}\\else\n {$\\scriptscriptstyle >$}\\fi}}}\n \\kern -.4ex{\\ifmmode{\\scriptscriptstyle \\sim}\\else\n {$\\scriptscriptstyle\\sim$}\\fi}}}\n\\def\\ltaprx {\\lower .1ex\\hbox{\\rlap{\\raise .6ex\\hbox{\\hskip .3ex\n {\\ifmmode{\\scriptscriptstyle <}\\else\n {$\\scriptscriptstyle <$}\\fi}}}\n \\kern -.4ex{\\ifmmode{\\scriptscriptstyle \\sim}\\else\n {$\\scriptscriptstyle\\sim$}\\fi}}}\n\\def\\etal {et al. }\n\\def\\littleprime{\\ifmmode{\\scriptscriptstyle \\prime }\n \\else{\\hbox{$\\scriptscriptstyle \\prime$ }}\\fi}\n\\def\\littless{\\ifmmode{\\scriptscriptstyle s }\n \\else{\\hbox{$\\scriptscriptstyle s $ }}\\fi}\n\\def\\littlemm{\\ifmmode{\\scriptscriptstyle m }\n \\else{\\hbox{$\\scriptscriptstyle m $ }}\\fi}\n\\def\\littlehh{\\ifmmode{\\scriptscriptstyle h }\n \\else{\\hbox{$\\scriptscriptstyle h $ }}\\fi}\n\\def\\littlecirc{\\ifmmode{\\scriptscriptstyle \\circ }\n \\else{\\hbox{$\\scriptscriptstyle \\circ $ }}\\fi}\n\\def\\rasec{\\raise .9ex \\hbox{\\littless}}\n\\def\\arcsec{\\raise .9ex\n \\hbox{\\littleprime\\hskip-3pt\\littleprime\\hskip-3pt}}\n\\def\\ramin{\\raise .9ex \\hbox{\\littlemm}}\n\\def\\arcmin{\\raise .9ex \\hbox{\\littleprime}}\n\\def\\hrs{\\raise .9ex \\hbox{\\littlehh}}\n\\def\\deg{\\hbox{$^\\circ$}}\n\\def\\degree{\\raise .9ex \\hbox{\\littlecirc}}\n\\def\\magpoint{\\hbox to 2pt{}\\rlap{\\hskip -.5ex \\arcmm}.\\hbox to 2pt{}}\n\\def\\arcsspoint{\\hbox to 1pt{}\\rlap{\\arcss}.\\hbox to 2pt{}}\n\\def\\arcsecpoint{\\hbox to 1pt{}\\rlap{\\arcsec}.\\hbox to 2pt{}}\n\\def\\arcminpoint{\\hbox to 1pt{}\\rlap{\\arcmin}.\\hbox to 2pt{}}\n\\def\\degreepoint{\\hbox to 1pt{}\\rlap{\\degree}.\\hbox to 2pt{}}\n\n\\slugcomment{Accepted by {\\it The Astrophysical Journal Supplements}.}\n\n\\begin{document}\n\n\\title{The Nature of Composite LINER/H\\,II Galaxies, As Revealed from \nHigh-Resolution VLA Observations}\n\n\\author{Mercedes E. Filho}\n\\affil{Lisbon Observatory and Kapteyn Astronomical Institute}\n\\authoraddr{P.O.~Box 800, NL--9700 AV Groningen, The~Netherlands}\n%%\\email{Mercedes Esteves Filho (mercedes@astro.rug.nl)}\n\n\\author{Peter D. Barthel}\n\\affil{Kapteyn Astronomical Institute}\n\\authoraddr{P.O.~Box 800, NL--9700 AV Groningen, The~Netherlands}\n\n\\author{Luis C. Ho}\n\\affil{Observatories of the Carnegie Institution of Washington}\n\\authoraddr{813 Santa Barbara Street, Pasadena, CA 91101, USA}\n\n\n\\begin{abstract}\n\nA sample of 37 nearby galaxies displaying composite LINER/H~II and pure\nH~II spectra was observed with the VLA in an investigation of the nature\nof their weak radio emission. The resulting radio contour maps overlaid\non optical galaxy images are presented here, together with an\nextensive literature list and discussion of the individual galaxies.\nRadio morphological data permit assessment of the ``classical AGN''\ncontribution to the global activity observed in these ``transition'' LINER\ngalaxies. One in five of the latter objects display clear AGN\ncharacteristics: these occur exclusively in bulge-dominated hosts.\n\n\\end{abstract}\n\n\\keywords{galaxies: active --- galaxies: nuclei --- galaxies: Seyfert --- \nradio continuum: galaxies}\n\n\\section{Introduction}\n\nLINER galaxies are a class of active galaxies characterized by the presence of \nstrong, nuclear, low-ionization emission lines (Heckman 1980). Like \nSeyfert nuclei, LINERs emit much stronger optical low-ionization forbidden \nlines compared to H~II nuclei, whose line emission is powered by \nphotoionization from young massive stars, but LINERs have a characteristically\nlower ionization state than Seyferts. In a recent optical survey of nearly \n500 nearby galaxies, Ho, Filippenko, \\& Sargent (1995, 1997a, 1997b) find that\n$\\sim$20\\% of all galaxies brighter than $B_T$ = 12.5\\,mag display\nLINER-type spectra. An additional 13\\% of the objects show spectra \nintermediate between those of ``pure'' LINERs and ``pure'' H\\,II nuclei. \nHo, Filippenko, \\& Sargent (1993; see also Ho 1996) dubbed this class as \n``transition objects,'' and they hypothesized that these might be composite \nsystems in which the optical signal of a weak active nucleus (the LINER \ncomponent) has been spatially blended by circumnuclear star-forming regions \n(the H~II component).\n\nModels have shown that photoionization by hot stars are able to reproduce the\noptical spectra of LINERs (Terlevich \\& Melnick 1985), especially those of \nthe transition-type variety (Shields 1992; Filippenko \\& Terlevich 1992). \nOther researchers have advocated shock-wave heating as a viable excitation \nmechanism for LINERs (Fosbury \\etal 1978; Heckman 1980; Dopita \\& Sutherland \n1995). At the same time, an increasing body of evidence suggests that a \nsignificant fraction of LINERs do contain irrefutable AGN characteristics \n(see reviews by Filippenko 1996 and Ho 1999b). Radio surveys, in particular, \nhave shown that many LINERs exhibit weak nuclear radio emission (Heckman 1980;\nSadler, Jenkins, \\& Kotanyi 1989; Wrobel \\& Heeschen 1991; Slee \\etal 1994; \nFalcke, Wilson, \\& Ho 1997; Van Dyk \\& Ho 1998). As discussed in detail by\nHo (1999a), weak nuclear radio emission in early-type (elliptical and S0) \ngalaxies is most likely related to accretion-driven energy production in these \nobjects, but at a very low level compared to powerful radio galaxies, which \nare also usually hosted by early-type systems. \n\nRadio observations provide an expecially attractive tool to further our \nunderstanding of the LINER phenomenon. Since radio frequencies are not plagued\nby dust obscuration and photoelectric absorption, high-resolution radio\nobservations potentially offer the cleanest and most efficient method to\nisolate an AGN core. Although radio emission also arises from supernova\nremnants and H\\,II regions, AGN cores can be identified through their \nhigh degree of central concentration, small angular size, flat spectral \nindices, and high brightness temperatures.\n\nGiven that LINERs are so numerous, they may be the most common type of\nAGN known. Their large space densities could make a major impact on the faint \nend of the local AGN luminosity function, which in turn has ramifications for \nmany astrophysical issues ranging from the cosmological evolution of AGN to\nthe contribution of AGN to the cosmic X-ray background. We are\ntherefore conducting high-resolution radio observations of selected\nLINER samples in order to investigate the interrelation between LINERs\nand classical AGN. For the present paper --- the first in a series ---\nwe have concentrated on transition-type LINERs. We report on sensitive \nVery Large Array (VLA)\\footnote{The VLA is a facility of the National Radio \nAstronomy Observatory (NRAO) which is a facility of the National Science \nFoundation operated under cooperative agreement by Associated Universities, \nInc.} C-array observations of a sample of 25 such transition LINERs at \n8.4\\,GHz. The resulting images, having angular resolution of about \n2\\arcsecpoint5, allow us to assess the strength and spatial distribution of \nthe nuclear radio emission. For comparison, we have also observed a small\nsample of 12 pure H\\,II nuclei. \n\nIn the following discussion and in upcoming papers, we adopt a\nHubble constant of H$_{0}$ = 75~km~s$^{-1}$~Mpc$^{-1}$.\n\n\\section{Sample Selection}\n\nThe sample of 25 transition LINER/H\\,II galaxies and 12 pure H\\,II\nnuclei was extracted from the original magnitude-limited Palomar survey of \n486 bright northern galaxies (Ho \\etal 1995), following the classification \ncriteria outlined in Ho et al. (1997a). The Palomar sample contains 65 \ntransition nuclei (Ho et al. 1997a), from which we chose a subset of 25 that \nhad little or no arcsec-scale resolution radio continuum data published, and\nthat fell within the observation window assigned to us by the VLA. In \naddition, we selected for comparison a small sample of 12 pure H\\,II nuclei \n(out of 206 such objects in the full Palomar sample). These were chosen to\nmimic the Hubble type distribution of the sample of transition objects, \nagain taking into consideration scheduling constraints.\nWe are not aware of any strong biases introduced by our sample selection. \n\nTable~1 lists the 37 sample objects. In addition to the optical positions of \nthe galaxies (columns 3 and 4), this table lists their distance (column~5) \nand their Hubble type (column~6). The Hubble types and distances are taken \nfrom Ho \\etal (1997a). The ``reference'' column (7), together with Table~2,\nsupplies references to earlier radio studies; it is readily apparent that\nseveral of the sample objects are well-studied objects, while some are\nnot. We will discuss our observational results in light of these existing \ndata in Section~4. The sample galaxies span a wide range of Hubble types, but \nthe majority are spirals.\n\n\\medskip \\centerline{\\bf -- TABLEs~1/2: Sample of transition LINER\n galaxies and H\\,II nuclei --}\n\n\\section {Observations and Data Reduction}\n\nThe resulting sample of 25 composite LINER/H\\,II and 12 pure H\\,II galaxies was\nobserved with the X-band (8.4\\,GHz) system of the VLA in two\nobserving sessions, on 1997 August~21 and August~25. The array was in its\nC-configuration, yielding a typical resolution of 2\\arcsecpoint5. Two\nbands of 50\\,MHz each were combined, yielding a total bandwidth of\n100\\,MHz. Snapshot observations combining two scans of 8--9~minutes\neach, at different hour angles, were obtained in order to improve the\nshape of the synthesized beam.\n\nSecondary phase and amplitude calibrators were observed before and after\neach scan. The primary calibrator was 3C\\,286, with appropriate\nbaseline constraints, and the adopted 8.4\\,GHz flux densities, as provided\nby the VLA staff, were 5.22~Jy and 5.20~Jy, at IF1 and IF2, respectively. \nThe calibration uncertainty is dominated by the uncertainty in the\nabsolute flux density of the primary calibrator, which is a few percent. \nThe array performed well: judging from the calibration sources,\nthe antenna phase and amplitude calibration appeared stable to within a\nfew percent. \n\nThe radio data are of high quality, and there was no need for\nextensive flagging of discrepant points. Reduction of the data was\nperformed using standard NRAO AIPS (version 15OCT98) image processing\nroutines. AIPS task IMAGR was employed to Fourier transform the\nmeasured visibilities and obtain CLEAN (H\\\"ogbom 1974; Clark 1980) maps of the sources. \nFull-resolution\nmaps, having synthesized beams of roughly 2\\arcsecpoint5, and tapered\nmaps, having beams between about 5\\arcsec~and 12\\arcsec, were\nmade. This proved useful to detect weak low surface brightness\nemission. As a rule of thumb, 1\\arcsec~corresponds to 50--100~pc for the \ntypical distances involved. Most images reach\nthe theoretical noise level of $\\sim 0.04$~mJy/beam (Perley, Schwab, \\& Bridle \n1989) to within a factor of two. Self-calibration was employed in\nthe analysis of two of the stronger sources (NGC\\,4552 and NGC\\,5354), \nleading to considerable improvements.\n\n\\section {Results}\n\n\\subsection {Radio Maps}\n\nNoting that a non-detection should be taken to imply no correlated flux\ndensity in excess of 0.5~mJy on the arcsec scale, radio contour maps of\nthe detected galaxies are presented in Figures 1--7, at the end of the\npaper. The radio maps are overlayed on optical images taken from the\nDigitized Sky Survey (DSS). In a number of cases only the\nhigh-resolution map (typical beamsize 2\\arcsecpoint5) or the\nlow-resolution map (typical beamsize 7\\arcsec~-- 10\\arcsec) are shown. \nUnrelated background radio sources were found in several fields; their\nnumber is entirely as expected given the size of the primary beam and\nthe sensitivity of the observations. In cases of large distances from\nthe field center, primary beam corrections were applied. Some of the\nbackground sources have been identified using NED (NASA/IPAC\nExtragalactic Database) and the Cambridge APM (Automatic Plate\nMeasuring) facility. Where possible, we have included them by their\nname in the tables below. Previously uncatalogued background sources\nare designated by their sky orientation with respect to the field center\nfor the relevant galaxy. All maps use contouring according to CLEV\n$\\times $ (--3, 3, 6, ..., MLEV) mJy/beam where MLEV are powers $3\n\\times 2^{\\rm n}$ up to a maximum of 96 and CLEV is the typical noise\nlevel on each radio map (see Table~3). \n\nTable~3 lists the various map parameters, with the following column\nheadings: the source name (1), the applied taper (2), the resulting\nrestoring beam (3), the position angle of the beam (4), the image noise \nlevel (5), and the relevant figure number (6). The H\\,II nuclei \nappear at the bottom of the table.\n\n\\medskip \\centerline{\\bf -- TABLE~3: Radio map parameters --}\n\nGiven that good phase stability was obtained, as judged from the VLA phase\ncalibrators, the astrometric accuracy of our overlay procedure must be\ndominated by the DSS accuracy, which is known to be about 0.6\\arcsec~ \n(V\\'eron-Cetty \\& V\\'eron 1996). This is born out by the images of several\nunresolved and slightly resolved nuclei (NGC\\,4552, NGC\\,5354, \nNGC\\,5838, NGC\\,5846) which appear accurate to within a few tenths of an arcsec. \n\n\\subsection {Comments on Individual Galaxies}\n\nWith reference to the images in the Appendix, we proceed by discussing\nthe results of our VLA imaging in the light of earlier studies of the\nsample objects. This discussion also deals with the detected background\nsources and includes important bibliographic information. We will\nfrequently compare our measurements with sample galaxy flux densities\nobtained within the VLA 1.4\\,GHz NVSS and FIRST surveys, having typical\nresolution of 45\\arcsec~ and 5\\arcsec, respectively (Condon \\etal 1998a;\nBecker, White, \\& Helfand 1995), as well as with the Green Bank 20~cm\nand 6~cm surveys, having typical resolution of $\\sim$700\\arcsec~and\n3\\arcminpoint5, respectively (White \\& Becker 1992, WB92 hereafter;\nBecker, White, \\& Edwards 1991, BWE91 hereafter). \n\n{\\bf IC\\,520 :} No compact structure was seen in this object, not even\non the tapered map. It was also not detected in the NVSS. However,\nCondon (1987) reports a detection at 1.49\\,GHz: at\n0\\arcminpoint8~resolution, he measured a 3.1~mJy radio source. \n\n{\\bf NGC\\,2541 :} We did not detect compact structure, not even on the\ntapered map. This source was also not detected in the FIRST or in the\nNVSS survey. However, Condon (1987) reports a possible detection at \n1.49\\,GHz, 0\\arcminpoint8~resolution, of a 3.2~mJy source, slightly\nextended to the SW relative to the optical position of the galaxy.\n\n{\\bf NGC\\,2985 :} We detect a 1.9~mJy source. At\n2\\arcsecpoint5~resolution, the source is slightly extended in the N-S\ndirection, along the orientation of the optical galaxy. The tapered map\nshows a 2.7~mJy core and about 1~mJy weak low surface brightness\nemission to the SW. The object was also detected in the NVSS: 44.1~mJy. \nAt 1.49\\,GHz, 1\\arcminpoint0~resolution, Condon (1987) measured a total\nflux of 61.9~mJy: the radio emission of NGC\\,2985 must be extended over\ntens of arcseconds. \n\n{\\bf NGC\\,3593 :} On both the untapered and tapered maps we measure\nabout 20~mJy of diffuse, 45\\arcsec~E-W elongated emission, oriented\nalong the major axis of the host of this H\\,II nucleus. NVSS measured\n87~mJy emission, WB92 measured 132~mJy (hence the radio source exceeds\none arcminute in size), whereas BWE91 measured 53~mJy. The 1.4\\,GHz,\n5\\arcsec~resolution map of Condon \\etal (1990) shows an E-W oriented\nsource of 63.4~mJy: these and our VLA data imply a steep-spectrum\nradio source.\n\nWe also detect an unrelated 10.6~mJy source, 3\\arcmin~to the N, extended\ntowards the E. As judged from the APM survey, the POSS plates show an as \nyet unclassified nonstellar source at this position: background source\nNGC\\,3593N is most likely a weak distant radio galaxy.\n\n{\\bf NGC\\,3627, M\\,66 :} This interacting galaxy belongs to the Leo\ntriplet. The 8.4\\,GHz maps show a 2\\arcmin~triple source aligned with\nthe inner bar of the optical galaxy. The outer radio components are\nrelated to star formation in the disk of the galaxy (Urbanik, Gr\\\"ave, \n\\& Klein 1985). We measure 3.9~mJy integrated emission in the compact central\ncomponent, while $\\sim$25~mJy are distributed in the NW and SE components.\nFrom comparison with low-resolution surveys (NVSS: 324.9~mJy; WB92:\n434~mJy; BWE91: 141~mJy) we infer that most of the radio emission of\nthis steep-spectrum radio source is resolved out by our observations.\nThe triple radio structure was also observed by Saikia \\etal (1994),\nat 5\\,GHz with 2\\arcsec~resolution. Combining our data with the Saikia\n\\etal (1994) and the Hummel \\etal (1987) data, we conclude that the\nnuclear radio source in NGC3627 must be of variable, flat-spectrum\nnature. More recently, high resolution (0\\arcsecpoint15) 15\\,GHz\nobservations detected an unresolved 1.4~mJy core (N. Nagar, private\ncommunication).\n\n{\\bf NGC\\,3628 :} Like NGC\\,3627, this galaxy also belongs to the Leo\ntriplet. Our 8.4\\,GHz full-resolution map shows some extended emission\nto the N and an eastern extension that is roughly aligned with the\nprojected disk of the galaxy. The nuclear region is clearly resolved. \nThe total flux density on our low-resolution map is about 70~mJy, 70$\\%$\nof which is in $\\sim$15\\arcsec~diffuse emission. The NVSS measured\n292~mJy whereas WB92, at lower resolution, detected 402~mJy, indicating\nresolved large-scale emission. At 1.4\\,GHz Condon \\etal (1990) measured\n203~mJy and 205~mJy at 5\\arcsec~and 1\\arcsecpoint5~resolution,\nrespectively. These and our data imply a steep-spectrum radio source,\nin agreement with the results from the Effelsberg 100m telescope\n(Schlickeiser, Werner, \\& Wielebinski 1984). Carral, Turner, \\& Ho\n(1990) observed this object at 15\\,GHz using the VLA in A-array and\nmeasured a total flux of 23~mJy. These authors sampled the innermost\npart of the source and obtain a $\\sim4$\\arcsec~string of a dozen\ncomponents aligned with the major axis of the galaxy, that they suggest\ncould be star-forming regions in the disk. \n\n{\\bf NGC\\,3675 :} We detect about 1.5~mJy of low surface brightness\nemission on our tapered maps. NVSS detected a 48.9~mJy source, whereas\nFIRST measured 8.04~mJy: the source must be strongly resolved. \n1.49\\,GHz VLA D-array observations (Condon 1987; Gioia \\& Fabbiano 1987)\ndetected a $\\sim$50~mJy source, oriented N-S, along the major axis of\nthe optical galaxy. Condon, Frayer, \\& Broderick (1991) report a flux\ndensity of 27~mJy at 4.85\\,GHz and a steep spectral index between 4.8\nand 1.4\\,GHz. \n\n{\\bf NGC\\,3681 :} We did not detect a radio source on the untapered or\ntapered maps. In contrast, NVSS measured a weak source of about\n4.2~mJy -- at much lower resolution.\n\n{\\bf NGC\\,3684 :} This H\\,II nucleus had no radio source detected,\neither on the untapered or on the tapered maps, but NVSS detected a\n15.9~mJy source. The radio emission of NGC\\,3684 must be diffuse.\n\nWe do, however, detect a partially resolved 18.1~mJy background\nsource, 3\\arcmin~to the SW, which APM identifies with a 19.5 mag\nstellar-like object. Further identification is still lacking.\n\n{\\bf NGC\\,4013 :} We detect a moderately resolved 1.1~mJy core and a small\nextension to the NE, parallel to the projected disk of this edge-on\ngalaxy. There is an additional 3~mJy of weak disk emission. On the\nbasis of the widely different NVSS and FIRST detections (40.5 vs. \n11.9~mJy), this disk emission must extend tens of arcseconds. Hummel,\nBeck, \\& Dettmar (1991) present 10\\arcsec~resolution 5\\,GHz data of\nNGC\\,4013 (UGC\\,6963) which show both the prominent core and the\nextended disk emission. Recent high resolution (0\\arcsecpoint15) 15\\,GHz\nobservations did not detect NGC\\,4013 above a 10$\\sigma$ limit of 1~mJy\n(N.~Nagar, private communication).\n\nWe also detect a slightly resolved 3.8~mJy background source,\n2\\arcmin~to the far SE. This source is also clearly seen in the map of\nCondon (1987). The APM facility reveals a 19.6 mag stellar-like object,\nwhich lacks further identification as yet. \n\n{\\bf NGC\\,4100 :} We detect about 7~mJy of low surface brightness\nemission associated with this H\\,II nucleus. The tapered map shows a\nslight extension to the SE along the major axis of the optical\ngalaxy. NVSS detected a 50.3~mJy source and FIRST detected 17.8~mJy,\nindicating resolution effects.\n\n{\\bf NGC\\,4217 :} We detect about 22~mJy, distributed along\n$\\sim$1\\arcminpoint5~of the projected galactic disk of this H\\,II\nnucleus. From low-resolution observations (NVSS: 123~mJy; WB92:\n139~mJy; BWE91: 40~mJy) we conclude that NGC\\,4217 harbours extended\nlow surface brightness radio emission, which must have a steep radio\nspectrum.\n \n{\\bf NGC\\,4245 :} No radio source associated with this H\\,II nucleus\nwas detected on the untapered or tapered maps. Neither NVSS nor FIRST\nhas detected this object at 1.4\\,GHz.\n\n{\\bf NGC\\,4321, M\\,100 :} We detect about 16~mJy of low surface\nbrightness emission in the nuclear region of this well-known grand\ndesign spiral in the Virgo cluster. The tapered map shows emission\nslightly extended to the NW. NVSS detected 87~mJy, while WB92 measured\n323~mJy and BWE91 87~mJy. At 1.49\\,GHz, 0\\arcminpoint9~resolution\nCondon (1987) measured 180\\,mJy total flux in a $\\sim $ 3\\arcmin\n$\\times $ 2\\arcmin region. At 4.9\\,GHz, 1\\arcsecpoint5~resolution\nCollison \\etal (1994) detect a ring-like structure coincident with our\nmain feature. At 8.5\\,GHz, 0\\arcsecpoint2 resolution, these authors\ndetect two unresolved sources, having peaks of 0.37~mJy/beam (E) and\n0.22\\,mJy/beam (W), respectively. The eastern radio source is\ncoincident with their 4.9\\,GHz main component while the one to the W\nis coincident with the optical nucleus and has a flat spectrum\n(Collison \\etal 1994).\n\nWe also detect an unresolved source, 1.5\\arcmin~to the SE, with 1.3~mJy\nintegrated flux, apparently located near the middle of the southern\nspiral arm of the galaxy. It is clearly visible on the NGC\\,4321 map. \nWe have identified this object with SN\\,1979C (Weiler \\etal 1981). \nCollison \\etal (1994) measured 2~mJy for this SN\\,1979C, at 4.9\\,GHz. \n\n{\\bf NGC\\,4369, Mrk\\,439 :} We detect 3.8~mJy of low surface brightness\ndisk emission associated with this H\\,II nucleus. On the basis of\nwidely different NVSS and FIRST detections (24.3 vs. 4.67\\,~mJy), this\ndisk emission must extend over tens of arcsec. The Condon \\etal (1990)\n1.49\\,GHz image, at 15\\arcsec~resolution, shows a 18.3~mJy source with\nextended emission to the E. \n\n{\\bf NGC\\,4405, IC\\,788 :} No compact emission was detected in the\nuntapered or tapered maps. NVSS detected weak (4.5~mJy) emission for\nthis H\\,II galaxy. \n\nWe did, however, detect a partially resolved 10.1~mJy source,\n2\\arcmin~SW of the NGC\\,4405 target position. As judged from the APM,\nthe POSS plates show a 19.2 mag stellar-like object at this position,\nwhich we subsequently identify as the $z=1.929$ QSO, LBQS\\,1223+1626\n(e.g., Hewett, Foltz, \\& Chaffee 1995). \n\n{\\bf NGC\\,4414 :} We detect $\\sim$29~mJy of low surface brightness\nemission, distributed along $\\sim$1\\arcminpoint5, in a structure aligned\nwith the galaxy's major axis. NVSS detected a 242~mJy source while\nFIRST detected a double-peaked source with 44 and 64~mJy components. \nThe Condon (1983), 1.465\\,GHz, 12\\arcsecpoint5~resolution map and the\nCondon (1987), 1.49\\,GHz, 1\\arcminpoint0~resolution map show comparable\nN-S structure, measuring $\\sim$0.22~Jy. Using this last value plus the\n78~mJy measured at 4.85\\,GHz, 15\\arcsec~resolution, Condon \\etal (1991)\nobtain a steep spectral index. \n\n{\\bf NGC\\,4424 :} On the tapered map we detect a resolved $\\sim$1~mJy core \nplus 1.5~mJy weak low surface brightness emission to the E along the\nprojected disk of this candidate merger galaxy (Kenney \\etal 1996). \nNVSS detected a weak 4.5~mJy source. Our full-resolution data show the\ncore of this H\\,II nucleus to be somewhat resolved. This is borne out of\nour recent high resolution\n(0\\arcsecpoint25) 8.4\\,GHz observations which did not detect NGC\\,4424 above\na 3$\\sigma$ limit of 0.2~mJy.\n\nWe also detect an unrelated, slightly resolved 13.3~mJy source,\n2\\arcminpoint5~to the SE. The APM identifies it with a 20.2 mag\nstellar-like object. Further properties of this background source\nremain as yet unknown. \n\n{\\bf NGC\\,4470 :} We detect $\\sim$3~mJy of weak low surface\nbrightness emission, extending 30\\arcsec~along the galaxy major \naxis. NVSS detected 17.1 mJy associated with this H\\,II nucleus.\n\nWe also detect an unrelated, resolved 16.0~mJy radio source,\n1\\arcminpoint5~to the NE of NGC\\,4470, which is not identified on the\nPOSS plate (APM). We identify this object with the radio source\nTXS\\,1227+081 (Douglas \\etal 1996), which has as yet no optical\nidentification.\n\n{\\bf NGC\\,4552, M\\,89 :} We detect about 77~mJy in a strong core plus \npossibly a jet-like structure to the NE. NVSS\ndetected a 103~mJy source. Since BWE91 measured 64~mJy at 5\\,GHz, the\nradio source in NGC\\,4552 must have a relatively flat radio spectrum,\nwhich is in agreement with findings by Condon \\etal (1991). The radio\nsource appears to be variable (Wrobel \\& Heeschen 1984; Ekers, Fanti, \\&\nMiley 1983; Sramek 1975a, 1975b; Ekers \\& Ekers 1973). Our recent\nsubarcsec resolution 8.4\\,GHz images have confirmed this object's compactness. \n\n{\\bf NGC\\,4643 :} No compact radio structure was detected on the\nuntapered or the tapered maps. NVSS also did not detect this source. \nHowever, we have detected several very weak sources ($\\sim$1~mJy) on the\ntapered maps, some of which may be due to weak diffuse disk emission. \n\n{\\bf NGC\\,4710 :} We detect about 6~mJy of weak disk emission\nassociated with this H\\,II nucleus. NVSS measured a 19.3~mJy source.\nAt 1.49\\,GHz, Condon \\etal (1990) measure 17.2~mJy and 14.7~mJy at 15\nand 5\\arcsec~resolution, respectively. The data imply a resolved\nsteep-spectrum radio source.\n\nWe also detect a 4.8~mJy resolved background source, 2.5\\arcmin~to the\nE of NGC\\,4710. No indentification could be found on the POSS.\n\n{\\bf NGC\\,4713 :} We detect $\\sim$1.2~mJy weak low surface brightness disk\nemission on our tapered maps. NVSS measured a 46.9~mJy source: our \nobservations must have resolved out much of the flux.\n\n{\\bf NGC\\,4800 :} We detect about 1.2~mJy of weak low surface brightness\nemission, stretching $\\sim30$\\arcsec~along the galaxy major axis. NVSS\ndetected a 23.5~mJy source and FIRST 12.2~mJy. Therefore, our\nobservations are resolving out much of the emission of this H\\,II\nnucleus. \n\n{\\bf NGC\\,4826 , M\\,64:} We detect about 21~mJy of low surface\nbrightness emission. The central region on the full-resolution map (not\npresented here) shows a double-peaked component, which can be compared\nto the complex inner triple structure of the 15 and 5\\,GHz,\n2\\arcsec~resolution maps of Turner \\& Ho (1994). Combining the data\nindicates that this is a steep spectrum source. NVSS detected a 101~mJy\nsource and BWE91 detected a 56~mJy source. The 1.49\\,GHz,\n1\\arcminpoint0~resolution data of Condon \\etal (1998b) and Condon (1987)\nshow a $\\sim$100~mJy source, as do the data of Gioia \\& Fabbiano (1987)\nat 40\\arcsec~resolution. \n\n{\\bf NGC\\,4845 :} On our tapered maps we detect a 2~mJy core and some\nemission to the N, perpendicular to the galaxy major axis, plus 10~mJy\nof $\\sim20$\\arcsec~elongated disk emission. NVSS detected a 43.8~mJy\nsource associated with this H\\,II nucleus. The data of Condon \\etal\n(1990) imply resolution effects on the 10~arcsec scale. \n\n{\\bf NGC\\,5012 :} We detect some very weak ($\\sim$1~mJy) features\nnear the target phase center. NVSS detected a 31.4~mJy source, but \nas FIRST did not detect it, we must be dealing with extended low\nsurface brightness emission.\n\n{\\bf NGC\\,5354 :} We detect an unresolved 11.7~mJy core. NVSS and\nFIRST detected a 8.4 and 8.0~mJy source, respectively, implying that the\nNGC\\,5354 radio source is unresolved at a resolution of 5\\arcsec. The\n4.85\\,GHz, 15\\arcsec~resolution maps of Condon \\etal (1991) show 7~mJy\nemission, implying that the nuclear radio source has an inverted\nspectrum. Our recent\nsubarcsec resolution 8.4\\,GHz images have confirmed this object's compactness. \n\n\nPaired galaxy NGC\\,5353 is also detected, 1\\arcminpoint25~to the S,\nwith a 26.7~mJy core. Condon \\etal (1991) measure 29~mJy at 4.85\\,GHz,\n15\\arcsec~resolution, implying that NGC\\,5353 also hosts a flat\nspectrum radio source.\n\n{\\bf NGC\\,5656 :} We detect $\\sim$1~mJy of weak low surface brightness\nemission, stretching over $\\sim$25\\arcsec~along the major axis of the\ngalaxy. NVSS detected a 22~mJy source.\n\n{\\bf NGC\\,5678 :} We detect about 8.5~mJy of low surface brightness\nemission stretching over $\\sim$1\\arcminpoint2~along the major axis of\nthe galaxy. The tapered map shows what could be a double-peaked source,\nsimilar to the 6\\arcsec~resolution, 1.4\\,GHz map of Condon (1983). NVSS\ndetected a 112~mJy source while BWE91 measured 68~mJy. The NVSS and\nBWE91 results, combined with Condon (1983) reporting 109~mJy at\n1.4\\,GHz, imply a steep spectrum source. \n\n{\\bf NGC\\,5838 :} We have detected a slightly resolved 2.2~mJy source. \nNVSS detected 3.0~mJy, while Wrobel \\& Heeschen (1991) report a 2 mJy\nsource (5\\,GHz, 5\\arcsec~resolution): the nuclear radio source in\nNGC\\,5838 must have a flat radio spectrum. Our recent\nsubarcsec resolution 8.4\\,GHz images have confirmed this object's compactness. \n\n \nThere is also an unrelated, unresolved 1.3~mJy source, about\n1\\arcminpoint5~to the S of NGC\\,5838. The POSS plates reveal an 18.4\nmag star-like object at that position, for which as yet no redshift is\navailable. \n\n{\\bf NGC\\,5846 :} We have detected a partially resolved 7.1~mJy source. \nNVSS measured a 22~mJy source. 1.4\\,GHz VLA observations by\nM\\\"ollenhoff, Hummel, \\& Bender (1992) measured an unresolved core of\n9~mJy plus 10~mJy of additional diffuse emission: NGC\\,5846 must possess\na compact flat-spectrum core component. Our recent\nsubarcsec resolution 8.4\\,GHz images have confirmed this object's compactness. \n\n \n{\\bf NGC\\,5879 :} No radio structure was detected on the untapered or\nthe tapered maps. NVSS detected a 21~mJy source, which hence must arise \nin an extended low surface brightness region.\n\nHowever, we did detect a 292.1~mJy, slightly resolved background\nsource, about 2\\arcmin~NE of our target. It shows up only on the POSS\nred plate as a noise-like source. We have identified this source as\nQSO 1508+5714, at a redshift of 4.301 (Hook \\etal 1995). It is in the\nWENSS (Rengelink \\etal 1997) and in BWE91 (282~mJy) as well as in WB92\n(149~mJy). Patnaik \\etal (1992) have observed the source with the VLA\nA-array at 8.5\\,GHz and measured 153~mJy: 1508+5714 must be a variable \nflat-spectrum quasar.\n \n{\\bf NGC\\,5921 :} We have detected a very weak 0.5~mJy core and some\nadditional weak extended emission. At 1.49\\,GHz and 0\\arcminpoint9\nresolution, Condon (1987) measured a 20.8~mJy source with an\nadditional 2.8~mJy eastern component which we do not detect at\n8.4\\,GHz. All emission must be of low surface brightness nature.\n\n{\\bf NGC\\,6384 :} Following the NVSS non-detection, we also do not\ndetect (compact) radio emission from NGC\\,6384. However, Condon\n(1987), at 1.49\\,GHz and 1\\arcminpoint2~resolution, found the radio\nsource, having $\\sim$ 35~mJy, to be very extended.\n\n{\\bf NGC\\,6482 :} We have not detected this source at 8.4\\,GHz and\nneither did NVSS.\n\nWe did, however, detect a slightly resolved 23.6~mJy background\nsource, about 3\\arcmin~to the S of NGC\\,6482. On the full-resolution\nmap this source is slightly extended. The POSS plates show a 20.9 mag\nstellar object. We have identified this source with the radio source\n1749+2302 included in GB6, with 26~mJy flux density.\n\n{\\bf NGC\\,6503 :} We do not detect radio emission from this galaxy on\nthe full-resolution or on the tapered maps. 1.4\\,GHz data (NVSS and Condon\n1987) indicate a NW-SE extended $\\sim$40~mJy source, which\nconsequently must be diffuse.\n \nWe also detect a background source, about 6\\arcmin~to the SW. Due to\nthe large distance from the phase center, which implies a large and uncertain\nprimary beam correction, we cannot assess the flux density of this\nsource. The source appears as a 16.9 mag stellar-like object on the POSS\nplates. We have identified this object with the BL Lacertae source\n1749+701 at redshift 0.77 (Hughes, Aller, \\& Aller 1992). This object has been\nextensively observed at other radio-frequencies and is included in the\nWENSS (Rengelink \\etal 1997) as well as BWE91 and WB92. The only other\n8.5\\,GHz measurement of this source comes from Patnaik \\etal (1992). They\nmeasure 558~mJy with the VLA A-array. \n\nTable~4 summarizes the properties of the background sources, including\nthe previously identified, as well as the new, identifications. Tabulated \n8.4\\,GHz fluxes have been corrected for primary beam attenuation. \n\n\\medskip \\centerline{\\bf -- TABLE~4: Field/background sources --}\n\n\\subsection {Radio Source Parameters}\n\nFor each galaxy with a 8.4\\,GHz detection, we list in Table~5 the radio\nsource parameters, measured both from the full-resolution and the\ntapered maps. Peak and integrated values (columns~3 and 6), as well as \nwell as sky positions of bidimensional gaussian fits (columns~4 and 5)\nare tabulated. These values were obtained using the AIPS task IMFIT. \nAs we are often dealing with resolved and/or asymmetric emission, such \nmeasurements are often inaccurate and must represent lower limits. \nIn such cases, we have estimated the integrated\n8.4\\,GHz flux density from inspection of the map and the relevant clean\ncomponent file and we have given it the prefix ``$\\geq$'' (column~6). \nAlso, given the fact that we have fitted single gaussian to the brightest\nsource components, the accuracy of the radio peak positions is judged to be\n\\ltaprx1\\arcsec~(see images). For NGC\\,3627, the quoted peak and integrated \nvalue are of the central core. In parentheses we include the total flux \nof the three components (see Section~4.2). \n\n\n\n \n\n\\medskip \n\\centerline{\\bf -- TABLE~5: Radio parameters of detected sources --}\n\nFrom a quick comparison with the integrated NVSS 1.4\\,GHz flux\ndensities, it is found that in many cases the high-resolution\nobservations must have resolved a substantial fraction of the emission. \nThis can be quantified by examination of the spectral index values. \nTable~6 lists spectral indices $\\alpha^{8.4}_{1.4}$ ($S_{\\nu } \\propto\n\\nu ^{-\\alpha}$) (column~5), obtained by combining the NVSS flux \ndensities (column~2)\nand the integrated 8.4\\,GHz flux densities (column~3) taken from Table~5. \nDue to the fact that the NVSS beam\n(45\\arcsec) exceeds the 8.4\\,GHz beam (7\\arcsec--10\\arcsec) by a\nsubstantial factor, these spectral index values should be considered\nas upper limits. It indeed\nappears that in most of these cases the radio emission was documented to\nbe extended over tens of arcseconds. \nWe also compile calculated NVSS radio luminosities (column~4) for the \n37 galaxies under consideration. \nAgain, for NGC\\,3627 quoted values refer to\nthe compact core except when in parentheses, in which case the values refer \nto all three source components. \n\n\n\n\\medskip \\centerline{\\bf -- TABLE~6: summary --}\n\nMost sample galaxies are seen to display steep spectral indices, as\ncommonly found for star-forming late-type galaxies (Condon 1992). The\nfollowing objects have flat ($\\alpha \\leq 0.6$) spectra: NGC\\,4552,\nNGC\\,5354, NGC\\,5838 and NGC\\,5846 and the H\\,II nucleus in NGC\\,4424. \nWe will return to this issue in the next Section. \n\n\\section {Discussion}\n\nOur VLA imaging observations have yielded X-band detections of 27 of the\n37 sample galaxies. These 27 include NGC\\,4643 and NGC\\,5012, which\nwere marginally detected. As for the non-detections, they are equally\ndistributed over the transition LINERs and the H\\,II nuclei. It appears\nthat non-detection at X-band, at a resolution of\n2\\arcsecpoint5--12\\arcsec, correlates with 1.4\\,GHz (NVSS) weakness\nand/or low surface brightness. Table~6 indicates that the NVSS radio\nluminosity distributions of the subsamples are comparable. The\nintegrated 1.4\\,GHz radio luminosities imply that the sample sources\nspan the usual luminosity range for nearby galaxies (10$^{26}$ --\n10$^{30.5}$ erg s$^{-1}$ Hz$^{-1}$; see, e.g., Condon 1987, 1992). \nWith the exception of NGC\\,4424 (see Section~4.2), none of the H\\,II \nnuclei display compact nuclear emission and/or a flat radio spectrum.\nThis is in strong contrast to the transition LINER galaxies.\n\nPurely based on the radio morphology, the transition LINER objects can\nbe divided into two categories. The first is made up of galaxies\ndisplaying extended, steep-spectrum, low surface brightness radio\nemission, usually tracing the optical isophotes of the host galaxy. The\nsecond category refers to objects that, in addition to extended\nemission, also show compact nuclear radio emission. The first category displays\nradio morphologies that are consistent with their being due to\nlarge-scale star formation; in several cases the radio morphology is\nseen to trace the H\\,II regions in the host. However, we stress that\nthe presence of a very weak nuclear component in these objects may still \nbe masked by the more dominant radio emission from star-forming regions. \nThe second category, which we will refer to in the following as AGN\ncandidates, is comprised of NGC\\,3627, NGC\\,4552, NGC\\,5354,\nNGC\\,5838, and NGC\\,5846. The last four of these are characterized with\na flat radio spectral index between 1.4 and 8.4 GHz (see end of Section~4.3). \nJudging from high-resolution observations which isolate the nuclear\nemission, the compact nucleus of NGC\\,3627 also displays a flat radio\nspectrum (see Section~4.2). These AGN candidates are on average more\nluminous than the non-AGN and, as we shall see below, their hosts\nare early rather than late-type galaxies. While at first sight the H\\,II nucleus\nNGC\\,4424 also belongs in this AGN candidate class, the radio image (Fig.~3d)\nshows it to be resolved. Higher resolution observations\nrecently carried out by us indeed resolve all the nuclear emission in \nNGC\\,4424 (see Section~4.2), in contrast to the AGN candidates \nfrom the transition LINER sample. As such there is a clear separation between\nthe non-AGN and AGN candidate classes. \n\nApparently, galaxies with composite LINER and star-formation spectra\nseparate out into objects with and without a clear signature of an\nAGN, that is to say, a compact, flat-spectrum radio source. The prime\nquestion to address, of course, is whether the optical spectra of\nthese classes differ in any way. Deferring the full analysis of this\nissue to another paper, we here just note that the class of AGN\ncandidates indeed displays somewhat stronger [N~II] and [S~II] lines\nin their optical spectra. As we will demonstrate in the forthcoming\npaper in this series, the behavior of the so called $u$-parameter,\nwhich measures the radio/far-IR ratio, also supports the weak AGN\nclassification. However, like in the case of Seyfert galaxies showing\na $\\sim$30\\% incidence rate of compact radio cores (e.g., Norris et\nal. 1990), there is not a one-to-one correspondence between compact\nradio emission and nuclear activity. We conclude that the radio\nproperties permit to isolate AGN candidates among the sample of\ntransition LINERs, although the absence of radio cores cannot be used to \nargue against their being AGN. These conclusions strongly support the \nhypothesis which resulted from the VLA observations of transition LINER\nNGC\\,7331 by Cowan et al. (1994).\n\nInspection of Table~6 readily shows that these AGN candidates are\nhosted by rather early-type galaxies (E--Sb). The relevant radio core\nluminosities L$_{\\rm 8.4\\,GHz}$ range from $\\sim$ 10$^{26.2}$ --\n10$^{28.5}$ erg s$^{-1}$ Hz$^{-1}$, which is several orders of\nmagnitude less than the core luminosities in FR\\,I or FR\\,II type\n(Fanaroff \\& Riley 1974) radio galaxies and quasars, and in the range\nof the weakest radio cores in Seyfert galaxies (Giuricin et al.\n1996). This, then, implies that weak LINER AGN preferentially occur\nin bulge-dominated hosts, not necessarily just in ellipticals,\nconsistent with statistical results from other lines of evidence (Ho\net al. 1997b; Ho 1999b). This is in agreement with the case of\nSeyfert galaxies, for which the radio core emission was also found to\nbe stronger in early-type hosts (Giuricin et al. 1996). As such,\nthese weak AGN differ from the more powerful FR\\,I radio galaxies,\nwhich are commonly associated with elliptical galaxies, not seldom\nbrightest cluster galaxies (Zirbel \\& Baum 1995). They exceed the\nvery weak nuclear source in the nearby transition LINER NGC\\,7331\n(Cowan et al. 1994) by a factor of $\\sim 15$, and are comparable in\nstrength to the well-known variable radio core of the LINER nucleus in\nM\\,81 (e.g., Ho et al. 1999). Hence, it must be concluded that at least some \nweak LINER AGN reveal themselves by low-power radio cores. This supports\nthe analysis of Ho (1999a), who proposed that the weak nuclear radio\nsources (radio power 10$^{26}$ -- 10$^{29}$ erg s$^{-1}$ Hz$^{-1}$) in\nnearby elliptical and S0 galaxies are the low-luminosity counterparts\nof more powerful AGN.\n\nFinally, it is intriguing that the transition LINER in the elliptical\ngalaxy NGC\\,6482 remained undetected in our observations (as well as in\nthe NVSS). Given that NGC 6482 is the most distant object in our\nsample, our non-detection would still allow a $\\leq 10^{27}$ erg\ns$^{-1}$ Hz$^{-1}$ compact radio source to reside in this object. \n\nFull analysis of our sample, including optical emission-line and infrared\nluminosities, will be presented in forthcoming papers. To address the\nphysical origin behind the findings presented here will be the challenge\nfor future work. \n\n\\section{Conclusions}\n\nA sample of composite LINER/H\\,II galaxies and pure H\\,II nuclei was\nstudied using the VLA (C-array) at 8.4\\,GHz. On the basis of their\nradio morphological properties, the composite sources can be divided\ninto objects with low surface brightness emission confined mainly to\nthe plane of the galaxy and objects displaying compact nuclear\ncomponents. The former\nobjects are similar in radio morphology to the H\\,II nuclei in our\nsample, whereas the latter show morphologies consistent with AGN. All\nfive of the LINER AGN are hosted by bulge-dominated galaxies (Hubble\ntype E--Sb), and four of them show flat spectral indices between 8.4 and\n1.4\\,GHz. In terms of radio luminosity, the present LINER AGN populate\nthe range of low core radio luminosities, which implies that classical AGN \nof low luminosity exist in a wide range of galaxy types.\n\n\\acknowledgments\n\nM.~E.~F. is supported by grant PRAXIS XXI/BD/15830/98 from the \nFunda\\c c\\~ao para a Ci\\^encia e Tecnologia, Minist\\'erio da Ci\\^encia e\nTecnologia, Portugal. P.~D.~B. acknowledges a visitor's grant from the\nSpace Telescope Science Institute, where a large part of this paper\ncould be written. L.~C.~H. is partly funded by NASA grant NAG 5-3556,\nand by NASA grants GO-06837.01-95A and AR-07527.02-96A from the Space\nTelescope Science Institute (operated by AURA, Inc., under NASA contract\nNAS5-26555). We want to thank Neil Nagar for providing us with \nsome of his preliminary results.\n\nThis research was supported in part by the European\nCommission TMR Programme, Research Network Contract ERBFMRXCT96-0034\n``CERES.'' We made extensive use of the APM (Automatic Plate Measuring)\nFacility, run by the Institute of Astronomy in Cambridge, the STScI DSS\n(Digitized Sky Survey), produced under US government grant NAGW -- 2166,\nand NED (NASA/IPAC Extragalactic Database), which is operated by the Jet\nPropulsion Laboratory, California Institute of Technology, under\ncontract with NASA. \n\n\\begin{references}\n\n\\reference{}\nBecker, R.~H., White, R.~L., \\& Edwards, A.~L. 1991, \n\\apjs, 75, 1\n\n\\reference{}\nBecker, R.~H., White, R.~L., \\& Helfand, D.~J. 1995,\n\\apj, 450, 559\n\n\\reference{}\nCarral, P., Turner, J.~L., \\& Ho, P.~T.~P. 1990, \\apj, 362, 434\n\n\\reference{}\nClark, B.~G., 1980, \\aap, 89, 377\n\n%Clark, R.~N., 1980, PASP, 92, 221\n\n\\reference{}\nCollison, P.~M., Saikia, D.~J., Pedlar, A., Axon, D.~J., \\& Unger, S.~W. 1994,\n\\mnras, 268, 203\n \n\\reference{}\nCondon, J.~J. 1983, \\apjs, 53, 459\n\n\\reference{}\nCondon, J.~J. 1987, \\apjs, 63, 485\n\n\\reference{}\nCondon, J.~J. 1992, ARA\\&A, 30, 575\n\n\\reference{}\nCondon, J.~J., \\& Broderick, J.~J. 1988, \\aj, 96, 30\n\n\\reference{}\nCondon, J.~J., Condon, M.~A., Gisler, G., \\& Puschell, J.~J. 1982, \n\\apj, 252, 102\n\n\\reference{}\nCondon, J.~J., Cotton, W.~D., Greisen, E.~W., Yin, Q.~F., \nPerley, R.~A., Taylor, G.~B., \\& Broderick, J.~J. 1998a, \\aj, 115, 1693\n\n\\reference{}\nCondon, J.~J., Frayer, D.~T., \\& Broderick, J.~J. 1991,\n\\aj, 101, 362\n\n\\reference{}\nCondon, J.~J., Helou, G., Sanders, D.~B., \\& Soifer, B.~T. 1990, \n\\apjs, 73 359\n\n\\reference{}\nCondon, J.~J., Yin, Q.~F., Thuan, T.~X., \\& Boller, Th. 1998b,\n\\aj, 116, 2682\n\n\\reference{}\nCowan, J.~J., Romanishin, W., \\& Branch, D. 1994, \\apj, 436, L139\n\n\\reference{}\nDopita, M.~A., \\& Sutherland, R.~S. 1995, \\apj, 102, 161\n\n\\reference{}\nDouglas, J.~N., Bash, F. N., Bozyan, F.~A., Torrence, G.~W., \\& \nWolfe, C. 1996, \\aj, 111, 1945\n\n\\reference{}\nDressel, L.~L., \\& Condon, J.~J. 1978, \\apjs, 36, 53\n\n\\reference{}\nDumke, M.~K., Krause, M., Wielebinski, R., \\& Klein, U. 1995,\n\\aap, 302, 691\n\n\\reference{}\nEkers, R.~D., \\& Ekers, J.~A. 1973, \\aap, 24, 247\n\n\\reference{}\nEkers, R.~D., Fanti, R., \\& Miley, G.~K. 1983, \\aap, 120, 297\n\n\\reference{}\nFabbiano, G., Gioia, I.~M., \\& Trinchieri, G. 1989, \\apj, 347, 127\n\n\\reference{}\nFalcke, H., Wilson, A.~S., \\& Ho, L.~C. 1997, in Relativistic\nJets in AGN, ed. M. Sikora \\& M. Ostrowski, 13\n\n\\reference{}\nFanaroff, B.~L., \\& Riley, J.~M. 1974, \\mnras, 167, 31P\n\n\\reference{}\nFilippenko, A.~V 1996, in The Physics of LINERs in View of Recent Observations, \ned. M. Eracleous et al. (San Francisco: ASP), 17\n\n\\reference{}\nFilippenko, A.~V., \\& Terlevich, R. 1992, \\apj, 397, L79\n\n\\reference{}\nFosbury, R.~A.~E., Melbold, U., Goss, W.~M., \\& Dopita, M.~A. 1978, MNRAS, 183,\n549\n\n\\reference{}\nGioia, I.~M., \\& Fabbiano, G. 1987, \\apjs, 63, 771\n\n\\reference{}\nGiuricin, G., Fadda, D., \\& Mezzetti, M. 1996, \\apj, 468, 475\n\n\\reference{}\nGregory, P.~C., \\& Condon, J.~J. 1991,\n\\apjs, 75, 1011\n\n\\reference{}\nHaynes, M., \\& Sramek, R.~A. 1975, \\aj, 80, 673\n\n\\reference{}\nHeckman, T.~M. 1980, \\aap, 87, 152\n\n\\reference{}\nHeckman, T.~M., Balick, B., \\& Crane, P.~C. 1980, \\aaps, 40, 295\n\n\\reference{}\nHewett, P.~C., Foltz, C.~B., \\& Chaffee, F.~H. 1995, \\aj, 109, 1498\n\n\\reference{}\nHo, L.~C. 1996, in The Physics of LINERs in View of Recent Observations, \ned. M. Eracleous et al. (San Francisco: ASP), 103\n\n\\reference{}\nHo, L.~C. 1999a, \\apj, 510, 631 \n\n\\reference{}\nHo, L.~C. 1999b, Advances in Space Research, 23 (5-6), 813\n\n\\reference{}\nHo, L.~C., Filippenko, A.~V., \\& Sargent, W.~L.~W. 1993, \\apj, 417, 63\n\n\\reference{}\nHo, L.~C., Filippenko, A.~V., \\& Sargent, W.~L.~W. 1995, \\apjs, 98, 477\n\n\\reference{}\nHo, L.~C., Filippenko, A.~V., \\& Sargent, W.~L.~W. 1997a, \\apjs, 112, 315\n\n\\reference{}\nHo, L.~C., Filippenko, A.~V., \\& Sargent, W.~L.~W. 1997b, \\apj, 487, 568\n\n\\reference{}\nHo, L.~C., Van Dyk, S.~D., Pooley, G.~G., Sramek, R.~A., \\& Weiler, K.~W. 1999,\n\\aj, 118, 843\n\n\\reference{}\nH\\\"ogbom, J.~A., 1974, \\aaps, 15, 417\n\n\\reference{}\nHook, I.~M., McMahon, R.~G., Patnaik, A.~R., Browne, I.~W.~A., Wilkinson, \nP.~N., Irwin, M.~J.,\\& Hazard, C. 1995, \\mnras, 273, L63\n\n\\reference{}\nHughes, P.~A., Aller, H.~D., \\& Aller, M.~F. 1992, \\apj, 396, 469\n\n\\reference{}\nHummel, E. 1980, \\aaps, 41, 151\n\n\\reference{}\nHummel, E., Beck, R., \\& Dettmar, R.-J. 1991,\n\\aaps, 87, 309\n\n\\reference{}\nHummel, E., \\& Kotanyi, C.~G. 1982, \\aap, 106, 183\n \n\\reference{}\nHummel, E., van der Hulst, J.~M., Keel, W.~C., \\& Kennicutt, R.~C., Jr.\n1987, \\aaps, 70, 517\n\n\\reference{}\nJenkins, C.~R. 1982, \\mnras, 200, 705\n\n\\reference{}\nJones, D.~L., Terzian, Y., \\& Sramek, R.~A. 1981a, \\apj, 246, 28\n\n\\reference{}\nJones, D.~L., Terzian, Y., \\& Sramek, R.~A. 1981b, \\apj, 247, L57\n\n\\reference{}\nKenney, J.~D.~P., Koopmann, R.~A., Rubin, V.~C., \\& Young, J.~S. 1996,\n\\aj, 111, 152\n\n\\reference{}\nKlein, U., \\& Emerson, D.~T. 1981, \\aap, 94, 29\n\n\\reference{}\nM\\\"ollenhoff, C., Hummel, E., \\& Bender, R. 1992,\n\\aap, 255, 35\n\n\\reference{}\nNiklas, S., Klein, U., Braine, J., \\& Wielebinski, R. 1995,\n\\aaps, 114, 21\n\n\\reference{}\nNorris, R.~P., Allen, D.~A., Sramek, R.~A., Kesteven, M.~J., \\& Troup, E.~R. \n1990, \n\\apj, 359, 291\n\n\\reference{}\nPatnaik, A.~R., Browne, I.~W.~A., Wilkinson, P.~N., \\& Wrobel, J.~M. 1992, \n\\mnras, 254, 655\n\n\\reference{}\nPerley, R.~A., Schwab, F.~R., \\& Bridle, A.~H. 1989, in Synthesis Imaging in \nRadio Astronomy: A Collection of Lectures from the Third NRAO Synthesis\nImaging Summer School (San Francisco: ASP), 6\n\n\\reference{}\nRengelink, R.~B., Tang, Y., de Bruyn, A.~G., Miley, G.~K., Bremer, M.~N., \nR\\\"ottgering, H.~J.~A., \\& Bremer, M.~A.~R. 1997, \\aaps, 124, 259\n\n\\reference{}\nReuter, H.-P., Krause, M., Wielebinski, R., \\& Lesch, H. 1991,\n\\aap, 248, 12 \n\n\n\\reference{}\nSadler, E.~M., Jenkins, C.~R., \\& Kotanyi, C.~G. 1989, \\mnras, 240, 591\n\n\\reference{}\nSaikia, D.~J., Pedlar, A., Unger, S.~W., \\& Axon, D.~J. 1994,\n\\mnras, 270, 46\n\n\\reference{}\nSchlickeiser, R., Werner, W., \\& Wielebinski, R. 1984, \\aap, 140, 227\n\n\\reference{}\nShields, J. C. 1992, \\apj, 399, L27\n\n\\reference{}\nSlee, O.~B., Sadler, E.~M., Reynolds, J.~E., \\& Ekers, R.~D. 1994,\n\\mnras, 269, 928\n\n\\reference{}\nSramek, R.~A. 1975a, \\aj, 80, 771\n\n \\reference{}\nSramek, R.~A. 1975b, \\apj, 198, L13\n\n\\reference{}\nTerlevich, R., \\& Melnick, J. 1985, \\mnras, 213, 841\n\n\\reference{}\nTurner, K.~C., Helou, G., \\& Terzian, Y. 1988, PASP, 100, 452\n\n\\reference{}\nTurner, J.~L., \\& Ho, P.~T.~P. 1994,\n\\apj, 421, 122\n\n\\reference{}\nUrbanik, M., Gr\\\"ave, R., \\& Klein, U. 1985, \\aap, 152, 291\n\n\\reference{}\nUrbanik, M., Klein, U., \\& Gr\\\"ave, R. 1986, \\aap, 166, 107\n\n\\reference{}\nvan Breugel, W.~J.~M., Schilizzi, R.~T., Hummel, E., \\& Kapahi, V.~K. 1981, \n\\aap, 96, 310\n\n\\reference{}\nvan der Hulst, J.~M., Crane, \\& P.~C., Keel, W.~C. 1981, \\aj, 86, 1175\n\n\\reference{}\nvan der Kruit, P.~C. 1973a, \\aap, 29, 231\n\n\\reference{}\nvan der Kruit, P.~C. 1973b, \\aap, 29, 249\n\n\\reference{}\nVan Dyk, S.~D., \\& Ho, L.~C. 1998, in IAU Symp. 184, The Central Regions of\nthe Galaxy and Galaxies, ed. Y. Sofue (Dordrecht: Kluwer), 489\n\n\\reference{}\nV\\'eron-Cetty, M.-P., \\& V\\'eron, P. 1996, \\aaps, 115, 97\n\n\\reference{}\nVila, M.~B., Pedlar, A., Davies, R.~D., Hummel, E., \\& Axon, D.~J. 1990, \n\\mnras, 242, 379\n\n\\reference{}\nWeiler, K.~W., van der Hulst, J.~M., Sramek, R.~A., \\& Panagia, N. 1981,\n\\apj, 243, L151\n\n\\reference{}\nWhite, R.~L., \\& Becker, R.~J. 1992,\n\\apjs, 79, 331\n\n\\reference{}\nWrobel, J.~M., \\& Heeschen, D.~S. 1984, \\apj, 287, 41\n\n\\reference{}\nWrobel, J.~M., \\& Heeschen, D.~S. 1991,\n\\aj, 101, 148\n\n\\reference{}\nZirbel, E.~L., \\& Baum, S.~A. 1995, \\apj, 448, 521 \n \n\\end{references}\n\n\\clearpage \n\n% TABLE 1\n%\\setcounter{table}{0}\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{l c c c c c c r}\n\\tableline\n\\tableline\n\nGalaxy & Other & R.A.(J2000) & Dec(J2000) & D & & Hubble Type & Reference \\\\\n & name & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ}$ $^{'}$ $^{''}$ & Mpc & & & \\\\\n\\tableline \nIC\\,520 & & 08 53 42.3 & +73 29 29 & 47.0 & & SAB(rs)ab? & 26\\\\\nNGC\\,2541 & & 08 14 40.2 & +49 03 42 & 10.6 & & SA(s)cd & 26,41\\\\\nNGC\\,2985 & & 09 50 20.9 & +72 16 44 & 22.4 & & (R')SA(rs)ab & 1,2,5,26,41,42 \\\\\nNGC\\,3627 & M\\,66 & 11 20 14.9 & +12 59 21 & 6.6 & & SAB(s)b & 1,5,6,11,13,14\\\\\n & & & & & & & 17,24,26,28,41,44\\\\\nNGC\\,3628 & & 11 20 16.2 & +13 35 22 & 7.7 & & SAb pec spin & 1,4,5,11,13,14,16\\\\\n &&&&&&& 17,18,19,24,26,30\\\\\n &&&&&&& 34,36,38,41,44,45\\\\\nNGC\\,3675 & & 11 26 08.0 & +43 34 58 & 12.8 & & SA(s)b & 1,3,17,25,26,41\\\\\n &&&&&&& 42,47\\\\\nNGC\\,3681 & & 11 26 29.4 & +16 51 51 & 24.2 & & SAB(r)bc & 1\\\\\nNGC\\,4013 & & 11 58 31.1 & +43 56 50 & 17.0 & & SAb spin & 1,3,15,26,41\\\\\nNGC\\,4321 & M\\,100& 12 22 54.8 & +15 49 20 & 16.8 & & SAB(s)bc & 1,5,7,11,13,14,17\\\\\n &&&&&&& 18,20,22,24,26,27\\\\\n &&&&&&& 35,36,41,47\\\\\nNGC\\,4414 & & 12 26 27.2 & +31 13 24 & 16.8 & & SA(rs)c? & 1,3,5,11,13,14\\\\\n &&&&&&& 17,18,24,26,31,36\\\\\nNGC\\,4552 & M\\,89 & 12 35 39.9 & +12 33 25 & 9.7 & & E & 1,13,14,17,22,29\\\\\n &&&&&&& 37,38,39,41,43,44\\\\\nNGC\\,4643 & & 12 43 20.2 & +01 58 41 & 16.8& & SB(rs)0/a & 21,24,41\\\\\nNGC\\,4713 & & 12 49 57.8 & +05 18 39 & 25.7 & & SAB(rs)d & 1\\\\\nNGC\\,4826 & M\\,64 & 12 56 44.2 & +21 41 05 & 17.9 & & (R)SA(rs)ab & 1,2,8,13,14,17,24,25\\\\\n &&&&&&& 26,36,40,41,44,46\\\\\nNGC\\,5012 & &13 11 36.8 & +22 54 56 & 4.1 & & SAB(rs)c & 1\\\\\nNGC\\,5354 && 13 53 26.7 & +40 18 09 & 32.8 & & SA0 spin & 1,3,12,17,32,41,44\\\\\nNGC\\,5656 && 14 30 25.5 & +35 19 17 & 42.6 & & SAab & 1\\\\\nNGC\\,5678 && 14 32 05.2 & +57 55 23 & 35.6 & & SAB(rs)b & 1,13,14,17,18,31\\\\\nNGC\\,5838 && 15 05 26.5 & +02 06 01 & 28.5 & & SA0$^{-}$ & 1\\\\\nNGC\\,5846 && 15 06 29.2 & +01 36 21 & 28.5 & & E0$^{-}$ & 1,9,10,12,41\\\\\nNGC\\,5879 && 15 09 47.1 & +57 00 05 & 16.8 & & SA(rs)bc? & 1,41\\\\\nNGC\\,5921 && 15 21 56.3 & +05 04 11 & 25.2 & & SB(r)bc & 1,24,26,41\\\\\nNGC\\,6384 && 17 32 24.5 & +07 03 37 & 26.6 & & SAB(r)bc & 5,17,24,26,41\\\\\nNGC\\,6482 && 17 51 48.9 & +23 04 20 & 52.3 & & E: & \\nodata \\\\\nNGC\\,6503 && 17 49 27.5 & +70 08 41 & 6.1 & & SA(s)cd & 1,5,26,41,42\\\\\n\n\\tableline\n\\end{tabular}\n\\end{center}\n\\setcounter{table}{0}\n\\caption{Sample sources -- the 25 transition LINERs.}\n\\end{table}\n\n\\clearpage\n\n% TABLE 1 - (cont.)\n%\\setcounter{table}{0}\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{l c c c c c c r}\n\n\\tableline\n\\tableline\n\n\nGalaxy & Other & R.A.(J2000) & Dec(J2000) & D & & Hubble Type & Reference \\\\\n & name & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ}$ $^{'}$ $^{''}$ & Mpc & & & \\\\\n\\tableline\nNGC\\,3593 & & 11 14 36.0 & +12 49 06 & 5.5 & & SA(S)0/a: & 1,5,11,13,14,17\\\\\n & & & & & & & 18,24,26,33,41\\\\\nNGC\\,3684 & & 11 27 11.1 & +17 01 49 & 23.4 & & SA(rs)bc & 1\\\\\nNGC\\,4100 & & 12 06 08.1 & +49 34 59 & 17.0 & & (R')SA(rs)bc & 1,3,5,26,41,42\\\\\nNGC\\,4217 & & 12 15 50.7 & +47 05 37 & 17.0 & & SAb spin & 1,3,5,11,13,14\\\\\n &&&&&&& 15,17,26,41\\\\\nNGC\\,4245 & & 12 17 36.7 & +29 36 29 & 9.7 & & SB(r)0/a & \\nodata\\\\\nNGC\\,4369 & Mrk\\,439 & 12 24 36.1 & +39 22 58 & 21.6 & & (R)SA(rs)a & 1,3,18,41\\\\\nNGC\\,4405 & IC\\,788 & 12 26 07.1 & +16 10 51 & 31.5 & & SA(rs)0: & 1\\\\\nNGC\\,4424 & & 12 27 11.4 & +09 25 15 & 16.8 & & SA(s)a: & 1\\\\\nNGC\\,4470 & & 12 29 37.9 & +07 49 25 & 31.4 & & Sa ? & 1\\\\\nNGC\\,4710 & & 12 49 38.9 & +15 09 55 & 16.8 & & SA(r)0+? spin & 1,12,15,18,32,36\\\\\n &&&&&&& 41,43\\\\\nNGC\\,4800 && 12 54 38.0 & +46 31 52 & 15.2 & & SA(rs)b & 1,3,41\\\\\nNGC\\,4845 & & 12 58 01.3 & +01 34 30& 15.6 & & SA(s)ab spin & 1,18\\\\\n\\tableline\n \n\\end{tabular}\n\\end{center}\n\\setcounter{table}{0}\n\\caption{Sample sources -- the 12 H\\,II nuclei (cont.).}\n\\end{table}\n\n\n%Table 2\n\\begin{table}\n\\small\n\\begin{center}\n\\begin{tabular}[h]{ll|ll}\n\\tableline\n\\tableline\nNo. & Reference & No. & Reference \\\\\n\\tableline\n\n1 & Condon \\etal 1998a & 25 & Gioia \\& Fabbiano 1987 \\\\\n2 & Condon \\etal 1998b & 26 & Condon 1987 \\\\\n3 & Becker \\etal 1995 & 27 & Urbanik \\etal 1986\\\\\n4 & Dumke \\etal 1995 & 28 & Urbanik \\etal 1985\\\\\n5 & Niklas \\etal 1995 & 29 & Wrobel \\& Heeschen 1984\\\\\n6 & Saikia \\etal 1994 & 30 & Schlickeiser et al. 1984\\\\\n7 & Collison \\etal 1994 & 31 & Condon 1983\\\\\n8 & Turner \\& Ho 1994 & 32 & Hummel \\& Kotanyi 1982\\\\\n9 & Slee \\etal 1994 & 33 & Jenkins \\etal 1982 \\\\\n10 & M\\\"ollenhoff \\etal 1992 & 34 & Condon \\etal 1982\\\\\n11 & White \\& Becker 1992 & 35 & Weiler \\etal 1981\\\\\n12 & Wrobel \\& Heeschen 1991 & 36 & van der Hulst \\etal 1981\\\\\n13 & Becker \\etal 1991 & 37 & van Breugel \\etal 1981\\\\\n14 & Gregory \\& Condon 1991 & 38 & Jones \\etal 1981a\\\\\n15 & Hummel \\etal 1991 & 39 & Jones \\etal 1981b\\\\\n16 & Reuter \\etal 1991 & 40 & Klein \\& Emerson 1981\\\\\n17 & Condon \\etal 1991 & 41 & Hummel \\etal 1980\\\\\n18 & Condon \\etal 1990 & 42 & Heckman \\etal 1980 \\\\\n19 & Carral \\etal 1990 & 43 & Dressel \\& Condon 1978 \\\\\n20 & Vila \\etal 1990 & 44 & Sramek 1975a \\\\\n21 & Fabbiano \\etal 1989 & 45 & Haynes \\& Sramek 1975\\\\\n22 & Turner \\etal 1988 & 46 & van der Kruit 1973a\\\\\n23 & Condon \\& Broderick 1988 & 47 & van der Kruit 1973b\\\\ \n24 & Hummel \\etal 1987 & & \\\\\n\n\\tableline \n\\end{tabular}\n\\end{center}\n\\setcounter{table}{1}\n\\caption{References for the radio data (see Table~1).}\n\\end{table}\n\n\n\\clearpage\n\n\n%TABLE 3\n\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{lccrcr}\n\\tableline\n\\tableline\n\nGalaxy & Taper & Beamsize & PA & $rms$ & Fig. No. \\\\\n & K$\\lambda $ & arcsec$^2$ & $^{\\circ }$ & mJy/beam & \\\\ \n\\tableline \nNGC\\,2985 & 0 & 2.98 $\\times $ 2.15 & $-$7.19 & 0.08 & \\\\\n & 20 & 9.30 $\\times $ 7.20 & $-$84.28 & 0.09 & 1a\\\\\nNGC\\,3627 & 0 & 2.55 $\\times $ 2.29 & $-$25.24 & 0.10 & \\\\\n & 15 & 10.96 $\\times $ 9.93 & $-$64.54 & 0.25 & 1c\\\\\t \nNGC\\,3628 & 0 & 2.54 $\\times $ 2.30 & $-$14.68 & 0.45 & \\\\\n & 20 & 8.78 $\\times $ 7.48 & $-$76.82 & 0.80 & 1d\\\\\nNGC\\,3675 & 25 & 7.27 $\\times $ 5.81 & 71.04 & 0.09 & 2a\\\\\nNGC\\,4013 & 0 & 2.52 $\\times $ 2.26 & $-$19.39 & 0.07 & \\\\\n & 30 & 5.90 $\\times $ 5.26 & 77.17 & 0.09 & 2b\\\\\nNGC\\,4321 & 0 & 2.52 $\\times $ 2.33 & $-$11.27 & 0.07 & \\\\\n & 30 & 7.25 $\\times $ 5.14 & $-$89.95 & 0.08 & 3a\\\\\nNGC\\,4414 & 0 & 2.43 $\\times $ 2.32 & $-$37.18 & 0.08 &\\\\\n & 10 & 18.70 $\\times $ 17.70 & $-$62.41 & 0.15 & 3c\\\\\nNGC\\,4552 & 0 & 2.93 $\\times $ 2.54 & 11.27 & 0.08 & 4b\\\\\nNGC\\,4643 & 15 & 12.04 $\\times $ 11.13 & 52.57 & 0.07 & 4c\\\\\nNGC\\,4713 & 15 & 12.12 $\\times $ 10.95 & 44.22 & 0.08 & 5a\\\\\nNGC\\,4826 & 0 & 2.76 $\\times $ 2.29 & $-$6.23 & 0.08 & \\\\\n & 20 & 9.62 $\\times $ 8.26 & 62.33 & 0.10 & 5c\\\\\nNGC\\,5012 & 15 & 11.59 $\\times $ 11.18 & 74.66 & 0.08 & 6a\\\\\nNGC\\,5354 & 0 & 2.84 $\\times $ 2.37 & $-$42.75 & 0.06 & 6b \\\\\n \nNGC\\,5656 & 20 & 9.54 $\\times $ 8.39 & 75.33 & 0.08 & 6c\\\\\nNGC\\,5678 & 0 & 2.99 $\\times $ 2.21 & $-$27.47 & 0.07 &\\\\\n & 15 & 11.09 $\\times $ 10.75 & $-$34.43 & 0.10 & 6d\\\\\nNGC\\,5838 & 0 & 3.13 $\\times $ 2.43 & 1.94 & 0.07 & \\\\\n & 35 & 5.62 $\\times $ 5.23 & 51.83 & 0.07 & 7a\\\\\nNGC\\,5846 & 0 & 3.13 $\\times $ 2.49 & 3.94 & 0.07 &\\\\\n & 30 & 7.06 $\\times $ 5.67 & 68.01 & 0.07 & 7b\\\\\nNGC\\,5921 & 20 & 7.12 $\\times $ 5.63 & 67.8 & 0.06 & 7c \\\\\n\\tableline\n\\tableline\n\nGalaxy & Taper & Beamsize & PA & $rms$ & Fig. No. \\\\\n & K$\\lambda $ & arcsec$^2$ & $^{\\circ }$ & mJy/beam & \\\\ \n\\tableline\n\nNGC\\,3593 & 0 & 2.58 $\\times $ 2.36 & $-$17.94 & 0.09 & \\\\ \n & 20 & 9.70 $\\times $ 7.17 & $-$80.16 & 0.15 & 1b \\\\\nNGC\\,4100 & 0 & 2.61 $\\times $ 2.35 & $-$29.79 & 0.07 & \\\\\n & 20 & 7.83 $\\times $ 7.40 & 84.07 & 0.08 & 2c \\\\\nNGC\\,4217 & 20 & 7.30 $\\times $ 5.41 & 76.75 & 0.09 & 2d\\\\\nNGC\\,4369 & 0 & 2.48 $\\times $ 2.34 & $-$14.62 & 0.07 & \\\\\n & 30 & 6.94 $\\times $ 5.51 & 88.71 & 0.10 & 3b \\\\\nNGC\\,4424 & 0 & 3.00 $\\times $ 2.46 & 12.14 & 0.09 & \\\\\n & 30 & 7.21 $\\times $ 5.60 & 76.27 & 0.07 & 3d\\\\\nNGC\\,4470 & 15 & 9.95 $\\times $ 7.99 & 59.70 & 0.07 & 4a\\\\\nNGC\\,4710 & 0 & 2.86 $\\times $ 2.48 & 3.88 & 0.10 &\\\\\n & 30 & 5.50 $\\times $ 5.16 & 72.46 & 0.08 & 4d\\\\\nNGC\\,4800 & 30 & 5.28 $\\times $ 5.15 & $-$82.56 & 0.10 & 5b\\\\\nNGC\\,4845 & 0 & 3.27 $\\times $ 2.44 & 15.08 & 0.08 & \\\\\n & 30 & 7.08 $\\times $ 5.69 & 64.51 & 0.10 & 5d \\\\\n\n\\tableline\n\\end{tabular}\n\\end{center}\n\\setcounter{table}{2}\n\\caption {Map parameters of the detected sources. The H\\,II nuclei appear\nbelow the transition LINERs.}\n\\end{table}\n\n\\clearpage \n\n\n\n%TABLE 4\n\n\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{lcccccrr}\n\\tableline\n\\tableline\n\n\nField Source & R.A.(J2000) & Dec(J2000) & z & NVSS & F$_{\\rm 8.4}^{\\rm int}$ & $\\alpha ^{\\rm 8.4}_{\\rm 1.4}$ & \nReference \\\\\n & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ }$ $^{'}$ $^{''}$ & & mJy & mJy & & \\\\ \n\\tableline\n\nNGC\\,3593N & 11 14 37.20 & +12 52 15.0 & \\nodata & 18.7 & 10.6 & 0.3 & \\nodata\\\\\nNGC\\,3684SW & 11 27 02.42 & +16 58 34.8 & \\nodata & 41.4 & 18.1 & 0.5 & \\nodata\\\\\nNGC\\,4013SE & 11 58 38.61 & +43 55 05.5 & \\nodata & \\nodata & 3.8 & \\nodata & \\nodata\\\\\nSN\\,1979C & 12 22 58.67 & +15 47 51.6 & 0.0052 & \\nodata & 1.3 & \\nodata & Weiler \\etal 1981 \\\\\nLBQS\\,1223+1626 & 12 25 59.09 & +16 10 21.2 & 1.9290 & 8.9 & 10.1 & $-$0.1 & Hewett \\etal 1995 \\\\\nNGC\\,4424SE & 12 27 19.83 & +09 23 03.0 & \\nodata & 11.0 & 13.3 & $-$0.1 & \\nodata \\\\\nTXS\\,1227+081 & 12 29 47.64 & +07 50 26.7 & \\nodata & 110.9 & 16.0 & 1.1 & Douglas \\etal 1996 \\\\\nNGC\\,4710E & 12 49 48.63 & +15 09 33.3 & \\nodata & 4.1 & 4.8 & $-$0.1& \\nodata \\\\ \nNGC\\,5353 & 13 53 26.69 & +40 16 58.7 & 0.0077 & 41.0 & 26.7 & 0.2 & Hummel \\& Kotanyi 1982\\\\\nNGC\\,5838S & 12 05 28.11 & +02 04 16.2 & \\nodata & 7.5 & 1.3 & 1.0 & \\nodata \\\\ \n87GB\\,1508+5714 & 15 10 02.97 & +57 02 43.6 & 4.3010 & 202.4 & 292.1 & $-$0.2 & Hook \\etal 1995 \\\\\n87GB\\,1749+2302 & 17 51 49.10 & +23 01 26.7 & 0.7700 & 45.3 & 23.6 & 0.4 & Becker \\etal 1991 \\\\\nBL\\,1749+701 & 17 48 32.87 & +70 05 52.5 & \\nodata & 735.6 & \\nodata & \\nodata & Hughes \\etal 1992 \\\\\n\n\\tableline \n\\end{tabular}\n\\end{center}\n\\setcounter{table}{3}\n\\caption{The field source parameters. The integrated 8.4\\,GHz flux densities \n(column~6) have been corrected for primary beam attenuation.}\n\\end{table}\n\n\\clearpage\n\n%TABLE 5\n\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{lccc cr}\n\\tableline\n\\tableline\nGalaxy & Taper & F$_{\\rm max}$ & R.A.(J2000) & Dec(J2000) & F$_{\\rm int}$ \\\\\n & K$\\lambda $ & mJy/beam & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ }$ $^{'}$ $^{''}$ & mJy \\\\ \n\\tableline \n\nNGC\\,2985 & 0 & 1.07 & 09 50 22.1 & +72 16 44 & $\\geq$1.9\\\\\n & 20 & 1.30 & 09 50 22.0 & +72 16 44 & $\\geq$2.7 \\\\\t\nNGC\\,3627 & 0 & 1.30 & 11 20 15.0 & +12 59 30 & 3.7 ($\\geq$22.1) \\\\\n & 15 & 2.99 & 11 20 15.1 & +12 59 31 & 3.9 ($\\geq$25.7)\\\\\nNGC\\,3628 & 0 & 15.31 & 11 20 17.0 & +13 35 20 & 61.4 \\\\\n & 20 & 41.07 & 11 20 17.0 & +13 35 19 & 69.1\\\\\nNGC\\,3675 & 25 & 0.37 & 11 26 08.7 & +43 35 01 & $\\geq$1.3 \\\\\n\nNGC\\,4013 & 0 & 1.08 & 11 58 31.4 & +43 56 51 & $\\geq$3.8 \\\\\n & 30 & 2.28 & 11 58 31.4 & +43 56 51 & $\\geq$4.1 \\\\\nNGC\\,4321 & 0 & 0.34 & 12 22 55.4 & +15 49 21 & 7.5\\\\\n & 30 & 1.64 & 12 22 55.3 & +15 49 21 & 15.7\\\\\nNGC\\,4414 & 0 & 0.65 & 12 26 27.5 & +31 13 40 & 2.3 \\\\\n & 10 & 3.72 & 12 26 26.7 & +31 13 42 & 29.4\\\\\nNGC\\,4552 & 0 & 76.51 & 12 35 39.8 & +12 33 23 & 76.8 \\\\\n \nNGC\\,4643 & 15 & \\nodata & \\nodata & \\nodata & $\\sim$1 \\\\\nNGC\\,4713 & 15 & 0.32 & 12 49 58.4 & +05 18 39 & $\\geq$1.2\\\\\nNGC\\,4826 & 0 & 1.8 & 12 56 43.4 & +21 41 01 & 18.9\\\\\n & 20 & 4.03 & 12 56 43.7 & +21 41 00 & 21.1\\\\\nNGC\\,5012 & 15 & \\nodata& \\nodata & \\nodata & $\\sim$1 \\\\\nNGC\\,5354 & 0 & 11.61 & 13 53 26.7 & +40 18 10 & 11.7 \\\\\n \nNGC\\,5656 & 20 & 0.40 & 14 30 26.9 & +35 19 25 & $\\geq$0.7\\\\\nNGC\\,5678 & 0 & 0.74 & 14 32 05.9 & +57 54 51 & $\\geq$2.0 \\\\\n & 15 & 1.31 & 14 32 05.5 & +57 54 51 & $\\geq$8.6\\\\\n\nNGC\\,5838 & 0 & 1.85 & 15 05 26.3 & +02 05 57 & 2.1\\\\\n & 35 & 1.88 & 15 05 26.3 & +02 05 57 & 2.2 \\\\\n\nNGC\\,5846 & 0 & 6.03 & 15 06 29.3 & +01 36 21 & 6.4 \\\\\n & 30 & 6.36 & 15 06 29.3 & +01 36 21 & 7.1\\\\\n\nNGC\\,5921 & 20 & 0.46 & 15 21 56.4 & +05 04 14 & $\\geq$0.8 \\\\\n\\tableline\n\\tableline\n\nGalaxy & Taper & F$_{\\rm max}$ & R.A.(J2000) & Dec(J2000) & F$_{\\rm int}$ \\\\\n & K$\\lambda $ & mJy/beam & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ }$ ' '' & mJy \\\\ \n\\tableline \n\nNGC\\,3593 & 0 & 1.82 & 11 14 36.4 & +12 49 06 & 16.4 \\\\ \n & 20 & 4.79 & 11 14 36.6 & +12 49 05 & 20.0 \\\\\nNGC\\,4100 & 0 & 0.93 & 12 06 08.6 & +49 34 58 & $\\geq$3.9 \\\\\n & 20 & 3.58 & 12 06 08.4 & +49 34 59 & $\\geq$7.3 \\\\\nNGC\\,4217 & 20 & 0.55 & 12 15 51.0 & +47 05 29 & $\\geq$22.0 \\\\\nNGC\\,4369 & 0 & 0.31 & 12 24 36.3 & +39 22 56 & 1.3 \\\\\n & 30 & 1.31 & 12 24 36.3 & +39 22 57 & 3.8 \\\\\nNGC\\,4424 & 0 & 0.60 & 12 27 11.2 & +09 25 17 & 2.0 \\\\\n & 30 & 0.80 & 12 27 11.7 & +09 25 17 & 2.5 \\\\\n\nNGC\\,4470 & 15 & 0.38 & 12 29 37.8 & +07 49 24 & $\\geq$2.6 \\\\\nNGC\\,4710 & 0 & 0.71 & 12 49 38.9 & +15 09 59 & $\\geq$6.0 \\\\\n & 30 & 1.64 & 12 49 39.0 & +15 09 58 & 6.1 \\\\\nNGC\\,4800 & 30 & 0.36 & 12 54 37.8 & +46 31 52 & $\\geq$1.2 \\\\\nNGC\\,4845 & 0 & 1.76 & 12 58 01.2 & +01 34 32 & $\\geq$9.9 \\\\\n & 30 & 5.15 & 12 58 01.1 & +01 34 32 & 12.5 \\\\\n\n\n\\tableline \n\\end{tabular}\n\\end{center}\n\\setcounter{table}{4}\n\\caption{The 8.4\\,GHz radio parameters of the detected sources. The \nH\\,II nuclei appear below the transition LINERs.}\n\\end{table}\n\n\\clearpage\n\n\n%TABLE 6\n\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{l c r c r c}\n\\tableline\n\\tableline\n\nGalaxy & NVSS & F$_{\\rm 8.4}^{\\rm int}$ & Log L$_{\\rm 1.4}^{\\rm tot}$ & \n$\\alpha_{\\rm 1.4}^{\\rm 8.4}$ & Hubble Type \\\\\n & mJy & mJy & erg s$^{-1}$ Hz$^{-1}$ & & \\\\\n\\tableline \nIC\\,520 & \\nodata & \\nodata & \\nodata & \\nodata & SAB(rs)ab?\\\\\nNGC\\,2541 & \\nodata & \\nodata & \\nodata & \\nodata & SA(s)cd \\\\\nNGC\\,2985 & 44.1 & 2.7 & 28.4 & 1.6 & (R')SA(rs)ab \\\\\nNGC\\,3627 & 324.9 & 3.9 (25.7) & 28.2 & 2.5 (1.5) & SAB(s)b \\\\\nNGC\\,3628 & 291.7 & 69.1 & 28.3 & 0.8 & SAb pec spin \\\\ \nNGC\\,3675 & 48.9 & 1.3 & 27.9 & 2.0 & SA(s)b \\\\\nNGC\\,3681 & 4.2 & \\nodata & 27.5 & \\nodata & SAB(r)bc \\\\\nNGC\\,4013 & 40.5 & 4.1 & 28.2 & 1.3 & SAb spin \\\\\nNGC\\,4321 & 87.1 & 15.7 & 28.5 & 1.0 & SAB(s)bc\\\\\nNGC\\,4414 & 242.2 & 29.4 & 28.4 & 1.2 & SA(rs)c? \\\\\nNGC\\,4552 & 103.1 & 76.8 & 28.5 & 0.2 & E \\\\\nNGC\\,4643 & \\nodata & $\\sim$1 & \\nodata & \\nodata & SB(rs)0/a \\\\\nNGC\\,4713 & 46.9 & 1.2 & 28.3 & 2.0 & SAB(rs)d \\\\\nNGC\\,4826 & 101.1 & 21.1 & 27.3 & 0.9 & (R)SA(rs)ab\\\\\nNGC\\,5012 & 31.4 & $\\sim$1 & 28.8 & \\nodata & SAB(rs)c \\\\\nNGC\\,5354 & 8.4 & 11.7 & 28.0 & $-$0.2 & SA0 spin \\\\\nNGC\\,5656 & 22.0 & 0.7 & 28.7 & 2.0 & SAab \\\\\nNGC\\,5678 & 111.5 & 8.6 & 29.2 & 1.4 & SAB(rs)b \\\\\nNGC\\,5838 & 3.0 & 2.2 & 27.5 & 0.2 & SA0$^{-}$ \\\\\nNGC\\,5846 & 22.1 & 7.1 & 28.3 & 0.6 & E0$^{-}$ \\\\\nNGC\\,5879 & 21.1 & \\nodata & 27.9 & \\nodata & SA(rs)bc?\\\\\nNGC\\,5921 & 24.2 & 0.8 & 28.3 & 1.9 & SB(r)bc\\\\\nNGC\\,6384 & \\nodata & \\nodata & \\nodata & \\nodata & SAB(r)bc\\\\\nNGC\\,6482 & \\nodata & \\nodata & \\nodata & \\nodata & E: \\\\\nNGC\\,6503 & 40.0 & \\nodata & 27.3 & \\nodata & SA(s)cd\\\\\n\n\\tableline\n\\tableline\nGalaxy & NVSS & F$_{\\rm 8.4}^{\\rm int}$ & Log L$_{\\rm 1.4}^{\\rm tot}$& \n$\\alpha_{\\rm 1.4}^{\\rm 8.4}$ & Hubble Type \\\\\n & mJy & mJy & erg s$^{-1}$ Hz$^{-1}$ & & \\\\\n\\tableline \n \nNGC\\,3593 & 87.3 & 20.0 & 27.5 & 0.8 & SA(S)0/a: \\\\\nNGC\\,3684 & 15.9 & \\nodata & 28.0 & \\nodata & SA(rs)bc \\\\\nNGC\\,4100 & 50.3 & 7.3 & 28.2 & 1.1 & (R')SA(rs)bc \\\\\nNGC\\,4217 & 122.8 & 22.0 & 28.6 & 1.0& SAb spin \\\\\nNGC\\,4245 & \\nodata & \\nodata & \\nodata & \\nodata & SB(r)0/a \\\\\nNGC\\,4369 & 24.3 & 3.8 & 28.1 & 1.0 & (R)SA(rs)a \\\\\nNGC\\,4405 & 4.5 & \\nodata & 27.7 & \\nodata & SA(rs)0: \\\\\nNGC\\,4424 & 4.5 & 2.5 & 27.2 & 0.3 & SA(s)a: \\\\\nNGC\\,4470 & 17.1 & 2.6 & 28.3 & 1.1 & Sa ? \\\\\nNGC\\,4710 & 19.3 & 6.1 & 27.8 & 0.7 & SA(r)0+? spin \\\\\nNGC\\,4800 & 23.5 & 1.2 & 27.8 & 1.7 & SA(rs)b \\\\\nNGC\\,4845 & 43.8 & 12.5 & 28.1 & 0.7 & SA(s)ab spin \\\\\n\n\\tableline\n\\end{tabular}\n\\end{center}\n\\setcounter{table}{5}\n\\caption{Summary of the detected sources. The H\\,II nuclei appear\n below the transition LINERs. All tabulated spectral index values are upper\nlimits (see Section~4.3).}\n\\end{table}\n\n\n\n\n\\clearpage\n\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f1a.ps}\n(a) \n\\epsfxsize=7.3cm\n\\raisebox{1.4cm}{\n\\epsffile{f1b.ps}\n(b)\n}\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{1}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f1c.ps}\n(c)\n\\epsfxsize=7.3cm\n\\raisebox{1.4cm}{\n\\epsffile{f1d.ps}\n(d)\n}\n}\n\n\\caption{Radio emission (contours) superimposed on optical images from \nthe Digitized Sky Survey (greyscale). Contour levels are CLEV $\\times$ \n(--3, 3, 6, 12, 24, 48, 96), where CLEV is the $rms$ noise level (see Table~3). \nThe grey scale levels are arbitrary. The size of the restoring \nbeam is given in parentheses after each object name (see Table~3).\n{\\bf (a)} NGC\\,2985 (9\\arcsecpoint30 $\\times$ 7\\arcsecpoint20), {\\bf (b)} \nNGC\\,3593 (9\\arcsecpoint70 $\\times$ 7\\arcsecpoint17), {\\bf (c)} NGC\\,3627 (10\\arcsecpoint96 $\\times$ 9\\arcsecpoint93) and {\\bf (d)} NGC\\,3628 \n(8\\arcsecpoint78 $\\times$ 7\\arcsecpoint48). NGC\\,3593 is an H\\,II nucleus. }\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f2a.ps}\n(a)\n\\epsfxsize=7.3cm\n\\raisebox{1.8cm}{\n\\epsffile{f2b.ps}\n(b)\n}\n}\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{2}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f2c.ps}\n(c)\n\\epsfxsize=7.3cm\n\\raisebox{1cm}{\n\\epsffile{f2d.ps}\n(d)\n}\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,3675 (7\\arcsecpoint27 $\\times$ 5\\arcsecpoint81), {\\bf (b)} NGC\\,4013\n(5\\arcsecpoint90 $\\times$ 5\\arcsecpoint26), {\\bf (c)} NGC\\,4100 (7\\arcsecpoint83 $\\times$ 7\\arcsecpoint40) and {\\bf (d)}\nNGC\\,4217 (7\\arcsecpoint30 $\\times$ 5\\arcsecpoint41). NGC\\,4100 and NGC\\,4217 are H\\,II nuclei.}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\raisebox{0.1cm}{\n\\epsffile{f3a.ps}\n(a)\n}\n\\epsfxsize=7.3cm\n\\epsffile{f3b.ps}\n(b)\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{3}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f3c.ps}\n(c)\n\\raisebox{1.6cm}{\n\\epsfxsize=7.3cm\n\\epsffile{f3d.ps}\n(d)\n}\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,4321 (7\\arcsecpoint25 $\\times$ 5\\arcsecpoint14), {\\bf (b)} NGC\\,4369\n(6\\arcsecpoint94 $\\times$ 5\\arcsecpoint51), {\\bf (c)} NGC\\,4414 (18\\arcsecpoint17 $\\times$ 17\\arcsecpoint70) and {\\bf (d)} NGC\\,4424\n(7\\arcsecpoint21 $\\times$ 5\\arcsecpoint60). NGC\\,4369 and NGC\\,4424 are H\\,II nuclei.}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f4a.ps}\n(a)\n\\epsfxsize=7.3cm\n\\raisebox{0.4cm}{\n\\epsffile{f4b.ps}\n(b)\n}\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{4}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\raisebox{1.8cm}{\n\\epsffile{f4c.ps}\n(c)\n}\n\\epsfxsize=7.3cm\n\\epsffile{f4d.ps}\n(d)\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,4470 (9\\arcsecpoint95 $\\times$ 7\\arcsecpoint99), {\\bf (b)} NGC\\,4552\n(2\\arcsecpoint93 $\\times$ 2\\arcsecpoint54), {\\bf (c)} NGC\\,4643 (12\\arcsecpoint04 $\\times$ 11\\arcsecpoint13) and {\\bf (d)}\nNGC\\,4710 (5\\arcsecpoint50 $\\times$ 5\\arcsecpoint16). NGC\\,4470 and NGC\\,4710 are H\\,II nuclei.}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\raisebox{1cm}{\n\\epsffile{f5a.ps}\n(a)\n}\n\\epsfxsize=7.3cm\n\\epsffile{f5b.ps}\n(b)\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{5}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f5c.ps}\n(c)\n\\epsfxsize=7.3cm\n\\raisebox{0.6cm}{\n\\epsffile{f5d.ps}\n(d)\n}\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,4713 (12\\arcsecpoint12 $\\times$ 10\\arcsecpoint95), {\\bf (b)} NGC\\,4800\n(5\\arcsecpoint28 $\\times$ 5\\arcsecpoint15), {\\bf (c)} NGC\\,4826 (9\\arcsecpoint62 $\\times$ 8\\arcsecpoint26) and {\\bf (d)} NGC\\,4845\n(7\\arcsecpoint08 $\\times$ 5\\arcsecpoint69). NGC\\,4845 is an H\\,II nucleus.}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f6a.ps}\n(a)\n\\epsfxsize=7.3cm\n\\raisebox{1.1cm}{\n\\epsffile{f6b.ps}\n(b)\n}\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{6}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\raisebox{0.6cm}{\n\\epsffile{f6c.ps}\n(c)\n}\n\\epsfxsize=7.3cm\n\\epsffile{f6d.ps}\n(d)\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,5012 (11\\arcsecpoint59 $\\times$ 11\\arcsecpoint18), {\\bf (b)} NGC\\,5354\n(2\\arcsecpoint84 $\\times$ 2\\arcsecpoint37), {\\bf (c)} NGC\\,5656 (9\\arcsecpoint54 $\\times$ 8\\arcsecpoint39) and {\\bf (d)} NGC\\,5678\n(11\\arcsecpoint09 $\\times$ 10\\arcsecpoint75).}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f7a.ps}\n(a)\n\\epsfxsize=7.3cm\n\\raisebox{0.3cm}{\n\\epsffile{f7b.ps}\n(b)\n}\n}\n\\end{figure}\n\n\\begin{figure}\n\\figurenum{7}\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f7c.ps}\n(c)\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,5838 (5\\arcsecpoint62 $\\times$ 5\\arcsecpoint23), {\\bf (b)} NGC\\,5846\n(7\\arcsecpoint06 $\\times$ 5\\arcsecpoint67) and {\\bf (c)} NGC\\,5921 (7\\arcsecpoint12 $\\times$ 5\\arcsecpoint63).}\n\n\\end{figure}\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"}],"string":"[\n {\n \"name\": \"ms.tex\",\n \"string\": \"% VERSION MEF JULY 7\\n% EDITED BY PDB JULY 7\\n% EDITED MEF JULY 12\\n% more editing pdb, july 13-14\\n% EDITED MEF JULY 15\\n% more editing PDB, July 18-19\\n% VERSION MEF JULY 21 with PDB's July 20th stuff\\n% more editing PDB July 25, MEF (tables)\\n% polishing PDB July 26\\n% MEF July 27 with PDB's STUFF\\n% EDITED + 3 TRANSITION OBJECTS (SEP 16) (suppressed)\\n% EDITED + PBCOR (SEP 17) \\n% EDITED NEW VERSION (OCT. 11)\\n% EDITED (OCT. 28) PICTURES INSERTED\\n% NEW INTRODUCTION \\n% MORE EDITING PDB/MEF NOVEMBER 26\\n% EDITED LCH, Nov. 30 1999\\n% LAST POLISHING PDB, MEF DEC.8\\n% Few more typos fixed, LCH, Dec. 8 1999\\n% REVISED FEB. 7TH 2000\\n% REVISED FEB. 11TH 2000\\n% VERSION 50944 - FINAL VERSION FEB. 14TH 2000\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%\\\\documentstyle[12pt,aasms4]{article}\\n\\\\documentstyle[11pt,aaspp4,tighten]{article}\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\\\def\\\\gtaprx {\\\\lower .1ex\\\\hbox{\\\\rlap{\\\\raise .6ex\\\\hbox{\\\\hskip .3ex\\n {\\\\ifmmode{\\\\scriptscriptstyle >}\\\\else\\n {$\\\\scriptscriptstyle >$}\\\\fi}}}\\n \\\\kern -.4ex{\\\\ifmmode{\\\\scriptscriptstyle \\\\sim}\\\\else\\n {$\\\\scriptscriptstyle\\\\sim$}\\\\fi}}}\\n\\\\def\\\\ltaprx {\\\\lower .1ex\\\\hbox{\\\\rlap{\\\\raise .6ex\\\\hbox{\\\\hskip .3ex\\n {\\\\ifmmode{\\\\scriptscriptstyle <}\\\\else\\n {$\\\\scriptscriptstyle <$}\\\\fi}}}\\n \\\\kern -.4ex{\\\\ifmmode{\\\\scriptscriptstyle \\\\sim}\\\\else\\n {$\\\\scriptscriptstyle\\\\sim$}\\\\fi}}}\\n\\\\def\\\\etal {et al. }\\n\\\\def\\\\littleprime{\\\\ifmmode{\\\\scriptscriptstyle \\\\prime }\\n \\\\else{\\\\hbox{$\\\\scriptscriptstyle \\\\prime$ }}\\\\fi}\\n\\\\def\\\\littless{\\\\ifmmode{\\\\scriptscriptstyle s }\\n \\\\else{\\\\hbox{$\\\\scriptscriptstyle s $ }}\\\\fi}\\n\\\\def\\\\littlemm{\\\\ifmmode{\\\\scriptscriptstyle m }\\n \\\\else{\\\\hbox{$\\\\scriptscriptstyle m $ }}\\\\fi}\\n\\\\def\\\\littlehh{\\\\ifmmode{\\\\scriptscriptstyle h }\\n \\\\else{\\\\hbox{$\\\\scriptscriptstyle h $ }}\\\\fi}\\n\\\\def\\\\littlecirc{\\\\ifmmode{\\\\scriptscriptstyle \\\\circ }\\n \\\\else{\\\\hbox{$\\\\scriptscriptstyle \\\\circ $ }}\\\\fi}\\n\\\\def\\\\rasec{\\\\raise .9ex \\\\hbox{\\\\littless}}\\n\\\\def\\\\arcsec{\\\\raise .9ex\\n \\\\hbox{\\\\littleprime\\\\hskip-3pt\\\\littleprime\\\\hskip-3pt}}\\n\\\\def\\\\ramin{\\\\raise .9ex \\\\hbox{\\\\littlemm}}\\n\\\\def\\\\arcmin{\\\\raise .9ex \\\\hbox{\\\\littleprime}}\\n\\\\def\\\\hrs{\\\\raise .9ex \\\\hbox{\\\\littlehh}}\\n\\\\def\\\\deg{\\\\hbox{$^\\\\circ$}}\\n\\\\def\\\\degree{\\\\raise .9ex \\\\hbox{\\\\littlecirc}}\\n\\\\def\\\\magpoint{\\\\hbox to 2pt{}\\\\rlap{\\\\hskip -.5ex \\\\arcmm}.\\\\hbox to 2pt{}}\\n\\\\def\\\\arcsspoint{\\\\hbox to 1pt{}\\\\rlap{\\\\arcss}.\\\\hbox to 2pt{}}\\n\\\\def\\\\arcsecpoint{\\\\hbox to 1pt{}\\\\rlap{\\\\arcsec}.\\\\hbox to 2pt{}}\\n\\\\def\\\\arcminpoint{\\\\hbox to 1pt{}\\\\rlap{\\\\arcmin}.\\\\hbox to 2pt{}}\\n\\\\def\\\\degreepoint{\\\\hbox to 1pt{}\\\\rlap{\\\\degree}.\\\\hbox to 2pt{}}\\n\\n\\\\slugcomment{Accepted by {\\\\it The Astrophysical Journal Supplements}.}\\n\\n\\\\begin{document}\\n\\n\\\\title{The Nature of Composite LINER/H\\\\,II Galaxies, As Revealed from \\nHigh-Resolution VLA Observations}\\n\\n\\\\author{Mercedes E. Filho}\\n\\\\affil{Lisbon Observatory and Kapteyn Astronomical Institute}\\n\\\\authoraddr{P.O.~Box 800, NL--9700 AV Groningen, The~Netherlands}\\n%%\\\\email{Mercedes Esteves Filho (mercedes@astro.rug.nl)}\\n\\n\\\\author{Peter D. Barthel}\\n\\\\affil{Kapteyn Astronomical Institute}\\n\\\\authoraddr{P.O.~Box 800, NL--9700 AV Groningen, The~Netherlands}\\n\\n\\\\author{Luis C. Ho}\\n\\\\affil{Observatories of the Carnegie Institution of Washington}\\n\\\\authoraddr{813 Santa Barbara Street, Pasadena, CA 91101, USA}\\n\\n\\n\\\\begin{abstract}\\n\\nA sample of 37 nearby galaxies displaying composite LINER/H~II and pure\\nH~II spectra was observed with the VLA in an investigation of the nature\\nof their weak radio emission. The resulting radio contour maps overlaid\\non optical galaxy images are presented here, together with an\\nextensive literature list and discussion of the individual galaxies.\\nRadio morphological data permit assessment of the ``classical AGN''\\ncontribution to the global activity observed in these ``transition'' LINER\\ngalaxies. One in five of the latter objects display clear AGN\\ncharacteristics: these occur exclusively in bulge-dominated hosts.\\n\\n\\\\end{abstract}\\n\\n\\\\keywords{galaxies: active --- galaxies: nuclei --- galaxies: Seyfert --- \\nradio continuum: galaxies}\\n\\n\\\\section{Introduction}\\n\\nLINER galaxies are a class of active galaxies characterized by the presence of \\nstrong, nuclear, low-ionization emission lines (Heckman 1980). Like \\nSeyfert nuclei, LINERs emit much stronger optical low-ionization forbidden \\nlines compared to H~II nuclei, whose line emission is powered by \\nphotoionization from young massive stars, but LINERs have a characteristically\\nlower ionization state than Seyferts. In a recent optical survey of nearly \\n500 nearby galaxies, Ho, Filippenko, \\\\& Sargent (1995, 1997a, 1997b) find that\\n$\\\\sim$20\\\\% of all galaxies brighter than $B_T$ = 12.5\\\\,mag display\\nLINER-type spectra. An additional 13\\\\% of the objects show spectra \\nintermediate between those of ``pure'' LINERs and ``pure'' H\\\\,II nuclei. \\nHo, Filippenko, \\\\& Sargent (1993; see also Ho 1996) dubbed this class as \\n``transition objects,'' and they hypothesized that these might be composite \\nsystems in which the optical signal of a weak active nucleus (the LINER \\ncomponent) has been spatially blended by circumnuclear star-forming regions \\n(the H~II component).\\n\\nModels have shown that photoionization by hot stars are able to reproduce the\\noptical spectra of LINERs (Terlevich \\\\& Melnick 1985), especially those of \\nthe transition-type variety (Shields 1992; Filippenko \\\\& Terlevich 1992). \\nOther researchers have advocated shock-wave heating as a viable excitation \\nmechanism for LINERs (Fosbury \\\\etal 1978; Heckman 1980; Dopita \\\\& Sutherland \\n1995). At the same time, an increasing body of evidence suggests that a \\nsignificant fraction of LINERs do contain irrefutable AGN characteristics \\n(see reviews by Filippenko 1996 and Ho 1999b). Radio surveys, in particular, \\nhave shown that many LINERs exhibit weak nuclear radio emission (Heckman 1980;\\nSadler, Jenkins, \\\\& Kotanyi 1989; Wrobel \\\\& Heeschen 1991; Slee \\\\etal 1994; \\nFalcke, Wilson, \\\\& Ho 1997; Van Dyk \\\\& Ho 1998). As discussed in detail by\\nHo (1999a), weak nuclear radio emission in early-type (elliptical and S0) \\ngalaxies is most likely related to accretion-driven energy production in these \\nobjects, but at a very low level compared to powerful radio galaxies, which \\nare also usually hosted by early-type systems. \\n\\nRadio observations provide an expecially attractive tool to further our \\nunderstanding of the LINER phenomenon. Since radio frequencies are not plagued\\nby dust obscuration and photoelectric absorption, high-resolution radio\\nobservations potentially offer the cleanest and most efficient method to\\nisolate an AGN core. Although radio emission also arises from supernova\\nremnants and H\\\\,II regions, AGN cores can be identified through their \\nhigh degree of central concentration, small angular size, flat spectral \\nindices, and high brightness temperatures.\\n\\nGiven that LINERs are so numerous, they may be the most common type of\\nAGN known. Their large space densities could make a major impact on the faint \\nend of the local AGN luminosity function, which in turn has ramifications for \\nmany astrophysical issues ranging from the cosmological evolution of AGN to\\nthe contribution of AGN to the cosmic X-ray background. We are\\ntherefore conducting high-resolution radio observations of selected\\nLINER samples in order to investigate the interrelation between LINERs\\nand classical AGN. For the present paper --- the first in a series ---\\nwe have concentrated on transition-type LINERs. We report on sensitive \\nVery Large Array (VLA)\\\\footnote{The VLA is a facility of the National Radio \\nAstronomy Observatory (NRAO) which is a facility of the National Science \\nFoundation operated under cooperative agreement by Associated Universities, \\nInc.} C-array observations of a sample of 25 such transition LINERs at \\n8.4\\\\,GHz. The resulting images, having angular resolution of about \\n2\\\\arcsecpoint5, allow us to assess the strength and spatial distribution of \\nthe nuclear radio emission. For comparison, we have also observed a small\\nsample of 12 pure H\\\\,II nuclei. \\n\\nIn the following discussion and in upcoming papers, we adopt a\\nHubble constant of H$_{0}$ = 75~km~s$^{-1}$~Mpc$^{-1}$.\\n\\n\\\\section{Sample Selection}\\n\\nThe sample of 25 transition LINER/H\\\\,II galaxies and 12 pure H\\\\,II\\nnuclei was extracted from the original magnitude-limited Palomar survey of \\n486 bright northern galaxies (Ho \\\\etal 1995), following the classification \\ncriteria outlined in Ho et al. (1997a). The Palomar sample contains 65 \\ntransition nuclei (Ho et al. 1997a), from which we chose a subset of 25 that \\nhad little or no arcsec-scale resolution radio continuum data published, and\\nthat fell within the observation window assigned to us by the VLA. In \\naddition, we selected for comparison a small sample of 12 pure H\\\\,II nuclei \\n(out of 206 such objects in the full Palomar sample). These were chosen to\\nmimic the Hubble type distribution of the sample of transition objects, \\nagain taking into consideration scheduling constraints.\\nWe are not aware of any strong biases introduced by our sample selection. \\n\\nTable~1 lists the 37 sample objects. In addition to the optical positions of \\nthe galaxies (columns 3 and 4), this table lists their distance (column~5) \\nand their Hubble type (column~6). The Hubble types and distances are taken \\nfrom Ho \\\\etal (1997a). The ``reference'' column (7), together with Table~2,\\nsupplies references to earlier radio studies; it is readily apparent that\\nseveral of the sample objects are well-studied objects, while some are\\nnot. We will discuss our observational results in light of these existing \\ndata in Section~4. The sample galaxies span a wide range of Hubble types, but \\nthe majority are spirals.\\n\\n\\\\medskip \\\\centerline{\\\\bf -- TABLEs~1/2: Sample of transition LINER\\n galaxies and H\\\\,II nuclei --}\\n\\n\\\\section {Observations and Data Reduction}\\n\\nThe resulting sample of 25 composite LINER/H\\\\,II and 12 pure H\\\\,II galaxies was\\nobserved with the X-band (8.4\\\\,GHz) system of the VLA in two\\nobserving sessions, on 1997 August~21 and August~25. The array was in its\\nC-configuration, yielding a typical resolution of 2\\\\arcsecpoint5. Two\\nbands of 50\\\\,MHz each were combined, yielding a total bandwidth of\\n100\\\\,MHz. Snapshot observations combining two scans of 8--9~minutes\\neach, at different hour angles, were obtained in order to improve the\\nshape of the synthesized beam.\\n\\nSecondary phase and amplitude calibrators were observed before and after\\neach scan. The primary calibrator was 3C\\\\,286, with appropriate\\nbaseline constraints, and the adopted 8.4\\\\,GHz flux densities, as provided\\nby the VLA staff, were 5.22~Jy and 5.20~Jy, at IF1 and IF2, respectively. \\nThe calibration uncertainty is dominated by the uncertainty in the\\nabsolute flux density of the primary calibrator, which is a few percent. \\nThe array performed well: judging from the calibration sources,\\nthe antenna phase and amplitude calibration appeared stable to within a\\nfew percent. \\n\\nThe radio data are of high quality, and there was no need for\\nextensive flagging of discrepant points. Reduction of the data was\\nperformed using standard NRAO AIPS (version 15OCT98) image processing\\nroutines. AIPS task IMAGR was employed to Fourier transform the\\nmeasured visibilities and obtain CLEAN (H\\\\\\\"ogbom 1974; Clark 1980) maps of the sources. \\nFull-resolution\\nmaps, having synthesized beams of roughly 2\\\\arcsecpoint5, and tapered\\nmaps, having beams between about 5\\\\arcsec~and 12\\\\arcsec, were\\nmade. This proved useful to detect weak low surface brightness\\nemission. As a rule of thumb, 1\\\\arcsec~corresponds to 50--100~pc for the \\ntypical distances involved. Most images reach\\nthe theoretical noise level of $\\\\sim 0.04$~mJy/beam (Perley, Schwab, \\\\& Bridle \\n1989) to within a factor of two. Self-calibration was employed in\\nthe analysis of two of the stronger sources (NGC\\\\,4552 and NGC\\\\,5354), \\nleading to considerable improvements.\\n\\n\\\\section {Results}\\n\\n\\\\subsection {Radio Maps}\\n\\nNoting that a non-detection should be taken to imply no correlated flux\\ndensity in excess of 0.5~mJy on the arcsec scale, radio contour maps of\\nthe detected galaxies are presented in Figures 1--7, at the end of the\\npaper. The radio maps are overlayed on optical images taken from the\\nDigitized Sky Survey (DSS). In a number of cases only the\\nhigh-resolution map (typical beamsize 2\\\\arcsecpoint5) or the\\nlow-resolution map (typical beamsize 7\\\\arcsec~-- 10\\\\arcsec) are shown. \\nUnrelated background radio sources were found in several fields; their\\nnumber is entirely as expected given the size of the primary beam and\\nthe sensitivity of the observations. In cases of large distances from\\nthe field center, primary beam corrections were applied. Some of the\\nbackground sources have been identified using NED (NASA/IPAC\\nExtragalactic Database) and the Cambridge APM (Automatic Plate\\nMeasuring) facility. Where possible, we have included them by their\\nname in the tables below. Previously uncatalogued background sources\\nare designated by their sky orientation with respect to the field center\\nfor the relevant galaxy. All maps use contouring according to CLEV\\n$\\\\times $ (--3, 3, 6, ..., MLEV) mJy/beam where MLEV are powers $3\\n\\\\times 2^{\\\\rm n}$ up to a maximum of 96 and CLEV is the typical noise\\nlevel on each radio map (see Table~3). \\n\\nTable~3 lists the various map parameters, with the following column\\nheadings: the source name (1), the applied taper (2), the resulting\\nrestoring beam (3), the position angle of the beam (4), the image noise \\nlevel (5), and the relevant figure number (6). The H\\\\,II nuclei \\nappear at the bottom of the table.\\n\\n\\\\medskip \\\\centerline{\\\\bf -- TABLE~3: Radio map parameters --}\\n\\nGiven that good phase stability was obtained, as judged from the VLA phase\\ncalibrators, the astrometric accuracy of our overlay procedure must be\\ndominated by the DSS accuracy, which is known to be about 0.6\\\\arcsec~ \\n(V\\\\'eron-Cetty \\\\& V\\\\'eron 1996). This is born out by the images of several\\nunresolved and slightly resolved nuclei (NGC\\\\,4552, NGC\\\\,5354, \\nNGC\\\\,5838, NGC\\\\,5846) which appear accurate to within a few tenths of an arcsec. \\n\\n\\\\subsection {Comments on Individual Galaxies}\\n\\nWith reference to the images in the Appendix, we proceed by discussing\\nthe results of our VLA imaging in the light of earlier studies of the\\nsample objects. This discussion also deals with the detected background\\nsources and includes important bibliographic information. We will\\nfrequently compare our measurements with sample galaxy flux densities\\nobtained within the VLA 1.4\\\\,GHz NVSS and FIRST surveys, having typical\\nresolution of 45\\\\arcsec~ and 5\\\\arcsec, respectively (Condon \\\\etal 1998a;\\nBecker, White, \\\\& Helfand 1995), as well as with the Green Bank 20~cm\\nand 6~cm surveys, having typical resolution of $\\\\sim$700\\\\arcsec~and\\n3\\\\arcminpoint5, respectively (White \\\\& Becker 1992, WB92 hereafter;\\nBecker, White, \\\\& Edwards 1991, BWE91 hereafter). \\n\\n{\\\\bf IC\\\\,520 :} No compact structure was seen in this object, not even\\non the tapered map. It was also not detected in the NVSS. However,\\nCondon (1987) reports a detection at 1.49\\\\,GHz: at\\n0\\\\arcminpoint8~resolution, he measured a 3.1~mJy radio source. \\n\\n{\\\\bf NGC\\\\,2541 :} We did not detect compact structure, not even on the\\ntapered map. This source was also not detected in the FIRST or in the\\nNVSS survey. However, Condon (1987) reports a possible detection at \\n1.49\\\\,GHz, 0\\\\arcminpoint8~resolution, of a 3.2~mJy source, slightly\\nextended to the SW relative to the optical position of the galaxy.\\n\\n{\\\\bf NGC\\\\,2985 :} We detect a 1.9~mJy source. At\\n2\\\\arcsecpoint5~resolution, the source is slightly extended in the N-S\\ndirection, along the orientation of the optical galaxy. The tapered map\\nshows a 2.7~mJy core and about 1~mJy weak low surface brightness\\nemission to the SW. The object was also detected in the NVSS: 44.1~mJy. \\nAt 1.49\\\\,GHz, 1\\\\arcminpoint0~resolution, Condon (1987) measured a total\\nflux of 61.9~mJy: the radio emission of NGC\\\\,2985 must be extended over\\ntens of arcseconds. \\n\\n{\\\\bf NGC\\\\,3593 :} On both the untapered and tapered maps we measure\\nabout 20~mJy of diffuse, 45\\\\arcsec~E-W elongated emission, oriented\\nalong the major axis of the host of this H\\\\,II nucleus. NVSS measured\\n87~mJy emission, WB92 measured 132~mJy (hence the radio source exceeds\\none arcminute in size), whereas BWE91 measured 53~mJy. The 1.4\\\\,GHz,\\n5\\\\arcsec~resolution map of Condon \\\\etal (1990) shows an E-W oriented\\nsource of 63.4~mJy: these and our VLA data imply a steep-spectrum\\nradio source.\\n\\nWe also detect an unrelated 10.6~mJy source, 3\\\\arcmin~to the N, extended\\ntowards the E. As judged from the APM survey, the POSS plates show an as \\nyet unclassified nonstellar source at this position: background source\\nNGC\\\\,3593N is most likely a weak distant radio galaxy.\\n\\n{\\\\bf NGC\\\\,3627, M\\\\,66 :} This interacting galaxy belongs to the Leo\\ntriplet. The 8.4\\\\,GHz maps show a 2\\\\arcmin~triple source aligned with\\nthe inner bar of the optical galaxy. The outer radio components are\\nrelated to star formation in the disk of the galaxy (Urbanik, Gr\\\\\\\"ave, \\n\\\\& Klein 1985). We measure 3.9~mJy integrated emission in the compact central\\ncomponent, while $\\\\sim$25~mJy are distributed in the NW and SE components.\\nFrom comparison with low-resolution surveys (NVSS: 324.9~mJy; WB92:\\n434~mJy; BWE91: 141~mJy) we infer that most of the radio emission of\\nthis steep-spectrum radio source is resolved out by our observations.\\nThe triple radio structure was also observed by Saikia \\\\etal (1994),\\nat 5\\\\,GHz with 2\\\\arcsec~resolution. Combining our data with the Saikia\\n\\\\etal (1994) and the Hummel \\\\etal (1987) data, we conclude that the\\nnuclear radio source in NGC3627 must be of variable, flat-spectrum\\nnature. More recently, high resolution (0\\\\arcsecpoint15) 15\\\\,GHz\\nobservations detected an unresolved 1.4~mJy core (N. Nagar, private\\ncommunication).\\n\\n{\\\\bf NGC\\\\,3628 :} Like NGC\\\\,3627, this galaxy also belongs to the Leo\\ntriplet. Our 8.4\\\\,GHz full-resolution map shows some extended emission\\nto the N and an eastern extension that is roughly aligned with the\\nprojected disk of the galaxy. The nuclear region is clearly resolved. \\nThe total flux density on our low-resolution map is about 70~mJy, 70$\\\\%$\\nof which is in $\\\\sim$15\\\\arcsec~diffuse emission. The NVSS measured\\n292~mJy whereas WB92, at lower resolution, detected 402~mJy, indicating\\nresolved large-scale emission. At 1.4\\\\,GHz Condon \\\\etal (1990) measured\\n203~mJy and 205~mJy at 5\\\\arcsec~and 1\\\\arcsecpoint5~resolution,\\nrespectively. These and our data imply a steep-spectrum radio source,\\nin agreement with the results from the Effelsberg 100m telescope\\n(Schlickeiser, Werner, \\\\& Wielebinski 1984). Carral, Turner, \\\\& Ho\\n(1990) observed this object at 15\\\\,GHz using the VLA in A-array and\\nmeasured a total flux of 23~mJy. These authors sampled the innermost\\npart of the source and obtain a $\\\\sim4$\\\\arcsec~string of a dozen\\ncomponents aligned with the major axis of the galaxy, that they suggest\\ncould be star-forming regions in the disk. \\n\\n{\\\\bf NGC\\\\,3675 :} We detect about 1.5~mJy of low surface brightness\\nemission on our tapered maps. NVSS detected a 48.9~mJy source, whereas\\nFIRST measured 8.04~mJy: the source must be strongly resolved. \\n1.49\\\\,GHz VLA D-array observations (Condon 1987; Gioia \\\\& Fabbiano 1987)\\ndetected a $\\\\sim$50~mJy source, oriented N-S, along the major axis of\\nthe optical galaxy. Condon, Frayer, \\\\& Broderick (1991) report a flux\\ndensity of 27~mJy at 4.85\\\\,GHz and a steep spectral index between 4.8\\nand 1.4\\\\,GHz. \\n\\n{\\\\bf NGC\\\\,3681 :} We did not detect a radio source on the untapered or\\ntapered maps. In contrast, NVSS measured a weak source of about\\n4.2~mJy -- at much lower resolution.\\n\\n{\\\\bf NGC\\\\,3684 :} This H\\\\,II nucleus had no radio source detected,\\neither on the untapered or on the tapered maps, but NVSS detected a\\n15.9~mJy source. The radio emission of NGC\\\\,3684 must be diffuse.\\n\\nWe do, however, detect a partially resolved 18.1~mJy background\\nsource, 3\\\\arcmin~to the SW, which APM identifies with a 19.5 mag\\nstellar-like object. Further identification is still lacking.\\n\\n{\\\\bf NGC\\\\,4013 :} We detect a moderately resolved 1.1~mJy core and a small\\nextension to the NE, parallel to the projected disk of this edge-on\\ngalaxy. There is an additional 3~mJy of weak disk emission. On the\\nbasis of the widely different NVSS and FIRST detections (40.5 vs. \\n11.9~mJy), this disk emission must extend tens of arcseconds. Hummel,\\nBeck, \\\\& Dettmar (1991) present 10\\\\arcsec~resolution 5\\\\,GHz data of\\nNGC\\\\,4013 (UGC\\\\,6963) which show both the prominent core and the\\nextended disk emission. Recent high resolution (0\\\\arcsecpoint15) 15\\\\,GHz\\nobservations did not detect NGC\\\\,4013 above a 10$\\\\sigma$ limit of 1~mJy\\n(N.~Nagar, private communication).\\n\\nWe also detect a slightly resolved 3.8~mJy background source,\\n2\\\\arcmin~to the far SE. This source is also clearly seen in the map of\\nCondon (1987). The APM facility reveals a 19.6 mag stellar-like object,\\nwhich lacks further identification as yet. \\n\\n{\\\\bf NGC\\\\,4100 :} We detect about 7~mJy of low surface brightness\\nemission associated with this H\\\\,II nucleus. The tapered map shows a\\nslight extension to the SE along the major axis of the optical\\ngalaxy. NVSS detected a 50.3~mJy source and FIRST detected 17.8~mJy,\\nindicating resolution effects.\\n\\n{\\\\bf NGC\\\\,4217 :} We detect about 22~mJy, distributed along\\n$\\\\sim$1\\\\arcminpoint5~of the projected galactic disk of this H\\\\,II\\nnucleus. From low-resolution observations (NVSS: 123~mJy; WB92:\\n139~mJy; BWE91: 40~mJy) we conclude that NGC\\\\,4217 harbours extended\\nlow surface brightness radio emission, which must have a steep radio\\nspectrum.\\n \\n{\\\\bf NGC\\\\,4245 :} No radio source associated with this H\\\\,II nucleus\\nwas detected on the untapered or tapered maps. Neither NVSS nor FIRST\\nhas detected this object at 1.4\\\\,GHz.\\n\\n{\\\\bf NGC\\\\,4321, M\\\\,100 :} We detect about 16~mJy of low surface\\nbrightness emission in the nuclear region of this well-known grand\\ndesign spiral in the Virgo cluster. The tapered map shows emission\\nslightly extended to the NW. NVSS detected 87~mJy, while WB92 measured\\n323~mJy and BWE91 87~mJy. At 1.49\\\\,GHz, 0\\\\arcminpoint9~resolution\\nCondon (1987) measured 180\\\\,mJy total flux in a $\\\\sim $ 3\\\\arcmin\\n$\\\\times $ 2\\\\arcmin region. At 4.9\\\\,GHz, 1\\\\arcsecpoint5~resolution\\nCollison \\\\etal (1994) detect a ring-like structure coincident with our\\nmain feature. At 8.5\\\\,GHz, 0\\\\arcsecpoint2 resolution, these authors\\ndetect two unresolved sources, having peaks of 0.37~mJy/beam (E) and\\n0.22\\\\,mJy/beam (W), respectively. The eastern radio source is\\ncoincident with their 4.9\\\\,GHz main component while the one to the W\\nis coincident with the optical nucleus and has a flat spectrum\\n(Collison \\\\etal 1994).\\n\\nWe also detect an unresolved source, 1.5\\\\arcmin~to the SE, with 1.3~mJy\\nintegrated flux, apparently located near the middle of the southern\\nspiral arm of the galaxy. It is clearly visible on the NGC\\\\,4321 map. \\nWe have identified this object with SN\\\\,1979C (Weiler \\\\etal 1981). \\nCollison \\\\etal (1994) measured 2~mJy for this SN\\\\,1979C, at 4.9\\\\,GHz. \\n\\n{\\\\bf NGC\\\\,4369, Mrk\\\\,439 :} We detect 3.8~mJy of low surface brightness\\ndisk emission associated with this H\\\\,II nucleus. On the basis of\\nwidely different NVSS and FIRST detections (24.3 vs. 4.67\\\\,~mJy), this\\ndisk emission must extend over tens of arcsec. The Condon \\\\etal (1990)\\n1.49\\\\,GHz image, at 15\\\\arcsec~resolution, shows a 18.3~mJy source with\\nextended emission to the E. \\n\\n{\\\\bf NGC\\\\,4405, IC\\\\,788 :} No compact emission was detected in the\\nuntapered or tapered maps. NVSS detected weak (4.5~mJy) emission for\\nthis H\\\\,II galaxy. \\n\\nWe did, however, detect a partially resolved 10.1~mJy source,\\n2\\\\arcmin~SW of the NGC\\\\,4405 target position. As judged from the APM,\\nthe POSS plates show a 19.2 mag stellar-like object at this position,\\nwhich we subsequently identify as the $z=1.929$ QSO, LBQS\\\\,1223+1626\\n(e.g., Hewett, Foltz, \\\\& Chaffee 1995). \\n\\n{\\\\bf NGC\\\\,4414 :} We detect $\\\\sim$29~mJy of low surface brightness\\nemission, distributed along $\\\\sim$1\\\\arcminpoint5, in a structure aligned\\nwith the galaxy's major axis. NVSS detected a 242~mJy source while\\nFIRST detected a double-peaked source with 44 and 64~mJy components. \\nThe Condon (1983), 1.465\\\\,GHz, 12\\\\arcsecpoint5~resolution map and the\\nCondon (1987), 1.49\\\\,GHz, 1\\\\arcminpoint0~resolution map show comparable\\nN-S structure, measuring $\\\\sim$0.22~Jy. Using this last value plus the\\n78~mJy measured at 4.85\\\\,GHz, 15\\\\arcsec~resolution, Condon \\\\etal (1991)\\nobtain a steep spectral index. \\n\\n{\\\\bf NGC\\\\,4424 :} On the tapered map we detect a resolved $\\\\sim$1~mJy core \\nplus 1.5~mJy weak low surface brightness emission to the E along the\\nprojected disk of this candidate merger galaxy (Kenney \\\\etal 1996). \\nNVSS detected a weak 4.5~mJy source. Our full-resolution data show the\\ncore of this H\\\\,II nucleus to be somewhat resolved. This is borne out of\\nour recent high resolution\\n(0\\\\arcsecpoint25) 8.4\\\\,GHz observations which did not detect NGC\\\\,4424 above\\na 3$\\\\sigma$ limit of 0.2~mJy.\\n\\nWe also detect an unrelated, slightly resolved 13.3~mJy source,\\n2\\\\arcminpoint5~to the SE. The APM identifies it with a 20.2 mag\\nstellar-like object. Further properties of this background source\\nremain as yet unknown. \\n\\n{\\\\bf NGC\\\\,4470 :} We detect $\\\\sim$3~mJy of weak low surface\\nbrightness emission, extending 30\\\\arcsec~along the galaxy major \\naxis. NVSS detected 17.1 mJy associated with this H\\\\,II nucleus.\\n\\nWe also detect an unrelated, resolved 16.0~mJy radio source,\\n1\\\\arcminpoint5~to the NE of NGC\\\\,4470, which is not identified on the\\nPOSS plate (APM). We identify this object with the radio source\\nTXS\\\\,1227+081 (Douglas \\\\etal 1996), which has as yet no optical\\nidentification.\\n\\n{\\\\bf NGC\\\\,4552, M\\\\,89 :} We detect about 77~mJy in a strong core plus \\npossibly a jet-like structure to the NE. NVSS\\ndetected a 103~mJy source. Since BWE91 measured 64~mJy at 5\\\\,GHz, the\\nradio source in NGC\\\\,4552 must have a relatively flat radio spectrum,\\nwhich is in agreement with findings by Condon \\\\etal (1991). The radio\\nsource appears to be variable (Wrobel \\\\& Heeschen 1984; Ekers, Fanti, \\\\&\\nMiley 1983; Sramek 1975a, 1975b; Ekers \\\\& Ekers 1973). Our recent\\nsubarcsec resolution 8.4\\\\,GHz images have confirmed this object's compactness. \\n\\n{\\\\bf NGC\\\\,4643 :} No compact radio structure was detected on the\\nuntapered or the tapered maps. NVSS also did not detect this source. \\nHowever, we have detected several very weak sources ($\\\\sim$1~mJy) on the\\ntapered maps, some of which may be due to weak diffuse disk emission. \\n\\n{\\\\bf NGC\\\\,4710 :} We detect about 6~mJy of weak disk emission\\nassociated with this H\\\\,II nucleus. NVSS measured a 19.3~mJy source.\\nAt 1.49\\\\,GHz, Condon \\\\etal (1990) measure 17.2~mJy and 14.7~mJy at 15\\nand 5\\\\arcsec~resolution, respectively. The data imply a resolved\\nsteep-spectrum radio source.\\n\\nWe also detect a 4.8~mJy resolved background source, 2.5\\\\arcmin~to the\\nE of NGC\\\\,4710. No indentification could be found on the POSS.\\n\\n{\\\\bf NGC\\\\,4713 :} We detect $\\\\sim$1.2~mJy weak low surface brightness disk\\nemission on our tapered maps. NVSS measured a 46.9~mJy source: our \\nobservations must have resolved out much of the flux.\\n\\n{\\\\bf NGC\\\\,4800 :} We detect about 1.2~mJy of weak low surface brightness\\nemission, stretching $\\\\sim30$\\\\arcsec~along the galaxy major axis. NVSS\\ndetected a 23.5~mJy source and FIRST 12.2~mJy. Therefore, our\\nobservations are resolving out much of the emission of this H\\\\,II\\nnucleus. \\n\\n{\\\\bf NGC\\\\,4826 , M\\\\,64:} We detect about 21~mJy of low surface\\nbrightness emission. The central region on the full-resolution map (not\\npresented here) shows a double-peaked component, which can be compared\\nto the complex inner triple structure of the 15 and 5\\\\,GHz,\\n2\\\\arcsec~resolution maps of Turner \\\\& Ho (1994). Combining the data\\nindicates that this is a steep spectrum source. NVSS detected a 101~mJy\\nsource and BWE91 detected a 56~mJy source. The 1.49\\\\,GHz,\\n1\\\\arcminpoint0~resolution data of Condon \\\\etal (1998b) and Condon (1987)\\nshow a $\\\\sim$100~mJy source, as do the data of Gioia \\\\& Fabbiano (1987)\\nat 40\\\\arcsec~resolution. \\n\\n{\\\\bf NGC\\\\,4845 :} On our tapered maps we detect a 2~mJy core and some\\nemission to the N, perpendicular to the galaxy major axis, plus 10~mJy\\nof $\\\\sim20$\\\\arcsec~elongated disk emission. NVSS detected a 43.8~mJy\\nsource associated with this H\\\\,II nucleus. The data of Condon \\\\etal\\n(1990) imply resolution effects on the 10~arcsec scale. \\n\\n{\\\\bf NGC\\\\,5012 :} We detect some very weak ($\\\\sim$1~mJy) features\\nnear the target phase center. NVSS detected a 31.4~mJy source, but \\nas FIRST did not detect it, we must be dealing with extended low\\nsurface brightness emission.\\n\\n{\\\\bf NGC\\\\,5354 :} We detect an unresolved 11.7~mJy core. NVSS and\\nFIRST detected a 8.4 and 8.0~mJy source, respectively, implying that the\\nNGC\\\\,5354 radio source is unresolved at a resolution of 5\\\\arcsec. The\\n4.85\\\\,GHz, 15\\\\arcsec~resolution maps of Condon \\\\etal (1991) show 7~mJy\\nemission, implying that the nuclear radio source has an inverted\\nspectrum. Our recent\\nsubarcsec resolution 8.4\\\\,GHz images have confirmed this object's compactness. \\n\\n\\nPaired galaxy NGC\\\\,5353 is also detected, 1\\\\arcminpoint25~to the S,\\nwith a 26.7~mJy core. Condon \\\\etal (1991) measure 29~mJy at 4.85\\\\,GHz,\\n15\\\\arcsec~resolution, implying that NGC\\\\,5353 also hosts a flat\\nspectrum radio source.\\n\\n{\\\\bf NGC\\\\,5656 :} We detect $\\\\sim$1~mJy of weak low surface brightness\\nemission, stretching over $\\\\sim$25\\\\arcsec~along the major axis of the\\ngalaxy. NVSS detected a 22~mJy source.\\n\\n{\\\\bf NGC\\\\,5678 :} We detect about 8.5~mJy of low surface brightness\\nemission stretching over $\\\\sim$1\\\\arcminpoint2~along the major axis of\\nthe galaxy. The tapered map shows what could be a double-peaked source,\\nsimilar to the 6\\\\arcsec~resolution, 1.4\\\\,GHz map of Condon (1983). NVSS\\ndetected a 112~mJy source while BWE91 measured 68~mJy. The NVSS and\\nBWE91 results, combined with Condon (1983) reporting 109~mJy at\\n1.4\\\\,GHz, imply a steep spectrum source. \\n\\n{\\\\bf NGC\\\\,5838 :} We have detected a slightly resolved 2.2~mJy source. \\nNVSS detected 3.0~mJy, while Wrobel \\\\& Heeschen (1991) report a 2 mJy\\nsource (5\\\\,GHz, 5\\\\arcsec~resolution): the nuclear radio source in\\nNGC\\\\,5838 must have a flat radio spectrum. Our recent\\nsubarcsec resolution 8.4\\\\,GHz images have confirmed this object's compactness. \\n\\n \\nThere is also an unrelated, unresolved 1.3~mJy source, about\\n1\\\\arcminpoint5~to the S of NGC\\\\,5838. The POSS plates reveal an 18.4\\nmag star-like object at that position, for which as yet no redshift is\\navailable. \\n\\n{\\\\bf NGC\\\\,5846 :} We have detected a partially resolved 7.1~mJy source. \\nNVSS measured a 22~mJy source. 1.4\\\\,GHz VLA observations by\\nM\\\\\\\"ollenhoff, Hummel, \\\\& Bender (1992) measured an unresolved core of\\n9~mJy plus 10~mJy of additional diffuse emission: NGC\\\\,5846 must possess\\na compact flat-spectrum core component. Our recent\\nsubarcsec resolution 8.4\\\\,GHz images have confirmed this object's compactness. \\n\\n \\n{\\\\bf NGC\\\\,5879 :} No radio structure was detected on the untapered or\\nthe tapered maps. NVSS detected a 21~mJy source, which hence must arise \\nin an extended low surface brightness region.\\n\\nHowever, we did detect a 292.1~mJy, slightly resolved background\\nsource, about 2\\\\arcmin~NE of our target. It shows up only on the POSS\\nred plate as a noise-like source. We have identified this source as\\nQSO 1508+5714, at a redshift of 4.301 (Hook \\\\etal 1995). It is in the\\nWENSS (Rengelink \\\\etal 1997) and in BWE91 (282~mJy) as well as in WB92\\n(149~mJy). Patnaik \\\\etal (1992) have observed the source with the VLA\\nA-array at 8.5\\\\,GHz and measured 153~mJy: 1508+5714 must be a variable \\nflat-spectrum quasar.\\n \\n{\\\\bf NGC\\\\,5921 :} We have detected a very weak 0.5~mJy core and some\\nadditional weak extended emission. At 1.49\\\\,GHz and 0\\\\arcminpoint9\\nresolution, Condon (1987) measured a 20.8~mJy source with an\\nadditional 2.8~mJy eastern component which we do not detect at\\n8.4\\\\,GHz. All emission must be of low surface brightness nature.\\n\\n{\\\\bf NGC\\\\,6384 :} Following the NVSS non-detection, we also do not\\ndetect (compact) radio emission from NGC\\\\,6384. However, Condon\\n(1987), at 1.49\\\\,GHz and 1\\\\arcminpoint2~resolution, found the radio\\nsource, having $\\\\sim$ 35~mJy, to be very extended.\\n\\n{\\\\bf NGC\\\\,6482 :} We have not detected this source at 8.4\\\\,GHz and\\nneither did NVSS.\\n\\nWe did, however, detect a slightly resolved 23.6~mJy background\\nsource, about 3\\\\arcmin~to the S of NGC\\\\,6482. On the full-resolution\\nmap this source is slightly extended. The POSS plates show a 20.9 mag\\nstellar object. We have identified this source with the radio source\\n1749+2302 included in GB6, with 26~mJy flux density.\\n\\n{\\\\bf NGC\\\\,6503 :} We do not detect radio emission from this galaxy on\\nthe full-resolution or on the tapered maps. 1.4\\\\,GHz data (NVSS and Condon\\n1987) indicate a NW-SE extended $\\\\sim$40~mJy source, which\\nconsequently must be diffuse.\\n \\nWe also detect a background source, about 6\\\\arcmin~to the SW. Due to\\nthe large distance from the phase center, which implies a large and uncertain\\nprimary beam correction, we cannot assess the flux density of this\\nsource. The source appears as a 16.9 mag stellar-like object on the POSS\\nplates. We have identified this object with the BL Lacertae source\\n1749+701 at redshift 0.77 (Hughes, Aller, \\\\& Aller 1992). This object has been\\nextensively observed at other radio-frequencies and is included in the\\nWENSS (Rengelink \\\\etal 1997) as well as BWE91 and WB92. The only other\\n8.5\\\\,GHz measurement of this source comes from Patnaik \\\\etal (1992). They\\nmeasure 558~mJy with the VLA A-array. \\n\\nTable~4 summarizes the properties of the background sources, including\\nthe previously identified, as well as the new, identifications. Tabulated \\n8.4\\\\,GHz fluxes have been corrected for primary beam attenuation. \\n\\n\\\\medskip \\\\centerline{\\\\bf -- TABLE~4: Field/background sources --}\\n\\n\\\\subsection {Radio Source Parameters}\\n\\nFor each galaxy with a 8.4\\\\,GHz detection, we list in Table~5 the radio\\nsource parameters, measured both from the full-resolution and the\\ntapered maps. Peak and integrated values (columns~3 and 6), as well as \\nwell as sky positions of bidimensional gaussian fits (columns~4 and 5)\\nare tabulated. These values were obtained using the AIPS task IMFIT. \\nAs we are often dealing with resolved and/or asymmetric emission, such \\nmeasurements are often inaccurate and must represent lower limits. \\nIn such cases, we have estimated the integrated\\n8.4\\\\,GHz flux density from inspection of the map and the relevant clean\\ncomponent file and we have given it the prefix ``$\\\\geq$'' (column~6). \\nAlso, given the fact that we have fitted single gaussian to the brightest\\nsource components, the accuracy of the radio peak positions is judged to be\\n\\\\ltaprx1\\\\arcsec~(see images). For NGC\\\\,3627, the quoted peak and integrated \\nvalue are of the central core. In parentheses we include the total flux \\nof the three components (see Section~4.2). \\n\\n\\n\\n \\n\\n\\\\medskip \\n\\\\centerline{\\\\bf -- TABLE~5: Radio parameters of detected sources --}\\n\\nFrom a quick comparison with the integrated NVSS 1.4\\\\,GHz flux\\ndensities, it is found that in many cases the high-resolution\\nobservations must have resolved a substantial fraction of the emission. \\nThis can be quantified by examination of the spectral index values. \\nTable~6 lists spectral indices $\\\\alpha^{8.4}_{1.4}$ ($S_{\\\\nu } \\\\propto\\n\\\\nu ^{-\\\\alpha}$) (column~5), obtained by combining the NVSS flux \\ndensities (column~2)\\nand the integrated 8.4\\\\,GHz flux densities (column~3) taken from Table~5. \\nDue to the fact that the NVSS beam\\n(45\\\\arcsec) exceeds the 8.4\\\\,GHz beam (7\\\\arcsec--10\\\\arcsec) by a\\nsubstantial factor, these spectral index values should be considered\\nas upper limits. It indeed\\nappears that in most of these cases the radio emission was documented to\\nbe extended over tens of arcseconds. \\nWe also compile calculated NVSS radio luminosities (column~4) for the \\n37 galaxies under consideration. \\nAgain, for NGC\\\\,3627 quoted values refer to\\nthe compact core except when in parentheses, in which case the values refer \\nto all three source components. \\n\\n\\n\\n\\\\medskip \\\\centerline{\\\\bf -- TABLE~6: summary --}\\n\\nMost sample galaxies are seen to display steep spectral indices, as\\ncommonly found for star-forming late-type galaxies (Condon 1992). The\\nfollowing objects have flat ($\\\\alpha \\\\leq 0.6$) spectra: NGC\\\\,4552,\\nNGC\\\\,5354, NGC\\\\,5838 and NGC\\\\,5846 and the H\\\\,II nucleus in NGC\\\\,4424. \\nWe will return to this issue in the next Section. \\n\\n\\\\section {Discussion}\\n\\nOur VLA imaging observations have yielded X-band detections of 27 of the\\n37 sample galaxies. These 27 include NGC\\\\,4643 and NGC\\\\,5012, which\\nwere marginally detected. As for the non-detections, they are equally\\ndistributed over the transition LINERs and the H\\\\,II nuclei. It appears\\nthat non-detection at X-band, at a resolution of\\n2\\\\arcsecpoint5--12\\\\arcsec, correlates with 1.4\\\\,GHz (NVSS) weakness\\nand/or low surface brightness. Table~6 indicates that the NVSS radio\\nluminosity distributions of the subsamples are comparable. The\\nintegrated 1.4\\\\,GHz radio luminosities imply that the sample sources\\nspan the usual luminosity range for nearby galaxies (10$^{26}$ --\\n10$^{30.5}$ erg s$^{-1}$ Hz$^{-1}$; see, e.g., Condon 1987, 1992). \\nWith the exception of NGC\\\\,4424 (see Section~4.2), none of the H\\\\,II \\nnuclei display compact nuclear emission and/or a flat radio spectrum.\\nThis is in strong contrast to the transition LINER galaxies.\\n\\nPurely based on the radio morphology, the transition LINER objects can\\nbe divided into two categories. The first is made up of galaxies\\ndisplaying extended, steep-spectrum, low surface brightness radio\\nemission, usually tracing the optical isophotes of the host galaxy. The\\nsecond category refers to objects that, in addition to extended\\nemission, also show compact nuclear radio emission. The first category displays\\nradio morphologies that are consistent with their being due to\\nlarge-scale star formation; in several cases the radio morphology is\\nseen to trace the H\\\\,II regions in the host. However, we stress that\\nthe presence of a very weak nuclear component in these objects may still \\nbe masked by the more dominant radio emission from star-forming regions. \\nThe second category, which we will refer to in the following as AGN\\ncandidates, is comprised of NGC\\\\,3627, NGC\\\\,4552, NGC\\\\,5354,\\nNGC\\\\,5838, and NGC\\\\,5846. The last four of these are characterized with\\na flat radio spectral index between 1.4 and 8.4 GHz (see end of Section~4.3). \\nJudging from high-resolution observations which isolate the nuclear\\nemission, the compact nucleus of NGC\\\\,3627 also displays a flat radio\\nspectrum (see Section~4.2). These AGN candidates are on average more\\nluminous than the non-AGN and, as we shall see below, their hosts\\nare early rather than late-type galaxies. While at first sight the H\\\\,II nucleus\\nNGC\\\\,4424 also belongs in this AGN candidate class, the radio image (Fig.~3d)\\nshows it to be resolved. Higher resolution observations\\nrecently carried out by us indeed resolve all the nuclear emission in \\nNGC\\\\,4424 (see Section~4.2), in contrast to the AGN candidates \\nfrom the transition LINER sample. As such there is a clear separation between\\nthe non-AGN and AGN candidate classes. \\n\\nApparently, galaxies with composite LINER and star-formation spectra\\nseparate out into objects with and without a clear signature of an\\nAGN, that is to say, a compact, flat-spectrum radio source. The prime\\nquestion to address, of course, is whether the optical spectra of\\nthese classes differ in any way. Deferring the full analysis of this\\nissue to another paper, we here just note that the class of AGN\\ncandidates indeed displays somewhat stronger [N~II] and [S~II] lines\\nin their optical spectra. As we will demonstrate in the forthcoming\\npaper in this series, the behavior of the so called $u$-parameter,\\nwhich measures the radio/far-IR ratio, also supports the weak AGN\\nclassification. However, like in the case of Seyfert galaxies showing\\na $\\\\sim$30\\\\% incidence rate of compact radio cores (e.g., Norris et\\nal. 1990), there is not a one-to-one correspondence between compact\\nradio emission and nuclear activity. We conclude that the radio\\nproperties permit to isolate AGN candidates among the sample of\\ntransition LINERs, although the absence of radio cores cannot be used to \\nargue against their being AGN. These conclusions strongly support the \\nhypothesis which resulted from the VLA observations of transition LINER\\nNGC\\\\,7331 by Cowan et al. (1994).\\n\\nInspection of Table~6 readily shows that these AGN candidates are\\nhosted by rather early-type galaxies (E--Sb). The relevant radio core\\nluminosities L$_{\\\\rm 8.4\\\\,GHz}$ range from $\\\\sim$ 10$^{26.2}$ --\\n10$^{28.5}$ erg s$^{-1}$ Hz$^{-1}$, which is several orders of\\nmagnitude less than the core luminosities in FR\\\\,I or FR\\\\,II type\\n(Fanaroff \\\\& Riley 1974) radio galaxies and quasars, and in the range\\nof the weakest radio cores in Seyfert galaxies (Giuricin et al.\\n1996). This, then, implies that weak LINER AGN preferentially occur\\nin bulge-dominated hosts, not necessarily just in ellipticals,\\nconsistent with statistical results from other lines of evidence (Ho\\net al. 1997b; Ho 1999b). This is in agreement with the case of\\nSeyfert galaxies, for which the radio core emission was also found to\\nbe stronger in early-type hosts (Giuricin et al. 1996). As such,\\nthese weak AGN differ from the more powerful FR\\\\,I radio galaxies,\\nwhich are commonly associated with elliptical galaxies, not seldom\\nbrightest cluster galaxies (Zirbel \\\\& Baum 1995). They exceed the\\nvery weak nuclear source in the nearby transition LINER NGC\\\\,7331\\n(Cowan et al. 1994) by a factor of $\\\\sim 15$, and are comparable in\\nstrength to the well-known variable radio core of the LINER nucleus in\\nM\\\\,81 (e.g., Ho et al. 1999). Hence, it must be concluded that at least some \\nweak LINER AGN reveal themselves by low-power radio cores. This supports\\nthe analysis of Ho (1999a), who proposed that the weak nuclear radio\\nsources (radio power 10$^{26}$ -- 10$^{29}$ erg s$^{-1}$ Hz$^{-1}$) in\\nnearby elliptical and S0 galaxies are the low-luminosity counterparts\\nof more powerful AGN.\\n\\nFinally, it is intriguing that the transition LINER in the elliptical\\ngalaxy NGC\\\\,6482 remained undetected in our observations (as well as in\\nthe NVSS). Given that NGC 6482 is the most distant object in our\\nsample, our non-detection would still allow a $\\\\leq 10^{27}$ erg\\ns$^{-1}$ Hz$^{-1}$ compact radio source to reside in this object. \\n\\nFull analysis of our sample, including optical emission-line and infrared\\nluminosities, will be presented in forthcoming papers. To address the\\nphysical origin behind the findings presented here will be the challenge\\nfor future work. \\n\\n\\\\section{Conclusions}\\n\\nA sample of composite LINER/H\\\\,II galaxies and pure H\\\\,II nuclei was\\nstudied using the VLA (C-array) at 8.4\\\\,GHz. On the basis of their\\nradio morphological properties, the composite sources can be divided\\ninto objects with low surface brightness emission confined mainly to\\nthe plane of the galaxy and objects displaying compact nuclear\\ncomponents. The former\\nobjects are similar in radio morphology to the H\\\\,II nuclei in our\\nsample, whereas the latter show morphologies consistent with AGN. All\\nfive of the LINER AGN are hosted by bulge-dominated galaxies (Hubble\\ntype E--Sb), and four of them show flat spectral indices between 8.4 and\\n1.4\\\\,GHz. In terms of radio luminosity, the present LINER AGN populate\\nthe range of low core radio luminosities, which implies that classical AGN \\nof low luminosity exist in a wide range of galaxy types.\\n\\n\\\\acknowledgments\\n\\nM.~E.~F. is supported by grant PRAXIS XXI/BD/15830/98 from the \\nFunda\\\\c c\\\\~ao para a Ci\\\\^encia e Tecnologia, Minist\\\\'erio da Ci\\\\^encia e\\nTecnologia, Portugal. P.~D.~B. acknowledges a visitor's grant from the\\nSpace Telescope Science Institute, where a large part of this paper\\ncould be written. L.~C.~H. is partly funded by NASA grant NAG 5-3556,\\nand by NASA grants GO-06837.01-95A and AR-07527.02-96A from the Space\\nTelescope Science Institute (operated by AURA, Inc., under NASA contract\\nNAS5-26555). We want to thank Neil Nagar for providing us with \\nsome of his preliminary results.\\n\\nThis research was supported in part by the European\\nCommission TMR Programme, Research Network Contract ERBFMRXCT96-0034\\n``CERES.'' We made extensive use of the APM (Automatic Plate Measuring)\\nFacility, run by the Institute of Astronomy in Cambridge, the STScI DSS\\n(Digitized Sky Survey), produced under US government grant NAGW -- 2166,\\nand NED (NASA/IPAC Extragalactic Database), which is operated by the Jet\\nPropulsion Laboratory, California Institute of Technology, under\\ncontract with NASA. \\n\\n\\\\begin{references}\\n\\n\\\\reference{}\\nBecker, R.~H., White, R.~L., \\\\& Edwards, A.~L. 1991, \\n\\\\apjs, 75, 1\\n\\n\\\\reference{}\\nBecker, R.~H., White, R.~L., \\\\& Helfand, D.~J. 1995,\\n\\\\apj, 450, 559\\n\\n\\\\reference{}\\nCarral, P., Turner, J.~L., \\\\& Ho, P.~T.~P. 1990, \\\\apj, 362, 434\\n\\n\\\\reference{}\\nClark, B.~G., 1980, \\\\aap, 89, 377\\n\\n%Clark, R.~N., 1980, PASP, 92, 221\\n\\n\\\\reference{}\\nCollison, P.~M., Saikia, D.~J., Pedlar, A., Axon, D.~J., \\\\& Unger, S.~W. 1994,\\n\\\\mnras, 268, 203\\n \\n\\\\reference{}\\nCondon, J.~J. 1983, \\\\apjs, 53, 459\\n\\n\\\\reference{}\\nCondon, J.~J. 1987, \\\\apjs, 63, 485\\n\\n\\\\reference{}\\nCondon, J.~J. 1992, ARA\\\\&A, 30, 575\\n\\n\\\\reference{}\\nCondon, J.~J., \\\\& Broderick, J.~J. 1988, \\\\aj, 96, 30\\n\\n\\\\reference{}\\nCondon, J.~J., Condon, M.~A., Gisler, G., \\\\& Puschell, J.~J. 1982, \\n\\\\apj, 252, 102\\n\\n\\\\reference{}\\nCondon, J.~J., Cotton, W.~D., Greisen, E.~W., Yin, Q.~F., \\nPerley, R.~A., Taylor, G.~B., \\\\& Broderick, J.~J. 1998a, \\\\aj, 115, 1693\\n\\n\\\\reference{}\\nCondon, J.~J., Frayer, D.~T., \\\\& Broderick, J.~J. 1991,\\n\\\\aj, 101, 362\\n\\n\\\\reference{}\\nCondon, J.~J., Helou, G., Sanders, D.~B., \\\\& Soifer, B.~T. 1990, \\n\\\\apjs, 73 359\\n\\n\\\\reference{}\\nCondon, J.~J., Yin, Q.~F., Thuan, T.~X., \\\\& Boller, Th. 1998b,\\n\\\\aj, 116, 2682\\n\\n\\\\reference{}\\nCowan, J.~J., Romanishin, W., \\\\& Branch, D. 1994, \\\\apj, 436, L139\\n\\n\\\\reference{}\\nDopita, M.~A., \\\\& Sutherland, R.~S. 1995, \\\\apj, 102, 161\\n\\n\\\\reference{}\\nDouglas, J.~N., Bash, F. N., Bozyan, F.~A., Torrence, G.~W., \\\\& \\nWolfe, C. 1996, \\\\aj, 111, 1945\\n\\n\\\\reference{}\\nDressel, L.~L., \\\\& Condon, J.~J. 1978, \\\\apjs, 36, 53\\n\\n\\\\reference{}\\nDumke, M.~K., Krause, M., Wielebinski, R., \\\\& Klein, U. 1995,\\n\\\\aap, 302, 691\\n\\n\\\\reference{}\\nEkers, R.~D., \\\\& Ekers, J.~A. 1973, \\\\aap, 24, 247\\n\\n\\\\reference{}\\nEkers, R.~D., Fanti, R., \\\\& Miley, G.~K. 1983, \\\\aap, 120, 297\\n\\n\\\\reference{}\\nFabbiano, G., Gioia, I.~M., \\\\& Trinchieri, G. 1989, \\\\apj, 347, 127\\n\\n\\\\reference{}\\nFalcke, H., Wilson, A.~S., \\\\& Ho, L.~C. 1997, in Relativistic\\nJets in AGN, ed. M. Sikora \\\\& M. Ostrowski, 13\\n\\n\\\\reference{}\\nFanaroff, B.~L., \\\\& Riley, J.~M. 1974, \\\\mnras, 167, 31P\\n\\n\\\\reference{}\\nFilippenko, A.~V 1996, in The Physics of LINERs in View of Recent Observations, \\ned. M. Eracleous et al. (San Francisco: ASP), 17\\n\\n\\\\reference{}\\nFilippenko, A.~V., \\\\& Terlevich, R. 1992, \\\\apj, 397, L79\\n\\n\\\\reference{}\\nFosbury, R.~A.~E., Melbold, U., Goss, W.~M., \\\\& Dopita, M.~A. 1978, MNRAS, 183,\\n549\\n\\n\\\\reference{}\\nGioia, I.~M., \\\\& Fabbiano, G. 1987, \\\\apjs, 63, 771\\n\\n\\\\reference{}\\nGiuricin, G., Fadda, D., \\\\& Mezzetti, M. 1996, \\\\apj, 468, 475\\n\\n\\\\reference{}\\nGregory, P.~C., \\\\& Condon, J.~J. 1991,\\n\\\\apjs, 75, 1011\\n\\n\\\\reference{}\\nHaynes, M., \\\\& Sramek, R.~A. 1975, \\\\aj, 80, 673\\n\\n\\\\reference{}\\nHeckman, T.~M. 1980, \\\\aap, 87, 152\\n\\n\\\\reference{}\\nHeckman, T.~M., Balick, B., \\\\& Crane, P.~C. 1980, \\\\aaps, 40, 295\\n\\n\\\\reference{}\\nHewett, P.~C., Foltz, C.~B., \\\\& Chaffee, F.~H. 1995, \\\\aj, 109, 1498\\n\\n\\\\reference{}\\nHo, L.~C. 1996, in The Physics of LINERs in View of Recent Observations, \\ned. M. Eracleous et al. (San Francisco: ASP), 103\\n\\n\\\\reference{}\\nHo, L.~C. 1999a, \\\\apj, 510, 631 \\n\\n\\\\reference{}\\nHo, L.~C. 1999b, Advances in Space Research, 23 (5-6), 813\\n\\n\\\\reference{}\\nHo, L.~C., Filippenko, A.~V., \\\\& Sargent, W.~L.~W. 1993, \\\\apj, 417, 63\\n\\n\\\\reference{}\\nHo, L.~C., Filippenko, A.~V., \\\\& Sargent, W.~L.~W. 1995, \\\\apjs, 98, 477\\n\\n\\\\reference{}\\nHo, L.~C., Filippenko, A.~V., \\\\& Sargent, W.~L.~W. 1997a, \\\\apjs, 112, 315\\n\\n\\\\reference{}\\nHo, L.~C., Filippenko, A.~V., \\\\& Sargent, W.~L.~W. 1997b, \\\\apj, 487, 568\\n\\n\\\\reference{}\\nHo, L.~C., Van Dyk, S.~D., Pooley, G.~G., Sramek, R.~A., \\\\& Weiler, K.~W. 1999,\\n\\\\aj, 118, 843\\n\\n\\\\reference{}\\nH\\\\\\\"ogbom, J.~A., 1974, \\\\aaps, 15, 417\\n\\n\\\\reference{}\\nHook, I.~M., McMahon, R.~G., Patnaik, A.~R., Browne, I.~W.~A., Wilkinson, \\nP.~N., Irwin, M.~J.,\\\\& Hazard, C. 1995, \\\\mnras, 273, L63\\n\\n\\\\reference{}\\nHughes, P.~A., Aller, H.~D., \\\\& Aller, M.~F. 1992, \\\\apj, 396, 469\\n\\n\\\\reference{}\\nHummel, E. 1980, \\\\aaps, 41, 151\\n\\n\\\\reference{}\\nHummel, E., Beck, R., \\\\& Dettmar, R.-J. 1991,\\n\\\\aaps, 87, 309\\n\\n\\\\reference{}\\nHummel, E., \\\\& Kotanyi, C.~G. 1982, \\\\aap, 106, 183\\n \\n\\\\reference{}\\nHummel, E., van der Hulst, J.~M., Keel, W.~C., \\\\& Kennicutt, R.~C., Jr.\\n1987, \\\\aaps, 70, 517\\n\\n\\\\reference{}\\nJenkins, C.~R. 1982, \\\\mnras, 200, 705\\n\\n\\\\reference{}\\nJones, D.~L., Terzian, Y., \\\\& Sramek, R.~A. 1981a, \\\\apj, 246, 28\\n\\n\\\\reference{}\\nJones, D.~L., Terzian, Y., \\\\& Sramek, R.~A. 1981b, \\\\apj, 247, L57\\n\\n\\\\reference{}\\nKenney, J.~D.~P., Koopmann, R.~A., Rubin, V.~C., \\\\& Young, J.~S. 1996,\\n\\\\aj, 111, 152\\n\\n\\\\reference{}\\nKlein, U., \\\\& Emerson, D.~T. 1981, \\\\aap, 94, 29\\n\\n\\\\reference{}\\nM\\\\\\\"ollenhoff, C., Hummel, E., \\\\& Bender, R. 1992,\\n\\\\aap, 255, 35\\n\\n\\\\reference{}\\nNiklas, S., Klein, U., Braine, J., \\\\& Wielebinski, R. 1995,\\n\\\\aaps, 114, 21\\n\\n\\\\reference{}\\nNorris, R.~P., Allen, D.~A., Sramek, R.~A., Kesteven, M.~J., \\\\& Troup, E.~R. \\n1990, \\n\\\\apj, 359, 291\\n\\n\\\\reference{}\\nPatnaik, A.~R., Browne, I.~W.~A., Wilkinson, P.~N., \\\\& Wrobel, J.~M. 1992, \\n\\\\mnras, 254, 655\\n\\n\\\\reference{}\\nPerley, R.~A., Schwab, F.~R., \\\\& Bridle, A.~H. 1989, in Synthesis Imaging in \\nRadio Astronomy: A Collection of Lectures from the Third NRAO Synthesis\\nImaging Summer School (San Francisco: ASP), 6\\n\\n\\\\reference{}\\nRengelink, R.~B., Tang, Y., de Bruyn, A.~G., Miley, G.~K., Bremer, M.~N., \\nR\\\\\\\"ottgering, H.~J.~A., \\\\& Bremer, M.~A.~R. 1997, \\\\aaps, 124, 259\\n\\n\\\\reference{}\\nReuter, H.-P., Krause, M., Wielebinski, R., \\\\& Lesch, H. 1991,\\n\\\\aap, 248, 12 \\n\\n\\n\\\\reference{}\\nSadler, E.~M., Jenkins, C.~R., \\\\& Kotanyi, C.~G. 1989, \\\\mnras, 240, 591\\n\\n\\\\reference{}\\nSaikia, D.~J., Pedlar, A., Unger, S.~W., \\\\& Axon, D.~J. 1994,\\n\\\\mnras, 270, 46\\n\\n\\\\reference{}\\nSchlickeiser, R., Werner, W., \\\\& Wielebinski, R. 1984, \\\\aap, 140, 227\\n\\n\\\\reference{}\\nShields, J. C. 1992, \\\\apj, 399, L27\\n\\n\\\\reference{}\\nSlee, O.~B., Sadler, E.~M., Reynolds, J.~E., \\\\& Ekers, R.~D. 1994,\\n\\\\mnras, 269, 928\\n\\n\\\\reference{}\\nSramek, R.~A. 1975a, \\\\aj, 80, 771\\n\\n \\\\reference{}\\nSramek, R.~A. 1975b, \\\\apj, 198, L13\\n\\n\\\\reference{}\\nTerlevich, R., \\\\& Melnick, J. 1985, \\\\mnras, 213, 841\\n\\n\\\\reference{}\\nTurner, K.~C., Helou, G., \\\\& Terzian, Y. 1988, PASP, 100, 452\\n\\n\\\\reference{}\\nTurner, J.~L., \\\\& Ho, P.~T.~P. 1994,\\n\\\\apj, 421, 122\\n\\n\\\\reference{}\\nUrbanik, M., Gr\\\\\\\"ave, R., \\\\& Klein, U. 1985, \\\\aap, 152, 291\\n\\n\\\\reference{}\\nUrbanik, M., Klein, U., \\\\& Gr\\\\\\\"ave, R. 1986, \\\\aap, 166, 107\\n\\n\\\\reference{}\\nvan Breugel, W.~J.~M., Schilizzi, R.~T., Hummel, E., \\\\& Kapahi, V.~K. 1981, \\n\\\\aap, 96, 310\\n\\n\\\\reference{}\\nvan der Hulst, J.~M., Crane, \\\\& P.~C., Keel, W.~C. 1981, \\\\aj, 86, 1175\\n\\n\\\\reference{}\\nvan der Kruit, P.~C. 1973a, \\\\aap, 29, 231\\n\\n\\\\reference{}\\nvan der Kruit, P.~C. 1973b, \\\\aap, 29, 249\\n\\n\\\\reference{}\\nVan Dyk, S.~D., \\\\& Ho, L.~C. 1998, in IAU Symp. 184, The Central Regions of\\nthe Galaxy and Galaxies, ed. Y. Sofue (Dordrecht: Kluwer), 489\\n\\n\\\\reference{}\\nV\\\\'eron-Cetty, M.-P., \\\\& V\\\\'eron, P. 1996, \\\\aaps, 115, 97\\n\\n\\\\reference{}\\nVila, M.~B., Pedlar, A., Davies, R.~D., Hummel, E., \\\\& Axon, D.~J. 1990, \\n\\\\mnras, 242, 379\\n\\n\\\\reference{}\\nWeiler, K.~W., van der Hulst, J.~M., Sramek, R.~A., \\\\& Panagia, N. 1981,\\n\\\\apj, 243, L151\\n\\n\\\\reference{}\\nWhite, R.~L., \\\\& Becker, R.~J. 1992,\\n\\\\apjs, 79, 331\\n\\n\\\\reference{}\\nWrobel, J.~M., \\\\& Heeschen, D.~S. 1984, \\\\apj, 287, 41\\n\\n\\\\reference{}\\nWrobel, J.~M., \\\\& Heeschen, D.~S. 1991,\\n\\\\aj, 101, 148\\n\\n\\\\reference{}\\nZirbel, E.~L., \\\\& Baum, S.~A. 1995, \\\\apj, 448, 521 \\n \\n\\\\end{references}\\n\\n\\\\clearpage \\n\\n% TABLE 1\\n%\\\\setcounter{table}{0}\\n\\\\begin{table}\\n\\\\footnotesize\\n\\\\begin{center}\\n\\\\begin{tabular}[h]{l c c c c c c r}\\n\\\\tableline\\n\\\\tableline\\n\\nGalaxy & Other & R.A.(J2000) & Dec(J2000) & D & & Hubble Type & Reference \\\\\\\\\\n & name & $^{h}$ $^{m}$ $^{s}$ & $^{\\\\circ}$ $^{'}$ $^{''}$ & Mpc & & & \\\\\\\\\\n\\\\tableline \\nIC\\\\,520 & & 08 53 42.3 & +73 29 29 & 47.0 & & SAB(rs)ab? & 26\\\\\\\\\\nNGC\\\\,2541 & & 08 14 40.2 & +49 03 42 & 10.6 & & SA(s)cd & 26,41\\\\\\\\\\nNGC\\\\,2985 & & 09 50 20.9 & +72 16 44 & 22.4 & & (R')SA(rs)ab & 1,2,5,26,41,42 \\\\\\\\\\nNGC\\\\,3627 & M\\\\,66 & 11 20 14.9 & +12 59 21 & 6.6 & & SAB(s)b & 1,5,6,11,13,14\\\\\\\\\\n & & & & & & & 17,24,26,28,41,44\\\\\\\\\\nNGC\\\\,3628 & & 11 20 16.2 & +13 35 22 & 7.7 & & SAb pec spin & 1,4,5,11,13,14,16\\\\\\\\\\n &&&&&&& 17,18,19,24,26,30\\\\\\\\\\n &&&&&&& 34,36,38,41,44,45\\\\\\\\\\nNGC\\\\,3675 & & 11 26 08.0 & +43 34 58 & 12.8 & & SA(s)b & 1,3,17,25,26,41\\\\\\\\\\n &&&&&&& 42,47\\\\\\\\\\nNGC\\\\,3681 & & 11 26 29.4 & +16 51 51 & 24.2 & & SAB(r)bc & 1\\\\\\\\\\nNGC\\\\,4013 & & 11 58 31.1 & +43 56 50 & 17.0 & & SAb spin & 1,3,15,26,41\\\\\\\\\\nNGC\\\\,4321 & M\\\\,100& 12 22 54.8 & +15 49 20 & 16.8 & & SAB(s)bc & 1,5,7,11,13,14,17\\\\\\\\\\n &&&&&&& 18,20,22,24,26,27\\\\\\\\\\n &&&&&&& 35,36,41,47\\\\\\\\\\nNGC\\\\,4414 & & 12 26 27.2 & +31 13 24 & 16.8 & & SA(rs)c? & 1,3,5,11,13,14\\\\\\\\\\n &&&&&&& 17,18,24,26,31,36\\\\\\\\\\nNGC\\\\,4552 & M\\\\,89 & 12 35 39.9 & +12 33 25 & 9.7 & & E & 1,13,14,17,22,29\\\\\\\\\\n &&&&&&& 37,38,39,41,43,44\\\\\\\\\\nNGC\\\\,4643 & & 12 43 20.2 & +01 58 41 & 16.8& & SB(rs)0/a & 21,24,41\\\\\\\\\\nNGC\\\\,4713 & & 12 49 57.8 & +05 18 39 & 25.7 & & SAB(rs)d & 1\\\\\\\\\\nNGC\\\\,4826 & M\\\\,64 & 12 56 44.2 & +21 41 05 & 17.9 & & (R)SA(rs)ab & 1,2,8,13,14,17,24,25\\\\\\\\\\n &&&&&&& 26,36,40,41,44,46\\\\\\\\\\nNGC\\\\,5012 & &13 11 36.8 & +22 54 56 & 4.1 & & SAB(rs)c & 1\\\\\\\\\\nNGC\\\\,5354 && 13 53 26.7 & +40 18 09 & 32.8 & & SA0 spin & 1,3,12,17,32,41,44\\\\\\\\\\nNGC\\\\,5656 && 14 30 25.5 & +35 19 17 & 42.6 & & SAab & 1\\\\\\\\\\nNGC\\\\,5678 && 14 32 05.2 & +57 55 23 & 35.6 & & SAB(rs)b & 1,13,14,17,18,31\\\\\\\\\\nNGC\\\\,5838 && 15 05 26.5 & +02 06 01 & 28.5 & & SA0$^{-}$ & 1\\\\\\\\\\nNGC\\\\,5846 && 15 06 29.2 & +01 36 21 & 28.5 & & E0$^{-}$ & 1,9,10,12,41\\\\\\\\\\nNGC\\\\,5879 && 15 09 47.1 & +57 00 05 & 16.8 & & SA(rs)bc? & 1,41\\\\\\\\\\nNGC\\\\,5921 && 15 21 56.3 & +05 04 11 & 25.2 & & SB(r)bc & 1,24,26,41\\\\\\\\\\nNGC\\\\,6384 && 17 32 24.5 & +07 03 37 & 26.6 & & SAB(r)bc & 5,17,24,26,41\\\\\\\\\\nNGC\\\\,6482 && 17 51 48.9 & +23 04 20 & 52.3 & & E: & \\\\nodata \\\\\\\\\\nNGC\\\\,6503 && 17 49 27.5 & +70 08 41 & 6.1 & & SA(s)cd & 1,5,26,41,42\\\\\\\\\\n\\n\\\\tableline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\setcounter{table}{0}\\n\\\\caption{Sample sources -- the 25 transition LINERs.}\\n\\\\end{table}\\n\\n\\\\clearpage\\n\\n% TABLE 1 - (cont.)\\n%\\\\setcounter{table}{0}\\n\\\\begin{table}\\n\\\\footnotesize\\n\\\\begin{center}\\n\\\\begin{tabular}[h]{l c c c c c c r}\\n\\n\\\\tableline\\n\\\\tableline\\n\\n\\nGalaxy & Other & R.A.(J2000) & Dec(J2000) & D & & Hubble Type & Reference \\\\\\\\\\n & name & $^{h}$ $^{m}$ $^{s}$ & $^{\\\\circ}$ $^{'}$ $^{''}$ & Mpc & & & \\\\\\\\\\n\\\\tableline\\nNGC\\\\,3593 & & 11 14 36.0 & +12 49 06 & 5.5 & & SA(S)0/a: & 1,5,11,13,14,17\\\\\\\\\\n & & & & & & & 18,24,26,33,41\\\\\\\\\\nNGC\\\\,3684 & & 11 27 11.1 & +17 01 49 & 23.4 & & SA(rs)bc & 1\\\\\\\\\\nNGC\\\\,4100 & & 12 06 08.1 & +49 34 59 & 17.0 & & (R')SA(rs)bc & 1,3,5,26,41,42\\\\\\\\\\nNGC\\\\,4217 & & 12 15 50.7 & +47 05 37 & 17.0 & & SAb spin & 1,3,5,11,13,14\\\\\\\\\\n &&&&&&& 15,17,26,41\\\\\\\\\\nNGC\\\\,4245 & & 12 17 36.7 & +29 36 29 & 9.7 & & SB(r)0/a & \\\\nodata\\\\\\\\\\nNGC\\\\,4369 & Mrk\\\\,439 & 12 24 36.1 & +39 22 58 & 21.6 & & (R)SA(rs)a & 1,3,18,41\\\\\\\\\\nNGC\\\\,4405 & IC\\\\,788 & 12 26 07.1 & +16 10 51 & 31.5 & & SA(rs)0: & 1\\\\\\\\\\nNGC\\\\,4424 & & 12 27 11.4 & +09 25 15 & 16.8 & & SA(s)a: & 1\\\\\\\\\\nNGC\\\\,4470 & & 12 29 37.9 & +07 49 25 & 31.4 & & Sa ? & 1\\\\\\\\\\nNGC\\\\,4710 & & 12 49 38.9 & +15 09 55 & 16.8 & & SA(r)0+? spin & 1,12,15,18,32,36\\\\\\\\\\n &&&&&&& 41,43\\\\\\\\\\nNGC\\\\,4800 && 12 54 38.0 & +46 31 52 & 15.2 & & SA(rs)b & 1,3,41\\\\\\\\\\nNGC\\\\,4845 & & 12 58 01.3 & +01 34 30& 15.6 & & SA(s)ab spin & 1,18\\\\\\\\\\n\\\\tableline\\n \\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\setcounter{table}{0}\\n\\\\caption{Sample sources -- the 12 H\\\\,II nuclei (cont.).}\\n\\\\end{table}\\n\\n\\n%Table 2\\n\\\\begin{table}\\n\\\\small\\n\\\\begin{center}\\n\\\\begin{tabular}[h]{ll|ll}\\n\\\\tableline\\n\\\\tableline\\nNo. & Reference & No. & Reference \\\\\\\\\\n\\\\tableline\\n\\n1 & Condon \\\\etal 1998a & 25 & Gioia \\\\& Fabbiano 1987 \\\\\\\\\\n2 & Condon \\\\etal 1998b & 26 & Condon 1987 \\\\\\\\\\n3 & Becker \\\\etal 1995 & 27 & Urbanik \\\\etal 1986\\\\\\\\\\n4 & Dumke \\\\etal 1995 & 28 & Urbanik \\\\etal 1985\\\\\\\\\\n5 & Niklas \\\\etal 1995 & 29 & Wrobel \\\\& Heeschen 1984\\\\\\\\\\n6 & Saikia \\\\etal 1994 & 30 & Schlickeiser et al. 1984\\\\\\\\\\n7 & Collison \\\\etal 1994 & 31 & Condon 1983\\\\\\\\\\n8 & Turner \\\\& Ho 1994 & 32 & Hummel \\\\& Kotanyi 1982\\\\\\\\\\n9 & Slee \\\\etal 1994 & 33 & Jenkins \\\\etal 1982 \\\\\\\\\\n10 & M\\\\\\\"ollenhoff \\\\etal 1992 & 34 & Condon \\\\etal 1982\\\\\\\\\\n11 & White \\\\& Becker 1992 & 35 & Weiler \\\\etal 1981\\\\\\\\\\n12 & Wrobel \\\\& Heeschen 1991 & 36 & van der Hulst \\\\etal 1981\\\\\\\\\\n13 & Becker \\\\etal 1991 & 37 & van Breugel \\\\etal 1981\\\\\\\\\\n14 & Gregory \\\\& Condon 1991 & 38 & Jones \\\\etal 1981a\\\\\\\\\\n15 & Hummel \\\\etal 1991 & 39 & Jones \\\\etal 1981b\\\\\\\\\\n16 & Reuter \\\\etal 1991 & 40 & Klein \\\\& Emerson 1981\\\\\\\\\\n17 & Condon \\\\etal 1991 & 41 & Hummel \\\\etal 1980\\\\\\\\\\n18 & Condon \\\\etal 1990 & 42 & Heckman \\\\etal 1980 \\\\\\\\\\n19 & Carral \\\\etal 1990 & 43 & Dressel \\\\& Condon 1978 \\\\\\\\\\n20 & Vila \\\\etal 1990 & 44 & Sramek 1975a \\\\\\\\\\n21 & Fabbiano \\\\etal 1989 & 45 & Haynes \\\\& Sramek 1975\\\\\\\\\\n22 & Turner \\\\etal 1988 & 46 & van der Kruit 1973a\\\\\\\\\\n23 & Condon \\\\& Broderick 1988 & 47 & van der Kruit 1973b\\\\\\\\ \\n24 & Hummel \\\\etal 1987 & & \\\\\\\\\\n\\n\\\\tableline \\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\setcounter{table}{1}\\n\\\\caption{References for the radio data (see Table~1).}\\n\\\\end{table}\\n\\n\\n\\\\clearpage\\n\\n\\n%TABLE 3\\n\\n\\\\begin{table}\\n\\\\footnotesize\\n\\\\begin{center}\\n\\\\begin{tabular}[h]{lccrcr}\\n\\\\tableline\\n\\\\tableline\\n\\nGalaxy & Taper & Beamsize & PA & $rms$ & Fig. No. \\\\\\\\\\n & K$\\\\lambda $ & arcsec$^2$ & $^{\\\\circ }$ & mJy/beam & \\\\\\\\ \\n\\\\tableline \\nNGC\\\\,2985 & 0 & 2.98 $\\\\times $ 2.15 & $-$7.19 & 0.08 & \\\\\\\\\\n & 20 & 9.30 $\\\\times $ 7.20 & $-$84.28 & 0.09 & 1a\\\\\\\\\\nNGC\\\\,3627 & 0 & 2.55 $\\\\times $ 2.29 & $-$25.24 & 0.10 & \\\\\\\\\\n & 15 & 10.96 $\\\\times $ 9.93 & $-$64.54 & 0.25 & 1c\\\\\\\\\\t \\nNGC\\\\,3628 & 0 & 2.54 $\\\\times $ 2.30 & $-$14.68 & 0.45 & \\\\\\\\\\n & 20 & 8.78 $\\\\times $ 7.48 & $-$76.82 & 0.80 & 1d\\\\\\\\\\nNGC\\\\,3675 & 25 & 7.27 $\\\\times $ 5.81 & 71.04 & 0.09 & 2a\\\\\\\\\\nNGC\\\\,4013 & 0 & 2.52 $\\\\times $ 2.26 & $-$19.39 & 0.07 & \\\\\\\\\\n & 30 & 5.90 $\\\\times $ 5.26 & 77.17 & 0.09 & 2b\\\\\\\\\\nNGC\\\\,4321 & 0 & 2.52 $\\\\times $ 2.33 & $-$11.27 & 0.07 & \\\\\\\\\\n & 30 & 7.25 $\\\\times $ 5.14 & $-$89.95 & 0.08 & 3a\\\\\\\\\\nNGC\\\\,4414 & 0 & 2.43 $\\\\times $ 2.32 & $-$37.18 & 0.08 &\\\\\\\\\\n & 10 & 18.70 $\\\\times $ 17.70 & $-$62.41 & 0.15 & 3c\\\\\\\\\\nNGC\\\\,4552 & 0 & 2.93 $\\\\times $ 2.54 & 11.27 & 0.08 & 4b\\\\\\\\\\nNGC\\\\,4643 & 15 & 12.04 $\\\\times $ 11.13 & 52.57 & 0.07 & 4c\\\\\\\\\\nNGC\\\\,4713 & 15 & 12.12 $\\\\times $ 10.95 & 44.22 & 0.08 & 5a\\\\\\\\\\nNGC\\\\,4826 & 0 & 2.76 $\\\\times $ 2.29 & $-$6.23 & 0.08 & \\\\\\\\\\n & 20 & 9.62 $\\\\times $ 8.26 & 62.33 & 0.10 & 5c\\\\\\\\\\nNGC\\\\,5012 & 15 & 11.59 $\\\\times $ 11.18 & 74.66 & 0.08 & 6a\\\\\\\\\\nNGC\\\\,5354 & 0 & 2.84 $\\\\times $ 2.37 & $-$42.75 & 0.06 & 6b \\\\\\\\\\n \\nNGC\\\\,5656 & 20 & 9.54 $\\\\times $ 8.39 & 75.33 & 0.08 & 6c\\\\\\\\\\nNGC\\\\,5678 & 0 & 2.99 $\\\\times $ 2.21 & $-$27.47 & 0.07 &\\\\\\\\\\n & 15 & 11.09 $\\\\times $ 10.75 & $-$34.43 & 0.10 & 6d\\\\\\\\\\nNGC\\\\,5838 & 0 & 3.13 $\\\\times $ 2.43 & 1.94 & 0.07 & \\\\\\\\\\n & 35 & 5.62 $\\\\times $ 5.23 & 51.83 & 0.07 & 7a\\\\\\\\\\nNGC\\\\,5846 & 0 & 3.13 $\\\\times $ 2.49 & 3.94 & 0.07 &\\\\\\\\\\n & 30 & 7.06 $\\\\times $ 5.67 & 68.01 & 0.07 & 7b\\\\\\\\\\nNGC\\\\,5921 & 20 & 7.12 $\\\\times $ 5.63 & 67.8 & 0.06 & 7c \\\\\\\\\\n\\\\tableline\\n\\\\tableline\\n\\nGalaxy & Taper & Beamsize & PA & $rms$ & Fig. No. \\\\\\\\\\n & K$\\\\lambda $ & arcsec$^2$ & $^{\\\\circ }$ & mJy/beam & \\\\\\\\ \\n\\\\tableline\\n\\nNGC\\\\,3593 & 0 & 2.58 $\\\\times $ 2.36 & $-$17.94 & 0.09 & \\\\\\\\ \\n & 20 & 9.70 $\\\\times $ 7.17 & $-$80.16 & 0.15 & 1b \\\\\\\\\\nNGC\\\\,4100 & 0 & 2.61 $\\\\times $ 2.35 & $-$29.79 & 0.07 & \\\\\\\\\\n & 20 & 7.83 $\\\\times $ 7.40 & 84.07 & 0.08 & 2c \\\\\\\\\\nNGC\\\\,4217 & 20 & 7.30 $\\\\times $ 5.41 & 76.75 & 0.09 & 2d\\\\\\\\\\nNGC\\\\,4369 & 0 & 2.48 $\\\\times $ 2.34 & $-$14.62 & 0.07 & \\\\\\\\\\n & 30 & 6.94 $\\\\times $ 5.51 & 88.71 & 0.10 & 3b \\\\\\\\\\nNGC\\\\,4424 & 0 & 3.00 $\\\\times $ 2.46 & 12.14 & 0.09 & \\\\\\\\\\n & 30 & 7.21 $\\\\times $ 5.60 & 76.27 & 0.07 & 3d\\\\\\\\\\nNGC\\\\,4470 & 15 & 9.95 $\\\\times $ 7.99 & 59.70 & 0.07 & 4a\\\\\\\\\\nNGC\\\\,4710 & 0 & 2.86 $\\\\times $ 2.48 & 3.88 & 0.10 &\\\\\\\\\\n & 30 & 5.50 $\\\\times $ 5.16 & 72.46 & 0.08 & 4d\\\\\\\\\\nNGC\\\\,4800 & 30 & 5.28 $\\\\times $ 5.15 & $-$82.56 & 0.10 & 5b\\\\\\\\\\nNGC\\\\,4845 & 0 & 3.27 $\\\\times $ 2.44 & 15.08 & 0.08 & \\\\\\\\\\n & 30 & 7.08 $\\\\times $ 5.69 & 64.51 & 0.10 & 5d \\\\\\\\\\n\\n\\\\tableline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\setcounter{table}{2}\\n\\\\caption {Map parameters of the detected sources. The H\\\\,II nuclei appear\\nbelow the transition LINERs.}\\n\\\\end{table}\\n\\n\\\\clearpage \\n\\n\\n\\n%TABLE 4\\n\\n\\n\\\\begin{table}\\n\\\\footnotesize\\n\\\\begin{center}\\n\\\\begin{tabular}[h]{lcccccrr}\\n\\\\tableline\\n\\\\tableline\\n\\n\\nField Source & R.A.(J2000) & Dec(J2000) & z & NVSS & F$_{\\\\rm 8.4}^{\\\\rm int}$ & $\\\\alpha ^{\\\\rm 8.4}_{\\\\rm 1.4}$ & \\nReference \\\\\\\\\\n & $^{h}$ $^{m}$ $^{s}$ & $^{\\\\circ }$ $^{'}$ $^{''}$ & & mJy & mJy & & \\\\\\\\ \\n\\\\tableline\\n\\nNGC\\\\,3593N & 11 14 37.20 & +12 52 15.0 & \\\\nodata & 18.7 & 10.6 & 0.3 & \\\\nodata\\\\\\\\\\nNGC\\\\,3684SW & 11 27 02.42 & +16 58 34.8 & \\\\nodata & 41.4 & 18.1 & 0.5 & \\\\nodata\\\\\\\\\\nNGC\\\\,4013SE & 11 58 38.61 & +43 55 05.5 & \\\\nodata & \\\\nodata & 3.8 & \\\\nodata & \\\\nodata\\\\\\\\\\nSN\\\\,1979C & 12 22 58.67 & +15 47 51.6 & 0.0052 & \\\\nodata & 1.3 & \\\\nodata & Weiler \\\\etal 1981 \\\\\\\\\\nLBQS\\\\,1223+1626 & 12 25 59.09 & +16 10 21.2 & 1.9290 & 8.9 & 10.1 & $-$0.1 & Hewett \\\\etal 1995 \\\\\\\\\\nNGC\\\\,4424SE & 12 27 19.83 & +09 23 03.0 & \\\\nodata & 11.0 & 13.3 & $-$0.1 & \\\\nodata \\\\\\\\\\nTXS\\\\,1227+081 & 12 29 47.64 & +07 50 26.7 & \\\\nodata & 110.9 & 16.0 & 1.1 & Douglas \\\\etal 1996 \\\\\\\\\\nNGC\\\\,4710E & 12 49 48.63 & +15 09 33.3 & \\\\nodata & 4.1 & 4.8 & $-$0.1& \\\\nodata \\\\\\\\ \\nNGC\\\\,5353 & 13 53 26.69 & +40 16 58.7 & 0.0077 & 41.0 & 26.7 & 0.2 & Hummel \\\\& Kotanyi 1982\\\\\\\\\\nNGC\\\\,5838S & 12 05 28.11 & +02 04 16.2 & \\\\nodata & 7.5 & 1.3 & 1.0 & \\\\nodata \\\\\\\\ \\n87GB\\\\,1508+5714 & 15 10 02.97 & +57 02 43.6 & 4.3010 & 202.4 & 292.1 & $-$0.2 & Hook \\\\etal 1995 \\\\\\\\\\n87GB\\\\,1749+2302 & 17 51 49.10 & +23 01 26.7 & 0.7700 & 45.3 & 23.6 & 0.4 & Becker \\\\etal 1991 \\\\\\\\\\nBL\\\\,1749+701 & 17 48 32.87 & +70 05 52.5 & \\\\nodata & 735.6 & \\\\nodata & \\\\nodata & Hughes \\\\etal 1992 \\\\\\\\\\n\\n\\\\tableline \\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\setcounter{table}{3}\\n\\\\caption{The field source parameters. The integrated 8.4\\\\,GHz flux densities \\n(column~6) have been corrected for primary beam attenuation.}\\n\\\\end{table}\\n\\n\\\\clearpage\\n\\n%TABLE 5\\n\\n\\\\begin{table}\\n\\\\footnotesize\\n\\\\begin{center}\\n\\\\begin{tabular}[h]{lccc cr}\\n\\\\tableline\\n\\\\tableline\\nGalaxy & Taper & F$_{\\\\rm max}$ & R.A.(J2000) & Dec(J2000) & F$_{\\\\rm int}$ \\\\\\\\\\n & K$\\\\lambda $ & mJy/beam & $^{h}$ $^{m}$ $^{s}$ & $^{\\\\circ }$ $^{'}$ $^{''}$ & mJy \\\\\\\\ \\n\\\\tableline \\n\\nNGC\\\\,2985 & 0 & 1.07 & 09 50 22.1 & +72 16 44 & $\\\\geq$1.9\\\\\\\\\\n & 20 & 1.30 & 09 50 22.0 & +72 16 44 & $\\\\geq$2.7 \\\\\\\\\\t\\nNGC\\\\,3627 & 0 & 1.30 & 11 20 15.0 & +12 59 30 & 3.7 ($\\\\geq$22.1) \\\\\\\\\\n & 15 & 2.99 & 11 20 15.1 & +12 59 31 & 3.9 ($\\\\geq$25.7)\\\\\\\\\\nNGC\\\\,3628 & 0 & 15.31 & 11 20 17.0 & +13 35 20 & 61.4 \\\\\\\\\\n & 20 & 41.07 & 11 20 17.0 & +13 35 19 & 69.1\\\\\\\\\\nNGC\\\\,3675 & 25 & 0.37 & 11 26 08.7 & +43 35 01 & $\\\\geq$1.3 \\\\\\\\\\n\\nNGC\\\\,4013 & 0 & 1.08 & 11 58 31.4 & +43 56 51 & $\\\\geq$3.8 \\\\\\\\\\n & 30 & 2.28 & 11 58 31.4 & +43 56 51 & $\\\\geq$4.1 \\\\\\\\\\nNGC\\\\,4321 & 0 & 0.34 & 12 22 55.4 & +15 49 21 & 7.5\\\\\\\\\\n & 30 & 1.64 & 12 22 55.3 & +15 49 21 & 15.7\\\\\\\\\\nNGC\\\\,4414 & 0 & 0.65 & 12 26 27.5 & +31 13 40 & 2.3 \\\\\\\\\\n & 10 & 3.72 & 12 26 26.7 & +31 13 42 & 29.4\\\\\\\\\\nNGC\\\\,4552 & 0 & 76.51 & 12 35 39.8 & +12 33 23 & 76.8 \\\\\\\\\\n \\nNGC\\\\,4643 & 15 & \\\\nodata & \\\\nodata & \\\\nodata & $\\\\sim$1 \\\\\\\\\\nNGC\\\\,4713 & 15 & 0.32 & 12 49 58.4 & +05 18 39 & $\\\\geq$1.2\\\\\\\\\\nNGC\\\\,4826 & 0 & 1.8 & 12 56 43.4 & +21 41 01 & 18.9\\\\\\\\\\n & 20 & 4.03 & 12 56 43.7 & +21 41 00 & 21.1\\\\\\\\\\nNGC\\\\,5012 & 15 & \\\\nodata& \\\\nodata & \\\\nodata & $\\\\sim$1 \\\\\\\\\\nNGC\\\\,5354 & 0 & 11.61 & 13 53 26.7 & +40 18 10 & 11.7 \\\\\\\\\\n \\nNGC\\\\,5656 & 20 & 0.40 & 14 30 26.9 & +35 19 25 & $\\\\geq$0.7\\\\\\\\\\nNGC\\\\,5678 & 0 & 0.74 & 14 32 05.9 & +57 54 51 & $\\\\geq$2.0 \\\\\\\\\\n & 15 & 1.31 & 14 32 05.5 & +57 54 51 & $\\\\geq$8.6\\\\\\\\\\n\\nNGC\\\\,5838 & 0 & 1.85 & 15 05 26.3 & +02 05 57 & 2.1\\\\\\\\\\n & 35 & 1.88 & 15 05 26.3 & +02 05 57 & 2.2 \\\\\\\\\\n\\nNGC\\\\,5846 & 0 & 6.03 & 15 06 29.3 & +01 36 21 & 6.4 \\\\\\\\\\n & 30 & 6.36 & 15 06 29.3 & +01 36 21 & 7.1\\\\\\\\\\n\\nNGC\\\\,5921 & 20 & 0.46 & 15 21 56.4 & +05 04 14 & $\\\\geq$0.8 \\\\\\\\\\n\\\\tableline\\n\\\\tableline\\n\\nGalaxy & Taper & F$_{\\\\rm max}$ & R.A.(J2000) & Dec(J2000) & F$_{\\\\rm int}$ \\\\\\\\\\n & K$\\\\lambda $ & mJy/beam & $^{h}$ $^{m}$ $^{s}$ & $^{\\\\circ }$ ' '' & mJy \\\\\\\\ \\n\\\\tableline \\n\\nNGC\\\\,3593 & 0 & 1.82 & 11 14 36.4 & +12 49 06 & 16.4 \\\\\\\\ \\n & 20 & 4.79 & 11 14 36.6 & +12 49 05 & 20.0 \\\\\\\\\\nNGC\\\\,4100 & 0 & 0.93 & 12 06 08.6 & +49 34 58 & $\\\\geq$3.9 \\\\\\\\\\n & 20 & 3.58 & 12 06 08.4 & +49 34 59 & $\\\\geq$7.3 \\\\\\\\\\nNGC\\\\,4217 & 20 & 0.55 & 12 15 51.0 & +47 05 29 & $\\\\geq$22.0 \\\\\\\\\\nNGC\\\\,4369 & 0 & 0.31 & 12 24 36.3 & +39 22 56 & 1.3 \\\\\\\\\\n & 30 & 1.31 & 12 24 36.3 & +39 22 57 & 3.8 \\\\\\\\\\nNGC\\\\,4424 & 0 & 0.60 & 12 27 11.2 & +09 25 17 & 2.0 \\\\\\\\\\n & 30 & 0.80 & 12 27 11.7 & +09 25 17 & 2.5 \\\\\\\\\\n\\nNGC\\\\,4470 & 15 & 0.38 & 12 29 37.8 & +07 49 24 & $\\\\geq$2.6 \\\\\\\\\\nNGC\\\\,4710 & 0 & 0.71 & 12 49 38.9 & +15 09 59 & $\\\\geq$6.0 \\\\\\\\\\n & 30 & 1.64 & 12 49 39.0 & +15 09 58 & 6.1 \\\\\\\\\\nNGC\\\\,4800 & 30 & 0.36 & 12 54 37.8 & +46 31 52 & $\\\\geq$1.2 \\\\\\\\\\nNGC\\\\,4845 & 0 & 1.76 & 12 58 01.2 & +01 34 32 & $\\\\geq$9.9 \\\\\\\\\\n & 30 & 5.15 & 12 58 01.1 & +01 34 32 & 12.5 \\\\\\\\\\n\\n\\n\\\\tableline \\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\setcounter{table}{4}\\n\\\\caption{The 8.4\\\\,GHz radio parameters of the detected sources. The \\nH\\\\,II nuclei appear below the transition LINERs.}\\n\\\\end{table}\\n\\n\\\\clearpage\\n\\n\\n%TABLE 6\\n\\n\\\\begin{table}\\n\\\\footnotesize\\n\\\\begin{center}\\n\\\\begin{tabular}[h]{l c r c r c}\\n\\\\tableline\\n\\\\tableline\\n\\nGalaxy & NVSS & F$_{\\\\rm 8.4}^{\\\\rm int}$ & Log L$_{\\\\rm 1.4}^{\\\\rm tot}$ & \\n$\\\\alpha_{\\\\rm 1.4}^{\\\\rm 8.4}$ & Hubble Type \\\\\\\\\\n & mJy & mJy & erg s$^{-1}$ Hz$^{-1}$ & & \\\\\\\\\\n\\\\tableline \\nIC\\\\,520 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & SAB(rs)ab?\\\\\\\\\\nNGC\\\\,2541 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & SA(s)cd \\\\\\\\\\nNGC\\\\,2985 & 44.1 & 2.7 & 28.4 & 1.6 & (R')SA(rs)ab \\\\\\\\\\nNGC\\\\,3627 & 324.9 & 3.9 (25.7) & 28.2 & 2.5 (1.5) & SAB(s)b \\\\\\\\\\nNGC\\\\,3628 & 291.7 & 69.1 & 28.3 & 0.8 & SAb pec spin \\\\\\\\ \\nNGC\\\\,3675 & 48.9 & 1.3 & 27.9 & 2.0 & SA(s)b \\\\\\\\\\nNGC\\\\,3681 & 4.2 & \\\\nodata & 27.5 & \\\\nodata & SAB(r)bc \\\\\\\\\\nNGC\\\\,4013 & 40.5 & 4.1 & 28.2 & 1.3 & SAb spin \\\\\\\\\\nNGC\\\\,4321 & 87.1 & 15.7 & 28.5 & 1.0 & SAB(s)bc\\\\\\\\\\nNGC\\\\,4414 & 242.2 & 29.4 & 28.4 & 1.2 & SA(rs)c? \\\\\\\\\\nNGC\\\\,4552 & 103.1 & 76.8 & 28.5 & 0.2 & E \\\\\\\\\\nNGC\\\\,4643 & \\\\nodata & $\\\\sim$1 & \\\\nodata & \\\\nodata & SB(rs)0/a \\\\\\\\\\nNGC\\\\,4713 & 46.9 & 1.2 & 28.3 & 2.0 & SAB(rs)d \\\\\\\\\\nNGC\\\\,4826 & 101.1 & 21.1 & 27.3 & 0.9 & (R)SA(rs)ab\\\\\\\\\\nNGC\\\\,5012 & 31.4 & $\\\\sim$1 & 28.8 & \\\\nodata & SAB(rs)c \\\\\\\\\\nNGC\\\\,5354 & 8.4 & 11.7 & 28.0 & $-$0.2 & SA0 spin \\\\\\\\\\nNGC\\\\,5656 & 22.0 & 0.7 & 28.7 & 2.0 & SAab \\\\\\\\\\nNGC\\\\,5678 & 111.5 & 8.6 & 29.2 & 1.4 & SAB(rs)b \\\\\\\\\\nNGC\\\\,5838 & 3.0 & 2.2 & 27.5 & 0.2 & SA0$^{-}$ \\\\\\\\\\nNGC\\\\,5846 & 22.1 & 7.1 & 28.3 & 0.6 & E0$^{-}$ \\\\\\\\\\nNGC\\\\,5879 & 21.1 & \\\\nodata & 27.9 & \\\\nodata & SA(rs)bc?\\\\\\\\\\nNGC\\\\,5921 & 24.2 & 0.8 & 28.3 & 1.9 & SB(r)bc\\\\\\\\\\nNGC\\\\,6384 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & SAB(r)bc\\\\\\\\\\nNGC\\\\,6482 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & E: \\\\\\\\\\nNGC\\\\,6503 & 40.0 & \\\\nodata & 27.3 & \\\\nodata & SA(s)cd\\\\\\\\\\n\\n\\\\tableline\\n\\\\tableline\\nGalaxy & NVSS & F$_{\\\\rm 8.4}^{\\\\rm int}$ & Log L$_{\\\\rm 1.4}^{\\\\rm tot}$& \\n$\\\\alpha_{\\\\rm 1.4}^{\\\\rm 8.4}$ & Hubble Type \\\\\\\\\\n & mJy & mJy & erg s$^{-1}$ Hz$^{-1}$ & & \\\\\\\\\\n\\\\tableline \\n \\nNGC\\\\,3593 & 87.3 & 20.0 & 27.5 & 0.8 & SA(S)0/a: \\\\\\\\\\nNGC\\\\,3684 & 15.9 & \\\\nodata & 28.0 & \\\\nodata & SA(rs)bc \\\\\\\\\\nNGC\\\\,4100 & 50.3 & 7.3 & 28.2 & 1.1 & (R')SA(rs)bc \\\\\\\\\\nNGC\\\\,4217 & 122.8 & 22.0 & 28.6 & 1.0& SAb spin \\\\\\\\\\nNGC\\\\,4245 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & SB(r)0/a \\\\\\\\\\nNGC\\\\,4369 & 24.3 & 3.8 & 28.1 & 1.0 & (R)SA(rs)a \\\\\\\\\\nNGC\\\\,4405 & 4.5 & \\\\nodata & 27.7 & \\\\nodata & SA(rs)0: \\\\\\\\\\nNGC\\\\,4424 & 4.5 & 2.5 & 27.2 & 0.3 & SA(s)a: \\\\\\\\\\nNGC\\\\,4470 & 17.1 & 2.6 & 28.3 & 1.1 & Sa ? \\\\\\\\\\nNGC\\\\,4710 & 19.3 & 6.1 & 27.8 & 0.7 & SA(r)0+? spin \\\\\\\\\\nNGC\\\\,4800 & 23.5 & 1.2 & 27.8 & 1.7 & SA(rs)b \\\\\\\\\\nNGC\\\\,4845 & 43.8 & 12.5 & 28.1 & 0.7 & SA(s)ab spin \\\\\\\\\\n\\n\\\\tableline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\setcounter{table}{5}\\n\\\\caption{Summary of the detected sources. The H\\\\,II nuclei appear\\n below the transition LINERs. All tabulated spectral index values are upper\\nlimits (see Section~4.3).}\\n\\\\end{table}\\n\\n\\n\\n\\n\\\\clearpage\\n\\n\\n\\\\begin{figure}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f1a.ps}\\n(a) \\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{1.4cm}{\\n\\\\epsffile{f1b.ps}\\n(b)\\n}\\n}\\n\\n\\\\end{figure}\\n\\n\\n\\\\begin{figure}\\n\\\\figurenum{1}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f1c.ps}\\n(c)\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{1.4cm}{\\n\\\\epsffile{f1d.ps}\\n(d)\\n}\\n}\\n\\n\\\\caption{Radio emission (contours) superimposed on optical images from \\nthe Digitized Sky Survey (greyscale). Contour levels are CLEV $\\\\times$ \\n(--3, 3, 6, 12, 24, 48, 96), where CLEV is the $rms$ noise level (see Table~3). \\nThe grey scale levels are arbitrary. The size of the restoring \\nbeam is given in parentheses after each object name (see Table~3).\\n{\\\\bf (a)} NGC\\\\,2985 (9\\\\arcsecpoint30 $\\\\times$ 7\\\\arcsecpoint20), {\\\\bf (b)} \\nNGC\\\\,3593 (9\\\\arcsecpoint70 $\\\\times$ 7\\\\arcsecpoint17), {\\\\bf (c)} NGC\\\\,3627 (10\\\\arcsecpoint96 $\\\\times$ 9\\\\arcsecpoint93) and {\\\\bf (d)} NGC\\\\,3628 \\n(8\\\\arcsecpoint78 $\\\\times$ 7\\\\arcsecpoint48). NGC\\\\,3593 is an H\\\\,II nucleus. }\\n\\n\\\\end{figure}\\n\\n\\\\clearpage\\n\\n\\\\begin{figure}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f2a.ps}\\n(a)\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{1.8cm}{\\n\\\\epsffile{f2b.ps}\\n(b)\\n}\\n}\\n\\\\end{figure}\\n\\n\\n\\\\begin{figure}\\n\\\\figurenum{2}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f2c.ps}\\n(c)\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{1cm}{\\n\\\\epsffile{f2d.ps}\\n(d)\\n}\\n}\\n\\n\\\\caption{As in Figure~1. {\\\\bf (a)} NGC\\\\,3675 (7\\\\arcsecpoint27 $\\\\times$ 5\\\\arcsecpoint81), {\\\\bf (b)} NGC\\\\,4013\\n(5\\\\arcsecpoint90 $\\\\times$ 5\\\\arcsecpoint26), {\\\\bf (c)} NGC\\\\,4100 (7\\\\arcsecpoint83 $\\\\times$ 7\\\\arcsecpoint40) and {\\\\bf (d)}\\nNGC\\\\,4217 (7\\\\arcsecpoint30 $\\\\times$ 5\\\\arcsecpoint41). NGC\\\\,4100 and NGC\\\\,4217 are H\\\\,II nuclei.}\\n\\n\\\\end{figure}\\n\\n\\\\clearpage\\n\\n\\\\begin{figure}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{0.1cm}{\\n\\\\epsffile{f3a.ps}\\n(a)\\n}\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f3b.ps}\\n(b)\\n}\\n\\n\\\\end{figure}\\n\\n\\n\\\\begin{figure}\\n\\\\figurenum{3}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f3c.ps}\\n(c)\\n\\\\raisebox{1.6cm}{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f3d.ps}\\n(d)\\n}\\n}\\n\\n\\\\caption{As in Figure~1. {\\\\bf (a)} NGC\\\\,4321 (7\\\\arcsecpoint25 $\\\\times$ 5\\\\arcsecpoint14), {\\\\bf (b)} NGC\\\\,4369\\n(6\\\\arcsecpoint94 $\\\\times$ 5\\\\arcsecpoint51), {\\\\bf (c)} NGC\\\\,4414 (18\\\\arcsecpoint17 $\\\\times$ 17\\\\arcsecpoint70) and {\\\\bf (d)} NGC\\\\,4424\\n(7\\\\arcsecpoint21 $\\\\times$ 5\\\\arcsecpoint60). NGC\\\\,4369 and NGC\\\\,4424 are H\\\\,II nuclei.}\\n\\n\\\\end{figure}\\n\\n\\\\clearpage\\n\\n\\\\begin{figure}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f4a.ps}\\n(a)\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{0.4cm}{\\n\\\\epsffile{f4b.ps}\\n(b)\\n}\\n}\\n\\n\\\\end{figure}\\n\\n\\n\\\\begin{figure}\\n\\\\figurenum{4}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{1.8cm}{\\n\\\\epsffile{f4c.ps}\\n(c)\\n}\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f4d.ps}\\n(d)\\n}\\n\\n\\\\caption{As in Figure~1. {\\\\bf (a)} NGC\\\\,4470 (9\\\\arcsecpoint95 $\\\\times$ 7\\\\arcsecpoint99), {\\\\bf (b)} NGC\\\\,4552\\n(2\\\\arcsecpoint93 $\\\\times$ 2\\\\arcsecpoint54), {\\\\bf (c)} NGC\\\\,4643 (12\\\\arcsecpoint04 $\\\\times$ 11\\\\arcsecpoint13) and {\\\\bf (d)}\\nNGC\\\\,4710 (5\\\\arcsecpoint50 $\\\\times$ 5\\\\arcsecpoint16). NGC\\\\,4470 and NGC\\\\,4710 are H\\\\,II nuclei.}\\n\\n\\\\end{figure}\\n\\n\\\\clearpage\\n\\n\\\\begin{figure}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{1cm}{\\n\\\\epsffile{f5a.ps}\\n(a)\\n}\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f5b.ps}\\n(b)\\n}\\n\\n\\\\end{figure}\\n\\n\\n\\\\begin{figure}\\n\\\\figurenum{5}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f5c.ps}\\n(c)\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{0.6cm}{\\n\\\\epsffile{f5d.ps}\\n(d)\\n}\\n}\\n\\n\\\\caption{As in Figure~1. {\\\\bf (a)} NGC\\\\,4713 (12\\\\arcsecpoint12 $\\\\times$ 10\\\\arcsecpoint95), {\\\\bf (b)} NGC\\\\,4800\\n(5\\\\arcsecpoint28 $\\\\times$ 5\\\\arcsecpoint15), {\\\\bf (c)} NGC\\\\,4826 (9\\\\arcsecpoint62 $\\\\times$ 8\\\\arcsecpoint26) and {\\\\bf (d)} NGC\\\\,4845\\n(7\\\\arcsecpoint08 $\\\\times$ 5\\\\arcsecpoint69). NGC\\\\,4845 is an H\\\\,II nucleus.}\\n\\n\\\\end{figure}\\n\\n\\\\clearpage\\n\\n\\\\begin{figure}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f6a.ps}\\n(a)\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{1.1cm}{\\n\\\\epsffile{f6b.ps}\\n(b)\\n}\\n}\\n\\n\\\\end{figure}\\n\\n\\n\\\\begin{figure}\\n\\\\figurenum{6}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{0.6cm}{\\n\\\\epsffile{f6c.ps}\\n(c)\\n}\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f6d.ps}\\n(d)\\n}\\n\\n\\\\caption{As in Figure~1. {\\\\bf (a)} NGC\\\\,5012 (11\\\\arcsecpoint59 $\\\\times$ 11\\\\arcsecpoint18), {\\\\bf (b)} NGC\\\\,5354\\n(2\\\\arcsecpoint84 $\\\\times$ 2\\\\arcsecpoint37), {\\\\bf (c)} NGC\\\\,5656 (9\\\\arcsecpoint54 $\\\\times$ 8\\\\arcsecpoint39) and {\\\\bf (d)} NGC\\\\,5678\\n(11\\\\arcsecpoint09 $\\\\times$ 10\\\\arcsecpoint75).}\\n\\n\\\\end{figure}\\n\\n\\\\clearpage\\n\\n\\\\begin{figure}\\n\\\\leavevmode\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f7a.ps}\\n(a)\\n\\\\epsfxsize=7.3cm\\n\\\\raisebox{0.3cm}{\\n\\\\epsffile{f7b.ps}\\n(b)\\n}\\n}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\figurenum{7}\\n\\\\centerline{\\n\\\\epsfxsize=7.3cm\\n\\\\epsffile{f7c.ps}\\n(c)\\n}\\n\\n\\\\caption{As in Figure~1. {\\\\bf (a)} NGC\\\\,5838 (5\\\\arcsecpoint62 $\\\\times$ 5\\\\arcsecpoint23), {\\\\bf (b)} NGC\\\\,5846\\n(7\\\\arcsecpoint06 $\\\\times$ 5\\\\arcsecpoint67) and {\\\\bf (c)} NGC\\\\,5921 (7\\\\arcsecpoint12 $\\\\times$ 5\\\\arcsecpoint63).}\\n\\n\\\\end{figure}\\n\\n\\\\end{document}\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[],"string":"[]"}}},{"rowIdx":399,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002405"},"title":{"kind":"string","value":"Recovering the Topology of the Initial Density Fluctuations Using the {\\em IRAS} Point Source Catalogue Redshift Survey"},"authors":{"kind":"list like","value":[{"author":"A. Canavezes"},{"author":"$^1$ J. Sharpe"},{"author":"$^2$"},{"author":"$^1$ Centro de Astrof\\'{i}sica da Universidade do Porto"},{"author":"Rua das Estrelas s/n"},{"author":"4150 Porto"},{"author":"Portugal"},{"author":"$^2$ Imperial College of Science Technology and Medicine"},{"author":"Blackett Laboratory"},{"author":"Prince Consort Road"},{"author":"London SW7 2BZ"},{"author":"UK"}],"string":"[\n {\n \"author\": \"A. Canavezes\"\n },\n {\n \"author\": \"$^1$ J. Sharpe\"\n },\n {\n \"author\": \"$^2$\"\n },\n {\n \"author\": \"$^1$ Centro de Astrof\\\\'{i}sica da Universidade do Porto\"\n },\n {\n \"author\": \"Rua das Estrelas s/n\"\n },\n {\n \"author\": \"4150 Porto\"\n },\n {\n \"author\": \"Portugal\"\n },\n {\n \"author\": \"$^2$ Imperial College of Science Technology and Medicine\"\n },\n {\n \"author\": \"Blackett Laboratory\"\n },\n {\n \"author\": \"Prince Consort Road\"\n },\n {\n \"author\": \"London SW7 2BZ\"\n },\n {\n \"author\": \"UK\"\n }\n]"},"abstract":{"kind":"string","value":"We apply the reconstruction technique of Nusser \\& Dekel (1992) to the recently available Point Source Catalogue Redshift Survey (PSCz) in order to subtract the phase correlations that are expected to develop in the mild non-linear regime of gravitational evolution. We study the evolution of isodensity contours defined using an adaptive smoothing algorithm in order to minimize the problems derived from the non-comutivity of operators. We study the genus curves of these isodensity contours and concentrate on the evolution of the amplitude drops, a meta-statistic able to quatify the level of phase-correlation present in the field. In order to test the method and to quatify the level of statistical uncertainty, we apply the method to a set of mock PSCz catalogues derived from the N-body simulations of two 'standard' CDM models, kindly granted to us by the Virgo consortium. We find the method to be reliable in recovering the right amplitude drops. When applied to PSCz the level of phase correlations observed is very low on all scales ranging from $5\\lu$ to $60\\lu$, providing support to the theory that structure originated from gaussian initial conditions."},"latex":{"kind":"list like","value":[{"name":"reconstruction.tex","string":"\\label{rec}\n\nThe {\\em IRAS} Point Source Catalogue Redshift Survey \\cite{Sa99} lends itself to topological studies because of its high sampling densities and large volume. It countains approximately $15000$ galaxies to the full depth of the PSC ($0.6 Jy$). Its sky coverage is $84.1$ per cent, where only the zone of avoidance is excluded, here defined as an infrared background exceeding $25 \\rm{MJy sr}^{-1}$ at $100\\mu\\rm{m}$, and a few unobserved or contaminated patches at higher latitude. The excluded regions are coded in an angular mask, as shown in Fig. \\ref{figMask}. Canavezes et al. \\shortcite{Ca98} analysed the topology of PSCz and showed that it is consistent with the topology of CDM models: The genus curves retain the w-shape characteristic of random-phase density fields even at small smoothing lengths, where non-linear evolution has already generated significant skewness of the 1-point PDF. These non-linearities are, however, detected by a depressed amplitude of the genus curves - amplitude drops - consistent with those detected for the CDM models. Above $10 \\lu$ strong phase correlations were not detected in PSCz and those that were detected at smaller scales are expected in the framework of mildly non-linear gravitational evolution. This supports the hypothesis that structure grew from random-phase initial conditions.\n\n\\begin{figure*}\n\\bc\n\\resizebox{14cm}{!}{\\includegraphics{plots/aitoffcrop.eps}}\n\\caption\n{Sky coverage of the PSCz survey in an aitoff projection. The dots represent the galaxies in the survey, the shaded regions are unobserved and comprise the angular mask. The galactic centre lies in the centre of the plot.\n\\label{figMask}}\n\\ec\n\\end{figure*}\n\nIn this paper we attempt to subtract these phase correlations by reversing gravity. If it is true that structure does indeed originate in random-phase fluctuations, then reversing gravitational evolution should provide us with an initial density fluctuation field free from phase correlations on any scale.\n\nThere are several methods to achieve this goal. Nusser \\& Dekel \\shortcite{ND92}, showed how to express the Zel'dovich approximation in a set of Eulerian coordinates and reverse it to obtain a reconstructed density field. They tested the method with N-body simulations and found satisfactory results. Recently, some improvements have been made on the original method (e.g. Gramann \\shortcite{Gr93}). Nusser, Dekel \\& Yahil \\shortcite{Nu95} applied the Nusser \\& Dekel \\shortcite{ND92} approximation to the $1.2$ Jy $IRAS$ redshift survey to recover the 1-point probability distribution function of the initial density field. Their results were consistent with Gaussian initial conditions. The PSCz presents us with an unprecedented number of resolution elements and should constitute therefore the best available data set on which to apply a reconstruction technique. \n\nThe method we choose to follow here is the quasi-linear method proposed by Nusser \\& Dekel \\shortcite{ND92}. In section \\ref{recmethod} we describe this method; In section \\ref{recdenmaps} we describe the construction of the density maps used as the input of the {\\em time-machine} and describe our error estimates; Section \\ref{recnbody} is devoted to testing the method using N-body simulations of a CDM model and in section \\ref{recpscz} we apply the method to the PSCz and present our results.\n\n\\section{THE RECONSTRUCTION METHOD}\n\\label{recmethod}\n\nThe reconstruction method we follow is based on two premises: The velocity field is, when smoothed on a scale of a few Mpc, irrotational, and the Zel'dovich approximation is accurate over the mildly non-linear regime. \n\nOur first step is to try to express the Zel'dovich approximation in a set of Eulerian coordinates.\n\nGiven an initial comoving position $\\bf{q}$ for a given particle, a final position $\\bf{x}(\\bf{q},t)$ will have the form\n\\be \n{\\bf x}({\\bf q},t)={\\bf q}+P({\\bf q},t).\n\\ee\nThe Zel'dovich approximation states that the displacement term $P({\\bf q},t)$ can be written as a product of two functions, each a function only of one of the variables ${\\bf q}$ or $t$, i.e., we can separate the variables $q$ and $t$:\n\\be\n{\\bf x}({\\bf q},t)={\\bf q}+D(t)\\Psi({\\bf q}).\n\\ee\nThis is simply a linear approximation with respect to the particle displacements rather than density. Particles in the Zel'dovich approximation follow straight lines:\n\\be\n{\\bf v}({\\bf q},t)=a(t)\\frac{d{\\bf x}}{dt}=a(t)\\dot{D}(t)\\Psi({\\bf q}).\n\\ee\nThe density fluctuation is given by\n\\be\n\\delta({\\bf q},t)=\\bar{\\rho}/J({\\bf q},t)-1,\n\\ee\nwhere $J({\\bf q},t)$ is the Jacobian of the coordinate transformation ${\\bf q}\\rightarrow {\\bf x}$.\n\nAs long as second order terms in $\\delta$ and ${\\bf v}$ are negligible, $\\delta(t) \\propto D(t)$, where $D(t)$ is the growing mode solution in linear perturbation theory (see e.g. Peebles \\shortcite{Pe80}).\n\nUnlike linear theory, where the density at a given position evolves according to the linear growth rate, under the Zel'dovich approximation infinite density can develop in a finite time as a result of the convergence of particle trajectories into a {\\em pancake}. in order to integrate a density field back in time, Nusser \\& Dekel \\shortcite{ND92} found the differential equation in Eulerian space which contains the Zel'dovich approximation. This is derived from the standard equation of motion of dust particles in an expanding Universe (e.g. Peebles \\shortcite{Pe80}):\n\\be\n\\frac{d{\\bf v}}{dt} + H{\\bf v}=-\\frac{1}{a}\\nabla\\Phi_{g} .\n\\label{eqmotion}\n\\ee\nHere ${\\bf v}$ stands for the {\\em peculiar} velocity of the particle, i.e., ${\\bf v}=a(t)\\frac{d{\\bf x}}{dt}$, where ${\\bf x}$ are the comoving positions; $\\nabla=\\left( \\partial /\\partial x,\\partial/\\partial y,\\partial /\\partial z \\right)$ and $\\Phi_{g}$ is the gravitational potential which is related to the local density fluctuation via the Poisson equation\n\\be\n\\nabla^{2}\\Phi_{g}=\\frac{3}{2}H^{2}\\Omega a^{2} \\delta .\n\\label{poisson}\n\\ee\n\nUsing the normalized variables $\\theta$ and $\\varphi_{g}$ defined thus:\n\\begin{eqnarray}\n\\theta({\\bf x},t)&\\equiv &\\frac{{\\bf v}({\\bf x},t)}{a\\dot{D}}={\\bf \\psi}({\\bf q}) \\label{renormtheta}\n\\\\\n\\phi_{g}({\\bf x},t)&\\equiv & \\frac{\\Phi_{g}({\\bf x},t)}{a^{2}\\dot{D}} \\label{renormphi} ,\n\\end{eqnarray}\nequations \\ref{eqmotion} and \\ref{poisson} reduce to\n\\be\n\\dot{\\theta} + \\frac{3H\\Omega}{2f(\\Omega)}\\theta=-\\nabla\\varphi_{g} ,\n\\label{motiontheta}\n\\ee\nwhere $f(\\Omega)\\equiv \\dot{D}/HD \\sim \\Omega^{0.6}$ \\cite{Pe80}.\n\nNotice that the Zel'dovich approximation is contained in \\ref{renormtheta}, which is to say \n\\be\n\\dot{\\theta}=0\n\\label{zeld}\n\\ee\n along the trajectory of a given particle, i.e., along a line of constant ${\\bf q}$. Hence, \\ref{motiontheta} is reduced, under the Zel'dovich approximation, to\n\\be\n\\frac{3H\\Omega}{2f(\\Omega)}\\theta=-\\nabla\\varphi_{g} .\n\\ee\n$\\theta$ is therefore the gradient of a potential:\n\\be\n\\theta=-\\nabla\\varphi_{v},\n\\label{gradient}\n\\ee\nwith\n\\be \n\\phi_{v}=\\frac{2f(\\Omega)}{3H\\Omega}\\varphi_{g} + F(t) .\n\\ee\nWe can obviously set $F(t)\\equiv 0$ since $\\theta$ is the only physical (measurable) quantity.\n\nEquation \\ref{zeld} can now be expanded in Eulerian coordinates:\n\\begin{eqnarray}\n\\frac{d\\theta}{dt}=0&\\Leftrightarrow & \\left[ \\frac{\\partial}{\\partial t} + \\frac{d{\\bf x}}{dt}\\cdot \\nabla \\right] \\theta({\\bf x},t) = 0 \\nonumber \\\\\n& \\Leftrightarrow & \\frac{\\partial \\theta}{\\partial t} + \\dot{D}(t) {\\bf \\psi}({\\bf q}) \\cdot \\nabla \\theta=0 \\nonumber \\\\\n& \\Leftrightarrow & \\frac{\\partial \\theta}{\\partial t} + \\dot{D} \\left( \\theta\\cdot \\nabla \\right) \\theta =0 .\n\\end{eqnarray}\nMaking use of the identity $\\left( \\theta\\cdot \\nabla \\right) \\theta = 1/2 \\left( \\nabla \\theta \\right) ^{2} - \\theta \\wedge \\left( \\nabla \\wedge \\theta \\right) $, taking into account the irrotationality of $\\theta$, and substituting \\ref{gradient} we arrive at\n\\begin{eqnarray}\n-\\nabla \\frac{\\partial \\varphi_{v}}{\\partial t} + \\dot{D}\\frac{1}{2} \\left(\\nabla \\theta\\right)^{2} = 0 & \\Leftrightarrow & -\\nabla \\left[ \\frac{\\partial \\varphi_{v}}{\\partial t} + \\frac{\\dot{D}}{2} \\left(\\nabla \\varphi\\right)^{2} \\right] = 0 \\nonumber \\\\\n& \\Leftrightarrow & \\frac{\\partial \\varphi_{v}}{\\partial t} + \\frac{\\dot{D}}{2} \\left( \\nabla \\varphi_{v}\\right) ^{2} = F(t) .\n\\end{eqnarray}\nAgain, because only gradients of $\\varphi_{v}$ have a physical meaning, we can take $F(t)$ to be zero. We finally arrive at the equation:\n\\be\n\\frac{\\partial \\varphi_{v}}{\\partial D} + \\frac{1}{2} \\left( \\nabla \\varphi_{v}\\right) ^{2} =0 .\n\\label{motion}\n\\ee \n\nThis is the differential equation which expresses the Zel'dovich approximation in Eulerian coordinates. Knowing $\\varphi_{v}$ at any time enables us to compute $\\varphi_{v}$ at any other time simply by integrating \\ref{motion} forwards or backwards.\n\nThe first step is to calculate $\\varphi_{v}$ at the present time. That can be easily achieved using Poisson's equation, which in Fourier space reads:\n\\be\n-k^{2} \\tilde{\\Phi}_{g}=\\frac{3}{2}H^{2}\\Omega a^{2} \\tilde{\\delta} ,\n\\ee\nwhere the tildes denote the Fourier transforms. Using \\ref{renormphi} we arrive at:\n\\be\n-Dk^{2}\\tilde{\\varphi}_{v}=\\tilde{\\delta} .\n\\label{potenti}\n\\ee\nSo, in order to obtain the velocity potential of a given smooth density field with periodic boundary conditions, we first transform it to Fourier space using some FFT code, we then divide the obtained field by $-k^{2}$ (normalizing D to unity at present), and then transform back to real space to obtain $\\varphi_{v}$. $\\varphi_{v}$ is then integrated back in time in the most trivial way: At every step, we calculate $1/2 \\left( \\nabla \\varphi_{v} \\right) ^{2}$ from the potential field; this is then used as a first order Taylor correction to predict the value of $\\varphi_{v}$ at the next step. Once a suitable number of integration steps has been performed, we use equation \\ref{potenti} again to obtain the value of $\\delta$ at the corresponding value of $D$.\n\nFor our application - topology, we expect the exact number of integrations\nto be irrelevant. After a certain number of iterations we expect to reach the linear\nregime in all scales, which means that the genus curves of the density fields will no longer change. This particular characteristic of the genus can in fact be useful to test the convergence of the method. We obtained several reconstructed density fields for different values of the number of integration steps, and found the topologies to converge. This result is shown is Fig. \\ref{convergence}.\n\n\\section{CONSTRUCTION OF THE DENSITY MAPS}\n\\label{recdenmaps}\n\nThe construction of the density maps we follow is, to a large extent, equivalent to the method followed by Canavezes et al. \\shortcite{Ca98}. We employ the same fit for the PSCz selection function $s(z)$:\n\\be\ns(z)=\\frac{\\psi}{z^{\\alpha}\\left( 1+\\left( \\frac{z}{z^{\\star}}\\right) ^{\\gamma} \\right)^{\\beta/\\gamma}} ,\n\\ee\nwith the parameters shown in Table \\ref{tab1} \\cite{Sp98a}, and estimate the density $\\rho(r)$ by\n\\be\n\\rho(r)\\propto\\frac{m(r)}{s(r)} ,\n\\ee\n\n\\begin{table}\n\\bc\n\\caption{Parameters of the selection function of PSCz.\\label{tab1}}\n\\vspace{0.5cm}\n\n\\begin{tabular}{ccc}\n$\\alpha$ & $\\beta$ & $\\gamma$ \\\\\n$0.991^{+0.068}_{-0.073}$ \n& $3.445^{+0.173}_{-0.158}$ \n& $1.925^{+0.162}_{-0.153}$ \\\\\n\\\\\n$z^{\\star}$ & $\\psi \\;\\;[h^3{\\rm Mpc}^{-3}]$ & \\\\\n$0.02534^{+0.00130}_{-0.00116}$ \n&$(141.3\\pm 2.4 ) \\times 10^{-6}$ & \\\\\n\\end{tabular}\n\\ec\n\\end{table}\n\n\\begin{table}\n\\bc\n\\caption{The smoothing lengths adopted for the topological analysis of the PSCz\nsurvey. Listed are the adopted survey depth $R_{\\rm max}$, the\nresulting number\n$N_{\\rm res}$ of resolution elements and the number $N_{\\rm gal}$ \nof galaxies inside the survey volume.\n\\label{tab2}\n}\n\\vspace{0.5cm}\n\\begin{tabular}{c|c|r|r|r}\n$\\lambda\\;\\;[\\lu]$ & $R_{\\rm max}\\;\\;[\\lu]$ &\n$N_{\\rm res}$ & $N_{\\rm gal}$ \\\\\n 5& 34.92& 215.5& 2295\\\\\n 6& 47.16& 307.3& 3550\\\\\n 7& 58.35& 366.3& 4928\\\\\n 8& 68.58& 398.5& 5909\\\\\n10& 86.91& 415.3& 7510\\\\\n12& 103.19& 402.3& 8775\\\\\n14& 118.04& 379.2& 9681\\\\\n16& 131.81& 353.7& 10356\\\\\n20& 156.96& 305.8& 11309\\\\\n24& 179.79& 266.0& 11968\\\\\n28& 200.97& 233.9& 12496\\\\\n32& 221.79& 210.6& 12833\\\\\n40& 263.44& 180.7& 13339\\\\\n48& 305.09& 162.4& 13684\\\\\n50& 315.50& 158.9& 13748\\\\\n56& 346.73& 150.2& 13924\\\\\n\\end{tabular}\n\\ec\n\\end{table}\n\n\nwhere $m(r)$ is the discrete point distribution. However, the angular mask needs to be treated with care. Because the structure we can see behind the mask will have a significant effect on the evolution of structure on the whole observable area, we need to resort to some sort of filling, prior to using the time-machine. \n\nWe consider two different types of filling: One, a random filling, in which fake objects are placed randomly over the masked region with an average number density equal to the average number density of the whole survey (weighted by the selection function); And another, a {\\em cloning}, in which fake objects are placed randomly in each bin, but with an average number density equal to the average number density of the neighbouring observable bins, again weighted by the selection function. \n\nOn both cases, we create a box containing a sphere of radius $R_{max}$ as defined in Table \\ref{tab2}. $R_{max}$ is the maximum distance up to which the average distance between two neighbouring galaxies in PSCz is smaller than the adopted smoothing length. The size of the box will then be $\\frac{2}{\\sqrt{3}}Rmax$. Although boundary conditions are not periodic, we smooth the density field in Fourier space assuming periodic boundary conditions. We consider this to be preferable to zero padding, as this would create an artificial boundary that would eventually affect the gravitational time-machine.\n\nWe then apply the Zel'dovich time-machine on the box thus obtained for both filling techniques. In the subsequent topological analysis, we limit ourselves to the sphere inside the box with radius $R_{max}$. \n\n\\subsection*{Smoothing Procedure}\n\nIdeally, one would want to apply the operator {\\em time-reverse} directly upon the unsmoothed density field obtained from PSCz, and only then smooth it on a range of scales to be able to calculate its genus curve. However, in order to obtain meaningful results, we need a smooth field {\\em a priori}. This poses a very important problem: These operators ({\\em time-reverse} and {\\em smoothing}) do not in general commute. In other words, the topology of the final density field can be significantly different whether the smoothing operation is performed before or after applying the {\\em time-machine} to our original field.\n\nTo illustrate this point, let us consider a Gaussian random density field smoothed on some scale $\\lambda$. After applying the {\\em time-machine} this density field will still be Gaussian. However, if we are to naively calculate its genus curve choosing for isodensity contours the same isodensity contours defined {\\em prior} to applying te {\\em time-machine}, we would wrongly conclude that the field is not Gaussian. In order to circumvent this problem we would be forced to smooth the final field once again on a larger scale, thus reducing considerably the statistical significance of our results.\n\nThere is, however, an alternative way to solve this dilemma: One can try to find a smoothing operator that comutes with our reconstruction operator.\n\nHow can we look for such a smoothing operator? One way of ensuring this is to find an operator that does not change the density field if applied once again at a latter stage. By other words, if we ensure that our final density field remains the same regardless of how many times we perform the smoothing operation throughout the time-reversing process, then it is because these two operators do indeed comute. A class of such operators are the adaptive smoothing operators. By adaptive smoothing, we understand a {\\em local} smoothing of variable smoothing length according to the local structure. There are several types of adaptive smoothing. The ideal adaptive smoothing operator ensures that the total mass enclosed by isodensity contours remains constant throughout the time-reversing process. A simplified version assumes spherical symmetry. At each point we employ a smoothing length $\\lambda$ such that $\\lambda^{3}\\propto 1/\\rho=1/\\left( \\rho_{0}+\\delta \\right)$. The proportionality constant defines the characteristic smoothing length, which is the smoothing length employed when the overdensity $\\delta$ vanishes. For highly dense regions, a smaller value of $\\lambda$ will be chosen, whereas voids will be smoothed with a larger value of $\\lambda$.\n\nWhen we apply the time-machine operator on a map smoothed in this way, the isodensity contours around a cluster will move, but the total mass enclosed by them will remain approximately constant, as long as the spherical symmetry hypothesis is a good approximation. \n\nIn our application to the PSCz we use a spherically symmetric adaptive smoothing algorithm. We start by creating a set of maps obtained from the original map (this might be either the PSCz data or simulation data) by smoothing it on a range of scales around a given characteristic scale $l_{0}$, using Gaussian filters of the form\n\\be\nG_{\\lambda}(x)=\\frac{1}{\\pi^{3/2}\\lambda^{3}} e^{-x^{2}/\\lambda^{2}}\n\\ee\nwhere $\\lambda$ varies around $l_{0}$. We then look for the appropriate value of $\\lambda$ at each position $x$ by enforcing the equation\n\\be\n(1+\\delta_{\\lambda})\\lambda^{3}=l_{0}^{3} ,\n\\ee \nwhere $\\delta_{\\lambda}$ is the density contrast when the original map is smoothed on a scale $\\lambda$. This ensures that the mass enclosed on a sphere of radius $\\lambda$ is, to first order in a Taylor expansion, constant throughout the whole map.\n\n\n\\subsection*{Error Estimates}\n\nThere are three different sources of error that enter our results: Shot noise, cosmic variance and the errors associated with the Zel'dovich approximation itself.\n\nThe most accurate and realistic way of estimating these errors, which ultimately enter the genus curves of the reconstructed PSCz density fields, is to analyse the topology of fake PSCz catalogues drawn from N-body simulations of some {\\em standard} CDM model. Since we intend to test the validity of the Zel'dovich time-machine with N-body simulations, it seems reasonable to extent this philosophy to the calculation of the statistical errors themselves. This is achieved by seeking a galaxy number density field with a Poisson distribution, whose expectation value is identical to the density field of the N-body simulation multiplied by the PSCz selection function. This is equivalent to {\\em observing} the density field of the N-body simulation in a similar way to the way PSCz observes the density field of the real Universe. This galaxy number density field is then divided by the PSCz selection function again to obtain a \"PSCZ-noisy\" distance-independent estimate of the real galaxy number density. Each of the {\\em mock} PSCz catalogues is adaptively smoothed using the algorithm described above and then used as input in the Zel'dovich time-machine. The genus curves of the reconstructed fields are calculated and the variance obtained over 10 mock PSCz catalogues is used as the statistical error estimate. \n\n\n\\section{TESTING THE METHOD WITH N-BODY SIMULATIONS OF CDM MODELS.}\n\\label{recnbody}\n\nAs we mentioned previously, we intend to test the regime of validity of the Zel'dovich time-machine by means of an N-body simulation of a CDM model. We apply the time-machine on the present density field drawn from the simulation and compare the density field thus obtained with the density field drawn from the original test-mass positions used as input in the simulation. More specifically, we need only to compare the topologies of the reconstructed and original fields through their genus curves.\n\nFor this purpose, we use two N-body simulations corresponding to two cold dark matter models, kindly provided by the Virgo consortium \\cite{Col97,Je97}.The simulations have been performed with an AP$^{3}$M-SPH code \nnamed {\\small HYDRA} \\cite{Cou95}. Here we consider the SCDM model and the $\\tau$CDM model, which parameters are shown in Table \\ref{modelparameters}. Because this simulations contain CDM on periodic boxes of size $239.5\\lu$ and use such a large number of particles, they constitute an ideal ground for this test.\n\n\\begin{table}\n\\bc\n\\caption{Parameters of the examined CDM models. The simulations have\nbeen done by the \nVirgo collaboration.\\label{modelparameters}\n}\n\\begin{tabular}{l|c|c|c|c|}\n\\multicolumn{1}{l|}{ }& $\\tau$CDM & $\\Lambda$CDM\n\\vspace{0.1cm}\\\\ \n\\multicolumn{1}{l|}{Number of particles } & $256^{3}$ & $256\n^{3}$ \\\\\n\\multicolumn{1}{l|}{Box size$[\\lu]$ } & $239.5$ & $239.5$\\\\\n$z_{start}$& $50$ & $30$ & \\\\\n$\\Omega_{0}$ & $1.0$ & $0.3$ \\\\\n$\\Omega_{\\Lambda}$& $0.0$ & $0.7$\\\\\n \\multicolumn{1}{l|}{Hubble constant $h$} & $0.5$ & $0.7$\\\\\n$\\Gamma$ & 0.21 & 0.21 \\\\\n$\\sigma_{8}$ & $0.60$ & $0.90$ \\\\\n \\multicolumn{1}{l|}{Mass per particle [$10^{10}h^{-1}M_{\\odot}$]} & $22.7$ &$5.8$ & \\\\\n\n\\end{tabular}\n\\ec\n\\end{table}\n\nWe start by binning the particles in cells of side length $2\\lu$ and smooth further on some characteristic smoothing length $\\lambda$, using the adaptive smoothing algorithm described in section \\ref{recdenmaps}, in an analogous procedure to the way we treat the PSCz galaxies. This \"double\" smoothing is required in the real Universe in order to minimize shot noise effects, but it is also necessary in order to eliminate severe non-linearities since the Zel'dovich time-machine is expected not to work over such regimes. It is also needed to smooth out regions of orbit-crossing.\n\nThe next step is to calculate the genus curves of both the original density field that is used as input in the simulation, smoothed in the same manner as described above, and the reconstructed density field obtained after applying the Zel'dovich time-machine to the present density field smoothed in the same way. In order to compare both genus curves we compute their amplitudes and their amplitude drops. It is very important to note that if we are to obtain gaussianized versions of the density fields at the present time, they will not have, in principle, the same genus amplitudes as the density fields themselves, even when these are in the Gaussian regime. This is so because of the very nature of adaptive smoothing. When a given density field is smoothed adaptively its genus curve will have a different shape and amplitude than the shape and amplitude of the genus curve of the same field when this is smoothed with a constant Gaussian window. We need to be extremely careful not to draw the wrong conclusions about the Gaussian or non-Gaussian nature of our density fields. After applying the time-machine, however, the amplitude of fluctuations will be reduced significantly. In fact they will be reduced to such an extent as to make the field look almost homogeneous. This means that the isodensity contours on adaptively smoothed maps will be very close to the isodensity contours on maps smoothed using a constant Gaussian window. Hence, it is possible to calculate amplitude drops and determine the Gaussian (or non-Gaussian) nature of our density maps {\\em after} applying the Zel'dovich time-machine, i.e., to determine the Gaussian (or non-Gaussian) nature of the {\\em reconstructed} fields.\n\nIn order to test the convergence of the reconstruction method, we obtained several reconstructed density fields for diffent values of the total number of integration steps, as mentioned in \\ref{recmethod}. Fig. \\ref{convergence} shows a particular slice of the reconstructed density fields at different integration steps when the method is applied to the maps at $z=0$ obtained from the $\\tau$CDM simulation by smoothing on characteristic lengths of $8\\lu$ and $10\\lu$. As it is evident from this Figure, the topology of the density fields is undistinguishable for values of $z$ greater than $4$ on smoothing scales of both $8\\lu$ and $10\\lu$. Only the amplitude of the density fluctuations changes, indicating that we are now in the linear regime. In Fig. \\ref{convscater} this is made even clearer. Here we show a point-by-point comparison of the reconstructed $\\tau$CDM density fields at redshifts $z=4$ and $z=9$, for the characteristic smoothing lengths of $8\\lu$ and $10\\lu$. We only show one in eight of all points, chosen randomly. It is obvious from this plot that the shape of fluctuations did not change from $z=4$ to $z=9$, for either of the smoothing lengths adopted. It is also obvious that the amplitude of fluctuations was reduced by a factor of $2$, as it is expected in the linear regime (notice that in the linear regime the growing mode of fluctuations varies as $1/(1+z)$). Hence, our time-machine shows the correct assimptotic behaviour.\n\n\\begin{figure*}\n\\bc\n\\resizebox{6cm}{!}{\\includegraphics{plots/d8tcdmcrop_test50.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d10tcdmcrop_test50.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d8tcdmcrop_test80.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d10tcdmcrop_test80.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d8tcdmcrop_test90.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d10tcdmcrop_test90.eps}}\n\\caption{A particular slice of the reconstructed fields for the $\\tau$CDM simulation for different values of $z$. The left panels show the fields smoothed adaptively with a characteristic smoothing length of $8\\lu$, whereas the panels on the right show the fields smoothed with a characteristic smoothing length of $10\\lu$ \\label{convergence}}\n\\ec\n\\end{figure*}\n\n\\begin{figure*}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/d8tcdm_scater.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/d10tcdm_scater.eps}}\n\n\\caption{ Point-by-point comparison of the reconstructed $\\tau$CDM density field at redshift $z=4$ and the reconstructed $\\tau$CDM density field at redshift $z=9$, when the adopted characteristic smoothing lengths are of $8\\lu$ and $10\\lu$. \\label{convscater}}\n\\ec\n\\end{figure*}\n\n\\begin{figure*}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/cont8tcdm_now.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/cont8tcdm_back80.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/cont8tcdm_orig.eps}}\n\n\\caption{Isodensity contours of the $\\tau$CDM simulation. The characteristic smoothing length adopted was $8\\lu$. The separation between contour levels is $0.2/(1+z)$. The zero contour is heavy; positive contours are solid; negative contours are dashed. \\label{nbodycontours}}\n\\ec\n\\end{figure*}\n\n\\subsection*{Results} \n\nFigure \\ref{nbodycontours} shows the isodensity contours obtained for the SCDM simulation and the $\\tau$CDM simulation, when the fields are adaptively smoothed on a characteristic scale of $5\\lu$ in a comoving box of size $240\\lu$. The first row shows the fields at the present time. The second row shows the fields after applying the Zel'dovich time-machine back to a redshift of 10 and the third row shows the original fields used as input in the simulations. In each panel the thick line represents the contour where the density contrast is zero. Dashed lines represent contours of negative density contrast whereas solid lines represent positive density contrasts. The contour spacing is $0.2/(1+z)$. Because this is normalized to the linear reconstruction case where $\\delta\\propto 1/(1+z)$, the linear theory reconstruction density maps look exactly like the present day maps (first row), albeit their much lower fluctuation amplitude. From the contours on both the reconstructed maps and the original maps we notice that their fluctuation amplitudes are larger than the fluctuation amplitude of a linearly reconstructed map. This result is expected because fluctuations will grow faster at the later stages of evolution, in the mildly non-linear regime. It is obvious from Fig. \\ref{nbodycontours} that the Zel'dovich time-machine is able to change the rank order of isodensity contours. This means that the genus curves will also be changed. In fact we can predict, just by looking at Fig. \\ref{nbodycontours} that the amplitude of the genus curves will increase after applying the Zel'dovich time-machine, as it is expected.\n\n\\begin{figure*}\n\\bc\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm_exp5.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm00_exp5.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm00_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm_exp14.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm00_exp14.eps}}\n\n\\caption{Genus curves for the SCDM model, at selected smoothing lengths. The left column shows the genus curves of the reconstructed field (thick solid lines) and of the randomized version of that field (thin solid lines), whereas the right column shows the genus curves of the original density field used as input for the N-body simulations. The dashed and dotted lines are the best fit random-phase curves to each of the fields. \\label{SCDMgenus}}\n\\ec \n\\end{figure*}\n\n\n\\begin{figure*}\n\\bc\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm_exp5.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm00_exp5.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm00_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm_exp14.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm00_exp14.eps}}\n\n\\caption{Genus curves for the $\\tau$CDM model, at selected smoothing lengths. The left column shows the genus curves of the reconstructed field (thick solid lines) and of the randomized version of that field (thin solid lines), whereas the right column shows the genus curves of the original density field used as input for the N-body simulations. The dashed and dotted lines are the best fit random-phase curves to each of the fields.\\label{TCDMgenus}}\n\\ec\n\\end{figure*}\n\\begin{figure}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/recdropmodels.eps}}\n\\caption{Amplitude drops measured for the reconstructed SCDM simulation and $\\tau$CDM simulation. Also show for comparison are the amplitude drops measured for the simulations at $z=0$\\label{recdropbody}.}\n\\ec\n\\end{figure}\n\\begin{figure}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/recampmodels.eps}}\n\\caption{Genus amplitudes measured for the reconstructed SCDM simulation and $\\tau$CDM simulation. Also shown are the genus amplitudes of the original fields\\label{recampbody}.}\n\\ec\n\\end{figure}\n\n\n\nFigures \\ref{SCDMgenus} and \\ref{TCDMgenus} show the genus curves obtained for the SCDM model and the $\\tau$CDM model respectively, at selected characteristic smoothing lengths, namely at $5\\lu$, $8\\lu$ and $14\\lu$. We restrict our analysis to this range of smoothing lengths, as we know {\\em a priori} that the Zel'dovich time-machine is only relevant in the mildly non-linear regime. In both figures, the first column shows the genus curves of the reconstructed field and its randomized counterpart, whereas the second column shows the genus curves of the original fields, used as input for the simulations. We deliberately do not show the genus curves of the present day {\\em adaptively smoothed} density fields, since, as we argued in the previous chapter, the isodensity contours are, at this stage, different from the isodensity contours of the fields smoothed using a constant kernel.\n\nIt is striking in Fig. \\ref{SCDMgenus} and Fig. \\ref{TCDMgenus} the consistency between the genus curves of the reconstructed field and of its randomized counterpart. This is particularly true for the genus amplitudes, which indicates that there is very little phase correlation in the reconstructed fields on all scales, as it is expected from Gaussian initial conditions. With regard to the genus amplitudes {\\em per se}, we find consistency with the genus amplitudes of the original density fields, although we notice a tendency for these to be slightly higher in the reconstructed fields. These means that the second moment of the power spectrum is recovered slightly {\\em in excess}. This becomes more important as we approach the smaller scales, which is to say as the system becomes more non-linear.\n\nIt is also interesting to notice a depression at high values of $\\nu$ on the genus curves of the reconstructed fields. We find this depression to be present in all cases, both for the Virgo simulations and the PSCz data. We expect this to be a particular feature of the reconstruction technique, i.e., ultimately dependent on the Zel'dovich approximation itself. At high values of $\\nu$ the regime is considerably non-linear and so we expect the Zel'dovich approximation to perform rather poorly. This problem is enhanced by the fact that the density fields have been smoothed adaptively. Nevertheless, we do not expect this feature to affect our results considerably as the calculation of the amplitude of the genus curves is restricted to the range $-1<\\nu<1$.\n\nNote that there is no sampling noise in these density fields. The tremble in the genus curves is ultimately due to cosmic variance.\n\nIn Fig. \\ref{recdropbody} we plot the amplitude drops obtained for the reconstructed SCDM model and for the reconstructed $\\tau$CDM model as a function of smoothing length. Also shown are the amplitude drops obtained for the models at $z=0$ \\cite{Ca98}. In all scales, the values obtained for the reconstructed fields are closer to unity than those of the present-day fields. This indicates that the Zel'dovich time-machine is a good tool in recovering Gaussian initial density fields. However, at small scales, we detect a slight departure from the expected value of unity, even for the reconstructed fields. This is not surprising since at this scales non-linearities become strong. The degree of strength of the non-linearities depends on the particular model. As we see from Fig. \\ref{recdropbody} they are more important in the $\\tau$CDM model than in the SCDM model, in agreement to what was found by Canavezes et al. \\shortcite{Ca98}.\n\nFig. \\ref{recampbody} shows the genus amplitudes of the reconstructed fields for both the SCDM model and the $\\tau$CDM model, together with the genus amplitudes of the original fields. In the case of the $\\tau$CDM model the agreement between the original genus amplitude and the genus amplitude of the reconstructed field, is striking, in particular when we consider scales above $\\sim 7\\lu$. For the SCDM model the agreement is not as good. The reconstructed genus amplitudes appear to be slightly higher than the true original ones.\n\nThese results indicate that the Zel'dovich time-machine is effective in recovering the right genus amplitude {\\em drops} on scales larger than $\\sim 8\\lu$, although recovered amplitudes cannot be considered reliable in the strict sense of the word. \n\n\n\n\\section{RECOVERING THE INITIAL DENSITY FIELD FROM PSCZ}\n\\label{recpscz}\n\nAs mentioned previously, one of the difficulties in using the PSCz in an attempt to recover the initial density fluctuations in the Universe, is the fact that the masked region can make up to $\\sim 20\\%$ of the whole observable area. Since this region will have a definite gravitational influence on the observable area when we attempt to reconstruct to original density field, some sort of filling is essential. As mentioned in \\ref{recdenmaps} we employ two different techniques: The random filling and the cloning. Fig. \\ref{randcloned} shows how the two different fillings appear to the eye. On the upper panel we show the map where the mask has been filled randomly and on the lower panel we show the map where the mask has been cloned. Although it is impossible to the eye to recognize any significant difference, we will be able to detect some noticeable differences on the topologies of the reconstructed density fields.\n\n\\begin{figure*}\n\\bc\n\\resizebox{6cm}{!}{\\includegraphics{plots/gcloned_exp6.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/grand_exp6.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gcloned_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/grand_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gcloned_exp12.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/grand_exp12.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gcloned_exp16.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/grand_exp16.eps}}\n\\caption{Genus curves of the reconstructed PSCz fields. \\label{PSCzgenus}}\n\\ec\n\\end{figure*}\n\\begin{figure*}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/randomcrop.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/clonedcrop.eps}}\n\\caption{Aitoff projections of PSCz galaxies and filled masks.In the upper panel the mask is filled randomly whereas in the lower panel the mask is filled using a cloning technique.\\label{randcloned}}\n\\ec\n\\end{figure*}\n\\begin{figure*}\n\\bc\n\\resizebox{10cm}{!}{\\includegraphics{plots/droppscznow.eps}}\n\\caption{The amplitude drop $R$ measured for PSCz. Also shown are the results\nobtained by Vogeley et al.$1994$ for the CfA survey. Here the \nerrors are taken to be the uncertainty Vogeley et al.$1994$ report \nfor mock catalogues extracted from a LCDM model\\label{drpscznow}}\n\\ec\n\\end{figure*}\n\\begin{figure*}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/dropcloned.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/droprandom.eps}}\n\\caption{The amplitude drops measured for the reconstructed PSCz density fields. In the upper panel the mask has been cloned, whereas in the lower panel the mask has been filled randomly. Also shown are the amplitude drops obtained for the reconstructed N-body simulations. \\label{psczdrops}}\n\\ec\n\\end{figure*}\n\n\\subsection*{Results \\& Discussion} \n\nFig. \\ref{PSCzgenus} shows the genus curves obtained for the reconstructed PSCz fields. On the first column we plot the genus curves of the fields for which the mask has been filled using a cloning technique, and on the second column we plot the genus curves of the fields where the mask has been filled randomly. The thick solid lines refer to the reconstructed PSCz fields {\\em proper}, whereas the thin solid lines refer to the randomized versions of those fields,i.e., the fields obtained from the reconstructed density fields by randomizing phases in Fourier space subject to the reality constraint $\\delta_{{\\bf k}}=\\delta_{-{\\bf k}}^{\\ast}$ and keeping the same power spectrum. The dotted and dashed lines are the best fitting random-phase curves to both the reconstructed PSCz density fields and their randomized versions.\n\nIt is striking to notice the proximity between genus curves, even at small smoothing lengths. The statistical errors drawn from the N-body simulation are not shown in Fig. \\ref{PSCzgenus} because of the high degree of correlation between the points in the genus curves.\n\nIndependently of whether the mask has been randomly filled or cloned, the recovered genus curves seem consistent with random-phase Gaussian fluctuations because the amplitude drops appear small. However, the amplitude themselves seem to depend on the mask filling technique.\n\n\nIn Fig. \\ref{psczdrops} we plot the amplitude drops obtained for the reconstructed PSCz density fields, as a function of smoothing length, as well as the error bars drawn from the $\\tau$CDM model following the method outlined in chapter \\ref{recdenmaps}. The amplitude drops of the reconstructed N-body simulations are also shown for comparison.\n\nIn contrast with Fig. \\ref{drpscznow}, where phase correlations were found for PSCz at small smoothing lengths, the reconstructed PSCz fields do not show any significant phase correlations on scales ranging from $5\\lu$ to $14\\lu$. This reinforces the hypothesis that density fluctuation originate from random-phase Gaussian initial conditions. \n \n\n\n\n\n"},{"name":"zeld.tex","string":" \n\n\\documentstyle[epsfig]{mn}\n%\n% Preamble\n%\n\n\n\\newcommand{\\iras} {{\\it IRAS \\/}}\n\\newcommand{\\et} {{\\em et al.}}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bea}{\\begin{eqnarray}}\n\\newcommand{\\eea}{\\end{eqnarray}}\n\\newcommand{\\bc}{\\begin{center}}\n\\newcommand{\\ec}{\\end{center}}\n\\newcommand{\\ol}[1]{ {\\overline{#1}}}\n\\newcommand{\\lu}{\\,h^{-1}{\\rm Mpc}}\n\\renewcommand{\\vec}[1]{ {\\bmath #1} } \n\\newcommand{\\dd}{{\\rm d}}\n\\newcommand{\\ls}{\\raisebox{-.8ex}{$\\buildrel{\\textstyle<}\\over\\sim$}}\n\\newcommand{\\props}{\\raisebox{-.8ex}{$\\buildrel{\\textstyle\\propto}\\over\\sim$}}\n\\newcommand{\\gs}{\\raisebox{-.8ex}{$\\buildrel{\\textstyle>}\\over\\sim$}}\n\n\n\\title{Recovering the Topology of the Initial Density Fluctuations Using the {\\em IRAS} Point Source Catalogue Redshift Survey}\n\n\n\\author[A. Canavezes J. Sharpe]{A. Canavezes,$^1$ J. Sharpe,$^2$ \\\\\n$^1$ Centro de Astrof\\'{i}sica da Universidade do Porto, Rua das Estrelas s/n, 4150 Porto, Portugal\\\\\n$^2$ Imperial College of Science Technology and Medicine, Blackett Laboratory, Prince Consort Road, London SW7 2BZ, UK}\n\n\\begin{document}\n\\maketitle\n\n\\begin{abstract}\n\nWe apply the reconstruction technique of Nusser \\& Dekel (1992) to the recently available Point Source Catalogue Redshift Survey (PSCz) in order to subtract the phase correlations that are expected to develop in the mild non-linear regime of gravitational evolution. We study the evolution of isodensity contours defined using an adaptive smoothing algorithm in order to minimize the problems derived from the non-comutivity of operators. We study the genus curves of these isodensity contours and concentrate on the evolution of the amplitude drops, a meta-statistic able to quatify the level of phase-correlation present in the field. In order to test the method and to quatify the level of statistical uncertainty, we apply the method to a set of mock PSCz catalogues derived from the N-body simulations of two 'standard' CDM models, kindly granted to us by the Virgo consortium. We find the method to be reliable in recovering the right amplitude drops. When applied to PSCz the level of phase correlations observed is very low on all scales ranging from $5\\lu$ to $60\\lu$, providing support to the theory that structure originated from gaussian initial conditions.\n\n\\end{abstract}\n \n\\begin{keywords}\ngalaxies:clusters:general -- cosmology:observations -- cosmology:large-scale-structure of the Universe\n\\end{keywords}\n\n\\section*{INTRODUCTION}\n\n \\input{reconstruction.tex}\n\n\\section*{AKNOWLEDGEMENTS}\n\nWe are grateful to the Virgo consortium (J. Colberg, H. Couchman, G. Efstathiou, C. S. Frenk, A. Jenkins, A. Nelson, J. Peacock, F. Pearce, P. Thomas and S. D. M. White) for provinding simulation data ahead of publication. AC aknowledges the support of FCT (Portugal).\n\n\\bibliography{zeld}\n\n\n \n\\end{document}\n\n\n"}],"string":"[\n {\n \"name\": \"reconstruction.tex\",\n \"string\": \"\\\\label{rec}\\n\\nThe {\\\\em IRAS} Point Source Catalogue Redshift Survey \\\\cite{Sa99} lends itself to topological studies because of its high sampling densities and large volume. It countains approximately $15000$ galaxies to the full depth of the PSC ($0.6 Jy$). Its sky coverage is $84.1$ per cent, where only the zone of avoidance is excluded, here defined as an infrared background exceeding $25 \\\\rm{MJy sr}^{-1}$ at $100\\\\mu\\\\rm{m}$, and a few unobserved or contaminated patches at higher latitude. The excluded regions are coded in an angular mask, as shown in Fig. \\\\ref{figMask}. Canavezes et al. \\\\shortcite{Ca98} analysed the topology of PSCz and showed that it is consistent with the topology of CDM models: The genus curves retain the w-shape characteristic of random-phase density fields even at small smoothing lengths, where non-linear evolution has already generated significant skewness of the 1-point PDF. These non-linearities are, however, detected by a depressed amplitude of the genus curves - amplitude drops - consistent with those detected for the CDM models. Above $10 \\\\lu$ strong phase correlations were not detected in PSCz and those that were detected at smaller scales are expected in the framework of mildly non-linear gravitational evolution. This supports the hypothesis that structure grew from random-phase initial conditions.\\n\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{14cm}{!}{\\\\includegraphics{plots/aitoffcrop.eps}}\\n\\\\caption\\n{Sky coverage of the PSCz survey in an aitoff projection. The dots represent the galaxies in the survey, the shaded regions are unobserved and comprise the angular mask. The galactic centre lies in the centre of the plot.\\n\\\\label{figMask}}\\n\\\\ec\\n\\\\end{figure*}\\n\\nIn this paper we attempt to subtract these phase correlations by reversing gravity. If it is true that structure does indeed originate in random-phase fluctuations, then reversing gravitational evolution should provide us with an initial density fluctuation field free from phase correlations on any scale.\\n\\nThere are several methods to achieve this goal. Nusser \\\\& Dekel \\\\shortcite{ND92}, showed how to express the Zel'dovich approximation in a set of Eulerian coordinates and reverse it to obtain a reconstructed density field. They tested the method with N-body simulations and found satisfactory results. Recently, some improvements have been made on the original method (e.g. Gramann \\\\shortcite{Gr93}). Nusser, Dekel \\\\& Yahil \\\\shortcite{Nu95} applied the Nusser \\\\& Dekel \\\\shortcite{ND92} approximation to the $1.2$ Jy $IRAS$ redshift survey to recover the 1-point probability distribution function of the initial density field. Their results were consistent with Gaussian initial conditions. The PSCz presents us with an unprecedented number of resolution elements and should constitute therefore the best available data set on which to apply a reconstruction technique. \\n\\nThe method we choose to follow here is the quasi-linear method proposed by Nusser \\\\& Dekel \\\\shortcite{ND92}. In section \\\\ref{recmethod} we describe this method; In section \\\\ref{recdenmaps} we describe the construction of the density maps used as the input of the {\\\\em time-machine} and describe our error estimates; Section \\\\ref{recnbody} is devoted to testing the method using N-body simulations of a CDM model and in section \\\\ref{recpscz} we apply the method to the PSCz and present our results.\\n\\n\\\\section{THE RECONSTRUCTION METHOD}\\n\\\\label{recmethod}\\n\\nThe reconstruction method we follow is based on two premises: The velocity field is, when smoothed on a scale of a few Mpc, irrotational, and the Zel'dovich approximation is accurate over the mildly non-linear regime. \\n\\nOur first step is to try to express the Zel'dovich approximation in a set of Eulerian coordinates.\\n\\nGiven an initial comoving position $\\\\bf{q}$ for a given particle, a final position $\\\\bf{x}(\\\\bf{q},t)$ will have the form\\n\\\\be \\n{\\\\bf x}({\\\\bf q},t)={\\\\bf q}+P({\\\\bf q},t).\\n\\\\ee\\nThe Zel'dovich approximation states that the displacement term $P({\\\\bf q},t)$ can be written as a product of two functions, each a function only of one of the variables ${\\\\bf q}$ or $t$, i.e., we can separate the variables $q$ and $t$:\\n\\\\be\\n{\\\\bf x}({\\\\bf q},t)={\\\\bf q}+D(t)\\\\Psi({\\\\bf q}).\\n\\\\ee\\nThis is simply a linear approximation with respect to the particle displacements rather than density. Particles in the Zel'dovich approximation follow straight lines:\\n\\\\be\\n{\\\\bf v}({\\\\bf q},t)=a(t)\\\\frac{d{\\\\bf x}}{dt}=a(t)\\\\dot{D}(t)\\\\Psi({\\\\bf q}).\\n\\\\ee\\nThe density fluctuation is given by\\n\\\\be\\n\\\\delta({\\\\bf q},t)=\\\\bar{\\\\rho}/J({\\\\bf q},t)-1,\\n\\\\ee\\nwhere $J({\\\\bf q},t)$ is the Jacobian of the coordinate transformation ${\\\\bf q}\\\\rightarrow {\\\\bf x}$.\\n\\nAs long as second order terms in $\\\\delta$ and ${\\\\bf v}$ are negligible, $\\\\delta(t) \\\\propto D(t)$, where $D(t)$ is the growing mode solution in linear perturbation theory (see e.g. Peebles \\\\shortcite{Pe80}).\\n\\nUnlike linear theory, where the density at a given position evolves according to the linear growth rate, under the Zel'dovich approximation infinite density can develop in a finite time as a result of the convergence of particle trajectories into a {\\\\em pancake}. in order to integrate a density field back in time, Nusser \\\\& Dekel \\\\shortcite{ND92} found the differential equation in Eulerian space which contains the Zel'dovich approximation. This is derived from the standard equation of motion of dust particles in an expanding Universe (e.g. Peebles \\\\shortcite{Pe80}):\\n\\\\be\\n\\\\frac{d{\\\\bf v}}{dt} + H{\\\\bf v}=-\\\\frac{1}{a}\\\\nabla\\\\Phi_{g} .\\n\\\\label{eqmotion}\\n\\\\ee\\nHere ${\\\\bf v}$ stands for the {\\\\em peculiar} velocity of the particle, i.e., ${\\\\bf v}=a(t)\\\\frac{d{\\\\bf x}}{dt}$, where ${\\\\bf x}$ are the comoving positions; $\\\\nabla=\\\\left( \\\\partial /\\\\partial x,\\\\partial/\\\\partial y,\\\\partial /\\\\partial z \\\\right)$ and $\\\\Phi_{g}$ is the gravitational potential which is related to the local density fluctuation via the Poisson equation\\n\\\\be\\n\\\\nabla^{2}\\\\Phi_{g}=\\\\frac{3}{2}H^{2}\\\\Omega a^{2} \\\\delta .\\n\\\\label{poisson}\\n\\\\ee\\n\\nUsing the normalized variables $\\\\theta$ and $\\\\varphi_{g}$ defined thus:\\n\\\\begin{eqnarray}\\n\\\\theta({\\\\bf x},t)&\\\\equiv &\\\\frac{{\\\\bf v}({\\\\bf x},t)}{a\\\\dot{D}}={\\\\bf \\\\psi}({\\\\bf q}) \\\\label{renormtheta}\\n\\\\\\\\\\n\\\\phi_{g}({\\\\bf x},t)&\\\\equiv & \\\\frac{\\\\Phi_{g}({\\\\bf x},t)}{a^{2}\\\\dot{D}} \\\\label{renormphi} ,\\n\\\\end{eqnarray}\\nequations \\\\ref{eqmotion} and \\\\ref{poisson} reduce to\\n\\\\be\\n\\\\dot{\\\\theta} + \\\\frac{3H\\\\Omega}{2f(\\\\Omega)}\\\\theta=-\\\\nabla\\\\varphi_{g} ,\\n\\\\label{motiontheta}\\n\\\\ee\\nwhere $f(\\\\Omega)\\\\equiv \\\\dot{D}/HD \\\\sim \\\\Omega^{0.6}$ \\\\cite{Pe80}.\\n\\nNotice that the Zel'dovich approximation is contained in \\\\ref{renormtheta}, which is to say \\n\\\\be\\n\\\\dot{\\\\theta}=0\\n\\\\label{zeld}\\n\\\\ee\\n along the trajectory of a given particle, i.e., along a line of constant ${\\\\bf q}$. Hence, \\\\ref{motiontheta} is reduced, under the Zel'dovich approximation, to\\n\\\\be\\n\\\\frac{3H\\\\Omega}{2f(\\\\Omega)}\\\\theta=-\\\\nabla\\\\varphi_{g} .\\n\\\\ee\\n$\\\\theta$ is therefore the gradient of a potential:\\n\\\\be\\n\\\\theta=-\\\\nabla\\\\varphi_{v},\\n\\\\label{gradient}\\n\\\\ee\\nwith\\n\\\\be \\n\\\\phi_{v}=\\\\frac{2f(\\\\Omega)}{3H\\\\Omega}\\\\varphi_{g} + F(t) .\\n\\\\ee\\nWe can obviously set $F(t)\\\\equiv 0$ since $\\\\theta$ is the only physical (measurable) quantity.\\n\\nEquation \\\\ref{zeld} can now be expanded in Eulerian coordinates:\\n\\\\begin{eqnarray}\\n\\\\frac{d\\\\theta}{dt}=0&\\\\Leftrightarrow & \\\\left[ \\\\frac{\\\\partial}{\\\\partial t} + \\\\frac{d{\\\\bf x}}{dt}\\\\cdot \\\\nabla \\\\right] \\\\theta({\\\\bf x},t) = 0 \\\\nonumber \\\\\\\\\\n& \\\\Leftrightarrow & \\\\frac{\\\\partial \\\\theta}{\\\\partial t} + \\\\dot{D}(t) {\\\\bf \\\\psi}({\\\\bf q}) \\\\cdot \\\\nabla \\\\theta=0 \\\\nonumber \\\\\\\\\\n& \\\\Leftrightarrow & \\\\frac{\\\\partial \\\\theta}{\\\\partial t} + \\\\dot{D} \\\\left( \\\\theta\\\\cdot \\\\nabla \\\\right) \\\\theta =0 .\\n\\\\end{eqnarray}\\nMaking use of the identity $\\\\left( \\\\theta\\\\cdot \\\\nabla \\\\right) \\\\theta = 1/2 \\\\left( \\\\nabla \\\\theta \\\\right) ^{2} - \\\\theta \\\\wedge \\\\left( \\\\nabla \\\\wedge \\\\theta \\\\right) $, taking into account the irrotationality of $\\\\theta$, and substituting \\\\ref{gradient} we arrive at\\n\\\\begin{eqnarray}\\n-\\\\nabla \\\\frac{\\\\partial \\\\varphi_{v}}{\\\\partial t} + \\\\dot{D}\\\\frac{1}{2} \\\\left(\\\\nabla \\\\theta\\\\right)^{2} = 0 & \\\\Leftrightarrow & -\\\\nabla \\\\left[ \\\\frac{\\\\partial \\\\varphi_{v}}{\\\\partial t} + \\\\frac{\\\\dot{D}}{2} \\\\left(\\\\nabla \\\\varphi\\\\right)^{2} \\\\right] = 0 \\\\nonumber \\\\\\\\\\n& \\\\Leftrightarrow & \\\\frac{\\\\partial \\\\varphi_{v}}{\\\\partial t} + \\\\frac{\\\\dot{D}}{2} \\\\left( \\\\nabla \\\\varphi_{v}\\\\right) ^{2} = F(t) .\\n\\\\end{eqnarray}\\nAgain, because only gradients of $\\\\varphi_{v}$ have a physical meaning, we can take $F(t)$ to be zero. We finally arrive at the equation:\\n\\\\be\\n\\\\frac{\\\\partial \\\\varphi_{v}}{\\\\partial D} + \\\\frac{1}{2} \\\\left( \\\\nabla \\\\varphi_{v}\\\\right) ^{2} =0 .\\n\\\\label{motion}\\n\\\\ee \\n\\nThis is the differential equation which expresses the Zel'dovich approximation in Eulerian coordinates. Knowing $\\\\varphi_{v}$ at any time enables us to compute $\\\\varphi_{v}$ at any other time simply by integrating \\\\ref{motion} forwards or backwards.\\n\\nThe first step is to calculate $\\\\varphi_{v}$ at the present time. That can be easily achieved using Poisson's equation, which in Fourier space reads:\\n\\\\be\\n-k^{2} \\\\tilde{\\\\Phi}_{g}=\\\\frac{3}{2}H^{2}\\\\Omega a^{2} \\\\tilde{\\\\delta} ,\\n\\\\ee\\nwhere the tildes denote the Fourier transforms. Using \\\\ref{renormphi} we arrive at:\\n\\\\be\\n-Dk^{2}\\\\tilde{\\\\varphi}_{v}=\\\\tilde{\\\\delta} .\\n\\\\label{potenti}\\n\\\\ee\\nSo, in order to obtain the velocity potential of a given smooth density field with periodic boundary conditions, we first transform it to Fourier space using some FFT code, we then divide the obtained field by $-k^{2}$ (normalizing D to unity at present), and then transform back to real space to obtain $\\\\varphi_{v}$. $\\\\varphi_{v}$ is then integrated back in time in the most trivial way: At every step, we calculate $1/2 \\\\left( \\\\nabla \\\\varphi_{v} \\\\right) ^{2}$ from the potential field; this is then used as a first order Taylor correction to predict the value of $\\\\varphi_{v}$ at the next step. Once a suitable number of integration steps has been performed, we use equation \\\\ref{potenti} again to obtain the value of $\\\\delta$ at the corresponding value of $D$.\\n\\nFor our application - topology, we expect the exact number of integrations\\nto be irrelevant. After a certain number of iterations we expect to reach the linear\\nregime in all scales, which means that the genus curves of the density fields will no longer change. This particular characteristic of the genus can in fact be useful to test the convergence of the method. We obtained several reconstructed density fields for different values of the number of integration steps, and found the topologies to converge. This result is shown is Fig. \\\\ref{convergence}.\\n\\n\\\\section{CONSTRUCTION OF THE DENSITY MAPS}\\n\\\\label{recdenmaps}\\n\\nThe construction of the density maps we follow is, to a large extent, equivalent to the method followed by Canavezes et al. \\\\shortcite{Ca98}. We employ the same fit for the PSCz selection function $s(z)$:\\n\\\\be\\ns(z)=\\\\frac{\\\\psi}{z^{\\\\alpha}\\\\left( 1+\\\\left( \\\\frac{z}{z^{\\\\star}}\\\\right) ^{\\\\gamma} \\\\right)^{\\\\beta/\\\\gamma}} ,\\n\\\\ee\\nwith the parameters shown in Table \\\\ref{tab1} \\\\cite{Sp98a}, and estimate the density $\\\\rho(r)$ by\\n\\\\be\\n\\\\rho(r)\\\\propto\\\\frac{m(r)}{s(r)} ,\\n\\\\ee\\n\\n\\\\begin{table}\\n\\\\bc\\n\\\\caption{Parameters of the selection function of PSCz.\\\\label{tab1}}\\n\\\\vspace{0.5cm}\\n\\n\\\\begin{tabular}{ccc}\\n$\\\\alpha$ & $\\\\beta$ & $\\\\gamma$ \\\\\\\\\\n$0.991^{+0.068}_{-0.073}$ \\n& $3.445^{+0.173}_{-0.158}$ \\n& $1.925^{+0.162}_{-0.153}$ \\\\\\\\\\n\\\\\\\\\\n$z^{\\\\star}$ & $\\\\psi \\\\;\\\\;[h^3{\\\\rm Mpc}^{-3}]$ & \\\\\\\\\\n$0.02534^{+0.00130}_{-0.00116}$ \\n&$(141.3\\\\pm 2.4 ) \\\\times 10^{-6}$ & \\\\\\\\\\n\\\\end{tabular}\\n\\\\ec\\n\\\\end{table}\\n\\n\\\\begin{table}\\n\\\\bc\\n\\\\caption{The smoothing lengths adopted for the topological analysis of the PSCz\\nsurvey. Listed are the adopted survey depth $R_{\\\\rm max}$, the\\nresulting number\\n$N_{\\\\rm res}$ of resolution elements and the number $N_{\\\\rm gal}$ \\nof galaxies inside the survey volume.\\n\\\\label{tab2}\\n}\\n\\\\vspace{0.5cm}\\n\\\\begin{tabular}{c|c|r|r|r}\\n$\\\\lambda\\\\;\\\\;[\\\\lu]$ & $R_{\\\\rm max}\\\\;\\\\;[\\\\lu]$ &\\n$N_{\\\\rm res}$ & $N_{\\\\rm gal}$ \\\\\\\\\\n 5& 34.92& 215.5& 2295\\\\\\\\\\n 6& 47.16& 307.3& 3550\\\\\\\\\\n 7& 58.35& 366.3& 4928\\\\\\\\\\n 8& 68.58& 398.5& 5909\\\\\\\\\\n10& 86.91& 415.3& 7510\\\\\\\\\\n12& 103.19& 402.3& 8775\\\\\\\\\\n14& 118.04& 379.2& 9681\\\\\\\\\\n16& 131.81& 353.7& 10356\\\\\\\\\\n20& 156.96& 305.8& 11309\\\\\\\\\\n24& 179.79& 266.0& 11968\\\\\\\\\\n28& 200.97& 233.9& 12496\\\\\\\\\\n32& 221.79& 210.6& 12833\\\\\\\\\\n40& 263.44& 180.7& 13339\\\\\\\\\\n48& 305.09& 162.4& 13684\\\\\\\\\\n50& 315.50& 158.9& 13748\\\\\\\\\\n56& 346.73& 150.2& 13924\\\\\\\\\\n\\\\end{tabular}\\n\\\\ec\\n\\\\end{table}\\n\\n\\nwhere $m(r)$ is the discrete point distribution. However, the angular mask needs to be treated with care. Because the structure we can see behind the mask will have a significant effect on the evolution of structure on the whole observable area, we need to resort to some sort of filling, prior to using the time-machine. \\n\\nWe consider two different types of filling: One, a random filling, in which fake objects are placed randomly over the masked region with an average number density equal to the average number density of the whole survey (weighted by the selection function); And another, a {\\\\em cloning}, in which fake objects are placed randomly in each bin, but with an average number density equal to the average number density of the neighbouring observable bins, again weighted by the selection function. \\n\\nOn both cases, we create a box containing a sphere of radius $R_{max}$ as defined in Table \\\\ref{tab2}. $R_{max}$ is the maximum distance up to which the average distance between two neighbouring galaxies in PSCz is smaller than the adopted smoothing length. The size of the box will then be $\\\\frac{2}{\\\\sqrt{3}}Rmax$. Although boundary conditions are not periodic, we smooth the density field in Fourier space assuming periodic boundary conditions. We consider this to be preferable to zero padding, as this would create an artificial boundary that would eventually affect the gravitational time-machine.\\n\\nWe then apply the Zel'dovich time-machine on the box thus obtained for both filling techniques. In the subsequent topological analysis, we limit ourselves to the sphere inside the box with radius $R_{max}$. \\n\\n\\\\subsection*{Smoothing Procedure}\\n\\nIdeally, one would want to apply the operator {\\\\em time-reverse} directly upon the unsmoothed density field obtained from PSCz, and only then smooth it on a range of scales to be able to calculate its genus curve. However, in order to obtain meaningful results, we need a smooth field {\\\\em a priori}. This poses a very important problem: These operators ({\\\\em time-reverse} and {\\\\em smoothing}) do not in general commute. In other words, the topology of the final density field can be significantly different whether the smoothing operation is performed before or after applying the {\\\\em time-machine} to our original field.\\n\\nTo illustrate this point, let us consider a Gaussian random density field smoothed on some scale $\\\\lambda$. After applying the {\\\\em time-machine} this density field will still be Gaussian. However, if we are to naively calculate its genus curve choosing for isodensity contours the same isodensity contours defined {\\\\em prior} to applying te {\\\\em time-machine}, we would wrongly conclude that the field is not Gaussian. In order to circumvent this problem we would be forced to smooth the final field once again on a larger scale, thus reducing considerably the statistical significance of our results.\\n\\nThere is, however, an alternative way to solve this dilemma: One can try to find a smoothing operator that comutes with our reconstruction operator.\\n\\nHow can we look for such a smoothing operator? One way of ensuring this is to find an operator that does not change the density field if applied once again at a latter stage. By other words, if we ensure that our final density field remains the same regardless of how many times we perform the smoothing operation throughout the time-reversing process, then it is because these two operators do indeed comute. A class of such operators are the adaptive smoothing operators. By adaptive smoothing, we understand a {\\\\em local} smoothing of variable smoothing length according to the local structure. There are several types of adaptive smoothing. The ideal adaptive smoothing operator ensures that the total mass enclosed by isodensity contours remains constant throughout the time-reversing process. A simplified version assumes spherical symmetry. At each point we employ a smoothing length $\\\\lambda$ such that $\\\\lambda^{3}\\\\propto 1/\\\\rho=1/\\\\left( \\\\rho_{0}+\\\\delta \\\\right)$. The proportionality constant defines the characteristic smoothing length, which is the smoothing length employed when the overdensity $\\\\delta$ vanishes. For highly dense regions, a smaller value of $\\\\lambda$ will be chosen, whereas voids will be smoothed with a larger value of $\\\\lambda$.\\n\\nWhen we apply the time-machine operator on a map smoothed in this way, the isodensity contours around a cluster will move, but the total mass enclosed by them will remain approximately constant, as long as the spherical symmetry hypothesis is a good approximation. \\n\\nIn our application to the PSCz we use a spherically symmetric adaptive smoothing algorithm. We start by creating a set of maps obtained from the original map (this might be either the PSCz data or simulation data) by smoothing it on a range of scales around a given characteristic scale $l_{0}$, using Gaussian filters of the form\\n\\\\be\\nG_{\\\\lambda}(x)=\\\\frac{1}{\\\\pi^{3/2}\\\\lambda^{3}} e^{-x^{2}/\\\\lambda^{2}}\\n\\\\ee\\nwhere $\\\\lambda$ varies around $l_{0}$. We then look for the appropriate value of $\\\\lambda$ at each position $x$ by enforcing the equation\\n\\\\be\\n(1+\\\\delta_{\\\\lambda})\\\\lambda^{3}=l_{0}^{3} ,\\n\\\\ee \\nwhere $\\\\delta_{\\\\lambda}$ is the density contrast when the original map is smoothed on a scale $\\\\lambda$. This ensures that the mass enclosed on a sphere of radius $\\\\lambda$ is, to first order in a Taylor expansion, constant throughout the whole map.\\n\\n\\n\\\\subsection*{Error Estimates}\\n\\nThere are three different sources of error that enter our results: Shot noise, cosmic variance and the errors associated with the Zel'dovich approximation itself.\\n\\nThe most accurate and realistic way of estimating these errors, which ultimately enter the genus curves of the reconstructed PSCz density fields, is to analyse the topology of fake PSCz catalogues drawn from N-body simulations of some {\\\\em standard} CDM model. Since we intend to test the validity of the Zel'dovich time-machine with N-body simulations, it seems reasonable to extent this philosophy to the calculation of the statistical errors themselves. This is achieved by seeking a galaxy number density field with a Poisson distribution, whose expectation value is identical to the density field of the N-body simulation multiplied by the PSCz selection function. This is equivalent to {\\\\em observing} the density field of the N-body simulation in a similar way to the way PSCz observes the density field of the real Universe. This galaxy number density field is then divided by the PSCz selection function again to obtain a \\\"PSCZ-noisy\\\" distance-independent estimate of the real galaxy number density. Each of the {\\\\em mock} PSCz catalogues is adaptively smoothed using the algorithm described above and then used as input in the Zel'dovich time-machine. The genus curves of the reconstructed fields are calculated and the variance obtained over 10 mock PSCz catalogues is used as the statistical error estimate. \\n\\n\\n\\\\section{TESTING THE METHOD WITH N-BODY SIMULATIONS OF CDM MODELS.}\\n\\\\label{recnbody}\\n\\nAs we mentioned previously, we intend to test the regime of validity of the Zel'dovich time-machine by means of an N-body simulation of a CDM model. We apply the time-machine on the present density field drawn from the simulation and compare the density field thus obtained with the density field drawn from the original test-mass positions used as input in the simulation. More specifically, we need only to compare the topologies of the reconstructed and original fields through their genus curves.\\n\\nFor this purpose, we use two N-body simulations corresponding to two cold dark matter models, kindly provided by the Virgo consortium \\\\cite{Col97,Je97}.The simulations have been performed with an AP$^{3}$M-SPH code \\nnamed {\\\\small HYDRA} \\\\cite{Cou95}. Here we consider the SCDM model and the $\\\\tau$CDM model, which parameters are shown in Table \\\\ref{modelparameters}. Because this simulations contain CDM on periodic boxes of size $239.5\\\\lu$ and use such a large number of particles, they constitute an ideal ground for this test.\\n\\n\\\\begin{table}\\n\\\\bc\\n\\\\caption{Parameters of the examined CDM models. The simulations have\\nbeen done by the \\nVirgo collaboration.\\\\label{modelparameters}\\n}\\n\\\\begin{tabular}{l|c|c|c|c|}\\n\\\\multicolumn{1}{l|}{ }& $\\\\tau$CDM & $\\\\Lambda$CDM\\n\\\\vspace{0.1cm}\\\\\\\\ \\n\\\\multicolumn{1}{l|}{Number of particles } & $256^{3}$ & $256\\n^{3}$ \\\\\\\\\\n\\\\multicolumn{1}{l|}{Box size$[\\\\lu]$ } & $239.5$ & $239.5$\\\\\\\\\\n$z_{start}$& $50$ & $30$ & \\\\\\\\\\n$\\\\Omega_{0}$ & $1.0$ & $0.3$ \\\\\\\\\\n$\\\\Omega_{\\\\Lambda}$& $0.0$ & $0.7$\\\\\\\\\\n \\\\multicolumn{1}{l|}{Hubble constant $h$} & $0.5$ & $0.7$\\\\\\\\\\n$\\\\Gamma$ & 0.21 & 0.21 \\\\\\\\\\n$\\\\sigma_{8}$ & $0.60$ & $0.90$ \\\\\\\\\\n \\\\multicolumn{1}{l|}{Mass per particle [$10^{10}h^{-1}M_{\\\\odot}$]} & $22.7$ &$5.8$ & \\\\\\\\\\n\\n\\\\end{tabular}\\n\\\\ec\\n\\\\end{table}\\n\\nWe start by binning the particles in cells of side length $2\\\\lu$ and smooth further on some characteristic smoothing length $\\\\lambda$, using the adaptive smoothing algorithm described in section \\\\ref{recdenmaps}, in an analogous procedure to the way we treat the PSCz galaxies. This \\\"double\\\" smoothing is required in the real Universe in order to minimize shot noise effects, but it is also necessary in order to eliminate severe non-linearities since the Zel'dovich time-machine is expected not to work over such regimes. It is also needed to smooth out regions of orbit-crossing.\\n\\nThe next step is to calculate the genus curves of both the original density field that is used as input in the simulation, smoothed in the same manner as described above, and the reconstructed density field obtained after applying the Zel'dovich time-machine to the present density field smoothed in the same way. In order to compare both genus curves we compute their amplitudes and their amplitude drops. It is very important to note that if we are to obtain gaussianized versions of the density fields at the present time, they will not have, in principle, the same genus amplitudes as the density fields themselves, even when these are in the Gaussian regime. This is so because of the very nature of adaptive smoothing. When a given density field is smoothed adaptively its genus curve will have a different shape and amplitude than the shape and amplitude of the genus curve of the same field when this is smoothed with a constant Gaussian window. We need to be extremely careful not to draw the wrong conclusions about the Gaussian or non-Gaussian nature of our density fields. After applying the time-machine, however, the amplitude of fluctuations will be reduced significantly. In fact they will be reduced to such an extent as to make the field look almost homogeneous. This means that the isodensity contours on adaptively smoothed maps will be very close to the isodensity contours on maps smoothed using a constant Gaussian window. Hence, it is possible to calculate amplitude drops and determine the Gaussian (or non-Gaussian) nature of our density maps {\\\\em after} applying the Zel'dovich time-machine, i.e., to determine the Gaussian (or non-Gaussian) nature of the {\\\\em reconstructed} fields.\\n\\nIn order to test the convergence of the reconstruction method, we obtained several reconstructed density fields for diffent values of the total number of integration steps, as mentioned in \\\\ref{recmethod}. Fig. \\\\ref{convergence} shows a particular slice of the reconstructed density fields at different integration steps when the method is applied to the maps at $z=0$ obtained from the $\\\\tau$CDM simulation by smoothing on characteristic lengths of $8\\\\lu$ and $10\\\\lu$. As it is evident from this Figure, the topology of the density fields is undistinguishable for values of $z$ greater than $4$ on smoothing scales of both $8\\\\lu$ and $10\\\\lu$. Only the amplitude of the density fluctuations changes, indicating that we are now in the linear regime. In Fig. \\\\ref{convscater} this is made even clearer. Here we show a point-by-point comparison of the reconstructed $\\\\tau$CDM density fields at redshifts $z=4$ and $z=9$, for the characteristic smoothing lengths of $8\\\\lu$ and $10\\\\lu$. We only show one in eight of all points, chosen randomly. It is obvious from this plot that the shape of fluctuations did not change from $z=4$ to $z=9$, for either of the smoothing lengths adopted. It is also obvious that the amplitude of fluctuations was reduced by a factor of $2$, as it is expected in the linear regime (notice that in the linear regime the growing mode of fluctuations varies as $1/(1+z)$). Hence, our time-machine shows the correct assimptotic behaviour.\\n\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/d8tcdmcrop_test50.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/d10tcdmcrop_test50.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/d8tcdmcrop_test80.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/d10tcdmcrop_test80.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/d8tcdmcrop_test90.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/d10tcdmcrop_test90.eps}}\\n\\\\caption{A particular slice of the reconstructed fields for the $\\\\tau$CDM simulation for different values of $z$. The left panels show the fields smoothed adaptively with a characteristic smoothing length of $8\\\\lu$, whereas the panels on the right show the fields smoothed with a characteristic smoothing length of $10\\\\lu$ \\\\label{convergence}}\\n\\\\ec\\n\\\\end{figure*}\\n\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/d8tcdm_scater.eps}}\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/d10tcdm_scater.eps}}\\n\\n\\\\caption{ Point-by-point comparison of the reconstructed $\\\\tau$CDM density field at redshift $z=4$ and the reconstructed $\\\\tau$CDM density field at redshift $z=9$, when the adopted characteristic smoothing lengths are of $8\\\\lu$ and $10\\\\lu$. \\\\label{convscater}}\\n\\\\ec\\n\\\\end{figure*}\\n\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/cont8tcdm_now.eps}}\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/cont8tcdm_back80.eps}}\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/cont8tcdm_orig.eps}}\\n\\n\\\\caption{Isodensity contours of the $\\\\tau$CDM simulation. The characteristic smoothing length adopted was $8\\\\lu$. The separation between contour levels is $0.2/(1+z)$. The zero contour is heavy; positive contours are solid; negative contours are dashed. \\\\label{nbodycontours}}\\n\\\\ec\\n\\\\end{figure*}\\n\\n\\\\subsection*{Results} \\n\\nFigure \\\\ref{nbodycontours} shows the isodensity contours obtained for the SCDM simulation and the $\\\\tau$CDM simulation, when the fields are adaptively smoothed on a characteristic scale of $5\\\\lu$ in a comoving box of size $240\\\\lu$. The first row shows the fields at the present time. The second row shows the fields after applying the Zel'dovich time-machine back to a redshift of 10 and the third row shows the original fields used as input in the simulations. In each panel the thick line represents the contour where the density contrast is zero. Dashed lines represent contours of negative density contrast whereas solid lines represent positive density contrasts. The contour spacing is $0.2/(1+z)$. Because this is normalized to the linear reconstruction case where $\\\\delta\\\\propto 1/(1+z)$, the linear theory reconstruction density maps look exactly like the present day maps (first row), albeit their much lower fluctuation amplitude. From the contours on both the reconstructed maps and the original maps we notice that their fluctuation amplitudes are larger than the fluctuation amplitude of a linearly reconstructed map. This result is expected because fluctuations will grow faster at the later stages of evolution, in the mildly non-linear regime. It is obvious from Fig. \\\\ref{nbodycontours} that the Zel'dovich time-machine is able to change the rank order of isodensity contours. This means that the genus curves will also be changed. In fact we can predict, just by looking at Fig. \\\\ref{nbodycontours} that the amplitude of the genus curves will increase after applying the Zel'dovich time-machine, as it is expected.\\n\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gscdm_exp5.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gscdm00_exp5.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gscdm_exp8.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gscdm00_exp8.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gscdm_exp14.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gscdm00_exp14.eps}}\\n\\n\\\\caption{Genus curves for the SCDM model, at selected smoothing lengths. The left column shows the genus curves of the reconstructed field (thick solid lines) and of the randomized version of that field (thin solid lines), whereas the right column shows the genus curves of the original density field used as input for the N-body simulations. The dashed and dotted lines are the best fit random-phase curves to each of the fields. \\\\label{SCDMgenus}}\\n\\\\ec \\n\\\\end{figure*}\\n\\n\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gtcdm_exp5.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gtcdm00_exp5.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gtcdm_exp8.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gtcdm00_exp8.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gtcdm_exp14.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gtcdm00_exp14.eps}}\\n\\n\\\\caption{Genus curves for the $\\\\tau$CDM model, at selected smoothing lengths. The left column shows the genus curves of the reconstructed field (thick solid lines) and of the randomized version of that field (thin solid lines), whereas the right column shows the genus curves of the original density field used as input for the N-body simulations. The dashed and dotted lines are the best fit random-phase curves to each of the fields.\\\\label{TCDMgenus}}\\n\\\\ec\\n\\\\end{figure*}\\n\\\\begin{figure}\\n\\\\bc\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/recdropmodels.eps}}\\n\\\\caption{Amplitude drops measured for the reconstructed SCDM simulation and $\\\\tau$CDM simulation. Also show for comparison are the amplitude drops measured for the simulations at $z=0$\\\\label{recdropbody}.}\\n\\\\ec\\n\\\\end{figure}\\n\\\\begin{figure}\\n\\\\bc\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/recampmodels.eps}}\\n\\\\caption{Genus amplitudes measured for the reconstructed SCDM simulation and $\\\\tau$CDM simulation. Also shown are the genus amplitudes of the original fields\\\\label{recampbody}.}\\n\\\\ec\\n\\\\end{figure}\\n\\n\\n\\nFigures \\\\ref{SCDMgenus} and \\\\ref{TCDMgenus} show the genus curves obtained for the SCDM model and the $\\\\tau$CDM model respectively, at selected characteristic smoothing lengths, namely at $5\\\\lu$, $8\\\\lu$ and $14\\\\lu$. We restrict our analysis to this range of smoothing lengths, as we know {\\\\em a priori} that the Zel'dovich time-machine is only relevant in the mildly non-linear regime. In both figures, the first column shows the genus curves of the reconstructed field and its randomized counterpart, whereas the second column shows the genus curves of the original fields, used as input for the simulations. We deliberately do not show the genus curves of the present day {\\\\em adaptively smoothed} density fields, since, as we argued in the previous chapter, the isodensity contours are, at this stage, different from the isodensity contours of the fields smoothed using a constant kernel.\\n\\nIt is striking in Fig. \\\\ref{SCDMgenus} and Fig. \\\\ref{TCDMgenus} the consistency between the genus curves of the reconstructed field and of its randomized counterpart. This is particularly true for the genus amplitudes, which indicates that there is very little phase correlation in the reconstructed fields on all scales, as it is expected from Gaussian initial conditions. With regard to the genus amplitudes {\\\\em per se}, we find consistency with the genus amplitudes of the original density fields, although we notice a tendency for these to be slightly higher in the reconstructed fields. These means that the second moment of the power spectrum is recovered slightly {\\\\em in excess}. This becomes more important as we approach the smaller scales, which is to say as the system becomes more non-linear.\\n\\nIt is also interesting to notice a depression at high values of $\\\\nu$ on the genus curves of the reconstructed fields. We find this depression to be present in all cases, both for the Virgo simulations and the PSCz data. We expect this to be a particular feature of the reconstruction technique, i.e., ultimately dependent on the Zel'dovich approximation itself. At high values of $\\\\nu$ the regime is considerably non-linear and so we expect the Zel'dovich approximation to perform rather poorly. This problem is enhanced by the fact that the density fields have been smoothed adaptively. Nevertheless, we do not expect this feature to affect our results considerably as the calculation of the amplitude of the genus curves is restricted to the range $-1<\\\\nu<1$.\\n\\nNote that there is no sampling noise in these density fields. The tremble in the genus curves is ultimately due to cosmic variance.\\n\\nIn Fig. \\\\ref{recdropbody} we plot the amplitude drops obtained for the reconstructed SCDM model and for the reconstructed $\\\\tau$CDM model as a function of smoothing length. Also shown are the amplitude drops obtained for the models at $z=0$ \\\\cite{Ca98}. In all scales, the values obtained for the reconstructed fields are closer to unity than those of the present-day fields. This indicates that the Zel'dovich time-machine is a good tool in recovering Gaussian initial density fields. However, at small scales, we detect a slight departure from the expected value of unity, even for the reconstructed fields. This is not surprising since at this scales non-linearities become strong. The degree of strength of the non-linearities depends on the particular model. As we see from Fig. \\\\ref{recdropbody} they are more important in the $\\\\tau$CDM model than in the SCDM model, in agreement to what was found by Canavezes et al. \\\\shortcite{Ca98}.\\n\\nFig. \\\\ref{recampbody} shows the genus amplitudes of the reconstructed fields for both the SCDM model and the $\\\\tau$CDM model, together with the genus amplitudes of the original fields. In the case of the $\\\\tau$CDM model the agreement between the original genus amplitude and the genus amplitude of the reconstructed field, is striking, in particular when we consider scales above $\\\\sim 7\\\\lu$. For the SCDM model the agreement is not as good. The reconstructed genus amplitudes appear to be slightly higher than the true original ones.\\n\\nThese results indicate that the Zel'dovich time-machine is effective in recovering the right genus amplitude {\\\\em drops} on scales larger than $\\\\sim 8\\\\lu$, although recovered amplitudes cannot be considered reliable in the strict sense of the word. \\n\\n\\n\\n\\\\section{RECOVERING THE INITIAL DENSITY FIELD FROM PSCZ}\\n\\\\label{recpscz}\\n\\nAs mentioned previously, one of the difficulties in using the PSCz in an attempt to recover the initial density fluctuations in the Universe, is the fact that the masked region can make up to $\\\\sim 20\\\\%$ of the whole observable area. Since this region will have a definite gravitational influence on the observable area when we attempt to reconstruct to original density field, some sort of filling is essential. As mentioned in \\\\ref{recdenmaps} we employ two different techniques: The random filling and the cloning. Fig. \\\\ref{randcloned} shows how the two different fillings appear to the eye. On the upper panel we show the map where the mask has been filled randomly and on the lower panel we show the map where the mask has been cloned. Although it is impossible to the eye to recognize any significant difference, we will be able to detect some noticeable differences on the topologies of the reconstructed density fields.\\n\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gcloned_exp6.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/grand_exp6.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gcloned_exp8.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/grand_exp8.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gcloned_exp12.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/grand_exp12.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/gcloned_exp16.eps}}\\n\\\\resizebox{6cm}{!}{\\\\includegraphics{plots/grand_exp16.eps}}\\n\\\\caption{Genus curves of the reconstructed PSCz fields. \\\\label{PSCzgenus}}\\n\\\\ec\\n\\\\end{figure*}\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/randomcrop.eps}}\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/clonedcrop.eps}}\\n\\\\caption{Aitoff projections of PSCz galaxies and filled masks.In the upper panel the mask is filled randomly whereas in the lower panel the mask is filled using a cloning technique.\\\\label{randcloned}}\\n\\\\ec\\n\\\\end{figure*}\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{10cm}{!}{\\\\includegraphics{plots/droppscznow.eps}}\\n\\\\caption{The amplitude drop $R$ measured for PSCz. Also shown are the results\\nobtained by Vogeley et al.$1994$ for the CfA survey. Here the \\nerrors are taken to be the uncertainty Vogeley et al.$1994$ report \\nfor mock catalogues extracted from a LCDM model\\\\label{drpscznow}}\\n\\\\ec\\n\\\\end{figure*}\\n\\\\begin{figure*}\\n\\\\bc\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/dropcloned.eps}}\\n\\\\resizebox{8cm}{!}{\\\\includegraphics{plots/droprandom.eps}}\\n\\\\caption{The amplitude drops measured for the reconstructed PSCz density fields. In the upper panel the mask has been cloned, whereas in the lower panel the mask has been filled randomly. Also shown are the amplitude drops obtained for the reconstructed N-body simulations. \\\\label{psczdrops}}\\n\\\\ec\\n\\\\end{figure*}\\n\\n\\\\subsection*{Results \\\\& Discussion} \\n\\nFig. \\\\ref{PSCzgenus} shows the genus curves obtained for the reconstructed PSCz fields. On the first column we plot the genus curves of the fields for which the mask has been filled using a cloning technique, and on the second column we plot the genus curves of the fields where the mask has been filled randomly. The thick solid lines refer to the reconstructed PSCz fields {\\\\em proper}, whereas the thin solid lines refer to the randomized versions of those fields,i.e., the fields obtained from the reconstructed density fields by randomizing phases in Fourier space subject to the reality constraint $\\\\delta_{{\\\\bf k}}=\\\\delta_{-{\\\\bf k}}^{\\\\ast}$ and keeping the same power spectrum. The dotted and dashed lines are the best fitting random-phase curves to both the reconstructed PSCz density fields and their randomized versions.\\n\\nIt is striking to notice the proximity between genus curves, even at small smoothing lengths. The statistical errors drawn from the N-body simulation are not shown in Fig. \\\\ref{PSCzgenus} because of the high degree of correlation between the points in the genus curves.\\n\\nIndependently of whether the mask has been randomly filled or cloned, the recovered genus curves seem consistent with random-phase Gaussian fluctuations because the amplitude drops appear small. However, the amplitude themselves seem to depend on the mask filling technique.\\n\\n\\nIn Fig. \\\\ref{psczdrops} we plot the amplitude drops obtained for the reconstructed PSCz density fields, as a function of smoothing length, as well as the error bars drawn from the $\\\\tau$CDM model following the method outlined in chapter \\\\ref{recdenmaps}. The amplitude drops of the reconstructed N-body simulations are also shown for comparison.\\n\\nIn contrast with Fig. \\\\ref{drpscznow}, where phase correlations were found for PSCz at small smoothing lengths, the reconstructed PSCz fields do not show any significant phase correlations on scales ranging from $5\\\\lu$ to $14\\\\lu$. This reinforces the hypothesis that density fluctuation originate from random-phase Gaussian initial conditions. \\n \\n\\n\\n\\n\\n\"\n },\n {\n \"name\": \"zeld.tex\",\n \"string\": \" \\n\\n\\\\documentstyle[epsfig]{mn}\\n%\\n% Preamble\\n%\\n\\n\\n\\\\newcommand{\\\\iras} {{\\\\it IRAS \\\\/}}\\n\\\\newcommand{\\\\et} {{\\\\em et al.}}\\n\\\\newcommand{\\\\be}{\\\\begin{equation}}\\n\\\\newcommand{\\\\ee}{\\\\end{equation}}\\n\\\\newcommand{\\\\bea}{\\\\begin{eqnarray}}\\n\\\\newcommand{\\\\eea}{\\\\end{eqnarray}}\\n\\\\newcommand{\\\\bc}{\\\\begin{center}}\\n\\\\newcommand{\\\\ec}{\\\\end{center}}\\n\\\\newcommand{\\\\ol}[1]{ {\\\\overline{#1}}}\\n\\\\newcommand{\\\\lu}{\\\\,h^{-1}{\\\\rm Mpc}}\\n\\\\renewcommand{\\\\vec}[1]{ {\\\\bmath #1} } \\n\\\\newcommand{\\\\dd}{{\\\\rm d}}\\n\\\\newcommand{\\\\ls}{\\\\raisebox{-.8ex}{$\\\\buildrel{\\\\textstyle<}\\\\over\\\\sim$}}\\n\\\\newcommand{\\\\props}{\\\\raisebox{-.8ex}{$\\\\buildrel{\\\\textstyle\\\\propto}\\\\over\\\\sim$}}\\n\\\\newcommand{\\\\gs}{\\\\raisebox{-.8ex}{$\\\\buildrel{\\\\textstyle>}\\\\over\\\\sim$}}\\n\\n\\n\\\\title{Recovering the Topology of the Initial Density Fluctuations Using the {\\\\em IRAS} Point Source Catalogue Redshift Survey}\\n\\n\\n\\\\author[A. Canavezes J. Sharpe]{A. Canavezes,$^1$ J. Sharpe,$^2$ \\\\\\\\\\n$^1$ Centro de Astrof\\\\'{i}sica da Universidade do Porto, Rua das Estrelas s/n, 4150 Porto, Portugal\\\\\\\\\\n$^2$ Imperial College of Science Technology and Medicine, Blackett Laboratory, Prince Consort Road, London SW7 2BZ, UK}\\n\\n\\\\begin{document}\\n\\\\maketitle\\n\\n\\\\begin{abstract}\\n\\nWe apply the reconstruction technique of Nusser \\\\& Dekel (1992) to the recently available Point Source Catalogue Redshift Survey (PSCz) in order to subtract the phase correlations that are expected to develop in the mild non-linear regime of gravitational evolution. We study the evolution of isodensity contours defined using an adaptive smoothing algorithm in order to minimize the problems derived from the non-comutivity of operators. We study the genus curves of these isodensity contours and concentrate on the evolution of the amplitude drops, a meta-statistic able to quatify the level of phase-correlation present in the field. In order to test the method and to quatify the level of statistical uncertainty, we apply the method to a set of mock PSCz catalogues derived from the N-body simulations of two 'standard' CDM models, kindly granted to us by the Virgo consortium. We find the method to be reliable in recovering the right amplitude drops. When applied to PSCz the level of phase correlations observed is very low on all scales ranging from $5\\\\lu$ to $60\\\\lu$, providing support to the theory that structure originated from gaussian initial conditions.\\n\\n\\\\end{abstract}\\n \\n\\\\begin{keywords}\\ngalaxies:clusters:general -- cosmology:observations -- cosmology:large-scale-structure of the Universe\\n\\\\end{keywords}\\n\\n\\\\section*{INTRODUCTION}\\n\\n \\\\input{reconstruction.tex}\\n\\n\\\\section*{AKNOWLEDGEMENTS}\\n\\nWe are grateful to the Virgo consortium (J. Colberg, H. Couchman, G. Efstathiou, C. S. Frenk, A. Jenkins, A. Nelson, J. Peacock, F. Pearce, P. Thomas and S. D. M. White) for provinding simulation data ahead of publication. AC aknowledges the support of FCT (Portugal).\\n\\n\\\\bibliography{zeld}\\n\\n\\n \\n\\\\end{document}\\n\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"zeld.bbl","string":"\\begin{thebibliography}{}\n\n\n\n\n\n\\bibitem[\\protect\\citename{Canavezes et al. }1998]{Ca98}\nCanavezes A., Springel V., Oliver S. J., Rowan-Robinson M., Keeble O., White S. D. M., Saunders W., Efstathiou G., Frenk C., McMahon R. G., Maddox S., Sutherland w., Tadros H., 1998, MNRAS, 297, 777\n \n\\bibitem[\\protect\\citename{Colberg et al. }1997]{Col97}\nColberg J.~M., White S.~D.~M., Jenkins A., Pearce F.~R., Frenk C.~S.,\nThomas P.~A., Hutchings R., Couchman H.~M.~P., Peacock J.~A.,\nEfstathiou G.~P., Nelson A.~H., 1997, in Hamilton D., ed, Ringberg Workshop,\nLarge-scale structure in the Universe. Cluver, Dordrecht, in press\n\n\\bibitem[\\protect\\citename{Couchman \\& Pearce }1995]{Cou95}\nCouchman H. M. P., Thomas P. A., Pearce F. R., 1995, ApJ, 452, 797\n\n\\bibitem[\\protect\\citename{Dekel et al. }1993]{De93}\nDekel A., Bertschinger E., Yahil A., Strauss M.~A., Davis M., Huchra\nJ.~P., 1993, ApJ, 412, 1\n\n\\bibitem[\\protect\\citename{Gramann }1993]{Gr93}\nGramann M., 1993, ApJ,405, 449\n\n\n\\bibitem[\\protect\\citename{Jenkins et al. }1997]{Je97}\nJenkins A. R., Frenk C. S., Pearce F. R., Thomas P. A.,\nColberg J. M., White S. D. M., Couchman H. M. P.,\nPeacock J. A., Efstathiou G. P., Nelson A. H., \n1997, ApJ, submitted\n\n\n\\bibitem[\\protect\\citename{Nusser \\& Davies }1994]{Nu94}\nNusser A., Davis M., 1994, ApJ, 421, L1 \n\n\\bibitem[\\protect\\citename{Nusser \\& Dekel }1992]{ND92}\nNusser A.,Dekel A, 1992, ApJ, 391, 443\n\n\\bibitem[\\protect\\citename{Nusser, Dekel \\& Yahil }1995]{Nu95}\nNusser A., Dekel A., Yahil A., 1995, ApJ, 449, 439\n\n\n\\bibitem[\\protect\\citename{Peebles }1980]{Pe80}\nPeebles J., 1980, {\\em Large Scale Struture of the Universe}, Princeton University Press\n\n\n\\bibitem[\\protect\\citename{Saunders et al. }1999]{Sa99}\nSaunders W. et al., 1999, MNRAS, submited, astro-ph/0001117 \n\n\n\\bibitem[\\protect\\citename{Springel \\& White }1998]{Sp98a}\nSpringel V., White S. D. M., 1998, MNRAS, in press\n\n\n\\bibitem[\\protect\\citename{Vogeley et al. }1994]{Vo94}\nVogeley M. S., Park C., Geller M. J., Huchra J.P., Gott J. R., 1994, ApJ, 420, 525\n\n\n\\end{thebibliography}\n"}],"string":"[\n {\n \"name\": \"zeld.bbl\",\n \"string\": \"\\\\begin{thebibliography}{}\\n\\n\\n\\n\\n\\n\\\\bibitem[\\\\protect\\\\citename{Canavezes et al. }1998]{Ca98}\\nCanavezes A., Springel V., Oliver S. J., Rowan-Robinson M., Keeble O., White S. D. M., Saunders W., Efstathiou G., Frenk C., McMahon R. G., Maddox S., Sutherland w., Tadros H., 1998, MNRAS, 297, 777\\n \\n\\\\bibitem[\\\\protect\\\\citename{Colberg et al. }1997]{Col97}\\nColberg J.~M., White S.~D.~M., Jenkins A., Pearce F.~R., Frenk C.~S.,\\nThomas P.~A., Hutchings R., Couchman H.~M.~P., Peacock J.~A.,\\nEfstathiou G.~P., Nelson A.~H., 1997, in Hamilton D., ed, Ringberg Workshop,\\nLarge-scale structure in the Universe. Cluver, Dordrecht, in press\\n\\n\\\\bibitem[\\\\protect\\\\citename{Couchman \\\\& Pearce }1995]{Cou95}\\nCouchman H. M. P., Thomas P. A., Pearce F. R., 1995, ApJ, 452, 797\\n\\n\\\\bibitem[\\\\protect\\\\citename{Dekel et al. }1993]{De93}\\nDekel A., Bertschinger E., Yahil A., Strauss M.~A., Davis M., Huchra\\nJ.~P., 1993, ApJ, 412, 1\\n\\n\\\\bibitem[\\\\protect\\\\citename{Gramann }1993]{Gr93}\\nGramann M., 1993, ApJ,405, 449\\n\\n\\n\\\\bibitem[\\\\protect\\\\citename{Jenkins et al. }1997]{Je97}\\nJenkins A. R., Frenk C. S., Pearce F. R., Thomas P. A.,\\nColberg J. M., White S. D. M., Couchman H. M. P.,\\nPeacock J. A., Efstathiou G. P., Nelson A. H., \\n1997, ApJ, submitted\\n\\n\\n\\\\bibitem[\\\\protect\\\\citename{Nusser \\\\& Davies }1994]{Nu94}\\nNusser A., Davis M., 1994, ApJ, 421, L1 \\n\\n\\\\bibitem[\\\\protect\\\\citename{Nusser \\\\& Dekel }1992]{ND92}\\nNusser A.,Dekel A, 1992, ApJ, 391, 443\\n\\n\\\\bibitem[\\\\protect\\\\citename{Nusser, Dekel \\\\& Yahil }1995]{Nu95}\\nNusser A., Dekel A., Yahil A., 1995, ApJ, 449, 439\\n\\n\\n\\\\bibitem[\\\\protect\\\\citename{Peebles }1980]{Pe80}\\nPeebles J., 1980, {\\\\em Large Scale Struture of the Universe}, Princeton University Press\\n\\n\\n\\\\bibitem[\\\\protect\\\\citename{Saunders et al. }1999]{Sa99}\\nSaunders W. et al., 1999, MNRAS, submited, astro-ph/0001117 \\n\\n\\n\\\\bibitem[\\\\protect\\\\citename{Springel \\\\& White }1998]{Sp98a}\\nSpringel V., White S. D. M., 1998, MNRAS, in press\\n\\n\\n\\\\bibitem[\\\\protect\\\\citename{Vogeley et al. }1994]{Vo94}\\nVogeley M. S., Park C., Geller M. J., Huchra J.P., Gott J. R., 1994, ApJ, 420, 525\\n\\n\\n\\\\end{thebibliography}\\n\"\n }\n]"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":3,"numItemsPerPage":100,"numTotalItems":1318468,"offset":300,"length":100}},"jwt":"eyJhbGciOiJFZERTQSJ9.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc2NTYwODkwNCwic3ViIjoiL2RhdGFzZXRzL3N5bnRoZXRpeC1pbnN0aXR1dGUvbGF0ZXgtZGF0YS1wdWIiLCJleHAiOjE3NjU2MTI1MDQsImlzcyI6Imh0dHBzOi8vaHVnZ2luZ2ZhY2UuY28ifQ.7HUNMDSGm4oTY3Qz0E1jEUOUKa66PCNExL6PkjcNNg9zETjrxhidTCoOh_dOpdb4he7aA7B7FyK_334H6WLGDw","displayUrls":true,"splitSizeSummaries":[{"config":"default","split":"train","numRows":1318468,"numBytesParquet":110673004212}]},"discussionsStats":{"closed":0,"open":1,"total":1},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[],"user":[]}}">
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astro-ph0002305
|
On dust-correlated Galactic emission in the Tenerife data
|
[
{
"author": "P. Mukherjee"
},
{
"author": "A.W. Jones"
},
{
"author": "R. Kneissl \\& A.N. Lasenby"
},
{
"author": "Astrophysics Group"
},
{
"author": "Cavendish Laboratory"
},
{
"author": "Madingley Road"
},
{
"author": "Cambridge CB3 OHE"
},
{
"author": "UK"
}
] |
Recently correlation analyses between Galactic dust emission templates and a number of CMB data sets have led to differing claims on the origin of the Galactic contamination at low frequencies. de Oliviera-Costa {\em et al} (1999) have presented work based on Tenerife data supporting the spinning dust hypothesis. Since the frequency coverage of these data is ideal to discriminate spectrally between spinning dust and free-free emission, we used the latest version of the Tenerife data, which have lower systematic uncertainty, to study the correlation in more detail. We found however that the evidence in favor of spinning dust originates from a small region at low Galactic latitude where the significance of the correlation itself is low and is compromised by systematic effects in the Galactic plane signal. The rest of the region was found to be uncorrelated. Regions that correlate with higher significance tend to have a steeper spectrum, as is expected for free-free emission. Averaging over all correlated regions yields dust-correlation coefficients of $180\pm47$ and $123\pm16$ $\mu$K /MJy sr$^{-1}$ at 10 and 15~GHz respectively. These numbers however have large systematic uncertainties that we have identified and care should be taken when comparing with results from other experiments. We do find evidence for synchrotron emission with spectral index steepening from radio to microwave frequencies, but we cannot make conclusive claims about the origin of the dust-correlated component based on the spectral index estimates. Data with higher sensitivity are required to decide about the significance of the dust-correlation at high Galactic latitudes and other Galactic templates, in particular H$_\alpha$ maps, will be necessary for constraining its origin.
|
[
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"name": "paper_spin.tex",
"string": "\\documentstyle[epsfig,mathptm]{mn}\n%\\renewcommand{\\baselinestretch}{2.0}\n\\DeclareMathVersion{bold}\n%==============================================================================%\n% Extra fonts for MNRAS papers, assuming files are processed with LaTeX2e with %\n% NFSS. Adapted from mnsample.tex (taking out the non-NFSS 2 code), explicitly %\n% switching on the AMS fonts, and adding a bold maths version (which is needed %\n% if mathptm is also used). %\n% %\n% Dave Green --- MRAO --- 1998 October 13th %\n%==============================================================================%\n\\newif\\ifAMStwofonts\n\\AMStwofontstrue % <- comment this out if AMS fonts not available\n%\n\\newcommand{\\rmn}[1] {\\mathrm{#1}}\n\\newcommand{\\itl}[1] {\\mathit{#1}}\n\\newcommand{\\bld}[1] {\\mathbf{#1}}\n%\n\\def\\textbfit{\\protect\\txtbfit}\n\\def\\textbfss{\\protect\\txtbfss}\n\\def\\deg{\\nobreak^\\circ}\n\\long\\def\\txtbfit#1{{\\fontfamily{cmr}\\fontseries{bx}\\fontshape{it}%\n \\selectfont #1}}\n\\long\\def\\txtbfss#1{{\\fontfamily{cmss}\\fontseries{bx}\\fontshape{n}%\n \\selectfont #1}}\n%\n\\DeclareMathVersion{bold} % <- seems to be needed with mathptm\n%\n\\DeclareMathAlphabet{\\mathbfit}{OT1}{cmr}{bx}{it}\n\\SetMathAlphabet\\mathbfit{bold}{OT1}{cmr}{bx}{it}\n\\DeclareMathAlphabet{\\mathbfss}{OT1}{cmss}{bx}{n}\n\\SetMathAlphabet\\mathbfss{bold}{OT1}{cmss}{bx}{n}\n%\n\\ifAMStwofonts\n %\n \\ifCUPmtlplainloaded \\else\n \\DeclareSymbolFont{UPM}{U}{eur}{m}{n}\n \\SetSymbolFont{UPM}{bold}{U}{eur}{b}{n}\n \\DeclareSymbolFont{AMSa}{U}{msa}{m}{n}\n \\DeclareMathSymbol{\\upi}{0}{UPM}{\"19}\n \\DeclareMathSymbol{\\umu}{0}{UPM}{\"16}\n \\DeclareMathSymbol{\\upartial}{0}{UPM}{\"40}\n \\DeclareMathSymbol{\\leqslant}{3}{AMSa}{\"36}\n \\DeclareMathSymbol{\\geqslant}{3}{AMSa}{\"3E}\n %\n \\let\\oldle=\\le \\let\\oldleq=\\leq\n \\let\\oldge=\\ge \\let\\oldgeq=\\geq\n \\let\\leq=\\leqslant \\let\\le=\\leqslant\n \\let\\geq=\\geqslant \\let\\ge=\\geqslant\n %\n \\fi\n\\fi\n\\title[Galactic emission in Tenerife data]{On dust-correlated \nGalactic emission in the Tenerife data}\n\\author[P. Mukherjee et al.]\n{P. Mukherjee, A.W. Jones, R. Kneissl \\& A.N. Lasenby\\\\\nAstrophysics Group, Cavendish Laboratory, Madingley Road, \nCambridge CB3 OHE, UK\\\\}\n\\date{Accepted . Received ; in original form 15th of February 2000}\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\pubyear{2000} \n\n\\def\\LaTeX{L\\kern-.36em\\raise.3ex\\hbox{a}\\kern-.15em\n T\\kern-.1667em\\lower.7ex\\hbox{E}\\kern-.125emX}\n\n\\newtheorem{theorem}{Theorem}[section]\n\n\\begin{document} \n\n\\maketitle\n\n\\label{firstpage}\n\n\\begin{abstract}\nRecently correlation analyses between Galactic dust emission templates \nand a number of CMB data sets have led to differing claims on the origin \nof the Galactic contamination at low frequencies. de Oliviera-Costa \n{\\em et al} (1999) have presented work based on Tenerife data supporting the \nspinning dust hypothesis. Since the frequency coverage of these data is \nideal to discriminate spectrally between spinning dust and free-free \nemission, we used the latest version of the Tenerife data, which have \nlower systematic uncertainty, to study the correlation in more detail. We \nfound however that the evidence in favor of spinning dust originates \nfrom a small region at low Galactic latitude where the significance of \nthe correlation itself is low and is compromised by systematic \neffects in the Galactic plane signal. The rest of the region was found to be \nuncorrelated. Regions that correlate with higher significance \ntend to have a steeper spectrum, as is expected for free-free \nemission. Averaging over all correlated regions yields dust-correlation\n coefficients of $180\\pm47$ and $123\\pm16$ $\\mu$K /MJy sr$^{-1}$ at 10 and \n15~GHz respectively.\n These numbers however have large systematic uncertainties that we have\n identified and care should be taken when comparing with results from other\n experiments. We do find evidence for \nsynchrotron emission with spectral index steepening from radio to microwave \nfrequencies, but we cannot make conclusive claims \nabout the origin of the dust-correlated component based on the spectral \nindex estimates. Data with higher sensitivity \nare required to decide about the significance of the dust-correlation \nat high Galactic latitudes and other Galactic templates, in particular \nH$_\\alpha$ maps, will be necessary for constraining its origin. \n\\end{abstract}\n\\begin{keywords}\ncosmic microwave background - methods: data analysis - radio continuum: general - radiation mechanisms: thermal and non-thermal \n\\end{keywords}\n\n\\section{Introduction}\n\\label{intro}\nA small, but significant correlation of existing Cosmic Microwave\nBackground (CMB) data with maps of Galactic dust emission has been \ndetected. It is important to understand the origin, and hence the\ncharacteristics of any Galactic emission present in CMB maps with\nstructure on angular scales relevant to CMB measurements.\nWith such information, we can attempt to remove these contaminating\nemissions from the data, to be left with a pure CMB map. \n\nCross-correlating the COBE DMR maps with\nDIRBE far-infrared maps, Kogut {\\em et al} (1996a,b) discovered that \nstatistically significant correlations did exist at each DMR frequency, \nbut that the frequency dependence was inconsistent with vibrational dust \nemission alone and strongly suggestive of additional dust-correlated \nfree-free emission ($\\beta_{ff} = -2.15$). A number of recent microwave \nobservations have also shown that these \ncorrelations are not strongly dependent on angular scale. \nDifferent experiments ( DMR: Kogut et al. 1996b; 19GHz: de\nOliviera-Costa et al. 1998; Saskatoon: de Oliviera-Costa et al. 1997;\nMAX5: Lim et al. 1996; OVRO: Leich et al. 1997), together give, with\n$95\\%$ confidence, $-3.6 < \n\\beta_{radio} < -1.3$, consistent with free-free emission over the\nfrequency range 15-50~GHz. However if the source of this correlated\nemission is indeed free-free, it is expected that a similar\ncorrelation should exist between $H_\\alpha$ and dust maps. Several\nauthors have found that these data sets are only marginally correlated\n(McCallough 1997 and Kogut 1997). Thus, most of the correlated\nemission appears to come from another source. \n\nDraine and Lazarian (1998a,b) suggest that the correlated emission could\noriginate from spinning dust grains. This model predicts a microwave\nemission spectrum that peaks at low microwave frequencies, the exact \nlocation of the peak depending \non the size distribution of dust grains, \nand has a spectral index between\n-3.3 and -4, over the frequency range 15-50~GHz (Draine and Lazarian 1998b, \nKogut 1999).\n The spectral indices\nobtained from various experiments do not seem to conform too well to\nthe spinning dust model alone. However, recently de Oliveira-Costa\n{\\em et al}\n(1999) (hereafter DOC99) claim to have found evidence of the spinning\ndust origin of DIRBE-correlated emission using the Tenerife 10 and\n15GHz data. They find a rising spectrum from 10GHz to\n15GHz, which is indicative of a spinning dust origin, as opposed to a\nfree-free origin, for the dust-correlated Galactic foreground at these\nfrequencies. In this paper, we use the most recent Tenerife data to show\nthat the correlated emission is not necessarily indicative of spinning\ndust. \n\n\\section{The data and Galactic templates}\n\nTenerife is a double differencing experiment that takes data by drift\nscanning in right-ascension at each declination. Data are taken every \n$1\\deg$ in RA \nand at intervals of $2.5\\deg$ in Dec. We used the Tenerife\n10GHz and 15GHz data in the region, $32.5\\deg < $Dec$ < 42.5\\deg$, \nand $0\\deg < $RA$ <360\\deg$, with point sources subtracted and \nbaselines removed. The Tenerife experiment has beams of \nFWHM $4.9\\deg$ and $5.2\\deg$ for the 10 and 15GHz experiments \nrespectively, with a differencing angle of $8.1\\deg$ between east and \nwest positions on the sky to make up the final triple beam (Jones {\\em et al}\n (1998)).\n\nFigure 1 shows the patch of sky covered by the experiment in Galactic \nprojection. Figure 2 shows the dust data and the Tenerife data at \nall the five declinations where data have been taken. \nWe have extended the \nanalysis presented in Gutierrez {\\em et al} (1999) to also cover a region \noutside the high latitude range ($b>40\\deg$) that they use to \nconstrain CMB\nfluctuations. Therefore, the data we have used are different from \nthat used in DOC99 as they did not extend the coverage of the raw data\nprocessing to be outside this range. This is one of the reasons we would \nexpect \ndifferences between our results and those of DOC99. A great advantage of \nusing the Tenerife data to constrain the spectral index of the \ndust-correlated component lies in the fact that similar angular scales \nand the same patch of the sky can be used. This is not the case when the \ncorrelation from different experiments are compared. Therefore, we have \nnot used the two further declinations covered by the 15GHz data set \n(Decs $30\\deg$ and $45\\deg$), but not by the 10GHz data, avoiding any \neffect from features present in these declination strips. However, \nwe have redone the calculations using these extra declinations and there \nwas no significant difference with the results presented in this paper. \n\nWhen looking at Figure 2, a difference between the two sides of the \nRA range, at almost all declinations is apparent. \nThe rise (drop because of the double differencing) of the \nGalactic signal towards low Galactic latitude seen in the \nconvolved dust maps on both sides of the RA range is \nonly followed on one side by the \nTenerife data. The Tenerife Galactic signal shows a stronger Galactic \ncentre / anti-centre difference and a variation with declination which\nis different compared to the dust template with a particularly strong \nfeature at Dec $42.5\\deg$. \nAlso note that the noisier 10GHz \ndata show a wider spread toward low Galactic latitude, which does not \nappear systematically Galactic, at least when compared to the Galactic \ndust template. This may be due to a systematic error in the Tenerife\ndata that is not fully represented by the error bars. \n\nThe Galactic templates used are the destriped DIRBE+IRAS $100\\mu$m \ntemplate of \ndust emission (Schlegel, Finkbeiner and Davis 1998), the 408MHz \nsurvey of synchrotron emission (Haslam \net. al. 1981), and the 1420MHz survey of synchrotron emission (Reich \n$\\&$ Reich, 1988, hereafter $R \\& R$). We used the cleaned and \ndestriped versions of the synchrotron emission maps by Lawson, \nMayer, Osborne \\& Parkinson (1987). \n\n\\begin{figure}\n\\centerline{\\epsfig{\nfile=dirbemapforpaper.ps,width=7.7cm,angle=0}}\n\\caption{The Figure shows the patch of sky covered by the Tenerife\nexperiment in black, overlayed on the DIRBE template (smoothed to\n$5\\deg$) to show the position of the Galactic plane.}\n \\label{fig:plot1}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfig{\nfile=figure2_recomp.ps,width=7.cm,angle=0}}\n%file=alldata.eps,width=8.5cm,height=10cm,angle=0}}\n\\caption{The figure shows the Tenerife and dust data in the RA \nrange that lies above the Galactic cut \nof $b>20\\deg$, for all five declination strips. The filled \ncircles and the dashed line represent the Tenerife 10GHz data, \nthe empty circles and thin solid line represent the 15GHz \ndata. The data have been binned every 5 points in RA. The \ncorresponding $1\\sigma$ error bars are shown. Units are mK. The thick solid \nline is the $100\\mu m$ data convolved with the Tenerife\nbeam. This data has been plotted in units of \n$0.13\\times 1$ MJy/sr.}\n\\label{fig:plot2} \n\\end{figure}\n\n\\section{Correlation analysis and results}\n\\subsection{The method}\n\nAssuming that the microwave data consist of a super-position of CMB,\nnoise and Galactic components, we can write \n$$y = aX + x_{CMB} + n.$$ \nHere $y$ is a data vector of $N$ pixels, $X$ is an $N\\times M$ \nelement matrix \ncontaining $M$ foreground templates convolved with the \nTenerife beam, $a$ is a vector of size $M$ that represents \nthe levels at which \nthese foreground templates are present in the Tenerife data,\n$n$ is the noise in the data and $x_{CMB}$ is due to the CMB \nconvolved with the\nbeam. The noise and CMB are treated as uncorrelated. \n\nThe minimum variance estimate of a is\n$$ \\hat{a} = [X^{T} C^{-1} X]^{-1} X^{T} C^{-1} y,$$\nwith errors given by $\\Delta \\hat{a}_i = \\Sigma_{ii}^{1/2}$ \nwhere $\\Sigma$ is given as,\n$$ \\Sigma = <\\hat{a}^2> - <\\hat{a}>^2 = [X^{T} C^{-1} X]^{-1}. $$\n$C$ above is the total covariance matrix (the sum of the noise\ncovariance matrix and the CMB covariance matrix). The noise\ncovariance matrix of the Tenerife data is taken to be diagonal, and\nthe CMB covariance matrix is obtained through Monte-Carlo simulations\nwith 10000 CMB realizations (this can of course be found analytically\nas well, as in DOC99). In all the above equations\n$X$ and $y$ are actually deviations of the corresponding quantities\nfrom the weighted mean with weights\\footnote{\\small{We have tried \na variety\nof different weighting schemes, including uniform\nweights, to check our method and all results found were within the\n$68\\%$ confidence limits of those presented in the paper.}}\ngiven by $C^{-1}$ (this is \ndifferent to DOC99 who use the actual $X$ and $y$ in the analysis). \nIt should be noted that there may be other components of emission \npresent in the data so that \nthe errors we consider here are only lower limits. Also, the templates\nthat we are using may not be perfect and we do not account for\npossible uncorrelated structure in $C$. If there are other\nnon-Gaussian components present in the data then the minimum variance\nestimate of $a$ will be incorrect. \n\n \n\\subsection{Results}\n\nListed in Table 1 are the correlation coefficients obtained for\nthe Tenerife data sets and the $100\\mu m$ DIRBE template, the Haslam,\nand the $R\\& R$, with each Galactic template taken individually.\nTable 2 shows the correlation coefficients obtained when fits\nare done for two templates jointly. The DIRBE and Haslam correlations\ncorrespond to joint $100\\mu m$-Haslam fits, whereas the $R\\&R$ values\ncorrespond to joint $100\\mu m-R\\&R$ fits. $\\Delta T= (\\hat{a}\\pm \\Delta\n\\hat{a})\\sigma_{Gal}$ is the amplitude of fluctuations in temperature in\nthe Tenerife data, that results from the correlation ($\\sigma_{Gal}$\nbeing the $rms$ deviation of the template map). The analysis is done\nfor different Galactic cuts. Only positive Galactic latitudes are\nused in these tables as the Tenerife data do not extend below\na $b$ of $-32\\deg$. \n\nFrom Table 1, we see that correlations with each of the three\ntemplates are detected with high significance. However these\ncorrelations fall off in significance towards higher Galactic\nlatitudes. For comparison, the {\\em rms} of the 10GHz data (after\nsubtracting noise) for $b > 20\\deg$ is $181\\pm 9\n\\mu K$ (the error is due to a \n$5\\%$ calibration uncertainty). If the templates are not significantly\ncorrelated with each other, one would conclude that 40\\%\nof the signal at 10~GHz is Galactic emission from Table 1. \nIt should be noted that the correlation between the DIRBE and Haslam\nGalactic templates is significant for all Galactic cuts although if the\ndust and free-free emissions (or spinning dust) are 100\\% correlated then\nthe Galactic emission would still only account for 50\\% of the total\nemission (assuming that all of the Galactic foregrounds present at this\nfrequency are present in either the Haslam or DIRBE templates).\n\nWe also see that the DIRBE-correlated component has slightly higher \nsignificance\nthan the Haslam or $R\\&R$-correlated components near the Galactic\nplane for both the data sets. Away from the Galactic plane, at 10~GHz,\nthe component correlated to the Haslam map becomes dominant \n(for $b > 20\\deg$) whereas at 15~GHz\nthe DIRBE component remains dominant. However, there is almost no significant\ncorrelated emission beyond this Galactic cut. \n \n\\subsection{Discussion}\n\nIt is seen from Table 1 that individual correlations with dust\ndo not show a rising (spinning dust) spectrum with significance\nbetween 10 and 15~GHz for any Galactic cut. From the joint $100\\mu m -\nHaslam$ correlations (Table 2), we see that it appears as if there is \nsome evidence for a rising spectrum of dust-correlated emission only\nfor the $b > 20\\deg$ cut (as reported by \nDOC99). Spectral indices inferred from the correlation coefficients are listed\nin Table 3. Errors are small close to the Galactic plane.\nHowever, the values do not consistently agree with the spectral \nindices of any one of the three Galactic emission components,\n -2.8 for synchrotron, -2.1 for\nfree-free and positive for spinning dust, for example +1 \nif the peak is at 20 GHz, that could be expected to be present \nas contaminating emissions in CMB data. \n\nFrom Table 3 we see that the value of the spectral index inferred from\nthe DIRBE-correlated component at 10 and 15~GHz is negative for most\nGalactic cuts (the correlations for $b>30\\deg$ and $b>40\\deg$ are not\nsignificant, so it was not possible to infer a spectral index\\footnote{\\small{\nNo significant correlations were obtained even for the $b>25\\deg$ cut, \nindicating that only a small region near $b$~$20\\deg$ Galactic latitude is \ncorrelated.}}).\nFrom the positive value of the spectral index for $b > 20\\deg$ DOC99\nconclude that spinning dust is responsible for producing the major\npart of the DIRBE-correlated emission. However, since the \nspectral indices inferred for all other Galactic cuts are negative, \na specific model of the spatial distribution of spinning dust would \nbe required to explain the data. On the other hand it could also \nbe that in the $b$-range where the Galactic signal in the Tenerife \ndata drops the estimation of the spectral index becomes more sensitive \nto systematic effects we have not accounted for. To decide this we \nfocus in on the $b > 20\\deg$ range and divide the data further. \nIt should be noted that these spectral indices were found \nusing the values for $\\hat{a}$ and not\n$\\Delta T$ as the beam sizes between the 10 and 15GHz data sets are\nslightly different giving rise to a lower expected $\\Delta T$\n(although the same relative level of contamination and hence $\\hat{a}$) \nat 15~GHz than at 10~GHz which would systematically bias the values\nobtained. \n\nWhen we examine the spectral indices obtained from the component \ncorrelated to the Haslam map at the two frequencies, we find that the\nvalues from the individual analysis are less negative than \nexpected for synchrotron emission (Table 3).\nJoint correlation of the $100\\mu$m dust and Haslam maps with\nthe data result in spectral indices that are steeper than expected\nfor synchrotron. This seems to imply that most of the emission in the 15GHz \ndata that is\n correlated with the Haslam map is also correlated with the DIRBE maps (this \nis expected as the region that correlates lies close to the Galactic plane), \nleading to a much lower value of $\\hat{a}$ for the synchrotron-correlated\n component than expected at 15GHz (and hence a much steeper spectrum). \nThis may simply be because dust-correlated \nemission is more significant in the 15GHz data. Similarily since the Haslam\n-correlated emission is more significant at 10~GHz, the joint correlation \nmethod gives a lower value of $\\hat{a}$ for the dust-correlated component and\n a correspondingly higher value for the synchrotron-correlated component.\n Being able to correct for this effect might therefore sort the systematic \ndiscrepancy. However, since we see this discrepancy with the synchrotron \nspectral index we should be wary of the dust template correlation as well. \n\nIf we now consider the DIRBE template to be an exact predictor for either\nspinning dust or free-free emission (so that all the features present\nin this template are present in the Tenerife data; as we are assuming\nwhen performing the correlation analysis) then the level of\n`contamination' $a$ will be independent of the region tested. This\nmeans that each value of $a$ in Table 1 should be the same for\nthe 10 and 15GHz data respectively. We can therefore take the variance\nof $a$ across the different regions analysed as a measure of the error\nin this method, and find that weighted mean and rms \nat 10~GHz and 15~GHz are 157 (20) and \n122 (10) $\\mu$K / (MJy sr$^{-1}$) respectively. This would correspond\nto a spectral index of $-0.6^{+0.5}_{-0.5}$.\n\n\\subsection{Further study of the $b > 20\\deg$ cut region}\n\nWe now divide the data into halves in RA, which gives two regions, \none towards the Galactic centre and one towards the Galactic \nanticentre, at each declination. Repeating our analysis on these \ndata we quantify the visual impression from Figure 2. \nAlthough the rise of the Galactic plane signal is equally strong in both \nregions of the dust template, we only find a significant correlation \nwith the 10 and 15GHz data in the Galactic centre region, in spite of the fact \nthat the noise errors in both regions are comparable.\nThe results of this analysis are listed in table 4. \nIt is seen that of the five declination \nstripes in the centre region only the three \nat higher declination are significantly correlated. \nThe anticentre regions are found to be uncorrelated or even \nsignificantly anticorrelated in two stripes, \nwhich again demonstrates that the structure is not correlated \nrather than that our sensitivity is reduced when dividing the data. \nAgain if we take the weighted mean and rms \nin the value of $a$ between declinations, we get \n197 (66) and 157 (91) $\\mu$K / (MJy sr$^{-1}$) \nfor the centre regions at 10 and 15~GHz respectively, \ngiving a spectral index of \n$-0.6^{+2.2}_{-2.8}$. The variation between declinations \nis high and the spectral index thus obtained is consistent \nwith both free-free and spinning dust models.\n\nWe perform yet another split of the data in an attempt to identify \nthe region where the correlation mainly comes from. It was found \nthat the 20 pixels at lowest Galactic latitude of \nall declinations taken together (100 pixels) gave \nsignificant correlations, while the remaining pixels (750) gave \nno correlation (see table 5). Again the spectral index for \ndust-correlated emission is small and negative, while that \nfor emission correlated to the Haslam map is steeper than expected. \nSince it is clear that the different \ndeclinations correlate differently, correlating them together is incorrect. \nHence, shown also in table 5 are the values obtained for the \nsame analysis on the 20 pixels at lowest Galactic latitude of each \ndeclination. Even though the signal to noise is much lower here, \nit is clear that the Galactic plane signal correlates with a free-free \nlike spectral index while the rest of the pixels shows a significant \nanti-correlation with dust at 10~GHz for some declinations. The Galaxy \ncorrelates positively while the remaining regions correlate \nnegatively or insignificantly. It is clear from analysing \nsuch splits that the correlation coefficients obtained when taking \nall declinations together as in tables 1 \\& 2 ($b>20\\deg$) and in table \n4 \\& 5, and \nwhich seem to indicate an almost flat or less negative spectral index \nbetween 10 and 15~GHz, are composed of regions that correlate \nwith a negative spectral index and regions that do not correlate \nsignificantly at all. The anti-correlation, which \noccurs mostly in the 10GHz data, lowers the combined best fit $a$ \nvalue at that frequency, and hence raises the spectral index of \ndust-correlated emission. \nNote here that the high values of 'a' obtained need not to be in \ncontradiction to the level of free-free allowed \nby H$_\\alpha$ as the detections are all close to the Galactic plane, \nwhere the level of free-free is expected to be high. \nWe still see a large variance between the three declinations \nwhich correlate significantly. If we take the\nweighted mean and rms of the highest three declinations\nas indicative of a composite correlation, we get 313 (172) \nand 219 (83) $\\mu$K / (MJy sr$^{-1}$) at 10~GHz and 15~GHz respectively,\n giving a spectral index of $-0.9^{+2.8}_{-2.2}$, again consistent\nwith both free-free and spinning dust. Note that this value was obtained \nfrom the weighted average of three pairs of numbers shown in table 5, \nwhere each pair indicated a negative spectral\nindex. The spectral index obtained simultaneously for the component \ncorrelated to the Haslam map is consistent within 1~$\\sigma$ with the \nsynchrotron spectral index. \n\nGiven that the dust templates correlate with the data only in a small \npart of the Tenerife patch above $b = 20\\deg$ we further \ntest, how physically meaningful the detection is. This is important \nbecause the spectral index of a component in this method is inferred \nby assuming that the difference in the correlation amplitude between the \nfrequencies is solely due to the change of emissivity of a single \nphysical component and is not due to a spurious change in the strength \nof the correlation. \n\n\\section{Sky rotations}\n\nAnother way to test for systematic errors in the method is to \ntake random samples from the Galactic templates themselves as \n\"Monte Carlo\" simulations. The advantage is that we can test \nagainst chance correlations with typical structure in the templates \nwithout having to understand the templates to a degree that would \nallow us to model this structure. Since the rise of the signal towards \nthe Galactic plane clearly is a strong feature in the data and \nhigh Galactic latitude correlations are at best weak, we correlate \nto rotated / flipped maps in the northern and southern hemispheres, \nwhich all have the same orientation relative to the Galactic plane. \nFigure 3 shows $\\hat{a}$ and its significance for 10 and 15~GHz, for \nthe $b = 20\\deg$ Galactic cut, the Galactic centre region of all declination\n strips taken together, \nand the spectral indices derived from these values. We find that the \nreal patch does not correlate most significantly at either frequency. \nGiven the number of patches that correlate more significantly we \nconclude that the real correlation is at most typical and only \ndue to the Galactic plane signal. Further we see \nthat the 15~GHz real correlation although less \nsignificant than the neighbouring points has a higher value of \n$\\hat{a}$. It seems that the real dust patch, although it does not \nrepresent the observed 15~GHz structure particularly well, \nhappens to produces a high correlation amplitude. Indeed the \nreal dust patch shows no strong features (low intensity rms), \nwhich explains the weak correlation and results in an overestimate \nof $\\hat{a}$ at 15~GHz. An interesting point is that the mean \nspectral index which could be interpreted as the spectral index \nderived from correlations to typical Galactic plane dust signals, \ncorrelations which are about as significant as the real correlation, \nhas a value of $-1.5\\pm 1.2$, well consistent with free-free emission.\nThe $rms$ variation in the value of the correlation coefficient at \n10 and 15~GHz can be taken as an estimate of the error in $\\hat{a}$ for \nthe real patch. The error estimates obtained in this way range from about\n $20\\%$ for $a$\n at both 10 and 15~GHz for the $b>0$ Galactic cut, to $64\\%$ and $30\\%$\n at 10 and 15~GHz respectively for the Galactic centre regions in the $b>20$ \nGalactic cut. As expected, the errors from sky-rotation increase with \ndecreasing signal and size of the region and are very large \nfor the individual declinations. Note that the lower Galactic cuts give the \nhighest correlation with the highest significance for the real patch \nshowing that the correlations there are not just due to aligned structure \nof the typical Galactic plane. The error estimates presented in this section\nare similar whether we include or exclude the rotated patches near the \nGalactic centre and anti-centre, where significantly different \nstructure could be expected, though in the first case errors increase \nslightly for both 10 and 15~GHz. Henceforth we use results corresponding to \nthe second case. \n\nSince we have strong indication that the correlations between \ndust and the Tenerife data results only from the Galactic plane \nsignal which will be similarly present in many \nphysical components of Galactic emission we further investigate \nthis particular feature of spatial distribution by modelling it \nin the next section. \n\n\\begin{figure}\n\\centerline{\\epsfig{\nfile=skyrots2.eps,width=7cm,height=9cm,angle=0}}\n\\caption{The top four panels show the correlation coefficients and \ntheir significances when the 10 and 15~GHz data are correlated with \ndifferent rotated patches of the dust template. These are joint \ncorrelations of the centre regions of all declinations combined, when the \nHaslam map is held fixed. The bottom panel shows the corresponding \nspectral indices. The first point in each panel corresponds to the real \npatch.}\n\\end{figure}\n\n\\section{Galaxy modelling}\n\nA problem with the interpretation of the correlation results\nat different frequencies purely as a spectral dependence is that it\nneglects the possibility of variations in the shape of the Galaxy\ndue to different components at different frequencies, and the resulting \nchange of spatial alignment. \nFor example, this method for obtaining the spectral index of correlated \nemission does not take into account the varying extent of the galaxy \nin the different data sets and template maps, so that the errors that \nwe are quoting in the above tables might be too small and could be \nsystematically wrong. If the Galaxy has a different spatial extent at \n10~GHz, 15~GHz and 3~THz ($100~\\mu$m), it will result \nin a higher or lower value for the overall correlation coefficient\nthan is actually the case. We investigate this effect by modelling\nthe spatial distribution of Galactic emission in the next section. \n\n\\begin{figure}\n\\centerline{\\epsfig{file=fwhm_3740_witherrors.eps,height=3cm,angle=0}}\n\\caption{The Figure shows the FWHM of the Gaussian model for the Galaxy \nthat gave the most significant correlation (or minimum $\\chi^2$) plotted \nagainst the different data sets for the $b > 20\\deg$ Galactic cut and \nfor Dec 40.0 (triangles) and Dec 37.5 (squares). \nThe model was correlated with the Galactic centre regions of the data only.}\n\\end{figure}\n\n\\begin{figure*}\n\\centerline{\\epsfig{\nfile=fittings10.eps,height=4.5cm,width=15cm,angle=0}}\n\\caption{Fitting the structure in the Tenerife data with the Gaussian model \nand the Galactic templates. Examples are shown for the 10 GHz data \nat Dec 42.5: (a) shows the best fit Gaussian model to the \ndata and residuals \n(b) shows the Haslam (dashed) and dust (dotted) templates with amplitudes \nfrom the joint fit result and the thick dot-dashed line is the \nsum of the two \n(c) an equally acceptable fit, given the goodness of fit, is achieved \nwhen the spectra are normalised with the amplitudes of the templates \nat 15 GHz and are constrained to free-free and synchrotron spectral \nindices.} \n\\end{figure*}\n\\begin{figure*}\n\\centerline{\\epsfig{\nfile=fittings15.eps,height=4.5cm,width=12cm,angle=0}}\n\\caption{The Gaussian model (a) and the joint fit result (b) \nfor the 15 GHz data at Dec 42.5} \n\\end{figure*}\n\nA significant correlation between the Tenerife data and the\nDIRBE dust template only occurs close to the Galactic plane where\nthere is a rise in the overall Galactic signal. This rise may be frequency\ndependent if different physical components are present (for example\nfree-free and synchrotron) so that care must be taken when comparing \ncorrelation results between different frequencies. \nWe take a simple model of the Galaxy \n$$S(b)=S_\\circ \\exp\\left(-{b^2 4 \\ln2 \\over FWHM^2}\\right)$$\nwhere $b$ is the Galactic latitude, $S$ is the amplitude and $FWHM$ is\nthe full width half maximum of the Gaussian model for the Galactic plane. \nThe value of $S_\\circ$ is arbitrary as \nit will only scale the estimate for $a$ for the various correlation\nresults and not affect the relative value between models with different \nwidth. Each model is then convolved with the appropriate\nexperimental beam, and correlated with the data, while varying FWHM. \n\nFigure 4 shows the widths of the Galactic models which correlated best with \nthe data and the Galactic templates for the two declination strips \nin the centre region which do show convincing correlation. Two strips \nshowed no significant correlation between the data and the templates, \nand Dec $= 42.5\\deg$ has the strong feature at 10~GHz, which is also \nincompatible with the templates. It can be seen that the most significant\ncorrelation between the dust/Haslam template and the model occurs with \nGalactic models of different sizes (FWHM), which are also different \nfrom the sizes obtained for the 10 and 15GHz data. However there seems to be a \nclear trend of decreasing width with increasing frequency compatible \nwith more synchrotron emission at 10~GHz and more dust-correlated \nstructure at 15~GHz. The combined fit to all declination stripes \nsimultaneously also shows this expected trend of increasing Galactic \nwidth with wavelength. If this systematic change is real we might \nbe able to fit for two distinct components with different width and \nspectral index. Although our fits of a single Gaussian component are \nall well acceptable the quality of the data is however not good enough \nto fit for two such components, if they are \npresent independently of templates.\n\nIn Figure 4 the points for the dust correlations lie closer to the \n15~GHz points than to the 10~GHz points, implying a better match of \nthe Galactic shape for 15 GHz. When correlating the dust template to \nthe data, the significance of any correlation will drop and $\\hat{a}$ will \nchange systematically, because the structure at each frequency is \ndifferent. When correcting for this mismatch, assuming that the correlated \ncomponent we are looking for has identical appearance at any frequency, \nwe find that the correlation amplitudes for both 10 and 15 GHz shift \nupwards. However the 10 GHz amplitude, because of the larger difference \nin size with dust, gets a larger shift, which results in a drop of the \nspectral index for the dust-correlated emission by typically about 0.2. \nTaking this effect of mismatched structure into account for the Haslam \ncorrelations results in a less steep spectral index, which is more \nconsistent with synchrotron emission.\n\nWhen we subtract the best fitting Galactic models from the data and the \ntemplates no correlations remain between the residuals, neither between \nthe data and the templates nor between the templates, showing again that \nany correlation is only due to the Galactic plane signal, which we are \nable to model. Figure 5 shows these best fit models for the 10 and 15GHz \ndata, for Dec 42.5, and the residuals. The fit achieved by the single \ncomponent Gaussian model is indeed good and in fact better than the joint \ncorrelation fit, which we show for comparison. Further we find that since \nthe joint fit to the 10 GHz data is rather poor in terms of goodness of fit, \nsynchrotron and free-free components with the expected spectral indices\n (-2.8 and -2.1) can be \nfitted with an almost similar goodness of fit, based on the reduced $\\chi^2$. \nWhen the same is done for the other declinations the goodness of fit \nis generally better for both the joint fit as well as the model fitting. \nFurther in the other declinations also we generally find equally \nacceptable fits for a dust-correlated component which is constrained \nto give a free-free spectral index. \n\n%\\onecolumn \t\t\n\n\\section{Template errors}\n\nAnother yet unaccounted source of error is an intrinsic error in the \ndust template itself, which can be instrument noise or data reduction \nerrors due to point source subtraction etc., but also systematic variations \nin the dust emissivity, which might not be followed in the same way by the \ncomponents at 10 and 15~GHz. Note that the DIRBE maps at different frequencies \nare correlated with each other to not more than $95 \\%$. If we assume that \nthere is a $5\\%$ Gaussian error in the flux at $100~\\mu$m due to these errors \nwe can model this effect to quantify any change that would occur in the \ncorrelation. To do this we added a $5\\%$ error in the flux (on the Tenerife \nangular scales) to the maps and calculated the new values of $a$. \nWe performed 300 Monte-Carlo simulations and found that there was \na systematic drop in $a$ for the 10 and 15~GHz data by factors of \n$1.6$ and $1.4$ respectively, when the centre regions of all declinations \nwere taken together for the $b>20\\deg$ cut (similar values are obtained when \nthe entire $b>20\\deg$ region is taken). Turning this effect around for\n the real data, assuming \nthat there is an intrinsic $5\\%$ error present in the template map, we need \nto increase the values of $a$ given in the tables by these factors. The \nvalue of $a$ at 10~GHz has to be increased relative to 15~GHz, which results \nin a significantly steeper spectral index, again more consistent with \nfree-free emission. However, it should be noted \nthat we do not have error maps for the templates at present and thus in this current paper we have not attempted a quantitative evaluation of this effect\nPresumably template errors, given that we have an\n idea of the likely causes, will be greater towards the Galactic plane. \nSince we have found that the only correlations we have to report result for \npixels close to the Galactic centre, this will be an important source of \nsystematic error.\n\n\\section{Conclusions} \n\nSpinning dust emission can be identified and discriminated from free-free \nemission {\\em if} indications for a peak in the emission spectrum can be found \nat low microwave frequencies, which are probed by the Tenerife experiment. \nA rising spectrum between 10 and 15~GHz can be taken as a prediction of \nthe spinning dust hypothesis, although the exact location of the emission \npeak depends on details of the model. Tentative evidence for a turnover in the \nspectrum of the Galactic dust-correlated \nmicrowave component between 10 and 15~GHz has been presented by DOC99. \nWe however find that the spectral index of dust-correlated emission is \nnegative for all Galactic cuts \nexcept for the $b > 20\\deg$ cut. The Galactic signal, and with it the \nsignificance of the correlation, decreases with increasing Galactic latitude, \nand no correlations are detected in the higher Galactic latitude regions of \n$b > 30\\deg$. The variance in the value of $\\hat{a}$ between \nregions with different Galactic cuts is rather large.\nWe further find that the correlation detected in the $b> 20\\deg$ region\ncomes only from a small number of pixels at low Galactic latitude and \ntowards the Galactic centre, where signal from the Galactic plane is \npresent. This correlation shows a free-free like spectral index, whereas \nthe rest of the region was found to be uncorrelated, or even significantly \nanticorrelated. \n\n%A systematic effect arises due to the presence of significant correlation \n%between the dust and Haslam templates close to the Galactic plane.\nUsing sky rotations we show that the correlation we see at $b > 20\\deg$ \nis only an alignment of structure due to the rise of the Galactic plane \nsignal. Employing a simple model for this structure we were able to \ndemonstrate that the spatial distribution of Galactic emission is in fact \ndifferent in the templates and in the data, giving rise to a systematic \nerror. We were also able to show that \nthis simple model of the Galaxy fits the data generally \nbetter than the templates. \nFurther, modelling a Galactic free-free component, which correlates with the \ndust template, generally yields an equally acceptable fit to the data. Another \nsignificant systematic effect arises due to intrinsic errors in the \ntemplates, and all these effects cause a misleading increase in the \ninferred spectral index of the dust-correlated component between 10 and \n15~GHz. \n\nA comparison of our results with \nother experiments is presented in Figure 7. Here the data points for the \nTenerife experiment, obtained by taking a weighted \naverage of all detections (all regions of all Galactic cuts, joint analyses)\n with errors taken from the sky rotations, correspond\n to values of $180\\pm47$ and $123\\pm16$ $\\mu$K /MJy sr$^{-1}$ at 10 and 15~GHz \nrespectively.\nNote that the 10GHz point on the plot is significantly higher, as compared to \nthat plotted in DOC99 and the value quoted in our table 2\nThis is because this region consists \nof parts that are correlated as well as parts that do not correlate or even \nanticorrelate, as in the case of the 10GHz data. Here, since we are \n focussing only on the regions that correlate (these regions are the same for \nboth 10 and 15~GHz data and have been found \nto lie close to the Galactic plane), the value is significantly higher. \nNote that the high values of $a$ that we get need not be in \ncontradiction to the typical level of free-free allowed by \n$H_{\\alpha}$ maps of other regions as our \ndetections are close to the Galactic plane, where the level of Galactic \nemission is expected to be high. \n\n\\begin{figure}\n\\centerline{\\epsfig{\nfile=spectra.eps,height=8cm,width=8cm,angle=0}}\n\\caption{Summary of our results on the dust-correlated (top panel) and \nsynchrotron-correlated (bottom panel) emission compared to results from other \nexperiments (COBE DMR-filled circles, 19GHz-empty triangle, OVRO-filled \ntriangle, Saskatoon-filled square). The straight lines \nrepresent synchrotron (solid), free-free (dotted) and vibrational dust \n(dashed) spectral indices. The thick solid curve shows a combination of \nfree-free emission with a small spinning dust contribution with a peak at \n15 GHz in an attempt to fit all \nthe data. This fit appears acceptable, as does the single free-free \ncomponent fit, but it should be kept in mind that the data from different \nexperiments might not be directly comparable, since they were taken on \ndifferent angular scales and towards different regions of the sky. The \nTenerife data points are an average derived from our various results, see text\n for details.} \n\\end{figure}\n\nThe spectral index for dust-correlated emission as \ndeduced from the 10 and 15 GHz points is less negative (by about $1\\sigma$) \nthan expected for free-free emission. \nThe spectral index deduced simultaneously from \nsynchrotron-correlated emission is systematically steeper than expected. \nThis could be attributed \nto the effects that we have identified \n and which have all been shown to influence the correlation in the \nsame direction. Note also that in this plot only the Tenerife and \nCOBE DMR points, at different frequencies, each represent data which \nprobe the same angular scales and were taken with the same sky coverage. \nInferring a spectral index by comparing different experiments assumes \nthat the Galactic component is traced by a given fixed template and \ndoes not depend on parameters which vary over the sky, but our analysis \nof the Tenerife data shows large variations of Galactic correlation \nwith the sky region. \n\nWith the present analysis of Tenerife data we are not \nable to make a firm claim about the origin of the dust-correlated component, \nsince we do not find convincing support for a spinning dust component. \nThis does not have to rule out this hypothesis, since \nenvironmental conditions or grain sizes, \nwhich affect the position of the \nspectral peak, could change systematically \nwith location on the sky, particularly in the transition region between low \nand high Galactic latitude. The spatial variation in the correlation \namplitude and the possibility of the presence of some spinning dust emission \nalong with free-free emission need to be dealt with. \nThe separation task is difficult for two reasons. Firstly neither \nthe frequency dependence nor the spatial distribution of any of the Galactic \ncomponents at low microwave frequencies is particularly well known. And further\n we would expect these components to be correlated, since we find their\n templates to be correlated, at least at low Galactic latitudes.\nThe combination of the results from the other experiments, shown in Figure 7, \nmight not be strongly constraining, but nevertheless, does \nnot give conclusive evidence for spinning dust emission either, without \nan expectation of the amplitude of free-free emission based on dust-correlated \nH$_\\alpha$ emission. \n\nIn order to make more reliable inferences, a pixel by pixel separation\nof components would have to be performed, using the Maximum Entropy\nmethod for example. In a forthcoming paper we shall perform such a\nseparation incorporating information about spinning dust. \nAlso, including other data at frequencies lower than 10~GHz and adding\nother templates of Galactic emission such as the $H_\\alpha$ maps from\nthe Wisconsin H-Alpha mapper (Tufte, Reynolds and Haffner 1998)\nwould be useful.\n\n\\section*{Acknowledgements} \n\\label{lastpage}\n\nWe wish to thank all the people involved in taking the Tenerife\ndata set, and Juan Francisco Macias-Perez for useful comments.\n PM acknowledges financial support from the Cambridge Commonwealth Trust. \nAWJ acknowledges King's College, Cambridge for support in the\nform of a Research Fellowship. RK acknowledges support from an EU\nMarie Curie Fellowship. \n\n\n\n\\begin{thebibliography}{99}\n\n\\bibitem{deOliviera97}\nde Oliviera-Costa, A. et al. 1997, ApJ, 482, L17\n\\bibitem{deOliviera98} \nde Oliviera-Costa, A. et al. 1998, ApJ, 509, L9\n\\bibitem{deOliviera99} \nde Oliviera-Costa, A. et al. 1999, Submitted to ApJ (astro-ph/9904296) (DOC99)\n\\bibitem{draine98a}\nDraine, B.T., and Lazarian, A. 1998a, ApJ, 494, L19\n\\bibitem{draine98b}\nDraine, B.T., and Lazarian, A. 1998b, ApJ, 508, 157\n\\bibitem{gutierrez99}\nGutierrez, C.M. et al. 1999, astro-ph/9903196\n\\bibitem{haslam81}\nHaslam, C.G.T., et al 1981, $A\\&A$, 100, 209\n\\bibitem{Jones98}\nJones, A.W. et al. 1998, MNRAS, 294, 582\n\\bibitem{kogut96a}\nKogut, A. et al. 1996a, ApJ, 460, 1\n\\bibitem{kogut96b}\nKogut, A. et al. 1996b, ApJ, 464, L5\n\\bibitem{kogut97}\nKogut, A., 1997, AJ, 114, 1127\n\\bibitem{kogut99}\nKogut, A., 1999, in Microwave foregrounds, ed.A. de Oliviera-Costa and M. \nTegmark, in press, (astro-ph/9902307)\n\\bibitem{bib:lawson}\nLawson, K.D., Mayer, C.J., Osborne, J.L. \\& Parkinson, M.L. 1987,\nMNRAS, 225, 307\n\\bibitem{leich97}\nLeitch, E.M., et al. 1997, ApJ, 486, L23\n\\bibitem{Lim96}\nLim, M.A., et al. 1996, ApJ, 469, L69\n\\bibitem{mccullough97}\nMcCullough, P.R. 1997, AJ, 113, 2186\n\\bibitem{Schlegel98}\nSchlegel, D.J., Finkbeiner, D.P. and Davis, M. 1998, ApJ, 500, 525\n\\bibitem{tufte98}\nTufte, S.L., Reynolds, R.J. and Haffner, L.M. 1998, ApJ, 504, 773\n\\end{thebibliography}\n\n\n%\\onecolumn\n%\\begin{table}\n%\\begin{center}\n% {\\small\n%\\caption{The following table shows the correlation coefficients $\\hat{a}\\pm \\Delta(\\hat{a})$ obtained when only the Galactic centre half of the data at Dec $42.5$ was correlated with dust, and when the Galactic centre half of all the declinations together was correlated with dust. At Dec $42.5$ there seems to be a strong synchrotron feature. Also note that the value of $\\hat{a}$ changes lot between declinations. Though all the declinations are not shown here, the variance in $\\hat{a}$, for correlation with dust, between declinations is large. See text.}\n%\\label{tab:table_zero} \n%\\begin{tabular}{|c|c|c|c|c|c|} \\hline\n%\\multicolumn{2}{c}{} & \\multicolumn{2}{c}{10GHz} &\n%\\multicolumn{2}{c}{15GHz} \\\\ \\cline{3-6}\n%region & & $with dust$ & $with haslam$ & $with dust$ & $with haslam$\\\\ \\hline\n%DEC 42 & individual & $1016\\pm 72$ & $382\\pm 20$ & $437\\pm 36$ & $143\\pm 12$\\\\[-0mm]\n%centre & joint & $225\\pm 95$ & $341\\pm 27$ & $261\\pm 55$ & $78\\pm 18$ \\\\ \\hline\n%all DECs & individual & $307\\pm 29$ & $110\\pm 8$ & $213\\pm 18$ & $47\\pm 6$\\\\[-0mm]\n%centre & joint & $160\\pm 33$ & $89\\pm 9$ & $182\\pm 22$ & $27\\pm 7$ \\\\ \\hline\n%\\end{tabular}\n%}\n%\\end{center}\n%\\end{table}\n\n\\onecolumn\n\\begin{table}\n\\begin{center}\n {\\small\n\\caption{Individual correlations for the Tenerife data. $\\hat{a}$ is the\ncorrelation coefficient, and has units $\\mu K(MJy/sr)^{-1}$ for the\n$100\\mu$m template, and $\\mu K/K$ for the Haslam and $R\\&R$ templates.}\n\\label{tab:table_one} \n\\begin{tabular}{|c|c|c|c|c|c|} \\hline\n\\multicolumn{2}{c}{} & \\multicolumn{2}{c}{10GHz} &\n\\multicolumn{2}{c}{15GHz} \\\\ \\cline{3-6}\nb & Template & $\\hat{a}\\pm \\Delta(\\hat{a})$ & $\\Delta T \\mu K$ & $\\hat{a}\\pm \\Delta(\\hat{a})$\n& $\\Delta T \\mu K$ \\\\ \\hline\n$b > 0\\deg$ & $100\\mu m$ & $214\\pm 0$ & $6435\\pm 13$ & $119\\pm 0$ & $3430\\pm 6$ \\\\[-0mm]\n & Has & $591\\pm 1$ & $5850\\pm 12$ & $333\\pm 1$ & $3189\\pm 6$ \\\\[-0mm]\n & $R\\&R$ & $26140\\pm 64$ & $4684\\pm 11$ & $14176\\pm 33$ & $2476\\pm\n5$ \\\\ \\hline\n\n$b > 5\\deg$ & $100\\mu m$ & $209\\pm 1$ & $3127\\pm 10$ & $123\\pm 0$ &\n $1770\\pm 5$ \\\\\n & Has & $545\\pm 2$ & $2617\\pm 9$ & $323\\pm 1$ & $1502 \\pm 4$ \\\\\n & $R\\&R$ & $17324\\pm 86$ & $1773\\pm 9$ & $10790\\pm 41$ & $1077\\pm 4$ \\\\ \\hline\n\n$b > 10\\deg$ & $100\\mu m$ & $268\\pm 1$ & $1918\\pm 11$ & $136\\pm 1$ & $967\\pm 4$ \\\\[-0mm]\n & Has & $431\\pm 3$ & $1422\\pm 9$& $259\\pm 1$ & $839\\pm 4$ \\\\[-0mm]\n & $R\\&R$ & $13209 \\pm 98$ & $1079\\pm 8$& $8654\\pm 47$ & $692\\pm 4$ \\\\ \\hline\n\n$b > 15\\deg$ & $100\\mu m$ & $259\\pm 9$ & $199\\pm 7$& $132\\pm 4$ &$106\\pm 3$ \\\\\n & Has & $142\\pm 5$ & $161\\pm 6$ & $81\\pm 3$ &$90\\pm 3$ \\\\ \n & $R\\&R$ & $4727\\pm 148$ & $207\\pm 6$& $2883\\pm 84$ & $125\\pm 4$\\\\ \\hline\n\n$b > 20\\deg$ & $100 \\mu m$ & $131\\pm 21$ & $41\\pm 7$& $140\\pm 13$ & $43\\pm 4$ \\\\[-0mm]\n & Has & $71\\pm 6$ & $70\\pm 6$& $29\\pm 4$ & $28\\pm 4$\\\\[-0mm]\n & $R\\&R$ & $2294\\pm 256$ & $54\\pm 6$ & $1514\\pm 165$ &$35\\pm 4$\\\\ \\hline\n\n$b > 30\\deg$ & $100 \\mu m$ & $18\\pm 38$ & $4\\pm 8$& $32\\pm 26$ &$6\\pm 5$ \\\\[-0mm]\n & Has & $20\\pm 8$ & $20\\pm 8$ & $7\\pm 4$ &$6\\pm 4$\\\\[-0mm]\n & $R\\&R$ & $897\\pm 390$ & $17\\pm 7$ & $379\\pm 255$ &$7\\pm 5$\\\\ \\hline\n\n$b > 40\\deg$ & $100 \\mu m$ & $39\\pm 43$ & $8\\pm 8$ & $13\\pm 30$ &$2\\pm 6$ \\\\\n & Has & $18\\pm 10$ & $14\\pm 8$ & $10\\pm 7$ &$8\\pm 5$\\\\[-0mm]\n & $R\\&R$ & $964\\pm 432$ & $18\\pm 8$ & $531\\pm 304$ &$10\\pm 5$\\\\ \\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\begin{center}\n{\\small\n\\caption{Joint correlations for the Tenerife data. $\\hat{a}$ is the\ncorrelation coefficient, and has units $\\mu K(MJy/sr)^{-1}$ for the\n$100\\mu$m template, and $\\mu K/K$ for the Haslam and $R\\&R$ templates.}\n\\label{tab:table_three} \n\\begin{tabular}{|c|c|c|c|c|c|} \\hline\n\\multicolumn{2}{c}{} & \\multicolumn{2}{c}{10GHz} &\n\\multicolumn{2}{c}{15GHz} \\\\ \\cline{3-6}\nb & Template & $\\hat{a}\\pm \\Delta(\\hat{a})$ & $\\Delta T \\mu K$& $\\hat{a}\\pm \\Delta(\\hat{a})$ & $\\Delta T \\mu K$\\\\ \\hline\n$b > 0\\deg$ & $100\\mu m$ & $151\\pm 1$ & $4535\\pm 36$ & $114\\pm 1$ &$3281\\pm 19$\\\\\n & Has & $191\\pm 3$ & $1895\\pm 33$ & $16\\pm 2$ &$157\\pm 18$ \\\\\n & $R\\&R$ & $6829\\pm 90$ & $1224\\pm 16$ & $1645\\pm 52$ &$287\\pm 9$\\\\ \\hline\n\n$b > 5\\deg$ & $100\\mu m$ & $154\\pm 1$ & $2311\\pm 21$ & $116\\pm 1$ &$1669\\pm 10$\\\\\n & Has & $171\\pm 4$ & $821\\pm 19$ & $23\\pm 2$ &$106\\pm 10$\\\\\n & $R\\&R$ & $5587\\pm 99$ & $572\\pm 10$ & $1405\\pm 54$ &$140\\pm 5$\\\\ \\hline\n\n$b > 10\\deg$ & $100\\mu m$ & $238\\pm 3$ & $1704\\pm 20$ & $136\\pm 1$ &$961\\pm 10$\\\\\n & Has & $64\\pm 5$ & $213\\pm 17$& $0\\pm 3$ &$0\\pm 10$ \\\\\n & $R\\&R$ & $1701\\pm 140$ & $139\\pm 11$ & $394\\pm 79$ &$31\\pm 6$\\\\ \\hline\n\n$b > 15\\deg$ & $100\\mu m$ & $200\\pm 10$ & $154\\pm 7$ & $110\\pm 5$ &$88\\pm 4$\\\\\n & Has & $94\\pm 6$ & $106\\pm 7$ & $26\\pm 4$ &$29\\pm 4$\\\\\n & $R\\&R$ & $3393\\pm 211$ & $148\\pm 9$ & $1858\\pm 140$ &$81\\pm 6$\\\\ \\hline\n\n$b > 20\\deg$ & $100\\mu m$ & $67\\pm 22$ & $21\\pm 7$ & $122\\pm 14$ &$38\\pm 4$\\\\\n & Has & $65\\pm 7$ & $64\\pm 6$ & $12\\pm 4$ &$11\\pm 4$\\\\\n & $R\\&R$ & $1983\\pm 288$ & $47\\pm 7$& $726\\pm 203$ & $17\\pm 5$\\\\ \\hline\n\n$b > 30\\deg$ & $100\\mu m$ & $-16\\pm 40$ & $-3\\pm 8$& $18\\pm 28$ &$4\\pm 6$ \\\\\n & Has & $21\\pm 8$ & $19\\pm 7$ & $6\\pm 5$ &$5\\pm 5$\\\\\n & $R\\&R$ & $1087\\pm 455$ & $20\\pm 8$ & $291\\pm304$ &$5\\pm 5$\\\\ \\hline\n\n$b > 40\\deg$ & $100\\mu m$ & $0\\pm 49$ & $0\\pm 10$ & $-21\\pm 37$ &$-4\\pm 7$\\\\\n & Has & $18\\pm 11$ & $14\\pm 9$ & $13\\pm 8$ &$10\\pm 6$\\\\\n & $R\\&R$ & $1245\\pm 576$ & $23\\pm 10$ & $842\\pm 421$ &$15\\pm 8$\\\\ \\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\begin{center}\n{\\small\n\\caption{Spectral indices obtained from individual and joint correlations. No \nnumber is given when the correlation is insignificant.}\n\\label{tab:table_five} \n\\begin{tabular}{|c|c|c|c|c|} \\hline\n\\multicolumn{1}{c}{} & \\multicolumn{2}{c}{Individual analysis} &\n\\multicolumn{1}{c}{joint analysis} \\\\ \\cline{2-5}\ncut & dust & Haslam & dust & Haslam \\\\ \\hline\n$b > 0\\deg$ & $-1.45^{+0.01}_{-0.01}$ & $-1.41^{+0.01}_{-0.01}$ & $-0.69^{+0.04}_{-0.04}$ & $-6.11^{+0.34}_{-0.37}$ \\\\ [2mm]\n$b > 5\\deg$ & $-1.31^{+0.01}_{-0.01}$ & $-1.29^{+0.02}_{-0.02}$ & $-0.70^{+0.04}_{-0.04}$ & $-4.95^{+0.27}_{-0.28}$ \\\\ [2mm]\n$b > 10\\deg$ & $-1.67^{+0.03}_{-0.03}$ & $-1.25^{+0.02}_{-0.03}$ & $-1.38^{+0.05}_{-0.05}$ & $-$ \\\\ [2mm]\n$b > 15\\deg$ & $-1.66^{+0.16}_{-0.16}$ & $-1.38^{+0.17}_{-0.18}$ & $-1.47^{+0.23}_{-0.24}$ & $-3.17^{+0.52}_{-0.56}$ \\\\ [2mm]\n$b > 20\\deg$ & $0.16^{+0.65}_{-0.60}$ & $-2.21^{+0.54}_{-0.56}$ & $1.48^{+1.35}_{-1.00}$ & $-4.17^{+1.00}_{-1.25}$ \\\\ [2mm]\n$b > 30\\deg$ & $-$ & $-2.56^{+2.35}_{-2.95}$ & $-$ & $-3.09^{+2.68}_{-5.21}$ \\\\ [2mm]\n$b > 40\\deg$ & $-$ & $-1.45^{+3.31}_{-4.06}$ & $-$ & $-0.80^{+3.51}_{-3.53}$ \\\\ \\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\begin{center}\n {\\small\n\\caption{Joint correlations obtained for data at different declinations when the data at each declination are divided into two halves, one half being towards the Galactic centre (marked C) and the other towards the anticentre (marked AC).}\n\\label{tab:table_zero} \n\\begin{tabular}{|c|c|c|c|c|c|c|c|} \\hline\n\\multicolumn{2}{c}{} & \\multicolumn{3}{c}{10GHz} &\n\\multicolumn{2}{c}{15GHz} \\\\ \\cline{3-8}\nregion & number of pixels & $dust$ & $Haslam$ & $\\chi^2$ & $dust$ & $Haslam$ & $\\chi^2$\\\\ \\hline\nall Decs, C & 426 & $160\\pm 33$ & $89\\pm 9$ & $856$ & $182\\pm 22$ & $27\\pm 7$ & $530$ \\\\\nall Decs, AC & 424 & $-80\\pm 32$ & $15\\pm 10$ & $481$ & $43\\pm 21$ & $-50\\pm 6$ & $469$ \\\\ \\hline\nDec 42.5, C & 88 & $225\\pm 95$ & $341\\pm27$ & $259$ & $261\\pm 55$ & $78\\pm 18$ & $122$ \\\\\nDec 42.5, AC & 87 & $-185\\pm 73$ & $29\\pm 19$ & $107$ & $24\\pm 43$ & $-12\\pm 12$ & $88$ \\\\ \\hline\nDec 40.0, C & 86 & $276\\pm 56$ & $74\\pm 33$ & $94$ & $225\\pm 41$ & $83\\pm 22$ & $93$ \\\\\nDec 40.0, AC & 86 & $-148\\pm 55$ & $-12\\pm 18$ & $94$ & $21\\pm 34$ & $-1\\pm 12$ & $79$ \\\\ \\hline\nDec 37.5, C & 85 & $177\\pm 50$ & $89\\pm 22$ & $100$ & $173\\pm 32$ & $25\\pm 14$ & $69$ \\\\\nDec 37.5, AC & 85 & $36\\pm 52$ & $37\\pm 17$ & $100$ & $17\\pm 32$ & $-5\\pm 10$ & $79$ \\\\ \\hline\nDec 35.0, C & 84 & $75\\pm 74$ & $50\\pm 13$ & $85$ & $72\\pm 45$ & $12\\pm 10$ & $86$ \\\\\nDec 35.0, AC & 84 & $0\\pm 54$ & $-8\\pm 21$ & $86$ & $17\\pm 33$ & $-13\\pm 10$ & $106$ \\\\ \\hline\nDec 32.5, C & 83 & $215\\pm 94$ & $-12\\pm 20$ & $57$ & $-77\\pm 69$ & $38\\pm 15$ &$71$ \\\\\nDec 32.5, AC & 82 & $-75\\pm 92$ & $7\\pm 24$ & $79$ & $128\\pm 43$ & $13\\pm 11$ & $89$ \\\\ \\hline \n\\end{tabular}\n}\n\\end{center}\n\\end{table}\n\n\n\\begin{table}\n\\begin{center}\n {\\small\n\\caption{The following table shows the correlation coefficients $\\hat{a}\\pm \\Delta(\\hat{a})$ obtained when the 20 pixels with lowest Galactic latitude in the Galactic centre region in each declination are correlated with the corresponding structure in the template maps, and those obtained when the remaining pixels are correlated. All these are joint fits. }\n\\label{tab:table_zero} \n\\begin{tabular}{|c|c|c|c|c|c|c|c|} \\hline\n\\multicolumn{2}{c}{} & \\multicolumn{3}{c}{10GHz} &\n\\multicolumn{2}{c}{15GHz} \\\\ \\cline{3-8}\nregion & number of pixels & $dust$ & $Haslam$ & $\\chi^2$ & $dust$ & $Haslam$ & $\\chi^2$\\\\ \\hline\nall Decs & 100 & $178\\pm 44$ & $111\\pm 14$ & $479$ & $167\\pm 31$ & $18\\pm 11$ & $159$ \\\\\nall Decs & 750 & $-52\\pm 27$ & $22\\pm 8$ & $821$ & $29\\pm 19$ & $47\\pm 51$ & $808$ \\\\ \\hline\nDec 42.5 & 20 & $1148\\pm 374$ & $279\\pm 49$ & $40$ & $466\\pm 141$ & $24\\pm 29$ & $24$ \\\\\nDec 42.5 & 155 & $-147\\pm 57$ & $37\\pm 17$ & $187$ & $54\\pm 35$ & $-14\\pm 11$ & $174$\\\\ \\hline\nDec 40.0 & 20 & $264\\pm 90$ & $48\\pm 10$ & $26$ & $177\\pm 59$ & $35\\pm 65$ & $24$ \\\\\nDec 40.0 & 152 & $-75\\pm 47$ & $0\\pm 16$ & $160$ & $26\\pm 30$ & $10\\pm 10$ & $139$ \\\\ \\hline\nDec 37.5 & 20 & $315\\pm 144$ & $163\\pm 92$ & $19$ & $217\\pm 75$ & $64\\pm 54$ & $10$ \\\\\nDec 37.5 & 150 & $10\\pm 46$ & $51\\pm 15$ & $180$ & $6\\pm 29$ & $1\\pm 8$ & $129$ \\\\ \\hline\nDec 35.0 & 20 & $23\\pm 121$ & $53\\pm 21$ & $20$ & $34\\pm 77$ & $3\\pm 18$ & $23$ \\\\\nDec 35.0 & 148 & $21\\pm 48$ & $14\\pm 15$ & $150$ & $7\\pm 30$ & $-6\\pm 8$ & $170$ \\\\ \\hline\nDec 32.5 & 20 & $152\\pm 200$ & $9\\pm 58$ & $18$ & $32\\pm 152$ & $8\\pm 42$ & $10$ \\\\\nDec 32.5 & 145 & $34\\pm 73$ & $0\\pm 17$ & $125$ & $79\\pm 39$ & $18\\pm 9$ & $155$ \\\\ \\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table}\n\n\n%\\label{lastpage}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002305.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{deOliviera97}\nde Oliviera-Costa, A. et al. 1997, ApJ, 482, L17\n\\bibitem{deOliviera98} \nde Oliviera-Costa, A. et al. 1998, ApJ, 509, L9\n\\bibitem{deOliviera99} \nde Oliviera-Costa, A. et al. 1999, Submitted to ApJ (astro-ph/9904296) (DOC99)\n\\bibitem{draine98a}\nDraine, B.T., and Lazarian, A. 1998a, ApJ, 494, L19\n\\bibitem{draine98b}\nDraine, B.T., and Lazarian, A. 1998b, ApJ, 508, 157\n\\bibitem{gutierrez99}\nGutierrez, C.M. et al. 1999, astro-ph/9903196\n\\bibitem{haslam81}\nHaslam, C.G.T., et al 1981, $A\\&A$, 100, 209\n\\bibitem{Jones98}\nJones, A.W. et al. 1998, MNRAS, 294, 582\n\\bibitem{kogut96a}\nKogut, A. et al. 1996a, ApJ, 460, 1\n\\bibitem{kogut96b}\nKogut, A. et al. 1996b, ApJ, 464, L5\n\\bibitem{kogut97}\nKogut, A., 1997, AJ, 114, 1127\n\\bibitem{kogut99}\nKogut, A., 1999, in Microwave foregrounds, ed.A. de Oliviera-Costa and M. \nTegmark, in press, (astro-ph/9902307)\n\\bibitem{bib:lawson}\nLawson, K.D., Mayer, C.J., Osborne, J.L. \\& Parkinson, M.L. 1987,\nMNRAS, 225, 307\n\\bibitem{leich97}\nLeitch, E.M., et al. 1997, ApJ, 486, L23\n\\bibitem{Lim96}\nLim, M.A., et al. 1996, ApJ, 469, L69\n\\bibitem{mccullough97}\nMcCullough, P.R. 1997, AJ, 113, 2186\n\\bibitem{Schlegel98}\nSchlegel, D.J., Finkbeiner, D.P. and Davis, M. 1998, ApJ, 500, 525\n\\bibitem{tufte98}\nTufte, S.L., Reynolds, R.J. and Haffner, L.M. 1998, ApJ, 504, 773\n\\end{thebibliography}"
}
] |
astro-ph0002306
|
Flash-Heating of Circumstellar Clouds by Gamma Ray Bursts
|
[
{
"author": "Charles D. Dermer\\altaffilmark{1} \\& Markus B\\\"ottcher\\altaffilmark{2,3}"
}
] |
The blast-wave model for gamma-ray bursts (GRBs) has been called into question by observations of spectra from GRBs that are harder than can be produced through optically thin synchrotron emission. If GRBs originate from the collapse of massive stars, then circumstellar clouds near burst sources will be illuminated by intense $\gamma$ radiation, and the electrons in these clouds will be rapidly scattered to energies as large as several hundred keV. Low-energy photons that subsequently pass through the hot plasma will be scattered to higher energies, thus hardening the intrisic spectrum. This effect resolves the ``line-of-death'' objection to the synchrotron shock model. Illuminated clouds near GRBs will form relativistic plasmas containing large numbers of electron-positron pairs that can be detected within $\sim$ 1-2 days of the explosion before expanding and dissipating. Localized regions of pair annihilation radiation in the Galaxy would reveal past GRB explosions.
|
[
{
"name": "ms.tex",
"string": "%\\documentclass[preprint2,epsf]{aastex}\n%\\documentstyle[12pt,aasms4,epsf,rotate]{article}\n\\documentstyle[11pt,aaspp4,epsf,rotate]{article}\n%\\documentstyle[aas2pp4]{article} \n%\\tighten \n%\\eqsecnum \n%\\received{}\n%\\accepted{} \n%\\journalid{}{} \n%\\articleid{}{} \n\\newcommand\\D{{\\cal D}}\n\\def\\psim{\\lower.5ex\\hbox{$\\; \\buildrel \\propto \\over\\sim \\;$}}\n\\def\\gtrsim{\\lower.5ex\\hbox{$\\; \\buildrel > \\over\\sim \\;$}}\n\\def\\lesssim{\\lower.5ex\\hbox{$\\; \\buildrel < \\over\\sim \\;$}}\n\\def\\gm{\\gamma_m} \n\\def\\g2{\\gamma_2} \n\\def\\tT{\\tau_T}\n\\def\\elnumax{L_{\\nu,{\\rm max}}} \n\\def\\e{{\\epsilon}}\n\\def\\ag{\\alpha_{\\gamma}}\n%\\slugcomment{}\n\\begin{document}\n\n\\title{Flash-Heating of Circumstellar Clouds by Gamma Ray Bursts}\n\n\\author{Charles D. Dermer\\altaffilmark{1} \\& Markus\nB\\\"ottcher\\altaffilmark{2,3}}\n\n\\altaffiltext{1}{E. O. Hulburt Center for Space Research, Code 7653,\nNaval Research Laboratory, Washington, DC 20375-5352}\n\\altaffiltext{2}{Department of Space Physics and Astronomy, Rice\nUniversity, Houston, TX 77005-1892} \\altaffiltext{3}{Chandra Fellow}\n\n\n\\begin{abstract}\n\nThe blast-wave model for gamma-ray bursts (GRBs) has been called into\nquestion by observations of spectra from GRBs that are harder than can\nbe produced through optically thin synchrotron emission. If GRBs originate \nfrom the collapse of massive stars, then circumstellar clouds near burst\nsources will be illuminated by intense $\\gamma$ radiation, and the\nelectrons in these clouds will be rapidly scattered to energies as\nlarge as several hundred keV. Low-energy photons that subsequently\npass through the hot plasma will be scattered to higher energies, thus\nhardening the intrisic spectrum. This effect resolves the\n``line-of-death'' objection to the synchrotron shock model. Illuminated\nclouds near GRBs will form relativistic plasmas containing large\nnumbers of electron-positron pairs that can be detected within $\\sim$\n1-2 days of the explosion before expanding and dissipating. Localized\nregions of pair annihilation radiation in the Galaxy would reveal past\nGRB explosions. \\end{abstract}\n\n\\keywords{gamma rays: bursts -- massive stars -- nonthermal radiation\nprocesses }\n\n\\section{Introduction}\n\nThe identification of flaring and fading X-ray, optical and radio\ncounterparts to gamma-ray burst (GRB) sources (e.g., Costa et al.\\\n\\markcite{cea97}1997; van Paradijs et al.\\ \\markcite{vpea97}1997;\nDjorgovski et al.\\ \\markcite{dea97}1997; Frail et al.\\\n\\markcite{fea97}1997), and the large energy releases implied by\nredshift measurements, find a consistent explanation in an expanding\nrelativistic blast-wave model (Paczy\\'nski \\& Rhoads\n\\markcite{pr93}1993; M\\'esz\\'aros \\& Rees \\markcite{mr97}1997). As a\nresult of Beppo-SAX and optical follow-on observations, the redshifts\nof about one dozen GRBs with durations greater than $\\sim 1$ s have\nbeen measured. The distribution of redshifts is broad and centered\nnear $z\\sim 1$, corresponding to the cosmological epoch of active star\nformation (Hogg \\& Fruchter \\markcite{hf99}1999). GRBs are extremely\nluminous and energetic at hard X-ray and $\\gamma$-ray energies. The\ndegree of GRB collimation is unknown, but peak directional\n$\\gamma$-ray luminosities and energy releases as large as $\\partial\nL/\\partial \\Omega\\simeq 3\\times 10^{51}$ ergs (s-sr)$^{-1}$ and $\\partial\nE/\\partial \\Omega \\simeq 3\\times 10^{53}$ ergs sr$^{-1}$, respectively,\nhave been measured (Kulkarni et al.\\ \\markcite{kea99}1999). Less\npowerful GRBs and less luminous episodes during the GRB produce\nsmaller $\\gamma$-ray powers, but the apparent isotropic $\\gamma$-ray\nluminosities from typical GRBs could regularly reach values exceeding\n$10^{50}L_{50}$ ergs s$^{-1}$ with $L_{50} \\sim 1$, with some GRBs\nreaching $L_{50} > 10^2$. Because the energy radiated in $\\gamma$\nrays is less than the total energy released by a GRB, the apparent\nisotropic energy release of GRB sources could often reach values of\n$10^{54}E_{54}$ ergs, with $E_{54} \\sim$1.\n\nCosmological gamma-ray burst and afterglow observations are best\nexplained through the fireball/blast-wave model, where the deposition\nof large quantities of energy into a small region yields a fireball\nthat expands until it reaches a relativistic speed determined by the\namount of baryons mixed into the fireball (see, e.g., Piran\n\\markcite{tp99}1999 for a review). Nonthermal synchrotron radiation\nfrom energetic electrons in the relativistic blast wave is thought to\naccount for the origin of the prompt $\\gamma$-ray emission and\nafterglow radiation. This paradigm has been called into question,\nhowever, by observations of very hard X-ray emission during the prompt\n$\\gamma$-ray luminous phase of a significant number of GRBs (Crider et al.\\\n\\markcite{crider97}1997; Preece et al.\\ \\markcite{pea98}1998). Photon\nfluxes $\\phi(\\e ) \\propto \\e^{-\\alpha_X}$ with $\\alpha_X \\sim$ 0,\nwhere $\\e = h\\nu/m_ec^2$ is the dimensionless photon energy, have been\nobserved in 5-10\\% of GRBs that are bright enough to permit spectral\nanalysis. This strongly contradicts the optically-thin synchrotron \nshock model, which predicts that only radiation spectra with \n$\\alpha_X \\geq 2/3$ can emerge from the blast wave. In view \nof the severity of this challenge to the model, these observations \nhave been termed the ``line-of-death\" to the synchrotron shock model. \nPossible explanations for this phenomeonon involve photoelectric \nabsorption by optically thick cold matter (Liang \\& Kargatis\n\\markcite{lk94}1994; Brainerd \\markcite{jb94}1994; B\\\"ottcher \net al.\\ \\markcite{bea99}1999), synchrotron self-absorption \n(Crider \\& Liang \\markcite{cl99}1999, Granot, Piran, \\& Sari\n\\markcite{granot00}2000, Lloyd \\& Petrosian \\markcite{lp99}1999), \nCompton scattering (Liang \\markcite{liang97}1997; Liang et al.\\ \n\\markcite{lcbs99}1999), or the existence of a\npair-photosphere (M\\'esz\\'aros \\& Rees \\markcite{mr00}2000) within the\nblast wave. Except for the last model cited, these explanations\nare inconsistent with the standard synchrotron shock model. Here we offer a\nsolution to this problem that is consistent with the standard model\nand recent observations pointing to a massive star origin of GRBs.\n\n\\section{Massive Star Origin of GRBs}\n\nConsiderable evidence linking the sources of GRBs with star-forming\nregions has recently been obtained (e.g., Lamb \\markcite{lamb99}1999).\nFor example, the associated host galaxies have blue colors, consistent\nwith galaxy types that are undergoing active star formation. GRB\ncounterparts are found within the optical radii and central regions of\nthe host galaxies (e.g. Bloom et al.\\ \\markcite{bea99a}1999a), rather\nthan far outside the galaxies' disks, as might be expected in a\nscenario of merging neutron stars and black holes (Narayan, Paczy\\'nski,\n\\& Piran \\markcite{npp92}1992). Lack of optical counterparts in some\nGRBs could be due to extreme reddening from large quantities of gas\nand dust in the host galaxy. This, together with the appearance of\nsupernova-like emissions in the late time optical decay curves of a\nfew GRBs (e.g., Bloom et al.\\ \\markcite{bea99b}1999b) and weak X-ray\nevidence for Fe K$_\\alpha$-line signatures (Piro et al.\\\n\\markcite{pea99}1999), supports a massive star hypernova/collapsar\n(Woosley \\markcite{sw93}1993; Paczy\\'nski \\markcite{bp98}1998)\norigin for the long duration gamma-ray bursters.\n\nThe observations thus favor a model for GRBs involving the collapse of\nthe core of a $\\gtrsim 30 M_\\odot$ star to a black hole, with the\ncollapse events producing fireballs and relativistic outflows with\nlarge directed energy releases. Earlier treatments of the blast-wave\nmodel considered systems where the density of the surrounding medium\nis either uniform or monotonically decreasing as a result of a\ncircumstellar medium formed by a hot stellar wind (M\\'esz\\'aros, Rees,\n\\& Wijers \\markcite{mrw98}1998). Until recently (Chevalier \\&\nLi \\markcite{cl99}1999; Li \\& Chevalier \\markcite{lc99}1999),\nless attention has been paid to the actual \nenvironment found in the vicinity of massive stars. For this\nwe consider $\\eta$ Carinae (Davidson \\& Humphreys\n\\markcite{dh97}1997), the best-studied massive star that might\ncorrespond to a GRB progenitor. It is an evolved star with\npresent-day mass $\\geq 90 M_\\odot$, distance of $2300\\pm 200$ pc, and\nlifetime of about 3 million years. It anisotropically ejects mass at\na current rate of $\\lesssim 0.003 M_\\odot$ yr$^{-1}$ to form its\nunusual ``homonculus nebula.\" Several Solar masses of material\nsurround $\\eta$ Carinae. In the immediate vicinity of the central\nstar, dense clouds of slow-moving gas with radii $r \\sim 10^{15}$ cm\nand densities between $10^7$ and $10^{10}$ cm$^{-3}$ were discovered\nwith speckle techniques (Hofman \\& Weigelt \\markcite{hw88}1988) and\nconfirmed with high-resolution HST observations (Davidson et al.\\\n\\markcite{dea95}1995). This material, moving with speeds of $\\sim 50$\nkm s$^{-1}$, is apparently ejected nonuniformly from the equatorial\nzone, but may remain trapped by the gravitational field of the star.\nInferences (Davidson \\& Humphreys \\markcite{dh97}1997) from [FeII]\nobservations suggest that $\\gtrsim 0.02 M_\\odot$ of gas are contained\nwithin $\\sim 2\\times 10^{16}$ cm, implying a volume-averaged gas\ndensity $\\gtrsim 7\\times 10^5$ cm$^{-3}$. Model results (B\\\"ottcher\n\\markcite{mb99}1999) imply that a dense ($n \\sim 10^{12}$ cm$^{-3}$)\ntorus of gas at mean distance $d\\sim 2\\times 10^{15}$ cm and with a\n10-fold enhancement of Fe relative to Solar abundance is required to\nexplain the Fe K$_\\alpha$ emission weakly detected from GRB 970508\nwith Beppo-SAX (Piro et al.\\ \\markcite{pea99}1999).\n\nGuided by the optical observations of $\\eta$ Carinae, we assume that\nthe volume-averaged density of gas at $d \\lesssim 10^{16}$ cm of a GRB\nsource is $\\langle n \\rangle = 10^6 n_6$ cm$^{-3}$. Dense clouds of\nradius $10^{15}r_{15}$ cm and radial Thomson depths $\\tT = n_c\\sigma_T\nr$ are assumed to be embedded within this region, so that the mean\ndensity of particles in a cloud is $n_c = 1.5\\times 10^9 \\tT /r_{15}$\ncm$^{-3}$. Thus $\\tT \\sim 1$ clouds located very close to a GRB\nsource are consistent with the observations of dense blobs near $\\eta$\nCarinae. The deceleration length scale of a blast wave with initial\nLorentz factor $\\Gamma_0 = 100\\Gamma_2$ in a uniform medium is $x_d =\n(3E_0/4\\pi \\Gamma_0^2 \\langle n \\rangle m_pc^2)^{1/3} = 2.5\\times\n10^{15}(E_{54}/\\Gamma_2^2 n_6)^{1/3}$ cm; hence the blast wave would\nemit a significant fraction of its energy before reaching distances of\n$\\sim 10^{16}$ cm. The deceleration time, which corresponds to the\nduration of the prompt $\\gamma$-ray luminous phase of a GRB in the\nexternal shock model (Rees \\& M\\'esz\\'aros \\markcite{rm92}1992), is\n$t_d = (1+z) x_d/(c \\Gamma_0^2) \\cong 8(1+z) (E_{54}/\\Gamma_2^8\nn_6)^{1/3}$ s. These parameters are not unique, and we expect that\nGRBs display a wide range of energies, Lorentz factors and surrounding\nmean densities that could accommodate the diverse range of GRB\nobservations.\n\n\\section{Blast-Wave/Cloud Interaction}\n\nA wave of photons impinging on a cloud located $10^{16} d_{16}$ cm\nfrom the explosion center will photoionize and Compton-scatter the\nambient electrons to energies characteristic of the incident $\\gamma$\nrays (Madau \\& Thompson \\markcite{mt99}1999). The $\\gamma$-ray photon\nfront has a width of $\\sim$10-100 lt-s, corresponding to the duration\nof the GRB, whereas the plasma cloud has a width of $\\sim 3\\times 10^4\nr_{15}$ lt-s, so that the radiation effects must be treated locally.\nThe radiation force driving the electrons outward is balanced by\nstrong electrostatic forces from the more massive protons and ions\nthat anchor the system until the net impulse is sufficient to drive\nthe entire plasma cloud outward. The Compton back-scattered photons\nprovide targets for successive waves of incident GRB photons through\n$\\gamma\\gamma$ pair-production interactions (Thompson \\& Madau\n\\markcite{tm99}1999). Higher-energy photons are preferentially\nattenuated, forming an additional injection source of $\\gtrsim 1$ MeV\nelectron-positron pairs. The nonthermal electrons and pairs will\nCompton scatter successive waves of photons, thereby modifying the\nincident spectrum. The pairs, no longer bound by electrostatic\nattraction with the ions, will be driven outward by both radiation\nforces and restoring electrostatic fields to form a mildly\nrelativistic pair wind passing through the more slowly moving normal\nplasma. Shortly after the $\\gamma$-ray photon front has passed, the\ndecelerating blast wave from the GRB will plow into the cloud,\nshock-heating the relativistic plasma.\n\nNonthermal synchrotron photons with energy $\\e$ impinge on the atoms\nin the cloud with a flux which can be parametrized as\n\\begin{equation} \n\\Phi(\\e) = (4\\pi d^2)^{-1}\\; {L \\over m_ec^2 \\e_0^2 \\zeta_1}\n\\;\\big[{1\\over (\\e/\\e_0)^{2/3}+(\\e/\\e_0)^{\\alpha_\\gamma}}\\bigr]\\; \n\\label{Phi}\n\\end{equation}\n(Dermer, Chiang, \\& B\\\"ottcher \\markcite{dcb99}1999), where $\\e_0 \\sim\n1$ is the photon energy of the peak of the $\\nu F_\\nu$ spectrum,\n$\\alpha_\\gamma \\sim 2$-3 is the photon spectral index at energies\n$\\e\\gg \\e_0$, and $\\zeta_1 \\cong [3/4 + (\\ag-2)^{-1}]$. Hydrogen, the most\nabundant species in the cloud, will be ionized on a time scale of\n$5\\times 10^{-5} (1+z) d_{16}^2 \\zeta_1 \\e_0^{4/3}/L_{50}$~s. Fe\nfeatures might persist briefly during the early periods of very weak\nGRBs on a time scale of $4\\times 10^{-3} (1+z) d_{16}^2 \\zeta_1\n\\e_0^{4/3}/L_{50}$~s, and would be identified by a rapidly evolving Fe\nabsorption feature at $9.1/(1+z)$ keV. After the H and Fe are\nionized, the coupling between the GRB photons and gas is dominated by\nCompton scattering interactions. Pair production through\nphoton-particle processes are negligible by comparison with Compton\ninteractions except for photons with $\\e \\gtrsim 200$. A lower limit\nto the time scale for an electron to be scattered by a photon is\n$t_T(s) \\approx 15 (1+z) d_{16}^2 \\zeta_1\\e_0/\\zeta_2 L_{50}$, where\n$\\zeta_2 = [3 + (\\alpha_\\gamma -1)^{-1}]$, assuming that all Compton\nscattering events occur in the Thomson limit. The Klein-Nishina \ndecline in the Compton cross section will increase this\nestimate by a factor of $\\sim 1$-3, depending on the incident\nspectrum. Most of the electrons in the cloud will therefore be\nscattered to high energies during a very luminous ($L_{50}\\gg 1$) GRB,\nor when the cloud is located at $d_{16} \\ll 1$.\n\nThe average energy transferred to an electron at rest when\nCompton-scattered by a photon with energy $\\e$ is $\\Delta\\e \\cong\n\\e^2/(1+1.5\\e )$ (this expression is accurate to better than 18\\% for\n$\\e < 10^3$). Defining $\\eta = \\gamma -1$ as the dimensionless\nelectron kinetic energy, we can easily estimate the production rate\n$f(\\eta )$ of electrons scattered to energy $\\eta$ in the\nnonrelativistic ($\\eta \\ll 1$) and extreme relativistic ($\\eta \\gg 1$)\nlimits, noting that $f(\\eta)d\\eta \\propto \\Phi(\\e)\\sigma_C(\\e)d\\e$ and\nletting $\\eta\\cong \\Delta\\e$. In the former limit, the Compton cross\nsection $\\sigma_C(\\e)\\rightarrow \\sigma_T$ and $\\Phi(\\e) \\propto\n\\e^{-2/3}$, so that $f(\\eta)\\propto \\eta^{-5/6}$ when $\\eta\\ll$ min(1,\n$\\e_0^2$). In the high energy limit, $\\sigma_C(\\e)\\propto\n\\ln(3.3\\e)/\\e$ and $\\Phi(\\e) \\propto \\e^{-\\alpha_\\gamma}$, so that\n$f(\\eta )\\propto \\eta^{-(\\alpha_\\gamma+1)} \\ln(2.2\\eta)$ when\n$\\eta\\gg$ max$(1, \\e_0^2$). Thus electrons are Compton-scattered on\nthe time scale derived above to form a hard spectrum that turns over\nat kinetic energies of $\\gtrsim 500\\times$min($1,\\e_0^2$) keV. For a\nGRB with $\\e_0 \\sim 1$, most of the kinetic energy is therefore\ncarried by nonthermal electrons with energies of $\\sim 500$ keV.\nSuccessive waves of photons that pass through this plasma will\ncontinue to Compton-scatter the nonthermal electrons. Only the lowest\nenergy photons, however, will be strongly affected by the radiative\ntransfer because both the Compton scattering cross section and energy\nchange per scattering is largest for the lowest energy photons.\n\nFollowing the initial wave of photons, successive photon fronts also\nencounter the back-scattered radiation (Madau \\& Thompson\n\\markcite{mt99}1999; Thompson \\& Madau \\markcite{tm99}1999). The\nkinematics of the Compton process dictate that the energy $\\e_s$ of a\nphoton back-scattered through $180^\\circ$ by an electron at rest is\n$\\e_s = \\e/(1+ 2\\e)$; thus $\\e_s$ cannot exceed 1/2 the electron\nrest-mass energy. Head-on collisions of the back-scattered photons by\nprimary GRB photons with $\\e_1 > 2/\\e_s = 2+2\\sqrt{3}$ can thus produce\nnonthermal e$^+$-$e^-$ pairs. The cross section for $\\gamma\\gamma$\npair production peaks near threshold with a value of $\\sim \\sigma_T/3$.\nThe $\\gamma\\gamma$ pair-production optical depth $\\tau_{\\gamma\\gamma}\n(\\e_1)$ of a photon that trails the onset of the GRB by $\\Delta t$\nseconds can be estimated by noting that the photon traverses a\ndistance $\\sim r$ through a backscattered radiation field of spectral\ndensity $n_s(\\e_s)\\approx n_e \\sigma_T \\cdot \\Delta t \\cdot \\Phi [\\e_s\n/(1-2\\e_s )]$ -- a more accurate calculation would replace the term\n$\\Delta t \\cdot \\Phi [\\e_s/(1-2\\e_s)]$ by an integral over the\ntime-varying flux. Approximating $\\tau_{\\gamma\\gamma} (\\e_1)\\approx r\n(\\sigma_T/3) \\Delta\\e_s n_s(2/\\e_1)$, where $\\Delta \\e_s \\simeq 2/\\e_1$ is\nthe bandwidth that is effective for producing pairs, we obtain\n\\begin{equation} \n\\tau_{\\gamma\\gamma} (\\e_1) \\approx 0.02 \\; {\\tau_T \\Delta t [s] \\, \nL_{50} k(\\e_1) \\over d_{16}^2 \\e_1\\e_0^2\\zeta_1}\\;\\big[{1\\over \n(\\e^\\prime/\\e_0)^{2/3} + (\\e^\\prime/\\e_0)^{\\alpha_\\gamma}}\\bigr]\\; , \n\\label{tau_gg}\n\\end{equation}\nwhere $\\e^\\prime = 2/(\\e_1-4)$. The coefficient results from a more\ndetailed derivation, and the term $k(\\e_1) = 1-4\\e_1^{-1} + \\e_1\n/(\\e_1 -4)$ is a Klein-Nishina correction. Eq.\\ (\\ref{tau_gg}) shows \nthat photons with energies above several MeV will be severely attenuated \nin Thomson thick clouds if $L_{50}\\gg 1$ or $d_{16}\\ll 1$. Photons with\nMeV energies are most severely attenuated, and $\\tau_{\\gamma\\gamma}\n(\\e_1)\\propto \\e_1^{-1/3}$ at energies $\\e_1 \\gg \\max (1, \\e_0)$.\nThe $\\gamma\\gamma$ pair injection process provides another source of\nnonthermal leptons with $\\eta \\sim 1$. The pairs will not, however,\nbe electrostatically bound but will be accelerated by the photon\npressure and electrostatic field. \n\nFig.\\ 1 shows Monte Carlo simulations of radiation spectra \ndescribed by eq.\\ (\\ref{Phi}) that pass through a hot electron \nscattering medium. For simplicity, we approximate the \nhard nonthermal electron spectrum by a thermal\ndistribution with temperatures of 100 and 300~keV. These\ncalculations show that the lowest energy photons of the primary\nsynchrotron spectrum are most strongly scattered, and that the \n``line-of-death\" problem of the synchrotron shock model of \nGRBs (Preece et al.\\ \\markcite{pea98}1998) can be solved by \nradiation transfer effects through a hot scattering cloud \nwith $\\tT \\gtrsim$ 1-2. \n\nAccording to this interpretation, GRBs \ndisplaying very hard spectra could display one break from the \nintrinsic synchrotron shock spectrum and a second break\nfrom the scattering process. In the examples shown in Fig. 1,\nthese two breaks are so close to each other that they appear\nas one smooth turnover. Two breaks are observed from GRB\n970111 (Crider \\& Liang \\markcite{cl99}1999), a GRB that strongly\nviolates the ``line of death.\" A prediction of this model is\nthat GRBs showing such flat X-ray spectra should also display softer\nMeV spectra than typical GRBs due to $\\gamma\\gamma$ attenuation\nprocesses in the hot scattering cloud.\n\n\\section{Observational Signatures of the Flash-Heated Cloud}\n\nThe Compton-scattered electrons transfer momentum to the $N_p =\n4\\times 10^{54}r_{15}^3n_9$ protons of the cloud through their\nelectrostatic coupling. If the radiation efficiency is $\\xi_r$, then\nthe Compton impulse gives each proton in the cloud $\\approx \\xi_r\n[1-\\exp(-\\tT )]E \\pi r^2/(4\\pi d^2N_p) \\approx 40 [1-\\exp(-\\tT )]\n(\\xi_r/0.1) E_{54}/(d_{16}^2 r_{15}n_9)$ MeV of directed energy.\nPairs, by contrast, will be accelerated to mildly relativistic speeds\nuntil Compton drag or streaming instabilities limit further\nacceleration. In the simplification that the medium interior to the\ncloud is uniform, and neglecting pair-loading of the swept-up material\n(Thompson \\& Madau \\markcite{tm99}1999), the decelerating blast wave\nfollows the dynamical equation $\\Gamma(x) = \\Gamma_0(x/x_d)^{-g}$,\nwhere $g = 3/2$ and 3 for adiabatic and radiative blast waves,\nrespectively. Using the standard parameters adopted here, the blast\nwave slows to between $\\xi= 0.01 - 0.1$ of its initial Lorentz factor\nbefore reaching a cloud at $d = 10^{16}$ cm. Even considering the\nradiative acceleration of the cloud, the blast wave reaches the cloud\nat time $t_{bw} = t_d(d/x_d)^{(2g+1)}/(2g+1) \\lesssim t_{\\rm dyn}$,\nwhere the dynamical time scale of the cloud is $t_{\\rm dyn} = r/c =\n3\\times 10^4 r_{15}$ s. Because the cloud is so dense, a large\nfraction of the residual energy of the blast wave is deposited into\nthe $N_p$ particles of the cloud. Thus each proton in the cloud\nreceives an additional $m_p\\beta_p^2 c^2 \\approx \\xi E \\pi r^2/(4\\pi\nd^2N_p) \\approx 40 (\\xi/0.1) E_{54}/(d_{16}^2 r_{15}n_9$) MeV of\nkinetic energy, divided roughly equally into directed outflow and\nrandom thermal energy.\n\nIf the circumstellar medium at $d_{16}\\gg 1$ is much more dilute than\nthe interior region, as suggested by observations of $\\eta$ Carinae,\nthen we can neglect further interactions of the cloud/blast wave\nsystem with their surroundings. The observational signatures and fate\nof the cloud at late times can be outlined by comparing time scales.\nThe cloud expands on a time scale $t_{\\rm ex} = t_{\\rm dyn}/\\beta =\n1.5\\times 10^5 r_{15}/(\\beta/0.2)$ s. The basic time scale\ngoverning radiative processes in the cloud is the Thomson time $t_{\\rm\nT} = (n_e\\sigma_T c)^{-1} = 5\\times 10^4/n_9$~s $= t_{\\rm dyn} /\\tau_{\\rm\nT}$. The electrons thermalize on a time scale $t_{\\rm T}/\\ln\\Lambda\n\\ll t_{\\rm dyn}$, where the Coulomb logarithm $\\ln\\Lambda \\approx 20$.\nThe protons transfer their energy to the electrons on the time\nscale $t_{ep}\\cong \\theta^{3/2}(m_p/m_e)t_{\\rm T}/\\ln\\Lambda$, \nwhere $\\theta = kT/m_ec^2$ is an effective dimensionless\nelectron temperature, and we assume collective plasma processes for\nenergy exchange to be negligible.\n\nThe flash-heated cloud can evolve in two limiting regimes. When the\nexternal soft-photon energy density is small, the system emits by a\nhard bremsstrahlung spectrum with $\\theta \\sim$ 1 and luminosity\n$L_{ff}\\cong N_e\\alpha_f m_ec^2\\theta^{1/2}/t_{\\rm T} \\approx 5\\times\n10^{41} r_{15}^3 n_9^2\\theta^{1/2}$ ergs s$^{-1}$. In the more likely\ncase when abundant soft photons are present, for example, from the\nCompton echo (Madau, Blandford, \\& Rees \\markcite{mbr99}1999), then\nCompton cooling will balance ion heating to produce a luminous\nComptonized soft-photon spectrum with effective temperature $\\theta\n\\sim 0.1$ and luminosity $L_{\\rm C}\\cong \\xi E \\pi r^2/(4\\pi d^2\nt_{ep}) \\approx 2\\times 10^{45} (\\xi/0.1) E_{54} r_{15}^2 n_9\nd_{16}^{-2}(\\theta/0.1)^{-3/2}$ ergs s$^{-1}$. In either case, the\nspectra persist until the plasma expands and adiabatically cools, that\nis, for a period $\\sim t_{ex} \\sim$ day. The hot bremsstrahlung\nplasma will be too dim to be detectable with current instrumentation,\nbut a 50-100 keV Comptonized plasma at redshift $z \\sim 1$ and luminosity \ndistance of $10^{28}D_{28}$ cm would have\na flux of $\\sim 1.6\\times 10^{-12} (\\xi/0.1) E_{54} r_{15}^2 n_9\nd_{16}^{-2}(\\theta/0.1)^{-3/2} D_{28}^{-2}$ ergs cm$^{-2}$ s$^{-1}$.\nThe hot plasma formed by a nearby GRB at $z \\sim 0.1$ would be\n easily detectable with the\nINTEGRAL and Swift missions at hard X-ray and soft $\\gamma$-ray\nenergies. In either case, e$^+$-e$^-$\npairs would be formed with moderate efficiency, \nand the cooling, expanding plasma\nwould produce a broad pair annihilation feature (Guilbert \\& Stepney\n\\markcite{gs85}1985). The residual pairs formed in the relativistic\nplasma and the pair wind would diffuse into the dilute interstellar\nmedium with density $n_{\\rm ISM}$ to annihilate on a time scale\n$(n_{\\rm ISM} \\sigma_{\\rm T} c)^{-1} \\sim 2 \\times 10^6/n_{\\rm ISM}$\nyr. If the energy intercepted by a single cloud is converted to pairs\nwith a conservative 1\\% pair yield, past GRBs in the Milky Way would\nbe revealed by localized regions of annihilation radiation with flux\n$\\sim 2\\times 10^{-5} E_{54} n_{\\rm ISM} ~(d/10 {\\rm kpc})^{-2}$ 0.511\nMeV ph cm$^{-2}$ s$^{-1}$. The high-latitude annihilation feature\ndiscovered with OSSE on the Compton Gamma Ray Observatory (Purcell et\nal.\\ \\markcite{pea97}1997), or other localized hot spots of\nannihilation radiation that will be mapped in detail with INTEGRAL,\ncould reveal sites of past GRB explosions. \n\n\\acknowledgments{CD thanks B. Paczy\\'nski for stressing the importance\nof massive star observations in developing blast-wave models of GRBs.\nThe work of CD is supported by the Office of Naval Research and NASA\nAstrophysical Theory Program (DPR S-13756G). The work of MB is\nsupported by NASA through Chandra Postdoctoral Fellowship grant\nPF~9-10007, awarded by the Chandra X-ray Center, which is operated\nby the Smithsonian Astrophysical Observatory for NASA under\ncontract NAS~8-39073.}\n\n\\begin{references}\n\n\\reference{bea99a} Bloom, J. S. et al.\\ 1999a, ApJ, 518, L1\n\n\\reference{bea99b} Bloom, J. S. et al.\\ 1999b, Nature 401, 453\n\n\\reference{bdcl} B\\\"ottcher, M., Dermer, C. D., Crider, A. W. \\&\nLiang, E. P. 1999, A\\&A 343, 111 \n\n\\reference{mb99} B\\\"ottcher, M. 1999, ApJ, submitted (astro-ph/9912030) \n\n\\reference{jb94} Brainerd, J. J. 1994, ApJ, 428, 21 \n\n\\reference{cl99} Chevalier, R. A., \\& Li, Z.-Y., 1999, ApJ, 520, L29\n\n\\reference{crider97} Crider, A. et al.\\ 1997, ApJ 479, L39 \n\n\\reference{cl99} Crider, A. W., \\& Liang, E. P. 1999, A\\&AS, 138, 405 \n\n\\reference{cea97} Costa, E. et al.\\ 1997, Nature, 387, 783 \n\n\\reference{dh97} Davidson, K., \\& Humphreys, R. M. 1997, ARAA, 35, 1 \n\n\\reference{dea95} Davidson, K. et al.\\ 1995, AJ, 109, 1784 \n\n\\reference{dcb99} Dermer, C. D., Chiang, J., \\& B\\\"ottcher, M. 1999, \nApJ 513, 656 \n\n\\reference{dea97} Djorgovski, S. G. et al.\\ 1997, Nature, 387, 876 \n\n\\reference{fea97} Frail, D. A., Kulkarni, S. R., Nicastro, L., \nFeroci, M. \\& Taylor, G. B. 1997, Nature 389, 261\n\n\\reference{granot00} Granot, J., Piran, T., \\& Sari, R., 2000, ApJ,\nsubmitted (astro-ph/0001160)\n\n\\reference{gs85} Guilbert, P. W., \\& Stepney, S., 1985, MNRAS, 212, 523 \n\n\\reference{hw88} Hofmann, K. H., \\& Weigelt, G. 1988, A\\&A, 203, L21 \n\n\\reference{hf99} Hogg, D. W., \\& Fruchter, A. S. 1999, ApJ 520, 54 \n\n\\reference{kea99} Kulkarni, S. R. et al.\\ 1999, Nature 398, 389 \n\n\\reference{lamb99} Lamb, D. Q. 1999, A\\&AS, 138, 607 \n\n\\reference{lc99} Li, Z.-Y., \\& Chevalier, R. A., 1999, ApJ, 526, 716\n\n\\reference{liang97} Liang, E. P., 1997, ApJ, 491, L15\n\n\\reference{lcbs99} Liang, E. P., Crider, A. W., B\\\"ottcher, M., \\& \nSmith, I. 1999, ApJ 519, L21 \n\n\\reference{lk94} Liang, E. P., \\& Kargatis, V. E., 1994, ApJ, 432, L111\n\n\\reference{lp99} Lloyd, N. M., \\& Petrosian, V., 1999, in proc. of 5$^{th}$\nHuntsville Symposium on Gamma-Ray Bursts, AIP proc. in press (astro-ph/9912205)\n\n\\reference{mt99} Madau, P. \\& Thompson, C. 1999, ApJ, in press \n(astro-ph/9909060)\n\n\\reference{mbr99} Madau, P., Blandford, R. D., \\& Rees, M. J. 1999,\nApJ, submitted (astro-ph/9912276) \n\n\\reference{mr00} M\\'esz\\'aros, P. \\& Rees, M. J. 2000, ApJL, in press \n\n\\reference{mrw98} M\\'esz\\'aros, P., Rees, M. J. \\& Wijers, R. A. M. J. \n1998, ApJ 499, 301\n\n\\reference{mr97}M\\'esz\\'aros, P., \\& Rees, M. J. 1997, ApJ, 476, 232\n\n\\reference{npp92} Narayan, R., Paczy\\'nski, B., \\& Piran, T. 1992, ApJ\n395, L83 \n\n\\reference{bp98} Paczy\\'nski, B. 1998, ApJ, 494, L4\n\n\\reference{pr93}Paczy\\'nski, B., \\& Rhoads, J. 1993, ApJ, 418, L5\n\n\\reference{tp99} Piran, T. 1999, Phys Rpts, 314, 575\n\n\\reference{pea99} Piro, L. et al.\\ 1999, ApJ, 514, L73\n\n\\reference{pea98} Preece, R. D. et al.\\ 1998, ApJ, 506, L23\n\n\\reference{pea97} Purcell, W. R., et al.\\ 1997, ApJ 491, 725\n\n\\reference{rm92} Rees, M. J., \\& M\\'esz\\'aros, P. 1992, MNRAS, 258, 41P \n\n\\reference{tm99} Thompson, C., \\& Madau, P. 1999, ApJ, submitted\n(astro-ph/9909111) \n\n\\reference{vpea97} van Paradijs, J. et al.\\ 1997, Nature, 386, 686 \n\n\\reference{sw93} Woosley, S. E. 1993, ApJ, 405, 273\n\n\\end{references} \n\n\\eject\n\n\\setcounter{figure}{0}\n\\begin{figure} \n\\rotate[r]{ \\epsfysize=12cm\n\\epsffile[150 0 550 500]{fig1.ps} }\n\n\\caption[]{Radiation transfer\neffects on GRB emission that passes through electrons energized by an\nearlier portion of the photon front. The intrinsic spectrum eq.(1),\nwith $\\alpha_X = 2/3$, $\\alpha_\\gamma = 2.5$ and $\\e_0 = 0.5$, is\nshown by the thick dashed curve. The nonthermal electrons are\napproximated by a thermal distribution with temperatures of 100 keV\n(thin curves) and 300 keV (thick curves), and Thomson depths $\\tT = 1$\n(solid curves) and $\\tT = 2$ (dotted curves). Spectral indices\n$\\alpha_X$ calculated at 50 keV are 0.5 ($T = 100$ keV, $\\tT = 1$),\n0.44 ($T = 300$ keV, $\\tT = 1$), 0.14 ($T = 100$ keV, $\\tT = 2$), and\n0.05 ($T = 300$ keV, $\\tT = 2$). } \n \n\\label{figure1} \n\\end{figure}\n\\end{document}\n"
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"name": "cosmorev.tex",
"string": "\\documentclass[12pt]{article}\n\\usepackage{epsfig}\n\\usepackage{rotating}\n\\textheight 8.5in\n\\textwidth 6.25in\n\\oddsidemargin 0.07in\n\\evensidemargin 0.25in\n\\topmargin -.25in\n\\newcommand{\\gsim}{\\lower.7ex\\hbox{$\\;\\stackrel{\\textstyle>}{\\sim}\\;$}}\n\\newcommand{\\lsim}{\\lower.7ex\\hbox{$\\;\\stackrel{\\textstyle<}{\\sim}\\;$}}\n\\newcommand{\\bm}[1]{{\\mbox{\\boldmath $#1$}}}\n\\renewcommand{\\AA}{{\\bf A}\\kern-1.5mm\\raisebox{.7mm}{$\\scriptstyle\n\\backslash$}}\n\\newcommand{\\tc}{t_{\\rm c}}\n\\def\\sidno{\\ifcase\\arabic{page}\\or\n 1\\or 2\\or 3\\or 4\\or \\or 6\\or 7\\or 8\\or 9\\fi }\n\\renewcommand{\\thepage}{\\sidno}\n\n\\hyphenation{equals ob-serv-ations mech-an-ism Fourier Dimo-poulos\n equa-tions electro-weak}\n\n\\begin{document}\n\\footnotesep=14pt\n\\begin{flushright}\n\\baselineskip=14pt\n{\\normalsize DAMTP-1999-180}\\\\\n{\\normalsize {astro-ph/0002307}}\n\\end{flushright}\n\n\\vspace*{.5cm}\n\\renewcommand{\\thefootnote}{\\fnsymbol{footnote}}\n\\setcounter{footnote}{0}\n\\begin{center}\n{\\Large\\bf The origin of cosmic magnetic fields\\footnote{Talk presented\nat the Third International Conference on Particle Physics and the\nEarly Universe (COSMO-99), Trieste, Italy, 27 Sept - 3 Oct, 1999, to\nappear in the proceedings.}}\n\\end{center}\n\\setcounter{footnote}{2}\n\\begin{center}\n\\baselineskip=16pt\n{\\bf Ola T\\\"{o}rnkvist}\\footnote{E-mail:\n{\\tt o.tornkvist@damtp.cam.ac.uk}}\\\\\n\\vspace{0.4cm}\n{\\em Department of Applied Mathematics and Theoretical Physics,}\\\\\n{\\em Centre for Mathematical Sciences, University of Cambridge,}\\\\\n{\\em Wilberforce Road, Cambridge CB3 0WA, United Kingdom}\\\\\n\\vspace*{0.25cm}{31 January 2000}\n\\end{center}\n\\baselineskip=20pt\n\\vspace*{.5cm}\n\\begin{quote}\n\\begin{center}\n{\\bf\\large Abstract}\n\\end{center}\n\\vspace{0.2cm}\n{\\baselineskip=10pt%\nIn this talk,\nI review a number of particle-physics models that lead to\nthe creation of magnetic fields in the early universe and address the\ncomplex problem of evolving such primordial magnetic fields into\nthe fields observed today. Implications for future observations of the\nCosmic Microwave Background (CMB) are discussed. Focussing\non first-order phase transitions in the early universe, I describe\nhow magnetic fields arise in the collision of expanding true-vacuum\nbubbles both in Abelian and non-Abelian gauge theories.}\n\\end{quote}\n\\renewcommand{\\thefootnote}{\\arabic{footnote}}\n\\setcounter{footnote}{0}\n\\newpage\n\\baselineskip=16pt\n\\section{Introduction to Cosmic Magnetic Fields}\n\nA large number of spiral galaxies, including the Milky Way, carry\nmagnetic fields \\cite{Kronberg}.\nWith few exceptions,\nthe galactic field strengths are measured to be\na few times $10^{-6}$ G. This particular value\nhas also been found at a redshift of\n$z=0.395$ \\cite{redshift}\nand between the galaxies in clusters.\n\n\nStudies of the polarisation of synchrotron radiation emitted by\ngalaxies with a face-on view, such as M51, reveal that their magnetic\nfields are aligned\nwith spiral arms and density waves in the disk.\nA plausible explanation is that\ngalactic magnetic\nfields were\ncreated by a mean-field dynamo mechanism \\cite{dynamo}, in which a\nmuch smaller seed\nfield was exponentially amplified by the turbulent motion of ionised gas\nin conjunction with the differential rotation of the galaxy.\n\nFor the\ndynamo to work, the initial seed\nfield must be correlated on a scale of $100$ pc, corresponding to the\nlargest turbulent eddy \\cite{dynamo}.\nThe required strength of the seed field is subject to large uncertainties;\npast authors have quoted\n$10^{-21\\pm 2}$ G as the lower bound\nat the time of completed galaxy formation.\nThis would present a problem for most particle-physics and field-theory\ninspired mechanisms of magnetic field generation. However, in recent\nwork with A.-C.\\ Davis and M.J.\\ Lilley \\cite{bbounds}, I have shown that\nthe lower bound on the dynamo seed field can be significantly\nrelaxed if the universe is flat with a cosmological constant, as\nis suggested by recent supernovae observations \\cite{supernovae}.\nIn particular, for\nthe same dynamo parameters that give a lower bound of\n$10^{-20}$ G for $\\Omega_0=1$, $\\Omega_\\Lambda=0$,\nwe obtain\n$10^{-30}$ G for $\\Omega_0=0.2=1-\\Omega_\\Lambda$, implying that\nparticle-physics mechanisms could still be viable.\nThe observation at redshift $z=0.395$~\\cite{redshift} can also be\naccounted for with these parameters, but\nrequires a seed field of at least $10^{-23}$ G \\cite{bbounds}.\n\nThe dynamo amplifies the magnetic field until\nits energy\nreaches equipartition with the kinetic energy of\nthe\nionised gas, $\\langle B^2/2\\rangle=\\langle\\rho v^2/2\\rangle$, when further\ngrowth is suppressed by dynamical back reaction.\nThus\na\nfinal field of\n$B_0\\approx 10^{-6}$ G\nresults\nfor any seed field of sufficient strength.\n\nIn order to explain the galactic field strength without a\ndynamo mechanism,\none would require a strong primordial field of\n$10^{-3} (\\Omega_0 h^2)^{1/3}$ G at the epoch of radiation\ndecoupling $t_{\\rm dec}$, corresponding to a\nfield\nstrength $10^{-9} (\\Omega_0 h^2)^{1/3}$ G\non comoving scales of $1$ Mpc. Future precision measurements\nof the CMB will put\nsevere constraints on such a primordial field \\cite{CMB}.\nMoreover,\nmagnetic fields on Mpc scales\nhave been probed by observations\nof the Faraday rotation of polarised light from distant luminous\nsources, which give an upper bound of about $10^{-9}$ G \\cite{Kronberg}.\nThe observation of micro-Gauss fields between galaxies\nin clusters presents an interesting dilemma. Because such regions are\nconsiderably less dense than galaxies, it is doubtful whether a dynamo\ncould have been operative. Thus the intra-cluster magnetic fields, unless\nsomehow ejected from\ngalaxies, have formed directly from a primordial field stronger\nthan $10^{-3} (\\Omega_0 h^2)^{1/3}$ G at $t_{\\rm dec}$. Such a field would\ncertainly leave a signature in future CMB data \\cite{CMB}.\n\nParticle-physics\ninspired models, which typically produce weak\nseed fields,\nlead to precise predictions and\nthere\nhave an advantage over astrophysical mechanisms,\nwhere the magnetic field strength is determined by complicated\nnonlinear dynamics,\nor solutions of general relativity with a magnetic field \\cite{Thorne},\nwhere the field strength must be fixed by observations.\nWith the possible exception of the last-mentioned model,\nthere is no compelling scenario that produces a\nprimordial\nfield strong enough to eliminate the need for\na dynamo.\n\nSeed fields for the dynamo can be astrophysical or primordial.\nIn the former category there is\nthe important possibility that a seed field may arise spontaneously\ndue to non-parallel gradients\nof pressure and charge density\nduring the collapse of a protogalaxy \\cite{Kulsrud}. For the rest of\nthis talk, however, I shall assume that the seed field is primordial.\n\n\\section{Primordial Seed Fields}\n\n\nIt is\nuseful to\ndistinguish between primordial seed fields that are produced\nwith correlation\nlength smaller than\nvs.\\ larger than the horizon size.\n\n{\\sl Subhorizon-scale seed fields} typically arise\nin first-order phase transitions and from causal processes involving\ndefects. For example, magnetic fields may be created on the surface\nof bubble walls \\cite{Hogan} due to local charge separation\ninduced by baryon-number gradients. The magnetic fields are then\namplified by plasma turbulence near the bubble wall. This possibility has been\nexplored for the QCD \\cite{Cheng} as well as for the\nelectroweak \\cite{baym-sigl}\nphase transition.\n\nThe production of magnetic fields in\ncollisions of expanding true-vacuum\nbubbles will be discussed\nin Sec.~\\ref{bubs}. Fields can also be generated\nin the wakes of, or due to the wiggles of, GUT-scale cosmic strings during\nstructure formation, resulting in a large correlation\nlength \\cite{supercond}. Joyce and Shaposhnikov have shown that an\nasymmetry of right-handed electrons, possibly generated at the GUT scale,\nwould become unstable to the generation of a hypercharge magnetic field\nshortly before the electroweak phase transition \\cite{Joyce}, leading to a\ncorrelation length of order $10^{6}/T$.\n\n{\\sl Horizon-scale seed fields} emerge naturally in second-order phase\ntransitions of gauge theories\nfrom the failure of\ncovariant derivatives of the Higgs field to correlate on superhorizon\nscales \\cite{Vacha}.\n\n{\\sl Superhorizon-scale seed fields} can arise as a solution of\nthe Einstein equations for axisymmetric universes \\cite{Thorne} and\nin inflationary or pre-Big Bang (superstring) scenarios. In the latter case,\nvacuum fluctuations of the field tensor are amplified by the\ndynamical\ndilaton field \\cite{Gasperini}. Inflationary models produce extremely\nweak magnetic fields unless conformal invariance is explicitly\nbroken \\cite{TurWid}, but even then great difficulties remain.\nAn exciting new possibility is that magnetic fields may be produced\nvia parametric resonance with an oscillating field \\cite{Finelli}\ne.g.\\ during\npreheating after inflation.\nBecause the inflaton is initially coherent on\nsuperhorizon scales, large correlations can arise without violating\ncausality.\nA similar proposal involves\ncharged scalar particles, minimally coupled to\ngravity, that are created from the vacuum due to the changing\nspace-time geometry at the end of inflation. The particles give\nrise to fluctuating electric currents which are claimed to produce\nsuperhorizon-scale (indeed, galactic-scale) fields of sufficient\nstrength to satisfy the galactic dynamo bound \\cite{Calzetta}.\nThis mechanism deserves further investigation.\n\n\\section{Evolution of Primordial Magnetic Fields}\n\nA serious problem with many\nparticle-physics and field-theory scenarios for producing primordial\nmagnetic fields is that the resulting correlation length $\\xi$ is\nvery small.\nIf the fields are produced\nat the QCD phase transition or earlier with sub-horizon correlation\nlength, then the expansion\nof the universe cannot stretch\n$\\xi$ to more than 1 pc today (see Fig.~1).\nThis is far short of the\ngalactic dynamo lower bound of 5-10 kpc (comoving), corresponding\nto 100 pc in a virialised galaxy \\cite{bbounds}.\n\n\n\\begin{sidewaysfigure}\n\\epsfig{figure=evolrot.eps,width=\\textheight}\n\\end{sidewaysfigure}\n\nNevertheless, many authors \\cite{brandenburg,Son,carroll,kostas}\nhave argued that the correlation length\nwill grow more rapidly due to magnetohydrodynamic (MHD) turbulence\nand inverse cascade, which transfers power from\nsmall-scale to large-scale Fourier modes. Several non-relativistic\nmodels for this\nevolution are analysed in Fig.~1. The most conservative estimate is\nobtained by assuming that\nthe magnetic field strength on the scale of one correlation\nlength at any time\nequals the volume average of fields that were produced on smaller\nscales but have\nsince decayed \\cite{Son}.\nThis leads to a growth $\\xi\\sim t^{7/10}$ (obtained from\nthe Minkowski-space growth $\\xi\\sim t^{2/5}$ via the substitution\n$t\\to \\tau=t^{1/2}$ and multiplication by the scale factor). The most\noptimistic estimate corresponds to the case\nwhen the magnetic field has maximal\nhelicity in relation to the energy density \\cite{Son,carroll}. As magnetic\nhelicity is approximately conserved\nin the high-conductivity early-universe environment, one obtains\nthe growth law $\\xi\\sim t^{5/6}$.\nTurbulence ends, freezing the growth (in comoving coordinates)\nwhen the kinetic Reynolds number drops\nbelow unity\nat the $e^+e^-$ annihilation or later, depending on the model and\nthe parameters of the initial field.\n\n\nAn intermediate and rather plausible estimate has been given by\nDimopoulos and Davis \\cite{kostas}, who use the fact that\nthe magnetic flux enclosed by a (sufficiently large) comoving closed\ncurve is conserved. The correlation length here increases at a rate\ngiven by the Alfv\\'{e}n velocity, so that $\\xi\\sim t^{3/4}$.\n\nAs Fig.~1 shows, only the most optimistic of these growth laws\nleads to a correlation length today\nthat satisfies the galactic dynamo bound. This occurs\n for fields correlated over the horizon scale at the QCD phase transition.\nBeware, however, that the growth laws were derived\nusing {\\sl non-relativistic\\/} MHD equations assuming\nthat the magnetic field energy density remains\nin equipartition with the\nkinetic energy density\n$\\rho\\bar{v}^2/2$, where $\\bar{v}$ is the presumed {\\sl non-relativistic\\/}\n``bulk velocity'' of\nthe {\\sl ultra-relativistic\\/} plasma.\nIt seems plausible that a relativistic treatment could alter the predicted\nevolution dramatically.\nIn this light, I\nfind it too early to reject the idea that also subhorizon fields\nmight evolve into fields sufficiently correlated to seed the galactic\ndynamo.\n\nAt the same time, Fig.~1 demonstrates\nthe intrinsic advantage of\nsuperhorizon field generation mechanisms.\nFor these,\nthe principal problem is not the correlation length,\n but to achieve sufficient strength of the magnetic field.\n\n\\section{Magnetic Fields From Bubble Collisions}\n\\label{bubs}\n\nFirst-order phase transitions in the early\nuniverse proceed through the nucleation of bubbles \\cite{Coleman},\nwhich subsequently expand and collide.\nIn order to study the generation of magnetic fields,\nthe initial field strength\nis assumed to vanish.\nOne may then choose\na gauge in which the vector potential $V_\\mu$ is initially zero.\nIn this gauge, the nucleation probability is peaked around bubbles\nwith constant orientation (phase) of the Higgs field.\n\nWe consider first a U(1) toy model.\nLet the Higgs field in two colliding bubbles be given by\n$\\phi_1=\\rho_1(x) e^{i\\theta_1}$ and\n$\\phi_2=\\rho_2(x) e^{i\\theta_2}$, respectively,\nwhere $\\theta_1\\neq\\theta_2$.\nWhen the bubbles meet, the phase gradient establishes a\ngauge-invariant current $j_k=iq[\\phi^{\\dagger} D_k \\phi -\n(D_k\\phi)^\\dagger \\phi]$ across the surface of intersection of the\ntwo bubbles, where $D_k=\\partial_k-iqV_k$. This current, in turn,\ngives rise to\na ring-like flux of the field strength $F_{ij}=\\partial_i V_j-\n\\partial_j V_i$, which takes the shape of a girdle encircling the\nbubble intersection region.\n\nIn recent work we have obtained accurate,\nbut rather complicated,\n analytical solutions for the\nfield evolution\nin U(1) bubble collisions \\cite{u1bub}\n using an analytical expression for the\nbubble-wall ``bounce'' profile \\cite{Coleman}.\nA simpler analytical solution was found by Kibble and\nVilenkin [KV] \\cite{KibVil}, who\nmade\nthree rather crude\napproximations: (1)\nThe bubble walls move through the plasma without friction,\n(2) the modulus of the Higgs field in the\ninterior of the bubbles\nequals a constant, and (3) the phase $\\theta$ of the Higgs field is\na step function at the moment of collision. The first of these\nassumptions leads to a simple equation of motion for the bubble wall,\nwhich endows the system\nwith a dynamical O(1,2) symmetry \\cite{Hawking}.\nAll quantities are then functions only of two coordinates:\n$z$, the position along the axis through the bubble centres, and\n$\\tau=\\sqrt{t^2-x^2-y^2}$, combining time with the perpendicular directions.\nThe solutions can be written\ndown explicitly in terms of Bessel functions\nand,\ndespite the crudeness of the approximations,\ncapture correctly the qualitative behaviour\nof the fields in the bubble overlap\nregion \\cite{u1bub}.\n\nThe simplicity of the KV approach makes it ideal for\nattacking the more complicated problem of non-Abelian bubble collisions.\nThese could occur in a first-order electroweak phase transition\n(e.g.\\ in the MSSM for $M_h\\lsim 116$ GeV) or in a GUT phase transition.\nField strengths created in an early phase transition naturally project\nonto the electromagnetic U(1) subgroup at the electroweak transition.\nI will here concentrate on \\mbox{SU(2)$\\times$U(1) $\\to$U(1)$_{\\rm EM}$}\nand the minimal Standard Model as a\nsolvable example.\n\nThe initial Higgs field\nin the two bubbles can be written in the form\n\\begin{equation}\n\\Phi_1=\\exp(-i\\theta_0\\bm{n}\\cdot\\bm{\\sigma})\n\\left(\\begin{array}{c}0\\\\*\\rho_1(x)\\end{array}\\right)~,\\quad\\quad\n\\Phi_2=\\exp(i\\theta_0\\bm{n}\\cdot\\bm{\\sigma})\n\\left(\\begin{array}{c}0\\\\*\\rho_2(x)\\end{array}\\right)~.\n\\end{equation}\nAs the bubbles collide, non-Abelian currents\n$j_k^A=i[\\Phi^\\dagger T^A D_k\\Phi - (D_k\\Phi)^\\dagger T^A \\Phi]$\ndevelop across the surface of their intersection, where\n$T^A=(g'/2,g\\sigma^a/2)$, $D_k=\\partial_k-iW_k^A T^A$ and\n$W_k^A=(Y_k,W_k^a)$. In analogy with the U(1) case, one obtains\na ring-like flux of non-Abelian fields. The recipe for projecting\nout the electromagnetic field\namongst the non-Abelian fields in an\narbitrary gauge has been given elsewhere \\cite{bdef}.\n\nIn the special cases $\\bm{n}=(0,0,\\pm 1)$ and $\\bm{n}=(n_1,n_2,0)$\nit is known \\cite{SafCop} that the non-Abelian flux consists of\npure Z and W vector fields, respectively.\nThe absence of an electromagnetic field\nhas its explanation in\nthe fact that the normalised Higgs\nfield $\\hat{\\Phi}\\equiv\n\\Phi/(\\Phi^\\dagger\\Phi)^{1/2}$ maps to a geodesic on the\nHiggs vacuum manifold and the gauge fields map to a line\nin the Lie algebra spanned by the generator of that same geodesic:\n\\begin{equation}\n\\hat{\\Phi}(x)=\\exp(i\\theta(x)\\bm{n}\\cdot\\bm{\\sigma})\n(0~~1)^\\top\n{}~,\\quad\n\\AA_\\mu(x)\\equiv W_\\mu^A(x) T^A= f_\\mu(x)\\bm{n}\\cdot\\bm{\\sigma}~.\n\\end{equation}\nWhen $n_3\\neq 0,\\pm1$, both $Z$ and $W$ fields are excited. Because\nthey have unequal masses\n$M_W\\neq M_Z$, they evolve\ndifferently \\cite{Grasso} and the fields $\\hat{\\Phi}$ and\n$\\AA_\\mu$ stray from the geodesic and its tangent, producing\nan electromagnetic current.\n\nI have used a KV approach to derive a\nperturbative analytical\nsolution for the evolution of gauge fields in an electroweak\nbubble collision, valid as long as the fields are small and higher-order\nnonlinearities can be neglected. The space allotted here\nallows me only to indicate the structure of the solution for the\nelectromagnetic field, which is\n\\begin{eqnarray}\nF^{\\alpha z}&=& x^\\alpha \\frac{\\sin\\theta_{\\rm w}}{g} n_3(1-n_3^2)\n\\int_0^z dz' \\left(\\rule{0pt}{5mm}\n h_3(\\tau,z')\\right.\\nonumber\\\\*\n &+& \\int_{\\tc}^\\tau \\!\\!d\\tau''\\!\\!\n\\int_{z'-\\tau''+\\tc}^{z'+\\tau''-\\tc} \\hspace*{-2mm}\ndz'' h_1(\\sqrt{(\\tau-\\tau'')^2 -\n(z'-z'')^2}) h_2(\\tau'',z'')\\!\\!\\left.\\rule{0pt}{5mm}\\right),\n\\end{eqnarray}\nwhere $\\tc$ is the time of collision and the functions $h_i$ contain\nproducts of $i$ Bessel functions. As expected, the\nresulting field strength is\nof the order of $M_W^2/g$ with a correlation length $\\xi\\sim M_W^{-1}$.\nHowever, when\nplasma friction and conductivity are taken into account, the magnetic\nfield spreads over the interior of a bubble \\cite{lilley}\nleading to an appreciable increase in correlation length.\n\n\\subsection*{Acknowledgments}\nThe author is supported by the European Commission's TMR programme under\nContract No.~ERBFMBI-CT97-2697.\n\n\n\\begin{thebibliography}{99}\n\n\\bibitem{Kronberg}P.\\,P.\\ Kronberg, Rep.\\ Prog.\\ Phys.\\ {\\bf 57}, 325 (1994).\n\\bibitem{redshift} P.\\,P.\\ Kronberg and J.\\,J.\\ Perry, Ap.\\ J.\\ {\\bf\n263}, 518 (1982); P.\\,P.\\ Kronberg, J.\\,J.\\ Perry and\n E.\\,L.\\,H.\\ Zukowski,\n{\\em ibid.\\/} {\\bf 387}, 528 (1992).\n\\bibitem{dynamo} Ya.\\,B.\\ Zeldovich, A.\\,A.\\ Ruzmaikin and D.\\,D.\\ Sokolov,\n{\\em Magnetic Fields in Astrophysics\\/} (Gordon and Breach, New York,\n1983).\n\\bibitem{bbounds} A.-C.\\ Davis, M.\\ Lilley and O.\\ T\\\"{o}rnkvist,\nPhys.\\ Rev.\\ D {\\bf 60}, 021301 (1999).\n\\bibitem{supernovae} S.\\ Perlmutter et al.,\nAp.\\ J. {\\bf 517}, 565P (1999);\nP.\\,M.\\ Garnavich et al.,\n{\\em ibid.\\/} {\\bf 509}, 74G (1998).\n\\bibitem{CMB}\nJ.\\ Adams, U.\\,H.\\ Danielsson, D.\\ Grasso, and H.\\ Rubinstein,\nPhys.\\ Lett.\\ {\\bf B388}, 253 (1996);\nJ.\\,D.\\ Barrow, P.\\,G.\\ Ferreira and J.\\ Silk,\nPhys.\\ Rev.\\ Lett.\\ {\\bf 78}, 3610 (1997);\nA.\\ Kosowsky and A.\\ Loeb, Ap.\\ J.\\ {\\bf 469}, 1 (1996).\n\\bibitem{Thorne} Ya.\\,B.\\ Zeldovich, Zh.\\ Eksp.\\ Teor.\\ Fiz.\\ {\\bf 48},\n986 (1964) [Sov.\\ Phys.\\ JETP {\\bf 21}, 656 (1965)];\nK.\\ Thorne, Bull.\\ Am.\\ Phys.\\ Soc.\\ {\\bf 11}, 340 (1966),\nAp.\\ J.\\ {\\bf 148}, 51 (1967).\n\\bibitem{Kulsrud} H.\\ Lesch and M.\\ Chiba,\nAstron.\\ Astrophys.\\ {\\bf 297}, 305L (1995);\nR.M.~Kulsrud, R.\\ Cen, J.P.\\ Ostriker and D.\\ Ryu,\nAp.\\ J.\\ {\\bf 480}, 481 (1997).\n\\bibitem{Hogan}\nC.\\,J.\\ Hogan, Phys.\\ Rev.\\ Lett.\\ {\\bf 51}, 1488 (1983)\n\\bibitem{Cheng}\nB.\\ Cheng and A.\\,V.\\ Olinto, Phys.\\ Rev.\\ D {\\bf 50}, 2421 (1994).\n\\bibitem{baym-sigl}\nG.\\ Baym, D.\\ B\\\"{o}deker and L.\\ McLerran, Phys.\\ Rev.\\ D {\\bf 53},\n662 (1996); G.\\ Sigl, A.\\ Olinto and K.\\ Jedamzik, {\\em ibid.\\/} {\\bf 55},\n4582 (1997).\n\\bibitem{supercond}\nT.\\ Vachaspati and A.\\ Vilenkin, Phys.\\ Rev.\\ Lett.\\ {\\bf 67}, 1057 (1991);\nK.\\ Dimopoulos, Phys.\\ Rev.\\ D {\\bf 57}, 4629 (1998).\n\\bibitem{Joyce} M.\\ Joyce and M.\\ Shaposhnikov, Phys.\\ Rev.\\ Lett.\\\n{\\bf 79}, 1193 (1997).\n\\bibitem{Vacha} T.\\ Vachaspati, Phys.\\ Lett.\\ B {\\bf 265}, 258 (1991).\n\\bibitem{Gasperini} M.\\ Gasperini, M.\\ Giovannini and G.\\ Veneziano,\nPhys.\\ Rev.\\ Lett.\\ {\\bf 75}, 3796 (1995); D.\\ Lemoine and M.\\ Lemoine,\nPhys.\\ Rev.\\ D {\\bf 52}, 1955 (1995).\n\\bibitem{TurWid} M.\\,S.\\ Turner and L.\\,M.\\ Widrow, Phys.\\ Rev.\\ D {\\bf 37},\n 2743 (1988); W.\\,D.\\ Garretson, G.\\,B.\\ Field and S.\\,M.\\ Carroll,\n{\\em ibid.\\/} {\\bf 46}, 5346 (1992).\n\n\\bibitem{Finelli} R.\\ Brustein and D.H.\\ Oaknin, Phys.\\ Rev.\\ D {\\bf 60},\n023508 (1999), Phys.\\ Rev.\\ Lett.\\ {\\bf 82}, 2628 (1999);\nF.\\ Finelli and A.\\ Gruppuso, hep-ph/0001231.\n\\bibitem{Calzetta}\nE.A.\\ Calzetta, A.\\ Kandus, and F.D.\\ Mazzitelli, Phys.\\ Rev.\\ D {\\bf\n57}, 7139 (1998); A.\\ Kandus, E.A.\\ Calzetta, F.D.\\ Mazzitelli and\nC.E.M.\\ Wagner, Phys.\\ Lett.\\ B {\\bf 472}, 287 (2000).\n\\bibitem{brandenburg}\nA.\\ Brandenburg, K.\\ Enqvist and P.\\ Olesen, Phys.\\ Rev.\\ D {\\bf 54},\n1291 (1996);\nT.\\ Shiromizu, Phys.\\ Lett.\\ B {\\bf 443}, 127 (1998).\n\\bibitem{Son}\nD.\\,T.\\ Son, Phys.\\ Rev.\\ D {\\bf 59}, 063008 (1999).\n\\bibitem{carroll}\nG.\\,B.\\ Field and S.\\,M.\\ Carroll, astro-ph/9811206.\n\\bibitem{kostas} K.\\ Dimopoulos and A.-C.\\ Davis,\nPhys.\\ Lett.\\ {\\bf B390} 87 (1997).\n\\bibitem{Coleman} S. Coleman,\nPhys. Rev. D {\\bf 15}, 2929 (1977);\n{\\it ibid.\\/} D {\\bf 16}, 1248 (1977).\n\\bibitem{u1bub} E.\\,J.\\ Copeland, P.\\,M.\\ Saffin and O.\\ T\\\"{o}rnkvist,\nhep-ph/9907437, to appear in Phys.\\ Rev.\\ D.\n\\bibitem{KibVil} T.\\,W\\,B.\\ Kibble and A.\\ Vilenkin, Phys.\\ Rev.\\ {\\bf D52},\n679 (1995).\n\\bibitem{Hawking}\nS.\\ Hawking, I.\\ Moss, and J.\\ Stewart,\nPhys.\\ Rev.\\ D {\\bf 26}, 2681 (1982).\n\\bibitem{bdef} O.\\ T\\\"{o}rnkvist, hep-ph/9805255,\nto be published in Phys.\\ Rev.\\ D.\n\\bibitem{SafCop} P.\\ Saffin and E.\\ Copeland,\nPhys. Rev. D {\\bf 56}, 1215 (1997).\n\\bibitem{Grasso} D.\\ Grasso and A.\\ Riotto, Phys.\\ Lett.\\ B {\\bf 418},\n258 (1998).\n\\bibitem{lilley} A.-C.\\ Davis and M.\\ Lilley,\nPhys.\\ Rev.\\ D {\\bf 61}, 043502 (2000).\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002307.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{Kronberg}P.\\,P.\\ Kronberg, Rep.\\ Prog.\\ Phys.\\ {\\bf 57}, 325 (1994).\n\\bibitem{redshift} P.\\,P.\\ Kronberg and J.\\,J.\\ Perry, Ap.\\ J.\\ {\\bf\n263}, 518 (1982); P.\\,P.\\ Kronberg, J.\\,J.\\ Perry and\n E.\\,L.\\,H.\\ Zukowski,\n{\\em ibid.\\/} {\\bf 387}, 528 (1992).\n\\bibitem{dynamo} Ya.\\,B.\\ Zeldovich, A.\\,A.\\ Ruzmaikin and D.\\,D.\\ Sokolov,\n{\\em Magnetic Fields in Astrophysics\\/} (Gordon and Breach, New York,\n1983).\n\\bibitem{bbounds} A.-C.\\ Davis, M.\\ Lilley and O.\\ T\\\"{o}rnkvist,\nPhys.\\ Rev.\\ D {\\bf 60}, 021301 (1999).\n\\bibitem{supernovae} S.\\ Perlmutter et al.,\nAp.\\ J. {\\bf 517}, 565P (1999);\nP.\\,M.\\ Garnavich et al.,\n{\\em ibid.\\/} {\\bf 509}, 74G (1998).\n\\bibitem{CMB}\nJ.\\ Adams, U.\\,H.\\ Danielsson, D.\\ Grasso, and H.\\ Rubinstein,\nPhys.\\ Lett.\\ {\\bf B388}, 253 (1996);\nJ.\\,D.\\ Barrow, P.\\,G.\\ Ferreira and J.\\ Silk,\nPhys.\\ Rev.\\ Lett.\\ {\\bf 78}, 3610 (1997);\nA.\\ Kosowsky and A.\\ Loeb, Ap.\\ J.\\ {\\bf 469}, 1 (1996).\n\\bibitem{Thorne} Ya.\\,B.\\ Zeldovich, Zh.\\ Eksp.\\ Teor.\\ Fiz.\\ {\\bf 48},\n986 (1964) [Sov.\\ Phys.\\ JETP {\\bf 21}, 656 (1965)];\nK.\\ Thorne, Bull.\\ Am.\\ Phys.\\ Soc.\\ {\\bf 11}, 340 (1966),\nAp.\\ J.\\ {\\bf 148}, 51 (1967).\n\\bibitem{Kulsrud} H.\\ Lesch and M.\\ Chiba,\nAstron.\\ Astrophys.\\ {\\bf 297}, 305L (1995);\nR.M.~Kulsrud, R.\\ Cen, J.P.\\ Ostriker and D.\\ Ryu,\nAp.\\ J.\\ {\\bf 480}, 481 (1997).\n\\bibitem{Hogan}\nC.\\,J.\\ Hogan, Phys.\\ Rev.\\ Lett.\\ {\\bf 51}, 1488 (1983)\n\\bibitem{Cheng}\nB.\\ Cheng and A.\\,V.\\ Olinto, Phys.\\ Rev.\\ D {\\bf 50}, 2421 (1994).\n\\bibitem{baym-sigl}\nG.\\ Baym, D.\\ B\\\"{o}deker and L.\\ McLerran, Phys.\\ Rev.\\ D {\\bf 53},\n662 (1996); G.\\ Sigl, A.\\ Olinto and K.\\ Jedamzik, {\\em ibid.\\/} {\\bf 55},\n4582 (1997).\n\\bibitem{supercond}\nT.\\ Vachaspati and A.\\ Vilenkin, Phys.\\ Rev.\\ Lett.\\ {\\bf 67}, 1057 (1991);\nK.\\ Dimopoulos, Phys.\\ Rev.\\ D {\\bf 57}, 4629 (1998).\n\\bibitem{Joyce} M.\\ Joyce and M.\\ Shaposhnikov, Phys.\\ Rev.\\ Lett.\\\n{\\bf 79}, 1193 (1997).\n\\bibitem{Vacha} T.\\ Vachaspati, Phys.\\ Lett.\\ B {\\bf 265}, 258 (1991).\n\\bibitem{Gasperini} M.\\ Gasperini, M.\\ Giovannini and G.\\ Veneziano,\nPhys.\\ Rev.\\ Lett.\\ {\\bf 75}, 3796 (1995); D.\\ Lemoine and M.\\ Lemoine,\nPhys.\\ Rev.\\ D {\\bf 52}, 1955 (1995).\n\\bibitem{TurWid} M.\\,S.\\ Turner and L.\\,M.\\ Widrow, Phys.\\ Rev.\\ D {\\bf 37},\n 2743 (1988); W.\\,D.\\ Garretson, G.\\,B.\\ Field and S.\\,M.\\ Carroll,\n{\\em ibid.\\/} {\\bf 46}, 5346 (1992).\n\n\\bibitem{Finelli} R.\\ Brustein and D.H.\\ Oaknin, Phys.\\ Rev.\\ D {\\bf 60},\n023508 (1999), Phys.\\ Rev.\\ Lett.\\ {\\bf 82}, 2628 (1999);\nF.\\ Finelli and A.\\ Gruppuso, hep-ph/0001231.\n\\bibitem{Calzetta}\nE.A.\\ Calzetta, A.\\ Kandus, and F.D.\\ Mazzitelli, Phys.\\ Rev.\\ D {\\bf\n57}, 7139 (1998); A.\\ Kandus, E.A.\\ Calzetta, F.D.\\ Mazzitelli and\nC.E.M.\\ Wagner, Phys.\\ Lett.\\ B {\\bf 472}, 287 (2000).\n\\bibitem{brandenburg}\nA.\\ Brandenburg, K.\\ Enqvist and P.\\ Olesen, Phys.\\ Rev.\\ D {\\bf 54},\n1291 (1996);\nT.\\ Shiromizu, Phys.\\ Lett.\\ B {\\bf 443}, 127 (1998).\n\\bibitem{Son}\nD.\\,T.\\ Son, Phys.\\ Rev.\\ D {\\bf 59}, 063008 (1999).\n\\bibitem{carroll}\nG.\\,B.\\ Field and S.\\,M.\\ Carroll, astro-ph/9811206.\n\\bibitem{kostas} K.\\ Dimopoulos and A.-C.\\ Davis,\nPhys.\\ Lett.\\ {\\bf B390} 87 (1997).\n\\bibitem{Coleman} S. Coleman,\nPhys. Rev. D {\\bf 15}, 2929 (1977);\n{\\it ibid.\\/} D {\\bf 16}, 1248 (1977).\n\\bibitem{u1bub} E.\\,J.\\ Copeland, P.\\,M.\\ Saffin and O.\\ T\\\"{o}rnkvist,\nhep-ph/9907437, to appear in Phys.\\ Rev.\\ D.\n\\bibitem{KibVil} T.\\,W\\,B.\\ Kibble and A.\\ Vilenkin, Phys.\\ Rev.\\ {\\bf D52},\n679 (1995).\n\\bibitem{Hawking}\nS.\\ Hawking, I.\\ Moss, and J.\\ Stewart,\nPhys.\\ Rev.\\ D {\\bf 26}, 2681 (1982).\n\\bibitem{bdef} O.\\ T\\\"{o}rnkvist, hep-ph/9805255,\nto be published in Phys.\\ Rev.\\ D.\n\\bibitem{SafCop} P.\\ Saffin and E.\\ Copeland,\nPhys. Rev. D {\\bf 56}, 1215 (1997).\n\\bibitem{Grasso} D.\\ Grasso and A.\\ Riotto, Phys.\\ Lett.\\ B {\\bf 418},\n258 (1998).\n\\bibitem{lilley} A.-C.\\ Davis and M.\\ Lilley,\nPhys.\\ Rev.\\ D {\\bf 61}, 043502 (2000).\n\n\\end{thebibliography}"
}
] |
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astro-ph0002308
|
Collisional versus collisionless dark matter
|
[
{
"author": "Ben Moore\\altaffilmark{1}"
},
{
"author": "Sergio Gelato\\altaffilmark{1}"
},
{
"author": "Adrian Jenkins\\altaffilmark{1}"
},
{
"author": "F. R. Pearce\\altaffilmark{1} \\& Vicent Quilis\\altaffilmark{1}"
}
] |
We compare the structure and substructure of dark matter halos in model universes dominated by collisional, strongly self interacting dark matter (SIDM) and collisionless, weakly interacting dark matter (CDM). While SIDM virialised halos are more nearly spherical than CDM halos, they can be rotationally flattened by as much as 20\% in their inner regions. Substructure halos suffer ram-pressure truncation and drag which are more rapid and severe than their gravitational counterparts tidal stripping and dynamical friction. Lensing constraints on the size of galactic halos in clusters are a factor of two smaller than predicted by gravitational stripping, and the recent detection of tidal streams of stars escaping from the satellite galaxy Carina suggests that its tidal radius is close to its optical radius of a few hundred parsecs --- an order of magnitude smaller than predicted by CDM models but consistent with SIDM. The orbits of SIDM satellites suffer significant velocity bias $\sigma_{_{SIDM}}/\sigma_{_{CDM}}=0.85$ and are more circular than CDM, $\beta_{_{SIDM}} \approx 0.5$, in agreement with the inferred orbits of the Galaxy's satellites. In the limit of a short mean free path, SIDM halos have singular isothermal density profiles, thus in its simplest incarnation SIDM is inconsistent with galactic rotation curves.
|
[
{
"name": "sidm.tex",
"string": "% $Id: sidm.tex,v 1.3 2000/02/16 15:59:19 gelato Exp gelato $\n\\documentclass{article}\n\\usepackage{emulateapj,psfig}\n%usepackage{eulergreek}\n\n\\def\\cf{cf.}\n\\def\\eg{{\\it e.g.}}\n\\def\\ie{{\\it i.e.}}\n\\def\\etal{{\\it et al.}}\n\\def\\kms{\\ensuremath{\\mbox{km}\\,\\mbox{s}^{-1}}}\n\\def\\kmsmpc{\\ensuremath{\\mbox{km}\\,\\mbox{s}^{-1}\\,\\mbox{Mpc}^{-1}}}\n\\def\\hmpc{\\ensuremath{h^{-1}\\,\\mbox{Mpc}}}\n\\def\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n' \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\\def\\gsim{ \\lower .75ex \\hbox{$\\sim$} \\llap{\\raise .27ex \\hbox{$>$}} }\n\\def\\lsim{ \\lower .75ex \\hbox{$\\sim$} \\llap{\\raise .27ex \\hbox{$<$}} }\n\n\n\\accepted{}\n\n\\long\\def\\***#1{{\\scshape ***#1***}}\n\\def\\arraystretch{1.25}\n\n\\makeatletter\n\\newenvironment{inlinetable}{%\n\\def\\@captype{table}%\n\\noindent\\begin{minipage}{0.999\\linewidth}\\begin{center}\\footnotesize}\n{\\end{center}\\end{minipage}\\smallskip}\n\n\\newenvironment{inlinefigure}{%\n\\def\\@captype{figure}%\n\\noindent\\begin{minipage}{0.999\\linewidth}\\begin{center}}\n{\\end{center}\\end{minipage}\\smallskip}\n\\makeatother\n\n\\begin{document}\n\\lefthead{Moore et al.}\n\\righthead{Collisional dark matter}\n\\submitted{Submitted to ApJ Letters, February 16th, 2000}\n\n\\title{Collisional versus collisionless dark matter} \n \\author{Ben Moore\\altaffilmark{1}, Sergio Gelato\\altaffilmark{1}, \nAdrian Jenkins\\altaffilmark{1}, \nF. R. Pearce\\altaffilmark{1} \n\\& Vicent Quilis\\altaffilmark{1}}\n\n\\altaffiltext{1}{Physics Department, University of Durham, Durham City, UK}\n\n\n\\begin{abstract}\n\nWe compare the structure and substructure of dark matter halos in\nmodel universes dominated by collisional, strongly self interacting\ndark matter (SIDM) and collisionless, weakly interacting dark matter\n(CDM). While SIDM virialised halos are more nearly spherical than CDM\nhalos, they can be rotationally flattened by as much as 20\\% in their\ninner regions. Substructure halos suffer ram-pressure truncation and\ndrag which are more rapid and severe than their gravitational\ncounterparts tidal stripping and dynamical friction. Lensing\nconstraints on the size of galactic halos in clusters are a factor of\ntwo smaller than predicted by gravitational stripping, and the recent\ndetection of tidal streams of stars escaping from the satellite galaxy\nCarina suggests that its tidal radius is close to its optical radius\nof a few hundred parsecs --- an order of magnitude smaller than\npredicted by CDM models but consistent with SIDM. The orbits of SIDM\nsatellites suffer significant velocity bias $\\sigma_{_{\\rm\nSIDM}}/\\sigma_{_{\\rm CDM}}=0.85$ and are more circular than CDM,\n$\\beta_{_{\\rm SIDM}} \\approx 0.5$, in agreement with the inferred\norbits of the Galaxy's satellites. In the limit of a short mean free\npath, SIDM halos have singular isothermal density profiles, thus in\nits simplest incarnation SIDM is inconsistent with galactic rotation\ncurves.\n\n\\end{abstract}\n\n\\keywords{dark matter --- galaxies: halos --- galaxies: formation ---\ngalaxies: kinematics and dynamics --- galaxies: evolution --- galaxies:\nclusters: general}\n\n\n\\section{Introduction}\n\nThe nature of dark matter is still far from being resolved. Primordial\nnucleosynthesis and observational data suggest that the baryonic\nmaterial accounts for just a fraction of the matter density in the\nuniverse. Fundamental particles remain the most likely candidate for\nthe dark matter and much effort has been devoted to\nresearching a class of weakly interacting, collisionless dark matter\n(CDM) (\\eg, Davis \\etal{} 1985). However, the hierarchical gravitational\ncollapse of cold collisionless particles leads to dense, \nsingular dark matter halos -- a result that is central to several \nfundamental problems with this model on small scales \n(\\eg~Hogan \\& Dalcanton 2000 and references within).\n\nIt may be possible to solve the current problems with CDM by appealing\nto extreme astrophysical processes. Alternatively, we can explore\nother dark matter candidates that behave differently on non-linear\nscales. One possibility is strongly self interacting dark matter\n(hereafter SIDM). Originally proposed to suppress small scale power in\nthe standard CDM model (Carlson \\etal{} 1992, Machaceck \\etal{} 1994, de\nLaix \\etal{} 1995), SIDM was recently revived by Spergel \\& Steinhardt\n(1999) to solve some of the outstanding problems with CDM. The\nbehaviour of this component depends on the particles' collisional\ncross-section. Large cross-sections imply short mean free paths, so\nthat the dark matter can be described as a fluid that does not cool\nbut can shock heat. Particles with a mean free path of order the scale\nlength of a dark matter halo offers the possibility of conductive heat\ntransfer to the halo cores (Spergel \\& Steinhardt 1999). In this\nLetter we contrast the dynamics and structure of ``halos within\nhalos'' between collisional and collisionless dark matter and compare\npredictions with current observational constraints.\n\n\\\n\n\\section{Simulating the structure of SIDM halos}\n\nIn this section we present the first numerical calculations of the\nstructure of dark matter halos in which the particles have a large\ninteraction cross-section. Self interacting dark matter behaves like\na collisional gas and its evolution can be simulated using standard\ncomputational fluid dynamics techniques. We model the collisional dark\nmatter fluid by approximating its behaviour as an ideal gas where the\nratio of specific heats is 5/3. We use the smoothed-particle\nhydro-dynamics (SPH) code Hydra (Couchman \\etal{} 1995) to follow the\nhierarchical growth of a massive dark matter halo. For added\nconfidence in the robustness of key results, we perform independent\ncollapse tests using an evolution of the Benz-Navarro SPH code\n(\\cf~Gelato \\& Sommer-Larsen 1999). \n\n%%%%%%%%%%%%%%%%\n\\begin{figure*}\n%%%\\centerline{\\includegraphics[width=1.0\\linewidth]{sidm_panel.ps}}\n%{\\large\\bf \\hskip 5cm www.nbody.net}\n%\\vskip -2.5cm\n\\centerline{\\psfig{figure=sidm_panel.ps,height=0.4\\textheight}}\n\\caption{\nPanel (a) is a view of the central 32 Mpc region of our SIDM\nsimulation at a redshift z=0. \nPanel (b) shows the velocity vectors of particles within the central 500\nkpc of one of the SIDM halos. The system is viewed face on to the most\nflattened plane demonstrating the coherent rotation.\nDense, but heavily stripped substructure halos can be found sinking deep\ninto the central regions - frequently prograde with the halo angular momentum. \nPanel (c) shows the high resolution halo in the CDM simulation to be compared\nwith panel (d) that shows the corresponding halo from the SIDM simulation.\nBoth of these halos are plotted to their virial radius.\n}\n\\label{fig:a:opt}\n\\end{figure*}\n%%%%%%%%%%%%%%%%\n\nOur cosmological initial conditions were adapted from the ``cluster\ncomparison'' simulation (Frenk \\etal{} 1999), in which a massive dark\nmatter halo forms within a 64 Mpc box of a critical density universe.\n(We adopt $H_0=50\\,\\kmsmpc$ throughout.) We carry out\ntwo simulations; the first is a CDM plus 10\\% non-radiative gas and\nthe second run is 100\\% non-radiative gas ($\\equiv$ SIDM). The\nparticle mass is approximately $8.6\\times 10^9M_\\odot$ and the\neffective force resolution is 0.3\\% of the virial radius of the final\ncluster $r_{\\rm vir}=2.7$ Mpc (see Figure~\\ref{fig:a:opt}).\n\nThe CDM run behaves as expected and as characterised\nby many previous authors (\\eg, Barnes \\& Efstathiou 1987, Frenk \\etal{}\n1999). One interesting point to highlight from this and similar\nsimulations is that the gas ends up with a shallower density profile\nthan the dark matter (\\cf~Figure~\\ref{fig:b:opt}). \nThis is due to energy transfer\nbetween the two components and the fact that the entropy of the gas\ncan increase through shocks that occur during the gravitational\ncollapse. On large scales the SIDM run is similar to the CDM run\nalthough we note that the filaments appear narrower. On non-linear\nscales the two models behave very differently and we now discuss the\nsalient features in more detail.\n\n\\subsection{Density profiles}\n\nThe final density profile of the most massive SIDM halo is shown next \nto its collisionless counterpart in Figure~\\ref{fig:b:opt}. This halo has\nmore than $10^5$ particles within its virial radius.\nThe profile is close to a\nsingular isothermal sphere with slope $\\rho(r) \\propto r^{-2}$, even\nin the very central region. The hierarchical collapse imparts\nthermal energy into the particles which leads to a small amount of\npressure support, however this is not sufficient\nto flatten their inner profiles.\n\nTo check these results we performed 3D spherical collapses of\npower-law spheres with zero initial kinetic energy and density\nprofiles $\\rho(r)\\propto r^n$ with $n=-1, 0, +1$. \nWe found consistent results with 100 and 5000 particles,\nindicating that the singular profile in the cosmological SIDM\nsimulation is \\emph{not} purely an artifact of the high-redshift\nprogenitor collapses being inadequately resolved.\nThe collapse with $n=-1$ leads to a singular\nspherical isothermal structure. In this case the central particles\nare not strongly shocked and stay at a low entropy. The $n=0$ and\n$n=+1$ collapes generate much higher entropies throughout the\nsystem. SIDM particles fall in from larger radii achieving higher velocities\nand significant thermal energy is generated during the collapse\nresulting in a pressure supported constant density core. \nA similar point has been made by Bertschinger (1985). Our\ncosmological Gaussian flucuations resemble the former collapse\nwhich results in singular isothermal structures --- what is needed is\na mechanism that prevents low entropy material surviving, such as we\nfind in more violent collapses.\n\n\\subsection{Ram pressure truncation and viscous drag}\n\nHalos of SIDM suffer ram-pressure truncation and ram-pressure/viscous\ndrag, however dynamical friction is largely suppressed in SIDM models\nsince the bow shocks and the collisional nature of the fluid \ninhibit the formation of trailing density wakes.\nA good approximation is to adopt isothermal profiles for the\nsubstructure halo (subscript $s$) and parent halo (subscript $p$) such\nthat $\\rho(r)=v^2/(4\\pi Gr^2)$. The ram pressure, $\\rho(r_p) v_p^2$,\ncan be equated to the force required to retain a shell of material at\nradius $r_s$ from the centre of the substructure halo $F \\approx\nm_sv_s^2/r_s$. Thus the stripping radius at position $r_p$ in the parent\nhalo is $r_{\\rm strip}=k r_p(v_s/v_p)^2$ where $k$ is a constant of order\n$\\pi$. This can be contrasted with the tidal radius of embedded\nisothermal halos, $r_{\\rm tidal}=r_p (v_s/v_p)$. Therefore, substructure\nhalos of SIDM will be stripped to substantially smaller sizes than\ntheir CDM counterparts.\n\nIt is also interesting to compare the timescale for a substructure\nhalo to sink to the centre of a larger system due to hydro-dynamical drag,\n$F_{\\rm drag}=\\rho(r_p) v_p^2 4\\pi r_s^2$. For a circular orbit, $L=r_p v_p$,\nand the rate of specific angular momentum loss, $dL/dt = r_p F/m_s$, therefore\n$r_p^{-1} dr_p/dt = F/(m_s v_p)$. As the substructure is dragged\ndeeper into the central potential, its radius decreases as calculated\nabove and we can substitute for $v_s$. Thus we find $dr_p/dt=k v_p$ such\nthat the drag timescale is simply of order of the crossing time\n$t_{\\rm drag}=k\nr_p/v_p$. All SIDM substructure halos sink at a similar rate\nindependent of their mass and on a timescale that is typically faster\nthan that due to dynamical friction.\n\n\n\n\n\n%%%%%%%%%%%%%%%%\n\\begin{inlinefigure}\n\\centerline{\\includegraphics[width=1.0\\linewidth]{rho.ps}}\n\\caption{\nThe radial density profiles of CDM versus SIDM halos. The spherical\ncollapse halos are plotted using an arbitrary scale at the upper\nright. In this case, the solid curve is the CDM density\nprofile, the dotted and dashed curves are the the spherical SIDM collapses\nwith $n=0$ and $n=-1$ respectively. The density profiles of the\nhierarchical collapses are shown for SIDM (dotted curve) and for CDM\n(solid curve) with 10\\% non-radiative gas (dashed curve).\n}\n\\label{fig:b:opt}\n\\end{inlinefigure}\n%%%%%%%%%%%%%%%%\n\n\n\n\\subsection{Orbital and velocity bias}\n\n\nThese results have fascinating implications for biasing and the\nsurvival of substructure within dense environments. In dynamically\nold objects, such as galaxy halos, there may have been time for most\nof their substructure to sink to the centre. Any surviving\nsubstructure that passes close to the Galactic disk will be stripped\nto a negligible mass, therefore disk heating is not a problem in SIDM\nmodels. Hydro-dynamical destruction may be happening to the\nSagittarius dwarf right now: its current SIDM halo radius would be\napproximately 100~pc. We may also expect that galaxies orbiting\nthrough the central regions of rich clusters will have lost most of\ntheir dark matter halos. Younger systems, such as galaxy clusters\nhave only had sufficient time to concentrate and bias their\n``satellites'' towards the central regions. SIDM satellites suffer\nsignificant velocity bias due to drag: an analysis of the 20 most massive\nsatellites within the largest dark matter halo yields\n$\\sigma_{_{\\rm SIDM}}/\\sigma_{_{\\rm CDM}}=0.85$.\n\nThe orbits of the Milky Way's satellites with known\nproper motions are surprisingly circular (\\eg,\nGrebel \\etal{} 1998, van den Bosch \\etal{} 1999), \nwhereas circular orbits are rare in CDM models (Ghigna \\etal{}\n1998). We find that the anisotropy parameter for SIDM satellites,\n$\\beta_{_{\\rm SIDM}}=0.5$, compared with $\\beta_{_{\\rm CDM}}=0.32$ (where \n$\\beta=v_t^2/(v_t^2+v_r^2)$), which\nresults from the efficient angular momentum loss of satellites at\npericentre. SIDM may also account for the ``Holmberg--Zaritsky''\neffect (Holmberg 1969, Zaritsky \\etal{} 1997). The angular momentum of\nSIDM halos is re-distributed differently than in the CDM halos\nleading to a rotationally flattened central core.\nThe baryons are most likely to dissipate into this plane\nthat aligns with the large scale filamentary structure. It is\nmaterial that flows from these cold filaments into the larger halos\nthat spins up the dark matter: satellites infalling along this\n``special'' plane will rapidly sink once they make contact with the\nSIDM galaxy halos. Furthermore, those satellites sinking in the\nretrograde direction to the parent halo's angular momentum will be\npreferentially destroyed due to the enhanced drag which is $\\propto v^2$\n(\\cf~Figure~\\ref{fig:a:opt}b).\n\n\\subsection{Halo shapes}\n\nThe shapes of dark matter halos provide another clear discriminant\nbetween SIDM and CDM. The typical ratio of short to long axis for \nCDM halos is\n0.5 with a log-normal distribution (Barnes \\& Efstathiou\n1987). Figure~\\ref{fig:c:opt} \nshows the ratio of short to long axis, $c/a$, and\nintermediate to long axis, $b/a$, as a function of radius for a well\nresolved halo in the simulation. The virialised part of the halo is\nrotationally flattened into an oblate shape such that $\\epsilon_{\\rm max}\n\\approx 0.2$. This is typical of the other SIDM halos which are generally\nflattened in the range $0.0\\lsim \\epsilon \\lsim 0.2$. For comparison\nwe also show the shape of the same halo in the collisionless CDM\nsimulation which has a prolate configuration with $c/a \\approx\nb/a=0.6$ within $r_{\\rm vir}$.\n\n%%%%%%%%%%%%%%%%\n\\begin{inlinefigure}\n\\centerline{\\includegraphics[width=1.0\\linewidth]{shape.ps}}\n\\caption{\nThe axial ratios of a CDM and an SIDM halo are plotted as a function of\nradius from the centre. Within the virial radius, this CDM halo is\nprolate, whereas the SIDM halo is slightly flattened by\nrotation into an oblate configuration.\n}\n\\label{fig:c:opt}\n\\end{inlinefigure}\n%%%%%%%%%%%%%%%%\n\nAnalyses of polar ring galaxies and X-ray isophotes tend to give\nflattened dark matter potentials, whereas techniques that use disk\nflaring and the precession of warps yield spherical mass distributions\n(Olling \\& Merrifield 1998). Ultimately, gravitational lensing\nwill resolve this issue, but for now we note that a lensing study of\nCL0024+1645 constrains the assymetry of the projected mass\ndistribution to be less than 3\\% (Tyson \\etal{} 1998). With the notion\nthat collisional halos should be spherical, Miralda-Escude (2000)\nargued that the cluster MS2137-23 rules out SIDM since analysis of its\ngravitational arcs demonstrates that its mass distribution must be\nflattened such that $\\epsilon \\gsim 0.1$ in the central region. \nAt the moment, SIDM and CDM are both consistent with these data.\n\n\\subsection{The extent of halos within halos}\n\nThe dwarf satellites of the Milky Way have internal velocities of\norder 10--30~\\kms, that in isolation would extend to 10--30~kpc\nbut are tidally limited according to their orbits within the\nMilky Way's potential. Numerical simulations confirm this simple\nexpectation (Ghigna \\etal{} 1998). For example, the dark matter halo\nsurrounding the Carina satellite would be truncated to $r_{\\rm tidal}\n\\approx (r_{\\rm peri}/50\\,{\\rm kpc}) (v_{_{\\rm Carina}}/v_{_{\\rm MW}}) = 2.7\\,{\\rm kpc}$\nat its current position. In an SIDM universe, the halo of Carina would\nbe reduced to a size $r_{\\rm strip} \\approx 400\\,{\\rm pc}$.\n\nObservations of stars escaping from satellites constrain the extent\nof their dark matter halos (Moore 1996, Burkert 1997). Tidal\nstreams have recently been spectroscopically confirmed for Carina\n(Majewski \\etal{} 1999) and are also claimed for Draco and Ursa~Minor\n(Irwin \\& Hatzidimitriou 1993). These observations imply that the\ndark matter extends only as far as the optical radii, about 300\nparsecs for all of these satellites and much smaller than their\nexpected sizes if they had halos of CDM. \n\nSimilarly, the dark matter halos of cluster galaxies are truncated by\nthe global cluster potential and their sizes can be constrained by\nquantifying their effects on strongly and weakly lensed images of\nbackground galaxies. Natarajan \\etal{} (1999) have analysed several of\nthe clusters imaged by the Hubble Space Telescope and claim that the\ndark matter halos of bright cluster galaxies are severely truncated to\nbetween 15--30 kpc. These galaxies have typical internal velocity\ndispersions of $150\\,\\kms$ and sample the projected central 500~kpc\nregion of the clusters (else they wouldn't lie in the HST frames). \nThus we expect $r_{\\rm tidal}\\approx$~30--60~kpc from gravitational stripping, but\n$r_{\\rm strip}\\approx$~10--30~kpc from maximal collisional stripping.\n\n\n\\section{Discussion}\n\nThe properties of dark matter halos of strongly interacting particles\nare markedly different from their collisionless counterparts. SIDM\nhalos are close to spherical with a modest degree of rotational\nflattening. Observations of halo shapes cannot currently distinguish\nbetween the models examined here; however, future lensing observations\nwill determine if SIDM is a viable dark matter candidate. Halos\nwithin halos suffer ram-pressure truncation that decreases their sizes\nto less than the tidal radius. Current observational data on\ngalactic halos in clusters and satellite galaxies in the Galactic halo\nare naturally reproduced in SIDM models: the extent of Carina's halo is\nan order of magnitude smaller than predicted by CDM. Ram-pressure\ndrag creates significant velocity and orbital bias in the substructure\nhalos which sink on a short timescale---of order the crossing\ntime---independent of their mass. Another positive feature of SIDM is\nthe ability to\nproduce satellite systems on near circular orbits which are very rare\nin CDM models.\n\nBoth CDM and SIDM with a large cross-section fail to reproduce\nobserved rotation curves of dwarf and LSB galaxies. We have seen that\nthe final density profiles are sensitive to the shape of the initial\nfluctuations: more violent collapses end up with constant density\ncores. Alternatively, SIDM with a mean free path between kiloparsec\nand megaparsec scales may solve this problem (Spergel \\& Steinhardt\n1999). In this case, particles could transfer heat to the cold\ncentral regions that occur in standard CDM collapses, creating an\ninitial expanding phase with lower central density. It is not obvious\nthat a cold core would be generated and maintained in a hierarchical\nscenario since the dense mini-halos collapsing at high redshift may\nform singular isothermal structures. The dense substructure halos\nwould rapidly sink to the centres of the parent halos by\nhydro-dynamical drag, depositing high density low entropy material \nand conserving isothermal profiles.\n\nSimulating intermediate mean free paths is relatively straightforward.\nOne technique would be to use the neighbour lists to choose random\nparticles to collide (Burkert 2000). Simulations in progress will\ndemonstrate whether SIDM can reproduce the observed rotation curves of\ndwarf galaxies. A solution to this problem will naturally resolve the\nabundance of dark matter substructure in the Galactic halo since \nsubstructure with shallow potentials would be easily disrupted.\n\n\\acknowledgments\n\n%{\\bf Acknowledgments} \\ \\ \\ \nBM would like to thank Marc Davis for many discussions of the\nastrophysical consequences of strongly interacting dark matter while a\nNATO fellow in Berkeley and the Royal Society for support. VQ is a\nMarie Curie research fellow (grant HPMF-CT-1999-00052). Computations\nwere carried out as part of the Virgo consortium. \n\n\\begin{references}\n\n%%%\\doublespace\n\n\\reference{} Barnes, J. \\& Efstathiou, G.P. 1987, ApJ, 319, 575.\n\n\\reference{} van den Bosch, F.C., Lewis, G.F., Lake, G. \\& Stadel, J. 1999,\nApJ, 515, 50.\n\n\\reference{} Bertschinger, E. 1985, ApJS, 85, 31\n\n\\reference{} Burkert, A. 1997, ApJ, 474, L99.\n\n\\reference{} Burkert, A. 2000, submitted to ApJLetters.\n\n%\\reference{} Carlberg, R. 1994, {\\it ApJ}, {\\bf 433}, 468.\n\n\\reference{} Carlson, E.D., Machacek, M.E. \\& Hall, L.J. 1992, ApJ, 398, 43.\n\n\\reference{} Couchman, H.M.P., Thomas, P.A. \\& Pearce, F.R. 1995, ApJ, 452, 797.\n\n\\reference{} Davis, M., Efstathiou, G., Frenk, C.S. \\& White, S.D.M. 1985, \nApJ, 292, 371.\n\n%\\reference{} Dubinski, J. \\& Carlberg, R. 1991, {\\it ApJ}, {\\bf 378}, 496.\n\n%\\reference{} Flores, R.A. \\& Primack, J.R. 1994, {\\it ApJLett., 457, L5.\n\n\\reference{} Frenk, C.S. et.al. 1999, ApJ, 525, 554.\n\n\\reference{} Gelato, S. \\& Sommer-Larsen, J. 1999, MNRAS, 303, 321.\n\n\\reference{} Ghigna, S., Moore, B., Governato, F., Lake, G., Quinn, T. \\& Stadel, J.\n1998, MNRAS, 300, 146.\n\n%\\reference{} Ghigna S., {\\bf Moore B.}, Lake, G. Quinn T. \\& Stadel J. 1999,\n%Ap.J, submitted, astro-ph/9910166\n\n\\reference{} Grebel, E.K., Kolatt, T. \\& Brandner, W. 1998, \nI.A.U. Symp. 192, 30, ed. Whitelock, P. \\$ Cannon, R.\n\n\\reference{} Hogan, C. \\& Dalcanton, J.J. 2000, astro-ph/0002330.\n\n\\reference{} Holmberg, E. 1969, Ark. Astron., 5, 305.\n\n\\reference{} Irwin, M.J. \\& Hatzidimitriou, D. 1993, ASP Conference series, 48, 322.\n\n%\\reference{} Klypin, A., Kravtsov, A.V., Valenzuela, O. \\& Prada, F. 1999, ApJ 523, 32. \n\n\\reference{} de Laix, A.A., Scherrer, R.J. \\& Schaeffer, R.K. 1995, ApJ, 452, 495.\n\n\\reference{} Machacek, M.E. 1994, ApJ, 431, 41.\n\n\\reference{} Majewski, S.R., Ostheimer, J.C., Patterson, R.J., Kunkel, W.E., Johnston,\nK.V. \\& Geisler, D. astro-ph/9911191.\n\n\\reference{} Miralde-Escude, J. 2000, astro-ph/0002013.\n\n%\\reference{} Mohapatra, R.M. \\& Teplitz, V.L. astro-ph/0001362.\n\n%\\reference{} Moore, B., 1994, {\\it Nature}, {\\bf 370}, 620.\n\n\\reference{} Moore, B. 1996, ApJ, 461, L13.\n\n%\\reference{} Moore, B., Katz N. \\& Lake G. 1996, {\\it ApJ}, {\\bf 457}, 455.\n\n%\\reference{} Moore, B., Governato, F., Quinn, T., Stadel, J. \\& Lake, G. 1998, \n%{\\it ApJLett.}, 499, L5.\n\n%\\references{} Moore B., Ghigna S., Governato F., Lake G., Quinn T., Stadel J. \\& \n%Tozzi P. 1999a, ApJLett., {\\bf 524}, L19.\n\n%\\reference{} Moore, B., Quinn, T. Governato, F., Stadel, J. \\& Lake, G. 1999b,\n% MNRAS, 310, 1147.\n\n\\reference{} Natarajan, P., Kneib, J.P. \\& Smail, I. 1999, astro-ph/9909349.\n\n%\\reference{} Navarro, J.F., Frenk, C.S. \\& White, S.D.M. 1996, {\\it ApJ}, {\\bf 462}, 563.\n\n\\reference{} Olling, R.P. \\& Merrifield, M.R. 1998,\nin {\\it Galactic Halos}, ASP Conference series, Vol. 136, 219, ed. D. Zaritsky.\n\n%\\reference{} Ostriker, J.P. astro-ph/9912548.\n\n%\\reference{} Peebles, P.J.E. 1984, {\\it ApJ}, {\\bf 277}, 470.\n\n\\reference{} Spergel, D.N. \\& Steinhardt, P.J. 1999, astro-ph/9909386.\n\n%\\reference{} Steinmetz, M. 1999, astro-ph/9910002.\n\n\\reference{} Tyson, J.A., Kochanksi, G.P. \\& dell'Antonio, I.P. 1998, ApJ, 498, L107.\n\n%\\reference{} Quinn, P.J., Salmon, J.K. \\& Zurek, W.H. 1986, {\\it Nature}, {\\bf 322}, 329.\n\n%\\reference{} Warren, S.W., Quinn, P.J., Salmon, J.K. \\& Zurek, H.W. 1992, {\\it ApJ}, \n%{\\bf 399}, 405.\n\n\\reference{} Zaritsky, D. Smith, R., Frenk, C.S. \\& White, S.D.M. 1997, ApJ, 478, L53. \n\n\\end{references}\n\n\\end{document}\n\n\n\n\n\n\n--Nq2Wo0NMKNjxTN9z--\n\n"
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astro-ph0002309
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Formation and evolution of disk galaxies within cold dark matter halos
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[
{
"author": "Vladimir Avila-Reese"
},
{
"author": "Claudio Firmani\\altaffilmark{1}"
}
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We present results of extensive model calculations of disk galaxy evolution within an hierarchical inside-out formation scenario. We first compare properties of the dark halos identified in a cosmological N-body simulation with predictions of a seminumerical method based on an extended collapse model and find a good agreement. We then describe detailed modelling of the formation and evolution of disks within these growing halos and predictions for the main properties, correlations and evolutionary features of normal disk galaxies. The shortcomings of the scenario are discussed.
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"name": "avilav1.tex",
"string": "\\documentstyle[11pt,newpasp,twoside]{article}\n\\markboth{Avila-Reese, Firmani, Klypin, \\& Kravtsov}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\\def\\lesssim{{_ <\\atop{^\\sim}}}\n\\def\\grtsim{{_ >\\atop{^\\sim}}}\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{Formation and evolution of disk galaxies within cold dark matter halos }\n\\author{Vladimir Avila-Reese, Claudio Firmani\\altaffilmark{1}}\n\\affil{Instituto de Astronom\\'\\i a-UNAM, A.P. 70-264, 04510 \nM\\'exico, D. F.}\n\\author{Anatoly Klypin and Andrey V. Kravtsov\\altaffilmark{2}}\n\\affil{Astronomy Department, NMSU, P.O. Box 30001/Dept. 4500, Las Cruces, \nNM 88003-8001, USA}\n\n\\altaffiltext{1}{Also Osservatorio Astronomico di Brera, via E.Bianchi \n46, I-23807 Merate, Italy}\n\n\\altaffiltext{2}{Hubble Fellow. Current address: Department of Astronomy, \nThe Ohio State University, 140 West 18th Av., Columbus, OH 43210-1173, USA}\n\n\\begin{abstract}\n We present results of extensive model calculations of disk galaxy\n evolution within an hierarchical inside-out formation scenario. We\n first compare properties of the dark halos identified in a\n cosmological N-body simulation with predictions of a seminumerical\n method based on an extended collapse model and find a good\n agreement. We then describe detailed modelling of the formation and\n evolution of disks within these growing halos and predictions for\n the main properties, correlations and evolutionary features of\n normal disk galaxies. The shortcomings of the scenario are\n discussed.\n \n\\end{abstract}\n\n\\section{Introduction}\n\nThe hierarchical cosmic structure formation picture based on the\ninflationary cold dark matter (CDM) provides a solid framework for\nmodels of galaxy formation and evolution. On the other hand, the\nunprecedented observations of galaxies at different redshifts make it\npossible to probe and constrain these models. Here we discuss some of\nthe results obtained with a self-consistent scenario of disk galaxy\nformation and evolution within the context of the hierarchical picture\n(the extended collapse scenario).\n\n\\section{Dark matter halos}\n\nUsing the extended Press-Schechter approximation, we generate the mass\naggregation histories (MAHs) of the dark matter (DM) halos. Collapse\nand virialization of these halos are then calculated assuming\nspherical symmetry and adiabatic invariance, using a method based on a\ngeneralization of the secondary infall model (Avila-Reese, Firmani, \\&\nHern\\'andez 1998). These halos will mainly correspond to isolated\nsystems. The diversity of MAHs results in {\\it diversity} of density\nprofiles which, in our model, mainly depend on the MAH. The density\nprofile corresponding to the average MAH is well described by the\nNavarro et al. (1996) profile. In Avila-Reese et al. (1999) we have\ncompared the outer density profiles, concentrations and structural\nrelations of thousands of halos identified as isolated in a\ncosmological ($\\Lambda$CDM) N-body simulation with those obtained with\nour seminumerical method. We found a good agreement between the model\nand simulation results.\n\nWe have found that $\\sim 13\\%$ of the halos in the numerical\nsimulation at $z=0$ are contained within larger halos and $\\sim 17\\%$\nhave significant companions within three virial radii. The remaining\n70\\% of the halos are isolated objects. The slope $\\beta$ of the outer\ndensity profile ($\\rho \\propto r^{-\\beta}$) and the halo concentration\ndefined as $c_{1/5}=r_h/r(M_h/5)$, where $r_h$ and $M_h$ are the\nvirial radius and mass, depend on the halo environment. For a given\n$M_h$, halos in clusters have typically steeper outer profiles and are\nmore concentrated than the isolated halos (for the latter $\\beta\n\\approx 2.9$ in average and $\\beta$ between 2.5 and 3.8 for 68\\% of\nthe halos). Contrary to naive expectations, halos in galaxy and group\nsystems as well as the halos with significant companions,\nsystematically have flatter and less concentrated density profiles\nthan isolated halos. A tight correlation between $M_h$ and the maximum\ncircular velocity $V_{m}$ is observed: $M_h\\propto V_m^n$, $n\\approx\n3.2$. This is roughly the slope of the infrared Tully-Fisher relations\n(TFR). Thus, it seems that there is no room for the mass dependence\nof the infrared $M_h/L$ ratio.\n\n\\section{Galaxy evolutionary models}\n\nWe model the formation and evolution of baryon disks in centrifugal\nequilibrium within the growing CDM halos formed as described in \\S 2. \nWe assume that halos acquire angular momentum from large-scale torques\nwith the spin parameter $\\lambda$ distributed log-normally and\nconstant in time. The disks are built inside-out with the gas infall\nrate (no mergers) proportional to the cosmological mass aggregation\nrate and assuming detailed angular momentum conservation. The\ngravitational drag of the disk on the DM halo is calculated. The local\nSF is assumed to be induced by disk instabilities and regulated by\nenergy balance within the disk turbulent ISM (no SF feedback and\nself-regulation at the level of the interhalo medium is allowed). We\nalso calculate the secular formation of a bulge. This way, {\\it at\n each epoch and at each radius}, the growing disk is characterized by\nthe infall rate of fresh gas, the gas and stellar surface density\nprofiles, the total rotation curve (including the DM component), the\nlocal SF rate, and the size of the inner region transformed into bulge\ncomponent.\n\n\\section{Highlights of the model results}\n\nResults on the structure and dynamics of our model disk galaxies were\ndiscussed in Firmani \\& Avila-Reese (2000); the luminosity properties\nand topics related to the disk Hubble sequence were treated in\nAvila-Reese \\& Firmani (2000), while some evolutionary aspects of the\ngalaxies were presented in Firmani \\& Avila-Reese (1999). In the\nfollowing, we highlight some of the results.\n\n{\\bf Local properties.} The (stellar) surface density and brightness\nprofiles are exponential, the sequence of high to low surface\nbrightness (SB) being mainly determined by $\\lambda$. The gas profiles\nat $z=0$ are also exponential although much lower in density and with\na scale radius $\\sim 2-4$ times larger than the stellar profiles. \nThere is a negative radial gradient of the color index: stars in the\nouter regions of the disk form later than stars in the inner regions. \nWe find that the local SF rate per unit area correlates with the gas\nsurface density as $\\Sigma _{\\rm SFR}(r)\\propto \\Sigma_g^n(r)$ with\n$n\\approx 2$ for most of the models and over a major portion of the\ndisks. The shape of the rotation curves correlates with the SB\n($\\lambda$) and in most cases is approximately flat. The dark halo\ndominates in the rotation curve decomposition down to very central\nregions.\n\n{\\bf The infrared Tully-Fisher relations (TFR).} The slope of the\n$M_h-V_m$ relation of the CDM halos remains imprinted in the TFR and\nagrees with observations. This slope is almost independent of the\nassumed disk mass fraction $f_d$ when the disk component in the\nrotation curve decomposition is gravitationally important ($f_d\\grtsim\n0.03$ for the $\\Lambda$CDM model used here). The zero point of the\nmodel TFR is only slightly larger than the observed zero point. The\nrms scatter in our TFR slightly decreases with mass; from $V_m=70$ to\n300 km/s the scatter is between 0.38 and 0.31 mag. We have found that\na major contribution to this scatter is from the scatter in the DM\nhalo structures due to the dispersion of the MAHs; a minor\ncontribution to the scatter is due to the dispersion of $\\lambda$. The\nTFR for high and low SB models is approximately the same. The slope of\nthe correlation among the residuals of the TF and luminosity-radius\nrelations is small and non-monotonic, although the shape of the\nrotation curves of our models correlates with the SB. For a given\ntotal (star+gas) disk mass, the $V_m$ decreases with decreasing SB. \nHowever, owing to the dependence of the SF efficiency on the disk\nsurface density, the stellar mass $M_s$ (luminosity) also decreases. \nThis combined influence of the SB ($\\lambda$) on $V_m$ and $M_s$ puts\nmodels of different SB on the same $M_s-V_m$ relation. As a result,\nhigh and low SB models follow similar TFRs.\n\n{\\bf The Hubble sequence. } The main properties of the high and low SB\ndisk galaxies and their correlations are determined by the combination\nof three fundamental physical factors and their dispersions: the halo\nvirial mass, the MAH and the angular momentum given through $\\lambda$.\nThe MAH determines mainly the halo structure, the integral color\nindex, and the gas fraction $f_g$ while $\\lambda$ determines mainly\nthe disk SB, the bulge-to-disk (b/d) ratio and the shape of the\nrotation curve. Our models show that the redder and more concentrated\n(higher SB) is the disk, the smaller is $f_g$ and the larger is the\nb/d ratio (disk Hubble sequence). The values of all these magnitudes\nare in good agreement with observations.\n\n{\\bf Evolutionary features.} In the inside-out hierarchical disk\nformation scenario galaxies undergo not only luminosity but also\nstructural (size, SB, b/d ratio) evolution. For an Einstein- de Sitter\nuniverse we find that the scale radius for normal disk galaxies\ndecreases roughly as $(1+z)^{-0.5}$ up to $z\\approx 1.5$, while the\ncentral $B-$band SB from $z=0$ to $z=1$ increases by $\\approx 1.2$ mag.\n\nThe SF history in the models is driven both by the MAH and the disk\ngas surface density. For the average MAH and $\\lambda=0.05$, the SF\nrate reaches a maximum at $z\\approx 1.5-2.5$ which is a factor of\n2.5-4.0 higher than the rate at $z=0$. In the same way, $L_B$\nincreases towards the past by factors slightly smaller than the SF\nrate. The less massive galaxies present a slightly more active\nluminosity evolution than the massive galaxies. The model galaxies are\nsomewhat bluer in the past; from $z=0$ to $z=1$ the $B-V$ decreases on\naverage 0.25-0.30 magnitudes. The total mass-to-$L_B$ ratio also\ndecreases towards higher redshifts: from $z=0$ to $z=1$ it decreases\non average by a factor $\\sim 3.3$, i.e. a galaxy at $z=1$ is more\nluminous in the $B-$band and less massive than at $z=0$. Again, this\nis a result related to the hierarchical MAHs of the protogalaxies.\n\nOwing to the mass (size) evolution, {\\it for a fixed $V_m$}, the\n$H-$band luminosity is a factor $\\approx $2.2 less at $z=1$ than at\n$z=0$; however, owing to the luminosity evolution, $L_B$ is a factor\n$\\approx$ 2.1 larger. Therefore, while the zero-point of the $H-$band\nTFR increases towards the past, in the case of the $B-$band TFR,\ncompensation due to the $L_B$ evolution results in the zero-point\nremaining approximately constant with time. The slopes in both cases\nalso remain constant.\n\n\\section{Potential difficulties of the hierarchical scenario}\n\nAlthough several main properties, correlations, and evolutionary\nfeatures of normal disk galaxies have been successfully predicted \nby our models, it is important to remark on their problems.\nWe find the following potential conflicts with the observations:\n{\\bf 1)} the size and SB evolution of the disks is too pronounced, {\\bf 2)} \nthe radial color index gradients are too steep and the $f_g$ is \nslightly over-abundant, {\\bf 3)} the DM component dominates in the \nrotation curve decompositions almost down to the center and the \nhalos are too cuspy. \n\nRegarding item 1), if selection effects in the deep field are not so\nsignificant as Simard et al. (1999) have claimed, then probably it is\nnot so serious. In fact, some physical ingredients not considered in\nour models (e.g., merging, angular momentum transfer, and\nnon-stationary SF) all work in the direction to improve models\nregarding problems 1) and 2). The problem 3) can probably be solved if\nthe inner density profile of the CDM halos can be shallower than\npredicted (several solutions such as self-interacting CDM, warm DM,\nnon-Gaussian fluctuations, have been proposed). Nevertheless, it is\npossible that all these problems together with those of the dearth of\nsatellites and the high frequency of disk disruptive mergers, are in\ngeneral pointing out to serious problems for the Gaussian CDM-based\nhierarchical picture of structure formation. More observational tests\nregarding the problems mentioned above and more theoretical effort in\nmodeling galaxy formation and evolution are urgently required.\n\n\\begin{references}\n\n\\reference Avila-Reese, V., Firmani, C., \\& Hern\\'{a}ndez X. 1998, \\apj,\n{\\bf 505}, 37\n\n\\reference Avila-Reese, V, Firmani, C., Klypin A., \\& Kravtsov A. 1999, \n\\mnras, 309, 527\n\n\\reference Avila-Reese, V, \\& Firmani, C. 2000, RevMexA\\&A, v. 36, in press \n\n\\reference Firmani, C., \\& Avila-Reese, V. 1999, ASP Conf. Series 176, 406\n\n\\reference Firmani, C., \\& Avila-Reese, V. 2000, \\mnras, in press\n\n\\reference Navarro, J., Frenk, C.S. \\& White, S.D.M. 1997, \\apj, 462, 563\n\n\\reference Simard, L. et al. 1999, \\apj, 519, 563 \n\n\\end{references} \n\n\\end{document}\n\n\n"
}
] |
[] |
astro-ph0002310
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THE MASS-TO-LIGHT FUNCTION: \ ANTIBIAS AND $\Omega _{m}$
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[
{
"author": "N.A. Bahcall"
},
{
"author": "R. Cen"
},
{
"author": "R. Dav\\'{e}"
},
{
"author": "J.P. Ostriker"
},
{
"author": "Q. Yu"
}
] |
We use large-scale cosmological simulations to estimate the mass-to-light ratio of galaxy systems as a function of scale, and compare the results with observations of galaxies, groups, clusters, and superclusters of galaxies. We find remarkably good agreement between observations and simulations. Specifically, we find that the simulated mass-to-light ratio increases with scale on small scales and flattens to a constant value on large scales, as suggested by observations. We find that while mass typically follows light on large scales, high overdensity regions --- such as rich clusters and superclusters of galaxies --- exhibit higher $M/L_{B}$ values than average, while low density regions exhibit lower $M/L_{B}$ values; high density regions are thus antibiased in $M/L_{B}$, with mass more strongly concentrated than blue light. This is true despite the fact that the galaxy mass density is unbiased or positively biased relative to the total mass density in these regions. The $M/L_{B}$ antibias is likely due to the relatively old age of the high density regions, where light has declined significantly since their early formation time, especially in the blue band which traces recent star formation. Comparing the simulated results with observations, we place a powerful constraint on the mass density of the universe; using, for the first time, the entire observed mass-to-light function, from galaxies to superclusters, we find $\Omega =0.16\pm0.05$.
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[
{
"name": "msnew.tex",
"string": "%\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[aas2pp4,tighten]{article}\n%\\documentstyle[11pt,eqsecnum,aaspp4]{article}\n\\documentstyle[11pt,amssym,aasms4]{article}\n\n%\\received{4 August 1999}\n%\\revised{4 August 1999}\n%\\accepted{23 September 1999}\n%\\cpright{type}{year}\n%\\journalid{337}{15 January 1999}\n%\\articleid{11}{14}\n%\\paperid{manuscriptid}\n%\\ccc{code}\n\n%pagestyle\n\n%\\lefthead{to be inserted }\n%\\righthead{to be inserted}\n\n\\begin{document}\n\n%\\begin{document}\n\n\\title{THE MASS-TO-LIGHT FUNCTION: \\ ANTIBIAS AND $\\Omega _{m}$}\n\\author{N.A. Bahcall, R. Cen, R. Dav\\'{e}, J.P. Ostriker, Q. Yu}\n\\affil{Princeton University Observatory, Princeton, NJ 08544}\n\n\\begin{abstract}\n\nWe use large-scale cosmological simulations to estimate the\nmass-to-light ratio of galaxy systems as a function of scale, and\ncompare the results with observations of galaxies, groups, clusters, and\nsuperclusters of galaxies. We find remarkably good agreement between\nobservations and simulations. Specifically, we find that the simulated\nmass-to-light ratio increases with scale on small scales and flattens to a\nconstant value on large scales, as suggested by observations. We find that\nwhile mass typically follows light on large scales, high overdensity regions\n--- such as rich clusters and superclusters of galaxies --- exhibit higher\n$M/L_{\\rm B}$ values than average, while low density regions exhibit lower\n$M/L_{\\rm B}$ values; high density regions are thus \\emph{antibiased} in \n$M/L_{\\rm B}$, with mass more strongly concentrated than blue light. This\nis true despite the fact that the galaxy mass density is unbiased or\npositively biased relative to the total mass density in these regions.\nThe $M/L_{\\rm B}$ antibias is likely due to the relatively old age of the high \ndensity regions, where light has declined significantly since their early \nformation time, especially in the blue band which traces recent star formation.\nComparing the simulated results with observations, we place a powerful\nconstraint on the mass density of the universe; using, for the first time,\nthe entire observed mass-to-light function, from galaxies to superclusters,\nwe find $\\Omega =0.16\\pm0.05$.\n\n\\end{abstract}\n\n\\section{ INTRODUCTION}\nOne of the oldest - and simplest - techniques for estimating the mass\ndensity of the universe is the mass-to-light method. In this method, the\naverage ratio of the observed mass to light of the largest possible systems\nis used; assuming it is a fair sample, it can then be multiplied by the\ntotal luminosity density of the universe to yield the universal mass\ndensity. When the method is applied to rich clusters of galaxies --- the\nlargest virilized systems for which a mass has been reliably determined --- the\ntotal mass density of the universe adds up to only $\\Omega \\simeq 0.2\\,\\ $%\n(where $\\Omega $ is the mass density in units of the critical density)\n(Zwicky 1957, Abell 1965, Ostriker, Peebles \\& Yahil 1974, Bahcall 1977,\nFaber \\& Gallagher 1979, Trimble 1987, Peebles 1993,\nBahcall, Lubin \\& Dorman 1995, Carlberg \\emph{et al.} 1996, 1997, and\nreferences therein). A fundamental assumption in this determination,\nhowever, is that the mass-to-light ratio ($M/L$) of clusters is a fair\nrepresentation of the universal value. If the mass-to-light ratio of\nclusters is larger or smaller than the universal mean, then the resulting $%\n\\Omega $ will be an over- or under- estimate, respectively. It is\nnot clear whether this classic assumption of an unbiased\nrepresentation by clusters is correct. More generally, if mass follows\nlight (i.e., galaxies) on large scales --- thus $M/L\\simeq $ constant --- the\ngalaxy distribution is considered to be unbiased with respect to mass; if\nmass is distributed more broadly than light, as is generally believed, then\nthe galaxy distribution is biased (i.e., more clustered) with respect to\nmass, and the above determination of $\\Omega $ is an underestimate. \\ We\ninvestigate these questions of cluster representation and bias, and the\nimpact they have on the measurement of $\\Omega $.\n\nObservations of galaxies, groups and clusters of galaxies suggest that \n$M/L$ increases as a function of scale up to scales of hundreds\nof kiloparsecs (Schwarzschild 1954, Rubin \\& Ford 1970, Roberts \\& Rots 1973,\nOstriker \\emph{et al.} 1974, Einasto \\emph{et al.} 1974, Davis \\emph{et al.}\n1980, Trimble 1987, Gramann 1990, Zaritzky \\emph{et al.} 1993, Fischer \\emph{et al }$1999$),\nbut then flattens out and remains approximately constant on larger scales\n(Bahcall, Lubin \\& Dorman 1995). In the modern context we normally interpret\nthis fact as indicating that luminous galaxies are more concentrated in peak\ndensity regions than the dark matter because baryons are dissipational. The\nshape and amplitude of the mass-to-light function --- that is, the dependence\nof $M/L$ on scale, $(M/L)(R)$ --- can place powerful constraints on\nthe amount and distribution of dark matter in the universe, as well as on\nthe amount of bias and its dependence on scale. The $M/L$ function thus provides\na direct, model-independent census of the total mass density of the universe.\n\nWhat is the expected dependence of $M/L$ on scale? In this paper we\ninvestigate this question using large-scale, high resolution hydrodynamic\ncosmological simulations that contain dark matter and gas, and compare the\nresults with observations. We find an excellent agreement between models\nand observations in the shape of the $M/L$ function; both data and models show\nan increase on small scales (hundreds of kpc) and a flattened $(M/L)(R)$\ndistribution on large scales. We use the comparison between data and\nsimulations to determine the mass density of the universe. The amount of\nbias and its dependence on scale are also revealed. \\ We find that clusters\nof galaxies are mildly \\emph{antibiased, } in the sense that mass is more\nconcentrated than light on average. Previous determinations of $\\Omega$\nusing clusters of galaxies have thus \\emph{overestimated} $\\Omega $ due\nto this unaccounted antibias. The present investigation attempts to provide\nan unbiased determination of $\\Omega$\nusing, for the first time, the entire observed mass-to-light function.\nThe above results do not disagree with previous estimates that the mass density of galaxies is unbiased or positively biased with respect to\nthe total mass density in the high\ndensity regions; it is the light density that is shown here to be antibiased.\n\n\\section{ OBSERVATIONS}\nThe observed mass-to-light ratio of galaxies, groups and clusters as a\nfunction of scale, $(M/L_{\\rm B})(R)$, is taken from Bahcall, Lubin and Dorman\n(1995, hereafter BLD). In these data, masses are determined using different\nmethods including velocity dispersion, gravitational lensing, and X-ray gas\ntemperature. The luminosity L$_{B}$ throughout this paper refers to the\n\\emph{total } blue luminosity, corrected for both Galactic and internal\nextinction. The data for rich clusters (at $R=1.5h^{-1}$Mpc) and for groups\n($R\\simeq 20$kpc to $1h^{-1}$Mpc), shown in the figures below, represent\nmedian $M/L_{\\rm B}$ values of large samples, as does the $M/L_{\\rm B}$ ratio\nfor the luminous parts of typical $L_*$ elliptical and spiral galaxies\n(see BLD for details). More recent observations of rich clusters from the\nCNOC cluster survey (Carlberg \\emph{et al. 1996, 1997}) yield consistent\nresults. Based on the available data, BLD find that the $M/L_{\\rm B}$ ratio\nof galaxy systems increases linearly with scale up to the scale of very\nlarge galactic halos ($R\\sim 0.2h^{-1}$Mpc), but then flattens on larger\nscales; they suggest that $M/L_{\\rm B}$ does not increase significantly with\nscale beyond $\\sim0.2h^{-1}$Mpc. Furthermore, BLD show that $M/L_{\\rm B}$ of\nelliptical galaxies is approximately three times larger than that of spirals\n(at the same radius); both increase linearly with scale up to \n$R\\sim0.2h^{-1}$Mpc. The total mass of groups and clusters can then be\naccounted for by the combined mass of their elliptical and spiral galaxy\nmembers, including their large halos, plus the intracluster gas. The large\nhalos are likely to be stripped off in the dense environments of clusters,\nbut their mass still remains in the clusters. Observations of weak\ngravitational lensing by foreground galaxies using the Sloan Digital Sky\nSurvey (Fischer \\emph{et al}. 1999) find consistent results indicating large\nhalos around galaxies.\n\nRecently, the first determination of the mass and mass-to-light ratio of a\nlarge supercluster ($\\sim6h^{-1}$Mpc), MS0302, was obtained using\nweak gravitational lensing (Kaiser \\emph{et al.}1999). The mass and \n$M/L_{\\rm B}$ ratio of three individual clusters in the supercuster as well\nas the mass and $M/L_{\\rm B}$ of the supercluster itself were all determined\nfrom the weak lensing observations. The results show, quite remarkably, the\n\\emph{ same }$M/L_{\\rm B}$ ratio for both the individual clusters and the\nlarge supercluster ($260\\pm40$ and $280\\pm40h\\ M_{\\odot }/L_{\\odot }$,\nrespectively) thus directly confirming a flat $(M/L_{\\rm B})(R)$ function on\nlarge scales, as suggested by BLD. This new supercluster result is added\nin the figures below (converted to our standard L$_{B}$ system by adding the \n30\\% contribution to the luminosity from spiral galaxies \n(Kaiser \\emph{et al.} 1999), correcting for passive luminosity evolution from\n$z=0.42$ to $z\\simeq0$ following $L_{\\rm B}\\propto(1+z)$, and correcting for\ninternal extinction ($\\sim$10\\%; BLD); the net correction factor is 1$\\pm$0.2). \nWe also show (for illustration only) the $M/L_{\\rm B}$ ratio determined from\nthe Least Action Method at $30h^{-1}$Mpc by Tully, Shaya and Peebles (1994)\nand the observed range of Virgo Infall measurements (see BLD). While these\nprovide less direct measures of mass than the supercluster weak lensing\nresult (and are thus not included in our fits), they are all consistent with\neach other and with the observed flattening of $M/L_{\\rm B}$ with scale. The\ndata are presented in the figures below. \n\n\\section{ SIMULATIONS}\n\n We investigate the expected behavior of $M/L_{\\rm B}$ as a function of\nscale using two sets of cosmological simulations which include both dark \nmatter and gas: a large-scale, $100h^{-1}$Mpc box simulation to study the\nlarge-scale behavior of $M/L_{\\rm B}$, and a smaller, higher resolution\nsimulation with a box size of $11.1h^{-1}$Mpc, to investigate smaller scales.\nThe large-scale hydrodynamic simulation, described by Cen and Ostriker (1999),\nuses the shock-capturing Total Variation Diminishing method on a Cartesian\ngrid for gas dynamics (Ryu \\emph{et al, } 1993). A Particle-Mesh (PM) code\nis used for dark matter particles. An FFT is used to solve Poisson's\nequation. In addition, the code accounts for cooling processes including\nmetal cooling and heating and incorporates a heuristic galaxy formation scheme\ndescribed by Cen and Ostriker (1999) (see also below). The cosmological model\nused is a flat Cold-Dark-Matter (CDM) model, with mass density $\\Omega =0.37,$\ncosmologial constant density $\\Omega _{\\Lambda }=0.63,$ baryon density\n$\\Omega_{\\rm b}=0.039,$ and a Hubble constant $h=0.7$ (where $H_{0}=100h$\nkms s$^{-1}$Mpc$^{-1}$). A power-spectrum slope of $n= 0.95$ and\nnormalization $\\sigma _{8}=0.8$ (the mass rms fluctuations on $8h^{-1}$Mpc\nscale at $z=0$ ) were used, consistent with the cluster abundance normalization\nand the COBE microwave background\nfluctuations (White \\emph{et al.} 1993, Ostriker and Steinhardt 1995,\nBahcall and Fan 1998). This model fits well current observational data\n(e.g., Ostriker and Steinhardt 1995, Krauss \\emph{et al.} 1995, Bahcall \n\\emph{et al.} 1999). A periodic box of $100h^{-1}$Mpc on a side is used, \nwith $512^{3}$ fluid cells and $256^{3}$ dark matter particles. The dark\nmatter mass resolution is $6\\times10^{9}h^{-1}M_{\\odot }$ and the grid cell\nsize is $0.2h^{-1}$Mpc. We consider only scales with radii $R \\gtrsim\n1h^{-1}$Mpc in this simulation, which is considerably larger than the cell\nsize; on these scales, the relevant gravitational and hydrodynamical physics\nare accurately computed. On smaller scales we use the smaller,\nhigher-resolution simulation described below.\n\nGalaxies are ``identified'' in the simulation by the procedure described in\nCen and Ostriker (1999): if a cell's mass is higher than the Jean's mass, and\nif the cooling time of the gas in it is shorter than its dynamical time, \nand if the flow around the cell is\nconverging, then it will have stars forming inside that cell. \\ The code\nturns the baryonic fluid component into collisionless stellar particles\n(``galaxy particles'') at a rate proportional to $m_{b}/t_{\\rm dyn}$, where\n$m_{\\rm b}$ is the mass of gas in the cell and $t_{\\rm dyn}$ is the local\ndynamical time. These galaxy particles subsequently contribute to metal\nproduction, SN energy feedback and the background ionizing UV radiation. \nThis algorithm is essentially the same as in Cen and Ostriker (1992) and also\nused by Katz, Hernquist and Weinberg (1996), Gnedin (1996) and Steinmetz\n(1996). The masses of the galaxy particles range from $\\sim10^{6}$ to\n$\\sim10^{9}M_{\\odot }$; thus many galaxy particles are contained in a single\nluminous galaxy in the real universe. Rather than group the particles into\ngalaxies, we simply use the galaxy particles themselves, which makes\nthe results less dependent on resolution.\n\nLuminosities (in the relevant bands) are assigned to each cell following the\nBruzual and Charlot (1993, 1998; hereafter BC) model; we use their instantaneous\nstar-formation model, which best fits observations (Nagamine, Cen \\&\nOstriker 1999). We also analyze our results using other BC models; the\nmain conclusions are insensitive to the specific star-formation model used.\nThe luminosities determined for each cell are summed over the galaxy\nparticles in the cell and evolve with time as given by the BC model.\nThe simulated luminosities are in excellent agreement with the observed\nluminosity density in the universe at different redshifts\n(Nagamine, Cen \\& Ostriker 1999; see also below).\n\nWith the above information we can now determine the mass-to-light ratio, \n$M/L_{\\rm B}$ (where $L_{\\rm B}$ is the light in the blue band) at different\nlocations in the simulation volume and study it as a function of scale. In\norder to minimize possible uncertainties due to model luminosities, we\nnormalize all luminosities - and thus $M/L_{\\rm B}$ - to the \\emph{observed}\nluminosity density of the universe, as discussed below; this ensures that\nour results are largely independent of the specific luminosity model used.\n\nThe behavior of $M/L_{\\rm B}$ on small scales is determined in a similar\nmanner using smaller ($11.1h^{-1}$Mpc box), higher-resolution ($5h^{-1}$kpc)\nTree SPH simulations (see Dave \\emph{et al.} 1999). This simulation uses a\nsimilar cosmological model ($\\Omega =0.4$, $\\Omega_{\\wedge }=0.6$,\n$h=0.65$, $\\sigma_{8}=0.8$); the small difference between the models is\nadjusted in the final normalization of $M/L_{\\rm B}$, but is insignificant. \nAn $\\Omega=1$ CDM model, tilted with $n=0.8$, is also investigated using this\nsimulation size. Galaxies are identified using SKID (see Katz, Weinberg \\&\nHernquist 1996), and luminosities are assigned to each galaxy using the\nsame BC model described above.\n\n\\section{DEFINITION OF BIAS}\n\nThe term ``bias\" has been used with different explicit\nand implicit definitions, so it is essential that we be clear.\nKaiser (1984) introduced bias as the difference between the amplitude\nof the correlation function of high density regions (such as galaxies\nand clusters) relative to that of the mass in order to explain the\nexceptionally strong correlation function observed for rich clusters\nof galaxies (Bahcall \\& Soneria 1983, Klypin \\& Kopylov 1983). Similarly,\nDavis et al. (1985) introduced bias as the proportionality constant\nbetween the observed fluctuations in the number density of galaxies\nand the mass fluctuations found in simulations:\n$(\\Delta N/N)_{\\rm gal}\\equiv b_{\\rm gal} (\\Delta \\rho/\\rho)_{m}$.\nSince some smoothing scale ($R$) must be utilized to calculate\neither side of the equation, bias must be explicitly a function\nof scale, $b_{\\rm gal}(R)$. Implicit were observational criteria\nlimiting the counted galaxies to be above a certain luminosity\nand surface brightness. If (and it is a substantial assumption)\none identifies the number density of halos in simulations with the number\ndensity of galaxies then good dark matter simulations (e.g., Jenkins\n\\emph{et al.} 1998, Kravtsov \\& Klypin 1999, Colin \\emph{et al.} 1999),\nwhich can compute $(\\Delta N/N)_{\\rm halo}=b_{\\rm halo}(R)(\\Delta\\rho/\n\\rho)_{m}$, provide useful information and indicate low bias at large scales\n($b_{\\rm halo}\\sim 1$), significant positive bias (b$_{\\rm halo}>1$) at\nintermediate scales, and antibias ($b_{\\rm halo}<1$) on small ($R<5h^{-1}$Mpc)\nscales due to merging of halos.\n\nHydrodynamic simulations which seek to identify the site of galaxy\nformation and estimate the formation rate can compute the mass overdensity\nin galaxies, $(\\Delta \\rho/\\rho)_{\\rm gal}$, although poor resolution limits\ntheir ability to identify individual objects and to compute the galaxy number \noverdensity $(\\Delta N/N)_{\\rm gal}$. Recent papers by Katz \\emph{et al}\n(1999) and Cen \\& Ostriker (2000) find significant positive bias on\nintermediate scales. Blanton \\emph{et al} (1999) discuss in detail the\nphysical origin of this bias, and its dependence on scale. Einasto et al.\n(1999) discuss the physical origin of bias in terms of the fraction of mass\nthat exists in the voids. The ``semi-analytic\" approach seeks to combine\nin simplified form elements of the physical approach utilized in the\nhydrodynamic modelling with the detailed resolution obtainable from pure\nN-body work and has produced suggestive and most useful comparisons with\nobservations (Cole \\emph{et al.} 1994, Kauffmann \\emph{et al.} 1997). All\nof the above work find positive (but small) bias on large scales so it is\nimportant to understand the sense in which we will identify antibias in\nthis work.\n\nThe best way of comparing simulations to observations is neither through\n$(\\Delta N/N)_{\\rm halo}$ nor $(\\Delta \\rho/\\rho)_{\\rm gal}$, but via \n$(\\Delta j/j)_{\\rm gal}$, where $j$ is the light emitted by the galaxies\nin some band (here we use $j_{\\rm B}$ in the blue band). We then compare\n$(\\Delta j_{\\rm B}/j_{\\rm B})_{\\rm gal}$ with the same observed quantity\n(after correction for obscuration).\n\nFigure 1 shows in three panels (for top-hat smoothing scales\n$1.5, 5, 10h^{-1}$Mpc) the average and the dispersion of \n$(\\Delta \\rho/\\rho)_{\\rm gal}$ and $(\\Delta j_{\\rm B}/j_{\\rm B})_{\\rm gal}$\nversus the total mass overdensity $(\\Delta \\rho/\\rho)_{m}$. Points above\nthe diagonal line are positively biased and those below the line are antibiased.\nThe $(\\Delta \\rho/\\rho)_{\\rm gal}$ curves are similar to those shown\nin Cen \\& Ostriker (1992, 2000) as well as Blanton \\emph{et al} (1999)\nand indicate positive bias on all scales in our dense regions\n(approaching no bias in the highest density regions on these scales),\nand negative bias (antibias) in underdense regions (i.e., little or no\ngalaxies in the `voids').\n\nBut we see that the light density $j_{\\rm B}$ is antibiased, both relatively\nand absolutely, in the highest density regions at 1.5, 5 and $10h^{-1}$Mpc\nscales: $(\\Delta j_{\\rm B}/j_{\\rm B})/(\\Delta\\rho/\\rho)_{m}<1$.\nThe effect is small but real and easily understood. At low redshift\nthe highest density regions typically represent rich clusters and superclusters\n(for large smoothing scales of $\\sim 1$ to $10h^{-1}$Mpc); the stars and\ngalaxies in such regions tend to be old. This well-known observational\nfact is clearly seen in the simulations (Blanton \\emph{et al} 1999; Cen\n\\& Ostriker 2000); after clusters form (at $z\\simeq1-2$) the member galaxies\nreside within a hot medium ($T=10^7-10^8$K) for which cooling is inefficient\nand further star formation is inhibited. In such old dense regions massive\nyoung blue stars are rare, and the light diminishes sharply with increasing\ntime, especially in the blue. Our Bruzual-Charlot (BC) models, which\nincorporate standard stellar evolution, thus show relatively low blue light\nlevels in the highest density regions at the present time; {\\it the age effect}\novercomes the slight bias to bring the typical values of\n$(\\Delta j_{\\rm B}/j_{\\rm B})$ below $(\\Delta \\rho/\\rho)_{m}$ \nand yield a small {\\it antibias in the highest density regions}.\nThe large amount of intracluster gas in these systems may also contribute \nto the antibias.\n\nFor observers who, in general, have no direct access to the ordinate in\nFigure 1, $(\\Delta\\rho/\\rho)_m$, it is interesting to consider the\nratio of the bias in the high density regions (rich clusters and \nsuperclusters) to the bias in the more normal regions where most \ngalaxies live at moderate overdensities. Since these latter have a\nsignificant positive bias, the {\\it relative antibias} of high density \nregions as compared to low density regions is a factor of $\\sim$2-4\n(depending on scale).\n\n\\section{THE MASS-TO-LIGHT FUNCTION}\n\nWe now turn to the determination of the expected mass-to-light ratio of\ngalaxy systems as a function of scale by investigating $M/L_{\\rm B}$ for\ndifferent size volumes in the simulations. In the $100h^{-1}$Mpc box, we\ninvestigate volumes with radii ranging from $R \\sim1h^{-1}$Mpc to $62h^{-1}$Mpc\n(the volume-equivalent radius of the full box). For each volume of radius $R$\nwe determine the total mass $M$ and the total light $L_{\\rm B}$ within the\nvolume, and hence $M/L_{\\rm B}$. The volumes are centered on\nrandomly selected ``galaxies'' in the box, for proper comparison with \nobservations (i.e., we center on random cells with total galaxy\nparticle mass exceeding 10$^{11}$ or 10$^{12}$ M$_{\\odot }$; the results are\ninsensitive to the specific threshold). For a given radius, a large number\nof volumes are selected; these random volumes represent a wide range of mass\noverdensities. Rich clusters and superclusters of galaxies populate the\nhighest overdensity regions (at their respective scales), while loose groups\nand other galactic systems correspond to regions of lower overdensities.\n\nThe first questions we ask are: How does $M/L_{\\rm B}$ depend on scale and on\nthe local overdensity - does it flatten and become constant on large scales?\nAnd, does it vary with overdensity (at a given scale)?\n\nThe results are presented in Figure 2, together with the observational data\ndiscussed in \\S 2. The immediately apparent result is that $(M/L)(R)$ increases\nwith scale on small scales and flattens on large scales, as seen in the \nobservations. Each of the $(M/L_{\\rm B})(R)$ curves for $R \\geq 0.9h^{-1}$%\nMpc represents the simulation results for the mean of all volumes with\noverdensity above a given threshold (at any given scale, as indicated in\nFig. 2). \\ The highest overdensities are selected to correspond to\nobserved rich clusters of galaxies ($\\Delta \\rho /\\rho \\gtrsim $190 and $%\n\\gtrsim $ 250 at $R=1.5h^{-1}$Mpc, where $\\Delta\\rho/\\rho$ is the total mass\noverdensity; this corresponds approximately to richness\nclass $\\gtrsim $ 0 and $\\gtrsim $ 1 clusters; Abell 1958); these are shown\nby the top solid and dashed curves. The lower overdensity regions are presented\nby the dot-dashed curves; these are typical for loose groups of\ngalaxies at $R \\sim1h^{-1}$Mpc. To illustrate the trend of $(M/L_{\\rm B})(R)$\nwith overdensity, we scale the density thresholds with radius (from\n$R = 1.5h^{-1}$Mpc) assuming a density profile f $\\rho (r)\\propto r^{-2.4}$,\nas suggested by observations (e.g., Bahcall 1977, 1999, Peebles 1993, Carlberg\n\\emph{et al.} 1997); the results are similar for other reasonable extrapolations.\n\nVoids, which contain little or no light (galaxies) but do contain some\nmass, exhibit very large $M/L_{\\rm B}$ ratios (e.g., Figure 1); their \ncontribution is of course included in the total $(M/L_{\\rm B})_{\\rm box}$\nand $\\Omega$ values discussed below since these values refer to the entire \namount of mass in the box.\n\nThe solid curve marked $\\Omega $ = 0.37 represents the mean $M/L_{\\rm B}$\nfunction for $\\Delta \\rho /\\rho (R \\leq 1.5h^{-1}{\\rm Mpc}) \\geq \\ 190$\nfor the $\\Omega $ = 0.37 simulation (converted to h = 1 for comparison with\nthe data). \\ The same solid line is then scaled up and down to $\\Omega $ = 1\nand $\\Omega $ = 0.16 respectively (the latter, as shown below, is our\nbest-fit value), using linear scaling with $\\Omega$, as expected (see below).\nThe entire set of $(M/L_{\\rm B})(R)$ curves for different overdensities is\npresented only once, for clarity, for $\\Omega $ = 0.16.\n\nThe shape of the $(M/L_{\\rm B})(R)$ function is nearly independent of\nthe specific model luminosities used; all models, including models with\ndifferent but observationally acceptable initial mass function (eg.,\nSalpeter 1955, Miller \\& Scalo 1979, Scalo 1986, for $\\gtrsim0.1M_{\\odot}$),\nyield essentially the same function shape. In order to be independent of\npossible uncertainties also in the normalization of the model luminosities,\nwe normalize $L_{\\rm B}$ of the entire simulation---and thus $M/L_{\\rm B}$ of\nthe full box--- to the \\emph{observed} luminosity density of the universe. \nThe local luminosity density of the universe (in total B band luminosity, \ncorrected for extinction) is observed to be $j_{\\rm B}=(2\\pm0.4)10^8hL_{\\odot ({\n\\rm B})}{\\rm Mpc}^{-3}$ (Efstathiou \\emph{et al.} 1988, Lin \\emph{et al.}\n1996, Carlberg \\emph{et al.} 1997, Ellis 1997, Small \\emph{et al.} 1998 and\nreferences therein). Since the mass density of the universe is\n$\\rho=3\\Omega H_0^2/8\\pi G=\\Omega\\rho_{\\rm crit}=2.78\\times10^{11}\\Omega\nh^2M_{\\odot}{\\rm Mpc}^{-3}$, the universal mass-to-light can be expressed as\n$M/L_{\\rm B}\\equiv\\rho/j_{\\rm B}=(1400\\pm280)\\Omega h M_{\\odot}/L_{\\odot ({\\rm B})}$, where $L_{\\rm B}$ is the total, extinction corrected blue luminosity at\n$z\\simeq0$. We normalize our simulation box to have the observed luminosity\ndensity of the universe, $j_{\\rm B}$, as listed above; the $M/L_{\\rm B}$ of\nthe full box is thus fixed at $(M/L_{\\rm B})_{\\rm box}=518h$ (for\n$\\Omega=0.37$). Our results are therefore independent of\nthe absolute value of the simulated luminosities. In fact, the\ndirect simulation yields $M/L_{\\rm B} =520h$ for the box, strongly supporting\nthe appropriateness of the luminosity model used. Similarly, for $\\Omega $%\n=1, $M/L_{\\rm B}$ is normalized to be $M/L_{\\rm B} =1400h$ ($\\Omega $=1), as\nrequired. \n\nOn scales smaller than $0.9h^{-1}$Mpc, the smaller, higher-resolution\nsimulation is used (\\S 3) to determine $(M/L_{\\rm B})(R)$ from $R \\sim20$\nkpc to $\\sim6h^{-1}$Mpc. Since the box is small, no high-density\nregions such as rich clusters are found (since these are rare objects).\nThe $(M/L_{\\rm B})(R)$ presented in Figure 2 represents the average of\ntypical bright galaxies (corresponding approximately to \noverdensities above the threshold indicated by the dot-dash curve, as\nextrapolated to the smaller radii). The results are presented for $\\Omega\n= 0.16$ (scaled down from $\\Omega=0.4$). The two sets of simulations agree\nwell with each other in the overlap region of $\\sim$1 to $6h^{-1}$Mpc, thus\nstrongly supporting these independent results.\n\nThe results of Figure 2 show that the simulated $(M/L_{\\rm B})(R)$ function\nincreases on small scales and then flattens on large scales as suggested by\nobservations (Bahcall \\emph{et al.} 1995); the data and simulations exhibit\nthe same overall shape of the $(M/L_{\\rm B})(R)$ function. This result is\nindependent of the specific luminosity model used; all models yield the\nsame basic $(M/L_{\\rm B})(R)$ shape. Even though $M/L_{\\rm B}$ flattens to a\nconstant value on large scales, a clear dependence of $(M/L_{\\rm B})(R)$ on\nthe local overdensity (within a given radius R) is apparent; high overdensity\nregions exhibit higher $M/L_{\\rm B}$ ratios than lower density regions. The\nresults indicate that high density regions (such as rich clusters and\nsuperclusters) are \\emph{ antibiased} with respect to the mean, exhibiting\nhigher $M/L_{\\rm B}$ ratios than average; this implies that mass is more\nconcentrated than light in the high density regions. This effect, as noted in\nthe previous section, is likely caused by the age effect: high density\nclusters and superclusters are old systems, with low recent star-formation\n(and thus lower than average blue luminosity); the old galaxies that dominate\nthese system have significantly reduced luminosities at this late time in\ntheir evolution. Since all measures of $\\Omega$ that utilize the $M/L_{\\rm B}$\nmethod use clusters and superclusters of galaxies --- which\nare shown here to overestimate the mean $M/L_{\\rm B}$ of the universe --- \nthese measures also overestimate $\\Omega$.\n\nWe can now determine an unbiased $\\Omega $ by properly matching the simulated\n$(M/L_{\\rm B})(R)$ function to the data. As illustrated in Figure 2, both\n$\\Omega=1$ and $\\Omega=0.37$ greatly overestimate the observed $M/L_{\\rm B}$\nratio of groups, clusters, and superclusters, on all scales, by a factor of\n$\\sim 6$ (for $\\Omega $ = 1) and $\\sim$2 (for $\\Omega $ = 0.37). \\ This\noverestimate is seen for the \\emph{entire }observed range of the $M/L_{\\rm B}$\nfunction, not just for the classical case of clusters at $\\sim1h^{-1}$Mpc. \nBy fitting the entire observed and simulated mass-to-light\nfunction - properly matching to the relevant overdensities - we can \ndetermine an unbiased measure of $\\Omega ;$ we discuss this below (\\S 6).\n\nIn Figure 3 we compare the observed $(M/L_{\\rm B})(R)$ data with the simulated\nresults for the relevant high- and low- overdensity regions. The high\noverdensity region (represented by the higher of the two bands at $R\\gtrsim\n1 h^{-1}$Mpc) corresponds to typical rich clusters and superclusters of\ngalaxies (at $\\sim1.5h^{-1}$ and $5-20h^{-1}$Mpc respectively;\nsee specific overdensities listed in Figure 3). The low density region reflects\nenvironments typical of looser groups and other galaxy systems. The\nresults are presented for both $\\Omega $ = 0.16 and $\\Omega $ = 1, as scaled\nfrom the $\\Omega $ = 0.37 simulation. \\ On small scales, $R \\simeq $ \\ 20\nkpc to $\\sim6 h^{-1}$Mpc, the results from the high-resolution simulation\nreflect the full $M/L_{\\rm B}$ range obtained for individual galaxies\nand groups. These results are in full agreement with the large-scale\nsimulations; the two independent results merge nicely with each other in the\noverlap region. The $\\Omega=1$ results on small scales\n($\\lesssim6h^{-1}$Mpc) are obtained directly from the $\\Omega $ = 1 high \nresolution simulations; these direct simulation results\nagree well with the scaled-up results from low $\\Omega $ \nthus supporting the linear scaling of $M/L_{\\rm B}$ with $\\Omega $ on large\nscales.\n\n\\section{DETERMINING $\\Omega$}\n\nThe results presented in Fig. 3 provide a powerful illustration that an $\\Omega\n$ = 1 model significantly overestimates $M/L_{\\rm B}$ on \\emph{all scales}.\nOn large scales, the high overdensity band that represents typical rich\nclusters (at $R \\simeq 1.5h^{-1}$Mpc, $\\Delta \\rho /\\rho \\gtrsim 250$)\noverestimates the observed $M/L_{\\rm B}$ value for clusters by a factor of\n$\\sim$6--- a familiar result. A similar overestimate is seen for smaller\ngroups of galaxies, for individual galaxies, and for superclusters. Even an\n$\\Omega $ = 0.37 model appears to overestimate $(M/L_{\\rm B})(R)$, by a factor\nof $\\sim$2 (with lower significance). \n\nTo determine the best fit value of $\\Omega $, we use two methods. In the\nfirst method, we use the observed $M/L_{\\rm B}$ ratio of rich clusters of\ngalaxies, and correct it to the proper global universal value (i.e., correct\nfor the cluster antibias) by using the simulation's ratio of $M/L_{\\rm B}$\nfor the entire box to that of rich clusters. This ratio, $b_{\\rm cl}^{^{M/L_{\\rm B}}}\\equiv[(M/L_{\\rm B})_{\\rm box}/<M/L_{\\rm B}>_{\\rm cl}]_{\\rm sim}$,\nis the bias factor (in $M/L_{\\rm B}$) of clusters. For rich clusters (richness\nclass $\\gtrsim $ 1) at $R \\simeq 1.5h^{-1}$Mpc, we find \n\\begin{equation}\nb_{\\rm cl}^{^{M/L_{\\rm B}}}\\equiv\\left[\\frac{<M/L_{\\rm B}>_{\\rm box}}{<M/L_{\\rm B}>_{\\rm cl}}\\right]_{\\rm sim}=0.75\\pm0.15.\\\\\n\\end{equation}\nThe universal $M/L_{\\rm B}$ value is thus given by $<M/L_{\\rm B}>_{\\rm cl}\n\\times b_{\\rm cl}$; rich clusters overestimate the mean value by\na factor of $1/b_{\\rm cl}\\simeq 1.3$. The error-bar in (1) reflects the rms\nscatter among the simulated cluster $M/L_{\\rm B}$ values and the scatter\namong the different luminosity models investigated. Since only the relative\nratio between the simulated $(M/L_{\\rm B})_{\\rm box}$ and $<M/L_{\\rm B}>_{\\rm\ncl}$ is used in this method, the luminosity normalization is unimportant. The\nmass density of the universe can be determined from the mean observed \n$M/L_{\\rm B}$ of rich clusters (richness $\\gtrsim $ 1) at $R\\simeq 1.5h^{-1}$%\nMpc, $<M/L_{\\rm B}>^{\\rm obs}_{\\rm cl} = 300 \\pm 70h M _{\\odot }/L_{\\odot }$\n(BLD; Carlberg \\emph{et al.} 1997; with $L_{\\rm B}$ in our standard system,\nat $z=0$), and the observed luminosity density of the universe, $j_{\\rm B}$,\n\\begin{equation}\n\\rho_m=<M/L_{\\rm B}>_o\\times j_{\\rm B}=<M/L_{\\rm B}>_{\\rm cl}^{\\rm obs}\\times\nb_{\\rm cl}^{^{M/L_{\\rm B}}}\\times j_{\\rm B}\n\\end{equation}\nwhere $<M/L_{\\rm B}>_o$ is the universal value. Therefore\n\\begin{equation}\n\\Omega\\equiv\\frac{\\rho_m}{\\rho_{\\rm crit}}=\\frac{<M/L_{\\rm B}>_{\\rm cl}^{\\rm obs}\\times b_{\\rm cl}^{M/L_{\\rm B}}}{(M/L_{\\rm B})_{\\rm crit}},\n\\end{equation}\nwhere $(M/L_{\\rm B})_{\\rm crit}\\equiv\\rho_{\\rm crit}/j_{\\rm B}$ is the value\nrequired for a critical density universe ($\\Omega $ = 1; see \\S 5). Recent\nobservations of the local galaxy luminosity function, corrected to the\nstandard system of luminosity used here, yield $j_{\\rm B}=(2\\pm0.4)\\times10^8h\nL_{\\odot}{\\rm Mpc}^{-3}$ and thus $(M/L_{\\rm B})_{\\rm crit}=1400\\pm280h M_{\\odot}/L_{\\odot}$ (Lin \\emph{et al.} 1996, Carlberg \\emph{et al.} 1997, Ellis 1997,\nSmall \\emph{et al.} 1998). The conservative error-bar used above reflects the\nscatter among the different measurements as well as their uncertainties. We\nthus find\n\\begin{equation}\n\\Omega= \\frac{(300\\pm70)(0.75\\pm0.15)}{1400\\pm280} = 0.16\\pm0.06.\n\\end{equation}\nThe representative $M/L_{\\rm B}$ value of the universe is $<M/L_{\\rm B}>_o$\n=225 $\\pm $ 70, as given by the numerator of (4).\n\nA second method of determining $\\Omega $ is fitting the entire observed\n$M/L_{\\rm B}$ function of galaxies, groups, clusters, and superclusters\n(MS0302) to the simulated function, for the relevant overdensities. Here we\nuse the high $\\Delta \\rho /\\rho $ band (Fig. 3) for rich clusters, the lower\nbound of this band for the MS0302 supercluster, and the low $\\Delta\n\\rho /\\rho $ band for groups (the upper sub-band is used since it best\nmatches the group overdensities). The small-scale $R < 1h^{-1}$Mpc band is\nused for fitting the observed galaxies and small groups of galaxies (at\n$\\lesssim 0.5h^{-1}$Mpc). Fitting the observed to simulated $M/L_{\\rm B}$\nfunction has a single free parameter: $\\Omega$; the best $\\chi^2$ fit\nyields $\\Omega $ = 0.16 $\\pm $ 0.02. Since the box normalization is fixed at\nthe observed value of $j_{\\rm B}=(2\\pm0.4)10^8h$, corresponding to\n$(M/L_{\\rm B})_{\\rm box} = (1400\\pm280)\\Omega h$ (\\S 5), the\nresult is essentially independent of the luminosity models. The result does\ndepend however on the observed normalization $j_{\\rm B}$; therefore \n$\\Omega=0.16\\pm0.02(j_{\\rm B}/(2\\pm0.4)10^8h$), or equivalantly,\n$\\Omega =0.16\\pm0.02[(1400\\pm 280)h/(M/L_{\\rm B})_{\\rm crit}]$. Allowing for\nthe normalization uncertainty as well as for uncertainties in the overdensities\nand in model luminosities, we find\n\\begin{equation}\n\\Omega =0.16\\pm 0.05.\n\\end{equation}\n\nThis value is consistent with the one obtained earlier using clusters of\ngalaxies alone. Additional systematic uncertainties, while difficult to\naccurately determine, may contribute an additional $\\sim$ 20\\%($\\pm$ 0.03) to\nthe above uncertainty (see below). The $M/L_{\\rm B}$ function for this\nbest-fit value, plotted in Fig. 3, reproduces well the entire observed \n$M/L_{\\rm B}$ function, from galaxies to superclusters.\n\n%Several points should be highlighted following the above results:%\n\n%\\begin{enumerate}\n%\\item The above analysis uses overdensities selected in the\n%$\\Omega =0.37$ simulation (keeping the same overdensities for the different\n%$\\Omega$'s). \n%The actual overdensities (of groups, clusters, superclusters) in the lower\n%$\\Omega\\simeq0.16$ universe are of course twice as large, which can further \n%reduce $\\Omega$ by $20\\%$, to $\\Omega\\simeq0.13$. However, \n%the overdensities are expected to simply reflect the internal temperature (or galaxy formation\n%epoch) of these systems, which depends mostly on their mass and not \n%significantly on the exact value of $\\Omega$. If so, the overdensities need\n%not be re-scaled. If they are re-scaled, the best-fit $\\Omega$ may be lower than given above (by $\\sim20$\\%).\n%\n%\\item \nThe error-bars given in (4,5) above may not include all possible systematic\nuncertainties. For example, if low surface brightness galaxies contribute\nsignificantly to the total luminosity density of the universe (over and above\nthe extrapolated luminosity function), but not to the luminosity in clusters,\nthis will increase $j_{\\rm B}$ (thus decrease $(M/L_{\\rm B})_{\\rm crit}$) from\nthe value used, therefore increasing $\\Omega $. However, if such galaxies\nexist also in groups, clusters, and superclusters --- this effect will cancel\nout. The effect, if exists, is expected to be small, and is at least partially\ncovered by the large uncertainty adopted for $j_{\\rm B}$ and $(M/L_{\\rm B})_{\\rm crit}$. Similarly, a diffuse intracluster light, which may\naccount for $\\sim$ 15\\% of the total cluster luminosity (Feldmeier et al. 2000),\nis not included in the observed cluster luminosity (it may in fact compensate\nfor the contribution of low surface brightness galaxies in the field). If\nincluded, this will lower $<M/L_{\\rm B}>^{\\rm obs}_{\\rm cl}$ \nand thus lower $\\Omega $ (by $\\sim$ 15\\%). Systematic uncertainties in the\nsimulations may also contribute --- but only if they are scale dependent\n(since the overall normalization is independent of the simulations).\nIt is unlikely that significant shape changes exist on the scales considered\nhere. While difficult to accurately determine such possible systematic\nuncertainties, we estimate that they may contribute an additional \n$\\sim$ 20\\% uncertainty to $\\Omega $.\n\n%\\item Due to the antibias trend of increased M/L$_{B}$ with overdensity, we\n%expect higher overdensity clusters (i.e., richer clusters) to have larger M/L$%\n%_{B}$ ratios, on average, than poorer clusters. \\ Therefore, M/L$_{B}$\n%ratios for clusters are expected to vary by a factor of up to\n%$\\sim$2 among individual clusters, depending, on average, on\n%their overdensity. \n\nFigure 2 and 3 illustrate that the $(M/L_{\\rm B})(R)$ function of high density \nregions increases with scale to an above-average peak at a\nclusters-superclusters scale of few Mpc, then decreases to the mean universal\nvalue. Conversely, low density regions reveal lower $M/L_{\\rm B}$ values. \nThis is consistent with observations of rich clusters (high density) versus\ngroups (low density); groups exhibit lower $M/L_{\\rm B}$ ratios than typical\nrich clusters by a factor of nearly two, as seen in both data and simulations.\nBased on the present results we also expect that observations of weak lensing\nin the ``field'', which are currently underway, will reveal lower $M/L_{\\rm B}$\nratios than seen in clusters or superclusters of galaxies by a factor of up to\n$\\sim$2, depending on the specific overdensities.\n\nOur best-fit $\\Omega$ (eq. 5) is lower than previous estimates due to\nthe antibias discussed above as well as the more robust use of the entire $M/L$\nfunction --- not just clusters ---in constraining $\\Omega$.\nA mass-density of $\\Omega \\simeq 0.35,$ frequently regarded as a current\n''most popular'' value, appears to overestimate the entire observed $M/L$\nfunction, \\emph{on all scales}$,$ for galaxies, groups, clusters and\nsuperclusters.\n\nThe above analysis uses overdensities selected in the\n$\\Omega =0.37$ simulation (keeping the same overdensities for the different\n$\\Omega$'s).\nThe actual overdensities (of groups, clusters, superclusters) in the lower\n$\\Omega\\simeq0.16$ universe are of course twice as large, which can further\nreduce $\\Omega$ by $20\\%$, to $\\Omega\\simeq0.13$. However, this effect,\nwhich is caused mainly by the earlier cluster formation time in lower $\\Omega$\nmodels is minimized by the fact that {\\it all} objects form earlier in such\nmodels.\nIf so, the \noverdensities need not be re-scaled. If they are re-scaled, the best-fit\n$\\Omega$ may be lower than given above (by $\\sim20$\\%).\n\n\n\\section{ELLIPTICAL AND SPIRAL GALAXIES}\n\nOn small scales, the data show that $M/L_{\\rm B}$ of elliptical galaxies is\nlarger than that of spirals by a factor of $\\sim$3 (BLD; see also Tully and\nShaya 1998); this is mostly due to lower blue luminosity in the older\nellipticals, but could also be partially due to higher elliptical\nmass. To test this observation in the simulations, we identify old\nand young galaxies (thus mostly ellipticals and spirals respectively) by\nselecting galactic systems based on their redshift of formation. For\nexample, in the large simulation box we define regions of ``old'' galaxies\nas those where the total galactic particle mass formed at high redshift\n(e.g., $z > 1.9$) exceeds that which formed at low redshift\n(e.g., $z < 0.6$) by a factor of five. \\ Thus regions dominated\nby old galaxies satisfy: $M_{\\rm gal}(z<0.6)/M_{\\rm gal}(z >1.9) < 0.2$. \nSimilarly, regions dominated by ``young'' galaxies satisfy $M_{\\rm gal}(z<0.6)/M_{\\rm gal}(z >1.9) > 0.2$. \\ Varying the specific redshift cuts\nand the fractional threshold (0.2, 0.4, 0.6) does not affect the final\nresults discussed below.\n\n In Figure 4 we present the $M/L_{\\rm B}$ function for the old and young\ngalaxies as discussed above (for $R \\geq 0.9 h^{-1}$Mpc; solid and dashed\ncurves). \\ These curves are superimposed on the high and low overdensity\nbands from Fig. 3. \\ The results show a strong correlation: \\ the old galaxy\n$(M/L_{\\rm B})(R)$ function traces remarkably well the high overdensity regions\n(such as clusters and superclusters), while the young galaxies trace well\nthe low overdensity regions. \\ No re-normalization has been applied, and the\nresults are insensitive to reasonable changes in the redshift and threshold\ndefinitions of the young and old regions. \\ This result is consistent with\nobservations in the sense that high density regions are indeed best traced\nby old galaxies. \\ The difference between $M/L_{\\rm B}$ of the old and young\ngalactic regions is approximately a factor of 2 to 3, consistent with\nobservations. \\ Extending the results to smaller scales of individual\ngalaxies, we select old and young galaxies in the high-resolution\nsimulations based on their colors: $B-V > 0.65$ (old) and $B-V\n< 0.65$ (young). \\ We plot in Fig. 4 the mean 10\\% highest and\nlowest $(M/L_{\\rm B})(R)$ for galaxies in these respective color cuts, for \n$R \\simeq 20$ kpc to 6 Mpc. \\ The results depend only slightly on the exact\ncuts. \\ The results are consistent with those obtained from the large\nsimulation; they merge with each other in the overlap regions. The simulated\nresults are consistent with the data for the entire $(M/L_{\\rm B})(R)$\nfunction if - and only if - $\\Omega $ $\\simeq$0.16, as shown in Figs. 2-4.\n\n\\section{ CONCLUSIONS}\n\\qquad We use large-scale cosmological simulations to determine the expected\nmass-to-light ratio of galaxy systems and its dependence on scale. \nThe $(M/L_{\\rm B})(R)$ function is investigated from small scales of galaxies\n($R \\simeq 20$ kpc) to large scales ($R \\simeq 60h^{-1}$Mpc), and compared with\nobservations of galaxies, groups, clusters, and superclusters. We use the\nresults to evaluate the amount of bias on different scales (i.e., how mass\ntraces light), and use the comparison with observations to determine the\nmass density of the universe, $\\Omega $.\n\nWe find the following results:\n\n\\begin{enumerate}\n\\item In high density regions the galaxy blue light is antibiased (i.e., lower) relative to the total mass density (while the galaxy mass density is not). This is due to the old age of the high density systems which leads to a relative decrease in their\npresent-day luminosity, especially in the blue band that traces recent star formation.\n\n\\item The shape of the simulated $(M/L_{\\rm B})(R)$ function is in excellent\nagreement with observations.\nThe simulated $M/L_{\\rm B}(R)$ function increases with\nscale on small scales and flattens on large scales, where $M/L_{\\rm B}$ reaches\na constant value, as observed.\nThe mean flattening of $(M/L_{\\rm B})(R)$ on large scales indicates that, on\naverage, mass follows light on large scales (i.e., $M \\propto L$).\n\n\\item Even though $M/L_{\\rm B}$ is approximately constant on large scales, we\nfind that the actual value of $M/L_{\\rm B}$ depends on the local mass\noverdensity, $\\Delta \\rho /\\rho (<R)$, at a given scale. \\ High\noverdensity regions exhibit higher $M/L_{\\rm B}$ ratios than lower density\nregions. \\ The difference can typically be a factor of 2 to 3, consistent\nwith observations of groups and clusters of galaxies (representing low and\nhigh density regions, respectively).\nThe dependence of $M/L_{\\rm B}(R)$ on overdensity indicates that high\ndensity regions such as rich clusters and superclusters are relatively \\emph{antibiased%\n} - they exhibit higher than average $M/L_{\\rm B}$ values, implying that mass is\nmore concentrated than light in these regions (see 1 above). In the blue luminosity band, the\ncluster $M/L_{\\rm B}$ antibias is $b_{\\rm cl}^{^{M/L_{\\rm B}}}=<M/L_{\\rm B}>_o/<M/L_{\\rm B}>_{\\rm cl}=0.75\\pm0.15$.\n\n\\item We find that the $(M/L_{\\rm B})(R)$ function of high density regions is\ntraced well by $(M/L_{\\rm B})(R)$ of old (elliptical) galaxies; low density\nregions are traced well by young (spiral) galaxies. \\ These results are\nconsistent with observations.\n\n\\item We determine the mass density of the universe by fitting the simulated\n$(M/L_{\\rm B})(R)$ function to observations. \nThe best fit $\\Omega$ is lower than previous estimates based on cluster $M/L$\nvalues because of the antibias discussed above as well as the more robust use \nof the entire $M/L$ function --- not just clusters --- in constraining $\\Omega$.\nWe find a best-fit value of \n$\\Omega=0.16\\pm0.05$ (with an additional estimated uncertainty of $\\pm0.03$ for possible additional systematics); this \nvalue provides a remarkably good match to the\ndata for galaxies, groups, clusters, and superclusters. \\ The results are\nindependent of the details of the models and provide a\npowerful measure of $\\Omega$.\nThe only significant uncertainty we are aware of is due to the possibility\nthat current observations may systematically underestimate the global\nmean luminosity density of the universe. This will produce a corresponding\nunderestimate in our computation of $\\Omega$ unless there was also a \ncorresponding underestimate in the luminosity of groups, clusters, and\nsuperclusters of galaxies.\n\\end{enumerate}\n\n\\acknowledgments{\nWe thank J. Peebles, D. Spergel, P. Steinhardt, and M. Strauss for helpful\ndiscussions. This work was supported by NSF grants AST-9803137 and ASC-9740300.\n}\n\n\n\\begin{thebibliography}{99}\n\\bibitem{}Abell, G.O. 1958, \\emph{ApJS}, 3, 211.\n\\bibitem{}Abell, G.O. 1965, \\araa, 3, 1.\n\\bibitem{}Bahcall, N.A. 1977, \\araa, 15, 505.\n\\bibitem{}Bahcall, N.A., \\& Soneria, R.M., 1983, \\apj, 270, 20\n\\bibitem{}Bahcall, N.A. 1999, \\emph{Astrophysical Quantities, }ed. A. Cox, Springer Publishing\n\\bibitem{}Bahcall, N.A., Lubin, L.M., and Dorman, V. 1995, \\emph{ApJL}, 447, L81 (hereafter BLD).\n\\bibitem{}Bahcall, N.A. and Fan, X. 1998, \\emph{ApJ}, 504, 1.\n\\bibitem{}Bahcall, N.A., Ostriker, J.P., Perlmutter, S., and Steinhardt, P.J. 1999, \\emph{Science, } 284, 1481.\n\\bibitem{}Blanton, M., Cen, R., Ostriker, J.P., Strauss, M.A., and Tegmark, M. 1999, \\emph{ApJ}, in press (astro-ph/9903165).\n\\bibitem{}Bruzal, A.G. and Charlot, S. 1993, \\emph{ApJ,} 405, 538; 1998, private communication (hereafter BC).\n\\bibitem{}Carlberg, R.G., Yee, H.K., Ellingson, E., Abraham, R. Gravel, P., Morris, S., and Pritchet, C.J. 1996, \\emph{ApJ, } 462, 32. [Also astro-ph/9704060]\n\\bibitem{}Carlberg, R.G., Yee, H.K., and Ellingson, E. 1977, \\emph{ApJ, } 478, 462.\n%\\bibitem[Cen~\\&~Ostriker]{CO92} Cen,~R.~\\&~Ostriker,~J.~P., 1992, ApJ, {393}, 22\n\\bibitem{}Cen, R. and Ostriker, J.P. 1992, \\emph{ApJ, } 399, L113\n%\\bibitem[Cen~\\&~Ostriker]{CO93} Cen,~R.~\\&~Ostriker,~J.~P., 1993, ApJ, {417}, 404\n%\\bibitem{}Cen, R. and Ostriker, J.P. 1998\n\\bibitem[Cen and Ostriker]{CO99} Cen,~R. and Ostriker,~J.~P., 1999, \\emph{ApJ}, 514, 1\n\\bibitem{}Cen, R. and Ostriker, J.P., 2000, \\emph{ApJ}, in press\n\\bibitem{} Cole, S., Aragon-Salamanca, Frenk, C.S., Navarro, J., Zepf, S.E. 1994, \\emph{MNRAS}, 271, 781\n\\bibitem{}Colin P., Klypin, A.A., Kravtsov, M.V., and Khokhlov, A.M., 1999, \\emph{ApJ},\n523, 32\n\\bibitem{}Davis, M., Tonry, J., Huchra, J., and Latham, D., 1980, \\emph{ApJ}, 238, L113\n\\bibitem{} Davis, M., Efstathiou, G., Frenk, C.S., and White, S.D.M. 1985, \\emph{ApJ}, 292, 371\n\\bibitem{}Dav\\'{e}, R., Hernquist, L., Katz, N., and Weinberg, D., 1999, \\emph{ApJ}, 511, 521\n\\bibitem{}Efstathiou, G., Ellis, R.S., and Peterson, B.A. 1988, \\emph{MNRAS, }232, 431.\n\\bibitem{}Einasto, J., Einasto, M., Tago, E., Muller, V., Knebe, A., Cen, R., Starobinsky, A.A., and Atrio-Barandela F., 1999, \\emph{ApJ}, 519, 456\n\\bibitem{}Einasto J., Kaasik, A., and Saar, E., 1974, \\emph{Nature}, 250, 309\n\\bibitem{}Ellis, R. S., 1997, ARA\\&A 35, 389\n\\bibitem{}Faber, S.M. and Gallagher, J. S., 1979, ARA\\&A, 17, 135\n\\bibitem{} Feldmeier, A. et al., 2000, BASS, Jan. 2000\n\\bibitem{}Fischer, P., \\emph{et al.} 1999, \\emph{AJ} submitted \\ (astro-ph/9912119).\n\\bibitem{}Gnedin, N.Y. 1996, \\emph{ApJ, }456, 1.\n\\bibitem{}Gramann, M., 1990, \\emph{MNRAS}, 244, 214\n\\bibitem{}Jenkins, A., \\emph{et al}, 1998, \\emph{ApJ}, 499, 20\n\\bibitem{}Kaiser, N., 1984, \\emph{ApJ}, 284, L9\n\\bibitem{}Kaiser, N., Wilson, G., Luppino, G., Kofman, L., Gioia, I., Metzger, M., and Dahle, H. 1999, \\emph{ApJ}, in press (astro-ph/9809268)\n\\bibitem{}Katz, N., Weinberg, D.H., and Hernquist, L., 1996, \\emph{ApJS}, 105, 19\n\\bibitem[Katz, Hernquist, \\& Weinberg 1999]{khw99} Katz, N., Hernquist, L. and \nWeinberg, D.H 1999, \\emph{ApJ}, 523, 463\n\\bibitem[Kauffmann, Nusser, \\& Steinmetz 1997]{kns97} Kauffmann, G., Nusser, A. and Steinmetz, M. 1997, \\mnras, 286, 795\n\\bibitem{}Klypin, A.A., \\& Kopylov, A.I., 1983, Sov. Astron. Lett., 9, 41\n\\bibitem{}Kravtsov, A. and Klypin, A. 1999, \\emph{ApJ,} 520, 437.\n\\bibitem{}Krauss, L. and Turner, M.S. 1995, \\emph{Gen.Rel.Grav.,} 27, 1135.\n\\bibitem{}Lin \\emph{et al.} 1996, \\emph{ApJ}, 464, 60\n\\bibitem{}Miller, G.E. and Scalo, J.M., 1979, \\emph{ApJS}, 41, 573\n\\bibitem{}Nagamine, K., Cen, R., and Ostriker, J.P. 1999, \\emph{ApJ}, submitted\n(astro-ph/9902372).\n\\bibitem{}Ostriker, J.P., Peebles, P.J.E., and Yahil, A. 1974, \\emph{ApJL, } 193, L1.\n\\bibitem{}Ostriker, J.P. and Steinhardt, P.J. 1995, \\emph{Nature, } 377, 600.\n\\bibitem{}Peebles, P.J.E. 1993, \\emph{Principles of Physical Cosmology}, (Princeton University Press, Princeton).\n\\bibitem{}Roberts, M.S. and Rots, A.H. 1973, \\emph{ApJL, }186, L95.\n\\bibitem{}Rubin, V.C. and Ford, W.K. 1970, \\emph{ApJ, }159, 379.\n\\bibitem[Ryu \\emph{et al.} 1993]{rokc93} Ryu, D., Ostriker, J.P., Kang, H., \\& Cen, R. 1993, \\emph{ApJ}, 414, 1\n\\bibitem{}Salpeter, E.E.,1955, \\emph{ApJ}, 121,161\n\\bibitem{}Scalo, J.M., 1986, FunCosP, 11, 1\n\\bibitem{}Schwarzchild, M., 1954, \\emph{AJ}, 59, 273\n\\bibitem{}Small, T.A., Ma, C., Sargent, W. and Hamilton,D. 1998, \\emph{ApJ}, 492, 45 [See also \\emph{ApJ}, 487, 512(1997)]\n\\bibitem{}Steinmetz, M., 1996, \\emph{MNRAS}, 278, 1005\n\\bibitem{}Trimble, V. 1987, ARA\\&A, 25, 423\n\\bibitem{}Tully, R.B. and Shaya, E.L., 1998, in Proceedings of Evolution\nof large Scale Structure, Garching (astro-ph/9810298)\n\\bibitem{}Tully, R.B., Shaya, E.L., and Peebles, P.J.E. 1994, in Proc. Yamada\nConference 23, ed. K. Sato (Tokyo: Universal Academy Press), 217.\n\\bibitem{}White, S.D.M., Efstathiou, G., and Frenk, C. 1993, \\emph{MNRAS, }262, 1023.\n\\bibitem{}Zaritzky, D., Smith, R., Frenk, C., and White, S.D.M. 1993, \\emph{ApJ, } 405, 464.\n\\bibitem{}Zwicky, F. 1957, \\emph{Morphological Astronomy}, (Berlin: Springer-Verlag).\n\n\\end{thebibliography}\n\n\\newpage\n\\figcaption[fig1.ps]{\nThe galaxy mass overdensity, $\\rho_{\\rm gal}/<\\rho_{\\rm gal}>$ (=1+$(\\Delta\\rho/\\rho)_{\\rm gal}$), and the galaxy \nluminosity overdensity, $j_{\\rm B}/<j_{\\rm B}>$, are presented as a function of the total \nmass overdensity, $\\rho_m/<\\rho_m>$ (=1+$(\\Delta\\rho/\\rho)_{m}$), for volumes with radii 1.5, 5, \nand $10h^{-1}$ Mpc (left to right panels) in the $100h^{-1}$ Mpc simulation. \n(The denominators represent the values of the full box.) \nRegions above the dotted diagonal line represent\npositive bias ($b_{\\rm gal}$ or $b_{j_{\\rm B}}$ $>$1 ), while regions below the line are \nantibiased ($b_{\\rm gal}$ or $b_{j_{\\rm B}}$ $<$ 1); see \\S 4.}\n\n\\figcaption[fig2.ps]{The mass-to-light function of galaxy systems from observations ($%\n\\S $2) and simulations ($\\S $3,5). \\ The data points include galaxies\n(spirals and ellipticals, as indicated by the different symbols), groups,\nrich clusters (at $R = 1.5h^{-1}$Mpc), supercluster (MS0302 at $\\sim6h\n^{-1}$Mpc, from weak lensing observations), and the Virgo infall and Least\nAction analysis (shown on the largest scales) (from BLD; $\\S $2). \\ The\ncurves are the mean simulations results for regions above different\nmass overdensity thresholds (listed above). \\ The simulated $(M/L_{\\rm B})(R)$ function\nfor $\\Omega $ = 0.37 is scaled up and down to $\\Omega $ = 1 and $\\Omega $ =\n0.16 respectively. \\ Only the high-density solid curve is repeated for all\nthree models; the complete set of curves is shown for one case only ($\\Omega \n$ = 0.16, our best-fit value). \\ (The overdensities $\\Delta \\rho /\\rho $\nrefer to the $\\Omega $ = 0.37 simulation.) \\ On small scales, the curve\nrepresents the mean high-resolution simulation results for typical galaxies\nand small groups.}\n\n\\figcaption[fig3.ps]{The mass-to-light function of galaxy systems from observations\nand simulations. \\ The simulated results (for $\\Omega $ = 1 and 0.16, scaled\nfrom $\\Omega $ = 0.37) are presented for high- and low- density regions (for\n$R \\gtrsim 1h^{-1}$Mpc) typical of rich clusters/superclusters and small\ngroups of galaxies, respectively. \\ The high-density region (top band)\nrepresents the overdensities listed in the highest overdensity column (and\nis bounded, bottom and top curves, by the mean 30\\% lowest and 30\\% highest\n$M/L_{\\rm B}$ values, respectively). The low-density band is outlined by\nthree $(M/L_{\\rm B})(R)$ curves representing, bottom to top, the mean \n$(M/L_{\\rm B})(R)$ for mass overdensities between the lowest\nand next overdensity listed in the figure (from right to left; e.g., the\nbottom curve is the mean for $\\Delta \\rho /\\rho $ = 55 - 110 at $R = 0.9h\n^{-1}$Mpc, etc.). \\ The upper part of the band represents typical overdensities of small groups of\ngalaxies. \\ On small scales, the wide band at $R \\simeq $ 20kpc to 6Mpc\nreflects $(M/L_{\\rm B})(R)$ for the full range of typical galaxies and groups in\nthe high-resolution simulations (for $\\Omega $ = 1 and $\\Omega $ = 0.16). \\\nThe, entire observed $M/L_{\\rm B}$ function is well fit by the simulations only\nif $\\Omega \\simeq 0.16.$}\n\n\\figcaption[fig4.ps]{The mass-to-light function from observations, simulations (for\nhigh- and low- density regions; Fig. 3), and for simulated old and young\ngalaxies ($\\sim$ ellipticals and spirals; \\S 7). \\ Old galaxies trace\nwell the high-density regions (with high $M/L_{\\rm B}$ ratios) while young\ngalaxies trace well low-density regions (with lower $M/L_{\\rm B}$ values). \\ The\nresults are consistent with observations.}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002310.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{}Abell, G.O. 1958, \\emph{ApJS}, 3, 211.\n\\bibitem{}Abell, G.O. 1965, \\araa, 3, 1.\n\\bibitem{}Bahcall, N.A. 1977, \\araa, 15, 505.\n\\bibitem{}Bahcall, N.A., \\& Soneria, R.M., 1983, \\apj, 270, 20\n\\bibitem{}Bahcall, N.A. 1999, \\emph{Astrophysical Quantities, }ed. A. Cox, Springer Publishing\n\\bibitem{}Bahcall, N.A., Lubin, L.M., and Dorman, V. 1995, \\emph{ApJL}, 447, L81 (hereafter BLD).\n\\bibitem{}Bahcall, N.A. and Fan, X. 1998, \\emph{ApJ}, 504, 1.\n\\bibitem{}Bahcall, N.A., Ostriker, J.P., Perlmutter, S., and Steinhardt, P.J. 1999, \\emph{Science, } 284, 1481.\n\\bibitem{}Blanton, M., Cen, R., Ostriker, J.P., Strauss, M.A., and Tegmark, M. 1999, \\emph{ApJ}, in press (astro-ph/9903165).\n\\bibitem{}Bruzal, A.G. and Charlot, S. 1993, \\emph{ApJ,} 405, 538; 1998, private communication (hereafter BC).\n\\bibitem{}Carlberg, R.G., Yee, H.K., Ellingson, E., Abraham, R. Gravel, P., Morris, S., and Pritchet, C.J. 1996, \\emph{ApJ, } 462, 32. [Also astro-ph/9704060]\n\\bibitem{}Carlberg, R.G., Yee, H.K., and Ellingson, E. 1977, \\emph{ApJ, } 478, 462.\n%\\bibitem[Cen~\\&~Ostriker]{CO92} Cen,~R.~\\&~Ostriker,~J.~P., 1992, ApJ, {393}, 22\n\\bibitem{}Cen, R. and Ostriker, J.P. 1992, \\emph{ApJ, } 399, L113\n%\\bibitem[Cen~\\&~Ostriker]{CO93} Cen,~R.~\\&~Ostriker,~J.~P., 1993, ApJ, {417}, 404\n%\\bibitem{}Cen, R. and Ostriker, J.P. 1998\n\\bibitem[Cen and Ostriker]{CO99} Cen,~R. and Ostriker,~J.~P., 1999, \\emph{ApJ}, 514, 1\n\\bibitem{}Cen, R. and Ostriker, J.P., 2000, \\emph{ApJ}, in press\n\\bibitem{} Cole, S., Aragon-Salamanca, Frenk, C.S., Navarro, J., Zepf, S.E. 1994, \\emph{MNRAS}, 271, 781\n\\bibitem{}Colin P., Klypin, A.A., Kravtsov, M.V., and Khokhlov, A.M., 1999, \\emph{ApJ},\n523, 32\n\\bibitem{}Davis, M., Tonry, J., Huchra, J., and Latham, D., 1980, \\emph{ApJ}, 238, L113\n\\bibitem{} Davis, M., Efstathiou, G., Frenk, C.S., and White, S.D.M. 1985, \\emph{ApJ}, 292, 371\n\\bibitem{}Dav\\'{e}, R., Hernquist, L., Katz, N., and Weinberg, D., 1999, \\emph{ApJ}, 511, 521\n\\bibitem{}Efstathiou, G., Ellis, R.S., and Peterson, B.A. 1988, \\emph{MNRAS, }232, 431.\n\\bibitem{}Einasto, J., Einasto, M., Tago, E., Muller, V., Knebe, A., Cen, R., Starobinsky, A.A., and Atrio-Barandela F., 1999, \\emph{ApJ}, 519, 456\n\\bibitem{}Einasto J., Kaasik, A., and Saar, E., 1974, \\emph{Nature}, 250, 309\n\\bibitem{}Ellis, R. S., 1997, ARA\\&A 35, 389\n\\bibitem{}Faber, S.M. and Gallagher, J. S., 1979, ARA\\&A, 17, 135\n\\bibitem{} Feldmeier, A. et al., 2000, BASS, Jan. 2000\n\\bibitem{}Fischer, P., \\emph{et al.} 1999, \\emph{AJ} submitted \\ (astro-ph/9912119).\n\\bibitem{}Gnedin, N.Y. 1996, \\emph{ApJ, }456, 1.\n\\bibitem{}Gramann, M., 1990, \\emph{MNRAS}, 244, 214\n\\bibitem{}Jenkins, A., \\emph{et al}, 1998, \\emph{ApJ}, 499, 20\n\\bibitem{}Kaiser, N., 1984, \\emph{ApJ}, 284, L9\n\\bibitem{}Kaiser, N., Wilson, G., Luppino, G., Kofman, L., Gioia, I., Metzger, M., and Dahle, H. 1999, \\emph{ApJ}, in press (astro-ph/9809268)\n\\bibitem{}Katz, N., Weinberg, D.H., and Hernquist, L., 1996, \\emph{ApJS}, 105, 19\n\\bibitem[Katz, Hernquist, \\& Weinberg 1999]{khw99} Katz, N., Hernquist, L. and \nWeinberg, D.H 1999, \\emph{ApJ}, 523, 463\n\\bibitem[Kauffmann, Nusser, \\& Steinmetz 1997]{kns97} Kauffmann, G., Nusser, A. and Steinmetz, M. 1997, \\mnras, 286, 795\n\\bibitem{}Klypin, A.A., \\& Kopylov, A.I., 1983, Sov. Astron. Lett., 9, 41\n\\bibitem{}Kravtsov, A. and Klypin, A. 1999, \\emph{ApJ,} 520, 437.\n\\bibitem{}Krauss, L. and Turner, M.S. 1995, \\emph{Gen.Rel.Grav.,} 27, 1135.\n\\bibitem{}Lin \\emph{et al.} 1996, \\emph{ApJ}, 464, 60\n\\bibitem{}Miller, G.E. and Scalo, J.M., 1979, \\emph{ApJS}, 41, 573\n\\bibitem{}Nagamine, K., Cen, R., and Ostriker, J.P. 1999, \\emph{ApJ}, submitted\n(astro-ph/9902372).\n\\bibitem{}Ostriker, J.P., Peebles, P.J.E., and Yahil, A. 1974, \\emph{ApJL, } 193, L1.\n\\bibitem{}Ostriker, J.P. and Steinhardt, P.J. 1995, \\emph{Nature, } 377, 600.\n\\bibitem{}Peebles, P.J.E. 1993, \\emph{Principles of Physical Cosmology}, (Princeton University Press, Princeton).\n\\bibitem{}Roberts, M.S. and Rots, A.H. 1973, \\emph{ApJL, }186, L95.\n\\bibitem{}Rubin, V.C. and Ford, W.K. 1970, \\emph{ApJ, }159, 379.\n\\bibitem[Ryu \\emph{et al.} 1993]{rokc93} Ryu, D., Ostriker, J.P., Kang, H., \\& Cen, R. 1993, \\emph{ApJ}, 414, 1\n\\bibitem{}Salpeter, E.E.,1955, \\emph{ApJ}, 121,161\n\\bibitem{}Scalo, J.M., 1986, FunCosP, 11, 1\n\\bibitem{}Schwarzchild, M., 1954, \\emph{AJ}, 59, 273\n\\bibitem{}Small, T.A., Ma, C., Sargent, W. and Hamilton,D. 1998, \\emph{ApJ}, 492, 45 [See also \\emph{ApJ}, 487, 512(1997)]\n\\bibitem{}Steinmetz, M., 1996, \\emph{MNRAS}, 278, 1005\n\\bibitem{}Trimble, V. 1987, ARA\\&A, 25, 423\n\\bibitem{}Tully, R.B. and Shaya, E.L., 1998, in Proceedings of Evolution\nof large Scale Structure, Garching (astro-ph/9810298)\n\\bibitem{}Tully, R.B., Shaya, E.L., and Peebles, P.J.E. 1994, in Proc. Yamada\nConference 23, ed. K. Sato (Tokyo: Universal Academy Press), 217.\n\\bibitem{}White, S.D.M., Efstathiou, G., and Frenk, C. 1993, \\emph{MNRAS, }262, 1023.\n\\bibitem{}Zaritzky, D., Smith, R., Frenk, C., and White, S.D.M. 1993, \\emph{ApJ, } 405, 464.\n\\bibitem{}Zwicky, F. 1957, \\emph{Morphological Astronomy}, (Berlin: Springer-Verlag).\n\n\\end{thebibliography}"
}
] |
astro-ph0002311
|
On the origin of the color Tully-Fisher and color-magnitude relations of disk galaxies
|
[
{
"author": "Vladimir Avila-Reese and Claudio Firmani\\altaffilmark{1}"
}
] |
[
{
"name": "avilav2.tex",
"string": "\\documentstyle[11pt,newpasp,twoside]{article}\n\\markboth{Avila-Reese and Firmani}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\\def\\lesssim{{_ <\\atop{^\\sim}}}\n\\def\\grtsim{{_ >\\atop{^\\sim}}}\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{On the origin of the color Tully-Fisher and \ncolor-magnitude relations of disk galaxies}\n\n\\author{Vladimir Avila-Reese and Claudio Firmani\\altaffilmark{1}}\n\\affil{Instituto de Astronom\\'\\i a-UNAM, A.P. 70-264, 04510 \nM\\'exico, D. F.}\n\n\\altaffiltext{1}{Also Osservatorio Astronomico di Brera, via E.Bianchi \n46, I-23807 Merate, Italy}\n\n\\vspace*{0.7cm}\n\n$\\bullet$ The increment of the slope of the T-F relation (TFR)\nwith the passband wavelength has been called the \n{\\bf color TFR}. For example,\nfrom the observed $K-$ and $B-$band TFRs one obtains that \n$L_K/L_B\\propto V_m^{0.6}$ (Pierce \\& Tully1999, \\apj, 387,47).\nSince $L_K$ traces the stellar disk mass $M_s$, then $M_s/L_B\\propto\nV_m^{0.6}$. \nThe empirical fact that more luminous galaxies tend to be redder\nhave been called the {\\bf color-magnitude relation}: $(B-H)\\propto\n\\gamma$log$L_B$, $\\gamma\\approx 0.4-1.2$. \n\n$\\bullet$ {\\bf Why the mass-to-luminosity ratio and the color \nindex of disk galaxies do depend on $V_m$ (or luminosity)?}\nAt least there are three alternatives: the star formation (SF) efficiency,\nthe gas infall efficiency and/or the internal face-on dust extinction \ndepend on the galaxy mass. We explore the last\nalternative since self-consistent models of disk galaxy\nevolution within the hierarchical formation scenario show that the \n$M_s/L_B$ ratio and $B-H$ do not significantly depend on mass or \nluminosity (Avila-Reese \\& Firmani 2000, RevMexA\\&A, v. 36, in press;\nAvila-Reese et al., this volume).\n\n$\\bullet$ Observations indeed show that dust and metallicity increase\nwith $L_B$. In a more quantitative fashion, Wang \\& Heckman \n(1996: \\apj, 457, 645, WH) have established that the UV(young massive\nstars)-to-FIR (the same young stars {\\bf +dust absorption}) ratio \ndecreases rapidly with $L_B$ $\\Rightarrow$ {\\bf the dust opacity increases\nwith $L_B$:} $\\tau_B=\\tau_{B,o}(L_B/L_{B,o})^\\beta$ (eq. 1), with $L_{B,o}=\n1.3\\times 10^{10}L_{B\\odot}$, $\\tau_{B,o}=0.8\\pm 0.3$, and $\\beta=\n0.5\\pm 0.2$ (WH). \n\n$\\bullet$ Applying the uniform slab model, and using eq. (1) with \nthe central values for the constants, a good approximation for the\nextinction in the range of $10^8-10^{11}L_{B\\odot}$ is: \n$A_B\\approx 0.38+0.42$log$L_{B,10}+0.14($log$L_{B,10})^2$ (eq. 2). \nAssuming that in the $H$ band dust absorption is negligible, this result\nshows that $(B-H)$ will redden due to dust extinction roughly \nas $\\propto 0.42$log$L_B$, which reasonable agrees \nwith that is observed. On the other hand, in the understanding that\nthe origin of the TFR in the different bands is common, the fact that\n$L_K/L_B\\propto V_m^{0.6}$ is easily accounted for the $B-$band extinction\ngiven by eq. (2). In the hierarchical scenario of galaxy formation\nindeed the TFR for any band is a common imprint of the mass-velocity \nrelation of the CDM halos.\n\n$\\bullet$ In conclusion, {\\it the luminosity-dependent dust extinction \nreported by WH easily explains the color TF and color-magnitude\nrelations of disk galaxies;} there is not necessity to evoke\nmass dependent SF and gas infall efficiencies. The extinction \ncould depend on mass\nbecause the efficiency of metal ejection out of the disk might\nbe larger for smaller galaxies and/or because more massive\ngalaxies have higher surface densities than the smaller ones. \n\n\n\\end{document}"
}
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[] |
|
astro-ph0002312
|
Gamma-Ray Bursts via the Neutrino Emission from Heated Neutron Stars
|
[
{
"author": "Jay D. Salmonson\\altaffilmark{1} and James R. Wilson"
}
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A model is proposed for gamma-ray bursts based upon a neutrino burst of $\sim 10^{52}$ ergs lasting a few seconds above a heated collapsing neutron star. This type of thermal neutrino burst is suggested by relativistic hydrodynamic studies of the compression, heating, and collapse of close binary neutron stars as they approach their last stable orbit, but may arise from other sources as well. We present a spherically symmetric hydrodynamic simulation of the formation and evolution of the pair plasma associated with such a neutrino burst. This pair plasma leads to the production of $\sim 10^{51} - 10^{52}$ ergs in $\gamma$-rays with spectral and temporal properties consistent with many observed gamma-ray bursts.
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"string": "%\\documentclass[manuscript,12pt]{aastex}\n\\documentclass[preprint]{aastex}\n\\usepackage{amsmath}\n\\usepackage{epsfig}\n%\\usepackage{longtable}\n%\\usepackage{multicol}\n\n\\shorttitle{Neutron Star Binary Gamma-Ray Burst}\n\\shortauthors{Salmonson, Wilson, Mathews}\n\n\\begin{document}\n\n\\title{Gamma-Ray Bursts via the Neutrino Emission from Heated Neutron Stars}\n\n\\author{Jay D. Salmonson\\altaffilmark{1} and James R. Wilson}\n\\affil{Lawrence Livermore National Laboratory, Livermore, CA 94550}\n\n\\author{Grant J. Mathews}\n\\affil{University of Notre Dame, Notre Dame, IN 46556}\n\n\\altaffiltext{1}{e-mail: salmonson@llnl.gov}\n\n\\begin{abstract}\nA model is proposed for gamma-ray bursts based upon a neutrino burst\nof $\\sim 10^{52}$ ergs lasting a few seconds above a heated collapsing\nneutron star. This type of thermal neutrino burst is suggested by\nrelativistic hydrodynamic studies of the compression, heating, and\ncollapse of close binary neutron stars as they approach their last\nstable orbit, but may arise from other sources as well. We present a\nspherically symmetric hydrodynamic simulation of the formation and\nevolution of the pair plasma associated with such a neutrino burst.\nThis pair plasma leads to the production of $\\sim 10^{51} - 10^{52}$\nergs in $\\gamma$-rays with spectral and temporal properties consistent\nwith many observed gamma-ray bursts.\n\\end{abstract}\n\n\\keywords{binaries: close --- gamma rays: bursts --- gamma rays: theory --- stars: neutron}\n\n\\section{Introduction}\n\nUnderstanding the origin of gamma-ray bursts (GRBs) has been a perplexing\nproblem since they were first detected almost three decades\nago \\citep{kso73}. The fact that GRBs are \ndistributed isotropically \\citep{mfw+92} suggests a cosmological origin.\nFurthermore, arcminute burst locations from BeppoSax have \nrevealed that at least some $\\gamma$-ray bursts\ninvolve weak X-ray, optical, or radio transients, and are of\ncosmological origin \\citep{1997IAUC.6584}. The Mg I absorption and [O II]\nemission lines along the line of sight from the GRB970508 optical\ntransient, for example, indicate a redshift $Z \\ge 0.835$\n\\citep{1997IAUC.6655}. The implied distance means that this burst must have\nreleased of order $_>^\\sim 10^{51}$ ergs in $\\gamma$-rays on a time\nscale $\\sim$ seconds. This energy requirement has been rendered even more\ndemanding by other events such as GRB971214 \\citep{kfw+98} which\nappears to be centered on a galaxy at redshift 3.42. This implies\nthat the energy of a $4\\pi$ burst would have to be as much as $ 3\n\\times 10^{53}$ ergs, comparable to the visible light output of $\\sim\n10^9$ galaxies.\n\n Based upon the accumulated\nevidence one can can now conclude that the following four\nfeatures probably characterize the source environment: 1) \nIf the total burst energies are in the\nrange of $10^{51}-10^{52}$ ergs, then a beaming factor of 10 to 100\nis necessary; 2) The multiple peak\ntemporal structure of most bursts probably requires \neither multiple colliding\nshocks \\citep{rm94,kps98} or a single shock impinging\nupon a clumpy interstellar medium \\citep{mr93b,dm99}; \n3) The observed afterglows imply some surrounding\nmaterial on a scale of light hours; and 4) the presence of [O II] emission\nlines suggests that the bursts occur in a young, \nmetal-enriched stellar population.\n\nSome proposed sources for the production of GRBs include accretion\nonto supermassive black holes, AGN's, relativistic stellar collisions,\nhypernovae, and binary neutron star coalescence. Each of these\npossibilities, however, remain speculative until realistic models can\nbe constructed for their evolution. In this paper we construct a\nmodel for GRBs produced by energetic neutrino emission from\na heated neutron star. Our specific model for the emission\nderives from the relativistic compression and heating of neutron\nstars near their last stable orbit, however any scenario by which\nenergetic neutrino emission above a neutron star can endure for several\nseconds (e.g. tidal heating, MHD induced heating, accretion shocks, \netc) might also power the gamma-ray burst paradigm described herein. \n\nOur model is as follows. A compressionally heated neutron star emits\nthermal neutrino pairs which, in turn, annihilate to produce a hot\nelectron-positron pair plasma. We model the expansion of the plasma\nwith a spherically symmetric relativistic hydrodynamics computer\nprogram. This simplification is justified at this stage of the\ncalculations since the rotational velocity of the stars is about one\nthird of the sound speed in the $e^+e^-$ pair plasma. We then analyze\nand compare the contributions of photons from $e^+e^-$ pair\nannihilation as well as from an external synchrotron shock as the\nplasma plows into the interstellar medium. We show that the\ncharacteristic features of GRBs, i.e. total energy, duration and\ngamma-ray spectrum, can be accounted for in the context of this model.\n\n\n\\section{ Compression in Close Neutron Star Binaries }\n\nIt has been speculated for some time that inspiraling neutron stars\ncould provide a power source for cosmological gamma-ray bursts.\nHowever, previous Newtonian and post Newtonian studies\n\\citep{jr96,rj98,ruffert99} of the final merger of two neutron stars\nhave found that the neutrino emission time scales are so short that it\nwould be difficult to drive a gamma-ray burst from this source. It is\nclear that a mechanism is required for extending the duration of\nenergetic neutrino emission. A number of possibilities could be\nenvisioned, for example, neutrino emission powered by accretion\nshocks, MHD or tidal interactions between the neutron stars, etc. The\npresent study, however, has been primarily motivated by numerical\nstudies of the strong field relativistic hydrodynamics of close\nneutron-star binaries in three spatial dimensions. These studies\n\\citep{wm95, wmm96, mw97, mmw98a, mw99} suggest that neutron stars in\na close binary can experience relativistic compression and heating\nover a period of seconds. During the compression phase released\ngravitational binding energy can be converted into internal energy.\nSubsequently, up to $10^{53}$ ergs in thermally produced neutrinos can\nbe emitted before the stars collapse \\citep{mw97,mw99}. Here we\nbriefly summarize the physical basis of this model and numerically\nexplore its consequences for the development of an $e^+e^-$ plasma and\nassociated GRB.\n\nIn \\citep{mw97,mw99} properties of equal-mass neutron-star binaries were\ncomputed as a function of mass and EOS (Equation of State). From\nthese studies it was deduced that compression, heating and collapse\ncould occur at times from a few seconds to tens of seconds before\nbinary merger. Our calculation of the rates of released binding\nenergy and neutron star cooling suggests that interior temperatures as\nhot as 70 MeV are achieved. This leads to a high neutrino luminosity\nwhich peaks at $L_\\nu \\sim 10^{53}$ ergs sec$^{-1}$. This much\nneutrino luminosity would partially convert to an $e^+e^-$ pair plasma\nabove the stars as is also observed above the nascent neutron star in\nsupernova simulations \\citep{wm93}.\n\nWe should point out, however, that many papers have been published\nclaiming the compression is nonexistent. In \\citet{mmw98a} we\npresented a rebuttal to the critics. Subsequently, however,\n\\citet{flan99} pointed out a spurious term in our formula for the\nmomentum constraint. We \\citep{mw99} have corrected the momentum\nconstraint equation and redone a sequence of calculations for a binary\nneutron star system with various angular momenta. A compression\neffect still exists which is able to release $10^{52}$ - $10^{53}$\nergs of gravitational binding energy. The compression does not occur\nfor corotating stars with a polytropic equation of state. For\nirrotational binary stars our compression effect is consistent\nwith the results of at least two other groups \\citep{bonazzola99a,\nbonazzola99b, mmw99, uryu99} using different numerical methods to\ncompute the relativistic hydrostatic equilibrium \\citep{bonazzola97}.\nHowever, these calculations were done with a polytropic equation of\nstate and found only very small compression; much less than 1\\%. For\nthe polytropic equation of state \\citet{mw99} also found a compression\nless than 1\\%. In simulations with the realistic, somewhat soft, EOS \ndescribed below we\nfound clear evidence \\citep{mw99} that significant compression, heating\nand collapse still occurs for sufficiently close orbits. The reason for\nthis EOS dependence is straightforward. Table \\ref{eostable} shows the\nrealistic EOS used in the present work and the\n\\citep{mw99} studies. The key difference between the polytropic and\nrealistic EOSs is that the adiabatic index $\\Gamma$ is not constant\nbut decreases at low density for a realistic EOS.\nThis causes the outer regions of the star to be more compact, and\ntherefore, less affected by tidal stabilization than for polytropes.\nAt the same time, the maximum central density tends to be larger for\na neutron star of a fixed baryon mass. Therefore the relativistic\neffects are more dramatic when a realistic EOS is employed.\n\nThe hydrodynamic calculations that demonstrate\ncompression have been made with the stars constrained to remain at \nzero temperature (i.e. efficient radiators). \nAs the compression rate increases, however, it is expected\nthat the rate of released binding energy will exceed the\nability of the star to radiate and internal heating will result. Large\nscale off-center vortices are observed to form \\citep{mmw98a}\nwithin the stars with a characteristic\ncirculation time scale of $\\sim 0.005$ sec. \nThe maximum velocities are nearly sonic. \nAmong other things, this circulatory motion\nshould help dissipate the compressional motion into thermal energy by shocks\nthereby heating the interior of the stars.\n\nWe have run several sets of calculations with realistic neutron-star\nequations of state. We first considered stars like our earlier bench\nmark cases \\citep{mmw98a} with a baryon mass of 1.548 $M_\\odot$\ncorresponding to a typical (cf. Appendix A)\ngravitational mass of M$_G$ = 1.39 M$_\\odot$ and a central\ndensity of $\\rho_c = 1.34 \\times 10^{15}$ g cm$^{-3}$ in isolation.\nThese stars are based upon the ``realistic'' EOS of table\n\\ref{eostable}\nfor which the maximum critical mass is $M_c = 1.575$ M$_\\odot$. \nAs summarized in Appendix A, this maximum mass is typical of the\nsomewhat soft EOS's in which relativistic particles and/or\n condensates have been included.\nParameters for this EOS were motivated by the necessity of such \na soft EOS to obtain the correct neutrino signal in simulations \nof SN 1987A (Wilson \\& Mayle 1993).\nAs noted in Table 5 of the Appendix this maximum mass is consistent with\nthe measured masses of all binary pulsar systems for which the\norbits have been well determined.\n\nAs noted above, the stars calculated using this realistic EOS \nshow significant compression and released binding energy before\ninspiral but do not individually collapse. The released gravitational\nenergy from this calculation is summarized in Table\n\\ref{tableheat}. Even without the collapse instability enough internal\nheating occurs to produce a significant gamma-ray burst.\n\n\nWe also found \\citep{mw99} that the\nindividual collapse of stars would occur if the stars \nare increased in mass\nfrom M$_G = 1.39$ to 1.44 M$_\\odot$ (M$_B = 1.61$ M$_\\odot$) for this\nEOS. Collapse of this star system is observed to occur for very\nclose separation ($d = 2.4 R$) near (but before) the final stable orbit.\nThus, collapse is a reasonable possibility for typical\nmasses and a moderately soft EOS. For example, collapse\nwould always occur prior to inspiral for\nstars in the typically observed mass range modeled with the EOS of \\citet{bb95}.\nFor a critical mass of 1.54, even stars of initial mass of 1.35\ncollapse before reaching the innermost stable orbit.\n\nBased upon the above results, we model the thermal energy deposition\ndue to neutron star compression as follows: we expect that the fluid\nmotion within the stars will quickly convert released gravitational\nbinding energy into thermal energy in the interior of the stars.\nThus, we estimate that the rate of thermal energy deposition is\ncomparable to the rate of released binding energy due to compression.\nThe amount of released binding energy scales with the orbital four\nvelocity \\citep{mw97,mw99}. An estimate of the rate of increase of\nthe orbital four velocity can be obtained \\citep{mw97} from the\ngravitational radiation timescale. Then, from the relation between\nreleased binding energy and increasing four velocity\n\\citep{mw97,mw99}, the energy deposition rate into the stars can be\ndeduced in approximate analytic form \\citep{mw97}. We write,\n\\begin{equation}\n\\dot E_{th} = \\frac{ (32/5) (M f)^{5/3} f E^0_{th} }\n{ [1 - (64/5) (M f)^{5/3} f t]^{3/2}}~~,\n\\label{jay:E:energydot}\n\\end{equation}\nwhere $f$ is the orbital angular frequency and $E_{th}^0$ is the total \nthermal energy deposited into the stars. \nIn the hydrodynamic pair plasma discussions below\nwe consider a range of\ndeposited thermal energy of $E^0_{th} = 10^{51}$, $10^{52}$, $10^{53}$\nergs, consistent with the hydrodynamics simulations. \nWe use the convention that\n$t < 0$ and $t = 0$ is the end of energy deposition when the\nneutron stars either have collapsed into two black holes or have reached \nthe last stable orbit and collapsed to a single black hole. \nAt the time that a typical neutron star binary system is near the last stable\nobit, the orbital frequency is $\\sim$ a few$\\times 10^3$ sec$^{-1}$.\nHence, by Equation (\\ref{jay:E:energydot}), the energy deposition rate \nwould be \n\\begin{equation}\n\\dot E_{th} \\approx 10^2 \\times E^0_{th} ~~{\\rm erg~sec^{-1}}~~.\n\\end{equation}\nThus, for $E^0_{th} = 2 \\times 10^{52}$ ergs, $\\dot E_{th} \\approx 2 \\times 10^{54}$\nergs sec$^{-1}$.\n\nThe magnitude of the neutrino\n luminosity is very critical since the subsequent fireball is formed\n by neutrino-antineutrino annihilation. In order\nto model the thermal energy emitted by neutrinos before either\n stellar or orbital collapse we have constructed a computer model\n which treats the diffusion of energy in a static neutron star.\nThis energy transport occurs by a combination\n of neutrino diffusion \n plus energy diffusion\n via a convective velocity-dependent diffusion coefficient. \nFor the neutrino energy diffusion we write:\n\\begin{equation}\n{d E_\\nu \\over dt} = \\vec \\nabla \\cdot D_\\nu \\vec \\nabla E_\\nu\n\\end{equation}\nwhere the coefficient for neutrino diffusion is just the form,\n\\begin{equation}\nD_\\nu^{rad} = {c \\over 3 \\rho \\kappa_\\nu } + {R V_c \\over 3}~~,\n\\end{equation}\nwhere a simple estimate for the neutrino opacity $\\kappa_\\nu$ is used,\n$\\kappa_\\nu \\approx 9 \\times 10^{43} T_{MeV}^2$ cm$^{2}$ g$^{-1}$\nbased upon the cross section for neutrino nuclear absorption and\nscattering. Characteristic convective velocities $V_c$ were deduced\nfrom simulations using our three-dimensional binary neutron star code\n\\citep{mw99}. We calculated an angle averaged radial\ncomponent of the fluid velocity in the frame of the star,\n\\begin{equation}\nV_c = { 1 \\over 4 \\pi} \\int \\vert V_r \\vert d(\\cos \\theta) d\\phi ~~.\n\\end{equation}\nFor our studies, these velocities were fit with an ansatz of the form\n\\begin{equation}\nV_c \\equiv {32 \\over 105} V_{c,ave} {r \\over R} \\sqrt{1 - r/R} ~~,\n%V_c \\propto {r \\over R} \\sqrt{1-r/R} ~~,\n%V_c ={V_c^{max}\\over 2}3^{3/2} {r \\over R} \\sqrt{1-r/R} ~~,\n\\end{equation}\nwhere $r$ is the radial position inside a star of radius $R$ and\n$V_{c,ave}$ is the volume averaged $V_c$. This gives a good fit to\nthe numerical results and has the correct form in that the velocity\ngoes to zero at the surface and also at $r = 0$.\n\n Energy was deposited in accordance with equation\n\\ref{jay:E:energydot} and the calculations terminated at time=0. In\nFigure \\ref{efig} the fraction of energy released, the peak\nluminosity, and $\\bar L$ the average luminosity weighted by $L^{5/4}$\n(see next section) are shown. The Energy input was $2\\times 10^{52}$\nergs and the orbital frequency was 4000 rad sec$^{-1}$\n\\citep[see][]{mw99}. The average convective velocity was found to be\n$\\approx 0.003~c$ by analyzing the hydrodynamical calculations\n\\citet{mw99} of neutron star binaries. From Figure \\ref{efig} we see\nthat a high emission efficiency and luminosity are obtained from this\nconvective velocity. These produced lower thermal energies but about\nthe same fraction of the energy emitted, $\\approx 68\\%$, but the $\\bar\nL$ is reduced. For $E^0_{th} =0.5$ ($1.0$) $\\times 10^{52}$ ergs $\\bar\nL= 0.75$ ($1.5$) $\\times10^{53}$ ergs sec$^{-1}$. From these\ncalculations we estimate that the conversion of compressional energy\nto fireball energy is probably $^>_\\sim 20\\%$.\n\n%\\placefigure{efig}\n\\begin{figure}[tb]\n\\centering \\epsfig{figure=f1.eps, width = 9cm, angle =-90}\n%\\plotone{f1.eps}\n%\\figcaption[Fig1.ps]\n\\caption{Luminosity from a compressed, heated neutron star as a\nfunction of average convective velocity within the star. Convection\nsubstantially improves the efficiency of transport of energy to the\nsurface. \\label{efig}} \n\\end{figure}\n\n\n\\section{ Neutrino Annihilation and Pair Creation } \\label{neutrinoannihilation}\n\n In the previous section we have outlined a mechanism by which\nneutrino luminosities of $\\sim 10^{53}$ erg sec$^{-1}$ may arise from\nbinary neutron stars approaching their final orbits. Here we argue\nthat the efficiency for converting these neutrinos into pair plasma is\nprobably quite high. Neutrinos emerging from the stars will deposit\nenergy outside the stars predominantly by $\\nu\\overline{\\nu}$\nannihilation to form electron pairs. A secondary mechanism for energy\ndeposition is the scattering of neutrinos from the $e^+e^-$ pairs.\nStrong gravitational fields near the stars will bend the neutrino\ntrajectories. This greatly enhances the annihilation and scattering\nrates \\citep{sw99}. Figure \\ref{plotQ} taken from \\citet{sw99} shows\nthe relativistic enhancement factor, ${\\mathcal{F}}(R/M)$, of the rate\nof annihilation by gravitational bending versus the radius to mass\nratio (in units $G=c=1$). For our employed neutron-star equations of\nstate the radius to mass ratio is typically between $R/M \\sim 3$ and 4\njust before stellar collapse. Thus, the enhancement factor ranges\nfrom $\\sim$ 8 to 28. Defining the efficiency of energy deposition as\nthe ratio of energy deposition to neutrino luminosity, then from\nEquation 24 of \\citet{sw99} we obtain,\n\\begin{equation}\n \\frac{ \\dot{Q} }{ L_\\nu } \\approx 0.03 {\\mathcal{F}}(R/M)\nL_{53}^{5/4}~~.\n\\end{equation}\n Thus, the efficiency of annihilation ranges from $\\approx$0.1 to $ 0.84\n\\times L_{53}^{5/4}$. For the upper range of luminosity the efficiency is\nquite large. \n\n%\\placefigure{plotQ}\n\\begin{figure}[tb]\n\\centering \\epsfig{figure=f2.eps, width=9cm}\n%\\plotone{f2.eps}\n\\caption{General relativistic neutrino heating\naugmentation ${\\mathcal{F}} \\equiv \\dot{Q}_{GR}/\\dot{Q}_{Newt}$ as a\nfunction of neutron star neutrinosphere radius down to $R = 3M$, where\ngeneral relativistic energy deposition is $\\dot{Q}_{GR}$, and\nNewtonian energy deposition is $\\dot{Q}_{Newt}$. \\label{plotQ}}\n\\end{figure}\n\nTo better analyze the annihilation process we have\nadapted the Mayle-Wilson \\citep{wm93} supernova model to this problem.\nWe emphasize that the Mayle-Wilson model is fully general\nrelativistic. To investigate this problem, a hot neutron star of the\nappropriate $R/M$ was constructed and the internal temperature\nadjusted to achieve the correct neutrino luminosities. The Courant\ncondition requires that the time steps be quite small ($\\sim 10^{-9}$\nsecond), and zonal masses as low as $10^{-13} M_\\odot$ are required \njust outside of the neutrinosphere. Hence, the calculations could\nonly be evolved for a short time. The entropy per baryon $s/k$ of the\n$e^+e^-$ pair plasma is the\ncritical quantity for gamma-ray production. It can be written,\n\\begin{equation}\ns/k = \\frac{4 m_b c^2 (a e^3)^{1/4} }{ 3 k \\rho }~~,\n\\label{entropyperbaryon}\n\\end{equation}\nwhere $\\rho$ is the baryon density and $e$ is the total energy\ndensity. The entropy per baryon was found to be in the range of $10^5\n- 10^6$ for the high luminosities. For a luminosity of $10^{53}$ ergs\nsec$^{-1}$, an efficiency of energy transfer from the neutrinos to the\n$e^+e^-$ pair plasma due to annihilation and electron scattering was\nfound to be about 50 \\%. This efficiency of neutrino annihilation\ndetermines the total energy of the pair plasma and the entropy. This\nprovides the initial conditions for the subsequent fireball expansion.\n\n\\section{Pair Plasma Expansion}\n\nHaving determined the initial conditions of the hot $e^+e^-$ pair\nplasma near the surface of a neutron star, we wish to follow its\nevolution and characterize the observable gamma-ray emission. To\nstudy this we have developed a spherically symmetric, general\nrelativistic hydrodynamic computer code to track the flow of baryons,\n$e^+e^-$ pairs, and photons. For the present discussion we consider\nthe plasma deposited at the surface of a $1.45 M_\\odot$ neutron star\nwith a radius of 10 km.\n\nThe fluid is modeled by evolving the following spherically\nsymmetric general relativistic hydrodynamic\nequations:\n\n\\begin{equation}\n\\frac{\\partial D }{ \\partial t} = - \\frac{\\alpha }{ r^2} \n\\frac{ \\partial }{ \\partial r} (\\frac{r^2 }{ \\alpha} D V^r)\n+ \\dot D_{in}\n\\label{jay:E:ddiff}\n\\end{equation}\n\n\\begin{equation}\n\\frac{\\partial E }{ \\partial t} = - \\frac{\\alpha }{ r^2} \\frac{ \\partial }{\n\\partial r} (\\frac{r^2 }{ \\alpha} E V^r) - P \\biggl[ \\frac{\\partial W }{\n\\partial t} + \\frac{\\alpha }{ r^2} \\frac{\\partial }{ \\partial r} (\\frac{ r^2\n}{ \\alpha} W V^r) \\biggr]\n + \\dot E_{in}\n\\label{jay:E:ediff}\n\\end{equation}\n\n\\begin{equation}\n\\frac{\\partial S_r }{ \\partial t} = - \\frac{\\alpha }{ r^2} \\frac{ \\partial }\n{ \\partial r} (\\frac{r^2 }{ \\alpha} S_r V^r) - \\alpha \\frac{\\partial P }\n{ \\partial r} - \\alpha \\frac{M }{ r^2} \\biggl(\\frac{D + \\Gamma E }{ W}\n\\biggr) \\biggl[ \\biggl(\\frac{W }{ \\alpha} \\biggr)^2 + \\frac{(U^r)^2 }{\n\\alpha^4} \\biggr] \n\\label{jay:E:sdiff}\n%\\biggl[ \\frac{ 1 - \\frac{2 M }{ r} + 2 (U^r)^2 }{ \\alpha^4 } \\biggr]\n\\end{equation}\nwhere $D = \\rho W$ and $E = \\epsilon \\rho W$\n are the Lorentz contracted coordinate densities of \nbaryonic and thermal mass\nenergy ($e^+e^-$ and photons) respectively. The quantities $\\dot D_{in}$ and\n$\\dot E_{in}$ refer to the injected plasma from neutrino pair annihilation, and\n$S_r$ is the radial\ncoordinate momentum density. $U_r$ is the radial component of the\ncovariant 4-velocity. $W\\equiv \\alpha U^t$ is\nthe generalized Lorentz factor, $V^r$ is the radial\ncoordinate three velocity, and $\\Gamma$ is an\nequation of state index.\nThese quantities are defined by\n\\begin{eqnarray}\n\\alpha \\equiv \\sqrt{1 - \\frac{2 M }{ r}} \\quad ; \\quad U_r & \\equiv &\n\\frac{S_r }{ D + \\Gamma E} \\quad ; \\quad W \\equiv \\sqrt{ 1 + U^r U_r}\n\\nonumber \\\\ & & \\\\ V^r \\equiv \\frac{U^r }{ W} \\quad & ; & \\quad \\Gamma\n\\equiv 1 + \\frac{ P W }{ E} \\nonumber\n\\label{jay:E:defu}\n\\end{eqnarray}\nTo evolve the $e^+e^-$ pair plasma, we define a pair equation. The observed\npair annihilation rate must be corrected for relativistic effects;\nspecifically, time dilation slows the apparent pair\nannihilation process for a fast moving fluid with respect to an observer.\n Thus, we construct\na continuity equation analogous to Equation (\\ref{jay:E:ddiff}) and add\na term to account for annihilation and pair-production reactions:\n\\begin{equation}\n\\frac{\\partial N_{pairs} }{ \\partial t} = - \\frac{\\alpha }{ r^2} \\frac{\n\\partial }{ \\partial r} (\\frac{r^2 }{ \\alpha} N_{pairs} V^r) +\n\\overline{\\sigma v} ((N_{pairs}^0 (T))^2 - N_{pairs}^2)/W^2 ~~.\n\\label{jay:E:ndiff}\n\\end{equation}\nHere, $N_{pairs}$ is the coordinate pair number density, and\n$\\overline{\\sigma v}$ is the Maxwellian averaged mean pair\nannihilation rate per particle. Although $\\overline{\\sigma v}$\ndepends on $T$, it varies little in the temperature range of interest,\nand thus, can be taken as constant: $\\overline{\\sigma v} = 2.5 \\times\n10^{-25}$ cm$^3$ sec$^{-1}$. $N_{pairs}^0 (T) = n_{pairs}^0 (T) W$,\nwhere $n_{pairs}^0 (T)$ is the local proper equilibrium $e^+e^-$ pair\ndensity at temperature T given by the appropriate Fermi integral with\na chemical potential of zero. Zero chemical potential is a good\napproximation when $N^0_{pairs}(T)$ of Equation (\\ref{jay:E:ndiff}) is\nimportant.\n\nThe total proper energy equation, including photons and $e^+e^-$ pairs\n(baryon thermal energy is negligible), is\n\\begin{equation}\ne_{tot} = a T^4 + e_{pairs}\n\\end{equation}\nwhere coordinate energy in Equation (\\ref{jay:E:ediff}) is related to\nproper energy by $E = e_{tot} W$ and $e_{pairs}$ is the\nappropriate zero chemical potential Fermi integral normalized to give\nthe proper $e^+e^-$ pair density $n_{pair} = N_{pairs}/W$ as\ndetermined by Equation (\\ref{jay:E:ndiff}).\n\nThe entropy per baryon (Equation \\ref{entropyperbaryon}) of the wind\nis crucial to the behavior of the burst. An entropy that is too high\nwill create a burst which is much hotter than those observed, while an\nentropy that is too low will extinguish the burst with baryons. We\nfind that entropies of the order $10^7$ to $10^8$ are ideal for\nproducing an isotropic burst directly from the expanding pair-photon plasma.\nIn the calculations shown below\n(Sections \\ref{analysespecltcrv} \\& \\ref{resultspplsma}) we cover a\nrange of possible entropies per baryon from $10^6$ to $10^8$. Other\npossible sources of high entropy-per-baryon plasmas include the\nformation of magnetized black holes \\citep{rswx98,rswx99} and the\nhigh-energy collisions ($\\gamma \\approx 2$) of stars in collapsing\nglobular clusters, which we are studying in a separate work.\n\nWe will deal with two paradigms for $\\gamma-$ray production.\nFirst, we treat the high entropy case ($s/k > 10^7$)\nwhere the emission is from the fireball. Secondly, we present a\nlow entropy case in which gamma emission arises from the collision of\nthe fireball with the local interstellar medium.\n\nIn the first case, the hydrodynamic equations are evolved as the\nplasma expands. Once the system becomes transparent to Thomson\nscattering, ($\\int N_{pair}(r) \\sigma_T dr ^<_\\sim 1$ where $\\sigma_T$\nis the Thomson cross-section) we assume the photons are\nfree-streaming, the calculation is stopped and the photon gas is\nanalyzed to determine the photon signal.\n\n\\section{ Analysis of the Spectrum and Light curve } \\label{analysespecltcrv}\n\nWe find that the photons and $e^+e^-$ pairs appear to decouple at\nvirtually the same time throughout the entire photon-$e^+e^-$ pair\nplasma (when the cloud has reached a radius $\\sim 10^{12} - 10^{13}$\ncm and the temperature is typically a few 10's of eV). As such, the\nphotons will be well approximated as thermal and so we neglect any\nradiation transport effects. Thus, we take decoupling to be\ninstantaneous and to occur when the plasma becomes optically thin to\nThomson scattering. Furthermore, we find that virtually none of the\nenergy deposited in the $e^+e^-$ pair plasma remains in the pairs\n($\\sim .001$\\%). Thus, the conversion of $e^+e^-$ pair energy to\nphotons and baryons is very efficient. From this simulation we derive\ntwo observables, the time integrated energy spectrum $N(\\epsilon)$ and\nthe total energy received as a function of observer time\n$\\varepsilon(t)$.\n\n\\subsection{The Spectrum}\n\nAs mentioned above, we assume that the $e^+e^-$\npairs and photons are equilibrated to the same $T$ when they decouple.\nThus, the photons in the fluid frame (denoted with a prime: $'$) make up a\nPlanck distribution of the form\n\\begin{equation}\n{u'}_{\\epsilon'}(T') \\approx \\frac{ {\\epsilon'}^3 }{ exp({\\epsilon' / T'}) - 1}\n~~,\n\\end{equation}\nbut ${u_\\epsilon / \\epsilon^3}$ is a relativistic\ninvariant \\citep{rl75}. This implies $\\epsilon / T$ is\nalso a relativistic invariant. So a Planck distribution in an\nemitter's rest-frame with temperature $T'$ will appear Planckian to a\nmoving observer, but with boosted temperature $T = T'/(\\gamma (1 - v \\cos\n\\theta))$ where $v \\cos \\theta$ is the component of fluid velocity (c=1)\ndirected toward the observer. Thus,\n\\begin{equation}\nu_\\epsilon (\\theta,v,T') \\approx \\frac{ \\epsilon^3 }{ exp(\\gamma (1 - v \\cos \\theta) \\frac{ \\epsilon }{ T'}) - 1 }\n\\label{jay:E:planck}\n\\end{equation}\ngives the observed spectrum of a blackbody with rest-frame temperature\n$T'$ moving at velocity $v$ and angle $\\theta$ with respect to the\nobserver.\n\nIn the present case we wish to calculate the spectrum from a\nspherical, relativistically expanding shell as seen by a distant\nobserver. Since we know $v$, $T'$ and the radius $R$ of the shell, we\nintegrate over volume (i.e., shell, angle) with respect to\nthe observer. We thus obtain the observed photon energy spectrum $N_\\epsilon =\n{\\int (u_\\epsilon / \\epsilon)\\ d^3x}$, from\n a relativistically expanding spherical\nshell with radius $R$, thickness $dR$, velocity $v$, Lorentz factor\n$\\gamma$ and fluid-frame temperature $T'$,\n to be (in photons/eV/steradian)\n\\begin{equation}\nN_\\epsilon(v,T',R) = (5.23 \\times 10^{11}) 4\\pi R^2 dR \\frac{\\epsilon T' }{ v\n\\gamma} \\log \\Biggl[ \\frac{1 - exp[- \\gamma \\epsilon (1 + v)/T' ] }{ 1 -\nexp[ - \\gamma \\epsilon (1 - v)/T' ] } \\Biggr]~~({\\rm eV^{-1}} sr^{-1}),\n\\end{equation}\nwhere $R$ is in cm. Note, that this spectrum has a maximum at\n$\\epsilon_{max} \\cong 1.39 \\gamma T'\\ eV$ for $\\gamma \\gg 1$. We may\nthen sum this spectrum over all shells (the zones in our computer\ncode) of the fireball to get the total spectrum. Figure\n\\ref{fireballspec} shows an example of such a spectrum up to 500 keV.\nSince we assume {\\it a priori} that the photons are thermal, our\nspectrum has a high frequency exponential tail, but the resultant\ntotal spectrum is clearly not thermal in the high energies.\n\n%\\placefigure{fireballspec}\n\\begin{figure}[tb]\n\\centering \\epsfig{figure=f3.eps, width=9cm}\n%\\plotone{f3.eps}\n%\\figcaption[fireballspec.eps] %[fireballspec_bw.eps] <- black and white figure\n\\caption\n{ A spectrum of a relativistically expanding spherical fireball. A\nPlanck spectrum is shown for reference to show that the gamma-ray\nburst spectrum is not a black-body out to several 100\nkeV. \\label{fireballspec}}\n\\end{figure}\n\n\\subsection{The Light Curve}\n\nTo construct the observed light curve $\\varepsilon(t)$ we again\ndecompose the spherical plasma into concentric shells and consider two\neffects: First, is the relative arrival time of the first light from\neach shell: light from outer shells will be observed before light from\ninner shells; Second, is the shape of the light curve from a single\nshell.\n\nEmission from moving pair plasma is beamed along the direction of travel\nwithin an angle $\\theta \\sim 1/\\gamma$. The surface of simultaneity\nof a relativistically expanding spherical shell, as seen by an observer,\nis an ellipsoid \\citep{fmn96}. The observer time of intersection of an\nexpanding ellipse with a fixed shell of radius R as a function of\n$\\theta$ (i.e. the time at which emission from this intersection\ncircle is received) is:\n\\begin{equation}\nt = \\frac{R }{ v}(1 - v \\cos \\theta) \\cong \\frac{R }{ 2 \\gamma^2 c}~~,\n\\label{ltcurvetimescale}\n\\end{equation}\nfor $\\theta \\ll 1, \\gamma \\gg 1$. Integrating our boosted Planck\ndistribution of photons (Equation \\ref{jay:E:planck}) over frequency,\nwe find that a relativistically expanding shell of radius R will have\na time profile (energy/time/steradian)\n\\begin{equation}\n\\varepsilon(\\tau,v,T',R) = \\frac{a }{ 2} \\biggl(\\frac{T' }{ \\gamma \\tau}\n\\biggr)^4 c~ R~ dR \\sim 1/\\tau^4~~,\n\\label{jay:E:ltcurve}\n\\end{equation}\nfor $\\tau > 1$ and where $\\tau \\equiv \\frac{vt }{ R}$. Emission\nstarts at $\\tau_{i} = (1-v/c)$ and ends at $\\tau_{f} = (1 + v/c)$.\nThe final light curve is constructed by summing the signal from all\nshells. The total thickness of the expanding plasma is $\\sim c J/\n\\dot{J}$ because it expands at near the speed of light and $J/\\dot{J}$\nis the timescale of compression and coalescence which sets the\nemission timescale. Typically $R \\sim 10^{12}$ cm and $J/\\dot{J}\n\\sim$ a few seconds, so $c J/\\dot{J} \\ll R$ and the emitting plasma is\na thin shell. The duration of the burst is determined by the duration\nof emission because the observed timescale of emission from the plasma\nshell is very short, $R/2\\gamma^2 c \\sim 0.01$ seconds (Equation\n\\ref{ltcurvetimescale}) for $\\gamma \\sim 100$, compared to\n$J/\\dot{J}$.\n\n\\section{ Results of Pair Plasma Emission } \\label{resultspplsma}\n\nWe have run a variety of models over a range of entropies per baryon\nand total energies. The results are summarized in Figures\n\\ref{date52}, \\ref{date53} \\& \\ref{dats7}. We see that more powerful\nbursts are derived from higher entropies per baryon and higher total\nenergies. In particular, entropies per baryon of a few $\\times 10^7$\nallow a burst with a spectral peak $\\sim 100$ keV and efficiencies\n$E_\\gamma/E_{tot} \\sim 10$\\%. This is consistent with, although at\nthe upper end of the range of, the entropies calculated for the\n$e^+e^-$ plasma deposited above the neutron stars. Much further work\nneeds to be done to better characterize the nature of the stellar\ncompression and energy transport within the stars. Also, more\nelaborate simulations must be done to resolve the plasma flow in three\ndimensions and to consider the effects of magnetic fields. In Table\n\\ref{gammatable} we see the final Lorentz factor for a range of\nexpanding fireballs. This data will be used when we look at the\ncollision of the fireball into an external medium.\n\n%\\placefigure{date52}\n\\begin{figure}\n\\centering \\epsfig{figure=f4.eps, width=9cm}\n%\\plotone{f4.eps}\n%\\figcaption[e52.eps]\n\\caption{The photon energy at the spectrum peak, and gamma-ray\nefficiency are plotted for a total energy $E_{tot} = 10^{52}$ ergs\nover a range of entropies $10^6$ to $10^8$. \\label{date52}}\n\\end{figure}\n\n%\\placefigure{date53}\n\\begin{figure}\n\\centering \\epsfig{figure=f5.eps, width=9cm} \n%\\plotone{f5.eps}\n%\\figcaption[e53.eps]\n\\caption{The photon energy at the spectrum peak, and gamma-ray\nefficiency are plotted for a total energy $E_{tot} = 10^{53}$ ergs\nover a range of entropies $10^6$ to $10^8$. \\label{date53}}\n\\end{figure}\n\n%\\placefigure{dats7}\n\\begin{figure}\n\\centering \\epsfig{figure=f6.eps, width=9cm}\n%\\plotone{f6.eps}\n%\\figcaption[s7.eps]\n\\caption{The photon energy at the spectrum peak, and gamma-ray\nefficiency are plotted for an entropy per baryon $s = 10^7$ over a\nrange of energies $10^{51}$ to $10^{53}$ ergs. \\label{dats7}}\n\\end{figure}\n\n\\section{ External Shock Emission }\n\nIn previous sections the emission from an expanding fireball was\nstudied. We found that the resulting emission spectrum and total\nenergy strongly depends upon the energy of the plasma\ndeposited near the surface of the neutron stars; entropies of\n$\\lesssim 10^6$ resulted in weak emission with most of the original\nenergy manifesting itself as kinetic energy of the baryons. Thus, for\nthe low entropy per baryon fireballs ($s \\sim 10^5 - 10^6$) produced\nby NSBs it is necessary to examine the emission due to the interaction\nof the relativistically expanding baryon wind with the interstellar\nmedium (ISM).\n\nAfter becoming optically thin and decoupling with the photons, the\nmatter component of the fireball continues to expand and interact with\nthe ISM via collisionless shocks. As the ISM is swept up, the matter\ndecelerates. We model this process as an inelastic collision between\nthe expanding fireball and the ISM as in, for example,\n\\citet{piran98}. We assume that the absorbed internal energy is\nimmediately radiated away. From this we construct a simple picture of\nthe emission due to the matter component of the fireball\n``snowplowing'' into the ISM of baryon number density $n$.\n\nFor a shell of a given rest mass $M$ expanding at Lorentz factor\n$\\gamma$, the conservation of momentum leads to\nthe following constraint equation:\n\\begin{equation}\n\\frac{d\\gamma }{ \\gamma^2 - 1} = - \\frac{dM }{ M} ~,\n\\end{equation}\nwhich has the solution\n\\begin{equation}\n\\frac{M}{M_0} = \\sqrt{\\frac{(\\gamma_0 - 1) (\\gamma + 1)}{(\\gamma_0 +\n1) (\\gamma - 1)}} ~.\n\\end{equation}\nNow we can put this in terms of radius by noting\n\\begin{equation}\nM = M_0 + \\frac{4 \\pi}{3} n m_p c^2 R^3 ~.\n\\end{equation}\nThus,\n\\begin{equation}\nR(\\gamma) = R_0 \\biggl( \\frac{M}{M_0} - 1 \\biggr)^{1/3} \\cong R_0\n\\biggl(\\frac{1}{\\gamma} - \\frac{1}{\\gamma_0} \\biggr)^{1/3} \\quad\n\\text{for $\\gamma$, $\\gamma_0 \\gg 1$} \\label{Rgamma}~~,\n\\end{equation}\nwhere \n\\begin{equation}\nR_0 \\equiv \\sqrt[3]{\\frac{3 M_0}{ 4 \\pi n m_p c^2}}~~,\n\\end{equation}\nis the radius at which $M = 2 M_0$. This is the characteristic radius\nat which the shock decelerates.\n\nWe assume that the local thermal energy radiated away after a thin\nshell of ISM mass $dM$ is swept up by the shock is\n\\begin{equation}\ndE' = (\\gamma - 1) dM ~. \\label{dE}\n\\end{equation}\nThe observer time elapsed for the mass to expand a distance $dR$ is\n\\begin{equation}\ndt_{obs} = \\frac{ dR }{ 2 \\gamma^2 c } ~. \\label{dtobs}\n\\end{equation}\nEquations (\\ref{Rgamma},\\ref{dtobs}) can be solved in the relativistic limit\nto give\n\\begin{equation}\nt(\\gamma,\\gamma_0) \\cong \\frac{R_0}{28 c} \\biggl(\\frac{9}{\\gamma_0^2}\n+ \\frac{3}{\\gamma \\gamma_0} + \\frac{2}{\\gamma^2} \\biggr) \\biggl(\n\\frac{1}{\\gamma} - \\frac{1}{\\gamma_0} \\biggr)^{1/3} \\quad \\text{for\n$\\gamma$, $\\gamma_0 \\gg 1$}~ . \\label{tgamma}\n\\end{equation}\nThe implied observer luminosity, from Equations (\\ref{dtobs}, \\ref{dE}), is\n\\begin{equation}\nL = \\frac{dE }{ dt_{obs}} = \\frac{\\gamma dE' }{ dt_{obs}} \\approx 8 \\pi R^2\n\\gamma^4 n m_p c^3 \\label{LumDE}\n\\end{equation}\nfor $\\gamma \\gg 1$. Using Equation (\\ref{tgamma}), a relativistic\n($\\gamma \\gg 1$) solution for observed luminosity, in ergs sec$^{-1}$,\nover several epochs is\n\\begin{equation}\nL(t) \\cong\n \\begin{cases}\n 2.68 \\times 10^{50} n \\gamma_{300}^8 t^2 ({1 - {6.27 \\times 10^{-3}} \n \\gamma_{300}^8 n E^{-1}_{52} t^3})^{10/3}& t<t_1\\\\ \\\\\n 7.88 \\times 10^{51} n^{1/3} E_{52}^{2/3} \\gamma^{8/3}_{300} \n (0.32 \\frac{t }{ t_{max}} - 0.15)^{2/3} \n (1.15 - 0.32 \\frac{t }{ t_{max}})^{10/3}& t_1<t<t_2\\\\ \\\\\n 5.3 \\times 10^{51} n \\gamma_{300}^4 \n \\bigl[\\frac{E_{52} }{ n \\gamma_{300}}\\bigr]^{4/7} t^{2/7} \n \\bigl(1 - \\sqrt{f(t)} \\bigr)^4 \n {\\bigl({f(t) + \\sqrt{f(t)}} \\bigr)^{2/3}}& t>t_2\n \\end{cases} \\label{Lequation}\n\\end{equation}\nwhere constant parameters are, $ E_{52} \\equiv E/10^{52}$ ergs,\n$\\gamma_{300} \\equiv \\gamma_0/300$ and $n$ is in baryons cm$^{-3}$.\nFor $t > t_2$:\n\\begin{equation}\nf(t) \\equiv 1 - 1.05 \\biggl( \\frac{ t_{max} }{ t} \\biggr)^{3/7} \n\\end{equation}\nand\n\\begin{equation}\nt_{max} \\equiv 3.5~ \\sqrt[3]{\\frac{ E_{52} }{ n \\gamma_{300}^8 }}\n \\qquad \\text{seconds}\n\\end{equation}\nis the observer time at maximum luminosity $L_{max}$:\n\\begin{equation}\nL(t_{max}) = L_{max} = 1.3 \\times 10^{51} n^{1/3} \\gamma^{8/3}_{300} \n E_{52}^{2/3} \\qquad \\text{ergs/sec}~.\n\\end{equation}\nThe times at which the solutions for each epoch are spliced together\nare roughly\n\\begin{align}\nt_1 &\\sim 0.6 t_{max} \\\\\nt_2 &\\sim 1.5 t_{max} ~.\n\\end{align}\n\nFigure \\ref{xltcrv} shows the light curve for a $10^{52}$ erg fireball\nexpanding at $\\gamma = 300$ for a range of ISM densities. This\ncorresponds to an initial energy deposition above the neutron stars\nwith an entropy per baryon of $s = 10^5$ as seen in Table\n\\ref{gammatable}. The expansion can be divided into a free-expansion\nphase and a deceleration phase:\n\\begin{equation}\nL(t) \\propto\n \\begin{cases}\n t^2& \\text{free expansion phase $(t < t_{max})$} \\\\\n t^{-10/7}& \\text{deceleration phase $(t > t_{max})$}\n \\end{cases}\n\\end{equation}\nFigure \\ref{xltcrv2} shows a linear plot of the light curve for ISM\ndensity $n = 1.0$ baryons cm$^{-3}$. The ``fast-rise, exponential-decay''\nor ``FRED''-like shape is evident and is in good qualitative agreement\nwith ``smooth'' GRBs.\n\n%\\placefigure{xltcrv}\n\\begin{figure}\n\\centering \\epsfig{figure=f7.eps, width=9cm}\n%\\plotone{f7.eps}\n%\\figcaption[ltcrv.eps] % [ltcrv_bw.eps] <- black and white figure\n\\caption{The light curve for a $10^{52}$ erg fireball expanding at $\\gamma =\n300$ into interstellar media with three different baryon number\ndensities $n$. \\label{xltcrv}}\n\\end{figure}\n\n%\\placefigure{xltcrv2}\n\\begin{figure}[tb]\n\\centering \\epsfig{figure=f8.eps, width=9cm}\n%\\plotone{f8.eps}\n%\\figcaption[ltcrv2.eps] % [ltcrv2_bw.eps] <- black and white figure\n\\caption{The light curve for a $10^{52}$ erg fireball expanding at $\\gamma =\n300$ into interstellar media with baryon density $n = 1.0$\ncm$^{-3}$. This curve is similar in its ``fast-rise, exponential\ndecay'' shape and $\\sim 10$ second duration to the light curves of\nmany of the smooth-type GRBs. \\label{xltcrv2}}\n\\end{figure}\n\n\\subsection{ Synchrotron Shock Spectrum }\n\nNow we wish to model the spectrum of light emitted as the fireball\nexpands into the ISM. To do this we assume an external synchrotron\nshock model \\citep{sm90,rm92,mr93b,rm94}. This analysis is analogous to\nafterglow models in the radiative limit. Thus, the spectrum will have\nthe form \\citep{spn98}\n\\begin{equation}\nL_\\nu =\n \\begin{cases}\n (\\nu/\\nu_c)^{1/3} L_{\\nu,max}& \\nu<\\nu_c\\\\\n (\\nu/\\nu_c)^{-1/2} L_{\\nu,max}& \\nu_m > \\nu>\\nu_c\\\\\n (\\nu_m/\\nu_c)^{-1/2} (\\nu/\\nu_m)^{-p/2} L_{\\nu,max}& \\nu>\\nu_m ~.\n \\end{cases} \\label{Lnu}\n\\end{equation}\nPhoton frequency $\\nu_m$ is the frequency corresponding to the minimum\nenergy of the electron distribution above which the electrons are\nassumed to have a power law functional form $n(\\gamma) \\sim\n\\gamma^{-p}$. In the numerical examples that follow, we take \nthe spectral index to be \n$p = 2.5$. This is consistent with that calculated for\nultrarelativistic shocks \\citep{bo98}. The ``cooling frequency''\n$\\nu_c$ corresponds to the energy below which the electrons cannot cool\non a hydrodynamic timescale. The peak of the luminosity\nspectrum is\n\\begin{equation}\n L_{\\nu,max} \\cong \\biggl(\\frac{p-2}{2 p - 2}\\biggr)\n \\frac{L}{\\sqrt{\\nu_m \\nu_c}}~~,\n\\end{equation}\nassuming $\\nu_m \\gg \\nu_c$, which is valid throughout the burst\nduration. \n\nThere are two free parameters in this model. $\\epsilon_e$ is the\nfraction of the kinetic energy of the baryons that is deposited into\nthe electrons by the shock. $\\epsilon_B$ is the ratio of the magnetic\nfield energy density to the kinetic energy density of the baryons. In\nthese simulations we take each of these values to be $1/4$.\n\nThe evolution of the characteristic frequency $\\nu_m$ is described by\n\\begin{equation}\n \\nu_m \\cong 1.4 \\times 10^{4} \\epsilon^2_e \\epsilon_B^{1/2}\n\\sqrt{n} \\gamma_{300}^4~ \\text{keV}\n \\begin{cases}\n (1 - \\bigl(\\frac{2 c t}{R_0}\\bigr)^3 \\gamma_0^7)^4&\nt<t_1\\\\ \\\\\n (1.15 - 0.32 t/t_{max})^4& t_1<t<t_2\\\\ \\\\\n \\biggl(1 - \\sqrt{1 - \\frac{2}{\\gamma_0} (\\frac{14 c\nt}{R_0})^{-3/7}}\\biggr)^4& t>t_2 ~.\n \\end{cases} \\label{numequation}\n\\end{equation}\n\nThe behavior of the cooling frequency $\\nu_c$ is more difficult to\ncharacterize since it depends on the hydrodynamical timescale of the\nfluid. Fortunately, however, $\\nu_c$ is much smaller than $\\nu_m$.\nTherefore, its exact behavior is not important for this analysis. \nThus, we assume\n$\\nu_c$ to be constant at early times and follow its asymptotic\npower-law at later times:\n\\begin{equation}\n \\nu_c \\cong 2.7 \\times 10^{-3} \\epsilon_B^{-3/2} E_{52}^{-4/7}\n\\gamma_{300}^{4/7} n^{-13/14}~ \\text{keV}\n \\begin{cases}\n t_{max}^{-2/7}& t \\leq t_{max}\\\\ \n t^{-2/7}& t > t_{max} ~~.\n\\end{cases} \n\\label{nucequation}\n\\end{equation} \nThe spectrum of the burst at peak luminosity $L_{max}$ is shown in\nFigure \\ref{xspec}. For $n = 1.0$ baryons cm$^{-3}$, most of the energy is\nemitted at photon energies $\\sim 100$ keV. Using Equations\n(\\ref{Lequation},\\ref{numequation},\\ref{nucequation}) for $L$, $\\nu_m$\nand $\\nu_c$ respectively, we can determine the spectrum (Equation\n\\ref{Lnu}). The fluence spectrum of the burst is obtained by integrating the\nevolving luminosity spectrum (Equation \\ref{Lnu}) in time. This is shown in\nFigure \\ref{xfluence}. This figure again shows that most of the burst energy is\nin photons of several hundred keV energy.\n\n%\\placefigure{xspec}\n\\begin{figure}\n\\centering \\epsfig{figure=f9.eps, width=9cm}\n%\\plotone{f9.eps}\n%\\figcaption[spec.eps] % [spec_bw.eps] <- black and white figure\n\\caption{The synchrotron spectrum for a $10^{52}$ erg fireball expanding at\n$\\gamma = 300$ into interstellar media with three different baryon\nnumber densities $n$. \\label{xspec}}\n\\end{figure}\n\n%\\placefigure{xfluence}\n\\begin{figure}\n\\centering \\epsfig{figure=f10.eps, width=9cm}\n%\\plotone{f10.eps}\n%\\figcaption[fluence.eps] % [fluence_bw.eps] <- black and white figure\n\\caption{The total energy spectrum of a $10^{52}$ erg fireball expanding at\n$\\gamma = 300$ into an interstellar medium with baryon number density\n$n$ = 1.0 cm$^{-3}$. \\label{xfluence}}\n\\end{figure}\n\nNow we can ask what the efficiency is of gamma-ray production by the\nshock compared to other wavelengths. At any time, the fraction of\nluminosity above a given minimum frequency $\\nu_{min}$ is\n\n\\begin{equation}\n\\varepsilon_{ff} = \n \\begin{cases} \n \\frac{\\bigl[ \\bigl( \\frac{2 p -\n 2}{p-2} \\bigr) \\nu_m^{-1/2} - 2 \\nu_{min}^{1/2}\n \\bigr]}{\\bigl[ \\bigl(\\frac{2 p - 2}{p-2} \\bigr)\n \\nu_m^{-1/2} - \\frac{5}{4} \\nu_c^{1/2} \\bigr]}&\n \\nu_c < \\nu_{min} < \\nu_m\\\\ \\\\\n \\frac{ \\bigl(\\frac{2}{p - 2} \\bigr)\n \\biggl(\\frac{\\nu_m^{p-1}}{\\nu_{min}^{p-2}} \\biggr)^{1/2}}\n {\\bigl[ \\bigl(\\frac{2 p - 2}{p-2} \\bigr)\n \\nu_m^{-1/2} - \\frac{5}{4} \\nu_c^{1/2} \\bigr]}&\n \\nu_{min} > \\nu_c ~.\n \\end{cases}\n\\end{equation}\nThus, we can calculate the duration, $t_{90}$, of the luminosity at\nenergies above this minimum energy. This is done in Table\n\\ref{t90table} for the various fireballs shown in Table\n\\ref{gammatable}. There is a competition between factors limiting the\n duration; lower energy fireballs simply have fewer high energy photons,\nand thus, shorter duration; while higher energy fireballs expand and\nevolve faster and thus have shorter duration. Fireballs with energy\nof order $10^{52}$ ergs and entropies per baryon of order $10^5$ yield\na value for $t_{90}$ which is consistent with observation.\n\nThe overall efficiency of the production of photons above a frequency\n$\\nu_{min}$ is \n\\begin{equation}\n\\begin{split}\n\\varepsilon_{ff tot} &\\equiv \\frac{ \\int_0^\\infty\n \\int_{\\nu_{min}}^\\infty L_\\nu d \\nu dt } { \\int_0^\\infty\n \\int_0^\\infty L_\\nu d \\nu dt } \\\\ &\\approx 1 -\n \\biggl(\\frac{\\nu_{min}}{\\nu_{max}} \\biggr)^{1/6} \\quad\n \\text{for } \\nu_{min} \\ll \\nu_{max}~~,\n\\end{split}\n\\end{equation}\nwhere $\\nu_{max}$ is the value of $\\nu_m$ (Equation \\ref{numequation})\nat $t = t_{max}$. For $\\nu_{min} = 10$ keV we have an overall\nefficiency of about $\\varepsilon_{ff tot} \\approx 75$ \\%. Thus, the\nradiative external shock GRB is quite efficient at producing\ngamma-rays if our assumptions are reasonable.\n\n\n\\section{Conclusions}\n\nIn this paper we have argued that heated neutron stars\n(perhaps by compression of close \nneutron-star binaries) are \nviable candidates for the production of large, high entropy per baryon,\n$e^+e^-$ pair plasma fireballs, and thus, for the creation of gamma-ray\nbursts. We find that fireballs of total energy $E \\sim 10^{51}$ to \n$3 \\times 10^{52}$ ergs and an entropy per baryon of $s/k \\sim 10^5 - 10^6$ are\npossible. Values for the entropy as high as $10^7$ may be realized\nduring the peak $\\nu\n\\overline{\\nu}$ luminosity (of $\\approx 10^{53}$ ergs sec$^{-1}$).\nEmergent gamma-rays yield\na quasi-thermal spectrum peaked at $\\sim 100$ keV with an efficiency\nof conversion from pair plasma to photons of $\\sim 30$\\%. \nThe lower entropy component of the fireball will\ninitiate a shock which propagates into the ISM, generating an external\nshock GRB.\n\nThe calculation utilizing the supernova computer program (Section\n\\ref{neutrinoannihilation}) to describe the neutrino and matter transport,\nproduces a baryonic wind that \ncontains $\\sim 90$\\% neutrons. The decay of the neutrons to protons occurs on the same\ntime scale as that for which the protons are decelerated by the\nintersteller medium. This delayed conversion of neutrons to protons\nwill broaden the gamma-ray signal by a factor of a few. In\naddition, the decay electrons will strongly increase the entropy of the\nexpanding plasma at the late times. In future work we will quantify the role\nof neutrons and explore the possibility of fireball photons\ninverse-Compton up-scattering off of the accelerated electron\ndistribution of the external shock. This corresponds to the emission scenario\nput forward by \\citet{lksc97}.\n\nAs of yet this model is spherically symmetric. Thus, it can only generate\nbursts with a smooth light-curve structure. However, we expect a large variety\nof GRB morphologies with varied time structure due to: 1) three\ndimensional resolution of the plasma flow; 2) plasma instabilities due\nto increased heating of the deposited plasma with time; and 3)\nvariation in the ratio of star mass in the NSB, effecting the relative\ncompression and heating rate of each star.\n\nIn future work we will numerically model, in three dimensions, the flow\nof the $e^+e^-$ pair plasma in the midst of the orbiting neutron\nstars. We have written a three-dimensional general relativistic\nhydrodynamic code to study this three-dimensional behavior. In\nparticular, we wish to study the possible formation of jets along the\norbital axis due to the collision of plasma blowing away\nfrom each star. Also, we have done simulations which suggest that the\ninternal magnetic field of the neutron stars may be high.\nThus, the inclusion of \nmagnetohydrodynamic plasma effects including Alfv\\'en instabilities\nand reconnections may ultimately be necessary.\n\n\nThe authors wish to thank the late Jean-Alain Marck for his inciteful and\nencouraging remarks on an earlier version of this manuscript. \nThis work was performed under the auspices of the U.S. Department of\nEnergy by University of California Lawrence Livermore National\nLaboratory under contract W-7405-ENG-48. J.R.W. was partly supported\nby NSF grant PHY-9401636. Work at University of Notre Dame supported\nin part by DOE grant DE-FG02-95ER40934, NSF grant PHY-97-22086, and by\nNASA CGRO grant NAG5-3818. \\\\\n\n%\\clearpage\n\n%\\bibliographystyle{apjbib}\n%\\bibliography{nsbpaper6} %journals,grb,grb2,nsbpaper,psrrefs,thesis} %nsbgm} \n\n\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\astroncite{{Akmal} et~al.}{1999}]{pandharipande99}\n{Akmal} A., {Pandharipande} V.~R., {Ravenhall} D.~G. 1999, \\prc, 58, 1804\n\n\\bibitem[\\protect\\astroncite{{An} et~al.}{1998}]{alp98}\n{An} P., {Lattimer} J., {Prakash} M. 1998, BAAS, 192, 8207\n\n\\bibitem[\\protect\\astroncite{Arnett \\& Bowers}{1977}]{ab77}\nArnett W.~D., Bowers R.~L. 1977, Astrophys.\\ J.\\ Suppl.\\ Ser., 33, 415\n\n\\bibitem[\\protect\\astroncite{Bednarz \\& Ostrowski}{1998}]{bo98}\nBednarz J., Ostrowski M. 1998, \\prl, 80(18)\n\n\\bibitem[\\protect\\astroncite{Bethe \\& Brown}{1995}]{bb95}\nBethe H.~A., Brown G.~E. 1995, \\apj, 445, L29\n\n\\bibitem[\\protect\\astroncite{{Blaizot}}{1980}]{blais80}\n{Blaizot} J.~P. 1980, Phys. Rep., 64, 171\n\n\\bibitem[\\protect\\astroncite{{Bonazzola} et~al.}{1997}]{bonazzola97}\n{Bonazzola} S., {Gourgoulhon} E., {Marck} J.-A. 1997, \\prd, 56, 7740\n\n\\bibitem[\\protect\\astroncite{{Bonazzola} et~al.}{1999a}]{bonazzola99a}\n{Bonazzola} S., {Gourgoulhon} E., {Marck} J.-A. 1999a,\n\\newblock in Proceedings of the 19th Texas Symposium on Relativistic\n Astrophysics and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.: J.\n Paul, T. Montmerle, and E. Aubourg (CEA Saclay).\n\n\\bibitem[\\protect\\astroncite{{Bonazzola} et~al.}{1999b}]{bonazzola99b}\n{Bonazzola} S., {Gourgoulhon} E., {Marck} J.-A. 1999b, \\prl, 82, 892\n\n\\bibitem[\\protect\\astroncite{{Brown} \\& {Bethe}}{1994}]{bb94}\n{Brown} G.~E., {Bethe} H.~A. 1994, \\apj, 423, 659\n\n\\bibitem[\\protect\\astroncite{{Collins} et~al.}{1998}]{chv98}\n{Collins} T. J.~B., {Helfer} H.~L., {Van Horn} H.~M. 1998, \\apjl, 508, L159\n\n\\bibitem[\\protect\\astroncite{{Dermer} \\& {Mitman}}{1999}]{dm99}\n{Dermer} C.~D., {Mitman} K.~E. 1999, \\apjl, 513, L5\n\n\\bibitem[\\protect\\astroncite{{Fenimore} et~al.}{1996}]{fmn96}\n{Fenimore} E.~E., {Madras} C.~D., {Nayakshin} S. 1996, \\apj, 473, 998\n\n\\bibitem[\\protect\\astroncite{{Flanagan}}{1999}]{flan99}\n{Flanagan} E.~E. 1999, \\prl, 82(7), 1354\n\n\\bibitem[\\protect\\astroncite{{Friedman} et~al.}{1986}]{fip86}\n{Friedman} J.~L., {Isper} J.~R., {Parger} L. 1986, \\apj, 304, 115\n\n\\bibitem[\\protect\\astroncite{{Galama} et~al.}{1997}]{1997IAUC.6655}\n{Galama} T.~J., {Groot} P.~J., {Van Paradijs} J., {Kouveliotou} C., {Centurion}\n M., {Telting} J.~H. et~al. 1997, \\iaucirc, 6655, 1\n\n%, {Smith} P., {Mackey} C., {Heise} J., {In 'T Zand} J.,\n% {Djorgovski} S.~G., {Metzger} M.~R., {Odewahn} S.~C., {Gal} R.~R., {Kulkarni}\n% S.~R., {Pahre} M.~A., {Frail} D.~A., {Costa} E., {Feroci} M., {Steidel}\n% C.~C., {Adelberger} K.~L. 1997, \\iaucirc, 6655, 1\n\n\\bibitem[\\protect\\astroncite{{Gotthelf} et~al.}{1999}]{gvd99}\n{Gotthelf} E.~V., {Vasisht} G., {Dotani} T. 1999, \\apj, 522, 115\n\n\\bibitem[\\protect\\astroncite{{Groot} et~al.}{1997}]{1997IAUC.6584}\n{Groot} P.~J., {Galama} T.~J., {Van Paradijs} J., {Strom} R., {Telting} J.,\n {Rutten} R. G.~M. et~al. 1997, \\iaucirc, 6584, 1\n\n%, {Pettini} M., {Tanvir} N., {Naber} R., {Kouveliotou} C.,\n% {In 'T Zand} J., {Heise} J., {Costa} E., {Feroci} M., {Piro} L., {Frontera}\n% F., {Zavattini} G., {Nicastro} L., {Palazzi} E. 1997, \\iaucirc, 6584, 1\n\n\\bibitem[\\protect\\astroncite{{Haberl} et~al.}{1997}]{h+97}\n{Haberl} F. et~al. 1997, \\aap, 326, 662\n\n\\bibitem[\\protect\\astroncite{{Janka} \\& {Ruffert}}{1996}]{jr96}\n{Janka} H.~T., {Ruffert} M. 1996, \\aap, 307, L33\n\n\\bibitem[\\protect\\astroncite{Klebesadel et~al.}{1973}]{kso73}\nKlebesadel R.~W., Strong I.~B., Olson R.~A. 1973, Astrophys.\\ J.\\ Lett., 182,\n L85\n\n\\bibitem[\\protect\\astroncite{{Kobayashi} et~al.}{1998}]{kps98}\n{Kobayashi} S., {Piran} T., {Sari} R. 1998,\n\\newblock in Huntsville Gamma-Ray Burst Symposium, p.~672\n\n\\bibitem[\\protect\\astroncite{{Kouveliotou} et~al.}{1998}]{k+98}\n{Kouveliotou} C. et~al. 1998, \\nat, 391, 235\n\n\\bibitem[\\protect\\astroncite{{Kulkarni} et~al.}{1998}]{kfw+98}\n{Kulkarni} S.~R., {Frail} D.~A., {Wieringa} M.~H., {Ekers} R.~D., {Sadler}\n E.~M., {Wark} R.~M., {Higdon} J.~L., {Phinney} E.~S., {Bloom} J.~S. 1998,\n \\nat, 395, 663\n\n\\bibitem[\\protect\\astroncite{{Lattimer}}{1998}]{lattimer98}\n{Lattimer} J.~M. 1998,\n\\newblock in N. {Shibazaki} et~al. (eds.), Neutron Stars and Pulsars Thirty\n Years after the Discovery, Universal Acadamy Press, Tokyo, Japan, p.~103\n\n\\bibitem[\\protect\\astroncite{{Liang} et~al.}{1997}]{lksc97}\n{Liang} E., {Kusunose} M., {Smith} I.~A., {Crider} A. 1997, \\apjl, 479, L35\n\n\\bibitem[\\protect\\astroncite{{Link} et~al.}{1999}]{lel99}\n{Link} B., {Epstein} R.~L., {Lattimer} J.~M. 1999, \\prl, 83, 3362\n\n\\bibitem[\\protect\\astroncite{{Marronetti} et~al.}{1999}]{mmw99}\n{Marronetti} P., {Mathews} G.~J., {Wilson} J.~R. 1999, \\prd, 60, 087301\n\n\\bibitem[\\protect\\astroncite{{Mathews} et~al.}{1998}]{mmw98a}\n{Mathews} G.~J., {Marronetti} P., {Wilson} J.~R. 1998, \\prd, 58, 043003\n\n\\bibitem[\\protect\\astroncite{{Mathews} \\& {Wilson}}{1997}]{mw97}\n{Mathews} G.~J., {Wilson} J.~R. 1997, \\apj, 482, 929\n\n\\bibitem[\\protect\\astroncite{{Mathews} \\& {Wilson}}{2000}]{mw99}\n{Mathews} G.~J., {Wilson} J.~R. 2000, \\prd, 61, 127304\n\n\\bibitem[\\protect\\astroncite{McAbee \\& Wilson}{1994}]{mw94b}\nMcAbee T.~L., Wilson J.~R. 1994, Nuclear Physics A, 576, 626\n\n\\bibitem[\\protect\\astroncite{Meegan et~al.}{1992}]{mfw+92}\nMeegan C.~A., Fishman G.~J., Wilson R.~B., Horack J.~M., Brock M.~N., Paciesas\n W.~S., Pendleton G.~N., Kouveliotou C. 1992, Nature, 355, 143\n\n\\bibitem[\\protect\\astroncite{{Merloni} et~al.}{1999}]{mvsb99}\n{Merloni} A., {Vietri} M., {Stella} L., {Bini} D. 1999, \\mnras, 304, 155\n\n\\bibitem[\\protect\\astroncite{{M{\\'e}sz{\\'a}ros} \\& {Rees}}{1993}]{mr93b}\n{M{\\'e}sz{\\'a}ros} P., {Rees} M.~J. 1993, \\apj, 405, 278\n\n\\bibitem[\\protect\\astroncite{{Miller} et~al.}{1998}]{mlp98}\n{Miller} M.~C., {Lamb} F.~K., {Psaltis} D. 1998, \\apj, 508, 791\n\n\\bibitem[\\protect\\astroncite{{Morsink} \\& {Stella}}{1999}]{ms99}\n{Morsink} S.~M., {Stella} L. 1999, \\apj, 513, 827\n\n\\bibitem[\\protect\\astroncite{{Page}}{1998}]{page98}\n{Page} D. 1998,\n\\newblock in N. {Shibazaki} et~al. (eds.), Neutron Stars and Pulsars Thirty\n Years after the Discovery, Universal Acadamy Press, Tokyo, Japan, p.~183\n\n\\bibitem[\\protect\\astroncite{{Piran}}{1999}]{piran98}\n{Piran} T. 1999, astro-ph/9907392\n\n\\bibitem[\\protect\\astroncite{{Rees} \\& {M{\\'e}sz{\\'a}ros}}{1992}]{rm92}\n{Rees} M.~J., {M{\\'e}sz{\\'a}ros} P. 1992, \\mnras, 258, 41P\n\n\\bibitem[\\protect\\astroncite{{Rees} \\& {M{\\'e}sz{\\'a}ros}}{1994}]{rm94}\n{Rees} M.~J., {M{\\'e}sz{\\'a}ros} P. 1994, \\apjl, 430, L93\n\n\\bibitem[\\protect\\astroncite{{Ruffert} \\& {Janka}}{1998}]{rj98}\n{Ruffert} M., {Janka} H.-T. 1998, \\aap, 338, 535\n\n\\bibitem[\\protect\\astroncite{{Ruffert} \\& {Janka}}{1999}]{ruffert99}\n{Ruffert} M., {Janka} H.-T. 1999, \\aap, 344, 573\n\n\\bibitem[\\protect\\astroncite{{Ruffini} et~al.}{1998}]{rswx98}\n{Ruffini} R., {Salmonson} J.~D., {Wilson} J.~R., {Xue} S.~S. 1998,\n\\newblock in Abstracts of the 19th Texas Symposium on Relativistic Astrophysics\n and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.: J. Paul, T.\n Montmerle, and E. Aubourg (CEA Saclay)., p.~E39\n\n\\bibitem[\\protect\\astroncite{{Ruffini} et~al.}{1999}]{rswx99}\n{Ruffini} R., {Salmonson} J.~D., {Wilson} J.~R., {Xue} S.~S. 1999, \\aap, 350, 334\n\n\\bibitem[\\protect\\astroncite{{Rybicki} \\& {Lightman}}{1975}]{rl75}\n{Rybicki} J.~B., {Lightman} A.~P. 1975,\n\\newblock Radiative Processes in Astrophysics,\n\\newblock USA: John Wiley \\& Sons, Inc.\n\n\\bibitem[\\protect\\astroncite{{Salmonson} \\& {Wilson}}{1999}]{sw99}\n{Salmonson} J.~D., {Wilson} J.~R. 1999, \\apj, 517, 859\n\n\\bibitem[\\protect\\astroncite{{Sari} et~al.}{1998}]{spn98}\n{Sari} R., {Piran} T., {Narayan} R. 1998, \\apjl, 497, L17\n\n\\bibitem[\\protect\\astroncite{{Schaab} \\& {Weigel}}{1999}]{schaabw99}\n{Schaab} C., {Weigel} M.~K. 1999, \\mnras, 308, 718\n\n\\bibitem[\\protect\\astroncite{{Shemi} \\& {Piran}}{1990}]{sm90}\n{Shemi} A., {Piran} T. 1990, \\apjl, 365, L55\n\n\\bibitem[\\protect\\astroncite{{Strohmayer} et~al.}{1996}]{szss+96}\n{Strohmayer} T.~E., {Zhang} W., {Swank} J.~H., {Smale} A., {Titarchuk} L.,\n {Day} C., {Lee} U. 1996, \\apjl, 469, L9\n\n\\bibitem[\\protect\\astroncite{{Thorsett} \\& {Chakrabarty}}{1999}]{tc99}\n{Thorsett} S.~E., {Chakrabarty} D. 1999, \\apj, 512, 288\n\n\\bibitem[\\protect\\astroncite{{Titarchuk} \\& {Osherovich}}{1999}]{to99}\n{Titarchuk} L., {Osherovich} V. 1999, \\apjl, 518, L95\n\n\\bibitem[\\protect\\astroncite{{Uryu} \\& {Eriguchi}}{1999}]{uryu99}\n{Uryu} K., {Eriguchi} Y. 1999, \\prd, 61, 024039\n\n\\bibitem[\\protect\\astroncite{{Van Der Klis} et~al.}{1996}]{vszj+96}\n{Van Der Klis} M., {Swank} J.~H., {Zhang} W., {Jahoda} K., {Morgan} E.~H.,\n {Lewin} W. H.~G., {Vaughan} B., {Van Paradijs} J. 1996, \\apjl, 469, L1\n\n\\bibitem[\\protect\\astroncite{{Van Der Klis} et~al.}{1997}]{vwhc97}\n{Van Der Klis} M., {Wijnands} R. A.~D., {Horne} K., {Chen} W. 1997, \\apjl, 481,\n L97\n\n\\bibitem[\\protect\\astroncite{{Vietri} \\& {Stella}}{1998}]{vs98}\n{Vietri} M., {Stella} L. 1998, \\apj, 503, 350\n\n\\bibitem[\\protect\\astroncite{{Walter} et~al.}{1996}]{wwn96}\n{Walter} F.~M., {Wolk} S.~J., {Neuhauser} R. 1996, \\nat, 379, 233\n\n\\bibitem[\\protect\\astroncite{{Wang} et~al.}{1999}]{wlr+99}\n{Wang} J. C.~L., {Link} B., {Van Riper} K., {Arnaud} K.~A., {Miralles} J.~A.\n 1999, \\aa, 345, 869\n\n\\bibitem[\\protect\\astroncite{{Wilson} \\& {Mathews}}{1995}]{wm95}\n{Wilson} J.~R., {Mathews} G.~J. 1995, \\prl, 75(23), 4161\n\n\\bibitem[\\protect\\astroncite{{Wilson} et~al.}{1996}]{wmm96}\n{Wilson} J.~R., {Mathews} G.~J., {Marronetti} P. 1996, \\prd, 54, 1317\n\n\\bibitem[\\protect\\astroncite{{Wilson} \\& {Mayle}}{1993}]{wm93}\n{Wilson} J.~R., {Mayle} R.~W. 1993, \\physrep, 227, 97\n\n\\bibitem[\\protect\\astroncite{{Yancopoulos} et~al.}{1994}]{yhh94}\n{Yancopoulos} S., {Hamilton} T.~T., {Helfand} D.~J. 1994, \\apj, 429, 832\n\n\\end{thebibliography}\n\n\\appendix\n\\section{Appendix: Neutron Star EOS}\n\n A key requirement of a gamma-ray burst paradigm based upon collapsing\nneutron stars in binaries is that the equation of state be relatively\nsoft so that significant compression and heating can occur before\ninspiral. Therefore, for completeness in this Appendix we review\narguments for and against a ``soft'' neutron star EOS.\n\nThe neutron star EOS must\nextend from normal iron nuclei on the surface to as much as 15 times\nnuclear matter density in the interior. At the same time, one must\nconsider that neutron stars in weak-interaction equilibrium are highly\nisospin asymmetric. They may also carry net strangeness. Therefore,\nonly pieces of the neutron-star equation of state, e.g. the nuclear\ncompressibility, are accessible in laboratory experiments. \nThe value for the nuclear\ncompressibility $K_s$ can be derived from the nuclear monopole\nresonance \\citep{blais80}. The present value ($K_s = $ 230 MeV) is\nconsistent with a modestly soft nuclear equation of state. \n\nNuclear heavy-ion collision data can also be used to shed some insight, particularly for\nthe heated neutron-star equation of state. For example,\n\\citet{mw94b} studied heavy ion\ncollisions of $^{139}$La on $^{139}$La as a means to constrain the\nsupernova EOS. The electron fraction for $^{139}_{57}$La ($Y_e = 0.41$)\noverlaps that of supernovae which range from $Y_e = 0.05$ to 0.50.\nThey showed that the pion contribution to the EOS could be constrained\nby the observed pion multiplicities from central collisions. The formation and\nevolution of pions was computed in the context of Landau-Migdal theory\nto model the effective energy and momenta of the pions. A key\naspect of hydrodynamic simulations of the heavy-ion data was the\ndetermination of the Landau parameter $g'$. Their determination of\nthe pion contribution to the equation of state implies a \nrelatively soft\nequation of state after pion condensation such that\na maximum neutron-star mass of $M \\le 1.64$\nM$_\\odot$ is inferred.\n\nThere have been dozens of nuclear equations of state introduced over\nthe years. Summaries of some of them can be found in\n\\citet{schaabw99} and \\citet{ab77}. As far as the maximum mass of a\nneutron star is concerned, most theoretical equations of state fall\ninto two groups, those which only describe the mean nuclear field even\nat high density and those which allow for various condensates,\ne.g. pions, kaons, hyperons, and even quark-gluon plasma. Table\n\\ref{tableos} summarizes the basic neutron star properties based upon\nmost available nuclear equations of state \\citep{lattimer98}.\n\nEquations of state which are based upon the mean nuclear field tend to\nbe ``stiff'' at high density. Therefore, they reach lower interior\ndensities for the same baryonic mass and tend to allow a higher\nmaximum neutron-star mass $m_{max} \\sim 1.8-2.2$ M$_\\odot$. Such\nequations of state also tend to become acausal at the high densities\nassociated with the maximum neutron-star mass. On the other hand, the\nrelativistic equations of state are generally causal at high density.\nThey also tend to be somewhat ``soft'', therefore allowing a higher\ncentral density for a given baryon mass and generally implying a\nmaximum neutron-star mass in the range $m_{max} \\sim 1.3-1.7 $\nM$_\\odot$. We note, however, that recent 3-body corrections to a\nrelativistic EOS \\citep{pandharipande99} tend to stiffen an otherwise\nsoft relativistic EOS.\n\nFor the most part, constraints on the neutron star equation of state\nmust ultimately come from observations of neutron stars themselves. Over the\nyears attempts have been made with limited success to constrain the\nequation of state based upon the maximum observed rotation frequency\n\\citep[e.g.][]{fip86} or the thermal response to neutron star glitches\n\\citep[e.g.][]{page98}. In recent years, however, new observational\nconstraints on the structure and properties of neutron stars are\nbecoming available \\citep{lattimer98}. Observations of quasi-periodic\noscillations (QPOs) \\citep{szss+96,vszj+96,vwhc97}, pulsar light\ncurves \\citep{yhh94,tc99}, and glitches \\citep{lel99}, studies of\nsoft-gamma repeaters \\citep{k+98,gvd99}; and even the identification\nof an isolated non-pulsing neutron stars \\citep{wwn96,h+97} have all\nled to the hope that significant constraints on the mass-radius relation and maximum\nmass of neutron stars may be soon coming.\n\n\\subsection{Pulsars}\n\nTwo possible constraints come from measured pulsar systems. The most\nprecisely measured property of any pulsar system is its spin\nfrequency. The frequencies of the fastest pulsars (PSR B1937+21 at\n641.9 Hz and B1957+20 at 622.1 Hz) already constrain the equation of\nstate under the assumption that these pulsars are near their maximum\nspin frequency \\citep{fip86}. In particular, the equation of\nstate cannot be too stiff, though maximum masses as large as 3\nM$_\\odot$ are still allowed.\n\nA much more stringent constraint may come from the numerous\ndeterminations of neutron-star masses in pulsar binaries. There are\nnow about 50 known pulsars in binary systems. Of these 50,\napproximately 15 of them have significantly constrained masses. These\nare summarized in Table \\ref{tablnsmass}. The measured masses are all\nconsistent with low neutron-star masses in the range $m \\approx 1.35\n\\pm 0.10$ M$_\\odot$ \\citep{tc99}. Even though these masses are low,\nthis does not necessarily mean that the maximum neutron-star\nmass is in this range. If one adopts these masses as approaching\nthe maximum neutron-star mass, then the softer equations of state are\npreferred. However, this narrow mass range may be the result of the\nmechanism of neutron-star formation in supernovae and not an\nindication of the maximum neutron-star mass.\n\n In a recent paper, \\citet{lel99} have proposed that glitches\nobserved in the Vela pulsar and six other pulsars may place some\nconstraint on the nuclear EOS. In particular, if the glitches\noriginate from the liquid of the inner crust, and if the mass of the\nVela pulsar is 1.35 consistent with Table 2, then the radius of the\nVela pulsar must be $R ^>_\\sim 8.9$ km. This result is consistent\nwith either a soft or stiff equations of state. A better theoretical\ndetermination of the pressure at the crust-core interface might lead\nto a more stringent constraint.\n\n\\subsection{QPO's}\nThe identification of kilohertz QPO's with the last stable orbit\naround a neutron star also could significantly constrain the\nneutron-star equation of state \\citep[e.g.][]{schaabw99}. For example,\ndemanding that the 1.2 khz QPO from source KS 1731-260 be the last\nstable orbit requires a neutron-star mass of 1.8 M$_\\odot$, On the\nother hand, other interpretations are possible for the origin of QPO's.\nFor example, they could be a harmonic of a lower frequency outer\norbit, or they might result from effects closer to the neutron-star\nsurface. Among proposals for the source of the QPO phenomenon are:\nboundary layer oscillations \\citep{chv98}; radial oscillations and\ndiffusive propagation in the transition region between the neutron\nstar and the last Keplerian orbit \\citep{to99}; Lense-Thirring\nprecession for fluid particles near the last stable orbit\n\\citep{mlp98,mvsb99,ms99}; and nonequitorial resonant oscillations of\nmagnetic fluid blobs \\citep{vs98}.\n\n\n\\subsection{Supernova constraints}\n\nThe lack of a radio pulsar in SN1987A, along with nucleosynthesis\nconstraints on the observed change of helium abundance with\nmetallicity has led to the suggestion \\citep{bb94,bb95} that the\nmaximum neutron-star mass must be $_\\sim^< 1.56$ M$_\\odot$. In this\npicture, the development of a kaon condensate tends to greatly soften\nthe EOS after $\\sim 12$ sec. Thus, even though neutrinos were\nemitted, the core subsequently collapses to a black hole.\n\nOne constraint comes from the\nneutrino signal itself observed to arise from supernova SN1987A.\nThe fact that the neutrinos arrived over an interval of at least\ntwelve seconds implies a significant cooling and neutrino diffusion\ntime from the core. This favors a soft equation of state in which\nthe core is more compact and at higher temperature in the supernova\nmodels. For example, the simulations of \\citet{wm93} require\na maximum neutron-star mass of $^<_\\sim 1.6$ M$_\\odot$.\n\n\\subsection{Isolated Neutron Star}\nA most promising constraint on the neutron-star EOS may come from the\ndetermination of the radius for the isolated nonpulsing neutron star\nRX J185635-3754, first detected by ROSAT \\citep{wwn96}. The inferred\n(redshifted) surface temperature from the X-ray emission is about 35\neV. Atmospheric models of this emission then imply \\citep{lattimer98,\nalp98, wlr+99} that for a distance between 31 and 41 pc, a radius\nbetween $5.75 < R/{\\rm km} < 11.4$ and a mass of $1.3 < M < 1.8$, is\nmost consistent with the observed emission. This is suggestive of a\nsoft equation of state. However, this constraint requires that the\ndistance be less than 41 kpc. On the other hand, \\citet{wlr+99} find\nthat the cooling properties of the soft X-ray source RX J0720.4-3125\nare most consistent with a moderately stiff or stiff EOS provided that\nthe age of this star is less than 10$^5$ yr. Proper motion studies\nwith HST are currently underway to determine a reliable distance to RX\nJ185635-3754. These studies will provide a key constraint on the\nnuclear equation of state.\n\n\n%\\tabletypesize{<size command>}\n%where \n%<size command> := \\small | \\footnotesize | \\scriptsize | \\tiny\n\n\n\\begin{deluxetable}{ccc|ccc}\n% \\tabletypesize{\\footnotesize}%\n\\tablecolumns{6} \n\\tablewidth{0pc} \n\n\\tablecaption{Table of the equation of state for a neutron star with\ncritical mass $M_c = 1.575 M_\\odot$. Values are baryonic\ndensity $\\rho$, specific energy $\\epsilon$ and $\\Gamma \\equiv 1 +\nP/\\rho \\epsilon$ where $P$ is the pressure. \\label{eostable}}\n\n\\tablehead{\\colhead{$\\rho$ gm/cm$^{-3}$} & \\colhead{$\\epsilon$ ergs/gm} & \\colhead{$\\Gamma$} & \\colhead{$\\rho$ gm/cm$^{-3}$} & \\colhead{$\\epsilon$ ergs/gm} & \\colhead{$\\Gamma$} }\n\\startdata\n1.00 $\\times 10^{9}$ & $1.11 \\times 10^{18}$ & 1.386 & $1.46 \\times 10^{13}$ & $1.94 \\times 10^{19}$ & 1.150 \\\\\n$1.46 \\times 10^{9}$ & $1.28 \\times 10^{18}$ & 1.380 & $2.15 \\times 10^{13}$ & $2.03 \\times 10^{19}$ & 1.108 \\\\\n$2.15 \\times 10^{9}$ & $1.47 \\times 10^{18}$ & 1.372 & $3.16 \\times 10^{13}$ & $2.09 \\times 10^{19}$ & 1.057 \\\\\n$3.16 \\times 10^{9}$ & $1.69 \\times 10^{18}$ & 1.367 & $4.64 \\times 10^{13}$ & $2.13 \\times 10^{19}$ & 1.052 \\\\\n$4.64 \\times 10^{9}$ & $1.94 \\times 10^{18}$ & 1.363 & $6.81 \\times 10^{13}$ & $2.17 \\times 10^{19}$ & 1.061 \\\\\n$6.81 \\times 10^{9}$ & $2.22 \\times 10^{18}$ & 1.358 & $1.00 \\times 10^{14}$ & $2.23 \\times 10^{19}$ & 1.093 \\\\\n$1.00 \\times 10^{10}$ & $2.54 \\times 10^{18}$ & 1.352 & $1.46 \\times 10^{14}$ & $2.36 \\times 10^{19}$ & 1.213 \\\\\n$1.46 \\times 10^{10}$ & $2.90 \\times 10^{18}$ & 1.346 & $2.15 \\times 10^{14}$ & $2.68 \\times 10^{19}$ & 1.468 \\\\\n$2.15 \\times 10^{10}$ & $3.30 \\times 10^{18}$ & 1.341 & $3.16 \\times 10^{14}$ & $3.39 \\times 10^{19}$ & 1.778 \\\\\n$3.16 \\times 10^{10}$ & $3.75 \\times 10^{18}$ & 1.336 & $4.64 \\times 10^{14}$ & $4.75 \\times 10^{19}$ & 1.992 \\\\\n$4.64 \\times 10^{10}$ & $4.26 \\times 10^{18}$ & 1.330 & $6.81 \\times 10^{14}$ & $7.09 \\times 10^{19}$ & 2.103 \\\\\n$6.81 \\times 10^{10}$ & $4.82 \\times 10^{18}$ & 1.322 & $1.00 \\times 10^{15}$ & $1.09 \\times 10^{20}$ & 2.16 \\\\\n$1.00 \\times 10^{11}$ & $5.44 \\times 10^{18}$ & 1.314 & $1.46 \\times 10^{15}$ & $1.69 \\times 10^{20}$ & 2.145 \\\\\n$1.46 \\times 10^{11}$ & $6.13 \\times 10^{18}$ & 1.307 & $2.15 \\times 10^{15}$ & $2.58 \\times 10^{20}$ & 2.063 \\\\\n$2.15 \\times 10^{11}$ & $6.88 \\times 10^{18}$ & 1.300 & $3.16 \\times 10^{15}$ & $3.87 \\times 10^{20}$ & 2.061 \\\\\n$3.16 \\times 10^{11}$ & $7.71 \\times 10^{18}$ & 1.294 & $4.64 \\times 10^{15}$ & $5.81 \\times 10^{20}$ & 2.059 \\\\\n$4.64 \\times 10^{11}$ & $8.62 \\times 10^{18}$ & 1.288 & $6.81 \\times 10^{15}$ & $8.67 \\times 10^{20}$ & 2.03 \\\\\n$6.81 \\times 10^{11}$ & $9.61 \\times 10^{18}$ & 1.280 & $1.00 \\times 10^{16}$ & $1.28 \\times 10^{21}$ & 2.015 \\\\\n$1.00 \\times 10^{12}$ & $1.06 \\times 10^{19}$ & 1.270 & $1.46 \\times 10^{16}$ & $1.88 \\times 10^{21}$ & 2.007 \\\\\n$1.46 \\times 10^{12}$ & $1.17 \\times 10^{19}$ & 1.261 & $2.15 \\times 10^{16}$ & $2.76 \\times 10^{21}$ & 2.003 \\\\\n$2.15 \\times 10^{12}$ & $1.29 \\times 10^{19}$ & 1.250 & $3.16 \\times 10^{16}$ & $4.05 \\times 10^{21}$ & 2.001 \\\\\n$3.16 \\times 10^{12}$ & $1.41 \\times 10^{19}$ & 1.236 & $4.64 \\times 10^{16}$ & $5.94 \\times 10^{21}$ & 2.001 \\\\ \n$4.64 \\times 10^{12}$ & $1.54 \\times 10^{19}$ & 1.224 & $6.81 \\times 10^{16}$ & $8.71 \\times 10^{21}$ & 2 \\\\\n$6.81 \\times 10^{12}$ & $1.67 \\times 10^{19}$ & 1.216 & $1.00 \\times 10^{17}$ & $1.27 \\times 10^{22}$ & 2 \\\\\n$1.00 \\times 10^{13}$ & $1.81 \\times 10^{19}$ & 1.211 \\\\\n\\enddata\n\\end{deluxetable}\n \n\n\\begin{deluxetable}{ccc}\n\\tablecolumns{3} \n\\tablewidth{0pc} \n\\tablecaption{Central density and released gravitational energy \nas a function of the binary angular momentum $J$ in geometrized units.\nThis calculation \\citep{mw99} is for\na neutron star with M$_B = 1.548$ M$_\\odot$, M$_G = 1.39$ M$_\\odot$,\n and and EOS for\nwhich M$_c = 1.575$ M$_\\odot$.}\n%\\begin{tabular}{ccc}\n%\\tableline \n%\\tableline \\\\\n\\tablehead{\\colhead{J ($10^{11}$ cm$^{2}$)} & \\colhead{$\\rho$ ($10^{15}$ g cm$^{-3}$)} & \\colhead{$E$ ($10^{52}$ erg)}} \n%\\tableline \\\\\n\\startdata\n1.65 & 1.48 & 4.3\\\\\n1.80 & 1.46 & 2.4\\\\\n2.0 & 1.45 & 1.5\\\\\n2.2 & 1.43 & 1.0\\\\\n2.4 & 1.40 & 0.7\\\\\n2.6 & 1.38 & 0.6\\\\\n$\\infty$ & 1.34 & 0\\\\\n\\enddata\n%\\tableline \\\\\n\\label{tableheat}\n%\\end{tabular}\n\\end{deluxetable}\n\n\\begin{deluxetable}{cccc}\n\\tablecolumns{4} \n\\tablewidth{0pc} \n\\tablecaption{Final Lorentz factor of the baryon wind for a range\nof initial total energies and entropies per\nbaryon. \\label{gammatable}}\n\n\\tablehead{\n\\colhead{} &\\multicolumn{3}{c}{Entropy per Baryon} \\\\\\cline{2-4}\n\\colhead{Energy (ergs)} & \\colhead{$10^5$} & \\colhead{$10^6$} & \\colhead{$10^7$}}\n\\startdata\n$10^{51}$ &175 &1750 & $1.6 \\times 10^4$ \\\\\n$10^{52}$ &350 &3100 & $2.9 \\times 10^4$ \\\\\n$10^{53}$ &525 &5500 & $5.3 \\times 10^4$ \\\\\n\\enddata\n\\end{deluxetable}\n\n\\begin{deluxetable}{cccc}\n\\tablecolumns{4} \n\\tablewidth{0pc} \n\\tablecaption{ The $t_{90}$ duration, in seconds, of external shock\nGRBs corresponding to the fireballs outlined in Table\n\\ref{gammatable}. This $t_{90}$ is calculated energy emitted in photons\ngreater than 10 keV. \\label{t90table}}\n\n\\tablehead{\n\\colhead{} &\\multicolumn{3}{c}{Entropy per Baryon} \\\\\\cline{2-4}\n\\colhead{Energy (ergs)} & \\colhead{$10^5$} & \\colhead{$10^6$} & \\colhead{$10^7$}}\n\\startdata\n$10^{51}$ &40.3 &0.7 & $3.7 \\times 10^{-3}$ \\\\\n$10^{52}$ &21.6 &7.2 & $1.6 \\times 10^{-3}$ \\\\\n$10^{53}$ &23.8 &0.17 & $1.8 \\times 10^{-3}$ \\\\\n\\enddata\n\\end{deluxetable}\n\n\\begin{center}\n\\begin{table}\n\\caption{Neutron star properties from various equations of state}\n\\begin{tabular}{lccc}\n\\tableline \n\\tableline \\\\\nEquation of State & Composition & Maximum Mass (M$_\\odot$)& R (km)\\\\\n\\tableline \\\\\nMean Nuclear Field& $p,n,e^-, \\mu^-$ & $\\approx 2.0 \\pm 0.20 $ & $ \\approx 13 \\pm 3$\\\\\n\n\\tableline \\\\\nExotic Particles/ & $p,n,e^-, \\mu^-, \\Lambda, \\Sigma^{\\pm,0},\n\\Xi^{0,-}$, & $\\approx 1.5 \\pm 0.2 $ & $\\approx 9 \\pm 1$ \\\\\nCondensates & $ \\Delta^{\\pm,0.++}, K^{\\pm,0}, \\pi^{\\pm,0}$, quarks, etc. \\\\\n\n\\tableline \\\\\n\\end{tabular}\n\\label{tableos}\n\\end{table}\n\\end{center}\n\n\n\\begin{table}\n\\caption{Summary of masses of observed pulsars in binaries.} \n\\begin{tabular}{lccc}\n\\tableline \n\\tableline \\\\\nPulsar & Mass (M$_\\odot$)& &\\\\\n\\tableline \\\\\n{\\it Double Neutron Star Systems} \\\\\n\\tableline \\\\\nJ1518+4904 & 1.56 $^{0.13}_{0.44}$ \\\\\nJ1518+4904 & 1.05 $^{0.45}_{0.11}$ \\\\\nB1534+12 & 1.339 $\\pm 0.0003$ \\\\\nB1534+12 & 1.339 $\\pm 0.0003$ \\\\\nB1913+16 & 1.4411 $\\pm 0.00035 $ \\\\\nB1913+16 & 1.3874 $\\pm 0.00035$ \\\\\nB2127+11C & 1.349 $\\pm 0.040$ \\\\\nB2127+11C & 1.363 $\\pm 0.040$ \\\\\nB2303+46 & 1.30 $^{+0.13}_{-0.46}$ \\\\\nB2303+46 & 1.34 $^{+0.47}_{-0.13}$ \\\\\n\\tableline \\\\\n{\\it Neutron Star/White-Dwarf Systems} \\\\\n\\tableline \\\\\nJ1012+5307 & 1.7 $\\pm 0.5$ \\\\\nJ1713+0747 & 1.45 $\\pm 0.31$ \\\\\nJ1713+0747 & 1.34 $\\pm 0.20$ \\\\\nB1802-07 & 1.26 $^{+0.08}_{-0.17}$ \\\\\nB1855+09 & 1.41 $\\pm 0.10$ \\\\\n\\tableline \\\\\n{\\it Neutron Star/Main-Sequence Systems} \\\\\n\\tableline \\\\\nJ0045-7319 & 1.58 $\\pm 0.34$ \\\\\n\\tableline \\\\\n\\end{tabular}\n\\label{tablnsmass}\n\\end{table}\n\n%\\end{multicols}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002312.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\astroncite{{Akmal} et~al.}{1999}]{pandharipande99}\n{Akmal} A., {Pandharipande} V.~R., {Ravenhall} D.~G. 1999, \\prc, 58, 1804\n\n\\bibitem[\\protect\\astroncite{{An} et~al.}{1998}]{alp98}\n{An} P., {Lattimer} J., {Prakash} M. 1998, BAAS, 192, 8207\n\n\\bibitem[\\protect\\astroncite{Arnett \\& Bowers}{1977}]{ab77}\nArnett W.~D., Bowers R.~L. 1977, Astrophys.\\ J.\\ Suppl.\\ Ser., 33, 415\n\n\\bibitem[\\protect\\astroncite{Bednarz \\& Ostrowski}{1998}]{bo98}\nBednarz J., Ostrowski M. 1998, \\prl, 80(18)\n\n\\bibitem[\\protect\\astroncite{Bethe \\& Brown}{1995}]{bb95}\nBethe H.~A., Brown G.~E. 1995, \\apj, 445, L29\n\n\\bibitem[\\protect\\astroncite{{Blaizot}}{1980}]{blais80}\n{Blaizot} J.~P. 1980, Phys. Rep., 64, 171\n\n\\bibitem[\\protect\\astroncite{{Bonazzola} et~al.}{1997}]{bonazzola97}\n{Bonazzola} S., {Gourgoulhon} E., {Marck} J.-A. 1997, \\prd, 56, 7740\n\n\\bibitem[\\protect\\astroncite{{Bonazzola} et~al.}{1999a}]{bonazzola99a}\n{Bonazzola} S., {Gourgoulhon} E., {Marck} J.-A. 1999a,\n\\newblock in Proceedings of the 19th Texas Symposium on Relativistic\n Astrophysics and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.: J.\n Paul, T. Montmerle, and E. Aubourg (CEA Saclay).\n\n\\bibitem[\\protect\\astroncite{{Bonazzola} et~al.}{1999b}]{bonazzola99b}\n{Bonazzola} S., {Gourgoulhon} E., {Marck} J.-A. 1999b, \\prl, 82, 892\n\n\\bibitem[\\protect\\astroncite{{Brown} \\& {Bethe}}{1994}]{bb94}\n{Brown} G.~E., {Bethe} H.~A. 1994, \\apj, 423, 659\n\n\\bibitem[\\protect\\astroncite{{Collins} et~al.}{1998}]{chv98}\n{Collins} T. J.~B., {Helfer} H.~L., {Van Horn} H.~M. 1998, \\apjl, 508, L159\n\n\\bibitem[\\protect\\astroncite{{Dermer} \\& {Mitman}}{1999}]{dm99}\n{Dermer} C.~D., {Mitman} K.~E. 1999, \\apjl, 513, L5\n\n\\bibitem[\\protect\\astroncite{{Fenimore} et~al.}{1996}]{fmn96}\n{Fenimore} E.~E., {Madras} C.~D., {Nayakshin} S. 1996, \\apj, 473, 998\n\n\\bibitem[\\protect\\astroncite{{Flanagan}}{1999}]{flan99}\n{Flanagan} E.~E. 1999, \\prl, 82(7), 1354\n\n\\bibitem[\\protect\\astroncite{{Friedman} et~al.}{1986}]{fip86}\n{Friedman} J.~L., {Isper} J.~R., {Parger} L. 1986, \\apj, 304, 115\n\n\\bibitem[\\protect\\astroncite{{Galama} et~al.}{1997}]{1997IAUC.6655}\n{Galama} T.~J., {Groot} P.~J., {Van Paradijs} J., {Kouveliotou} C., {Centurion}\n M., {Telting} J.~H. et~al. 1997, \\iaucirc, 6655, 1\n\n%, {Smith} P., {Mackey} C., {Heise} J., {In 'T Zand} J.,\n% {Djorgovski} S.~G., {Metzger} M.~R., {Odewahn} S.~C., {Gal} R.~R., {Kulkarni}\n% S.~R., {Pahre} M.~A., {Frail} D.~A., {Costa} E., {Feroci} M., {Steidel}\n% C.~C., {Adelberger} K.~L. 1997, \\iaucirc, 6655, 1\n\n\\bibitem[\\protect\\astroncite{{Gotthelf} et~al.}{1999}]{gvd99}\n{Gotthelf} E.~V., {Vasisht} G., {Dotani} T. 1999, \\apj, 522, 115\n\n\\bibitem[\\protect\\astroncite{{Groot} et~al.}{1997}]{1997IAUC.6584}\n{Groot} P.~J., {Galama} T.~J., {Van Paradijs} J., {Strom} R., {Telting} J.,\n {Rutten} R. G.~M. et~al. 1997, \\iaucirc, 6584, 1\n\n%, {Pettini} M., {Tanvir} N., {Naber} R., {Kouveliotou} C.,\n% {In 'T Zand} J., {Heise} J., {Costa} E., {Feroci} M., {Piro} L., {Frontera}\n% F., {Zavattini} G., {Nicastro} L., {Palazzi} E. 1997, \\iaucirc, 6584, 1\n\n\\bibitem[\\protect\\astroncite{{Haberl} et~al.}{1997}]{h+97}\n{Haberl} F. et~al. 1997, \\aap, 326, 662\n\n\\bibitem[\\protect\\astroncite{{Janka} \\& {Ruffert}}{1996}]{jr96}\n{Janka} H.~T., {Ruffert} M. 1996, \\aap, 307, L33\n\n\\bibitem[\\protect\\astroncite{Klebesadel et~al.}{1973}]{kso73}\nKlebesadel R.~W., Strong I.~B., Olson R.~A. 1973, Astrophys.\\ J.\\ Lett., 182,\n L85\n\n\\bibitem[\\protect\\astroncite{{Kobayashi} et~al.}{1998}]{kps98}\n{Kobayashi} S., {Piran} T., {Sari} R. 1998,\n\\newblock in Huntsville Gamma-Ray Burst Symposium, p.~672\n\n\\bibitem[\\protect\\astroncite{{Kouveliotou} et~al.}{1998}]{k+98}\n{Kouveliotou} C. et~al. 1998, \\nat, 391, 235\n\n\\bibitem[\\protect\\astroncite{{Kulkarni} et~al.}{1998}]{kfw+98}\n{Kulkarni} S.~R., {Frail} D.~A., {Wieringa} M.~H., {Ekers} R.~D., {Sadler}\n E.~M., {Wark} R.~M., {Higdon} J.~L., {Phinney} E.~S., {Bloom} J.~S. 1998,\n \\nat, 395, 663\n\n\\bibitem[\\protect\\astroncite{{Lattimer}}{1998}]{lattimer98}\n{Lattimer} J.~M. 1998,\n\\newblock in N. {Shibazaki} et~al. (eds.), Neutron Stars and Pulsars Thirty\n Years after the Discovery, Universal Acadamy Press, Tokyo, Japan, p.~103\n\n\\bibitem[\\protect\\astroncite{{Liang} et~al.}{1997}]{lksc97}\n{Liang} E., {Kusunose} M., {Smith} I.~A., {Crider} A. 1997, \\apjl, 479, L35\n\n\\bibitem[\\protect\\astroncite{{Link} et~al.}{1999}]{lel99}\n{Link} B., {Epstein} R.~L., {Lattimer} J.~M. 1999, \\prl, 83, 3362\n\n\\bibitem[\\protect\\astroncite{{Marronetti} et~al.}{1999}]{mmw99}\n{Marronetti} P., {Mathews} G.~J., {Wilson} J.~R. 1999, \\prd, 60, 087301\n\n\\bibitem[\\protect\\astroncite{{Mathews} et~al.}{1998}]{mmw98a}\n{Mathews} G.~J., {Marronetti} P., {Wilson} J.~R. 1998, \\prd, 58, 043003\n\n\\bibitem[\\protect\\astroncite{{Mathews} \\& {Wilson}}{1997}]{mw97}\n{Mathews} G.~J., {Wilson} J.~R. 1997, \\apj, 482, 929\n\n\\bibitem[\\protect\\astroncite{{Mathews} \\& {Wilson}}{2000}]{mw99}\n{Mathews} G.~J., {Wilson} J.~R. 2000, \\prd, 61, 127304\n\n\\bibitem[\\protect\\astroncite{McAbee \\& Wilson}{1994}]{mw94b}\nMcAbee T.~L., Wilson J.~R. 1994, Nuclear Physics A, 576, 626\n\n\\bibitem[\\protect\\astroncite{Meegan et~al.}{1992}]{mfw+92}\nMeegan C.~A., Fishman G.~J., Wilson R.~B., Horack J.~M., Brock M.~N., Paciesas\n W.~S., Pendleton G.~N., Kouveliotou C. 1992, Nature, 355, 143\n\n\\bibitem[\\protect\\astroncite{{Merloni} et~al.}{1999}]{mvsb99}\n{Merloni} A., {Vietri} M., {Stella} L., {Bini} D. 1999, \\mnras, 304, 155\n\n\\bibitem[\\protect\\astroncite{{M{\\'e}sz{\\'a}ros} \\& {Rees}}{1993}]{mr93b}\n{M{\\'e}sz{\\'a}ros} P., {Rees} M.~J. 1993, \\apj, 405, 278\n\n\\bibitem[\\protect\\astroncite{{Miller} et~al.}{1998}]{mlp98}\n{Miller} M.~C., {Lamb} F.~K., {Psaltis} D. 1998, \\apj, 508, 791\n\n\\bibitem[\\protect\\astroncite{{Morsink} \\& {Stella}}{1999}]{ms99}\n{Morsink} S.~M., {Stella} L. 1999, \\apj, 513, 827\n\n\\bibitem[\\protect\\astroncite{{Page}}{1998}]{page98}\n{Page} D. 1998,\n\\newblock in N. {Shibazaki} et~al. (eds.), Neutron Stars and Pulsars Thirty\n Years after the Discovery, Universal Acadamy Press, Tokyo, Japan, p.~183\n\n\\bibitem[\\protect\\astroncite{{Piran}}{1999}]{piran98}\n{Piran} T. 1999, astro-ph/9907392\n\n\\bibitem[\\protect\\astroncite{{Rees} \\& {M{\\'e}sz{\\'a}ros}}{1992}]{rm92}\n{Rees} M.~J., {M{\\'e}sz{\\'a}ros} P. 1992, \\mnras, 258, 41P\n\n\\bibitem[\\protect\\astroncite{{Rees} \\& {M{\\'e}sz{\\'a}ros}}{1994}]{rm94}\n{Rees} M.~J., {M{\\'e}sz{\\'a}ros} P. 1994, \\apjl, 430, L93\n\n\\bibitem[\\protect\\astroncite{{Ruffert} \\& {Janka}}{1998}]{rj98}\n{Ruffert} M., {Janka} H.-T. 1998, \\aap, 338, 535\n\n\\bibitem[\\protect\\astroncite{{Ruffert} \\& {Janka}}{1999}]{ruffert99}\n{Ruffert} M., {Janka} H.-T. 1999, \\aap, 344, 573\n\n\\bibitem[\\protect\\astroncite{{Ruffini} et~al.}{1998}]{rswx98}\n{Ruffini} R., {Salmonson} J.~D., {Wilson} J.~R., {Xue} S.~S. 1998,\n\\newblock in Abstracts of the 19th Texas Symposium on Relativistic Astrophysics\n and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.: J. Paul, T.\n Montmerle, and E. Aubourg (CEA Saclay)., p.~E39\n\n\\bibitem[\\protect\\astroncite{{Ruffini} et~al.}{1999}]{rswx99}\n{Ruffini} R., {Salmonson} J.~D., {Wilson} J.~R., {Xue} S.~S. 1999, \\aap, 350, 334\n\n\\bibitem[\\protect\\astroncite{{Rybicki} \\& {Lightman}}{1975}]{rl75}\n{Rybicki} J.~B., {Lightman} A.~P. 1975,\n\\newblock Radiative Processes in Astrophysics,\n\\newblock USA: John Wiley \\& Sons, Inc.\n\n\\bibitem[\\protect\\astroncite{{Salmonson} \\& {Wilson}}{1999}]{sw99}\n{Salmonson} J.~D., {Wilson} J.~R. 1999, \\apj, 517, 859\n\n\\bibitem[\\protect\\astroncite{{Sari} et~al.}{1998}]{spn98}\n{Sari} R., {Piran} T., {Narayan} R. 1998, \\apjl, 497, L17\n\n\\bibitem[\\protect\\astroncite{{Schaab} \\& {Weigel}}{1999}]{schaabw99}\n{Schaab} C., {Weigel} M.~K. 1999, \\mnras, 308, 718\n\n\\bibitem[\\protect\\astroncite{{Shemi} \\& {Piran}}{1990}]{sm90}\n{Shemi} A., {Piran} T. 1990, \\apjl, 365, L55\n\n\\bibitem[\\protect\\astroncite{{Strohmayer} et~al.}{1996}]{szss+96}\n{Strohmayer} T.~E., {Zhang} W., {Swank} J.~H., {Smale} A., {Titarchuk} L.,\n {Day} C., {Lee} U. 1996, \\apjl, 469, L9\n\n\\bibitem[\\protect\\astroncite{{Thorsett} \\& {Chakrabarty}}{1999}]{tc99}\n{Thorsett} S.~E., {Chakrabarty} D. 1999, \\apj, 512, 288\n\n\\bibitem[\\protect\\astroncite{{Titarchuk} \\& {Osherovich}}{1999}]{to99}\n{Titarchuk} L., {Osherovich} V. 1999, \\apjl, 518, L95\n\n\\bibitem[\\protect\\astroncite{{Uryu} \\& {Eriguchi}}{1999}]{uryu99}\n{Uryu} K., {Eriguchi} Y. 1999, \\prd, 61, 024039\n\n\\bibitem[\\protect\\astroncite{{Van Der Klis} et~al.}{1996}]{vszj+96}\n{Van Der Klis} M., {Swank} J.~H., {Zhang} W., {Jahoda} K., {Morgan} E.~H.,\n {Lewin} W. H.~G., {Vaughan} B., {Van Paradijs} J. 1996, \\apjl, 469, L1\n\n\\bibitem[\\protect\\astroncite{{Van Der Klis} et~al.}{1997}]{vwhc97}\n{Van Der Klis} M., {Wijnands} R. A.~D., {Horne} K., {Chen} W. 1997, \\apjl, 481,\n L97\n\n\\bibitem[\\protect\\astroncite{{Vietri} \\& {Stella}}{1998}]{vs98}\n{Vietri} M., {Stella} L. 1998, \\apj, 503, 350\n\n\\bibitem[\\protect\\astroncite{{Walter} et~al.}{1996}]{wwn96}\n{Walter} F.~M., {Wolk} S.~J., {Neuhauser} R. 1996, \\nat, 379, 233\n\n\\bibitem[\\protect\\astroncite{{Wang} et~al.}{1999}]{wlr+99}\n{Wang} J. C.~L., {Link} B., {Van Riper} K., {Arnaud} K.~A., {Miralles} J.~A.\n 1999, \\aa, 345, 869\n\n\\bibitem[\\protect\\astroncite{{Wilson} \\& {Mathews}}{1995}]{wm95}\n{Wilson} J.~R., {Mathews} G.~J. 1995, \\prl, 75(23), 4161\n\n\\bibitem[\\protect\\astroncite{{Wilson} et~al.}{1996}]{wmm96}\n{Wilson} J.~R., {Mathews} G.~J., {Marronetti} P. 1996, \\prd, 54, 1317\n\n\\bibitem[\\protect\\astroncite{{Wilson} \\& {Mayle}}{1993}]{wm93}\n{Wilson} J.~R., {Mayle} R.~W. 1993, \\physrep, 227, 97\n\n\\bibitem[\\protect\\astroncite{{Yancopoulos} et~al.}{1994}]{yhh94}\n{Yancopoulos} S., {Hamilton} T.~T., {Helfand} D.~J. 1994, \\apj, 429, 832\n\n\\end{thebibliography}"
}
] |
astro-ph0002313
|
Resolving the extragalactic hard X-ray background
|
[
{
"author": "R. F. Mushotzky$^{\\ast}$"
},
{
"author": "L. L. Cowie$^{\\dag}$"
},
{
"author": "A. J. Barger$^{\\dag}$"
},
{
"author": "K. A. Arnaud$^{\\ast\\ddag}$"
}
] |
[
{
"name": "chandra.tex",
"string": "%CHANDRA.TEX -- AASTeX 4.0 \"Resolving the extragalactic X-ray\n%background: source counts from Chandra observations of the SSA13 field''\n% by R. F. Mushotzky, L. L. Cowie, A. J. Barger, & K. A. Arnaud\n% Contact: Lennox L. Cowie, Institute for Astronomy, 2680 Woodlawn Dr.,\n% Honolulu, HI 96822; email:cowie@ifa.hawaii.edu; phone: (808)956-8134;\n% FAX: (808)946-3467\n%\n% Files: chandra.tex [Manuscript, with 1 table]\n% chandra_fig1a.eps Number counts in 2-10 keV band\n% chandra_fig1b.eps Number counts in 0.5-2 keV band\n% chandra_fig2.eps Thumbnail Keck I images of hard-selected sources\n% chandra_fig3.eps I mag vs. X-ray photon indices\n% chandra_fig4.eps Sample LRIS spectra of X-ray detected sources\n\n%\\documentstyle[12pt,aj_pt4,overcite,psfig,flushrt,times]{article}\n\\documentstyle[12pt,aaspp4,lscape,overcite,psfig,flushrt]{article}\n\n% version for mach: changed epsfig to psfig throughout document, and\n% apjfonts to times in documentstyle declaration (to avoid loading the\n% add'l needed fonts to mach's font distribution). One weird additional\n% fix: removed all \"\\small\" commands at start of \\caption{ }; this version\n% of TeX runs out of space when the command is given to use small fonts\n% in the caption\n\n% Integrated text, table, and figures 31-Dec-1999. To have table notes\n% fit into page and adopt the aj_pt4 font + spacing, use aj_pt4 in the\n% documentstyle option list, but reset \\hoffset, \\textwidth, \\parskip,\n% and \\baselinestretch to match aaspp4 values.\n% Note that the LaTeX2e version of the new aastex5.0 style macros force\n% use of \\bibitem fields which disable the overcite.sty operation.\n\n\\hoffset=0.0in\n\\setlength{\\textwidth}{6.5in}\n\\setlength{\\textheight}{8.4in}\n\\renewcommand\\baselinestretch{1.1}\n\\parskip=1.5ex\n\n% aaspp4,aj_pt4, and flushrt are standard style files for aastex4.0\n% epsfig and lscape are standard style files under the teTeX\n% distribution of LaTeX{2e}; epsfig supercedes\n% the old psfig.sty file\n% overcite is Don Arseneau's supported style macro\n% which works under both LaTeX2e and 2.09\n\n% Added the following redefinition of \\thebibliography to get numbered entries\n% 31-Dec-1993 EMH\n\\renewcommand{\\thebibliography}[1]{\\clearpage\\subsection*{REFERENCES}\\list\n {\\arabic{enumi}.}{\\settowidth\\labelwidth{[#1]}\\leftmargin\\labelwidth\n \\advance\\leftmargin\\labelsep\n \\usecounter{enumi}}\n \\def\\newblock{\\hskip .11em plus .33em minus .07em}\n \\sloppy\\clubpenalty4000\\widowpenalty4000\n \\sfcode`\\.=1000\\relax}\n \\let\\endthebibliography=\\endlist\n\\def\\aanat#1{{\\it Astron. Astrophys.\\/} {\\bf #1}}\n%\\def\\aasupnat#1{{\\it Astron. Astrophys. Suppl. Ser.\\/} {\\bf #1}}\n\\def\\ajnat#1{{\\it Astron. J.\\/} {\\bf #1}}\n\\def\\apjnat#1{{\\it Astrophys. J.\\/} {\\bf #1}}\n\\def\\apjsupnat#1{{\\it Astrophys. J. Suppl. Ser.\\/} {\\bf #1}}\n\\def\\araanat#1{{\\it Annu. Rev. Astron. Astrophys.\\/} {\\bf #1}}\n\\def\\mnnat#1{{\\it Mon. Not. R. Astron. Soc.\\/} {\\bf #1}}\n%\\def\\paspnat#1{{\\it Publ. Astron. Soc. Pacif.\\/} {\\bf #1}}\n\\def\\natnat#1{{\\it Nature\\/} {\\bf #1}}\n\\def\\pasjnat#1{{\\it Publ. Astron. Soc. Jpn\\/} {\\bf #1}}\n\\def\\prlnat#1{{\\it Phys. Rev. Lett.\\/} {\\bf #1}}\n%\\def\\annat#1{{\\it Astron. Nach.\\/} {\\bf #1}}\n\n\n\\begin{document}\n\n\\title{Resolving the extragalactic hard X-ray background\n}\n\n\\author{R. F. Mushotzky$^{\\ast}$, L. L. Cowie$^{\\dag}$,\nA. J. Barger$^{\\dag}$, K. A. Arnaud$^{\\ast\\ddag}$}\n\n\\leftline{$^{\\ast}$\\ NASA Goddard Space Flight Center, Code 662,\nGreenbelt, MD 20771}\n\n\\leftline{$^{\\dag}$\\ Institute for Astronomy, University of Hawaii, 2680\nWoodlawn Drive, Honolulu, HI 96822}\n\n\\leftline{$^{\\ddag}$\\ Astronomy Department, University of Maryland,\nCollege Park, MD 20742}\n\n\\vskip 0.2cm\n\n\\centerline{To be published in {\\it Nature}}\n%\\centerline{B05651 \\ LS/lf}\n\n%\\vfill\\eject\n\n{\\bf\nThe origin of the hard (${\\bf 2-10}$\\ keV) X-ray background has \nremained mysterious for over 35 years. Most of the soft\n(${\\bf 0.5-2}$\\ keV) X-ray background has been resolved into \ndiscrete sources, which are primarily quasars; however, these \nsources do not have the flat spectral shape required to \nmatch the X-ray background spectrum. Here we report the results \nof an X-ray survey 30 times more sensitive than previous studies \nin the hard band and four times more sensitive in the soft\nband. The sources detected in our survey account for at least \n75 per cent of the hard X-ray background. The mean X-ray \nspectrum of these sources is in good agreement with that of the \nbackground. The X-ray emission from the majority of the detected \nsources is unambiguously associated with either the nuclei\nof otherwise normal bright galaxies or optically faint sources,\nwhich could either be active nuclei of dust enshrouded \ngalaxies or the first quasars at very high redshifts.\n}\n\n\nFor some time after the discovery of the\ncosmic X-Ray background (XRB)\\cite{giacconi}, there was\nconsiderable controversy over whether the background\narose from a superposition of discrete sources or from\nthermal bremsstrahlung emission from a hot intergalactic gas.\nWe now know that the bulk of the XRB cannot originate in\na uniform hot intergalactic medium\nsince a strong Compton distortion on the cosmic microwave\nbackground spectrum\nwas not observed by the FIRAS instrument on {\\it COBE}\n\\cite{mather2,wright}.\n\nAt soft X-ray energies ($0.5-2$\\ keV) the XRB has been extensively\nstudied with the {\\it ROSAT} satellite. The deepest {\\it ROSAT}\nsource counts reach $\\sim 1000$\\ per square degree at a limiting\nflux of $10^{-15}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$, and at this level\n$70-80$ per cent of the XRB is resolved into discrete sources\n\\cite{hasinger}. The great majority of the optical identifications\nof a complete sample of 50 {\\it ROSAT} sources, at\na limiting flux of $5\\times 10^{-15}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$,\nare unobscured active galactic nuclei (AGN) \\cite{schmidt1}.\nHowever, because the objects detected in the soft band do not have\nthe spectrum of the XRB, a new population of absorbed or\nflat spectrum objects are needed to make up the background at\nhigher energies. Detailed models developed\nto resolve this ``spectral paradox'' assumed that\nmost of the flux in the XRB is produced by active galaxies that \nare obscured by dust. When deep imaging sky surveys with the \n{\\it ASCA}\\cite{ueda,ueda1,ueda2,cagnoni} and {\\it BeppoSAX}\\cite{fiore} \nsatellites became possible in the hard ($>2$\\ keV) X-ray band,\n$\\sim 30$\\ per cent of the hard XRB was resolved, but only \nindirect identifications of the optical counterparts could be made.\n\nThe {\\it Chandra} satellite\\cite{weisskopf}, \nwith its great sensitivity over a wide energy range,\nexcellent image quality, superb positional accuracy,\nand reasonable field-of-view, can directly image the sources that\nmake up the hard XRB. We have therefore carried out a deep imaging \nsurvey of the Hawaii Deep Survey Field SSA13 with the ACIS-S \ninstrument on {\\it Chandra} to resolve\nthe hard XRB and to identify the nature of the sources that produce it.\nWe chose to centre on the SSA13 field\\cite{lilly}, which has existing\nmultiwavelength observations\\cite{windhorst,songaila,barger},\nto maximize the immediate identification of optical/near-infrared (NIR)\ncounterparts and redshifts for the X-ray source detections.\nWe find that above a flux threshold of\n$2.5\\times 10^{-15}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$ ($2-10$\\ keV),\nwe can account for at least $75$ per cent of the sky flux,\nwith the main uncertainty being the sky flux itself.\nOur deep optical observations show a rich assortment\nof hard X-ray sources which could not have been discovered by\nprevious satellites.\n\n\\vskip 0.5cm\n\\centerline{\\bf {\\it Chandra} X-ray Survey of SSA13}\n\\vskip 0.2cm\n\nThe SSA13 observation was performed on 1999 December 3--4 for an\nelapsed time of 100.9\\ ks. The optical axis of the telescope at\nRA(2000)$=13^h\\ 12^m\\ 21.40^s$,\nDec(2000)$=42^{\\circ}\\ 41^{'}\\ 20.96^{''}$ was positioned on\nthe back illuminated CCD (S3) of ACIS since\nthis detector has a much better soft X-ray sensitivity than the\nfront illuminated chips. Furthermore, since the back illuminated\ndetectors did not suffer the radiation damage which affected the\nfront illuminated chips in orbit, they are well\ncharacterised by extensive ground-based calibrations.\n\nThe overall sensitivity of the instrument spans\na wide energy range from 0.2 to 10\\ keV.\nTwo energy-dependent images of the S3 chip were generated in\nthe hard ($2-10$\\ keV) and soft ($0.5-2$\\ keV) bands, as was\na $2-10$\\ keV image of the front illuminated S2 chip that\ncovered a neighboring region.\nWe extracted sources independently for the hard\nand soft band images. Sources brighter than \n$3.2\\times 10^{-15}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$ ($2-10$\\ keV) \nor $3\\times 10^{-16}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$ ($0.5-2$\\ keV; S3 chip\nonly) which lie within 6 arcminutes of the optical axis are \ngiven in Table~1, ordered by right ascension; the table contains 22 \nsources selected in the hard band and a further 15 sources \nselected solely in the soft band.\nDetails of the extraction and calibration of the X-ray data and\nof the optical photometry may be found in the table footnote.\n\n\\vskip 0.5cm\n\\centerline{\\bf Number Counts and the Resolution of the X-ray Background}\n\\label{secbkgd}\n\\vskip 0.2cm\n\nThe cumulative counts per square degree, $N(>S)$,\nare the sum of the inverse areas of all\nsources brighter than flux $S$. Sources at the faintest\nfluxes can be detected only at smaller off-axis angles\nwhere the PSF and vignetting corrections are smaller; thus,\nthe area diminishes with flux.\nIn Fig.~\\ref{figcounts}a, b we present our cumulative\ncounts per square degree (filled squares) in the soft and hard \nbands, respectively, with $1\\sigma$\nuncertainties from the Poisson error in the number of detected\nsources (jagged solid lines). To the limiting flux levels\nof $2.3\\times 10^{-16}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$ ($0.5-2$\\ keV) \nand $2.5\\times 10^{-15}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$ ($2-10$\\ keV),\nsimulations show that the counts are nearly complete and that\nEddington bias is unimportant; thus,\nthe raw counts accurately represent the true counts.\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=chandra_fig1a.eps,height=2.3in}\n\\psfig{file=chandra_fig1b.eps,height=2.3in}}\n\\caption{\nIntegral number counts per square degree\nof X-ray sources in the SSA13 field versus flux\nfor (a)\\ the hard and (b)\\ the soft energy bands.\nThe soft counts are based on 30 sources in the $10^{-7}$ probability sample\ncovering an area of 59 square arcminutes on the S3 chip.\nThe hard counts are based on the $10^{-7}$ probability sample of the S2 chip\nin the $2-10$\\ keV band and\na $10^{-7}$ probability sample of the S3 chip chosen in the $2-6$\\ keV band\n(to minimise background) and corrected to $2-10$\\ keV fluxes.\nThe total area is 84 square arcminutes. At fluxes greater than\n$2\\times 10^{-14}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$, sources were drawn\nfrom the S2, S3, I2, and I3 chips, which increased the area\nto 227 square arcminutes. The combined hard sample contains 35 sources.\nIn (a)\\ the solid line at bright fluxes is the\n$N(>S)\\propto S^{-3/2}$ representation of the\n{\\it ASCA} counts from Ueda et al.\\cite{ueda2}\n(sensitivity limit $7\\times 10^{-14}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$);\nthese data lie on the extrapolation from previous results by\n{\\it HEAO1} A2\\cite{picc} with a Euclidean slope of $-1.5$.\nThe dotted line shows the extrapolation of this line to fainter fluxes.\nThe solid line at fainter fluxes is the $-1.05$ power-law fit\nto the present data below $2\\times 10^{-14}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$.\nThe dashed line shows the normalisation at a given flux at which\nintegral counts with the observed shape would exceed a $2-10$\\ keV sky\nflux\\cite{chen}\nof $1.9\\times 10^{-11}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$\\ deg$^{-2}$.\n%using the recent higher estimates of the background.\nIn (b)\\ the open and filled circles show the counts determined from\nthe {\\it ROSAT} PSPC\n(sensitivity limit $2\\times 10^{-15}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$)\nand HRI (sensitivity limit $10^{-15}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$)\ndata of the Lockman Hole from Hasinger et al.\\cite{hasinger}.\nThe dotted line shows the fluctuation limits from\nHasinger et al.\\cite{hasinger93}. The solid lines are the $-0.7$\nindex power-law fit to the data below\n$7\\times 10^{-14}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$\nand the $-1.5$ index power-law fit above that flux.\nThe dashed line shows\nthe normalisation at a given flux at which integral counts with\nthe observed shape would exceed the $0.5-2$\\ keV XRB\\cite{chen}.\n}\n\\label{figcounts}\n\\end{figure}\n\nOur soft band counts are in excellent agreement with the deep\n{\\it ROSAT} counts in the Lockman Hole from\nHasinger et al.\\cite{hasinger} in the region of overlap.\nAt fainter fluxes our new counts fall at the lower limit of their\nfluctuation analysis, which suggests an ongoing flattening. \n\nAn area-weighted maximum likelihood fit\\cite{murdoch} of a single \npower-law to the \n$0.5-2$\\ keV counts over the flux range \n$2.3-70\\times 10^{-16}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$ is\ngiven by the relation\n\n\\begin{equation}\nN(>S)=185 \\times (S/7 \\times 10^{-15})^{-0.7 \\pm 0.2}\n\\end{equation}\n\n\\noindent\nwhere the errors on the power-law index are 68\\% confidence.\nLikewise, a power-law fit to the $2-10$\\ keV counts over\nthe flux range $2.5-20\\times 10^{-15}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$\nis given by\n\n\\begin{equation}\nN(>S)=170 \\times (S/2 \\times 10^{-14})^{-1.05 \\pm 0.35}\n\\label{hardpleq}\n\\end{equation}\n\n\\noindent\nwhere the counts intercept the {\\it ASCA} extrapolation at the \nupper end of the flux range. Though the range\nin indices is consistent with the power-law index of 1.5\nseen at brighter fluxes, the counts are significantly lower \nthan an extrapolation of the {\\it ASCA} counts.\n\nThe source contributions to the XRB can be obtained by summing\nthe individual fluxes divided by area or, more indirectly, by\nintegrating $S dN$ using the power-law fits. We list the\ndirectly summed source contributions to the XRB in the two bands \nin Table~2, along with previous determinations by {\\it ROSAT}\nand {\\it ASCA}. With the additional 10 per cent contribution\nfrom our data to the soft band, a maximum flux of\n$1.1\\times 10^{-12}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$\\ deg$^{-2}$\nremains to be accounted for. In the hard band, the combination\nof the present results with the {\\it ASCA} measurements at\nhigher fluxes means that at least $75$\\ per cent of the background \n(using the highest published normalisation) is resolved to the \ncurrently observed flux limits.\n\n\\vskip 0.5cm\n\\centerline{\\bf Optical Properties of the X-ray Sources}\n\\vskip 0.2cm\n\nWe have compared our X-ray images with existing\\cite{cowie96,wilson}\ndeep $HK'$, $I$, $B$, and $U'$\nimages obtained with the Keck 10\\ m and UH 2.2\\ m telescopes.\nBecause of the excellent $\\sim 1$\\ arcsec X-ray positional accuracy,\nwe can, in most cases, securely identify the optical counterparts\nto the X-ray sources. In Fig.~\\ref{figimages}a, b we show thumbnail\n$I$-band images of all of the X-ray sources in Table~1.\nOnly one source,\nCXO J131159.3+423928 (significant in both the hard and soft\nX-ray images), is significantly extended in the X-ray images;\nit is probably a high redshift cluster.\nThe optical image (thumbnail 35 of Fig.~\\ref{figimages}a)\nis centred on a faint ($I=23$) galaxy which lies at the centre\nof a region of enhanced galaxy density.\nIn addition to the probable cluster, the hard sample contains\ntwo quasars, eight bright galaxies, and eleven optically faint\n($I>23$) objects, while the soft sample\ncontains five quasars, five bright galaxies, and fifteen \nunidentified optically faint objects.\nMorphologically the X-ray selected bright galaxy population\nconsists of a mixture of early spirals and elliptical galaxies.\nThree of the bright galaxies show possible signs of interaction\nwith nearby bright neighbors while the remainder are clearly\nisolated.\n\nOur Keck spectra for the quasars\nshow broad MgII or CIV and Lyman alpha lines.\nIn some of the bright galaxy spectra clear AGN signatures are \npresent (e.g., a broad absorption line galaxy with \nP-Cygni profiles at $z=1.320$). However,\nalthough subtle AGN signatures may be present in their optical\nspectra, most of the bright galaxies\nwould not have been identified in an optical survey as AGN.\nWe illustrate this in Fig.~\\ref{figspectra} with\nspectra for three of the bright galaxies.\n\n\\begin{figure}[p]\n\\figurenum{2}\n\\centerline{\\psfig{file=chandra_fig2.eps,width=5.0in,angle=90}}\n\\caption{\n$9''\\times 9''$ $I$-band images of the X-ray sources of Table~1.\nMost of the images are from ultradeep\ndata obtained with LRIS on the Keck 10\\ m telescope, but those marked\nwide are from shallower wide-field UH 2.2\\ m data,\nand those marked hst are from deep (approximately 16000 s of exposure)\nF814W {\\it HST} data. The astrometry of the optical images\nis tied to deep 20\\ cm VLA images currently being analysed by\nRichards et al. (in preparation).\nThe absolute offset from the nominal {\\it Chandra}\nastrometry ($2.2''$\\ W, $0.2''$\\ N) was obtained from the quasar\nCXO J131215.3+423901. A small adjustment to the pixel\nsize ($0.4908''$ versus $0.492''$) was also made to optimize the\nagreement between the X-ray and optical sources, but no adjustment\nof the roll angle. In this system the\n{\\it r.m.s.} dispersion between the 8 objects in the soft sample with\n$I<23$ optical counterparts in the deep LRIS data is $0.36''$.\nIntercomparison of the independent positions determined from the\nhard and soft mages suggests that the error\nmay rise to as much as $1.7''$ in the faintest X-ray sources.\nThe ID numbers are as in Table~1, and the sources are ordered from\nthe lower left by right ascension.\nThe upper panel shows a circle of $1.5''$ radius\ntypical of the maximum positional uncertainty.\n\\label{figimages}\n}\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{3}\n\\vskip-2in\n\\centerline{\\psfig{file=chandra_fig3.eps,height=8.9in}}\n\\vskip-0.4in\n\\caption{\nKeck LRIS spectra of three of the X-ray detected bright galaxies\nthat have redshifts (\\#30 at $z=0.180$ and \\#12 at $z=0.585$ are from\nthe hard-selected sample and \\#14 at $z=0.234$ is from the\nsoft-selected sample). These objects do not show strong\nemission features, except for H$\\alpha$, NII, and SII in the\n$z=0.234$ spectrum and [OII\\}3727 in the $z=0.585$ spectrum.\nThe resolution of the spectra is $14$\\ km/s and the shaded regions\nshow the positions of the strong 5577\\ \\AA\\ night sky line and\nthe atmospheric bands.\n\\label{figspectra}\n}\n\\end{figure}\n\n\n\n\\vskip 0.5cm\n\\centerline{\\bf The X-ray Spectrum}\n\\vskip 0.2cm\n\n\\begin{figure}[p]\n\\figurenum{4}\n\\centerline{\\psfig{file=chandra_fig4.eps,height=5.2in}}\n\\caption{\n$I$ magnitudes versus X-ray photon indices.\nSolid symbols represent the hard ($2-10$\\ keV) selected sample,\nand open symbols represent the soft ($0.5-2$\\ keV) selected sample.\nFor objects with redshift identifications, quasars\nare represented by circles and galaxies by squares.\nSources without redshifts are represented by triangles.\nIn cases where the objects were significantly detected in both samples,\nthe hard-selected magnitudes and indices were used; these objects\nare indicated by solid symbols surrounded by larger open symbols.\n\\label{figmagvsindex}\n}\n\\end{figure}\n\n\nThe photon intensity of the XRB, $P(E)$, where $E$ is the photon\nenergy in keV and $P(E)$ has units of\n[photons\\ cm$^{-2}$\\ s$^{-1}$\\ keV$^{-1}$\\ sr$^{-1}$],\ncan be approximated by a power-law, $P(E)=AE^{-\\Gamma}$.\nThe {\\it HEAO1} A-2 experiment\\cite{marshall} found that the XRB\nspectrum from $3-15$\\ keV was well described by a photon index\n$\\Gamma\\simeq 1.4$, and this result has been confirmed and extended to\nlower energies by recent analyses of {\\it ASCA}\\cite{gendreau,chen,\nmiyaji,ishisaki} and {\\it BeppoSAX}\\cite{vecchi} data.\n\nThe photon indices of the individual sources given in Table~1 were \ncomputed from the ratios of the counts in the $0.5-2$\\ keV band\nto those in the $2-10$\\ keV band, assuming each source\ncould be described by a single power-law.\nThere is an extremely wide range of hardness in both samples,\nranging from negative indices to $\\Gamma=1.8$ in the hard-selected\nsample and from $\\Gamma=0.1$ to values above 2 in the soft sample.\nThe composite (counts-weighted) photon index is $1.22\\pm 0.03$\nin the hard sample and $1.42\\pm 0.04$\nin the soft sample. The progressive hardening of the soft sample\nas we move to fainter fluxes is a continuation of a trend seen\nin the {\\it ROSAT} samples\\cite{hasinger93,almaini}.\nThe combined spectrum of all the soft X-ray sources of Table~1\nis well fit by a single power-law over the $0.3-10$\\ keV range\nwith an index of $1.42 \\pm 0.07$ and an extinction corresponding\nto the galactic $N(H)= 1.4 \\times 10^{20}$ cm$^{-2}$.\nIf we assume that 75 per cent of the $2-10$\\ keV\nbackground has an index of 1.22 and that the remaining\n25 per cent of the background comes from sources that have\nfluxes greater than $1\\times 10^{-13}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$\n($2-10$\\ keV) and an average photon index\\cite{ueda1} of 1.63, \nthen the index of the combined sample is 1.38, which agrees\nextremely well with the spectrum of the hard X-ray background\n\\cite{marshall,gendreau,chen,miyaji,ishisaki,vecchi}.\n\nInspection of Table~1 suggests that the hardest sources\ntend to correspond to the bright galaxies, with the optically\nfaint objects having intermediate hardness, and the quasars\nbeing the softest of the sources observed.\nWe illustrate this more clearly in Fig.~\\ref{figmagvsindex} where\nwe have plotted $I$-band magnitude versus photon index. Of the\n$I\\lesssim 22$ objects, more than half are galaxies,\nand the majority of these have $\\Gamma<1$. The five known quasars all\nlie in the $\\Gamma>1.7$ range, consistent with that of most\nbrighter AGN. The faint sources spread\nover a wide range of indices that overlap both of the other populations.\nWe can quantify this by generating the counts-weighted averages\nfor each population separately. For the hard-selected sample,\nwe find that the bright galaxies (\\#9, 12, 26, 29) have\nan average photon index of $0.59 \\pm 0.06$, the faint objects\n(\\#1, 6, 7, 8, 9, and 22) have $1.33 \\pm 0.06$, and the\ntwo quasars have $1.76 \\pm 0.07$. For the soft-selected sample, \nthe 15 unidentified objects with $I>23$ have a composite index of\n$1.35 \\pm 0.06$, which is almost identical to that of the\noptically faint objects in the hard sample, and the quasars\nhave a composite index of $1.80 \\pm 0.12$.\n\n\\vskip 0.5cm\n\\centerline{\\bf The Source of the Background}\n\\vskip 0.2cm\n\n\nOur data conclusively show that AGN are the major\ncontributors to the hard X-ray background.\nMany of our sources agree with the predictions\nof XRB synthesis\nmodels\\cite{setti,madau,matt,comastri,zdziarski,smith,gilli,schmidt2,miyaji2}\nconstructed within the framework of AGN\nunification schemes to account for the spectral intensity\nof the hard XRB and to explain\nthe X-ray source counts in the hard and soft energy bands.\nIn the unified scheme, the orientation of a molecular torus\nsurrounding the nucleus determines the classification of the\nsource. The models invoke, along with a population of unobscured\nAGN, whose nuclear emission we see directly, a substantial\npopulation of intrinsically obscured AGN whose hydrogen column\ndensities of $N_H\\sim 10^{21}-10^{25}$\\ cm$^{-2}$\naround the nucleus block our line-of-sight.\n\nThe AGN that make up the hard XRB come in two main flavors:\nroughly 40 per cent are luminous early-type galaxies (both\nellipticals and early spirals) in the\nredshift range from $z=0$ to just beyond $z=1$, and\nroughly 50 per cent have faint or, in some cases, undetectable\noptical counterparts. Most of these objects would not have been\nfound even in sensitive optical surveys for AGN.\n\nThe bright galaxy population is extremely hard with an\naverage photon index of $\\Gamma=0.59$. The X-ray sources\nare point-like and centred on the galaxy nuclei, which suggests \nthat they are produced by accretion onto the central black\nholes that are known to be present in such systems.\nThe hardness of the X-ray spectra indicates that these X-ray\nsources are highly obscured. Such sources were described by\nMoran et al.\\cite{moran} based on {\\it Einstein} data. After \nhard X-ray components were discovered by Allen et al.\\cite{allen} \nin {\\it ASCA} spectra of six nearby giant elliptical \ngalaxies, a model\\cite{dm1} was constructed which\nwas able to account for a large fraction of the XRB \nwith objects of this type. The model \npredicted that a significant fraction of the hard number \ncounts at fluxes $<10^{-14}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$ could arise \nfrom sources at low redshift, as is indeed now observed to be the case.\nThe absolute $K$ magnitudes of these sources lie between\n$\\sim -24$ and $\\sim -26$\n(${\\rm H_o}=65$\\ km\\ s$^{-1}$\\ Mpc$^{-1}$ and $q_o=0.5$),\nor from just below to several times the $L_{\\ast}$ luminosity,\nand their rest-frame $2-10$\\ keV luminosities range from $5\\times\n10^{41}$ to $3\\times 10^{43}$\\ erg\\ s$^{-1}$.\nThese sources are at too low redshifts to be likely\nsubmillimeter candidates; however, they should be far-infrared\nsources, which SIRTF and other upcoming airborne\nand space missions should be able to detect.\n\nThe optically faint sources have an average photon\nindex of $\\Gamma=1.3$. These sources could either be a\nsmooth continuation to $z>1$ of the bright early-type\ngalaxies with obscured luminous X-ray nuclei, more\ndistant obscured AGN, or something more exotic,\nsuch as extremely high redshift ($z\\gg 5$) quasars.\nFor this final possibility, the objects would be invisible in the \n$B$-band because of scattering by the foreground intergalactic \nneutral hydrogen.\nIn the soft sample, eleven of the optically faint sources have\n$B>26$ and could lie in this category. This places an upper\nlimit on the surface density of this type of source of 0.26 per\nsquare arcminute to the $3\\times10^{-16}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$\nlimit of the $0.5-2$\\ keV sample, which is slightly lower than\nthe predictions of the toy model of Haiman and Loeb\\cite{haiman}\nfor X-ray selected high-redshift quasars.\nThe handful of objects which are detected in the NIR\nbut absent in $B$ are the most promising candidates for this\ntype of object and, in some cases (e.g., object 19 in the soft\nsample) may be bright enough for follow-up with NIR\nspectroscopy to test the hypothesis.\n\n%optical spectra of the optically brighter objects and \nComparison with submillimeter\\cite{barger1,hughes,gunn}, \nfar-infrared, and radio\nsamples should allow us to determine what fraction of\nobjects in these surveys are X-ray emitting AGN.\nAs near-infrared spectra and photometric redshift estimates of \nthe optically faint sources are established, \nwe will be able to refine the obscured AGN models and determine\nwhether any of the faint sources are indeed very high redshift\nquasars. With the X-ray, \noptical, and submillimeter samples all now approaching the full \nresolution of their respective backgrounds, we are close to achieving \na complete cosmic census of the population of galaxies and AGN.\n\n\n\\vskip 0.5cm\n\\centerline{\\bf Acknowledgements}\n\\vskip 0.2cm\n\n We thank J. Halpern and G. Hasinger for comments which\n greatly improved the first draft of this paper.\n We acknowledge E. Boldt for his many years of pioneering\n work concerning the X-ray background and \n R. Giacconi, whose insight and enthusiasm have\n inspired this subject. We thank the CXC, L. Van Speybroeck, \n M. Weisskopf and the MSFC team, M. Bautz, G. Garmire, and \n the ACIS team for building and operating such an excellent \n observatory. We acknowledge the use of HEASARC software.\n A.J. Barger acknowledges support from\n the Hubble and Chandra fellowship programs. \n\n\\newpage\n\n\\begin{thebibliography}{50}\n\n\\bibitem {giacconi} Giacconi, R., Gursky, H., Paolini, F.,\n\\& Rossi, B.\\ Evidence for X-rays from sources outside the Solar system.\n\\prlnat{9}, 439--443 (1962).\n\n\\bibitem {mather2} Mather, J.C.\\ et al.\\ Measurement of the cosmic\nmicrowave background spectrum by the {\\it COBE} FIRAS instrument.\n\\apjnat{420}, 439--444 (1994).\n\n\\bibitem {wright} Wright, E.L.\\ et al.\\ Interpretation of the\n{\\it COBE} FIRAS CMBR spectrum.\n\\apjnat{420}, 450--456 (1994).\n\n\\bibitem {hasinger} Hasinger, G., Burg, R., Giacconi, R., Schmidt, M.,\nTr\\\"umper, J., \\& Zamorani, G.\\\nThe {\\it ROSAT} Deep Survey.\\ I.\\ X-ray sources in the Lockman Field.\n\\aanat{329}, 482--494 (1998).\n\n\\bibitem {schmidt1} Schmidt, M.\\ et al.\\\nThe {\\it ROSAT} deep survey.\\ II.\\ Optical identification,\nphotometry and spectra of X-ray sources in the Lockman field.\n\\aanat{329}, 495--503 (1998).\n\n\\bibitem{ueda} Ueda, Y.\\ et al.\\\nA population of faint galaxies that contribute to the cosmic\nX-ray background.\n\\natnat{391}, 866--868 (1998).\n\n\\bibitem {ueda1} Ueda, Y.\\ et al.\\\nLOG N-LOG S relations and spectral properties of sources\nfrom the {\\it ASCA} large sky survey: their implications\nfor the origin of the cosmic X-ray background (CXB).\n\\apjnat{518}, 656--671 (1999).\n\n\\bibitem {ueda2} Ueda, Y., Takahashi, T., Ishisaki, Y.,\nOhashi, T., Makishima, K.\\\nThe {\\it ASCA} medium sensitivity survey (the GIS catalog project):\nsource counts and evidence for emerging population of hard\nsources. \\apjnat{524}, L11--L14 (1999).\n\n\\bibitem {cagnoni} Cagnoni, I., Della Ceca, R., Maccacaro, T.\\\nA Medium Survey of the Hard X-Ray Sky with the {\\it ASCA}\nGas Imaging Spectrometer: The ($2-10$\\ keV) Number Counts\nRelationship. \\apjnat{493}, 54--61 (1998).\n\n\\bibitem {fiore} Fiore, F., La Franca, F., Giommi, P., Elvis, M.,\nMatt, G., Comastri, A., Molendi, S., \\& Gioia, I.\\\nThe contribution of faint AGN to the hard X-ray background.\n\\mnnat{306}, L55--L60 (1999).\n\n\\bibitem {weisskopf} Weisskopf, M.C.\\\nThe Chandra X-ray Observatory (CXO): an overview.\nIn the proceedings of the NATO-ASI held in Crete,\nGreece (in the press); also as preprint\nastro-ph/9912097 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n\\bibitem {lilly} Lilly, S.J., Cowie, L.L., \\& Gardner J.P.\\\nA deep imaging and spectroscopic survey of faint galaxies.\n\\apjnat{369}, 79--105 (1991).\n\n\\bibitem {songaila} Songaila, A., Cowie, L.L., Hu, E.M., \\& Gardner J.P.\\\nThe Hawaii K band Galaxy Survey III. Spectroscopy of $K<20$ galaxies.\n\\apjsupnat{94}, 461--515 (1994).\n\n\\bibitem {windhorst} Windhorst, R.A.\\ et al.\\\nIdentification of faint radio sources with optically luminous\ninteracting disk galaxies.\n\\natnat{365}, 471--474 (1995).\n\n\\bibitem {barger} Barger, A.J., Cowie, L.L., \\& Sanders, D.B.\\\nResolving the submillimeter background.\n\\apjnat{518}, L5--L8 (1999).\n\n%\\bibitem {wainscoat} Wainscoat R.J. \\& Cowie, L.L.\\\n%An optimized filter for deep near-infrared imaging\n%(in preparation) (2000).\n\n\\bibitem {picc} Piccinotti, G., Mushotzky, R.F., Boldt, E.A.,\nHolt, S.S., Marshall, F.E., Serlemitsos, P.J., Shafer, R.A.\\\nA complete X-ray sample of the high-latitude ($|{b}|>20^{\\circ}$)\nsky from {\\it HEAO 1} A-2: $\\log{N}-\\log{S}$ and luminosity functions.\n\\apjnat{253}, 485--503 (1982).\n\n\\bibitem {chen} Chen, L.-W., Fabian, A.C., \\& Gendreau, K.C.\\\n{\\it ASCA} and {\\it ROSAT} observations of the QSF3 field: the\nX-ray background in the $0.1-7$\\ keV band.\n\\mnnat{285}, 449--471 (1997).\n\n\\bibitem {hasinger93} Hasinger, G., Burg, R., Giacconi, R.,\nHartner, G., Schmidt, M., Tr${\\rm \\ddot{u}}$mper, J., \\&\nZamorani, G.\\\nA deep X-ray survey in the Lockman Hole and the soft\nX-ray $\\log N-\\log S$.\n\\aanat{275}, 1--15 (1993).\n\n\\bibitem {murdoch} Murdoch, H.S., Crawford, D.F., \\& Jauncey, D.L.\\\nMaximum Likelihood estimation of the Number-Flux density distribution\nof radio sources in the presence of noise and comfusion.\n\\apjnat{183}, 1--13 (1973).\n\n\\bibitem {gendreau} Gendreau, K.C.\\ et al.\\\nASCA Observations of the Spectrum of the X-Ray Background.\n\\pasjnat{47}, L5--L9 (1995).\n\n\\bibitem {marshall} Marshall, F.\\ et al.\\ The diffuse X-ray\nbackground spectrum from 3 to 50\\ keV.\n\\ajnat{235}, 4--10 (1980).\n\n\\bibitem {vecchi} Vecchi, A., Molendi, S., Guainazzi, M.,\nFiore, F., \\& Parmar, A.N.\\\nThe BeppoSAX 1-8 keV cosmic background spectrum.\n\\aanat{349}, L73--L76 (1999).\n\n\\bibitem {cowie96} Cowie, L.L., Songaila, A., Hu, E.M., \\&\nCohen, J.G.\\\nNew insight on galaxy formation and evolution from Keck\nspectroscopy of the Hawaii Deep Fields.\n\\ajnat{112}, 839--864 (1996).\n\n\\bibitem {wilson} Wilson, G., Cowie, L.L., Barger, A.J., \\&\nBurke, D.J.\\\nThe evolution of the universal ultraviolet luminosity density\nwith redshift. \\apjnat (submitted) (2000).\n\n%\\bibitem {richards} Richards E.\\ et al.\\\n%An extremely deep 20\\ cm study of the SSA13 field (in preparation) (2000).\n\n\\bibitem {miyaji} Miyaji, T.\\ et al.\\\nThe cosmic X-ray background spectrum observed with {\\it ROSAT}\nand {\\it ASCA}.\n\\aanat{334}, L13--L16 (1998).\n\n\\bibitem {ishisaki} Ishisaki, Y., Makishima, K., Takahashi, T.,\nUeda, Y., Ogasaka, Y., \\& Inoue, H.\\\n\\apjnat (submitted) (1999).\n\n\\bibitem {almaini} Almaini, O.\\ et al.\\\nA deep {\\it ROSAT} survey. XII. The X-ray spectra of faint\n{\\it ROSAT} sources.\n\\mnnat{282}, 295--303 (1996).\n\n\\bibitem {setti} Setti, G. \\& Woltjer, L.\\\nActive galactic nuclei and the spectrum of the X-ray background.\n\\aanat{224}, L21--L23 (1989).\n\n\\bibitem {madau} Madau, P., Ghisellini, G., \\& Fabian, A.C.\\\nThe unified Seyfert scheme and the origin of the cosmic X-ray\nbackground. \\mnnat{270}, L17--L21 (1994).\n\n\\bibitem {matt} Matt, G. \\& Fabian, A.C.\\\nSpectral constraints on Seyfert 2 galaxies as major contributors\nto the hard (3--100\\ keV) X-ray background.\\\n\\mnnat{267}, 187--192 (1994).\n\n\\bibitem {comastri} Comastri, A., Setti, G., Zamorani, G., \\&\nHasinger, G.\\\nThe contribution of AGNs to the X-ray background.\\\n\\aanat{296}, 1--12 (1995).\n\n\\bibitem {zdziarski} Zdziarski, A.A., Johnson, W.N., Done, C.,\nSmith, D., \\& McNaron-Brown, K.\\\nThe average X-ray/gamma-ray spectra of Seyfert galaxies from\n{\\it GINGA} and OSSE and the origin of the cosmic X-ray background.\n\\apjnat{438}, L63--L66 (1995).\n\n\\bibitem {smith} Smith, D.A. \\& Done, C.\\\nUnified theories of active galactic nuclei: a hard X-ray sample\nof Seyfert 2 galaxies.\n\\mnnat{280}, 355--377 (1996).\n\n\\bibitem {gilli} Gilli, R., Risaliti, G., \\& Salvati, M.\\\nBeyond the standard model for the cosmic X-ray background.\n\\aanat{347}, 424--433 (1999).\n\n\\bibitem {schmidt2} Schmidt, M., Giacconi, R., Hasinger, G.,\nTr$\\rm{\\ddot{u}}$mper, J., \\& Zamorani, G.\\\nThe X-ray luminosity function of active galactic nuclei.\nIn {\\it Highlights in X-ray Astronomy}.\nMPE report (in the press); also as preprint\nastro-ph/9908295 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n\\bibitem {miyaji2} Miyaji, T., Hasinger, G., Schmidt, M.\\\nSoft X-ray AGN luminosity function from {\\it ROSAT} surveys I.\n\\aanat (in the press); also as preprint\nastro-ph/9910410 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n\\bibitem {moran} Moran, E.C., Helfand D.J., Becker R.H., \\& White, R.L.\\\nThe Einstein two-sigma catalog: silver needles in the X-ray haystack.\n\\apjnat{461}, 127-145 (1996).\n\n\\bibitem {allen} Allen, S.W., Di Matteo, T., \\& Fabian, A.C.\\\nHard X-ray emission from elliptical galaxies\n\\mnnat (in the press); also as preprint\nastro-ph/9905052 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n\\bibitem {dm1} Di Matteo, T. \\& Allen, S.W.\\\nHard X-ray emission from elliptical galaxies and its\ncontribution to the X-ray background.\n\\apjnat{527}, L21--L24 (1999).\n\n\\bibitem {haiman} Haiman, Z. \\& Loeb, A.\\\nX-ray emission from the first quasars.\n\\apjnat{521}, L9--L13 (1999).\n\n\\bibitem {hughes} Hughes, D.H., et al.\\\nHigh-redshift star formation in the Hubble Deep Field revealed by\na submillimetre-wavelength survey.\n\\natnat{394}, 241--247 (1998).\n\n\\bibitem {barger1} Barger, A.J., et al.\\\nSubmillimetre-wavelength detection of dusty star-forming galaxies\nat high redshift.\n\\natnat{394}, 248--251 (1998).\n\n\\bibitem {gunn} Gunn, K.F. \\& Shanks, T.\\\nImplications of an obscured AGN model for the X-ray background\nat submillimeter and far-infrared wavelengths.\n\\mnnat (submitted); also as preprint\nastro-ph/9909089 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n%\\bibitem {almaini} Almaini, O., Lawrence, A., \\& Boyle, B.J.\\\n%The AGN contribution to deep submillimetre surveys and the\n%far-infrared background.\n%\\mnnat{305}, L59--L63 (1999).\n\n%\\bibitem {smail} Smail, I., Ivison, R.J., \\& Blain, A.W.\\\n%A deep submillimeter survey of lensing clusters: a new window\n%on galaxy formation and evolution.\n%\\apjnat{490}, L5--L8 (1997).\n\n%\\bibitem {eales} Eales, S. et al.\\\n%The Canada-UK deep submillimeter survey: first submillimeter images,\n%the source counts, and resolution of the background.\n%\\apjnat{515}, 518--524 (1999).\n\n%\\bibitem {sanders} Sanders, D.B. \\& Mirabel, I.F.\\\n%Luminous infrared galaxies.\n%\\araanat{34}, 749--792 (1996).\n\n%\\bibitem {bargersp} Barger, A.J., Cowie, L.L., Smail, I.,\n%Ivison, R.J., Blain, A.W., \\& Kneib, J.-P.\\\n%Redshift distribution of the faint submillimeter galaxy population.\n%\\ajnat{117}, 2656--2665 (1999).\n\n%\\bibitem {hasinger98} Hasinger, G.\\\n%The X-ray background and the AGN X-ray luminosity function.\n%{\\it Astron. Nachr.}, 319, 37 (1998).\n\n\\end{thebibliography}\n\n\\newpage\n\n\\noindent\n%{\\small \\parskip=0.0ex\n{\\bf Notes to Table~1}\nX-ray sources in the SSA13 field selected in the hard \n($2-10$\\ keV; S2 and S3 chips)\nor soft ($0.5-2$\\ keV; S3 chip) bands.\nThe X-ray images were prepared using xselect \nand associated ftools at GSFC. ACIS grades 0, 2, 3, 4, and 6 were \nused, and columns at the boundaries of the readout nodes were rejected.\n%The S3 data were trimmed to exclude background\n%spikes, giving a total exposure of 95.9\\ ks; for the S2 chip\n%the full exposure time of 100.9\\ ks was used.\nCounts lying within a $5''$ diameter aperture\nwere measured, together with the background in a\n$5''-7.5''$ radius annulus, at $2''$ intervals along the field.\n%The average background was 4.7 counts in a $5''$ cell\n%in the $2-10$\\ keV S3 image, 1.3 counts in the\n%$0.5-2$\\ keV S3 image, and 1.5 counts in the $2-10$\\ keV S2\n%image.\nThe distribution of detected counts is Poisson.\nA cut of 17 counts in the hard S3 image\nand 10 counts in the other two images represents a \n$<10^{-7}$ probability threshold against background fluctuations and \nensures a $<20$\\% probability of a single spurious\nsource detection in the entire sample. \n%The cells were searched\n%to locate all positions that were at or above these levels.\nThe source counts were corrected for the enclosed energy fraction\nwithin the aperture. For the S3 chip the flux calibrations\nwere made using an array of effective areas versus energy at 12\npositions and an assumed power-law spectrum having counts-weighted\nmean photon indices $\\Gamma=1.2$ ($2-10$\\ keV) and\n$\\Gamma=1.4$ ($0.5-2$\\ keV).\nThe galactic $N(H)= 1.4 \\times 10^{20}$ cm$^{-2}$ is too\nlow to affect the flux conversions.\nFor the S2 chip a single conversion factor of\n$2.6\\times 10^{-11}$\\ erg\\ cm$^{-2}$\\ ct$^{-1}$ was used.\nUsing the on-axis flux calibrations of\n$2.5\\times 10^{-11}$ ($2-10$\\ keV)\nand $2.9\\times 10^{-12}$ ($0.5-2$\\ keV)\nto convert the S3 counts per second to flux,\nwe determine limiting minimum fluxes of\n$3.2\\times 10^{-15}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$ ($2-10$\\ keV)\nand $3.0\\times 10^{-16}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$ ($0.5-2$\\ keV).\nThe table is restricted to sources with off-axis angles \n$<6'$, where $>50$\\% of the energy is enclosed within a $\\sim2.5''$ \nradius, and to sources where the noise, computed from the variance of\nthe background and signal, is less than one third the signal.\nThe $15''$ borders of each chip have incomplete\nexposure times due to the spacecraft dither so objects detected\nin these borders were not included in our counts analysis.\n%The areas are 84\\ arcmin$^2$ ($2-10$\\ keV) and 59\\ arcmin$^2$\n%($0.5-2$\\ keV).\nThe NIR and optical magnitudes are computed in $1.5''$\nradii intervals. $I$ is Kron-Cousins, $B$ is Johnson,\n$HK'$ is a broad filter centred at $1.9$\nmicrons, and $U'$ is a $300$\\ \\AA\\\nfilter centred at $3400$\\ \\AA. Lower limits are $1\\sigma$.\n%}\n\n\\noindent\n%{\\small \\parskip=0.0ex\n{\\bf Notes to Table~2}\nThe statistical errors on our observed sky brightnesses dominate\nthe systematic errors, which are expected to be less than \n10 per cent. To be consistent with Hasinger et al.\\cite{hasinger},\nwe converted our soft band sky brightness of\n$6.0\\pm 1.5\\times 10^{-13}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$\\ deg$^{-2}$\nto the $1-2$\\ keV range using the measured mean photon index.\nThis result was then compared with the $1-2$\\ keV background\n(where galactic contamination is less than at lower energies) of\n$3.7-4.4\\times 10^{-12}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$\\ deg$^{-2}$\nfrom Gendreau et al.\\cite{gendreau}, using a fit to {\\it ASCA}\ndata, and Chen et al.\\cite{chen}, using a fit to joint\n{\\it ASCA}/{\\it ROSAT} data.\nIn the hard band the summed counts are compared with\nthe $2-10$\\ keV background of\n$1.6-2.3\\times 10^{-11}$\\ erg\\ cm$^{-2}$\\ s$^{-1}$\\ deg$^{-2}$\nfrom Marshall et al.\\cite{marshall},\nusing a fit to {\\it HEAO1} A2 data, and Vecchi et al.\\cite{vecchi},\nusing a fit to {\\it BeppoSAX} data.\n%}\n\n\\newpage\n\n\\begin{deluxetable}{lrrrrrrrrrrrrrr}\n\\tablewidth{0pt}\n\\scriptsize\n\\tablenum{1}\n\\tablehead{\n\\colhead{\\#} & \\multicolumn{3}{c}{RA(2000)} &\n\\multicolumn{3}{c}{Dec(2000)} &\n$f$(2--10\\ keV) & $f$(0.5--2\\ keV) & \\colhead{$\\Gamma$} &\n\\colhead{$HK'$} & \\colhead{$I$} & \\colhead{$B$} & \\colhead{$U'$} &\n\\colhead{$z$} \\cr\n& & & & & & & ($10^{-16}$\\ cgs) & ($10^{-17}$\\ cgs) & & & & & &\n}\n\\startdata\n0\\tablenotemark{S2} & 13 & 12 & 43.38 & 42 & 44 & 36.73 & $82.5 \\pm 21.0$ & \\nodata\n& \\nodata & 20.13 & 24.60 & \\nodata & \\nodata & \\nodata \\cr\n1\\tablenotemark{b} & 13 & 12 & 40.24 & 42 & 39 & 35.55 & $43.0 \\pm 14.1$ & $79.0 \\pm 16.7$ & 0.93\n& \\nodata & 24.43 & 25.19 & \\nodata & \\nodata \\cr\n2\\tablenotemark{S2} & 13 & 12 & 39.62 & 42 & 45 & 48.77 & $89.9 \\pm 25.2$ & \\nodata\n& \\nodata & 24.36 & $>26.7$ & \\nodata & \\nodata & \\nodata \\cr\n3\\tablenotemark{S2} & 13 & 12 & 39.50 & 42 & 42 & 48.83 & $39.2 \\pm 11.4$ & \\nodata\n& \\nodata & 17.08 & 19.89 & \\nodata & \\nodata & 0.111 \\cr\n4\\tablenotemark{s} & 13 & 12 & 37.94 & 42 & 40 & 5.53 & $32.1\\pm 11.8$ & $32.8\\pm 10.8$ & 0.45\n& \\nodata & 24.10 & $25.76$ & \\nodata & \\nodata \\cr\n5\\tablenotemark{S2} & 13 & 12 & 37.16 & 42 & 43 & 21.08 & $50.0 \\pm 12.5$ & \\nodata\n& \\nodata & $>25.4$ & $>26.7$ & \\nodata & \\nodata & \\nodata\\cr\n6\\tablenotemark{b} & 13 & 12 & 36.86 & 42 & 38 & 44.55 & $46.2 \\pm 14.2$ & $39.2 \\pm 12.1$ & 0.28\n& \\nodata & $>25.4$ & $>26.7$ & \\nodata & \\nodata \\cr\n7\\tablenotemark{b} & 13 & 12 & 36.58 & 42 & 40 & 2.80 & $384 \\pm 34.0$ & $1480 \\pm 67.1$ & 1.54\n& \\nodata & $>25.4$ & $26.70$ & \\nodata & \\nodata \\cr\n8\\tablenotemark{h} & 13 & 12 & 36.00 & 42 & 40 & 44.11 & $41.6 \\pm 12.3$ & $23.1 \\pm 9.22$ & $-0.06$\n& \\nodata & 23.94 & 25.40 & $>25.5$ & \\nodata \\cr\n9\\tablenotemark{b,S3e} & 13 & 12 & 35.68 & 42 & 41 & 50.67 & $232 \\pm 26.0$ & $408 \\pm 35.3$ & 0.90\n& \\nodata & 20.91 & 22.95 & 23.40 & 1.320 \\cr\n10\\tablenotemark{S2} & 13 & 12 & 34.48 & 42 & 43 & 9.27 & $78.1 \\pm 14.9$ & \\nodata\n& \\nodata & 16.38 & 19.26 & 23.22 & 24.19 & 0.241 \\cr\n11\\tablenotemark{s} & 13 & 12 & 32.36 & 42 & 39 & 49.39 & $15.7\\pm 8.86$ & $50.0\\pm 12.9$ & 1.38\n& 20.16 & 24.37 & 25.82 & $>25.5$ & \\nodata \\cr\n12\\tablenotemark{h} & 13 & 12 & 31.34 & 42 & 39 & 2.19 & $48.4 \\pm 13.1$ & $19.8 \\pm 8.60$ & $-0.40$\n& 18.02 & 20.54 & 23.37 & 23.76 & 0.586 \\cr\n13\\tablenotemark{s} & 13 & 12 & 30.83 & 42 & 39 & 42.73 & $4.71\\pm 6.69$ & $38.2\\pm 11.3$ & 2.12\n& 19.75 & 23.94 & 25.80 & 25.36 & \\nodata \\cr\n14\\tablenotemark{s} & 13 & 12 & 29.26 & 42 & 37 & 32.33 & $14.5\\pm 10.6$ & $112\\pm 20.1$ & 2.09\n& 16.04 & 18.39 & 20.91 & 21.35 & 0.234 \\cr\n15\\tablenotemark{S2} & 13 & 12 & 28.25 & 42 & 44 & 54.52 & $56.7 \\pm 13.7$ & \\nodata\n& \\nodata & 21.64 & 24.41 & 25.33 & $>25.5$ & \\nodata \\cr\n16\\tablenotemark{b} & 13 & 12 & 26.00 & 42 & 37 & 35.86 & $49.9 \\pm 15.2$ & $170 \\pm 24.6$ & 1.43\n& 19.73 & 22.67 & 24.53 & 25.14 & \\nodata \\cr\n17\\tablenotemark{s} & 13 & 12 & 25.29 & 42 & 41 & 19.53 & $13.7\\pm 8.14$ & $49.6\\pm 12.8$ & 1.45\n& 21.68 & $>25.9$ & 26.93 & $>25.5$ & \\nodata \\cr\n18\\tablenotemark{S2e} & 13 & 12 & 22.48 & 42 & 44 & 49.97 & $42.1 \\pm 11.7$ & \\nodata & \\nodata\n& 20.73 & 24.98 & 26.26 & $>25.5$ & \\nodata \\cr\n19\\tablenotemark{b} & 13 & 12 & 22.32 & 42 & 38 & 13.89 & $116 \\pm 19.8$ & $622 \\pm 44.6$ & 1.80\n& 17.80 & 19.84 & 21.53 & 22.23 & 2.565\\tablenotemark{q} \\cr\n20\\tablenotemark{s} & 13 & 12 & 21.63 & 42 & 35 & 49.97 & $45.4\\pm 28.4$ & $203\\pm 33.9$ & 1.65\n& \\nodata & 25.06 & $>26.7$ & \\nodata & \\nodata \\cr\n21\\tablenotemark{s} & 13 & 12 & 21.50 & 42 & 44 & 5.41 & $17.3\\pm 8.92$ & $78.7\\pm 16.1$ & 1.60\n& 19.23 & 22.06 & 23.36 & 23.98 & 1.305\\tablenotemark{q} \\cr\n22\\tablenotemark{b} & 13 & 12 & 20.11 & 42 & 42 & 22.42 & $49.0 \\pm 12.3$ & $196 \\pm 24.6$ & 1.53\n& $>22.5$ & 24.14 & 25.75 & $>25.5$ & \\nodata \\cr\n23\\tablenotemark{s} & 13 & 12 & 19.19 & 42 & 38 & 8.36 & $28.3\\pm 11.5$ & $36.1\\pm 11.6$ & 0.62\n& $>22.5$ & 24.56 & 26.72 & $>25.5$ & \\nodata \\cr\n24\\tablenotemark{b} & 13 & 12 & 15.32 & 42 & 39 & 0.22 & $190 \\pm 23.3$ & $986 \\pm 54.4$ & 1.75\n& 16.18 & 17.92 & 18.66 & 19.00 & 2.565\\tablenotemark{q} \\cr\n25\\tablenotemark{s} & 13 & 12 & 11.72 & 42 & 44 & 12.59 & $19.5\\pm 10.0$ & $175\\pm 24.3$ & 2.16\n& 18.65 & 20.70 & 22.22 & 22.27 & 0.950\\tablenotemark{q} \\cr\n26\\tablenotemark{b} & 13 & 12 & 10.02 & 42 & 41 & 29.94 & $151 \\pm 20.3$ & $246 \\pm 27.8$ & 0.76\n& 16.74 & 19.47 & 22.50 & 24.15 & 0.212 \\cr\n27\\tablenotemark{s} & 13 & 12 & 9.93 & 42 & 36 & 15.30 & $15.9\\pm 25.8$ & $77.3\\pm 22.2$ & 1.72\n& 19.66 & 23.50 & 27.32 & $>25.5$ & \\nodata \\cr\n28\\tablenotemark{s} & 13 & 12 & 8.38 & 42 & 41 & 43.08 & $2.37\\pm 6.18$ & $53.1\\pm 13.4$ & 2.88\n& 20.39 & 23.24 & 25.64 & $>25.5$ & \\nodata \\cr\n29\\tablenotemark{b} & 13 & 12 & 6.55 & 42 & 41 & 41.31 & $138 \\pm 20.2$ & $95.8 \\pm 17.7$ & 0.05\n& 17.80 & 20.50 & 23.66 & 24.82 & 0.696 \\cr\n30\\tablenotemark{h} & 13 & 12 & 6.55 & 42 & 41 & 25.16 & $38.4 \\pm 11.8$ & $8.17 \\pm 6.45$ & $-1.72$\n& 15.22 & 17.47 & 20.52 & 22.31 & 0.180 \\cr\n31\\tablenotemark{s} & 13 & 12 & 5.18 & 42 & 41 & 23.45 & $7.29\\pm 7.77$ & $33.8\\pm 11.3$ & 1.62\n& 21.16 & $>25.9$ & 28.02 & $>25.5$ & \\nodata \\cr\n32\\tablenotemark{h} & 13 & 12 & 4.18 & 42 & 41 & 13.59 & $48.2 \\pm 13.7$ & $25.9 \\pm 10.2$ & $-0.17$\n& 22.39 & $>25.9$ & $>27.6$ & $>25.5$ & \\nodata \\cr\n33\\tablenotemark{s} & 13 & 12 & 1.23 & 42 & 42 & 7.78 & $5.28\\pm 8.64$ & $83.3\\pm 17.9$ & 2.60\n& 21.08 & 23.65 & 26.67 & $>25.5$ & 3.405\\tablenotemark{q} \\cr\n34\\tablenotemark{s} & 13 & 11 & 59.66 & 42 & 41 & 52.89 & $34.3\\pm 13.9$ & $42.1\\pm 13.5$ & 0.53\n& \\nodata & $>25.9$ & 26.21 & $>25.5$ & \\nodata \\cr\n35\\tablenotemark{b} & 13 & 11 & 59.36 & 42 & 39 & 28.17 & $273 \\pm 36.5$ & $612 \\pm 51.2$ & 1.01\n& \\nodata & 23.04 & $>27.6$ & $>25.5$ & \\nodata \\cr\n36\\tablenotemark{s} & 13 & 11 & 59.19 & 42 & 38 & 34.12 & $55.5\\pm 22.6$ & $107\\pm 23.3$ & 0.93\n& \\nodata & $>25.9$ & 27.29 & $>25.5$ & \\nodata \\cr\n\\enddata\n\\tablenotetext{s}{S3 source detected only in soft band sample.}\n\\tablenotetext{h}{S3 source detected only in hard band sample.}\n\\tablenotetext{b}{Significant detection in both samples.}\n\\tablenotetext{S3e}{In the S3 $15''$ excluded border.}\n\\tablenotetext{S2}{Detected in the S2 chip.}\n\\tablenotetext{S2e}{In the S2 $15''$ excluded border.}\n\\tablenotetext{q}{Quasar spectrum.}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{ccccc}\n\\tablewidth{0pt}\n\\tablenum{2}\n\\tablecaption{Source Contributions to the XRB\\label{tab2}}\n\\tablehead{\n\\colhead{Energy range} &\n\\colhead{Flux range} & \\colhead{Source Contribution} &\n\\colhead{Percentage} & \\colhead{Reference} \\\\\n\\colhead{(keV)} & \\colhead{(erg\\ cm$^{-2}$\\ s$^{-1}$)} &\n\\colhead{(erg\\ cm$^{-2}$\\ s$^{-1}$\\ deg$^{-2}$)} & \n\\colhead{of XRB\\tablenotemark{1}} &\n}\n\\startdata\n$1-2$ & $>10^{-15}$ & $3.0\\times 10^{-12}$ & $68-81$ &\nHasinger et al.\\cite{hasinger} \\\\\n$1-2$ & $(2.3-10)\\times 10^{-16}$ & $(3.8\\pm 1.0)\\times 10^{-13}$ & $6-13$ &\npresent paper\\\\\n$2-10$ & $>10^{-13}$ & $4.5\\times 10^{-12}$ & $20-28$ &\nUeda et al.\\cite{ueda1}\\\\\n$2-10$ & $(2.5-100)\\times 10^{-15}$ & $(1.30\\pm 0.3)\\times 10^{-11}$ &\n$56-81$ & present paper\\\\\n\\enddata\n\\tablenotetext{1}{The range given is a combination of the uncertainty\nin the source contribution (from the third column) and the variation in\nthe published sky flux.}\n\\end{deluxetable}\n\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002313.extracted_bib",
"string": "\\begin{thebibliography}{50}\n\n\\bibitem {giacconi} Giacconi, R., Gursky, H., Paolini, F.,\n\\& Rossi, B.\\ Evidence for X-rays from sources outside the Solar system.\n\\prlnat{9}, 439--443 (1962).\n\n\\bibitem {mather2} Mather, J.C.\\ et al.\\ Measurement of the cosmic\nmicrowave background spectrum by the {\\it COBE} FIRAS instrument.\n\\apjnat{420}, 439--444 (1994).\n\n\\bibitem {wright} Wright, E.L.\\ et al.\\ Interpretation of the\n{\\it COBE} FIRAS CMBR spectrum.\n\\apjnat{420}, 450--456 (1994).\n\n\\bibitem {hasinger} Hasinger, G., Burg, R., Giacconi, R., Schmidt, M.,\nTr\\\"umper, J., \\& Zamorani, G.\\\nThe {\\it ROSAT} Deep Survey.\\ I.\\ X-ray sources in the Lockman Field.\n\\aanat{329}, 482--494 (1998).\n\n\\bibitem {schmidt1} Schmidt, M.\\ et al.\\\nThe {\\it ROSAT} deep survey.\\ II.\\ Optical identification,\nphotometry and spectra of X-ray sources in the Lockman field.\n\\aanat{329}, 495--503 (1998).\n\n\\bibitem{ueda} Ueda, Y.\\ et al.\\\nA population of faint galaxies that contribute to the cosmic\nX-ray background.\n\\natnat{391}, 866--868 (1998).\n\n\\bibitem {ueda1} Ueda, Y.\\ et al.\\\nLOG N-LOG S relations and spectral properties of sources\nfrom the {\\it ASCA} large sky survey: their implications\nfor the origin of the cosmic X-ray background (CXB).\n\\apjnat{518}, 656--671 (1999).\n\n\\bibitem {ueda2} Ueda, Y., Takahashi, T., Ishisaki, Y.,\nOhashi, T., Makishima, K.\\\nThe {\\it ASCA} medium sensitivity survey (the GIS catalog project):\nsource counts and evidence for emerging population of hard\nsources. \\apjnat{524}, L11--L14 (1999).\n\n\\bibitem {cagnoni} Cagnoni, I., Della Ceca, R., Maccacaro, T.\\\nA Medium Survey of the Hard X-Ray Sky with the {\\it ASCA}\nGas Imaging Spectrometer: The ($2-10$\\ keV) Number Counts\nRelationship. \\apjnat{493}, 54--61 (1998).\n\n\\bibitem {fiore} Fiore, F., La Franca, F., Giommi, P., Elvis, M.,\nMatt, G., Comastri, A., Molendi, S., \\& Gioia, I.\\\nThe contribution of faint AGN to the hard X-ray background.\n\\mnnat{306}, L55--L60 (1999).\n\n\\bibitem {weisskopf} Weisskopf, M.C.\\\nThe Chandra X-ray Observatory (CXO): an overview.\nIn the proceedings of the NATO-ASI held in Crete,\nGreece (in the press); also as preprint\nastro-ph/9912097 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n\\bibitem {lilly} Lilly, S.J., Cowie, L.L., \\& Gardner J.P.\\\nA deep imaging and spectroscopic survey of faint galaxies.\n\\apjnat{369}, 79--105 (1991).\n\n\\bibitem {songaila} Songaila, A., Cowie, L.L., Hu, E.M., \\& Gardner J.P.\\\nThe Hawaii K band Galaxy Survey III. Spectroscopy of $K<20$ galaxies.\n\\apjsupnat{94}, 461--515 (1994).\n\n\\bibitem {windhorst} Windhorst, R.A.\\ et al.\\\nIdentification of faint radio sources with optically luminous\ninteracting disk galaxies.\n\\natnat{365}, 471--474 (1995).\n\n\\bibitem {barger} Barger, A.J., Cowie, L.L., \\& Sanders, D.B.\\\nResolving the submillimeter background.\n\\apjnat{518}, L5--L8 (1999).\n\n%\\bibitem {wainscoat} Wainscoat R.J. \\& Cowie, L.L.\\\n%An optimized filter for deep near-infrared imaging\n%(in preparation) (2000).\n\n\\bibitem {picc} Piccinotti, G., Mushotzky, R.F., Boldt, E.A.,\nHolt, S.S., Marshall, F.E., Serlemitsos, P.J., Shafer, R.A.\\\nA complete X-ray sample of the high-latitude ($|{b}|>20^{\\circ}$)\nsky from {\\it HEAO 1} A-2: $\\log{N}-\\log{S}$ and luminosity functions.\n\\apjnat{253}, 485--503 (1982).\n\n\\bibitem {chen} Chen, L.-W., Fabian, A.C., \\& Gendreau, K.C.\\\n{\\it ASCA} and {\\it ROSAT} observations of the QSF3 field: the\nX-ray background in the $0.1-7$\\ keV band.\n\\mnnat{285}, 449--471 (1997).\n\n\\bibitem {hasinger93} Hasinger, G., Burg, R., Giacconi, R.,\nHartner, G., Schmidt, M., Tr${\\rm \\ddot{u}}$mper, J., \\&\nZamorani, G.\\\nA deep X-ray survey in the Lockman Hole and the soft\nX-ray $\\log N-\\log S$.\n\\aanat{275}, 1--15 (1993).\n\n\\bibitem {murdoch} Murdoch, H.S., Crawford, D.F., \\& Jauncey, D.L.\\\nMaximum Likelihood estimation of the Number-Flux density distribution\nof radio sources in the presence of noise and comfusion.\n\\apjnat{183}, 1--13 (1973).\n\n\\bibitem {gendreau} Gendreau, K.C.\\ et al.\\\nASCA Observations of the Spectrum of the X-Ray Background.\n\\pasjnat{47}, L5--L9 (1995).\n\n\\bibitem {marshall} Marshall, F.\\ et al.\\ The diffuse X-ray\nbackground spectrum from 3 to 50\\ keV.\n\\ajnat{235}, 4--10 (1980).\n\n\\bibitem {vecchi} Vecchi, A., Molendi, S., Guainazzi, M.,\nFiore, F., \\& Parmar, A.N.\\\nThe BeppoSAX 1-8 keV cosmic background spectrum.\n\\aanat{349}, L73--L76 (1999).\n\n\\bibitem {cowie96} Cowie, L.L., Songaila, A., Hu, E.M., \\&\nCohen, J.G.\\\nNew insight on galaxy formation and evolution from Keck\nspectroscopy of the Hawaii Deep Fields.\n\\ajnat{112}, 839--864 (1996).\n\n\\bibitem {wilson} Wilson, G., Cowie, L.L., Barger, A.J., \\&\nBurke, D.J.\\\nThe evolution of the universal ultraviolet luminosity density\nwith redshift. \\apjnat (submitted) (2000).\n\n%\\bibitem {richards} Richards E.\\ et al.\\\n%An extremely deep 20\\ cm study of the SSA13 field (in preparation) (2000).\n\n\\bibitem {miyaji} Miyaji, T.\\ et al.\\\nThe cosmic X-ray background spectrum observed with {\\it ROSAT}\nand {\\it ASCA}.\n\\aanat{334}, L13--L16 (1998).\n\n\\bibitem {ishisaki} Ishisaki, Y., Makishima, K., Takahashi, T.,\nUeda, Y., Ogasaka, Y., \\& Inoue, H.\\\n\\apjnat (submitted) (1999).\n\n\\bibitem {almaini} Almaini, O.\\ et al.\\\nA deep {\\it ROSAT} survey. XII. The X-ray spectra of faint\n{\\it ROSAT} sources.\n\\mnnat{282}, 295--303 (1996).\n\n\\bibitem {setti} Setti, G. \\& Woltjer, L.\\\nActive galactic nuclei and the spectrum of the X-ray background.\n\\aanat{224}, L21--L23 (1989).\n\n\\bibitem {madau} Madau, P., Ghisellini, G., \\& Fabian, A.C.\\\nThe unified Seyfert scheme and the origin of the cosmic X-ray\nbackground. \\mnnat{270}, L17--L21 (1994).\n\n\\bibitem {matt} Matt, G. \\& Fabian, A.C.\\\nSpectral constraints on Seyfert 2 galaxies as major contributors\nto the hard (3--100\\ keV) X-ray background.\\\n\\mnnat{267}, 187--192 (1994).\n\n\\bibitem {comastri} Comastri, A., Setti, G., Zamorani, G., \\&\nHasinger, G.\\\nThe contribution of AGNs to the X-ray background.\\\n\\aanat{296}, 1--12 (1995).\n\n\\bibitem {zdziarski} Zdziarski, A.A., Johnson, W.N., Done, C.,\nSmith, D., \\& McNaron-Brown, K.\\\nThe average X-ray/gamma-ray spectra of Seyfert galaxies from\n{\\it GINGA} and OSSE and the origin of the cosmic X-ray background.\n\\apjnat{438}, L63--L66 (1995).\n\n\\bibitem {smith} Smith, D.A. \\& Done, C.\\\nUnified theories of active galactic nuclei: a hard X-ray sample\nof Seyfert 2 galaxies.\n\\mnnat{280}, 355--377 (1996).\n\n\\bibitem {gilli} Gilli, R., Risaliti, G., \\& Salvati, M.\\\nBeyond the standard model for the cosmic X-ray background.\n\\aanat{347}, 424--433 (1999).\n\n\\bibitem {schmidt2} Schmidt, M., Giacconi, R., Hasinger, G.,\nTr$\\rm{\\ddot{u}}$mper, J., \\& Zamorani, G.\\\nThe X-ray luminosity function of active galactic nuclei.\nIn {\\it Highlights in X-ray Astronomy}.\nMPE report (in the press); also as preprint\nastro-ph/9908295 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n\\bibitem {miyaji2} Miyaji, T., Hasinger, G., Schmidt, M.\\\nSoft X-ray AGN luminosity function from {\\it ROSAT} surveys I.\n\\aanat (in the press); also as preprint\nastro-ph/9910410 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n\\bibitem {moran} Moran, E.C., Helfand D.J., Becker R.H., \\& White, R.L.\\\nThe Einstein two-sigma catalog: silver needles in the X-ray haystack.\n\\apjnat{461}, 127-145 (1996).\n\n\\bibitem {allen} Allen, S.W., Di Matteo, T., \\& Fabian, A.C.\\\nHard X-ray emission from elliptical galaxies\n\\mnnat (in the press); also as preprint\nastro-ph/9905052 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n\\bibitem {dm1} Di Matteo, T. \\& Allen, S.W.\\\nHard X-ray emission from elliptical galaxies and its\ncontribution to the X-ray background.\n\\apjnat{527}, L21--L24 (1999).\n\n\\bibitem {haiman} Haiman, Z. \\& Loeb, A.\\\nX-ray emission from the first quasars.\n\\apjnat{521}, L9--L13 (1999).\n\n\\bibitem {hughes} Hughes, D.H., et al.\\\nHigh-redshift star formation in the Hubble Deep Field revealed by\na submillimetre-wavelength survey.\n\\natnat{394}, 241--247 (1998).\n\n\\bibitem {barger1} Barger, A.J., et al.\\\nSubmillimetre-wavelength detection of dusty star-forming galaxies\nat high redshift.\n\\natnat{394}, 248--251 (1998).\n\n\\bibitem {gunn} Gunn, K.F. \\& Shanks, T.\\\nImplications of an obscured AGN model for the X-ray background\nat submillimeter and far-infrared wavelengths.\n\\mnnat (submitted); also as preprint\nastro-ph/9909089 at $\\langle$http:\\/\\/xxx.lanl.gov$\\rangle$ (1999).\n\n%\\bibitem {almaini} Almaini, O., Lawrence, A., \\& Boyle, B.J.\\\n%The AGN contribution to deep submillimetre surveys and the\n%far-infrared background.\n%\\mnnat{305}, L59--L63 (1999).\n\n%\\bibitem {smail} Smail, I., Ivison, R.J., \\& Blain, A.W.\\\n%A deep submillimeter survey of lensing clusters: a new window\n%on galaxy formation and evolution.\n%\\apjnat{490}, L5--L8 (1997).\n\n%\\bibitem {eales} Eales, S. et al.\\\n%The Canada-UK deep submillimeter survey: first submillimeter images,\n%the source counts, and resolution of the background.\n%\\apjnat{515}, 518--524 (1999).\n\n%\\bibitem {sanders} Sanders, D.B. \\& Mirabel, I.F.\\\n%Luminous infrared galaxies.\n%\\araanat{34}, 749--792 (1996).\n\n%\\bibitem {bargersp} Barger, A.J., Cowie, L.L., Smail, I.,\n%Ivison, R.J., Blain, A.W., \\& Kneib, J.-P.\\\n%Redshift distribution of the faint submillimeter galaxy population.\n%\\ajnat{117}, 2656--2665 (1999).\n\n%\\bibitem {hasinger98} Hasinger, G.\\\n%The X-ray background and the AGN X-ray luminosity function.\n%{\\it Astron. Nachr.}, 319, 37 (1998).\n\n\\end{thebibliography}"
}
] |
|
astro-ph0002314
|
DETECTION OF MULTI-TeV GAMMA RAYS FROM MARKARIAN 501 DURING AN UNFORESEEN FLARING STATE IN 1997 WITH THE TIBET AIR SHOWER ARRAY
|
[
{
"author": "M.~Amenomori\\altaffilmark{1}"
},
{
"author": "S.~Ayabe\\altaffilmark{2}"
},
{
"author": "P.Y.~Cao\\altaffilmark{3}"
},
{
"author": "Danzengluobu\\altaffilmark{4}"
},
{
"author": "L.K.~Ding\\altaffilmark{5}"
},
{
"author": "Z.Y.~Feng\\altaffilmark{6}"
},
{
"author": "Y.~Fu\\altaffilmark{3}"
},
{
"author": "H.W.~Guo\\altaffilmark{4}"
},
{
"author": "M.~He\\altaffilmark{3}"
},
{
"author": "K.~Hibino\\altaffilmark{7}"
},
{
"author": "N.~Hotta\\altaffilmark{8}"
},
{
"author": "Q.~Huang\\altaffilmark{6}"
},
{
"author": "A.X.~Huo\\altaffilmark{5}"
},
{
"author": "K.~Izu\\altaffilmark{9}"
},
{
"author": "H.Y.~Jia\\altaffilmark{6}"
},
{
"author": "F.~Kajino\\altaffilmark{10}"
},
{
"author": "K.~Kasahara\\altaffilmark{11}"
},
{
"author": "Y.~Katayose\\altaffilmark{9}"
},
{
"author": "Labaciren\\altaffilmark{4}"
},
{
"author": "J.Y.~Li\\altaffilmark{3}"
},
{
"author": "H.~Lu\\altaffilmark{5}"
},
{
"author": "S.L.~Lu\\altaffilmark{5}"
},
{
"author": "G.X.~Luo\\altaffilmark{5}"
},
{
"author": "X.R.~Meng\\altaffilmark{4}"
},
{
"author": "K.~Mizutani\\altaffilmark{2}"
},
{
"author": "J.~Mu\\altaffilmark{12}"
},
{
"author": "H.~Nanjo\\altaffilmark{1}"
},
{
"author": "M.~Nishizawa\\altaffilmark{13}"
},
{
"author": "M.~Ohnishi\\altaffilmark{9}"
},
{
"author": "I.~Ohta\\altaffilmark{8}"
},
{
"author": "T.~Ouchi\\altaffilmark{7}"
},
{
"author": "J.R.~Ren\\altaffilmark{5}"
},
{
"author": "T.~Saito\\altaffilmark{14}"
},
{
"author": "M.~Sakata\\altaffilmark{10}"
},
{
"author": "T.~Sasaki\\altaffilmark{10}"
},
{
"author": "Z.Z.~Shi\\altaffilmark{5}"
},
{
"author": "M.~Shibata\\altaffilmark{15}"
},
{
"author": "A.~Shiomi\\altaffilmark{9}"
},
{
"author": "T.~Shirai\\altaffilmark{7}"
},
{
"author": "H.~Sugimoto\\altaffilmark{16}"
},
{
"author": "K.~Taira\\altaffilmark{16}"
},
{
"author": "Y.H.~Tan\\altaffilmark{5}"
},
{
"author": "N.~Tateyama\\altaffilmark{7}"
},
{
"author": "S.~Torii\\altaffilmark{7}"
},
{
"author": "T.~Utsugi\\altaffilmark{2}"
},
{
"author": "C.R.~Wang\\altaffilmark{3}"
},
{
"author": "H.~Wang\\altaffilmark{5}"
},
{
"author": "X.W.~Xu\\altaffilmark{5}"
},
{
"author": "Y.~Yamamoto\\altaffilmark{10}"
},
{
"author": "G.C.~Yu\\altaffilmark{6}"
},
{
"author": "A.F.~Yuan\\altaffilmark{4}"
},
{
"author": "T.~Yuda\\altaffilmark{9}"
},
{
"author": "C.S.~Zhang\\altaffilmark{5}"
},
{
"author": "H.M.~Zhang\\altaffilmark{5}"
},
{
"author": "J.L.~Zhang\\altaffilmark{5}"
},
{
"author": "N.J.~Zhang\\altaffilmark{3}"
},
{
"author": "X.Y.~Zhang\\altaffilmark{3}"
},
{
"author": "Zhaxiciren\\altaffilmark{4}"
},
{
"author": "Zhaxisangzhu\\altaffilmark{4}"
},
{
"author": "and W.D.~Zhou\\altaffilmark{12} (The Tibet AS${\\gamma}$ Collaboration)"
}
] |
In 1997, the BL Lac Object Mrk 501 entered a very active phase and was the brightest source in the sky at TeV energies, showing strong and frequent flaring. Using the data obtained with a high density air shower array that has been operating successfully at Yangbajing in Tibet since 1996, we searched for $\gamma$-ray signals from this source during the period from February through August in 1997. Our observation detected multi-TeV $\gamma$-ray signals at the 3.7~$\sigma$ level during this period. The most rapid increase of the excess counts was observed between April 7 and June 16 and the statistical significance of the excess counts in this period was 4.7~$\sigma$. Among several observations of flaring TeV $\gamma$-rays from Mrk 501 in 1997, this is the only observation using a conventional air shower array. We present the energy spectrum of $\gamma$-rays which will be worthy to compare with those obtained by imaging atmospheric Cerenkov telescopes.
|
[
{
"name": "Mrk501s.tex",
"string": "% SAMPLE2.TEX -- AASTeX macro package tutorial paper.\n\\documentstyle[12pt,aaspp4]{article}\n%\\documentstyle[12pt,aasms4]{article}\n%\\documentstyle[aas2pp4]{article}\n%\\slugcomment{Not to appear in Nonlearned J., 45.}\n\n\\begin{document}\n\n\\title{DETECTION OF MULTI-TeV GAMMA RAYS FROM MARKARIAN 501 DURING AN UNFORESEEN \nFLARING STATE IN 1997 \nWITH THE TIBET AIR SHOWER ARRAY}\n\n\\author{ M.~Amenomori\\altaffilmark{1}, S.~Ayabe\\altaffilmark{2}, \n P.Y.~Cao\\altaffilmark{3}, Danzengluobu\\altaffilmark{4},\n L.K.~Ding\\altaffilmark{5}, Z.Y.~Feng\\altaffilmark{6}, \n Y.~Fu\\altaffilmark{3}, H.W.~Guo\\altaffilmark{4}, \n M.~He\\altaffilmark{3}, K.~Hibino\\altaffilmark{7},\n N.~Hotta\\altaffilmark{8}, Q.~Huang\\altaffilmark{6},\n A.X.~Huo\\altaffilmark{5}, K.~Izu\\altaffilmark{9},\n H.Y.~Jia\\altaffilmark{6}, F.~Kajino\\altaffilmark{10}, \n K.~Kasahara\\altaffilmark{11}, Y.~Katayose\\altaffilmark{9},\n Labaciren\\altaffilmark{4}, J.Y.~Li\\altaffilmark{3},\n H.~Lu\\altaffilmark{5}, S.L.~Lu\\altaffilmark{5},\n G.X.~Luo\\altaffilmark{5}, X.R.~Meng\\altaffilmark{4}, \n K.~Mizutani\\altaffilmark{2}, J.~Mu\\altaffilmark{12}, \n H.~Nanjo\\altaffilmark{1}, M.~Nishizawa\\altaffilmark{13},\n M.~Ohnishi\\altaffilmark{9}, I.~Ohta\\altaffilmark{8},\n T.~Ouchi\\altaffilmark{7}, J.R.~Ren\\altaffilmark{5},\n T.~Saito\\altaffilmark{14}, M.~Sakata\\altaffilmark{10},\n T.~Sasaki\\altaffilmark{10}, Z.Z.~Shi\\altaffilmark{5},\n M.~Shibata\\altaffilmark{15}, A.~Shiomi\\altaffilmark{9}, \n T.~Shirai\\altaffilmark{7}, H.~Sugimoto\\altaffilmark{16},\n K.~Taira\\altaffilmark{16}, Y.H.~Tan\\altaffilmark{5},\n N.~Tateyama\\altaffilmark{7}, S.~Torii\\altaffilmark{7}, \n T.~Utsugi\\altaffilmark{2}, C.R.~Wang\\altaffilmark{3},\n H.~Wang\\altaffilmark{5}, \n X.W.~Xu\\altaffilmark{5}, Y.~Yamamoto\\altaffilmark{10},\n G.C.~Yu\\altaffilmark{6}, A.F.~Yuan\\altaffilmark{4}, \n T.~Yuda\\altaffilmark{9}, C.S.~Zhang\\altaffilmark{5},\n H.M.~Zhang\\altaffilmark{5}, J.L.~Zhang\\altaffilmark{5},\n N.J.~Zhang\\altaffilmark{3}, X.Y.~Zhang\\altaffilmark{3}, \n Zhaxiciren\\altaffilmark{4}, Zhaxisangzhu\\altaffilmark{4},\n and W.D.~Zhou\\altaffilmark{12}\n (The Tibet AS${\\bf \\gamma}$ Collaboration)}\n\n\\altaffiltext{1}{ Department of Physics, Hirosaki University, Hirosaki 036-8561, Japan}\n\\altaffiltext{2}{ Department of Physics, Saitama University, Urawa 338-8570, Japan}\n\\altaffiltext{3}{ Department of Physics, Shangdong University, Jinan 250100, China}\n\\altaffiltext{4}{ Department of Mathematics and Physics, Tibet University, Lhasa 850000, China}\n\\altaffiltext{5}{ Institute of High Energy Physics, Academia Sinica, Beijing 100039, China}\n\\altaffiltext{6}{ Department of Physics, South West Jiaotong University, Chengdu 610031, China}\n\\altaffiltext{7}{ Faculty of Engineering, Kanagawa University, Yokohama 221-8686, Japan}\n\\altaffiltext{8}{ Faculty of Education, Utsunomiya University, Utsunomiya 321-8505, Japan}\n\\altaffiltext{9}{ Institute for Cosmic Ray Research, University of Tokyo, Tanashi 188-8502, Japan}\n\\altaffiltext{10}{ Department of Physics, Konan University, Kobe 658-8501, Japan}\n\\altaffiltext{11}{ Faculty of Systems Engineering, Shibaura Institute of Technology, Omiya 330-8570, Japan}\n\\altaffiltext{12}{ Department of Physics, Yunnan University, Kunming 650091, China}\n\\altaffiltext{13}{ National Center for Science Information Systems, Tokyo 112-8640, Japan}\n\\altaffiltext{14}{ Tokyo Metropolitan College of Aeronautical Engineering, Tokyo 116-0003, Japan}\n\\altaffiltext{15}{ Faculty of Engineering, Yokohama National University, Yokohama 240-0067, Japan}\n\\altaffiltext{16}{ Shonan Institute of Technology, Fujisawa 251-8511, Japan}\n\n\\begin{abstract}\n\n In 1997, the BL Lac Object Mrk 501 entered a very active phase and was the brightest \nsource in the sky at TeV energies, showing strong and frequent flaring. \nUsing the data obtained with a high density air shower array that has been \noperating successfully at Yangbajing in Tibet since 1996, we searched for $\\gamma$-ray signals \nfrom this source during the period from February through August in 1997. \nOur observation detected multi-TeV $\\gamma$-ray signals at the 3.7~$\\sigma$ level \nduring this period. The most rapid increase of the excess counts was observed \nbetween April 7 and June 16 and the statistical significance of the excess counts\n in this period was 4.7~$\\sigma$. Among several observations of flaring TeV \n$\\gamma$-rays from Mrk 501 in 1997, this is the only observation using a conventional \nair shower array. We present the energy spectrum of $\\gamma$-rays which will be worthy \nto compare with those obtained by imaging atmospheric Cerenkov telescopes. \n\n\\end{abstract}\n\n\\keywords{ gamma rays : observations -- BL Lacertae objects : individual (Markarian 501) }\n\n\\section{INTRODUCTION}\n\n Mrk 501 and Mrk 421 have been well detected as extra-galactic TeV $\\gamma$-ray sources by\nWhipple and subsequent ground-based Cerenkov detectors (\\cite{ong98}). They are the \nso-called BL Lac objects, which are radio-loud AGNs (Active Galactic Nuclei) whose \nrelativistic jets are aligned along our line of sight. Flux variability on various \nscales is a common feature of BL Lac objects as already seen in Mrk 501 and Mrk 421, \nand spectral variations of $\\gamma$-rays coming from these sources are considered to be\na very powerful tool for understanding the physics of BL Lac objects.\nWhen Mrk 501 was first detected by the Whipple Collaboration in 1995 (\\cite{quin96}), \nit showed rather low fluxes at a level significantly below the Crab flux. In March of 1997, \nhowever, this source went into a state of remarkably flaring activity and its high state \nlasted for almost half a year with highly variable and strong $\\gamma$-ray emission. \nThe maximum flux reached roughly 10 times that of the Crab. During this period, \nseveral groups (\\cite{prot97}) observed strong $\\gamma$-ray emission from this source \nwith imaging atmospheric Cerenkov detectors. Independent measurements of the \n$\\gamma$-ray spectrum seem to show a gradual softening towards higher energy, while \nthe systematic uncertainties in the flux estimates remain too large to reach a common \nunderstanding. The energy spectrum and its shape are very important quantities for clarifying the\nmechanism of $\\gamma$-ray production or particle acceleration at the source, and\n eventually to lead to the actual measurement of the intergalactic infrared or \nfar-infrared background field (\\cite{steck93}). Hence, confirmation of the detection of $\\gamma$-rays \nwith a different technique will be strongly required.\n\nThe Tibet air shower array, operating since 1990, is located at Yangbajing (4300 m above\nsea level) in Tibet (\\cite{ame92}). This array has a capability of detecting $\\gamma$-rays \nin the TeV energy region with high efficiency and good angular resolution. Using \nthis array, we have succeeded in detecting the Crab at the 5.5~$\\sigma$ level (\\cite{ame99}). \nIn this paper we present the observation of multi-TeV $\\gamma$-ray flares from Mrk 501 \nin 1997. The result obtained with well established air shower technique is important for \ncomparing with those by imaging atmospheric Cerenkov telescopes. \n\n\\section{EXPERIMENT}\n\n The Tibet air shower array consists of two overlapping arrays (Tibet-II and HD) as \ndescribed elsewhere (\\cite{yuda96}). The Tibet-II array comprises 185 scintillation \ndetectors (BICRON 408A) of 0.5 m$^2$ each placed on a 15 m square grid with an \nenclosed area of 36,900 m$^2$, and the HD (high density) array is operating inside \nthe Tibet-II array to detect cosmic ray showers with energies lower than 10 TeV. This HD array \nconsists of 109 scintillation detectors (some of detectors are commonly used in \nboth arrays), placed on a 7.5 m square grid covering an area of 5,175 m$^2$. \nThe detector arrangement of the Tibet air shower array is schematically shown in \nFig. 1. Every detector, except those placed with a 30 m spacing on the\noutskirts of the inner detector matrix of the Tibet-II array, is equipped with a\n fast timing (FT) phototube (HPK H1161) and is thus referred to as an ^^ ^^ FT-detector''.\n A lead plate of 5 mm thickness is placed on the top \nof each detector to improve the fast timing data by converting $\\gamma$-rays in the \nshowers to electron pairs. This lead converter typically increases the shower size \nby a factor of about 2 and improves the angular resolution by about 30 \\% (\\cite{ame90}). \n\n\\placefigure{fig1}\n\nAll the TDCs (time-to-digital converters) and ADCs (analog-to-digital converters) are \nregularly monitored by using a calibration module in the FASTBUS system at every \n20 minutes. The length of each signal cable is also monitored by measuring a \nmismatched-reflection pulse from each detector. \n The data-taking system has been operating under any 4-fold coincidence in the\nFT-detectors, resulting in that the trigger rate of the events is about 200~Hz for\nthe Tibet-II while being about 115~Hz for the HD array. \n\nThe observation presented here was made by using the data taken between\n 1997 February and 1997 August. The event selection was done by imposing the \nfollowing three conditions to the recorded data : 1) Each of any four FT detectors \nshould record a signal of more than 1.25 particles ; 2) among the four detectors recording the\nhighest particles, two or more should be within each detector area of the Tibet II \nand HD arrays denoted by the dotted and solid lines, respectively, in Fig.1 ;\n and 3) the zenith angle of the incident direction should be less than 45$^\\circ$.\nAfter data processing and quality cuts, the total number of events selected were\n$5.5 \\times 10^8$ for the HD array and $1.0 \\times 10^9$ for the Tibet-II array,\n respectively, with the effective running time of 155.3 days.\n\n\\section{ARRAY PERFORMANCE}\n\n Since the background cosmic rays are isotropic and $\\gamma$-rays from a source are \napparently centered on the source direction, a bin size for collecting on-source \ndata should be determined based on the array's angular resolution so as to optimize \nthe signal to noise ratio. In order to achieve a good resolution, a study of \ncore-finding techniques and shower-front curvature corrections has been done (\\cite{ame90}).\nThe angular accuracy of the Tibet array can be checked thoroughly by observing the shadow \nthat the Moon casts in the cosmic rays (\\cite{ame93}).\nThe Tibet II and HD arrays have a capability of observing the Moon's shadow with good statistics. \n The mode energies of primary protons to be detected are about 3 TeV and about 8 TeV \nfor the Tibet HD and II arrays, respectively. \nHence the angular resolution of each array can be independently examined in respective \nenergy regions. The statistical significance of the Moon's shadow observed with both arrays \nbecomes about 10$\\sigma$ or more for half a year observation. From this observation,\n we estimated the angular resolution of both arrays to be better than 0.9$^\\circ$ for all events. \nWe have also found that the angular resolution scales with $\\sum \\rho$, where \n $\\sum \\rho$ stands for \nthe sum of the number of shower particles per {\\rm m$^2$} detected in each counter.\n The resolution increases with increasing $\\sum\\rho$ as\n $0.8^\\circ \\times ((\\ge\\sum\\rho)/20)^{-0.3}$ ( $15 < \\sum \\rho < 300$ ).\n\n The Moon's shadow by the events with $\\sum\\rho$ = 15-50 was found at the position \nshifted from the Moon center to the west by 0.32$^\\circ$ ($\\pm 0.10^\\circ$). \n The primary cosmic rays \ncasting the Moon's shadow are almost protons and the mean energy of protons capable of \ngenerating these events at Yangbajing is estimated to be about 4.7 TeV by the simulation.\nOn the other hand, a proton of energy E impinging at normal angle on the Earth is \ndeflected by the geomagnetic field and its deflection angle is calculated \nas $ \\Delta \\theta E \\simeq 1.6^\\circ$ TeV. \nSo, the observed shift of the Moon's shadow is consistent with that expected from\n the effect of\nthe geomagnetic field. A more elaborate study of the Moon's shadow using a Monte \nCarlo technique shows almost same results as those by the experiment\n (\\cite{suga99}). \nThus, the results obtained by assigning primary energies to the\nobserved events can be directly checked by observing the Moon's shadow. \n\n The pointing of the array is inferred from the position of the Moon's shadow by \nhigh energy cosmic rays ($> 20$ TeV) which are negligibly affected by the geomagnetic field. \nThis estimation can also be done by examining the deviations of the Moon's\n shadow in the north-south direction, since the effect of the geomagnetic field acts\nonly in the east-west direction. It is then found to be smaller than 0.1$^\\circ$ \nfor both arrays.\n\n\\placefigure{fig2}\n\nFigure 2 shows the cumulative deficit counts of the events coming from the direction\nof the Moon as a function of MJD, obtained with the HD array. The data set used are \nbetween February 1997 and August 1997, just corresponding to the observation period of \nMrk 501. A linearly increasing of the deficit events may be a sure guarantee \nagainst the long-term stability of the array operation. \nTh meridian zenith angle of the Moon at Yangbajing changes between 12$^\\circ$ and 50$^\\circ$\nevery 27.3 days. Naturally the most efficient observations are done when the Moon \ncomes in sight around the smallest zenith angle of about 12$^\\circ$ every 27.3 days. \nThis effect will be found as a tier-like structure on the deficit curve, as seen in Fig. 2.\n\n\\section{RESULTS AND DISCUSSIONS}\n\n A circular window was used to search for signals and then its size was determined \nbased on the angular resolution estimated by the experiment.\n The window size is chosen to optimize the significance of signals defined by \n$N_s/N_B^{1/2}$, where $N_S$ is the number of signals and $N_B$ the number of\nbackground events, and to contain more than 50~\\% of the signals from a source. \nThe radii of search windows used for the events with $\\sum\\rho >$ 15, 50 and 100\nwere 0.9$^\\circ$, 0.8$^\\circ$ and 0.5$^\\circ$, respectively.\nThe signals were searched for by counting the number of events coming from the \non-source window. The background was estimated by averaging over events falling \nin the ten off-source windows adjacent to the source, but without overlapping\neach other. \nThe source window traverses a path in local coordinates expressed by the zenith angle \nand azimuth angle through every day. In order to reduce a strong zenith angle dependence \nof the background, \nthese off-source windows were taken in the azimuth angle directions with the same zenith \nangle, except two windows adjacent to the on-source window.\n\n\\placefigure{fig3}\n\nFigure 3 shows the cumulative excess counts for all events as a function of MJD\nand background, obtained with\nthe HD array. No excess counts were observed until the middle of March 1997. However,\n excess events rapidly increased in the period from April through June and then it\n became slightly dull. The operation of the array was stopped on August 25 of 1997 to\n calibrate the operation system. As discussed in \\S 3, one should first note that \nthe observed excess counts are by no means due to some artificial noise or unstable \noperation of the system.\nThe statistical significance of the excess counts reached a 3.7~$\\sigma$ level during \nthis period. The excess counts very rapidly increased during the period from April 7 \nthrough June 16 and the statistical significance of the excess counts was a 4.7~$\\sigma$.\n These observed features are almost consistent with other observations by atmospheric Cerenkov \ntelescopes (\\cite{prot97}).\n\n\\placefigure{fig4}\n\nShown in Fig. 4 is the contour map of the excess event densities around Mrk 501 for\n the events with $\\sum\\rho >$ 15 observed between April 7 and June 16 in 1997. \nThis map was obtained using the same method as done for the Moon and Sun shadows \n(\\cite{ame93}). Mrk 501 is well observed in the right direction by our air shower array. \n\n\\placefigure{fig5}\n\n Figure 5 shows the distribution of the opening angles relative to the Mrk 501 direction\nfor all events with $\\sum\\rho >$ 15 in the HD array. The excess in the small opening angle \nregion (less than 0.5$^\\circ$) could be attributed to $\\gamma$-rays from Mrk 501. \nThe simulation result done for $\\gamma$-ray events coming from Mrk 501 can well reproduce\n the experiment as shown in Fig.~5, when we take account of the systematic pointing errors \nestimated in \\S 3.\nFor the observation period from 1997 February to 1997 August, the statistical \nsignificances of the excess events with $\\sum\\rho >$ 15, 30 and 50\nwere 3.7~$\\sigma$, 2.3~$\\sigma$ and 1.6~$\\sigma$, respectively.\n\n We also searched for $\\gamma$-ray emission using the entire Tibet-II array, but no excess \nwas found in this period and upper limits on the excess number of the events at the \n90 \\% confidence level were obtained.\n\nWe estimated the $\\gamma$-ray spectrum from Mrk 501 by a Monte Carlo simulation \n(we used a GENAS code by Kasahara \\& Torii (\\cite{kasa91}).), assuming \na differential power-law spectrum with the form $E^{-\\beta}$ and the\ncut-off at a certain energy, $E_c$, where the cut-off means that the spectral slope \nsteepens by 1.0 at $E_c$. The value of $\\beta$ was changed between 2.4 and 2.7 and \nalso the effect of $E_c$ was examined between 7 TeV and 30 TeV. \nPrimary $\\gamma$-rays with energies between 0.2 TeV and 50 TeV were thrown from \nthe direction of Mrk 501. Observation of simulated events at Yangbajing level was done\nas in our experiment, estimating the collecting area, trigger efficiency and\nthreshold energy for $\\gamma$-rays generating the events at observation level. \n Simulated events in respective size ($\\sum\\rho$) bins were then compared with those \nby the experiment.\nThe energy of $\\gamma$-rays was defined as the energy of the maximum flux of\nsimulated events observed in each size bin. These steps were repeated\nuntil the observed results are well reproduced. A combination of $\\beta \\cong 2.6$\nand $E_c \\sim$ 20-30 TeV can reproduce the data well. We examined that the \nabsolute flux values except the highest energy bin stay almost unchanged for above trials, \nbut it is of course difficult to settle the spectral slope from this experiment \nbecause of very small energy range fitted here. The systematic errors on the flux arise\nmainly from the event selection procedure, which depends upon the array performance, \nand from the calculations of the collecting area and the air shower size \ndistribution by the simulation. They are estimated to be 13 \\% and 8 \\%, \nrespectively (\\cite{ame99}).\n\n\\placefigure{fig6}\n\n\\placefigure{fig7}\n\n Shown in Figs. 6 and 7 are the energy spectra averaged in the period from February \n15 to August 25 in 1997 and from February 15 to June 8 in 1997, respectively.\nThe latter observation time corresponds to that of the Whipple Collaboration (\\cite{samu98}).\nIt is seen that the results reported recently by other experiments (\\cite{samu98} \n; \\cite{haya98} \\& \\cite{kon99}) are almost compatible with ours,\nalthough these do not cover the same observation times. It should pay attention, \nhowever, that our results were obtained by the continuous observation of Mrk 501 \nextending February through August in 1997, while those by Cerenkov telescopes\n were obtained for very limited periods of moonless and cloudless nights.\n \n Mrk 501 and Mrk 421, nearby AGNs, are at almost the same red-shift (0.033 and 0.031, \nrespectively) and have been detected in TeV energies (\\cite{ong98}). \nIn particular, Mrk 501 during the strong, long-lasting 1997 flare provided a good \nopportunity to study the energy spectrum of $\\gamma$-rays from this source in detail \n(\\cite{prot97}), suggesting a spectral feature different with that of Mrk 421 (\\cite{kren99}). \nIn both sources, it is likely that a synchrotron-inverse Compton picture plays an important \npart (\\cite{prot97}). Since the attenuation mechanism of TeV $\\gamma$-rays by intergalactic \ninfra-red photon field is almost the same for both sources, a difference of spectral \nfeatures, if any, could be attributed to the production mechanism of $\\gamma$-rays at \nthe sources. Therefore, it is very important to continue the observation of high energy \n $\\gamma$-rays from both sources with as small uncertainties as possible.\n \n\\section{SUMMARY}\n\n Mrk 501 suddenly came into a very active phase from March in 1997, with several large \nflares and lasted for $\\sim 1/2$ yr. The maximum $\\gamma$-ray flux during this period \nreached about 10 times as high as the Crab Nebula.\nFollowing a successful observation of steady emission of multi-TeV $\\gamma$-rays \nfrom the Crab(\\cite{ame99}), we further detected multi-TeV $\\gamma$-rays from Mrk 501\nwhich was in a high flaring state between March 1997 and August 1997, and estimated \nthe absolute fluxes of $\\gamma$-rays around multi-TeV region,\nusing the high resolution Tibet air shower array. The detection of a signal from this\nsource was achieved by the improvement of the array performance, which can be directly\nchecked by observing the Moon's shadow. Monthly observations of the Moon's shadow provide\na direct check of the angular resolution, pointing accuracy, and\nalso the stable operation of the array over a long period. Furthermore, the\nobservation of the displacement of the Moon's shadow due the effect of\nthe geomagnetic field\nprovides an important check of the results obtained by assigning energies to all the\nevents. This is the first attempt to be done in the air shower experiments,\nand it suggests that the Moon is a unique cosmic-ray anti-source capable of calibrating\nthe array performance thoroughly. \nHence, the results obtained by the Tibet \nexperiment using a different technique will be a great help to \nunderstand the possible bias and errors involved in the Cerenkov observations. \n\nThe area of the present HD array will be extended by a factor of about five in 1999, while its\neffective area will be increased by a factor of about seven by the reduction of edge effects.\n Then, the Tibet array could cover the energy range from 3~TeV to \n$\\sim$100~TeV with \n significantly better statistics and angular resolution at high energies.\n Air shower arrays are wide aperture and high duty cycle instruments, in contrast\nto atmospheric Cerenkov telescopes with relatively narrow fields of view and small duty\ncycle of $\\sim$10 \\%. These features will be indispensable for understanding a time\nvariability of emission of high energy $\\gamma$-rays from point sources such as AGNs\nand GRBs (gamma ray bursts).\nThe Tibet experiment, therefore, will have unique capabilities for the discovery of new, relatively bright sources and for a general survey of the overhead sky.\n\n\\acknowledgments\n\n This work is supported in part by Grants-in-Aid for Scientific\nResearch and also for International Science Research from the Ministry\nof Education, Science, Sports and Culture in Japan and for International\nScience Research from the Committee\nof the Natural Science Foundation and the Academy of Sciences in\nChina.\n\n\\begin{thebibliography}{}\n\\bibitem[Amenomori et al.\\ 1990]{ame90} Amenomori, M. et al. 1990, Nucl. Instrum. \nMethods Phys. Res., A,288, 619 \n\\bibitem[Amenomori et al.\\ 1992]{ame92} Amenomori, M. et al. 1992, \\prl, 69, 2468\n\\bibitem[Amenomori et al.\\ 1993]{ame93} Amenomori, M. et al. 1993, \\prd, 47, 2675\n\\bibitem[Amenomori et al.\\ 1999]{ame99} Amenomori, M. et al. 1999, \\apj, 525, \nL93\n\\bibitem[Hayashida et al.\\ 1998]{haya98} Hayashida, N. et al. 1998, \\apj, 504, L71\n\\bibitem[Kasahara \\& Torii\\ 1991]{kasa91} Kasahara, K. \\& Torii, S. 1991, Comput. Phys. \nCommun., 64, 109 \n\\bibitem[Konopelko et al.\\ 1999]{kon99} Konopelko, A.K. et al. 1999, astro-ph/9901093\n\\bibitem[Krennrich et al.\\ 1999]{kren99} Krennrich et al. 1999, \\apj, 511, 149 \n\\bibitem[Ong\\ 1998]{ong98} Ong, R.A. 1998, Phys. Rep., 305, 93\n\\bibitem[Protheroe et al.\\ 1997]{prot97} Protheroe, R.J. et al. 1997, Proc. 25th \nInt. Cosmic Ray Conf. (Durban), 8, 317\n\\bibitem[Quinn et al.\\ 1996]{quin96} Quinn, J. et al. 1996, \\apj, 456, L83\n\\bibitem[Samuelson et al.\\ 1998]{samu98} Samuelson, F.W. et al. 1998, \\apj, 501, L17\n\\bibitem[Stecker \\& de Jager\\ 1993]{steck93} Stecker, F.W. \\& de Jager, O.C.\n1993, \\apj, 415, L71\n\\bibitem[Suga et al.\\ 1999]{suga99} Suga, Y. et al. 1999, Proc. 26th Int. \nCosmic-Ray Conf. (Salt Lake City), 7, 202\n\\bibitem[Yuda\\ 1996]{yuda96} Yuda, T. 1996, Proc. Int. Symp. on Extremely High \nEnergy Cosmic Rays : Astrophysics and Future Observations, \ned. M. Nagano (Tokyo : Univ. Tokyo/Inst. Cosmic-Ray Res.), 175 \n\\end{thebibliography}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig1.eps}\n\\caption{Schematical view of the Tibet-II/HD shower array operating at Yangbajing. \nOpen and filled squares : FT-detectors ; filled circles : density detectors equipped with \nwide dynamic range phototube. We selected the events whose cores are within the detector \nmatrix enclosed with the solid (HD) or dotted (Tibet-II) line. \\label{fig1}}\n\\end{figure}\n\n\\begin{figure}\n\\plotone{fig2.ps}\n\\caption{Cumulative deficit counts of events with $\\sum\\rho >$ 15 coming from \nthe direction of the Moon as a function of MJD (solid line).\n The radius of search window is taken to be 0.9$^\\circ$ and its center is\nput on the most deficit posittion of the Moon shadow. The dotted and dashed lines \ndenote the expected curves when the angular resolutions are assumed to \nbe 0.8$^\\circ$ and 0.9$^\\circ$, respectively. \\label{fig2}}\n\\end{figure}\n\n\\begin{figure}\n\\plotone{fig3.ps}\n\\caption{Cumulative excess of the events with $\\sum\\rho >$ 15. The dotted lines\ndenote the excess counts at the 1, 2, 3 and 4~$\\sigma$ level, respectively.\n \\label{fig3}}\n\\end{figure}\n\n\\begin{figure}\n\\plotone{fig4.ps}\n\\caption{Contour map of the weights of excess event densities around\nMrk 501, observed between April 7 and June 16 in 1997, in the area of $4^\\circ \\times 4^\\circ$\ncentered on the direction of Mrk 501. The contour lines are drawn with a step of \n1$\\sigma$. Angle distance is measured from the direction of Mrk 501 along the right \nascension (abscissa) and the declination (ordinate). \\label{fig4}}\n\\end{figure}\n\n\\begin{figure}\n\\plotone{fig5.eps}\n\\caption{Opening angle distribution of the events with $\\sum\\rho >$ 15\ncoming from the directions around Mrk 510. The simulation result done\nfor $\\gamma$-ray events is shown by the dashed line. \\label{fig5}}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig6.eps}\n\\caption{Energy spectrum of $\\gamma$-rays from Mrk 501 averaged in \nthe period from 1997 February 15 to 1997 August 25. The error bars \nindicate 1~$\\sigma$ ranges, excluding systematic errors.\nUpper limits at the 90~\\% \nconfidence level, obtained from the Tibet-II and HD arrays, are also plotted in this \nfigure. Our data are compared with other results by Whipple (Samuelson et al. 1998 ),\nHEGRA (Konopelko et al. 1999) and TAP (Hayashida et al. 1998). \\label{fig6}}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig7.eps}\n\\caption{Energy spectrum of $\\gamma$-rays from Mrk 501 averaged in the period from \n1997 February 15 to 1997 June 9. Upper limits, obtained from the Tibet-II and HD arrays,\n are at the 90~\\% confidence level. Our data are compared with the \nWhipple results. \\label{fig7}}\n\\end{figure}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002314.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Amenomori et al.\\ 1990]{ame90} Amenomori, M. et al. 1990, Nucl. Instrum. \nMethods Phys. Res., A,288, 619 \n\\bibitem[Amenomori et al.\\ 1992]{ame92} Amenomori, M. et al. 1992, \\prl, 69, 2468\n\\bibitem[Amenomori et al.\\ 1993]{ame93} Amenomori, M. et al. 1993, \\prd, 47, 2675\n\\bibitem[Amenomori et al.\\ 1999]{ame99} Amenomori, M. et al. 1999, \\apj, 525, \nL93\n\\bibitem[Hayashida et al.\\ 1998]{haya98} Hayashida, N. et al. 1998, \\apj, 504, L71\n\\bibitem[Kasahara \\& Torii\\ 1991]{kasa91} Kasahara, K. \\& Torii, S. 1991, Comput. Phys. \nCommun., 64, 109 \n\\bibitem[Konopelko et al.\\ 1999]{kon99} Konopelko, A.K. et al. 1999, astro-ph/9901093\n\\bibitem[Krennrich et al.\\ 1999]{kren99} Krennrich et al. 1999, \\apj, 511, 149 \n\\bibitem[Ong\\ 1998]{ong98} Ong, R.A. 1998, Phys. Rep., 305, 93\n\\bibitem[Protheroe et al.\\ 1997]{prot97} Protheroe, R.J. et al. 1997, Proc. 25th \nInt. Cosmic Ray Conf. (Durban), 8, 317\n\\bibitem[Quinn et al.\\ 1996]{quin96} Quinn, J. et al. 1996, \\apj, 456, L83\n\\bibitem[Samuelson et al.\\ 1998]{samu98} Samuelson, F.W. et al. 1998, \\apj, 501, L17\n\\bibitem[Stecker \\& de Jager\\ 1993]{steck93} Stecker, F.W. \\& de Jager, O.C.\n1993, \\apj, 415, L71\n\\bibitem[Suga et al.\\ 1999]{suga99} Suga, Y. et al. 1999, Proc. 26th Int. \nCosmic-Ray Conf. (Salt Lake City), 7, 202\n\\bibitem[Yuda\\ 1996]{yuda96} Yuda, T. 1996, Proc. Int. Symp. on Extremely High \nEnergy Cosmic Rays : Astrophysics and Future Observations, \ned. M. Nagano (Tokyo : Univ. Tokyo/Inst. Cosmic-Ray Res.), 175 \n\\end{thebibliography}"
}
] |
astro-ph0002315
|
Perturbative Analysis of Adaptive Smoothing Methods in Quantifying Large-Scale Structure
|
[
{
"author": "\\sc Naoki Seto"
}
] |
Smoothing operation to make continuous density field from observed point-like distribution of galaxies is crucially important for topological or morphological analysis of the large-scale structure, such as, the genus statistics or the area statistics (equivalently the level crossing statistics). It has been pointed out that the adaptive smoothing filters are more efficient tools to resolve cosmic structures than the traditional spatially fixed filters. We study weakly nonlinear effects caused by two representative adaptive methods often used in smoothed hydrodynamical particle (SPH) simulations. Using framework of second-order perturbation theory, we calculate the generalized skewness parameters for the adaptive methods in the case of initially power-law fluctuations. Then we apply the multidimensional Edgeworth expansion method and investigate weakly nonlinear evolution of the genus statistics and the area statistics. Isodensity contour surfaces are often parameterized by the volume fraction of the regions above a given density threshold. We also discuss this parameterization method in perturbative manner. \keywords{cosmology: theory --- large-scale structure of the universe}
|
[
{
"name": "p1.tex",
"string": "\n\\documentstyle[12pt,aaspp4]{article}\n%\\documentstyle[aasms4]{article}\n\n\\begin{document}\n%\\baselineskip 7.5mm\n\n\\newcommand{\\gsim}{\\mbox{\\raisebox{-1.0ex}{$~\\stackrel{\\textstyle >}\n{\\textstyle \\sim}~$ }}}\n\\newcommand{\\lsim}{\\mbox{\\raisebox{-1.0ex}{$~\\stackrel{\\textstyle <}\n{\\textstyle \\sim}~$ }}}\n\\newcommand{\\psim}{\\mbox{\\raisebox{-1.0ex}{$~\\stackrel{\\textstyle \\propto}\n{\\textstyle \\sim}~$ }}}\n\\newcommand{\\vect}[1]{\\mbox{\\boldmath${#1}$}}\n\\newcommand{\\lmk}{\\left(}\n\\newcommand{\\rmk}{\\right)}\n\\newcommand{\\lnk}{\\left\\{ }\n\\newcommand{\\nn}{\\nonumber}\n\\newcommand{\\rnk}{\\right\\} }\n\\newcommand{\\lkk}{\\left[}\n\\newcommand{\\rkk}{\\right]}\n\\newcommand{\\lla}{\\left\\langle}\n\\newcommand{\\p}{\\partial}\n\\newcommand{\\rra}{\\right\\rangle}\n\\newcommand{\\vex}{{\\vect x}}\n\\newcommand{\\vek}{{\\vect k}}\n\\newcommand{\\vel}{{\\vect l}}\n\\newcommand{\\vem}{{\\vect m}}\n\\newcommand{\\ven}{{\\vect n}}\n\\newcommand{\\vep}{{\\vect p}}\n\\newcommand{\\veq}{{\\vect q}}\n\\newcommand{\\veX}{{\\vect X}}\n\\newcommand{\\veV}{{\\vect V}}\n\\newcommand{\\beq}{\\begin{equation}}\n\\newcommand{\\eeq}{\\end{equation}}\n\\newcommand{\\beqa}{\\begin{eqnarray}}\n\\newcommand{\\eeqa}{\\end{eqnarray}}\n\\newcommand{\\mpc}{\\rm Mpc}\n\\newcommand{\\kmpc}{Omega_0 h^2 {\\rm Mpc}}\n\n\n\\title{Perturbative Analysis of Adaptive Smoothing Methods in\n Quantifying Large-Scale Structure}\n\\author{\\sc Naoki Seto }\n\\affil{Department of Physics, Faculty of Science, Kyoto University,\nKyoto 606-8502, Japan }\n\n\n\\begin{abstract}\nSmoothing operation to make continuous density field from observed\npoint-like distribution of galaxies is crucially important for\ntopological or morphological analysis of the large-scale structure, such\nas, the genus statistics or the area statistics (equivalently the level\ncrossing statistics). \nIt has been pointed out that the adaptive smoothing filters are more\nefficient tools to resolve cosmic\nstructures\n than the \ntraditional spatially fixed filters. We study weakly nonlinear effects\ncaused by two representative \nadaptive methods often used in smoothed hydrodynamical particle (SPH)\nsimulations. Using framework of second-order perturbation theory, we \ncalculate the generalized skewness parameters for the adaptive methods\nin the case of initially power-law fluctuations.\n Then we apply the multidimensional Edgeworth expansion method\n and investigate weakly\n nonlinear evolution of the genus statistics and the area statistics.\nIsodensity contour surfaces are often parameterized by the volume fraction\nof the regions above a given density threshold.\nWe also discuss this parameterization method in perturbative manner.\n\\keywords{cosmology: theory --- large-scale structure of the universe}\n\\end{abstract}\n\n\n\n\\section{Introduction}\nThe large-scale distribution of galaxies is one of the most important\nsources to study formation and evolution of cosmic structures. Now\nthere are two ongoing large-scale redshift surveys of \ngalaxies, the Sloan Digital \nSky Survey (SDSS, Gunn \\& Weinberg 1995) and the Anglo-Australian\nTelescope 2dF Survey (Colless 1998). These\nsurveys will bring us enormous information of three-dimensional galaxy\ndistribution and \nare expected to revolutionarily improve our knowledge of\nthe large-scale structure in the universe. \n\nThe two-point correlation function of galaxies, or its Fourier\ntransform, the \npower spectrum are simple as well as powerful tools, and have been \nwidely used to quantify\n clustering of galaxies ({\\it e.g.} \nTotsuji \\& Kihara 1969, Peebles 1974, Davis \\& Peebles 1983). These two\nquantities \nare based on the \nsecond-order moments of matter fluctuations. When the fluctuations are \nRandom Gaussian distributed, the two-point correlation function or the power\nspectrum contains full statistical information of the fluctuations.\n Even though the \ninitial seed of structure\nformation is often assumed to be random Gaussian distributed as\npredicted by the standard inflation scenarios (Guth \\& Pi 1982, Hawking\n1982, Starobinsky 1982), this simple assumption has not been\nobservationally established. Moreover, the cosmic structures observed today\nare more or less affected by nonlinear gravitational evolution. \nTherefore, only with\n these two quantities, we cannot study the large-scale structure properly.\n\n\nOther\nstatistical methods have been proposed and is expected to play\ncomplimentary roles to the \ntraditional analyses based on the second-order moment. The\nskewness parameter characterizes the asymmetry of one point\nprobability distribution function (PDF) of the density field and\nhas been investigated in deep (Peebles 1980, Fry 1984, Juszkiewicz,\nBouchet \\& Colombi 1993, Bernardeau 1994, Scoccimarro 1998, Seto\n1999). Beside higher-order moments \n(such as skewness),\nthere are other statistical \napproaches designed to directly measure the geometrical or \nmorphological aspects of galaxy clustering. Connectivity of the isodensity \ncontour is an interesting target for these approaches. For example,\n the genus statistics were proposed by\nGott, Melott \\& Dickinson (1986), the area statistics (equivalently the level\ncrossing statistics) by Ryden (1988), and percolation analysis by Klypin \n(1988). In addition, the Minkowski functionals recently attain much attention\n({\\it e.g.} Minkowski 1903, Mecke, Buchert \\& Wagner 1994, Schmalzing\n\\& Buchert 1997, Kerscher et al. 1997).\n\nTo analyze observed cosmic structures, \nsmoothing operation becomes crucially important in some cases. The\nobserved galaxies are \ndistributed in point-like manner, but geometrical or\nmorphological analyses, such as, the genus statistics, are usually based on \ncontinuous (smoothed) density field (see also Babul \\& Starkman 1992, \nLuo \\& Vishniac 1995). We have traditionally used filters\nwith spatially fixed smoothing \nradius for analyzing the large-scale\nstructure. \nEven though this method is the simplest from theoretical\npoint of views, other possibilities are worth investigated. \nThe local statistical fluctuations due to the discreteness of particles\nare determined by the number of particles contained in \n the smoothing kernel. If \nwe use a spatially fixed filter, we can measure smoothed quantities at\noverdensity regions relatively more accurately than at underdense\nregions. As a result, quality of information becomes\ninhomogeneous. This inhomogeneity is caused by the simple choice to\nspatially fix the smoothing radius.\nThere must be more efficient methods to resolve cosmic \nstructure from particle distribution (Hernquist \\& Katz 1989).\nActually,\nSpringel et al. (1998) have pointed out that the signal to noise ratio of\nthe genus statistics is considerably improved by using adaptive smoothing\nmethods.\nAdaptive methods are based on Lagrangian description, use nearly \nsame number of ``particles\" (mass elements) to construct smoothed\ndensity field (Hernquist \\& Katz 1989) and are expected to be less affected\nby discreteness of mass \nelements. Therefore, it seems reasonable that we can resolve cosmic structures\nmore efficiently, using these methods.\n\nIn this article, we perturbatively analyzed quantitative effects\ncaused by adaptive smoothing\nmethods. We pay \nspecial attention to three representative examples,\n the skewness parameter, the genus statistics and the area statistics.\n As the skewness is basically \n defined by the one point PDF, we can, in principle, \n discuss it without making\n continuous density field. But its analysis is very instructive to see \n nonlinear effects accompanied with adaptive smoothing methods.\n As a first step, \nwe mainly study the density field in real space and \ndo not discuss the effects of biasing (Kaiser 1984, Bardeen, Bond, Kaiser\n\\& Szalay 1986, Dekel \\& Lahav 1999). \n\nThis article is organized as follows. In \\S 2 we describe basic properties of\nthe adaptive smoothing and introduce its two main approaches. Then\nperturbative formulas are derived for each of them. In \\S 3 we discuss \nthe skewness parameters of the density field smoothed by these two \nadaptive methods.\nWe evaluate them using second-order \nperturbation theory. Some of results in this section can be\nstraightforwardly\n applied\nto the density field in the redshift space.\nThen we discuss weakly nonlinear effects of the genus and the area\nstatistics using the multidimensional Edgeworth expansion method explored by\nMatsubara (1994). To characterize the isodensity contour,\nparameterization based on the volume fraction above a given density\nthreshold is often adopted. In \\S 4.1 we discuss this parameterization in \nperturbative manner. In \\S 4.2 we explicitly evaluate the generalized\nskewness which is closely related to the genus and the area statistics. In\n\\S 4.3 and \\S 4.4, we\nshow the weakly nonlinear effects on these two statistics with various\nsmoothing methods. We make a brief summary in \\S 5.\n\n\n\n\n\n\n\\section{Adaptive Smoothing Method}\nThe (unsmoothed) density contrast field $\\delta(\\vex)$ at a point\n$\\vex$ is defined in terms\nof the mean density of the universe $\\bar{\\rho}$ and the local density\n$\\rho(\\vex)$ \nas\n\\beq\n\\delta(\\vex)=\\frac{\\rho(\\vex)-\\bar{\\rho}}{\\bar{\\rho}}.\n\\eeq\nIn this article we assume that the primordial density fluctuations obey\nRandom Gaussian distribution which is completely characterized by the (linear) \nmatter power \nspectrum. Unless we state explicitly, we limit our analysis in the real \nspace density field. But some of our\nresults are straightforwardly applied to the redshift space quantities, \nas shown in the next section.\n\nIsotropic filters with spatially constant smoothing radius $R$ have been\ntraditionally used to obtain continuous smoothed density field\n$\\delta_{FR}(\\vex) $ as follows\n\\beq\n\\delta_{FR}(\\vex)=\\int d\\vex' \\delta(\\vex')W(|\\vex'-\\vex|;R).\n\\eeq\nHere the function $W(\\vex;R)$ is a spatial filter function and the\nsubscript $F$ indicate the fixed smoothing. Most of theoretical\nanalyses in the large-scale structure have been based on this fixed smoothing \nmethod. As for the functional shape of $W(\\vex;R)$, two\nkinds of functions are often used ({\\it e.g.} Bardeen et al. 1986,\nMatsubara 1995).\n One is the Gaussian filter and defined as\n\\beq\nW(\\vex;R)=(2 \\pi)^{-3/2}R^{-3} \\exp\\lmk - {\\vex^2}/{2R^2}\\rmk.\n\\eeq\nThe other one is the top-hat filter and has a compact support as\n\\beqa \\\nW(\\vex;R)=\\cases{\n3/(4\\pi R^3) & $(|\\vex|\\le R)$ \\cr\n0 & $(|\\vex|> R).$ \\cr\n}\\eeqa\nIn this article we mainly use the Gaussian filter. This filter is useful \nfor quantifying the large-scale structure from observed noisy data sets.\nIn addition, algebraic\nmanipulations for the Gaussian filter are generally\n much simpler than for the top-hat filter. \n\nNext let us discuss the basic properties of adaptive smoothing methods \n(Hernquist \\& Katz 1989, Thomas \\& Couchman 1992, Springel et al. 1998).\nThe essence of these methods is to change the smoothing radius\n$R$ as a function of position $\\vex$ according to its local density contrast.\nWith a given spherically symmetric kernel $W$, we determine the\nsmoothing radius \n$R(\\vex)$ so that the total \nmass included within the kernel becomes constant.\n\\beq\n\\bar{\\rho}\\int d\\vex' (1+\\delta(\\vex'))R(\\vex)^3\nW(|\\vex'-\\vex|;R(\\vex))=\\bar{\\rho}R^3. \n\\eeq\nThe radius $R(\\vex)$ becomes smaller than the standard value\n$R$ in a overdense region and becomes\nlarger in a underdense region. In a system constituted by equal mass\nparticles as in standard N-body simulations, the smoothing radius $R(\\vex)$ is\ndetermined so that the total number of particles in a filter becomes \n constant. Thus adaptive smoothing is basically Lagrangian\n description and their smoothing radii \nare closely related to the resolution of spatial structures. \n\n \nWe can solve the variable smoothing radius \n $R(\\vex)$ in equation (5) by perturbatively expanding \nthe deviation \n$\\delta R(\\vex)\\equiv R(\\vex)-R$. In this procedure we regard\nthe density contrast $\\delta$ as the order\nparameter of the perturbative expansion. After some calculations we\n obtain the first-order solution \nas follows\n\\beq\n\\delta R(\\vex)=-\\frac13\\delta_{FR}(\\vex)R+O(\\delta^2).\n\\eeq\nThis simple result seems quite reasonable with the \nrelation below. \n\\beq\nR(\\vex)^3 (1+\\delta_{FR}(\\vex))=R^3 (1+O(\\delta^2)).\n\\eeq\nThis relation\n roughly shows that the total mass within the smoothing radius \n$R(\\vex)$ does not\ndepend on position $\\vex$.\n\nWith the variable smoothing radius $R(\\vex)$ (solution\nfor eq.[5]) we can\npractice adaptive smoothing. \nAs pointed out by Hernquist \\& Katz (1989) for the smoothed\nparticle hydrodynamics (SPH), there exist two different methods \n({\\it gather} and {\\it scatter} approaches) to\nassign the smoothed density contrast field\nat each point $\\vex$. The gather approach is simply use the solution\n$R(\\vex)$ at the point $\\vex$ in interest and the smoothed field is\n formally written as \n\\beq\n\\delta_{GR}(\\vex)=\\int d\\vex' \\delta(\\vex')W(|\\vex'-\\vex|;R(\\vex))-C(R),\n\\eeq\nthe subscript $G$ indicates the gather approach. In this case, the volume\naverage of the first term in the right hand side dose not vanish and we\nhave added a term $C(R)$ so that the total volume \naverage of $\\delta_{GR}(\\vex)$ becomes zero.\n\nIn the scatter approach we use the solution $R(\\vex')$ for each point where \na mass element exists. We can write down the smoothed field at $\\vex$ as\n\\beq\n\\delta_{SR}(\\vex)=\\int d\\vex' \\delta(\\vex')W(|\\vex'-\\vex|;R(\\vex')),\n\\eeq\nthe subscript $S$ represents the scatter approach. In this case the\nvolume average becomes zero. We only dilute the mass element at point\n$\\vex'$ with the density profile proportional to \n$W(|\\vex'-\\vex|;R(\\vex'))$ around that\npoint. \nNote that the spatial dependence of the smoothing radius $R(\\cdot)$ is\ndifferent between equations (8) and (9).\n\n\n\nNext we evaluate \n equations for $\\delta_{GR}(\\vex)$ and $\\delta_{SR}(\\vex)$ up to \nsecond-order of the density contrast \n$\\delta$ using perturbative solution of the smoothing radius \n $R(\\vex)=R+\\delta R(\\vex)$\ngiven in equation (6). The results are given as \n\\beqa\n\\delta_{GR}(\\vex)&=&\\delta_{FR}(\\vex)-\\frac13\\delta_{FR}(\\vex)R\\frac{\\p}{\\p \n R}\\delta_{FR}(\\vex)+\\frac16 R\\frac{d}{d \n R}\\sigma_R^2+O(\\delta^3),\\\\\n\\delta_{SR}(\\vex)&=&\\delta_{FR}(\\vex)-\\frac{R}3\\int d\\vex' \\p_R\nW(|\\vex'-\\vex|;R)\\delta(\\vex')\\delta_{FR}(\\vex') +O(\\delta^3).\n\\eeqa\nThe formula for the scatter approach is somewhat complicated, compared\nwith the gather approach. Also in numerical analysis, the scatter approach \nrequires higher computational costs (Springel et al. 1998). This reflects\n nonlocal character of the smoothing radius.\n\nEquations (10) and (11) show apparently that \n the corrections due to the adaptive methods start from \nsecond-order of $\\delta$. Therefore, their effects are expected to be\n comparable to \nsecond-order (nonlinear) effects predicted by cosmological gravitational\nperturbation theory (Peebles 1980, Fry 1984, Goroff et al. 1986).\n Adaptive smoothing methods modify the quantities \n which characterize the \nnonlinear mode couplings, such as the skewness parameter of density field.\n\n\nIf we use the Gaussian filter, the leading-order correction for the \n scatter approach is expressed \n as follows\n\\beq\n\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\n\\exp\\lkk-\\frac{(2\\vel^2+\\vek^2+2\\vek\\cdot \\vel)R^2}{2} \\rkk \\delta(\\vek)\n\\delta(\\vel)\\exp[i(\\vek+\\vel)\\cdot \\vex]\\frac{(\\vek+\\vel)^2R^2}{3}, \n\\eeq\nwhere $\\delta(\\vek)$ and $\\delta(\\vel)$ are the Fourier coefficients of\n the density contrast and defined as \n\\beq\n\\delta(\\vek)=\\int d\\vex\\delta(\\vex)\n\\exp(-i\\vek\\cdot\\vex).\n\\eeq\nFormula (12) is useful to quantitatively evaluate nonlinear effects\n caused by the scatter approach.\n\n\n\\section{Skewness}\nIn this section we investigate modifications of the skewness\nparameter $S$ caused by the two adaptive methods. Skewness is a fundamental\nquantities to \ncharacterize asymmetry of the one point PDF of the density \nfield (Peebles 1980, Fry 1984, Juszkiewicz,\nBouchet \\& Colombi 1993, Bernardeau 1994). It is defined as\n\\beq\nS=\\frac{\\lla \\delta^3\\rra}{\\sigma^4},\n\\eeq\nwhere the angular bracket $\\lla \\cdot\\rra$ represents to take the ensemble\naverage and $\\sigma(\\equiv\\lla \\delta^2\\rra^{1/2})$ is the rms\nfluctuation of $\\delta$. Here, we \ndiscuss the leading-order contributions for the numerator $\\lla\n\\delta^3\\rra$ and denominator $\\sigma^4$.\nAs we have already commented in \\S 1, the skewness\nparameter can be discussed \n without making continuous density field. It can be basically\ndefined by the count probability distribution function, and spatial\nrelation between one region and another one is unnecessary ({\\it e.g.}\nGazta$\\tilde{\\rm n}$aga 1992, Bouchet et al. 1993, Kim \\& Strauss 1998, and\nreferences therein, see also Colombi, Szapudi \\& Szalay 1998).\n Therefore our \neffort in this article to resolve cosmic structures by using the adaptive\nsmoothing might be irrelevant for observational determination of\nthe skewness parameter. But perturbative analysis in this section is\nvery useful to \ngrasp nonlinear effects caused by the adaptive smoothing methods and\nbecome basis for\nstudying statistics of isodensity contours such as the genus statistics or\nthe area statistics discussed in the next section.\n\n\nThe leading-order contribution for the rms fluctuation \n $\\sigma$ is written in terms of the linear (primordial) power\nspectrum $\\lla \\delta_1(\\vek) \\delta_1(\\vel)\\rra=(2\\pi)^3\\delta_{Drc}(\\vek+\\vel)P(k)$ ($ \\delta_1(\\vek)$ : linear\nmode, $\\delta_{Drc}(\\cdot)$: Dirac's delta function). With the Fourier transformed filter function $w(kR)$ we have\n\\beq\n\\sigma_R^2=\\lla \\delta^2_R(\\vex)\\rra=\\int\n\\frac{d\\vek}{(2\\pi)^3}P(k)w(kR)^2,\n\\eeq\nwhere the suffix $R$ is added to explicitly indicate the\nsmoothing radius $R$.\nThroughout in this article, we use power-law spectra $P(k)$ as\n\\beq\nP(k)=Ak^n,~~~-3<k\\le 1.\n\\eeq\nfor these scale-free models the normalization factor $A$ becomes\n irrelevant and we can \nsimply put $A=1$ below. Furthermore, as shown later, \n the skewness parameter does not\n depend on the smoothing radius in our leading-order analysis.\n From equation (15) we have the variance $\\sigma_R^2$ for the Gaussian\nfilter as\n\\beq\n\\sigma_R^2=\\int_0^{\\infty}\\frac{dk}{2\\pi^2}k^{n+2}e^{-k^2 R^2}=\\frac{R^{-n-3}}{(2\\pi)^{2}}\\Gamma\\lmk\\frac{3+n}{2} \\rmk. \n\\eeq\nThe integral (15) logarithmically diverges for $n=-3$, but skewness $S$\n is well-behaved in the limit\n $n\\to -3$ from above. As it shows interesting behavior at this specific\n spectral index, we also discuss quantities at $n=-3$ regarding them\n as the limit values.\n\nCalculation of the third-order moment $\\lla\\delta^3\\rra$ is more\ncomplicated than that of the variance $\\sigma^2$ discussed so far.\n When the initial fluctuation is random Gaussian distributed as\nassumed in this article, the \nlinear contribution for the third-order moment \nbecomes exactly zero due to the symmetric\ndistribution of the density contrast $\\delta$ around the origin\n$\\delta=0$. Nonlinear mode \ncouplings induce asymmetry in this distribution.\nTherefore, we resort to higher-order perturbation theory. The\nleading-order contribution for the \nskewness parameter without smoothing operation is\ngiven by Peebles (1980) in the case of Einstein de-Sitter background as\n\\beq\nS=\\frac{34}7.\n\\eeq\nIt is convenient to use the Fourier space representation to calculate\nthe third-order moment \n for the smoothed density field. Following the standard procedure, \nwe expand a nonlinear Fourier modes of overdensity $\\delta$ and the \n(irrotational) peculiar velocity field $\\veV$ as (Fry 1984, Goroff et al. 1986)\n\\beqa\n\\delta(\\vex)&=&\\delta_1(\\vex)+\\delta_2(\\vex)+\\cdots,\\nonumber\\\\\n\\veV(\\vex)&=&\\veV_1(\\vex)+\\veV_2(\\vex)+\\cdots,\n\\eeqa\nwhere $\\delta_1(\\vex)$ and $\\veV_1(\\vex)$ are the linear modes and\n$\\delta_2(\\vex)$ and $\\veV_2(\\vex)$ the\nsecond-order modes.\nWe perturbatively solve the continuity, Euler and Poisson\nequations,\n\\beqa\n\\frac{\\p}{\\p\n t}\\delta(\\vex)+\\frac{1}{a}\\nabla[\\veV(\\vex)\\{1+\\delta(\\vex)\\}]&=&0,\\nonumber\\\\ \n\\frac{\\p}{\\p\n t}\\veV(\\vex)+\\frac1a[\\veV(\\vex)\\cdot\\nabla]\\veV(\\vex)+\\frac{\\p_t\n a}a\\veV(\\vex)+\\frac1a\\nabla\\phi(\\vex)&=&0,\\nonumber\\\\\n\\nabla^2\\phi(\\vex)-4\\pi a^2\\rho(t)\\delta(\\vex)&=&0,\\nonumber\n\\eeqa\nwhere $a$ represents the scale factor.\nThe second-order solution in $\\vek$-space is given as \n\\beq\n\\delta_2(\\vek)=\\int\\frac{d\\vel}{(2\\pi)^3}\\delta_1(\\vel)\\delta_1(\\vek-\\vel) \nJ(\\vel,\\vek-\\vel),\n\\eeq\nor in $\\vex$-space\n\\beq\n\\delta_2(\\vex)=\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}e^{i\\vek\\cdot \n \\vex}\\delta_1(\\vel)\\delta_1(\\vek-\\vel) \nJ(\\vel,\\vek-\\vel),\n\\eeq\nwhere the kernel $J$ is defined by \n\\beq\nJ(\\vek,\\vel)=\n\\frac12(1+K)+\\frac{\\vek\\cdot\\vel}2\\lmk\\frac1{k^2}+\\frac1{l^2}\\rmk\n+\\frac12(1-K) \\frac{(\\vek\\cdot\\vel)^2}{k^2l^2}.\n\\eeq\nThe factor $K(\\Omega,\\lambda)$ weakly depends on the\ndensity parameter $\\Omega$ and cosmological constant $\\lambda$ as shown \nin the fitting formula (Matsubara 1995, see also Bouchet et al. 1992)\n\\beq\nK(\\Omega,\\lambda)\\simeq\\frac37\\Omega^{-1/30}-\\frac{\\lambda}{80}\\lmk1\n-\\frac32\\lambda\\log_{10}\\Omega\\rmk. \n\\eeq\nIn the ranges of two parameters $\\Omega$ and $\\lambda$\n\\beq\n0.1\\le \\Omega\\le1,~~~0.1\\le \\lambda\\le1,\n\\eeq\n the\ndifference of $K(\\Omega,\\lambda)$ from \n$K=3/7$ is within\n$8\\%$. Therefore, in the following analysis we basically study the \nEinstein de-Sitter background and use $K=3/7$.\n\nUsing the second-order solution (21) we can derive the well known formula for the\nthird-order moment as follows (Juszkiewicz et al. 1993) \n\\beq\n\\lla\\delta_R^3\\rra=6\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\nP(k) P(l)J(\\vek,\\vel)w(kR)w(lR) w(|\\vek+\\vel|R).\n\\eeq\nLet us simplify this six-dimensional integral $d\\vek d\\vel$. In the case of the\nGaussian filter \n\\beq\nw(kR)=\\exp(-k^2R^2/2),\n\\eeq\nwe can change $\\lla\\delta_R^3\\rra $ to the following form (Matsubara 1994)\n\\beq\n\\lla\\delta_R^3\\rra=\\frac3{28\\pi^4}(5I_{220}+7I_{131}+2I_{222}),\n\\eeq\nwhere we have defined\n\\beq\nI_{abc}=\\int_0^\\infty dk \\int_0^\\infty dl\\int_{-1}^1\ndu\\exp[-R^2(k^2+l^2+ukl)]k^al^bu^c P(k) P(l).\n\\eeq\nFor a power-law initial fluctuation $P(k)=k^n$, we obtain a final closed\nformula\n(Matsubara 1994, $\\L$okas et al. 1995)\n\\beq\nS_F(n)=3F\\lmk \\frac{n+3}2,\n\\frac{n+3}2,\\frac32;\\frac14\\rmk-\\lmk n+\\frac87\\rmk F\\lmk \\frac{n+3}2,\n\\frac{n+3}2,\\frac52;\\frac14\\rmk,\\label{a26}\n\\eeq\nwhere $F$ is the Hypergeometric function.\n\nIn the case of the top-hat filter whose Fourier transform is given by \n\\beq\nw(kR)=\\frac3{(kR)^3}(\\sin kR-kR\\cos kR),\n\\eeq\nthe final form of $S$ becomes very simple as follows (Juszkiewicz et al. 1993,\nBernardeau 1994)\n\\beq\nS_F(n)=\\frac{34}7-(n+3).\n\\eeq\nThis formula is not only valid for pure power-law initial fluctuations but\nalso for general power spectra with effective spectral index defined at \nthe smoothing radius $R$ as\n\\beq\nn\\equiv-\\frac{d\\ln \\sigma_R^2}{d\\ln R}-3.\n\\eeq\n\nEquations (29) and (31) are only the leading-order contribution and more\nhigher-order effects might \nchange them considerably. Thus it is quite important \nto compare these analytic formulas with fully nonlinear numerical\nsimulations and \nclarify validity of the perturbative formulas.\n There are many works on this topic and the\nanalytic predictions show surprisingly good agreement with numerical\nsimulations, even at $\\sigma\\sim1$ ({\\it e.g.} Baugh,\nGazta$\\tilde{\\rm n}$aga \\& Efstathiou 1995, Hivon et al. 1995,\nJuszkiewicz et al. 1995, $\\L$okas et al. 1995).\n\nSo far we have discussed skewness $S$ with fixed smoothing methods. For the\nthird-order moments $\\lla\\delta_R^3\\rra$, the second-order effects\ncaused by the \ngravitational evolution and that caused by the adaptive smoothing are\ndecoupled, as we can see from equations (10) and (11). Thus we can write the\nskewness parameter for adaptive methods in the following forms\n\\beqa\nS_{G}&=&S_{F}+\\Delta S_{G},\\\\\nS_{S}&=&S_{F}+\\Delta S_{S}.\n\\eeqa\nHere $\\Delta S_{G}$ and $\\Delta S_{S}$ are the correction terms caused\nby \nthe adaptive smoothing methods. In the next two subsections we\ncalculated these \nterms explicitly.\n\n\n\n\\subsection{Gather Approach}\nFirst we calculate the correction term $\\Delta S_{G}$ for the gather\napproach. With equation (10) this term is easily transformed to the\n following equation (see Appendix A.1 \nfor \nderivation)\n\\beq\n\\Delta S_G=-\\frac{d\\ln \\sigma_R^2}{d\\ln R}.\n\\eeq\nFor a power-law spectrum we have simple equation below \n\\beq\n\\Delta S_{G}(n)=(n+3).\n\\eeq\nIn derivation of equation (35)\n we only use Gaussianity of the one point PDF of\nthe linear smoothed field $\\delta_R$. Therefore, these formulas\n do not depend on the shape of the smoothing\nfilter nor the cosmological parameters $\\Omega$ or\n$\\lambda$. Furthermore they are valid also \n in the redshift space, if we use the the distant observer\napproximation. Thus equation (35) has strong predictability.\n\n\nHivon et al. (1995) perturbatively examined the skewness parameters in\nredshift space \nand evaluate them both for the top-hat filter and the \n Gaussian filter. They also compared their analytic results with\n numerical results. They found that\n these two show agreement only in the range $\\sigma\\lsim 0.1$, in\n contrast to the skewness parameter in the real space \n $\\sigma\\lsim1.0$. They commented that this limitation is mainly due to the\n finger of god effects ({\\it e.g.} Davis \\& Peebles 1983).\n\n\nHere we use their analytic results\n and combine our new formula with them. In figure 1 we\npresent the skewness parameters for various spectral indexes $n$ both in\n the real\nand redshift spaces. For simplicities we limit our analysis for the Einstein\n de-Sitter background.\n\nFor the Gaussian filter, the skewness parameter \n by the gather method is a increasing\nfunction of spectral index $n$ both in real and redshift spaces. This\ndependence is contrast to the skewness with\nthe fixed smoothing method. \nComparing the skewness in the real and the redshift spaces, \n$n$ dependence of the gather method is \n somewhat weaker in real space than in redshift space, but this tendency is\n also different \n from the fixed smoothing. \n\n\nFor the top-hat filter, there is no spectral index $n$- dependence in\n the real space.\n We have $S=34/7$ which is the same as the unsmoothed value (Peebles\n 1980). Bernardeau (1994) pointed out that the skewness $S$ filtered with\n the top-hat filter in\n Lagrangian space does not depend on the power spectrum and is given by\n $S=34/7$.\nAs the adaptive smoothing is basically Lagrangian description, this fact\nseems reasonable. \nIn the case of the \nredshift space we have a fitting formula below\n\\beq\nS_G(n)=\\frac{35.2}7-0.15(n+3),~~~({\\rm Einstein~de~Sitter~background})\n\\eeq\nwhich is based on formula (49) of Hivon et al (1995).\nAgain $n$ dependence is very weak and\n becomes weaker for $\\Omega<1$ (see Fig.4 of Hivon et\nal. 1995). \n Finally, we comment the possibility that our\nperturbative treatment of the redshift space skewness becomes\nworse in the adaptive methods than in the fixed smoothing method. In the\nadaptive methods, smoothing radius of a high density region becomes\nsmaller and the (strongly nonlinear) finger of god effects might not be\nsuppressed well. \n\n\n\n\n\\subsection{Scatter Approach}\nNext we calculate the correction term $\\Delta S_S$ for the scatter\napproach. We only discuss the real space density field smoothed with the\nGaussian filter (eq.[3]). From\nequation (12) we obtain the following equation (see Appendix A.1),\n\\beq\n\\Delta S_{SR}(n)\\sigma_R^4=2\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\n\\exp\\lkk-\\frac{(3\\vel^2+2\\vek^2+2\\vek\\cdot \\vel)R^2}{2} \\rkk\nP(k)P(l){(\\vek+\\vel)^2} R^2.\n\\eeq \nThe six dimensional integral $d\\vek d\\vel$ is simplified to a\nthree dimensional integral $dkdldu$ as in equations (25) and (28). Then we\nhave the following relation\n\\beqa\n\\Delta S_{SR}(n)\\sigma_R^4&=&\\frac1{4\\pi^4}\\int_0^\\infty\n{dk}\\int_0^\\infty{dl}\\int_{-1}^1du \n\\exp\\lkk-\\frac{(3l^2+2k^2+2klu)R^2}{2} \\rkk \\nn\\\\\n& &\\times k^2 l^2\nP(k)P(l){(k^2+l^2+2klu)} R^2.\n\\eeqa\nFor a pure-power law fluctuation we obtain the following\nanalytic formula\n\\beqa\n\\Delta S_{S}(n)&=&-2^{(n+3)/2}3^{-(n+5)/2} (n+3) \\bigg\\{\n \\frac23(n+3)F\\lmk\\frac{5+n}{2}, \\frac{5+n}{2},\\frac{5}{2},\\frac{1}{6} \\rmk \\nn\\\\\n& & - {5}\nF\\lmk \\frac{3+n}{2}, \\frac{5+n}{2},\\frac{3}{2},\\frac{1}{6}\\rmk \\bigg\\}.\n\\eeqa\n\\if0%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\beqa\n\\Delta S_{S}(n)&=&-2^{(n+3)/2}3^{-(n+5)/2} \\bigg\\{ 12F\\lmk\\frac{3+n}{2},\n \\frac{3+n}{2},\\frac{1}{2},\\frac{1}{6}\\rmk\\nn\\\\ & & - 12F\\lmk\\frac{3+n}{2},\n \\frac{3+n}{2},\\frac{3}{2},\\frac{1}{6} \\rmk\n- {5(3+n)} \nF\\lmk \\frac{3+n}{2}, \\frac{5+n}{2},\\frac{3}{2},\\frac{1}{6}\\rmk \\bigg\\}\n\\eeqa\n\\fi%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nIn contrast to the previous gather approach, this result is valid only to\n the real space skewness with the Gaussian filter. In table 1 we\n present numerical values of $\\Delta S_{S}(n)$. In figure 2 we show\n $ S_{S}(n)$ as a function of the spectral index $n$.\nWe can see that \n$n$ dependence is similar to the gather approach but now it becomes weaker.\nIf we change $n$ from $-3$ to $-1$, skewness $S$ changes $\\sim 25\\%$ for the \n scatter approach, $\\sim 45\\%$ for the gather approach, and $\\sim 38\\%$\n for the fixed smoothing.\n\n\n\\section{Statistics of Isodensity Contour}\nThe genus number is a topological quantity and defined\nby the number of the homotopy classes of closed curves that may be drawn \non a surface without cutting them into two pieces. This definition\nseems highly mathematical, but there are more intuitive methods to count \nthe \ngenus number. First one is to notice the number of holes and\nisolated regions of the surface in interest. Second one is to count \nstationary points of the surface along one spatial direction (Adler\n1981, Bardeen et al. 1986).\nWith these equivalent methods, we can calculate the genus density as\nfollows\n\\beqa\n{\\rm Genus~ density}&=&\\frac{N({\\rm holes})-N({\\rm isolated\n ~regions})}{\\rm volume}\\\\\n &=&-\\frac{N({\\rm maxima})+N({\\rm minima})-N({\\rm saddle~\n points})}{\\rm2\\times volume}.\n\\eeqa\n For example, in the case\nof one-sphere, we have $N({\\rm holes})=0$ and $N({\\rm isolated\n ~regions})=1$ and genus number becomes $-1$. We obtain the same result \n with equation (42). \nThe genus number density of isodensity contour of the large-scale\nstructure is a powerful measure to quantify connectivity of galaxy\nclustering, such as, filamentary networks, sheet-like or bubble-like\nstructures. The genus density of a high density contours\nis expected to be\n negative as the surfaces would \nshow disconnected meatball-like structure. But the genus density for\ncontours around the mean density $\\delta\\sim0$ would be positive as\nthey would \nlook like highly connected sponge-like structure (Gott, Melott \\&\nDickinson 1986). \nThe genus density as a function of the matter density threshold is called\nthe genus \nstatistics and has been widely investigated both numerically and\nobservationally \n(Gott, Weinberg \\& Melott 1987, Weinberg, Gott \\& Melott 1987, Melott,\nWeinberg \\& Gott 1988, Gott et al. 1989, Park \\& Gott 1991, Park, Gott\n\\& da Costa 1992, Weinberg \\& Cole 1992, Moore et al. 1992, Vogeley,\nPark, Geller, Huchra \\& Gott 1994, Rhoads, Gott \\& Postman 1994,\nMatsubara \\& Suto 1996, Coles, Davies \\& Pearson 1996, Sahni et\nal. 1997, \nProtogeros \\& Weinberg 1997, Coles, Pearson, Borgani, Plionis \\&\nMoscardini 1998, Canavezes et\nal. 1998, Springel et al. 1998)\n\nUsually we use the local expression (42) to analytically study the genus\nstatistics. For the genus density of isodensity contour at\n$\\nu\\equiv \\delta/\\sigma$, this expression is written as follows\n(Doroshkevich 1970, Adler 1981, Bardeen et al. 1986, Hamilton, Gott \\&\nWeinberg 1986)\n\\beq\nG(\\nu)=-\\frac12\\lla\\delta_{Drc}[\\delta(\\vex)-\\nu\\sigma]\\delta_{Drc}[\\p_1\\delta(\\vex)]\\delta_{Drc}[\\p_2\\delta(\\vex)]|\\p_3\\delta(\\vex)|(\\p_{11}\\delta(\\vex)\\p_{22}\\delta(\\vex)- \n\\p_{12}\\delta(\\vex)^2 \n) \\rra,\n\\eeq \nwhere $\\delta_{Drc}(\\cdot)$ represents the Dirac's delta function. The\nfirst one $\\delta_{Drc}[\\delta(\\vex)-\\nu\\sigma]$ specifies the contour\n$\\nu\\equiv \\delta/\\sigma$. The second and third ones\n$\\delta_{Drc}[\\p_1\\delta(\\vex)]$, $\\delta_{Drc}[\\p_2\\delta(\\vex)]$\nspecify the stationary points along $x_3$ direction. The term \n$(\\p_{11}\\delta(\\vex)\\p_{22}\\delta(\\vex)- \n\\p_{12}\\delta(\\vex)^2 \n)$ is the determinant of the Hesse-matrix and assigns proper\nsignatures for the stationary points corresponding to signs of equation \n(42). Even though equation (43) introduces a specific spatial direction\n($x_3$-axis), Seto et al. (1997) derived a\nrotationarilly symmetric formula, and studied nonlinear evolution of\nthe genus statistics using the Zeldovich approximation (Zeldovich 1970)\n\nIn the case of an isotropic random Gaussian fluctuation which is usually\nassumed as the initial condition of the structure formation, the\ncomplicated formula (43) is simplified to (Doroshkevich 1970, Adler 1981,\nBardeen et al. 1986, Hamilton, Gott \\& \nWeinberg 1986)\n\\beq\nG(\\nu)=\\frac1{(2\\pi)^2}\\lmk\\frac{\\sigma_1^2}{3\n \\sigma^2}\\rmk^{3/2} e^{-\\nu^2/2}(1-\\nu^2),\n\\eeq\nwhere $\\sigma_1^2$ is defined as\n\\beq\n\\sigma_1^2=\\lla(\\nabla\\delta)^2 \\rra=\\frac1{2\\pi^2}\\int_0^\\infty dk\nP(k)k^4 w(kR)^2.\n\\eeq\nNonlinear evolution of the genus statistics had been studied using N-body\nsimulations, but most analytical predictions for the genus statistics have been based on\nthe linear formula (44). To compare it with observed distribution of\ngalaxies we have to use sufficiently large smoothing radius to reduce\nnonlinearities. However, such a large smoothing radius is not\nstatistically preferable for the finiteness of our survey volume. \n\nMatsubara (1994) improved this difficulty by taking into account of weakly \nnonlinear \neffects in the genus statistics (see also Hamilton 1988, Okun 1990, \nMatsubara \\& Yokoyama 1996,\nSeto et al. 1997). He used the multidimensional Edgeworth\nexpansion method and added the first-order nonlinear correction to\nthe linear formula. His result is written as \n\\beq\nG(\\nu)=-\\frac1{(2\\pi)^2}\\lmk \\frac{\\sigma_1^2}{3\n \\sigma^2}\\rmk^{3/2}e^{-\\nu^2/2}\\lkk H_2(\\nu)+\\sigma \\lmk\\frac{S}6\nH_5(\\nu) +\\frac{3T}{2} H_3(\\nu) +3UH_1(\\nu) \\rmk+O(\\sigma^2)\\rkk.\n\\eeq\nThis formula is valid for statistically isotropic and homogeneous\nweakly random Gaussian fields.\nHere functions \n$H_n(\\nu)\\equiv (-1)^ne^{\\nu^2/2}(d/d\\nu)^n e^{-\\nu^2/2}$\nare the Hermite polynomials,\n\\beqa\nH_0(x)&=&1,~~H_1(x)=x,~~~H_2(x)=x^2-1,\\nn \\\\\nH_3(x)&=&x^3-3x,~~H_5(x)=x^5-10x^3+15x.\n\\eeqa\nIn equation (46), $S$ is the skewness parameter discussed in the previous\nsection. $T$ and $U$ are called the generalized skewness parameters and \ndefined by\n\\beqa\nT&=&-\\frac1{2\\sigma^2\\sigma_1^2}\\lla\\delta^2\\Delta\\delta\\rra, \\nn \\\\\nU&=&-\\frac3{4\\sigma_1^4}\\lla\\nabla\\delta\\cdot\\nabla\\delta\\Delta\\delta\\rra. \n\\eeqa\nMatsubara \\& Suto (1996) examined the perturbative formula (46) using\nN-body simulations. For power-law spectra with $n=1,0$ and $-1$, they found\nthat this formula are in reasonable agreement with numerical results\n in the range $-0.2\\lsim\n\\nu\\sigma\\lsim 0.4$. \n\nNext let us briefly summarize the area statistics $N_3(\\nu)$ which were\nproposed by Ryden (1988) and investigated detailedly by Ryden et \nal. (1989).\nThe area statistics are defined as the mean area of isodensity contour\nsurface per unit volume. For statistically homogeneous and isotropic\nfluctuations, the area statistics are equal to twice the mean number of\nisodensity contour crossings along a straight line of unit length. \nThese two statistics are thus equivalent (beside factor 2), but the\ncontour crossing statistics are easier to compute numerically (Ryden 1988). \n\nAs in equation (43), the area statistics for isodensity contour\n$\\delta=\\nu\\sigma$ is \nwritten as\n\\[\nN_3(\\nu)=\\lla \\delta_{Drc}[\\delta(\\vex)-\\nu\\sigma]|\\nabla\\delta(\\vex)|\\rra.\n\\]\nIn the case of isotropic Random Gaussian fluctuations, we have the following \nformula (Ryden 1988)\n\\beq\nN_3(\\nu)=\\frac2\\pi \\lmk\\frac{\\sigma_1^2}{3\\sigma^2} \\rmk^{1/2}e^{-\\nu^2/2}.\n\\eeq\n\nWeakly nonlinear effects on the area statistics can be discussed \n with a similar technique used to derive equation (46) (Matsubara\n 1995). In this \ncase, we need information of the density field up to its first spatial\nderivative and nonlinear correction is expressed in terms of\n two parameters $S$ and $T$ as follows\n\\beq\nN_3(\\nu)=\\frac2\\pi \\lmk\\frac{\\sigma_1^2}{3\\sigma^2}\n\\rmk^{1/2}e^{-\\nu^2/2}\n\\lkk 1+\\sigma\\lmk\\frac{S}6 H_3(\\nu)+\\frac{T}2H_1(\\nu) \\rmk +O(\\sigma^2)\\rkk.\n\\eeq\n\n\nIn the rest of this section we consider nonlinear effects of the\nadaptive smoothing methods on the \ngenus and the area statistics. We calculate the generalized skewness parameters $T$\nand $U$ both for the gather approach and the scatter approach.\nWe limit our analysis to the real space density field smoothed by\nGaussian filters.\n\n\n\\subsection{Reparameterization of Isodensity Contour}\n\nEquation (46) is weakly non-Gaussian genus density for isodensity\ncontour surfaces\nparameterized by the simple definition $\\nu=\\delta/\\sigma$. There is another \nconventional \nmethod to name contour surfaces. In this method, we notice the volume\nfraction \n$f$ above the density threshold of the contour in interest ({\\it e.g.}\nGott, Melott \\& Dickinson 1986, Gott et al. 1989), and \nparameterize the\ncontour using value $\\nu_r$ defined by \n\\beq\n\\nu_r\\equiv {\\rm erf}^{-1}(f),\n\\eeq\nwhere the suffix $r$ indicates `` reparameterization'' and ${\\rm erf}(x)$\nis the error \nfunction defined by\n\\beq\n{\\rm erf}(x)\\equiv \\frac1{\\sqrt{2\\pi}}\\int_x^\\infty dy e^{-y^2/2}.\n\\eeq\nThis procedure is a kind of Gaussianization. Two methods coincide\n$\\nu=\\nu_r$ when the one point PDF\n$P(\\nu)$ is Gaussian distributed. If we use this new parameterization,\nthe \ngenus curve is \napparently \ninvariant under a monotonic mapping of the density contrast field\n$\\delta$. Furthermore, it has been long known that the genus curve\nwith $\\nu_r$\nparameterization\n(51) nearly keeps its original symmetric shape (eq.[44]) in the course of\n weakly nonlinear gravitational\nevolution \nof density field ({\\it e.g.} Springel et al. 1998 and references\ntherein). Almost the same \nkind of tendency has been confirmed for the area statistics (Ryden et\nal. 1989). Weakly nonlinear area density with $\\nu_r$ parameterization \n remains at its linear shape very well. Here, let us\nrelate these two parameterization methods for \n weakly nonlinear regime. Using the Edgeworth expansion method, the one\npoint PDF $P(\\nu)$ is written in terms of the skewness $S$ up to the\nfirst-order \nnonlinear correction \n\\beq\nP(\\nu)=\\frac1{\\sqrt{2\\pi}}e^{-\\nu^2/2}\\lkk\n1+\\frac{\\sigma S}6H_3(\\nu)+O(\\sigma^2)\\rkk. \n\\eeq\nJuszkiewicz et al. (1995) examined this approximation using N-body\nsimulations. They found that the above formula is accurate until\n$\\sigma S$ reaches 1. Therefore the inequality\n\\beq\n\\sigma\\lsim S^{-1}\\sim0.2,\n\\eeq\n would be a standard for the validity of the\nperturbative analysis in this subsection.\nThe volume fraction $f(\\nu)$ above the threshold $\\delta=\\nu\n\\sigma$ is given by\n\\beq\nf(\\nu)=\\int_\\nu^\\infty dx P(x)=\n{\\rm erf}(\\nu)+\\frac{\\sigma S}{6\\sqrt{2\\pi}}\\lnk e^{-\\nu^2}(\\nu^2-1)\n\\rnk+O(\\sigma^2).\n\\eeq\nWith equations (51) and (55) we obtain correspondence\nbetween $\\nu$ and $\\nu_r$ as follows\n\\[\n\\nu=\\nu_r+\\frac{\\sigma S}6 \\lnk\\nu_r^2-1 \\rnk+O(\\sigma^2).\n\\]\nFinally the genus density $G_r(\\nu_r)$ in this new parameterization is\ngiven by $G(\\nu)=G_r(\\nu_r)$ and written as\n\\beqa\nG_r(\\nu_r)&=&-\\frac1{(2\\pi)^2}\\lmk \\frac{\\sigma_1^2}{3\n \\sigma^2}\\rmk^{3/2}e^{-\\nu_r^2/2}\\bigg[ H_2(\\nu_r)+\\sigma \\bigg(\nH_3(\\nu)\\lmk-S+\\frac32 T\\rmk \\nn\\\\\n& & +H_1(\\nu)(-S+3U) \\bigg)+O(\\sigma^2)\\bigg].\n\\eeqa\n\nSimilarly we have the following result for the area statistics\n\\beq\nN_{3r}(\\nu_r)=\\frac2\\pi \\lmk\\frac{\\sigma_1^2}{3\\sigma^2}\n\\rmk^{1/2}e^{-\\nu_r^2/2}\n\\lkk 1+\\sigma\\lmk-\\frac{S}3 +\\frac{T}2 \\rmk H_1(\\nu_r)+O(\\sigma^2) \\rkk.\n\\eeq\nIn this case, the first nonlinear correction is simply proportional to\n$\\nu_r$ (see eq.[47]) and it completely vanishes when we have $S=3/2T$.\n\n\n\nLater in \\S 4.3 and \\S4.4, we will confirm that the nonlinear correction\n(proportional to $\\sigma$) for the genus and area statistics with the \n fixed smoothing method are very small for $\\nu_r$ parameterization,\nas experientally known in N-body simulations. \nIn the followings, we use these two parameterizations $\\nu$ and $\\nu_r$.\n\n\n\n\\subsection{Generalized Skewness}\nThe generalized skewness $T$ and $U$ are basic ingredients to\nperturbatively evaluate the weakly non-Gaussian effects on the\n genus and the area statistics. For the Gaussian\nfilter with a fixed smoothing radius, explicit formulas\nvalid for the power-law initial\nfluctuations\n were derived by Matsubara\n(1994).\nThey are given as follows\n\\beqa\nT_{FR}&=&\n3F\\lmk \\frac{n+3}2,\\frac{n+5}2,\\frac3 2,\\frac14 \\rmk\n-\\lmk n+\\frac{18}7\\rmk F\\lmk \\frac{n+3}2,\\frac{n+5}2,\\frac5 2,\\frac14\n\\rmk\\nn\\\\\n& &+\\frac{4(n-2)}{105}F\\lmk \\frac{n+3}2,\\frac{n+5}2,\\frac7 2,\\frac14\n\\rmk,\\\\\nU_{FR}&=&F\\lmk \\frac{n+5}2,\\frac{n+5}2,\\frac5 2,\\frac14\\rmk\n-\\frac{7n+16}{35} F\\lmk \\frac{n+5}2,\\frac{n+5}2,\\frac7 2,\\frac14\n\\rmk.\n\\eeqa\nAs shown in the case of \n the skewness parameter $S$ analyzed in \\S 3.1 and \\S 3.2, the \nsecond-order (first nonlinear) effects caused by the adaptive smoothing \nmethods are decoupled from those induced by gravitational mode\ncouplings. Thus we can calculate them separately and express the total\nvalues in forms similar to equations (33) and (34). \n\nFirst, we analyze correction terms $\\Delta T_{GR}$\nand $\\Delta U_{GR}$ for the gather approach. We define these terms\nby the following equations\n\\beq\n T_{GR}= T_{FR}+\\Delta T_{GR},~~ U_{GR}= U_{FR}+\\Delta U_{GR}.\n\\eeq\n After some tedious algebra using equation (10), we obtain the\n leading-order correction terms as follows (Appendix A.2)\n\\beqa\n\\Delta T_{GR}&=&\\frac23(n+4),\\\\\n\\Delta U_{GR}&=&\\frac13(n+5).\n\\eeqa\nThese results are similar to the correction term for the \nskewness $\\Delta S_{GR}=n+3$ (eq.[36]) which\ndoes not depend on the shape of the filter function. However, \nsituation is not so much \nsimple here. For the Gaussian filter we have the following relation, \n\\beq\nR\\frac{\\p \\delta_R(\\vex)}{\\p R}=R^2\\Delta_{x} \\delta_R(\\vex).\n\\eeq \nThis relation plays important roles to derive equations (61) and (62). But\nit does not hold for general filter functions and the simple results given in \nequations (61) and (62) are\nspecific to the Gaussian filter.\nWe summarize numerical data for the parameters$T_{GR}$ and $U_{GR}$ in Table 3.\n\nGeneralized skewness for the gather approach is much more\ncomplicated. If we write down them in the form \n\\beq\nT_{SR}=T_{SR}+\\Delta T_{SR},~~~\nU_{SR}=U_{SR}+\\Delta U_{SR},\n\\eeq\ncorrection terms $\\Delta T_{SR}$ and $\\Delta U_{SR}$ are written in the manner similar to equation (39) as\nfollows (Appendix A.3)\n\\beqa\n-2\\Delta T_{SR}(n)\\sigma_R^2\\sigma_{1R}^2&=&\\frac1{6\\pi^4}\\int_0^\\infty\n{dk}\\int_0^\\infty{dl}\\int_{-1}^1du \n\\exp\\lkk-\\frac{(3l^2+2k^2+2klu)R^2}{2} \\rkk \\nn\\\\\n& &\\times k^2 l^2\nP(k)P(l){(k^2+l^2+2klu)}{(k^2+l^2+klu)} R^2,\\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%\n-\\frac43\\Delta U_{SR}(n)\\sigma_{1R}^4&=&\\frac1{6\\pi^4}\\int_0^\\infty\n{dk}\\int_0^\\infty{dl}\\int_{-1}^1du \n\\exp\\lkk-\\frac{(3l^2+2k^2+2klu)R^2}{2} \\rkk \\nn\\\\\n& &\\times k^4 l^4\nP(k)P(l){(k^2+l^2+klu)} (1-u^2) R^2.\n\\eeqa\nWe can calculate them explicitly as follows\n\\beqa\n\\Delta T_{SR}&=&{2^{(n+5)/2} 3^{-(n+9)/2}}\\bigg[4(n+3)F\\lmk\n\\frac{n+5}2,\\frac{n+5}2,\\frac52,\\frac16 \\rmk\\nn \\\\\n& &~~~+\\frac52{(n+3)(n+5)}F\\lmk\n\\frac{n+5}2,\\frac{n+7}2,\\frac52,\\frac16 \\rmk \\nn\\\\\n& &~~~-\\frac{13(n+5)}2F\\lmk\\frac{n+3}2,\\frac{n+7}2,\\frac32,\\frac16\n\\rmk\\nn\\\\\n& &~~~\n-12(n+3)F\\lmk\\frac{n+5}2,\\frac{n+5}2,\\frac32,\\frac16 \\rmk\\bigg],\\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\Delta U_{SR}&=& -2^{(n+5)/2} 3^{-(n+5)/2}\\bigg[4\nF\\lmk\\frac{n+5}2,\\frac{n+5}2,\\frac52,\\frac16 \\rmk \\nn \\\\\n& &~~~+\\frac{5(n+5)}9\nF\\lmk\\frac{n+5}2,\\frac{n+7}2,\\frac52,\\frac16 \\rmk\\nn \\\\\n& &~~~-4F\\lmk\\frac{n+5}2,\\frac{n+5}2,\\frac32,\\frac16 \\rmk\n\\bigg].\n\\eeqa\n\n\nWe present numerical data of the parameters $T_{SR}$ and $U_{SR}$ in Table 4.\nNote that the magnitude of\n generalized skewness $T$ and $U$ becomes very small in the\nscatter approach. \nThis fact becomes important in the next subsection.\n\n\n\\subsection{Weakly Nonlinear Genus Statistics}\nIn figures 3 to 5, we show the weakly nonlinear genus density smoothed\n by\n three\ndifferent methods (fixed, gather and scatter), using two types of\nparameterizations $\\nu$ and $\\nu_r$. All of these curves\nare smoothed by the Gaussian filter (eq.[3]). We plot the normalized \ngenus curves \\footnote{Note that the amplitude of $G(0)$ or $G_r(0)$ are\n not changed by the \n first-order correction of $\\sigma$.} $G(\\nu)/G(0)$ or $G_r(\\nu_r)/G_r(0)$ to see deviation\n from the symmetric\nlinear genus curve $\\propto (1-\\nu^2)\\exp(-\\nu^2/2)$. \n Upper panel of figure 3 is essentially same as Fig.1 of\nMatsubara (1994).\n\nFirst, comparing upper and bottom panels of \nFig.3, we can confirm the fact experientally \nknown in N-body\nsimulations. Weakly nonlinear genus curves for the fixed smoothing method\n are very close to the linear\nsymmetric shape in the case of $\\nu_r$ parameterization ({\\it e.g.}\nSpringel et al. 1998). For a spectral index with\n$n\\sim -1$, three curves for \n$\\sigma=0,0.2$ and $0.4$ are nearly degenerated.\n\nIn Fig.4 we present genus curves with the gather smoothing. From Figs.3 and\n4 it is apparent that deviations from the linear curves become larger in the\ngather approach, especially in tail parts. But these deviations become\nsmaller with using parameter $\\nu_r$.\n\nBottom panel of \nFig.4 is calculated under conditions (gather approach and parameter\n$\\nu_r$) similar to Fig.7 of Springel et al. (1998) which is\n obtained from N-body\nsimulations. However overall shapes of these two are different. The minimum\nvalue of $G_r(\\nu_r)$ are attained around the point \n$\\nu_r\\sim1.5$ in our result, but\nthis point is $\\nu_r \\sim -1.5$ in theirs. \nThis difference might be caused by the difference of adopted filter\nfunction. We use the Gaussian filter but a different kernel (a spline\nkernel that is often used in SPH simulations) is adopted in their calculation\n(Monaghan \\& Lattanzio 1985).\n\n \nIn figure 5 we show results for the scatter approach. Nonlinear effects \nare more prominent than two cases analyzed earlier. As shown in\nequations (46) and (56), nonlinear correction of the genus curves are\nwritten by combination of terms proportional to parameters $S$, $T$ and\n$U$. Some \nof their contribution cancel out, as realized in the case of the fixed or gather smoothing\nmethods. However, amplitude of parameters $T$ and $U$ for the scatter\napproach \nbecomes very small (see\nTable 4), and cancellation becomes weaker.\n\nBased on the definition of the genus density (eq.[41]), nonlinear evolution\nof isodensity contours is sometimes described with such terminologies as,\nsponge-like (connected topology) or meatball like (disconnected\ntopology). In the case of Random Gaussian initial \nfluctuations, linear theory predicts symmetry of the genus statistics\n with respect to the sign \nof density contrast $\\delta$,\n and geometry of both high and low density tails look \n meat-ball like with negative genus density. \nIf we use the fixed or gather smoothing methods, nonlinear\n effects make the genus number of a high density contour ({\\it e.g.}\n $\\nu=2$) smaller, and topology of that region \nbecomes more meatball-like (see figures 3 and 4). In contrast,\ncontour of low density threshold ({\\it e.g.} $\\nu=-2$) is transformed\nin the direction of \nsponge-like topology, as quantified by the increase of genus number density (see\nfigures 3 and 4). \n\nIt is not easy to understand behaviors of Fig.5 for the scatter\napproach. But, changing point of views, we can discuss characters of\nthis approach by comparing figures for various smoothing methods. To\ncharacterize nonlinear effects \naccompanied with the scatter approach, we apply the topological\ninterpretation mentioned \nin the last paragraph. As shown in Fig.6 where various smoothing\nmethods are compared, the scatter approach makes low density regions more\nmeatball-like.\nBut high density regions are transformed in the opposite direction.\nThis trend shows remarkable contrast to the nonlinear gravitational effects\ntraced by the simple fixed smoothing method. \n\n\\if0%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n This is a remarkable difference from nonlinear\ngravitational effects traced by the simple fixed smoothing method. \n This drastic change is mainly due to large value of the\nparameter $U$ in this approach. Around the origin $\\nu\\sim 0$, the\nmagnitude of the weakly nonlinear correction is decided by the\ncoefficient of $\\nu$ in equation (46). They are given by (see \neqs.[46][47])\n\\beq\n\\sigma(2.5S-4.5T+3U).\n\\eeq\nFor $\\nu_r$ parameterization, we have\n\\beq\n\\sigma(2S-4.5T+3U).\n\\eeq\nAs shown in Tables 3 and 4, we typically have $U_F\\sim1.3$ and\n$U_G\\sim4.1$, but $U_S$ is as large \nas $\\sim9$. From these results, we can state that perturbative analysis \nof the genus statistics \nbased on the multidimensional Edgeworth expansion is not suitable for\nthe scatter approach.\n\\fi%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\n\\subsection{Weakly Nonlinear Area Statistics}\nIn Figs.7 to 9, we plot the weakly nonlinear area statistics, using equation\n(50) for $\\nu$ parameterization and equation (57) for $\\nu_r$\nparameterization. As in the analysis of the genus statistics, we\nnormalize amplitude of the area density by $N_3(0)$ or $N_{3r}(0)$.\nComparing upper and bottom panels of figure 7, it is apparent that \n$\\nu_r$ parameterization is very effective to keep the original \nlinear shape against\nweakly nonlinear effects. This fact has been confirmed experimentally in \nN-body simulations (Ryden et al. 1989) and is quite\n similar to the situation in the\ngenus statistics explained in previous subsection. With $\\nu_r$ parameterization (bottom panel of Fig.7), three\ncurves for $\\sigma=0,0.2$ and $0.4$ are almost completely\noverlapped for all spectral indexes $n$. This fact seems reasonable as we have $S_F\\simeq3/2T_F$ for\nthe fixed smoothing method (see eq.[57] and Tables 1, 3).\n\n\nIf we use the adaptive smoothing methods, weakly nonlinear correction on\n$N_3(\\nu)$ ($\\nu$ parameterization) are considerable as\nshown in upper panels of Figs.8 and 9. \nThis correction becomes apparently smaller for the gather approach, but\nnot for the scatter approach.\n We have already commented\nthat the first-order nonlinear correction for the area statistics is\ncharacterized by two parameters $S$ and $T$. For the scatter approach,\n$T$ parameter is very small for spectral indexes $n>-1$, and cancellation\nmentioned in \\S 4.3 is not effective.\n\n\n\\if0%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nFor the adaptive smoothing methods, $\\nu_r$ parameterization does not\nremove the nonlinear effects so clearly as in the case of\n the fixed smoothing method.\nBut this parameterization is very effective, compared with its\nperformance in the genus statistics. Even for $\\sigma=0.4$, deviation of \n$N_{3r}(\\nu)/N_{3r}(0)$ from its linear value $e^{-\\nu_r^2/2}$ (eq.[49]) \nis within $0.1$ for two adaptive methods. For the scatter\napproach this deviation\n becomes smaller for a larger spectral\nindex $n$ ($-2\\le n\\le1$), but it very weakly depends on $n$ for the gather\napproach. \n\\fi%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\n\\section{Summary}\nObservational analysis of galaxy clustering is one of the central issues \nin modern cosmology. Various methods have been proposed to quantify the\nclustering, and many of them ({\\it e.g.} topological analyses of isodensity\ncontour) are based on continuous smoothed density field.\n However what we can observe\n directly is distribution of point-like\n galaxies. Thus smoothing operation is crucially important in\nthe analyses of the large-scale structure. From theoretical point of\nviews, filters with spatially constant\n smoothing \n radii are natural choice and\nhave been widely adopted so far. But we should notice that\n there are no strong\nconvincing reasons \n to stick to this traditional method.\n\nThere are few galaxies in void regions even at semi-nonlinear\nscales. In these regions density field obtained with fixed smoothing radius\n might be considerably affected by the \ndiscreteness of (point-like) mass elements, and might\n hamper our analyses of \nthe cosmic structures. Adaptive smoothing is basically Lagrangian description, \nand we use nearly same number of particles to construct smoothed density\nfield at each point. Thus it is quite possible that \n the adaptive methods are more efficient than the fixed\nmethods to analyze the large-scale structure.\nActually, Springel et al. (1998) have recently \npointed out that using adaptive filters,\nsignal to noise ratio of the genus statistics is improved \neven at weakly nonlinear scales $\\gsim 10h^{-1}{\\rm Mpc}$. \n\nIn this article, we have developed a perturbative analysis of adaptive \nsmoothing methods that are applied to quantify the large-scale\nstructure. Even \nthough adaptive methods might be promising approaches in \nobservational cosmology, this kind of analytic investigation\n has not been done so far.\nOur targets are weakly nonlinear effects induced by \n two typical adaptive approaches, the gather approach and the scatter\napproach (Hernquist \\& Katz 1989). The concept of these methods is\neasily understood with \nequations (8) and (9). The gather approach is easier to handle\nanalytically. Numerical costs dealing with discrete particles' systems \n are also lower in this approach (Springel et al. 1998). \nEffects caused by these two adaptive methods start from second-order\nof $\\delta$ in perturbative sense. \nThey modify quantities which characterize the \n nonlinear mode couplings induced by gravity ({\\it e.g.} Peebles 1980). \n\nIn \\S 3 we have investigated the skewness parameter $S$ which is a\nfundamental measure to quantify asymmetry of one point PDF.\nWe have shown that the skewness for a gather top-hat \nfilter does not depend on the spectral index $n$ in real space, and\n very weakly depends on it ($S\\simeq 35.2-0.15n$: Einstein de-Sitter\nbackground) in redshift space. \nIn the case of Gaussian filter, the skewness parameters \nshow similar behaviors both in the scatter and gather approaches. They are \n increasing functions of $n$, in contrast to the fixed \n smoothing method.\n\nNext in \\S 4, the genus and area statistics have been\n studied with Gaussian adaptive\nfilters. Our \nanalysis is based on the \nmultidimensional Edgeworth expansion explored by Matsubara\n(1994).\nWe use two quantities $\\nu(\\equiv\\delta/\\sigma)$ and $\\nu_r$ to \n parameterize isodensity contours. The latter $\\nu_r$ is defined by the volume \n fraction above a given density threshold (Gott, Melott, \\& Dickinson\n 1986). It is explicitly shown that \nusing this parameterization, two statistics with the fixed smoothing method\n are very weakly affected by semi-nonlinear gravitational dynamics, as\n experientally \n confirmed by\n N-body simulations. \nFor the gather smoothing, we found that the $\\nu_r$- parameterization is more \neffective to keep original linear shape of the area statistics than of the\ngenus statistics.\n\n\nThe parameters $S, T$ and $U$ \n which characterize the nonlinear\ncorrections of isodensity contour depend largely on the filtering methods. \n We can characterize nonlinear effects of these methods in somewhat\n intuitive manner, using results for the genus statistics.\nThe scatter approach makes low density tails more\n meatball-like, but high density tails are transformed in the direction\n of\n sponge-like (connected) topology. This is a remarkable difference\n from fixed or gather smoothing methods.\n\n\\if0\n Therefore nonlinear effects for these statistics are also\n larger in adaptive approaches. \nWe have shown that perturbative analyses of genus statistics \nare not suitable for the scatter approach. In this approach, the\nparameter $U$ becomes too large to treat nonlinear effects perturbatively\neven in the case of $\\sigma\\sim0.2$.\n\\fi\n\nOur investigation in this article has been fully analytical one, using\nperturbative technique of cosmological density field. Numerical analyses \nbased on N-body simulations would play complementary roles to results\nobtained here, and thus are very important. Apart from numerical\ninvestigations, \nperturbative treatment given in this article would be also\n developed further\nin several ways. The smoothed velocity field is crucially important\nmaterial in observational cosmology as it is supposed to be less\ncontaminated by effects of \nbiasing (Dekel 1994, Strauss \\& Willick 1995). But our observational\n information is limited to the \nline of sight peculiar velocities only at points where astrophysical objects\nexist. Thus construction of smoothed velocity field \ncontains similar characters as discussed in this article ({\\it e.g.}\nBernardeau \\& van de Weygaert 1996).\nThere is another (more technical) problem that has not mentioned so far.\nIn this article we have only studied spherically symmetric filter\nfunctions. Springel et al. (1998) have shown that\nsignal to noise ratio of the genus curves is further improved by\nusing a triaxial kernel, taking account of tensor information\nof local density field. This point must be also\nworth studying.\n\n\n\n \\acknowledgments\nThe author would like to thank J. \\ Yokoyama \nfor discussion and an anonymous referee for useful comments. \n He also thanks H.\\ Sato and N. \\ Sugiyama \nfor their continuous encouragement.\nThis work was partially supported by the Japanese Grant\nin Aid for Science Research Fund of the Ministry of Education, Science,\nSports and Culture No.\\ 3161.\n\n\\newpage\n\n\\appendix\n\n\\section{Derivations of Parameters}\n\nIn this appendix we derive expressions for the correction terms \n$\\Delta S$, $\\Delta T$\nand $\\Delta U$ given in the main text.\n First we perturbatively expand the density contrast field smoothed by an\n adaptive filter as\n\\beq\n\\delta_A(\\vex)=\\delta_1(\\vex)+\\delta_2(\\vex)+\\delta_{2A}(\\vex)+\\cdots,\n\\eeq\n where $\\delta_1(\\vex)$ is the linear mode, $\\delta_2(\\vex)$ is the\n second-order mode induced by gravity, and $\\delta_{2A}$ is the\n second-order correction term caused by an adaptive \n smoothing (the suffix $A$ represents ``adaptive''). Then the\n third-order moment for $\\delta_A(\\vex)$ is given as\n\\beq\n\\lla \\delta_A^3\\rra=3\\lla \\delta_2\\delta_1^2\\rra +3\\lla\n\\delta_{2A}\\delta_1^2\\rra+\\cdots.\n\\eeq\n Thus the first-order correction term for\n the third-order \n moment is given as \n%\\footnote{In this appendix the notation $\\delta$\n% means ``difference'' not the Laplacian operator ($\\nabla^2$).}\n\\beq\n 3\\lla\n\\delta_{2A}\\delta_1^2\\rra.\n\\eeq\nIn the same manner we have the following correction terms for $\\lla\n \\delta_A^2\\nabla^2\\delta_A\\rra$ and $\\lla\n \\nabla \\delta_A\\cdot\\nabla\\delta_a \\nabla^2\\delta_A\\rra$ as\n\\beqa\n& & \\lla \\delta_1^2\\nabla^2\n \\delta_{2A}\\rra +2 \\lla \\delta_1 \\delta_{2A} \\nabla^2 \\delta_1\\rra,\\\\\n& &\n \\lla \\nabla \\delta_1 \\cdot \\nabla \\delta_1 \\nabla^2 \n \\delta_{2A}\\rra +2 \\lla\\nabla \\delta_1\\nabla \\delta_{2A} \\nabla^2\\delta_1\\rra.\n \\eeqa\n\nWe can write down the second-order correction terms $\\delta_{2A}$ for the \n gather and scatter\napproaches with smoothing radius $R$ (see eqs. [10] and [11]) \n\\beqa\n\\delta_{2GR}(\\vex)&=&-\\frac13\\delta_{1R}(\\vex)R\\frac{\\p}{\\p \n R}\\delta_{1R}(\\vex)+\\frac16 R\\frac{d}{d \n R}\\sigma_R^2,\\\\\n\\delta_{2SR}(\\vex)&=&-\\frac{R}3\\int d\\vex' \\p_R\nW(|\\vex'-\\vex|;R)\\delta_1(\\vex')\\delta_{1R}(\\vex').\n\\eeqa\nwhere $\\delta_{1R}(\\vex)$ represents the smoothed linear mode,\n$W(|\\vex'-\\vex|;R) $ is a filter function. The variance $\\sigma_R$ of\n the matter\n fluctuations is given as \n\\beqa\n\\sigma_{R}^2&=&\\lla \\delta_{1R}^2\\rra+O(\\delta^4)\\\\\n&=&\\int\\frac{d\\vek}{(2\\pi)^3}w(kR)^2 P(k)+O(\\delta^4),\n\\eeqa \nwhere $w(kR)$ is a Fourier transformed filter function. \n%Without\n%loss of generalities, we can discuss statistical aspects of equations\n%() and () using only at point $\\vex=0$.\n \nFor the Gaussian filter (see eq.[3]) the above equations are given\nwith the linear Fourier modes \n$\\delta_1(\\vek)$ as \n\\beqa\n\\delta_{2GR}(\\vex)&=&\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\n\\exp\\lkk-\\frac{(\\vel^2+\\vek^2)R^2}{2} \\rkk \\delta_1(\\vek)\n\\delta_1(\\vel)\\frac{\\vek^2R^2}3\\exp[i(\\vek+\\vel)\\cdot \\vex]\\nn\\\\\n& & +\\frac16 R\\frac{d}{d R}\\sigma_R^2,\\\\\n\\delta_{2SR}(\\vex)&=& -\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\n\\exp\\lkk-\\frac{(2\\vel^2+\\vek^2+2\\vek\\cdot \\vel)R^2}{2} \\rkk \\delta_1(\\vek)\n\\delta_1(\\vel)\\frac{(\\vek+\\vel)^2R^2}{3}\\nn\\\\\n& &\\times\\exp[i(\\vek+\\vel)\\cdot \\vex], \n\\eeqa\n\nNext we comment on the ensemble average of variables.\nWe assume that the linear Fourier modes of density fluctuation are\nrandom Gaussian distributed.\nIf variables $\\{A,B,C,D\\}$ obeys multivariable Gaussian distribution, we\ngenerally \nhave the following relation\n\\beq\n\\lla ABCD\\rra=\\lla AB\\rra \\lla CD\\rra + \\lla AC\\rra \\lla BD\\rra+\\lla\nAD\\rra \\lla BC\\rra.\n\\eeq\nFor the linear Fourier modes the above equation becomes\n\\beqa\n\\lla\\delta_1(\\vek)\\delta_1(\\vel)\\delta_1(\\vem)\\delta_1(\\ven)\\rra&=&\n(2\\pi)^6P(k)P(l)\\delta_{Drc}(\\vek+\\vem)\\delta_{Drc}(\\vel+\\ven)\\nn\\\\\n& & +(2\\pi)^6P(k)P(m)\\delta_{Drc}(\\vek+\\vel)\\delta_{Drc}(\\vem+\\ven)\\nn\\\\\n& &+(2\\pi)^6P(k)P(l)\\delta_{Drc}(\\vek+\\ven)\\delta_{Drc}(\\vel+\\vem).\n\\eeqa\nHere $\\delta_{Drc}(\\cdot)$ is the Dirac's delta function and $P(k)$ is\nthe matter power spectrum.\nWe evaluate expressions (A3)-(A5) using relations \n(A12)-(A13).\n\n\n\\subsection {Skewness}\nFor the gather approach the real-space representation (A6) is more\nconvenient. Using property (A12) we obtain the following result\n\\beqa\n\\lla \\delta_{2SR}\\delta_{1R}^2\\rra &=&\\lla -\\delta_{1R}^3 \\lmk R \\frac{\\p}{\\p\n R}\\delta_{1R} \\rmk \\rra +\\frac12 \\lla \\delta_{1R}^2 \\rra \\frac{d}{d \n R}\\sigma_R^2\\\\\n&=&-3\\sigma_{1R}^2\\lla\\delta_{1R} \\frac{\\p}{\\p\n R}\\delta_{1R}\\rra +\\frac12 \\sigma_R^2 \\frac{d}{d \n R}\\sigma_R^2\\\\\n&=& -\\sigma_R^2\\frac{d}{d \n R}\\sigma_R^2.\n\\eeqa\nThe correction term for the skewness $S_G$ is written as equation (35)\n\\beq\n\\Delta S_G=\\frac{\\lla \\delta_{2GR}\\delta_{1R}^2\\rra}{\\sigma_R^4}\n=-\\frac1{\\sigma_R^2}\\frac{d}{d \n R}\\sigma_R^2=-\\frac{d\\ln \\sigma_R^2}{d\\ln R}.\n \\eeq\nFor power-law models we have a simple relation $\\sigma_R^2\\propto\nR^{-n-3}$, and the above\nexpression becomes\n\\beq\n\\Delta S_G=(n+3).\n\\eeq\nHere we should notice that relations (A17) and (A18) do not depend on the\nchoice of filter functions.\n\nNext let us evaluate the correction term for the skewness parameter in\nthe case of \nthe scatter approach. In this case we limit our analysis for a \nGaussian filter (eq.[3]). From equation (A11) we have\n\\beqa\n3\\lla\\delta_{2SR}(\\vex)\\delta_{1R}(\\vex)^2\\rra &=&\n\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\\frac{d\\vem}{(2\\pi)^3}\\frac{d\\ven}{(2\\pi)^3}{(\\vek+\\vel)^2R^2}\\nn\\\\\n& &\\exp\\lkk-\\frac{(2\\vel^2+\\vek^2+\\vem^2+\\ven^2+2\\vek\\cdot \\vel)R^2}{2}\n\\rkk \\nn\\\\\n& & \\times\\lla \\delta_1(\\vek)\n\\delta_1(\\vel)\\delta_1(\\vem)\\delta_1(\\ven)\\rra\\exp[i(\\vek+\\vel+\\vem+\\ven)\\cdot \\vex].\\nn\\\\ \n\\eeqa\nUsing equation (A13) we can simplify the above integral as \n\\beq\n2\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\n\\exp\\lkk-\\frac{(3\\vel^2+2\\vek^2+2\\vek\\cdot \\vel)R^2}{2} \\rkk\nP(k)P(l){(\\vek+\\vel)^2} R^2.\n\\eeq\nNote that the integrad of this expression depends only on the\ninformation of the shape of the triangle determined by two vectors\n$\\vek$ and $\\vel$. \nThis triangle is characterized by three quantities, namely, two sides $k=|\\vek|$,\n$l=|\\vel|$ and cosine between them $u\\equiv\\vek\\cdot\\vel/(kl)$ with $-1\\le u\\le 1$. We\nchange variables from $\\{\\vek, \\vel\\}$ to $\\{k,l,u\\}$. The volume\nelement is deformed as\n\\beq\nd\\vek d\\vel \\Rightarrow 8\\pi^2 dk dl du.\n\\eeq\nThus we obtain equation (39). This equation looks somewhat\ncomplicated. For power-law models, however, \nwe can easily evaluate it using {\\it mathematica} (Wolfram 1996) and\nfinally \nobtain analytical expression (40) given in the main text.\n\n\n\\subsection {Generalized Skewness for the Gather Approach}\nFor this approach we have the following relation for a Gaussian filter\n\\beq\nR \\frac{\\p}{\\p R} \\delta_{1R}(\\vex)=R^2\\nabla^2\\delta_{1R}(\\vex).\n\\eeq\nTherefore the correction terms (A4) and (A5) can be written by\ncombinations of the following five variables \\footnote{In this subsection we denote\n $\\delta_{1R}(\\vex)$ simply by $\\delta$.}\n\\beq\n\\{\\delta,~\\nabla\\delta,~\\nabla^2\\delta,~\\nabla^3\\delta,~\\nabla^4\\delta\\}.\n\\eeq\nFor example, equation (A4) is written as\n\\beq\n-\\frac13 R^2\\lkk \\lla\\delta^2\\nabla^2(\\delta\\nabla^2\\delta)\\rra+2\\lla\n\\delta^2 (\\nabla^2\\delta)(\\nabla^2\\delta) \\rra-2\n\\lla\\delta\\nabla^2\\delta \\rra\\lla\\delta\\nabla^2\\delta \\rra \\rkk\n\\eeq\nUsing property (A12), the above expression is deformed as \n\\beq\n-\\frac13 R^2\\lkk 3\\lla \\nabla^2\\delta \\nabla^2\\delta\\rra\\lla \\delta\n\\delta\\rra+2 \\lla\\nabla\\delta \\nabla^3\\delta \\rra \\lla \\delta \\delta\\rra \n+3\\lla \\delta \\nabla^4 \\delta \\rra \n\\lla \\delta \\delta\\rra +4\\lla \\delta\\nabla^2 \\delta \\rra^2 \\rkk\n\\eeq\nThe moments appeared in the above equation can be written in terms of\n$P(k)$ as\n\\beqa\n-\\lla \\delta\\nabla^2 \\delta \\rra &=&\\lla\\nabla \\delta\\nabla\n\\delta\\rra=\\int \\frac{dk}{2\\pi^2}k^4P(k)e^{-k^2R^2}\\\\\n \\lla \\nabla^2 \\delta\\nabla^2 \\delta \\rra &=&-\\lla\\nabla^3 \\delta\\nabla\n\\delta\\rra= \\lla \\nabla^4 \\delta \\delta \\rra=\\int \\frac{dk}{2\\pi^2}k^6P(k)e^{-k^2R^2}\n\\eeqa \nFor a power-law models ($P(k)\\propto k^n$). These integrals are evaluated respectively as\n\\beq\n\\sigma^2_R R^{-2}\\lmk\\frac{n+3}2\\rmk, ~~~\\sigma_R^2 R^{-4} \\lmk\\frac{n+3}2\\rmk\\lmk \\frac{n+5}2\\rmk. \n\\eeq\n\nWith the definition of $T$ parameter (eq.[48]) we obtain the final\nresult that is \ngiven in equation (61) as \n\\beq\n\\Delta T_{GR}=\\frac23 (n+4)\n\\eeq\n\nTo calculate the correction term (A5), let us use the Fourier space\nrepresentation (A10).\\footnote{We obtain the same result\n starting from equation (A6).} It is straightforward to get\n\\beqa\n \\lla \\nabla \\delta_1 \\cdot \\nabla \\delta_1 \\nabla^2 \n \\delta_{2A}\\rra +2 \\lla\\nabla \\delta_1\\nabla \\delta_{2A}\n \\nabla^2\\delta_1\\rra\n &=&\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\\frac{d\\vem}{(2\\pi)^3}\\frac{d\\ven}{(2\\pi)^3}\n\\frac{k^2R^2}{3}\\nn\\\\\n& &\\times \\exp\\lkk-\\frac{(\\vel^2+\\vek^2+\\vem^2+\\ven^2)R^2}{2}\n\\rkk \\nn\\\\\n& & \\times\\lla \\delta_1(\\vek)\n\\delta_1(\\vel)\\delta_1(\\vem)\\delta_1(\\ven)\\rra\\nn\\\\\n& & \\times\\exp[i(\\vek+\\vel+\\vem+\\ven)\\cdot \\vex],\\nn\\\\ \n& &\\times\n[-(\\vem\\cdot\\ven)(\\vek+\\vel)^2\\nn\\\\\n& &~~-(\\vem\\cdot(\\vek+\\vel)\\ven^2)-(\\ven\\cdot(\\vek+\\vel)\\vem^2) \n].\n\\eeqa\nWith equation (A13), the above integral becomes\n\\beqa\n& &-\\frac13\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\n{k^2R^2}\n \\exp\\lkk-{(\\vel^2+\\vel^2)R^2}\n\\rkk P(k) P(l) \n [4k^2 l^2-4(\\vek\\cdot\\vel)^2 ]\\nn\\\\\n&=&-\\frac1{6\\pi^4}\\int_0^\\infty\n{dk}\\int_0^\\infty{dl}\\int_{-1}^1du \n\\exp\\lkk-{(l^2+k^2)R^2} \\rkk k^6 l^4\nP(k)P(l){(1-u^2)} R^2\\nn\\\\\n&=&-\\frac2{9\\pi^4}\\int_0^\\infty k^6 P(k) \\exp[-k^2 R^2]\\int dl l^4 P(l) \\exp[-l^2 R^2].\n\\eeqa\nFor power-law models this expression becomes (see eqs.[A26]-[A28])\n\\beq\n-\\frac89 \\sigma_R^4 \\lmk\\frac{n+3}2 \\rmk^2 \\lmk\\frac{n+5}2 \\rmk.\n\\eeq\nUsing definition of $U$ parameter (eq.[48]) we obtain equation (62) as\n\\beq\n\\Delta U_{GR}=\\frac13 (n+5).\n\\eeq\n\n\n\nNote that results (A29) and (A33) are not valid for general filters. Equation\n(A22) that holds for the Gaussian filter plays crucial roles to derive them.\n\n\\subsection {Generalized Skewness for the Scatter Approach}\nFirst we evaluate the correction term given in equation (A4). With the\nFourier space representation (A10) we obtain the following equation\n\\beqa\n \\lla \\delta_1^2\\nabla^2\n \\delta_{2A}\\rra +2 \\lla \\delta_1 \\delta_{2A} \\nabla^2\n \\delta_1\\rra&=&\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\\frac{d\\vem}{(2\\pi)^3}\\frac{d\\ven}{(2\\pi)^3}\\frac{(\\vek+\\vel)^2R^2}{3}\\nn\\\\\n& &\\times\\exp\\lkk-\\frac{(2\\vel^2+\\vek^2+\\vem^2+\\ven^2+2\\vek\\cdot \\vel)R^2}{2}\n\\rkk \\nn\\\\\n& & \\times\\lla \\delta_1(\\vek)\n\\delta_1(\\vel)\\delta_1(\\vem)\\delta_1(\\ven)\\rra\\exp[i(\\vek+\\vel+\\vem+\\ven)\\cdot \\vex],\\nn\\\\ \n& &\\times [(\\vek+\\vel)^2+\\vem^2+\\ven^2]\n\\eeqa\nWith the formula (A13), this twelfth-dimensional integral becomes\n\\beq\n\\frac23\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\n\\exp\\lkk-\\frac{(3\\vel^2+2\\vek^2+2\\vek\\cdot \\vel)R^2}{2} \\rkk\nP(k)P(l){(\\vek+\\vel)^2} R^2[(\\vek+\\vel)^2+\\vel^2+\\vek^2].\n\\eeq\nchanging variables from $d\\vek d\\vel$ to $dk dl du$ as shown in relation \n(A21), we obtain the result essentially same as equation (65) as\n\\beqa\n \\lla \\delta_1^2\\nabla^2\n \\delta_{2A}\\rra +2 \\lla \\delta_1 \\delta_{2A} \\nabla^2\n \\delta_1\\rra&=&\\frac1{6\\pi^4}\\int_0^\\infty\n{dk}\\int_0^\\infty{dl}\\int_{-1}^1du \n\\exp\\lkk-\\frac{(3l^2+2k^2+2klu)R^2}{2} \\rkk \\nn\\\\\n& &\\times k^2 l^2\nP(k)P(l){(k^2+l^2+2klu)}{(k^2+l^2+klu)} R^2,\n\\eeqa\nAs in the case of skewness parameter, we can evaluate this complicated\nintegrals with {\\it mathematica} and obtain equation (67).\n\nIn the same manner, equation (A5) is written as\n\\beqa\n \\lla \\nabla \\delta_1 \\cdot \\nabla \\delta_1 \\nabla^2 \n \\delta_{2A}\\rra +2 \\lla\\nabla \\delta_1\\nabla \\delta_{2A}\n \\nabla^2\\delta_1\\rra\n &=&\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\\frac{d\\vem}{(2\\pi)^3}\\frac{d\\ven}{(2\\pi)^3}\n\\frac{(\\vek+\\vel)^2R^2}{3}\\nn\\\\\n& &\\times \\exp\\lkk-\\frac{(2\\vel^2+\\vek^2+\\vem^2+\\ven^2+2\\vek\\cdot \\vel)R^2}{2}\n\\rkk \\nn\\\\\n& & \\times\\lla \\delta_1(\\vek)\n\\delta_1(\\vel)\\delta_1(\\vem)\\delta_1(\\ven)\\rra\\nn\\\\\n& &\\times\\exp[i(\\vek+\\vel+\\vem+\\ven)\\cdot \\vex],\\nn\\\\ \n& &\\times\n[-(\\vem\\cdot\\ven)(\\vek+\\vel)^2\\nn\\\\\n& &~~-(\\vem\\cdot(\\vek+\\vel)\\ven^2)-(\\ven\\cdot(\\vek+\\vel)\\vem^2) \n].\n\\eeqa\nThis expression is simplified to the following form\n\\beqa\n& &\\frac13\\int\\frac{d\\vek}{(2\\pi)^3}\\frac{d\\vel}{(2\\pi)^3}\n{(\\vek+\\vel)^2R^2}\n \\exp\\lkk-\\frac{(2\\vel^2+\\vek^2+\\vem^2+\\ven^2+2\\vek\\cdot \\vel)R^2}{2}\n\\rkk \\nn\\\\\n& & \\times P(k) P(l) \n [4k^2 l^2-4(\\vek\\cdot\\vel)^2 ].\n\\eeqa\nAgain, changing variables, we obtain the expression (66) as\n\\beqa\n\\lla \\nabla \\delta_1 \\cdot \\nabla \\delta_1 \\nabla^2 \n \\delta_{2A}\\rra +2 \\lla\\nabla \\delta_1\\nabla \\delta_{2A}\n \\nabla^2\\delta_1\\rra\n &=&\\frac1{6\\pi^4}\\int_0^\\infty\n{dk}\\int_0^\\infty{dl}\\int_{-1}^1du {(1-u^2)} R^2\\nn\\\\\n& &\\times\\exp\\lkk-\\frac{(3l^2+2k^2+2klu)R^2}{2} \\rkk \\nn\\\\\n& &\\times k^4 l^4\nP(k)P(l){(k^2+l^2+2klu)}.\n\\eeqa\nFor power-law\nmodels we can evaluate this integral using {\\it mathematica} and\nobtain equation (68).\n\n\n\n\n\\newpage\n%\\begin{references}\n\\begin{thebibliography}{}\n\n\\bibitem[]{} Adler,~R.~J. 1981, The Geometry of Random Fields\n (Chichester: Wiley)\n\n\\bibitem[]{} Babul, A. \\& Starkman, G. D. 1992, ApJ, 401, 28\n\n\\bibitem[]{} Baugh, C. M, Gazta$\\tilde{\\rm n}$aga, E. \\& Efstathiou,\n G. 1995, MNRAS, 274, 1049\n\n\\bibitem[]{} Bardeen, J. M., Bond, J. R., Kaiser, N. \\& Szalay, A S. 1986, ApJ, 305, \n15\n\n\\bibitem[]{} Bernardeau, F. 1994, A\\&A, 291, 697\n\n\\bibitem[]{} Bernardeau, F. \\& van de Weygaert, R. 1996, MNRAS, 279, 693\n\n\\bibitem[]{} Bouchet, F. Juszkiewicz, R. Colombi, S. \\& Pellat, R. 1992, ApJ, 394, L5\n\n\\bibitem[]{} Bouchet, F. et al. 1993, ApJ, 417, 36\n\n\\bibitem[]{} Canavezes, A. et al. 1998, MNRAS, 297, 17\n\n\\bibitem[]{} Coles, P., Davies, A. \\& Pearson, R. C. 1996, MNRAS, 281, 1375\n\n\\bibitem[]{} Coles, P., Pearson, R. C., Borgani, S. Plionis, M. \\&\n Moscardini, L. 1998, MNRAS, 294, 245\n\n\n\\bibitem[]{} Colless, M. 1998, Phil. Trans. R. Soc. Lond. A. in press (astro-ph/9804079)\n\n\\bibitem[]{} Colombi, S., Szapudi, I. \\& Szalay, A. S. 1998, MNRAS, 296, \n 253\n\n\\bibitem[]{} Davis, M. \\& Peebles, P. J. E. 1983, ApJ, 267, 465\n\n\\bibitem[]{} Dekel, A., 1994, ARA\\&A, 32, 371\n\n\\bibitem[]{} Dekel, A. \\& Lahav, O. 1999, ApJ, 520, 24\n\n\\bibitem[]{} Doroshkevich, A. G. 1970, Astrofizika, 6, 581 (English\n transl. Astrophysics, 6, 320)\n\n\\bibitem[]{} Fry, J. N. 1984, ApJ, 279, 499\n\n\\bibitem[]{} Gazta$\\tilde{\\rm n}$aga, E. 1992, ApJ, 398, L17\n\n\\bibitem[]{} Goroff, M. H., Grinstein, B., Rey, S. -J., \\& Wise, M. B., 1986, ApJ,\n 311, 6\n\n\\bibitem[]{} Gott, J. R., Melott, A. L. \\& Dickinson, M. 1986, ApJ, 306, 341\n\n\\bibitem[]{} Gott,~J.~R., Weinberg,~D.~H. \\& Melott,~A.~L. 1987, ApJ, 319, 1\n\n\\bibitem[]{} Gott, J. R. et al. 1989, ApJ, 340, 625 \n\n\\bibitem[]{} Gunn, J. E. \\& Weinberg, D. H. 1995, in Wide-Field Specroscopy\n and the Distant Universe eds. S.J. Maddox and\n A. Aragon-Salamanca.(World Sientific: Singapore), 3\n\n\\bibitem[]{} Guth, A. \\& Pi, S.-Y. 1982, Phys. Rev. Lett., 49, 1110\n\n\\bibitem[]{} Hamilton, A. J. S., Gott, J. R. \\& Weinberg, D. H. 1986, ApJ, 309, 1\n\n\\bibitem[]{} Hamilton, A. J. S. 1988, PASP, 100, 1343\n\n\\bibitem[]{} Hawking, S. W. 1982, Phys. Lett., 115B, 295\n\n\\bibitem[]{} Hernquist, L. \\& Katz, N. 1989, ApJS, 70, 419\n\n\\bibitem[]{} Hivon, E., Bouchet, F. R., Colombi, S., \\& Juszkiewicz, R. 1995,\n A\\&A, 298, 643\n\n\\bibitem[]{} Juszkiewicz, R., Bouchet, F. R., \\& Colombi, S. 1993,\n ApJ, 412, L9 \n\n\\bibitem[]{} Juszkiewicz, R. et al. 1995, ApJ, 442, 39\n\n\\bibitem[]{} Kaiser, N. 1984, ApJ, 284, L9\n\n\\bibitem[]{} Kerscher, M. et al. 1997, MNRAS, 284, 73\n\n\\bibitem[]{} Kim, R. S. J., \\& Strauss, M. A. 1998, ApJ, 493, 39\n\n\\bibitem[]{} Klypin, A. A. 1988, ActaCosmologica, 15, 101\n\n\\bibitem[]{} {\\L}okas, E. L., Juszkiewicz, R., Weinberg, D. H. \\& Bouchet, F. R. 1995,\n MNRAS, 274, 730\n\n\n\\bibitem[]{} Luo, S. \\& Vishniac, E. T. 1995, ApJS, 96, 429\n\n\\bibitem[]{} Matsubara, T. 1994, ApJ, 434, L43\n\n\\bibitem[]{} Matsubara, T. 1995, Ph.D. Thesis, Hiroshima Univ\n\n\\bibitem[]{} Matsubara, T. \\& Suto, Y. 1996, ApJ, 460, 51\n\n\\bibitem[]{} Matsubara, T. \\& Yokoyama, J. 1996, ApJ, 463, 409\n\n\\bibitem[]{} Mecke, K. R., Buchert, T. \\& Wagner, H. 1994, A\\&A, 288, \n 697\n\n\\bibitem[]{} Melott,~A.~L., Weinberg,~D.~H., \\& Gott,~J.~R. 1988, ApJ,\n 328, 50\n\n\\bibitem[]{} Minkowski, H. 1903, Math. Ann., 57, 447\n\n\\bibitem[]{} Moore,~B. et al. 1992, MNRAS, 256, 477\n\n\\bibitem[]{} Monaghan, J. J. \\& Lattanzio, J. J. 1985, A\\&A, 149, 135\n\n\\bibitem[]{} Okun, B. L. 1990, J. Stat. Phys., 59, 523\n\n\\bibitem[]{} Park,~C. \\& Gott,~J.~R. 1991, ApJ, 378, 457\n\n\\bibitem[]{} Park,~C., Gott,~J.~R., \\& da Costa,~L.~N. 1992, ApJ, 392, L51\n\n% Peacock, J. A. \\& Dodds, S. J. 1996, MNRAS, 280, L19\n\n\\bibitem[]{} Protogeros, Z. A. M. \\& Weinberg D. H., 1997, ApJ, 489, 457\n\n\\bibitem[]{} Peebles, P. J. E. 1974, A\\&A, 32, 197\n\n\\bibitem[]{} Peebles, P. J. E. 1980, {\\ The Large Scale Structure of the Universe}\n (Princeton University Press: Princeton)\n\n\\bibitem[]{} Rhoads,~J.~E., Gott,~J.~R., \\& Postman,~M. 1994, ApJ, 421, 1\n\n\\bibitem[]{} Ryden, B. S. 1988, ApJ, 333, L41\n\n\\bibitem[]{} Ryden, B. S. et al. 1989, ApJ, 340, 647\n\n\\bibitem[]{} Sahni, V. Sathyprakash,B. S. \\& Shandarin, S. F. 1997, ApJ, 467, L1\n\n\\bibitem[]{} Schmalzing, J. \\& Buchert, T. 1997, ApJ, 482, L1\n\n\\bibitem[]{} Scoccimarro, R. 1998, MNRAS, 299, 1097\n\n\\bibitem[]{} Seto, N., Yokoyama, J., Matsubara, T. \\& Siino, M. 1997, ApJS, 110, 177\n\n\\bibitem[]{} Seto, N. 1999, ApJ, 523, 24\n\n\\bibitem[]{} Springel, V. et al. 1998, MNRAS, 298, 1169\n\n\\bibitem[]{} Starobinsky, A. A. 1982, Phys. Lett., 117B, 175\n\n\\bibitem[]{} Strauss, M. A. \\& Willick, J. A. 1995, Phys. Rep., 261, 271\n\n\\bibitem[]{} Thomas, P. A. \\& Couchman, H. M. P. 1992, MNRAS, 257, 11\n\n\\bibitem[]{} Totsuji, H \\& Kihara, T. 1969, PASJ, 21 221\n \n\\bibitem[]{} Vogeley,~M.~S. et al. 1994, ApJ, 420, 525\n\n\\bibitem[]{} Weinberg, D.~H., Gott, J.~R., \\& Melott, A.~L. 1987, ApJ, 321, 2\n\n\\bibitem[]{} Weinberg,~D.~H. \\& Cole,~S. 1992, MNRAS, 259, 652\n\n\\bibitem[]{} Wolfram, S. 1996, {\\ The Mathematica Book, 3rd ed.}\n (Cambridge University Press: Cambridge)\n\n\\bibitem[]{} Zeldovich, Ya.~B. 1970, A\\&A, 5, 84\n\n\n%\\end{references}\n\\end{thebibliography}\n\n\\newpage\n\n\n\\begin{center}\nTABLE 1\\\\\n{\\sc skewness for the\n gather approach (Gaussian filter)}\\\\ \n\\ \\\\\n\\begin{tabular}{ccccccc}\n\\hline\\hline\n spectral index $n$ &1& 0 &-1& -2& -3 \\\\\n\\hline\n $S_F(n)$ ~~ &~~ 3.029~~ &~~ 3.144~~ &~~3.468 ~~ &~~4.022\n ~~&4.857 \\\\\n $\\Delta S_G(n)$ ~~ &~~ 4.000~~ &~~ 3.000~~ &~~2.000 ~~ &~~1.000\n ~~&0 \\\\\n $S_G(n)$ ~~ &~~ 7.029~~ &~~ 6.144~~ &~~5.468 ~~ &~~5.022 ~~&4.857 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\n\n\\begin{center}\nTABLE 2\\\\\n{\\sc skewness for the\n scatter approach}\\\\ \n\\ \\\\\n\\begin{tabular}{ccccccc}\n\\hline\\hline\n spectral index $n$ &1& 0 &-1& -2& -3 \\\\\n\\hline\n $S_F(n)$ ~~ &~~ 3.029~~ &~~ 3.144~~ &~~3.468 ~~ &~~4.022\n ~~&4.857 \\\\\n $\\Delta_S S(n)$ ~~ &~~ 3.031~~ &~~ 2.576~~ &~~2.045 ~~ &~~1.277\n ~~&0 \\\\\n $S_S(n)$ ~~ &~~ 6.060~~ &~~ 5.720~~ &~~5.513 ~~ &~~5.299 ~~&4.857 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n%\\newpage\n\n\\begin{center}\nTABLE 3\\\\\n{\\sc generalized skewness for the\n gather approach}\\\\ \n\\ \\\\\n\\begin{tabular}{ccccccc}\n\\hline\\hline\n spectral index $n$ &1& 0 &-1& -2& -3 \\\\\n\\hline\n $T_F(n)$ ~~ &~~ 2.020~~ &~~ 2.096~~ &~~2.312 ~~ &~~2.681\n ~~&3.238 \\\\\n $\\Delta T_G(n)$ ~~ &~~ 3.333~~ &~~ 2.667~~ &~~2.000 ~~ &~~1.333\n ~~&0.667 \\\\\n $T_G(n)$ ~~ &~~ 5.353~~ &~~ 4.763~~ &~~4.312 ~~ &~~4.014 ~~&3.905 \\\\\n\\hline\n $U_G(n)$ ~~ &~~ 1.431~~ &~~ 1.292~~ &~~1.227 ~~ &~~1.222\n ~~&1.272 \\\\\n $\\Delta U_G(n)$ ~~ &~~ 2.000~~ &~~ 1.667~~ &~~1.333 ~~ &~~1.000\n ~~&0.667 \\\\\n $U_G(n)$ ~~ &~~ 3.431~~ &~~ 2.959~~ &~~2.560 ~~ &~~2.222 ~~&1.929 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\nTABLE 4\\\\\n{\\sc generalized skewness for the\n scatter approach}\\\\ \n\\ \\\\\n\\begin{tabular}{ccccccc}\n\\hline\\hline\n spectral index $n$ &1& 0 &-1& -2& -3 \\\\\n\\hline\n $T_F(n)$ ~~ &~~ 2.020~~ &~~ 2.096~~ &~~2.312 ~~ &~~2.681\n ~~&3.238 \\\\\n $\\Delta T_S(n)$ ~~ &~~ -2.082~~ &~~ -1.908~~ &~~-1.723 ~~ &~~-1.451\n ~~&-0.963 \\\\\n $T_S(n)$ ~~ &~~ -0.0623~~ &~~ 0.1882~~ &~~0.5892 ~~ &~~1.230 ~~&2.275 \\\\\n\\hline\n $U_F(n)$ ~~ &~~ 1.431~~ &~~ 1.292~~ &~~1.227 ~~ &~~1.222\n ~~&1.272 \\\\\n $\\Delta U_S(n)$ ~~ &~~ -1.265~~ &~~ -1.145~~ &~~-1.027 ~~ &~~-0.8916\n ~~&-0.7105 \\\\\n $U_S(n)$ ~~ &~~ 0.1662~~ &~~ 0.1474~~ &~~0.2000 ~~&~~0.3301~~&0.5611\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n%\\if0%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=15.2cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{fig1.eps} \\end{minipage}\n \\end{center}\n\\caption[]{Skewness for the gather approach in real and\n redshift spaces. We use two kinds of filters (Gaussian\n and top-hat filters).\n The dashed-lines represent \n results for the traditional \nfixed smoothing method and the solid lines for the gather approach.\nNumerical data in the redshift space are based on Table 2 and 3 of Hivon et\nal. (1995). }\n\\end{figure}\n\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=15.2cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{fig2.eps} \\end{minipage}\n \\end{center}\n\\caption[]{Real space skewness for the scatter approach with the \n Gaussian filters. The dashed-line represents results for \n the fixed smoothing method and the solid line for the scatter approach.}\n\\end{figure}\n\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=15.2cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{fig3.eps} \\end{minipage}\n \\end{center}\n\\caption[]{Normalized genus density for the fixed Gaussian smoothing (see\n Matsubara 1994). Upper panel corresponds to \n $\\nu$- parameterization and lower to $\\nu_r$- parameterization. The solid curves represent linear curves\n (eq.[45]). Dotted-lines, dashed-lines show $\\sigma=0.2$, and\n $\\sigma=0.4$ respectively.}\n\\end{figure}\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=15.2cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{fig4.eps} \\end{minipage}\n \\end{center}\n\\caption[]{Same as Fig.3 but with the gather approach. }\n\\end{figure}\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=15.2cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{fig5.eps} \\end{minipage}\n \\end{center}\n\\caption[]{Same as Fig.3 but with the scatter approach. }\n\\end{figure}\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=15.2cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{fig6.eps} \\end{minipage}\n \\end{center}\n\\caption[]{Nonlinear Genus curves for various smoothing methods. The\n solid line corresponds to the linear analysis, dotted to the fixed smoothing,\n short-dased to the gather approach, and long-dased to the scatter\n approach. We fix the spectral index at $n=0$ and nonlinearity at $\\sigma=0.2$. }\n\\end{figure}\n\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=15.2cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{fig7.eps} \\end{minipage}\n \\end{center}\n\\caption[]{Normalized area statistics for the fixed Gaussian smoothing. Upper panel corresponds to \n $\\nu$ parameterization and lower to $\\nu_r$ parameterization. The\n solid curves represent the linear prediction \n (eq.[45]). Dotted-lines, dashed-lines show $\\sigma=0.2$, and\n $\\sigma=0.4$ respectively. }\n\\end{figure}\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=15.2cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{fig8.eps} \\end{minipage}\n \\end{center}\n\\caption[]{Same as Fig.6 but for the gather approach. }\n\\end{figure}\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=15.2cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{fig9.eps} \\end{minipage}\n \\end{center}\n\\caption[]{Same as Fig.6 but for the scatter approach. }\n\\end{figure}\n\\end{document}\n%\\fi%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\newpage\n\\centerline{\\bf FIGURE CAPTIONS}\n\\begin{description}\n\\item[Figs.\\ 1]\nSkewness for the gather approach in real and\n redshift spaces. We use two kinds of filters (Gaussian\n and top-hat filters).\n The dashed-lines represent \n results for the traditional \nfixed smoothing method and the solid lines for the gather approach.\nNumerical data in the redshift space are based on Table 2 and 3 of Hivon et\nal. (1995). \n\n\n\\item[Figs.\\ 2]\nReal space skewness for the scatter approach with the \n Gaussian filters. The dashed-line represents results for \n the fixed smoothing method and the solid line for the scatter approach.\n\n\\item[Figs.\\ 3]\nNormalized genus density for the fixed Gaussian smoothing (see\n Matsubara 1994). Upper panel corresponds to \n $\\nu$- parameterization and lower to $\\nu_r$- parameterization. The solid cur\nves represent linear curves\n (eq.[45]). Dotted-lines, dashed-lines show $\\sigma=0.2$, and\n $\\sigma=0.4$ respectively.\n\n\\item[Figs.\\ 4]\nSame as Fig.3 but with the gather approach.\n\n\\item[Figs.\\ 5]\nSame as Fig.3 but with the scatter approach.\n\n\\item[Figs.\\ 6]\nNonlinear Genus curves for various smoothing methods. The\n solid line corresponds to the linear analysis, dotted to the fixed smoothing,\n short-dased to the gather approach, and long-dased to the scatter\n approach. We fix the spectral index at $n=0$ and nonlinearity at\n $\\sigma=0.2$.\n\n\\item[Figs.\\ 7]\nNormalized area statistics for the fixed Gaussian smoothing. Upper p\nanel corresponds to \n $\\nu$ parameterization and lower to $\\nu_r$ parameterization. The\n solid curves represent the linear prediction \n (eq.[45]). Dotted-lines, dashed-lines show $\\sigma=0.2$, and\n $\\sigma=0.4$ respectively.\n\n\\item[Figs.\\ 8]\nSame as Fig.6 but for the gather approach.\n\n\\item[Figs.\\ 9]\nSame as Fig.6 but for the scatter approach. \n\n\n\\end{description}\n\\end{document}\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002315.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[]{} Adler,~R.~J. 1981, The Geometry of Random Fields\n (Chichester: Wiley)\n\n\\bibitem[]{} Babul, A. \\& Starkman, G. D. 1992, ApJ, 401, 28\n\n\\bibitem[]{} Baugh, C. M, Gazta$\\tilde{\\rm n}$aga, E. \\& Efstathiou,\n G. 1995, MNRAS, 274, 1049\n\n\\bibitem[]{} Bardeen, J. M., Bond, J. R., Kaiser, N. \\& Szalay, A S. 1986, ApJ, 305, \n15\n\n\\bibitem[]{} Bernardeau, F. 1994, A\\&A, 291, 697\n\n\\bibitem[]{} Bernardeau, F. \\& van de Weygaert, R. 1996, MNRAS, 279, 693\n\n\\bibitem[]{} Bouchet, F. Juszkiewicz, R. Colombi, S. \\& Pellat, R. 1992, ApJ, 394, L5\n\n\\bibitem[]{} Bouchet, F. et al. 1993, ApJ, 417, 36\n\n\\bibitem[]{} Canavezes, A. et al. 1998, MNRAS, 297, 17\n\n\\bibitem[]{} Coles, P., Davies, A. \\& Pearson, R. C. 1996, MNRAS, 281, 1375\n\n\\bibitem[]{} Coles, P., Pearson, R. C., Borgani, S. Plionis, M. \\&\n Moscardini, L. 1998, MNRAS, 294, 245\n\n\n\\bibitem[]{} Colless, M. 1998, Phil. Trans. R. Soc. Lond. A. in press (astro-ph/9804079)\n\n\\bibitem[]{} Colombi, S., Szapudi, I. \\& Szalay, A. S. 1998, MNRAS, 296, \n 253\n\n\\bibitem[]{} Davis, M. \\& Peebles, P. J. E. 1983, ApJ, 267, 465\n\n\\bibitem[]{} Dekel, A., 1994, ARA\\&A, 32, 371\n\n\\bibitem[]{} Dekel, A. \\& Lahav, O. 1999, ApJ, 520, 24\n\n\\bibitem[]{} Doroshkevich, A. G. 1970, Astrofizika, 6, 581 (English\n transl. Astrophysics, 6, 320)\n\n\\bibitem[]{} Fry, J. N. 1984, ApJ, 279, 499\n\n\\bibitem[]{} Gazta$\\tilde{\\rm n}$aga, E. 1992, ApJ, 398, L17\n\n\\bibitem[]{} Goroff, M. H., Grinstein, B., Rey, S. -J., \\& Wise, M. B., 1986, ApJ,\n 311, 6\n\n\\bibitem[]{} Gott, J. R., Melott, A. L. \\& Dickinson, M. 1986, ApJ, 306, 341\n\n\\bibitem[]{} Gott,~J.~R., Weinberg,~D.~H. \\& Melott,~A.~L. 1987, ApJ, 319, 1\n\n\\bibitem[]{} Gott, J. R. et al. 1989, ApJ, 340, 625 \n\n\\bibitem[]{} Gunn, J. E. \\& Weinberg, D. H. 1995, in Wide-Field Specroscopy\n and the Distant Universe eds. S.J. Maddox and\n A. Aragon-Salamanca.(World Sientific: Singapore), 3\n\n\\bibitem[]{} Guth, A. \\& Pi, S.-Y. 1982, Phys. Rev. Lett., 49, 1110\n\n\\bibitem[]{} Hamilton, A. J. S., Gott, J. R. \\& Weinberg, D. H. 1986, ApJ, 309, 1\n\n\\bibitem[]{} Hamilton, A. J. S. 1988, PASP, 100, 1343\n\n\\bibitem[]{} Hawking, S. W. 1982, Phys. Lett., 115B, 295\n\n\\bibitem[]{} Hernquist, L. \\& Katz, N. 1989, ApJS, 70, 419\n\n\\bibitem[]{} Hivon, E., Bouchet, F. R., Colombi, S., \\& Juszkiewicz, R. 1995,\n A\\&A, 298, 643\n\n\\bibitem[]{} Juszkiewicz, R., Bouchet, F. R., \\& Colombi, S. 1993,\n ApJ, 412, L9 \n\n\\bibitem[]{} Juszkiewicz, R. et al. 1995, ApJ, 442, 39\n\n\\bibitem[]{} Kaiser, N. 1984, ApJ, 284, L9\n\n\\bibitem[]{} Kerscher, M. et al. 1997, MNRAS, 284, 73\n\n\\bibitem[]{} Kim, R. S. J., \\& Strauss, M. A. 1998, ApJ, 493, 39\n\n\\bibitem[]{} Klypin, A. A. 1988, ActaCosmologica, 15, 101\n\n\\bibitem[]{} {\\L}okas, E. L., Juszkiewicz, R., Weinberg, D. H. \\& Bouchet, F. R. 1995,\n MNRAS, 274, 730\n\n\n\\bibitem[]{} Luo, S. \\& Vishniac, E. T. 1995, ApJS, 96, 429\n\n\\bibitem[]{} Matsubara, T. 1994, ApJ, 434, L43\n\n\\bibitem[]{} Matsubara, T. 1995, Ph.D. Thesis, Hiroshima Univ\n\n\\bibitem[]{} Matsubara, T. \\& Suto, Y. 1996, ApJ, 460, 51\n\n\\bibitem[]{} Matsubara, T. \\& Yokoyama, J. 1996, ApJ, 463, 409\n\n\\bibitem[]{} Mecke, K. R., Buchert, T. \\& Wagner, H. 1994, A\\&A, 288, \n 697\n\n\\bibitem[]{} Melott,~A.~L., Weinberg,~D.~H., \\& Gott,~J.~R. 1988, ApJ,\n 328, 50\n\n\\bibitem[]{} Minkowski, H. 1903, Math. Ann., 57, 447\n\n\\bibitem[]{} Moore,~B. et al. 1992, MNRAS, 256, 477\n\n\\bibitem[]{} Monaghan, J. J. \\& Lattanzio, J. J. 1985, A\\&A, 149, 135\n\n\\bibitem[]{} Okun, B. L. 1990, J. Stat. Phys., 59, 523\n\n\\bibitem[]{} Park,~C. \\& Gott,~J.~R. 1991, ApJ, 378, 457\n\n\\bibitem[]{} Park,~C., Gott,~J.~R., \\& da Costa,~L.~N. 1992, ApJ, 392, L51\n\n% Peacock, J. A. \\& Dodds, S. J. 1996, MNRAS, 280, L19\n\n\\bibitem[]{} Protogeros, Z. A. M. \\& Weinberg D. H., 1997, ApJ, 489, 457\n\n\\bibitem[]{} Peebles, P. J. E. 1974, A\\&A, 32, 197\n\n\\bibitem[]{} Peebles, P. J. E. 1980, {\\ The Large Scale Structure of the Universe}\n (Princeton University Press: Princeton)\n\n\\bibitem[]{} Rhoads,~J.~E., Gott,~J.~R., \\& Postman,~M. 1994, ApJ, 421, 1\n\n\\bibitem[]{} Ryden, B. S. 1988, ApJ, 333, L41\n\n\\bibitem[]{} Ryden, B. S. et al. 1989, ApJ, 340, 647\n\n\\bibitem[]{} Sahni, V. Sathyprakash,B. S. \\& Shandarin, S. F. 1997, ApJ, 467, L1\n\n\\bibitem[]{} Schmalzing, J. \\& Buchert, T. 1997, ApJ, 482, L1\n\n\\bibitem[]{} Scoccimarro, R. 1998, MNRAS, 299, 1097\n\n\\bibitem[]{} Seto, N., Yokoyama, J., Matsubara, T. \\& Siino, M. 1997, ApJS, 110, 177\n\n\\bibitem[]{} Seto, N. 1999, ApJ, 523, 24\n\n\\bibitem[]{} Springel, V. et al. 1998, MNRAS, 298, 1169\n\n\\bibitem[]{} Starobinsky, A. A. 1982, Phys. Lett., 117B, 175\n\n\\bibitem[]{} Strauss, M. A. \\& Willick, J. A. 1995, Phys. Rep., 261, 271\n\n\\bibitem[]{} Thomas, P. A. \\& Couchman, H. M. P. 1992, MNRAS, 257, 11\n\n\\bibitem[]{} Totsuji, H \\& Kihara, T. 1969, PASJ, 21 221\n \n\\bibitem[]{} Vogeley,~M.~S. et al. 1994, ApJ, 420, 525\n\n\\bibitem[]{} Weinberg, D.~H., Gott, J.~R., \\& Melott, A.~L. 1987, ApJ, 321, 2\n\n\\bibitem[]{} Weinberg,~D.~H. \\& Cole,~S. 1992, MNRAS, 259, 652\n\n\\bibitem[]{} Wolfram, S. 1996, {\\ The Mathematica Book, 3rd ed.}\n (Cambridge University Press: Cambridge)\n\n\\bibitem[]{} Zeldovich, Ya.~B. 1970, A\\&A, 5, 84\n\n\n%\\end{references}\n\\end{thebibliography}"
}
] |
astro-ph0002316
|
PERFORMANCE RESULTS OF THE AMS-01 AEROGEL THRESHOLD \Cher
|
[
{
"author": "F. MAYET"
},
{
"author": "(for the AMS collaboration)"
}
] |
The Alpha Magnetic Spectrometer (AMS) was flown in june 1998 on board of the space shuttle Discovery (flight STS-91) at an altitude ranging between 320 and 390 km. This preliminary version of AMS included an Aerogel Threshold \cher detector (ATC) to separate $\bar{p}$ from $e^{-}$ background, for momenta less than 3.5 \GeVc. In this paper, the design and physical principles of ATC will be discussed briefly, then the performance results of ATC will be presented.
|
[
{
"name": "blois_proc.tex",
"string": "%====================================================================%\n% MORIOND.TEX 2-Feb-1995 %\n% This latex file rewritten from various sources for use in the %\n% preparation of the standard proceedings Volume, latest version %\n% for the Neutrino'96 Helsinki conference proceedings %\n% by Susan Hezlet with acknowledgments to Lukas Nellen. %\n% Some changes are due to David Cassel. %\n%====================================================================%\n\n\\documentstyle[11pt,blois_proc,epsfig]{article}\n%\\documentclass[11pt]{article}\n%\\usepackage{moriond,epsfig}\n\n\n\\bibliographystyle{unsrt} \n% for BibTeX - sorted numerical labels by order of\n% first citation.\n\n% A useful Journal macro\n\\def\\Journal#1#2#3#4{{#1} {\\bf #2}, #3 (#4)}\n\n% Some useful journal names\n\\def\\NCA{\\em Nuovo Cimento}\n\\def\\NIM{\\em Nucl. Instrum. Methods}\n\\def\\NIMA{{\\em Nucl. Instrum. Methods} A}\n\\def\\NPB{{\\em Nucl. Phys.} B}\n\\def\\PLB{{\\em Phys. Lett.} B}\n\\def\\PRL{\\em Phys. Rev. Lett.}\n\\def\\PRD{{\\em Phys. Rev.} D}\n\\def\\ZPC{{\\em Z. Phys.} C}\n\n% Some other macros used in the sample text\n\\def\\st{\\scriptstyle}\n\\def\\sst{\\scriptscriptstyle}\n\\def\\mco{\\multicolumn}\n\\def\\epp{\\epsilon^{\\prime}}\n\\def\\vep{\\varepsilon}\n\\def\\ra{\\rightarrow}\n\\def\\ppg{\\pi^+\\pi^-\\gamma}\n\\def\\vp{{\\bf p}}\n\\def\\ko{K^0}\n\\def\\kb{\\bar{K^0}}\n\\def\\al{\\alpha}\n\\def\\ab{\\bar{\\alpha}}\n\\def\\be{\\begin{equation}}\n\\def\\ee{\\end{equation}}\n\\def\\bea{\\begin{eqnarray}}\n\\def\\eea{\\end{eqnarray}}\n\\def\\CPbar{\\hbox{{\\rm CP}\\hskip-1.80em{/}}}\n%\n\\newcommand{\\GeVc} {\\mbox{$ {\\mathrm{GeV}}/c $}}\n\\newcommand{\\GeVcc} {\\mbox{$ {\\mathrm{GeV}}/c^2 $}}\n\\newcommand{\\MeVc} {\\mbox{$ {\\mathrm{MeV}}/c $}}\n\n%\n%temp replacement due to no font\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% %\n% BEGINNING OF TEXT %\n% %\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{document}\n\\vspace{-3.cm}\n\\noindent\nXIth Rencontres de Blois (Frontiers of Matter) proceedings.\\\\\nISN-99.98\\\\\n\\vspace*{2.cm}\n\\title{PERFORMANCE RESULTS OF THE AMS-01 AEROGEL THRESHOLD \\Cher}\n\n\\author{ F. MAYET \\\\ (for the AMS collaboration)}\n\n\\address{Institut des Sciences Nucl\\'eaires, 53 avenue des Martyrs, 38026 Grenoble cedex, France\\\\\nE-mail: Frederic.Mayet@isn.in2p3.fr}\n\n\\maketitle\\abstracts{\nThe Alpha Magnetic Spectrometer (AMS) was flown in june 1998 on board of the space shuttle Discovery (flight STS-91) \nat an altitude ranging between 320 and 390 km.\nThis preliminary version of AMS included an Aerogel Threshold \\cher detector (ATC) to separate \n$\\bar{p}$ from $e^{-}$ background, for momenta less than 3.5 \\GeVc.\nIn this paper, the design and physical principles of ATC will be discussed briefly, then the performance results of\nATC will be presented.}\n\n\\section{Role of ATC in AMS-01}\nOne of the purposes of the AMS Shuttle flight was to search for cosmic $\\bar{p}$ and to measure \n${\\bar{p}}/p$ ratio for momenta(P) below 3.5~\\GeVc. The major background component to the $\\bar{p}$ sample is expected to be $e^{-}$ (${\\bar{p}}/e^{-} \\sim 10^{-2}$ for the considered\nP range).\\\\\nUsing AMS-01 momentum resolution~\\cite{bill} (${\\Delta P}/P=7.\\%$) and $\\beta$ resolution~\\cite{chou} (${\\Delta \\beta }/\\beta \\simeq\n3.3\\%$), it can be shown~\\cite{atc} that\nAMS electron rejection falls sharply above 1.5-2 \\GeVc~. ATC is used to extend $\\bar{p}/e^{-}$ discrimination range up to 3.5\n\\GeVc. As a secondary result, ${p}/{e^{+}}$ separation can also be improved using appropriate ATC selections.\n\n\n\\noindent\nMany balloon-borne experiments (CAPRICE, BESS,...) have included a \\cher counter and a Ring Imaging \\cher counter \nis under study for the next phase of the AMS experiment~\\cite{thom,fer}.\\\\\nUsing an aerogel material with a low refractive index (n=1.035), \nthe ATC counter profits from \\cher effect to separate $\\bar{p}$ from $e^{-}$ at low energy.\nIndeed, the momentum threshold is 1.9 \\MeVc~for $e^{\\pm}$ and 3.5 \\GeVc~for $p$($\\bar{p}$). \nHence, in the GeV range and up to this momentum, $p$($\\bar{p}$) are not expected to produce any signal, while $e^{\\pm}$ will give a full signal.\n\\begin{figure}\n\\psfig{figure=newatc.ps,height=6.5in,angle=270}\n{\\noindent\n\\caption{ATC detector design. The 2 shifted layers (in x and y directions) can be seen together\twith \nthe structure allowing to mount the ATC directly on the Space Shuttle. On the detailed view of the ATC cell, \nthe eight blocks of aerogel are shown together with three teflon layers and the PMP wavelength shifter in the middle of the cell.\n\\label{fig:atcfig}}}\n\\end{figure}\n\n\n\\noindent\nThe design of ATC will be described in detail elsewhere~\\cite{atc}.\nThe elementary component of the ATC detector is the aerogel cell \n(11 $\\times$ 11 $\\times$ 8.8 $cm^{3}$, see figure \\ref{fig:atcfig}), filled with eight $1.1 cm$ thick aerogel blocks.\nThe emitted photons are reflected by three $250 \\mu m$ teflon layers surrounding the blocks, until they reach \nthe photomultiplier's window (Hamamatsu R-5900).\\\\\nThe 168 cells are arranged in 2 layers (80 cells in the upper one and 88 cells in the lower one). \nDue to the direct photon detection used, the Rayleigh diffusion ($L_{R} \\propto \\lambda_{\\gamma}^{4}$) and \nthe absorption ($L_{abs} \\propto \\lambda_{\\gamma}^{2}$) are known to be the most limiting processes.\nThese two effects are decreasing with increasing photons wavelength. For this purpose, a wavelength shifter is placed in the middle of each cell. \nIt consists of a thin layer of tedlar (25 $\\mu m$) soaked in a PMP solution.\nThis allows to shift~\\footnote{It should be noticed that maximum efficiency \nof the R-5900 photomultipier tube is also at $\\lambda \\sim 420 nm$.} wavelength from 300$nm$ up to 420$nm$. \nThe use of the shifter leads to an overall increase in number of p.e, estimated to be $\\sim 40.\\%$.\\\\\n\n\\section{ATC performance results}\n\nMore detailed results may be found in reference 3. First, ATC was not affected neither by the launch nor the space\nconditions, which is a success because of the natural fragility of the aerogel material. Then, some basic checks have been done, to ensure\nthat the ATC response is consistent with the main physical dependences. Namely, the number of photons created by \\cher effect, in a \nmaterial of refractive index $n$, is known to be :\n\\begin{equation}\nN_{pe} \\propto L_{aero}\\times Z^{2} \\times (1-\\frac{1}{n^{2} \\beta^{2}})\n\\label{cherequa} \n\\end{equation}\nAs shown in reference 3, the ATC signal as a linear dependence with the square of the particle's charge ($Z^{2}$) and the path length in the material\n($L_{aero}$). Moreover, using flight data, the refractive index has been evaluated to be $n=1.034$, which is in good agreement with the known value.\n\n\\noindent\nThe ATC rejection and efficiency for particle selection is evaluated by defining two control samples:\nElectrons (positrons) are simulated by high energy protons ($P \\geq 15 $ and $\\beta \\geq 0.99$), \ndetected near equator by AMS, thus taking advantage on the geomagnetic cutoff which ensure that most of the particles \nin this region are high energy ones.\nAntiprotons are simulated by low energy protons ($P \\leq 3.5$ \\GeVc~, $\\beta \\leq 0.97$ and $0.6 \\leq M \\leq1.2$ \\GeVcc).\n\n\\noindent\nUsing these two control samples, one gets 7.5 p.e for $e^{\\pm}$ (after correction on various effects such as electronic\nthreshold and $\\beta$ effect). On the other hand, most of the $p$($\\bar{p}$) give 0 p.e, although ATC\nencountered a residual light problem due to after-pulses \nin the PMT, \\cher effect in the PMT window and scintillation effect in various materials.\n\n\\noindent\nAntiprotons are selected as particles crossing two cells, leading to an overall \ngeometrical efficiency of 72 $\\%$, and giving less than 0.15 p.e . \nUsing this selection, ATC provides a rejection of 330 against electrons, with a maximum \nefficiency of $48\\%$ (shown in fig. \\ref{fig:atcperf}).\n\n\\noindent\nATC may also be used to select positrons out of proton background. In this case, the ATC conditions require that the particle crosses \n2 cells and produce, in each cell, more than 2 p.e . In order to avoid contamination \\footnote{For more details, see ref. 3} due to\nprotons passing close to the PMT, and thus producing \\cher effect in the window, the closest distance \nto the PMT should be greater than 1.5 $cm$. Using this selection, ATC provides a separation between positrons and proton background, \nwith an efficiency of $41 \\%$ and a maximum rejection of 260 (see fig. \\ref{fig:atcperf}).\n%\n\n\\noindent\nThe first AMS test flight has been largely successful for AMS in general and ATC in particular. No major problems were encountered, and ATC allows \nto extend $\\bar{p}/e^{-}$ discrimination range up to 3.5 \\GeVc, with a good efficiency and a high rejection, as shown above.\nFurthermore, ATC may be used as a redundant way of selecting $e^{+}$ out of proton background.\n%\n\\section*{Acknowledgments}\nThe AMS Aerogel Threshold \\cher is the result of the contributions of physicists, engineers and\ntechnicians from ISN Grenoble and LAPP Annecy (France), INFN Firenze and INFN Bologna \n(Italy), ITEP Moscow (Russia), Academia Sinica (Taiwan), LIP Lisboa (Portugal).\\\\\nThe author wishes to thank Daniel Santos, Jean Favier and Fernando Barao, for the fruitful collaboration on ATC\nanalysis.\n%\n\n\\begin{figure}\n\\begin{center}\n\\psfig{figure=effpro_bw.epsi,height=2.5in}\n\\psfig{figure=eplus_bw.epsi,height=2.5in}\n{\\noindent\n\\caption{Antiproton efficiency (left) as a function of P(\\GeVc) for different cuts on $n_{p.e}$. \nThe $e^{-}$ rejection (R) is also indicated for each cut. \nProton rejection (right) as a function of P(\\GeVc), together with $e^{+}$ efficiency($\\epsilon$).\n\\label{fig:atcperf}}}\n\\end{center}\n\\end{figure}\n\n%\n\\section*{References}\n\\begin{thebibliography}{99}\n\\bibitem{bill}J. Alcaraz \\textit{et al.}, {\\em Contribution to ICRC 99 (Salt Lake City, USA), session OG.4.2.02}\n\\bibitem{chou}E. Choumilov, \\textit{private communication}\n\\bibitem{atc}F. Barao, J. Favier, F. Mayet {\\it et al.}, in preparation.\n\\bibitem{thom}T. Thuillier {\\it et al.}, {\\em Proc. Beaune 99}, to be published.\n\\bibitem{fer}F. Barao, {\\em Proc. New Worlds in Astrop. Physics 98}, to be published.\n\n\\end{thebibliography}\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002316.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{bill}J. Alcaraz \\textit{et al.}, {\\em Contribution to ICRC 99 (Salt Lake City, USA), session OG.4.2.02}\n\\bibitem{chou}E. Choumilov, \\textit{private communication}\n\\bibitem{atc}F. Barao, J. Favier, F. Mayet {\\it et al.}, in preparation.\n\\bibitem{thom}T. Thuillier {\\it et al.}, {\\em Proc. Beaune 99}, to be published.\n\\bibitem{fer}F. Barao, {\\em Proc. New Worlds in Astrop. Physics 98}, to be published.\n\n\\end{thebibliography}"
}
] |
astro-ph0002317
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Analytic solutions for coupled linear perturbations
|
[
{
"author": "Adi Nusser"
},
{
"author": "Physics Department"
},
{
"author": "Technion"
},
{
"author": "Haifa 32000"
},
{
"author": "Israel"
}
] |
Analytic solutions for the evolution of cosmological linear density perturbations in the baryonic gas and collisionless dark matter are derived. The solutions are expressed in a closed form in terms of elementary functions, for arbitrary baryonic mass fraction. They are obtained assuming $\Omega=1$ and a time independent comoving Jeans wavenumber, $k_J$. By working with a time variable $\tau\equiv \ln(t^{2/3})$, the evolution of the perturbations is described by linear differential equations with constant coefficients. The new equations are then solved by means of Laplace transformation assuming that the gas and dark matter trace the same density field before a sudden heating epoch. In a dark matter dominated Universe, the ratio of baryonic to dark matter density perturbation decays with time roughly like $\exp(-5\tau/4)\propto t^{-5/6}$ to the limiting value $1/[1+(k/k_J)^2]$. For wavenumbers $k>k_J/\sqrt{24}$, the decay is accompanied with oscillations of a period $ 8\pi/\sqrt{24 (k/k_J)^2 -1}$ in $\tau$. In comparison, as $\tau $ increases in a baryonic matter dominated Universe, the ratio approaches $1-(k/k_J)^2$ for $k\le k_J$, and zero otherwise.
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[
{
"name": "jeans.tex",
"string": "%\\documentstyle[twocolumn]{mn}\n%\\documentstyle[twocolumn,referee]{mn}\n%\\documentstyle[onecolumn,referee]{mn}\n%\\documentstyle[onecolumn,psfig,rotating]{mnv2}\n\\documentstyle[onecolumn,psfig,rotating]{mnv2}\n\n\\parskip 6pt\n\\def\\cl{\\centerline}\n\\def\\no{\\noindent}\n\\def\\bk{\\hfill\\break}\n% The following macros should be used only in math mode.\n\\def\\lsim{~\\rlap{$<$}{\\lower 1.0ex\\hbox{$\\sim$}}}\n\\def\\bsim{~\\rlap{$>$}{\\lower 1.0ex\\hbox{$\\sim$}}}\n\n\\def\\ergcms{\\,{\\rm erg\\,cm^{-3}\\,s^{-1}}}\n\\def\\kms{\\ {\\rm km\\,s^{-1}}}\n\\def\\hmpc{\\ {\\rm h^{-1}Mpc}}\n\\def\\hh{\\ {\\rm h_{50}}}\n\\def\\hmmpc{\\ {\\rm hMpc^{-1}}}\n\\def\\gcc{\\,{\\rm g\\,cm^{-3}}}\n\\def\\tl{ {\\tilde l}}\n\\def\\pcc{\\,{\\rm cm^{-3}}}\n\\def\\kel{\\,{\\rm K}}\n\\def\\dd{{\\rm d}}\n\\def\\ln{{\\rm ln}}\n\\def\\pa{\\partial}\n\\def\\rarrow{\\rightarrow}\n\\def\\larrow{\\leftarrow}\n\\def\\la{\\langle}\n\\def\\ra{\\rangle}\n\\def\\grad{\\nabla}\n%\n\\def\\pmb#1{\\setbox0=\\hbox{#1}%\n\\kern-.025em\\copy0\\kern-\\wd0\n\\kern.05em\\copy0\\kern-\\wd0\n\\kern-.025em\\raise.0433em\\box0}\n\\def\\th{\\vartheta}\n%\\def\\divv{\\vnabla \\cdot \\vv}\n%\\def\\vth{\\vec\\th}\n\\def\\vth{\\pmb{$\\th$}}\n\\def\\ph{\\varphi}\n\\def\\phv{\\ph_v}\n\\def\\phg{\\ph_g}\n\\def\\vV{\\pmb{$V$}}\n\\def\\vv{\\pmb{$V$}}\n\\def\\valpha{\\pmb{$\\theta$}}\n\\def\\tvalpha{\\pmb{$\\tilde {\\alpha} $}}\n\\def\\vtheta{\\pmb{$\\theta$}}\n\\def\\vq{\\pmb{$q$}}\n\\def\\vg{\\pmb{$g$}}\n\\def\\tvg{\\pmb{${\\tilde g}$}}\n\\def\\vx{\\pmb{$x$}}\n\\def\\vs{{\\pmb{$s$}}}\n\\def\\vk{\\pmb{$k$}}\n\\def\\vC{\\pmb{$C$}}\n\\def\\vA{\\pmb{$A$}}\n\\def\\tvC{\\pmb{$\\tilde {C}$}}\n\\def\\vkp{{\\vk^\\prime}}\n\\def\\vpsi{\\pmb{$\\psi$}}\n\\def\\phiv{\\phi_v}\n\\def\\phig{\\phi_g}\n\\def\\pot {\\Phi}\n\\def\\db {\\delta_b}\n\\def\\dx {\\delta_x}\n\\def\\ldb {\\Delta_b}\n\\def\\ldx {\\Delta_x}\n\\def\\trh {\\frac{3}{2}}\n\\def\\sterm {s^2+\\frac{1}{2}s}\n\\def\\omtot {f_x \\ldx + f_b \\ldb}\n% notation change!! MD\n\\def\\ip {i^\\prime}\n\\def\\da {{\\dot a}}\n\\def\\rh {{\\rm H}}\n\\def\\rp {{\\tau}}\n\n\\def\\etal{{\\it et al.\\ }}\n\\def\\con {5\\log {\\rm e}}\n%\\def\\vnabla{\\vec\\nabla}\n\\def\\vnabla{\\pmb{$\\nabla$}}\n\\def\\divv{\\vnabla \\cdot \\vv}\n\\def\\dvx{\\pmb{${\\dot x}$}}\n\\def\\xpar{{\\vx^\\parallel}}\n\\def\\xper{{\\vx^\\perp}}\n\\def\\cpar{{\\vC^\\parallel}}\n\\def\\cper{{\\vC^\\perp}}\n% Make sure sections dont begin at bottom of page\n\\def\\secpush{\\vskip0pt plus 2.0\\baselineskip\\penalty-250\n \\vskip0pt plus -2.0\\baselineskip }\n\n\n\\begin{document}\n\\title[Analytic solutions for coupled perturbations]\n{Analytic solutions for coupled linear perturbations}\n\\author[Nusser ]{Adi Nusser\n\\\\\nPhysics Department,\nTechnion, Haifa 32000, Israel\\\\\nE-mail: adi@physics.technion.ac.il\n}\n\\maketitle\n\n\\begin{abstract}\nAnalytic solutions for the evolution of cosmological linear density\nperturbations in the baryonic gas and collisionless dark matter are\nderived. The solutions are expressed in a closed form in terms of\nelementary functions, for arbitrary baryonic mass fraction. They are\nobtained assuming $\\Omega=1$ and a time independent comoving Jeans\nwavenumber, $k_J$. By working with a time variable $\\tau\\equiv\n\\ln(t^{2/3})$, the evolution of the perturbations is described by\nlinear differential equations with constant coefficients. The new\nequations are then solved by means of Laplace transformation assuming\nthat the gas and dark matter trace the same density field before a sudden\nheating epoch. In a dark matter dominated Universe, the ratio of\nbaryonic to dark matter density perturbation decays with time roughly like\n$\\exp(-5\\tau/4)\\propto t^{-5/6}$ to the limiting value\n$1/[1+(k/k_J)^2]$. For wavenumbers $k>k_J/\\sqrt{24}$, the decay is\naccompanied with oscillations of a period $ 8\\pi/\\sqrt{24 (k/k_J)^2 -1}$ in\n$\\tau$. In comparison, as $\\tau $ increases in a baryonic matter\ndominated Universe, the ratio approaches $1-(k/k_J)^2$ for $k\\le k_J$,\nand zero otherwise.\n\\end{abstract}\n\\begin{keywords}\ncosmology: theory -- gravitation -- dark matter --intergalactic medium\n\\end{keywords}\n\\section {Introduction}\n\nSeveral methods (e.g., Croft et al. 1998; Gnedin 1998; Nusser \\&\nHaehnelt 1999) have recently been proposed for extracting\ninformation on the mass density field from the Lyman-$\\alpha$ forest.\nThe underlying physical picture behind these method is that the\nabsorbing Neutral hydrogen in the low density intergalactic medium\n(IGM) is tightly related to the mass density field on scales larger\nthan the Jeans length. Below the Jeans length gas pressure segregates\nthe baryons from the total mass fluctuations. On scales near the Jeans\nlength, the evolution of the baryonic perturbation can affect\nestimates of the clustering amplitude from observations of the\nLyman-$\\alpha$ forest.\n\nHydrodynamical simulations (Petitjean, M\\\"ucket \\& Kates 1995; Zhang,\nAnninos \\& Norman 1995; Hernquist et al.~1996; Miralda-Escud\\'e et\nal.~1996, Theuns et al. 1998) and semi-analytic models (e.g., Bi\net. al. 1992, Gnedin \\& Hui 1996) of the IGM have been successful at\nexplaining observations of the forest. Despite the success of the\nsimulations, it is usually difficult to use them to study in detail\nthe evolution of the gas below Jeans length (Theuns et al. 1998). The\nequations governing the evolution of baryons and dark matter in the\nnonlinear regime are extremely difficult to solve, even for special\nconfigurations like spherical collapse. Fortunately, since most of\nthe IGM is of moderate density, linear analysis can be a suitable tool\nfor understanding the evolution of the baryons (Gnedin \\& Hui 1998).\nHere we derive analytic solutions to the linear equations in a flat\nuniverse without a cosmological constant. Although the linear\nequations can readily be numerically integrated under a variety of\nconditions (Gnedin \\& Hui 1998), analytic treatment offers better\nunderstanding of the equations. Further, the paucity\nof analytic solutions makes their pursue worthwhile, even if tedious at\ntimes.\nThe analytic solutions we derive here are \nsubject to the condition that the baryonic and dark matter \ntrace the same density and\nvelocity fields before a sudden reionization epoch.\nAfter reionization the temperature of the IGM is\nassumed to be inversely proportional to the scale factor so that the\ncomoving Jeans length is constant. \n\n\nThe paper is organized as follows. \nIn section 2 we cast the equations in the form \nof linear differential equations with constant coefficients.\nIn Section 3 we present the solutions to these equations for \nseveral cases. We conclude in Section 4. \n\n\\section{The linear equations}\nLet $\\dx(t,k)$ and $\\db(t,k)$ be , respectively, the Fourier modes\nof baryonic and dark matter \ndensity fluctuations. Let also $f_X$ and $f_b=1-f_x$ be the \nthe mean mass fractions of these two types of matter. \nWe will restrict the analysis to perturbations in a flat universe \nwithout a cosmological constant.\nThe linear equations governing the evolution \nof $\\db$ and $\\dx$ are (e.g., Bi et. al. 1992, Padmanabhan 1993, \nGnedin \\& Hui 1998),\n\\begin{eqnarray}\n\\frac{\\dd^2 \\dx}{\\dd t^2} +2H\\frac{\\dd \\dx}{\\dd t}&=& \n\\frac{3}{2}H^2\\left(f_x \\dx + f_b \\db \\right) \\cr\n\\frac{\\dd^2 \\db}{\\dd t^2} +{2}H\\frac{\\dd \\db}{\\dd t}&=& \n\\frac{3}{2}H^2\\left(f_x \\dx + f_b \\db \\right) - \\frac{3}{2}H^2 \n\\left(\\frac{k}{k_J}\\right)^2 \\db \\; ,\n\\label{lint}\n\\end{eqnarray}\nwhere $a(t)\\propto t^{2/3}$ is the scale factor, $H(t)=2/(3t)$ the\nHubble function, and $k_J$ is the comoving Jeans wavenumber related to the\nspeed of sound $c_s$ and the mean total (baryons plus dark) density,\n$\\bar \\rho=3H^2/(8\\pi G)$, by\n\\begin{equation}\nk_J=\\frac{a}{c_s}\\sqrt{4\\pi G \\bar \\rho}=\\sqrt{\\frac{3}{2}}\\frac{a H}{c_s} .\n\\end{equation}\n\n\nFor $f_x$ close to unity the gravity of the baryons is negligible and\n$\\dx \\propto a$. If also $k_J=const$ (i.e., $c_s^2\\propto 1/a$) and we\nimpose, at some initial time $t_i$, the condition\n$\\db(t_i)=\\dx(t_i)/(1+(k/k_J)^2)$, then $\\db(t) =\\dx(t)/(1+(k/k_J)^2)$\nat any later time, $t$. In the next section we will show how to solve\nthese equations with $0<le f_x\\le $ assuming that \n$\\db(t)=\\dx(t)$ for $t\\le t_i$, which is appropriate for a\nsudden reionization of the IGM at $t_i$.\n\nIn order to solve these equations we work with a new time \nvariable $\\rp \\equiv \\ln (a)$ instead of $t$ (Nusser \\& Colberg 1998).\nIn terms of $\\tau$ the equations become,\n\\begin{eqnarray}\n\\frac{\\dd^2 \\dx}{\\dd \\rp^2} +\\frac{1}{2}\\frac{\\dd \\dx}{\\dd \\rp}&=& \\frac{3}{2}\\left(f_x \\dx +\nf_b \\db \\right) \\cr \n\\frac{\\dd^2 \\db}{\\dd \\rp^2} +\\frac{1}{2}\\frac{\\dd \\db}{\\dd \\rp}&=& \\frac{3}{2}\\left(f_x \\dx +\nf_b \\db \\right) -\\frac{3}{2} \\kappa^2 \\db \\; ,\n\\label{lintau}\n\\end{eqnarray}\nwhere have defined $\\kappa=k/k_J$.\n\nWhen $\\kappa$ is constant, the differential equations (\\ref{lintau}) \nare linear with constant coefficients and they can be solved\nby means of Laplace transformation.\nSince Laplace transforms are seldom used in cosmological studies, it seems \nprudent to briefly review\ntheir basic properties which are relevant to us. \nWe refer the reader to Arfkin (1985) and references therein\nfor mathematical details.\nThe Laplace transform, $f(s)$, of a function $F(t)$, where $t\\ge 0$,\nis defined as \n\\begin{equation}\nf(s)\\equiv {\\cal L}\\{F(t)\\}=\\int_0^\\infty \\exp\\left(-st\\right) F(t) \\dd t .\n\\label{laplace:def}\n\\end{equation} \nWe will need the Laplace transforms of first and second derivatives of a\nfunction. Using (\\ref{laplace:def}) these transforms can be related to the\n$f(s)$ by\n\\begin{eqnarray}\n{\\cal L} \\{ F'(t)\\} &=& s f(s)- F(0) \\cr\n{\\cal L} \\{ F''(t)\\} &=& s^2 f(s)- s F(0) - F'(0) \\; ,\n\\label{laplace:derv}\n\\end{eqnarray}\nwhere the prime and double prime denote first and second order \nderivatives, respectively. \nThe Bromwich integral expresses $F(t)$ in terms of $f(s)$\nas \n\\begin{equation}\nF(t)=\\frac{1}{2\\pi i}\\int_{\\gamma -i\\infty}^{\\gamma+i\\infty}\n\\exp\\left(s t\\right) f(s)\\dd s \n\\label{bowich}\n\\end{equation}\nwhere $i=\\sqrt{-1}$ and $\\gamma$ is a real number chosen so that\nall poles of $f(s)$ lie, in the complex plane, to the left of the \nvertical line defining the integration path. Therefore, by the residue\ntheorem we have\n\\begin{equation}\nF(t)=\\sum \\left[\n{\\rm residues} \\; {\\rm of} \\; \\exp\\left(s t\\right)f(s)\n\\right]\n\\label{resid}\n\\end{equation}\nAs an example consider $f(s)=1/(s-s_1)(s-s_2)$ which has two simple poles at \n$s=s_1 $ and $s_2$. The residues of $\\exp({s t}) f(s)$ at these poles are \n$\\exp({s_1 t}) /(s_1-s_2)$ and $-\\exp({s_2 t}) /(s_1-s_2)$ so that, by (\\ref{resid}),\n$F(t)=[\\exp({s_1 t})- \\exp({s_2 t})]/(s_1-s_2)$. If $s_1=s_2$, the function \nhas a pole of order two at $s_1$. The residue \nin this case is $\\dd[(s-s_1)^2 \\exp({st})f(s))]/\\dd s$ evaluated at $s=s_1$. \nTherefore, $F(t)=t \\exp({s_1 t})$.\n\n\n\\section{The solutions}\n\nDenote by $\\ldx$ and $\\ldx$ the Laplace transforms of $\\dx$ and $\\db$,\nrespectively. By taking the Laplace transform of (\\ref{lintau}) we can\nobtain relations between $\\ldx$ and $\\ldb$. The initial conditions\nare contained in the Laplace transforms of the first and second\nderivatives of the densities. So first we have to specify in\nmathematical terms our choice for the initial conditions. For\nsimplicity of notation we fix the initial conditions at $\\tau=1$\nassuming that before that time the temperature of the baryonic fluid\nis zero, i.e., $\\kappa=0$. The initial conditions are fixed by the\nvalues of $\\dx$ and $\\db$ and their first derivatives at $\\tau=1$.\nBefore $\\tau=1$, we have $\\dx=\\db=\\exp(\\tau)$, ignoring the decaying\nmode and setting arbitrarily $\\dx(\\tau=1)=1$. The first derivatives\nof $\\dx$ and $\\db$ are therefore equal to unity at $\\tau=1$. This\nfixes the initial conditions necessary for solving\n(\\ref{lintau}). Although we will present solutions satisfying only\nthese initial conditions, we will, for completeness, write the Laplace\ntransformation of (\\ref{lintau}) for $\\db=\\alpha\\dx $ and $\\dd \\db\n/\\dd \\tau=\\alpha \\dd \\dx /\\dd \\tau$, at $\\tau=1$. \nThen the Laplace transformation of (\\ref{lintau}) yields\n\\begin{eqnarray}\n\\left( \\sterm \\right) \\ldx &=& \n\\trh \\left( \\omtot \\right) +s +\\trh\\cr \n\\left( \\sterm \\right) \\ldb &=& \n\\trh \\left( \\omtot \\right) -\n\\trh \\kappa^2 \\ldb + \\alpha s +\\trh \\alpha \\; ,\n\\label{laplace:lin}\n\\end{eqnarray}\nwhere have have used (\\ref{laplace:derv}) to computed the \ntransforms of the first and second derivatives of $\\dx$ and $\\db$.\nFor $f_x=1$ the first of these equations yields\n\\begin{equation}\n\\ldx=\\frac{1}{s-1}\\; ,\n\\label{ldxfx}\n\\end{equation}\nwhich is the Laplace transform of $\\exp(\\tau)$. \nIf we take $\\alpha=(1+\\kappa^2)^{-1}$ and \nsubstitute (\\ref{ldxfx}) in \nthe second equation of (\\ref{laplace:lin}) we get \n\\begin{equation}\n\\ldb=\\frac{1}{s-1}\\frac{1}{1+\\kappa^2}=\\frac{\\ldx}{1+\\kappa^2} \\; ,\n\\end{equation}\nwhich leads to the well known solution $\\db=\\dx/(1+\\kappa^2)$. \n\nSubsequently we will present solutions only for $\\alpha=1$.\nIn this case,\nequations (\\ref{laplace:lin}) yield %IMPORT\n\\begin{equation}\n\\ldx= \\frac{\\left( s +\\trh\\right) \\left(\\trh \\kappa^2+\\sterm\\right)}\n{\\left(\\sterm\\right)\n\\left(\n\\trh \\kappa^2+\\sterm-\\trh\n\\right) -\\frac{9}{4}f_x\\kappa^2} \\; ,\n\\label{dxg} \n\\end{equation}\nand\n\\begin{equation}\n\\ldb=\\frac{\\sterm}{\\trh \\kappa^2 \n+\\sterm}\\ldx \\; .\n\\label{dbdx}\n\\end{equation}\n\nBefore solving these equations for any value\nof $f_x $ in the range 0--1, it is instructive to \nexamine the solutions for the special values $f_x=1$ and $0$.\n\n\n\n\\subsection{ Case I: $f_x=1$}\nIn this case $\\ldx=(s-1)^{-1}$ and equation \n(\\ref{dbdx}) can be written in the form \n\\begin{equation}\n\\ldb=\\frac{\\sterm}{(s-1)(s-s_{_-})(s-s_{_+})}\n\\end{equation}\nwhere $s_{_\\pm}$ are the roots of $3\\kappa^2/2+s^2+s/2$. They\nare given by\n\\begin{equation}\n s_{_\\pm}=-\\frac{1}{4}\\left(1 \\pm \\chi\\right) \n\\qquad ; \\qquad \\chi^2={1 -24 \\kappa^2}\n\\end{equation}\nWe will deal with the case $ \\chi^2=0$ at the end of this subsection.\nFor $\\chi^2 \\ne 0$, \nall three poles of $\\ldb$\nare simple and so,\nby (\\ref{resid}), its inverse transform is\n\\begin{equation}\n\\db=\\frac{\\exp\\left(\\rp\\right)}{1+\\kappa^2} +\n\\frac{1}{s_{_-}-s_{_+}}\\frac{\\kappa^2}{1+\\kappa^2} \n\\biggl[\n\\left(s_{_-}-1\\right) \\exp\\left(s_{_+} \\rp\\right) - \\left(s_{_+} -1\\right)\n\\exp\\left(s_{_-} \\rp\\right)\n\\label{dbcon}\n\\biggr]\n\\end{equation}\nFor $\\chi^2>0$ the roots $s_{_\\pm}$ are real and the \nresult is \n\\begin{equation}\n\\db=\\frac{\\exp\\left(\\rp\\right)}{1+\\kappa^2} +\n\\frac{1}{2\\chi}\\frac{\\kappa^2}{1+\\kappa^2}\n\\biggl[\\left(\\chi-5\\right) \\exp\\left(-\\frac{\\chi}{4}\\rp\\right) \n+\\left(5+\\chi\\right)\\exp\\left(+\\frac{\\chi}{4}\\rp\\right)\\biggr]\n\\exp\\left(-\\frac{\\rp}{4}\\right)\n\\label{dbexp}\n\\end{equation}\nThe first term is the solution given in the previous section \nfor $\\alpha=1/(1+\\kappa^2)$. \nThe maximum value $\\chi^2 $ attains is unity, so\nthe second and third\nterms are always decaying. \nIf $\\chi^2 <0$, then (\\ref{dbcon}) gives the solution \n\\begin{equation}\n\\db=\\frac{\\exp\\left(\\rp\\right)}{1+\\kappa^2} +\n\\frac{1}{\\tilde \\chi}\\frac{\\kappa^2}{1+\\kappa^2}\n\\biggl[5\\sin\\left(\\frac{\\tilde \\chi}{4}\\rp\\right) +\n\\chi\\cos\\left(\\frac{\\tilde \\chi}{4}\\rp\\right)\n\\biggr]\\exp\\left(-\\frac{\\rp}{4}\\right)\n\\label{dbsin}\n\\end{equation}\nwhere $\\tilde \\chi$ is the imaginary part of $\\chi$. The solution\nshows an oscillatory behavior with a period of $16\\pi/\\tilde \\chi$. The\nenvelope of these oscillations decays like $\\exp(-\\tau/4)\\propto\nt^{-1/6}$.\n\n\nWe deal now with the case $\\chi^2=0$, which occurs for $\\kappa^2=1/24$.\nHere special care is needed because $s_{_-}=s_{_+}=-1/4$. However \nthe contribution of the pole at $s=-1$ to the Bromwich integral \nremains unchanged and the\ncontribution of the second order pole at $s=-1/4$ is simply \nthe first derivative of $\\exp({s\\tau})\n(s+1/4)^2\\ldb$ at $s=-1/4$. The result is\n\\begin{equation}\n\\db=\\frac{24}{25}\\exp\\left(\\tau\\right) +\\frac{1}{20}\\left(\\tau + \\frac{4}{5}\\right)\n\\exp\\left(-\\frac{\\tau}{4}\\right) \\; .\n\\end{equation}\nThe first term on the left is the familiar $\\dx /(1+\\kappa^2)$ evaluated \nat $\\kappa^2=1/24$.\nThe expression can also be derived by taking the limit $\\chi^2\\rightarrow 0$ \nin either (\\ref{dbexp}) or (\\ref{dbsin}).\n\nIn the limit $\\tau\\rightarrow \\infty$ \nthe ratio $\\db/\\dx$ is $1/(1+\\kappa^2)$.\n% for $\\kappa \\le 1$ and zero otherwise.\n\n\n\\subsection{ Case II: $f_x=0$}\nThis is equivalent to ignoring the gravity of the \ndark matter. Of course here only the behavior of the \nperturbation in the baryons is relevant since the dark matter \nplays no role. \nHowever, for the sake of completeness and comparison with other situations\nwe will solve for the dark matter fluctuations as well.\n\nWe first find the solution for $\\dx$.\nIf $f_x=0$, we can express (\\ref{dxg}) in \nterms of $s_{_\\pm}$, the roots of\n$3\\kappa^2/2+s^2+s/2-3/2$, as\n\\begin{equation}\n\\ldx= \\frac{\\left( s +\\trh\\right) \\left(\\trh \\kappa^2+\\sterm\\right)}\n{s\\left(s+\\frac{1}{2}\\right)\n\\left(s-s_{_-}\n\\right)\n\\left(s-s_{_+}\n\\right)\n} \\; ,\n\\end{equation}\nwhere \n\\begin{equation}\n s_{_\\pm}=-\\frac{1}{4}\\left(1 \\pm \\chi\\right) \n\\qquad ; \\qquad \\chi^2={25 -24 \\kappa^2}\n\\end{equation}\n\nIf $\\kappa\\ne 1$, then the function $\\ldb$ has three simple \npoles at $s=0$, $s_{_-}$, and $s_{_+}$. \nSo for $\\kappa \\ne 1$ and $\\chi^2>0$, Bromwich integral \nyields\n\\begin{equation}\n\\dx=\n\\frac{\\kappa^2}{1-\\kappa^2}\\biggl[\n2 \\exp\\left(-\\frac{\\tau}{2}\\right)-3\n\\biggr]\n+\\frac{1}{2\\chi}\\frac{1}{1-\\kappa^2}\n\\biggl[\\left(\\chi-5\\right)\\exp\\left(-\\frac{\\chi}{4}\\tau\\right)\n+\\left(\\chi+5\\right)\\exp\\left(+\\frac{\\chi}{4}\\tau\\right)\\biggr]\n\\exp\\left(-\\frac{\\tau}{4}\\right) \\; .\n\\label{dxs2}\n\\end{equation}\nThe expression for $\\db$ is\n\\begin{equation}\n\\db=\\frac{1}{2\\chi}\\biggl[\n\\left(\\chi -5\\right) \\exp\\left(-\\frac{\\chi}{4}\\tau\\right)+\n\\left(\\chi+5\\right) \\exp\\left(\\frac{\\chi}{4}\\tau\\right)\\biggr]\n\\exp\\left(-\\frac{\\tau}{4}\\right) \\; .\n\\label{dbs2}\n\\end{equation}\n\n\nWhen $\\kappa=1$ the solution can be found either by taking the limit\n$\\kappa\\rightarrow 1$ in the previous two \nexpressions or by direct evaluation of the Bromwich integral\nwith a two poles of order two at $s=0$ and $-1/2$. The result is \n\\begin{equation}\n\\dx=-27+28\\exp\\left(-\\frac{\\tau}{2}\\right)+\n3\\tau\\left[3+2 \\exp\\left(-\\frac{\\tau}{2}\\right) \\right] \\qquad {\\rm and} \\qquad\n\\db=3-2 \\exp\\left(-\\frac{\\tau}{2}\\right) \\; .\n\\end{equation}\nThis implies that $\\dx$ grows\nlinearly with $\\tau$ at late times\nwhile $\\db$ reaches an asymptotic value of $3$.\n\nThe oscillatory behavior of $\\db$ and $\\dx$ appears when $\\chi^2<0$,\ni.e., for $\\kappa^2 >25/24$. The expressions in this case \ncan be obtained by replacing $\\chi$ with $i\\tilde \\chi$ in \n(\\ref{dxs2}) and (\\ref{dbs2}). For $\\kappa^2 >\\!> 25/24$, the solution\ncoincides with that given in Padmanabhan (1993)\n\nIn the limit $\\tau\\rightarrow \\infty$ \nthe ratio $\\db/\\dx$ is $1-\\kappa^2$\nfor $\\kappa \\le 1$ and, zero otherwise.\n\n\n\\subsection{ Case III: $0<f_x<1$}\nAgain we first derive $\\dx$.\nThe denominator and numerator in (\\ref{dxg}) do not \nhave any common roots. \nThen the poles of $\\ldx$ are the roots of the denominator.\nWe find these roots as follows. Denote $y(s)=s^2+s/2-3/2$ and equate\ndenominator to zero to obtain\n\\begin{equation}\ny^2+\\trh y \\left(1+\\kappa^2\\right) +\\frac{9}{4}f_b \\kappa^2=0\n\\end{equation}\nwhere we have used $1-f_x=f_b$.\nThis equation is satisfied for the following values of $y$,\n\\begin{equation}\ny_{p,m}=-\\frac{3}{4}\\left(1+\\kappa^2\\right)\\left(1\\pm \\Xi\\right) \n\\qquad ; \\qquad \\Xi^2=1-4f_b\\frac{\\kappa^2}{\\left(1+\\kappa^2\\right)^2} \\; ,\n\\end{equation}\nwhere the subscripts $p $ and $m$ correspond to the plus and minus sign,\nrespectively.\nSo the roots of the denominator in (\\ref{dxg}) are \nthe values of $s$ which make $y(s)=y_{p,m}$.\nLet $s_{p,\\pm}$ and $s_{_{m,\\pm}}$ be the roots of \n$y(s)-y_{p}=0$ and $y(s)-y_{m}=0$, respectively. They are given by\n\\begin{eqnarray}\ns_{_{m,\\pm}}=-\\frac{1}{4}\\left(1\\pm\\chi_m\\right) &;& \n{\\chi_m}^2=25-12 \n\\left(1+\\kappa^2\\right)\\left(1+\\Xi\\right) \\; ,\\cr\ns_{_{p,\\pm}}=-\\frac{1}{4}\\left(1\\pm\\chi_p\\right) &;& \n{\\chi_p}^2=25-12\n\\left(1+\\kappa^2\\right)\\left(1-\\Xi\\right) \\; .\n\\end{eqnarray}\n\nExcluding the values $f_b=0$ and $1$, which we have considered in the\nprevious subsections, we have $0<\\Xi^2<1-f_b$. This ensures that all\nfour roots, $s_{_{m,\\pm}}$ and $s_{_{p,\\pm}} $, are distinct. Also,\n$1<\\chi_p^2<25$ for any $\\kappa$, so the roots $s_{_{p,\\pm}}$ are\nreal. On the other hand, $0<\\chi^2_m<1$ when $\\kappa^2\n<25/(600-576f_b)$, and negative otherwise. So $s_{_{m,\\pm}}$ can be\ncomplex.\n\nFor $\\chi_m^2>0$, the Bromwich integral yields\n\\begin{equation}\n\\dx=\\frac{24\\kappa^2+\\chi_p^2-1}\n{2\\chi_p\n\\left(\n\\chi_p^2-\\chi_m^2\n\\right)}\n\\biggl[\\left( \\chi_p-5\\right)\\exp\\left(-\\frac{\\chi_p}{4}\\rp \\right)\n+\\left( \\chi_p+5\\right)\\exp\\left(+\\frac{\\chi_p}{4}\\rp \\right)\\biggr]\n\\exp\\left(-\\frac{\\tau}{4}\\right)\n + (\\chi_p \\longleftrightarrow \\chi_m) \\; ,\n\\end{equation}\nwith the second term on the r.h.s is obtained \ninterchanging $\\chi_p$ and $\\chi_m$ in the first term.\nThis result can be extended to $\\chi_m^2<0 $ \nby writing $\\chi_m=i \\tilde \\chi_m$ where $\\tilde \\chi_m$ is real.\n\nUsing (\\ref{dbdx}) we similarly obtain \n$\\db$\n\\begin{equation}\n\\db=\\frac{\\chi_p^2-1}\n{2\\chi_p\n\\left(\n\\chi_p^2-\\chi_m^2\n\\right)}\n\\biggl[\\left( \\chi_p-5\\right)\\exp\\left(-\\frac{\\chi_p}{4}\\rp \\right)\n+\\left( \\chi_p+5\\right)\\exp\\left(+\\frac{\\chi_p}{4}\\rp \\right)\\biggr]\n\\exp\\left(-\\frac{\\tau}{4}\\right)\n + (\\chi_p \\longleftrightarrow \\chi_m) \\; .\n\\end{equation}\n\n\n\n\nTo visualize these solutions,\nwe show in Fig.1 the density evolution for various values of $f_x$ and\n$\\kappa$. \nThe dark matter curve for $f_x=0.9$ is very close to \n$\\exp(\\tau)$. For $\\kappa=5$ the baryonic perturbations\nfor both values of $f_x$ show oscillations with similar period and amplitude.\nThis is simply because for high $\\kappa$, the evolution is mainly dictated \nby pressure forces.\n\n\nIn Fig.2 we the solid lines represent the ratio\n$\\db(\\kappa)/\\dx(\\kappa)$ as a function of $\\kappa$ at different\n$\\tau$ designated in the plot by the redshift, $z$. The initial\nconditions are satisfied at $z=6$ and $f_x=0.9$ was taken.\nAlso plotted, as the dotted line in each panel, the function\n$1/(1+\\kappa^2)$ which represents the limiting solution as $\\tau\\rightarrow \\infty$. The analytic\ncurves show more oscillations as they get closer to the limiting\nsolution, when the redshift is decreased.\n\n\nIn many applications (e.g., Bi et al 1992, Bi \\& Davidsen 1997, Nusser\n\\& Haehnelt 2000) the limiting ratio $1/(1+\\kappa^2)$ is often used to\nfilter the mass power spectrum in order to generate density\nfluctuations in the gas. As pointed out by Gnedin \\& Hui (1998) this\nmay lead to a significant bias in statistics of the gas density. As\nan illustration of this bias we compute the rms values of the gas\ndensity by filtering a scale free mass power spectrum of slope\n$n=-2.5$ with the ratio $(\\db/\\dx)^2 $ given from the analytic, and\nthe limiting solutions, respectively. Fig.3 shows the ratio of the\nformer to the latter rms value. As in the previous figure, $f_x=0.9$\nand initial conditions satisfied at $z=6$. Using the filter\n$1/(1+\\kappa^2)$ can seriously underestimate the amplitude of gas\ndensity fluctuations. Only when we approach $z=0$ the ratio gets\nclose to to unity.\n \n\\section{Summary}\nWe have found analytic solutions to the linear equations governing the\nevolution of baryonic and dark matter under four assumptions. First,\nthe Universe is flat without cosmological constant. Second,\nsudden reionization of the IGM. Third, the temperature of\nthe low density IGM drops like $1/a$ so that the comoving Jeans \nlength is time independent. Fourth, before reionization the IGM is cold and \nthe baryonic and dark matter trace the same density and velocity fields.\n\nOf these assumptions, only the fourth has a physical basis, at least\nbefore any heating has occurred and when the IGM temperature is low.\nThis is also the only assumption which if changed, the equations can\nstill be readily solved by Laplace transformation. Unfortunately,\nrelaxing any of the other assumptions complicates the analytic\ntreatment of equations (\\ref{lintau}) by means of Laplace\ntransformation. For example, suppose that the Jeans wavenumber changes\nwith time according to $a^\\beta$. Then the Laplace transformation of\nthe term involving $k_J$ will yield $\\ldb$ at $(s+\\beta)$ while other\nterms involve $\\ldb(s)$.\n\nYet the solutions can be useful for semi-analytic modeling of the\nIGM. They offer a convenient improvement over the commonly used filter\n$1/[1+(k/k_J)^2]$ for generating gas fluctuations associated with a\ngiven mass density field.\n\nThe analytic solutions presented here were verified by a comparison\nwith the solutions obtained by numerical integration of equations\n(\\ref{lint}). All numerical and analytic solutions agreed up to the\nnumerical accuracy.\n\n\\section{acknowledgement}\nThis research was supported by a grant from the Israeli Science Foundation.\n\n\\begin{thebibliography}{}\n\\bibitem{} Arfkin G., 1985 {\\it Mathematical\nMethods for Physicists}, Academic Press, INC., \nHarcourt Brace Jovanovich, Publishers.\n\\bibitem{} Bi H.G., B\\\"orner G., Chu Y., 1992, A\\&A, 266, 1 \n\\bibitem{} Bi H.G., Davidsen A.F., 1997, ApJ, 479, 523\n\\bibitem{} Croft R.A.C., Weinberg D.H., Katz N., Hernquist L., 1998, ApJ, \n495, 44 \n\\bibitem{} Hernquist L., Katz N., Weinberg D.H., Miralda-Escud\\'e J.,\n1996, ApJ, 457, L51 \n\\bibitem{} Gnedin N., Hui L., 1996, ApJ, 486, 599\n\\bibitem{} Gnedin N., Hui L., 1998, MNRAS, 296, 44\n\\bibitem{} Miralda-Escud\\'e J., Cen R., Ostriker J.P., Rauch M.,\n1996, ApJ, 471, 582\n \n\\bibitem{} Nusser A., Colberg J.M., 1998, MNRAS, 294, 457\n\\bibitem{} Nusser A., Haehnelt M., 1999, MNRAS, 303, 179\n\\bibitem{} Nusser A., Haehnelt M., 2000, MNRAS, in press, (astro-ph/9906406)\n\\bibitem{} Padmanabhan T., 1993, {\\it Structure Formation in the Universe},\nCambridge University Press, Cambridge.\n\\bibitem{} Peebles P.J.E., 1980, {\\it ``The Large Scale Structure in \nThe Universe''}, Princeton University Press, Princeton.\n\n\\bibitem{} Petitjean P., M\\\"ucket J.P., Kates R.E., 1995, A\\&A, 295, L9 \n\n\\bibitem {}Theuns T., Leonard A., Efstathiou G.,\n Pearce F.R., Thomas P.A., 1998, MNRAS, 301, 478 \n\\end{thebibliography}\n\n\\begin{figure}\n\\centering\n\\begin{sideways}\n\\mbox{\\psfig{figure=fig1.ps,height=6.0in}}\n\\end{sideways}\n\\caption{ Curves of $\\dx(\\tau)$ (solid lines) and $\\db(\\tau)$ (dotted) \nfor various values of $f_x$ and $\\kappa=k/k_J$. }\n\\label{fig:fig1}\n\\end{figure} \n\n\\begin{figure}\n\\centering\n\\begin{sideways}\n\\mbox{\\psfig{figure=fig2.ps,height=6.0in}}\n\\end{sideways}\n\\caption{ \nRatios of baryonic to dark matter density as a \nfunction of $\\kappa$ at different times, indicates by the redshift, $z$,\nin each panel.\nThe solid lines are the analytic solutions \nobtained with $f_x=0.9$ and where the initial conditions are satisfied \nat $z=6$.\nThe dotted line in each panel shows \n$1/(1+\\kappa^2)$, the ratio corresponding to the limiting solution.}\n\\label{fig:fig2}\n\\end{figure} \n\n\\begin{figure}\n\\centering\n\\begin{sideways}\n\\mbox{\\psfig{figure=fig3.ps,height=6.0in}}\n\\end{sideways}\n\\caption{ The ratio of the baryonic density $rms$ values \ncomputed by filtering\nthe mass power spectrum with $(\\db(\\tau,\\kappa)/\\dx(t,\\kappa))^2$ in the\nanalytic solution to that obtained by filtering with\n$1/(1+\\kappa^2)^2$.\nA scale free mass power spectrum with slope $n=-2.5$ is assumed.}\n\\label{fig:fig3}\n\\end{figure} \n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002317.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem{} Arfkin G., 1985 {\\it Mathematical\nMethods for Physicists}, Academic Press, INC., \nHarcourt Brace Jovanovich, Publishers.\n\\bibitem{} Bi H.G., B\\\"orner G., Chu Y., 1992, A\\&A, 266, 1 \n\\bibitem{} Bi H.G., Davidsen A.F., 1997, ApJ, 479, 523\n\\bibitem{} Croft R.A.C., Weinberg D.H., Katz N., Hernquist L., 1998, ApJ, \n495, 44 \n\\bibitem{} Hernquist L., Katz N., Weinberg D.H., Miralda-Escud\\'e J.,\n1996, ApJ, 457, L51 \n\\bibitem{} Gnedin N., Hui L., 1996, ApJ, 486, 599\n\\bibitem{} Gnedin N., Hui L., 1998, MNRAS, 296, 44\n\\bibitem{} Miralda-Escud\\'e J., Cen R., Ostriker J.P., Rauch M.,\n1996, ApJ, 471, 582\n \n\\bibitem{} Nusser A., Colberg J.M., 1998, MNRAS, 294, 457\n\\bibitem{} Nusser A., Haehnelt M., 1999, MNRAS, 303, 179\n\\bibitem{} Nusser A., Haehnelt M., 2000, MNRAS, in press, (astro-ph/9906406)\n\\bibitem{} Padmanabhan T., 1993, {\\it Structure Formation in the Universe},\nCambridge University Press, Cambridge.\n\\bibitem{} Peebles P.J.E., 1980, {\\it ``The Large Scale Structure in \nThe Universe''}, Princeton University Press, Princeton.\n\n\\bibitem{} Petitjean P., M\\\"ucket J.P., Kates R.E., 1995, A\\&A, 295, L9 \n\n\\bibitem {}Theuns T., Leonard A., Efstathiou G.,\n Pearce F.R., Thomas P.A., 1998, MNRAS, 301, 478 \n\\end{thebibliography}"
}
] |
astro-ph0002318
|
ROSAT HRI catalogue of X-ray sources in the LMC region\thanks{Table 4 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html}
|
[
{
"author": "Manami Sasaki"
},
{
"author": "Frank Haberl"
},
{
"author": "and Wolfgang Pietsch"
}
] |
%______________________________________ Do not leave a blank line here! All 543 pointed observations of the ROSAT High Resolution Imager (HRI) with exposure times higher than 50 sec and performed between 1990 and 1998 in a field of 10\degr\ x 10\degr\ covering the Large Magellanic Cloud (LMC) were analyzed. A catalogue was produced containing 397 X-ray sources with their properties measured by the HRI. The list was cross-correlated with the ROSAT Position Sensitive Propotional Counter (PSPC) source catalogue presented by Haberl \& Pietsch (1999) in order to obtain the hardness ratios for the X-ray sources detected by both instruments. 138 HRI sources are contained in the PSPC catalogue, 259 sources are new detections. The spatial resolution of the HRI was higher than that of the PSPC and the source position could be determined with errors mostly smaller than 15\arcsec\ which are dominated by systematic attitude errors. After cross-correlating the source catalogue with the SIMBAD data base and the TYCHO catalogue 94 HRI sources were identified with known objects based on their positional coincidence and X-ray properties. Whenever more accurate coordinates were given in catalogues or literature for identified sources, the X-ray coordinates were corrected and the systematic error of the X-ray position was reduced. For other sources observed simultaneously with an identified source the coordinates were improved as well. In total the X-ray position of 254 sources could be newly determined. The catalogue contains 39 foreground stars, 24 supernova remnants (SNRs), five supersoft sources (SSSs), nine X-ray binaries (XBs), and nine AGN well known from literature. Another eight sources were identified with known candidates for these source classes. Additional 21 HRI sources are suggested in the present work as candidates for SNR, X-ray binary in the LMC, or background AGN because of their extent, hardness ratios, X-ray to optical flux ratio, or flux variability. \keywords{Catalogues -- Galaxies: Magellanic Clouds -- Galaxies: stellar content -- X-rays: galaxies -- X-rays: stars}
|
[
{
"name": "ds1817.tex",
"string": "%\\documentclass[referee]{aa}\n\\documentclass{aa}\n\\usepackage{psfig,longtable,lscape}\n%\\usepackage{graphics}\n%\\addtolength{\\topmargin}{1.7cm}\n%\n% literature:\n\\newcommand{\\apj}[2]{ApJ #1, #2}\n\\newcommand{\\aj}[2]{AJ #1, #2}\n\\newcommand{\\aaa}[2]{A\\&A #1, #2}\n\\newcommand{\\aas}[2]{A\\&AS #1, #2}\n\\newcommand{\\pas}[2]{PASP #1, #2}\n\\newcommand{\\jap}[2]{PASJ #1, #2}\n\\newcommand{\\mon}[2]{MNRAS #1, #2}\n\\newcommand{\\nat}[2]{Nat #1, #2}\n% units:\n\\newcommand{\\ergcm}[1]{10$^{#1}$ erg cm$^{-2}$ s$^{-1}$}\n\\newcommand{\\ergs}[1]{10$^{#1}$ erg s$^{-1}$}\n\\newcommand{\\hcm}[1]{10$^{#1}$ cm$^{-2}$}\n%\n\\newcommand{\\nh}{\\hbox{N$_{\\rm H}$}}\n\\newcommand{\\fxfo}{\\hbox{f$_{\\rm x}$/f$_{\\rm opt}$}}\n\\newcommand{\\et}{et al.}\n\\newcommand{\\ct}{cts s$^{-1}$}\n\\newcommand{\\perr}{r$_{90}$}\n\\newcommand{\\derr}{d$_{90}$}\n\\newcommand{\\rerr}{r$_{\\rm BSC}$}\n\\newcommand{\\ext}{r$_{\\rm ext}$}\n\\newcommand{\\dext}{d$_{\\rm ext}$}\n\\newcommand{\\extl}{ML$_{\\rm ext}$}\n\\newcommand{\\exil}{ML$_{\\rm exi}$}\n\\newcommand{\\drib}{d$_{\\rm rib}$}\n%\n\\begin{document}\n\n\\thesaurus{\n 04.03.1; %Catalogues --\n 11.13.1; %Galaxies: Magellanic Clouds --\n 11.19.5; %Galaxies: stellar content --\n 13.25.2; %X-rays: galaxies --\n 13.25.5 %X-rays: stars\n }\n\n\\title{ROSAT HRI catalogue of X-ray sources in the LMC\nregion\\thanks{Table 4 is only available in electronic form\nat the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5)\nor via http://cdsweb.u-strasbg.fr/Abstract.html}\n}\n\n\\author{Manami Sasaki, Frank Haberl, and Wolfgang Pietsch}\n\\authorrunning{Sasaki et al.}\n\n\\offprints{M.\\ Sasaki (manami@mpe.mpg.de)}\n\n\\institute{Max--Planck--Institut f\\\"ur extraterrestrische Physik,\n Giessenbachstra{\\ss}e, 85748 Garching, Germany}\n\n\\date{Received date: 01 December 1999; accepted date: 18 January 2000}\n\n\\maketitle%\\markboth{}\n % {}\n\n\\begin{abstract}\n%______________________________________ Do not leave a blank line here!\nAll 543 pointed observations of the ROSAT High Resolution Imager (HRI)\nwith exposure times higher than 50 sec\nand performed between 1990 and 1998 in a field of 10\\degr\\ x\n10\\degr\\ covering the Large Magellanic Cloud (LMC) were analyzed.\nA catalogue was produced containing 397 X-ray sources with\ntheir properties measured by the HRI. The list was cross-correlated\nwith the ROSAT Position Sensitive Propotional \nCounter (PSPC) source catalogue presented by Haberl \\& Pietsch (1999)\nin order to obtain the hardness ratios for the X-ray sources detected\nby both instruments. 138 HRI sources are contained in the PSPC\ncatalogue, 259 sources are new detections. \nThe spatial resolution of the HRI was\nhigher than that of the PSPC and the source position could be\ndetermined with errors mostly smaller than 15\\arcsec\\ which are\ndominated by systematic attitude errors. \nAfter cross-correlating the source catalogue with the SIMBAD data base\nand the TYCHO catalogue 94 HRI sources were identified with \nknown objects based on their positional coincidence and X-ray\nproperties. Whenever more accurate coordinates were given in\ncatalogues or literature for identified sources, the X-ray coordinates\nwere corrected and the systematic error of the X-ray position was\nreduced. For other sources observed simultaneously with an identified\nsource the coordinates were improved as well. \nIn total the X-ray position of 254 sources could be newly determined.\nThe catalogue contains 39 foreground stars, 24 supernova remnants\n(SNRs), five supersoft sources (SSSs), nine X-ray binaries (XBs), and\nnine AGN well known from literature. Another eight sources\nwere identified with known candidates for these source classes. \nAdditional 21 HRI sources are suggested in the present work as\ncandidates for SNR, X-ray binary in the LMC, or background AGN\nbecause of their extent, hardness ratios, X-ray to optical flux ratio,\nor flux variability. \n\n\\keywords{Catalogues -- Galaxies: Magellanic Clouds --\n Galaxies: stellar content --\n X-rays: galaxies -- X-rays: stars}\n\\end{abstract}\n\n\\section{Introduction}\n\nThe Magellanic Clouds (MCs) as the nearest galaxies to the Milky Way\nallow us to resolve their stellar content in various wavelength\nbands. \nX-ray observations combined with optical and radio data can be used \nto investigate the physical properties of individual X-ray sources as \nwell as the statistical properties of different source classes in a \ngalaxy as a whole. The quantitative and positional distribution of \nX-ray sources in the MCs will help us to understand the unresolved\nX-ray emission from more distant galaxies.\n\nAfter the first observation of X-ray emission from the MCs in 1968 \n(Mark et al.\\ 1969) four permanent (LMC X-1, X-2, X-3, and X-4, Leong\net al.\\ 1971; Giacconi et al.\\ 1972) and\nfew transient X-ray sources were found in the LMC in several satellite\nmissions (UHURU, SAS-3, Copernicus, Ariel-V, HEAO-1). \nAn extensive pointed survey of the LMC was performed\nby the Einstein Observatory between 1979 and 1981. The two detectors\non board this satellite, the Imaging Proportional Counter and the High\nResolution Imager, were sensitive enough to detect \nX-ray binaries, SSSs, and SNRs at the distance of the LMC (55kpc). \nLong et al.\\ (1981)\npublished a list of 97 discrete X-ray sources in the direction of the\nLMC and the same data was re-analyzed by Wang et al.\\ (1991) finally\ngiving a list of 105 sources. 54 discrete X-ray sources were\nidentified with objects in the LMC, most of the remaining sources were\nassociated with foreground stars and background AGN. In EXOSAT\nobservations few additional X-ray sources were found (Jones et al.\\\n1985; Pakull et al.\\ 1985; Pietsch et al.\\ 1989). \n\nThe next thorough survey of the LMC was made by ROSAT in the energy\nrange of 0.1 -- 2.4 keV (Tr\\\"umper 1982). From 1990 to 1998 ROSAT\nperformed more than 700 \npointed observations in a 10 by 10 degree field centered on the\nLMC. Haberl \\& Pietsch (1999b, hereafter HP99b) analyzed 212 PSPC\nobservations and created a catalogue of 758 X-ray sources. \n\nIn this work results of the analysis of the ROSAT HRI data of the LMC\nare presented. A description of the HRI detector can be found in David\n\\et\\ (1996). A source catalogue was obtained in a\nsimilar way as in \nHP99b and many sources were identified by cross-correlating\nthe source list with other existing catalogues. With the help of \nknown properties of different source classes we looked for new\ncandidates for SNRs, stars, and hard X-ray sources which\nmainly consist of X-ray binaries and absorbed background AGN.\n\n\\section{ROSAT HRI data}\n\n\\subsection{Data analysis}\\label{data}\n\nThe LMC was observed by the ROSAT HRI in more than 500\npointings during the operational phase of ROSAT between 1990 and\n1998. 543 observations with exposure\ntimes of 50 to 110000 s (Fig.\\,\\ref{exphisto}) in a field of 10\\degr\\ x\n10\\degr\\ around RA = 05$^h$ 25$^m$ 00$^s$, Dec = --67\\degr\\ 43\\arcmin\\\n20\\arcsec\\ (J2000.0) were used for the analysis. The analysis was \ncarried out using three detection methods available in EXSAS (Zimmermann et\nal.\\ 1994). For each pointing X-ray sources were searched using the sliding\nwindow methods with local background and with a spline\nfitted background map. The resulting detection lists were merged and \na maximum likelihood algorithm was performed on this list.\nSources were accepted if their likelihood of existence was larger than\n10.0, i.e.\\ the existence probability was higher than P = 1 --\nexp(--\\exil) = 1 -- 4.5 $\\cdot$ 10$^{-5}$, and their telescope\noff-axis angle smaller than 15\\arcmin\\ during the observation. \n\nFor point and point like sources the source extent was determined\nby the maximum likelihood technique fitting the source intensity\ndistribution with a Gaussian profile. The count rates resulting from this\ncalculation are correct only for sources with small extent and a\nbrightness profile peaking in the center. For extended sources like\nSNRs with ringlike structure the net count rates were determined\ninteractively by integrating the counts within a circle around the\nsource. For the background the counts were averaged in a ring around\nthe source distant enough not to be influenced by the source emission. \n\nIn order to increase the sensitivity HRI observations\nwith pointing directions within a radius of 1\\arcmin\\ were\nmerged after adjusting their position. \nThis was possible for 56 different regions in the LMC.\nSource detection was also performed on these data and additional\nfaint sources were found which were not detectable in single\npointings.\n\nThe final source lists obtained for each pointing and co-added\nobservations were merged to one list and multiple detections of a source\nwere reduced to one detection for each source. For this purpose the\ndetection with the smallest positional error was chosen. After\nscreening manually in order to delete spurious detections like knots\nin extended emission, the catalogue finally contains 397 distinct sources. \n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=ds1817f1.ps,angle=270,width=9cm}}\n\\caption[]{\\label{exphisto} Histogram of HRI pointing exposure times.}\n\\end{figure}\n\n\\subsection{Positional corrections and error} \\label{poscorr}\n\n\\begin{table*}[t]\n\\include{ds1817t1}\\label{variable}\n\n\\vspace{2mm}\nNotes to columns No 2 and 3:\nFor point and point like sources count rates are the mean of output\nvalues from maximum likelihood algorithm for single pointings. For\nextended sources and bright sources with apparent extent (see text)\nthe average of integrated count rates in single pointings was taken (*\nin front of the number). \n\n\\vspace{1mm}\nNotes to column No 6:\nDegrees of freedom.\n\n\\vspace{1mm}\nNotes to column No 7:\nSource number from HP99b.\n\n\\vspace{1mm}\nNotes to column No 8:\nSources classified in this work are put in $<$ $>$.\nAbbreviations for references in square brackets are given in\nliterature list.\n\\end{table*}\n\nROSAT observations suffer from a systematic\npositional uncertainty of about 7\\arcsec\\ (K\\\"urster 1993). \nFor minimizing this systematic error the coordinates of\nidentified objects were compared to high accuracy positions available\nin the TYCHO catalogue obtained from the ESA Hipparcos space\nastrometry satellite (Hoeg \\et\\ 1997) or in the literature. \nFirst the X-ray position was corrected to TYCHO coordinates. For\nsources without any TYCHO counterpart, but identified on the ESO\nDigitized Sky Survey \n(DSS) frame with other stars on this frame which were listed in the\nTYCHO catalogue, more accurate coordinates were calculated for HRI \nsources by determining the offset between the TYCHO and DSS positions\nand between the HRI and DSS position. Other sources could be\nidentified with objects in the SIMBAD data base operated at the Centre\nde Donn\\'ees astronomiques de Strasbourg or in the literature and\ntheir positions were corrected after checking their positions on DSS\nframes. \nCorrection of coordinates for one source implied improved coordinates\nfor all detections of this source in different pointings\nand for other sources in same pointings.\nThose secondary corrections again allowed correction of further\npointings if the sources were detected several times.\nFinally for 254 out of 397 sources improved coordinates were \ndetermined. \n\nIn cases where positional correction was possible the remaining\nsystematic error consists of the error in former optical measurements\nand the statistical error of the identified source. \nFor not corrected sources the systematic error was set to 7\\arcsec. \nThe positional error was finally computed as a composite of the\nstatistical uncertainty with 90 \\% confidence and the systematic error.\nIt is used throughout the paper for the error circle. \nAfter the source detection procedure the mean positional error was 8\\farcs3. \nThe coordinate correction reduced the mean positional error of all\nsources to 6\\farcs4. For position corrected sources the mean\npositional error is 5\\farcs1. \n\n\\subsection{Correlation with existing catalogues} \\label{correlate}\n\n\\begin{figure*}[t]\n\\begin{center}\n\\begin{tabular}{lll}\n\\hspace{-1mm}\\mbox{\\psfig{figure=ds1817f2a.ps,angle=270,width=6.1cm}}& \n\\hspace{-6mm}\\mbox{\\psfig{figure=ds1817f2b.ps,angle=270,width=6.1cm}}&\n\\hspace{-7mm}\\mbox{\\psfig{figure=ds1817f2c.ps,angle=270,width=6.1cm}}\\\\\n\\hspace{7mm} a.\\ power law spectra with photon&\n\\hspace{2mm} b.\\ Raymond \\& Smith spectra with&\n\\hspace{1mm} c.\\ black body spectra with\\\\\n\\hspace{7mm} index: --2.5, --2.0, --1.5, --1.0, --0.5 &\n\\hspace{2mm} T = 0.1, 0.3, 1.0, 3.0, 10.0 keV &\n\\hspace{1mm} T = 10.0 -- 200.0 eV \\\\\n\\end{tabular}\n\\end{center}\n\\vspace{-3mm}\n\\caption[]{\\label{hri2pspc} PSPC/HRI conversion factor as \nfunction of N$_{\\rm H}$ for power law, Raymond \\& Smith, and black\nbody spectra.} \n\\end{figure*}\n\nThe catalogue was cross-correlated with the SIMBAD data\nbase and the TYCHO catalogue in order to identify HRI\nsources. The HRI catalogue contains samples of known SSSs,\nX-ray binaries, SNRs, Galactic foreground stars, and background AGN. \nThe catalogue was also cross-correlated with the source\nlist from the pointed PSPC observations (HP99b). 138 HRI sources are\nidentical with sources which were detected in PSPC data and thus for\nmost of them the hardness ratios (HR1, HR2) are known. Since the HRI\nhad no spectral resolution no information on the X-ray spectrum could\nbe obtained for HRI sources which are completely new detections. \nA total of 94 HRI sources were identified with known\nobjects like SSSs, X-ray binaries, SNRs, stars, and background AGN. \n\nWith the help of their X-ray properties like extent,\nextent likelihood, PSPC hardness ratios, X-ray to optical flux ratio\n(see Sec.\\,\\ref{newclass}), and X-ray variability 14 previously unknown\nHRI sources and 7 sources also listed in the PSPC catalogue were newly\nclassified. \n\nThe whole source catalogue from HRI observations with the corrected\ncoordinates, final positional error, existence likelihood, HRI\ncount rate, extent, extent likelihood, PSPC count rate and the\ncorresponding PSPC source number with hardness ratios (HP99b) is given\nin Table \\ref{wholecat}. \nFor each HRI and PSPC count rate the results for the pointing with the\nsmallest positional error, determined by the maximum likelihood\nalgorithm, were selected. \nTherefore HRI count rates in the table are representative for one single\nobservation for each source. For extended SNRs the given count rate may\ncorrespond to a knot within the source.\nPSPC count rates are taken from the PSPC catalogue (HP99b) if\navailable. For HRI sources without PSPC detection we derived\n2$\\sigma$ upper limit from the pointing with the highest exposure time. \nIf the source was too close to the rim or the window support structure\nof the PSPC detector, no count rate is given in Table \\ref{wholecat}.\nNeither was it possible to determine PSPC count rates or upper limits\nfor sources located in regions with diffuse emission. \n\n\\subsection{Flux variability}\n\nAbout 80 \\% of HRI sources were observed more than once and allow time\nvariability studies. For point and point like sources longterm\nlightcurves were produced with observation-average count rates or\nupper limits determined by the maximum likelihood algorithm, whereas\nfor extended sources integrated count rates within a circle were used\n(see Sec.\\,\\ref{data}). \nFor some very bright sources the count rates were integrated in the\nsame way, because an apparent extent resulted from the maximum\nlikelihood algorithm. An apparent extent is computed if the high photon\nstatistics of the bright sources cause a significant deviation from\nthe assumed model for the point spread function.\n\nA $\\chi^{2}$-test for a constant count rate was performed and the\nfactor between the maximum and minimum flux was computed for each\nlightcurve. Together with the reduced $\\chi^{2}$ this flux factor was\nused to characterize variability on long time scales of days to\nyears (see also HP99a). For SNRs we expect constant integrated flux,\nhowever the flux factor was in the range of 1.0 to 1.8. This may be\ncaused by different off-axis angles and/or different extraction of the\nextended source. Therefore variations below a\nfactor of 2.0 should be handled with care as they might indicate no\nreal variability but false integration of the source flux because of\nthe extent or existence of a nearby bright source.\n\nIn order to obtain a complete lightcurve of the ROSAT observations,\nalso PSPC count rates and upper limits were calculated for the HRI\nsources. In Figures \\ref{hri2pspc} a -- c the\nPSPC to HRI count rate conversion factor is plotted over N$_{\\rm H}$ =\n10$^{20}$ -- 10$^{23}$ cm$^{-2}$ for three different spectral models. \nSSSs with a soft black body spectrum can be modeled with T = 10.0 --\n50.0 eV and galactic N$_{\\rm H}$ = 10$^{20}$ -- 10$^{21}$ cm$^{-2}$ in\nthe direction of the LMC. XBs in general show a power law spectrum\nwith N$_{\\rm H}$ up to 10$^{22}$ cm$^{-2}$ because of intrinsic\nabsorption N$_{\\rm H}$. So for most of the point and point like X-ray\nsources PSPC count rates can be converted into HRI count rates by\ndividing by a typical value of 3, though for very soft sources this\nscale factor can be larger. \nSources in regions with extended emission (e.g.\\ 30 Dor or\nN44) or close to another source can not always be resolved in PSPC\ndata and may result in false large converting factor. \n\n$\\chi^{2}$ and the flux factor were again calculated for all\nlightcurves including PSPC count rates (divided by 3.0) and upper\nlimits. Finally 26 sources show significant variability with reduced\n$\\chi^{2} >$ 5 corresponding to a probability $>$ 0.9999 (see Table\n\\ref{variable}). \nFour of them are new classified HRI sources (for sources No 49 and 364\nsee Sec.\\,\\ref{classhard}, for No 300 and 313 see Sec.\\,\\ref{stellar}).\nAs example the lightcurve of source No 49, a new HRI candidate for\na variable X-ray binary or AGN is shown in Fig.\\,\\ref{lc0049}. \n\nPSPC count rates were determined in as many pointings as possible.\nThe mean value was calculated from these count rates and compared to\nthe HRI mean count rates (see Fig.\\,\\ref{rate}). The resulting\nconversion factor is close to 3.0, only variable sources marked with\ndots show bigger deviation. \n\n\\begin{figure}\n\\centerline{\\psfig{figure=ds1817f3.ps,angle=270,width=9cm}}\n\\caption[]{\\label{lc0049} Lightcurve of source No 49. \nCrosses for converted PSPC count rates, dots for HRI count rates. Zero\npoint of the space craft clock is 1990, June 21 21:06:50 UT.} \n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\psfig{figure=ds1817f4.ps,angle=270,width=9cm}}\n\\caption[]{\\label{rate} Mean of observation-averaged count rates from\nPSPC pointings over mean of observation-averaged count rates from HRI\npointings for ROSAT sources. \nSquares indicate SNRs, lozenges stars, hexagons XBs, triangles AGN,\nand asterisks SSSs. Crossed symbols are already known candidates. \nVariable sources are additionally marked\nwith filled dots. The line indicates a PSPC/HRI conversion factor of 3.}\n\\end{figure}\n\n\\section{Source classes}\n\nIn section \\ref{identifiedsou} we discuss HRI sources which were\nidentified either with sources already known from literature or with\ncandidates which were found in former X-ray studies and in PSPC data\n(HP99b). Section \\ref{newclass} deals with new classification of HRI\nsources based on their X-ray properties.\n\n\\subsection{Source identification}\\label{identifiedsou}\n\nFor 97 HRI sources out of 138 which were also detected by the PSPC the\nHRI observation yielded smaller positional error circles and\nconsequently more accurate source positions compared to the PSPC\nresults. Therefore for several sources likely optical counterparts\ncould be determined which was not possible only with PSPC data. \n \n94 HRI sources were identified with known objects in the LMC,\nforeground stars, or background objects mainly\nbased on their position (see\nSec.\\,\\ref{correlate}). As they comprise different source types\nX-ray properties characteristic for each source class could be derived from\nHRI and PSPC data. Table \\ref{identified} lists HRI sources\nwith identification. \n\nHP99b have shown that extent and extent likelihood as well as the\nhardness ratios measured by the PSPC have characteristic values for\ndifferent source classes and can be used as classification criteria.\n\n\\begin{figure}\n\\centerline{\\psfig{figure=ds1817f5.ps,angle=270,width=9cm}}\n\\caption[]{\\label{extent} Source extent and extent likelihood of HRI\nsources in the LMC. SNRs are marked with open squares, known point\nsources with open triangles. Crossed symbols are candidates for SNRs\nor point sources known from literature, filled symbols are new\nclassifications.}\n\\end{figure}\n\nIn Fig.\\,\\ref{extent} extent and extent likelihood of the HRI sources\nare shown. The extent was calculated in the maximum likelihood\nalgorithm and so gives the value resulting from fitting\nGaussians. Thus in some cases it may not be the extent of the whole\nsource but only of knots which were found within the extended source.\nIdentified SNRs, marked with open squares, are distributed in the region\nwith large extent and high extent likelihood. Crossed squares indicate\nknown SNR candidates and filled squares sources newly classified as\nSNR candidates in this work. \nPoint sources have lower extent likelihood unless they were extremely\nbright like AB Dor (No 180), LMC X-1 (No 311), or RX J0439.8-6809 (No\n4) where the deviation of the point spread function from the assumed \nGaussian profile becomes significant. \n\n\\subsubsection{Foreground stars}\n\nBy cross-correlating the HRI source catalogue with SIMBAD and\nTYCHO catalogues and using the finding charts presented by Schmidtke\net al.\\ (1994, hereafter SCF94), Cowley at al.\\ (1997, hereafter\nCSM97), and Schmidtke et al.\\ (1999, hereafter SCC99)\n39 sources were identified with Galactic foreground stars (Table\n\\ref{identified}). Most of them could also be identified with the\nhelp of UBV photometry results presented by Gochermann \\et\\ (1993) and\nGrothues \\et\\ (1997). On DSS-images there are point sources as very\nlikely optical counterparts at the positions of these HRI sources\nwithin the error circle. \n\nBased on hardness ratios of the PSPC observations two point sources\nwere suggested as foreground star candidates by HP99b (No 189 and 349).\nThey were detected in PSPC images and their hardness ratios\nare within the range characteristic of stars (HP99b). DSS images show\nan optical point source within the improved HRI error circle in both\ncases. \n\n\\subsubsection{Supernova Remnants}\n\nMost SNRs in the LMC are extended X-ray sources which could be resolved\nby the HRI. They typically show extents of about 5\\arcsec\\ --\n20\\arcsec\\ and high extent likelihood ($>$ 10.0). A total of 24 known\nSNRs were observed by the HRI, four HRI sources are identified with\nknown SNR candidates (No 50, 231, 310, and 315). For both No\n231 and 310 the measured hardness ratios are typical for SNRs. No 50\nhas a harder X-ray spectrum with HR1 = 1.00$\\pm$0.10 and HR2 =\n0.34$\\pm$0.07. \n\n\\subsubsection{Supersoft sources}\n\nSSSs have very soft X-ray spectra and so far seven SSSs have been\ndiscovered in the LMC (HP99b). Two of them were sources of the Einstein\nLMC survey (Long et al.\\ 1981) and five were found with the help of\nthe ROSAT PSPC. In the HRI pointings five LMC SSSs listed in Table\n\\ref{identified} were observed and detected with high existence\nlikelihood. \n\n\\subsubsection{X-ray binaries}\n\nCharacteristic for most X-ray binaries is the hard X-ray spectrum and\nflux variability. In HRI observations nine bright sources could be\nidentified with well known massive X-ray binaries (HMXB).\nThe point source RX J0532.7-6926, here No 238, has been suggested to\nbe a low mass X-ray binary (LMXB) candidate by Haberl \\& Pietsch\n(1999a, hereafter HP99a) and was also detected by the HRI. In HP99a a\nlightcurve with PSPC and HRI measurements is presented and variability\nis discussed in detail. Between 1990 and 1993 the source showed an\nexponential intensity decay. \n\n\\subsubsection{AGN}\n\nNine known background AGN with redshifts between 0.06 and 0.44 (SCF94;\nCSM97; Crampton et al.\\ 1997) were re-identified in the HRI pointings. \nBecause of its positional coincidence with the radio source PKS 0552-640\nand its hardness ratios measured by the PSPC the HRI source No 389 was\nclassified as AGN candidate (No 37 in HP99b). On the DSS frame an\noptical source with m$_{B}$ = 16.3 within the HRI error circle is\nidentified as the most likely optical counterpart.\n\n\\subsection{New classifications}\\label{newclass}\n\nThe extensive detection list produced from the HRI pointings towards\nthe LMC allowed us to search for new candidates for different source\ntypes. In the course of studying the newly discovered HRI sources the\nfollowing parameters were of prime importance: count rates, source\nextent, extent likelihood, flux variability, and counterparts in other\nwavelengths. \n\nIn addition to these X-ray properties we calculated the X-ray to optical\nflux ratio of HRI sources, for which possible optical counterparts could\nbe found. The flux ratio was computed according to \nthe equation log(f$_{x}$/f$_{opt}$) = log(3 $\\cdot$ HRI counts/s\n$\\cdot 10^{-11}$) + 0.4 m$_{B}$ + 5.37 (Maccacaro et al.\\ 1988; HP99b). \nThe relation used for PSPC observations in HP99b was applied here for\nHRI sources converting the HRI count rates to PSPC count rates by\nmultiplying by the factor of 3 which is typical for hard sources.\nB magnitudes from the USNO-A1.0 Catalogue produced by the\nUnited States Naval Observatory (Monet 1996) were used.\nFor several sources the optical counterpart could not be determined\nuniquely. In such a case the magnitude of the brightest optical object\nwithin the error circle was used resulting in lower\nlimits for log(f$_{x}$/f$_{opt}$). For the SNRs log(f$_{x}$/f$_{opt}$)\nin general gives no quantitative information, but is an indicator that\nthis source class is bright in X-ray (log(f$_{x}$/f$_{opt}$) $>$ --1). \n\nAs one can see in Fig.\\,\\ref{logfxfopt} stars in general have negative\nlog(f$_{x}$/f$_{opt}$), for AGN it is around zero, and for SSSs and XBs\nit is mostly positive in particular when they were observed in their\nX-ray active phase. Combination of f$_{x}$/f$_{opt}$ and the hardness\nratios provides a tool to exclude foreground stars. \n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=ds1817f6.ps,angle=270,width=9cm}}\n\\caption[]{\\label{logfxfopt} Flux ratio log(f$_{x}$/f$_{opt}$) as a\nfunction of hardness ratio 1. Open squares are SNRs, open\nlozenges stars, open hexagons XBs, open triangles AGN, and asterisks\nSSSs. Crossed symbols are already known\ncandidates and filled symbols are new classifications.} \n\\end{figure}\n\nNewly discovered HRI sources which are suggested as candidates for\ndifferent source classes in this work can be found in Table\n\\ref{classified} and are discussed in the following. \n\n\\subsubsection{SNR candidates}\n\nInvestigating the extent five HRI sources (No 197, 284, 288,\n307, 338) not classified with the help of PSPC observations are suggested\nas SNR candidates as their extent is larger than 8\\arcsec\\ (see\nFig.\\,\\ref{extent}).\nSince they were not detected by the PSPC because of short exposure\ntimes there is no spectral information about these sources which might\nbe crucial for further improvement of the classification. \n\n\\subsubsection{Sources classified as stellar}\\label{stellar}\n\nFor 11 HRI sources probable optical counterparts were found within the\nerror circle which are all bright (m$_{B} \\leq$ 12.5), and their\nlog(f$_{x}$/f$_{opt}$) is negative ($<$ --2.0). For this reason these\nsources are classified as stellar objects, and in particular the\nbrightest objects are likely foreground stars. Four sources were also\nobserved by the PSPC (No 90, 135, 217, 313), but as the errors of\ntheir hardness ratios are large, no spectral information is given.\n\nThe lightcurve of No 300 shows a strong decrease of the X-ray\nemission with a factor of 10 in 2 years indicating that the HRI\nobservations were performed after an emission maximum. \nThe point source in the optical DSS image at the HRI position is very\nlikely the optical counterpart with a B magnitude\nof m$_{B}$ = 12.4 according to the USNO-A1.0 Catalogue and\nlog(f$_{x}$/f$_{opt}$) = --2.75.\n\n\\subsubsection{LMC stars as candidates for high mass X-ray binaries}\n\nTwo X-ray point sources detected by the HRI were \nidentified with known LMC O and B stars (No 328, Sanduleak 1970,\nm$_{B}$ = 18.8 and No 332, Brunet \\et\\ 1975, m$_{B}$ = 13.6) because\nof the positional coincidence. With HRI data no variability\ninvestigations could be carried out for these X-ray sources, though\nthere exist many pointings in their direction, because they were both\ndetected only once and in other pointings the upper limits were\ntoo high for this purpose. But their identification with optically\nselected LMC stars allows us to classify them as candidates for high\nmass X-ray binaries. \n\n\\subsubsection{Sources with hard X-ray spectrum: Candidates for AGN or\nX-ray binary} \\label{classhard}\n\nWith the help of the hardness ratios and other characteristics\nmeasured by the HRI like flux variability or f$_{x}$/f$_{opt}$\nthree HRI sources which were also detected by the PSPC \ncould be classified as candidates either for X-ray binary or for AGN.\n\nThe point source No 49 shows significant flux variations, as it is shown in\nFig.\\,\\ref{lc0049}, and has a hard and/or highly absorbed X-ray spectrum\n(HR1 = 1.00$\\pm$0.71, HR2 = 0.26$\\pm$0.16). On the DSS image a likely optical\ncounterpart with a B magnitude of 16.4 (according to the USNO-A1.0\nCatalogue) is found. Therefore this source has been classified as\na candidate either for an X-ray binary or AGN.\n\nSources No 230 and 364 are further candidates for X-ray binary or\nAGN as they have a hard and/or absorbed X-ray spectrum (HR1 =\n1.00$\\pm$0.35, HR2 = 1.00$\\pm$0.98 and HR1 = 1.00$\\pm$0.21, HR2 =\n1.00$\\pm$0.60 respectively).\nSince source No 230 has a small positional error a probable\noptical counterpart can be found on the DSS image. This counterpart is\nfaint (m$_{B}$ = 22.6), and we obtain a high log(f$_{x}$/f$_{opt}$) of\n1.56. \nFor source No 364 there is a relatively faint optical source\n(m$_{B}$ = 18.2) within the error circle which might be the\ncounterpart (log(f$_{x}$/f$_{opt}$) = 0.43).\n\nAnother nine sources detected by the HRI were identified with sources in\nthe PSPC catalogue (HP99b) showing a hard X-ray spectrum. But from the\nHRI observations no additional information could be obtained. Thus the\nHRI sources are simply classified as hard X-ray sources because of the\nhardness ratios of their PSPC detections. \n\n\\subsection{Source distribution}\n\nDue to the high spatial resolution of the HRI many sources could be\ndetected both in the outer regions and in the optical bar region of\nthe LMC.\nIn Fig.\\,\\ref{known} HRI sources identified with known objects and\nknown candidates are plotted on a grey scale PSPC image (0.1 -- 2.4\nkeV) of the LMC (from HP99b). The sources are located in different\nregions of the \nLMC and show no spatial preferences, it is not only background AGN or\nforeground stars and candidates which are distributed over the whole\nLMC region. There are still more than 250 non-identified point sources\nwhich are homogeneously distributed in all LMC regions which were covered\nby ROSAT HRI pointings as it is shown in Fig.\\,\\ref{unidentified}. \nIn contrast, in PSPC observations not many additional sources could be\ndetected in the regions with strong diffuse emission, because the lower\nspatial resolution hindered in distinguishing between extended and\npoint like emission (HP99b).\n\nThe HRI allows to study the extent of the sources to scales of\narcseconds. Therefore SNR candidates could be\nfound not only in regions without surrounding diffuse\nemission. Four out of five newly suggested SNR candidates are located\nin regions with diffuse emission between 30 Dor and LMC X-1 (see\nFig.\\,\\ref{unidentified}). \n\nWithin and around the optical bar region several new stellar sources\nand candidates for X-ray binary or AGN were found.\n\n\\section{Summary}\n\nThe analysis of all 543 ROSAT HRI pointed observations performed\nbetween 1990 and 1998 with exposure times higher than 50 sec is\npresented. Using a maximum likelihood algorithm the\nsource detection resulted in a catalogue of 397 sources which was\ncross-correlated with the SIMBAD data base and the TYCHO catalogue. \nFurther X-ray properties could be obtained for HRI sources contained\nin the PSPC catalogue of HP99b. \n\nThe high spatial resolution of the HRI enabled\nthe identification of 94 HRI sources with well known objects based on the\npositional coincidence and considering their extent and hardness\nratios. The coordinates of most of the identified\nsources could be improved to more accurate positions and allowed the\npositional correction of other HRI sources. Thus for 254 sources the\nsystematic error for their coordinates could be reduced to values\nsmaller than 7\\arcsec\\ which is the standard systematic error of ROSAT\nobservations. \n\nFor different source classes like SSS, X-ray binary, SNR,\nGalactic stars, and background AGN classification\ncriteria could be derived from the extent and hardness ratios of the\nidentified sources. We looked for flux variability of the\nsources and for likely optical counterparts. Five newly detected HRI\nsources were classified as candidates for SNRs because of their\nextent, two HRI sources which were identified with an LMC O and a B\nstar as HMXB candidates. Eleven sources with probable bright optical\ncounterpart and small X-ray to optical flux ratio are classified as\nstellar sources. Three sources with hard and/or absorbed X-ray\nspectrum indicated by the PSPC hardness ratios are likely candidates\nfor X-ray binaries or AGN. Two of the hard X-ray sources show flux\nvariability and for each of these an optical counterpart was found. \n\nWith the help of HRI observations many new X-ray sources were found. \nFurther follow-up observations in X-ray, optical, or radio\nwavelengths with spectral information are needed to characterize these\nsources in more detail. \n\n\\acknowledgements\n%________________________________________ Do not leave a blank line here!\nThe ROSAT project is supported by the German\nBundesministerium f\\\"ur Bildung und Forschung (BMBF) and \nthe Max-Planck-Gesellschaft. This research has been carried out by\nmaking extensive use of the SIMBAD data base operated at CDS,\nStrasbourg, France. \n%_____________________________________________________________________\n \n\\begin{thebibliography}{}\n\n\\bibitem[Brunet \\et\\ (1975)]{BIM75}\n Brunet J.P., Imbert M., Martin N., Mianes P., Prevot L., Robeirot E.,\n Rousseau J., 1975, A\\&AS 21, 109\n\n\\bibitem[Chu (1997)]{C97}\n Chu Y.-H., 1997, AJ 113, 1815 [C97] \n %Supernova remnants in OB associations. \n\n\\bibitem[Chu \\et\\ (1997)]{CKS97}\n Chu Y.-H., Kennicutt R.C., Snowden S.L., Smith R.C., Williams R.M.,\n Bomans D.J., 1997, PASP 109, 554 [CKS97]\n\n\\bibitem[Cowley \\et\\ (1984)]{CCH84}\n Cowley A.P., Crampton D., Hutchings J.B., Helfand D.J., Hamilton T.T.,\n Thorstensen J.R., Charles P.A., 1984, ApJ 286, 196 [CCH84] \n %Optical counterparts of the Large Magellanic Cloud X-ray point sources.\n\n\\bibitem[Cowley \\et\\ (1997)]{CSM97} \n Cowley A.P., Schmidtke P.C., McGrath T.K., Ponder A.L., Fertig R.M.,\n 1997, PASP 109, 21 [CSM97]\n\n\\bibitem[Crampton \\et\\ (1997)]{CGC97}\n Crampton D., Gussie G., Cowley A.P., Schmidtke P.C., 1997, AJ 114,\n 2353 [CGC97] \n %Probes for Nearby Galaxies \n\n\\bibitem[David \\et\\ (1996)]{DHK96}\n David L.P., Harnden Jr.\\ F.R., Kearns K.E., and Zombeck M.V.,\n 1996, The ROSAT High Resolution Imager (HRI), USRSDC/SAO Calibration\n Report 1996 February, revised\n\n\\bibitem[Dennerl \\et\\ (1996)]{DHP96}\n Dennerl K., Haberl F., Pietsch W., 1996, in: Zimmermann H.U.,\n Tr\\\"umper J., Yorke H.\\ (eds.) Proceedings of `R\\\"ontgenstrahlung from\n the Universe', Sept.\\ 25-29 1995, MPE report 263, 131 [DHP96]\n\n\\bibitem[Giacconi \\et\\ (1972)]{GMG72}\n Giacconi R., Murray S., Gursky H., Kellogg E., Schreier E., \n Tananbaum H., 1972, ApJ 178, 281 \n\n\\bibitem[Gochermann \\et\\ (1993)]{GGO93}\n Gochermann J., Grothues H.-G., \\\"Ostreicher M.O., Bergh\\\"ofer T.,\n Schmidt-Kaler T., 1993, A\\&AS 99, 591 [GGO93] \n %UBV photometry of galactic foreground and LMC member\n %stars. I. Galactic foreground stars.\n\n\\bibitem[Grothues \\et\\ (1997)]{GOG97}\n Grothues H.-G., \\\"Ostreicher M.O., Gochermann J., Tappert C.,\n Zaum A., Brugger H.R., Schmidt-Kaler T., 1997, A\\&AS 121, 247 [GOG97]\n %UBV photometry of galactic foreground and LMC member\n %stars. II. Galactic foreground stars (supplement).\n\n\\bibitem[Haberl \\et\\ (1995a)]{HDP95a}\n Haberl F., Dennerl K., Pietsch W., 1995, A\\&A 302, L1 [HDP95a]\n\n\\bibitem[Haberl \\et\\ (1995b)]{HPD95b}\n Haberl F., Pietsch W., Dennerl K., 1995, A\\&A 303, L49 [HPD95b]\n\n\\bibitem[Haberl \\et\\ (1997)]{HDP97}\n Haberl F., Dennerl K., Pietsch W., 1997, A\\&A 318, 490 [HDP97]\n\n\\bibitem[Haberl \\& Pietsch (1999a)]{HP99a}\n Haberl F., Pietsch W., 1999a, A\\&A 344, 521 [HP99a]\n\n\\bibitem[Haberl \\& Pietsch (1999b)]{HP99b}\n Haberl F., Pietsch W., 1999b, A\\&AS 139, 277 [HP99b]\n\n\\bibitem[Hoeg \\et\\ (1997)]{HBB97}\n Hoeg E., B\\\"assgen G., Bastian U., Egret D., Fabricius C.,\n Gro{\\ss}mann V., Halbwachs J.L., Makarov V.V., Perryman M.A.C.,\n Schwekendiek P., Wagner K., Wicenec A., 1997, A\\&A 323, L57\n\n\\bibitem[Jones \\et\\ (1985)]{JPM85}\n Jones L.R., Pye J.P., McHardy I.M., Fairall A.P., 1985, \n Space Sci.\\ Rev.\\ 40, 693\n\n\\bibitem[K\\\"urster (1993)]{K93}\n K\\\"urster M., 1993, ROSAT Status Report No.\\ 67\n\n\\bibitem[Leong \\et\\ (1971)]{LKG71}\n Leong C., Kellogg E., Gursky H., Tananbaum H., Giacconi R., 1971, ApJ\n 170, L67\n\n\\bibitem[Long \\et\\ (1981)]{LHG81}\n Long K.S., Helfand D.J., Grabelsky D.A., 1981, ApJ 248, 925\n %A soft X-ray study of the Large Magellanic Cloud\n\n\\bibitem[Maccacaro \\et\\ (1988)]{MGW88}\n Maccacaro T., Gioia I.M., Wolter A., Zamorani G., Stocke J.T.,\n 1988, ApJ 326, 680\n %The X-ray spectra of the extragalactic sources in the Einstein\n %extended medium sensitivity survey\n\n\\bibitem[Mark \\et\\ (1969)]{MPR69}\n Mark H., Price R., Rodrigues R., Seward F.D., Swift C.D.,\n 1969, ApJ 155, L143\n\n\\bibitem[Monet (1996)]{M96}\n Monet D., 1996, American Astronomical Society Meeting, 188, 54.04 \n\n\\bibitem[Morgan (1994)]{M94b}\n Morgan D.H., 1994, A\\&AS 102, 235 [M94b]\n\n\\bibitem[Orio \\& Greiner (1999)]{OG99}\n Orio M., Greiner J., 1999, A\\&A 344, L13 [OG99]\n\n\\bibitem[Pakull \\et\\ (1985)]{PBS85}\n Pakull M., Brunner H., Staubert A., Pietsch W., Beuermann K.,\n 1985, Space Sci.\\ Rev.\\ 40, 379 \n\n\\bibitem[Pietsch \\et\\ (1989)]{PDR89}\n Pietsch W., Dennerl K., Rosso C., 1989, Proc.\\ 23rd ESLAB Symp.\\ \n on Two Topics in X-ray Astronomy, Bologna ESA SP-296, 573\n\n\\bibitem[Sanduleak (1970)]{S70}\n Sanduleak N., 1970, Contr.\\ Cerro-Tololo Obs., 89\n %A deep objective-prism survey for Large Magellanic Cloud members\n\n\\bibitem[Schmidtke \\et\\ (1994)]{SCF94}\n Schmidtke P.C., Cowley A.P., Frattare L.M., McGrath T.K.,\n Hutchings J.B., Crampton D., 1994, PASP 106, 843 [SCF94]\n %LMC Stellar X-ray Sources Observed With ROSAT: I. X-ray Data and\n %Search for Optical Counterparts\n\n\\bibitem[Schmidtke \\et\\ (1999)]{SCC99}\n Schmidtke P.C., Cowley A.P., Crane J.D., Taylor V.A., McGrath T.K.,\n 1999, AJ 117, 927 [SCC99]\n\n\\bibitem[Tr\\\"umper (1982)]{T82}\n Tr\\\"umper J., 1982, Adv.\\ Space Res.\\ 2, 241\n\n\\bibitem[Wang \\et\\ (1991)]{WHHW91}\n Wang Q., Hamilton T., Helfand D.J., Wu X., 1991, ApJ 374, 475\n [WHHW91]\n %The detection of X-rays from the hot interstellar medium of the \n %Large Magellanic Cloud. \n\n\\bibitem[Zimmermann \\et\\ (1994)]{ZBB94}\n Zimmermann H.U., Becker W., Belloni T., D\\\"obereiner S., Izzo C.,\n Kahabka P., Schwentker O., 1994, EXSAS User's Guide, MPE report 257\n\n\\end{thebibliography}\n\n\\onecolumn\n\n\\clearpage\n\n\\begin{figure}\n\\begin{center}\n\\begin{tabular}{c}\n\\\\[2cm]\n\\mbox{\\psfig{figure=ds1817f7.ps,angle=0,width=175mm}}\n\\\\[5mm]\\\\\n\\end{tabular}\n\\end{center}\n\\caption[]{\\label{known} Identified HRI sources are plotted on a grey\nscale PSPC image (0.1 -- 2.4 keV) of the LMC. Squares are SNRs,\ncircles are foreground stars, double squares SSSs, crossed squares\nXBs, crossed circles AGN. Candidates from literature are included for\neach source class.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\begin{center}\n\\begin{tabular}{c}\n\\\\[2cm]\n\\mbox{\\psfig{figure=ds1817f8.ps,angle=0,width=175mm}}\n\\\\[5mm]\\\\\n\\end{tabular}\n\\end{center}\n\\caption[]{\\label{unidentified} The distribution of unidentified HRI\nsources and new source classifications is shown. Unidentified HRI\nsources are plotted as dots, squares are sources classified as SNR\ncandidates, circles as stellar sources, crossed squares as XB\ncandidates and double circles as candidates for XB or AGN.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{landscape}\n\n\\begin{table}\n\\scriptsize\n\n\\include{ds1817t2}\\label{identified}\n\n\\include{ds1817t3}\\label{classified} \n\n\\end{table}\n\n\\clearpage\n\n\\include{ds1817t4}\\label{wholecat}\n\n\\end{landscape}\n\n\\end{document}\n"
},
{
"name": "ds1817t1.tex",
"string": "\\caption[]{HRI sources with significant flux variability}\n\\begin{tabular}{rrrrrrrl}\n\\hline\\noalign{\\smallskip}\n\\multicolumn{1}{c}{1} & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & \\multicolumn{1}{c}{4} &\n\\multicolumn{1}{c}{5} & \\multicolumn{1}{c}{6} & \\multicolumn{1}{c}{7} & ~~8 \\\\\n\\hline\\noalign{\\smallskip} \n\\multicolumn{1}{c}{No} & \\multicolumn{1}{c}{Rate} &\n\\multicolumn{1}{c}{Rate} & \n\\multicolumn{1}{c}{$\\frac{\\rm F_{max}}{\\rm F_{min}}$} &\n\\multicolumn{1}{c}{Red.\\ $\\chi^2$} & \\multicolumn{1}{c}{DOF} & \n\\multicolumn{1}{c}{No} & Remarks \\\\\n & \\multicolumn{1}{c}{HRI} & \\multicolumn{1}{c}{PSPC} & &\n & & \\multicolumn{1}{c}{PSPC} & \\\\\n & \\multicolumn{1}{c}{[\\ct]} & \\multicolumn{1}{c}{[\\ct]} & &\n & & & \\\\\n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n 19 & *4.6e-1 & *2.3e-3 & 598.1 &376.1 & 1 & 331 & HMXB RX J0502.9-6626 (CAL E)\\\\ \n 20 & 5.3e-2 & 7.7e-2 & 4.5 &163.5 & 2 & 380 & AGN RX J0503.1-6634, z=0.064 [SCF94]\\\\ \n 23 & 2.4e-2 & 2.1e-2 & 3.4 & 61.9 & 1 & 715 & \\\\ \n 49 & *4.9e-3 & *7.5e-3 & 4.3 &9.4 & 4 & 559 & $<$XB$>$ or $<$AGN$>$\\\\ \n 65 & 2.2e-3 & 1.9 & 25611.5 &663.9 & 45 & 1030 & SSS RX J0513.9-6951 \\\\ \n103 & 4.1e-3 & 2.8e-3 &10.5 & 10.2 & 6 && foreground star HD 35862 \\\\ \n124 & 1.8e-2 & 1.0e-1 & 4.9 & 19.6 & 20 & 1094 & AGN RX J0524.0-7011, z=0.151 [SCF94]\\\\ \n155 & *8.3e-3 & *4.2e-3 & 132.1 & 18.7 & 30 && Nova LMC 1995 [OG99] \\\\ \n167 & 1.4e-3 & 1.2e-1 & 256.1 & 51.6 & 26 & 1039 & SSS RX J0527.8-6954 \\\\ \n180 & *1.9 & *7.5 &11.2 &691.6 & 74 & 122 & foreground star K1III\\& HD 36705 (AB Dor)\\\\ \n193 & 3.4e-2 & 1.7e-1 & 2.6 &7.0 & 8 & 749 & foreground star G5 HD 269620 [CSM97]\\\\ \n202 & 2.0e-3 & 8.5e-2 & 1022.5 & 11.9 & 20 & 204 & HMXB Be/X \nRXJ0529.8-6556 [HDP97]\\\\ \n218 & 8.4e-3 & 3.7e-1 & 344.9 & 99.9 & 10 & 252 & HMXB Be/X \nEXO053109-6609 [HDP95a], [DHP96]\\\\ \n233 & 6.0e-3 & 2.2e-2 &66.1 &7.9 & 13 & 184 & HMXB RX J0532.5-6551 (Sk -65 66) [HPD95b]\\\\ \n239 & *8.9e-2 & *4.9 & 367.1 & 10247.6 & 25 & 316 & HMXB LMC X-4, HD 269743 O8III \\\\ \n293 & 4.4e-2 & 1.6e-1 & 2.1 &9.4 & 18 & 902 & foreground star dMe CAL 69 [CSM97] \\\\ \n300 & 5.4e-3 & &18.9 &414.6 & 2 && $<$stellar$>$, source not resolved by the PSPC\\\\ \n306 & *6.0 & *23.4 & 2.5 & 1838.8 & 22 & 41 & HMXB LMC X-3 \\\\ \n311 & 3.5 & 13.5 & 1.6 &576.1 & 29 & 1001 & HMXB LMC X-1, O8III \\\\ \n313 & *6.3e-3 & *8.3e-3 & 3.7 &9.3 & 3 & 668 & $<$stellar$>$\\\\ \n348 & 4.3e-2 & & 284.0 &775.9 & 6 & 654 & SSS CAL 83 [SCF94], one PSPC point., source near rim \\\\ \n349 & 3.0e-2 & 1.0e-1 &19.5 &7.2 & 5 & 61 & foreground star? [HP99a] \\\\ \n352 & 1.3e-3 & 1.2e-2 & 3.1 & 10.0 & 2 & 1225 & HMXB RX J0544.1-7100 [HP99b]\\\\ \n363 & 6.1e-2 & 1.3e-1 & 1.5 & 36.8 & 3 & 1240 & SSS CAL 87 \\\\ \n364 & 1.2e-2 & &30.5 &158.4 & 1 & 747 & $<$XB$>$ or $<$AGN$>$, one PSPC pointing, source near rib \\\\ \n375 & 3.3e-3 & 3.3e-2 & 4.5 &6.1 & 4 & 1127 & foreground star F3/F5IV/V HD 39756 \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n"
},
{
"name": "ds1817t2.tex",
"string": "\\caption[]{Identified HRI sources in the LMC}\n\\begin{tabular}{rrrrrccrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ & \\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} & \\multicolumn{1}{c}{9} & 10 & 11 & ~~~12 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{PSPC} & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n 9 & 04 53 43.5 & -68 24 23 & 4.4 & 15.3 & 5.99e-04$\\pm$1.63e-04 & 1.2$\\pm$ 1.9 & 0.1 & & & & foreground star G0 HD 268717 [GGO93] \\\\ \n 12 & 04 54 30.2 & -68 18 01 & 9.1 & 12.7 & 1.30e-03$\\pm$3.20e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & foreground star HD 31961 \\\\ \n 15 & 04 58 25.1 & -69 08 22 & 4.1 & 39.8 & 5.77e-03$\\pm$1.31e-03 & 2.3$\\pm$ 2.0 & 1.2 & 816 & 1.00$\\pm$0.51 & 0.29$\\pm$0.13 & foreground star F7V [CSM97] \\\\ \n 16 & 04 58 43.9 & -68 50 50 & 4.1 & 317.5 & 4.48e-02$\\pm$3.74e-03 & 0.0$\\pm$ 0.0 & 0.0 & 742 & -0.04$\\pm$0.05 & 0.09$\\pm$0.07 & foreground star dMe HD 268840 [CSM97] \\\\ \n 18 & 05 02 09.3 & -66 20 36 & 5.3 & 16.2 & 7.81e-03$\\pm$3.22e-03 & 0.4$\\pm$ 2.7 & 0.0& 304 & 0.68$\\pm$0.06 & 0.08$\\pm$0.08 & foreground star K0III [SCF94] \\\\ \n 24 & 05 05 27.1 & -67 43 14 & 7.1 & 425.8 & 1.48e-02$\\pm$1.10e-03\n& 0.0$\\pm$ 0.0 & 0.0 & 568 & 0.74$\\pm$0.06 & 0.18$\\pm$0.09 &\nforeground eclipsing binary star ASAS J050526-6743.2 \\\\ \n 63 & 05 13 39.4 & -69 32 00 & 6.5 & 33.1 & 6.14e-03$\\pm$1.40e-03 & 0.0$\\pm$ 0.0 & 0.0 & 943 & & & foreground star K1V [CSM97] \\\\ \n 71 & 05 14 26.8 & -69 57 05 & 1.7 & 160.7 & 3.52e-03$\\pm$3.08e-04 & 1.7$\\pm$ 1.4 & 1.3 & & & & foreground star HD 269255 \\\\ \n 79 & 05 16 07.2 & -68 15 35 & 2.4 & 691.7 & 7.17e-02$\\pm$4.31e-03 & 0.0$\\pm$ 0.0 & 0.0 & 636 & -0.03$\\pm$0.06 & -0.09$\\pm$0.09 & foreground star G1V [SCF94] \\\\ \n 87 & 05 17 25.8 & -71 31 58 & 15.1 & 17.3 & 7.26e-03$\\pm$1.82e-03 & 4.3$\\pm$ 6.2 & 0.1 & 1284 & 1.00$\\pm$0.79 & -0.09$\\pm$0.10 & foreground star K2III\\& HD 35324 \\\\ \n 91 & 05 18 32.3 & -68 13 33 & 1.7 & 201.4 & 1.47e-02$\\pm$1.85e-03\n& 1.7$\\pm$ 1.2 & 2.8 & 634 & -1.00$\\pm$1.37 & & foreground star\nK3V HD 269320 [GGO93], [SCF94] \\\\ \n 99 & 05 19 56.2 & -71 29 07 & 6.3 & 25.8 & 8.53e-03$\\pm$2.61e-03 & 0.4$\\pm$ 2.7 & 0.0& 1280 & 0.30$\\pm$0.13 & 0.35$\\pm$0.10 & foreground star K2III [SCF94] \\\\ \n103 & 05 22 08.2 & -68 04 28 & 2.4 & 124.0 & 5.61e-03$\\pm$5.50e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & foreground star HD 35862 \\\\ \n104 & 05 22 19.6 & -67 51 31 & 2.7 & 30.5 & 1.72e-03$\\pm$3.14e-04 & 1.4$\\pm$ 1.5 & 0.4 & & & & foreground star HD 269422 \\\\ \n117 & 05 23 13.3 & -69 33 43 & 3.7 & 39.8 & 9.61e-04$\\pm$1.36e-04 & 0.9$\\pm$ 3.2 & 0.0& 954 & 1.00$\\pm$0.50 & & foreground star GSC 09166-00446 \\\\ \n123 & 05 24 01.4 & -71 09 33 & 7.1 & 455.0 & 5.64e-02$\\pm$5.15e-03 & 3.0$\\pm$ 1.3 & 36.1 & 1242 & -0.17$\\pm$0.12 & 0.24$\\pm$0.19 & foreground star M5e 1E 0524.7-7112\\\\\n133 & 05 25 02.3 & -67 53 28 & 8.7 & 27.0 & 4.48e-03$\\pm$9.35e-04 & 0.0$\\pm$ 0.0 & 0.0 & 595 & 0.38$\\pm$0.10 & 0.08$\\pm$0.12 & foreground star K2IV, RS CVn? [CSM97] \\\\ \n140 & 05 25 38.4 & -69 35 43 & 0.6 & 1847.2 & 7.64e-03$\\pm$2.55e-04 & 2.5$\\pm$ 0.8 & 70.3 & 964 & 0.30$\\pm$0.08 & -0.01$\\pm$0.10 & foreground star F7V HD 36436 [CSM97] \\\\ \n145 & 05 25 58.1 & -70 11 07 & 2.1 & 259.6 & 7.57e-03$\\pm$6.45e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1093 & 0.68$\\pm$0.06 & 0.23$\\pm$0.07 & foreground star K2IV-V, RS CVn [SCF94] \\\\ \n154 & 05 26 34.9 & -63 41 34 & 3.5 & 21.5 & 8.72e-04$\\pm$2.44e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & foreground star HD 36355 \\\\ \n156 & 05 26 59.8 & -68 37 22 & 3.8 & 45.0 & 2.37e-03$\\pm$3.87e-04 & 0.0$\\pm$ 0.0 & 0.0 & 693 & -0.46$\\pm$0.09 & -0.47$\\pm$0.16 & foreground star F0IV-V HD 36584 \\\\ \n171 & 05 28 11.7 & -71 05 38 & 8.1 & 19.0 & 1.39e-03$\\pm$2.79e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & foreground star F3/F5V HD 36877 \\\\ \n176 & 05 28 26.8 & -70 54 02 & 8.3 & 24.1 & 2.81e-03$\\pm$5.26e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & foreground star G0V HD 36890 \\\\ \n178 & 05 28 32.5 & -68 36 13 & 1.5 & 734.8 & 1.18e-02$\\pm$7.34e-04 & 2.2$\\pm$ 1.1 & 12.0 & 687 & 1.00$\\pm$0.19 & 0.01$\\pm$0.05 & foreground star G1V [CSM97] \\\\ \n180 & 05 28 44.7 & -65 26 56 & 0.2 & 31209.6 & 2.36e+00$\\pm$2.90e-02 & 2.0$\\pm$ 0.4 & 421.5 & 122 & -0.00$\\pm$0.01 & 0.07$\\pm$0.01 & foreground star K1III\\& HD 36705 (AB Dor) \\\\ \n189 & 05 29 24.0 & -68 49 12 & 2.3 & 54.3 & 1.89e-03$\\pm$3.18e-04 & 2.1$\\pm$ 1.9 & 1.2 & 728 & 0.23$\\pm$0.14 & 0.02$\\pm$0.17 & foreground star? [HP99b]\\\\\n193 & 05 29 27.0 & -68 52 05 & 0.6 & 2800.3 & 3.33e-02$\\pm$1.21e-03 & 1.9$\\pm$ 0.8 & 26.9 & 749 & 0.06$\\pm$0.02 & 0.04$\\pm$0.03 & foreground star G5 HD 269620 [CSM97] \\\\ \n212 & 05 30 49.6 & -67 05 55 & 10.0 & 20.9 & 1.18e-02$\\pm$3.76e-03 & 0.0$\\pm$ 0.0 & 0.0 & 478 & -0.25$\\pm$0.18 & 0.34$\\pm$0.28 & foreground star dMe [SCF94] \\\\ \n216 & 05 31 03.1 & -71 06 10 & 3.5 & 25.4 & 9.92e-04$\\pm$2.34e-04 & 1.4$\\pm$ 1.8 & 0.2 & & & & foreground star GSC 09166-00859 \\\\ \n262 & 05 35 22.8 & -66 12 55 & 8.3 & 48.9 & 1.00e-02$\\pm$1.88e-03 & 0.0$\\pm$ 0.0 & 0.0 & 268 & -0.24$\\pm$0.13 & -1.00$\\pm$1.65 & foreground star dM4e [CCH84] \\\\ \n293 & 05 38 15.9 & -69 23 30 & 0.9 & 2548.9 & 4.30e-02$\\pm$1.46e-03 & 0.6$\\pm$ 1.1 & 0.0 & 902 & 0.02$\\pm$0.03 & -0.00$\\pm$0.04 & foreground star dMe CAL 69 [CSM97] \\\\ \n294 & 05 38 21.3 & -68 50 34 & 2.6 & 33.2 & 1.37e-03$\\pm$2.89e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & foreground star G5V HD 269916 \\\\ \n296 & 05 38 34.4 & -68 53 07 & 0.4 & 5091.1 & 5.56e-02$\\pm$1.64e-03 & 0.0$\\pm$ 0.0 & 0.0 & 752 & -0.04$\\pm$0.02 & 0.05$\\pm$0.02 & foreground star G2V, RS CVn? [CSM97] \\\\ \n305 & 05 38 50.0 & -69 44 27 & 4.1 & 36.0 & 1.46e-03$\\pm$2.48e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & foreground star F2V HD 38329 \\\\ \n308 & 05 39 29.2 & -69 57 09 & 4.4 & 20.3 & 8.84e-04$\\pm$2.24e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & foreground star HD 269934 \\\\ \n349 & 05 43 34.5 & -64 22 55 & 7.2 & 624.1 & 3.06e-02$\\pm$1.79e-03 & 0.0$\\pm$ 0.0 & 0.0 & 61 & -0.00$\\pm$0.13 & 0.05$\\pm$0.19 & foreground star? [HP99b] \\\\ \n356 & 05 44 46.4 & -65 44 07 & 3.9 & 15.3 & 1.43e-03$\\pm$5.16e-04 & 0.0$\\pm$ 0.0 & 0.0 & 157 & -0.20$\\pm$0.22 & -1.00$\\pm$0.63 & foreground star A7V HD 39014 \\\\ \n375 & 05 48 19.2 & -70 20 44 & 1.7 & 216.6 & 3.57e-03$\\pm$3.47e-04 & 2.3$\\pm$ 1.3 & 7.5 & 1127 & & & foreground star F3/F5IV/V HD 39756 \\\\ \n379 & 05 49 28.9 & -69 47 14 & 9.9 & 24.2 & 1.81e-03$\\pm$3.34e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1014 & -1.00$\\pm$0.89 & & foreground star F2V HD 39904 \\\\ \n383 & 05 49 46.5 & -71 49 36 & 7.1 & 570.5 & 9.56e-03$\\pm$5.97e-04 & 3.3$\\pm$ 1.2 & 62.1 & 1312 & -0.02$\\pm$0.06 & -0.16$\\pm$0.08 & foreground star dMe [SCC99] \\\\ \n386 & 05 51 00.5 & -69 54 08 & 4.4 & 106.0 & 1.20e-02$\\pm$1.73e-03 & 0.6$\\pm$ 3.0 & 0.0& 1036 & -0.11$\\pm$0.16 & -1.00$\\pm$3.23 & foreground star F5V HD 40156 \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\n\\vspace{2mm}\nNotes to column No 9 (Table \\ref{identified}), No 10 (Tables\n\\ref{classified} and \\ref{wholecat}): \nCatalogue number from [HP99b].\n\n\\vspace{1mm}\nNotes to column No 12 (Table \\ref{identified}), No 13\n(Tables \\ref{classified} and \\ref{wholecat}):\n\nfg: foreground.\n\nCandidates from literature are marked with ? behind the source class. \n\nNew classification of this work are put in $<$ $>$.\n\nAbbreviations for references in square brackets are given in the\nliterature list.\n\\end{table}\n\n\\clearpage\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\scriptsize\n\\caption[]{Continued}\n\\begin{tabular}{rrrrrccrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ & \\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} & \\multicolumn{1}{c}{9} & 10 & 11 & ~~~12 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil & Count rate & \\ext & \\extl & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{PSPC} & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n 8 & 04 53 38.0 & -68 29 20 & 3.2 & 392.8 & 1.66e-02$\\pm$7.28e-04 & 6.3$\\pm$ 1.4 & 687.9 & 670 & 0.86$\\pm$0.01 & -0.36$\\pm$0.01 & SNR 0453-68.5 \\\\ \n 13 & 04 54 47.3 & -66 25 44 & 8.3 & 96.2 & 8.53e-03$\\pm$7.03e-04 & 13.6$\\pm$ 4.5 & 46.7 & 329 & 0.84$\\pm$0.04 & -0.24$\\pm$0.05 & SNR LHA 120-N 11L \\\\ \n 25 & 05 05 42.0 & -67 52 29 & 7.0 & 2223.3 & 5.83e-02$\\pm$1.40e-03 & 6.8$\\pm$ 1.1 &4214.3 & 592 & 0.81$\\pm$0.01 & -0.21$\\pm$0.01 & SNR DEM L 71 \\\\ \n 27 & 05 05 55.5 & -68 01 51 & 7.0 & 7040.7 & 2.16e-01$\\pm$3.25e-03 & 12.2$\\pm$ 1.7 &5968.8 & 614 & 0.89$\\pm$0.01 & -0.19$\\pm$0.02 & SNR LHA 120-N 23 \\\\ \n 43 & 05 08 58.6 & -68 43 35 & 7.0 & 13431.0 & 5.04e-01$\\pm$7.44e-03 & 5.4$\\pm$ 0.8 &8288.7 & 707 & 0.97$\\pm$0.00 & 0.13$\\pm$0.01 & SNR LHA 120-N 103B \\\\ \n 47 & 05 09 31.3 & -67 31 17 & 7.0 & 5476.1 & 6.33e-02$\\pm$1.11e-03 & 6.5$\\pm$ 0.9 &7396.2 & 542 & 0.78$\\pm$0.01 & -0.27$\\pm$0.01 & SNR 0509.0-67.5 \\\\ \n 50 & 05 10 48.7 & -68 45 27 & 7.6 & 21.3 & 4.16e-03$\\pm$1.28e-03 & 0.0$\\pm$ 0.0 & 0.4 & 712 & 1.00$\\pm$0.10 & 0.34$\\pm$0.07 & SNR? [WHHW91]\\\\\n 97 & 05 19 34.3 & -69 02 01 & 7.0 & 8929.9 & 2.58e-01$\\pm$3.80e-03 & 6.2$\\pm$ 0.8 &9883.6 & 789 & 0.95$\\pm$0.00 & -0.02$\\pm$0.01 & SNR 0519-69.0 \\\\ \n 98 & 05 19 48.9 & -69 26 09 & 7.9 & 45.9 & 8.54e-03$\\pm$8.38e-04 & 10.4$\\pm$ 3.5 & 74.6 & 915 & 0.36$\\pm$0.08 & -0.14$\\pm$0.10 & SNR 0520-69.4 \\\\ \n114 & 05 23 02.4 & -67 53 00 & 4.9 & 17.4 & 3.13e-03$\\pm$5.53e-04 & 6.2$\\pm$ 2.8 & 6.5 & 594 & 1.00$\\pm$0.04 & 0.17$\\pm$0.06 & SNR 0523-67.9 [CMG93]\\\\\n132 & 05 25 01.9 & -69 38 51 & 0.5 & 7939.5 & 2.66e-01$\\pm$2.44e-03 & 6.4$\\pm$ 0.9 &9439.5 & 977 & 0.94$\\pm$0.00 & -0.04$\\pm$0.01 & SNR LHA 120-N 132D \\\\ \n136 & 05 25 22.9 & -65 59 17 & 7.0 & 2178.7 & 4.85e-02$\\pm$5.97e-04 & 10.0$\\pm$ 1.4 &5218.8 & 219 & 0.94$\\pm$0.01 & -0.14$\\pm$0.02 & SNR LHA 120-N 49B \\\\ \n146 & 05 26 00.1 & -66 05 19 & 7.0 & 5983.6 & 7.83e-02$\\pm$5.44e-04 & 6.8$\\pm$ 0.9 &8459.6 & 241 & 0.95$\\pm$0.00 & -0.02$\\pm$0.01 & SNR LHA 120-N 49 \\\\ \n166 & 05 27 45.6 & -69 11 51 & 7.9 & 23.4 & 1.74e-03$\\pm$3.23e-04 & 4.7$\\pm$ 2.5 & 8.7 & 836 & 1.00$\\pm$0.74 & 1.00$\\pm$6.84 & SNR 0528-69.2 \\\\ \n223 & 05 31 56.7 & -70 59 59 & 3.4 & 71.6 & 4.76e-03$\\pm$3.79e-04 & 8.2$\\pm$ 2.5 & 110.9 & 1222 & 1.00$\\pm$0.09 & -0.26$\\pm$0.04 & SNR LHA 120-N 206 \\\\ \n231 & 05 32 27.3 & -67 31 10 & 8.5 & 106.1 & 1.80e-02$\\pm$1.99e-03 & 9.1$\\pm$ 4.8 & 9.8 & 540 & 1.00$\\pm$0.49 & -0.45$\\pm$0.09 & SNR? 0532-67.5 [C97]\\\\\n248 & 05 33 55.7 & -69 54 47 & 8.1 & 102.9 & 4.42e-02$\\pm$3.39e-03 & 15.7$\\pm$ 4.7 & 153.6 & 1043 & 1.00$\\pm$0.11 & -0.20$\\pm$0.05 & SNR 0534-69.9 \\\\ \n252 & 05 34 16.3 & -70 33 43 & 10.6 & 10.5 & 3.99e-03$\\pm$1.08e-03 & 7.4$\\pm$ 4.5 & 4.8 & 1160 & 0.82$\\pm$0.03 & 0.08$\\pm$0.04 & SNR DEM L 238 \\\\ \n268 & 05 35 45.7 & -69 18 00 & 1.5 & 63.8 & 1.36e-03$\\pm$9.48e-05 & 5.8$\\pm$ 1.6 & 119.1 & 866 & 1.00$\\pm$0.09 & -0.14$\\pm$0.05 & SNR Honeycomb Nebula \\\\ \n269 & 05 35 46.5 & -66 02 23 & 7.0 & 3681.1 & 3.11e-01$\\pm$6.77e-03 & 7.2$\\pm$ 1.1 &5993.1 & 226 & 0.94$\\pm$0.00 & -0.01$\\pm$0.01 & SNR LHA 120-N 63A \\\\ \n270 & 05 35 48.9 & -69 09 31 & 2.8 & 47.9 & 9.83e-04$\\pm$9.34e-05 & 6.8$\\pm$ 2.4 & 37.3 & & & & SNR 0536-69.2, 30 DOR C: knot \\\\ \n274 & 05 36 06.6 & -70 38 57 & 9.2 & 11.0 & 3.46e-03$\\pm$1.06e-03 & 5.1$\\pm$ 3.5 & 4.0 & 1173 & 1.00$\\pm$0.02 & -0.17$\\pm$0.04 & SNR DEM L 249 \\\\ \n276 & 05 36 17.3 & -69 13 04 & 2.0 & 55.0 & 1.14e-03$\\pm$9.25e-05 & 6.1$\\pm$ 1.9 & 72.0 & 840 & 0.89$\\pm$ * & 0.11$\\pm$ * & SNR 0536-69.2, 30 DOR C: knot \\\\ \n277 & 05 36 19.0 & -69 09 30 & 3.2 & 64.0 & 1.37e-03$\\pm$1.15e-04 & 8.5$\\pm$ 2.7 & 43.2 & & & & SNR 0536-69.2, 30 DOR C: knot \\\\ \n289 & 05 37 46.9 & -69 10 18 & 0.4 & 8036.1 & 4.07e-02$\\pm$6.36e-04 & 5.1$\\pm$ 0.7 &3391.0 & 826 & 1.00$\\pm$0.02 & 0.47$\\pm$0.02 & SNR 0538-69.1, LHA 120-N 157B (CAL 67) \\\\ \n310 & 05 39 36.6 & -70 01 58 & 9.3 & 27.1 & 4.28e-03$\\pm$6.40e-04 & 10.1$\\pm$ 4.4 & 14.4 & 1063 & 1.00$\\pm$0.17 & -0.17$\\pm$0.10 & SNR? [HP99b]\\\\\n315 & 05 40 04.5 & -69 43 58 & 3.6 & 41.3 & 3.36e-03$\\pm$3.52e-04 & 5.8$\\pm$ 2.0 & 61.8 & & & & SNR? [CKS97] \\\\ \n318 & 05 40 10.9 & -69 19 52 & 0.7 & 17883.4 & 1.95e-01$\\pm$3.32e-03 & 2.7$\\pm$ 0.5 & 781.3 & 877 & 0.98$\\pm$0.00 & 0.58$\\pm$0.01 & SNR LHA 120-N 158A, PSR B0540-69 \\\\ \n365 & 05 46 57.1 & -69 42 40 & 10.7 & 32.2 & 7.62e-03$\\pm$8.64e-04 & 16.8$\\pm$ 6.2 & 29.9 & 993 & 0.95$\\pm$ * & 0.21$\\pm$ * & SNR LHA 120-N 135, shell B \\\\ \n366 & 05 47 18.5 & -69 41 28 & 7.4 & 29.7 & 3.41e-03$\\pm$3.51e-04 & 6.7$\\pm$ 2.2 & 85.5 & 987 & 1.00$\\pm$0.10 & 0.22$\\pm$0.07 & SNR LHA 120-N 135, shell A \\\\ \n372 & 05 47 47.6 & -70 24 46 & 3.0 & 37.3 & 8.31e-03$\\pm$1.11e-03 & 6.4$\\pm$ 2.5 & 60.3 & 1137 & 1.00$\\pm$0.05 & -0.10$\\pm$0.06 & SNR 0548-70.4 \\\\ \n\\noalign{\\smallskip}\n 4 & 04 39 49.6 & -68 09 01 & 0.4 & 6228.5 & 1.66e-01$\\pm$4.89e-03 & 2.1$\\pm$ 0.6 & 138.9 & 628 & -1.00$\\pm$0.01 & & SSS RX J0439.8-6809 \\\\ \n 65 & 05 13 50.7 & -69 51 46 & 1.2 & 16279.1 & 3.09e-01$\\pm$2.41e-03 & 2.8$\\pm$ 0.5 &1161.2 & 1030 & -0.86$\\pm$0.00 & -0.98$\\pm$0.01 & SSS RX J0513.9-6951 \\\\ \n167 & 05 27 49.4 & -69 54 05 & 4.3 & 21.1 & 5.08e-04$\\pm$1.24e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1039 & -1.00$\\pm$0.01 & & SSS RX J0527.8-6954 \\\\ \n348 & 05 43 34.2 & -68 22 21 & 1.1 & 17776.1 & 2.15e-01$\\pm$3.26e-03 & 2.2$\\pm$ 0.7 & 46.1 & 654 & -0.87$\\pm$0.02 & -1.00$\\pm$0.51 & SSS CAL 83 [SCF94] \\\\ \n363 & 05 46 46.9 & -71 08 52 & 7.0 & 3268.5 & 6.23e-02$\\pm$2.17e-03 & 3.0$\\pm$ 0.8 & 242.1 & 1240 & 0.80$\\pm$0.01 & -0.86$\\pm$0.01 & SSS CAL 87 \\\\ \n\\noalign{\\smallskip}\n 17 & 05 01 23.9 & -70 33 33 & 2.9 & 58.0 & 1.12e-02$\\pm$2.64e-03 & 1.1$\\pm$ 1.5 & 0.1 & & & & HMXB RX J0501.6-7034 (CAL 9) \\\\ \n 19 & 05 02 51.6 & -66 26 25 & 1.2 & 2361.6 & 4.35e-01$\\pm$2.26e-02 & 1.8$\\pm$ 0.8 & 23.0 & 331 & 1.00$\\pm$0.67 & 0.43$\\pm$0.18 & HMXB RX J0502.9-6626 (CAL E) \\\\ \n202 & 05 29 48.3 & -65 56 46 & 2.0 & 119.2 & 1.94e-03$\\pm$2.05e-04 & 0.0$\\pm$ 0.0 & 0.0 & 204 & 0.84$\\pm$0.04 & 0.49$\\pm$0.06 & HMXB Be/X transient RXJ0529.8-6556 \\\\\n218 & 05 31 13.5 & -66 07 09 & 0.8 & 1133.4 & 9.42e-03$\\pm$4.08e-04 & 0.0$\\pm$ 0.0 & 0.0 & 252 & 0.64$\\pm$0.03 & 0.27$\\pm$0.04 & HMXB Be/X transient EXO053109-6609 \\\\\n233 & 05 32 33.1 & -65 51 43 & 1.4 & 327.0 & 3.99e-03$\\pm$2.80e-04 & 0.0$\\pm$ 0.0 & 0.0 & 184 & 1.00$\\pm$0.10 & 0.43$\\pm$0.05 & HMXB RX J0532.5-6551 \\\\ \n238 & 05 32 42.8 & -69 26 18 & 3.9 & 29.3 & 1.35e-03$\\pm$2.82e-04 & 2.5$\\pm$ 2.1 & 1.1 & 914 & 1.00$\\pm$0.31 & 0.29$\\pm$0.19 & LMXB? RX J0532.7-6926 [HP99a] \\\\ \n239 & 05 32 49.5 & -66 22 13 & 0.2 & 30957.4 & 2.82e+00$\\pm$4.22e-02 & 1.6$\\pm$ 0.4 & 182.5 & 316 & 0.51$\\pm$0.01 & 0.12$\\pm$0.02 & HMXB LMC X-4, HD 269743 O8III \\\\ \n306 & 05 38 56.3 & -64 05 03 & 0.2 & 34020.7 & 7.37e+00$\\pm$6.88e-02 & 1.9$\\pm$ 0.4 & 367.4 & 41 & 0.84$\\pm$0.00 & 0.28$\\pm$0.01 & HMXB LMC X-3 \\\\ \n311 & 05 39 38.7 & -69 44 32 & 3.0 & 32679.3 & 3.77e+00$\\pm$4.68e-02 & 0.0$\\pm$ 0.0 & 0.0 & 1001 & 0.99$\\pm$0.00 & 0.74$\\pm$0.00 & HMXB LMC X-1, O8III \\\\ \n352 & 05 44 06.0 & -71 00 51 & 7.8 & 12.3 & 1.34e-03$\\pm$5.17e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1225 & 1.00$\\pm$0.03 & 0.65$\\pm$0.03 & HMXB RX J0544.1-7100 [HP99b] \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\scriptsize\n\\caption[]{Continued}\n\\begin{tabular}{rrrrrccrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ & \\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} & \\multicolumn{1}{c}{9} & 10 & 11 & ~~~12 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil & Count rate & \\ext & \\extl & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{PSPC} & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n 10 & 04 54 10.7 & -66 43 17 & 7.3 & 55.1 & 8.01e-03$\\pm$1.82e-03 & 1.5$\\pm$ 1.5 & 0.6 & 411 & 1.00$\\pm$0.24 & 0.29$\\pm$0.07 & AGN RX J0454.2-6643, z=0.228 [CGC97] \\\\ \n 20 & 05 03 04.0 & -66 33 44 & 2.2 & 188.8 & 5.35e-02$\\pm$8.03e-03 & 0.0$\\pm$ 0.0 & 0.0 & 380 & 0.83$\\pm$0.03 & 0.17$\\pm$0.03 & AGN RX J0503.1-6634, z=0.064 [SCF94] \\\\ \n 86 & 05 17 16.9 & -70 44 01 & 2.2 & 186.4 & 1.03e-02$\\pm$1.24e-03 & 2.5$\\pm$ 1.4 & 8.2 & & & & AGN RX J0517.3-7044, z=0.169 [CSM97] \\\\ \n124 & 05 24 02.5 & -70 11 09 & 1.6 & 800.1 & 1.57e-02$\\pm$8.88e-04 & 1.6$\\pm$ 1.2 & 2.0 & 1094 & 0.91$\\pm$0.02 & 0.27$\\pm$0.04 & AGN RX J0524.0-7011, z=0.151 [SCF94] \\\\ \n220 & 05 31 31.8 & -71 29 46 & 3.5 & 46.4 & 1.19e-02$\\pm$3.54e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & AGN RX J0531.5-7130, z=0.221 [SCF94] \\\\ \n224 & 05 31 59.9 & -69 19 51 & 3.5 & 46.4 & 2.81e-03$\\pm$5.53e-04 & 2.4$\\pm$ 1.9 & 2.3 & 876 & 1.00$\\pm$0.21 & 0.02$\\pm$0.09 & AGN RX J0532.0-6920, z=0.149 [SCF94] \\\\ \n257 & 05 34 44.6 & -67 38 56 & 8.5 & 41.1 & 6.03e-03$\\pm$1.13e-03 & 0.0$\\pm$ 0.0 & 0.0 & 561 & 1.00$\\pm$0.15 & -0.04$\\pm$0.15 & AGN RX J0534.8-6739, z=0.072 [CSM97] \\\\ \n371 & 05 47 45.2 & -67 45 05 & 2.6 & 89.0 & 9.63e-03$\\pm$1.75e-03 & 2.1$\\pm$ 1.5 & 3.4 & & & & AGN RX J0547.8-6745, z=0.391 [CSM97] \\\\ \n385 & 05 50 31.5 & -71 09 57 & 8.6 & 29.1 & 3.59e-03$\\pm$7.58e-04 & 0.5$\\pm$ 3.7 & 0.0& 1243 & 1.00$\\pm$0.75 & 1.00$\\pm$1.61 & AGN RX J0550.5-7110, z=0.443 [CGC97] \\\\ \n389 & 05 52 24.3 & -64 02 12 & 7.1 & 464.0 & 4.82e-02$\\pm$4.64e-03 & 2.3$\\pm$ 1.2 & 10.8 & 37 & 0.57$\\pm$0.11 & 0.17$\\pm$0.12 & AGN? PKS 0552-640 [HP99b] \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}"
},
{
"name": "ds1817t3.tex",
"string": "\\caption[]{Classified HRI sources}\n\\begin{tabular}{rrrrrccrrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ &\n\\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} &\n\\multicolumn{1}{c}{9} & \\multicolumn{1}{c}{10} & 11 & 12 & ~~~13 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & log(f$_{x}$/f$_{opt}$) & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& & \\multicolumn{1}{c}{PSPC} & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n 28 & 05 05 58.4 & -68 10 30 & 8.4 & 22.8 & 1.85e-03$\\pm$4.21e-04 & 2.7$\\pm$ 3.4 & 0.2 &-3.09 & & & & $<$stellar$>$ \\\\\n 29 & 05 06 16.7 & -68 15 09 & 9.7 & 30.5 & 3.82e-03$\\pm$6.81e-04 & 0.0$\\pm$ 0.0 & 0.0 &-2.77 & & & & $<$stellar$>$ \\\\ \n 49 & 05 10 28.7 & -67 37 41 & 7.1 & 484.0 & 5.01e-03$\\pm$3.10e-04 & 0.0$\\pm$ 0.0 & 0.0 &-0.89 & 559 & 1.00$\\pm$0.71 & 0.26$\\pm$0.16 & $<$XB$>$ or $<$AGN$>$ \\\\ \n 90 & 05 17 47.8 & -71 44 05 & 11.4 & 15.9 & 1.96e-03$\\pm$6.46e-04 & 1.9$\\pm$ 2.3 & 0.3 &-3.06 & 1305 & 1.00$\\pm$1.34 & 0.45$\\pm$0.15 & $<$stellar$>$ \\\\ \n135 & 05 25 22.5 & -69 49 16 & 4.9 & 29.6 & 2.12e-03$\\pm$3.86e-04 & 0.0$\\pm$ 0.0 & 0.0 &-3.23 & 1025 & 1.00$\\pm$0.64 & 1.00$\\pm$2.40 & $<$stellar$>$ \\\\ \n197 & 05 29 39.2 & -66 08 06 & 20.1 & 12.7 & 1.96e-03$\\pm$4.05e-04 & 17.1$\\pm$10.8 & 2.2 &-0.62 & & & & $<$SNR$>$ \\\\ \n217 & 05 31 13.1 & -68 25 48 & 7.7 & 21.8 & 1.09e-03$\\pm$2.78e-04 & 0.0$\\pm$ 0.0 & 0.0 &-3.11 & 661 & & 1.00$\\pm$1.10 & $<$stellar$>$ \\\\ \n229 & 05 32 15.6 & -71 04 26 & 4.8 & 14.1 & 8.18e-04$\\pm$2.30e-04 & 0.0$\\pm$ 0.0 & 0.0 &-3.48 & & & & $<$stellar$>$ \\\\ \n230 & 05 32 18.5 & -71 07 43 & 2.9 & 302.5 & 4.69e-03$\\pm$3.49e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.56 & 1238 & 1.00$\\pm$0.35 & 1.00$\\pm$0.98 & $<$XB$>$ or $<$AGN$>$ \\\\ \n254 & 05 34 27.7 & -69 25 40 & 5.9 & 11.0 & 2.65e-03$\\pm$9.41e-04 & 0.0$\\pm$ 0.0 & 0.0 &-2.77 & & & & $<$stellar$>$ \\\\ \n284 & 05 37 28.6 & -69 23 18 & 13.4 & 11.5 & 4.07e-03$\\pm$1.05e-03 & 9.8$\\pm$ 7.6 & 1.5 &-1.58 & & & & $<$SNR$>$ \\\\ \n287 & 05 37 35.9 & -68 25 57 & 7.4 & 115.8 & 3.15e-03$\\pm$3.26e-04 & 0.0$\\pm$ 0.0 & 0.0 &-3.34 & & & & $<$stellar$>$ \\\\ \n288 & 05 37 36.2 & -69 16 42 & 9.7 & 16.3 & 8.36e-04$\\pm$1.40e-04 & 11.5$\\pm$ 5.5 & 5.1 &-0.51 & & & & $<$SNR$>$ \\\\ \n300 & 05 38 42.4 & -68 52 41 & 1.5 & 103.8 & 2.75e-03$\\pm$3.86e-04 & 0.8$\\pm$ 1.3 & 0.1 &-2.75 & & & & $<$stellar$>$ \\\\ \n307 & 05 39 27.9 & -69 33 12 & 12.0 & 15.7 & 2.49e-03$\\pm$4.68e-04 & 12.8$\\pm$ 6.5 & 4.0 & 0.76 & & & & $<$SNR$>$ \\\\ \n313 & 05 39 59.9 & -68 28 42 & 7.1 & 315.3 & 6.31e-03$\\pm$5.22e-04 & 2.7$\\pm$ 1.2 & 26.9 &-2.79 & 668 & 1.00$\\pm$0.62 & 1.00$\\pm$1.88 & $<$stellar$>$ \\\\ \n328 & 05 41 22.2 & -69 36 29 & 6.6 & 11.1 & 7.28e-04$\\pm$2.03e-04 & 0.0$\\pm$ 0.0 & 0.0 &-0.77 & & & & $<$HMXB$>$ LMC B2 supergiant star \\\\ \n332 & 05 41 37.1 & -68 32 32 & 4.5 & 33.6 & 2.34e-03$\\pm$4.27e-04 & 0.0$\\pm$ 0.0 & 0.0 &-2.34 & & & & $<$HMXB$>$ LMC O star \\\\ \n338 & 05 42 01.2 & -69 24 44 & 11.9 & 11.5 & 2.43e-03$\\pm$5.91e-04 & 8.3$\\pm$ 5.6 & 2.8 & 0.47 & & & & $<$SNR$>$ \\\\ \n347 & 05 43 22.2 & -68 56 39 & 6.4 & 141.3 & 2.51e-03$\\pm$3.01e-04 & 1.2$\\pm$ 1.1 & 0.8 &-3.07 & & & & $<$stellar$>$ \\\\ \n364 & 05 46 55.7 & -68 51 35 & 7.0 & 1146.0 & 2.02e-02$\\pm$1.00e-03 & 3.6$\\pm$ 1.0 & 171.7 & 0.43 & 747 & 1.00$\\pm$0.21 & 1.00$\\pm$0.60 & $<$XB$>$ or $<$AGN$>$ \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n"
},
{
"name": "ds1817t4.tex",
"string": "\\begin{table}\n\\scriptsize\n\\caption[]{\\label{wholecat}HRI sources in the LMC region}\n\\begin{tabular}{rrrrrccrrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ &\n\\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} &\n\\multicolumn{1}{c}{9} & \\multicolumn{1}{c}{10} & 11 & 12 & ~~~13 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & Count rate & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & & & & & & & & \\multicolumn{1}{c}{PSPC} & \\multicolumn{1}{c}{PSPC} & & & \\\\ \n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{[\\ct]} & & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n 1 & 04 38 23.9 & -68 08 24 & 5.7 & 10.7 & 4.42e-03$\\pm$1.82e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.74E-03 & & & & \\\\ \n 2 & 04 38 31.3 & -68 12 01 & 3.0 & 32.7 & 2.81e-03$\\pm$6.18e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.71E-03 & & & & \\\\ \n 3 & 04 39 44.7 & -67 58 39 & 10.0 & 10.1 & 3.81e-03$\\pm$1.21e-03 & 5.2$\\pm$ 5.7 & 0.4 & & & & & \\\\ \n 4 & 04 39 49.6 & -68 09 01 & 0.4 & 6228.5 & 1.66e-01$\\pm$4.89e-03 & 2.1$\\pm$ 0.6 & 138.9 & 1.15E+00 & 628 & -1.00$\\pm$0.01 & & SSS RX J0439.8-6809 \\\\ \n 5 & 04 40 07.7 & -68 14 54 & 4.5 & 12.1 & 2.37e-03$\\pm$8.84e-04 & 1.8$\\pm$ 2.4 & 0.2 & $<$1.12E-03 & & & & \\\\ \n 6 & 04 42 04.6 & -68 08 30 & 12.0 & 11.1 & 1.11e-02$\\pm$3.92e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n 7 & 04 53 36.5 & -68 27 45 & 3.6 & 50.7 & 1.22e-03$\\pm$2.12e-04 & 1.7$\\pm$ 1.5 & 0.9 & & & & & \\\\ \n 8 & 04 53 38.0 & -68 29 20 & 3.2 & 392.8 & 1.66e-02$\\pm$7.28e-04 & 6.3$\\pm$ 1.4 & 687.9 & 5.00E-01 & 670 & 0.86$\\pm$0.01 & -0.36$\\pm$0.01 & SNR 0453-68.5 \\\\ \n 9 & 04 53 43.5 & -68 24 23 & 4.4 & 15.3 & 5.99e-04$\\pm$1.63e-04 & 1.2$\\pm$ 1.9 & 0.1 & & & & & foreground star G0 HD 268717 [GGO93] \\\\ \n 10 & 04 54 10.7 & -66 43 17 & 7.3 & 55.1 & 8.01e-03$\\pm$1.82e-03 & 1.5$\\pm$ 1.5 & 0.6 & 2.69E-02 & 411 & 1.00$\\pm$0.24 & 0.29$\\pm$0.07 & AGN RX J0454.2-6643, z=0.2279 [CGC97] \\\\ \n 11 & 04 54 27.8 & -68 33 53 & 4.5 & 13.2 & 5.60e-04$\\pm$1.62e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.31E-03 & & & & \\\\ \n 12 & 04 54 30.2 & -68 18 01 & 9.1 & 12.7 & 1.30e-03$\\pm$3.20e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & foreground star HD 31961 \\\\ \n 13 & 04 54 47.3 & -66 25 44 & 8.3 & 96.2 & 8.53e-03$\\pm$7.03e-04 & 13.6$\\pm$ 4.5 & 46.7 & 2.74E-02 & 329 & 0.84$\\pm$0.04 & -0.24$\\pm$0.05 & SNR LHA 120-N 11L \\\\ \n 14 & 04 55 39.6 & -66 30 01 & 7.7 & 16.8 & 1.11e-03$\\pm$3.35e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.56E-03 & & & & \\\\ \n 15 & 04 58 25.1 & -69 08 22 & 4.1 & 39.8 & 5.77e-03$\\pm$1.31e-03 & 2.3$\\pm$ 2.0 & 1.2 & 1.22E-02 & 816 & 1.00$\\pm$0.51 & 0.29$\\pm$0.13 & foreground star F7V [CSM97] \\\\ \n 16 & 04 58 43.9 & -68 50 50 & 4.1 & 317.5 & 4.48e-02$\\pm$3.74e-03 & 0.0$\\pm$ 0.0 & 0.0 & 1.23E-01 & 742 & -0.04$\\pm$0.05 & 0.09$\\pm$0.07 & foreground star dMe HD 268840 [CSM97] \\\\ \n 17 & 05 01 23.9 & -70 33 33 & 2.9 & 58.0 & 1.12e-02$\\pm$2.64e-03 & 1.1$\\pm$ 1.5 & 0.1 & & & & & HMXB RX J0501.6-7034 (CAL 9) \\\\ \n 18 & 05 02 09.3 & -66 20 36 & 5.3 & 16.2 & 7.81e-03$\\pm$3.22e-03 & 0.4$\\pm$ 2.7 & 0.0 & 2.74E-02 & 304 & 0.68$\\pm$0.06 & 0.08$\\pm$0.08 & foreground star K0III [SCF94] \\\\ \n 19 & 05 02 51.6 & -66 26 25 & 1.2 & 2361.6 & 4.35e-01$\\pm$2.26e-02 & 1.8$\\pm$ 0.8 & 23.0 & 3.23E-03 & 331 & 1.00$\\pm$0.67 & 0.43$\\pm$0.18 & HMXB RX J0502.9-6626 (CAL E) \\\\ \n 20 & 05 03 04.0 & -66 33 44 & 2.2 & 188.8 & 5.35e-02$\\pm$8.03e-03 & 0.0$\\pm$ 0.0 & 0.0 & 1.17E-01 & 380 & 0.83$\\pm$0.03 & 0.17$\\pm$0.03 & AGN RX J0503.1-6634, z=0.064 [SCF94] \\\\ \n 21 & 05 04 31.5 & -67 54 26 & 9.0 & 16.2 & 1.72e-03$\\pm$4.38e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$6.12E-03 & & & & \\\\ \n 22 & 05 05 02.3 & -65 42 50 & 8.2 & 10.3 & 8.15e-04$\\pm$2.83e-04 & 1.0$\\pm$ 2.2 & 0.0 & & & & & \\\\ \n 23 & 05 05 21.8 & -68 45 40 & 7.1 & 447.5 & 2.40e-02$\\pm$1.93e-03 & 1.2$\\pm$ 1.4 & 0.3 & 2.10E-02 & 715 & -0.03$\\pm$0.13 & -1.00$\\pm$0.66 & \\\\ \n 24 & 05 05 27.1 & -67 43 14 & 7.1 & 425.8 & 1.48e-02$\\pm$1.10e-03 & 0.0$\\pm$ 0.0 & 0.0 & 4.44E-02 & 568 & 0.74$\\pm$0.06 & 0.18$\\pm$0.09 & fg eclipsing binary star ASAS J050526-6743.2 \\\\ \n 25 & 05 05 42.0 & -67 52 29 & 7.0 & 2223.3 & 5.83e-02$\\pm$1.40e-03 & 6.8$\\pm$ 1.1 &4214.3 & 1.61E+00 & 592 & 0.81$\\pm$0.01 & -0.21$\\pm$0.01 & SNR DEM L 71 \\\\ \n 26 & 05 05 50.5 & -67 50 09 & 14.5 & 10.5 & 2.27e-03$\\pm$6.06e-04 & 7.3$\\pm$ 7.6 & 0.7 & & & & & \\\\ \n 27 & 05 05 55.5 & -68 01 51 & 7.0 & 7040.7 & 2.16e-01$\\pm$3.25e-03 & 12.2$\\pm$ 1.7 &5968.8 & 9.57E-01 & 614 & 0.89$\\pm$0.01 & -0.19$\\pm$0.02 & SNR LHA 120-N 23 \\\\ \n 28 & 05 05 58.4 & -68 10 30 & 8.4 & 22.8 & 1.85e-03$\\pm$4.21e-04 & 2.7$\\pm$ 3.4 & 0.2 & $<$9.57E-03 & & & & $<$stellar$>$ \\\\ \n 29 & 05 06 16.7 & -68 15 09 & 9.7 & 30.5 & 3.82e-03$\\pm$6.81e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.15E-02 & 635 & 1.00$\\pm$0.76 & -0.05$\\pm$0.19 & $<$stellar$>$ \\\\ \n 30 & 05 06 25.5 & -65 37 10 & 7.8 & 14.7 & 9.71e-04$\\pm$3.01e-04 & 1.2$\\pm$ 2.0 & 0.1 & & & & & \\\\ \n 31 & 05 06 33.9 & -69 10 47 & 7.1 & 249.1 & 6.66e-03$\\pm$7.07e-04 & 1.3$\\pm$ 1.0 & 1.9 & 3.26E-02 & 830 & 1.00$\\pm$0.08 & 0.22$\\pm$0.09 & hard [HP99b] \\\\ \n 32 & 05 06 55.0 & -69 00 32 & 9.0 & 11.1 & 1.09e-03$\\pm$3.50e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n 33 & 05 07 09.0 & -68 45 00 & 8.0 & 12.0 & 1.33e-03$\\pm$4.89e-04 & 0.6$\\pm$ 2.1 & 0.0 & $<$8.85E-03 & & & & \\\\ \n 34 & 05 07 11.7 & -67 43 14 & 11.8 & 15.0 & 9.46e-03$\\pm$3.57e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n 35 & 05 07 37.1 & -68 47 52 & 8.4 & 15.3 & 1.73e-03$\\pm$4.81e-04 & 0.0$\\pm$ 0.0 & 0.0 & 7.74E-03 & 724 & 1.00$\\pm$0.16 & -0.02$\\pm$0.16 & hard [HP99b] \\\\ \n 36 & 05 07 59.5 & -67 28 34 & 9.1 & 12.1 & 7.95e-04$\\pm$2.28e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.36E-03 & & & & \\\\ \n 37 & 05 08 06.2 & -69 13 43 & 8.3 & 16.6 & 1.48e-03$\\pm$3.97e-04 & 0.8$\\pm$ 2.7 & 0.0 & 7.91E-03 & 844 & 1.00$\\pm$1.22 & & \\\\ \n 38 & 05 08 15.0 & -69 18 27 & 8.4 & 54.6 & 4.86e-03$\\pm$7.26e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.84E-02 & 865 & & & \\\\ \n 39 & 05 08 22.0 & -67 34 12 & 8.2 & 12.6 & 4.02e-04$\\pm$1.11e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n 40 & 05 08 33.3 & -68 54 28 & 9.0 & 23.9 & 2.89e-03$\\pm$6.39e-04 & 0.0$\\pm$ 0.0 & 0.0 & 7.69E-03 & 756 & 1.00$\\pm$0.37 & 0.35$\\pm$0.16 & \\\\ \n 41 & 05 08 53.3 & -67 24 03 & 8.3 & 11.3 & 6.21e-04$\\pm$1.86e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.16E-03 & & & & \\\\ \n 42 & 05 08 54.5 & -67 37 33 & 7.8 & 15.5 & 4.38e-04$\\pm$1.11e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.51E-03 & & & & \\\\ \n 43 & 05 08 58.6 & -68 43 35 & 7.0 & 13431.0 & 5.04e-01$\\pm$7.44e-03 & 5.4$\\pm$ 0.8 &8288.7 & 1.92E+00 & 707 & 0.97$\\pm$0.00 & 0.13$\\pm$0.01 & SNR LHA 120-N 103B \\\\ \n 44 & 05 09 01.7 & -67 21 16 & 8.9 & 13.8 & 9.82e-04$\\pm$2.57e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.65E-03 & & & & \\\\ \n 45 & 05 09 11.1 & -67 33 55 & 7.7 & 18.2 & 4.66e-04$\\pm$1.11e-04 & 2.4$\\pm$ 2.1 & 0.8 & $<$3.24E-03 & & & & Planetary Nebula [M94b] 18 \\\\ \n 46 & 05 09 14.2 & -67 20 15 & 10.1 & 10.6 & 5.92e-04$\\pm$1.59e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.77E-03 & & & & \\\\ \n 47 & 05 09 31.3 & -67 31 17 & 7.0 & 5476.1 & 6.33e-02$\\pm$1.11e-03 & 6.5$\\pm$ 0.9 &7396.2 & 5.02E-01 & 542 & 0.78$\\pm$0.01 & -0.27$\\pm$0.01 & SNR 0509.0-67.5 \\\\ \n 48 & 05 10 24.6 & -67 29 04 & 8.0 & 12.2 & 3.72e-04$\\pm$1.03e-04 & 2.1$\\pm$ 2.2 & 0.5 & $<$2.06E-03 & & & & \\\\ \n 49 & 05 10 28.7 & -67 37 41 & 7.1 & 484.0 & 5.01e-03$\\pm$3.10e-04 & 0.0$\\pm$ 0.0 & 0.0 & 6.07E-03 & 559 & 1.00$\\pm$0.71 & 0.26$\\pm$0.16 & $<$XB$>$ or $<$AGN$>$ \\\\ \n 50 & 05 10 48.7 & -68 45 27 & 7.6 & 21.3 & 4.16e-03$\\pm$1.28e-03 & 0.0$\\pm$ 0.0 & 0.4 & 3.27E-02 & 712 & 1.00$\\pm$0.10 & 0.34$\\pm$0.07 & SNR? [WHHW91] \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\n\\vspace{2mm}\nNotes to column No 6: \nHRI count rate ist the output value from maximum likelihood algorithm\nwith the smallest positional error.\n\n\\vspace{1mm}\nNotes to column No 9:\nFor sources which are listed in [HP99b] PSPC count rates are taken from\nthe PSPC catalogue. \nOtherwise PSPC count rate is the 95.4\\% (2$\\sigma$) upper limit from\nmaximum likelihood algorithm of the pointing with maximum exposure. \n\n\\end{table}\n\n\\clearpage\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\scriptsize\n\\caption[]{Continued}\n\\begin{tabular}{rrrrrccrrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ &\n\\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} &\n\\multicolumn{1}{c}{9} & \\multicolumn{1}{c}{10} & 11 & 12 & ~~~13 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & Count rate & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & & & & & & & & \\multicolumn{1}{c}{PSPC} & \\multicolumn{1}{c}{PSPC} & & & \\\\ \n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{[\\ct]} & & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n 51 & 05 10 50.4 & -69 05 13 & 9.3 & 10.0 & 2.82e-03$\\pm$1.08e-03 & 3.0$\\pm$ 3.2 & 0.3 & $<$6.39E-03 & & & & \\\\ \n 52 & 05 10 56.1 & -69 22 14 & 7.9 & 16.5 & 3.49e-03$\\pm$1.31e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$8.88E-03 & & & & \\\\ \n 53 & 05 11 51.1 & -69 10 16 & 7.3 & 25.4 & 2.72e-03$\\pm$5.46e-04 & 2.3$\\pm$ 3.8 & 0.1 & $<$8.57E-03 & & & & \\\\ \n 54 & 05 12 21.3 & -69 08 29 & 7.5 & 10.7 & 1.11e-03$\\pm$3.46e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.21E-03 & & & & \\\\ \n 55 & 05 12 29.0 & -69 42 48 & 4.2 & 35.7 & 2.85e-03$\\pm$4.05e-04 & 0.0$\\pm$ 0.0 & 0.0 & 4.12E-03 & 992 & 1.00$\\pm$0.53 & 1.00$\\pm$0.49 & \\\\ \n 56 & 05 12 30.2 & -69 55 58 & 3.1 & 23.5 & 1.32e-03$\\pm$2.44e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.48E-03 & & & & \\\\ \n 57 & 05 12 45.4 & -69 39 01 & 14.0 & 11.0 & 5.03e-03$\\pm$1.50e-03 & 0.0$\\pm$ 0.0 & 0.0 & 6.24E-03 & 976 & 1.00$\\pm$0.27 & 0.15$\\pm$0.18 & \\\\ \n 58 & 05 12 47.4 & -69 49 23 & 6.0 & 11.7 & 4.67e-03$\\pm$1.59e-03 & 3.8$\\pm$ 3.3 & 1.7 & & & & & \\\\ \n 59 & 05 12 48.9 & -69 53 10 & 2.1 & 53.4 & 1.74e-03$\\pm$2.36e-04 & 1.5$\\pm$ 1.5 & 0.7 & $<$5.51E-03 & & & & \\\\ \n 60 & 05 12 52.0 & -70 05 18 & 14.4 & 15.1 & 1.00e-02$\\pm$2.96e-03 & 6.5$\\pm$ 8.6 & 0.2 & $<$2.40E-03 & & & & \\\\ \n 61 & 05 12 57.3 & -69 56 42 & 8.6 & 10.3 & 3.18e-03$\\pm$1.27e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n 62 & 05 13 29.8 & -69 59 30 & 10.8 & 12.6 & 5.57e-03$\\pm$1.85e-03 & 5.1$\\pm$ 4.7 & 1.2 & $<$2.22E-03 & & & & \\\\ \n 63 & 05 13 39.4 & -69 32 00 & 6.5 & 33.1 & 6.14e-03$\\pm$1.40e-03 & 0.0$\\pm$ 0.0 & 0.0 & 2.42E-02 & 943 & & & foreground star K1V [CSM97] \\\\ \n 64 & 05 13 40.2 & -69 44 23 & 8.4 & 12.2 & 4.92e-03$\\pm$1.84e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$8.99E-04 & & & & \\\\ \n 65 & 05 13 50.7 & -69 51 46 & 1.2 & 16279.1 & 3.09e-01$\\pm$2.41e-03 & 2.8$\\pm$ 0.5 &1161.2 & 1.94E+00 &1030 & -0.86$\\pm$0.00 & -0.98$\\pm$0.01 & SSS RX J0513.9-6951 \\\\ \n 66 & 05 13 59.1 & -69 46 04 & 8.6 & 11.2 & 3.55e-03$\\pm$1.82e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$6.36E-04 & & & & \\\\ \n 67 & 05 14 05.7 & -69 53 35 & 4.5 & 15.2 & 3.25e-03$\\pm$1.31e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.26E-03 & & & & \\\\ \n 68 & 05 14 11.9 & -69 44 47 & 3.8 & 14.4 & 9.16e-04$\\pm$2.11e-04 & 0.2$\\pm$ 2.9 & 0.0 & $<$4.82E-03 & & & & \\\\ \n 69 & 05 14 20.7 & -69 55 53 & 2.9 & 19.7 & 8.93e-04$\\pm$1.87e-04 & 1.6$\\pm$ 1.9 & 0.2 & $<$2.31E-03 & & & & \\\\ \n 70 & 05 14 25.9 & -70 00 55 & 10.2 & 10.1 & 5.47e-03$\\pm$2.13e-03 & 5.1$\\pm$ 5.2 & 0.5 & $<$1.59E-03 & & & & \\\\ \n 71 & 05 14 26.8 & -69 57 05 & 1.7 & 160.7 & 3.52e-03$\\pm$3.08e-04 & 1.7$\\pm$ 1.4 & 1.3 & $<$4.65E-03 & & & & foreground star HD 269255 \\\\ \n 72 & 05 14 38.4 & -69 48 56 & 1.4 & 385.7 & 5.79e-03$\\pm$3.67e-04 & 1.6$\\pm$ 1.0 & 4.3 & $<$6.21E-03 & & & & \\\\ \n 73 & 05 14 43.0 & -69 47 36 & 4.6 & 12.3 & 3.22e-03$\\pm$1.26e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.32E-03 & & & & \\\\ \n 74 & 05 15 04.3 & -71 43 44 & 11.2 & 41.0 & 4.53e-03$\\pm$9.72e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n 75 & 05 15 09.7 & -69 50 46 & 3.5 & 19.4 & 1.07e-03$\\pm$2.19e-04 & 1.9$\\pm$ 2.5 & 0.1 & $<$5.60E-04 & & & & \\\\ \n 76 & 05 15 28.8 & -69 49 51 & 9.0 & 10.0 & 5.09e-03$\\pm$2.24e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.30E-03 & & & & \\\\ \n 77 & 05 15 42.1 & -69 50 20 & 7.7 & 10.2 & 3.07e-03$\\pm$1.08e-03 & 2.6$\\pm$ 4.0 & 0.1 & $<$2.67E-03 & & & & \\\\ \n 78 & 05 16 00.1 & -69 16 09 & 7.3 & 30.3 & 7.25e-03$\\pm$1.58e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$5.86E-03 & & & & \\\\ \n 79 & 05 16 07.2 & -68 15 35 & 2.4 & 691.7 & 7.17e-02$\\pm$4.31e-03 & 0.0$\\pm$ 0.0 & 0.0 & 1.10E-01 & 636 & -0.03$\\pm$0.06 & -0.09$\\pm$0.09 & foreground star G1V [SCF94] \\\\ \n 80 & 05 16 10.8 & -69 54 38 & 11.2 & 10.6 & 7.64e-03$\\pm$3.02e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.70E-03 & & & & \\\\ \n 81 & 05 16 11.8 & -69 50 05 & 11.5 & 12.5 & 8.81e-03$\\pm$2.73e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$6.05E-03 & & & & \\\\ \n 82 & 05 16 26.2 & -69 48 19 & 2.7 & 238.1 & 1.23e-02$\\pm$6.89e-04 & 0.0$\\pm$ 0.0 & 0.0 & 7.41E-03 &1019 & 1.00$\\pm$0.28 & 0.36$\\pm$0.17 & \\\\ \n 83 & 05 16 37.0 & -70 05 12 & 4.6 & 21.1 & 1.48e-03$\\pm$3.44e-04 & 2.5$\\pm$ 3.0 & 0.2 & $<$4.49E-02 & & & & \\\\ \n 84 & 05 16 40.2 & -71 45 58 & 11.5 & 21.4 & 3.28e-03$\\pm$8.41e-04 & 4.2$\\pm$ 2.6 & 3.1 & 1.20E-02 &1308 & 1.00$\\pm$0.26 & 0.42$\\pm$0.13 & RX J0516.7-7146; B0517-7151 [FHW95] \\\\ \n 85 & 05 17 14.8 & -71 38 26 & 12.1 & 11.1 & 1.74e-03$\\pm$6.51e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n 86 & 05 17 16.9 & -70 44 01 & 2.2 & 186.4 & 1.03e-02$\\pm$1.24e-03 & 2.5$\\pm$ 1.4 & 8.2 & & & & & AGN RX J0517.3-7044, z=0.169 [CSM97] \\\\ \n 87 & 05 17 25.8 & -71 31 58 & 15.1 & 17.3 & 7.26e-03$\\pm$1.82e-03 & 4.3$\\pm$ 6.2 & 0.1 & 1.90E-02 &1284 & 1.00$\\pm$0.79 & -0.09$\\pm$0.10 & foreground star K2III\\& HD 35324 \\\\ \n 88 & 05 17 30.4 & -71 51 42 & 11.6 & 11.0 & 1.49e-03$\\pm$5.70e-04 & 0.0$\\pm$ 0.0 & 0.0 & 4.66E-03 &1318 & 1.00$\\pm$0.86 & 1.00$\\pm$2.32 & \\\\ \n 89 & 05 17 46.9 & -68 54 57 & 9.8 & 14.1 & 1.80e-03$\\pm$4.61e-04 & 0.0$\\pm$ 0.0 & 0.0 & 8.40E-03 & 760 & 1.00$\\pm$0.33 & -0.12$\\pm$0.23 & \\\\ \n 90 & 05 17 47.8 & -71 44 05 & 11.4 & 15.9 & 1.96e-03$\\pm$6.46e-04 & 1.9$\\pm$ 2.3 & 0.3 & 8.54E-03 &1305 & 1.00$\\pm$1.34 & 0.45$\\pm$0.15 & $<$stellar$>$ \\\\ \n 91 & 05 18 32.3 & -68 13 33 & 1.7 & 201.4 & 1.47e-02$\\pm$1.85e-03 & 1.7$\\pm$ 1.2 & 2.8 & 3.67E-02 & 634 & -1.00$\\pm$1.37 & & fg star K3V HD 269320 [GGO93], [SCF94] \\\\ \n 92 & 05 18 40.7 & -69 32 06 & 10.5 & 10.0 & 2.80e-03$\\pm$1.03e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.03E-02 & & & & \\\\ \n 93 & 05 18 52.2 & -68 15 54 & 3.0 & 16.0 & 2.04e-03$\\pm$7.09e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$6.65E-02 & & & & RX J0518.9-6816 \\\\ \n 94 & 05 18 55.3 & -69 56 01 & 2.4 & 69.3 & 2.56e-03$\\pm$3.99e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$8.78E-03 & & & & \\\\ \n 95 & 05 19 19.9 & -68 54 32 & 8.0 & 17.8 & 1.61e-03$\\pm$4.44e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.14E-02 & & & & Nova LMC 1992 \\\\ \n 96 & 05 19 33.4 & -69 17 49 & 9.3 & 46.1 & 4.95e-03$\\pm$7.26e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.38E-02 & 863 & -0.16$\\pm$0.18 & -1.00$\\pm$1.81 & \\\\ \n 97 & 05 19 34.3 & -69 02 01 & 7.0 & 8929.9 & 2.58e-01$\\pm$3.80e-03 & 6.2$\\pm$ 0.8 &9883.6 & 1.46E+00 & 789 & 0.95$\\pm$0.00 & -0.02$\\pm$0.01 & SNR 0519-69.0 \\\\ \n 98 & 05 19 48.9 & -69 26 09 & 7.9 & 45.9 & 8.54e-03$\\pm$8.38e-04 & 10.4$\\pm$ 3.5 & 74.6 & 1.13E-01 & 915 & 0.36$\\pm$0.08 & -0.14$\\pm$0.10 & SNR 0520-69.4 \\\\ \n 99 & 05 19 56.2 & -71 29 07 & 6.3 & 25.8 & 8.53e-03$\\pm$2.61e-03 & 0.4$\\pm$ 2.7 & 0.0 & 1.34E-02 &1280 & 0.30$\\pm$0.13 & 0.35$\\pm$0.10 & foreground star K2III [SCF94] \\\\ \n100 & 05 20 19.5 & -69 11 37 & 9.5 & 12.8 & 1.92e-03$\\pm$5.48e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$9.70E-03 & & & & \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\scriptsize\n\\caption[]{Continued}\n\\begin{tabular}{rrrrrccrrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ &\n\\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} &\n\\multicolumn{1}{c}{9} & \\multicolumn{1}{c}{10} & 11 & 12 & ~~~13 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & Count rate & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & & & & & & & & \\multicolumn{1}{c}{PSPC} & \\multicolumn{1}{c}{PSPC} & & & \\\\ \n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{[\\ct]} & & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n101 & 05 20 54.9 & -67 44 59 & 7.0 & 14.7 & 2.95e-03$\\pm$6.37e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.21E-03 & & & & \\\\ \n102 & 05 21 39.2 & -68 53 43 & 13.8 & 10.9 & 2.86e-03$\\pm$7.89e-04 & 2.9$\\pm$ 7.7 & 0.0 & $<$3.85E-03 & & & & \\\\ \n103 & 05 22 08.2 & -68 04 28 & 2.4 & 124.0 & 5.61e-03$\\pm$5.50e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$4.40E-03 & & & & foreground star HD 35862 \\\\ \n104 & 05 22 19.6 & -67 51 31 & 2.7 & 30.5 & 1.72e-03$\\pm$3.14e-04 & 1.4$\\pm$ 1.5 & 0.4 & $<$1.69E-03 & & & & foreground star HD 269422 \\\\ \n105 & 05 22 23.5 & -67 50 45 & 8.5 & 12.4 & 3.03e-03$\\pm$1.13e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$7.64E-04 & & & & \\\\ \n106 & 05 22 24.6 & -69 30 33 & 9.8 & 12.0 & 1.32e-03$\\pm$3.62e-04 & 5.0$\\pm$ 3.8 & 1.3 & $<$1.80E-03 & & & & \\\\ \n107 & 05 22 29.2 & -68 00 28 & 5.3 & 14.0 & 2.83e-03$\\pm$5.44e-04 & 6.4$\\pm$ 2.8 & 5.9 & & & & & knot in N44 \\\\ \n108 & 05 22 32.8 & -69 42 37 & 12.3 & 10.9 & 1.63e-02$\\pm$6.56e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.97E-03 & & & & \\\\ \n109 & 05 22 36.0 & -67 56 05 & 7.9 & 10.6 & 1.04e-03$\\pm$3.93e-04 & 0.8$\\pm$ 1.8 & 0.0 & & & & & knot in N44\\\\ \n110 & 05 22 37.8 & -67 47 44 & 4.2 & 13.9 & 1.55e-03$\\pm$3.74e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$4.89E-03 & & & & \\\\ \n111 & 05 22 42.7 & -69 15 55 & 11.2 & 13.9 & 4.60e-03$\\pm$1.36e-03 & 3.3$\\pm$ 5.2 & 0.1 & & & & & \\\\ \n112 & 05 22 46.2 & -69 28 35 & 7.3 & 78.6 & 3.33e-03$\\pm$4.82e-04 & 0.0$\\pm$ 0.0 & 0.0 & 8.87E-03 & 931 & 1.00$\\pm$0.19 & 0.32$\\pm$0.16 & hard [HP99b] \\\\ \n113 & 05 23 00.1 & -70 18 32 & 3.6 & 37.2 & 2.00e-03$\\pm$3.71e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.17E-02 & & & & \\\\ \n114 & 05 23 02.4 & -67 53 00 & 4.9 & 17.4 & 3.13e-03$\\pm$5.53e-04 & 6.2$\\pm$ 2.8 & 6.5 & 1.66E-02 & 594 & 1.00$\\pm$0.04 & 0.17$\\pm$0.06 & SNR 0523-67.9 [CMG93] \\\\ \n115 & 05 23 04.5 & -69 43 26 & 7.8 & 14.4 & 5.69e-03$\\pm$1.81e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.32E-03 & & & & \\\\ \n116 & 05 23 12.9 & -70 15 32 & 4.1 & 19.3 & 1.27e-03$\\pm$3.08e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.07E-02 &1109 & 1.00$\\pm$0.16 & 0.15$\\pm$0.14 & hard [HP99b] \\\\ \n117 & 05 23 13.3 & -69 33 43 & 3.7 & 39.8 & 9.61e-04$\\pm$1.36e-04 & 0.9$\\pm$ 3.2 & 0.0 & 7.13E-03 & 954 & 1.00$\\pm$0.50 & & foreground star GSC 09166-00446 \\\\ \n118 & 05 23 21.9 & -67 53 35 & 5.0 & 25.1 & 3.77e-03$\\pm$5.94e-04 & 6.4$\\pm$ 3.4 & 6.5 & & & & & knot in N44 \\\\ \n119 & 05 23 32.0 & -69 35 28 & 6.9 & 11.4 & 7.74e-03$\\pm$2.70e-03 & 3.2$\\pm$ 3.6 & 0.4 & $<$4.46E-03 & & & & \\\\ \n120 & 05 23 38.1 & -69 39 07 & 5.9 & 11.5 & 3.49e-03$\\pm$1.35e-03 & 2.1$\\pm$ 3.2 & 0.1 & $<$1.65E-03 & & & & \\\\ \n121 & 05 23 53.9 & -67 57 35 & 6.2 & 12.9 & 2.00e-03$\\pm$4.69e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.55E-03 & & & & \\\\ \n122 & 05 23 55.1 & -69 33 12 & 5.3 & 11.0 & 3.85e-03$\\pm$1.68e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.07E-02 & & & & \\\\ \n123 & 05 24 01.4 & -71 09 33 & 7.1 & 455.0 & 5.64e-02$\\pm$5.15e-03 & 3.0$\\pm$ 1.3 & 36.1 & 2.77E-01 &1242 & -0.17$\\pm$0.12 & 0.24$\\pm$0.19 & foreground star M5e 1E 0524.7-7112 \\\\ \n124 & 05 24 02.5 & -70 11 09 & 1.6 & 800.1 & 1.57e-02$\\pm$8.88e-04 & 1.6$\\pm$ 1.2 & 2.0 & 1.14E-01 &1094 & 0.91$\\pm$0.02 & 0.27$\\pm$0.04 & AGN RX J0524.0-7011, z=0.151 [SCF94] \\\\ \n125 & 05 24 11.1 & -70 22 36 & 3.4 & 26.4 & 1.38e-03$\\pm$2.94e-04 & 2.7$\\pm$ 2.3 & 1.8 & $<$6.75E-03 & & & & \\\\ \n126 & 05 24 12.8 & -66 00 33 & 13.1 & 10.9 & 2.69e-03$\\pm$7.55e-04 & 4.4$\\pm$ 6.2 & 0.1 & $<$3.79E-03 & & & & \\\\ \n127 & 05 24 19.4 & -66 05 20 & 7.6 & 42.9 & 7.75e-04$\\pm$1.09e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.16E-03 & & & & \\\\ \n128 & 05 24 26.3 & -69 36 13 & 1.6 & 76.9 & 9.41e-04$\\pm$1.07e-04 & 2.4$\\pm$ 1.5 & 4.4 & & & & & \\\\ \n129 & 05 24 29.9 & -66 11 35 & 8.0 & 44.3 & 9.87e-04$\\pm$1.31e-04 & 0.0$\\pm$ 0.0 & 0.0 & 3.52E-03 & 264 & 1.00$\\pm$0.48 & 0.28$\\pm$0.21 & \\\\ \n130 & 05 24 47.2 & -69 32 06 & 4.9 & 12.3 & 4.06e-03$\\pm$1.45e-03 & 2.3$\\pm$ 2.6 & 0.5 & $<$1.34E-03 & & & & \\\\ \n131 & 05 24 48.3 & -66 03 47 & 8.2 & 17.3 & 1.43e-03$\\pm$4.37e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.88E-03 & & & & \\\\ \n132 & 05 25 01.9 & -69 38 51 & 0.5 & 7939.5 & 2.66e-01$\\pm$2.44e-03 & 6.4$\\pm$ 0.9 &9439.5 & 7.37E+00 & 977 & 0.94$\\pm$0.00 & -0.04$\\pm$0.01 & SNR LHA 120-N 132D \\\\ \n133 & 05 25 02.3 & -67 53 28 & 8.7 & 27.0 & 4.48e-03$\\pm$9.35e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.81E-02 & 595 & 0.38$\\pm$0.10 & 0.08$\\pm$0.12 & foreground star K2IV, RS CVn? [CSM97] \\\\ \n134 & 05 25 06.6 & -70 16 42 & 2.1 & 81.9 & 2.74e-03$\\pm$3.83e-04 & 2.6$\\pm$ 1.5 & 8.9 & $<$9.08E-03 & & & & \\\\ \n135 & 05 25 22.5 & -69 49 16 & 4.9 & 29.6 & 2.12e-03$\\pm$3.86e-04 & 0.0$\\pm$ 0.0 & 0.0 & 3.99E-03 &1025 & 1.00$\\pm$0.64 & 1.00$\\pm$2.40 & $<$stellar$>$ \\\\ \n136 & 05 25 22.9 & -65 59 17 & 7.0 & 2178.7 & 4.85e-02$\\pm$5.97e-04 & 10.0$\\pm$ 1.4 &5218.8 & 4.56E-01 & 219 & 0.94$\\pm$0.01 & -0.14$\\pm$0.02 & SNR LHA 120-N 49B \\\\ \n137 & 05 25 28.1 & -69 14 24 & 7.2 & 73.0 & 1.94e-03$\\pm$3.00e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.09E-02 & & & & \\\\ \n138 & 05 25 28.7 & -63 40 41 & 7.6 & 12.3 & 1.26e-03$\\pm$3.61e-04 & 0.9$\\pm$ 4.0 & 0.0 & & & & & \\\\ \n139 & 05 25 38.1 & -69 37 20 & 3.5 & 11.0 & 2.34e-03$\\pm$9.50e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n140 & 05 25 38.4 & -69 35 43 & 0.6 & 1847.2 & 7.64e-03$\\pm$2.55e-04 & 2.5$\\pm$ 0.8 & 70.3 & 3.29E-02 & 964 & 0.30$\\pm$0.08 & -0.01$\\pm$0.10 & foreground star F7V HD 36436 [CSM97] \\\\ \n141 & 05 25 42.1 & -63 41 54 & 3.3 & 75.3 & 2.92e-03$\\pm$4.50e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n142 & 05 25 48.9 & -69 21 07 & 8.7 & 10.2 & 8.03e-03$\\pm$3.59e-03 & 2.9$\\pm$ 4.6 & 0.1 & $<$3.67E-02 & & & & \\\\ \n143 & 05 25 52.7 & -69 44 56 & 2.1 & 56.0 & 8.42e-04$\\pm$1.09e-04 & 0.8$\\pm$ 1.8 & 0.0 & 4.42E-03 &1002 & 1.00$\\pm$0.55 & 1.00$\\pm$1.20 & \\\\ \n144 & 05 25 55.4 & -68 51 56 & 8.5 & 13.6 & 1.20e-03$\\pm$3.32e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.86E-03 & & & & \\\\ \n145 & 05 25 58.1 & -70 11 07 & 2.1 & 259.6 & 7.57e-03$\\pm$6.45e-04 & 0.0$\\pm$ 0.0 & 0.0 & 4.14E-02 &1093 & 0.68$\\pm$0.06 & 0.23$\\pm$0.07 & foreground star K2IV-V, RS CVn [SCF94] \\\\ \n146 & 05 26 00.1 & -66 05 19 & 7.0 & 5983.6 & 7.83e-02$\\pm$5.44e-04 & 6.8$\\pm$ 0.9 &8459.6 & 2.06E+00 & 241 & 0.95$\\pm$0.00 & -0.02$\\pm$0.01 & SNR LHA 120-N 49 \\\\ \n147 & 05 26 12.2 & -69 33 59 & 5.0 & 13.1 & 4.59e-03$\\pm$1.70e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.59E-03 & & & & \\\\ \n148 & 05 26 15.2 & -63 46 59 & 3.0 & 51.8 & 1.66e-03$\\pm$3.31e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n149 & 05 26 17.8 & -66 02 32 & 7.8 & 11.8 & 7.99e-04$\\pm$2.80e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$6.15E-03 & & & & \\\\ \n150 & 05 26 20.1 & -69 37 04 & 8.8 & 11.3 & 7.71e-03$\\pm$3.08e-03 & 1.1$\\pm$ 2.6 & 0.0 & $<$2.41E-03 & & & & \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\scriptsize\n\\caption[]{Continued}\n\\begin{tabular}{rrrrrccrrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ &\n\\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} &\n\\multicolumn{1}{c}{9} & \\multicolumn{1}{c}{10} & 11 & 12 & ~~~13 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & Count rate & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & & & & & & & & \\multicolumn{1}{c}{PSPC} & \\multicolumn{1}{c}{PSPC} & & & \\\\ \n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{[\\ct]} & & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n151 & 05 26 31.5 & -66 01 04 & 8.1 & 11.1 & 5.62e-04$\\pm$1.79e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.46E-03 & & & & \\\\ \n152 & 05 26 32.1 & -69 44 48 & 8.6 & 10.5 & 2.12e-03$\\pm$7.00e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.28E-03 & & & & \\\\ \n153 & 05 26 32.9 & -69 54 12 & 4.7 & 18.1 & 6.00e-04$\\pm$1.46e-04 & 0.0$\\pm$ 0.0 & 0.0 & 2.46E-03 &1041 & 1.00$\\pm$0.94 & 1.00$\\pm$0.99 & \\\\ \n154 & 05 26 34.9 & -63 41 34 & 3.5 & 21.5 & 8.72e-04$\\pm$2.44e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.70E-02 & & & & foreground star HD 36355 \\\\ \n155 & 05 26 50.5 & -70 01 24 & 1.6 & 849.8 & 1.71e-02$\\pm$9.32e-04 & 1.8$\\pm$ 1.5 & 1.0 & & & & & Nova LMC 1995 [OG99] \\\\ \n156 & 05 26 59.8 & -68 37 22 & 3.8 & 45.0 & 2.37e-03$\\pm$3.87e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.13E-02 & 693 & -0.46$\\pm$0.09 & -0.47$\\pm$0.16 & foreground star F0IV-V HD 36584 \\\\ \n157 & 05 27 07.5 & -70 04 57 & 5.7 & 14.3 & 1.26e-03$\\pm$3.05e-04 & 3.7$\\pm$ 3.3 & 1.0 & 3.61E-03 &1078 & 1.00$\\pm$0.58 & 1.00$\\pm$1.82 & \\\\ \n158 & 05 27 14.8 & -63 49 07 & 2.9 & 92.5 & 2.61e-03$\\pm$4.09e-04 & 0.3$\\pm$ 1.3 & 0.0 & $<$1.89E-02 & & & & \\\\ \n159 & 05 27 16.6 & -69 39 31 & 4.3 & 26.0 & 1.27e-03$\\pm$2.39e-04 & 0.0$\\pm$ 0.0 & 0.0 & 5.27E-03 & 980 & 1.00$\\pm$0.89 & 1.00$\\pm$3.10 & \\\\ \n160 & 05 27 18.2 & -65 19 10 & 5.0 & 22.6 & 2.40e-03$\\pm$4.22e-04 & 0.0$\\pm$ 0.0 & 0.0 & 7.42E-03 & 108 & 1.00$\\pm$2.67 & -1.00$\\pm$0.50 & \\\\ \n161 & 05 27 19.0 & -65 52 46 & 10.8 & 15.4 & 1.64e-03$\\pm$3.76e-04 & 0.0$\\pm$ 0.0 & 0.0 & 9.57E-03 & 186 & 1.00$\\pm$0.36 & 0.29$\\pm$0.19 & \\\\ \n162 & 05 27 21.0 & -68 30 14 & 1.9 & 134.5 & 3.15e-03$\\pm$3.92e-04 & 0.8$\\pm$ 1.3 & 0.1 & 5.19E-02 & 672 & & -1.00$\\pm$0.58 & \\\\ \n163 & 05 27 21.1 & -63 52 29 & 3.5 & 53.2 & 2.26e-03$\\pm$3.99e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n164 & 05 27 25.4 & -65 29 42 & 6.3 & 10.9 & 3.67e-03$\\pm$1.46e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$5.11E-03 & & & & \\\\ \n165 & 05 27 45.6 & -70 18 08 & 2.4 & 68.7 & 2.31e-03$\\pm$3.39e-04 & 1.0$\\pm$ 1.6 & 0.1 & $<$2.43E-02 & & & & \\\\ \n166 & 05 27 45.6 & -69 11 51 & 7.9 & 23.4 & 1.74e-03$\\pm$3.23e-04 & 4.7$\\pm$ 2.5 & 8.7 & 4.37E-02 & 836 & 1.00$\\pm$0.74 & 1.00$\\pm$6.84 & SNR 0528-69.2 \\\\ \n167 & 05 27 49.4 & -69 54 05 & 4.3 & 21.1 & 5.08e-04$\\pm$1.24e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.11E-01 &1039 & -1.00$\\pm$0.01 & & SSS RX J0527.8-6954 \\\\ \n168 & 05 28 04.8 & -65 20 11 & 2.3 & 47.3 & 2.07e-03$\\pm$2.92e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.00E-03 & & & & \\\\ \n169 & 05 28 06.3 & -63 37 50 & 7.9 & 10.8 & 1.44e-03$\\pm$4.55e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n170 & 05 28 11.2 & -65 20 16 & 2.2 & 43.9 & 1.90e-03$\\pm$2.79e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.11E-03 & & & & \\\\ \n171 & 05 28 11.7 & -71 05 38 & 8.1 & 19.0 & 1.39e-03$\\pm$2.79e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & foreground star F3/F5V HD 36877 \\\\ \n172 & 05 28 12.7 & -63 36 27 & 7.0 & 29.9 & 3.08e-03$\\pm$5.75e-04 & 0.0$\\pm$ 0.0 & 0.0 & 3.21E-02 & 17 & & & \\\\ \n173 & 05 28 17.8 & -69 21 34 & 10.3 & 10.8 & 1.31e-03$\\pm$3.50e-04 & 2.7$\\pm$ 4.1 & 0.1 & $<$4.45E-02 & & & & \\\\ \n174 & 05 28 18.3 & -65 33 40 & 2.1 & 36.7 & 1.55e-03$\\pm$2.49e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.73E-03 & & & & \\\\ \n175 & 05 28 25.4 & -67 43 30 & 12.9 & 16.6 & 4.87e-03$\\pm$1.12e-03 & 7.9$\\pm$ 6.6 & 0.9 & $<$4.97E-03 & & & & \\\\ \n176 & 05 28 26.8 & -70 54 02 & 8.3 & 24.1 & 2.81e-03$\\pm$5.26e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$4.58E-03 & & & & foreground star G0V HD 36890 \\\\ \n177 & 05 28 29.6 & -63 50 15 & 8.7 & 12.4 & 1.67e-03$\\pm$4.79e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$7.31E-03 & & & & \\\\ \n178 & 05 28 32.5 & -68 36 13 & 1.5 & 734.8 & 1.18e-02$\\pm$7.34e-04 & 2.2$\\pm$ 1.1 & 12.0 & 5.75E-02 & 687 & 1.00$\\pm$0.19 & 0.01$\\pm$0.05 & foreground star G1V [CSM97] \\\\ \n179 & 05 28 39.0 & -69 21 03 & 5.1 & 16.1 & 1.33e-03$\\pm$3.23e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$6.24E-02 & & & & \\\\ \n180 & 05 28 44.7 & -65 26 56 & 0.2 & 31209.6 & 2.36e+00$\\pm$2.90e-02 & 2.0$\\pm$ 0.4 & 421.5 & 8.07E+00 & 122 & -0.00$\\pm$0.01 & 0.07$\\pm$0.01 & fg star K1III\\& HD 36705 (AB Dor) \\\\ \n181 & 05 28 47.3 & -65 39 57 & 2.7 & 150.0 & 7.81e-03$\\pm$6.05e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.58E-02 & 147 & 1.00$\\pm$0.15 & 0.27$\\pm$0.18 & hard [HP99b] \\\\ \n182 & 05 29 02.7 & -69 40 09 & 6.6 & 11.1 & 7.64e-04$\\pm$2.08e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.16E-03 & & & & \\\\ \n183 & 05 29 04.8 & -65 14 33 & 5.9 & 25.6 & 2.89e-03$\\pm$4.75e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.58E-03 & & & & \\\\ \n184 & 05 29 08.3 & -68 37 36 & 4.0 & 10.3 & 1.73e-03$\\pm$7.85e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.84E-02 & & & & \\\\ \n185 & 05 29 09.6 & -68 42 56 & 3.1 & 47.8 & 2.11e-03$\\pm$3.54e-04 & 0.0$\\pm$ 0.0 & 0.0 & 8.58E-03 & 705 & 1.00$\\pm$0.55 & 1.00$\\pm$0.77 & \\\\ \n186 & 05 29 16.0 & -71 08 43 & 4.2 & 32.8 & 1.15e-03$\\pm$2.05e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n187 & 05 29 22.6 & -65 20 33 & 2.7 & 29.9 & 1.52e-03$\\pm$2.63e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.72E-03 & & & & \\\\ \n188 & 05 29 23.8 & -65 32 37 & 2.3 & 36.5 & 1.53e-03$\\pm$2.49e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$4.81E-03 & & & & \\\\ \n189 & 05 29 24.0 & -68 49 12 & 2.3 & 54.3 & 1.89e-03$\\pm$3.18e-04 & 2.1$\\pm$ 1.9 & 1.2 & 7.17E-03 & 728 & 0.23$\\pm$0.14 & 0.02$\\pm$0.17 & foreground star? [HP99b] \\\\ \n190 & 05 29 24.8 & -65 57 28 & 6.5 & 17.2 & 8.72e-04$\\pm$1.86e-04 & 0.0$\\pm$ 0.0 & 0.0 & 4.37E-03 & 210 & 1.00$\\pm$0.59 & 0.01$\\pm$0.10 & \\\\ \n191 & 05 29 26.0 & -69 52 05 & 3.5 & 13.9 & 7.24e-04$\\pm$2.24e-04 & 0.0$\\pm$ 0.0 & 0.0 & 3.53E-03 &1032 & 1.00$\\pm$0.40 & 1.00$\\pm$0.57 & \\\\ \n192 & 05 29 26.6 & -69 46 58 & 3.3 & 34.3 & 2.85e-03$\\pm$6.69e-04 & 0.0$\\pm$ 0.0 & 0.0 & 3.48E-03 &1011 & 1.00$\\pm$0.70 & 1.00$\\pm$0.86 & \\\\ \n193 & 05 29 27.0 & -68 52 05 & 0.6 & 2800.3 & 3.33e-02$\\pm$1.21e-03 & 1.9$\\pm$ 0.8 & 26.9 & 1.44E-01 & 749 & 0.06$\\pm$0.02 & 0.04$\\pm$0.03 & foreground star G5 HD 269620 [CSM97] \\\\ \n194 & 05 29 28.2 & -65 31 40 & 5.7 & 12.3 & 7.89e-03$\\pm$3.84e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.87E-03 & & & & \\\\ \n195 & 05 29 31.8 & -69 12 18 & 8.4 & 11.1 & 7.33e-04$\\pm$2.20e-04 & 1.9$\\pm$ 2.9 & 0.1 & $<$1.32E-02 & & & & \\\\ \n196 & 05 29 32.0 & -65 35 27 & 8.5 & 10.4 & 6.41e-03$\\pm$2.10e-03 & 5.6$\\pm$ 4.5 & 2.1 & $<$1.74E-03 & & & & \\\\ \n197 & 05 29 39.2 & -66 08 06 & 20.1 & 12.7 & 1.96e-03$\\pm$4.05e-04 & 17.1$\\pm$10.8 & 2.2 & $<$1.63E-03 & & & & $<$SNR$>$ \\\\ \n198 & 05 29 41.0 & -65 53 23 & 7.2 & 10.4 & 6.01e-04$\\pm$1.60e-04 & 0.0$\\pm$ 0.0 & 0.0 & 2.11E-03 & 189 & 1.00$\\pm$0.80 & -0.22$\\pm$0.15 & \\\\ \n199 & 05 29 41.9 & -65 27 41 & 0.9 & 244.0 & 4.60e-03$\\pm$3.62e-04 & 0.2$\\pm$ 1.2 & 0.0 & 1.01E-02 & 124 & -1.00$\\pm$0.20 & & \\\\ \n200 & 05 29 44.0 & -69 35 42 & 2.0 & 109.1 & 2.55e-03$\\pm$2.87e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$5.69E-03 & & & & \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\scriptsize\n\\caption[]{Continued}\n\\begin{tabular}{rrrrrccrrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ &\n\\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} &\n\\multicolumn{1}{c}{9} & \\multicolumn{1}{c}{10} & 11 & 12 & ~~~13 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & Count rate & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & & & & & & & & \\multicolumn{1}{c}{PSPC} & \\multicolumn{1}{c}{PSPC} & & & \\\\ \n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{[\\ct]} & & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n201 & 05 29 45.0 & -65 16 03 & 6.6 & 18.9 & 2.47e-03$\\pm$4.65e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.15E-03 & & & & \\\\ \n202 & 05 29 48.3 & -65 56 46 & 2.0 & 119.2 & 1.94e-03$\\pm$2.05e-04 & 0.0$\\pm$ 0.0 & 0.0 & 2.43E-01 & 204 & 0.84$\\pm$0.04 & 0.49$\\pm$0.06 & HMXB RXJ0529.8-6556 [HP99a] \\\\ \n203 & 05 30 04.7 & -65 20 08 & 5.4 & 17.3 & 1.81e-03$\\pm$3.65e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.64E-03 & & & & \\\\ \n204 & 05 30 09.3 & -66 06 56 & 6.7 & 10.2 & 6.24e-04$\\pm$1.68e-04 & 0.0$\\pm$ 0.0 & 0.0 & 2.19E-03 & 251 & 1.00$\\pm$0.83 & 0.32$\\pm$0.16 & \\\\ \n205 & 05 30 11.9 & -65 51 27 & 1.9 & 133.0 & 2.09e-03$\\pm$2.10e-04 & 0.0$\\pm$ 0.0 & 0.0 & 6.00E-03 & 183 & 1.00$\\pm$0.21 & 0.62$\\pm$0.07 & hard [HP99b] \\\\ \n206 & 05 30 15.3 & -68 43 17 & 5.6 & 29.9 & 2.68e-03$\\pm$4.72e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.13E-03 & & & & 2E 0530.5-6845 \\\\ \n207 & 05 30 21.9 & -66 15 38 & 4.0 & 32.2 & 1.58e-03$\\pm$2.99e-04 & 0.0$\\pm$ 0.0 & 0.0 & 4.09E-03 & 281 & 1.00$\\pm$0.59 & 0.31$\\pm$0.18 & \\\\ \n208 & 05 30 22.4 & -65 29 32 & 9.1 & 11.0 & 3.36e-03$\\pm$9.94e-04 & 3.1$\\pm$ 5.2 & 0.0 & $<$1.61E-03 & & & & \\\\ \n209 & 05 30 25.9 & -69 08 08 & 5.3 & 24.5 & 1.68e-03$\\pm$3.61e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.65E-02 & & & & \\\\ \n210 & 05 30 40.2 & -66 05 37 & 7.7 & 12.3 & 1.39e-03$\\pm$3.54e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.65E-03 & & & & \\\\ \n211 & 05 30 40.3 & -71 00 32 & 4.1 & 16.3 & 5.73e-04$\\pm$1.38e-04 & 2.7$\\pm$ 2.3 & 1.8 & & & & & \\\\ \n212 & 05 30 49.6 & -67 05 55 & 10.0 & 20.9 & 1.18e-02$\\pm$3.76e-03 & 0.0$\\pm$ 0.0 & 0.0 & 4.77E-02 & 478 & -0.25$\\pm$0.18 & 0.34$\\pm$0.28 & foreground star dMe [SCF94] \\\\ \n213 & 05 31 00.3 & -66 12 37 & 2.7 & 28.4 & 9.63e-04$\\pm$2.16e-04 & 0.0$\\pm$ 0.0 & 0.0 & 6.00E-03 & 267 & 1.00$\\pm$0.44 & 0.30$\\pm$0.13 & \\\\ \n214 & 05 31 02.0 & -66 04 30 & 3.1 & 17.9 & 4.58e-04$\\pm$1.09e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.07E-03 & 237 & 1.00$\\pm$2.58 & & \\\\ \n215 & 05 31 02.9 & -66 06 55 & 2.5 & 76.0 & 1.57e-03$\\pm$1.94e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n216 & 05 31 03.1 & -71 06 10 & 3.5 & 25.4 & 9.92e-04$\\pm$2.34e-04 & 1.4$\\pm$ 1.8 & 0.2 & & & & & foreground star GSC 09166-00859 \\\\ \n217 & 05 31 13.1 & -68 25 48 & 7.7 & 21.8 & 1.09e-03$\\pm$2.78e-04 & 0.0$\\pm$ 0.0 & 0.0 & 5.32E-03 & 661 & & 1.00$\\pm$1.10 & $<$stellar$>$ \\\\ \n218 & 05 31 13.5 & -66 07 09 & 0.8 & 1133.4 & 9.42e-03$\\pm$4.08e-04 &\n0.0$\\pm$ 0.0 & 0.0 & 5.34E-01 & 252 & 0.64$\\pm$0.03 & 0.27$\\pm$0.04 &\nHMXB EXO053109-6609 [HP99a] \\\\ \n219 & 05 31 15.7 & -70 53 46 & 3.7 & 61.1 & 1.69e-03$\\pm$2.32e-04 & 1.8$\\pm$ 2.3 & 0.2 & 2.42E-03 &1210 & 1.00$\\pm$0.43 & 1.00$\\pm$1.22 & \\\\ \n220 & 05 31 31.8 & -71 29 46 & 3.5 & 46.4 & 1.19e-02$\\pm$3.54e-03 &\n0.0$\\pm$ 0.0 & 0.0 & & & & & AGN RX J0531.5-7130, z=0.2214 [SCF94] \\\\ \n221 & 05 31 38.1 & -68 47 48 & 3.4 & 22.4 & 1.48e-03$\\pm$3.01e-04 & 3.8$\\pm$ 2.4 & 6.5 & $<$1.02E-02 & & & & \\\\ \n222 & 05 31 54.4 & -66 02 21 & 3.8 & 11.8 & 3.50e-04$\\pm$9.86e-05 & 1.1$\\pm$ 2.3 & 0.0 & 2.90E-03 & 229 & 1.00$\\pm$0.27 & 1.00$\\pm$0.82 & \\\\ \n223 & 05 31 56.7 & -70 59 59 & 3.4 & 71.6 & 4.76e-03$\\pm$3.79e-04 & 8.2$\\pm$ 2.5 & 110.9 & 8.73E-02 &1222 & 1.00$\\pm$0.09 & -0.26$\\pm$0.04 & SNR LHA 120-N 206 \\\\ \n224 & 05 31 59.9 & -69 19 51 & 3.5 & 46.4 & 2.81e-03$\\pm$5.53e-04 & 2.4$\\pm$ 1.9 & 2.3 & 1.33E-02 & 876 & 1.00$\\pm$0.21 & 0.02$\\pm$0.09 & AGN RX J0532.0-6920, z=0.149 [SCF94] \\\\ \n225 & 05 32 11.9 & -70 04 54 & 7.6 & 25.2 & 1.02e-03$\\pm$2.34e-04 & 0.0$\\pm$ 2.0 & 0.0 & $<$4.61E-03 & & & & \\\\ \n226 & 05 32 12.8 & -69 31 37 & 3.1 & 51.2 & 2.02e-03$\\pm$3.80e-04 & 1.5$\\pm$ 1.4 & 0.9 & $<$4.88E-03 & & & & \\\\ \n227 & 05 32 13.4 & -69 29 53 & 4.1 & 10.8 & 4.50e-04$\\pm$1.62e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.32E-02 & & & & \\\\ \n228 & 05 32 14.0 & -71 10 10 & 3.7 & 110.3 & 2.95e-03$\\pm$3.07e-04 & 1.2$\\pm$ 2.6 & 0.0 & & & & & \\\\ \n229 & 05 32 15.6 & -71 04 26 & 4.8 & 14.1 & 8.18e-04$\\pm$2.30e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & $<$stellar$>$ \\\\ \n230 & 05 32 18.5 & -71 07 43 & 2.9 & 302.5 & 4.69e-03$\\pm$3.49e-04 & 0.0$\\pm$ 0.0 & 0.0 & 9.43E-03 &1238 & 1.00$\\pm$0.35 & 1.00$\\pm$0.98 & $<$XB$>$ or $<$AGN$>$ \\\\ \n231 & 05 32 27.3 & -67 31 10 & 8.5 & 106.1 & 1.80e-02$\\pm$1.99e-03 & 9.1$\\pm$ 4.8 & 9.8 & 6.67E-02 & 540 & 1.00$\\pm$0.49 & -0.45$\\pm$0.09 & SNR? 0532-67.5 [C97] \\\\ \n232 & 05 32 27.5 & -69 00 15 & 4.1 & 78.4 & 4.02e-03$\\pm$5.22e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.80E-02 & & & & \\\\ \n233 & 05 32 33.1 & -65 51 43 & 1.4 & 327.0 & 3.99e-03$\\pm$2.80e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.11E-02 & 184 & 1.00$\\pm$0.10 & 0.43$\\pm$0.05 & HMXB RX J0532.5-6551 (Sk -65 66) \\\\ \n234 & 05 32 34.4 & -66 07 31 & 8.6 & 10.4 & 7.70e-04$\\pm$1.98e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$8.31E-04 & & & & \\\\ \n235 & 05 32 35.7 & -65 54 47 & 5.6 & 10.7 & 5.00e-04$\\pm$1.35e-04 & 2.7$\\pm$ 3.2 & 0.3 & $<$4.27E-03 & & & & \\\\ \n236 & 05 32 37.1 & -65 55 57 & 5.0 & 12.6 & 4.57e-04$\\pm$1.21e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.64E-03 & & & & \\\\ \n237 & 05 32 42.7 & -71 48 51 & 5.9 & 13.0 & 2.55e-03$\\pm$8.38e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n238 & 05 32 42.8 & -69 26 18 & 3.9 & 29.3 & 1.35e-03$\\pm$2.82e-04 & 2.5$\\pm$ 2.1 & 1.1 & 1.84E-02 & 914 & 1.00$\\pm$0.31 & 0.29$\\pm$0.19 & LMXB? RX J0532.7-6926 [HP99a] \\\\ \n239 & 05 32 49.5 & -66 22 13 & 0.2 & 30957.4 & 2.82e+00$\\pm$4.22e-02 & 1.6$\\pm$ 0.4 & 182.5 & 4.30E-01 & 316 & 0.51$\\pm$0.01 & 0.12$\\pm$0.02 & HMXB LMC X-4, HD 269743 O8III \\\\ \n240 & 05 32 50.2 & -69 40 21 & 7.3 & 12.6 & 3.56e-03$\\pm$1.28e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$6.19E-03 & & & & \\\\ \n241 & 05 32 51.4 & -70 06 31 & 7.4 & 36.9 & 1.34e-03$\\pm$2.64e-04 & 1.3$\\pm$ 1.8 & 0.1 & 7.64E-03 &1082 & 1.00$\\pm$1.38 & 1.00$\\pm$2.45 & \\\\ \n242 & 05 32 52.0 & -66 28 39 & 2.8 & 17.6 & 5.91e-04$\\pm$1.50e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.49E-03 & & & & \\\\ \n243 & 05 33 02.2 & -66 11 32 & 7.3 & 10.5 & 3.40e-03$\\pm$1.25e-03 & 3.9$\\pm$ 4.0 & 0.6 & $<$1.59E-03 & & & & \\\\ \n244 & 05 33 05.3 & -66 12 41 & 3.5 & 18.9 & 8.75e-04$\\pm$2.20e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.41E-03 & & & & \\\\ \n245 & 05 33 34.8 & -68 54 54 & 2.0 & 141.5 & 4.94e-03$\\pm$5.22e-04 & 2.2$\\pm$ 2.0 & 0.7 & 4.80E-02 & 759 & 0.24$\\pm$0.22 & -1.00$\\pm$1.21 & \\\\ \n246 & 05 33 36.9 & -67 32 43 & 11.6 & 15.2 & 4.15e-03$\\pm$1.07e-03 & 6.3$\\pm$ 5.9 & 0.5 & $<$2.45E-02 & & & & \\\\ \n247 & 05 33 39.5 & -69 09 29 & 4.8 & 21.4 & 4.92e-04$\\pm$8.61e-05 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.17E-03 & & & & \\\\ \n248 & 05 33 55.7 & -69 54 47 & 8.1 & 102.9 & 4.42e-02$\\pm$3.39e-03 & 15.7$\\pm$ 4.7 & 153.6 & 2.81E-01 &1043 & 1.00$\\pm$0.11 & -0.20$\\pm$0.05 & SNR 0534-69.9 \\\\ \n249 & 05 33 59.7 & -71 45 26 & 3.5 & 139.0 & 1.53e-02$\\pm$1.86e-03 & 2.0$\\pm$ 2.2 & 0.4 & & & & & \\\\ \n250 & 05 34 08.2 & -70 19 00 & 8.2 & 62.9 & 5.27e-03$\\pm$7.29e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.31E-02 &1124 & 1.00$\\pm$0.19 & 0.46$\\pm$0.11 & hard [HP99b] \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\scriptsize\n\\caption[]{Continued}\n\\begin{tabular}{rrrrrccrrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ &\n\\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} &\n\\multicolumn{1}{c}{9} & \\multicolumn{1}{c}{10} & 11 & 12 & ~~~13 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & Count rate & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & & & & & & & & \\multicolumn{1}{c}{PSPC} & \\multicolumn{1}{c}{PSPC} & & & \\\\ \n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{[\\ct]} & & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n251 & 05 34 15.8 & -69 14 17 & 2.9 & 29.4 & 1.23e-03$\\pm$2.52e-04 & 0.8$\\pm$ 2.1 & 0.0 & $<$3.34E-03 & & & & \\\\ \n252 & 05 34 16.3 & -70 33 43 & 10.6 & 10.5 & 3.99e-03$\\pm$1.08e-03 & 7.4$\\pm$ 4.5 & 4.8 & 6.49E-02 &1160 & 0.82$\\pm$0.03 & 0.08$\\pm$0.04 & SNR DEM L 238 \\\\ \n253 & 05 34 26.4 & -69 28 56 & 6.1 & 10.4 & 2.25e-03$\\pm$8.76e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.46E-03 & & & & \\\\ \n254 & 05 34 27.7 & -69 25 40 & 5.9 & 11.0 & 2.65e-03$\\pm$9.41e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$8.05E-04 & & & & $<$stellar$>$ \\\\ \n255 & 05 34 42.3 & -69 21 14 & 3.1 & 12.3 & 1.75e-04$\\pm$4.24e-05 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.40E-03 & & & & \\\\ \n256 & 05 34 44.0 & -67 37 45 & 9.6 & 10.5 & 6.56e-03$\\pm$3.08e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n257 & 05 34 44.6 & -67 38 56 & 8.5 & 41.1 & 6.03e-03$\\pm$1.13e-03 & 0.0$\\pm$ 0.0 & 0.0 & 6.18E-02 & 561 & 1.00$\\pm$0.15 & -0.04$\\pm$0.15 & AGN RX J0534.8-6739, z=0.072 [CSM97] \\\\ \n258 & 05 35 03.3 & -66 10 40 & 10.3 & 11.5 & 1.06e-02$\\pm$3.97e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$4.07E-02 & & & & \\\\ \n259 & 05 35 03.5 & -69 21 03 & 2.9 & 12.9 & 1.57e-04$\\pm$3.80e-05 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.33E-03 & & & & \\\\ \n260 & 05 35 07.9 & -69 18 48 & 7.6 & 12.4 & 1.26e-03$\\pm$4.43e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n261 & 05 35 11.4 & -69 57 05 & 7.9 & 13.6 & 1.07e-03$\\pm$3.25e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.47E-02 & & & & \\\\ \n262 & 05 35 22.8 & -66 12 55 & 8.3 & 48.9 & 1.00e-02$\\pm$1.88e-03 & 0.0$\\pm$ 0.0 & 0.0 & 3.35E-02 & 268 & -0.24$\\pm$0.13 & -1.00$\\pm$1.65 & foreground star dM4e [CCH84] \\\\ \n263 & 05 35 26.9 & -68 32 38 & 7.5 & 13.1 & 4.01e-04$\\pm$1.18e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.36E-02 & 676 & & & \\\\ \n264 & 05 35 28.7 & -69 16 08 & 0.7 & 586.7 & 2.05e-03$\\pm$9.58e-05 & 3.1$\\pm$ 1.0 & 86.8 & 4.38E-03 & 854 & 1.00$\\pm$0.27 & 0.21$\\pm$0.20 & SN 1987A \\\\ \n265 & 05 35 33.7 & -69 44 56 & 8.2 & 11.3 & 2.49e-03$\\pm$9.84e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$5.65E-02 & & & & \\\\ \n266 & 05 35 34.2 & -69 08 25 & 4.7 & 11.6 & 7.04e-04$\\pm$2.10e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n267 & 05 35 41.2 & -69 53 08 & 7.6 & 20.2 & 1.25e-03$\\pm$3.34e-04 & 1.9$\\pm$ 1.9 & 0.8 & $<$1.84E-02 & & & & \\\\ \n268 & 05 35 45.7 & -69 18 00 & 1.5 & 63.8 & 1.36e-03$\\pm$9.48e-05 & 5.8$\\pm$ 1.6 & 119.1 & 3.28E-02 & 866 & 1.00$\\pm$0.09 & -0.14$\\pm$0.05 & SNR Honeycomb Nebula \\\\ \n269 & 05 35 46.5 & -66 02 23 & 7.0 & 3681.1 & 3.11e-01$\\pm$6.77e-03 & 7.2$\\pm$ 1.1 &5993.1 & 7.39E+00 & 226 & 0.94$\\pm$0.00 & -0.01$\\pm$0.01 & SNR LHA 120-N 63A \\\\ \n270 & 05 35 48.9 & -69 09 31 & 2.8 & 47.9 & 9.83e-04$\\pm$9.34e-05 & 6.8$\\pm$ 2.4 & 37.3 & & & & & SNR 0536-69.2, 30 DOR C: knot \\\\ \n271 & 05 35 53.1 & -69 34 58 & 3.0 & 16.0 & 7.53e-04$\\pm$2.25e-04 & 0.7$\\pm$ 1.9 & 0.0 & $<$4.17E-03 & & & & \\\\ \n272 & 05 36 00.7 & -70 41 28 & 7.6 & 27.0 & 3.02e-03$\\pm$8.02e-04 & 1.9$\\pm$ 2.0 & 0.7 & 1.03E-02 &1181 & 1.00$\\pm$0.14 & 0.39$\\pm$0.10 & hard [HP99b] \\\\ \n273 & 05 36 01.4 & -70 17 36 & 8.2 & 10.9 & 8.29e-04$\\pm$2.79e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.44E-02 & & & & \\\\ \n274 & 05 36 06.6 & -70 38 57 & 9.2 & 11.0 & 3.46e-03$\\pm$1.06e-03 & 5.1$\\pm$ 3.5 & 4.0 & 6.02E-02 &1173 & 1.00$\\pm$0.02 & -0.17$\\pm$0.04 & SNR DEM L 249 \\\\ \n275 & 05 36 17.2 & -69 03 43 & 9.1 & 10.2 & 2.32e-03$\\pm$7.22e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.05E-03 & & & & \\\\ \n276 & 05 36 17.3 & -69 13 04 & 2.0 & 55.0 & 1.14e-03$\\pm$9.25e-05 & 6.1$\\pm$ 1.9 & 72.0 & 2.47E-02 & 840 & 0.89$\\pm$ * & 0.11$\\pm$ * & SNR 0536-69.2, 30 DOR C: knot \\\\ \n277 & 05 36 19.0 & -69 09 30 & 3.2 & 64.0 & 1.37e-03$\\pm$1.15e-04 & 8.5$\\pm$ 2.7 & 43.2 & & & & & SNR 0536-69.2, 30 DOR C: knot \\\\ \n278 & 05 36 32.7 & -65 56 40 & 8.3 & 12.2 & 2.74e-03$\\pm$9.88e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.17E-02 & & & & \\\\ \n279 & 05 36 57.1 & -69 00 27 & 6.9 & 12.8 & 1.26e-03$\\pm$3.20e-04 & 4.4$\\pm$ 3.9 & 1.0 & & & & & \\\\ \n280 & 05 36 57.8 & -69 13 26 & 2.2 & 59.4 & 5.51e-04$\\pm$6.58e-05 & 0.6$\\pm$ 1.9 & 0.0 & & & & & \\\\ \n281 & 05 37 00.1 & -69 25 37 & 8.3 & 10.8 & 2.28e-03$\\pm$6.65e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n282 & 05 37 07.2 & -69 03 09 & 6.4 & 11.9 & 7.18e-04$\\pm$1.47e-04 & 7.5$\\pm$ 3.4 & 4.9 & & & & & knot in 30 Dor \\\\ \n283 & 05 37 07.5 & -69 18 54 & 10.4 & 13.0 & 9.60e-04$\\pm$2.05e-04 & 8.4$\\pm$ 6.2 & 1.5 & & & & & knot \\\\ \n284 & 05 37 28.6 & -69 23 18 & 13.4 & 11.5 & 4.07e-03$\\pm$1.05e-03 & 9.8$\\pm$ 7.6 & 1.5 & & & & & $<$SNR$>$ \\\\ \n285 & 05 37 31.8 & -69 28 26 & 6.1 & 10.5 & 2.58e-03$\\pm$9.41e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n286 & 05 37 33.6 & -69 18 43 & 6.8 & 18.2 & 4.89e-04$\\pm$9.24e-05 & 3.5$\\pm$ 4.8 & 0.2 & & & & & \\\\ \n287 & 05 37 35.9 & -68 25 57 & 7.4 & 115.8 & 3.15e-03$\\pm$3.26e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & $<$stellar$>$ \\\\ \n288 & 05 37 36.2 & -69 16 42 & 9.7 & 16.3 & 8.36e-04$\\pm$1.40e-04 & 11.5$\\pm$ 5.5 & 5.1 & & & & & $<$SNR$>$ \\\\ \n289 & 05 37 46.9 & -69 10 18 & 0.4 & 8036.1 & 4.07e-02$\\pm$6.36e-04 & 5.1$\\pm$ 0.7 &3391.0 & 2.34E-01 & 826 & 1.00$\\pm$0.02 & 0.47$\\pm$0.02 & SNR 0538-69.1, LHA 120-N 157B\\\\ \n290 & 05 37 50.3 & -69 04 23 & 2.4 & 21.2 & 3.83e-04$\\pm$8.80e-05 & 0.0$\\pm$ 0.0 & 0.0 & & & & & knot in 30 Dor \\\\ \n291 & 05 38 09.8 & -68 56 56 & 2.5 & 109.7 & 1.85e-03$\\pm$1.79e-04 & 1.5$\\pm$ 2.5 & 0.1 & & & & & \\\\ \n292 & 05 38 14.6 & -64 11 50 & 10.1 & 11.1 & 8.86e-03$\\pm$4.22e-03 & 1.2$\\pm$ 3.5 & 0.0 & $<$1.03E-03 & & & & \\\\ \n293 & 05 38 15.9 & -69 23 30 & 0.9 & 2548.9 & 4.30e-02$\\pm$1.46e-03 & 0.6$\\pm$ 1.1 & 0.0 & 1.72E-01 & 902 & 0.02$\\pm$0.03 & -0.00$\\pm$0.04 & foreground star dMe CAL 69 [CSM97] \\\\ \n294 & 05 38 21.3 & -68 50 34 & 2.6 & 33.2 & 1.37e-03$\\pm$2.89e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$8.35E-03 & & & & foreground star G5V HD 269916 \\\\ \n295 & 05 38 28.8 & -69 08 33 & 15.8 & 18.1 & 5.14e-03$\\pm$9.66e-04 & 16.1$\\pm$10.1 & 2.4 & & & & & knot in 30 Dor \\\\ \n296 & 05 38 34.4 & -68 53 07 & 0.4 & 5091.1 & 5.56e-02$\\pm$1.64e-03 & 0.0$\\pm$ 0.0 & 0.0 & 2.98E-01 & 752 & -0.04$\\pm$0.02 & 0.05$\\pm$0.02 & foreground star G2V, RS CVn? [CSM97] \\\\ \n297 & 05 38 38.4 & -68 28 09 & 7.9 & 13.2 & 6.62e-04$\\pm$2.00e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.75E-03 & & & & \\\\ \n298 & 05 38 41.0 & -69 55 54 & 11.7 & 11.7 & 9.82e-03$\\pm$3.41e-03 & 2.8$\\pm$ 5.8 & 0.0 & $<$3.56E-03 & & & & \\\\ \n299 & 05 38 41.4 & -69 05 13 & 0.7 & 505.0 & 3.46e-03$\\pm$2.23e-04 & 1.2$\\pm$ 1.0 & 1.5 & & & & & knot in 30 Dor \\\\ \n300 & 05 38 42.4 & -68 52 41 & 1.5 & 103.8 & 2.75e-03$\\pm$3.86e-04 & 0.8$\\pm$ 1.3 & 0.1 & & & & & $<$stellar$>$ \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\scriptsize\n\\caption[]{Continued}\n\\begin{tabular}{rrrrrccrrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ &\n\\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} &\n\\multicolumn{1}{c}{9} & \\multicolumn{1}{c}{10} & 11 & 12 & ~~~13 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & Count rate & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & & & & & & & & \\multicolumn{1}{c}{PSPC} & \\multicolumn{1}{c}{PSPC} & & & \\\\ \n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{[\\ct]} & & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n301 & 05 38 43.7 & -69 06 05 & 0.7 & 1523.9 & 8.47e-03$\\pm$3.04e-04 & 4.0$\\pm$ 1.1 & 165.4 & & & & & cluster of stars HD 38268; RMC 136 \\\\ \n302 & 05 38 43.8 & -69 10 12 & 2.1 & 41.7 & 2.44e-03$\\pm$1.98e-04 & 7.1$\\pm$ 2.0 & 107.4 & & & & & knot in 30 Dor \\\\ \n303 & 05 38 46.7 & -69 02 25 & 2.9 & 33.4 & 2.25e-03$\\pm$2.06e-04 & 8.1$\\pm$ 2.6 & 71.9 & & & & & knot in 30 Dor \\\\ \n304 & 05 38 49.8 & -68 35 04 & 7.4 & 39.1 & 1.50e-03$\\pm$2.80e-04 & 1.6$\\pm$ 2.0 & 0.2 & & & & & \\\\ \n305 & 05 38 50.0 & -69 44 27 & 4.1 & 36.0 & 1.46e-03$\\pm$2.48e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$5.74E-03 & & & & foreground star F2V HD 38329 \\\\ \n306 & 05 38 56.3 & -64 05 03 & 0.2 & 34020.7 & 7.37e+00$\\pm$6.88e-02 & 1.9$\\pm$ 0.4 & 367.4 & 2.04E+01 & 41 & 0.84$\\pm$0.00 & 0.28$\\pm$0.01 & HMXB LMC X-3 \\\\ \n307 & 05 39 27.9 & -69 33 12 & 12.0 & 15.7 & 2.49e-03$\\pm$4.68e-04 & 12.8$\\pm$ 6.5 & 4.0 & & & & & $<$SNR$>$ \\\\ \n308 & 05 39 29.2 & -69 57 09 & 4.4 & 20.3 & 8.84e-04$\\pm$2.24e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.47E-03 & & & & foreground star HD 269934 \\\\ \n309 & 05 39 31.3 & -69 05 12 & 4.7 & 31.4 & 2.05e-03$\\pm$2.25e-04 & 10.3$\\pm$ 3.5 & 31.7 & & & & & knot in 30 Dor \\\\ \n310 & 05 39 36.6 & -70 01 58 & 9.3 & 27.1 & 4.28e-03$\\pm$6.40e-04 & 10.1$\\pm$ 4.4 & 14.4 & 2.36E-02 &1063 & 1.00$\\pm$0.17 & -0.17$\\pm$0.10 & SNR? [HP99b] \\\\ \n311 & 05 39 38.7 & -69 44 32 & 3.0 & 32679.3 & 3.77e+00$\\pm$4.68e-02 & 0.0$\\pm$ 0.0 & 0.0 & 1.27E+01 &1001 & 0.99$\\pm$0.00 & 0.74$\\pm$0.00 & HMXB LMC X-1, O8III \\\\ \n312 & 05 39 50.1 & -69 08 03 & 7.4 & 18.9 & 1.44e-03$\\pm$2.13e-04 & 10.6$\\pm$ 4.8 & 13.3 & & & & & knot in 30 Dor \\\\ \n313 & 05 39 59.9 & -68 28 42 & 7.1 & 315.3 & 6.31e-03$\\pm$5.22e-04 & 2.7$\\pm$ 1.2 & 26.9 & 1.31E-02 & 668 & 1.00$\\pm$0.62 & 1.00$\\pm$1.88 & $<$stellar$>$ \\\\ \n314 & 05 40 03.2 & -68 20 36 & 8.4 & 25.3 & 1.65e-03$\\pm$3.35e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n315 & 05 40 04.5 & -69 43 58 & 3.6 & 41.3 & 3.36e-03$\\pm$3.52e-04 & 5.8$\\pm$ 2.0 & 61.8 & & & & & SNR? [CKS97] \\\\ \n316 & 05 40 06.6 & -70 14 21 & 7.4 & 24.1 & 1.04e-03$\\pm$2.58e-04 & 1.1$\\pm$ 1.6 & 0.1 & $<$2.12E-02 & & & & \\\\ \n317 & 05 40 07.8 & -69 17 11 & 2.2 & 56.6 & 2.25e-03$\\pm$3.87e-04 & 2.5$\\pm$ 1.7 & 3.1 & & & & & \\\\ \n318 & 05 40 10.9 & -69 19 52 & 0.7 & 17883.4 & 1.95e-01$\\pm$3.32e-03 & 2.7$\\pm$ 0.5 & 781.3 & 8.40E-01 & 877 & 0.98$\\pm$0.00 & 0.58$\\pm$0.01 & SNR LHA 120-N 158A, PSR B0540-69 \\\\ \n319 & 05 40 23.7 & -68 56 52 & 3.7 & 15.9 & 9.73e-04$\\pm$2.65e-04 & 0.5$\\pm$ 2.2 & 0.0 & & & & & \\\\ \n320 & 05 40 27.7 & -69 37 17 & 4.9 & 11.6 & 5.29e-04$\\pm$1.53e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n321 & 05 40 30.1 & -64 20 42 & 8.9 & 12.4 & 1.46e-03$\\pm$4.49e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$7.47E-03 & & & & \\\\ \n322 & 05 40 30.3 & -69 46 58 & 5.1 & 11.3 & 3.85e-03$\\pm$1.60e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n323 & 05 40 31.5 & -68 58 17 & 9.8 & 10.1 & 1.36e-03$\\pm$3.67e-04 & 2.7$\\pm$ 5.4 & 0.0 & & & & & \\\\ \n324 & 05 40 35.0 & -68 32 28 & 9.0 & 11.7 & 8.02e-04$\\pm$2.31e-04 & 3.3$\\pm$ 2.8 & 0.8 & $<$8.69E-03 & & & & \\\\ \n325 & 05 40 37.2 & -70 12 01 & 7.1 & 88.6 & 2.45e-03$\\pm$3.75e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$6.85E-03 & & & & \\\\ \n326 & 05 41 13.1 & -64 11 51 & 7.4 & 48.1 & 2.81e-03$\\pm$5.45e-04 & 0.0$\\pm$ 0.0 & 0.0 & 2.05E-02 & 50 & 1.00$\\pm$0.70 & 1.00$\\pm$0.43 & \\\\ \n327 & 05 41 16.0 & -69 41 36 & 3.8 & 20.8 & 5.97e-04$\\pm$1.48e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n328 & 05 41 22.2 & -69 36 29 & 6.6 & 11.1 & 7.28e-04$\\pm$2.03e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.34E-02 & & & & $<$HMXB$>$ LMC B2 supergiant SK -69 271 \\\\ \n329 & 05 41 27.6 & -69 44 53 & 4.2 & 12.5 & 4.44e-04$\\pm$1.34e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n330 & 05 41 29.9 & -69 04 45 & 8.9 & 14.9 & 1.14e-03$\\pm$2.76e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.59E-02 & & & & CAL 80 \\\\ \n331 & 05 41 35.4 & -68 26 17 & 8.6 & 10.5 & 1.96e-03$\\pm$5.94e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n332 & 05 41 37.1 & -68 32 32 & 4.5 & 33.6 & 2.34e-03$\\pm$4.27e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.23E-02 & & & & $<$HMXB$>$ LMC O star BI 267 \\\\ \n333 & 05 41 39.3 & -69 02 36 & 8.1 & 11.1 & 8.19e-04$\\pm$2.39e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.40E-01 & & & & \\\\ \n334 & 05 41 44.5 & -69 42 09 & 5.3 & 10.7 & 5.48e-04$\\pm$1.63e-04 & 1.9$\\pm$ 2.7 & 0.1 & $<$1.55E-02 & & & & \\\\ \n335 & 05 41 44.6 & -69 21 53 & 4.4 & 15.1 & 1.06e-03$\\pm$3.05e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$7.96E-03 & & & & \\\\ \n336 & 05 41 52.5 & -69 54 00 & 8.5 & 11.8 & 6.88e-04$\\pm$1.95e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.38E-03 & & & & \\\\ \n337 & 05 41 59.0 & -68 15 42 & 7.5 & 14.4 & 2.47e-03$\\pm$6.50e-04 & 2.1$\\pm$ 4.0 & 0.0 & & & & & \\\\ \n338 & 05 42 01.2 & -69 24 44 & 11.9 & 11.5 & 2.43e-03$\\pm$5.91e-04 & 8.3$\\pm$ 5.6 & 2.8 & $<$7.76E-03 & & & & $<$SNR$>$ \\\\ \n339 & 05 42 04.2 & -68 21 08 & 7.1 & 10.9 & 1.71e-03$\\pm$5.17e-04 & 4.2$\\pm$ 4.2 & 0.7 & & & & & \\\\ \n340 & 05 42 36.9 & -68 32 03 & 3.2 & 23.5 & 1.17e-03$\\pm$2.75e-04 & 2.0$\\pm$ 2.4 & 0.5 & & & & & \\\\ \n341 & 05 42 39.2 & -68 58 57 & 8.7 & 10.3 & 9.13e-04$\\pm$2.78e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.19E-03 & & & & \\\\ \n342 & 05 42 39.8 & -68 50 49 & 6.7 & 32.9 & 1.04e-03$\\pm$2.38e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$3.90E-03 & & & & \\\\ \n343 & 05 42 45.4 & -69 53 59 & 7.7 & 13.6 & 5.10e-04$\\pm$1.49e-04 & 0.6$\\pm$ 2.2 & 0.0 & $<$2.32E-03 & & & & \\\\ \n344 & 05 42 55.8 & -68 41 42 & 13.3 & 10.5 & 6.72e-03$\\pm$2.78e-03 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.40E-03 & & & & \\\\ \n345 & 05 43 04.3 & -69 26 32 & 8.1 & 16.4 & 1.20e-03$\\pm$3.31e-04 & 2.6$\\pm$ 2.8 & 0.4 & $<$6.08E-03 & & & & \\\\ \n346 & 05 43 15.1 & -69 49 52 & 8.0 & 10.6 & 1.78e-03$\\pm$7.63e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.51E-02 & & & & \\\\ \n347 & 05 43 22.2 & -68 56 39 & 6.4 & 141.3 & 2.51e-03$\\pm$3.01e-04 & 1.2$\\pm$ 1.1 & 0.8 & $<$1.67E-02 & & & & $<$stellar$>$ \\\\ \n348 & 05 43 34.2 & -68 22 21 & 1.1 & 17776.1 & 2.15e-01$\\pm$3.26e-03 & 2.2$\\pm$ 0.7 & 46.1 & 8.66E-01 & 654 & -0.87$\\pm$0.02 & -1.00$\\pm$0.51 & SSS CAL 83 [SCF94] \\\\ \n349 & 05 43 34.5 & -64 22 55 & 7.2 & 624.1 & 3.06e-02$\\pm$1.79e-03 & 0.0$\\pm$ 0.0 & 0.0 & 6.53E-02 & 61 & -0.00$\\pm$0.13 & 0.05$\\pm$0.19 & foreground star? [HP99b] \\\\ \n350 & 05 43 39.6 & -69 17 18 & 8.7 & 11.0 & 8.77e-04$\\pm$2.51e-04 & 4.1$\\pm$ 3.6 & 0.5 & $<$2.29E-03 & & & & \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\scriptsize\n\\caption[]{Continued}\n\\begin{tabular}{rrrrrccrrrccl}\n\\hline\\noalign{\\smallskip}\n1~ & \\multicolumn{1}{c}{2} & \\multicolumn{1}{c}{3} & 4~ &\n\\multicolumn{1}{c}{5} & 6 & 7 & \\multicolumn{1}{c}{8} &\n\\multicolumn{1}{c}{9} & \\multicolumn{1}{c}{10} & 11 & 12 & ~~~13 \\\\\n\\hline\\noalign{\\smallskip} \nNo & \\multicolumn{1}{c}{RA} & \\multicolumn{1}{c}{Dec} & \\perr & \\exil\n& Count rate & \\ext & \\extl & Count rate & \\multicolumn{1}{c}{No} & HR1 & HR2 & Remarks \\\\\n & & & & & & & & \\multicolumn{1}{c}{PSPC} & \\multicolumn{1}{c}{PSPC} & & & \\\\ \n & \\multicolumn{2}{c}{(J2000.0)} & [\\arcsec] & & [\\ct] & [\\arcsec] &\n& \\multicolumn{1}{c}{[\\ct]} & & & & \\\\ \n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n351 & 05 43 58.7 & -65 39 55 & 4.4 & 16.4 & 1.88e-03$\\pm$6.11e-04 & 0.0$\\pm$ 0.0 & 0.0 & 6.86E-03 & 148 & 1.00$\\pm$0.87 & 1.00$\\pm$0.66 & \\\\ \n352 & 05 44 06.0 & -71 00 51 & 7.8 & 12.3 & 1.34e-03$\\pm$5.17e-04 & 0.0$\\pm$ 0.0 & 0.0 & 4.41E-02 &1225 & 1.00$\\pm$0.03 & 0.65$\\pm$0.03 & HMXB RX J0544.1-7100 [HP99b] \\\\ \n353 & 05 44 10.5 & -69 46 49 & 7.9 & 11.3 & 6.22e-04$\\pm$2.01e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$2.21E-02 & & & & \\\\ \n354 & 05 44 29.3 & -71 11 55 & 10.5 & 11.8 & 1.73e-03$\\pm$5.03e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.51E-03 & & & & \\\\ \n355 & 05 44 34.8 & -69 46 25 & 8.8 & 10.8 & 7.12e-04$\\pm$2.01e-04 & 3.0$\\pm$ 3.1 & 0.5 & $<$1.08E-02 & & & & \\\\ \n356 & 05 44 46.4 & -65 44 07 & 3.9 & 15.3 & 1.43e-03$\\pm$5.16e-04 & 0.0$\\pm$ 0.0 & 0.0 & 6.57E-03 & 157 & -0.20$\\pm$0.22 & -1.00$\\pm$0.63 & foreground star A7V HD 39014 \\\\ \n357 & 05 45 00.4 & -69 54 15 & 9.1 & 12.9 & 4.70e-03$\\pm$1.90e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n358 & 05 45 08.7 & -68 19 37 & 7.2 & 10.7 & 6.64e-03$\\pm$2.94e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n359 & 05 45 43.4 & -68 25 26 & 9.3 & 13.3 & 1.15e-03$\\pm$3.21e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n360 & 05 45 52.7 & -69 54 45 & 16.3 & 10.5 & 2.01e-03$\\pm$5.51e-04 & 0.0$\\pm$ 8.0 & 0.0 & $<$3.10E-03 & & & & \\\\ \n361 & 05 45 56.2 & -69 43 55 & 7.1 & 188.7 & 3.07e-03$\\pm$3.11e-04 & 1.0$\\pm$ 1.4 & 0.1 & & & & & \\\\ \n362 & 05 46 15.3 & -68 35 23 & 7.3 & 90.4 & 2.94e-03$\\pm$4.31e-04 & 0.0$\\pm$ 0.0 & 0.0 & 1.24E-02 & 686 & & & RX J0546.3-6836 (CAL 86) \\\\ \n363 & 05 46 46.9 & -71 08 52 & 7.0 & 3268.5 & 6.23e-02$\\pm$2.17e-03 & 3.0$\\pm$ 0.8 & 242.1 & 1.24E-01 &1240 & 0.80$\\pm$0.01 & -0.86$\\pm$0.01 & SSS CAL 87 \\\\ \n364 & 05 46 55.7 & -68 51 35 & 7.0 & 1146.0 & 2.02e-02$\\pm$1.00e-03 & 3.6$\\pm$ 1.0 & 171.7 & 1.08E-02 & 747 & 1.00$\\pm$0.21 & 1.00$\\pm$0.60 & $<$XB$>$ or $<$AGN$>$ \\\\ \n365 & 05 46 57.1 & -69 42 40 & 10.7 & 32.2 & 7.62e-03$\\pm$8.64e-04 & 16.8$\\pm$ 6.2 & 29.9 & 4.54E-02 & 993 & 0.95$\\pm$ * & 0.21$\\pm$ * & SNR LHA 120-N 135 (DEM L 316), shell B \\\\ \n366 & 05 47 18.5 & -69 41 28 & 7.4 & 29.7 & 3.41e-03$\\pm$3.51e-04 & 6.7$\\pm$ 2.2 & 85.5 & 5.02E-02 & 987 & 1.00$\\pm$0.10 & 0.22$\\pm$0.07 & SNR LHA 120-N 135 (DEM L 316), shell A \\\\ \n367 & 05 47 19.9 & -68 31 33 & 7.5 & 21.7 & 8.99e-04$\\pm$2.45e-04 & 1.4$\\pm$ 1.8 & 0.2 & & & & & \\\\ \n368 & 05 47 21.7 & -70 26 55 & 4.3 & 10.6 & 2.85e-03$\\pm$1.46e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n369 & 05 47 27.2 & -70 06 27 & 7.7 & 26.1 & 1.42e-03$\\pm$3.30e-04 & 2.1$\\pm$ 2.5 & 0.4 & $<$1.82E-03 & & & & \\\\ \n370 & 05 47 34.7 & -71 55 19 & 12.4 & 10.7 & 3.46e-03$\\pm$1.04e-03 & 2.5$\\pm$ 6.0 & 0.0 & & & & & \\\\ \n371 & 05 47 45.2 & -67 45 05 & 2.6 & 89.0 & 9.63e-03$\\pm$1.75e-03 & 2.1$\\pm$ 1.5 & 3.4 & & & & & AGN RX J0547.8-6745, z=0.3905 [CSM97] \\\\ \n372 & 05 47 47.6 & -70 24 46 & 3.0 & 37.3 & 8.31e-03$\\pm$1.11e-03 & 6.4$\\pm$ 2.5 & 60.3 & 1.52E-01 &1137 & 1.00$\\pm$0.05 & -0.10$\\pm$0.06 & SNR 0548-70.4 \\\\ \n373 & 05 47 58.9 & -68 35 41 & 8.4 & 11.8 & 7.84e-04$\\pm$2.50e-04 & 1.6$\\pm$ 3.0 & 0.0 & & & & & \\\\ \n374 & 05 48 01.3 & -71 56 19 & 10.6 & 11.0 & 2.50e-03$\\pm$7.26e-04 & 4.6$\\pm$ 4.7 & 0.6 & $<$1.69E-03 & & & & \\\\ \n375 & 05 48 19.2 & -70 20 44 & 1.7 & 216.6 & 3.57e-03$\\pm$3.47e-04 & 2.3$\\pm$ 1.3 & 7.5 & 1.63E-02 &1127 & & & foreground star F3/F5IV/V HD 39756 \\\\ \n376 & 05 48 28.8 & -71 12 44 & 8.3 & 17.7 & 1.52e-03$\\pm$4.14e-04 & 0.0$\\pm$ 0.0 & 0.0 & 8.27E-03 &1247 & 1.00$\\pm$0.09 & 0.27$\\pm$0.08 & hard [HP99b] \\\\ \n377 & 05 48 58.9 & -68 54 08 & 8.5 & 23.0 & 1.40e-03$\\pm$3.27e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n378 & 05 49 12.5 & -70 06 56 & 9.7 & 12.8 & 1.75e-03$\\pm$4.63e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.29E-02 & & & & \\\\ \n379 & 05 49 28.9 & -69 47 14 & 9.9 & 24.2 & 1.81e-03$\\pm$3.34e-04 & 0.0$\\pm$ 0.0 & 0.0 & 9.33E-03 &1014 & -1.00$\\pm$0.89 & & foreground star F2V HD 39904 \\\\ \n380 & 05 49 40.5 & -69 44 12 & 13.7 & 14.3 & 1.52e-03$\\pm$3.45e-04 & 5.0$\\pm$ 6.2 & 0.2 & 1.17E-02 & 999 & 1.00$\\pm$0.73 & 0.48$\\pm$0.21 & \\\\ \n381 & 05 49 41.8 & -70 23 14 & 8.4 & 10.2 & 4.75e-03$\\pm$2.04e-03 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n382 & 05 49 46.0 & -69 38 40 & 12.2 & 12.4 & 2.06e-03$\\pm$5.30e-04 & 0.0$\\pm$ 0.0 & 0.0 & 6.39E-03 & 975 & 1.00$\\pm$3.30 & -1.00$\\pm$1.76 & \\\\ \n383 & 05 49 46.5 & -71 49 36 & 7.1 & 570.5 & 9.56e-03$\\pm$5.97e-04 & 3.3$\\pm$ 1.2 & 62.1 & 4.12E-02 &1312 & -0.02$\\pm$0.06 & -0.16$\\pm$0.08 & foreground star dMe [SCC99] \\\\ \n384 & 05 49 53.4 & -68 19 46 & 10.9 & 11.7 & 3.12e-03$\\pm$9.77e-04 & 0.0$\\pm$ 0.0 & 0.0 & & & & & \\\\ \n385 & 05 50 31.5 & -71 09 57 & 8.6 & 29.1 & 3.59e-03$\\pm$7.58e-04 & 0.5$\\pm$ 3.7 & 0.0 & 2.86E-03 &1243 & 1.00$\\pm$0.75 & 1.00$\\pm$1.61 & AGN RX J0550.5-7110, z=0.4429 [CGC97] \\\\ \n386 & 05 51 00.5 & -69 54 08 & 4.4 & 106.0 & 1.20e-02$\\pm$1.73e-03 & 0.6$\\pm$ 3.0 & 0.0 & 5.99E-02 &1036 & -0.11$\\pm$0.16 & -1.00$\\pm$3.23 & foreground star F5V HD 40156 \\\\ \n387 & 05 51 22.6 & -70 27 37 & 9.0 & 24.8 & 3.98e-03$\\pm$8.57e-04 & 0.0$\\pm$ 0.0 & 0.0 & $<$1.19E-02 & & & & \\\\ \n388 & 05 51 38.8 & -69 23 00 & 9.5 & 12.5 & 3.04e-03$\\pm$1.03e-03 & 3.7$\\pm$ 3.7 & 0.3 & 1.42E-02 & 893 & 0.03$\\pm$0.24 & -1.00$\\pm$2.55 & \\\\ \n389 & 05 52 24.3 & -64 02 12 & 7.1 & 464.0 & 4.82e-02$\\pm$4.64e-03 & 2.3$\\pm$ 1.2 & 10.8 & 1.75E-01 & 37 & 0.57$\\pm$0.11 & 0.17$\\pm$0.12 & AGN? PKS 0552-640 [HP99b] \\\\ \n390 & 05 52 32.0 & -69 49 06 & 4.5 & 36.5 & 5.16e-03$\\pm$1.12e-03 & 3.7$\\pm$ 2.3 & 6.8 & 7.30E-02 &1024 & 1.00$\\pm$0.14 & 0.46$\\pm$0.15 & 2E 0553.0-6949 \\\\ \n391 & 05 52 48.7 & -69 26 35 & 7.5 & 39.8 & 4.85e-03$\\pm$1.19e-03 & 1.9$\\pm$ 2.1 & 0.4 & $<$1.15E-02 & & & & RX J0552.8-6927 \\\\ \n392 & 05 53 02.2 & -70 17 51 & 8.9 & 10.7 & 3.49e-03$\\pm$1.29e-03 & 1.7$\\pm$ 3.0 & 0.1 & & & & & \\\\ \n393 & 05 53 34.9 & -70 30 24 & 7.9 & 21.8 & 2.38e-03$\\pm$6.02e-04 & 2.4$\\pm$ 2.3 & 0.9 & $<$5.16E-03 & & & & \\\\ \n394 & 05 54 13.5 & -69 19 56 & 9.0 & 12.3 & 2.63e-03$\\pm$9.49e-04 & 1.7$\\pm$ 3.0 & 0.0 & & & & & \\\\ \n395 & 05 54 52.0 & -67 51 10 & 9.1 & 10.3 & 5.05e-03$\\pm$2.44e-03 & 2.9$\\pm$ 2.8 & 0.3 & & & & & \\\\ \n396 & 06 08 50.6 & -65 43 58 & 7.3 & 53.7 & 6.19e-03$\\pm$6.36e-04 & 6.0$\\pm$ 2.1 & 85.2 & & & & & S0 galaxy ESO 86- 62 \\\\ \n397 & 06 08 55.0 & -65 53 00 & 9.2 & 11.6 & 1.14e-03$\\pm$3.18e-04 & 2.9$\\pm$ 3.4 & 0.4 & & & & & $<$galaxy$>$ \\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n"
}
] |
[
{
"name": "astro-ph0002318.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Brunet \\et\\ (1975)]{BIM75}\n Brunet J.P., Imbert M., Martin N., Mianes P., Prevot L., Robeirot E.,\n Rousseau J., 1975, A\\&AS 21, 109\n\n\\bibitem[Chu (1997)]{C97}\n Chu Y.-H., 1997, AJ 113, 1815 [C97] \n %Supernova remnants in OB associations. \n\n\\bibitem[Chu \\et\\ (1997)]{CKS97}\n Chu Y.-H., Kennicutt R.C., Snowden S.L., Smith R.C., Williams R.M.,\n Bomans D.J., 1997, PASP 109, 554 [CKS97]\n\n\\bibitem[Cowley \\et\\ (1984)]{CCH84}\n Cowley A.P., Crampton D., Hutchings J.B., Helfand D.J., Hamilton T.T.,\n Thorstensen J.R., Charles P.A., 1984, ApJ 286, 196 [CCH84] \n %Optical counterparts of the Large Magellanic Cloud X-ray point sources.\n\n\\bibitem[Cowley \\et\\ (1997)]{CSM97} \n Cowley A.P., Schmidtke P.C., McGrath T.K., Ponder A.L., Fertig R.M.,\n 1997, PASP 109, 21 [CSM97]\n\n\\bibitem[Crampton \\et\\ (1997)]{CGC97}\n Crampton D., Gussie G., Cowley A.P., Schmidtke P.C., 1997, AJ 114,\n 2353 [CGC97] \n %Probes for Nearby Galaxies \n\n\\bibitem[David \\et\\ (1996)]{DHK96}\n David L.P., Harnden Jr.\\ F.R., Kearns K.E., and Zombeck M.V.,\n 1996, The ROSAT High Resolution Imager (HRI), USRSDC/SAO Calibration\n Report 1996 February, revised\n\n\\bibitem[Dennerl \\et\\ (1996)]{DHP96}\n Dennerl K., Haberl F., Pietsch W., 1996, in: Zimmermann H.U.,\n Tr\\\"umper J., Yorke H.\\ (eds.) Proceedings of `R\\\"ontgenstrahlung from\n the Universe', Sept.\\ 25-29 1995, MPE report 263, 131 [DHP96]\n\n\\bibitem[Giacconi \\et\\ (1972)]{GMG72}\n Giacconi R., Murray S., Gursky H., Kellogg E., Schreier E., \n Tananbaum H., 1972, ApJ 178, 281 \n\n\\bibitem[Gochermann \\et\\ (1993)]{GGO93}\n Gochermann J., Grothues H.-G., \\\"Ostreicher M.O., Bergh\\\"ofer T.,\n Schmidt-Kaler T., 1993, A\\&AS 99, 591 [GGO93] \n %UBV photometry of galactic foreground and LMC member\n %stars. I. Galactic foreground stars.\n\n\\bibitem[Grothues \\et\\ (1997)]{GOG97}\n Grothues H.-G., \\\"Ostreicher M.O., Gochermann J., Tappert C.,\n Zaum A., Brugger H.R., Schmidt-Kaler T., 1997, A\\&AS 121, 247 [GOG97]\n %UBV photometry of galactic foreground and LMC member\n %stars. II. Galactic foreground stars (supplement).\n\n\\bibitem[Haberl \\et\\ (1995a)]{HDP95a}\n Haberl F., Dennerl K., Pietsch W., 1995, A\\&A 302, L1 [HDP95a]\n\n\\bibitem[Haberl \\et\\ (1995b)]{HPD95b}\n Haberl F., Pietsch W., Dennerl K., 1995, A\\&A 303, L49 [HPD95b]\n\n\\bibitem[Haberl \\et\\ (1997)]{HDP97}\n Haberl F., Dennerl K., Pietsch W., 1997, A\\&A 318, 490 [HDP97]\n\n\\bibitem[Haberl \\& Pietsch (1999a)]{HP99a}\n Haberl F., Pietsch W., 1999a, A\\&A 344, 521 [HP99a]\n\n\\bibitem[Haberl \\& Pietsch (1999b)]{HP99b}\n Haberl F., Pietsch W., 1999b, A\\&AS 139, 277 [HP99b]\n\n\\bibitem[Hoeg \\et\\ (1997)]{HBB97}\n Hoeg E., B\\\"assgen G., Bastian U., Egret D., Fabricius C.,\n Gro{\\ss}mann V., Halbwachs J.L., Makarov V.V., Perryman M.A.C.,\n Schwekendiek P., Wagner K., Wicenec A., 1997, A\\&A 323, L57\n\n\\bibitem[Jones \\et\\ (1985)]{JPM85}\n Jones L.R., Pye J.P., McHardy I.M., Fairall A.P., 1985, \n Space Sci.\\ Rev.\\ 40, 693\n\n\\bibitem[K\\\"urster (1993)]{K93}\n K\\\"urster M., 1993, ROSAT Status Report No.\\ 67\n\n\\bibitem[Leong \\et\\ (1971)]{LKG71}\n Leong C., Kellogg E., Gursky H., Tananbaum H., Giacconi R., 1971, ApJ\n 170, L67\n\n\\bibitem[Long \\et\\ (1981)]{LHG81}\n Long K.S., Helfand D.J., Grabelsky D.A., 1981, ApJ 248, 925\n %A soft X-ray study of the Large Magellanic Cloud\n\n\\bibitem[Maccacaro \\et\\ (1988)]{MGW88}\n Maccacaro T., Gioia I.M., Wolter A., Zamorani G., Stocke J.T.,\n 1988, ApJ 326, 680\n %The X-ray spectra of the extragalactic sources in the Einstein\n %extended medium sensitivity survey\n\n\\bibitem[Mark \\et\\ (1969)]{MPR69}\n Mark H., Price R., Rodrigues R., Seward F.D., Swift C.D.,\n 1969, ApJ 155, L143\n\n\\bibitem[Monet (1996)]{M96}\n Monet D., 1996, American Astronomical Society Meeting, 188, 54.04 \n\n\\bibitem[Morgan (1994)]{M94b}\n Morgan D.H., 1994, A\\&AS 102, 235 [M94b]\n\n\\bibitem[Orio \\& Greiner (1999)]{OG99}\n Orio M., Greiner J., 1999, A\\&A 344, L13 [OG99]\n\n\\bibitem[Pakull \\et\\ (1985)]{PBS85}\n Pakull M., Brunner H., Staubert A., Pietsch W., Beuermann K.,\n 1985, Space Sci.\\ Rev.\\ 40, 379 \n\n\\bibitem[Pietsch \\et\\ (1989)]{PDR89}\n Pietsch W., Dennerl K., Rosso C., 1989, Proc.\\ 23rd ESLAB Symp.\\ \n on Two Topics in X-ray Astronomy, Bologna ESA SP-296, 573\n\n\\bibitem[Sanduleak (1970)]{S70}\n Sanduleak N., 1970, Contr.\\ Cerro-Tololo Obs., 89\n %A deep objective-prism survey for Large Magellanic Cloud members\n\n\\bibitem[Schmidtke \\et\\ (1994)]{SCF94}\n Schmidtke P.C., Cowley A.P., Frattare L.M., McGrath T.K.,\n Hutchings J.B., Crampton D., 1994, PASP 106, 843 [SCF94]\n %LMC Stellar X-ray Sources Observed With ROSAT: I. X-ray Data and\n %Search for Optical Counterparts\n\n\\bibitem[Schmidtke \\et\\ (1999)]{SCC99}\n Schmidtke P.C., Cowley A.P., Crane J.D., Taylor V.A., McGrath T.K.,\n 1999, AJ 117, 927 [SCC99]\n\n\\bibitem[Tr\\\"umper (1982)]{T82}\n Tr\\\"umper J., 1982, Adv.\\ Space Res.\\ 2, 241\n\n\\bibitem[Wang \\et\\ (1991)]{WHHW91}\n Wang Q., Hamilton T., Helfand D.J., Wu X., 1991, ApJ 374, 475\n [WHHW91]\n %The detection of X-rays from the hot interstellar medium of the \n %Large Magellanic Cloud. \n\n\\bibitem[Zimmermann \\et\\ (1994)]{ZBB94}\n Zimmermann H.U., Becker W., Belloni T., D\\\"obereiner S., Izzo C.,\n Kahabka P., Schwentker O., 1994, EXSAS User's Guide, MPE report 257\n\n\\end{thebibliography}"
}
] |
astro-ph0002319
|
X-ray photoionized plasma diagnostics with Helium-like ions. Application to Warm Absorber-Emitter in Active Galactic Nuclei.
|
[
{
"author": "Delphine Porquet\\inst{1,2} \\& Jacques Dubau\\inst{3}"
}
] |
We present He-like line ratios (resonance, intercombination and forbidden lines) for totally and partially photoionized media. For solar plasmas, these line ratios are already widely used for density and temperature diagnostics of coronal (collisional) plasmas. In the case of totally and partially photoionized plasmas, He-like line ratios allow for the determination of the ionization processes involved in the plasma (photoionization with or without an additional collisional ionization process), as well as the density and the electronic temperature. \\ With the new generation of X-ray satellites, Chandra / AXAF, XMM and Astro-E, it will be feasible to obtain both high spectral resolution and high sensitivity observations. Thus in the coming years, the ratios of these three components will be measurable for a large number of non-solar objects.\\ In particular, these ratios could be applied to the Warm Absorber-Emitter, commonly present in Active Galactic Nuclei (AGN). A better understanding of the Warm Absorber connection to other regions (Broad Line Region, Narrow Line Region) in AGN (Seyferts type-1 and type-2, low- and high-redshift quasars...) will be an important key to obtaining strong constraints on unified schemes.\\ We have calculated He-like line ratios, for $Z$=6, 7, 8, 10, 12 and 14, taking into account the upper level radiative cascades which we have computed for radiative and dielectronic recombinations and collisional excitation. The atomic data are tabulated over a wide range of temperatures in order to be used for interpreting a large variety of astrophysical plasmas.\\ \keywords{Atomic data -- Atomic process -- Techniques: spectroscopic -- Galaxies: Active -- (Galaxies:) quasars: emission lines -- X-rays: galaxies}
|
[
{
"name": "ds1759.tex",
"string": "%\\documentclass[referee]{aa}\n%\\documentclass[referee,epsf,psfig]{aa}\n%\\documentclass[epsf,psfig]{aa}\n\\documentclass{aa}\n\\usepackage{graphics}\n\n\\begin{document}\n\n\\thesaurus{06\n (02.01.3; \n 02.01.4; \n 02.12.1; \n 03.20.8; \n 11.01.2;\n 11.17.2; \n 13.25.2)}\n\n\\title{X-ray photoionized plasma diagnostics with Helium-like ions. Application to Warm Absorber-Emitter in Active Galactic Nuclei.}\n\\author{Delphine Porquet\\inst{1,2} \\& Jacques Dubau\\inst{3}}\n\n\\offprints{D. Porquet}\n\\mail{Delphine.Porquet@obspm.fr}\n\\institute{DAEC, Observatoire de Paris, Section Meudon, F-92195 Meudon Cedex, France \n\\and CEA/DSM/DAPNIA, Service d'Astrophysique, CEA Saclay, F-91191 Gif sur Yvette Cedex, France\n\\and DARC, Observatoire de Paris, Section Meudon, F-92195 Meudon Cedex, France}\n\\date{Received ...; accepted ...}\n\n\\titlerunning{Photoionized plasma diagnostics with He-like ions}\n\n\\authorrunning{Porquet \\& Dubau}\n\\maketitle\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\large\n\\begin{abstract}\n\nWe present He-like line ratios (resonance, intercombination and forbidden lines) for totally and partially photoionized media. For solar plasmas, these line ratios are already widely used for density and temperature diagnostics of coronal (collisional) plasmas. In the case of totally and partially photoionized plasmas, He-like line ratios allow for the determination of the ionization processes involved in the plasma (photoionization with or without an additional collisional ionization process), as well as the density and the electronic temperature. \\\\ \nWith the new generation of X-ray satellites, Chandra / AXAF, XMM and Astro-E, it will be feasible to obtain both high spectral resolution and high sensitivity observations. Thus in the coming years, the ratios of these three components will be measurable for a large number of non-solar objects.\\\\ \nIn particular, these ratios could be applied to the Warm Absorber-Emitter, commonly present in Active Galactic Nuclei (AGN). A better understanding of the Warm Absorber connection to other regions (Broad Line Region, Narrow Line Region) in AGN (Seyferts type-1 and type-2, low- and high-redshift quasars...) will be an important key to obtaining strong constraints on unified schemes.\\\\\n We have calculated He-like line ratios, for $Z$=6, 7, 8, 10, 12 and 14, taking into account the upper level radiative cascades which we have computed for radiative and dielectronic recombinations and collisional excitation. The atomic data are tabulated over a wide range of temperatures in order to be used for interpreting a large variety of astrophysical plasmas.\\\\\n\\keywords{Atomic data -- Atomic process -- Techniques: spectroscopic -- Galaxies: Active -- (Galaxies:) quasars: emission lines -- X-rays: galaxies}\n\\end{abstract}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Introduction} \\label{sec:Introduction}\nThe new X-ray satellites (Chandra, XMM and Astro-E) will offer unprecedented high spectral resolution and high sensitivity spectra. Indeed, it will be possible to observe and to separate, in the X-ray range, the three most intense lines of He-like ions: the {\\bf resonance} line ({\\bf w}: 1s$^{2}$\\,\\element[][1]{S}$_{\\mathrm{0}}$ -- 1s2p\\,\\element[][1]{P}$_{\\mathrm{1}}$), the {\\bf intercombination} lines ({\\bf x,y}: 1s$^{2}$\\,\\element[][1]{S}$_{0}$ -- 1s2p \\element[][3]{P}$_{2,1}$ respectively) and the {\\bf forbidden} line ({\\bf z}: 1s$^{2}$\\,\\element[][1]{S}$_{0}$ -- 1s2s\\,\\element[][3]{S}$_{1}$). They correspond to transitions between the $n$=2 shell and the $n$=1 ground state shell (see Figure~\\ref{gotrian}).\\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 1\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nThe ratios of these lines are already widely used for collisional (coronal) plasma diagnostics of various types of objects: solar flares, supernovae remnants, the interstellar medium and tokamak plasmas, i.e. for very hot collisional plasmas (Mewe \\& Schrijver \\cite{Mewe78a} \\cite{Mewe78b}, Winkler et al. \\cite{Winkler81}, Doyle \\& Schwob \\cite{Doyle82}, and Pradhan \\& Shull \\cite{Pradhan81}). \nAs shown by Gabriel \\& Jordan (\\cite{Gabriel69}, \\cite{GabrielJordan72}, \\cite{Gabriel73}), these ratios are sensitive to electron density (R(n$_{\\mathrm{e}}$), equation~\\ref{eq:R}) and to electronic temperature (G(T$_{\\mathrm{e}}$), equation~\\ref{eq:G}):\n\\begin{equation}\n\\mathrm{ R~(n_e)~=~\\frac{z}{(x+y)}} \\label{eq:R}\n\\end{equation}\n%and\n\\begin{equation}\n\\mathrm{ G~(T_e)=\\frac{z+(x+y)}{w}} \\label{eq:G}\n\\end{equation}\nAs emphasized by Pradhan (\\cite{Pradhan85}), Liedahl (\\cite{Liedahl99}) and Mewe (\\cite{Mewe99}) (see also Paerels et al. \\cite{Paerelsetal98}), these plasma diagnostics could be also extended to study photoionized plasmas. Indeed, Pradhan has calculated the {\\bf R} and {\\bf G} ratios for highly charged ions (\\ion{Ar}{xvii} and \\ion{Fe}{xxv}) in ``recombination dominated non-coronal plasmas''. We present numerical calculations of these ratios, for six lighter ions, which could be applied directly for the first time to Chandra and XMM observations of the Warm Absorber present in Active Galactic Nuclei (AGN), and especially in Seyfert\\,1.\\\\\n\n\\indent The Warm Absorber (WA) is a totally or a partially photoionized medium (with or without an additional ionization process), first proposed by Halpern (\\cite{Halpern84}) in order to explain the shape of the X-ray spectrum of the \\object{QSO MR2251-178}, observed with the Einstein Observatory. Its main signatures are the two high-ionization oxygen absorption edges, \\ion{O}{vii} and \\ion{O}{viii} at 0.74 keV and 0.87 keV respectively, seen in fifty percent of Seyfert 1 galaxies at least (Nandra $\\&$ Pounds \\cite{Nandra94}, Reynolds \\cite{Reynolds97}, George et al. \\cite{George98}). According to Netzer (\\cite{Netzer93}), an emission line spectrum from the WA should also be observed. \nIndeed, He-like ion lines have been observed in different types of Seyfert galaxies (\\object{NGC 3783}: George et al. \\cite{George95}, \\object{MCG-6-30-15}: Otani et al. \\cite{Otani96}, \\object{E 1615+061}: Piro et al. \\cite{Piro97}, \\object{NGC 4151}: Leighly et al. {\\cite{Leighly97}, \\object{NGC 1068}: Ueno et al. {\\cite{Ueno94}, Netzer \\& Turner \\cite{Netzer97}, and Iwasawa et al. \\cite{Iwasawa97}). \nThe WA is supposed to be at least a two-zone medium with an inner part (called the ``inner WA'') associated with \\ion{O}{viii} and an outer part (called the ``outer WA''), less ionized, associated with \\ion{O}{vii} (Reynolds \\cite{Reynolds97}, Porquet et al. \\cite{Porquet99}). Furthermore, the \\ion{O}{vii} line is predicted to be the strongest line associated with the outer WA; the \\ion{Ne}{ix} line is predicted to be one of the strongest lines formed in the inner WA (Porquet et al. \\cite{Porquet98}).\\\\\nThe ionization processes, that occur in the Warm Absorber, are still not very well known. Indeed, even though the WA is commonly thought to be a photoionized gas, an additional ionization process cannot be ruled out (Porquet \\& Dumont \\cite{PorquetDumont98}, Porquet et al. \\cite{Porquet99}, Nicastro et al. \\cite{Nicastro99}). Thus, in the present paper, we do not restrict ourselves to only a single type of plasma, but rather study the following cases.\\\\ %\nWe consider a ``pure photoionized plasma'' to be a plasma ionized by high energy photons (external ionizing source). For such a plasma, H-like radiative recombination (and dielectronic recombination at high temperature) are dominant compared to electronic excitation from the ground level (1s$^{2}$) of He-like ions. The lines are formed by recombination.\\\\\nA ``hybrid plasma'' is a partially photoionized plasma, but with an additional ionization process, e.g. collisional (internal ionizing source). For this case, He-like electronic excitation processes from the ground level are usually as important as H-like recombinations, and may even dominate. The lines are formed by collisional excitation from the ground level with or without recombination.\\\\\n \nIn the next section, we introduce the atomic data calculations needed for such plasmas and we emphasize the role of upper-level radiative cascade contributions calculated in this paper for the populations of the $n$=2 shell levels. In section~\\ref{sec:diagnostics}, we develop line diagnostics of the ionization process (temperature) and the density for pure photoionized and hybrid plasmas. We give the corresponding numerical calculations of the line ratios for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi}, and \\ion{Si}{xiii}. In section~\\ref{sec:practical}, we give a practical method for using these results to determine the physical parameters of the WA, in the context of the expected data from the new X-ray satellites (section~\\ref{sec:satellite}).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Atomic data}\\label{sec:atomicdata}\n\nLiedahl (\\cite{Liedahl99}) described the basic mechanisms of density diagnostics for X-ray photoionized plasmas from He-like ions. As he noted, a proper calculation of the population of the $n$=2 shell levels depends upon a number of additional levels. We propose in this article to use extensive calculations of atomic data taking into account upper level (n$>$2) radiative cascade contribution on $n$=2 shell levels for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi}, and \\ion{Si}{xiii}, to give a much more precise treatment of this plasma diagnostic. \\\\\nWe consider in this paper, the main atomic processes involved in pure photoionized and hybrid plasmas: radiative recombination and dielectronic recombination (only important for high temperature plasmas), collisional excitation inside the $n$=2 shell, and collisional excitation from the ground level (important for high temperature plasmas). \n\n\\subsection{Energy levels, radiative transition probabilities}\n\nUsing the SUPERSTRUCTURE code (Eissner et al. \\cite{Eissner74}), we have calculated the energy levels for the first 49 fine-structure levels ($\\mathrm{^{2S+1}{L}_{J}}$) for the six ions. This corresponds to the levels of the first 15 configurations (from 1s$^{2}$ to 1s5g). Nevertheless, for the first seven levels, we have preferred to use the Vainshtein \\& Safronova (\\cite{Vainshtein85}) data which have a slightly better accuracy ($\\sim$10$^{-3}$).\\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 1\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nIn Table~\\ref{energielevel}}, in order to reduce the amount of data, we only report the energy levels for the first 17 levels ($n$=1 to $n$=3 shell). The values for the others levels are available on request.\nThe transition probabilities (A$_{\\mathrm{ki}}$ in s$^{-1}$) for the ``allowed'' transition (E1), are also calculated by the SUPERSTRUCTURE code; for the other transitions (M1, M2 \\& 2E1) the A$_{\\mathrm{ki}}$ values are from Lin et al. (\\cite{Lin77}). In a same way, only direct radiative contributions of the first 17 levels onto the first 7 levels are given in Table~\\ref{Aki1}.\\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 2\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Recombination coefficient rates}\n\nBlumenthal et al. (\\cite{Blumenthal72}) have noted that radiative and dielectronic recombination can have a significant effect on the populations of the $n$=2 states in He-like ions through radiative cascades from higher levels as well as through direct recombination. \n\n\\subsubsection{Radiative recombination (RR) coefficients rates}\\label{sec:RR}\n\n\\noindent For radiative recombination rate coefficients, we have used the method of Bely-Dubau et al. (\\cite{Bely-Dubau82a}). This method is based on $(Z-0.5)$ screened hydrogenic approximation of the Burgess (\\cite{Burgess58}) formulae, as we explain below.\\\\\n\n\\noindent For recombination of a bare nucleus of charge $Z$ to form H-like ions, Burgess (\\cite{Burgess58}) fitted simple power law expressions to the ``exact'' theoretical hydrogenic photoionization cross-sections $\\sigma_{\\mathrm{nl}}$(E) (in cm$^{2}$) for the {$n l$} levels ($1\\le n\\le 12$ and $0\\le l \\le n-1$). According to Burgess ``for moderately small $n$, the errors should be not more than about 5\\%. Such accuracy should be sufficient for most astrophysical applications''. \n\\begin{eqnarray}\\label{eq:sectBurgess}\n&\\sigma_{nl}(E)&=0.55597\\, \\frac {Z^2}{n^2}\\frac 1{2(2l+1)}\\nonumber\\\\\n&&\\times \\left[l~|\\sigma(nl,o~l-1)|^{2}\\left(\\frac {I_H Z^2}{n^2 E}\\right)^{\\gamma(nl,l-1)}\n\\right . \\nonumber \\\\ \n&& \\left . +~(l+1)~|\\sigma(nl,o~l+1)|^{2} \n\\left(\\frac{I_H Z^2}{n^2 E}\\right)^{\\gamma(nl,l+1)}\\right] \n\\end{eqnarray} \n\\noindent where E is the photon energy $ E\\ge I_H Z^2/n^2$.\\\\\nBely-Dubau et al. (\\cite{Bely-Dubau82a}) used this equation for He-like 1s$nl$ levels by replacing $Z$ with $(Z-0.5)$. The quantity $(Z-0.5)$ was chosen to take into account the screening of the $1s$ orbital. To check the validity of this assumption we compared the photoionization cross sections obtained from equation (3) to the recent calculations of the Opacity Project by Fernley et al. (\\cite{Fernley87}). In Figure~\\ref{photoionisation} are plotted photoionisation cross sections for 1s2s $^1$S $^3$S, 1s2p $^1$P $^3$P and 1s10d $^1$D $^3$D for $Z$ =6, 10, 14 (continuous curves), scaled as $(Z-0.5)$. With the exception of 1s2p $^1$P, the three continuous curves can hardly be distinguished. Furthermore, the curves do not differ when passing from singlet to triplet cases. This is strong evidence that for 1s$nl$, it is possible to use screened hydrogenic calculations. For comparison, we give the present calculation corresponding to formulae (3) modified (empty circles). \\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 2\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\noindent The Opacity Project data were taken from the Topbase Bank (Cunto et al. \\cite{Cunto93}). This bank includes the 1s$nl$ photoionization cross sections for $1 \\le n \\le 10$ and $l=0,1,2$. The Burgess data, $\\sigma(nl,o~l\\pm 1)$ and $\\gamma(nl,l\\pm 1)$, are more complete since they also include $3\\le l\\le n-1$. Formula (3) is also more convenient since being analytic one can derive directly the radiative recombination rates (cm$^{3}$\\,s$^{-1}$) from it. \n\n\\begin{equation}\\label{eq:alphaBurgess}\n\\mathrm{\\alpha_{nl}(Z,T_{e})~=~8.9671\\times10^{-23}~T_e^{3/2}~Z~f_{nl}(T_e)}\n\\end{equation}\nwhere\nT$_{\\mathrm{e}}$ is the electronic temperature, $Z$ is the atomic number and\n\\begin{eqnarray}\n&\\mathrm{f_{nl}(T_{e})}& = \\frac{x_\\mathrm{n}^3}{\\mathrm{n}^2}~[~\\mathrm{l}|\\sigma(\\mathrm{nl,o~l-1})|^{2}~\\Gamma_{\\mathrm{c}}(\\mathrm{x_n},3-\\gamma(\\mathrm{nl,l-1)})~ \\nonumber\\\\\n &+ (\\mathrm{l+1})& |\\sigma(\\mathrm{nl,o~l+1})|^{2}~\\Gamma_{\\mathrm{c}}(\\mathrm{x_{n}},3-\\gamma(\\mathrm{nl,l+1}))]\n\\end{eqnarray}\n\\begin{equation}\\label{eq:xn}\n{\\rm with} \\qquad \\mathrm{\\mathrm{x_{n}}~=~\\frac{\\mathrm{Z^{2}~I_{H}}}{\\mathrm{k~T_{e}~n}^{2}}~~~~\\left(\\frac{\\mathrm{I_H}}{\\mathrm{k}}=157\\,890 \\right)}\n\\end{equation}\n\\noindent The quantities $|\\sigma(\\mathrm{nl,o~l}\\pm1)|/{\\mathrm{n}}^{2}$ and $\\gamma(\\mathrm{nl,l}\\pm1)$ are given in Table\\,I of Burgess and \n\\begin{equation}\n\\mathrm{\\Gamma_{c}(x,p)=\\frac{e^{x}}{x^p}~\\int_{x}^{\\infty}t^{(p-1)}~e^{-t}~dt}\n\\end{equation}\n\n\\noindent Finally, to transform H-like data to He-like data, we used the two following expressions for 1s$^{2}$ and 1s\\,nl:\n\\begin{equation}\n\\mathrm{\\noindent \\alpha_{1s^{2}}~=~\\frac{1}{2}~\\alpha_{1s}\\mathrm{(Z,T_{e})}~~~(n=1, ground~level)}\n\\end{equation}\n\\begin{equation}\n\\mathrm{\\noindent \\alpha_{1s~nl~(LSJ)}=\\frac{(2J+1)}{(2L+1)~(2S+1)}~\\alpha_{nl}(Z,T_{e})~~(n\\geq2)}\n\\end{equation}\n\\noindent And we replace $Z$ by ($Z$-0.5) in formula (\\ref{eq:alphaBurgess}) and (\\ref{eq:xn}).\\\\\n\nFor 10$<$n$< \\infty$, we have used the Seaton (\\cite{Seaton59}) formula (see below) which gives RR rates for each quantum number $n$ (shell) of H-like ions. We have assumed that the $l$ recombination for such high $n$ is the same as for $n$=10. \\\\\nSeaton derived his formula by expanding the Gaunt factor, usually taken to be one, to third order (Menzel \\& Pekeris \\cite{MenzelPekeris35}, Burgess \\cite{Burgess58}). \nAccording to Seaton, the radiative recombination rates (in cm$^{3}$\\,s$^{-1}$) for the $n$ shell of H-like ions can be written as:\n\\begin{equation}\\label{eq:alphanl}\n\\mathrm{\\alpha_{n(Z,T)}~=~5.197\\times10^{-14}~Z~x_{n}^{3/2}~S_{n}(x_{n})}\n\\end{equation}\n\\begin{equation}\n\\mathrm{S(x_n)~=~X_0(x_n)+\\frac{0.1728}{n^{\\frac{2}{3}}}~{X_1(x_n})-\\frac{0.0496}{n^{\\frac{4}{3}}}~X_2(x_n)}\n\\end{equation}\n\\begin{equation}\n\\mathrm{X_0(x_n)=\\Gamma_{c}(x,0)}\\\\\n\\end{equation}\n\\begin{equation}\n\\mathrm{X_{1}(x_{n})=\\Gamma_{c}\\!\\left(x,\\frac{1}{3}\\right)-2~\\Gamma_{c}\\!\\left(x,-\\frac{2}{3}\\right)}\\\\\n\\end{equation}\n\\begin{equation}\n\\mathrm{X_2(x_n)=\\Gamma_{c}\\!\\left(x,\\frac{2}{3}\\right)-\\frac{2}{3}~\\Gamma_{c}\\!\\left(x,-\\frac{1}{3}\\right)+\\frac{2}{3}~\\Gamma_{c}\\!\\left(x,-\\frac{4}{3}\\right)}\n\\end{equation}\n\nNext, we have computed the effects of cascades from $n>$2 levels on each 1s2l level (1s\\,2s~$^{3}\\mathrm{S}_{1}$,\\,$^{1}\\mathrm{S}_{0}$; 1s\\,2p $^{3}\\mathrm{P}_{0}$, $^{3}\\mathrm{P}_{1}$, $^{3}\\mathrm{P}_{2}$, $^{1}\\mathrm{P}_{1}$; $n$=2 shell levels). The present study has shown that the radiative recombination (RR) is slowly convergent with $n$, thus the first 49 levels (n$\\leq$5) are considered as fine-structure levels (LSJ), the levels from $n$=6 to $n$=10 (l=9) shells are separated in LS term (Bely-Dubau et al. \\cite{Bely-Dubau82a}, \\cite{Bely-Dubau82b}), and finally levels from $n$=11 to $n$=$\\infty$ are taken into account inside $n$=10. Figure~\\ref{delphine2.ps} shows the scaled direct plus upper (n$>$2) level radiative cascade RR rates $\\alpha^{\\mathrm{s}}$=T$^{1/2}$\\,$\\alpha$/($Z$-0.5)$^{2}$ versus T$^{\\mathrm{s}}$=T/($Z$-0.5)$^{2}$ for 1s2l levels ($Z$= 8, 10, 12 and 14), and for comparison the direct RR contribution. T is in Kelvin. This points out the importance of the cascade contribution at low temperature. The $\\alpha^{\\mathrm{s}}$ curves are very well superposed and thus allows us to deduce the RR rate coefficients for other Z, as for example $Z=$ 9,11,13.\\\\\n\\noindent Tables~\\ref{cascadeC6},\\,~\\ref{cascadeO8},\\,~\\ref{cascadeNe9},\\,~\\ref{cascadeMg11} and\\,~\\ref{cascadeSi13} report separately the direct and the cascade contribution to the RR rate coefficients for each 1s2l level.\\\\\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 3\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nWe checked that the calculated rates summed over $n\\ge 2$ and $l$, added to the rate of the 1s$^2$ (ground level) level, are similar to the total RR rates calculated by Arnaud \\& Rothenflug (\\cite{Arnaud85}), Pequignot et al. (\\cite{Pequignot91}), Mazzotta et al. (\\cite{Mazzotta98}), Jacobs et al. (\\cite{Jacobs77}) (for He-like Fe ion) and Nahar (\\cite{Nahar99}) (for \\ion{O}{vii}). Since these authors used hydrogenic formulae, the RR rate coefficient depends on which screening value was used. As already noted, we have taken for our calculations a screening of 0.5 which is a realistic screening of the atomic nuclei by the 1s inner electron. Most probably, some of these authors have used a ($Z$-1) scaling. For example for \\ion{C}{v}, a screening of unity implies a lower value by some 20\\% with respect to the value obtained with a screening of 0.5. \\\\\n\n\\subsubsection{Dielectronic recombination (DR) coefficient rates}\n\nFor the low temperature range (photoionized plasma) considered in this paper the dielectronic recombination can be neglected. However at high temperatures, the contribution of DR is no longer negligible. Therefore, we have calculated DR coefficients rates (direct plus upper ($n>$2) level radiative cascade contribution).\\\\\n\n\\noindent We used the same method as Bely-Dubau et al. (\\cite{Bely-Dubau82a}). The AUTOLSJ code (including the SUPERSTRUCTURE code) was run with 42 configurations belonging to 1s$nl$, 2s$nl$ and 2p$nl$, with $n\\le 5$. All the fine-structure radiative and autoionization probabilities were calculated. For low $Z$ ions, it was necessary to do an extrapolation to higher $n$ autoionizing levels. Specifically, we extrapolate autoionization probabilities, as 1/$n^3$, while keeping the radiative probabilities constant. This extrapolation is not perfectly accurate, and we can estimate that the RD for C, N and O might be slightly over or under estimated.\\\\\n\nIn Table~\\ref{cascadeC6}~,\\ref{cascadeO8},~\\ref{cascadeNe9},~\\ref{cascadeMg11}, and \\ref{cascadeSi13}, the DR rates are reported for $Z$=6, 8, 10, 12, 14 over a wide range of temperature.\\\\\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 3\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 4\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 5\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 6\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 7\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 8\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Electron excitation rate coefficients}\\label{sec:exc}\n\nThe collisional excitation (CE) rate coefficient (in cm$^3$\\,s$^{-1}$) for each \ntransition is given by:\n\\begin{equation}\n\\mathrm{C_{ij}(T_{e})=\\frac{8.60 \\times 10^{-6}}{g_i~T^{1/2}}~exp\\left(-\\frac{\\Delta E_{ij}}{k~T}\\right)~\\Upsilon_{ij}(T_{e})}\n\\end{equation}\nWhere $\\Delta$E$_{\\mathrm{ij}}$ is the energy of the transition, g$_{\\mathrm{i}}$ is the statistical weight of the lower level of the transition, and $\\Upsilon_{\\mathrm{ij}}$ is the so-called effective collision strength of the transition i$\\to$j.\\\\\n\nThe 1s\\,2l--1s\\,2l${'}$ transitions (i.e. inside the $n$=2 shell) are very important for density diagnostic purpose. The data are from Zhang \\& Sampson (\\cite{Zhang87}). \\\\\n\\noindent Below, we report scaled effective collision strength $\\Upsilon^{\\mathrm{s}}_{\\mathrm{ij}}$=($Z$-0.5)$^{2}$\\,$\\Upsilon_{\\mathrm{ij}}$. We also use a scaled electronic temperature T$^{\\mathrm{s}}$ = T(K)/(1000 $Z^{2}$). The ($Z$-0.5)$^{2}$ coefficient has been chosen to obtain scaled $\\Upsilon^{\\mathrm{s}}$ almost independent of $Z$ (for 6\\,$\\leq Z \\leq$\\,14). In Figure~\\ref{figure1s21s2l}, $\\Upsilon^{\\mathrm{s}}$(T$^{\\mathrm{s}}$) is displayed for the four most important transitions (between 2$^{3}$S$_{1}$ and 2$^{3}$P$_{0,1,2}$ levels, and between 2$^{1}$S$_{0}$ and 2$^{1}$P$_{1}$ levels) including both direct and resonant contribution, and for comparison the direct contribution alone is shown for $Z$=8. We remark that the curves $\\Upsilon^{\\mathrm{s}}$(T$^{\\mathrm{s}}$) are nearly identical for different $Z$, and for these transitions the resonant contribution is quite negligible since the two curves for $Z$=8 are superposed. The rates for the transitions between 2$^{3}$S$_{1}$ and 2$^{3}$P$_{0,1,2}$ levels are proportional to their statistical weight. The curves for transitions 2$^{3}$S$_{1}$--2$^{3}$P$_{1}$ 2$^{1}$S$_{0}$--2$^{1}$P$_{1}$ are nearly identical.\\\\ \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 4\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nThese high values of $\\Upsilon^{\\mathrm{s}}$ inside the $n$=2 shell and the small energy difference between these levels, favour transitions by excitation between the $n$=2 shell levels. Thus the excitation inside the $n$=2 shell should be taken into account even for low temperature plasmas.\\\\\nExcitation from $n$=2 levels to higher shell levels can be neglected due to the weak population of the $n$=2 shell compared to the ground level ($n$=1) in a moderate density plasma and also due to the high $\\Upsilon^{\\mathrm{s}}$(T$^{\\mathrm{s}}$) values inside the $n$=2 shell which favour transitions between the $n$=2 levels, as we see below.\\\\\n\\indent CE from the 1s$^{2}$ (ground) level to excited levels are only important for high temperature such as the hybrid case, due to the high energy difference between these levels. For 1s$^{2}$--1s2l transitions, we have used the effective collision strength values from Zhang \\& Sampson (\\cite{Zhang87}). These values include both non-resonant and resonant contributions.\\\\ \n\\indent CE rates for the 1s$^{2}$--1snl (3$\\leq$n$\\leq$5) transitions are from Sampson et al. (\\cite{Sampson83}). Their calculations do not include resonance effects but these are expected to be relatively small (Dubau \\cite{Dubau94}). The rates converge as $n^{-3}$.\\\\\n\nWe have calculated the radiative cascade contribution from n$>$2 levels for each $n$=2 level. We have considered the first 49 levels, as fine-structure levels (LSJ); the contributions from the $n$=6 to $n$=$\\infty$ levels are considered to converge as $n^{-3}$. The cascade contributions become more important for high temperatures. The cascade contribution (from $n>$2 levels) increases steadily with temperature and has an effect mostly on the 1s\\,2s$^{3}$S$_{1}$ level. The resonant contribution increases then decreases with temperature. For high temperature plasmas, cascade effects should be taken into account. For very low temperature plasmas only the direct non-resonant contribution is important, except for the 1s\\,2s\\,$^{3}$S$_{1}$ level which also receives cascade from within the $n$=2 level, i.e. from 1s\\,2p\\,$^{3}$P$_{0,1,2}$ levels, as long as the density does not redistribute the level population, i.e. the density is not above the critical density. \\\\\nTables~\\ref{collcascadeC5},~\\ref{collcascadeO8},~\\ref{collcascadeNe9},~\\ref{collcascadeMg11} and \\ref{collcascadeSi13} report data which correspond respectively to the direct (b), the resonance (c), and the $n>$2 cascade (d) contributions.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 9\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 10\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 11\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 12\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 13\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Plasma diagnostics} \\label{sec:diagnostics}\n\n\\subsection{Computation of the line ratios}\nThe intensities of the three component lines (resonance, forbidden and intercombination) are calculated from atomic data presented in the former section. The ratios R(n$_{\\mathrm{e}}$) and G(T$_{\\mathrm{e}}$) are calculated for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi}, and \\ion{Si}{xiii}. The wavelengths of these three lines for each He-like ion treated in this paper are reported in Table~\\ref{lambda}.\\\\\n \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT TAB 14\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nWe note that for all temperatures (low and high), we have included in the line ratio calculations, RR contribution (direct + upper-level radiative cascade), and collisional excitations inside the $n$=2 shell. For high temperature plasmas, the CE contribution (direct + resonance + cascade) from the ground level ($n$=1 shell, 1s$^{2}$) should be included in the calculations as well as DR (direct + cascade). Figure~\\ref{exc_recomb} displays these different contributions which populate a given $n$=2 level.\\\\\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 5\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nAs emphasized previously, the cascade contribution from n$>$2 levels, especially for the $^{3}$S$_{1}$ level, should be taken into account in line ratio calculations since this level is responsible for the forbidden component ({\\bf z}) line, which appears in both ratios {\\bf R} and {\\bf G}. \nFor a pure photoionized plasma, when no upper level radiative cascade contribution is included in the RR rates, {\\bf R} and {\\bf G} could be underestimated by 6--10\\% (for \\ion{O}{vii}). In a hybrid plasma, where collisional processes from the ground level are not negligible, the ratio {\\bf R} is lower by $\\sim$20$\\%$ at T=3.6\\,10$^{6}$\\,K, when no cascades from upper levels are taken into account. In a similar way, the value of {\\bf G} would be underestimated.\\\\\n\nWe also point out the importance of taking into account the branching ratios in the calculations of {\\bf x} and {\\bf y} lines. B$_{\\mathrm{x}}$ = A$_{5\\to1}$ / (A$_{5\\to1}$ + A$_{5\\to2}$), and B$_{\\mathrm{y}}$ = A$_{4\\to1}$ / (A$_{4\\to1}$ + A$_{4\\to2}$) are respectively the branching ratios of the {\\bf x} and {\\bf y} lines (A$_{\\mathrm{j \\to i}}$ being the transition probability from level j to level i, see Fig.~\\ref{gotrian}). Branching ratios are very important in the case of light nuclear charge ($Z$), as shown in Figure~\\ref{BRCVSiXIII}, for \\ion{C}{v}, A$_{5\\to1}<<$A$_{5\\to2}$ as well A$_{4\\to1}<$A$_{4\\to2}$. When $Z$ increases, most branching ratios become less important but nevertheless some of them should be included in the calculations. Without these branching ratios the intensities of the intercombination lines {\\bf x} and {\\bf y} could be overestimated, resulting in an underestimate of the ratio {\\bf R}. This could lead to huge discrepancies for the value of {\\bf R} as well as for {\\bf G}.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 6\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\subsection{Ionizing process diagnostics}\\label{sec:process}\nFirst of all, the ionization processes that occur should be determined. High resolution spectra enable us to measure the intensities of the forbidden ({\\bf z}), intercombination ({\\bf x+y}) and resonance ({\\bf w}) lines of a He-like ion. They give an indication of the ionization processes which occur in the gas using the relative intensity of the resonance line {\\bf w} compared to those of the forbidden {\\bf z} and the intercombination {\\bf x+y} lines. This corresponds to the {\\bf G} ratio (see eq.~\\ref{eq:G}).\\\\\nRR to the $^{3}$S and $^{3}$P (triplet) levels is more than a factor 4 greater than the $^{1}$P (singlet) level, due to the higher statistical weights of the triplet levels. When RR dominates compared to CE from the ground level (1s$^{2}$), this results in a very intense forbidden {\\bf z} ($^{3}$S$_{1}$ level) or {\\bf (x+y)} ($^{3}$P$_{1,2}$ levels) lines, compared to the resonance {\\bf w} line ($^{1}$P$_{1}$ level). On the contrary, when CE from the ground level dominates compared to RR, the $^{1}$P$_{1}$ level is preferentially populated (high value of $\\Upsilon$(1s$^{2}$\\,$^{1}$S$_{0}\\to$1s2p\\,$^{1}$P$_{1}$)), thus implying an intense resonance {\\bf w} line.\\\\\nWe also introduce the parameter {\\bf X$_{\\mathrm{ion}}$} which is the relative ionic abundance of the H-like and He-like ions. As an example for oxygen, it corresponds to the ratio of \\ion{O}{viii}/\\ion{O}{vii} ground state population. A low value of {\\bf X$_{\\mathrm{ion}}$} means that the H-like ion relative abundance is small compared to the He-like one and thus CE from the 1s$^{2}$ ground level is dominant compared to RR (H-like$\\to$He-like), when the temperature is high enough to permit excitation from the ground level.\\\\\n Figure~\\ref{1surG} displays the ratios {\\bf G} as a function of electronic temperature (T$_{\\mathrm{e}}$) for different values of {\\bf X$_{\\mathrm{ion}}$}. The range of temperatures (low values) where the ratio ($>$4 see $\\S$\\ref{sec:process}) is almost independent of T$_{\\mathrm{e}}$ and {\\bf X$_{\\mathrm{ion}}$} occurs for a plasma dominated by RR (pure photoionized plasmas).\\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 7\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nAt higher temperatures, i.e. large enough to permit excitation from the ground level to upper levels, {\\bf G} becomes sensitive to both parameters (T$_{\\mathrm{e}}$, {\\bf X$_{\\mathrm{ion}}$}). High values of {\\bf X$_{\\mathrm{ion}}$} favour mainly DR (H-like ions towards He-like ions), but for photoionized plasma such high temperatures (where {\\bf G}$<$4) are probably extreme cases (i.e not realistic) for WA plasmas.\\\\\nOn the contrary, for lower values of {\\bf X$_{\\mathrm{ion}}$} the lines are produced mainly by collisional excitation (``hybrid'' plasma in our nomenclature). A value of {\\bf G$<$4} will be the signature of a plasma where collisional processes are no longer negligible and even be dominant compared to recombination. We should notice that this is no more the case when {\\bf G} is sensitive to n$_{\\mathrm{e}}$, i.e. when the resonance {\\bf w} line becomes sensitive to density due to the depopulation of the 1s2s\\,$^{1}$S$_{0}$ level to the 1s2p$^{1}$P$_{1}$ level (see also fig. 4--6--9 in Gabriel \\& Jordan \\cite{GabrielJordan72}).\\\\\nIn conclusion, the relative intensity of the resonance {\\bf w} line, compared to the forbidden {\\bf z} and the intercombination ({\\bf x+y}) lines, contains informations about the ionization processes that occur: a weak {\\bf w} line compared to the {\\bf z} or the ({\\bf x+y}) lines corresponds to a pure photoionized plasma. It leads to a ratio of {\\bf G}=(z+x+y)/w$>$4. On the contrary a strong {\\bf w} line corresponds to a hybrid plasma (or even a collisional plasma), where collisional processes are not negligible and may even dominate (see $\\S$\\ref{sec:hybrid}). In this case, {\\bf w} is at least as intense as the {\\bf z} or {\\bf x+y} lines.\n\n\\subsection{Density diagnostic}\\label{sec:calculations}\n\\indent In the low density limit, all $n$=2 states are populated by electron impact directly or via upper-level radiative cascade from He-like ground state and by H-like recombination (see Figure~\\ref{gotrian} and \\ref{exc_recomb}). These states decay radiatively directly or by cascade to the ground level. The relative intensities of the three intense lines are then independent of density. As n$_{\\mathrm{e}}$ increases from the low density limit, some of these states (1s2s\\,$^{3}$S$_{1}$ and $^{1}$S) are depleted by collision to the nearby states where n$_{\\mathrm{crit}}$\\,C\\,$\\sim$A, with C being the collisional coefficient rate, A being the radiative transition probabilities from $n$=2 to $n$=1 (ground state), and n$_{\\mathrm{crit}}$ being the critical density. Collisional excitation depopulates first the 1s2s\\,\\element[][3]{S}$_{1}$ level (metastable) to the 1s2p \\element[][3]{P}$_{0,1,2}$ levels. The intensity of {\\bf z} decreases and those of {\\bf x} and {\\bf y} increase, hence implying a reduction of the ratio {\\bf R} (according to eq.\\ref{eq:R}). For much higher densities, 1s2s\\,$^{1}$S$_{0}$ is also depopulated to 1s2p$^{1}$P$_{1}$.\n\\subsubsection{Pure photoionized plasmas}\nAs explained previously, pure photoionized plasmas are characterized by a weak resonance {\\bf w} line compared to the forbidden {\\bf z} or the intercombination ({\\bf x+y}) lines. The ratio {\\bf R} as a function of electronic density n$_{\\mathrm{e}}$ is reported in Figure~\\ref{Rphoto} for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi}, \\ion{Si}{xiii} at different values of T$_{\\mathrm{e}}$.\\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 8\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n For low values of T$_{\\mathrm{e}}$ corresponding to the density range where {\\bf G} is independent of {\\bf X$_{\\mathrm{ion}}$} (fig.~\\ref{Rphoto}), {\\bf R} is almost insensitive to temperature.\\\\\n But in the case of high temperature (with a high {\\bf X$_{\\mathrm{ion}}$} value so that the medium is dominated by recombination), the value of {\\bf R} is larger. Thus in the density range where {\\bf R} takes a constant value (i.e. low density values), a high value of {\\bf R} corresponds to a high temperature. This also imply a very intense H-like line (K$_{\\alpha}$) since the ratio X$_{\\mathrm{ion}}$=H-like/He-like need to be large enough so that the gas is dominated by recombinations (see caption of the Figure~\\ref{1surG}).\n\n\\subsubsection{Hybrid plasmas}\\label{sec:hybrid}\nHybrid plasmas, where both recombination and collisional processes occur, are characterized by {\\bf G}$<$4, i.e. an intense resonance {\\bf w} line.\\\\\nFor high temperature, the ratio {\\bf R} as a function of electronic density n$_{\\mathrm{e}}$ is reported in Figure~\\ref{Rhybrid} for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi}, \\ion{Si}{xiii} for different values of {\\bf X$_{\\mathrm{ion}}$}. {\\bf R} is calculated at the temperature corresponding to the maximum abundance of the He-like ion for a collisional plasma (see Arnaud \\& Rothenflug \\cite{Arnaud85}). In the low density limit, in the range where {\\bf R} is independent of density, its value is correlated with {\\bf X$_{\\mathrm{ion}}$}. However for intermediate values of {\\bf X$_{\\mathrm{ion}}$}, {\\bf R} is similar to the {\\bf R} calculated for photoionized plasmas (see also Figure~\\ref{Rphoto}), especially for low charge ions ({\\ion{C}{v}, \\ion{N}{vi} and \\ion{O}{vii}). Thus discriminating between ionization processes is difficult using this {\\bf R} ratio. As one can also see, at higher densities this ratio is almost insensitive to the {\\bf X$_{\\mathrm{ion}}$} value.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 9\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Practical use of the diagnostics} \\label{sec:practical}\n\\noindent The physical parameters which could be inferred are numerous:\\\\\n\\noindent - Firstly, we can determine which ionization processes occur in the medium, i.e. a whether photoionization dominates or if an additional process competes (such as a collisional one). Indeed, in the case of a pure photoionized plasma, the intensity of the resonance line {\\bf w}, is weak compared to those of the intercombination {\\bf x+y} and forbidden {\\bf z} lines. On the contrary, if there is a strong {\\bf w} line, this means that collisional processes are not negligible and may even dominate. This combined with the relative intensity of the K$_{\\alpha}$ line (H-like) can give an estimate of the ratio of the ionic abundance of H-like/He-like and according to Figure~\\ref{1surG}, this can also give an indication of the electronic temperature T$_{\\mathrm{e}}$ in the case of a hybrid plasma, since {\\bf G} is sensitive to T$_{\\mathrm{e}}$. Figure~\\ref{nedomaine} gives the temperature range where {\\bf G} is insensitive to {\\bf X$_{\\mathrm{ion}}$} and T$_{\\mathrm{e}}$ for pure photoionized plasmas. \\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 10\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\noindent - Next, density diagnostics can be used. The ratio {\\bf R = z/(x+y)} changes rapidly over approximatively two decades of density, around the critical value, which is different for each He-like ion (see Fig.\\ref{nedomaine}). In this narrow density range, when the density increases the 1s2s\\,\\element[][3]{S}$_{1}$ level (metastable) is depopulated by electron impact excitation to the 1s2p\\,\\element[][3]{P}$_{0,1,2}$ levels which imply that the intensity of the forbidden {\\bf z} line decreases while the intensity of the intercombination {\\bf x+y} lines increases (see Figure~\\ref{XMM}). Outside this range, at the low density limit (intense {\\bf z} and a constant {\\bf R} value), {\\bf R} gives an upper limit for the value of the gas density producing the He-like ion. At higher densities (the forbidden {\\bf z} line disappears since the density value is greater than the critical density and hence {\\bf R} tends to zero), {\\bf R} gives a lower density limit. Thus if the physical parameters deduced from each He-like ion do not correspond, this could be the signature of stratification of the WA.\\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%PLEASE INSERT FIG 11\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\noindent - Once the density is determined from the ratio {\\bf R}, an estimate of the size of the medium ($\\Delta r$) becomes possible, since N$_{\\mathrm{H}}$=n$_{\\mathrm{H}}~\\Delta r$, where N$_{\\mathrm{H}}$ is the column density of the WA.\\\\\n\\noindent - In addition, the distance $r$ of the medium from the central ionizing source could be deduced, since the density and the distance are related by the ``ionization parameter'' $\\xi$=L/n$_{\\mathrm{H}}$\\,r$^{2}$. Note that the determination of $\\xi$ is dependant of the shape of the incident continuum.\\\\\n%\\end{itemize}\n%newpage\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Current and future X-ray satellites opportunities}\\label{sec:satellite}\n\nThe high spectral resolution of the next generation of X-ray telescopes (Chandra, XMM and Astro-E) will enable us to detect and to separate the three main X-ray lines (resonance, intercombination and forbidden) of He-like ions.\\\\\nConcerning Chandra (AXAF), all the main lines (w, x+y, z) for the He-like ions treated in this paper (\\ion{C}{v} to \\ion{Si}{xiii}), can be resolved using either the HRC-S combined with the LETG (0.08--6.0 keV; 2--160\\,\\AA), or the ACIS-S with HETG (0.4-10\\,keV; 1.2--31\\AA).\\\\\nThe XMM mission, due to its high sensitivity and high spectral resolution (RGS: 0.35--2.5\\,keV; 5--35\\,\\AA), will enable us to detect these He-like ions, except for \\ion{C}{v} which is outside the detector's energy range. See Figure~\\ref{XMM} for cases illustrating a pure photoionized plasma and a hybrid plasma for \\ion{O}{vii} near 0.57\\,keV.\\\\\nThe Astro-E XRS will be the first X-ray micro-calorimeter in space. \nIt will have an energy resolution of 12\\,eV (FWHM) over a broad energy range, 0.4 - 10 keV. Although, this is not sufficient for detailed spectroscopy at low energies, it will be very useful for the study of He-like ions (see figure 8 in Paerels \\cite{Paerels99}) with E$>$2.5\\,keV (i.e. $Z>$16), i.e. complementary to the Chandra and XMM capabilities. \\\\\nAt some future date, XEUS (X-Ray Evolving Universe Spectroscopy mission), which is a potential follow-on to ESA's cornerstone XMM (Turner et al. \\cite{Turner97}), will offer to observers a high energy astrophysics facility with high resolving power (E/$\\Delta$E$\\sim$1\\,eV near 1\\,keV with its narrow field imager) combined with a unprecedented collecting area (initial mirror area of 6\\,m$^{2}$). This will enable observers to use these types of plasma diagnostics for Carbon to Iron He-like ions. And, in addition, for high $Z$, ($Z$=26 for iron) He-like lines and their corresponding dielectronic satellite lines will be resolved and give accurate temperature diagnostics in the case of hybrid plasmas. Satellite lines to the He-like 1s$^{2}$--1s2l$^{'}$ parent line are due to transitions of the type:\n\\begin{equation}\n1s^{2}nl-1s2l^{'}nl~~~~~~~n\\geq2\n\\end{equation}\nThe main dielectronic satellite lines of \\ion{Ca}{xix} and \\ion{Fe}{xxv} He-like ions correspond to $n$=2 and 3 and are most important for temperature diagnostic purposes. For more details see the review by Dubau \\& Volonte (\\cite{DubauVolonte80}).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Conclusion}\\label{sec:conclusion}\nWe have shown that the ratios of the three main lines (forbidden, intercombination and resonance) of He-like ions provide very powerful diagnostics for totally or partially photoionized media. For the first time, these diagnostics can be applied to non solar plasmas thanks to the high spectral resolution and the high sensitivity of the new X-ray satellites Chandra/AXAF, XMM and Astro-E.\\\\\nThese diagnostics have strong advantages. The lines are emitted by the same ionization stage of one element, thus eliminating any uncertainties due to elemental abundances. In addition, since the line energies are relatively close together, this minimizes wavelength dependent instrumental calibration uncertainties, thus ensuring that observed photon count rates can be used almost directly.\\\\\n For example, the determination of the physical parameters of the Warm Absorber component in AGN, such as the ionization process, the density and in some case the electronic temperature (``hybrid plasma''), will allow observers to deduce the size and the location (from the ionizing source) of the WA. In addition, since He-like ions are sensitive to different range of parameters (density, temperature), it could permit confirmation of the idea that the WA comes from a stratified, or a multi-zone medium (Reynolds \\cite{Reynolds97}, Porquet et al. \\cite{Porquet99}). As a consequence, a better understanding of the WA will be important for relating the WA to other regions (Broad Line Region, Narrow Line Region) in different AGN classes (Seyferts type-1 and type-2, low- and high-redshift quasars...). This will offer strong constraints on unified schemes.\n\n\\begin{acknowledgements}\nThe authors wish to acknowledge M. Cornille, J. Hughes and the anonymous referee for their careful reading of this paper. The authors greatly thank R. Mewe for his interest in this work and for very fruitful comparisons.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\\bibitem[1985]{Arnaud85} \nArnaud, M. \\& Rothenflug, R. 1985, A\\&AS, 60, 425 \n\\bibitem[1982a]{Bely-Dubau82a} \nBely-Dubau, F., Faucher, P., Dubau, J., Gabriel, A. H. 1982a, MNRAS, 198, 239 \n\\bibitem[1982b]{Bely-Dubau82b} \nBely-Dubau, F., Faucher, P., Steenman-Clark, L., Dubau, J., Loulergue, M., Gabriel, A. H., Antonucci, E., Volonte, S., Rapley, C. G. 1982b, MNRAS, 201, 1155 \n\\bibitem[1972]{Blumenthal72}\nBlumenthal, G. R., Drake, G. W. F., Tucker, W. H. 1972, ApJ, 172, 205 \n\\bibitem[1958]{Burgess58}\nBurgess, A. 1958, MNRAS, 118, 477\n\\bibitem[1960]{BurgessSeaton60}\nBurgess, A., Seaton, M. J. 1960, MNRAS, 121, 471 \n\\bibitem[1993]{Cunto93} \nCunto, W., Mendoza, C., Ochsenbein, F., Zeippen, C. J. 1993, A\\&A, 275, L5 \n\\bibitem[1980]{Doyle80} \nDoyle, J. G. 1980, A\\&A, 87, 184 \n\\bibitem[1982]{Doyle82}\nDoyle, J. G., Schwob, J. L. 1982, J. Phys B, 15, 813\n\\bibitem[1994]{Dubau94}\nDubau, J. 1994, ADNDT, 57, 21\n\\bibitem[1980]{DubauVolonte80} \nDubau, J. \\& Volonte, S. 1980, Reports of Progress in Physics, 43, 199\n\\bibitem[1974]{Eissner74}\nEissner, W., Jones M., Nussbaumer H., 1974, Comput. Phys. Commun., 8, 270\n\\bibitem[1987]{Fernley87} \nFernley, J.A., Taylor, K. T., Seaton, M. J. 1987, J. Phys. B: At. Mol. Phys., 20, 6457\n\\bibitem[1969]{Gabriel69}\nGabriel, A. H., Jordan, C. 1969, MNRAS, 145, 241\n\\bibitem[1972]{GabrielJordan72}\nGabriel, A. H., Jordan, C. 1972, in ``Case studies in atomic collision physics'', vol.2, p209, McDaniel, McDowell (eds.).\n\\bibitem[1973]{Gabriel73}\nGabriel, A. H., Jordan, C. 1973, ApJ, 186, 327 \n\\bibitem[1995]{George95}\nGeorge, I. M., Turner, T. J., Netzer, H. 1995, ApJ 438, L67\n\\bibitem[1998]{George98} \nGeorge, I. M., Turner, T. J., Netzer, H. , Nandra, K., Mushotzky, R. F., Yaqoob, T. 1998, ApJS, 114, 73 \n\\bibitem[1984]{Halpern84}\nHalpern, J. C. 1984, ApJ, 281, 90\n\\bibitem[1997]{Iwasawa97} \nIwasawa, K., Fabian, A. C., Matt, G. 1997, MNRAS, 289, 443\n\\bibitem[1977]{Jacobs77} \nJacobs, V. L., Davis, J., Kepple, P. C. \\& Blaha, M. 1977, ApJ, 211, 605 \n\\bibitem[1997]{Leighly97} \nLeighly, K. M., Matsuoka, M. , Cappi, M., Mihara, T. 1997, IAU Symposia 188, 249 \n\\bibitem[1999]{Liedahl99}\nLiedahl, D.A. 1999, in X-rays Spectroscopy in Astrophysics, EADN School proceeding, 1997, J.A. van Paradijs, J.A.M Bleeker (eds.), p.189\n\\bibitem[1977]{Lin77}\nLin, C. D., Johnson, W. R., Dalgarno, A. 1977, Physical Review A, vol. 15, 154\n\\bibitem[1998]{Mazzotta98} Mazzotta, P., Mazzitelli, G., Colafrancesco, S., Vittorio, N. 1998, A\\&AS, 133, 403 \n\\bibitem[1935]{MenzelPekeris35}\nMenzel, D.H, Pekeris, C.L. 1935, MNRAS, 96, 77\n\\bibitem[1978a]{Mewe78a} \nMewe, R. \\& Schrijver, J. 1978a, A\\&A, 65, 99\n\\bibitem[1978b]{Mewe78b} \nMewe, R. \\& Schrijver, J. 1978b, A\\&AS, 33, 311 \n\\bibitem[1999]{Mewe99}\nMewe, R. 1999, in X-rays Spectroscopy in Astrophysics, EADN School proceeding, 1997, J.A. van Paradijs, J.A.M Bleeker (eds.), p.109\n \\bibitem[1999]{Nahar99} \nNahar, S. N. 1999, ApJS, 120, 31 \n\\bibitem[1994]{Nandra94}\nNandra, K., Pounds, K. A. 1994, MNRAS, 268, 405\n\\bibitem[1993]{Netzer93}\nNetzer, H., 1993, ApJ 411, 594 \n\\bibitem[1997]{Netzer97}\nNetzer, H., Turner, T. J. 1997, ApJ, 488, 694 \n\\bibitem[1999]{Nicastro99} \nNicastro, F. , Fiore, F. , Perola, G. C., Elvis, M. 1999, ApJ, 512, 184 \n\\bibitem[1996]{Otani96}\nOtani, C. , Kii, T. , Reynolds, C. S., Fabian, A. C., Iwasawa, K. , Hayashida, K. , Inoue, H. , Kunieda, H., Makino, F. , Matsuoka, M., Tanaka, Y. 1996, PASJ, 48, 211 \n\\bibitem[1998]{Paerelsetal98}\nPaerels, F. et al. 1998, in Proceedings of the First XMM Workshop on \"Science with XMM\", held at Noordwijk, The Netherlands, M.Dahlem (ed.), URL http://astro.estec.esa.nl/XMM/news/ws1/ws1$_{}$papers.html\n\\bibitem[1999]{Paerels99}\nPaerels, F. 1999, in X-rays Spectroscopy in Astrophysics, EADN School proceeding, 1997, p.347, J.A. van Paradijs, J.A.M Bleeker (eds.)\n\\bibitem[1991]{Pequignot91} \nPequignot, D., Petitjean, P. \\& Boisson, C. 1991, A\\&A, 251, 680\n\\bibitem[1998]{PorquetDumont98}\nPorquet, D., Dumont, A.M. 1998, in \"Structure and Kinematics of Quasar Broad Line Regions\", Eds C. M. Gaskell, W. N. Brandt, M. Dietrich, D. Dultzin-Hacyan, and M. Eracleous, ASP Conf. Ser., in press\n\\bibitem[1998]{Porquet98}\nPorquet, D., Dumont, A.M., Mouchet, M. 1998, Author, I. 1998, in Proceedings of the First XMM Workshop on \"Science with XMM\", held at Noordwijk, The Netherlands, M. Dahlem (ed.), URL http://astro.estec.esa.nl/XMM/news/ws1/ws1$_{}$papers.html \n\\bibitem[1999]{Porquet99}\nPorquet, D., Dumont, A.M., Collin, S., Mouchet, M. 1999, A\\&A, 341, 58\n\\bibitem[1985]{Pradhan85} \nPradhan, A. K. 1985, ApJ, 288, 824 \n\\bibitem[1981]{Pradhan81} \nPradhan, A. K., Shull, J. M. 1981, ApJ, 249, 821 \n\\bibitem[1997]{Piro97}\nPiro, L., Balucinska-Church, M., Fink, H., Fiore, F., Matsuoka, M., Perola, G. C., Soffitta, P. 1997, A\\&A, 319, 74 \n\\bibitem[1997]{Reynolds97}\nReynolds, C. S., 1997, MNRAS, 286, 513 \n\\bibitem[1983]{Sampson83}\nSampson, D. H., Goett, S. J., Clarck, R. E. H. 1983, ADNDT, 29, 467\n\\bibitem[1959]{Seaton59}\nSeaton, M. J. 1959, MNRAS, 119, 81\n\\bibitem[1997]{Turner97} \nTurner, M. J. L., Bleeker, J. A. M., Hasinger, G., Peacock, A., Truemper, J. 1997, IAU Symposia, 188, E20\n\\bibitem[1994]{Ueno94}\nUeno, S., Mushotzky, R. F., Koyama, K., Iwasawa, K., Awaki, H., Hayashi, I. 1994, PASJ, 46, L71 \n\\bibitem[1985]{Vainshtein85}\nVainshtein, L. A. \\& Safronova U. I. 1985, Physica Scripta, vol. 31, 519\n\\bibitem[1981]{Winkler81} \nWinkler, P. F., Clark, G. W., Markert, T. H., Petre, R., Canizares, C. R. 1981, ApJ, 245, 574 \n\\bibitem[1987]{Zhang87}\nZhang, H. \\& Sampson, D. H. 1987, ApJS, 63, 487\n\\end{thebibliography}\n%*****************************************************************************************\n\\begin{figure*}[h]\n\\vspace{1cm}\\resizebox{8cm}{!}{\\includegraphics{ds1759_fig1.ps}} \n\\caption{Simplified Gotrian diagram for He-like ions. {\\bf w}, {\\bf x,y} and {\\bf z} correspond respectively to the resonance, intercombination and forbidden lines. {\\it Full curves}: collisional excitation transitions, {\\it broken curves}: radiative transitions and {\\it thick dot-dashed curves}: recombination (radiative and dielectronic). {\\it Note: the broken arrow ($^{1}$S$_{0}$ to the ground level) corresponds to the 2-photon continuum}.}\n\\label{gotrian}\n\\end{figure*}\n\n\\begin{figure*}[h]\n\\begin{center}\n\\rotatebox{90}{\\resizebox{8cm}{!}{\\includegraphics{ds1759_fig2a.ps}}}\\vspace{0.3cm}\n\\rotatebox{90}{\\resizebox{3.80cm}{!}{\\includegraphics{ds1759_fig2b.ps}}}\n\\end{center}\n\\caption{Scaled photoionization cross sections $\\sigma_{\\mathrm{s}}$=$\\sigma$\\,($Z$-0.5)$^{2}$ (in cm$^{-3}$\\,s$^{-1}$) as a function of E/($Z$-0.5)$^{2}$ (E is in Rydberg). {\\it Empty circles}: photoionisation cross sections calculated in the present work; {\\it solid lines}: photoionisation cross sections available in Topbase for different values of $Z$=6, 10, 14.}\n\\label{photoionisation}\n\\end{figure*}\n\n\n\\begin{figure*}[h]\n\\begin{center}\n\\rotatebox{90}{\\resizebox{12cm}{!}{\\includegraphics{ds1759_fig3.ps}}}\n\\end{center}\n\\caption{Scaled total radiative recombination rates (upper curves: direct plus cascade contribution from n$>$2 levels) $\\alpha^{\\mathrm{s}}$=T$^{1/2}$\\,$\\alpha$/($Z$-0.5)$^{2}$ ($\\times$10$^{12}$ cm$^{3}$\\,s$^{-1}$) versus T$^{\\mathrm{s}}$=T/($Z$-0.5)$^{2}$ ($\\times$10$^{-4}$) towards each $n$=2 level (Plus, star, circle and cross are respectively for $Z$=8,10,12,14), and for comparison the direct contribution (lower curve in each graph). T is in Kelvin.}\n\\label{delphine2.ps}\n\\end{figure*}\n\n\\begin{figure*}[h]\n\\rotatebox{180}{\\resizebox{16.5cm}{!}{\\includegraphics{ds1759_fig4.ps}}}\n\\caption{Scaled effective collision strengths $\\Upsilon^{\\mathrm{s}}$=($Z$-0.5)$^{2}$\\,$\\Upsilon$ versus T$^{\\mathrm{s}}$=T(K)/(1000\\,$Z^{2}$) for He-like ions with $Z$=\\,8,\\,10,\\,12,\\,14 inside the $n$=2 level. The upper curves represent $\\Upsilon^{\\mathrm{s}}$ with the resonance effect taken into account (plus, star, circle and cross respectively for $Z$=\\,8,\\,10,\\,12\\,and 14) and for comparison the lower curve (with plus) corresponds to $\\Upsilon^{\\mathrm{s}}$ without resonance effect for $Z$=8. {\\it Note: the two Z=8 curves (with plus) are superposed.}}\n\\label{figure1s21s2l}\n\\end{figure*}\n\n\\begin{figure*}[h]\n\\resizebox{8cm}{!}{\\includegraphics{ds1759_fig5.ps}}\n\\caption{Simplified Gotrian diagram reporting the different contributions for the population of a given $n$=2 shell level. \n(1): direct contribution due to collisional excitation (CE) from the ground level (1s$^{2}$) of He-like ions; (2)+(2'): CE upper level radiative cascade contribution; (3): direct RR or direct DR from H-like ions contribution; and (4)+(4'): RR or DR upper level radiative cascade contribution. {\\it Note: CE and DR are only effective at high temperature}.}\n\\label{exc_recomb}\n\\end{figure*}\n\n\\begin{figure*}[h]\n\\begin{tabular}{cc}\n\\resizebox{7.5cm}{!}{\\includegraphics{ds1759_fig6a.ps}} & \\resizebox{7.5cm}{!}{\\includegraphics{ds1759_fig6b.ps}}\\\\\n\\end{tabular}\n\\caption{Simplified Gotrian diagrams for \\ion{C}{v} and \\ion{Si}{xiii}. Thick curves correspond to the strongest radiative transitions (A$_{\\mathrm{i} \\to {\\mathrm{j}}}$ in s$^{-1}$), and thin curves correspond to lower values.}\n\\label{BRCVSiXIII}\n\\end{figure*}\n%\\clearpage\n%----------------------------------------------------------------------------------------\n\\begin{figure*}[h]\n\\begin{tabular}{cc}\n\\resizebox{7.75cm}{!}{\\includegraphics{ds1759_fig7a.ps}} &\\resizebox{7.5cm}{!}{\\includegraphics{ds1759_fig7d.ps}}\\\\\n\\resizebox{7.35cm}{!}{\\includegraphics{ds1759_fig7b.ps}} &\\resizebox{7.25cm}{!}{\\includegraphics{ds1759_fig7e.ps}}\\\\\n\\resizebox{7.5cm}{!}{\\includegraphics{ds1759_fig7c.ps}} &\\resizebox{7.25cm}{!}{\\includegraphics{ds1759_fig7f.ps}}\\\\\n\\end{tabular}\n\\caption{{\\bf G (=(x+y+z)/w)} is reported as a function of electronic temperature (T$_{\\mathrm{e}}$) for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi}, and \\ion{Si}{xiii} in the density range where {\\bf G} is not dependent on density (see $\\S$\\ref{sec:process}). The number ($m$) associated to each curves means {\\bf X$_{\\mathrm{ion}}$}=10$^{\\mathrm{m}}$, where {\\bf X$_{\\mathrm{ion}}$} is the ratio of H-like ions over He-like ions. As an example for Oxygen ($Z$=8) it corresponds to ratio of the relative ionic abundance of \\ion{O}{viii}/\\ion{O}{vii} ground state population.}\n\\label{1surG}\n\\end{figure*}\n\\clearpage\n%----------------------------------------------------------------------------------------\n\\begin{figure*}[h]\n\\begin{tabular}{cc}\n\\resizebox{7.15cm}{!}{\\includegraphics{ds1759_fig8a.ps}} & \\resizebox{7.25cm}{!}{\\includegraphics{ds1759_fig8d.ps}}\\\\ \n\\resizebox{7cm}{!}{\\includegraphics{ds1759_fig8b.ps}} & \\resizebox{7.45cm}{!}{\\includegraphics{ds1759_fig8e.ps}} \\\\\n\\resizebox{7.15cm}{!}{\\includegraphics{ds1759_fig8c.ps}} & \\resizebox{7.5cm}{!}{\\includegraphics{ds1759_fig8f.ps}}\\\\ \n\\end{tabular}\n\\caption{In case of pure photoionized plasmas (i.e. RR dominant at low temperature and DR dominant at high temperature), {\\bf ratio R (=z/(x+y))} is reported as a function of n$_{\\mathrm{e}}$ for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi}, and \\ion{Si}{xiii} at different electronic temperatures (T$_{\\mathrm{e}}$ in Kelvin). For low temperatures (the two first reported here: solid curves and dot-dashed curves), the value of {\\bf R} is independent of the value of {\\bf X$_{\\mathrm{ion}}$}. As the temperature increases, {\\bf X$_{\\mathrm{ion}}$} is high enough to maintain recombination dominant compared to collisional excitation from the ground level: $\\sim$ 10$^{2}$ and 10$^{3-4}$ (for increasing temperature: respectively for long-dashed curves and short-dashed curves).}\n\\label{Rphoto}\n\\end{figure*}\n\\clearpage\n%----------------------------------------------------------------------------------------\n\\begin{figure*}[h]\n\\begin{center}\n\\begin{tabular}{cc}\n\\resizebox{7cm}{!}{\\includegraphics{ds1759_fig9a.ps}} &\\resizebox{7.25cm}{!}{\\includegraphics{ds1759_fig9d.ps}}\\\\\n\\resizebox{7cm}{!}{\\includegraphics{ds1759_fig9b.ps}} &\\resizebox{7.35cm}{!}{\\includegraphics{ds1759_fig9e.ps}}\\\\ \n\\resizebox{7cm}{!}{\\includegraphics{ds1759_fig9c.ps}} &\\resizebox{7.35cm}{!}{\\includegraphics{ds1759_fig9f.ps}}\\\\ \n\\end{tabular}\n\\end{center}\n\\caption{In case of hybrid plasmas (partially photoionized: recombination plus collisional excitation from the ground level), the {\\bf ratio R (=z/(x+y))} is reported as a function of n$_{\\mathrm{e}}$ for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi}, and \\ion{Si}{xiii} at different values of {\\bf X$_{\\mathrm{ion}}$} (=H-like/He-like ionic fraction). {\\bf R} is calculated at the temperature corresponding to the maximum of the He-like ion abundance for a collisional plasma (see Arnaud \\& Rothenflug \\cite{Arnaud85}).\nSolid curves: the lowest values of {\\bf X$_{\\mathrm{ion}}$} corresponds to hybrid plasmas, and the highest value of {\\bf X$_{\\mathrm{ion}}$} to pure photoionized plasmas. Long-dashed curves: {\\bf X$_{\\mathrm{ion}}$} is equal to the ratio H-like/He-like in a case of collisional plasma (from Arnaud \\& Rothenflug \\cite{Arnaud85}). {\\it Note: for \\ion{C}{v}, \\ion{N}{vi} and \\ion{O}{vii} at these temperatures, the curves for X$_{\\mathrm{ion}}$=100 and 10\\,000 are indistinguishable}.}\n\\label{Rhybrid}\n\\end{figure*}\n\\clearpage\n%----------------------------------------------------------------------------------------\n\\begin{figure*}[h]\n\\begin{tabular}{cc}\n\\resizebox{7cm}{!}{\\includegraphics{ds1759_fig10a.ps}} &\\resizebox{7.15cm}{!}{\\includegraphics{ds1759_fig10b.ps}}\n\\end{tabular}\n\\caption{{\\it At left}: This figure reports for each ion treated in this paper the two decades (approximatively) where the ratio {\\bf R} is strongly sensitive to the density. {\\it At right}: the approximative range of temperatures for each ion where the plasma can be considered purely photoionized, independent of the {\\bf X$_{\\mathrm{ion}}$} value.}\n\\label{nedomaine}\n\\end{figure*}\n\\clearpage\n%----------------------------------------------------------------------------------------\n\\begin{figure*}[h]\n\\begin{tabular}{cc}\n\\resizebox{8cm}{!}{\\includegraphics{ds1759_fig11a.ps}} &\\resizebox{8cm}{!}{\\includegraphics{ds1759_fig11d.ps}}\\\\\n\\resizebox{8cm}{!}{\\includegraphics{ds1759_fig11b.ps}} &\\resizebox{8cm}{!}{\\includegraphics{ds1759_fig11e.ps}}\\\\\n\\resizebox{8cm}{!}{\\includegraphics{ds1759_fig11c.ps}} &\\resizebox{8cm}{!}{\\includegraphics{ds1759_fig11f.ps}}\\\\\n\\end{tabular}\n\\caption{\\ion{O}{vii} theoretical spectra constructed using the RGS (XMM) resolving power (E/$\\Delta$E) for three values of density (in cm$^{-3}$). This corresponds (approximatively) to the range where the ratio {\\bf R} is very sensitive to density. {\\bf z}: forbidden lines, {\\bf x+y}: intercombination lines and {\\bf w}: resonance line. {\\it At left}: ``hybrid plasma'' at T$_{\\mathrm{e}}$=1.5\\,10$^{6}$\\,K and X$_{\\mathrm{ion}}$=1; {\\it At right}: ``pure'' photoionized plasma at T$_{\\mathrm{e}}$=10$^{5}$\\,K (at this temperature this part of the spectra are independent of the value of X$_{\\mathrm{ion}}$, see Figure~\\ref{1surG}). {\\it Note: the intensities are normalized in order to have the sum of the lines equal to the unity}.}\n\\label{XMM}\n\\end{figure*}\n\\clearpage\n\n%***************************Table********************************\n%TABLE 1\n\\begin{table*}\n\\caption{Energy (in cm$^{-1}$) for the first 17 levels for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi} and \\ion{Si}{xiii} calculated by the SUPERSTRUCTURE code (except for the first seven levels which are from Vainshtein \\& Safronova 1985). Here X(Y) means X$\\times$10$^{Y}$.}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccccc}\n\\hline\n\\hline\n%% & & & & & & & \\\\\n% & & & & & & & \\\\\ni &conf &level & \\ion{C}{v} & \\ion{N}{vi} & \\ion{O}{vii} & \\ion{Ne}{ix} & \\ion{Mg}{xi} & \\ion{Si}{xiii}\\\\\n%% & & & & & & & \\\\\n\\hline \n\\hline\n% & & & & & & & \\\\\n1 &1s$^{2}$&$^{1}\\mathrm{S}_{0}$& 0. & 0. &0. & 0. & 0. & 0. \\\\\n2 &1s\\,2s &$^{3}\\mathrm{S}_{1}$&2.4114\\,(+6)&3.3859\\,(+6) &4.5253\\,(+6) &7.2996\\,(+6) &10.7358\\,(+6) &14.8357\\,(+6) \\\\\n3 &1s\\,2p &$^{3}\\mathrm{P}_{0}$&2.4553\\,(+6)&3.4383\\,(+6) &4.5863\\,(+6) &7.3779\\,(+6) &10.8317\\,(+6) &14.9495\\,(+6) \\\\\n4 &1s\\,2p &$^{3}\\mathrm{P}_{1}$&2.4552\\,(+6)&3.4383\\,(+6) &4.5863\\,(+6) &7.3782\\,(+6) &10.8325\\,(+6) &14.9513\\,(+6) \\\\\n5 &1s\\,2p &$^{3}\\mathrm{P}_{2}$&2.4554\\,(+6)&3.4386\\,(+6) &4.5869\\,(+6) &7.3798\\,(+6) &10.8361\\,(+6) &14.9585\\,(+6) \\\\\n6 &1s\\,2s &$^{1}\\mathrm{S}_{0}$&2.4551\\,(+6)&3.4393\\,(+6) &4.5884\\,(+6) &7.3824\\,(+6) &10.8385\\,(+6) &14.9585\\,(+6) \\\\\n7 &1s\\,2p &$^{1}\\mathrm{P}_{1}$&2.4833\\,(+6)&3.4737\\,(+6) &4.6291\\,(+6) &7.4361\\,(+6) &10.9062\\,(+6) &15.0417\\,(+6) \\\\\n8 &1s\\,3s &$^{3}\\mathrm{S}_{1}$&2.8239\\,(+6)&3.9765\\,(+6) &5.3251\\,(+6) &8.6105\\,(+6) &12.6824\\,(+6) &17.5435\\,(+6) \\\\\n9 &1s\\,3p &$^{3}\\mathrm{P}_{0}$&2.8352\\,(+6)&3.9902\\,(+6) &5.3441\\,(+6) &8.6314\\,(+6) &12.7081\\,(+6) &17.5741\\,(+6) \\\\\n10&1s\\,3p &$^{3}\\mathrm{P}_{1}$&2.8352\\,(+6)&3.9903\\,(+6) &5.3412\\,(+6) &8.6316\\,(+6) &12.7087\\,(+6) &17.5752\\,(+6) \\\\\n11&1s\\,3p &$^{3}\\mathrm{P}_{2}$&2.8353\\,(+6)&3.9904\\,(+6) &5.3414\\,(+6) &8.6322\\,(+6) &12.7099\\,(+6) &17.5775\\,(+6) \\\\\n12&1s\\,3s &$^{1}\\mathrm{S}_{0}$&2.8401\\,(+6)&3.9953\\,(+6) &5.3463\\,(+6) &8.6368\\,(+6) &12.7136\\,(+6) &17.5795\\,(+6) \\\\\n13&1s\\,3d &$^{3}\\mathrm{D}_{1}$&2.8408\\,(+6)&3.9973\\,(+6) &5.3497\\,(+6) &8.6433\\,(+6) &12.7238\\,(+6) &17.5942\\,(+6) \\\\\n14&1s\\,3d &$^{3}\\mathrm{D}_{2}$&2.8408\\,(+6)&3.9973\\,(+6) &5.3497\\,(+6) &8.6433\\,(+6) &12.7239\\,(+6) &17.5945\\,(+6) \\\\\n15&1s\\,3d &$^{3}\\mathrm{D}_{3}$&2.8408\\,(+6)&3.9973\\,(+6) &5.3498\\,(+6) &8.6435\\,(+6) &12.7244\\,(+6) &17.5953\\,(+6) \\\\\n16&1s\\,3d &$^{1}\\mathrm{D}_{2}$&2.8411\\,(+6)&3.9977\\,(+6) &5.3502\\,(+6) &8.6411\\,(+6) &12.7251\\,(+6) &17.5962\\,(+6) \\\\\n17&1s\\,3p &$^{1}\\mathrm{P}_{1}$&2.8433\\,(+6)&4.0004\\,(+6) &5.3534\\,(+6) &8.6480\\,(+6) &12.7294\\,(+6) &17.6005\\,(+6) \\\\\n%% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\label{energielevel}\n\\end{table*}\n\n\n%TABLE 2\n\\begin{table*}[h]\n\\caption{Radiative transitions probabilities (A$_{\\mathrm{ki}}$ in s$^{-1}$, i=1,7; k=2,17) for \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi} and \\ion{Si}{xiii} calculated by the SUPERSTRUCTURE code, except for marked values (a) which are from Lin et al. (1977) and (b) which are from Mewe \\& Schrijver (1978a). i and k correspond respectively to the lower and the upper level of the transition.}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{cccccccc}\n\\hline\n\\hline\n%% & & & & & & & \\\\\n & & \\multicolumn{6}{c}{A$_{ki}$ (s$^{-1}$)} \\\\\n%% & & & & & & & \\\\\n\\cline{3-8}\n%% & & & & & & & \\\\\n i & k & \\ion{C}{v} & \\ion{N}{vi} & \\ion{O}{vii} & \\ion{Ne}{ix} & \\ion{Mg}{xi} & \\ion{Si}{xiii}\\\\\n\\hline\n\\hline\n%% & & & & & & & \\\\\n1 & 2 &4.960\\,(+01)$^{\\mathrm{a}}$&2.530\\,(+02)$^{\\mathrm{b}}$ & 1.060\\,(+03)$^{\\mathrm{a}}$ &1.100\\,(+04)$^{\\mathrm{a}}$ & 7.330\\,(+04)$^{\\mathrm{a}}$ &3.610\\,(+05)$^{\\mathrm{a}}$\\\\\n1 & 4 &2.159\\,(+07) &1.100\\,(+08) &4.447\\,(+08) &4.470\\,(+09) & 2.867(+10) & 1.345\\,(+11) \\\\\n1 & 5 &2.650\\,(+04)$^{\\mathrm{a}}$&1.030\\,(+05)$^{\\mathrm{b}}$ &3.330\\,(+05)$^{\\mathrm{a}}$ &2.270\\,(+06)$^{\\mathrm{a}}$ & 1.060\\,(+07)$^{\\mathrm{a}}$ & 3.890\\,(+07)$^{\\mathrm{a}}$\\\\\n1 & 6 &3.310\\,(+05)$^{\\mathrm{a}}$&9.430\\,(+05)$^{\\mathrm{b}}$ &2.310\\,(+06)$^{\\mathrm{a}}$ &1.000\\,(+07)$^{\\mathrm{a}}$ & 3.220\\,(+07)$^{\\mathrm{a}}$ & 8.470\\,(+07)$^{\\mathrm{a}}$\\\\\n1 & 7 &9.477\\,(+11) &1.911\\,(+12) &3.467\\,(+12) &9.197\\,(+12) & 2.010\\,(+13) &3.857\\,(+13) \\\\\n1 & 10 &6.939\\,(+06) & 3.525\\,(+07) &1.423\\,(+08) &1.429\\,(+09) & 9.141\\,(+09) &4.268\\,(+10) \\\\\n1 & 17 &3.105\\,(+11) &6.061\\,(+11) & 1.073\\,(+12) &2.752\\,(+12) & 5.877\\,(+12) & 1.107\\,(+13) \\\\\n2 & 3 &5.616\\,(+07) &6.717\\,(+07) &7.818\\,(+07) &1.003\\,(+08) & 1.228\\,(+08) &1.460\\,(+08) \\\\\n2 & 4 &5.655\\,(+07) &6.794\\,(+07) &7.956\\,(+07) & 1.039\\,(+08) & 1.304\\,(+08) &1.602\\,(+08) \\\\\n2 & 5 &5.735\\,(+07) &6.955\\,(+07) &8.249\\,(+07) &1.118\\,(+08) & 1.486\\,(+08) &1.977\\,(+08) \\\\\n2 & 9 &1.376\\,(+10) & 2.872\\,(+10) & 5.342\\,(+10) &1.466\\,(+11) & 3.280\\,(+11) &6.406\\,(+11) \\\\\n2 & 10 &1.375\\,(+10) &2.870\\,(+10) & 5.337\\,(+10) &1.464\\,(+11) & 3.269\\,(+11) &6.366\\,(+11) \\\\\n2 & 11 &1.374\\,(+10) &2.867\\,(+10) &5.329\\,(+10) &1.461\\,(+11) & 3.262\\,(+11) &6.360\\,(+11) \\\\\n2 & 17 &2.898\\,(+05) & 1.607\\,(+06) &6.902\\,(+06) &7.514\\,(+07) & 5.061\\,(+08) & 2.452\\,(+09) \\\\\n3 & 8 &7.088\\,(+08) &1.366\\,(+09) & 2.398\\,(+09) & 6.079\\,(+09) & 1.290\\,(+10) & 2.426\\,(+10) \\\\\n3 & 13 &2.349\\,(+10) & 4.847\\,(+10) & 8.947\\,(+10) & 2.432\\,(+11) & 5.408\\,(+11) & 1.052\\,(+12) \\\\\n4 & 8 &2.129\\,(+09) & 4.106\\,(+09)& 7.211\\,(+09) &1.831\\,(+10) &3.890\\,(+10) & 7.315\\,(+10) \\\\\n4 & 13 &1.761\\,(+10) & 3.634\\,(+10) & 6.706\\,(+10) & 1.822\\,(+11) & 4.046\\,(+11) & 7.856\\,(+11) \\\\\n4 & 14 &3.165\\,(+10) &6.519\\,(+10) &1.199\\,(+11) & 3.213\\,(+11) & 6.967\\,(+11) &1.314\\,(+12) \\\\\n4 & 16 &5.150\\,(+07) &2.346\\,(+08) &8.525\\,(+08) &6.862\\,(+09) & 3.311\\,(+10) & 1.073\\,(+11) \\\\\n5 & 8 &3.557\\,(+09) & 6.870\\,(+09) & 1.208(+10) & 3.080(+10) & 6.583(+10) & 1.248(+11) \\\\\n5 & 13 &1.174\\,(+09) & 2.421\\,(+09) & 4.468(+09) &1.213(+10) & 2.695(+10) & 5.240(+10) \\\\\n5 & 14 &1.054\\,(+10) & 2.169\\,(+10) & 3.983(+10) &1.061(+11) & 2.268(+11) & 4.173(+11) \\\\\n5 & 15 &4.225\\,(+10) & 8.718\\,(+10) & 1.609(+11) &4.369(+11) & 9.708(+11) & 1.887(+12) \\\\\n5 & 16 &2.214\\,(+07) & 1.025\\,(+08) & 3.784(+08) &3.145(+09) &1.582(+10) &5.438(+10) \\\\\n6 & 7 &5.875\\,(+06) &9.199\\,(+06) & 1.307\\,(+07) &2.266\\,(+07) & 3.541\\,(+07) & 5.286\\,(+07) \\\\\n6 & 10 &4.013\\,(+05) &2.088\\,(+06) & 8.582\\,(+06) &8.838\\,(+07) & 5.759\\,(+08) &2.730\\,(+09) \\\\\n6 & 17 &1.457\\,(+10) & 2.982\\,(+10) & 5.478\\,(+10) &1.482\\,(+11) & 3.286\\,(+11) & 6.371\\,(+11) \\\\\n7 & 12 &5.646\\,(+09) &1.145\\,(+10) & 2.071\\,(+10) &5.436\\,(+10) & 1.175\\,(+11) &2.232\\,(+11) \\\\\n7 & 13 &3.673\\,(+05) &1.940\\,(+06) & 8.054\\,(+06) &8.401\\,(+07) & 5.522\\,(+08) &2.638\\,(+09) \\\\\n7 & 14 &6.862\\,(+07) &3.164\\,(+08) & 1.162\\,(+09) &9.519\\,(+09) & 4.675\\,(+10) &1.547\\,(+11) \\\\\n7 & 16 &3.950\\,(+10) &8.194\\,(+10) & 1.516\\,(+11) &4.092\\,(+11) & 8.896\\,(+11) & 1.674\\,(+12) \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\label{Aki1}\n\\end{table*}\n%\\newpage\n\n%TABLE 3\n\\begin{table*}[h]\n\\caption{Radiative and dielectronic recombination rates (respectively RR and DR) calculated in this work (in cm$^{3}$\\,s$^{-1}$) for each $n$=2 level of \\ion{C}{v}.}\n\\label{cascadeC6}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\nT$_{\\mathrm{e}}$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n%% & & & & & & \\\\\n\\hline\n\\hline\n 5.0\\,(+04) & 2.43\\,(-13)$^{\\mathrm{a}}$& 7.13\\,(-14)& 2.14\\,(-13) & 3.57\\,(-13) & 8.09\\,(-14) &2.14\\,(-13) \\\\\n & 8.97\\,(-13)$^{\\mathrm{b}}$& 2.51\\,(-13)& 7.51\\,(-13) & 1.25\\,(-12) & 1.69\\,(-14) &6.87\\,(-13) \\\\\n & 0$^{\\mathrm{c}}$ & 0 & 0 & 0 & 0 & 0 \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 1.0\\,(+05) & 1.71\\,(-13) &4.85\\,(-14) & 1.46\\,(-13) & 2.43\\,(-13) & 5.69\\,(-14) &1.46\\,(-13) \\\\\n & 5.78\\,(-13) & 1.43\\,(-13) & 4.30\\,(-13) & 7.16\\,(-13) & 1.09\\,(-14) &3.89\\,(-13) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 2.0\\,(+05) & 1.20\\,(-13) & 3.20\\,(-14) & 9.60\\,(-14) & 1.60\\,(-13) & 3.99\\,(-14) & 9.60\\,(-14) \\\\\n & 3.58\\,(-13) & 7.80\\,(-14) & 2.34\\,(-13) & 3.89\\,(-13) & 6.70\\,(-15) & 2.09\\,(-13) \\\\\n & 4.32\\,(-19) &1.34\\,(-20) & 3.81\\,(-20) & 5.13\\,(-20) & 1.33\\,(-19) & 5.61(-19) \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 5.0\\,(+05) & 7.35\\,(-14) & 1.71\\,(-14) & 5.12\\,(-14) & 8.54\\,(-14) & 2.45\\,(-14) & 5.12\\,(-14) \\\\\n & 1.75\\,(-13) & 3.19\\,(-14) & 9.58\\,(-14) & 1.60\\,(-13) & 3.30\\,(-15) & 8.38\\,(-14) \\\\\n & 2.75\\,(-15) & 4.72\\,(-16) & 1.28\\,(-15) & 1.55\\,(-15) & 6.77\\,(-16) & 4.56\\,(-15) \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 1.0\\,(+06) & 4.96\\,(-14) & 9.77\\,(-15) & 2.93\\,(-14) & 4.89\\,(-14) & 1.65\\,(-14) & 2.93\\,(-14) \\\\\n & 9.64\\,(-14) & 1.53\\,(-14) & 4.60\\,(-14) & 7.61\\,(-14) & 1.80\\,(-15) & 3.95\\,(-14) \\\\\n & 3.72\\,(-14) & 8.94\\,(-15) & 2.42\\,(-14) & 2.85\\,(-14) & 8.17\\,(-15) & 6.92\\,(-14) \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 2.0\\,(+06) & 3.24\\,(-14) & 5.10\\,(-15) & 1.53\\,(-14) & 2.55\\,(-14) & 1.08\\,(-14) & 1.53\\,(-14) \\\\\n & 4.98\\,(-14) & 7.10\\,(-15) & 2.12\\,(-14) & 3.53\\,(-14) & 9.00\\,(-16) & 1.79\\,(-14) \\\\\n & 8.57\\,(-14) & 2.32\\,(-14) & 6.26\\,(-14) & 7.31\\,(-14) & 1.80\\,(-14) & 1.68\\,(-13) \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$] RR direct contribution. \n\\item[$^{\\mathrm{b}}$] RR upper level radiative cascade contribution from the n$>$2 levels. \n\\item[$^{\\mathrm{c}}$] DR direct plus upper level radiative cascade from the n$>$2 levels contributions (when the value is equal to zero this means that the DR rate is negligible compared to the RR rates).\n\\end{list}\nNote: a+b+c represent the total recombination rates.\n\\end{table*}\n%\\clearpage\n\n\n%TABLE 4\n\\begin{table*}[h]\n\\caption{Same as Table~\\ref{cascadeC6} for \\ion{N}{vi}.}\n\\label{cascadeC6}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\nT$_{\\mathrm{e}}$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n%% & & & & & & \\\\\n\\hline\n\\hline\n 7.0\\,(+04)& 2.86\\,(-13) & 8.42\\,(-14) & 2.53\\,(-13) & 4.21\\,(-13) & 9.55\\,(-14) &2.53\\,(-13) \\\\\n & 1.07\\,(-12) & 2.94\\,(-13) & 8.77\\,(-13) & 1.47\\,(-12) & 2.35\\,(-14) &8.07\\,(-13) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 1.4\\,(+05)& 2.02\\,(-13) &5.73\\,(-14) & 1.72\\,(-13) & 2.86\\,(-13) & 6.72\\,(-14) &1.72\\,(-13) \\\\\n & 6.91\\,(-13) & 1.68\\,(-13) & 5.04\\,(-13) & 8.44\\,(-13) & 1.52\\,(-14) &4.58\\,(-13) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 2.8\\,(+05)& 1.41\\,(-13) & 3.78\\,(-14) & 1.13\\,(-13) & 1.89\\,(-13) & 4.71\\,(-14) & 1.13\\,(-13) \\\\\n & 4.28\\,(-13) & 9.12\\,(-14) & 2.74\\,(-13) & 4.56\\,(-13) & 9.30\\,(-15) & 2.46\\,(-13) \\\\\n & 8.56\\,(-18) &3.67\\,(-20) & 1.34\\,(-19) & 2.38\\,(-19) & 2.90\\,(-18) & 1.17\\,(-17) \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 7.0\\,(+05) & 8.68\\,(-14) & 2.02\\,(-14) & 6.05\\,(-14) & 1.01\\,(-13) & 2.89\\,(-14) & 6.05\\,(-14) \\\\\n & 2.10\\,(-13) & 3.72\\,(-14) & 1.12\\,(-13) & 1.86\\,(-13) & 4.60\\,(-15) & 9.85\\,(-14) \\\\\n & 6.58\\,(-15) & 5.98\\,(-16) & 1.50\\,(-15) & 1.75\\,(-15) & 2.00\\,(-15) & 9.76\\,(-15) \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 1.4\\,(+06) & 5.86\\,(-14) & 1.15\\,(-14) & 3.46\\,(-14) & 5.76\\,(-14) & 1.95\\,(-14) & 3.46\\,(-14) \\\\\n & 1.15\\,(-13) & 1.79\\,(-14) & 5.36\\,(-14) & 8.94\\,(-14) & 2.50\\,(-15) & 4.64\\,(-14) \\\\\n & 4.88\\,(-14) & 1.03\\,(-14) & 2.54\\,(-14) & 2.82\\,(-14) & 1.26\\,(-14) & 8.57\\,(-14) \\\\\n% & & & & & & \\\\\n\\hline\n%% & & & & & & \\\\\n\n 2.8\\,(+06) & 3.82\\,(-14) & 6.02\\,(-15) & 1.81\\,(-14) & 3.01\\,(-14) & 1.27\\,(-14) & 1.81\\,(-14) \\\\\n & 5.97\\,(-14) & 8.18\\,(-15) & 2.46\\,(-14) & 4.11\\,(-14) & 1.30\\,(-15) & 2.09\\,(-14) \\\\\n & 9.17\\,(-14) & 2.56\\,(-14) & 6.27\\,(-14) & 6.85\\,(-14) & 2.16\\,(-14) & 1.76\\,(-13) \\\\\n%% & & & & & & \\\\\n% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table*}\n%\\clearpage\n\n%TABLE 5\n\\begin{table*}[h]\n\\caption{Same as Table~\\ref{cascadeC6} for \\ion{O}{vii}.}\n\\label{cascadeO8}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\nT$_{\\mathrm{e}}$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n%% & & & & & & \\\\\n\\hline\n\\hline\n 9.0\\,(+04) & 3.36\\,(-13) & 9.90\\,(-14) & 2.97\\,(-13) & 4.95\\,(-13) & 1.12\\,(-13) & 2.97\\,(-13) \\\\\n & 1.24\\,(-12) & 3.51\\,(-13) & 1.05\\,(-12) & 1.75\\,(-12) & 2.50\\,(-14) & 9.63\\,(-13) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n%% & & & & & & \\\\\n \n 1.8\\,(+05) & 2.37\\,(-13) & 6.74\\,(-14) & 2.02\\,(-13) & 3.37\\,(-13) & 7.89\\,(-14) &2.02\\,(-13) \\\\\n & 8.03\\,(-13) & 2.02\\,(-13) & 6.05\\,(-13) & 1.01\\,(-12) & 1.63\\,(-14) &5.50\\,(-13) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n%% & & & & & & \\\\\n \n3.6\\,(+05) & 1.66\\,(-13) & 4.45\\,(-14) & 1.34\\,(-13) & 2.23\\,(-13) & 5.53\\,(-14) & 1.34\\,(-13) \\\\\n & 4.95\\,(-13) & 1.10\\,(-13) & 3.29\\,(-13) & 5.50\\,(-13) & 1.01\\,(-14) & 2.96\\,(-13) \\\\\n & 9.67\\,(-19) & 1.86\\,(-20) & 5.19\\,(-20) & 6.73\\,(-20) & 3.42\\,(-19) & 1.36\\,(-18) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 9.0\\,(+05) & 1.02\\,(-13) & 2.39\\,(-14) & 7.16\\,(-14) & 1.19\\,(-13) & 3.40\\,(-14) & 7.16\\,(-14) \\\\\n & 2.44\\,(-13) & 4.52\\,(-14) & 1.35\\,(-13) & 2.27\\,(-13) & 4.90\\,(-15) & 1.19\\,(-13) \\\\\n & 3.55\\,(-15) & 4.90(-16) & 1.32\\,(-15) & 1.54\\,(-15) & 1.05\\,(-15) & 6.02\\,(-15) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 1.8\\,(+06) & 6.90\\,(-14) &1.37\\,(-14) & 4.11\\,(-14) & 6.85\\,(-14) & 2.30\\,(-14) & 4.11\\,(-14) \\\\\n & 1.34\\,(-13) & 2.18\\,(-14) & 6.49\\,(-14) & 1.09\\,(-13) & 2.70\\,(-15) & 5.65\\,(-14) \\\\\n & 3.90\\,(-14) & 8.49\\,(-15) & 2.26\\,(-14) &2.57\\,(-14) & 1.01\\,(-14) & 7.43\\,(-14) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 3.6\\,(+06) &4.51\\,(-14) & 7.19\\,(-15) & 2.16\\,(-14) & 3.60\\,(-14) & 1.50\\,(-14) & 2.16\\,(-14) \\\\\n &6.99\\,(-14) & 1.00\\,(-14) & 3.01\\,(-14) & 5.02\\,(-14) & 1.40\\,(-15) & 2.56\\,(-14) \\\\\n &8.19\\,(-14) & 2.11\\,(-14) & 5.60\\,(-14) & 6.28\\,(-14) & 1.98\\,(-14) & 1.65\\,(-13) \\\\\n%% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table*}\n\n%TABLE 6\n\\begin{table*}[h]\n\\caption{Same as Table~\\ref{cascadeC6} for \\ion{Ne}{ix}.}\n\\label{cascadeNe9}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\n & & & & & & \\\\\nT$_{\\mathrm{e}}$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n%% & & & & & & \\\\\n\\hline\n\\hline\n 1.4\\,(+05) &4.33\\,(-13) & 1.27\\,(-13) & 3.82\\,(-13) & 6.37\\,(-13) & 1.44\\,(-13) & 3.82\\,(-13) \\\\\n & 1.59\\,(-12) & 4.57\\,(-13) & 1.37\\,(-12) & 2.28\\,(-12) & 3.40\\,(-14) & 1.26\\,(-12) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n \n 2.8\\,(+05) &3.05\\,(-13) & 8.69\\,(-14) & 2.61\\,(-13) & 4.35\\,(-13) & 1.02\\,(-13) & 2.61\\,(-13) \\\\\n & 1.02\\,(-12) & 2.62\\,(-13) & 7.89\\,(-13) & 1.31\\,(-12) & 2.20\\,(-14) & 7.19\\,(-13) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n%% & & & & & & \\\\\n \n 5.6\\,(+05) & 2.14\\,(-13) & 5.75\\,(-14) & 1.73\\,(-13) &2.88\\,(-13) & 7.12\\,(-14) & 1.73\\,(-13) \\\\\n & 6.35\\,(-13) & 1.43\\,(-13) & 4.31\\,(-13) & 7.22\\,(-13) & 1.36\\,(-14) & 3.88\\,(-13) \\\\\n & 1.22\\,(-18) & 1.19\\,(-20) & 3.74\\,(-20) & 5.73\\,(-20) & 5.29\\,(-19) & 2.01\\,(-18) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 1.4\\,(+06) & 1.31\\,(-13) & 3.09\\,(-14) & 9.28\\,(-14) & 1.55\\,(-13) & 4.38\\,(-14) & 9.28\\,(-14) \\\\\n & 3.15\\,(-13) & 5.93\\,(-14) & 1.78\\,(-13) & 2.97\\,(-13) & 6.70\\,(-15) & 1.57\\,(-13) \\\\\n & 3.65\\,(-15) & 2.68\\,(-16) & 8.31\\,(-16) & 1.19\\,(-15) & 1.38\\,(-15) & 6.78\\,(-15) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 2.8\\,(+06) & 8.90\\,(-14) & 1.78\\,(-14) & 5.35\\,(-14) & 8.91\\,(-14) & 2.97\\,(-14) & 5.35\\,(-14) \\\\\n & 1.73\\,(-13) & 2.86\\,(-14) & 8.55\\,(-14) & 1.43\\,(-13) & 3.60\\,(-15) & 7.45\\,(-14) \\\\\n & 3.66\\,(-14) & 4.47\\,(-15) & 1.38\\,(-14) & 1.96\\,(-14) & 1.23\\,(-14) & 7.45\\,(-14) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 5.6\\,(+06) & 5.83\\,(-14) & 9.39\\,(-15) & 2.82\\,(-14) & 4.70\\,(-14) & 1.94\\,(-14) & 2.82\\,(-14) \\\\\n & 8.97\\,(-14) & 1.32\\,(-14) & 3.96\\,(-14) & 6.60\\,(-14) & 1.90\\,(-15) & 3.40\\,(-14) \\\\\n & 7.37\\,(-14) & 1.09\\,(-14) & 3.37\\,(-14) & 4.75\\,(-14) & 2.32\\,(-14) & 1.57\\,(-13) \\\\\n%% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table*}\n\n%TABLE 7\n\\begin{table*}[h]\n\\caption{Same as Table~\\ref{cascadeC6} for \\ion{Mg}{xi}.}\n\\label{cascadeMg11}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\nT$_{\\mathrm{e}}$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n%% & & & & & & \\\\\n\\hline\n\\hline\n 2.0\\,(+05) &5.30\\,(-13) & 1.56\\,(-13) & 4.69\\,(-13) & 7.82\\,(-13) & 1.77\\,(-13) & 4.69\\,(-13) \\\\\n &1.94\\,(-12) & 5.65\\,(-13) & 1.70\\,(-12) & 2.83\\,(-12) & 4.30\\,(-14) & 1.56\\,(-12) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n%% & & & & & & \\\\\n \n 4.0\\,(+05) & 3.74\\,(-13) & 1.07\\,(-13) & 3.20\\,(-13) & 5.34\\,(-13) &1.25\\,(-13) &3.20\\,(-13) \\\\\n & 1.25\\,(-12) & 3.25\\,(-13) & 9.80\\,(-13) & 1.63\\,(-12) & 2.80\\,(-14) &8.90\\,(-13) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n%% & & & & & & \\\\\n \n 8.0\\,(+05) & 2.62\\,(-13) & 7.07\\,(-14) & 2.12\\,(-13) & 3.54\\,(-13) & 8.74\\,(-14) & 2.12\\,(-13) \\\\\n & 7.78\\,(-13) & 1.78\\,(-13) & 5.36\\,(-13) & 8.96\\,(-13) & 1.76\\,(-14) & 4.85\\,(-13) \\\\\n & 1.19\\,(-18) & 7.95\\,(-21) & 2.92\\,(-20) & 4.91\\,(-20) & 6.68\\,(-19) & 2.45\\,(-18) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 2.0\\,(+06) & 1.61\\,(-13) & 3.81\\,(-14) & 1.14\\,(-13) & 1.91\\,(-13) & 5.38\\,(-14) & 1.14\\,(-13) \\\\\n & 3.85\\,(-13) &7.39\\,(-14) & 2.22\\,(-13) & 3.70\\,(-13) & 8.60\\,(-15) & 1.98\\,(-13) \\\\\n & 3.36\\,(-15) & 1.71\\,(-16) & 6.40\\,(-16) & 9.60\\,(-16) & 1.61\\,(-15) & 7.10\\,(-15) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 4.0\\,(+06) & 1.09\\,(-13) & 2.21\\,(-14) & 6.62\\,(-14) & 1.10\\,(-13) & 3.64\\,(-14) & 6.62\\,(-14) \\\\\n & 2.13\\,(-13) & 3.56\\,(-14) & 1.07\\,(-13) & 1.79\\,(-13) & 4.80\\,(-15) & 9.38\\,(-14) \\\\\n & 3.31\\,(-14) & 2.83\\,(-15) & 1.07\\,(-14) & 1.59\\,(-14) & 1.36\\,(-14) & 7.11\\,(-14) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 8.0\\,(+06) & 7.17\\,(-14) & 1.17\\,(-14) & 3.50\\,(-14) & 5.83\\,(-14) & 2.39\\,(-14) & 3.50\\,(-14) \\\\\n & 1.11\\,(-13) & 1.64\\,(-14) & 4.95\\,(-14) & 8.27\\,(-14) & 2.50\\,(-15) & 4.27\\,(-14) \\\\\n & 6.62\\,(-14) & 6.90(\\,-15) & 2.62\\,(-14) & 3.88\\,(-14) & 2.47\\,(-14) & 1.44\\,(-13) \\\\\n%\\hline\n%% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table*}\n\n%TABLE 8\n\\begin{table*}[h]\n\\caption{Same as Table~\\ref{cascadeC6} for \\ion{Si}{xiii}.}\n\\label{cascadeSi13}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\nT$_{\\mathrm{e}}$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n%% & & & & & & \\\\\n\\hline\n\\hline\n 2.8\\,(+05) & 6.23\\,(-13) & 1.84\\,(-13) & 5.52\\,(-13) & 9.19\\,(-13) & 2.08\\,(-13) & 5.52\\,(-13) \\\\\n & 2.25\\,(-12) & 6.65\\,(-13) & 2.00\\,(-12) & 3.33\\,(-12) & 5.30\\,(-14) & 1.85\\,(-12) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n%% & & & & & & \\\\\n \n 5.5\\,(+05) & 4.39\\,(-13) & 1.25\\,(-13) & 3.76\\,(-13) & 6.27\\,(-13) & 1.46\\,(-13) & 3.76\\,(-13) \\\\\n & 1.44\\,(-12) & 3.84\\,(-13) & 1.15\\,(-12) & 1.92\\,(-12) & 3.50\\,(-14) & 1.05\\,(-12) \\\\\n & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n%% & & & & & & \\\\\n \n 1.1\\,(+06) & 3.08\\,(-13) & 8.32\\,(-14) & 2.49\\,(-13) & 4.16\\,(-13) & 1.03\\,(-13) & 2.49\\,(-13) \\\\\n & 8.92\\,(-13) & 2.10\\,(-13) & 6.32\\,(-13) & 1.05\\,(-12) & 2.10\\,(-14) & 5.74\\,(-13) \\\\\n & 1.29\\,(-18) & 8.47\\,(-21) &3.32\\,(-20) & 6.78\\,(-20) &9.70\\,(-19) & 3.46\\,(-18) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 2.8\\,(+06) & 1.90\\,(-13) & 4.49\\,(-14) & 1.35\\,(-13) & 2.24\\,(-13) & 6.32\\,(-14) & 1.35\\,(-13) \\\\\n & 4.45\\,(-13) & 8.71\\,(-14) & 2.61\\,(-13) & 4.37\\,(-13) & 1.06\\,(-14) &2.34\\,(-13) \\\\\n & 3.43\\,(-15) & 1.77\\,(-16) &6.55\\,(-16) &9.75\\,(-16) & 2.09\\,(-15 ) & 8.56\\,(-15) \\\\\n\\hline\n%% & & & & & & \\\\\n \n 5.5\\,(+06) & 1.29\\,(-13) & 2.59\\,(-14) & 7.78\\,(-14) & 1.30\\,(-13) & 4.28\\,(-14) & 7.78\\,(-14) \\\\\n & 2.46\\,(-13) & 4.20\\,(-14) & 1.26\\,(-13) & 2.11\\,(-13) & 5.90\\,(-15) & 1.11\\,(-13) \\\\\n & 2.97\\,(-14) & 2.50\\,(-15) & 9.28\\,(-15) & 1.35\\,(-14) & 1.48\\,(-14) & 6.93\\,(-14) \\\\ \n\\hline\n%% & & & & & & \\\\\n \n 1.1(+07) & 8.43\\,(-14) & 1.37\\,(-14) & 4.12\\,(-14) &6.86\\,(-14) & 2.81\\,(-14) &4.12\\,(-14) \\\\\n & 1.29\\,(-13) & 1.94\\,(-14) & 5.83\\,(-14) & 9.74\\,(-14) & 3.10\\,(-15) &5.07\\,(-14) \\\\\n & 5.84\\,(-14) & 5.93\\,(-15) & 2.21\\,(-14) & 3.20\\,(-14) & 2.55\\,(-14) & 1.30\\,(-13) \\\\\n%\\hline\n%% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table*}\n\n%TABLE 9\n\\begin{table*}\n\\caption{Effective collisions strengths ($\\Upsilon$) for each 1s$^{2}$--1s2l transition of \\ion{C}{v}.}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\nT$_{\\mathrm{e}}$/$Z^3$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n\\hline\n\\hline\n 400 &8.48\\,(-03)$^{\\mathrm{a}}$& 4.95\\,(-03) & 1.48\\,(-02) &2.47\\,(-02) & 1.42\\,(-02) &4.05\\,(-02) \\\\\n &7.53\\,(-06)$^{\\mathrm{b}}$& 7.67\\,(-07) & 2.31\\,(-06) &3.88\\,(-06) & 4.32\\,(-07) &9.86\\,(-06) \\\\\n\\hline\n%% & & & & & & \\\\\n\n 600 &9.09\\,(-03) & 5.04\\,(-03) & 1.51\\,(-02) &2.51\\,(-02) & 1.46\\,(-02) &4.26\\,(-02) \\\\\n &8.96\\,(-05) & 6.94\\,(-06) & 2.09\\,(-05) &3.50\\,(-05) & 4.40\\,(-06) &7.09\\,(-05) \\\\\n\\hline\n%% & & & & & & \\\\\n\n 900 &9.46\\,(-03) & 5.02\\,(-03) & 1.50\\,(-02) &2.51\\,(-02) & 1.50\\,(-02) &4.48\\,(-02) \\\\\n &4.76\\,(-04) & 3.12\\,(-05) & 9.37\\,(-05) &1.57\\,(-04) & 2.28\\,(-05) &2.73\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n 1\\,350 &9.39\\,(-03) & 4.85\\,(-03) & 1.46\\,(-02) &2.42\\,(-02) & 1.52\\,(-02) &4.76\\,(-02) \\\\\n &1.45\\,(-03) & 8.59\\,(-05) & 2.58\\,(-04) &4.32\\,(-04) & 7.53\\,(-05) &6.95\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n 2\\,000 &8.91\\,(-03) & 4.56\\,(-03) & 1.37\\,(-02) & 2.27\\,(-02) & 1.55\\,(-02) &5.13\\,(-02) \\\\\n &2.97\\,(-03) & 1.64\\,(-04) & 4.93\\,(-04) & 8.26\\,(-04) & 1.80\\,(-04) &1.31\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n 3\\,000 &8.14\\,(-03) & 4.15\\,(-03) & 1.25\\,(-02) & 2.08\\,(-02) & 1.58\\,(-02) & 5.65\\,(-02) \\\\\n &4.75\\,(-03) & 2.51\\,(-04) & 7.54\\,(-04) & 1.26\\,(-03) & 3.62\\,(-04) & 2.10\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n 4\\,500 &7.23\\,(-03) & 3.68\\,(-03) & 1.11\\,(-02) & 1.84\\,(-02) & 1.62\\,(-02) & 6.40\\,(-02) \\\\\n &6.23\\,(-03) & 3.20\\,(-04) & 9.60\\,(-04) & 1.61\\,(-03) & 6.36\\,(-04) & 2.97\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n 6\\,700 &6.30\\,(-03) & 3.20\\,(-03) & 9.60\\,(-03) & 1.60\\,(-02) & 1.68\\,(-02) & 7.38\\,(-02) \\\\\n &7.08\\,(-03) & 3.56\\,(-04) & 1.07\\,(-03) & 1.79\\,(-03) & 1.01\\,(-03) & 3.88\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n 10\\,000 &5.37\\,(-03) & 2.70\\,(-03) & 8.09\\,(-03) & 1.34\\,(-02) & 1.76\\,(-02) & 8.70\\,(-02) \\\\\n &7.23\\,(-03) & 3.59\\,(-04) & 1.08\\,(-03) & 1.80\\,(-03) & 1.50\\,(-03) & 4.82\\,(-03) \\\\\n% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$] direct + resonance contribution inferred from the data for \\ion{O}{vii} (from Zhang \\& Sampson 1987, see Table~\\ref{collcascadeO8}) with the scaling reported in Figure~\\ref{figure1s21s2l} . \n\\item[$^{\\mathrm{b}}$] cascade contribution calculated in this paper.\n\\item Note: here a+b corresponds to the total collision strength which populates the level considered. \n\\end{list}\n\\label{collcascadeC5}\n\\end{table*}\n\n%TABLE 10\n\\begin{table*}\n\\caption{Effective collisions strengths ($\\Upsilon$) for each 1s$^{2}$--1s2l transition of \\ion{O}{vii}.}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\nT$_{\\mathrm{e}}$/$Z^3$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n\\hline\n\\hline\n &4.06\\,(-03)$^{\\mathrm{a}}$& 2.51\\,(-03) & 7.50\\,(-03) &1.25\\,(-02) & 7.35\\,(-03) &2.10\\,(-02) \\\\\n 400 &5.01\\,(-04)$^{\\mathrm{b}}$& 1.53\\,(-04) & 4.60\\,(-04) &7.71\\,(-04) & 2.92\\,(-04) &7.53\\,(-04) \\\\\n &1.82\\,(-05)$^{\\mathrm{c}}$& 1.32\\,(-06) & 3.95\\,(-06) &6.67\\,(-06) & 9.42\\,(-07) &1.26\\,(-05) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &4.06\\,(-03) & 2.48\\,(-03) & 7.41\\,(-03) &1.23\\,(-02) & 7.45\\,(-03) &2.19\\,(-02) \\\\\n 600 &8.27\\,(-04) & 2.31\\,(-04) & 6.97\\,(-04) &1.16\\,(-03) & 4.06\\,(-04) &9.84\\,(-04) \\\\\n &1.33\\,(-04) & 8.38\\,(-06) & 2.51\\,(-05) &4.23\\,(-05) & 6.68\\,(-06) &6.98\\,(-05) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &4.04\\,(-03) & 2.42\\,(-03) & 7.26\\,(-03) &1.21\\,(-02) & 7.59\\,(-03) &2.30\\,(-02) \\\\\n 900 &1.05\\,(-03) & 2.75\\,(-04) & 8.31\\,(-04) &1.38\\,(-03) & 4.56\\,(-04) &1.06\\,(-03) \\\\\n &5.05\\,(-04) & 2.94\\,(-05) & 8.82\\,(-05) &1.48\\,(-04) & 2.71\\,(-05) &2.26\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &3.96\\,(-03) & 2.33\\,(-03) & 7.00\\,(-03) &1.16\\,(-02) & 7.75\\,(-03) &2.46\\,(-02) \\\\\n 1350 &1.09\\,(-03) & 2.74\\,(-04) & 8.29\\,(-04) &1.37\\,(-03) & 4.38\\,(-04) &9.83\\,(-04) \\\\\n &1.22\\,(-03) & 6.80\\,(-05) & 2.04\\,(-04) &3.42\\,(-04) & 7.61\\,(-05) &5.12\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &3.80\\,(-03) & 2.21\\,(-03) & 6.63\\,(-03) & 1.10\\,(-02) & 7.94\\,(-03) &2.68\\,(-02) \\\\\n 2000 &9.86\\,(-04) & 2.42\\,(-04) & 7.31\\,(-04) & 1.20\\,(-03) & 3.78\\,(-04) & 8.31\\,(-04) \\\\\n &2.14\\,(-03) & 1.15\\,(-04) & 3.45\\,(-04) & 5.79\\,(-04) & 1.63\\,(-04) &8.96\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &3.58\\,(-03) & 2.04\\,(-03) & 6.12\\,(-03) & 1.02\\,(-02) & 6.26\\,(-03) & 2.97\\,(-02) \\\\\n 3000 &8.04\\,(-04) & 1.93\\,(-04) & 5.86\\,(-04) & 9.73\\,(-04) & 2.28\\,(-04) & 6.47\\,(-04) \\\\\n &3.04\\,(-03) & 1.60\\,(-04) & 4.81\\,(-04) & 8.06\\,(-04) & 3.04\\,(-04) & 1.37\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &3.28\\,(-03) & 1.83\\,(-03) & 5.51\\,(-03) & 9.18\\,(-03) & 8.51\\,(-03) & 3.39\\,(-02) \\\\\n 4500 &6.09\\,(-04) & 1.45\\,(-04) & 4.42\\,(-04) & 7.32\\,(-04) & 2.23\\,(-04) & 4.81\\,(-04) \\\\\n &3.67\\,(-03) & 1.90\\,(-04) & 5.72\\,(-04) & 9.57\\,(-04) & 5.05\\,(-04) & 1.88\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &2.94\\,(-03) & 1.61\\,(-03) & 4.84\\,(-03) & 8.06\\,(-03) & 8.89\\,(-03) & 3.93\\,(-02) \\\\\n 6\\,700 &4.51\\,(-04) & 1.06\\,(-04) & 3.22\\,(-04) & 5.33\\,(-04) & 1.61\\,(-04) & 3.45\\,(-04) \\\\\n &3.91\\,(-03) & 2.01\\,(-04) & 6.04\\,(-04) & 1.01\\,(-03) & 7.70\\,(-04) & 2.41\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &2.57\\,(-03) & 1.37\\,(-03) & 4.12\\,(-03) & 6.85\\,(-03) & 9.34\\,(-03) & 4.65\\,(-02) \\\\\n 10\\,000 &3.16\\,(-04) & 7.53\\,(-05) & 2.28\\,(-04) & 3.76\\,(-04) & 1.14\\,(-04) & 2.42\\,(-04) \\\\\n &3.81\\,(-03) & 1.94\\,(-04) & 5.85\\,(-04) & 9.77\\,(-04) & 1.11\\,(-03) & 2.96\\,(-03) \\\\\n% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\begin{list}{}{}\n\\item[$^{\\mathrm{a}}$] direct contribution (from Zhang \\& Sampson 1987). \n\\item[$^{\\mathrm{b}}$] resonance contribution (from Zhang \\& Sampson 1987).\n\\item[$^{\\mathrm{c}}$] cascade contribution calculated in this paper.\n\\item Note: here a+b+c corresponds to the total collision strength which populates the level considered. \n\\end{list}\n\\label{collcascadeO8}\n\\end{table*}\n\n\n%TABLE 11\n\\begin{table*}\n\\caption{Same as Table~\\ref{collcascadeO8} but for the \\ion{Ne}{ix}.}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\n%% & & & & & & \\\\\nT$_{\\mathrm{e}}$/$Z^3$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n\\hline\n\\hline\n\n &2.53\\,(-03) & 1.56\\,(-03) & 4.67\\,(-03) & 7.77\\,(-03) &4.79\\,(-03) & 1.45\\,(-02) \\\\\n 400 &5.05\\,(-04) & 1.41\\,(-04) & 4.23\\,(-04) & 7.04\\,(-04) &2.44\\,(-04) & 5.92\\,(-04) \\\\\n &3.14\\,(-05) & 1.97\\,(-06) & 5.91\\,(-06) & 9.99\\,(-06) &1.63\\,(-06) & 1.64\\,(-05) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &2.53\\,(-03) & 1.53\\,(-03) & 4.59\\,(-03) & 7.65\\,(-03) & 4.88\\,(-03) & 1.51\\,(-02) \\\\\n 600 &6.75\\,(-04) &1.77\\,(-04) & 5.35\\,(-04) & 8.89\\,(-04) & 2.93\\,(-04) & 6.76\\,(-04) \\\\\n &1.64\\,(-04) &9.55\\,(-06) & 2.87\\,(-05) & 4.84\\,(-05) & 8.87\\,(-06) & 7.27\\,(-05) \\\\\n\\hline\n%% & & & & & & \\\\\n\n & 2.50\\,(-03) &1.49\\,(-03) & 4.47\\,(-03) & 7.43\\,(-03) & 4.96\\,(-03) &1.59\\,(-02) \\\\\n 900 & 7.34\\,(-04) &1.85\\,(-04) & 5.62\\,(-04) & 9.29\\,(-04) & 2.95\\,(-04) &6.63\\,(-04) \\\\\n & 4.96\\,(-04) &2.77\\,(-05) & 8.32\\,(-05) & 1.40\\,(-04) & 3.02\\,(-05) &2.03\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &2.43\\,(-03) &1.42\\,(-03) & 4.27\\,(-03) & 7.10\\,(-03) & 5.08\\,(-03) &1.71\\,(-02) \\\\\n 1350 &6.89\\,(-04) &1.69\\,(-04) & 5.11\\,(-04) & 8.44\\,(-04) & 2.62\\,(-04) &5.78\\,(-04) \\\\\n &1.03\\,(-03) &5.59\\,(-05) & 1.68\\,(-04) & 2.83\\,(-04) & 7.49\\,(-05) &4.15\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &2.31\\,(-03) &1.33\\,(-03) & 4.00\\,(-03) & 6.64\\,(-03) & 5.21\\,(-03) & 1.87\\,(-02) \\\\\n2000 &5.78\\,(-04) &1.40\\,(-04) & 4.25\\,(-04) & 6.96\\,(-04) & 2.14\\,(-04) & 4.67\\,(-04) \\\\\n &1.60\\,(-03) &8.61\\,(-05) & 2.59\\,(-04) & 4.35\\,(-04) & 1.48\\,(-04) & 6.83\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &2.15\\,(-03) &1.21\\,(-03) & 3.65\\,(-03) & 6.06\\,(-03) &5.39\\,(-03) & 2.09\\,(-02) \\\\\n3000 &4.49\\,(-04) &1.08\\,(-04) & 3.26\\,(-04) & 5.37\\,(-04) & 1.63\\,(-04) & 3.52\\,(-04) \\\\\n &2.10\\,(-03) &1.11\\,(-04) & 3.35\\,(-04) & 5.63\\,(-04) & 2.61\\,(-04) & 9.97\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &1.95\\,(-03) &1.08\\,(-03) & 3.24\\,(-03) & 5.39\\,(-03) & 5.61\\,(-03) & 2.40\\,(-02) \\\\\n4500 &3.30\\,(-04) &7.91\\,(-05) & 2.39\\,(-04) & 3.94\\,(-04) & 1.19\\,(-04) & 2.56\\,(-04) \\\\\n &2.39\\,(-03) &1.25\\,(-04) & 3.78\\,(-04) & 6.33\\,(-04) & 4.17\\,(-04) & 1.34\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &1.72\\,(-03) &9.32\\,(-04) & 2.81\\,(-03) & 4.66\\,(-03) & 5.86\\,(-03) &2.80\\,(-02) \\\\\n6700 &2.36\\,(-04) &5.65\\,(-05) & 1.70\\,(-04) & 2.80\\,(-04) & 8.50\\,(-05) &1.81\\,(-04) \\\\\n &2.43\\,(-03) &1.27\\,(-04) & 3.85\\,(-04) & 6.42\\,(-04) & 6.18\\,(-04) &1.68\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &1.49\\,(-03) &7.83\\,(-04) & 2.36\\,(-03) & 3.91\\,(-03) & 6.17\\,(-03) & 3.32\\,(-02) \\\\\n10000 &1.64\\,(-04) &3.93\\,(-05) & 1.19\\,(-04) & 1.97\\,(-04) & 5.92\\,(-05) & 1.26\\,(-04) \\\\\n &2.29\\,(-03) &1.19\\,(-04) & 3.62\\,(-04) & 6.01\\,(-04) & 8.73\\,(-04) & 2.05\\,(-03) \\\\\n%%\\hline\n%% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\label{collcascadeNe9}\n\\end{table*}\n\n%TABLE 12\n\\begin{table*}\n\\caption{Same as Table~\\ref{collcascadeO8} but for the \\ion{Mg}{xi}.}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\n%% & & & & & & \\\\\nT$_{\\mathrm{e}}$/$Z^3$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n\\hline\n\\hline\n\n & 1.74\\,(-03) & 1.05\\,(-03) & 3.18\\,(-03) & 5.28\\,(-03) & 3.39\\,(-03) &1.06\\,(-02) \\\\\n 400 & 4.41\\,(-04) & 1.16\\,-04) & 3.51\\,(-04) & 5.86\\,(-04) & 1.93\\,(-04) &4.49\\,(-04) \\\\\n & 4.40\\,(-05) & 2.59\\,(-06) & 7.75\\,(-06) & 1.32\\,(-05) & 2.40\\,(-06) &2.00\\,(-05) \\\\\n\\hline\n%% & & & & & & \\\\\n\n & 1.72\\,(-03) & 1.04\\,(-03) &3.11\\,(-03) & 5.18\\,(-03) & 3.44\\,(-03) &1.10\\,(-02) \\\\\n 600 & 5.17\\,(-04) & 1.32\\,(-04) &3.97\\,(-04) & 6.61\\,(-04) & 2.10\\,(-04) &4.74\\,(-04) \\\\\n & 1.81\\,(-04) & 1.02\\,(-05) & 3.06\\,(-05) & 5.21\\,(-05) & 1.07\\,(-05) &7.46\\,(-05) \\\\\n\\hline\n%% & & & & & & \\\\\n\n & 1.69\\,(-03) & 1.00\\,(-03) & 3.01\\,(-03) & 5.00\\,(-03) & 3.50\\,(-03) & 1.18\\,(-02) \\\\\n 900 & 5.11\\,(-04) & 1.28\\,(-04) & 3.84\\,(-04) & 6.35\\,(-04) & 1.97\\,(-04) & 4.39\\,(-04) \\\\\n & 4.65\\,(-04) & 2.56\\,(-05) & 7.68\\,(-05) & 1.30\\,(-04) & 3.19\\,(-05) &1.85\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n & 1.63\\,(-03) & 9.50\\,(-04) & 2.85\\,(-03) & 4.73\\,(-03) & 3.58\\,(-03) & 1.26\\,(-02) \\\\\n 1350 & 4.45\\,(-04) & 1.10\\,(-04) & 3.30\\,(-04) & 5.45\\,(-04) & 1.67\\,(-04) & 3.65\\,(-04) \\\\\n & 8.56\\,(-04) & 4.66\\,(-05) & 1.40\\,(-04) & 2.37\\,(-04) & 7.25\\,(-05) &3.50\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n & 1.53\\,(-03) &8.77\\,(-04) & 2.65\\,(-03) & 4.38\\,(-03) & 3.69\\,(-03) & 1.39\\,(-02) \\\\\n2000 & 3.60\\,(-04) &8.75\\,(-05) & 2.63\\,(-04) & 4.35\\,(-04) & 1.31\\,(-04) & 2.87\\,(-04) \\\\\n & 1.24\\,(-03) &6.66\\,(-05) &2.01\\,(-04) & 3.38\\,(-04) & 1.35\\,(-04) & 5.46\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n & 1.41\\,(-03) &7.92\\,(-04) & 2.40\\,(-03) & 3.96\\,(-03) & 3.82\\,(-02) & 1.57\\,(-02) \\\\\n3000 & 2.70\\,(-04) &6.57\\,(-05) & 1.85\\,(-04) & 3.25\\,(-04) & 9.77\\,(-05) & 2.12\\,(-04) \\\\\n & 1.52\\,(-03) &8.15\\,(-05) & 2.47\\,(-04) & 4.14\\,(-04) & 2.28\\,(-04) & 7.72\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n & 1.27\\,(-03) & 6.96\\,(-04) & 2.11\\,(-03) & 3.48\\,(-03) & 3.99\\,(-03) & 1.80\\,(-02) \\\\\n4500 & 1.94\\,(-04) & 4.72\\,(-05) & 1.42\\,(-04) & 2.34\\,(-4) & 7.04\\,(-05) & 1.52\\,(-04) \\\\\n & 1.65\\,(-03) & 8.78\\,(-05) & 2.68\\,(-04) & 4.47\\,(-04) & 3.54\\,(-04) & 1.01\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n & 1.11\\,(-03) & 5.95\\,(-04) & 1.81\\,(-03) & 2.98\\,(-03) & 4.18\\,(-03) & 2.12\\,(-02) \\\\\n6700 & 1.37\\,(-04) & 3.33\\,(-05) & 9.97\\,(-05) & 1.65\\,(-04) & 4.97\\,(-05) & 1.07\\,(-04) \\\\\n & 1.63\\,(-03) & 8.60\\,(-05) & 2.66\\,(-04) & 4.40\\,(-04) & 5.13\\,(-04) & 1.26\\,(-03) \\\\\n\\hline\n%% & & & & & & \\\\\n\n & 9.45\\,(-04) & 4.93\\,(-04) & 1.51\\,(-03) & 2.47\\,(-03) & 4.39\\,(-03) & 2.51\\,(-02) \\\\\n10000 & 9.47\\,(-05) & 2.31\\,(-05) & 6.91\\,(-05) & 1.14\\,(-04) & 3.42\\,(-05) & 7.37\\,(-05) \\\\\n & 1.49\\,(-03) & 7.83\\,(-05) & 2.46\\,(-04) & 4.02\\,(-04) & 7.12\\,(-04) & 1.52\\,(-03) \\\\\n%%\\hline\n%% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\label{collcascadeMg11}\n\\end{table*}\n\n%TABLE 13\n\\begin{table*}\n\\caption{Same as Table~\\ref{collcascadeO8} but for the \\ion{Si}{xiii}.}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n%\\hline\n\\hline\n\\hline\n%% & & & & & & \\\\\nT$_{\\mathrm{e}}$/$Z^3$&$^{3}\\mathrm{S}_{1}$&$^{3}\\mathrm{P}_{0}$&$^{3}\\mathrm{P}_{1}$&$^{3}\\mathrm{P}_{2}$&$^{1}\\mathrm{S}_{0}$& $^{1}\\mathrm{P}_{1}$\\\\ \n\\hline\n\\hline\n\n &1.26\\,(-03) & 7.63\\,(-04) &2.31\\,(-03) &3.81\\,(-03) & 2.51\\,(-03) & 8.07\\,(-03) \\\\\n 400 &3.62\\,(-04) & 9.39\\,(-05) &2.82\\,(-04) &4.69\\,(-04) & 1.50\\,(-04) & 3.41\\,(-04) \\\\\n &5.44\\,(-05) & 3.11\\,(-06) &9.32\\,(-06) &1.60\\,(-05) & 3.18\\,(-06) & 2.31\\,(-05) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &1.24\\,(-03) & 7.45\\,(-04) &2.25\\,(-03) &3.71\\,(-03) & 2.56\\,(-03) & 8.46\\,(-03) \\\\\n 600 &3.88\\,(-04) & 9.84\\,(-05) &2.95\\,(-04) &4.88\\,(-04) & 1.52\\,(-04) & 3.39\\,(-04) \\\\\n &1.87\\,(-04) & 1.04\\,(-05) &3.13\\,(-05) &5.34\\,(-05) & 1.22\\,(-05) & 7.49\\,(-05) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &1.21\\,(-03) & 7.13\\,(-04) &2.16\\,(-03) &3.57\\,(-03) & 2.60\\,(-03) & 9.00\\,(-03) \\\\\n 900 &3.59\\,(-04) & 9.00\\,(-05) &2.68\\,(-04) & 4.45\\,(-04) & 1.36\\,(-04) & 3.00\\,(-04) \\\\\n &4.23\\,(-04) & 2.34\\,(-05) &7.01\\,(-05) &1.19\\,(-04) & 3.28\\,(-05) & 1.69\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &1.16\\,(-03) & 6.70\\,(-04) &2.04\\,(-03) &3.34\\,(-03) & 2.67\\,(-03) & 9.79\\,(-03) \\\\\n 1350 &3.01\\,(-04) & 7.44\\,(-05) &2.22\\,(-04) &3.66\\,(-04) & 1.11\\,(-04) & 2.44\\,(-04) \\\\\n &7.14\\,(-04) & 3.91\\,(-05) &1.18\\,(-04) &2.00\\,(-04) & 6.96\\,(-05) & 3.00\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &1.09\\,(-03) & 6.16\\,(-04) & 1.88\\,(-03) &3.08\\,(-03) & 2.75\\,(-03) &1.08\\,(-02) \\\\\n2000 &2.34\\,(-04) & 5.78\\,(-05) & 1.72\\,(-04) &2.84\\,(-04) & 8.54\\,(-05) &1.87\\,(-04) \\\\\n &9.68\\,(-04) & 5.27\\,(-05) &1.60\\,(-04) & 2.69\\,(-04) & 1.24\\,(-04) &4.51\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &9.88\\,(-04) & 5.52\\,(-04) &1.69\\,(-03) &2.75\\,(-03) & 2.86\\,(-03) &1.22\\,(-02) \\\\\n3000 &1.72\\,(-04) & 4.25\\,(-05) &1.27\\,(-04) &2.09\\,(-04) & 6.26\\,(-05) & 1.36\\,(-04) \\\\\n &1.14\\,(-03) & 6.17\\,(-05) &1.89\\,(-04) &3.16\\,(-04) & 2.02\\,(-04) & 6.20\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &8.78\\,(-04) & 4.80\\,(-04) &1.48\\,(-03) &2.39\\,(-03) & 2.99\\,(-03) &1.41\\,(-02) \\\\\n4500 &1.22\\,(-04) & 3.03\\,(-05) &9.01\\,(-05) &1.48\\,(-04) & 4.35\\,(-05) &9.61\\,(-05) \\\\\n &1.19\\,(-03) & 6.42\\,(-05) &2.00\\,(-04) & 3.30\\,(-04) & 3.06\\,(-04) & 7.98\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &7.66\\,(-04) & 4.06\\,(-04) & 1.28\\,(-03) &2.03\\,(-03) & 3.13\\,(-03) &1.66\\,(-02) \\\\\n6700 &8.54\\,(-05) & 2.12\\,(-05) & 6.33\\,(-05) &1.03\\,(-04) & 3.10\\,(-05) &6.75\\,(-05) \\\\\n &1.14\\,(-03) & 6.13\\,(-05) & 1.95\\,(-04) &3.17\\,(-04) & 4.36\\,(-04) &9.81\\,(-04) \\\\\n\\hline\n%% & & & & & & \\\\\n\n &6.47\\,(-04) &3.32\\,(-04) & 1.07\\,(-03) & 1.66\\,(-03) & 3.29\\,(-03) &1.99\\,(-02) \\\\\n10000 &5.88\\,(-05) &1.46\\,(-05) & 4.35\\,(-05) & 7.15\\,(-05) & 2.14\\,(-05) &4.67\\,(-05) \\\\\n &1.02\\,(-03) &5.46\\,(-05) & 1.80\\,(-04) & 2.86\\,(-04) & 5.97\\,(-04) &1.17\\,(-03) \\\\\n%%\\hline\n%% & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\label{collcascadeSi13}\n\\end{table*}\n\n%TABLE 14\n\\begin{table*}[h]\n\\caption{Energy of the three main X-ray lines of \\ion{C}{v}, \\ion{N}{vi}, \\ion{O}{vii}, \\ion{Ne}{ix}, \\ion{Mg}{xi} and \\ion{Si}{xiii}, as well as the corresponding wavelength in \\AA, in parentheses. \n{\\bf w} corresponds to the resonance line, {\\bf x+y} corresponds to the intercombination lines (here too close to be separated) and {\\bf z} corresponds to the forbidden line.}\n\\label{lambda}\n\\begin{center}\n{\\scriptsize\n\\begin{tabular}{ccccccc}\n\\hline\n\\hline\n% & & & & & & \\\\ \nMultiplet & \\ion{C}{v}&\\ion{N}{vi}&\\ion{O}{vii} &\\ion{Ne}{ix} &\\ion{Mg}{xi} &\\ion{Si}{xiii}\\\\\n% & & & & & & \\\\ \n\\hline\nw & 307.88 & 430.65 & 574.00 & 921.82 & 1357.07 & 1864.44 \\\\ \n &(40.27) &(28.79) &(21.60) & (13.45) &(9.17) & (6.65) \\\\\nx+y & 304.41 & 426.36 & 568.74 & 915.02 &1343.28 & 1853.29 \\\\ \n &(40.73) &(29.08) &(21.80) &(13.55) &(9.23) &(6.69) \\\\\nz & 298.97 & 419.86 & 561.02 & 905.00 & 1331.74 & 1839.54 \\\\ \n & (41.47) &(29.53) &(22.10) &(13.70) &(9.31) &(6.74) \\\\\n\\hline\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table*}\n\n\n%***************************Table********************************\n\n%------------------------------------------------------------------------------------\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002319.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[1985]{Arnaud85} \nArnaud, M. \\& Rothenflug, R. 1985, A\\&AS, 60, 425 \n\\bibitem[1982a]{Bely-Dubau82a} \nBely-Dubau, F., Faucher, P., Dubau, J., Gabriel, A. H. 1982a, MNRAS, 198, 239 \n\\bibitem[1982b]{Bely-Dubau82b} \nBely-Dubau, F., Faucher, P., Steenman-Clark, L., Dubau, J., Loulergue, M., Gabriel, A. H., Antonucci, E., Volonte, S., Rapley, C. G. 1982b, MNRAS, 201, 1155 \n\\bibitem[1972]{Blumenthal72}\nBlumenthal, G. R., Drake, G. W. F., Tucker, W. H. 1972, ApJ, 172, 205 \n\\bibitem[1958]{Burgess58}\nBurgess, A. 1958, MNRAS, 118, 477\n\\bibitem[1960]{BurgessSeaton60}\nBurgess, A., Seaton, M. J. 1960, MNRAS, 121, 471 \n\\bibitem[1993]{Cunto93} \nCunto, W., Mendoza, C., Ochsenbein, F., Zeippen, C. J. 1993, A\\&A, 275, L5 \n\\bibitem[1980]{Doyle80} \nDoyle, J. G. 1980, A\\&A, 87, 184 \n\\bibitem[1982]{Doyle82}\nDoyle, J. G., Schwob, J. L. 1982, J. Phys B, 15, 813\n\\bibitem[1994]{Dubau94}\nDubau, J. 1994, ADNDT, 57, 21\n\\bibitem[1980]{DubauVolonte80} \nDubau, J. \\& Volonte, S. 1980, Reports of Progress in Physics, 43, 199\n\\bibitem[1974]{Eissner74}\nEissner, W., Jones M., Nussbaumer H., 1974, Comput. Phys. Commun., 8, 270\n\\bibitem[1987]{Fernley87} \nFernley, J.A., Taylor, K. T., Seaton, M. J. 1987, J. Phys. B: At. Mol. Phys., 20, 6457\n\\bibitem[1969]{Gabriel69}\nGabriel, A. H., Jordan, C. 1969, MNRAS, 145, 241\n\\bibitem[1972]{GabrielJordan72}\nGabriel, A. H., Jordan, C. 1972, in ``Case studies in atomic collision physics'', vol.2, p209, McDaniel, McDowell (eds.).\n\\bibitem[1973]{Gabriel73}\nGabriel, A. H., Jordan, C. 1973, ApJ, 186, 327 \n\\bibitem[1995]{George95}\nGeorge, I. M., Turner, T. J., Netzer, H. 1995, ApJ 438, L67\n\\bibitem[1998]{George98} \nGeorge, I. M., Turner, T. J., Netzer, H. , Nandra, K., Mushotzky, R. F., Yaqoob, T. 1998, ApJS, 114, 73 \n\\bibitem[1984]{Halpern84}\nHalpern, J. C. 1984, ApJ, 281, 90\n\\bibitem[1997]{Iwasawa97} \nIwasawa, K., Fabian, A. C., Matt, G. 1997, MNRAS, 289, 443\n\\bibitem[1977]{Jacobs77} \nJacobs, V. L., Davis, J., Kepple, P. C. \\& Blaha, M. 1977, ApJ, 211, 605 \n\\bibitem[1997]{Leighly97} \nLeighly, K. M., Matsuoka, M. , Cappi, M., Mihara, T. 1997, IAU Symposia 188, 249 \n\\bibitem[1999]{Liedahl99}\nLiedahl, D.A. 1999, in X-rays Spectroscopy in Astrophysics, EADN School proceeding, 1997, J.A. van Paradijs, J.A.M Bleeker (eds.), p.189\n\\bibitem[1977]{Lin77}\nLin, C. D., Johnson, W. R., Dalgarno, A. 1977, Physical Review A, vol. 15, 154\n\\bibitem[1998]{Mazzotta98} Mazzotta, P., Mazzitelli, G., Colafrancesco, S., Vittorio, N. 1998, A\\&AS, 133, 403 \n\\bibitem[1935]{MenzelPekeris35}\nMenzel, D.H, Pekeris, C.L. 1935, MNRAS, 96, 77\n\\bibitem[1978a]{Mewe78a} \nMewe, R. \\& Schrijver, J. 1978a, A\\&A, 65, 99\n\\bibitem[1978b]{Mewe78b} \nMewe, R. \\& Schrijver, J. 1978b, A\\&AS, 33, 311 \n\\bibitem[1999]{Mewe99}\nMewe, R. 1999, in X-rays Spectroscopy in Astrophysics, EADN School proceeding, 1997, J.A. van Paradijs, J.A.M Bleeker (eds.), p.109\n \\bibitem[1999]{Nahar99} \nNahar, S. N. 1999, ApJS, 120, 31 \n\\bibitem[1994]{Nandra94}\nNandra, K., Pounds, K. A. 1994, MNRAS, 268, 405\n\\bibitem[1993]{Netzer93}\nNetzer, H., 1993, ApJ 411, 594 \n\\bibitem[1997]{Netzer97}\nNetzer, H., Turner, T. J. 1997, ApJ, 488, 694 \n\\bibitem[1999]{Nicastro99} \nNicastro, F. , Fiore, F. , Perola, G. C., Elvis, M. 1999, ApJ, 512, 184 \n\\bibitem[1996]{Otani96}\nOtani, C. , Kii, T. , Reynolds, C. S., Fabian, A. C., Iwasawa, K. , Hayashida, K. , Inoue, H. , Kunieda, H., Makino, F. , Matsuoka, M., Tanaka, Y. 1996, PASJ, 48, 211 \n\\bibitem[1998]{Paerelsetal98}\nPaerels, F. et al. 1998, in Proceedings of the First XMM Workshop on \"Science with XMM\", held at Noordwijk, The Netherlands, M.Dahlem (ed.), URL http://astro.estec.esa.nl/XMM/news/ws1/ws1$_{}$papers.html\n\\bibitem[1999]{Paerels99}\nPaerels, F. 1999, in X-rays Spectroscopy in Astrophysics, EADN School proceeding, 1997, p.347, J.A. van Paradijs, J.A.M Bleeker (eds.)\n\\bibitem[1991]{Pequignot91} \nPequignot, D., Petitjean, P. \\& Boisson, C. 1991, A\\&A, 251, 680\n\\bibitem[1998]{PorquetDumont98}\nPorquet, D., Dumont, A.M. 1998, in \"Structure and Kinematics of Quasar Broad Line Regions\", Eds C. M. Gaskell, W. N. Brandt, M. Dietrich, D. Dultzin-Hacyan, and M. Eracleous, ASP Conf. Ser., in press\n\\bibitem[1998]{Porquet98}\nPorquet, D., Dumont, A.M., Mouchet, M. 1998, Author, I. 1998, in Proceedings of the First XMM Workshop on \"Science with XMM\", held at Noordwijk, The Netherlands, M. Dahlem (ed.), URL http://astro.estec.esa.nl/XMM/news/ws1/ws1$_{}$papers.html \n\\bibitem[1999]{Porquet99}\nPorquet, D., Dumont, A.M., Collin, S., Mouchet, M. 1999, A\\&A, 341, 58\n\\bibitem[1985]{Pradhan85} \nPradhan, A. K. 1985, ApJ, 288, 824 \n\\bibitem[1981]{Pradhan81} \nPradhan, A. K., Shull, J. M. 1981, ApJ, 249, 821 \n\\bibitem[1997]{Piro97}\nPiro, L., Balucinska-Church, M., Fink, H., Fiore, F., Matsuoka, M., Perola, G. C., Soffitta, P. 1997, A\\&A, 319, 74 \n\\bibitem[1997]{Reynolds97}\nReynolds, C. S., 1997, MNRAS, 286, 513 \n\\bibitem[1983]{Sampson83}\nSampson, D. H., Goett, S. J., Clarck, R. E. H. 1983, ADNDT, 29, 467\n\\bibitem[1959]{Seaton59}\nSeaton, M. J. 1959, MNRAS, 119, 81\n\\bibitem[1997]{Turner97} \nTurner, M. J. L., Bleeker, J. A. M., Hasinger, G., Peacock, A., Truemper, J. 1997, IAU Symposia, 188, E20\n\\bibitem[1994]{Ueno94}\nUeno, S., Mushotzky, R. F., Koyama, K., Iwasawa, K., Awaki, H., Hayashi, I. 1994, PASJ, 46, L71 \n\\bibitem[1985]{Vainshtein85}\nVainshtein, L. A. \\& Safronova U. I. 1985, Physica Scripta, vol. 31, 519\n\\bibitem[1981]{Winkler81} \nWinkler, P. F., Clark, G. W., Markert, T. H., Petre, R., Canizares, C. R. 1981, ApJ, 245, 574 \n\\bibitem[1987]{Zhang87}\nZhang, H. \\& Sampson, D. H. 1987, ApJS, 63, 487\n\\end{thebibliography}"
}
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astro-ph0002320
|
CHVCs: Galactic Building Blocks at z = 0
|
[
{
"author": "Robert Braun"
}
] |
A distinct sub-class of anomalous velocity \hi emission features has emerged from recent high quality surveys of the Local Group environment, namely the compact high velocity clouds (CHVCs). A program of high-resolution imaging with the Westerbork array and the Arecibo telescope has begun to provide many insights into the nature of these objects. Elongated core components with a velocity gradient consistent with rotation (V$_{Rot}\sim$ 15 \kms) are seen in many objects. Comparison of volume and column densities has allowed the first distance estimates to be made (600$\pm$300~kpc). The objects appear to be strongly dark-matter dominated with dark-to-gas mass ratios of 30--50 implied if the typical distance is 700~kpc.
|
[
{
"name": "braunr.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Braun \\& Burton}{CHVCs: Galactic Building Blocks at z = 0}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\NH{$N_{\\rm HI}$~} \n\\def\\kms{km\\,s$^{-1}$} \n\\def\\vlsr{$v_{\\rm LSR}$~}\n\\def \\hi {H\\,{\\sc i~}} \n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{CHVCs: Galactic Building Blocks at z = 0}\n \\author{Robert Braun}\n\\affil{Netherlands Foundation for Research in Astronomy, P.O. Box 2,\n 7990 AA Dwingeloo, The Netherlands}\n\\author{W. Butler Burton}\n\\affil{Sterrewacht Leiden, P.O. Box 9513, 2300 RA Leiden, The Netherlands}\n\n\\begin{abstract}\n A distinct sub-class of anomalous velocity \\hi emission features has\n emerged from recent high quality surveys of the Local Group\n environment, namely the compact high velocity clouds (CHVCs). A\n program of high-resolution imaging with the Westerbork array and the\n Arecibo telescope has begun to provide many insights into the nature\n of these objects. Elongated core components with a velocity gradient\n consistent with rotation (V$_{Rot}\\sim$ 15 \\kms) are seen in many\n objects. Comparison of volume and column densities has allowed the\n first distance estimates to be made (600$\\pm$300~kpc). The objects\n appear to be strongly dark-matter dominated with dark-to-gas mass\n ratios of 30--50 implied if the typical distance is 700~kpc. \n\\end{abstract}\n\n\\section{Introduction}\n\nThe nature of anomalous velocity \\hi discovered during $\\lambda$21~cm\nsurveys of the Galaxy has been the subject of much debate in the past\nthree decades. There appear to be at least four reasonably distinct\nclasses of this gas, namely: (1) Localized outflows and subsequent\ninflows associated with massive star formation which are commonly\nreferred to as a ``galactic fountain'' (Shapiro \\& Field, 1976;\nBregman, 1980). (2) The stream of tidal debris from the interaction of\nthe Galaxy with the Magellanic Clouds is another major source of\nanomalous velocity \\hi\\/. Recent imaging (Putman \\& Gibson, 1999) has\nbegun to reveal the true extent of this debris system, and allow it to\nbe distinguished from other components. (3) The extended HVC complexes\n(named A, C, H, M, \\dots) which span ten's of degrees on the sky and\nhave recently been determined to have both nearby distances of about\n10~kpc (Van Woerden et al. 1999) and rather low ($\\sim$0.1 solar) metal\nabundance (Wakker et al. 1999). These diffuse \\hi structures appear to\nbe currently merging with the Galaxy and each account for some 10$^7$\nM$\\odot$ of fresh gas. And finally (4) the system of compact high\nvelocity clouds (CHVCs) cataloged by Braun \\& Burton (1999).\n\nThe CHVCs form a distinct class of compact, high-contrast \\hi emission\nfeatures at anomalous velocity, which can be readily distinguished from\nthe more diffuse components in the recent high quality surveys; the\nLeiden/Dwingeloo Survey in the North (Hartmann \\& Burton 1997) and the\nParkes Multibeam Survey in the South (see Putman \\& Gibson 1999). Their\naverage angular size is only 1~degree FWHM and the total velocity width\n30~\\kms~ FWHM. The 65 confirmed members of the CHVC class share a\nwell-defined kinematic pattern. A global search for the reference frame\nthat minimizes the line-of-sight velocity dispersion of the system,\nreturns the Local Group Standard of Rest with high confidence. In this\nsystem the velocity dispersion of the population is only 70~\\kms,\nalthough it is in-falling toward the Local Group barycenter at about\n100~\\kms. These properties suggest that the objects are: (1) associated\nwith the Local Group rather than the Galaxy as such, (2) that they are\nlikely to reside at quite substantial distances and (3) have as yet had\nlittle tidal interaction with the more massive Local Group members.\n\n\\begin{figure}\n\\plotone{braunr1.eps}\n\n\\caption{{\\bf A:}~ Westerbork image of CHVC\\,$204\\!+\\!30\\!+\\!075$ \n showing \\NH at 1~arcmin\n resolution; contours are drawn at levels of 20, 50, 100,\n 200, and $300 \\times 10^{18}$~cm$^{-2}$. {\\bf B:}~\n Intensity--weighted line--of--sight velocity, with contours of\n $v_{\\rm LSR}$ drawn in steps of 5 \\kms~ from 40 to 85 \\kms. {\\bf C:}\n Rotation velocities fit to the two principal components of\n CHVC\\,$204\\!+\\!30\\!+\\!075$. The solid lines show the rotation curves\n of Navarro, Frenk, \\& White (1997) cold--dark--matter halos of the\n indicated mass and 0.7~Mpc distance. {\\bf D: top}~ Equilibrium\n temperature curves for \\hi in an intergalactic environment\n characterized by a metallicity of 10\\% of the solar value and a\n dust--to--gas ratio of 10\\% of that in the solar neighborhood,\n calculated for two values of the neutral shielding column depth,\n namely $10^{19}$~cm$^ {-2}$ (solid line) and $10^{20}$~cm$^{-2}$\n (dashed line). {\\bf D: bottom}~ Mass volume density, in units of\n hydrogen nuclei per cubic centimeter, as a function of radius for an\n NFW cold dark matter halo. }\n\\end{figure}\n\n\n\\section{High Resolution Imaging}\n\nA program of high resolution imaging of the CHVCs has begun to provide\nfurther insights into the nature of these sources. An initial\nsub-sample of six CHVCs was imaged with the upgraded Westerbork array\n(WSRT) in December 1998. A complete description of those results can be\nfound in Braun \\& Burton (2000). The sub-sample was chosen to span a\nwide range of positions on the sky and in line-of-sight velocity, as\nwell as gas content and \\hi linewidth. An additional eight sources\nhave been imaged with the WSRT during the summer of 1999, specifically\ntargeting objects suspected of having very bright and narrow \\hi\nemission features. A sample of ten CHVCs have also been imaged with\nthe upgraded Arecibo telescope in November of 1999. In addition to\nfully-sampled images of the central square degree, a very deep\ncross-cut of two degree length was obtained for each source reaching an\nrms sensitivity of about $\\Delta$\\NH~=~10$^{17}$~cm$^{-2}$ at 10~\\kms~\nresolution. Full accounts of these recent results will be given\nelsewhere.\n\n\n\\subsection{Core/Halo Morphology and Physics}\n\nAll of the imaged sources share a number of common properties. Each\nsource contains between one and ten compact cores (of 1 to 10 arcmin\nextent) embedded in a diffuse halo of about 1~degree diameter. An\naverage of 40\\% of the \\hi line flux arises in the compact cores\n(although the range varies between 1 and 60\\%). The peak column density\nin these cores varies between 10$^{19}$ and 10$^{21}$~cm$^{-2}$. The\nfractional surface area of each source which exceeds a column density\nof 5$\\times10^{18}$ is only 15\\% on average, although this also varies\ngreatly from source to source. The remainder of the \\hi emission arises\nin a diffuse halo which reaches peak column densities of\n$10^{18.5}$--$10^{19.5}$~cm$^{-2}$ but declines smoothly with an exponential\nprofile to values of $10^{17.5}$~cm$^{-2}$ or less (as illustrated in Fig.2).\n\nThe resolved \\hi linewidths toward the core components (with 1~arcmin\nresolution) are typically only 5~\\kms~ FWHM (but range from as little as\n2 to as much as 15~\\kms). All of the core linewidths are sufficiently\nnarrow that it is possible to unambiguously identify these with the\nCool Neutral Medium phase of \\hi, with typical kinetic temperature of\n100~K. The diffuse halos, on the other hand, all have resolved \\hi\nlinewidths (with 3~arcmin resolution) of 21--25~\\kms~ FWHM, as seen in\nFig.2d. The one-to-one correspondence of halo emission with linewidths\nequal to or exceeding the thermal linewidth of 8000~K gas (21~\\kms~\nFWHM) provides an unambiguous identification of these halos with the\nWarm Neutral Medium phase of \\hi. A shielding column of WNM is one\nprerequisite for the condensation of CNM cores in calculations of \\hi\nthermodynamics (eg. Wolfire et al. 1995). The second prerequisite for\nCNM condensation is a sufficiently high thermal pressure, in excess of\nabout P/k~=~100~cm$^{-3}$K. Both of these aspects are illustrated in\nthe \\hi phase diagram shown in Fig.1d. An adequate shielding column of WNM\nis clearly detected in the CHVCs, as just discussed above. We will\nreturn to the question of an adequate thermal pressure below.\n\nAnother general result is that the CNM core components are dynamically\ndecoupled from their WNM halos. This is illustrated in Fig.2, where a\nsubstantial velocity gradient of some 30~\\kms~ is seen within the major\ncore component of CHVC158$-$39$-$285. Such large gradients are not\nobserved in the halo gas, which instead is always centered near the\nsystemic velocity of the system. This dichotomy suggests that while the\ncores may represent flattened rotating disks, the halos are more nearly\nspherical distributions. \n\n\\begin{figure}\n\\plotone{braunr2.eps}\n\n\\caption{{\\bf A:} Arecibo image of CHVC\\,$158\\!-\\!39\\!-\\!285$\n showing \\NH at 3 arcmin resolution; contours are drawn at levels of\n 5, 10, 20, and $30 \\times 10^{18}$~cm$^{-2}$. {\\bf B:}~\n Intensity--weighted line--of--sight velocity, with contours of\n $v_{\\rm LSR}$ drawn at the indicated velocities. {\\bf C:} Position,\n velocity cut at a fixed declination of +16:17:30. Contours are in\n units of brightness temperature. {\\bf D:} Variation of line-of-sight\n velocity, velocity FWHM and \\NH with position. }\n\\end{figure}\n\n\\subsection{Distance, Metallicity and Dark Matter Content}\n\nOne of the objects imaged with the WSRT, CHVC125+41$-$207, has proven\nparticularly interesting for several reasons. This object has a number\nof opaque core components of only $\\theta$~=~90\\arcsec angular size, a\nbrightness temperature in \\hi emission of 75~K, and linewidths so\nnarrow (less than 2~\\kms~ FWHM) that the kinetic temperature\n(T$_k$~=~85~K), \\hi opacity ($\\tau$~=~2) and column density\n(\\NH~=~10$^{21}$cm$^{-2}$), can be accurately derived. A good estimate\nof the volume density (n$_{H}$~=~2$\\pm$1~cm$^{-3}$) for this object has\nbeen made by modeling the thermodynamics (Wolfire et al., priv. comm.).\nWith these quantities in hand and only the assumption of crude\nspherical symmetry for the cores, it is possible to estimate the source\ndistance from D~=~\\NH/(n$_{H}$$\\theta$)~=~600$\\pm$300~kpc.\n\nThe same object has also allowed the first measurement of CHVC\nmetallicity, since the bright UV source Mrk~205 is located behind its\ndiffuse \\hi halo. Bowen, Blades and Pettini (1995) detect unsaturated MgII\nabsorption, with 0.15 \\AA~EW at the CHVC velocity, while we detect\na neutral column \\NH~=~5$\\times$10$^{18}$ cm$^{-2}$ at the same\nposition. The implied metal abundance is about 0.05 solar.\n\nAlthough many of the CHVCs have only one or two core components, a\nhandful of these objects might best be called CHVC clusters. As many as\nten cores are seen in close proximity (within 30--50~arcmin), each with\nits own systemic velocity and internal kinematics (which we address\nbelow) but sharing the same diffuse halo of shielding gas. The most\nextreme case is that of CHVC115+13$-$275, where the cores have relative\nvelocities as high as 70 \\kms~ and angular separations as large as\n30~arcmin. If these are gravitationally bound systems (and their cool\ngas content and isolation on the sky make this seem plausible) then\nthey have a dynamical mass, $M_{\\rm dyn}=Rv^2/G=2.3\\times 10^5R_{\\rm\n kpc}v_{\\rm km/s}^2$, and gas mass $M_{\\rm gas}=1.4~M_{\\rm\n HI}=3.2\\times 10^5S~D_{\\rm Mpc}^2$. If for example the distance were\n0.7~Mpc, then $M_{\\rm dyn}=10^{8.93}$ M$_\\odot$ and $M_{\\rm\n gas}=10^{7.22}$ M$_\\odot$. The dark--to--gas mass ratio in this case\nhas the rather substantial value of $\\Gamma$~=~51, which scales with\n$1/D$ for other distance estimates.\n\nAs already noted above, many of the CHVC cores give an indication for\norganized internal kinematics. Many of the cores have a systematic\nvelocity gradient along the long axis of their elliptical distribution\nwhich is very suggestive of rotation in a flattened disk system.\nSeveral examples are shown in Figs.1 and 2. The best-resolved examples\nof this pattern have been subjected to the standard tilted ring fitting\nalgorithms used in deriving galactic rotation curves. Good solutions\nfor rotation are found (Fig.1c) which slowly rise over some 6~arcmin to\nconstant values of 15 to 20~\\kms. The shapes of these rotation curves\nare in very good agreement with those predicted by Navarro, Frenk \\&\nWhite (1997) for a CDM halo at 0.7~Mpc distance (as shown in Fig.1c).\nThe dark--to--visible mass ratios in these two cases are $\\Gamma$~=~36\nand 29. \n\nThe presence of a significant dark matter component is important not\nonly for understanding the kinematics of the individual cores and the\nCHVC clusters, but also for understanding the \\hi thermodynamics. As\nnoted earlier, a significant thermal pressure in excess of about\nP/k~=~100~cm$^{-3}$K is required to allow condensation of the cool\ncores observed in the CHVCs (see Fig.1d, upper). The mass density\nprovided within the central few kpc of an NFW halo in this mass range\n(Fig.1d, lower) is sufficient to provide the required hydrostatic\npressure in combination with the observed warm halo column densities of\nabout 10$^{19}$cm$^{-2}$ (see also Braun \\& Burton 2000). \n\n\n\\acknowledgments \n\nWe are grateful to M.G. Wolfire, A. Sternberg, D. Hollenbach, and C.F.\nMcKee for providing the equilibrium temperature curves shown in\nFig.1d. The Westerbork Synthesis Radio Telescope is operated by the\nNetherlands Foundation for Research in Astronomy, under contract with\nthe Netherlands Organization for Scientific Research. The Arecibo\nObservatory is part of the National Astronomy and Ionosphere Center,\nwhich is operated by Cornell University under a cooperative agreement\nwith the National Science Foundation.\n\n\n\\begin{references}\n\n\\reference Bowen, D.V., Blades, J.C., \\& Pettini, M. 1995, \\apj, 448, 662\n\\reference Braun R., \\& Burton W.B. 1999, \\aap, 341, 437 \n\\reference Braun R., \\& Burton W.B. 2000, \\aap, in press, astro-ph/9912417\n\\reference Bregman J. 1980, \\apj, 236, 577 \n\\reference Hartmann D., \\& Burton W.B. 1997, ``Atlas of \n Galactic Neutral Hydrogen'', Cambridge: Cambridge University Press \n\\reference Navarro J.F., Frenk C.S., \\& White S.D.M., 1997, \\apj, 490, 493\n\\reference Putman M.E., \\& Gibson B.K. 1999, PASA, 16, 70 \n\\reference Shapiro P.R., \\& Field G. 1976, \\apj, 205, 762 \n\\reference Wakker B.P., Howk J.C., Savage B.D., van Woerden H., Tufte\n S.L., Schwarz U.J., Benjamin R., Reynolds R.J., Peletier R.F. \\&\n Kalberla P.M.W. 1999, Nature, 402, 388\n\\reference van Woerden H., Schwarz U.J., Peletier R.F., Wakker B.P., \\&\n Kalberla P.M.W. 1999, Nature, 400, 138\n\\reference Wolfire M.G., Hollenbach D., McKee C.F., Tielens A.G.G.M., \\&\n Bakes E.L.O. 1995, \\apj, 443, 152 \n\n\\end{references} \n\n\\end{document}\n"
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astro-ph0002321
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Evidence for a Young Stellar Population in NGC~5018
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"author": "Andrew J. Leonardi\\altaffilmark{1}"
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Two absorption line indices, Ca II and H$\delta$/$\lambda$4045, measured from high-resolution spectra are used with evolutionary synthesis models to verify the presence of a young stellar population in NGC~5018. The derived age of this population is $\sim$ 2.8 Gyr with a metallicity roughly solar and it completely dominates the integrated light of the galaxy near 4000 \AA.
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"name": "ms.tex",
"string": "% SAMPLE2.TEX -- AASTeX macro package tutorial paper.\n\n% The first item in a LaTeX file must be a \\documentstyle command to\n% declare the overall style of the paper. The two \\documentstyle lines\n% that are relevant for the AASTeX macros are shown; one is commented out\n% so that the file can be processed.\n\n\\documentclass[preprint]{aastex}\n%\\documentstyle[12pt,aasms]{article}\n%\\documentstyle[11pt,aaspp]{article}\n%\\documentstyle[aaspptwo]{article}\n\\usepackage{natbib}\n\\bibpunct[;]{(}{)}{;}{a}{}{,}\n\n% There are two optional preamble declarations that enable to user to\n% control certain formatting options. \\tighten is used with the\n% aasms substyle to turn off double-spacing; don't do this for\n% actual manuscripts intended for editorial review, only for your friends.\n%\n% \\eqsecnum changes the way equations are numbered. Normally,\n% equations are just numbered sequentially through the entire paper.\n% If \\eqsecnum appears in the preamble, equation numbers will\n% be sequential through each section, and will be formatted \"(sec-eqn)\",\n% where sec is the current section number and eqn is the number of the\n% equation within that section. \\eqsecnum can be used with\n% either substyle.\n\n%\\tighten\n%\\eqsecnum\n\n% Here's some slug-line data. They're never printed out by these\n% substyles because they're only relevant to the actual publication\n% process, and these styles aren't used in publication (yet).\n% The receipt and acceptance dates would be filled in by the editorial\n% staff on the appropriate dates; they are commented out in this sample\n% so that the abstract environment prints out rules so that the dates\n% can be typed onto the manuscript according to current practice.\n\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n\\journalid{337}{15 January 1989}\n\\articleid{11}{14}\n\n% This is the end of the \"preamble\". Now we wish to start with the\n% real material for the paper, which we indicate with \\begin{document}.\n% Following the \\begin{document} command is the front matter for the\n% paper, viz., the title, author and address data, the abstract, and\n% any keywords or subject headings that are relevant.\n\n%\\slugcomment{Maybe ApJ Letter, maybe not}\n\n\\begin{document}\n\n\\title{Evidence for a Young Stellar Population in NGC~5018}\n\n\\author{Andrew J. Leonardi\\altaffilmark{1} }\n\\affil{CB \\#3255, Department of Physics \\& Astronomy, University of North\n Carolina, Chapel Hill, NC 27599-3255}\n\n\\and\n\n\\author{Guy Worthey}\n\\affil{Department of Physics \\& Astronomy, St. Ambrose University, \n518 W. Locust St., Davenport, IA 52803-2829}\n\n% Notice that each of these authors has alternate affiliations, which\n% are identified by the \\altaffilmark after each name. The actual alternate\n% affiliation information is typeset in footnotes at the bottom of the\n% first page, and the text itself is specified in \\altaffiltext commands.\n% There is a separate \\altaffiltext for each alternate affiliation\n% indicated above.\n\n\\altaffiltext{1}{Visiting Astronomer, Cerro Tololo Inter-American Observatory. \nCTIO is operated by AURA, Inc.\\ under contract to the National Science\nFoundation.} \n\n% The abstract environment prints out the receipt and acceptance dates\n% if they are relevant for the journal style. For the aasms style, they\n% will print out as horizontal rules for the editorial staff to type\n% on, so long as the author does not include \\received and \\accepted\n% commands. This should not be done, since \\received and \\accepted dates\n% are not known to the author.\n\n\\begin{abstract}\nTwo absorption line indices, Ca II and H$\\delta$/$\\lambda$4045, measured\nfrom high-resolution spectra are used with evolutionary synthesis\nmodels to verify the presence of a young stellar population\nin NGC~5018. The derived age of this population is $\\sim$ 2.8 Gyr with a \nmetallicity roughly solar and it completely\ndominates the integrated light of the galaxy near 4000 \\AA. \n\\end{abstract}\n\n\\keywords{line: profiles --- galaxies: abundances --- galaxies: elliptical\nand lenticular, cD --- galaxies: individual (NGC 5018) --- galaxies: \nstarburst --- galaxies: stellar content}\n\n% That's it for the front matter. On to the main body of the paper.\n% We'll only put in tutorial remarks at the beginning of each section\n% so you can see entire sections together.\n%\n% In the first two sections, you should notice the use of the LaTeX \\cite\n% command to identify citations. The citations are tied to the\n% reference list via symbolic tags. We have chosen the first three\n% characters of the first author's name plus the last two numeral of the\n% year of publication. The corresponding reference has a \\bibitem\n% command in the reference list below.\n%\n% Please go to the LaTeX manual for a complete description of the\n% \\cite-\\bibitem mechanism.\n\n\\section{Introduction}\n\nMorphological peculiarities in the optical images of galaxies are now almost\ninvariably taken to be signs of a past tidal interaction or merger. Though\ntheoretical models have had success reproducing tidal tails, shells, and\nother structures \\citep[e.g.,][]{tt72,q84,hq88,mbr93},\nin the absence of explicit details of the interaction such as the Hubble\ntypes of the progenitors, relative progenitor sizes, and impact parameter, a \nunique solution is difficult to come by.\n\nDynamical friction during a collision almost certainly leads to a merger of the\nstellar systems \\citep{s83} and simulations have shown that any\naccompanying gas will rapidly dissipate to the center during minor mergers involving\neither ellipticals \\citep{wh93} or disk galaxies\n\\citep{mh94a}. If the conditions are right, it is\nreasonable to expect that this gas inflow will result in star formation. The\nduration, intensity, and even the starting time of the star formation, however,\ndepend on the morphology of the progenitor and the details of the\ninteraction \\citep{mh94b}. As much post-merger \ninformation as possible is needed to help constrain the merger possibilities, \nincluding analysis of the resulting young stellar population (YSP).\n\nUnfortunately, unless the merger remnant is presently forming stars at a \nreasonably vigorous rate (hence producing readily apparent emission lines) or has\nexperienced a very recent and relatively strong episode of star formation placing\nit in the starburst regime, a YSP can be difficult to detect. Broadband colors\nand other YSP indicators return to pre-star formation levels very quickly\n\\citep{bas90,cs94} and\nmany indicators that imply the presence of a YSP can also be explained by\nintrinsic metallicity differences in the final population of the merger\nremnants \\citep[hereafter BBB]{bbb93}. Ambiguity\nabout whether a YSP even exists or not complicates the details of the merger\nconsiderably.\n\nIn this paper, we use spectral indices in conjunction with evolutionary synthesis models to \ndetect and determine the age and metallicity of a YSP in the particular case of\na possible merger remnant,\nNGC~5018. It represents an update to the age-dating technique introduced in\n\\citet[hereafter LR]{lr96}. NGC~5018 is appropriate to the\npresent discussion because there is ongoing uncertainty concerning the presence of\na YSP. Certain observations imply the existence of a YSP while others seem to be\ninconsistent with the presence of a YSP. NGC~5018 and the roots of the controversy \nare described\nin \\S2. In \\S3, a review of the age-dating technique and its \nrefinements are given. The results of the technique applied to NGC~5018 are\npresented in \\S4 and \\S5 contains the conclusions.\n\n\\section{NGC~5018}\n\nNGC~5018 is a member of the \\citet{mc83} catalog of\nshell elliptical galaxies and is considered a probable merger remnant\n\\citep{fpcmv86}. As noted by \\citet{ssfbdg90}\nand BBB, NGC~5018 has an abnormally weak $\\mathrm{Mg_{2}}$ index\nfor its luminosity: Its measured Mg$_2$ is 0.209 \\citep{twfbg98}\neven though the mean Mg$_2$-$\\sigma$ relation suggests Mg$_2 = 0.301$\nfor an elliptical galaxy with NGC 5018's measured velocity dispersion\nof $\\sigma = 223$ km s$^{-1}$ \\citep{bbf93}, about 6 standard\ndeviations away from the mean. \nAlthough deviations from the line-strength-luminosity\nrelation correlate well with the amount of morphological disturbance in\nelliptical galaxies \\citep{ssfbdg90}, NGC~5018 has\nabnormally weak line strengths even when this correlation is accounted for.\nFor a class of objects, these authors ruled out metallicity\nvariations in the galaxies as the cause for the correlation due to the \nphysical implausibility\nof stronger mergers leading to more metal-poor stellar populations in the\nremnants. \\citeauthor{ssfbdg90} concluded that mergers produce a YSP which is\nobserved in the decreased line strengths. On a galaxy-by-galaxy basis,\nhowever, an intrinsic metallicity variation cannot be ruled out by\na low $\\mathrm{Mg_{2}}$ index alone. In NGC~5018, a low $\\mathrm{Mg_{2}}$ \nindex coupled with the lack of an upturn\nin its UV spectral energy distribution (SED), led BBB to conclude that\nNGC~5018 consisted of a metal-poor old stellar population, in stark\ncontrast to other ellipticals of the same luminosity.\nBBB were unable to match both the UV SED observations and the $\\mathrm{Mg_{2}}$\nindex with composite populations created by mixing spectral templates of\nmetal-rich elliptical galaxies and a contaminating YSP template. Only\ntemplates containing metal-poor populations approached both observations.\n\nIndirect observational evidence that a YSP does in fact exist in NGC~5018 is\nextensive. The shells present in its optical image are photometrically\nbluer than the surrounding parts of the galaxy \\citep{fpcmv86}\nsuggesting a younger age for the shells.\nThe detection of an HI gas bridge connecting NGC~5018 with the nearby spiral\nNGC~5022 \\citep{kgvjk88} is evidence of an ongoing interaction\nwhile a possible past interaction is implied by a stellar\nbridge connecting the two and the embedded dust lane in NGC~5018\n\\citep{mh97}.\nPossible young globular cluster candidates, formed during a past interaction\nand perhaps only several hundred Myr old, have been observed \n\\citep{hk96}.\nFurthermore, \\citet{ghjn94} measured extended H$\\alpha$+[N II]\nemission in the central region coinciding with the embedded dust lane which\nthey associated with star forming regions.\nAlso, IR emission has been detected in the same area \n\\citep{jkkg87}. \n\\citet{tb87} showed in an IR two-color diagram that\nNGC~5018 lies in a region quite different\nfrom that occupied by infrared ``cirrus'', which is emission from diffuse\ndust in the interstellar medium of a galaxy. Instead, it is closer to\nthe region where the IR emission from warmer dust associated with HII \nregions dominates \\citep{h86,blw88}\n, suggesting a YSP source for the IR emission.\n\nWhile the observations are compelling, they are not conclusive. The\ndirect detection of the YSP is needed to resolve the issue. BBB chose\nto observe in the far-UV for exactly that reason, since in principle,\nthis region of the spectrum is dominated by young stars\n\\citep{o88} and the low UV flux level in NGC~5018 led\nthem to the metal-poor scenario. They discounted dust obscuration as\nthe cause because the best available photometry at that time\n\\citep{fpcmv86} showed that the dust lane in NGC~5018\ndoes not extend into the region where their IUE spectrum was taken.\nSubsequent observations, however \\citep{cd94,ghjn94}\n, indicate that not only is dust\npresent throughout the central region but also is patchy in nature,\nmaking the reddening effects difficult to ascertain.\n\\citet{cd94} showed that reasonable\nexpectations of dust obscuration and a YSP can explain both the low\n$\\mathrm{Mg_{2}}$ index and the UV flux depletion in the central\nregion of NGC~5018. Both sets of authors concluded that a YSP was a\nmore probable explanation for the observations. \n\nThe conflict is\nillustrated in Figure~\\ref{fig:lick} where we have plotted data from\nthe Lick group \\citep{twfbg98} for NGC~5018 and other\nsystems. The top panel shows a $\\lambda 2750-V$ color plotted against\nthe $\\mathrm{C_{2}}$4668 Lick index. The $\\mathrm{C_{2}}$4668 index is\nmore metal-sensitive than Mg$_2$ and is less subject, but not immune,\nto abundance ratio effects. BBB remarked that NGC~5018's\n$\\mathrm{Mg_{2}}$ index and UV spectrum resembles M32's, even though\nM32 is a much less luminous galaxy, which led them to surmise a system\nwith an abundance like that of a dwarf galaxy rather than a giant\nelliptical. The UV data here supports this view. As can be seen in\nthe top panel of Figure~\\ref{fig:lick}, NGC~5018 has approximately the\nsame UV color but a slightly weaker $\\mathrm{C_{2}}$$\\lambda$4668 index than M32\nindicating that NGC~5018 is about twice as old and more metal-poor\nthan M32. The bottom panel of Figure~\\ref{fig:lick} plots H$\\beta$\n(uncorrected for any emission fill-in) against $\\mathrm{C_{2}}$4668\nand shows NGC~5018 nearly on the same model grid line as M32 implying\nsimilar age, but still $\\sim$ 0.15 dex more metal-poor than M32.\nEmission corrections for H$\\beta$ would push NGC~5018 vertically\nupward to younger ages and higher metallicity, worsening the\ndiscrepancy in age between the two panels. On the other hand, a\ncorrection for UV extinction in the upper panel would make the two\npanels agree better.\n\nTo help resolve the still uncertain nature of NGC~5018, we utilize \nspectroscopic observations, along with an updated age-dating method to\nunambiguously show that a YSP is present in NGC~5018.\nThe modeling technique is discussed in \\S3. The \nlong-slit spectra of NGC~5018 were acquired at the KPNO 4m telescope in June~1995 by\nLewis Jones and kindly provided to us. Four 30-minute exposures were acquired\nwith the R-C spectrograph with grating KPC-22B at second order and the T2KB\n2048x2048 CCD. The slit width was 2 arcsec. A 14.5 pixel aperture was extracted\nfrom the raw spectrum and with a CCD spatial scale of $\\sim$ 0.69 arcsec/pixel,\nthe aperture size on NGC~5018 is 2''x10''. The dispersion of the spectra is \n0.7 \\AA/pxl and the resolution\nis FWHM $\\sim$ 1.8 \\AA. Data reductions were done in IRAF. For details see\n\\citet{j99}. A representative spectrum, emphasizing the wavelength\nregion of interest, is shown in Figure~\\ref{fig:spec}. It has been normalized\nto unity at 4040 \\AA.\n\n\\section{The Age-Dating Technique}\n\nThe age-dating technique as described in LR uses two spectral indices developed\nin \\citet{r84, r85}. Each index is defined by taking the ratio\nof counts in the bottoms of two neighboring absorption lines without reference\nto the continuum levels. The specific absorption lines used are identified on the\nNGC~5018 spectrum in Figure~\\ref{fig:spec}. The first index, H$\\delta$/$\\lambda$4045, \nmeasures\nthe integrated spectral type of a galactic stellar population and is produced\nfrom the ratio of the central intensity in H$\\delta$ relative to the central \nintensity in the neighboring\nFe I $\\lambda$4045 line. Note that the way the index is defined, \nH$\\delta$/$\\lambda$4045 \\emph{decreases} as H$\\delta$ gets stronger. The second \nindex, Ca II, formed from the ratio of\nthe central intensity of Ca II H+H$\\epsilon$ relative to Ca II K, is constant in\nstars with a spectral type later than F2 but then decreases dramatically for \nearlier type stars, reaching a minimum at spectral type A0. It provides an\nunambiguous signature for stars hotter than F2 in the integrated light of a \nstellar population. \n\nThe indices are computed for single-age theoretical populations from evolutionary\nsynthesis models. When plotted together in the two-dimensional index space, the\nindices resolve the well-known degeneracy between a YSP's age and light \ncontribution to a composite stellar population \\citep[e.g.,][LR]{cs87,bas90,cs94}.\nA valuable property of these indices particularly applicable to \nNGC~5018 is their virtual insensitivity to reddening. Since only neighboring\nspectral features are used, reddening does not affect their values and the\nembedded dust in the center of NGC~5018 will not obscure the evidence of a\nYSP.\n\nIn LR, the evolutionary synthesis models of \\citet{bc93}\nwere used with the spectral library updated to include the higher resolution\nstellar library of \\citet{jhc84}. The models\nwere restricted to solar abundance populations only, thus metallicity effects on the \nindices could only be explored crudely. To remedy this, the technique now employs\nthe evolutionary synthesis models of \\citet{w94}.\n\nThe Worthey models work as follows: For a given age and metallicity, a theoretical\nisochrone \\citep{bbcfn94} is consulted, with each point on\nthe isochrone representing a parcel of stars of known luminosity, temperature, \nand gravity. The spectral indices for that isochrone point are interpolated\nfrom empirical fitting functions of the indices from a high-resolution spectral\nlibrary \\citep[see also \\citealt{lea96}]{j99} that has been \nsmoothed to the resolution of the\nNGC~5018 spectra. The indices are weighted by luminosity and\nnumber and added up along the isochrone to get the spectral index values for the\nentire integrated population. The population is formed from an instantaneous\nburst of star formation. A finite burst, however, is more realistic and will become\na future feature of the models. These models were originally designed to disentangle\nage and metallicity effects in the integrated light of old stellar populations. To\nextend the age coverage to include very young ages ($<$ 1 Gyr) and also extend spectral\ncoverage to the blue, the empirical library was augmented with 2103 \ntheoretical stellar spectra computed with the \\citet{k95} SYNTHE \nprogram. The indices were computed for each synthetic spectrum and the values were\nused as a lookup table with specific isochrone points being found by interpolating\nbetween the synthetic grid points \\citep[for more details see][]{l00}.\n\nFigure~\\ref{fig:burst} shows the Ca II index plotted against the \nH$\\delta$/$\\lambda$4045 index\nfor two stellar populations with [Fe/H] = -0.7 and [Fe/H] =\n0.0 respectively. \nIn the figure, the solid squares represent the index values for an instantaneous\nburst of star formation that has evolved to the labeled age in Gyr, so each curve\nfollows the evolution of the indices for a stellar population of\nthe given metallicity. Both indices initially decrease for young systems as they \nage, reaching a minimum at about 0.25--0.5 Gyr as the O and B stars die\nout and A stars begin to dominate the integrated light, thus generating strong\nBalmer lines. Subsequently, as the Balmer lines weaken, the indices increase\nagain. Also plotted in Figure~\\ref{fig:burst} are \nthe index values observed\nfor a select Galactic globular cluster, 47 Tuc ([Fe/H] = -0.7). \nThe long-slit observation was acquired at the CTIO 1.5m telescope in November \n1995. A 10 minute exposure of 47~Tuc was acquired using the Cassegrain spectrograph\nwith the Loral 1200x800 CCD and the B\\&L grating \\#58 at second order. During the \nexposure, the slit was trailed across the core diameter of the cluster to obtain\na true integrated light\nmeasurement. The dispersion of the spectrum is 1.12 \\AA/pixel and the resolution is\nFWHM $\\sim$ 2.6 \\AA. Data reductions were done in IRAF. For details see \n\\citet{l00}. Although the Ca II index loses much of its\nage discriminating power at older ages, we still determine a reasonable \nglobular cluster age of approximately~15 Gyr for 47~Tuc at the appropriate\nmetallicity. Simultaneous age and metallicity discrimination with high S/N spectra is \nmost effective between\nthe ages of 0.25 Gyr and 4 Gyr. Since the Ca II and H$\\delta$/$\\lambda$4045 \nindices are insensitive to metallicity for ages less than $\\sim$ 0.25 Gyr, the ability to \nuniquely determine a metallicity is lost whereas for ages greater than $\\sim$ 4.0 Gyr, the\nCa II index approaches the constant value for late type stars and its evolution essentially\nhalts.\n\nUnfortunately, the isochrones used here only model the horizontal branch as a red\nclump. \nTo illustrate where such a population with a blue horizontal branch would fall on the\nCa II--H$\\delta$/$\\lambda$4045 diagram, also included\non Figure~\\ref{fig:burst} are the index values for a 20 minute\nexposure of the Galactic globular cluster M15 taken during the same observing \nrun as 47 Tuc and for a very metal-poor ([Fe/H] = -1.7) 15.1 Gyr model with\na red clump (note that both the models in \nFigure~\\ref{fig:burst} and the globular cluster spectra \nhave been smoothed out to the resolution and intrinsic velocity dispersion of \nthe NGC~5018 spectra described \nabove). While~47 Tuc has a predominantly red horizontal branch, M15 has a blue\nhorizontal branch \\citep{l89}. The agreement between the [Fe/H] = -1.7\nmodel and M15\nis poor. Blue horizontal branch stars are luminous enough to contribute significantly\nthe Ca II \nindex and drive it below what the models predict for this age and metallicity. \n\n\\section{Results}\n\n\\subsection{Composite Populations}\n\nThe question we must answer for NGC~5018 is whether a YSP is contaminating the\nlight of an old, underlying population or the light is originating from a solely\nold, metal-poor population. To create a composite population, we assume that the\nold population has an age of 15 Gyr but the metallicity can vary. We then \ninterpolate in the index space between the old population point and a YSP point in \nconstant increments to represent different levels of contamination by the YSP.\nThe flux\ncontributions for the two populations have been normalized at 4040 \\AA.\nThe computed indices for the theoretical composite populations are illustrated\nin Figures~\\ref{fig:yspm17}--\\ref{fig:yspp00}. In each figure, the full\nevolution of the YSP is plotted in a similar manner to Figure~\\ref{fig:burst},\none YSP metallicity per figure. A solid, colored circle represents the index\nvalues for the~15 Gyr population denoting the old underlying stellar\nsystem, each color a different old population metallicity which may or may\nnot be the same as the YSP's metallicity. The lines connecting the old\npopulation points with select ages along the YSP evolution curve represent\ncomposite stellar populations. The crosses along each line are interpolations\nbetween these two populations in 25\\% increments\nof the contribution of the YSP to the\nintegrated light near 4000 \\AA. The YSP points used for interpolation were chosen\nso that the resulting composite population would come as closely as possible to\nNGC~5018.\n\nThe mean indices for the four spectra of NGC~5018 are plotted as an open triangle \nwith error bars in Figures~\\ref{fig:yspm17}--\\ref{fig:yspp00}. Error bars for the \nNGC~5018 data points were calculated by computing the rms scatter among the four\nobservations. The model trajectories were computed after both the empirical and the \nsynthetic spectral libraries\nhad been smoothed with gaussians to match the resolution\nand intrinsic velocity dispersion of the NGC~5018 spectra which allows comparison between\nthe theoretical integrated indices and those of NGC~5018.\nThe observed indices for~47 Tuc and a spectrum of M32, obtained during the same observing\nrun as the globular cluster spectra, are also plotted in \nFigures~\\ref{fig:yspm17}--\\ref{fig:yspp00} for comparison purposes.\n\n\\subsection{Index Plots}\n\nFigure \\ref{fig:yspm17} shows the index values for a very metal-poor\nYSP ([Fe/H] = -1.7) mixed with two possible old, underlying\npopulations. Figure~\\ref{fig:yspm07} does the same for a moderately\nmetal-poor YSP ([Fe/H] = -0.7). If we also allow the old population\nto be metal-poor (red symbols), we have an extreme version of the case\nput forth by BBB of a strictly metal-poor population. If NGC~5018 were to\nhave such a\npopulation and yet still contain the large amount of structure\nattributed to the galaxy by \\citet{ssfbdg90}, BBB\npostulated that NGC~5018 would either have to be the result of the merging of many\nmetal-poor components or a large metal-poor elliptical\nthat experienced a recent merger. The figures show quite definitively\nthat an old stellar population with a globular cluster-like metallicity of -1.7 combined\nwith either the very metal-poor YSP or the moderately metal-poor YSP is \ndisallowed. Even by choosing\nan age of 13.2 Gyr for the ``young\" population to approach NGC~5018\nas close as possible, the set of allowed indices\ndefined by the possible composite populations are not near the location of \nNGC~5018 in the figures. No combination\nof metal-poor young and old populations nor a single coeval metal-poor\npopulation can reproduce the observed indices.\n\nIf a metal-poor YSP is mixed with a metal-rich old population, we have the\nsituation depicted with the blue symbols in Figures~\\ref{fig:yspm17} \nand~\\ref{fig:yspm07}. In this scenario, NGC~5018 could\nhave evolved as a normal elliptical galaxy but then interacted with a \nyoung, metal-poor disk galaxy. Dust obscuration as suggested by\n\\citet{cd94} would still be needed to explain the\nlack of an upturn in the UV SED. In any case, this population mixture\nis disallowed as well, in agreement with BBB. If a large percentage\nof the light is originating in the old population, the composite has a\nsimilar Ca II index value as NGC~5018 but its H$\\delta$/$\\lambda$4045\nindex is too weak compared to the dominant population in NGC~5018.\n\nIt is only when we allow the YSP to be metal-rich, i.e., solar or greater,\nthat the model indices match the observed values for NGC~5018. \nFigure~\\ref{fig:yspp00full} shows the solar YSP curve from Figure~\\ref{fig:burst}\nagain along with four old population points, two metal-poor (green and red\nsymbols) and two metal-rich (blue and magenta symbols). For clarity, the\ninterpolation curves between the old population points and the YSP curve have\nbeen omitted from Figure~\\ref{fig:yspp00full} and are instead shown on\nFigure~\\ref{fig:yspp00} which is identical to Figure~\\ref{fig:yspp00full} but\non an expanded scale. We derive an age of $\\sim$ 2.8 Gyr for the YSP in\nNGC~5018. Also it is interesting to note in Figure~\\ref{fig:yspp00} that the\nlight at 4000 \\AA\\ is completely dominated by the YSP with virtually 100\\% of the\nlight originating from the YSP regardless of the assumed old population metallicity.\nIn fact, for an old population with [Fe/H] = -1.7, \\emph{any} contribution\nto the light by the old population will drive the model indices away from\nNGC~5018. Even in the most likely scenario, a metal-rich old population with a\nmetal-rich YSP, the old population does not contribute to the integrated light.\nIn this picture, NGC~5018 can evolve as a normal elliptical galaxy and then \ninteract with a metal-rich companion requiring no unusual events to create the stellar\npopulation of NGC~5018.\n \\emph{Thus if an underlying old metal-poor population is present\nin NGC~5018, it cannot be contributing significantly to the integrated blue\nlight.} \n\nWe conclude on the basis of these results that there is a young stellar\npopulation in the central regions of NGC~5018. We infer that the age of\nthis YSP is on the order of 2.8 Gyr, the metallicity is near\nsolar, and it is providing virtually all of the light at 4000 \\AA. These\ndeterminations are reddening independent due to the nature of the spectral\nindices used.\n\n\\section{Discussion}\n\nThe two observations of BBB which led them to conclude that a YSP is\nnot present in NGC~5018 are a low $\\mathrm{Mg_{2}}$ index coupled with\nthe lack of an upturn in the UV SED both comparable to that found in M32. As seen\nin Figures~\\ref{fig:yspm17}--\\ref{fig:yspp00}, however, NGC~5018 lies in a \ndifferent region of the H$\\delta$/$\\lambda$4045--Ca II diagram than M32 hence\nit cannot be just a high luminosity version of M32. With the patchiness of \nthe dust in the central regions of NGC~5018, there may be as much as two\nmagnitudes of extinction in the far-UV part of the spectrum which\ncould explain the lack of an upturn \n\\citep{cd94}. The results\nderived here, however, indicate that large amounts of dust obscuration\nneed not be invoked, although a modest amount of extinction would\nbring Figure \\ref{fig:lick} into better harmony with the spectral\nindex results. The YSP age of~2.8 Gyr derived here is reddening\ninsensitive and thus robust regardless of the structure of the dust\ndistribution. Also, as Figure~\\ref{fig:yspp00} shows, the YSP is\ncompletely dominating the visible part of the spectrum of NGC~5018. A\nYSP of this age does not have an upturn in the UV part of the spectrum.\nHence the small far-UV upturn in NGC~5018 may simply reflect the\ncharacteristics of the 2.8-Gyr-old stellar population\ndominating the light.\n\nThe models predict that a YSP of this age is about 6 times brighter (at\n4000\\AA ) than an ancient population of the same metallicity and IMF. Hence if\nthe relative contributions from the old and young populations were only half\nand half, then the galaxy must be 6 parts old to 1 part\nyoung in the central region. This would qualify as a gas-rich\nmerger event with a rapid gas inflow to the center \\citep{wh93}\n of NGC 5018. If the light contribution is\nweighted even more heavily toward the young population as we suggest, this\nimplies a more violent event, perhaps a merger of two spiral \ngalaxies or some other event involving large amounts of gas consumed in\nstar formation, with an extremely high inflow to the nucleus. Note that,\nif nebular emission is filling in the Balmer lines, the derived age\ndecreases, the YSP is brighter, and so the size of the merging event\ndecreases.\n\nA solar-[Fe/H] population of age 2.8 Gyr has an Mg$_2 \\approx 0.20 $ mag,\nas is observed in NGC~5018. Aging this population to 15 Gyr raises the\nMg$_2$ to 0.27 mag, still about 2 standard deviations from the mean\nrelation for elliptical galaxies, though a dust-hidden YSP could be diluting\nthe Mg$_2$ index \\citep{cd94}. We note, however, \nthat compared to\nM32, NGC~5018's C$_2$4668 index is weaker but its Mg$_2$ index is\nstronger, implying that NGC~5018 may also participate in the general\ntrend for large ellipticals to have enhanced Mg abundance\n\\citep[e.g.,][]{w98}. This will further increase NGC~5018's Mg$_2$ line\nstrength as it ages so that it may one day fall among other\nellipticals in the Mg$_2$-$\\sigma$ relation.\n\nAs mentioned previously, significant emission has been observed in the\ncenter of NGC~5018 \\citep{ghjn94}. Since both of\nthe spectral indices we used depend on the intensity in the center of\na Balmer line, contamination by emission could affect the results\nsignificantly even though the contamination decreases as one moves\ntoward higher order lines in the Balmer sequence. Specifically,\nemission will weaken H$\\delta$ relative to Fe I $\\lambda$4045 and to a\nlesser degree weaken Ca II H+H$\\epsilon$ relative to Ca II K. Each\nindex, if contaminated, will therefore have a higher value than if\nthere were no emission. From\nFigures~\\ref{fig:yspm17}--\\ref{fig:yspp00}, it can be seen that if\nemission contamination were removed, the data points for NGC~5018\nwould shift toward younger ages. The determined YSP age of 2.8\nGyr represents therefore an \\emph{upper limit on the YSP age}. The limited\nspectral coverage does not permit a more detailed analysis of the\nemission contamination, but the fact that H$\\beta$ from Figure\n\\ref{fig:lick} gives the same age indicates that the emission must be\nrelatively modest.\n\nThe power of the method used in this paper is its ability to discriminate\nbetween different, plausible stellar populations. The verification of the \npresence of a YSP in\nNGC~5018 and its age of~2.8 Gyr are quite unambiguous, irrespective of the nature \nof the old, underlying population. Also, this type of determination is not\nunique to NGC~5018. A similar procedure can be applied to any galaxy with\nmorphological peculiarities suspected of harboring more than one coeval stellar\npopulation. With this tool, the effects of a dynamical interaction on the\nintegrated light of a galaxy can be analyzed more fully.\n\n\\acknowledgments\n\nAJL would like to thank Dr.\\ Jim Rose for a lot of guidance and many helpful\ndiscussions, Lewis Jones for providing the spectra of NGC 5018 and the referee,\nDr.\\ Scott Trager, for many helpful suggestions which improved the paper. This \nresearch was partially supported by NSF grant AST-9320723 to the University of \nNorth Carolina and by NASA through grant GO-06664.01-95A awarded by the Space\nTelescope Science Institute which is operated by the Association of\nUniversities for Research in Astronomy, Inc., for NASA under Contract\nNAS5-26555. \n\n\\clearpage\n\n% Now comes the reference list. In this document, we used \\cite to call\n% out citations, so we must use \\bibitem in the reference list, which\n% means we use the LaTeX thebibliography environment. Please note that\n% \\begin{thebibliography} is followed by a null argument. If you forget\n% this, mayhem ensues, and LaTeX will say \"Perhaps a missing item?\" when\n% you run it. Do not call us, do not send mail when this happens. Put\n% the silly {} after the \\begin{thebibliography}.\n%\n% Each reference has a \\bibitem command to define the citation format\n% and the symbolic tag, as well as a \\bibitem[]{} command which sets up\n% formatting parameters for the reference list itself.\n%\n% If we had not bothered with the \\cite-\\bibitem business, calling out\n% the references outselves, the reference list could be enclosed in\n% a references environment (\\begin{references} has no null argument),\n% and there would be no need for the leading \\bibitem's.\n\n\\begin{thebibliography}{}\n\\bibitem[Bender, Burstein, \\& Faber(1993)]{bbf93} Bender, R., Burstein, D., \\& Faber, S. M. 1993, \\apj, 411, 153\n\\bibitem[Bertelli et al.(1994)]{bbcfn94} Bertelli, G., Bressan, A., Chiosi, C., Fagotto, F., \\&\n Nasi, E., 1994, \\aaps, 106, 275\n\\bibitem[Bertola, Burstein, \\& Buson(1993)]{bbb93} Bertola, F., Burstein, D., \\& Buson, L. M., 1993, \\apj,\n 403, 573 (BBB)\n\\bibitem[Bica, Alloin, \\& Schmidt(1990)]{bas90} Bica, E., Alloin, D., \\& Schmidt, A., 1990, \\aap, 228, 23\n\\bibitem[Bruzual \\& Charlot(1993)]{bc93} Bruzual A., G., \\& Charlot, S., 1993, \\apj, 405, 538\n\\bibitem[Burstein et al.(1988)]{bbbfl88} Burstein, D., Bertola, F., Buson, L. M., Faber, S. M., \\& Lauer, T. R.\n1988, \\apj, 328, 440\n\\bibitem[Bushouse, Lamb, \\& Werner(1988)]{blw88} Bushouse, H. A., Lamb, S. A., \\& Werner, M. W., 1988, \\apj, 335, 74\n\\bibitem[Carollo \\& Danziger(1994)]{cd94} Carollo, C. M., \\& Danziger, I. J., 1994, \\mnras, 270, 743\n\\bibitem[Charlot \\& Silk(1994)]{cs94} Charlot, S., \\& Silk, J., 1994, \\apj, 432, 453\n\\bibitem[Couch \\& Sharples(1987)]{cs87} Couch, W. J., \\& Sharples, R. M., 1987, \\mnras, 229, 423\n\\bibitem[Fort et al.(1986)]{fpcmv86} Fort, B. P., Prieur, J.-L., Carter, D., Meatheringham, S. J.,\n \\& Vigroux, L., 1986, \\apj, 306, 110\n\\bibitem[Goudfrooij et al.(1994)]{ghjn94} Goudfrooij, P., Hansen, L., J\\mbox{\\o}rgensen, H. E., \\& \n N\\mbox{\\o}rgaard-Nielsen, H. U., 1994, \\aaps, 105, 341\n\\bibitem[Helou(1986)]{h86} Helou, G., 1986, \\apj, 311, L33\n\\bibitem[Hernquist \\& Quinn(1988)]{hq88} Hernquist, L., \\& Quinn, P. J., 1988, \\apj, 331, 682\n\\bibitem[Hilker \\& Kissler-Patig(1996)]{hk96} Hilker, M., \\& Kissler-Patig, M., 1996, \\aap, 314, 357\n\\bibitem[Jacoby, Hunter, \\& Christian(1984)]{jhc84} Jacoby, G. H., Hunter, D. A., \\& Christian, C. A., 1984, \\apjs,\n 56, 257\n\\bibitem[Jones(1999)]{j99} Jones, L. A., 1999, Ph.D. thesis Univ. of North Carolina\n\\bibitem[Jura et al.(1987)]{jkkg87} Jura, M., Kim, D.-W., Knapp, G. P., \\& Guhathakurta, P., 1987, \\apj,\n 312, L11\n\\bibitem[Kim et al.(1988)]{kgvjk88} Kim, D.-W., Guhathakurta, P., van Gorkom, J. H., Jura, M., \n \\& Knapp, G. R., 1988, \\apj, 330, 684\n\\bibitem[Kurucz(1995)]{k95} Kurucz, R. L., 1995, private communication\n\\bibitem[Lee(1989)]{l89} Lee, Y.-W., 1989, Ph.D. thesis Yale University\n\\bibitem[Leitherer et al.(1996)]{lea96} Leitherer, C., et al., 1996, \\pasp, 108, 996\n\\bibitem[Leonardi(2000)]{l00} Leonardi, A. J., 2000, in preparation\n\\bibitem[Leonardi \\& Rose(1996)]{lr96} Leonardi, A. J., \\& Rose, J. A., 1996, \\aj, 111, 182 (LR)\n\\bibitem[Malin \\& Carter(1983)]{mc83} Malin, D. F., \\& Carter, D., 1983, \\apj, 274, 534\n\\bibitem[Malin \\& Hadley(1997)]{mh97} Malin, D. F., \\& Hadley, B., 1997, Pub. Astro. Soc. of Aus., 14, 52\n\\bibitem[Mihos, Bothun, \\& Richstone(1993)]{mbr93} Mihos, J. C., Bothun, G. D., \\& Richstone, D. O., 1993, \\apj,\n 418, 82\n\\bibitem[Mihos \\& Hernquist(1994a)]{mh94a} Mihos, J. C., \\& Hernquist, L., 1994a, \\apj, 425, L13\n\\bibitem[Mihos \\& Hernquist(1994b)]{mh94b} Mihos, J. C., \\& Hernquist, L., 1994b, \\apj, 431, L9\n\\bibitem[O'Connell(1988)]{o88} O'Connell, R. W., 1988, in Towards Understanding Galaxies at High\n Redshift, ed. R. G. Kron \\& A. Renzini (Dordrecht: Kluwer), 177\n\\bibitem[Quinn(1984)]{q84} Quinn, P. J., 1984, \\apj, 279, 596\n\\bibitem[Rose(1984)]{r84} Rose, J. A., 1984, \\aj, 89, 1238\n\\bibitem[Rose(1985)]{r85} Rose, J. A., 1985, \\aj, 90, 1927\n\\bibitem[Schweizer(1983)]{s83} Schweizer, F., 1983, in Proc. IAU Symp. 100, Internal Kinematics\n and Dynamics of Galaxies, ed. E. Athanassoula (Dordrecht: Reidel), 319\n\\bibitem[Schweizer et al.(1990)]{ssfbdg90} Schweizer, F., Seitzer, P., Faber, S. M., Burstein, D., \n Dalle Ore, C. M., \\& Gonzalez, J. J., 1990, \\apj, 364, L33\n\\bibitem[Thronson \\& Bally(1987)]{tb87} Thronson, H. A., \\& Bally, J., 1987, \\apj, 319, L63\n\\bibitem[Toomre \\& Toomre(1972)]{tt72} Toomre, A., \\& Toomre, J., 1972, \\apj, 178, 623\n\\bibitem[Trager et al.(1998)]{twfbg98} Trager, S. C., Worthey, G., Faber, S. M., Burstein, D.,\n \\& Gonz\\'alez, J. J. 1998, \\apjs, 116, 1\n\\bibitem[Weil \\& Hernquist(1993)]{wh93} Weil, M. L., \\& Hernquist, L., 1993, \\apj, 405, 142\n\\bibitem[Worthey(1994)]{w94} Worthey, G., 1994, \\apjs, 95, 107\n\\bibitem[Worthey(1998)]{w98} Worthey, G., 1998, \\pasp, 110, 888\n\\bibitem[Worthey, Dorman, \\& Jones(1996)]{wdj96} Worthey, G., Dorman, B., \\& Jones, L. A. 1996, \\aj, 112, 948\n\n\\end{thebibliography}\n\n% Finally, we have figure captions. Usually these must be on a separate\n% page, although unlike table, it is often permissible to have several\n% figure captions on the same page. We force the page break between\n% the reference list and the figure captions.\n%\n% The \\caption command in the figure environment works like the one in the\n% table environment (it's the same one, actually), except that this one\n% produces identification text that reads \"Figure N.\"\n\n\\clearpage\n\n\\begin{figure}\n\\caption{Two age-sensitive indices, a UV-visual color and an\nH$\\beta$ index, are plotted versus metal-sensitive spectral index\nC$_2$4668. The color $\\lambda 2750 - V = {\\rm log} F_{\\lambda 2750} -\n{\\rm log} F_V$ following Burstein et al. 1988 and BBB, and has units of\ndex rather than magnitudes. The marked dust screen extinction also\nrefers to a straight logarithm, that is, $A_V = 0.1$ dex, or 0.25 mag. \nThe $\\lambda 2750$ passband is an average of BBB and Burstein et al.\ndata from $\\lambda 2650$ to $\\lambda 2850$ with their extinction\ncorrections applied. Optical spectral indices on the Lick system come\nfrom Trager et al. (1998). The optical data was taken from a\nsignificantly smaller aperture than the IUE UV data, so the C$_2$4668\nindex should be weakened somewhat (a few tenths of \\AA ) to compensate\nfor this mismatch in the upper panel. Error bars in bold refer to M32\nand M31 data, wider bars to the rest of the sample. Models from Worthey\n(1994) appear as a grid labeled by scaled solar metallicity and age in\nGyr. Models are scaled solar and thus do not track element\noverenhancements. Such an effect probably exists for the C$_2$4668\nindex; the larger galaxies have a C$_2$4668 index stronger than their\naverage abundance would dictate. In the upper panel, an arrow attached\nto M31 is an estimate of the effect of subtracting the hot star\ncomponent (which is not included in the models) from the spectrum, as\nmodeled by Worthey et al. (1996). The indicated effect is an\nunderestimate because Worthey et al. maximized the contribution from\nvery hot PAGB stars. Similar corrections should be made for NGC 3115 and\nNGC 3379, but we lack appropriate spectrophotometric data. NGC 3115 has\na UV upturn similar to M31, but NGC 3379 has considerably more UV flux,\nso its correction is likely to be quite large. The other galaxies have\nvery weak UV emission so that their corrections are negligible. Large\ncorrections for emission fill-in in the H$\\beta$ index are unlikely for\nthe galaxies plotted. If corrections are applied, galaxies move\nvertically to younger ages and somewhat higher abundance.}\n\\label{fig:lick}\n\\end{figure}\n \n\\begin{figure}\n\\caption{One of the long-slit spectra of NGC~5018 used to calculate the mean \nspectral indices.\nEach spectra was smoothed with a gaussian of 0.5 pixels. The absorption features\nused in the age-dating technique are identified.} \n\\label{fig:spec}\n\\end{figure}\n \n\\begin{figure}\n\\caption{The CaII index is plotted vs the H$\\delta$/$\\lambda$4045 index for an\ninstantaneous burst of star formation with [Fe/H] = -0.7 (red solid and \nshort-dashed line) and [Fe/H] = 0.0 (blue long-dashed line). The colored \nlines represent the evolution of the index values as the population ages. Various ages\n(in Gyr) have been marked by solid squares. For clarity, the path from \n0.004 Gyr to 0.5 Gyr on the [Fe/H] = -0.7 curve has been marked with a\nshort-dashed line while the evolution subsequent to 0.5 Gyr has been marked\nwith a solid line. An old, metal-poor model (green circle) is plotted to show the\neffects of horizontal branch morphology on the indices (see text). The error bars \nfor the labeled globular\ncluster points (open triangles) are smaller than the plotting symbol.} \\label{fig:burst}\n\\end{figure}\n\n\\begin{figure}\n\\caption{Ca II plotted vs H$\\delta$/$\\lambda$4045 for a composite population\nconsisting of a metal-poor young population ([Fe/H] = -1.7; evolution\nmarked by the solid black curve, with specific ages labeled by the solid squares) \nand one of two OSP (age = 15.1 Gyr) populations ([Fe/H] = -1.7, marked by the \nsolid red circle \nand [Fe/H] = 0.0, marked by the solid blue circle).\nDotted lines between the old population point and the 13.2 Gyr YSP point denote\ninterpolations between these two populations with each cross along the\nOSP [Fe/H] = 0.0 curve marked with the fractional contribution of the YSP\nto the total integrated light at 4000 \\AA. The crosses along the OSP [Fe/H] = -1.7\ncurve are similar but have been left off for clarity. The indices for NGC~5018, \nM32, and 47 Tuc are plotted as open triangles.} \\label{fig:yspm17}\n\\end{figure}\n\n\\begin{figure}\n\\caption{Same as Fig. \\ref{fig:yspm17} but with the YSP [Fe/H] = -0.7.} \n \\label{fig:yspm07}\n\\end{figure}\n\\begin{figure}\n\\caption{Same as Fig. \\ref{fig:yspm17} but with the YSP [Fe/H] = 0.0. Also,\ntwo other old populations have been added: [Fe/H] = -0.7 (green solid circle)\nand [Fe/H] = +0.4 (magenta solid circle). For clarity, the interpolations between\nthe OSPs and the YSP have been omitted and are shown in Fig. \\ref{fig:yspp00} on\nan expanded scale.} \\label{fig:yspp00full}\n\\end{figure}\n\n\\begin{figure}\n\\caption{Identical to Fig. \\ref{fig:yspp00full} but with an expanded scale on the\nCa II axis. Also, the interpolations between the OSP points and the YSP points\nnearest NGC~5018 are shown.\nThe increment crosses along the\n[Fe/H] = -0.7 and [Fe/H] = +0.0 curves have been omitted for clarity.}\n\\label{fig:yspp00}\n\\end{figure}\n\n\n% That's all, folks.\n%\n% The technique of segregating major semantic components of the document\n% within \"environments\" is a very good one, but you as an author have to\n% come up with a way of making sure each \\begin{whatzit} has a corresponding\n% \\end{whatzit}. If you miss one, LaTeX will probably complain a great\n% deal during the composition of the document. Occasionally, you get away\n% with it right up to the \\end{document}, in which case, you will see\n% \"\\begin{whatzit} ended by \\end{document}\".\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002321.extracted_bib",
"string": "\\begin{thebibliography} is followed by a null argument. If you forget\n% this, mayhem ensues, and LaTeX will say \"Perhaps a missing item?\" when\n% you run it. Do not call us, do not send mail when this happens. Put\n% the silly {} after the \\begin{thebibliography}.\n%\n% Each reference has a \\bibitem command to define the citation format\n% and the symbolic tag, as well as a \\bibitem[]{} command which sets up\n% formatting parameters for the reference list itself.\n%\n% If we had not bothered with the \\cite-\\bibitem business, calling out\n% the references outselves, the reference list could be enclosed in\n% a references environment (\\begin{references} has no null argument),\n% and there would be no need for the leading \\bibitem's.\n\n\\begin{thebibliography}{}\n\\bibitem[Bender, Burstein, \\& Faber(1993)]{bbf93} Bender, R., Burstein, D., \\& Faber, S. M. 1993, \\apj, 411, 153\n\\bibitem[Bertelli et al.(1994)]{bbcfn94} Bertelli, G., Bressan, A., Chiosi, C., Fagotto, F., \\&\n Nasi, E., 1994, \\aaps, 106, 275\n\\bibitem[Bertola, Burstein, \\& Buson(1993)]{bbb93} Bertola, F., Burstein, D., \\& Buson, L. M., 1993, \\apj,\n 403, 573 (BBB)\n\\bibitem[Bica, Alloin, \\& Schmidt(1990)]{bas90} Bica, E., Alloin, D., \\& Schmidt, A., 1990, \\aap, 228, 23\n\\bibitem[Bruzual \\& Charlot(1993)]{bc93} Bruzual A., G., \\& Charlot, S., 1993, \\apj, 405, 538\n\\bibitem[Burstein et al.(1988)]{bbbfl88} Burstein, D., Bertola, F., Buson, L. M., Faber, S. M., \\& Lauer, T. R.\n1988, \\apj, 328, 440\n\\bibitem[Bushouse, Lamb, \\& Werner(1988)]{blw88} Bushouse, H. A., Lamb, S. A., \\& Werner, M. W., 1988, \\apj, 335, 74\n\\bibitem[Carollo \\& Danziger(1994)]{cd94} Carollo, C. M., \\& Danziger, I. J., 1994, \\mnras, 270, 743\n\\bibitem[Charlot \\& Silk(1994)]{cs94} Charlot, S., \\& Silk, J., 1994, \\apj, 432, 453\n\\bibitem[Couch \\& Sharples(1987)]{cs87} Couch, W. J., \\& Sharples, R. M., 1987, \\mnras, 229, 423\n\\bibitem[Fort et al.(1986)]{fpcmv86} Fort, B. P., Prieur, J.-L., Carter, D., Meatheringham, S. J.,\n \\& Vigroux, L., 1986, \\apj, 306, 110\n\\bibitem[Goudfrooij et al.(1994)]{ghjn94} Goudfrooij, P., Hansen, L., J\\mbox{\\o}rgensen, H. E., \\& \n N\\mbox{\\o}rgaard-Nielsen, H. U., 1994, \\aaps, 105, 341\n\\bibitem[Helou(1986)]{h86} Helou, G., 1986, \\apj, 311, L33\n\\bibitem[Hernquist \\& Quinn(1988)]{hq88} Hernquist, L., \\& Quinn, P. J., 1988, \\apj, 331, 682\n\\bibitem[Hilker \\& Kissler-Patig(1996)]{hk96} Hilker, M., \\& Kissler-Patig, M., 1996, \\aap, 314, 357\n\\bibitem[Jacoby, Hunter, \\& Christian(1984)]{jhc84} Jacoby, G. H., Hunter, D. A., \\& Christian, C. A., 1984, \\apjs,\n 56, 257\n\\bibitem[Jones(1999)]{j99} Jones, L. A., 1999, Ph.D. thesis Univ. of North Carolina\n\\bibitem[Jura et al.(1987)]{jkkg87} Jura, M., Kim, D.-W., Knapp, G. P., \\& Guhathakurta, P., 1987, \\apj,\n 312, L11\n\\bibitem[Kim et al.(1988)]{kgvjk88} Kim, D.-W., Guhathakurta, P., van Gorkom, J. H., Jura, M., \n \\& Knapp, G. R., 1988, \\apj, 330, 684\n\\bibitem[Kurucz(1995)]{k95} Kurucz, R. L., 1995, private communication\n\\bibitem[Lee(1989)]{l89} Lee, Y.-W., 1989, Ph.D. thesis Yale University\n\\bibitem[Leitherer et al.(1996)]{lea96} Leitherer, C., et al., 1996, \\pasp, 108, 996\n\\bibitem[Leonardi(2000)]{l00} Leonardi, A. J., 2000, in preparation\n\\bibitem[Leonardi \\& Rose(1996)]{lr96} Leonardi, A. J., \\& Rose, J. A., 1996, \\aj, 111, 182 (LR)\n\\bibitem[Malin \\& Carter(1983)]{mc83} Malin, D. F., \\& Carter, D., 1983, \\apj, 274, 534\n\\bibitem[Malin \\& Hadley(1997)]{mh97} Malin, D. F., \\& Hadley, B., 1997, Pub. Astro. Soc. of Aus., 14, 52\n\\bibitem[Mihos, Bothun, \\& Richstone(1993)]{mbr93} Mihos, J. C., Bothun, G. D., \\& Richstone, D. O., 1993, \\apj,\n 418, 82\n\\bibitem[Mihos \\& Hernquist(1994a)]{mh94a} Mihos, J. C., \\& Hernquist, L., 1994a, \\apj, 425, L13\n\\bibitem[Mihos \\& Hernquist(1994b)]{mh94b} Mihos, J. C., \\& Hernquist, L., 1994b, \\apj, 431, L9\n\\bibitem[O'Connell(1988)]{o88} O'Connell, R. W., 1988, in Towards Understanding Galaxies at High\n Redshift, ed. R. G. Kron \\& A. Renzini (Dordrecht: Kluwer), 177\n\\bibitem[Quinn(1984)]{q84} Quinn, P. J., 1984, \\apj, 279, 596\n\\bibitem[Rose(1984)]{r84} Rose, J. A., 1984, \\aj, 89, 1238\n\\bibitem[Rose(1985)]{r85} Rose, J. A., 1985, \\aj, 90, 1927\n\\bibitem[Schweizer(1983)]{s83} Schweizer, F., 1983, in Proc. IAU Symp. 100, Internal Kinematics\n and Dynamics of Galaxies, ed. E. Athanassoula (Dordrecht: Reidel), 319\n\\bibitem[Schweizer et al.(1990)]{ssfbdg90} Schweizer, F., Seitzer, P., Faber, S. M., Burstein, D., \n Dalle Ore, C. M., \\& Gonzalez, J. J., 1990, \\apj, 364, L33\n\\bibitem[Thronson \\& Bally(1987)]{tb87} Thronson, H. A., \\& Bally, J., 1987, \\apj, 319, L63\n\\bibitem[Toomre \\& Toomre(1972)]{tt72} Toomre, A., \\& Toomre, J., 1972, \\apj, 178, 623\n\\bibitem[Trager et al.(1998)]{twfbg98} Trager, S. C., Worthey, G., Faber, S. M., Burstein, D.,\n \\& Gonz\\'alez, J. J. 1998, \\apjs, 116, 1\n\\bibitem[Weil \\& Hernquist(1993)]{wh93} Weil, M. L., \\& Hernquist, L., 1993, \\apj, 405, 142\n\\bibitem[Worthey(1994)]{w94} Worthey, G., 1994, \\apjs, 95, 107\n\\bibitem[Worthey(1998)]{w98} Worthey, G., 1998, \\pasp, 110, 888\n\\bibitem[Worthey, Dorman, \\& Jones(1996)]{wdj96} Worthey, G., Dorman, B., \\& Jones, L. A. 1996, \\aj, 112, 948\n\n\\end{thebibliography}"
}
] |
astro-ph0002322
|
Testing the connection between the X-ray and submillimetre source populations using {Chandra}
|
[
{
"author": "A.C.\\ Fabian$^1$"
},
{
"author": "Ian Smail$^2$"
},
{
"author": "K.\\ Iwasawa$^1$"
},
{
"author": "S.W.\\ Allen$^1$"
},
{
"author": "A.W.\\ Blain$^1$"
},
{
"author": "C.S.\\ Crawford$^1$"
},
{
"author": "S.\\ Ettori"
},
{
"author": "$^1$ R.J.\\ Ivison$^3$"
},
{
"author": "R.M.\\ Johnstone$^1$"
},
{
"author": "J.-P.\\ Kneib$^4$ and R.J.\\ Wilman$^1$"
},
{
"author": "\\vspace*{1mm}"
},
{
"author": "Madingley Road"
},
{
"author": "Cambridge CB3 0HA"
},
{
"author": "$^2$ Department of Physics"
},
{
"author": "South Road"
},
{
"author": "Durham"
},
{
"author": "DH1 3LE"
},
{
"author": "$^3$ Department of Physics \\& Astronomy"
},
{
"author": "Gower Street"
},
{
"author": "London"
},
{
"author": "WC1E 6BT"
},
{
"author": "$^4$ Observatoire Midi-Pyr\\'en\\'ees"
},
{
"author": "14 Avenue E.\\ Belin"
},
{
"author": "31400 Toulouse"
},
{
"author": "France"
}
] |
The powerful combination of the {Chandra} X-ray telescope, the SCUBA submillimetre-wave camera and the gravitational lensing effect of the massive galaxy clusters A\,2390 and A\,1835 has been used to place stringent X-ray flux limits on six faint submillimetre SCUBA sources and deep submillimetre limits on three {Chandra} sources which lie in fields common to both instruments. One further source is marginally detected in both the X-ray and submillimetre bands. For all the SCUBA sources our results are consistent with starburst-dominated emission. For two objects, including SMMJ\,14011+0252 at $z=2.55$, the constraints are strong enough that they can only host powerful active galactic nuclei if they are both Compton-thick and any scattered X-ray flux is weak or itself absorbed. The lensing amplification for the sources is in the range 1.5--7, assuming that they lie at $z\gs 1$. The brightest detected X-ray source has a faint extended optical counterpart ($I\approx22$) with colours consistent with a galaxy at $z\simeq 1$. The X-ray spectrum of this galaxy is hard, implying strong intrinsic absorption with a column density of about $10^{23}\psqcm$ and an intrinsic (unabsorbed) 2--10~keV luminosity of $3\times 10^{44}\ergps$. This source is therefore a Type-II quasar. The weakest detected X-ray sources are not detected in {HST} images down to $I\simeq 26$.
|
[
{
"name": "ma155.tex",
"string": "\\def\\cm{{\\rm\\thinspace cm}}\n\\def\\dyn{{\\rm\\thinspace dyn}}\n\\def\\erg{{\\rm\\thinspace erg}}\n\\def\\eV{{\\rm\\thinspace eV}}\n\\def\\MeV{{\\rm\\thinspace MeV}}\n\\def\\g{{\\rm\\thinspace g}}\n\\def\\ga{{\\rm\\thinspace gauss}}\n\\def\\K{{\\rm\\thinspace K}}\n\\def\\keV{{\\rm\\thinspace keV}}\n\\def\\km{{\\rm\\thinspace km}}\n\\def\\kpc{{\\rm\\thinspace kpc}}\n\\def\\Lsun{\\hbox{$\\rm\\thinspace L_{\\odot}$}}\n\\def\\m{{\\rm\\thinspace m}}\n\\def\\Mpc{{\\rm\\thinspace Mpc}}\n\\def\\Msun{\\hbox{$\\rm\\thinspace M_{\\odot}$}}\n\\def\\pc{{\\rm\\thinspace pc}}\n\\def\\ph{{\\rm\\thinspace ph}}\n\\def\\s{{\\rm\\thinspace s}}\n\\def\\yr{{\\rm\\thinspace yr}}\n\\def\\sr{{\\rm\\thinspace sr}}\n\\def\\Hz{{\\rm\\thinspace Hz}}\n\\def\\MHz{{\\rm\\thinspace MHz}}\n\\def\\GHz{{\\rm\\thinspace GHz}}\n\\def\\chisq{\\hbox{$\\chi^2$}}\n\\def\\delchi{\\hbox{$\\Delta\\chi$}}\n\\def\\cmps{\\hbox{$\\cm\\s^{-1}\\,$}}\n\\def\\cmpssq{\\hbox{$\\cm\\s^{-2}\\,$}}\n\\def\\cmsq{\\hbox{$\\cm^2\\,$}}\n\\def\\cmcu{\\hbox{$\\cm^3\\,$}}\n\\def\\pcmcu{\\hbox{$\\cm^{-3}\\,$}}\n\\def\\pcmcuK{\\hbox{$\\cm^{-3}\\K\\,$}}\n\\def\\dynpcmsq{\\hbox{$\\dyn\\cm^{-2}\\,$}}\n\\def\\ergcmcups{\\hbox{$\\erg\\cm^3\\ps\\,$}}\n\\def\\ergpcmps{\\hbox{$\\erg\\cm^{-3}\\s^{-1}\\,$}}\n\\def\\ergpcmsqps{\\hbox{$\\erg\\cm^{-2}\\s^{-1}\\,$}}\n\\def\\ergpcmsqpspA{\\hbox{$\\erg\\cm^{-2}\\s^{-1}$\\AA$^{-1}\\,$}}\n\\def\\ergpcmsqpspsr{\\hbox{$\\erg\\cm^{-2}\\s^{-1}\\sr^{-1}\\,$}}\n\\def\\ergpcmcups{\\hbox{$\\erg\\cm^{-3}\\s^{-1}\\,$}}\n\\def\\ergps{\\hbox{$\\erg\\s^{-1}\\,$}}\n\\def\\ergpspmp{\\hbox{$\\erg\\s^{-1}\\Mpc^{-3}\\,$}}\n\\def\\gpcm{\\hbox{$\\g\\cm^{-3}\\,$}}\n\\def\\gpcmps{\\hbox{$\\g\\cm^{-3}\\s^{-1}\\,$}}\n\\def\\gps{\\hbox{$\\g\\s^{-1}\\,$}}\n\\def\\Jy{{\\rm Jy}}\n\\def\\keVpcmsqpspsr{\\hbox{$\\keV\\cm^{-2}\\s^{-1}\\sr^{-1}\\,$}}\n\\def\\kmps{\\hbox{$\\km\\s^{-1}\\,$}}\n\\def\\kmpspmp{\\hbox{$\\km\\s^{-1}\\Mpc{-1}\\,$}}\n\\def\\Lsunppc{\\hbox{$\\Lsun\\pc^{-3}\\,$}}\n\\def\\Msunpc{\\hbox{$\\Msun\\pc^{-3}\\,$}}\n\\def\\Msunpkpc{\\hbox{$\\Msun\\kpc^{-1}\\,$}}\n\\def\\Msunppc{\\hbox{$\\Msun\\pc^{-3}\\,$}}\n\\def\\Msunppcpyr{\\hbox{$\\Msun\\pc^{-3}\\yr^{-1}\\,$}}\n\\def\\Msunpyr{\\hbox{$\\Msun\\yr^{-1}\\,$}}\n\\def\\pcm{\\hbox{$\\cm^{-3}\\,$}}\n\\def\\pcmsq{\\hbox{$\\cm^{-2}\\,$}}\n\\def\\pcmK{\\hbox{$\\cm^{-3}\\K$}}\n\\def\\phpcmsqps{\\hbox{$\\ph\\cm^{-2}\\s^{-1}\\,$}}\n\\def\\pHz{\\hbox{$\\Hz^{-1}\\,$}}\n\\def\\pmpc{\\hbox{$\\Mpc^{-1}\\,$}}\n\\def\\pmpccu{\\hbox{$\\Mpc^{-3}\\,$}}\n\\def\\ps{\\hbox{$\\s^{-1}\\,$}}\n\\def\\psqcm{\\hbox{$\\cm^{-2}\\,$}}\n\\def\\psr{\\hbox{$\\sr^{-1}\\,$}}\n\\def\\kmpspMpc{\\hbox{$\\kmps\\Mpc^{-1}$}}\n\n\\def\\gs{\\mathrel{\\raise0.35ex\\hbox{$\\scriptstyle >$}\\kern-0.6em\n\\lower0.40ex\\hbox{{$\\scriptstyle \\sim$}}}}\n\\def\\ls{\\mathrel{\\raise0.35ex\\hbox{$\\scriptstyle <$}\\kern-0.6em\n\\lower0.40ex\\hbox{{$\\scriptstyle \\sim$}}}}\n%\n\\documentstyle[psfig,times]{mn}\n%\n\\begin{document}\n\n\\title[{\\it Chandra}--SCUBA sources]\n{Testing the connection between the X-ray and submillimetre source\npopulations using {\\it Chandra}}\n\\author[Fabian et al.]\n{A.C.\\ Fabian$^1$, Ian Smail$^2$, K.\\ Iwasawa$^1$, S.W.\\ Allen$^1$,\nA.W.\\ Blain$^1$, C.S.\\ Crawford$^1$, \\and S.\\ Ettori,$^1$ R.J.\\\nIvison$^3$, R.M.\\ Johnstone$^1$, J.-P.\\ Kneib$^4$ and R.J.\\\nWilman$^1$\\\\\n\\vspace*{1mm}\\\\\n$^1$ Institute of Astronomy, Madingley Road, Cambridge CB3 0HA \\\\\n$^2$ Department of Physics, University of Durham, South Road, Durham,\nDH1 3LE\\\\\n$^3$ Department of Physics \\& Astronomy, University College London, Gower\nStreet, London, WC1E 6BT\\\\\n$^4$ Observatoire Midi-Pyr\\'en\\'ees, 14 Avenue E.\\ Belin, 31400 Toulouse, \nFrance\n}\n\\maketitle\n\n\\begin{abstract}\nThe powerful combination of the {\\it Chandra} X-ray telescope, the\nSCUBA submillimetre-wave camera and the gravitational lensing effect\nof the massive galaxy clusters A\\,2390 and A\\,1835 has been used to\nplace stringent X-ray flux limits on six faint submillimetre SCUBA\nsources and deep submillimetre limits on three {\\it Chandra} sources\nwhich lie in fields common to both instruments. One further source is\nmarginally detected in both the X-ray and submillimetre bands. For all\nthe SCUBA sources our results are consistent with starburst-dominated\nemission. For two objects, including SMMJ\\,14011+0252 at $z=2.55$, the\nconstraints are strong enough that they can only host powerful active\ngalactic nuclei if they are both Compton-thick and any scattered X-ray\nflux is weak or itself absorbed. The lensing amplification for the\nsources is in the range 1.5--7, assuming that they lie at $z\\gs 1$.\nThe brightest detected X-ray source has a faint extended optical\ncounterpart ($I\\approx22$) with colours consistent with a galaxy at\n$z\\simeq 1$. The X-ray spectrum of this galaxy is hard, implying\nstrong intrinsic absorption with a column density of about\n$10^{23}\\psqcm$ and an intrinsic (unabsorbed) 2--10~keV luminosity of\n$3\\times 10^{44}\\ergps$. This source is therefore a Type-II quasar.\nThe weakest detected X-ray sources are not detected in {\\it HST}\nimages down to $I\\simeq 26$.\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies:active -- quasars:general -- galaxies:Seyfert --\ngalaxies:formation -- galaxies:starburst -- infrared:galaxies\n-- X-rays:general\n\\end{keywords}\n\n\\section{Introduction}\nThe spectrum of the X-ray Background (XRB) over the 1-7~keV band is a\npower-law of energy index 0.4 (Gendreau et al.\\ 1995) which is flatter\nthan that of any known class of extragalactic source. Following the\noriginal suggestion of Setti \\& Woltjer (1989), it is commonly assumed\nthat this is due to the XRB being dominated by many absorbed sources.\nThese sources, with different absorbing column densities and\nredshifts, combine to give the observed XRB spectrum (Madau,\nGhisellini \\& Fabian 1994; Matt \\& Fabian 1994; Comastri et al.\\ 1995;\nWilman \\& Fabian 1999). The absorbed energy is presumably reradiated\nin the Far InfraRed (FIR) band, as observed in nearby heavily absorbed\nActive Galactic Nuclei (AGN) like that in the luminous {\\it IRAS}\ngalaxy NGC\\,6240 (Vignati et al.\\ 1999). The residual harder X-ray\nemission which penetrates the absorbing medium, and the tail of the\nreradiated emission in the submillimetre band from such an source both\nexhibit a negative K-correction. This means that obscured AGN should\nbe detectable to large redshifts in both bands.\n\nObservations of the XRB with {\\it Chandra} show that much (more than\n80 per cent) of it is resolved into point sources in the 2--8~keV band\n(Brandt et al.\\ 2000; Mushotzky et al.\\ 2000). More than half the\nintensity is due to a combination of hard sources identified with\neither otherwise normal bright galaxies or in optically faint or even\ninvisible galaxies. Deep 850-$\\mu$m submillimetre observations with\nSCUBA show that much (more than 80 per cent) of the submillimetre\nbackground seen by {\\it COBE}-FIRAS (Fixsen et al.\\ 1998) at this\nwavelength is resolved into discrete sources (Blain et al.\\ 1999).\n\nA key question is what fraction of the deep X-ray and submillimetre\nsource populations are related. The far-infrared and submillimetre\nbackground represents a significant part of the energy output of\nobjects in the Universe. If the contribution of starbursts and AGN to\nthe background can be separated using deep X-ray images, then the\nrelative importance of high-mass star formation and AGN in heating the\ndust responsible for this emission can be determined. Recent\nmodelling suggests that the AGN fraction in the submillimetre background is\nabout 20 per cent (Almaini, Lawrence \\& Boyle 1999; Fabian \\& Iwasawa\n1999; Gunn \\& Shanks 1999). The uncertainty is such that AGN may\ncontribute in total between 10--50 per cent of the total energy output\nof stars (Fabian 1999).\n\nSmail et al.\\ (1997, 1998) have used the SCUBA instrument at the JCMT\n(Holland et al 1999) to study the submillimetre sources in seven\nmassive clusters of galaxies at redshifts between 0.2 and 0.4,\nexploiting the gravitational lensing magnification from the clusters to\nmake an exceptionally deep 850-$\\mu$m survey for background sources.\n{\\it Chandra} images of two of the clusters, A\\,2390 and A\\,1835, have\nrecently been obtained which, owing to the superb angular resolution,\nprobe much deeper than any previous X-ray images of these regions, for\nexample the {\\it ROSAT}-HRI limit of $8 \\times\n10^{-14}$\\,erg\\s$^{-1}$\\,cm$^{-2}$ to the 0.1--2.0\\,keV X-ray flux of\nthe SCUBA source SMMJ\\,14011+0252 in A\\,1835 (Ivison et al.\\ 2000).\nHere we study the {\\it Chandra} X-ray limits to the flux of the SCUBA\nsources and conversely SCUBA limits on the {\\it Chandra} sources\nfound in the images. Only one source is marginally detected in both\nwavebands. We then discuss the implications for obscured AGN models.\n\n\\section{Observations and Results}\n\n{\\it Chandra} observed A\\,2390 on 1999 November 5 for a livetime of\n9,126~s and A\\,1835 on 1999 December 11 for a total of 19,626~s. For\neach observation the cluster lies close to the aimpoint of the\ntelescope on the ACIS-S back-illuminated CCD chip. Only mild temporal\nvariations in count rate are seen through the observations so we use\nthe whole exposure in this work. A 7-arcsec pointing offset evident in\nthe A\\,1835 field from the position of the cluster X-ray peak and\nseveral other source identified in the field has been removed. We estimate that\nthe source positions from the {\\it Chandra} images are accurate\nto 1$''$ rms.\n\nThe analysis of the cluster emission will be presented elsewhere;\nhere we restrict ourselves to the positions of the SCUBA sources and\nof three X-ray sources in the {\\it Chandra} fields which lie within the\nSCUBA field (i.e.\\ within 1.5~arcmin of the cluster centre; Table\n1). A further possible ($2.8\\sigma$) X-ray source in the A\\,2390 field\nis also discussed since it is spatially coincident with a tentative\n($2\\sigma$) SCUBA source. No point-like X-ray sources are seen in the\nSCUBA region of the {\\it Chandra} field of A\\,1835. \n\nThe X-ray data were analysed using images in the 0.5--2~keV and\n2--7~keV bands with one-arcsec pixels. The sources detected in the\nSCUBA field of A\\,2390 appear principally in just 4 neighbouring\nChandra pixels (a few counts from the brightest sources occupy 2\nfurther pixels). We therefore adopt a region of 4 sq.\\ arcsec when\nestimating source fluxes and limits. The cluster emission means that\nthe background is not flat, and so the background has been determined\nby averaging the 8 neighbouring pixels in images formed with 10 by 10\narcsec pixels, excluding the source pixel. Upper limits in the X-ray\nband have been obtained by using the Bayesian method of Kraft, Burrows\n\\& Nousek (1990) and are quoted at the 99 per cent confidence level\n(Table 2). We assume Galactic columns of $6.8\\times 10^{20}\\psqcm$\nfor A\\,2390 and $2.3\\times 10^{20}\\psqcm$ for A\\,1835.\n\nThe submillimetre, radio and optical imaging of A\\,1835 used here is\ndiscussed in detail in Ivison et al.\\ (2000), while the submillimetre\nobservations of A\\,2390 are detailed in Smail et al.\\ (1998; a new\nsources is reported here), the VLA 1.4-GHz radio map in Edge et al.\\\n(1999) and the optical imaging of this cluster with {\\it Hubble Space\nTelescope} (HST) is described in Pell\\'o et al.\\ (1999). In addition,\nthere is deep 6.7$\\mu$m and 15-$\\mu$m {\\it ISO} imaging of A\\,2390\n(Altieri et al.\\ 1999; Lemonon et al.\\ 1999), which is sensitive to\nhot dust emission from background galaxies out to $z\\sim 1$.\n\n\\begin{figure*}\n\\centerline{\\psfig{figure=fig1.ps,width=0.8\\textwidth}}\n\\caption{\nOptical, X-ray and submm views of the ten {\\it Chandra} and SCUBA\nsources lying within the SCUBA maps of A\\,2390 and A\\,1835. For each\nsource we show two panels, in the left-hand panel we overlay the {\\it\nChandra} image on the optical images of the field, the right-hand\npanel shows the equivalent view with the SCUBA map overlayed. The\noptical image for A\\,1835 is the ground-based $I$-band exposure from\nIvison et al.\\ (2000), while for A\\,2390 we have combined the {\\it\nHST} WFPC2 F555W and F814W images (Pell\\'o et al.\\ 1999) and rebinned\nthese to the scale of the A\\,1835 $I$-band image to enhance the\nvisibility of faint extended features. Each panel is 10 arcsec\nsquare, with north top and east left. The {\\it Chandra} images have\nbeen convolved with a 0.8$''$-FWHM gaussian for display purposes.}\n\\end{figure*}\n\n\nIn Fig.~1 we show overlays of the {\\it Chandra} and SCUBA images on\noptical images of A\\,1835 and A\\,2390. We note that the brightest {\\it\nChandra} source, CXOUJ215334.0+174240, is associated with a relatively\nlarge (4$''$ total extent) mid-type spiral with a blue nucleus and a\nfaint companion. This galaxy has a colour and apparent magnitude\nsimilar to those expected for a slightly reddened $L^\\ast$ mid-type spiral\nat $z=0.85\\pm0.15$. While the next brightest X-ray source,\nCXOUJ215333.2+174209 has a more amorphous counterpart, with a bright\ncompact nucleus and an asymmetric envelope and has a much bluer colour,\nits redshift is not strongly constrained by the current data.\nCounterparts to the remaining two {\\it Chandra} sources are not seen in\nthe optical imaging (although there is a very faint object in the\nvicinity of CXOUJ215334.4+174205); if they are background galaxies\nthen, after correction for lensing amplification, they must be fainter\nthan $I\\sim 27$. CXOUJ215334.0+174240 is the only one of the four {\\it\nChandra} sources detected at 1.4~GHz with the VLA, at a flux density of\n$2.6\\pm 0.1$ mJy, the 3-$\\sigma$ limits on the remainder being $<0.2$\nmJy.\n\nFor the two X-ray sources which are detected in both X-ray bands we\nhave determined an X-ray spectral index, $\\alpha_{\\rm x}$ from the\nflux ratios. These are both unphysically negative ($-0.8$ and $-0.3$;\nwe define all spectral indices according to $F\\propto \\nu^{-\\alpha}$)\nand thus indicate intrinsic absorption. The brightest source,\nCXOUJ215334.0+174240, has $\\sim 90$ counts, which enables a crude\nspectral analysis to be performed. A straight power-law spectrum with\nGalactic absorption is a poor fit and yields an energy index of\n$-0.3$. Including additional soft X-ray absorption allows a better\nfit, although with no firm constraints on the index. The absorption\nhowever must exceed $N=6\\times10^{21}\\psqcm$ at the 90 per cent\nconfidence level. Note that the intrinsic absorption will be\napproximately $(1+z)^3 N$, where $z$ is the redshift of the source.\nFor an assumed energy index of 1, typical of quasars, and the redshift\nindicated by the optical colours, we find\n$N=(6\\pm2)$--$(9\\pm3)\\times10^{22}\\psqcm$, and an unabsorbed intrinsic\n2--10~keV luminosity of 2.7--$6.8\\times 10^{44}\\ergps$, for\n$z=0.7$--1, respectively. After correction for the lensing\namplification factor of about 2, the source has an intrinsic\n$L(2$--$10\\keV)\\approx 2$--$3\\times10^{44}\\ergps$. This makes it a\nstrong contender to be one of the first genuine Type-II quasars (see\ndiscussions in Halpern et al.\\ 1999; Vignati et al.\\ 1999;\nFranceschini et al 1999).\n\nThe X-ray limits on the SCUBA sources in the A\\,1835 field are about\n100 times deeper than previously achieved using {\\it ROSAT} data\n(Ivison et al.\\ 2000). We have produced two submillimetre-to-X-ray\nspectral indices, $\\alpha_{SX}$, using the measured values at\n850$\\mu$m and 2~keV in our rest frame. Rather than obtain one X-ray\nestimate for the spectral flux at 2~keV from a whole band measurement,\nwhich would be biased by the most sensitive lower energy end of the\nband, we have estimated it by converting the observed counts to fluxes\nin the 0.5--2 and 2--7~keV bands (listed in Table 2), using the\nresponse matrix of the ACIS-S chip and assuming an intrinsic energy\nindex of 1 (which is roughly appropriate for the scattered flux from\nan absorbed AGN).\n\n\n\\begin{table*}\n\\begin{center}\n\\caption{Postions of the {\\it Chandra} (prefixed CXOU) and SCUBA\nsources (prefixed SMM) discussed here. We list the $1''$-diameter\nphotometry of the {\\it Chandra} sources from the {\\it HST} F555W and\nF814W frames and for all sources the gravitational lensing\namplification obtained by modelling the mass distribution of the\nclusters (see Blain et al.\\ 1999 for details: * indicates no solution\nat that redshift). Known spectroscopic redshifts are put in the left\ncolumn and the amplification at that redshift in the right.}\n\n\\begin{tabular}{lllcccc}\n%\\noalign{\\smallskip \\hrule \\smallskip}\nSource Name & R.A. & Dec & $V_{555}$ & $I_{814}$ & \\multicolumn{2}{c}{Amplification}\\\\\n& \\multicolumn{2}{c}{J2000} & & & $z=1$ & $z=2.5$ \\\\\n%\\noalign{\\smallskip \\hrule \\smallskip}\nCXOUJ215334.0+174240 & 21 53 34.0 & 17 42 40 & $25.6\\pm 0.1$ &\n$22.6\\pm 0.0$ & $z\\sim 1$ & 1.9 \\\\\nCXOUJ215333.2+174209 & 21 52 33.2 & 17 42 09 & $25.7\\pm 0.1$ & $24.2\\pm 0.1$ & 3.9 & 6.9 \\\\\nCXOUJ215333.8+174113 & 21 53 33.76 & 17 41 13 & $>26.2$ & $>24.5$ & 7.0 & * \\\\\nCXOUJ215334.4+174205 & 21 53 34.4 & 17 42 05 & $>26.9$ & $>26.2$ & 1.7 & 1.9 \\\\\nSMMJ\\,21536+1742 & 21~53~38.5 & 17~42~19 & ... & ... & 2.1 & 2.6 \\\\\nSMMJ\\,21535+1742 & 21~53~33.2 & 17~42~49 & ... & ... & 1.7 & 1.9 \\\\\nSMMJ\\,14011+0252 & 14~01~04.96 & 02~52~23.5 & ... & ... & $z=2.55$ & $3.0\\pm0.6$ \\\\\nSMMJ\\,14009+0252 & 14~00~57.55 & 02~52~48.6 & ... & ... & 1.4 & 1.5 \\\\\nSMMJ\\,14010+0253 & 14~01~03.09 & 02~53~12.0 & ... & ... & $z=2.22$ & $4.8\\pm2.8$ \\\\\nSMMJ\\,14010+0252 & 14~01~00.53 & 02~51~49.4 & ... & ... & 1.6 & 1.8 \\\\\n%\\noalign{\\smallskip \\hrule \\smallskip}\n\\end{tabular} \n\\end{center}\n\\end{table*}\n \n\\begin{table*}\n\\begin{center}\n\\caption{Count rates and fluxes of the {\\it Chandra} and SCUBA sources. The total \n{\\it Chandra} background-subtracted count for each source, the background \n(per square arcsec), and the flux, obtained assuming an X-ray energy \nindex of 1 are shown in two X-ray bands: 0.5--2~keV (no brackets) and \n2--7~keV (brackets). The final column give the submillimetre-to-X-ray index \n$\\alpha_{\\rm SX}$ obtained in the same bands (with the same bracket convention).}\n\n\\begin{tabular}{lccccc}\n%\\noalign{\\smallskip \\hrule \\smallskip}\nSource Name & \\multicolumn{3}{c}{X-ray flux -- at low (high) energy} & \n{SCUBA 850-$\\mu$m} & {$\\alpha_{SX}$} \\\\\n& Count & Background & Flux & Flux density & \\\\ \n& & & ($10^{-15}\\ergpcmsqps$) & (mJy) & (99\\% c.l.) \\\\\n%(0.5--2~keV)} & \\multicolumn{3}{c}{(2--7~keV)} &\n%$850\\mu{\\rm m}$ & (0.5--2~keV) & (2--7~keV) \\\\\n%& ct & bkgd & Flux & ct & bkgd & Flux & & & \\\\\n[5pt]\n%\\noalign{\\smallskip \\hrule \\smallskip}\nCXOUJ215334.0+174240 & $32\\pm5.8$ ($54.1\\pm7.3$) & 0.34 (0.15) & $9.9$\n($90$) & \n$<5.5$ & $<1.06$ ($<0.91$) \\\\\nCXOUJ215333.2+174209 & $19\\pm4.6$ ($14.3\\pm3.9$) & 0.5 (0.2) & 5.9 (23) & \n$<5.7$ & $<1.10$ ($<1.01$) \\\\\nCXOUJ215333.8+174113 & $11.9\\pm3.6$ ($<13$) & 0.28 (0.13) & 3.7 ($<17$) & \n$<5.7$ & $<1.14$ ($<1.03$) \\\\\nCXOUJ215334.4+174205 & $10.4\\pm3.7$ ($<7.9$) & 0.89 (0.18) & 3.2 ($<13$) & \n$3.9\\pm2.2$ & 1.12 (1.02) \\\\\nSMMJ\\,21536+1742 & $<10.6$ ($<4.6$) & 1.1 (0.68) & $<3.2$ ($<7.7$) & \n$6.7\\pm1.2$ & $>1.16$ ($>1.10$) \\\\\nSMMJ\\,21535+1742 & $<6.0$ ($<7.9$) & 2.4 (0.48) & $<1.8$ ($<13$) & \n$8.3\\pm 2.2$ & $>1.21$ ($>1.07$) \\\\\nSMMJ\\,14011+0252 & $<5.6$ ($<5.6$)& 7.3 (2.4) & $<0.78$ ($<4.4$) & \n$14.6\\pm 1.8$ & $>1.32$ ($>1.19$) \\\\\nSMMJ\\,14009+0252 & $<6.0$ ($<4.6$) & 1.1 (0.6) & $<0.84$ ($<3.6$) & \n$15.6\\pm 1.9$ & $>1.32$ ($>1.21$) \\\\\nSMMJ\\,14010+0253 & $<6.2$ ($<4.6$) & 7.6 (2.2) & $<0.87$ ($<0.87$) & \n$4.3\\pm 1.7$ & $>1.23$ ($>1.12$) \\\\\nSMMJ\\,14010+0252 & $<6.7$ ($<6.0)$ & 2.4 (1.0) & $<0.94$ ($<4.7$) & \n$4.2\\pm 1.7$ & $>1.22$ ($>1.10$) \\\\\n%\\noalign{\\smallskip \\hrule \\smallskip}\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\section{Discussion}\n\nWe compare expected values of $\\alpha_{\\rm SX}$ as a function of\nredshift in Fig.~2 for various classes of observed objects, both\nstarbursts and AGN. We select 3C\\,273 as an example of a powerful\nquasar, and use the submillimetre data of Neugebauer, Soifer \\& Miley\n(1985) in our model; Arp\\,220 as a starburst using the submillimetre\ndata of Sanders et al.\\ (1999) and the X-ray data of Iwasawa (1999);\nand NGC\\,6240 as a powerful obscured (Compton-thick) AGN using an\nestimate of the submillimetre spectrum based on that from Arp\\,220\nnormalised by the FIR luminosity and the {\\it BeppoSAX} spectrum from\nVignati et al.\\ (1999). We also show how $\\alpha_{\\rm SX}$ changes as\nthe absorption in NGC\\,6240 decreases from the measured value of\n$2\\times 10^{24}$ to $5\\times 10^{23}\\psqcm$ and also if the scattered\nfraction drops to 1 per cent. Data from several quasars at $z>4$ are\nshown for comparison with the 3C\\,273 prediction.\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig2.ps,width=0.5\\textwidth,angle=270}}\n\\caption{Submillimetre to X-ray spectral index, $\\alpha_{\\rm SX}$,\nplotted against redshift for a powerful quasar, 3C\\,273, an absorbed\nAGN, NGC\\,6240, and a starburst, Arp\\,220. The effects of decreasing\nthe scattered fraction from NGC\\,6240 to 1 per cent, and of its column\ndensity to $5\\times 10^{23}\\psqcm$ are indicated by the dash-dot and\ndash lines. The {\\it Chandra}/SCUBA sources with known redshifts are\nindicated by the squares. The $\\ast$ symbols represent the five $z>4$\nquasars for which both X-ray and SCUBA (850$mu$m) data are\navailable; monochromatic X-ray fluxes at 2 keV were calculated from\nthe (Galactic) absorption-corrected 0.1--2.0 keV fluxes in Kaspi et\nal.~(2000) assuming a power-law of $\\Gamma=2$; 850-$\\mu$m fluxes are\ntaken from the compilation in McMahon et al.~(1999).}\n\\end{figure}\n\nThe typical limits on $\\alpha_{\\rm SX}$ for the SCUBA galaxies are\n$\\alpha_{\\rm SX} \\ls 1.2$ (at 99 per cent confidence). Combining the\nlimits for the 6 galaxies we obtain a 99 per cent confidence limit on a\ntypical SCUBA galaxy of $\\alpha_{\\rm SX}> 1.34$, with the strongest\nconstraints for individual galaxies being $\\alpha_{\\rm SX} > 1.32$ for\nSMMJ\\,14011+0252 ($z=2.55$) and SMMJ\\,14009+0252 in the A\\,1835 field.\nThus the indices for this population are straightforwardly consistent\nwith starbursts. They do not resemble Compton-thin AGN at any redshift\nand are inconsistent with the spectrum of NGC\\,6240 at any redshift.\nIf these galaxies host a powerful AGN then either a) reprocessed\nradiation from the AGN provides only a minor fraction of the\nsubmillimetre luminosity, or b) the source must be Compton thick and in\naddition the fraction of any scattered X-ray emission must be less than\none per cent. We note that X-ray limits on the hyperluminous {\\it\nIRAS} galaxy F15307+3252 at $z=0.92$, which does contain an AGN since\nbroad scattered emission lines are seen (Hines et al.\\ 1995), show that\nit must have a very low X-ray scattered fraction ($<1$ per cent),\npossibly due to intrinsic absorption of the scattered emission (Fabian\net al.\\ 1996). If this is typical of obscured AGN more powerful than\nNGC\\,6240, then the present results would be consistent with obscured\nAGN provided that they are at relatively high redshift ($z\\gs 2$).\n\nOf the four {\\it Chandra} sources we identified in our fields, two have\nprobable optical counterparts suggesting that they are distant disk\ngalaxies. The colours and luminosity of the brightest of these suggest\nit is an $L^\\ast$ mid-type galaxy at $z\\sim 1$. If the two\noptically-unidentified {\\it Chandra} sources are AGN, and the host\ngalaxies have luminosities of $L^\\ast$ or greater, then they must be at\n$z>2$, or be intrinsically reddened. Obscuration of both AGN and\nsurrounding spheroid is required by some models for the XRB (Fabian\n1999). It is possible for these dust-enshrouded strongly-obscured AGN\nto be undetected in our 850-$\\mu$m SCUBA maps if their dust is\ntypically much hotter than 40\\,K. Comparing the radio flux and SCUBA\nlimit for the brightest {\\it Chandra} galaxy CXOUJ215334.0+174240\n(\\S2), the redshift $z$ and dust temperature $T_d$ of the source must\nsatisfy the relationship $T_d > 27(1+z)$\\,K. Taking the redshift\nconstraint from the optical, $z \\simeq 0.85\\pm 0.15$, we derive $T \\ge\n50$\\,K. Such sources would not contribute substantially to the\nsubmillimetre background at $\\sim 1$\\,mm, but might at shorter\nwavelengths. Eventual comparison with {\\it ISO} imaging may shed\nfurther light on the nature of the dust emission in these sources.\n\nIn summary, {\\it Chandra} and SCUBA observations have been combined to\nprobe the relation between the faint X-ray and submillimetre sky. Only\none marginal source is seen in both datasets, and so in general we\nfind deep submillimetre limits from SCUBA on the X-ray sources found\nusing {\\it Chandra} and deep X-ray limits from {\\it Chandra} on the\nSCUBA-selected sources. The limits on background sources in these\nfields are particularly strong due to amplification by gravitational\nlensing.\n\nFor the SCUBA galaxies, we cannot completely rule out the presence of\neither an obscured, weak AGN or a more powerful Compton-thick AGN in\nwhich any scattered flux is also very weak or absorbed. However, the\nsimplest explanation of our results on the SCUBA sources is that they\nare predominantly powered by starbursts. Clearly the current sample is\nsmall and so we cannot make any definitive statement about the whole\nSCUBA population. We note that at the moment our conclusions are not\ninconsistent with suggestions that AGN powering 20 per cent of the\nSCUBA population, although a substantially higher fraction would be\ndifficult to accommodate. \n\nFor the {\\it Chandra} sources in the A2390 field we find that they\nhave optically faint counterparts, $I\\gs 23$--27. We\nidentify one source as a probable Type-II obscured quasar at $z\\simeq\n1$. We suggest that the remaining, typically fainter sources are\neither more distant, $z>2$, or intrinsically reddened. Observations\nof these fields in the near-infrared are urgently needed to test the\nnature of these sources.\n\n\\section{Acknowledgements}\nWe thank L.\\ van Speybroeck and his colleagues for the superb X-ray\ntelescope and M.\\ Weisskopf and the project team for the {\\it Chandra}\nmission. ACF is grateful to NASA for the opportunity to participate in\n{\\it Chandra}. The Royal Society is thanked for support by ACF, IRS, SWA,\nCSC and SE and PPARC by RJI. AWB and JPK thank the Raymond \\&\nBeverly Sackler Foundation and the LENSNET European Network,\nrespectively. \n\n\\begin{thebibliography}{}\n\\bibitem []{} Almaini O., Lawrence A., Boyle B., 1998, MNRAS, 305,\n59\n\\bibitem []{} Altieri B. et al., 1999, A\\&A, 343, L65\n\\bibitem []{} Blain A.W., Kneib J-P., Ivison R.J., Smail I., 1999, ApJ, 512, \nL87\n%\\bibitem []{} Blain A.W., Smail I., Ivison R.J., Kneib J-P., 2000, in Bunker A.\\,J., \n%van Breughel W.\\,J.\\,M. eds, The Hy-Redshift\n%Universe: galaxy formation and evolution at high redshift, ASP conf. series. \n%vol.\\,193. ASP, San Francisco, in press (astro-ph/9908111)\n\\bibitem []{} Brandt W.N., et al, 2000, AJ, in press (astro-ph/0002121)\n\\bibitem []{} Edge A.C., Ivison R.J., Smail I., Blain A.W., Knieb\nJ.-P., 1999, MNRAS, 306, 599\n\\bibitem []{} Fabian A.C., 1999, MNRAS, 308, L39\n\\bibitem []{} Fabian A.C., 2000, astro-ph/0001178\n\\bibitem []{} Fabian A.C., Cutri R.M., Smith H.E., Crawford C.S.,\nBrandt W.N., 1996, MNRAS, 283, L95 \n\\bibitem []{} Fabian A.C., Iwasawa K., 1999, MNRAS, 303, L34\n\\bibitem []{} Fixsen D.\\,J., Dwek E., Mather J.\\,C., Bennett C.\\,L., \nShafer R.\\,A., 1998, ApJ, 508, 123\n%\\bibitem []{} Fiore F., et al 1999, MNRAS, 306, L55\n\\bibitem []{} Franceschini A., Bassani L., Cappi M., Granato G.L.,\nMalaguti G., Palazzi E., Persic M., 1999, A\\&A, 353, 910\n\\bibitem []{} Gendreau K., et al, 1995, PASJ, 47, L5\n\\bibitem []{} Gunn, K.F., \\& Shanks, T., MNRAS, submitted\n(astro-ph/9909089).\n\\bibitem []{} Halpern J.P., Turner T.J., George I.M., 1999, MNRAS in\npress (astro-ph 9905342)\n\\bibitem []{} Hines D.C., Schmidt G.D., Smith P.S., Cutri R.M., Low\nF.J., 1995, ApJ, 450, 1\n\\bibitem []{} Holland W.S., et al., 1999, MNRAS, 303,659\n%\\bibitem []{} Hughes D.H., et al 1998, Nature 394, 241\n\\bibitem []{} Ivison R.\\,J., Smail I., Barger A.\\,J., Kneib J.-P., Blain A.\\,W., Owen~F.\\,N.,\nKerr T.\\,H., Cowie L.\\,L., 2000, MNRAS, in press (astro-ph/9911069) \n\\bibitem []{} Iwasawa K., 1999, MNRAS, 302, 96\n\\bibitem []{} Kaspi~S., Brandt~W.N., Schneider~D.P., AJ accepted\n(astro-ph/0001299)\n\\bibitem []{} Kraft R.P., Burrows, D.N., Nousek J., 1991, ApJ, 374, 344\n\\bibitem[]{} Lemonon L., Pierre M., Cesarsky C.J., Elbaz D., Pell\\'o R.,\nSoucail G., \\& Vigroux L., 1998, A\\&A, 334, L21\n\\bibitem []{}Madau P., Ghisellini G., Fabian A.C., 1994, MNRAS, 270, L17 \n\\bibitem []{} Matt G., Fabian A.C., 1994, MNRAS, 267, 187\n\\bibitem []{} McMahon~R.G., Priddey~R.S., Omont~A., Snellen~I.,\nWithington~S., 1999, MNRAS, 309, L1\n\\bibitem []{} Mushotzky, R.F., Cowie, L.L., Barger, A., 2000, preprint\n\\bibitem []{} Neugebauer G., Soifer B.T., Miley G.K., 1985, ApJ, 295,\nL27 \n\\bibitem[]{} Pell\\'o, R., et al., 1999, A\\&A, 346, 359\n\\bibitem []{} Sanders D.B., 1999, Proc. of \"Space Infrared Telescopes and\nRelated Science\" at the 32nd COSPAR Meeting, Nagoya, Japan, eds. T.\nMatsumoto and T. de Graauw, Advances in Space Research (Oxford:\nElsevier) (astro-ph/9904292)\n\\bibitem []{} Setti G., Woltjer L., 1989, A\\&A, 224, L21\n\\bibitem []{} Smail I., Ivison R.\\,J., Blain A.\\,W., 1997, ApJ, 490, L5\n\\bibitem []{} Smail I., Ivison R.\\,J., Blain A.\\,W., Kneib J.-P., 1998, ApJ, 507, L21\n\\bibitem []{} Smail I., Ivison R.\\,J., Owen F.\\,N., Blain A.\\,W., Kneib J.-P., 2000, \nApJ, in press (astro-ph/9907083)\n\\bibitem []{} Vignati P., et al, 1999, A\\&A, 349, L57\n\\bibitem []{} Wilman R.J., Fabian A.C., 1999, MNRAS, 309, 862 \n%\\bibitem []{} Wilman R.J., Fabian A.C., Cutri R.M., Crawford C.S.,\n%Brandt W.N., 1999, MNRAS, 300, L7 \n\n\n\\end{thebibliography}\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002322.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem []{} Almaini O., Lawrence A., Boyle B., 1998, MNRAS, 305,\n59\n\\bibitem []{} Altieri B. et al., 1999, A\\&A, 343, L65\n\\bibitem []{} Blain A.W., Kneib J-P., Ivison R.J., Smail I., 1999, ApJ, 512, \nL87\n%\\bibitem []{} Blain A.W., Smail I., Ivison R.J., Kneib J-P., 2000, in Bunker A.\\,J., \n%van Breughel W.\\,J.\\,M. eds, The Hy-Redshift\n%Universe: galaxy formation and evolution at high redshift, ASP conf. series. \n%vol.\\,193. ASP, San Francisco, in press (astro-ph/9908111)\n\\bibitem []{} Brandt W.N., et al, 2000, AJ, in press (astro-ph/0002121)\n\\bibitem []{} Edge A.C., Ivison R.J., Smail I., Blain A.W., Knieb\nJ.-P., 1999, MNRAS, 306, 599\n\\bibitem []{} Fabian A.C., 1999, MNRAS, 308, L39\n\\bibitem []{} Fabian A.C., 2000, astro-ph/0001178\n\\bibitem []{} Fabian A.C., Cutri R.M., Smith H.E., Crawford C.S.,\nBrandt W.N., 1996, MNRAS, 283, L95 \n\\bibitem []{} Fabian A.C., Iwasawa K., 1999, MNRAS, 303, L34\n\\bibitem []{} Fixsen D.\\,J., Dwek E., Mather J.\\,C., Bennett C.\\,L., \nShafer R.\\,A., 1998, ApJ, 508, 123\n%\\bibitem []{} Fiore F., et al 1999, MNRAS, 306, L55\n\\bibitem []{} Franceschini A., Bassani L., Cappi M., Granato G.L.,\nMalaguti G., Palazzi E., Persic M., 1999, A\\&A, 353, 910\n\\bibitem []{} Gendreau K., et al, 1995, PASJ, 47, L5\n\\bibitem []{} Gunn, K.F., \\& Shanks, T., MNRAS, submitted\n(astro-ph/9909089).\n\\bibitem []{} Halpern J.P., Turner T.J., George I.M., 1999, MNRAS in\npress (astro-ph 9905342)\n\\bibitem []{} Hines D.C., Schmidt G.D., Smith P.S., Cutri R.M., Low\nF.J., 1995, ApJ, 450, 1\n\\bibitem []{} Holland W.S., et al., 1999, MNRAS, 303,659\n%\\bibitem []{} Hughes D.H., et al 1998, Nature 394, 241\n\\bibitem []{} Ivison R.\\,J., Smail I., Barger A.\\,J., Kneib J.-P., Blain A.\\,W., Owen~F.\\,N.,\nKerr T.\\,H., Cowie L.\\,L., 2000, MNRAS, in press (astro-ph/9911069) \n\\bibitem []{} Iwasawa K., 1999, MNRAS, 302, 96\n\\bibitem []{} Kaspi~S., Brandt~W.N., Schneider~D.P., AJ accepted\n(astro-ph/0001299)\n\\bibitem []{} Kraft R.P., Burrows, D.N., Nousek J., 1991, ApJ, 374, 344\n\\bibitem[]{} Lemonon L., Pierre M., Cesarsky C.J., Elbaz D., Pell\\'o R.,\nSoucail G., \\& Vigroux L., 1998, A\\&A, 334, L21\n\\bibitem []{}Madau P., Ghisellini G., Fabian A.C., 1994, MNRAS, 270, L17 \n\\bibitem []{} Matt G., Fabian A.C., 1994, MNRAS, 267, 187\n\\bibitem []{} McMahon~R.G., Priddey~R.S., Omont~A., Snellen~I.,\nWithington~S., 1999, MNRAS, 309, L1\n\\bibitem []{} Mushotzky, R.F., Cowie, L.L., Barger, A., 2000, preprint\n\\bibitem []{} Neugebauer G., Soifer B.T., Miley G.K., 1985, ApJ, 295,\nL27 \n\\bibitem[]{} Pell\\'o, R., et al., 1999, A\\&A, 346, 359\n\\bibitem []{} Sanders D.B., 1999, Proc. of \"Space Infrared Telescopes and\nRelated Science\" at the 32nd COSPAR Meeting, Nagoya, Japan, eds. T.\nMatsumoto and T. de Graauw, Advances in Space Research (Oxford:\nElsevier) (astro-ph/9904292)\n\\bibitem []{} Setti G., Woltjer L., 1989, A\\&A, 224, L21\n\\bibitem []{} Smail I., Ivison R.\\,J., Blain A.\\,W., 1997, ApJ, 490, L5\n\\bibitem []{} Smail I., Ivison R.\\,J., Blain A.\\,W., Kneib J.-P., 1998, ApJ, 507, L21\n\\bibitem []{} Smail I., Ivison R.\\,J., Owen F.\\,N., Blain A.\\,W., Kneib J.-P., 2000, \nApJ, in press (astro-ph/9907083)\n\\bibitem []{} Vignati P., et al, 1999, A\\&A, 349, L57\n\\bibitem []{} Wilman R.J., Fabian A.C., 1999, MNRAS, 309, 862 \n%\\bibitem []{} Wilman R.J., Fabian A.C., Cutri R.M., Crawford C.S.,\n%Brandt W.N., 1999, MNRAS, 300, L7 \n\n\n\\end{thebibliography}"
}
] |
astro-ph0002323
|
Ages of late spectral type Vega--like stars
|
[
{
"author": "Inseok Song"
},
{
"author": "J.-P. Caillault"
}
] |
We have estimated the ages of eight late--type Vega--like stars by using standard age dating methods for single late--type stars, e.g., location on the color magnitude diagram, Li~6708 \AA{} absorption, CaII~H\&K emission, X--ray luminosity, and stellar kinematic population. With the exception of the very unusual pre-main sequence star system HD~98800, all the late--type Vega-like stars are the same age as the Hyades cluster (600--800 Myr) or older.
|
[
{
"name": "LateVegas.tex",
"string": "%% This LaTeX-file was created by <song> Wed Feb 16 11:02:22 2000\n%% LyX 1.0 (C) 1995-1999 by Matthias Ettrich and the LyX Team\n\n%% Do not edit this file unless you know what you are doing.\n\\documentclass[preprint2]{aastex}\n\\usepackage[T1]{fontenc}\n\\usepackage{graphics}\n\n\\makeatletter\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.\n\\providecommand{\\LyX}{L\\kern-.1667em\\lower.25em\\hbox{Y}\\kern-.125emX\\@}\n%% Special footnote code from the package 'stblftnt.sty'\n%% Author: Robin Fairbairns -- Last revised Dec 13 1996\n\\let\\SF@@footnote\\footnote\n\\def\\footnote{\\ifx\\protect\\@typeset@protect\n \\expandafter\\SF@@footnote\n \\else\n \\expandafter\\SF@gobble@opt\n \\fi\n}\n\\expandafter\\def\\csname SF@gobble@opt \\endcsname{\\@ifnextchar[%]\n \\SF@gobble@twobracket\n \\@gobble\n}\n\\edef\\SF@gobble@opt{\\noexpand\\protect\n \\expandafter\\noexpand\\csname SF@gobble@opt \\endcsname}\n\\def\\SF@gobble@twobracket[#1]#2{}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.\n%\\usepackage[light,first]{draftcopy}\n\\usepackage[first]{draftcopy}\n\\draftcopyName{Accepted}{180}\n\n\\makeatother\n\n\\begin{document}\n\n\n\\title{Ages of late spectral type Vega--like stars}\n\n\n\\author{Inseok Song, J.-P. Caillault,}\n\n\n\\affil{Department of Physics and Astronomy, University of Georgia, Athens GA 30602-2451\nUSA}\n\n\n\\email{song@physast.uga.edu, jpc@akbar.physast.uga.edu}\n\n\n\\author{David Barrado y Navascu\\'{e}s,}\n\n\n\\affil{Max-Planck Institut f�r Astronomie, K�nigstuhl 17, Heidelberg, D-69117 Germany}\n\n\n\\email{barrado@mpia-hd.mpg.de}\n\n\n\\author{John R. Stauffer}\n\n\n\\affil{Harvard Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138\nUSA}\n\n\n\\email{stauffer@amber.harvard.edu}\n\n\n\\author{Sofia Randich}\n\n\n\\affil{Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125, Firenze Italy}\n\n\n\\email{randich@arcetri.astro.it}\n\n\\begin{abstract}\nWe have estimated the ages of eight late--type Vega--like stars by using standard\nage dating methods for single late--type stars, e.g., location on the color\nmagnitude diagram, Li~6708 \\AA{} absorption, CaII~H\\&K emission, X--ray luminosity,\nand stellar kinematic population. With the exception of the very unusual pre-main\nsequence star system HD~98800, all the late--type Vega-like stars are the same\nage as the Hyades cluster (600--800 Myr) or older.\n\\end{abstract}\n\n\\keywords{planetary system --- stars: activity --- stars: late--type}\n\n\n\\section{Introduction}\n\nVega--like stars are stars with IR excess emission due to optically thin dust\ndisks with little or no gas \\citep{BP93,LBA99}. It is important to know the\nages of Vega--like stars because they may provide crucial information about\nextra--solar planetary systems. Given the existence of a complete, flux--limited\nIR survey and a 100\\% success rate for identifying stars with IR excesses due\nto circumstellar disks, then if all identified Vega--like stars were young,\none could conclude that the timescale for the disks to ``go away'' is short.\nFurthermore, if the fraction of the number of Vega--like stars to the total\nnumber of stars (\\( N_{V}/N_{T} \\)) is similar to the fraction of the average\nages of Vega--like stars to the average ages of milky way disk stars (\\( T_{V}/T_{mw} \\)),\nthen one could also conclude that most stars are born with such disks. Hence,\nif such Vega disks are signposts of planet formation, then one could infer that\nmost stars have planetary systems. On the other hand, if Vega--like stars have\na wide range of ages and \\( N_{V}/N_{T}\\ll T_{V}/T_{mw} \\), then one could\nplausibly conclude that disk formation -- and hence possibly planet formation\n-- is not a common process, at least at the level of sensitivity of the IR survey\nused to identify the Vega--like stars.\n\nThere have been many efforts to determine the ages of Vega--like stars. \\citet{BP93}\nestimated the age of \\( \\beta \\)~\\-Pictoris as 100 Myr whereas \\citet{Jura93}\nclaimed that \\( \\beta \\)~\\-Pictoris is extremely young, \\( \\sim 2-3 \\) Myr.\nThey interpreted the same data in opposite ways, the latter group claiming that\n\\( \\beta \\)~\\-Pictoris is approaching the zero age main sequence (ZAMS) and\nthe former group believing that \\( \\beta \\)~\\-Pictoris is an old main sequence\n(MS) star. More recent studies of \\( \\beta \\)~Pictoris support its young age \\citep{Jura98,BSSC}.\nAnother conspicuous Vega-like star, HR~4796A, is believed to be even younger\nthan \\( \\beta \\)~\\-Pictoris \\citep{Jura93,Stauffer95} while Fomalhaut and\nVega are estimated to be much older, \\( \\sim 200 \\) Myr \\citep{BP93,Barrado97,David98}.\n\nIn order to increase the number of age estimates of Vega--like stars, we have\ncompiled a list of 361 Vega--like stars from the literature and have searched\nfor late--type binary companions in order to follow the techniques of \\citet{Stauffer95},\nwho determined the age of HR 4796A by using the properties of its late--type\ncompanion star HR 4796B. The complete results of our survey can be found in\n\\citet{myPhD}. However, there are eight late--type Vega--like stars in our list\nfor which we can estimate ages directly by using standard age dating methods\nfor single late--type stars, methods such as their location on the CMD, Li 6708\\AA\\\nabsorption, X--ray luminosity, rotation, CaII H\\&K emission, etc. \n\nIn section 2, we present the late--type Vega--like stars and their age related\ndata. The age determinations are discussed in section 3, and a conclusion is\nprovided in section 4.\n\n\n\\section{Data}\n\nIn Table 1, we list the eight late--type (\\( B-V>0.65 \\)) Vega--like stars\nalong with the data to be used for age estimations. All spectral types are taken\nfrom SIMBAD and X--ray luminosities are from the Rosat All Sky Survey data \\citep{Hunsch98,Hunsch99}.\nThe fractional IR luminosity \\( f \\) (in the 6th column of Table 1) is defined\nas \\( f\\equiv L_{IR}/L_{*} \\). IRAS PSC2/FSC fluxes were used to calculate\nthe \\( f \\) values. The values of the logarithm of the ratio between CaII~H\\&K\nfluxes and stellar bolometric luminosity, \\( \\log R^{'}(HK) \\), are from \\citet{Henry}\nand the sources of the other parameters are indicated by footnotes to Table\n\\ref{table1}. \n\nHD~98800 is a quadruple system consisting of two spectroscopic binaries \\citep{Torres}.\nSince the \\( L_{x} \\) flux includes the emission from all four components,\nwe divided the published value by four to take the multiplicity into account.\nThe Li abundance for this system is high, \\( \\log N(\\mathrm{Li})= \\)3.1, 2.3,\nand 3 for components Aa, Ba, and Bb, respectively \\citep{Soderblom98}, and the\nvalues for each component were used instead of the value from the whole system,\nwhen possible. \\( M_{v} \\) values for each component were taken from \\citet{Soderblom98},\nand, according to \\citet{Gehrz99}, component B emits most of the IR excess emission. \n\n\n\\section{Age estimations}\n\n\n\\subsection{Color--Magnitude Diagram (CMD) location}\n\nThe eight late--type Vega--like stars are plotted in Figure 1 with theoretical\nsolar abundance PMS evolutionary tracks from \\citet{DM97}. We have used a ``tuned''\ntemperature scale to convert \\( T_{eff} \\) to \\( (V-I)_{c} \\) \\citep{Stauffer95},\nwhich locates the 100 Myr isochrone onto the locus of Pleiades stars. Except\nfor the HD~98800 system, we used Hipparcos \\( (V-I)_{c} \\) colors to plot the\nCMD. With the exception of only HD~73752 and HD~98800, all the Vega--like stars\nare located on or close to the ZAMS which makes it difficult to get an age estimation\nwith precision smaller than the MS lifetime of the late--type stars. A star\nwhose position in the CMD is above the ZAMS can either be in the PMS stage or\nin the post ZAMS evolutionary stage. We need additional information to determine\nthe actual ages of these stars. As argued below, HD~73752 is probably in the\npost MS evolutionary stage whereas HD~98800 is almost certainly a PMS star.\nExcept for HD~73752 and HD~98800, we are only able to conclude that the stars\nin our sample are older than \\( \\sim 30 \\) Myr based solely in their locations\nin the CMD.\n\n\n\\subsection{Lithium abundance}\n\nFour stars (\\( \\epsilon \\) Eri, HD~73752, HD~98800, and HD~221354) have had\ntheir Li 6708\\AA{} absorption strengths measured. Those values and the Li data\nfor the Pleiades, the Hyades, and the M34 cluster members are plotted in Figure\n2. It appears that HD~98800 is younger than the Pleiades cluster and that HD~73752,\n\\( \\epsilon \\) Eri, and HD~221352 are about the same age as the Hyades cluster\n(\\( 600-800\\, \\mathrm{Myr} \\)). \n\n\n\\subsection{X-ray emission}\n\nHD~98800 is again located above the Pleiades cluster in a plot of \\( L_{x} \\)\nversus \\( (B-V) \\) (Fig. 3). HD~73752, HD~67199, and HD~69830 have X--ray luminosities\nmuch lower than those of Hyades stars with similar \\( (B-V) \\) colors, so we\nassign older ages to those stars. \\( \\epsilon \\) Eri, HD~53143, and HD~128400,\nhowever, show about the same X--ray activity as Hyades stars so their ages are\nprobably similar. \n\n\n\\subsection{CaII H\\&K}\n\nBy using the chromospheric activity -- age relation of \\citet{Donahue}: \n\\[\n\\log t=10.725-1.334R_{5}+0.4085R^{2}_{5}-0.0522R_{5}^{3},\\]\n where \\( t \\) is the age in years, and \\( R_{5} \\) is defined as \\( R_{HK}^{'}\\times 10^{5} \\),\nwe can obtain another estimate of the ages of \\( \\epsilon \\) Eri, HD~53143,\nHD~67199, and HD~128400. These ages agree with the age estimations from the\nprevious sections. The age uncertainty can be obtained from the measurement\nerror of \\( \\log R^{'}(HK) \\), \\( \\Delta \\log R^{'}(HK)=\\pm 0.052 \\) \\( (\\Delta \\tau \\sim 200\\, \\mathrm{Myr}) \\) \\citep{Henry}.\nWe adopted these ages as the final age estimations for the stars with CaII H\\&K\nmeasurements because this method is the only one that provides a quantitative\nestimate. Age estimation from the CMD can also be fairly accurate, but only\nwhen a star is in its PMS phase. Note that the calibration of this age formula\nis presumably tied to an age scale where the Pleiades is 75 Myr and \\( \\alpha \\)\nPersei is 50 Myr old. If the new lithium depletion ages for these clusters (125\nand 85 Myr, respectively -- \\citeauthor{Stauffer99} \\emph{et al.} {[}\\citeyear{Stauffer98}, \\citeyear{Stauffer99}{]})\nare correct, then the CaII H\\&K ages should be increased by \\( \\sim 50\\% \\).\n\n\n\\subsection{Kinematics}\n\nAll eight stars appear in the Hipparcos catalog but only six stars have radial\nvelocity measurements (from \\citealt{Duflot} and references therein). We have\nused these radial velocities and parallaxes, along with B1950 coordinates and\nproper motions, to calculate \\( (U,V,W) \\) galactic velocity components following\n\\citet{JohnsonUVW}. The kinematic population of the Vega--like stars is determined\nby using the population criteria from \\citet{Leggett} - young disk stars are\nthose with \\( -20<U<50 \\) and \\( -30<V<0, \\) while old disk stars have an\neccentricity less than 0.5 in the \\( UV \\) plane, but lie outside the young\ndisk ellipsoid. Of the six Vega--like stars with \\( (U,V,W) \\) velocities,\nonly HD~98800 is located inside of the young disk star regime (Fig. 4).\n\n\n\\subsection{Other criteria}\n\nSince all Vega-like stars with \\( v\\sin i \\) measurements in this study are\nslow rotators, we can not assign any meaningful ages from this method. Metallicities\nof the Vega-like stars with {[}Fe/H{]} measurements are very close to the solar\nvalue. Thus, the metallicity data cannot constrain ages of these stars, either. \n\n\n\\subsection{Final estimated ages}\n\nAll age estimations are summarized in Table~\\ref{table2}. Based on its X--ray\nluminosity, Li abundance, kinematics, and location on the CMD, we are confident\nthat HD~98800 is a PMS star, with a probable age of \\( \\sim 7\\, \\mathrm{Myr} \\),\nand almost certainly lying between 2 and 12 Myr old which is in good agreement\nwith \\citeauthor{Soderblom98}'s \\citeyear{Soderblom98} estimate of \\( 10^{\\, +10}_{\\, -5} \\)\nMyr. Based on a similar set of evidence, HD~73752 on the other hand is almost\ncertainly a post MS star whose IR excess emission mechanism may be different\nfrom that of the younger Vega--like stars. The six other stars in our study\nlie close to the ZAMS in the CMD and seem to have ages \\( \\sim 1\\, \\mathrm{Gyr} \\).\nFor HD~69830 and HD~73752, we assigned maximum ages of 2 Gyr because they have\nabout the same X-ray activity as HD~67199 which has an age determination from\nCaII H\\&K. However, the ages for these stars could be as small as the age of\nthe Hyades cluster (but not smaller than that). Therefore, we assign ages in\nthe range of \\( 600-2000\\, \\mathrm{Myr} \\) for these two stars. HD~221354 does\nnot have a good age estimation, but from the fact that it is on the MS and that\nit belongs kinematically to the old disk population stars, we assign an age\nof \\( 1.0\\pm 0.5 \\) Gyr. \n\n\\citet{Habing99} performed a study very similar to ours but mainly of early--type\nstars. They found that most Vega--disks disappear very sharply around an age\nof 400 Myr. \\citet{uvbyBpaper} have also found that early--type Vega--like stars\nare systematically young (\\( <400 \\) Myr) by using Str\\\"{o}mgren \\emph{uvby\\( \\beta \\)}\nphotometry. \n\n\n\\subsection{K stars with upper limit in \\protect\\( f\\protect \\)}\n\nAs seen from Table~\\ref{table2}, there are no Vega-like stars with ages in\nthe range between a few tens and a few hundreds of Myr in the spectral type\nrange in which we are interested. To have more data in that age range, we constructed\na list of young K stars based on their strong Li absorption or strong X-ray\nemission \\citep{Fisher,Jeff}. We collected age related data for these stars\nfrom which we estimated their ages (see \\citealt{myPhD}). Some of these stars\nwere detected with IRAS. Upper limits to \\( f \\) for these stars were calculated\nby assuming that each system has a dust disk with temperature of 100 K and that\nthe system was barely undetected at 60 \\( \\mu m \\). These stars are plotted\nas open downward pointing triangles in Figure~\\ref{f_age}, a plot of \\( f \\)\nversus age for early--type and late--type Vega--like stars with good age estimates.\nTwo stars in the list of young K stars, Gl~150 and HD~68586, lie above the ZAMS\nin a CMD, but, based on the other data available for these stars, we find that\nthey must be post MS stars; as a result, they are not plotted in Figure~\\ref{f_age}.\n\nWe find Figure~\\ref{f_age} both illuminating and puzzling. For the early--type\nstars, the correlation of age and IR excess plus the generally young ages for\nthese prototypical objects suggest that many A stars form with disks and the\ndisk excesses decrease with age due to some evolutionary process \\citep{BSSC}.\nFor the late--type Vega--like stars, the much older derived ages at least suggests\nthat the timescale for disk evolution is longer. \n\n\n\\section{Conclusion}\n\nWe have estimated ages of eight late-type Vega-like stars by using standard\nage dating methods for a late-type star. Except for the PMS star HD~98800, all\nVega-like stars in this study are the same age as the Hyades cluster or older. \n\nBecause we have only one late--type Vega--like star with an age less than \\( \\sim 500 \\)\nMyr, we cannot draw any strong conclusions about the evolutionary timescale\nfor disk evolution for K dwarfs. It would be very useful to obtain mid--IR data\n(with the very sensitive SIRTF, for example) for the stars in the list of young\nK stars. It would also be useful to obtain more complete age indicator data\nfor this sample in order to make the age estimation more precise.\n\n\n\\acknowledgements{IS and JPC acknowledge the support of NASA through grant NAG5--6902.}\n\n\\bibliographystyle{apjl}\n\\bibliography{Vegas}\n\n\n\\newpage\n\\onecolumn\n\n\\begin{table}\n\n\\caption{\\label{table1}Late-type Vega-like stars and their age related data.}\n{\\noindent \\centering \\begin{tabular}{ccccccccc}\n\\hline \n{\\scriptsize HD \\#}&\n{\\scriptsize Other Name}&\n{\\scriptsize Sp. Type}&\n{\\scriptsize \\( \\mathrm{M}_{\\mathrm{v}} \\)}&\n{\\scriptsize \\( (B-V) \\)}&\n{\\scriptsize \\( f(L_{IR}/L_{*})\\times 10^{3} \\)}&\n{\\scriptsize \\( \\log L_{x}(ergs/s) \\)}&\n{\\scriptsize \\( \\log R^{'}(HK) \\)}&\n{\\scriptsize \\( \\log N(\\mathrm{Li}) \\)}\\\\\n\\hline \n{\\scriptsize 22049}&\n{\\scriptsize \\( \\epsilon \\) Eri}&\n{\\scriptsize K2V}&\n{\\scriptsize \\( 6.18\\pm 0.11 \\)}&\n{\\scriptsize \\( 0.88 \\)}&\n{\\scriptsize 0.08}&\n{\\scriptsize 28.32}&\n{\\scriptsize -4.47}&\n{\\scriptsize 0.25\\( ^{a} \\)}\\\\\n{\\scriptsize 53143}&\n{\\scriptsize GL 260}&\n{\\scriptsize K1V}&\n{\\scriptsize \\( 5.49\\pm 0.14 \\)}&\n{\\scriptsize \\( 0.81 \\)}&\n{\\scriptsize 0.18}&\n{\\scriptsize 28.69}&\n{\\scriptsize -4.52}&\n{\\scriptsize --}\\\\\n{\\scriptsize 67199}&\n{\\scriptsize --}&\n{\\scriptsize K1V}&\n{\\scriptsize \\( 5.99\\pm 0.06 \\)}&\n{\\scriptsize \\( 1.0 \\)}&\n{\\scriptsize 0.24}&\n{\\scriptsize 27.87}&\n{\\scriptsize -4.72}&\n{\\scriptsize --}\\\\\n{\\scriptsize 69830}&\n{\\scriptsize GL 302}&\n{\\scriptsize K0V}&\n{\\scriptsize \\( 5.45\\pm 0.05 \\)}&\n{\\scriptsize \\( 0.76 \\)}&\n{\\scriptsize 0.61}&\n{\\scriptsize 27.48}&\n{\\scriptsize --}&\n{\\scriptsize -- }\\\\\n{\\scriptsize 73752}&\n{\\scriptsize HR 3430}&\n{\\scriptsize G3/5V}&\n{\\scriptsize \\( 3.55\\pm 0.11 \\)}&\n{\\scriptsize \\( 0.73 \\)}&\n{\\scriptsize 0.03}&\n{\\scriptsize 27.98}&\n{\\scriptsize --}&\n{\\scriptsize 1.3\\( ^{b} \\)}\\\\\n{\\scriptsize 98800Aa}&\n{\\scriptsize GL 2084}&\n{\\scriptsize K5V}&\n{\\scriptsize \\( 6.06 \\)}&\n{\\scriptsize \\( 1.17 \\)}&\n{\\scriptsize --}&\n{\\scriptsize 30.17}&\n{\\scriptsize --}&\n{\\scriptsize 3.1\\( ^{c} \\)}\\\\\n\\multicolumn{1}{r}{{\\scriptsize Ba}}&\n{\\scriptsize --}&\n{\\scriptsize K7V}&\n{\\scriptsize \\( 6.79 \\)}&\n{\\scriptsize \\( 1.37 \\)}&\n{\\scriptsize 230}&\n{\\scriptsize 30.17}&\n{\\scriptsize --}&\n{\\scriptsize 2.3\\( ^{c} \\)}\\\\\n\\multicolumn{1}{r}{{\\scriptsize Bb}}&\n{\\scriptsize --}&\n{\\scriptsize M1V}&\n{\\scriptsize \\( 8.5: \\)}&\n{\\scriptsize \\( 1.41 \\)}&\n{\\scriptsize --}&\n{\\scriptsize 30.17}&\n{\\scriptsize --}&\n{\\scriptsize 3:\\( ^{c} \\)}\\\\\n{\\scriptsize 128400}&\n{\\scriptsize --}&\n{\\scriptsize G5V}&\n{\\scriptsize \\( 5.19\\pm 0.07 \\)}&\n{\\scriptsize \\( 0.67 \\)}&\n{\\scriptsize 3.2}&\n{\\scriptsize 28.59}&\n{\\scriptsize -4.56}&\n{\\scriptsize --}\\\\\n{\\scriptsize 221354}&\n{\\scriptsize GL 895.4}&\n{\\scriptsize K2V}&\n{\\scriptsize \\( 5.63\\pm 0.15 \\)}&\n{\\scriptsize \\( 0.84 \\)}&\n{\\scriptsize 1.0}&\n{\\scriptsize --}&\n{\\scriptsize --}&\n{\\scriptsize 0.158\\( ^{d} \\)}\\\\\n\\hline \n\\end{tabular}\\scriptsize \\par}\n\\( ^{a} \\) \\citet{Mallik} \\( ^{b} \\) \\citet{Lebre} \\( ^{c} \\) \\citet{Soderblom93}\nand see section 2 \\( ^{d} \\) \\citet{Fisher}\n\\end{table}\n \n\n\\begin{table}\n\n\\caption{\\label{table2}Age estimations for the late--type Vega--like stars.}\n{\\centering \\begin{tabular}{ccccccc}\n\\hline \nName&\n\\multicolumn{5}{c}{age dating methods}&\nFinal age\\\\\n\\cline{2-6} \n&\n\\( L_{\\mathrm{x}} \\)&\nCaII H\\&K&\nLi&\nkinematics&\nCMD&\n(Myr)\\\\\n\\hline \n\\( \\epsilon \\) Eri&\n\\( \\sim \\mathrm{H} \\)&\n730&\n\\( \\sim \\mathrm{H} \\)&\nOD&\nMS&\n\\( 730\\pm 200 \\)\\\\\nHD 53143&\n\\( \\sim \\mathrm{H} \\)&\n965&\n--&\nOD&\nMS&\n\\( 965\\pm 200 \\)\\\\\nHD 67199&\n\\( >\\mathrm{H} \\)&\n2000&\n--&\n--&\n\\( > \\)MS&\n\\( 2000\\pm 200 \\)\\\\\nHD 69830&\n\\( >\\mathrm{H} \\)&\n--&\n--&\nOD&\nMS&\n\\( 600-2000 \\)\\\\\nHD 73752&\n\\( >\\mathrm{H} \\)&\n--&\n\\( \\sim \\mathrm{H} \\)&\nOD&\n\\( > \\)MS&\n\\( 600-2000 \\)\\\\\nHD 98800&\n\\( <\\mathrm{P} \\) &\n--&\n\\( <\\mathrm{P} \\)&\nYD&\n\\( 7\\pm 5 \\)&\n\\( 7\\pm 5 \\)\\\\\nHD 128400&\n\\( \\sim \\mathrm{H} \\)&\n1100&\n--&\n--&\nMS&\n\\( 1100\\pm 600 \\)\\\\\nHD 221354&\n--&\n--&\n\\( \\succeq \\mathrm{H} \\)&\nOD&\nMS&\n\\( 1500\\pm 1000 \\)\\\\\n\\hline \n\\multicolumn{7}{l}{ P=Pleiades, H=Hyades, OD=old disk population, YD=young disk population}\\\\\n\\end{tabular}\\par}\\end{table}\n \n\n\\begin{figure}\n{\\par\\centering \\resizebox*{0.9\\columnwidth}{!}{\\rotatebox{270}{\\includegraphics{CMD.eps}}} \\par}\n\n\n\\caption{CMD of late--type Vega--like stars (filled diamonds) and the Pleiades stars\n(crosses). Isochrones are from \\citet{DM97}.}\n\\end{figure}\n\\begin{figure}\n{\\par\\centering \\resizebox*{0.9\\columnwidth}{!}{\\rotatebox{270}{\\includegraphics{Li.eps}}} \\par}\n\n\n\\caption{Li abundances of late--type Vega--like stars (large crosses) as well as members\nof the Pleiades cluster (filled symbols, 125 Myr), M34 (plus signs, 250 Myr),\nand the Hyades (open symbols, 600--800 Myr). Downward pointing triangles indicate\nupper limits.}\n\\end{figure}\n\\begin{figure}\n{\\par\\centering \\resizebox*{0.9\\columnwidth}{!}{\\rotatebox{270}{\\includegraphics{Lx.eps}}} \\par}\n\n\n\\caption{X--ray luminosities of late--type Vega--like stars, as well as those in the\nPleiades and the Hyades. All symbols have the same meaning as in Figure 2.}\n\\end{figure}\n\\begin{figure}\n{\\par\\centering \\resizebox*{0.9\\columnwidth}{!}{\\rotatebox{270}{\\includegraphics{UVW.eps}}} \\par}\n\n\n\\caption{Kinematic population of late--type Vega--like stars. }\n\\end{figure}\n\\begin{figure}\n{\\par\\centering \\resizebox*{0.9\\columnwidth}{!}{\\rotatebox{270}{\\includegraphics{f_age.eps}}} \\par}\n\n\n\\caption{\\label{f_age}Fractional infrared luminosity versus age. Early--type Vega--like\nstars are plotted as solid circles and late--type Vega--like stars are plotted\nas filled diamonds. Field K stars with IR excess upper limits are represented\nwith downward pointing open triangles.}\n\\end{figure}\n\n\n\\end{document}\n"
}
] |
[
{
"name": "LateVegas.bbl",
"string": "\\begin{thebibliography}{29}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n\\bibitem[\\protect\\astroncite{Backman \\& Paresce}{1993}]{BP93}\nBackman, D.~E. \\& Paresce, F. 1993, in {\\em Protostars and Planets III\\/},\n edited by R.~H. {Levy} \\& J.~{Lunine}, (Tucson: University of Arizona Press),\n 1253\n\n\\bibitem[\\protect\\astroncite{{Barrado y Navascu�s}}{1998}]{David98}\n{Barrado y Navascu�s}, D. 1998, {\\em \\aap\\/}, {\\bf 339}, 831\n\n\\bibitem[\\protect\\astroncite{{Barrado y Navascu�s} {\\em\n et~al.\\/}}{1997}]{Barrado97}\n{Barrado y Navascu�s}, D., {Stauffer}, J.~R., {Hartmann}, L., \\&\n {Balachandran}, S.~C. 1997, {\\em \\apj\\/}, {\\bf 475}, 313\n\n\\bibitem[\\protect\\astroncite{{Barrado y Navascu�s} {\\em et~al.\\/}}{1999}]{BSSC}\n{Barrado y Navascu�s}, D., {Stauffer}, J.~R., {Song}, I., \\& {Caillault}, J.-P.\n 1999, {\\em \\apjl\\/}, {\\bf 520}, L123\n\n\\bibitem[\\protect\\astroncite{{D'Antona} \\& {Mazzitelli}}{1997}]{DM97}\n{D'Antona}, R.~A. \\& {Mazzitelli}, I. 1997, in {\\em Cool stars in Clusters and\n Associations\\/}, edited by R.~{Pallavicini} \\& G.~{Micela}, vol.~68 of {\\em\n Mem.S.A.It.\\/}, 807\n\n\\bibitem[\\protect\\astroncite{{Donahue}}{1993}]{Donahue}\n{Donahue}, R.~A. 1993, Ph.D. thesis, New Mexico State University\n\n\\bibitem[\\protect\\astroncite{{Duflot} {\\em et~al.\\/}}{1995}]{Duflot}\n{Duflot}, M., {Figon}, P., \\& {Meyssonnier}, N. 1995, {\\em \\aaps\\/}, {\\bf 114},\n 269\n\n\\bibitem[\\protect\\astroncite{{Fisher}}{1998}]{Fisher}\n{Fisher}, D. 1998, Ph.D. thesis, UC Santa Cruz\n\n\\bibitem[\\protect\\astroncite{{Gehrz}}{1999}]{Gehrz99}\n{Gehrz}, R. D. e.~a. 1999, {\\em \\apjl\\/}, {\\bf 512}, L55\n\n\\bibitem[\\protect\\astroncite{{Habing} {\\em et~al.\\/}}{1999}]{Habing99}\n{Habing}, H.~J., {\\em et~al.\\/} 1999, {\\em \\nat\\/}, {\\bf 401}, 456\n\n\\bibitem[\\protect\\astroncite{{Henry} {\\em et~al.\\/}}{1996}]{Henry}\n{Henry}, T.~J., {Soderblom}, D.~R., {Donahue}, R.~A., \\& {Baliunas}, S.~L.\n 1996, {\\em \\aj\\/}, {\\bf 111}, 439\n\n\\bibitem[\\protect\\astroncite{{H�nsch} {\\em et~al.\\/}}{1999}]{Hunsch99}\n{H�nsch}, M., {Schmitt}, J. H. M.~M., {Sterzik}, M.~F., \\& {Voges}, W. 1999,\n {\\em \\aaps\\/}, {\\bf 135}, 319\n\n\\bibitem[\\protect\\astroncite{{H�nsch} {\\em et~al.\\/}}{1998}]{Hunsch98}\n{H�nsch}, M., {Schmitt}, J. H. M.~M., \\& {Voges}, W. 1998, {\\em \\aaps\\/}, {\\bf\n 132}, 155\n\n\\bibitem[\\protect\\astroncite{{Jeffries} {\\em et~al.\\/}}{1995}]{Jeff}\n{Jeffries}, R.~D., {Bertram}, D., \\& {Spurgeon}, B.~R. 1995, {\\em \\mnras\\/},\n {\\bf 276}, 397\n\n\\bibitem[\\protect\\astroncite{{Johnson} \\& {Soderblom}}{1987}]{JohnsonUVW}\n{Johnson}, D. R.~H. \\& {Soderblom}, D.~R. 1987, {\\em \\aj\\/}, {\\bf 93}, 864\n\n\\bibitem[\\protect\\astroncite{{Jura} {\\em et~al.\\/}}{1998}]{Jura98}\n{Jura}, M., {Malkan}, M., {White}, R., {Telesco}, C., {Pina}, R., \\& {Fisher},\n R.~S. 1998, {\\em \\apj\\/}, {\\bf 505}, 897\n\n\\bibitem[\\protect\\astroncite{{Jura} {\\em et~al.\\/}}{1993}]{Jura93}\n{Jura}, M., {Zuckerman}, B., {Becklin}, E.~E., \\& {Smith}, R.~C. 1993, {\\em\n \\apjl\\/}, {\\bf 418}, L37\n\n\\bibitem[\\protect\\astroncite{{Lagrange} {\\em et~al.\\/}}{2000}]{LBA99}\n{Lagrange}, A.~M., {Backman}, D.~E., \\& {Artymowicz}, P. 2000, in {\\em\n Protostars and Planets IV\\/}, edited by V.~{Mannings}, A.~P. {Boss}, \\& S.~S.\n {Russell}, (Tucson: University of Arizona Press), in press\n\n\\bibitem[\\protect\\astroncite{{L�bre} {\\em et~al.\\/}}{1999}]{Lebre}\n{L�bre}, A., {de Laverny}, P., {de Medeiros}, J.~R., {Charbonnel}, C., \\& {da\n Silva}, L. 1999, {\\em \\aap\\/}, {\\bf 345}, 936\n\n\\bibitem[\\protect\\astroncite{{Leggett}}{1992}]{Leggett}\n{Leggett}, S.~K. 1992, {\\em \\apjs\\/}, {\\bf 82}, 351\n\n\\bibitem[\\protect\\astroncite{{Mallik}}{1998}]{Mallik}\n{Mallik}, S.~V. 1998, {\\em \\aap\\/}, {\\bf 338}, 623\n\n\\bibitem[\\protect\\astroncite{{Soderblom} {\\em et~al.\\/}}{1993}]{Soderblom93}\n{Soderblom}, D.~R., {Stauffer}, J.~R., {Macgregor}, K.~B., \\& {Jones}, B.~F.\n 1993, {\\em \\apj\\/}, {\\bf 409}, 624\n\n\\bibitem[\\protect\\astroncite{{Soderblom}}{1998}]{Soderblom98}\n{Soderblom}, D. R. e.~a. 1998, {\\em \\apj\\/}, {\\bf 498}, 385\n\n\\bibitem[\\protect\\astroncite{{Song}}{2000}]{myPhD}\n{Song}, I. 2000, Ph.D. thesis, University of Georgia\n\n\\bibitem[\\protect\\astroncite{{Song} {\\em et~al.\\/}}{2000}]{uvbyBpaper}\n{Song}, I., {Caillault}, J.-P., {Barrado y Navascu\\'es}, D., \\& {Stauffer}, J.\n 2000, {\\em ApJL\\/}, in preparation\n\n\\bibitem[\\protect\\astroncite{{Stauffer} {\\em et~al.\\/}}{1995}]{Stauffer95}\n{Stauffer}, J.~R., {Hartmann}, L.~W., \\& {Barrado Y Navascues}, D. 1995, {\\em\n \\apj\\/}, {\\bf 454}, 910\n\n\\bibitem[\\protect\\astroncite{{Stauffer} {\\em et~al.\\/}}{1998}]{Stauffer98}\n{Stauffer}, J.~R., {Schultz}, G., \\& {Kirkpatrick}, J.~D. 1998, {\\em \\apjl\\/},\n {\\bf 499}, L199\n\n\\bibitem[\\protect\\astroncite{{Stauffer} {\\em et~al.\\/}}{1999}]{Stauffer99}\n{Stauffer}, J.~R., {\\em et~al.\\/} 1999, {\\em {\\apj}\\/}, {\\bf 527}, 219\n\n\\bibitem[\\protect\\astroncite{{Torres} {\\em et~al.\\/}}{1995}]{Torres}\n{Torres}, G., {Stefanik}, R.~P., {Latham}, D.~W., \\& {Mazeh}, T. 1995, {\\em\n \\apj\\/}, {\\bf 452}, 870\n\n\\end{thebibliography}\n"
}
] |
astro-ph0002324
|
High Resolution Spectroscopy of the X-ray Photoionized Wind in Cygnus X-3 with the {Chandra} High Energy Transmission Grating Spectrometer
|
[
{
"author": "Frits Paerels\\altaffilmark{1,2}"
},
{
"author": "Jean Cottam\\altaffilmark{1}"
},
{
"author": "Masao Sako\\altaffilmark{1}"
},
{
"author": "Duane A. Liedahl\\altaffilmark{3}"
},
{
"author": "A. C. Brinkman\\altaffilmark{2}"
},
{
"author": "R. L. J. van der Meer\\altaffilmark{2}"
},
{
"author": "J. S. Kaastra\\altaffilmark{2}"
},
{
"author": "and P. Predehl\\altaffilmark{4}"
}
] |
We present a preliminary analysis of the 1--10 keV spectrum of the massive X-ray binary Cyg X-3, obtained with the High Energy Transmission Grating Spectrometer on the {Chandra X-ray Observatory}. The source reveals a richly detailed discrete emission spectrum, with clear signatures of photoionization-driven excitation. Among the spectroscopic novelties in the data are the first astrophysical detections of a number of He-like 'triplets' (Si, S, Ar) with emission line ratios characteristic of photoionization equilibrium, fully resolved narrow radiative recombination continua of Mg, Si, and S, the presence of the H-like Fe Balmer series, and a clear detection of a $\sim 800$ km s$^{-1}$ large scale velocity field, as well as a $\sim 1500$ km s$^{-1}$ FWHM Doppler broadening in the source. We briefly touch on the implications of these findings for the structure of the Wolf-Rayet wind. \keywords{atomic processes - techniques: spectroscopic - stars: individual (Cygnus X-3) - X-rays: stars}
|
[
{
"name": "ms_pp.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[11pt,aas2pp4]{article}\n%\\documentclass{article}\n%\\usepackage{emulateapj,pstricks,apjfonts}\n\n\\newbox\\grsign \\setbox\\grsign=\\hbox{$>$} \n\\newdimen\\grdimen \\grdimen=\\ht\\grsign\n\\newbox\\laxbox \\newbox\\gaxbox\n\\setbox\\gaxbox=\\hbox{\\raise.5ex\\hbox{$>$}\\llap\n {\\lower.5ex\\hbox{$\\sim$}}}\\ht1=\\grdimen\\dp1=0pt\n\\setbox\\laxbox=\\hbox{\\raise.5ex\\hbox{$<$}\\llap\n {\\lower.5ex\\hbox{$\\sim$}}}\\ht2=\\grdimen\\dp2=0pt\n\\def\\gax{\\mathrel{\\copy\\gaxbox}}\n\\def\\lax{\\mathrel{\\copy\\laxbox}}\n\n\\begin{document}\n\n\\title{\nHigh Resolution Spectroscopy of the X-ray Photoionized Wind in\nCygnus X-3 with the {\\it Chandra} High Energy Transmission Grating\nSpectrometer\n}\n\n\\author{\nFrits Paerels\\altaffilmark{1,2}, \nJean Cottam\\altaffilmark{1},\nMasao Sako\\altaffilmark{1},\nDuane A. Liedahl\\altaffilmark{3}, \nA. C. Brinkman\\altaffilmark{2},\nR. L. J. van der Meer\\altaffilmark{2},\nJ. S. Kaastra\\altaffilmark{2}, and\nP. Predehl\\altaffilmark{4}\n}\n\\altaffiltext{1}{Columbia Astrophysics Laboratory,\nColumbia University, 538 W. 120th St., New York, NY 10027, USA} \n\n\\altaffiltext{2}{SRON Laboratory for Space Research,\nSorbonnelaan 2, 3584 CA Utrecht, the Netherlands}\n\n\\altaffiltext{3}{Department of Physics,\nLawrence Livermore National Laboratory,\nP.O. Box 808, L-41, Livermore, CA 94550, USA}\n\n\\altaffiltext{4}{Max Planck Institut f\\\"ur Extraterrestrische\nPhysik, Postfach 1503, D-85740 Garching, Germany}\n\n\\begin{abstract}\n\nWe present a preliminary analysis of the 1--10 keV spectrum of the\nmassive X-ray binary Cyg X-3, obtained with the High Energy\nTransmission Grating Spectrometer on the {\\it Chandra X-ray\nObservatory}. The source reveals a richly detailed discrete emission\nspectrum, with clear signatures of photoionization-driven excitation. \nAmong\nthe spectroscopic novelties in the data are the first astrophysical\ndetections of a number of He-like 'triplets' (Si, S, Ar)\nwith emission line\nratios characteristic of photoionization equilibrium, fully resolved\nnarrow radiative recombination continua of Mg, Si, and S, \nthe presence of\nthe H-like Fe Balmer series, and a clear detection of a $\\sim 800$ km\ns$^{-1}$ large scale velocity field, as well as a $\\sim\n1500$ km s$^{-1}$\nFWHM Doppler broadening\nin the source. We briefly touch on\nthe implications of these findings for the structure of the Wolf-Rayet\nwind. \n\n\n\\keywords{atomic processes - techniques: spectroscopic -\n stars: individual (Cygnus X-3) - X-rays: stars}\n\n\\end{abstract}\n\n\n\\section{Introduction}\n\nIn a previous paper (Liedahl \\& Paerels 1996, 'LP96') we presented an\ninterpretation of the discrete spectrum of Cyg X-3 as observed with\nthe Solid State Imaging Spectrometers on {\\it ASCA} (cf. Kitamoto\net al. 1994; Kawashima \\& Kitamoto 1996). \nWe found clear spectroscopic evidence that the discrete emission is\nexcited by recombination in a tenuous X-ray\nphotoionized medium, presumably\nthe stellar wind from the Wolf-Rayet companion star (van Kerkwijk et \nal. 1992). \nSpecifically, the {\\it ASCA} spectrum revealed a narrow\nradiative recombination continuum (RRC) from H-like S, unblended\nwith any other transitions. On closer inspection, RRC features due to\nH-like Mg and Si were also found to be present in the data, although\nseverely blended with emission lines. These narrow continua are an\nunambiguous indicator of excitation by recombination in X-ray\nphotoionized gas, and their relative narrowness is a direct\nconsequence of the fact that a highly ionized photoionized \nplasma is generally much cooler than a collisionally ionized plasma of\ncomparable mean ionization (LP96, Liedahl 1999 and references\ntherein).\n\nWith the high spectral resolution of the {\\it Chandra} High Energy\nTransmission Grating Spectrometer, we now have the capability to fully\nresolve the discrete spectrum. \nApart from offering a unique way to determine the structure of the\nwind of a massive star, study of the spectrum may yield\nother significant benefits. Cyg X-3 shows a bright, purely\nphotoionization driven spectrum, and, as such, may provide a template\nfor the study of the spectra of more complex accretion-driven\nsources, such as AGN. The analysis will also allow us to verify\nexplicitly \nthe predictions for the structure of X-ray photoionized nebulae\nderived from widely applied X-ray photoionization codes.\n\n\n\\section{Data Reduction}\n\nA description of the High Energy Transmission Grating Spectrometer\n(HETGS) may be found in Markert et al. (1994).\nCyg X-3 was observed on October 20, 1999, for a total of 14.6 ksec\nexposure time, starting at 01:11:38 UT.\nThe observation covered approximate binary phases $-0.31$ to \n$+0.53$, which\nmeans that about half of the exposure in our observation occurs in the\nbroad minimum in the lightcurve at orbital phase zero.\nAspect-corrected data from the standard CXC pipeline \n(processing date October 30, 1999) was post-processed \nusing dedicated procedures written at Columbia. We used \n({\\it ASCA}-)grade \n0,2,3,4 events, \na spatial filter 30\nACIS pixels wide was applied to both the High Energy \nGrating (HEG) and Medium Energy Grating (MEG)\nspectra, and\nthe resulting events were plotted in a dispersion--CCD pulse height\ndiagram, in which the spectral orders are neatly separated. \n\nA second filter was applied in this dispersion--pulse height diagram.\nThe filter consisted of a narrow mask centered on each of the spectral\norders separately. The mask size and shape were optimized\ninteractively.\nThe\nresidual background in the extracted spectra is of order 0.5\ncounts/spectral bin of 0.005 \\AA\\ or \nless. \nThe current state of the calibration does not provide us with the\neffective area associated with our joint spatial/pulse height \nfilters to better than 25\\% accuracy, hence we have chosen not to\nflux-calibrate the spectrum at this time.\nAn additional correction to the flux in the chosen aperture\ndue to the (energy\ndependent) scattering of photons by interstellar dust has not yet\nbeen determined either.\n\nIn the resulting order-separated count spectra, we located the zero\norder and we determined its centroid position to find the zero of the\nwavelength scale. We then converted pixel number to wavelength based\non the geometry of the HETGS. In this procedure, we used ACIS/S chip\npositions that\nwere determined after launch from an analysis of the dispersion\nangles in the HETGS spectrum of Capella (Huenemoerder et al. 2000). \nThis preliminary wavelength\nscale appears to be accurate to approximately 2 m\\AA. \nThe spectral resolution was\ndetermined from a study of narrow, unblended\nemission lines in the spectrum of Capella.\nIt is approximately constant accross the entire HETGS band, and amounts\nto approximately 0.012 \\AA\\ (0.023 \\AA) FWHM for the HEG (MEG) (Dewey\n2000).\nThe resolution in the Cyg X-3 spectrum can be checked\nself-consistently by analyzing the width of the zero order image.\nUnfortunately, the zero order image is affected by pileup. \nHowever, enough\nevents arrive during the 41 ms CCD frame transfer, forming a\nstreak in the image, \nthat we can construct an unbiased 1D zero-order\ndistribution from them. The width of this distribution is consistent\nwith the widths of narrow lines in the spectrum of Capella, which\nindicates that the resolution in the Cyg X-3 spectrum is not affected\nby systematic effects ({\\it e.g.},\nincorrect aspect solution, defocusing).\n\n\\section{X-ray Photoionization in Cyg X-3}\n\nFigure 1 shows the HEG and MEG first order spectra; the higher order\nspectra are unfortunately very weak, and we will not discuss them\nhere.\nWe show the spectra as a function of wavelength, because this is the\nmost natural unit for a diffractive spectrometer: the instruments have\napproximately constant wavelength resolution.\nThe spectra have been smoothed with a 3-pixel boxcar average to\nbring out coherent features \n%(the source did not oblige us as far as\n%its total flux is concerned; at the time of the {\\it Chandra}\n%observation, its 2--10 keV flux was approximately a factor 5 below\n%that at the time of the {\\it ASCA} observation). \nWe have indicated the\npositions of expected strong H-- and He-like discrete features. A\ncursory examination of the spectrum strikingly confirms the\nphotoionization-driven origin of the discrete emission. \n\nWe detect the spectra of the H-like species of all abundant \nelements from Mg through Fe. In Si and S, we detect well-resolved \nnarrow radiative recombination continua. This is illustrated in Figure\n2, which shows the 3.0--7.0 \\AA\\ band on an enlarged scale. The \nSi XIV and\nS XVI continua are readily apparent.\nThe width of these features is a\ndirect measure of the electron temperature in the recombining plasma,\nand a simple eyeball fit to the shapes indicates $kT_e \\sim$ 50 eV,\nwhich is roughly in agreement with the result of model calculations\nfor optically thin X-ray photoionized nebulae (Kallman \\& McCray\n1982). A more detailed, fully quantitative analysis of the spectrum\nwill be required to see whether we can also detect the \nexpected temperature gradient in the source (more highly ionized zones\nare also expected to be hotter).\nIn the Si XIV and S XVI spectra we estimate the ratio between \nthe total photon flux in the RRC to that in Ly$\\alpha$ to be about \n0.8 and 0.7, respectively; here, we assume $kT_e =$ 50 eV, and we have\nmade an approximate correction for the differences in effective area\nat the various features. These measured ratios\nare in reasonable agreement with the expected ratio of \n$0.73 (kT_e/20\\ {\\rm eV})^{+0.17}$ (LP96), which indicates that the\nH-like spectra are consistent with pure recombination in optically\nthin gas.\n\nThe positions of the lowest members of the Fe XXVI Balmer series are\nindicated in Figure 1 (the fine structure splitting\nof these transitions is\nappreciable in H-like Fe, as is evident from the plot). The\nrelative brightness of the Balmer spectrum is yet another indication of\nrecombination excitation.\nThere is evidence for line emission at the position of H$\\beta$, and\npossibly at H$\\gamma$ and H$\\delta$; the spectrum is unfortunately too\nheavily absorbed to permit a detection of H$\\alpha$ ($\\lambda\\lambda\n9.52,9.74$ \\AA). Unfortunately, the long-wavelength member of the \nH$\\beta$ 'doublet'\n($\\lambda \\approx 7.17$ \\AA) almost precisely coincides\nwith the expected position of Al XIII Ly$\\alpha$, which precludes \na simple and neat direct detection of Al (the first detection of an\nodd-$Z$ triple-$\\alpha$ element in non-solar\nX-ray astronomy). Any limit on the\nAl/Si abundance ratio thus becomes dependent on an understanding of the\nintensity of the Fe XXVI spectrum.\n\nAs for the He-like species, we detect the $n=2-1$ complexes, consisting\nof the forbidden ('$f$'), intercombination ('$i$'), and resonance \n('$r$') transitions, in Si\nXIII, S XV, Ar XVII, Ca XIX, and Fe XXV (as well as the corresponding\nRRC in Si, S, and possibly Ar). The line complexes appear resolved\ninto blended resonance plus intercombination lines, and\nthe forbidden line (see Figures 1 and 2), up to Ar XVII.\n\nIn an optically thin, low density, \npurely photoionization-driven plasma, one expects the intensity ratio\n$f/(r+i) \\approx 1$\nfor the mid-$Z$ elements, very different from the pattern in the more\nfamiliar collisional equilibrium case, where the resonance transition\nis relatively much brighter ({\\it e.g.}, Gabriel \\& Jordan\n1969; Pradhan 1982; Liedahl 1999). We use the ratio $f/(r+i)$ rather\nthan the conventional $G \\equiv (i + f)/r$ and $R \\equiv f/i$,\nbecause the intercombination and resonance lines are unfortunately \nblended by significant Doppler broadening in the source\n(see Section 4).\nTheoretically, in a photoionized plasma \n$f/(r+i)$ is approximately equal to 1.3, 1.0, 0.83, for\nSi XIII, S XV, and Ar XVII, respectively, and \ndepends only weakly on electron temperature (LP96, Liedahl\n2000). The measured ratios $f/(r+i)$, derived by fitting three\nGaussians with common wavelength offset and broadening at the expected\npositions of $f, i$, and $r$, are approximately 1.1, 0.8, and 1.1\nwith the\nHEG, for Si, S, and Ar, respectively; the corresponding ratios for \nthe MEG are 1.3, 1.0, and 0.8. Since most of the lines contain at least\n100 photons, the statistical error on the ratios is generally less\nthan 15\\%. These measurements include a model for the Si XIII RRC in\nthe S XV triplet (assuming $kT_e = 50$ eV), and Mg XII Ly$\\gamma$\nemission in the Si XIII triplet.\n\nThe He-like line ratios are probably\naffected by systematic features in the efficiency of the\nspectrometer. The S XV triplet is superimposed on the Si XIII\nRRC, the Si XIII triplet straddles the Si K edge in the CCD\nefficiency, and the Ar XVII triplet straddles the Au M$_{\\rm IV}$ \nand Ir M$_{\\rm I}$ edges. \nCorrections for these effects will have to be carefully\nevaluated. Nevertheless, the raw ratios $f/(r+i)$ for the Si and Ar\ntriplets are already of the right magnitude for pure recombination. \nOur provisional conclusion is that the \nHe-like spectra are, very roughly, consistent with pure\nrecombination in optically thin gas.\n\nJust as in a collisional plasma, the relative strengths of the\nforbidden and intercombination lines are sensitive to density (Liedahl\n1999; Porquet \\& Dubau 2000), due to collisional transfer between the\nupper levels of $f$ and $i$ at high density. As mentioned above,\nthere are some systematic\nuncertainties in the measured line ratios, and we defer a discussion\nof possible constraints on the density in the wind to a future paper.\n\nThe detection of fluorescent Fe emission\nis a surprise, because virtually\nno fluorescence\nwas seen at the time of the {\\it ASCA} observation\n(Kitamoto et al. 1994). The apparent\ncentroid wavelength of the fluorescent line is $1.939$ \\AA\\\n(photon energy 6394 eV), with a\nformal error of less than $10^{-3}$ \\AA\\ (3 eV). \nThe width of the line is \n$0.022$ \\AA\\ FWHM, with a formal uncertainty of less than 5\\%.\nThis is wider than would be expected from the \nvelocity broadening to be discussed in the next section, and may\nbe an indication that a range of ionization stages contributes to the\nfluorescent emission. If we assume the same velocity broadening for\nthe Fe K$\\alpha$ feature as for the high-ionization lines (which may \nnot necessarily be correct if the low-- and high--ionization lines\noriginate in different parts of the stellar wind), we find that \nFe K$\\alpha$ has an intrinsic width (expressed as the FWHM of a\nGaussian distribution) of 0.018 \\AA\\ (corresponding to $\\Delta E \n\\approx 60$ eV). The fine structure split between K$\\alpha_1$ and \nK$\\alpha_2$ contributes slightly \nto this width ($\\Delta\\lambda \\approx 0.004$\n\\AA), but the measured width covers the full range of \nK$\\alpha$ wavelengths for charge states between fully neutral and \nNe-like (Decaux et al. 1995).\n\n\\section{Bulk Velocity Fields}\n\nWe find that all emission features are significantly\nbroadened and redshifted. The lines and radiative recombination continua\nare resolved by both the HEG and the MEG. The line widths for\nH-like Mg, Si, S, Ar, Ca, and Fe Ly$\\alpha$ were measured by\nfitting a simple Gaussian profile. Other than the negligibly small\nfine structure split ($\\Delta\\lambda \\sim 0.005$ \\AA), these lines are\nclean and unblended. \nThe resulting widths do not seem to exhibit a strong dependence on\nphase. Assuming that the\nspectrometer profile is well represented by a Gaussian of width\n0.012 \\AA\\ (0.023 \\AA) FWHM for the HEG (MEG), we find that the\nbroadening of the lines is roughly consistent with a Gaussian velocity\ndistribution, of width $\\Delta v \\sim 1500$ km s$^{-1}$ FWHM. \nThe scatter\nis too large to permit a meaningful test for any dependence of the\nvelocity broadening on ionization parameter. \nNote that no such broadening was\nseen in the spectrum of Capella. \n\nWe also measured the radial velocities for the Ly$\\alpha$ lines,\nassuming the dispersion relation obtained from an analysis of the\nspectrum of Capella. Wavelengths were calculated from the level\nenergies given by Johnson \\& Soff (1985); these should be accurate to\na few parts in $10^6$. There is a clear systematic redshift to all the\nemission lines and RRCs, in both the positive and negative spectral\norders and in both grating spectra. This is shown in Figure 3, where\nwe have segregated dim and bright state data, but have averaged\npositive and negative spectral orders, and HEG and MEG spectral data. \nAlso shown are the best fitting uniform\nvelocity offsets. These fits were\nforced to yield zero wavelength shift at zero wavelength. \nThe average redshift for the dim state is $\\sim 800$ km s$^{-1}$,\nand for the bright state is $\\sim 750$ km s$^{-1}$.\nWe thus\nfind a net redshift much smaller than the observed velocity \nspread, and essentially no\ndependence of the centroid velocity on the binary phase.\nWe should point out that our preliminary analysis,\nbased on fitting simple Gaussians, is admittedly crude,\nand may have biased the true nature of the velocity field somewhat.\nWe also note, with caution, that Doppler shifts due to a single, uniform\nvelocity do not appear to be a very good description of the data: the\nlongest wavelength lines appear to be offset at a significantly\nlarger than average radial velocity. A detailed analysis, taking into\naccount the actual lineshape, will be\nrequired to confirm or refute the possibility that these offsets\nrepresent the expected systematic correlation of average\nwind velocity and ionization parameter.\n\n\\section{Discussion}\n\nThe HETGS spectrum of Cyg X-3 has revealed a rich discrete spectrum,\nthe properties of which are consistent with pure recombination\nexcitation in cool, optically thin, low density X-ray photoionized gas\nin equilibrium. We fully resolve the narrow RRCs\nfor the first time, \nand estimate an average electron temperature in the\nphotoionized region of $kT_e \\sim 50$ eV, consistent with global\nphotoionization calculations.\n\nWe detect a net redshift in the emission lines of $v \\sim 750-800$\nkm s$^{-1}$, essentially independent of binary phase, \nand a distribution in velocity with a FWHM of $\\sim 1500$ km s$^{-1}$.\nIf the wind were photoionized throughout, we would expect to\nsee roughly equal amounts of\nblue-- and redshifted material, so evidently we are viewing\nan ionized region that is not symmetric with respect to the source of\nthe wind, as expected if only the part of the wind in the\nvicinity of the X-ray continuum source is ionized. \nHowever, in the simplest wind models, one would then \nexpect to see a strong\ndependence of the centroid velocity on binary phase, alternating\nbetween red-- and blueshifts, and this is decidedly not the case in\nour data. \nThe implications of this finding for the flow pattern and\ndistribution of material in the wind will be explored in a future paper.\n\nFinally, the Fe K$\\alpha$ fluorescent feature, which \nprobes a more neutral phase of the wind, has never been seen before in\nCyg X-3.\nUnfortunately, the exact range of ionization can not\nbe separated uniquely from systematic Doppler shifts through a\nmeasurement of the wavelengths of the K$\\alpha$ spectra, because the\nfeature, while clearly broadened, is not separated into its component\nionization stages. Still,\nthe width of the feature (the net effect of the\nvelocity field and the existence of a range of charge states)\nand its intensity\nwill impose strong constraints on the global properties \nof the wind. \n\n\n\\noindent\nAcknowledgements.\n\\newline\n\\noindent\nWe wish to express our gratitude to Dan Dewey and Marten van Kerkwijk,\nfor discussions and a careful reading of the manuscript, and to the\nreferee, Randall Smith, for a thorough review.\nJC acknowledges support from NASA under a GRSP fellowship.\nMS's contribution was supported by \nNASA under Long Term Space Astrophysics\ngrant no. NAG 5-3541. FP was supported under NASA Contract no. NAS\n5-31429.\nDL acknowledges support from NASA under Long Term Space Astrophysics\nGrant no. S-92654-F. Work at LLNL was performed under the auspices of\nthe US Department of Energy, Contract mo. W-7405-Eng-48.\n\n\n%\\clearpage\n\n\\begin{references}\n\n\\reference{} Decaux, V., Beiersdorfer, P., Osterheld, A., Chen, M., \\&\nKahn, S. M. 1995, \\apj, 443, 464.\n\n\\reference{} Dewey, D. 2000, priv. comm.\n\n\\reference{}Gabriel, A. H. \\& Jordan, C. 1969, \\mnras, 145, 241.\n\n\\reference{} Huenemoerder, D., et al., \\apj, in preparation.\n\n\\reference{} Johnson, W. R., \\& Soff, G. 1985, Atom. Data Nucl. Data\nTables, 33, 405.\n\n\\reference{} Kallman, T. R., \\& McCray, R. 1982, \\apjs, 50, 263.\n\n\\reference{}Kawashima, K., \\& Kitamoto, S. 1996, \\pasj, 48, L113.\n\n\\reference{} Kitamoto, S., Kawashima, K., Negoro, H., Miyamoto, S.,\nWhite, N. E., \\& Nagase, F. 1994, \\pasj, 46, L105\n\n\\reference{} Liedahl, D. A., \\& Paerels, F. 1996, \\apjl,468, L33.\n\n\\reference{} Liedahl, D. A. 1999, in {\\it X-ray Spectroscopy in\nAstrophysics},\nProceedings of the European Astrophysics Doctoral Network Tenth \nSummer School, J. van Paradijs \\& J. A. M. Bleeker (Eds.), \np.189 (Berlin:Springer)\n\n\\reference{} Liedahl, D. A. 2000, in preparation.\n\n\\reference{} Markert, T. H., Canizares, C. R., Dewey, D., McGuirk, M,\nPak, C., \\& Schattenburg, M. L. 1995, Proc. SPIE, 2280, 168.\n\n\\reference{} Porquet, D. \\& Dubau, J. 2000, Rev. Mex. A. A., 99, 167.\n\n\\reference{} Pradhan, A. 1982, \\apj, 263, 477.\n\n\\reference{} van Kerkwijk, M. H., Charles, P. A., Geballe, T. R.,\nKing, D. L., Miley, G. K., Molnar, L. A., van den Heuvel, E. P. J.,\nvan der Klis, M., \\& van Paradijs, J. 1992, Nature, 355, 703.\n\n\\end{references}\n\n\\newpage\n\nFigure Captions:\n\n\\noindent\nFig.1---The 1--10 \\AA\\ spectrum of Cyg X-3 as observed with the HEG\n(upper panel), and the MEG (lower panel), binned in 0.005 \\AA\\ bins.\nThe positive and negative first orders have been added, and the\nspectra have been smoothed with a 3 pixel boxcar filter. Labels\nindicate the positions of various discrete spectral features.\n'He$\\alpha$' is the inelegant label for the resonance, \nintercombination, and forbidden lines in the He-like ions, plotted at\nthe average wavelength for the complex.\nHigh-ionization features of interest \nthat were not detected have been labeled in\nbrackets. Horizontal bars indicate the nominal\npositions of the gaps between\nthe ACIS chips; the dithering of the spacecraft will broaden the gaps\nand soften their edges.\n\n\\noindent\nFig.2---The 3.0--7.0 \\AA\\ region of the spectrum enlarged; we show\nthe raw count rates, binned by two 0.005 \\AA\\ bins.\nThe most important transitions have been labeled; dashed lines mark\nthe expected positions of Si and S recombination edges. These markers\nhave been redshifted by 800 km s$^{-1}$.\nThe horizontal bar\nnear 4.5 \\AA\\ in the HEG spectrum marks the nominal position of the\ngap between chips S2 and S3 in ACIS.\nThe solid\nline in the MEG spectrum is a crude empirical fit to the continuum, with\nSi XIII, Si XIV, and S XVI narrow radiative recombination continua\nadded. The electron temperature was set to 50 eV, and the continua\nwere convolved with a 1500 km s$^{-1}$ FWHM velocity field, to match\nthe broadening observed in the emission lines.\n\n\\noindent\nFig.3--Measured wavelength shift for selected Ly$\\alpha$ features.\nFilled symbols refer to the 'dim' state data, open symbols to the\n'bright' state data. The velocities as measured with the HEG and the\nMEG have been averaged; velocities in\npositive and negative spectral orders were\naveraged. Error bars indicate the size of the rms variation between\nthese various measurements. In cases where only one or two velocities\nwere measurable due to low signal-to-noise, we instead indicate \nthe estimated\nstatistical error on these measurements. The solid lines are the\nweighted least squares Doppler velocities for both the dim and the\nbright states.\n\n\\vfill\\eject\n\n\\centerline{\\null}\n\\vskip7.5truein\n\\special{psfile=fig1.ps voffset=0 hoffset=0 vscale=70\nhscale=70 angle=0}\n\n\\vfill\\eject\n\n\\centerline{\\null}\n\\vskip7.5truein\n\\special{psfile=fig2.ps voffset=0 hoffset=0 vscale=70\nhscale=70 angle=0}\n\n\\vfill\\eject\n\n\\centerline{\\null}\n\\vskip7.5truein\n\\special{psfile=fig3.ps voffset=0 hoffset=0 vscale=70\nhscale=70 angle=0}\n\n\n\\end{document}\n\n\\end\n"
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astro-ph0002325
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Multi-colour $PL$-relations of Cepheids in the {\sc hipparcos} catalogue and the distance to the LMC \thanks{Based on data from the ESA \HP\ astrometry satellite.}
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[
{
"author": "M.A.T. Groenewegen \\inst{1}"
},
{
"author": "R.D. Oudmaijer \\inst{2,3} %"
},
{
"author": "H.-G. Ludwig \\inst{3}"
}
] |
We analyse a sample of 236 \C\ from the \HP\ catalog, using the method of ``reduced parallaxes'' in $V, I, K$ and the reddening-free ``Wesenheit-index''. We compare our sample to those considered by Feast \& Catchpole (1997) and Lanoix et al. (1999), and argue that our sample is the most carefully selected one with respect to completeness, the flagging of overtone pulsators, and the removal of \C\ that may influence the analyses for various reasons (double-mode \C, unreliable \HP\ solutions, possible contaminated photometry due to binary companions). From numerical simulations, and confirmed by the observed parallax distribution, we derive a (vertical) scale height of \C\ of 70 pc, as expected for a population of 3-10 \msol\ stars. This has consequences for Malmquist- and Lutz-Kelker (Lutz \& Kelker 1973, Oudmaijer et al. 1998) type corrections which are smaller for a disk population than for a spherical population. The $V$ and $I$ data suggest that the slope of the Galactic $PL$-relations may be shallower than that observed for LMC Cepheids, either for the whole period range, or that there is a break at short periods (near $\log P_0 \approx 0.7-0.8$). We stress the importance of two systematic effects which influence the distance to the LMC: the slopes of the Galactic $PL$-relations and metallicity corrections. In order to assess the influence of these various effects, we present 27 distance moduli (DM) to the LMC. These are based on three different colours ($V,I,K$), three different slopes (the slope observed for \C\ in the LMC, a shallower slope predicted from one set of theoretical models, and a steeper slope as derived for Galactic \C\ from the surface-brightness technique), and three different metallicity corrections (no correction as predicted by one set of theoretical models, one implying larger DM as predicted by another set of theoretical models, and one implying shorter DM based on empirical evidence). We derive DM between 18.45 $\pm$ 0.18 and 18.86 $\pm$ 0.12. The DM based on $K$ are shorter than those based on $V$ and $I$ and range from 18.45 $\pm$ 0.18 to 18.62 $\pm$ 0.19, but the DM in $K$ could be systematically too low by about 0.1 magnitude because of a bias due to the fact that NIR photometry is available only for a limited number of stars. From the Wesenheit-index we derive a DM of 18.60 $\pm$ 0.11, assuming the observed slope of LMC \C\ and no metallicity correction, for want of more information. The DM to the LMC based on the parallax data can be summarised as follows. Based on the $PL$-relation in $V$ and $I$, and the Wesenheit-index, the DM is \begin{displaymath} 18.60 \pm 0.11 \;\; (\pm 0.08 \;{slope})(^{+0.08}_{-0.15} \;{metallicity}), \end{displaymath} which is our current best estimate. Based on the $PL$-relation in $K$ the DM is $\;\;\;\; 18.52 \pm 0.18$ \begin{displaymath} \;\;(\pm 0.03 \;{slope}) (\pm 0.06 \;{metallicity}) (^{+0.10}_{-0} \;{sampling \;bias}). \end{displaymath} The random error is mostly due to the given accuracy of the \HP\ parallaxes and the number of Cepheids in the respective samples. The terms between parentheses indicate the possible systematic uncertainties due to the slope of the Galactic $PL$-relations, the metallicity corrections, and in the $K$-band, due to the limited number of stars. Recent work by Sandage et al. (1999) indicates that the effect of metallicity towards shorter distances may be smaller in $V$ and $I$ than indicated here. From this, we point out the importance of obtaining NIR photometry for more (closeby) \C, as for the moment NIR photometry is only available for 27\% of the total sample. This would eliminate the possible bias due to the limited number of stars, and would reduce the random error estimate from 0.18 to about 0.10 mag. Furthermore, the sensitivity of the DM to reddening, metallicity correction and slope are smallest in the $K$-band. \keywords{Stars: distances - Cepheids - Magellanic Clouds - distance scale}
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[
{
"name": "cepana.tex",
"string": "%\\documentstyle[referee,psfig]{l-aa}\n%\\documentstyle[psfig]{l-aa}\n\n% \\documentclass[referee]{aa}\n \\documentclass{aa}\n \\usepackage{psfig}\n\n\n\\renewcommand{\\topfraction}{0.999}\n\\renewcommand{\\textfraction}{0.001}\n\n\\newcommand{\\less}{\\raisebox{-1.1mm}{$\\stackrel{<}{\\sim}$}}\n\\newcommand{\\more}{\\raisebox{-1.1mm}{$\\stackrel{>}{\\sim}$}}\n\\newcommand{\\msol}{{M$_{\\odot}$}}\n\\newcommand{\\msolyr}{{M$_{\\odot}$}\\,yr$^{-1}$ }\n\\newcommand{\\lsol}{{L$_{\\odot}$}}\n\\newcommand{\\bdouble}{\\baselineskip 1.5\\baselineskip}\n\\newcommand{\\ratio}{$^{12}$C/$^{13}$C }\n\\newcommand{\\kks}{K km s$^{-1}$}\n\\newcommand{\\ks}{km s$^{-1}$}\n\\newcommand{\\HP}{{\\sc hipparcos}}\n\\newcommand{\\C}{Cepheids}\n\n%\\include{psfig.sty}\n\n\\begin{document}\n%\\bdouble\n%\\psdraft\n\n\\thesaurus{04(08.04.1, 08.22.1, 11.13.1, 12.04.3)}\n\\title{Multi-colour $PL$-relations of Cepheids in the \n{\\sc hipparcos} catalogue and the distance to the LMC\n\\thanks{Based on data from the ESA \\HP\\ astrometry satellite.}\n}\n\n\\author{M.A.T. Groenewegen \\inst{1} \\and R.D. Oudmaijer \\inst{2,3} \n%\\and H.-G. Ludwig \\inst{3}\n}\n\n\\offprints{Martin Groenewegen (groen@mpa-garching.mpg.de)}\n\n\\institute{\nMax-Planck Institut f\\\"ur Astrophysik, Karl-Schwarzschild-Stra{\\ss}e 1, \nD-85740 Garching, Germany\n\\and\nDepartment of Physics and Astronomy, University of Leeds, LS2 9JT Leeds, U.K.\n\\and\nBlackett Laboratory, Imperial College of Science, \nTechnology and Medicine, Prince Consort Road, London SW7 2BZ, U.K.\n%\\and\n%Astronomical Observatory, Niels Bohr Institute, \n%Juliane Maries Vej 30, DK-2100 Copenhagen, Denmark\n}\n\n\\date{received: Nov. 22nd, 1999, accepted: Feb. 3rd, 2000}\n\n\n\\authorrunning{Groenewegen \\& Oudmaijer}\n\\titlerunning{The distance to the LMC from \\HP\\ Cepheid parallaxes}\n\n\\maketitle\n \n\\begin{abstract}\n\nWe analyse a sample of 236 \\C\\ from the \\HP\\ catalog, using the method\nof ``reduced parallaxes'' in $V, I, K$ and the reddening-free\n``Wesenheit-index''. We compare our sample to those considered by\nFeast \\& Catchpole (1997) and Lanoix et al. (1999), and argue that our\nsample is the most carefully selected one with respect to\ncompleteness, the flagging of overtone pulsators, and the removal of\n\\C\\ that may influence the analyses for various reasons (double-mode\n\\C, unreliable \\HP\\ solutions, possible contaminated photometry due to\nbinary companions).\n\nFrom numerical simulations, and confirmed by the observed parallax\ndistribution, we derive a (vertical) scale height of \\C\\ of 70 pc, as\nexpected for a population of 3-10 \\msol\\ stars. This has consequences\nfor Malmquist- and Lutz-Kelker (Lutz \\& Kelker 1973, Oudmaijer et\nal. 1998) type corrections which are smaller for a disk population\nthan for a spherical population.\n\n\nThe $V$ and $I$ data suggest that the slope of the Galactic\n$PL$-relations may be shallower than that observed for LMC Cepheids,\neither for the whole period range, or that there is a break at short\nperiods (near $\\log P_0 \\approx 0.7-0.8$).\n\nWe stress the importance of two systematic effects which influence the\ndistance to the LMC: the slopes of the Galactic $PL$-relations and\nmetallicity corrections. In order to assess the influence of these\nvarious effects, we present 27 distance moduli (DM) to the LMC. These\nare based on three different colours ($V,I,K$), three different slopes\n(the slope observed for \\C\\ in the LMC, a shallower slope predicted\nfrom one set of theoretical models, and a steeper slope as derived for\nGalactic \\C\\ from the surface-brightness technique), and three\ndifferent metallicity corrections (no correction as predicted by one\nset of theoretical models, one implying larger DM as predicted by\nanother set of theoretical models, and one implying shorter DM based\non empirical evidence). We derive DM between 18.45 $\\pm$ 0.18 and\n18.86 $\\pm$ 0.12. The DM based on $K$ are shorter than those based on\n$V$ and $I$ and range from 18.45 $\\pm$ 0.18 to 18.62 $\\pm$ 0.19, but\nthe DM in $K$ could be systematically too low by about 0.1 magnitude\nbecause of a bias due to the fact that NIR photometry is available\nonly for a limited number of stars.\n\nFrom the Wesenheit-index we derive a DM of 18.60 $\\pm$ 0.11, assuming\nthe observed slope of LMC \\C\\ and no metallicity correction, for want\nof more information.\n\n\nThe DM to the LMC based on the parallax data can be summarised as\nfollows. Based on the $PL$-relation in $V$ and $I$, and the\nWesenheit-index, the DM is \n\\begin{displaymath}\n18.60 \\pm 0.11 \\;\\; (\\pm 0.08 \\;{\\rm slope})(^{+0.08}_{-0.15} \\;{\\rm\nmetallicity}), \n\\end{displaymath}\nwhich is our current best estimate.\nBased on the $PL$-relation in $K$ the DM is $\\;\\;\\;\\; 18.52 \\pm 0.18$\n\\begin{displaymath}\n \\;\\;(\\pm 0.03 \\;{\\rm slope}) (\\pm 0.06 \\;{\\rm metallicity})\n(^{+0.10}_{-0} \\;{\\rm sampling \\;bias}). \n\\end{displaymath}\nThe random error is mostly due to the given accuracy of the \\HP\\\nparallaxes and the number of Cepheids in the respective samples. The\nterms between parentheses indicate the possible systematic\nuncertainties due to the slope of the Galactic $PL$-relations, the\nmetallicity corrections, and in the $K$-band, due to the limited\nnumber of stars. Recent work by Sandage et al. (1999) indicates that\nthe effect of metallicity towards shorter distances may be smaller in\n$V$ and $I$ than indicated here.\n\nFrom this, we point out the importance of obtaining NIR photometry for\nmore (closeby) \\C, as for the moment NIR photometry is only available\nfor 27\\% of the total sample. This would eliminate the possible bias\ndue to the limited number of stars, and would reduce the random error\nestimate from 0.18 to about 0.10 mag. Furthermore, the sensitivity of\nthe DM to reddening, metallicity correction and slope are smallest in\nthe $K$-band.\n\n\n\n\\keywords{Stars: distances - Cepheids - Magellanic Clouds - distance scale}\n\n\\end{abstract}\n\n\\section{Introduction}\n\nCepheids are important standard candles in determining the\nextra-galactic distance scale. The results of the \\HP\\ mission allow,\nin principle, a calibration of the period-luminosity relation based on\nthe available parallaxes. Feast \\& Catchpole (1997; hereafter FC) did\njust that for the $M_{\\rm V} - \\log P$-relation based on pre-released\n\\HP\\ data of 223 Cepheids available to them at that time. Now that the\nentire catalog has become available (ESA 1997) it is timely to analyse\nthe full sample of Cepheids in it.\n\nIn a recent paper, Lanoix et al. (1999, hereafter L99) presented a\nstudy similar to ours and they derived the zero points of the $M_{\\rm\nV} - \\log P$- and $M_{\\rm I} - \\log P$-relations, without, however,\ndiscussing the distance to the LMC. We will indicate where the two\nstudies agree and differ.\n\nThe paper is organised as follows. In Sect.~2 the sample considered in\nthe present paper is presented, and compared to that in FC and L99.\nIn Sect.~3 several aspects involved in the analysis of parallax data\nare described, and the method of ``reduced parallaxes'' is outlined,\ntogether with all necessary recipes to obtain the reddening. In\nSect.~4 the zero points of the $PL$-relations in $V,I, K$ and the\nreddening-free ``Wesenheit-index'' (e.g. Tanvir 1999, and Eq.~(11)) are\npresented for different selections of the sample, which are discussed\nin Sect.~5. In Sect.~6 we construct and present the zero points for\nvolume complete samples of stars. In Sect.~7 we describe numerical\nsimulations that are first of all tuned to fit the observed properties\nof the \\C\\ in the \\HP\\ catalog, and then are used to show that the\nmethod of ``reduced parallaxes'' introduces a bias which is of the\norder of 0.01 mag or less. Based on these results we discuss in\nSect.~8 the distance to the LMC, and elaborate on the various\nuncertainties. \\\\\n\n\n\\section{Sample selection}\n\nThe number and some properties of the Cepheid population in the \\HP\\\ncatalog were discussed by Groenewegen (1999, hereafter G99). To\nsummarise: by cross-correlating the general \\HP\\ database, the \\HP\\\n``resolved variable catalog'' and the electronic database of Fernie et\nal. (1995; hereafter F95), a total of 280 \\C\\ was identified. Then, 9\nType {\\sc ii} \\C, 1 factual RR Lyrae variable, 1 CH-like carbon-rich\nCepheid, 10 double-mode \\C, 7 Cepheids with an unreliable \\HP\\\nsolution and 4 \\C\\ with no or unreliable optical photometry were\nexcluded. Note that for RY Sco and Y Lac we use the new determinations\nfor the parallax and its error from Falin \\& Mignard (1999). This\nleaves 248 stars, of which 32 are classified as overtone pulsators by\nF95, Antonello et al. (1990) or Sachkov (1997). Luri et al. (1999)\nhave classified \\C\\ in fundamental and overtone pulsators using the\n\\HP\\ lightcurves, but did not yet publish the results for individual\nstars. For the sample, G99 calculated intensity-mean $I$ (on the\nCousins system) and $V-I$ magnitudes for 189 stars, and collected\nmagnitude-mean colours for additional 14 stars, and provided $JHK$\nintensity-mean magnitudes on the Carter system for 69 stars. \\\\\n\n\nBy comparison, the FC dataset consisted of 223 stars of which 3 were\ndiscarded. These were DP Vel for lack of photometric data, and AW Per\nand AX Cir because they are in binaries and the photometry might be\naffected by the companions. However, in the F95 catalog there are many\nmore stars which are flagged for this reason. From the sample in G99\nare therefore excluded the stars flagged ``O C'' (RX Cam, AW Per, T\nMon, SS CMa, S Mus, AX Cir, W Sgr, V350 Sgr, U Aql, SU Cyg, V1334 Cyg)\nand ``O: C'' (VY Car) in F95. This leaves 32 overtone pulsators and\n204 fundamental mode pulsators in the sample considered here. They are\nlisted for completeness in Appendix A together with some adopted\nparameters. \\\\\n\n\nRecently, L99 also studied the \\C\\ in the \\HP\\ catalog. They selected\nstars listed as ``DCEP'' or ``DCEPS'' from the \\HP\\ catalog. \nInterestingly, they state that they selected 247 stars, while in\nreality there are 250 such stars (G99). After removing 9 \\C\\ for\nwhich there is no photometry listed in F95, their final sample\nconsists of of 238 stars (including 31 overtones). They did not\neliminate double-mode \\C, \\C\\ where the photometry is (likely)\ncontaminated by a binary companion or \\C\\ with unreliable \\HP\\\nsolutions. Furthermore, they assumed all \\C\\ classified as ``DCEPS''\nto be overtone pulsators, which is not the case. Their sample\ntherefore includes stars they consider overtones which we and FC\nconsider fundamental mode pulsators (e.g., SZ Cas, Y Oph, V496 Aql,\nV924 Cyg, V532 Cyg), and stars they consider fundamental mode\npulsators which are overtone pulsators (e.g., V465 Mon, DK Vel, V950\nSco, see Mantegazza \\& Poretti 1992). In addition, V473 Lyr is\nconsidered by them to be a first overtone pulsator, while it probably\nis a second overtone pulsator (Van Hoolst \\& Waelkens 1995;\nAndrievsky et al. 1998; also see below). \\\\\n\n\nOf the 236 stars in our sample there are 198 in common with the sample\nof FC. In other words, 22 stars in the FC sample would not have made\nit through the selection process outlined in G99 and\nhere. Specifically, their sample contains 7 stars with unreliable \\HP\\\nsolutions (we use the improved parallax values for RY Sco and Y Lac\nfrom Falin \\& Mignard (1999), information which was not available to\nFC), 9 binaries (in addition to AW Per and AX Cir) where the\nphotometry may be contaminated by the companions and 8 double-mode\n\\C. Another difference is that 7 more stars than in FC are flagged as\novertone pulsators following F95 and Sachkov (1997). \\\\\n\nFor the 198 stars in common we have compared the intensity-mean $V$\nand $B-V$. FC mention that they use F95, except when the data were in\nLaney \\& Stobie (1993). Our photometry was at first instance taken\nsolely from F95, except for RW Cas (see discussion in G99). In $V$,\nthe photometry is identical for 165 stars. For 18 stars $V$ differs by\n$>0.01$mag, for 8 by $>0.02$mag and for 5 by $>0.03$mag. The latter\ncases were inspected individually.\n\nFor RW Cas the difference in the sense ``Fernie et al $-$ FC'' is 0.101 mag. \nAs discussed in G99, there may be a typographical error in F95. \n\nFor X Pup the difference is $-0.047$. The F95 entry of $V$ =\n8.460 is close to the value derived in G99 for the dataset of Moffett\n\\& Barnes (1984). The other dataset considered in G99 gives a value of\n$V = 8.536$. The value by FC of $V = 8.507$ is intermediate. We have\nkept the F95 value.\n\nFor AQ Pup the difference is 0.122 mag. G99 calculated $V,I$ for 3\ndata sets. The entry in F95 ($V = 8.791$) is identical to the Moffett\n\\& Barnes (1984) dataset. The FC value of $V = 8.669$ is close to the\n2 other datasets (8.676, 8.686 mag), and one of these was the\npreferred one in G99 regarding the $V,I$ photometry. For AQ Pup we use\nthe $V$ and $B-V$ from FC.\n\nFor RS Pup the difference is $-0.081$. The value in F95 ($V$ = 6.947)\nis clearly off from both values in G99 (6.999 and 7.020 mag) which\nboth are in agreement with the value of $V$ = 7.028 used by FC. For RS\nPup we use $V$ and $B-V$ from FC.\n\nFor S Nor the difference is $-0.032$. The value used by FC is\nextremely close to the value derived in G99, and for S Nor we use the\n$V$ and $B-V$ from FC.\n\nAfter these changes in $V$ and $B-V$, there are 164 with identical\nvalues for $B-V$, for 12 stars $B-V$ differs by $>0.014$ mag, for 9\nby $>0.028$ mag, and for 5 by $>0.042$ mag (RW Cas, X Pup, U Nor, RY\nSco, RU Sct). These cases have not been considered separately. It\nmerely indicates that errors in $V$ and $B-V$ (and hence reddening)\ncan contribute to the uncertainties in the derivation of the zero\npoint of the $PL$-relation, as will be discussed below.\n\nFor V1162 Aql, we discovered an error in the $(B-V)$ value listed in F95.\nFrom the data in Berdnikov \\& Turner (1995) that was used in G99 to\ncalculate $(V-I)$ we derive and adopt an intensity weighted mean of\n$(B-V)$ = 0.879 magnitudes.\n\n\nIn G99, $V$ and $I$ photometry was presented for many \\C\\ in the \\HP\\\ncatalog, based on a literature search. When possible, intensity-mean\nmagnitudes were calculated based on the original published\ndatasets. Some magnitude-means were also presented. The $V - I$\nmagnitudes are taken from G99. When there are multiple entries the\nfirst one was taken following the considerations in G99. In total\nthere is $I$-band data for 191 stars (or 81\\% of the sample), 178 of\nwhich are intensity-mean magnitudes. In G99 it was shown that there is\nno significant difference between the intensity-mean and\nmagnitude-mean, and so the remaining 13 magnitude-means are used\nwithout correction.\n\nG99 also presented intensity-mean $JHK$ magnitudes in, or transformed\nto, the Carter system. When there are multiple entries the first one\nis taken, following the considerations in G99. In total there is\n$JHK$-band data for 63 stars, or 27\\% of the sample.\n\n\n\n\\section{Analysing parallax data}\n\n\nAnalysing parallax data is not a trivial exercise, and has led to some\nconfusion in the literature. Part of this confusion is probably\nrelated to the fact that parallax data suffer from many types of\nbiases (see Brown et al. 1997). For example, the most conspicuous\nbias, the Lutz-Kelker (LK; Lutz \\& Kelker 1973) bias, although known\nfor a long time, could not be empirically investigated due to a lack\nof data on which it could be tested.\n\nOne can visualize the LK effect by analogy with the well-known\nMalmquist bias. Malmquist bias occurs on samples of objects because\ndue to a particular magnitude cut, objects that are brighter than the\nmean will be included in a sample, while objects that are fainter than\nthe mean will be excluded. The net effect of this type of bias is that\nthe intrinsic magnitude for a certain sample will be too bright if no\ncorrections are applied. To investigate the presence of such biases,\none can look at so-called Spaenhauer diagrams, where the observed\nmagnitude is plotted as a function of, for example, distance. In such\na way it is relatively easy to find the point where the Malmquist bias\nstarts to dominate (see e.g. Sandage 1994).\n\n\nA similar, but opposite effect, is due to the LK bias. For a given\nparallax cut (or any selection based on the parallax, or its\nassociated error), on average, more objects that are located far away\nwill scatter into the sample, than stars will scatter out of the\nsample, as the sampled volume is larger for the former objects. Because \nthe distances to the objects scattered into the sample are then\nunderestimated, this effectively results in a too faint mean\n`intrinsic' magnitude of the entire sample. As with the Malmquist\nbias, the LK-bias depends on the space distribution of the sample of\nstars under consideration. Contrary also to the Malmquist bias is that\nalthough the error-bars on the parallax are symmetric, those on the\nderived distances and intrinsic magnitudes are a-symmetric, which\nseriously affects the analysis of the data. In addition, the relative\nerror-bars on the parallax increase with distance.\n\n\nThe LK bias was shown to exist empirically by Oudmaijer et al. (1998).\nFigure~1 gives an illustrative plot, showing the magnitudes of the\nCepheids under consideration, derived from their photometry and\nobserved parallax, as a function of parallax in the upper panel, and\nas function of relative error in the lower panel ($\\rho = V_0 + 5 \\log\n\\pi +5 - \\delta \\log P$, for $\\delta = -2.81$ -- see next Section for\ndetails). As the absolute error in the \\HP\\ data is more or less\nconstant, the two figures are equivalent. The inferred magnitude of\nthe objects in the Cepheid sample is not a random distribution around\nthe mean, but shows a clear trend as function of parallax. For large\nparallaxes (and small relative errors) the inferred magnitudes are too\nfaint, and then, for larger distances, the objects become too\nbright. It was only in Oudmaijer et al. (1998), that this was shown\nempirically for the first time.\n\n\n\n\n%BoundingBox: 106 54 475 711 (4 pla)\n%\\begin{figure*}\n%\\centerline{\\psfig{figure=span.ps,width=17.5cm,angle=-90}}\n%\\caption[]{blie de bla. KEEP ALL ?? . For comparison the derived value\n%for the zero point $\\rho$ derived for the full sample (Tab.~1,\n%solution 10) is indicated.}\n%\\end{figure*}\n\n%BoundingBox: 109 383 475 711 (2 plaatjes)\n\\begin{figure}\n\\centerline{\\psfig{figure=span.ps,width=8.5cm,angle=-90}}\n\\caption[]{$\\rho = V_0 + 5 \\log \\pi +5 - \\delta \\log P$ plotted\nagainst parallax, and relative parallax error, for the stars with\npositive observed \\HP\\ parallaxes. For comparison the derived value\nfor the zero point $\\rho$ derived for the full sample (Table~1,\nsolution 10) is indicated.}\n\\end{figure}\n\n\n\nIndeed, it is clear from this type of graph, which is a version of a\nSpaenhauer diagram, that a selection on parallax (or relative error in\nparallax) will not return the correct answer. In most cases the result\nwill be biased (but see Oudmaijer et al. 1999, for a counter-example).\n\nLutz \\& Kelker (1973) were the first to investigate this effect, and\nfound that the resulting bias can be substantial, increasing with\nincreasing relative error. For a relative error of 17.5\\% in the\nparallax, the bias is 0.43 magnitudes -- yet as Koen (1992) later\nshowed, the confidence intervals around these corrections are large.\nThe 17.5\\% limit was taken literally by subsequent authors, and often\nstars with worse determinations were deleted\n%(string of references) \nor individual stars were corrected with the\nvalues LK derived.\n%(other string of references)\n\n\n\n\nLK claimed that individual stars suffer from the same bias, a point\nthey emphasize strongly. Actually, it is quite a surprising result\nthat LK concluded that individual stars are biased. LK start their\ncalculations assuming that the observed parallax equals the true\nparallax with a random error, a standard procedure when investigating\nmeasurement errors and the main assumption for Monte-Carlo simulations\nas performed in e.g. Sect.~7 of this paper. It seems rather\ncontradictory then that LK infer from their results that individual\nstars are biased if their initial conditions assume otherwise.\n\n\nLet us first comment on whether the conjecture that the observed\nparallax is equal to the true parallax (plus a random observational\nerror) is correct. It is actually quite hard to investigate this in a\n`bias-free' manner, but the evidence provided by the \\HP\\ mission\nswings the balance towards answering this question with a\n`yes'. Measurements of stars beyond the detection limit of \\HP, such\nas those in the Magellanic Clouds (Van Leeuwen 1997, Arenou et\nal. 1995) consistently give average observed parallaxes close to zero\nmas with a scatter of order the observational error. This indicates\nthat the measurements are not biased, even though the relative errors\non the parallax are substantial -- and the results for individual\nstars can be widely off the true distance, but crucially, in the mean\nthey appear to give the right answer within the errors rather than \nshow a conspicuous bias in one direction. In addition, analyses of\nOpen Clusters, for which photometric distances are known, do not show\na deviation from the mean distance for increasing distances and thus\nlower quality data (Arenou et al. 1995, Robichon et al. 1999). Based\non this, it appears that individual stellar determinations are most\nlikely not biased.\n\nThere is one exception, mentioned briefly by Koen \\& Laney\n(1998). These authors argue that if a single star is the result of a\nselection on parallax, its measurement is biased. Although this sounds\ncounter-intuitive, it is a formal implication from the fact that a\nselection on parallax gives rise to a bias.\n%This may have been what LK\n%meant in their original paper on this bias. \n\n%{\\it ALS JE DIT ERUIT WIL HALEN, PRIMA: Its implication becomes almost\n%philosophical -- is a single star measurement biased because of the\n%fact that one uses it? This would appear to be the case if one\n%intuitively uses the parallax of a given star and derives a distance\n%from it, the measurement is biased in the sense because one takes a\n%selection on parallax subconsciously by deciding that it is of\n%sufficient quality.}\n\nA final comment concerns the use of parallaxes of a sample of which\none does not know that the objects should have the same intrinsic\nmagnitude, while their distances are not known.\n%as is e.g. the case for Galactic motion studies. \nThe trend observed in Fig.~1 that, for a\ngiven sample, large parallaxes return in principle too faint intrinsic\nmagnitudes, while small parallaxes return too bright magnitudes, can\nhave serious implications in the interpretation of the data.\n\n\n\n\\subsection{How to deal with the Lutz-Kelker bias?}\n\nThe remaining question is how one should deal with the effects of the\nbias. Should one, as often the case with Malmquist bias, introduce a\n(sample-dependent) correction factor, or are there ways to circumvent\nthe problem?\n\nIn a paper dealing with this problem, Turon Lacarrieu \\& Cr\\'ez\\'e\n(1977) discuss two different methods: \\footnote{Note that Turon\nLacarrieu \\& Cr\\'ez\\'e (1977) repeat the phrase by LK that `individual\nstars' suffer from the bias, without specifying whether this would\nmean {\\it all} stars (which contradicts their own assumption that the\nobserved parallax is equal to the true parallax with an associated\nerror-bar), or individual stars that are the result of a selection on\nparallax. }\n\nAccepting that a sample selected on parallax is inevitably biased,\nthey first considered using the better parallaxes, and investigate the\nresulting mean magnitudes, and provide corrections along similar lines\nas LK (also see Smith 1987a+b+c, Koen 1992).\n\nSecondly they considered a full sample, and, avoiding transformations\nfrom parallaxes to distances and magnitudes, they derive the mean\nparallax first and use the resulting mean parallax to derive the mean\nmagnitude of the sample. Since negative parallaxes can not be\nincorporated into a mean magnitude, one in principle has to discard\nthese data, in effect selecting on parallax and thus biasing the\nsample. Therefore, Turon Lacarrieu \\& Cr\\'ez\\'e (1977) introduced the\nso-called ``reduced parallax'' (10$^{0.2M_{\\rm V}} \\sim \\pi$), which\ncan take into account negative parallaxes, and hence the (weighted)\nmean of the reduced parallax can be converted into a mean magnitude.\nThis method, as will be discussed in Sect.~3.2, indeed appears to be\n``bias-free'', mainly because a weighting scheme puts less weight on\nthe larger deviations around the mean from the lower quality data,\nwhilst not being a formal selection on parallax.\n\nThe Cepheids in \\HP\\ were investigated previously by FC who used the\nsecond, reduced parallax method, and Oudmaijer et al. (1998), who used\na scheme based on the first method. Their results were equal within\nthe error-bars. Although FC used the reduced parallax method, which\nformally does not suffer from LK bias (Koen \\& Laney 1998), they still\nsuggested in a footnote that a LK correction of 0.02 mag should be\napplied on their final result. This is not necessary; the result only\nhas to be corrected for Malmquist bias, as FC also pointed out, but\ndid not actually apply, as they estimated it would essentially\ncounteract their proposed LK correction of 0.02 mag.\n\nThese, and other issues will be investigated in the remainder of this\npaper. First, we will outline the method for the reduced parallaxes again.\n\n\n\n\\subsection{The ``reduced parallax'' method}\n\nThe method of ``reduced parallax'' (discussed by Turon Lacarrieu \\&\nCr\\'ez\\'e 1977) was the one used by FC in analysing Cepheid data. \\\\\n\n\\noindent\nConsider a Period-Luminosity relation of the form:\n\\begin{equation}\n M_{\\rm V} = \\delta \\, \\log P + \\rho,\n\\end{equation}\nwhere $P$ is the fundamental period in days. If $\\langle V\\rangle$ is\nthe intensity-mean visual magnitude and $\\langle V_0 \\rangle$ its\nreddening corrected value, then one can write:\n\\begin{equation}\n10^{0.2\\rho} = \\pi \\times 0.01\\,\\;10^{0.2(\\langle V_0 \\rangle - \\delta\n\\;\\log \\;P)} \\equiv \\pi \\times {\\rm RHS},\n\\end{equation}\nwhich defines the expression {\\sc rhs} and where $\\pi$ is the parallax\nin milli-arcseconds. This method has the advantage that negative\nparallaxes can be used in the analyses as well. A weighted-mean, with\nerror, of the quantity 10$^{0.2 \\rho}$ is calculated, with the weight\n(weight = $\\frac{1}{{\\sigma}^2}$) for the individual stars derived\nfrom:\n\\begin{equation}\n{\\sigma}^2 = \\left( {\\sigma}_{\\pi} \\times {\\rm RHS} \\right)^2 + \n\\left(0.2\\,\\ln(10) \\,\\; \\pi\\; {\\sigma}_{\\rm H} \\times {\\rm RHS} \\right)^2,\n\\end{equation}\nwith ${\\sigma}_{\\pi}$ the standard error in the parallax. This follows\nfrom the propagation-of-errors in Eq.~(2). For the error (denoted\n${\\sigma}_{\\rm H}$) in $(\\langle V_0 \\rangle-\\delta \\; \\log \\;P)$ we\nfollow FC's ``solution B'' and adopt ${\\sigma}_{\\rm H} = 0.1$\nthroughout this paper. Recently, L99 considered alternative weighting\nschemes, but concluded that the one used by FC and the present paper\ngives the most reliable zero point and the lowest dispersion. \\\\\n\n\\noindent\nThe reddening is derived as follows. The intrinsic colours follow from\nthe relation in Laney \\& Stobie (1994):\n\\begin{equation}\n \\langle B \\rangle_0 - \\langle V \\rangle_0 \\;= 0.416 \\, \\log P + 0.314,\n%sigma = 0.091\n\\end{equation}\nwhich has a dispersion of 0.091 mag. The visual extinction\n($A_{\\rm V} = R_{\\rm V} \\times E(B-V)$) is calculated using (Laney\n\\& Stobie 1993):\n\\begin{equation}\n R_{\\rm V} = 3.07 + 0.28 \\; (B-V)_0 + 0.04\\; E(B-V). \n\\end{equation}\nNo dispersion is given for this relation, only an error of 0.03 in the\nzero point. We will assume that the dispersion in Eq.~(5) is \nslightly larger than this, namely 0.05 mag.\n\n\\noindent\nFor overtone pulsators, the fundamental period has to be estimated\nfrom the observed period. This was done, following FC, using:\n\\begin{equation}\n P_1/P_0 = 0.716 - 0.027\\; \\log P_1,\n\\end{equation}\nwith a dispersion we estimate from the original data (Alcock et\nal. 1995) to be of order 0.002.\n\n\\noindent\nFor pulsators in the second overtone, the fundamental period is\ncalculated, following FC, using:\n\\begin{equation}\n P_2/P_0 = 0.55.\n\\end{equation}\nThis completes the description of the method used by FC. \\\\\n\n\\noindent\nAlternative methods which are described now, follow this description\nclosely but are based on $\\langle V \\rangle$ and $\\langle I \\rangle$,\nrespectively $\\langle J \\rangle$ and $\\langle K \\rangle$ photometry\ninstead of $\\langle B \\rangle$ and $\\langle V \\rangle$. The rationale\nbeing that the extinction in $I$ and $K$ is less than in $V$, and that\nthe scatter in the $M_{\\rm I}-P$- and $M_{\\rm K}-P$-relations is less\nthan in the $M_{\\rm V}-P$-relation (Tanvir 1999, Laney \\& Stobie\n1994). \\\\\n\n\\noindent\nFirst consider the case based on $V$ and $I$. The intrinsic colour is\nderived from (Caldwell \\& Coulson 1986):\n\\begin{equation}\n \\langle V \\rangle_0 - \\langle I \\rangle_0 \\;= 0.292 \\, \\log P + 0.443\n\\end{equation}\nwhich has a dispersion of 0.064 mag. This relation was derived for\nmagnitude-mean $(V-I)_0$ but we will assume it to hold for\nintensity-mean magnitudes as well. In a recent paper, Feast (1999,\nAppendix D), presents a correction formula that implies that the\ndifference intensity-mean minus magnitude-mean $(V-I)$ colour \nis of order $-0.017$ mag for a typical $V$-band amplitude of 0.7 mag. \\\\\n\n\\noindent\nThere seems not to exist a relation similar to Eq.~(5), where $R(I)\n\\equiv A_{\\rm I}/E(V-I)$ is related to $(\\langle V \\rangle-\\langle I\n\\rangle)_0$ and/or $E(V-I)$. We have derived such a relation from the\navailable $BVI$ data.\n\n\\noindent\nFor each star with $BVI$ photometry, $(\\langle B \\rangle-\\langle V\n\\rangle)_0$ and $(\\langle V \\rangle-\\langle I \\rangle)_0$ can be\ncalculated from Eqs.~(4) and (8). Then, $A_{\\rm I}$ is calculated\nusing Gieren et al. (1998):\n\\begin{equation}\n R_{\\rm I} = 1.82 + 0.205 \\; (B-V)_0 + 0.022\\; E(B-V),\n\\end{equation}\nand $A_{\\rm I} = R_{\\rm I} \\times E(B-V)$. In Fig.~2 $R(I)$ is\nplotted versus $(V-I)_0$. A least-square fit to 183 data points gives:\n\\begin{equation}\n R(I) = 1.422\n\\end{equation}\nwith no significant dependence on $(V-I)_0$ and with a standard error\nof 0.19. For ${\\sigma}_{\\rm H}$ (in this case the error in $(\\langle\nI_0 \\rangle-{\\delta}_{\\rm I} \\; \\log \\;P$)) we adopt a value of 0.15\nmag (Tanvir 1999). \\\\\n\n\n%$R$ = 1.43, $\\beta$ is the coefficient of the colour term in the\n%period-luminosity-colour relation (BONO, BARAFFE) = 2.85 (Bono,\n%private communication), so ${\\sigma}_{\\rm H} = 0.15 (\\beta/R - 1) =0.15$.\n\n\\noindent\nA variation on this method that treats the problem of reddening in a\ndifferent way, is to use the reddening-free so-called\n``Wesenheit-index'' (see for example Tanvir 1999), that uses the {\\em\nobserved} colours but is essentially reddening-free when defined as:\n\\begin{equation}\n W = V - 2.42\\; (V-I).\n\\end{equation}\nFor ${\\sigma}_{\\rm H}$ (in this case the error in $(\\langle W\n\\rangle-{\\delta}_{\\rm W} \\; \\log \\;P$)) we adopt a value of 0.11\nmag (Tanvir 1999). \\\\\n\n\\noindent\nNow consider the case based on $J$ and $K$ colours. The intrinsic color is\nderived from Laney \\& Stobie (1994):\n%sigma = 0.044\n\\begin{equation}\n \\langle J \\rangle_0 - \\langle K \\rangle_0 \\;= 0.149 \\, \\log P + 0.310\n\\end{equation}\nwhich has a dispersion of 0.044 mag. Again, there seems not to exist a\nrelation similar to Eq.~(5), where $R(K) \\equiv A_{\\rm K}/E(J-K)$ is\nrelated to $(\\langle J \\rangle-\\langle K \\rangle)_0$ and/or\n$E(J-K)$. We have derived such a relation from the available $BVJK$\ndata.\n\n\\noindent\nFor each star with $BVJK$ photometry, $(\\langle B \\rangle-\\langle V\n\\rangle)_0$ and $(\\langle J \\rangle-\\langle K \\rangle)_0$ can be\ncalculated from Eqs.~(4) and (12). Then, $A_{\\rm K}$ is calculated\nusing Laney \\& Stobie (1993):\n\\begin{equation}\n A_{\\rm K} = 0.279 \\; E(B-V).\n\\end{equation}\nIn Fig.~3 $R(K)$ is plotted versus $(J-K)_0$. A least-square fit to 55\ndata points gives:\n\\begin{equation}\n R(K) = 1.035 - 1.063 \\; (J-K)_0 \n\\end{equation}\nwith a standard error of 0.091. For ${\\sigma}_{\\rm H}$ (in this case\nthe error in $(\\langle K_0 \\rangle-{\\delta}_{\\rm K} \\; \\log \\;P$)) we\nadopt a value of 0.12 mag (Gieren et al. 1998).\n\n%$R$ = 0.55, $\\beta$ is the coefficient of the colour term in the\n%period-luminosity-colour relation (BONO, BARAFFE) = 1.86 (Bono,\n%private communication), so ${\\sigma}_{\\rm H} = 0.** (\\beta/R - 1) = 0.12 $.\n\n\n%BoundingBox: 35 60 219 387\n\\begin{figure}\n\\centerline{\\psfig{figure=a_i.ps,width=8.8cm,angle=-90}}\n\\caption[]{The relation between $R(I)$ and $(\\langle V \\rangle-\\langle\nI \\rangle)_0$. The fit reported in Eq.~(10), is based on 183\nstars. Eight outliers (the crosses) were not considered in the\nfit. Three outliers are outside the plot range. There is no\ndependence on $(V-I)$. }\n\\end{figure}\n\n%BoundingBox: 35 60 219 387\n\\begin{figure}\n\\centerline{\\psfig{figure=a_k.ps,width=8.8cm,angle=-90}}\n\\caption[]{The relation between $R(K)$ and $(\\langle J \\rangle-\\langle\nK \\rangle)_0$. The fit reported in Eq.~(14), is based on 55\nstars. Eight outliers (the crosses) were not considered in the\nfit. Seven outliers are outside the plot range. There is a dependence\non $(J-K)$. }\n\\end{figure}\n\n\n\\section{Zero points of the $PL$-relations}\n\n\\subsection{Zero point of the $M_{\\rm V}-\\log P$-relation}\n\nIn Tables~1-4 we present the results from the ``reduced parallax''\nmethod presented in the previous section for different samples of\nstars, and based on different colors ($BV$, $VI$ or $JK$). To test the\nimplementation of the method we have calculated the zero point for\nsome of the solutions considered in FC, adopting a slope $\\delta =\n-2.81$ and working with $BV$ colours, as they did. The data for the\nsample used by FC come from Feast \\& Whitelock (1997; their\nTable~1). These are our solutions 1-7 in Table~1, and the value for\nthe zero point and total weight are in perfect agreement to within the\nlisted number of decimal places in FC. The error in the zero point\ndetermination is slightly different, ours being larger by a few\n1/100-th of a magnitude. Using the FC sample, we also calculated the\nsolution for the overtones only, and the overtones excluding Polaris\n(solutions 8-9). \\\\\n\nFor the present sample and using a slope $\\delta = -2.81$ solutions\n10-12 give the value for the zero point for the whole sample, and for\nfundamental mode and overtone pulsators separately. In this case, V473\nLyr was considered to be pulsating in the second overtone. This\ninteresting object is thought to be the only Galactic Cepheid\npulsating in the second overtone (Van Hoolst \\& Waelkens 1995 and\nAndrievsky et al. 1998). The values of $\\rho$ assuming that V473 Lyr\nis a fundamental mode, first overtone or second overtone pulsator,\nrespectively, are $-2.68$, $-2.07$ and $-1.61$, all with an error of\n0.70. With such a large error only fundamental mode pulsation can be\nexcluded from the \\HP\\ parallax alone. The zero point assuming second\novertone pulsation is consistent with the zero point obtained for the\nwhole sample, and we will hence assume in our zero point\ndeterminations that V473 Lyr is indeed a second overtone pulsator. \\\\\n\nThe zero point for the entire sample of $-1.41 \\pm 0.10$ compares to\nthe value of FC of $-1.43 \\pm 0.10$, and the value of L99 of $-1.44\n\\pm 0.05$ (they used a slightly different slope of $-2.77$). These\nvalues are all very similar, and the differences are mainly due to the\ndifferent samples of \\C, and to a lesser extent to the slight\ndifferences in the adopted photometry. We believe that the present\nsample is the most carefully selected sample of the three with respect\nto completeness, the flagging of overtone pulsators, and the removal\nof \\C\\ that may influence the analysis for various reasons\n(double-mode \\C, unreliable \\HP\\ solutions, possible contaminated\nphotometry due to binary companions), as explained in the\nintroduction.\n\n\\subsubsection{$P_0$ versus $P_1$}\n\nA first comment is on the different solution from the fundamental mode\nand overtone pulsators. In FC the difference between the solution\nusing the fundamental pulsators or the full sample was only 0.02\nmag. In our case it is about 0.08. FC did not present the solution for\nthe overtones only, but we have calculated it from their data\n(solution 8). The difference using only the overtones or the\nfundamental pulsators is 0.05 mag in their case. In our case it is\n0.15 mag, which is a difference at the 1$\\sigma$ level. This indicates\nhow important it is to carefully flag the overtone pulsators.\n\n\\subsubsection{Selecting on visual magnitude}\n\nL99 derive a zero point of $-1.44$ (after correcting for a bias of\n$-0.01$ mag) with a very small error of 0.05, using a selection on $V\n\\le 5.5$. We confirm (solutions 14 and 15) that the derived zero point\nis not significantly different from that for the whole sample, but we\ndo not confirm such a small error. In fact, Pont (1999) argues that\nthe error of 0.10 in FC is even underestimated based on his numerical\nsimulations. Our simulations confirm this (Sect.~7) and so it is not\nclear how L99 arrived at such a small error.\n\n\\subsubsection{Selecting on parallax}\n\nFor solutions 16-18 only positive parallaxes have been selected to\nhighlight the effect of LK-bias. The zero points are fainter, as\nexpected. Interestingly enough, the zero point for the overtone\npulsators is hardly changed. Only 5 overtones (15\\%) have negative\nobserved parallaxes and those carry very little weight, while for the\nfundamental mode pulsators a selection on positive parallaxes reduces\nthe number by 32\\%.\n\n\\subsubsection{Selecting on weight}\n\nFCs final choice for the zero point relied heavily on a subsample of\n26 stars, selected on weight. The question arises if this introduces\nsome bias. For solutions 19-24 we have made different selections on\nweight, in particular solutions 19-22 have been devised such that each\nbin selected on individual weight has about the same total weight, so\nthat the errors on the zero point are comparable. The differences are\nat the 1$\\sigma$ level. From numerical simulations performed in\nSect.~7 (see Table~6) we confirm that there are no indications at the\npresent level of accuracy that a selection on weight is an (indirect)\nselection on parallax, and so a sample selected on weight appears not\nto be subject to LK-bias. The error on the zero point determination is\nlarger when selecting on (individual) weight, simply because of the\nsmaller value of the total weight (see Table~6). This is different\nfrom the result in FC, who quote a {\\it smaller} error on the zero\npoint for the sample selected on weight compared to their full sample\n(cf. their solution 6 and 1).\n\n\n%Figure~3 gives a graphical representation how\n%the individual weights are correlated with parallax, parallax error,\n%and the ratio. Selecting on weight is essentially a selection on the\n%parallax error (see Eq.~3). Since the bottom panel in Fig.~3 shows\n%that for every parallax error, the range in parallax is about the same, \n%a selection on weight is not an (indirect) selection on\n%parallax, and so is not subject to LK-bias. \\\\\n\n\\subsubsection{Selecting on period}\n\nSolutions 25-36 represent cases where the sample was split up in bins\nin $\\log P$ carrying approximately equal weight, for the whole sample\n(solutions 25-28), and the fundamental pulsators only (solutions\n29-32, and 33-36 for a slope of $-2.22$). In both cases, the star with\nthe highest individual weight was excluded in defining the bins. There\nis a significant dependence of the zero point on $\\log P$. This is\nparticularly clear in the case of the fundamental mode pulsators where\nthe zero point for stars with $\\log P \\ge 0.85$ differs at the\n3$\\sigma$ level from the shortest period bin. \n\n\nTo expand on this matter further, we show in Fig.~4 how 10$^{0.2\n\\rho}$ depends on $\\log P$ for the full sample (top panel), and for\nthe 47 stars with an individual weight $>5$. Shown are the\nweighted-mean values of 10$^{0.2 \\rho}$ (solid lines), and weighted \nleast-square fits to the data of the form 10$^{0.2 \\rho} = \\alpha \\,\n\\log P + \\beta $ (dashed line). The ($\\alpha, \\beta$) found are\n(0.11 $\\pm$ 0.12, 0.44 $ \\pm$ 0.10) for the full sample, and (0.094\n$\\pm$ 0.115, 0.43 $ \\pm$ 0.09) for the 47 stars. The analysis was\nrepeated for the fundamental mode pulsators only, giving samples of\n204 and 35 stars, respectively. The ($\\alpha, \\beta$) found are (0.17\n$\\pm$ 0.15, 0.35 $ \\pm$ 0.14) for the full sample, and (0.17 $\\pm$\n0.15, 0.34 $ \\pm$ 0.14) for the stars with weight $>5$. The slopes\nderived are significant at the 1$\\sigma$ level only. \\\\\n\n\nThese results depend on the adopted slope in the $PL$-relation. For a\nslope $\\delta = -3.1$ we find that the effect of the dependence of the\nzero point on the binning in $\\log P$ is enhanced, and that the slope\nin the 10$^{0.2 \\rho}$ versus $\\log P$ relation becomes significant\nat the 2$\\sigma$ level. We also calculated the results for a slope of\n$\\delta = -2.22$ (Bono et al. 1999). The results are listed as\nsolutions 33-36 for the fundamental pulsators. The dependence on\nperiod is not significant in this case, although the shortest bin\nremains the brightest. Least-square fits give the following results\nfor ($\\alpha, \\beta$): all stars ($-0.039 \\,\\pm$ 0.090, 0.45 $\\pm$\n0.08), 56 stars with weight $>5$ ($-0.050 \\,\\pm$ 0.099, 0.45 $\\pm$\n0.08), all fundamental pulsators (0.00 $\\pm$ 0.11, 0.39 $\\pm$ 0.11),\n42 fundamental pulsators with weight $>5$ (0.00 $\\pm$ 0.13, 0.38 $\\pm$\n0.12). The slope derived is no longer significant. From this analysis\none may conclude that there is weak evidence for the fact that the\nslope in the $M_{\\rm V}-\\log P$-relation is shallower than in the LMC,\nor, alternatively that there is a change of slope at the short period\nend. A similar effect is found for the $M_{\\rm I}-\\log P$-relation\n(see next section). The implications are discussed further in\nSect.~8. \\\\\n\n\n\\begin{table*}\n\\caption[]{Values for the zero point from $BV$ photometry.}\n\n%\\scriptsize\n\n\\begin{tabular}{rrcrl} \\hline\nSolution& N & Zero point & Total & Remarks \\\\\n & & in $V$ & Weight & \\\\ \\hline\n1 &220 & -1.403 $\\pm$ 0.104 & 1598.1 & FC solution 1 (whole sample) \\\\\n2 &219 & -1.399 $\\pm$ 0.130 & 1002.2 & FC solution 2 (whole sample minus Polaris) \\\\\n3 &210 & -1.427 $\\pm$ 0.144 & 844.9 & FC solution 3 (whole sample minus overtones) \\\\\n4 & 25 & -1.442 $\\pm$ 0.154 & 751.0 & FC solution 4 (high weight minus Polaris) \\\\ \n5 & 20 & -1.499 $\\pm$ 0.177 & 595.4 & FC solution 5 (high weight minus overtones) \\\\\n6 & 26 & -1.428 $\\pm$ 0.144 & 1346.9 & FC solution 6 (high weight plus Polaris) \\\\\n7 & 1 & -1.410 $\\pm$ 0.170 & 595.9 & FC solution 10 (Polaris) \\\\\n & & & & \\\\\n8 & 10 & -1.377 $\\pm$ 0.149 & 753.2 & FC sample, only overtones \\\\\n9 & 9 & -1.254 $\\pm$ 0.308 & 157.3 & FC sample, overtones minus Polaris \\\\\n & & & & \\\\\n10 & 236 & -1.411 $\\pm$ 0.100 & 1718.6 & All stars \\\\\n11 & 204 & -1.492 $\\pm$ 0.150 & 824.5 & All fundamental modes \\\\\n12 & 32 & -1.339 $\\pm$ 0.135 & 894.1 & All overtones \\\\\n13 & 31 & -1.201 $\\pm$ 0.219 & 297.5 & All overtone minus Polaris \\\\\n14 & 10 & -1.417 $\\pm$ 0.128 & 1067.4 & $V_{\\rm obs} < 5.5$ \\\\\n15 & 19 & -1.461 $\\pm$ 0.122 & 1225.0 & $V_0 < 5.5$ \\\\\n16 & 165 & -1.248 $\\pm$ 0.095 & 1656.7 & $\\pi >0$, all stars \\\\\n17 & 138 & -1.154 $\\pm$ 0.134 & 764.2 & $\\pi >0$, fundamental modes\\\\\n18 & 27 & -1.332 $\\pm$ 0.134 & 892.6 & $\\pi >0$, overtones \\\\\n19 & 208 & -1.219 $\\pm$ 0.229 & 275.4 & weight $< 11$ \\\\\n20 & 17 & -1.541 $\\pm$ 0.267 & 272.8 & $11 \\le $ weight $< 29$ \\\\\n21 & 7 & -1.494 $\\pm$ 0.252 & 292.5 & $29 \\le $ weight $< 70$ \\\\\n22 & 3 & -1.401 $\\pm$ 0.247 & 281.3 & $70 \\le $ weight $< 500$ \\\\\n23 & 235 & -1.411 $\\pm$ 0.124 & 1122.1 & weight $< 500$ \\\\\n24 & 27 & -1.478 $\\pm$ 0.147 & 846.7 & $11 \\le $weight$ < 500$ \\\\\n25 & 50 & -1.680 $\\pm$ 0.274 & 296.3 & $\\log P <$ 0.65 \\\\\n26 & 54 & -1.251 $\\pm$ 0.226 & 292.9 & $0.65 \\le \\log P < 0.79$, no Polaris\\\\\n27 & 62 & -1.572 $\\pm$ 0.272 & 271.6 & $0.79 \\le \\log P < 0.98$\\\\\n28 & 69 & -1.165 $\\pm$ 0.223 & 261.3 & $0.98 \\le \\log P$\\\\\n29 & 66 & -2.016 $\\pm$ 0.412 & 177.7 & $\\log P < 0.73$, no $\\delta$ Cep\\\\\n30 & 40 & -1.607 $\\pm$ 0.376 & 146.7 & $0.73 \\le \\log P < 0.85$\\\\\n31 & 35 & -1.205 $\\pm$ 0.323 & 136.9 & $0.85 \\le \\log P < 0.99$\\\\\n32 & 62 & -1.254 $\\pm$ 0.250 & 239.2 & $0.99 \\le \\log P$\\\\\n33 & 66 & -2.367 $\\pm$ 0.410 & 247.6 & $\\delta = -2.22$, $\\log P < 0.73$, no $\\delta$ Cep\\\\\n34 & 40 & -2.085 $\\pm$ 0.376 & 227.7 & $\\delta = -2.22$, $0.73 \\le \\log P < 0.85$\\\\\n35 & 35 & -1.730 $\\pm$ 0.323 & 222.7 & $\\delta = -2.22$, $0.85 \\le \\log P < 0.99$\\\\\n36 & 62 & -1.994 $\\pm$ 0.252 & 446.8 & $\\delta = -2.22$, $0.99 \\le\n \\log P$\\\\\n37 & 204 & -2.019 $\\pm$ 0.149 & 1349.2 & $\\delta = -2.22$, all fundamental modes \\\\\n38 & 236 & -1.885 $\\pm$ 0.100 & 2662.2 & $\\delta = -2.22$, all stars \\\\\n39 & 47 & -1.495 $\\pm$ 0.110 & 1555.4 & ${\\pi}_{\\rm phot} >1$ mas,\n all stars, ZP=-1.411 \\\\\n40 & 45 & -1.481 $\\pm$ 0.109 & 1549.7 & ${\\pi}_{\\rm phot} >1$ mas,\n all stars, ZP=-1.485 \\\\\n41 & 35 & -1.643 $\\pm$ 0.177 & 684.1 & ${\\pi}_{\\rm phot} >1$ mas,\n fundamental modes, ZP=-1.411 \\\\\n42 & 27 & -1.615 $\\pm$ 0.181 & 638.1 & ${\\pi}_{\\rm phot} >1$ mas,\n fundamental modes, ZP=-1.615 \\\\\n43 & 12 & -1.386 $\\pm$ 0.139 & 871.3 & ${\\pi}_{\\rm phot} >1$ mas,\n overtones, ZP=-1.411 \\\\\n44 & 13 & -1.386 $\\pm$ 0.139 & 875.9 & ${\\pi}_{\\rm phot} >1$ mas,\n overtones, ZP=-1.386 \\\\\n45 & 12 & -1.434 $\\pm$ 0.123 & 1160.4 & ${\\pi}_{\\rm phot} >1.8$ mas,\n all stars \\\\\n46 & 8 & -1.388 $\\pm$ 0.199 & 429.1 & ${\\pi}_{\\rm phot} >1.8$ mas,\n fundamental modes \\\\\n47 & 3 & -1.444 $\\pm$ 0.159 & 708.1 & ${\\pi}_{\\rm phot} >1.8$ mas,\n overtones \\\\\n48 & 236 & -1.406 $\\pm$ 0.100 & 1710.7 & as (10), $V$ larger by 0.005\\\\\n49 & 236 & -1.434 $\\pm$ 0.100 & 1755.1 & as (10), $B-V$ larger by 0.007\\\\\n50 & 236 & -1.382 $\\pm$ 0.100 & 1673.2 & as (10), $(B-V)_0$ larger by 0.009\\\\\n51 & 236 & -1.417 $\\pm$ 0.100 & 1727.7 & as (10), $R_{\\rm V}$ larger by 0.05\\\\\n52 & 107 & -1.155 $\\pm$ 0.181 & 415.3 & All stars with $\\log P \\ge 0.846$ \\\\\n53 & 107 & -1.816 $\\pm$ 0.182 & 754.5 & $\\delta = -2.22$, All\n stars with $\\log P \\ge 0.846$ \\\\\n54 & 41 & -1.954 $\\pm$ 0.114 & 2213.4 & ${\\pi}_{\\rm phot} >1$ mas,\n $\\delta = -2.22$, $\\log P > 0.50$ \\\\\n55 & 42 & -1.299 $\\pm$ 0.115 & 1187.4 & ${\\pi}_{\\rm phot} >1$ mas,\n $\\delta = -3.04$, $\\log P > 0.50$ \\\\\n\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n%67 27 393 748 \n%\\begin{figure}\n%\\centerline{\\psfig{figure=weight_all.ps,width=8.8cm}}\n%\\caption[]{Weight versus various quantities for the sample of 236\n%stars using $BV$ colours.\n%\\vspace{3.cm}\n%}\n%\\end{figure}\n\n\n%65 386 388 749\n\\begin{figure}\n\\centerline{\\psfig{figure=rho_p.ps,width=8.8cm}}\n\\caption[]{10$^{0.2 \\rho}$ versus $\\log P$ based on $BV$ colours for\na slope of $-2.81$. In the top panel all 236 stars are plotted. The\novertones are marked by the filled symbols. In the bottom panel only\nthe 47 stars with an individual weight $>5$ are shown. The solid lines\nrepresent the weighted mean of 10$^{0.2 \\rho}$ for the respective\nsamples. The dashed lines represent the weighted least-squares fit to\nthe data for the respective samples (see text).\nThis provides weak evidence that the slope of $-2.81$ is too steep.\n}\n\\end{figure}\n\n\n\n\\subsection{Zero point of the $M_{\\rm I}-\\log P$-relation}\n\nIn Table~2 the zero points of the $M_{\\rm I}- \\log P$-relation are\nlisted based on $V,I$ photometry. Unless otherwise noted, a slope of\n$-3.05$ is used. This is the slope adopted in L99, and is based on\nwork of Tanvir (1999) and Gieren et al. (1998). In every case we have\ncalculated both the zero points for the $M_{\\rm I}- \\log P$- and\n$M_{\\rm V}- \\log P$-relation for the respective samples. For the whole\nsample we find $\\rho = -1.89 \\pm 0.11$. This is 0.08 mag brighter\nthan in L99, but within their and our quoted errors. L99 used the\nmagnitude-mean magnitudes in Caldwell \\& Coulson (1987), and then\napplied a correction of $-0.03$ mag to convert these to\nintensity-mean magnitudes. We use for most stars the intensity-mean\nmagnitudes as calculated in G99 from the original data. \\\\\n\nAs for the solutions based on $BV$ photometry we find that the zero\npoint using only the fundamental modes is brighter than using only the\novertone pulsators, but the difference is now less than 1$\\sigma$.\nPolaris again is the star with the highest individual weight.\nSolutions 6-8 illustrate the effect of LK-bias when selecting stars\nwith positive parallaxes.\n\n\n\\subsubsection{Selecting on period}\n\nAs before, we have split up the sample according to period in bins of\napproximate equal total weight, for all stars (solutions 9-12,\nexcluding Polaris), and for the fundamental pulsators (solutions\n13-16, excluding $\\delta$ Cep, the fundamental pulsator with the\nhighest individual weight). Again we see that the zero point depends\non the period bin chosen, but the effect is not as systematic as in\nthe $V$-band. In Fig.~5 10$^{0.2 \\rho}$ is plotted against $\\log\nP$. We have made least-square fits as before and find for the whole\nsample ($\\alpha, \\beta$) = (0.11 $\\pm$ 0.11, 0.331 $\\pm$ 0.091), for\nthe 48 stars with an individual weight $>5$ ($\\alpha, \\beta$) = (0.101\n$\\pm$ 0.098, 0.332 $\\pm$ 0.079), for all 163 fundamental mode\npulsators ($\\alpha, \\beta$) = (0.17 $\\pm$ 0.14, 0.26 $\\pm$ 0.13), and\nfor the 35 fundamental mode pulsators with a weight $>5$ ($\\alpha,\n\\beta$) = (0.17 $\\pm$ 0.12, 0.25 $\\pm$ 0.11). The slope is again\nsignificant at at most the 1$\\sigma$ level. \\\\\n\nSolutions 17-21 give the division in period bins for a slope of the\n$PL$-relation of $-2.35$ for the fundamental mode pulsators (the slope\nin the $PL$-relation in $V$ is $-2.22$). After taking into account the\ndifference in zero points in $V$, the dependence of the zero point in\n$I$ on period bin is not significant. The least-square fits give the\nfollowing results for ($\\alpha, \\beta$): the whole sample ($-0.024\n \\pm$ 0.076, 0.343 $\\pm$ 0.065), for the 62 stars with an individual\nweight $>5$ ($-0.013$ $\\pm$ 0.077, 0.317 $\\pm$ 0.069), for all 163\nfundamental mode pulsators (0.012 $\\pm$ 0.093, 0.294 $\\pm$ 0.089), and\nfor the 50 fundamental mode pulsators with a weight $>5$ (0.032 $\\pm$\n0.093, 0.264 $\\pm$ 0.090). As we found previously, a shallower slope\ngives rise to a smaller or no dependence of the zero point on period. \\\\\n\n\n\\begin{table*}\n\\caption[]{Values for the zero point from $VI$ photometry.}\n\\begin{tabular}{rrcrcl} \\hline\nSolution& N & Zero point & Total & Zero point & Remarks \\\\\n & & in $I$ & Weight & in $V$ & \\\\ \\hline\n1 & 191 & -1.892 $\\pm$ 0.111 & 2203.4 & -1.42 $\\pm$ 0.10 & All stars \\\\\n2 & 163 & -1.952 $\\pm$ 0.159 & 1131.9 & -1.49 $\\pm$ 0.16 & All fundamental modes \\\\\n3 & 28 & -1.830 $\\pm$ 0.154 & 1071.5 & -1.36 $\\pm$ 0.14 & All overtones \\\\\n4 & 1 & -1.859 $\\pm$ 0.204 & 629.3 & -1.41 $\\pm$ 0.17 & Polaris \\\\\n5 & 10 & -1.889 $\\pm$ 0.142 & 1328.4 & -1.42 $\\pm$ 0.13 & $V_{\\rm obs} < 5.5$ \\\\\n6 & 139 & -1.745 $\\pm$ 0.105 & 2137.9 & -1.29 $\\pm$ 0.10 & $\\pi >0$, all stars \\\\\n7 & 114 & -1.671 $\\pm$ 0.143 & 1068.9 & -1.22 $\\pm$ 0.14 & $\\pi >0$, fundamental modes\\\\\n8 & 25 & -1.821 $\\pm$ 0.154 & 1069.0 & -1.35 $\\pm$ 0.14 & $\\pi >0$, overtones\\\\\n9 & 35 & -1.974 $\\pm$ 0.270 & 398.0 & -1.51 $\\pm$ 0.27 & $\\log P < 0.66$ \\\\\n10& 36 & -2.039 $\\pm$ 0.284 & 383.4 & -1.50 $\\pm$ 0.28 & $0.66 \\le\n \\log P < 0.78$, no Polaris \\\\\n11& 44 & -2.131 $\\pm$ 0.286 & 409.5 & -1.61 $\\pm$ 0.29 & $0.78 \\le \\log P < 0.92$ \\\\\n12& 75 & -1.514 $\\pm$ 0.223 & 383.2 & -1.14 $\\pm$ 0.22 & $\\log P \\ge 0.92$ \\\\\n13& 38 & -2.148 $\\pm$ 0.397 & 216.6 & -1.72 $\\pm$ 0.40 & $\\log P < 0.72$ \\\\\n14& 35 & -2.408 $\\pm$ 0.451 & 213.4 & -1.99 $\\pm$ 0.46 & $0.72 \\le\n \\log P < 0.85$, no $\\delta$ Cep \\\\\n15& 29 & -1.731 $\\pm$ 0.351 & 188.7 & -1.21 $\\pm$ 0.34 & $0.85 \\le \\log P < 0.99$ \\\\\n16& 60 & -1.629 $\\pm$ 0.258 & 318.7 & -1.26 $\\pm$ 0.25 & $\\log P \\ge 0.99$ \\\\\n17& 38 & -2.581 $\\pm$ 0.396 & 323.7 & -2.09 $\\pm$ 0.40 & $\\delta = -2.35$, $\\log P < 0.72$ \\\\\n18& 35 & -2.976 $\\pm$ 0.451 & 358.9 & -2.47 $\\pm$ 0.46 & $\\delta = -2.35$, $0.72 \\le\n \\log P < 0.85$, no $\\delta$ Cep \\\\\n19& 29 & -2.349 $\\pm$ 0.349 & 335.1 & -1.73 $\\pm$ 0.34 & $\\delta = -2.35$, $0.85 \\le \\log P < 0.99$ \\\\\n20& 60 & -2.476 $\\pm$ 0.258 & 691.6 & -2.00 $\\pm$ 0.25 & $\\delta = -2.35$, $\\log P \\ge 0.99$ \\\\\n21& 163 & -2.571 $\\pm$ 0.158 & 2020.5 & -2.03 $\\pm$ 0.16 & $\\delta =\n -2.35$, all fundamental modes \\\\\n22& 191 & -2.454 $\\pm$ 0.110 & 3709.3 & -1.90 $\\pm$ 0.10 & $\\delta = -2.35$, all stars\\\\\n23& 12 & -1.924 $\\pm$ 0.139 & 1442.5 & -1.43 $\\pm$ 0.13 & ${\\pi}_{\\rm phot} >1.8$ mas, all stars \\\\\n24& 191 & -1.887 $\\pm$ 0.111 & 2193.3 & -1.42 $\\pm$ 0.10 & as (1), $I$ larger by 0.005\\\\\n25& 191 & -1.899 $\\pm$ 0.111 & 2217.6 & -1.42 $\\pm$ 0.10 & as (1), $V-I$ larger by 0.007\\\\\n26& 191 & -1.883 $\\pm$ 0.111 & 2186.1 & -1.42 $\\pm$ 0.10 & as (1), $(V-I)_0$ larger by 0.006\\\\\n27& 191 & -1.922 $\\pm$ 0.111 & 2262.5 & -1.42 $\\pm$ 0.10 & as (1), $R(I)$ larger by 0.19\\\\\n28& 10 & -2.469 $\\pm$ 0.143 & 2232.3 & -1.92 $\\pm$ 0.13 & ${\\pi}_{\\rm phot} >1.8$ mas, $\\delta = -2.35$, $\\log P > 0.50$ \\\\\n29& 11 & -1.689 $\\pm$ 0.144 & 1082.8 & -1.23 $\\pm$ 0.13 & ${\\pi}_{\\rm phot} >1.8$ mas, $\\delta = -3.33$, $\\log P > 0.50$ \\\\\n% & & & & & \\\\\n% & 95 & -1.944 $\\pm$ 0.137 & 1500.9 &$A_{\\rm I} < 0.68$ median $A_I$ no P.\\\\\n% & 95 & -2.333 $\\pm$ 0.503 & 159.9 & $A_{\\rm I} > 0.68$ \\\\\n% & 23 & -1.884 $\\pm$ 0.179 & 834.7 & $A_{\\rm I} < 0.30$, equal weight \\\\\n% & 167 & -2.078 $\\pm$ 0.197 & 826.2 & $A_{\\rm I} > 0.30$ \\\\\n% & 191 & -1.871 $\\pm$ 0.111 & 2134.7 & slope = $-$3.15 \\\\\n% & 191 & -1.799 $\\pm$ 0.111 & 1991.6 & slope = $-$3.25 \\\\\n% & 191 & -1.728 $\\pm$ 0.112 & 1859.0 & slope = $-$3.35 \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n%65 386 388 749\n\\begin{figure}\n\\centerline{\\psfig{figure=rho_p_i.ps,width=8.8cm}}\n\\caption[]{10$^{0.2 \\rho}$ versus $\\log P$ based on $VI$ colours for\na slope of $-3.05$. In the top panel all 191 stars are plotted. The\novertones are marked by the filled symbols. In the bottom panel only\nthe 48 stars with an individual weight $>5$ are shown. The solid lines\nrepresent the weighted mean of 10$^{0.2 \\rho}$ for the respective\nsamples. The dashed lines represent the weighted least-squares fit to\nthe data for the respective samples.}\n\\end{figure}\n\n\n\n\n\\subsection{Zero point of the $M_{\\rm K}-\\log P$-relation}\n\nTable~3 lists the results for the zero point of the $M_{\\rm K}-\\log\nP$-relation and the zero point for the $PL$-relations in $V$ and $I$\nfor the same samples. Unless noted otherwise we have used a slope of\n$\\delta = -3.27$ from Gieren et al. (1998). For the whole sample we\nfind a zero point of $-2.61 \\pm 0.17$, but note that the corresponding\nzero points in the $V$ and $I$ band of this sub-sample are too bright\nby about 0.11 magnitude compared to the full samples in $V$ and $I$,\nand so the true zero point is probably closer to $-2.50$. These\noff-sets indicate biases due to the small number of available\nmeasurements in the NIR. This is especially clear when further\nsub-divisions into smaller samples are made, like a division in period\n(solutions 9-13). Especially in one bin (solution 10) the result\ndepends very much on one star which was taken out (solution 11). After\nshifting the zero points in $K$ by an amount such as to make the zero\npoints in $V$ all equal there is no evidence for a dependence of the\nzero point on period.\n\n\n\n\\begin{table*}\n\\caption[]{Values for the zero point from $JK$ photometry.}\n\\begin{tabular}{rrcrccl} \\hline\nSolution& N & Zero point & Total & Zero point & Zero point & Remarks \\\\\n & & in $K$ & Weight & in $V$ & in $I$ & \\\\ \\hline\n1 & 63 & -2.607 $\\pm$ 0.169 & 1821.0 & -1.52 $\\pm$ 0.17 & -2.00 $\\pm$\n 0.17 & All stars \\\\\n2 & 56 & -2.645 $\\pm$ 0.192 & 1455.6 & -1.56 $\\pm$ 0.19 & -2.02 $\\pm$ 0.20 & All fundamental modes \\\\\n3 & 7 & -2.462 $\\pm$ 0.353 & 365.3 & -1.41 $\\pm$ 0.35 & -1.94 $\\pm$ 0.36 & All overtones \\\\\n4 & 1 & -2.692 $\\pm$ 0.398 & 355.5 & -1.52 $\\pm$ 0.39 & -2.09 $\\pm$ 0.41 & $\\delta$ Cep \\\\\n5 & 6 & -2.602 $\\pm$ 0.227 & 1006.9 & -1.50 $\\pm$ 0.22 & -1.97 $\\pm$\n 0.23 & $V_{\\rm obs} < 5.5$ \\\\\n6 & 52 & -2.476 $\\pm$ 0.161 & 1775.6 & -1.39 $\\pm$ 0.16 & -1.87 $\\pm$\n 0.16 & $\\pi >0$, all stars \\\\\n7 & 45 & -2.479 $\\pm$ 0.181 & 1410.2 & -1.39 $\\pm$ 0.18 & -1.85 $\\pm$\n 0.19 & $\\pi >0$, fundamental modes \\\\\n8 & 7 & -2.462 $\\pm$ 0.353 & 365.4 & -1.41 $\\pm$ 0.35 & -1.94 $\\pm$\n 0.36 & $\\pi >0$, overtones \\\\\n9 & 8 & -2.601 $\\pm$ 0.392 & 337.2 & -1.59 $\\pm$ 0.39 & -2.08 $\\pm$ 0.40 & $\\log P < 0.64$ \\\\\n10& 17 & -3.002 $\\pm$ 0.445 & 377.9 & -1.91 $\\pm$ 0.45 & -2.38 $\\pm$\n 0.45 & $0.64 \\le \\log P < 0.85$, no $\\delta$ Cep \\\\\n11& 16 & -2.746 $\\pm$ 0.400 & 370.4 & -1.61 $\\pm$ 0.40 & -2.11 $\\pm$\n 0.40 & $0.64 \\le \\log P < 0.85$, no $\\delta$ Cep, no V496 Aql \\\\\n12& 8 & -2.833 $\\pm$ 0.494 & 262.1 & -1.70 $\\pm$ 0.49 & -2.24 $\\pm$ 0.50 & $0.85 \\le \\log P < 0.99$ \\\\\n13& 29 & -2.195 $\\pm$ 0.270 & 485.3 & -1.18 $\\pm$ 0.27 & -1.50 $\\pm$\n 0.27 & $\\log P \\ge 0.99$ \\\\\n14& 3 & -2.635 $\\pm$ 0.271 & 725.1 & -1.49 $\\pm$ 0.27 & -2.01 $\\pm$\n 0.28 & ${\\pi}_{\\rm phot} >$ 2.6 mas, fundamental mode\\\\\n15& 63 & -2.599 $\\pm$ 0.169 & 1807.9 & -1.52 $\\pm$ 0.17 & -2.00 $\\pm$ 0.17 & as (1), $K$ larger by 0.005 \\\\\n16& 63 & -2.611 $\\pm$ 0.169 & 1827.7 & -1.52 $\\pm$ 0.17 & -2.00 $\\pm$ 0.17 & as (1), $J-K$ larger by 0.007 \\\\\n17& 63 & -2.604 $\\pm$ 0.169 & 1816.8 & -1.52 $\\pm$ 0.17 & -2.00 $\\pm$ 0.17 & as (1), $(J-K)_0$ larger by 0.004 \\\\\n18& 63 & -2.612 $\\pm$ 0.169 & 1830.9 & -1.52 $\\pm$ 0.17 & -2.00 $\\pm$ 0.17 & as (1), $R(K)$ larger by 0.097 \\\\\n19& 62 & -2.800 $\\pm$ 0.177 & 1979.3 & -2.06 $\\pm$ 0.18 & -2.60 $\\pm$ 0.18 & $\\delta = -3.05$, $\\log P > 0.5$ \\\\\n20& 62 & -2.321 $\\pm$ 0.178 & 1262.8 & -1.31 $\\pm$ 0.18 & -1.74 $\\pm$ 0.18 & $\\delta = -3.60$, $\\log P > 0.5$ \\\\\n% & & & & & & \\\\\n% & 32 & -2.585 $\\pm$ 0.176 & 1638.6 & $A_{\\rm K} < 0.091$, median\\\\\n% & 31 & -3.011 $\\pm$ 0.614 & 200.5 & $A_{\\rm K} \\ge 0.091$ \\\\\n% & 7 & -2.605 $\\pm$ 0.240 & 899.9 & $A_{\\rm K} < 0.016$, equal weight\\\\\n% & 56 & -2.649 $\\pm$ 0.240 & 939.2 & $A_{\\rm K} \\ge 0.016$ \\\\\n% & 63 & -2.359 $\\pm$ 0.170 & 1427.3 & as 1, slope $-3.60$ \\\\\n% & 63 & -2.488 $\\pm$ 0.170 & 1612.4 & as 1, slope $-3.44$ \\\\\n% & 63 & -2.831 $\\pm$ 0.170 & 2222.5 & as 1, slope $-3.03$ \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\\subsection{Zero point of the $M_{\\rm W}-\\log P$-relation}\n\nTable~4 lists the results for the zero point of the $M_{\\rm W}-\\log\nP$-relation. We have used a slope of $\\delta = -3.411$ (Tanvir\n1999). As before the sample is divided into period bins. After\nshifting the zero points in $W$ by an amount such as to make the zero\npoints in $V$ all equal (this value can be taken from the\ncorresponding solutions in Table~2) there is no evidence for a\ndependence of the zero point on period.\n\n\n\\begin{table*}\n\\caption[]{Values for the zero point from the Wesenheit-index.}\n\\begin{tabular}{rrcrl} \\hline\nSolution& N & Zero point & Total & Remarks \\\\\n & & in $W$ & Weight & \\\\ \\hline\n1 & 191 & -2.557 $\\pm$ 0.104 & 4554.1 & All stars \\\\\n2 & 163 & -2.622 $\\pm$ 0.156 & 2167.2 & All fundamental modes \\\\\n3 & 28 & -2.500 $\\pm$ 0.141 & 2387.0 & All overtones \\\\\n4 & 1 & -2.528 $\\pm$ 0.176 & 1555.8 & Polaris \\\\\n5 & 139 & -2.424 $\\pm$ 0.100 & 4431.9 & $\\pi > 0$, all stars \\\\\n6 & 35 & -2.626 $\\pm$ 0.267 & 743.3 & $\\log P < 0.66$, no Polaris \\\\\n7 & 36 & -2.704 $\\pm$ 0.277 & 737.2 & $0.66 \\ge \\log P < 0.78$ \\\\\n8 & 44 & -2.800 $\\pm$ 0.283 & 771.4 & $0.78 \\ge \\log P < 0.92$ \\\\\n9 & 75 & -2.204 $\\pm$ 0.219 & 746.5 & $\\log P \\ge 0.92$ \\\\\n10& 185 & -2.558 $\\pm$ 0.136 & 2676.9 & $\\log P \\ge 0.50$ \\\\\n11& 12 & -2.585 $\\pm$ 0.127 & 3118.8 & ${\\pi}_{\\rm phot} > 1.8$ mas \\\\\n12& 10 & -2.569 $\\pm$ 0.134 & 2808.9 & ${\\pi}_{\\rm phot} > 1.8$ mas,\n $\\log P \\ge 0.50$ \\\\\n13& 191 & -2.581 $\\pm$ 0.104 & 4656.6 & As (1), reddening coefficient\n of 2.45 in Eq.~(11) \\\\\n14& 191 & -2.564 $\\pm$ 0.104 & 4584.0 & As (1), $V$ larger by 0.005 \\\\\n15& 191 & -2.545 $\\pm$ 0.104 & 4503.7 & As (1), $I$ larger by 0.005 \\\\\n% -2.662 $\\pm$ 0.104 & 5019.1 & $\\delta = -3.278$, reddening coeff. 2.42 \\\\\n% -2.768 $\\pm$ 0.104 & 5530.6 & $\\delta = -3.278$, reddening coeff. 2.55 \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\n\n\n\n\\section{Summary of the results}\n\n\n\\subsection{On the use of longer wavelengths}\n\nOne argument to consider $PL$-relations in $I$ and $K$ besides the\ntraditional relation in $V$, is because of the smaller extinction at\nlonger wavelengths. We have calculated the zero points for the whole\nsample considering a systematic shift for all stars of 0.005 mag in\n$V$ (respectively $I$ and $K$), 0.007 in $B-V$ (resp. $V-I$, $J-K$), a\nshift in the period-colour relations (Eqs.~(4), (8), (12)) equal to\n1/10-th of the quoted dispersions, and a shift in the selective\nreddening (Eqs.~(5), (10), (14)) equal to the quoted dispersion. The\nresults are listed in Table~1 (solutions 48-51), Table~2 (solutions\n23-26), and Table~3 (solutions 15-18). Adding the differences between\nthese zero points and that for the default case in quadrature, one\narrives at estimated uncertainties due to errors in the photometry,\nreddening and period-colour relations of 0.038 mag in $V$, 0.032 mag\nin $I$, and 0.011 mag in $K$. This illustrates that the $K$-band\n$PL$-relation is indeed the least sensitive to these effects. For the\nWesenheit-index the error due to the photometry and reddening\ncoefficients amounts to 0.028 mag (solutions 13-15 in Table~4). \\\\\n\nUnfortunately, the advantages of using the infrared, like the\nintrinsically tighter $PL$-relation and the insensitivity to\nreddening, are countered by the fact that so few stars have been\nmeasured in the NIR so far. Of the approximately 48 stars with in 1\nkpc, $BV$ photometry is available for all of them, $VI$ for 41 of\nthem, but $JHK$ data (of sufficient quality) for only 24. It is\nestimated that determining the intensity-mean NIR magnitudes of the\nremaining 24 stars alone would bring the scatter in the zero point\ndetermination in the $K$-band down from about 0.17 to less than 0.1 mag. \\\\\n\n\n\\subsection{On the slopes of Galactic $PL$-relations}\n\nAnother important issue concerns the slopes in the respective Galactic\n$PL$-relations. Common practice is to adopt the slope determined for\n\\C\\ in the LMC, but the slope could be different for Galactic \\C. In\nTable~5 we have collected slopes of the $PL$-relations from the\nliterature for \\C\\ in the Galaxy, LMC and SMC, in $V,I,K$, both\nobservationally determined and from two recent theoretical papers\n(Alibert et al. 1999, Bono et al. 1999 and private communication). \nTable~5 includes ths slopes in $V$ and $I$ by Madore \\& Freedman (1991)\nused by the {\\sc hst} $H_0$ Key Project (see for example Gibson et\nal. 1999). From the results of Gieren et al. (1998) on the \\C\\ in the\nLMC, we have calculated the error in the slope using the data they\nkindly provided (their Tables 8 and 9). In addition we have calculated\nthe slope and zero point for their data set but using cut-offs in\nperiod, for reasons that will be explained later. \\\\\n\nThere are several interesting features to be noted about the slopes.\nObservationally, the slopes in the $V$ and $I$ $PL$-relations in the\nLMC are very well established, respectively, about $-2.81$ and\n$-3.05$, and these are the default slopes adopted in the present study,\nwith errors of about 0.08 and 0.06. For $M_{\\rm K}-\\log P$-relation\nthere are fewer observational data available but the slope in Gieren\net al. (1998) is determined very accurately and is in reasonable\nagreement with the result of Madore \\& Freedman (1991). \\\\\n \n\nOne fact needs to be mentioned however, and that is that the period\ndistribution of the calibrating \\C\\ in the LMC is very different from\nthat of the Galactic \\C\\ in the \\HP\\ catalog. In Table 8 in Gieren et\nal. (1998) there are 53 LMC \\C\\ listed with $V,I$ photometry that\ndefine their $PL$-relation. Nine have $\\log P \\le 0.555$, then there\nis a gap, and 42 have $\\log P \\ge 0.846$. In $JHK$ (their Table 9),\nthere are 59 \\C, including 5 that have $\\log P \\le 0.680$, then there\nis a gap, and 54 have $\\log P \\ge 0.834$. The same dichotomy of \\C\\\nin period can be seen from Tanvir (1999). Note that in more distant\nGalaxies than the Magellanic Clouds, due to observational bias, most\nknown Cepheids have periods longer than 10 days. We therefore have\nincluded in Table~5 the slopes in $V,I,K$ based on the data in Gieren\net al. (1998), but have divided the sample according to period. The\nslopes for the long period sub-sample differ only slightly from that\nfor the whole sample but are characterised by slightly larger\nerrors. The slopes for the short-period sample have larger errors\nbecause of the small number of stars involved but nevertheless are\nsystematically steeper at the 1$\\sigma$ level in all three\ncolours. For comparison, in our sample only 107 of the 236 \\C\\ have\n$\\log P \\ge 0.846$, and the zero point of this sample differs at the\n1.4$\\sigma$ level from that of the whole sample (solution 52 in\nTable~1). This is yet another indication that for the default slope of\n$-2.81$ the zero point may depend on the period range chosen. For a slope\nof $\\delta = -2.22$ (compare solutions 38, 53) this is not the case. \\\\\n\nA second issue concerns the predictions of the theoretical models and the\ncomparison with observations. In $V,K$ for the LMC, and in $I$ for the\nSMC the models of Bono et al. (1999) are in very good agreement with\nthe observed slope, in $I$ for the LMC and $V$ for the SMC the\nagreement is poor. In $I, K$ for the LMC, the models of Alibert et\nal. (1999) are in good agreement with the observed slopes; in $V$ the\nagreement for the LMC and $V,I$ for the SMC is fair. However, the\nprediction both models make for the Galaxy are very different. Gieren\net al. (1998) have derived $PL$-relations for Galactic \\C\\ using the\nsurface brightness technique. The slopes they find in all three bands\nare {\\it steeper} than the corresponding slopes in the LMC at the 2-3\n$\\sigma$ level. In their paper they ascribe this to small number\nstatistics, and in the end assume the LMC slopes to hold for the\nGalactic \\C\\ as well, also, they add, because the slopes for the LMC\n\\C\\ are better determined. The models of Alibert et al. (1999)\npredict slopes for the Galactic $PL$-relations that are {\\it steeper}\nthan the observed ones in the LMC in $V,I,K$ as well, although by a\nsmall amount only (the main conclusion of their paper is actually that\nthe slope and zero point of the $PL$-relations do not depend on\nmetallicity). By contrast, the Bono et al. (1999) paper predicts\nslopes that are significantly {\\it shallower} in the Galaxy compared\nto the LMC especially in $V,I$ but also in $K$. In addition, the Bono\net al. models actually predict a non-linear $PL$-relation in $V$, for\nall metallicities considered. Furthermore, Alibert et al. mention\nthat a change of slope in $PL$-relations is expected at short periods\ndue to the reduction of the blue loop during core He burning, and that\nthis change of slope occurs near $\\log P = 0.2$ for $Z$ = 0.004, $\\log\nP = 0.35$ for $Z$ = 0.01, and $\\log P = 0.5$ for $Z$ = 0.02. Such a\nchange of slope (in the sense that the slope of the $PL$-relation is\nsteeper for periods below this limit) was recently observed for SMC\n\\C\\ (Bauer et al. 1999) with the break occurring near $\\log P = 0.3$,\nnear the predicted value. \\\\\n\n\n\n\\begin{table*}\n\\caption[]{Slopes of the $PL$-relations.}\n\\begin{tabular}{ccll} \\hline\nSlope & Colour & System & Reference \\\\ \\hline\n$-3.037 \\pm 0.138$ & V & GAL & Gieren et al. (1998)\\\\\n $-2.22 \\pm 0.04$ & V & 0.02& Bono et al. (1999); non-linear, $\\log P<1.4$\\\\\n$-2.905$ & V & 0.02& Alibert et al. (1999) \\\\\n\n$-2.810 \\pm 0.082$ & V & LMC & Tanvir (1999) \\\\\n$-2.769 \\pm 0.073$ & V & LMC & Gieren et al. (1998) \\\\\n$-2.820 \\pm 0.118$ & V & LMC & this work; 44 stars with $\\log P >\n0.845$ from Gieren et al. (1998)\\\\\n $-3.54 \\pm 0.68$ & V & LMC & this work; 9 stars with $\\log P < 0.845$ from Gieren et al. (1998)\\\\\n $-2.88 \\pm 0.20$ & V & LMC & Madore \\& Freedman (1991)\\\\\n $-2.81 \\pm 0.06$ & V & LMC & Caldwell \\& Laney (1991)\\\\\n $-2.79 \\pm 0.06$ & V & 0.008& Bono et al. (1999); non-linear, $\\log P<1.4$\\\\\n$-2.951$ & V & 0.01& Alibert et al. (1999) \\\\\n\n$-2.63 \\pm 0.08$ & V & SMC & Caldwell \\& Laney (1991), \\\\\n$-3.04 \\pm 0.04$ & V & 0.004& Bono et al. (1999); non-linear, $\\log P<1.4$\\\\\n$-2.939$ & V & 0.004& Alibert et al. (1999) \\\\\n\n$-3.329 \\pm 0.132$ & I & GAL & Gieren et al. (1998)\\\\\n $-2.35 \\pm 0.08$ & I & 0.02& Bono et al. (1999) \\\\\n$-3.102$ & I & 0.02& Alibert et al. (1999)\\\\\n\n$-3.078 \\pm 0.059$ & I & LMC & Tanvir (1999) \\\\\n$-3.041 \\pm 0.054$ & I & LMC & Gieren et al. (1998)\\\\\n$-3.084 \\pm 0.088$ & I & LMC & this work; 44 stars with $\\log P > 0.845$ from Gieren et al. (1998)\\\\\n $-3.39 \\pm 0.39$ & I & LMC & this work; 9 stars with $\\log P < 0.845$ from Gieren et al. (1998)\\\\\n $-3.14 \\pm 0.17$ & I & LMC & Madore \\& Freedman (1991)\\\\\n $-3.01 \\pm 0.05$ & I & LMC & Caldwell \\& Laney (1991) \\\\\n $-2.63 \\pm 0.08$ & I & 0.008& Bono et al. (1999) \\\\\n $-3.140$ & I & 0.01& Alibert et al. (1999) \\\\\n\n $-2.92 \\pm 0.07$ & I & SMC & Caldwell \\& Laney (1991) \\\\\n $-2.73 \\pm 0.10$ & I & 0.004& Bono et al. (1999) \\\\\n $-3.124$ & I & 0.004& Alibert et al. (1999) \\\\\n\n$-3.598 \\pm 0.114$ & K & GAL & Gieren et al. (1998) \\\\\n $-3.03 \\pm 0.07$ & K & 0.02 & Bono et al. (1999) \\\\\n $-3.367$ & K & 0.02 & Alibert et al. (1999)\\\\\n\n$-3.267 \\pm 0.041$ & K & LMC & Gieren et al. (1998) \\\\\n$-3.304 \\pm 0.052$ & K & LMC & this work; 54 stars with $\\log P > 0.833$ from Gieren et al. (1998)\\\\\n $-3.37 \\pm 0.39$ & K & LMC & this work; 5 stars with $\\log P < 0.833$ from Gieren et al. (1998)\\\\\n $-3.42 \\pm 0.09$ & K & LMC & Madore \\& Freedman (1991) \\\\\n $-3.19 \\pm 0.09$ & K & 0.008 & Bono et al. (1999) \\\\\n $-3.395$ & K & 0.01& Alibert et al. (1999) \\\\\n\n $-3.27 \\pm 0.09$ & K & 0.004 & Bono et al. (1999) \\\\\n $-3.369$ & K & 0.004 & Alibert et al. (1999) \\\\\n\n$-3.411 \\pm 0.036$ & Wesenheit & LMC & Tanvir (1999) \\\\\n%$-3.278 \\pm 0.014$ & Wesenheit & LMC & Udalski et al. (1999) \\\\\n\n%Caldwell \\& Laney (1991), LMC: in $H$, $-3.72 \\pm 0.07$ \\\\\n%Caldwell \\& Laney (1991), SMC: in $H$, $-3.25 \\pm 0.07$ \\\\\n%Laney \\& Stobie (1994), mix of LMC, SMC, GAL: in $V$, $-2.874 \\pm 0.072$ \\\\\n%Laney \\& Stobie (1994), mix of LMC, SMC, GAL: in $K$, $-3.401 \\pm 0.045$ \\\\\n%Bono et al., all Z: in $V$, $-2.93 \\pm 0.14$, OVERTONES \\\\\n%Bono et al., all Z: in $I$, $-3.15 \\pm 0.09$, OVERTONES \\\\\n%Bono et al., all Z: in $K$, $-3.44 \\pm 0.05$, OVERTONES \\\\\n\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\n\\subsection{Consistency between individual distances based on \ndifferent colours}\n\nFor a given slope and zero point of the $PL$-relation one can\ncalculate the photometric distance, and since we have determined the\nzero point for three photometric band we can intercompare photometric\ndistances to individual \\C. This is illustrated in Fig.~6, for the\ndefault slopes of the $PL$-relations. The zero point of the $M_{\\rm\nV}-\\log P$ relation is fixed at $-1.411$ (solution 10, Table~1). The\nzero point of the $M_{\\rm I}-\\log P$ relation is determined to give a\nmean difference in $(m-M)_{\\rm 0,I} - (m-M)_{\\rm 0,V}$ of zero, and is\nfound to be $-1.918$ (top panel Fig.~6). The rms dispersion is 0.14\nmag. Similarly, to create the bottom panel, the zero point of the\n$M_{\\rm K}-\\log P$ relation was determined to give a mean difference\nin $(m-M)_{\\rm 0,K} - (m-M)_{\\rm 0,I}$ of zero, and is found to be\n$-2.600$, with an rms dispersion is 0.10. The values for the zero\npoints in $I$ and $K$ derived in this way differ only slightly from\nthe solutions 1 in Tables 2 and 3.\n\nInterestingly, least-square fitting shows that the slopes of the\nrelations are not unity, but 0.980 $\\pm$ 0.007 (top panel), and 0.965\n$\\pm$ 0.007 (bottom panel). Using the same procedure, but adopting\nsteeper slopes of $-3.04$, $-3.33$, $-3.60$ (see Sect.~8 for the\nreason of these choices) in, respectively, the $M_{\\rm V}-\\log P$,\n$M_{\\rm I}-\\log P$ and $M_{\\rm K}-\\log P$ relations and fixing the\nzero point of the $M_{\\rm V}-\\log P$ relation at $-1.234$ we find in\nthe same way the zero points of the $M_{\\rm I}-\\log P$ and $M_{\\rm\nK}-\\log P$-relations to be $-1.696$ and $-2.328$. The slopes are 0.983\n$\\pm$ 0.007 and 0.971 $\\pm$ 0.007.\n\nUsing the same procedure, but adopting shallower slopes of $-2.22$,\n$-2.35$, $-3.05$ in, respectively, the $M_{\\rm V}-\\log P$, $M_{\\rm\nI}-\\log P$ and $M_{\\rm K}-\\log P$ relations and fixing the zero point\nof the $M_{\\rm V}-\\log P$ relation at $-1.885$ (solution 38 in Table~1)\nwe find the zero point of the $M_{\\rm I}-\\log P$ and $M_{\\rm K}-\\log\nP$-relations to be $-2.491$ and $-2.692$. The slopes are 0.974 $\\pm$\n0.007 and 1.010 $\\pm$ 0.010.\n\nThe conclusion is the the photometric distances based on different\n$PL$-relations are consistent with each other at a level of 0.10-0.14\nmag, similar to the uncertainties in the individually derived zero\npoints in $V,I,K$ for the full sample. The data does not allow to\ndiscriminate between different choices of the slopes of the $PL$-relations.\n\n\n%BoundingBox: 67 54 388 712 idl/vergelijk.f\n\\begin{figure}\n\\centerline{\\psfig{figure=vergelijk.ps,width=8.8cm}}\n\\caption[]{Comparison of the distance moduli based on the\n$PL$-relations in $V$ and $I$ (top panel), assuming zero points of\nrespectively $-1.411$ and $-1.918$, and the default slopes, and $I$\nand $K$ (bottom panel) for zero points of $-1.918$ and $-2.600$, and\nthe default slopes. The solid line is the one-to-one relation,\nalthough a least-square fit indicates that the best fitting slope\ndiffers slightly from unity (see text).\n}\n\\end{figure}\n\n\n\n\n\\section{A volume complete sample}\n\nThe question remains how representative the \\HP\\ Cepheid sample is. As\nwith all stars that made it in the \\HP\\ catalog, they were proposed by\nPrincipal Investigators in solicited proposals. If proposers preferred\ntheir `favorite' objects to be observed, there may be a `Human' bias,\nwhich is impossible to correct for. For example, at some point in the\nselection process of the \\HP\\ Input Catalog the number of \\C\\ with\nmagnitudes between 9.5 and 11 were `tuned-up' (ESA 1989, page\n80). Also, the distribution in pulsation period of the about 72 \\C\\\nthat were proposed to be observed but did not end up in the \\HP\\ Input\nCatalog is somewhat different from the 270 that did make it (ESA 1989,\npage 96).\n\n\nIn view of this it may be instructive to try to construct a volume\ncomplete sample. The \\HP\\ Input Catalog (ESA 1989, page 94) mentions\nthat {\\it all} 55 \\C\\ within 1 kpc have been included. This depends of\ncourse on the adopted slope and zero point to calculate the\nphotometric parallax. The F95 database lists 51 stars within 1 kpc for\ntheir adopted relation of $M_{\\rm V} = -2.902 \\, \\log P -1.203$.\n\nIn Fig.~7 the cumulative (photometric) parallax distribution is\nplotted for the 236 stars in the sample, with distances from F95, or\ncalculated in the same way for the stars not listed there. Also\nindicated is a line with slope $-2$ as expected for a disk population\n(with $N(r)dr \\sim r$ it follows that $N(\\pi)d\\pi \\sim {\\pi}^{-3}$,\nand so the cumulative distribution is proportional to\n${\\pi}^{-2}$). From this figure it is confirmed that the \\HP\\ catalog\nis volume complete to approximately 1 kpc.\n\nOn the other hand, three new \\C\\ were discovered with \\HP. For the same\nslope and zero point as used in F95 the photometric parallaxes of CK\nCam, V898 Cen, V411 Lac are 1.77, 0.73 and 1.17 mas, respectively.\n\n%As a matter of interest we note that CK Cam is the star with the largest\n%photometric parallax that has an observed negative parallax.\n\n\nAs \\HP\\ discovered 2 \\C\\ that are closer than 1 kpc, it implies that\nthe present sample may now be indeed complete down to 1 mas, but is\npossibly only complete for stars with a parallax \\more 1.8 mas as no\nnew \\C\\ closer than this limit have been discovered.\n\nIn Tables~1-4 we include solutions for volume complete samples, or, in\nother words, complete in photometric parallax. Since this depends on\nthe zero point itself, this is an iterative process. For the $M_{\\rm\nV}-\\log P$-relation we give the results in Table~1 for a cut-off at 1\nand 1.8 mas. In solutions 39, 41, 43 we list the zero point for an\ninput zero point of $-1.411$ (solution 10) for the whole sample, the\nfundamental pulsators, and the overtones, respectively. The next line\n(solutions 40, 42, 44) lists the final result after iteration on the\nzero point. Solutions 45-47 give the final results for a higher\ncut-off in photometric parallax. In most cases the zero points are\nslightly brighter than the corresponding solutions 10, 11, 12. This is\na bit surprising because of the Malmquist bias one expects the volume\ncomplete sample to be dimmer. The expected Malmquist bias for a disk\npopulation with an intrinsic spread of ${\\sigma}_{\\rm H}$ = 0.10\naround the mean is about 0.009 mag (Stobie et al. 1989). This is much\nsmaller than the typical error estimate in the zero points, and so the\nfact that the volume complete sample is brighter probably reflects the\nslightly different nature of that sample. For example, the mean value\nof $\\log P_0$ for the whole sample is 0.86, while that for the volume\ncomplete sample is 0.77. As we noticed earlier, since the shortest\nperiod bins give brighter zero points this could be an explanation. \\\\\n\n\nFor the $M_{\\rm I}-\\log P$-relation the construction of a volume\ncomplete sample is slightly more complicated due to the fact that for\nsome of the 47 stars with $BV$ photometry and a photometric parallax\n$>1$ mas no $I$-band photometry is available. This implies that one has to\napply a more stringent criterion to obtain a volume complete sample of\nstars that also have $I$-band photometry. This turns out to be a\nphotometric parallax limit of 1.8 mas, and solution 23 lists the\nresult. The zero point is slightly brighter, and this again may be due\nto the fact that the average $\\log P_0$ value is smaller (0.74) than\nfor the whole sample (0.90). \\\\\n\n\nIn the $K$-band no meaningful volume complete sample can be\nconstructed. As there is no NIR data available for Polaris, any\nvolume complete sample could be constructed for fundamental pulsators\nonly. In any case, even then, a volume complete sample of stars with\nNIR data would have a cut-off at 2.6 mas, and would only include 3\nstars. For completeness, it has been included in Table~3 (sol. 14). \\\\\n\nThe conclusion is that the zero point of the $PL$-relation based on a\nvolume complete sample are within $1\\sigma$ of the results for the\nfull sample. Surprisingly, the zero points are brighter, contrary to\none would expect from Malmquist bias. However, the Malmquist\ncorrection is expected to be small (see the next section for an\nestimate based on numerical simulations), and certainly much smaller\nthan the error in the zero point, so that this effect is due to the\nslightly different nature of the volume complete samples compared to\nthe full samples.\n\n\n\n\n%BoundingBox: 35 60 219 387\n\\begin{figure}\n\\centerline{\\psfig{figure=pardistr.ps,width=8.8cm,angle=-90}}\n\\caption[]{Cumulative (photometric) parallax distribution of the 236\nstars in the sample with distances from F95 who calculated them using\n$M_{\\rm V} = -2.902 \\, \\log P -1.203$. The dashed line has a slope of\n$-2$, as expected for a disk population. It shows that \\HP\\ is volume\ncomplete down to a distance of about 1 kpc.}\n\\end{figure}\n\n\n\\section{Properties of the \\HP\\ \\C, and numerical simulations}\n\nIn this section we describe a numerical model to first of all construct\nsynthetic samples of stars that fit some observed properties of the\n\\HP\\ \\C. Second, this model is used to investigate the numerical bias\ninvolved in applying the ``reduced parallax'' method. \\\\\n\n\nThe observed distributions of the fundamental period, the $V$\nmagnitude, de-reddened $(B-V)_0$, colour excess, and absolute distance\nto the Galactic plane are plotted in Fig.~8 for the 236 \\C\\ in our\nsample (the dotted lines). For the overtones, the fundamental period\nwas calculated following Eqs.~(6-7). $(B-V)_0$ follows from Eq.~(4),\nand $E(B-V)$ from the observed value of $(B-V)$ minus $(B-V)_0$. The\nabsolute distance to the Galactic plane is calculated from the\ngalactic latitude combined with the de-reddened $V$-magnitude and a\nphotometric distance based on Eq.~(1) with $\\delta = -2.81$ and $\\rho\n= -1.43$. The distributions are compared to simulations described now.\n\nWe have devised a numerical code to simulate the distributions\ndescribed above. The input period distribution is (assumed ad-hoc to\nbe) a Gaussian in $\\log P$ with mean $X_{\\rm P}$, and spread $X_{\\rm\n\\sigma P}$. Based on the observed properties of the sample only $\\log\nP$ values between 0.43 and 1.66 are allowed. A random number is drawn\nand a $\\log P$ selected following this distribution. The values of\n$X_{\\rm P}$ and $X_{\\rm \\sigma P}$ directly influence the resulting\ndistribution and so are easily determined. We find that values of\n$X_{\\rm P}$ between 0.65 and 0.75 and of $X_{\\rm \\sigma P}$ between\n0.2 and 0.25 give acceptable fits.\n\nThe galactic distribution of \\C\\ is assumed to be a double exponential\ndisk with a scale height $H$ in the $z$-direction (the coordinate\nperpendicular to the galactic plane), and a scale height $R_{\\rm GC}$\nin the galacto-centric direction. The coordinate system used is\ncylindrical coordinates centered on the Galactic Centre. Three random\nnumbers are drawn to select the distance to the Galactic plane, the\ndistance to the Galactic centre and a random angle $\\phi$ between 0\nand 2$\\pi$ in the Galactic plane centered on the Galactic centre. From\nthis the distance $d$ to the Sun is calculated. Based on the observed\nphotometric parallaxes of the sample only stars closer than 7800 pc to\nthe Sun are allowed. We find no evidence for a gradient in the number\nof \\C\\ with galacto-centric radius, in other words $R_{\\rm GC} =\n\\infty$ gives good fits, probably indicating that the volume sampled\nis too small to detect such a gradient, or that the distribution of\n\\C\\ is at least equally determined by another factor, for example the\nlocation of the spiral arms. The value of $H$ is directly determined\nby the distribution of the number of stars as a function of $z$, and\nis found to be between 60 and 80 pc. This is consistent with the scale\nheight of a relative massive population of stars, as the \\C\\ are.\n\nThe value of $M_{\\rm V}$ and $(B-V)_0$ are correlated in the sense\nthat brighter \\C\\ are also bluer for a given period. Contrary to other\nstudies we do not assume a Gaussian spread around the $M_{\\rm V}- \\log\nP$ and $(B-V)_0 - \\log P$ relations, but instead a `box' like\ndistribution which is more physical because of the finite width of the\ninstability strip. However, this does assume that the instability\nstrip is uniformly filled (for all periods).\n\nA single uniform random number, $Rn$, is drawn and then\n\\begin{equation}\n M_{\\rm V} = -2.81 \\, \\log P - 1.43 + \\; (-0.42 + 0.84 \\times {\\rm Rn})\n\\end{equation}\nand\n\\begin{equation}\n (B-V)_0 \\;= 0.416 \\, \\log P + 0.314 + \\; (-0.15 + 0.3 \\times {\\rm Rn})\n\\end{equation}\nare calculated. The full width of the instability strip in $M_{\\rm V}$\nis taken to be 0.84 magnitude (derived from plots in Gieren et\nal. 1998, Tanvir 1999), and that of the $(B-V)_0$ relation to be 0.3 mag.\n(Laney \\& Stobie 1994).\n\n\\noindent\nThe reddening is calculated from:\n\\begin{equation}\n A_{\\rm V} = 0.09 \\, \\frac{1 - \\exp \\left( -0.0111 \\; d\\; \\sin b\n \\right)}{\\sin b}\n\\end{equation}\nwhere $b$ is the absolute value of the galactic latitude. The colour\nexcess is then calculated using Eq.~(5). The factor in front was varied to\nfit the $E(B-V)$ distribution. We also tried the reddening model of\nArenou et al. (1992), but found that it could not fit the $E(B-V)$\ndistribution.\n\nThe simulated `observed' visual magnitude is calculated from $V =\nM_{\\rm V}+ 5 \\; \\log d - 5 + A_{\\rm V}$. Then a term is added\nsimulating the uncertainty in the observed $V$, which is described\nby a Gaussian distribution with a dispersion of 0.005 mag.\n\n\\HP\\ was complete only down to about $V = 7$ and the following\nfunction was used to determine if a star was `observed' or not. A\nrandom number ($Rn$) was drawn to calculate:\n\\begin{equation}\n V_{\\rm lim} = 7.0 - \\frac{\\log (1.0 - {\\rm Rn} )}{C}\n\\end{equation}\nwith $C$ empirically determined to be:\n\\begin{equation}\n C = 0.107 -0.030\\; y -0.00482 \\; y^2 +0.00361 \\; y^3\n\\end{equation}\nwith $y = (V-7)$. A star is `observed' if $V < V_{\\rm lim}$.\n\nThe simulation is continued until 25 sets of 236 stars fulfill all\ncriteria. Typically 100~000 stars needed to be drawn to arrive at\nthis. The simulated distributions are depicted in Fig.~8 using the\nsolid lines (normalised to the observed number of 236 stars). Typical\nparameters $X_{\\rm P} = 0.70$, $X_{\\rm \\sigma P} = 0.25$, and $H = 70$\npc have been used. The overall fit is good. \\\\\n\nThis numerical code for the quoted parameters provides us with a tool\nwith which synthetic samples of Cepheids can be generated that obey the\nobserved distributions.\n\n\nThe main difference with the simulations of L99 is in the conclusion\nabout the space distribution of \\C. They assume a homogeneous 3D\ndistribution, and consider a box centered on the Sun of 4200 pc on a\nside. They justify this because of ``the relative small depth of the\n\\HP\\ survey [with respect to] the depth of the Galactic disk''. This\nis not true however. First of all, using any reasonable combination of\n$\\delta$ and $\\rho$ it is clear that \\HP\\ sampled \\C\\ to much greater\ndistances than 2.1 kpc, in fact out to 7-8 kpc. Furthermore, since\nthe scale height of 3-10 \\msol\\ main-sequence stars (the progenitors\nof the \\C\\ variables) is of order 100 pc it is clear that \\HP\\ sampled\nto distances much larger than the scale height of the Cepheid\npopulation. This is directly confirmed from our simulations from\nwhich we derive a scale height of about 70 pc. In other words, the\nspace distribution of the \\C\\ is a disk population, not a homogeneous\npopulation.\n\nThis might have consequences for the results of the L99 paper\nconcerning biases which are difficult to judge by us. Another\nconsequence is related to the fact that both Malmquist- and LK-bias\ndepend on the underlying distribution of stars. For example, Oudmaijer\net al. (1998) calculated the LK-bias assuming a homogeneous\ndistribution of \\C. For a disk population the values of both the\nMalmquist- and LK-bias are smaller (Stobie et al. 1989, Koen 1992). \\\\\n\n\n\n%BoundingBox: 70 22 322 705\n\\begin{figure}\n\\centerline{\\psfig{figure=hipp_sim.ps,width=7.8cm}}\n\\caption[]{Observed (dotted line) and numerical simulation (solid\nline) of the 236 \\C\\ in \\HP. Harmonic periods have been converted to\nthe fundamental period. For a description of the model, and the\nparameters see Sect.~6.\n}\n\\end{figure}\n\n\\noindent\nNow, we will discuss whether the zero points derived by the method\noutlined in Sect.~4 are subject to bias or not. Similar simulations\nwere also performed by L99 and Pont (1999). L99 concluded that zero\npoints derived for the whole sample in $V$ are too bright by 0.01\nmag. Pont (1999) concluded that any bias is less than 0.03 mag.\n\nWhat remains to be discussed in relation to our numerical model is how\nthe `observed' parallax and the error in the parallax are calculated.\n\nWe define several quantities. First of all a minimum error in the\nparallax, calculated from (in mas):\n\\begin{equation}\n\\begin{array}{llll}\n{\\sigma}_{\\pi}^{\\rm min} & = & 0.45 & V \\le 8 \\\\\n & = & 0.45 \\times (V/8)^{3.2} & {\\rm else} \\\\\n\\end{array}\n\\end{equation} \nSecond of all, an error in the error on the parallax, calculated from\n(in mas):\n\\begin{equation}\n\\begin{array}{llll}\n{\\sigma}_{\\sigma} & = & 0.18 & V \\le 8 \\\\\n & = & 0.18 - 0.2167\\, y + 0.325 \\, y^2 - 0.06833 \\, y^3 & {\\rm else} \\\\\n\\end{array}\n\\end{equation} \nwith $y = (V-8)$.\nThird, a `mean' error on the parallax, calculated from (in mas):\n\\begin{equation}\n\\begin{array}{llll}\n{\\sigma} & = & 0.80 & V \\le 5 \\\\\n & = & 0.80 - 0.0280 \\, y - 0.00229 \\,y^2 + 0.008651 \\,y^3 & {\\rm else} \\\\\n\\end{array}\n\\end{equation} \nwith $y = (V-5)$. All fits have been made with {\\sc idl} using the routine\n{\\sc polyfit} from the full sample of 236 stars. It was verified that\nthe synthetic samples have the same distribution of parallax and\nparallax error compared to the observed sample.\n\nThe error on the parallax, ${\\sigma}_{\\pi}$, was then determined from\n$\\sigma$ plus a quantity randomly selected from a Gaussian\ndistribution with dispersion ${\\sigma}_{\\sigma}$. The result is only\naccepted when ${\\sigma}_{\\pi} > {\\sigma}_{\\pi}^{\\rm min}$ however.\nFinally, the `observed' parallax (in mas) is calculated from 1000/$d$,\nwith $d$ the true distance in pc, plus a quantity randomly selected\nfrom a Gaussian distribution with dispersion ${\\sigma}_{\\pi}$.\n\nThe simulation is continued until 100 sets of 236, 191, or 63 stars\nfulfill all criteria, depending whether the simulation relates to\n$V$, $I$ or $K$. About 410~000 stars have to been drawn to arrive at\n23~600 `observed' stars in $V$. This was done with the parameter set\nthat best described the observed distributions, as discussed above,\ni.e. with $X_{\\rm P} = 0.70$, $X_{\\rm \\sigma P} = 0.25$, and $H = 70$ pc.\n\n\nIn the case the simulation relates to $I$ and $K$ the procedure is as\nfollows. First the stars are selected according to the procedure\noutlined above, that is, selection based on $V$-photometry. For the\nstars that fulfill the criteria, the `observed' $I$, $V-I$\n(respectively $K$, $J-K$) colours are determined, using the\nperiod-colour and reddening relations outlined in Sect.~4. The {\\it\nsame random number} that was used in Eqs.~(15-16) to calculate the true\n$M_{\\rm V}$ and $(B-V)$ is used to calculate $M_{\\rm I}$ and $(V-I)$,\nrespectively $M_{\\rm K}$ and $(J-K)$. This is to simulate the fact\nthat if the synthetic star is `observed' to be fainter and bluer than\nthe mean in $V$, this is also the case at other wavelengths. This\nprocedure ignores any phase shifts between the light curves at different\ncolours. For the full-width of the instability strip (cf. Eqs.~ (15-16))\nin $M_{\\rm I}$ we take 0.70 mag, in $(V-I)$ 0.20 mag, in $M_{\\rm K}$\n0.60 and in $(J-K)$ 0.16 mag (Gieren et al. 1998).\n\nFor every set of 236, 191, or 63 stars we apply the ``reduced\nparallax'' method and derive the zero point. From the distribution of\nthe zero points of the 100 sets, we determine the mean, and the\ndispersion. The results are given in Table~6, where we list the zero\npoint assumed in the numerical simulation, the zero point retrieved,\nthe average number of stars in the simulation that fulfilled the\nselection criteria, and to which solution the simulation refers\nto. From the results we see that the zero point of the volume complete\nsample is dimmer than for the whole sample, as expected from Malmquist\nbias. In any case, the biases are very small, of order 0.01 mag, or\nless, similar to the results found by L99 and Pont (1999). Second, we\nconfirm the result by Pont (1999) that the errors derived are somewhat\nlarger compared to the outcome of the ``reduced parallax''\nmethod. However the differences are not so large as compared to the\nerror bars quoted in FC.\n\nFrom the simulations we find that the smallest error is for the sample\nselected on parallax (as was found for the `real' sample), but that it is\nsubject to Lutz-Kelker bias.\n\n\n\n\n\\begin{table*}\n\\caption[]{Zero points from numerical simulations.}\n\\begin{tabular}{ccrcl} \\hline\nInput & Result & Number & Band & Remarks \\\\ \\hline\n$-1.43$ & $-1.425 \\pm 0.124$ & 236 & $V$ & all stars, solution 10 \\\\\n$-1.43$ & $-1.418 \\pm 0.140$ & 33 & $V$ & volume complete sample, solution 39 \\\\\n$-1.43$ & $-1.431 \\pm 0.175$ & 11 & $V$ & $V_{\\rm obs} < 5.5$, solution 14 \\\\\n$-1.43$ & $-1.197 \\pm 0.114$ & 165 & $V$ & $\\pi >0$, solution 16 \\\\\n$-1.43$ & $-1.457 \\pm 0.241$ & 215 & $V$ & weight $<$ 11, solution 19 \\\\\n$-1.43$ & $-1.421 \\pm 0.289$ & 13.3 & $V$ & 11 $<$ weight $<$ 29, solution 20 \\\\\n$-1.43$ & $-1.443 \\pm 0.327$ & 4.8 & $V$ & 29 $<$ weight $<$ 70, solution 21 \\\\\n$-1.43$ & $-1.400 \\pm 0.259$ & 2.4 & $V$ & 70 $<$ weight $<$ 500, solution 22 \\\\\n$-1.43$ & $-1.425 \\pm 0.130$ & 236 & $V$ & weight $<$ 500, solution 23 \\\\\n$-1.43$ & $-1.416 \\pm 0.157$ & 20 & $V$ & 11 $<$ weight $<$ 500, solution 24 \\\\\n & & & & \\\\\n$-1.90$ & $-1.907 \\pm 0.143$ & 191 & $I$ & all stars, solution 1 \\\\\n$-1.90$ & $-1.904 \\pm 0.206$ & 8.5 & $I$ & volume complete sample, solution 22 \\\\\n$-1.90$ & $-1.664 \\pm 0.131$ & 134 & $I$ & $\\pi >0$, solution 6 \\\\\n & & & & \\\\\n$-2.60$ & $-2.610 \\pm 0.261$ & 63 & $K$ & all stars, solution 1 \\\\\n$-2.60$ & $-2.617 \\pm 0.435$ & 1.3 & $K$ & volume complete sample, solution 14 \\\\\n$-2.60$ & $-2.339 \\pm 0.234$ & 45 & $K$ & $\\pi > 0$, solution 6 \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\n\n\n\n\\section{Discussion}\n\n\\subsection{The finally adopted zero points}\n\nBased on the results obtained in Sects.~4, 5 and 6, we will present\nthree sets of solutions, a `traditional' one, and two alternatives.\nThe traditional one follows FC and L99 closely. The zero point adopted\nis the one for the entire sample (which has the lowest error of the\nsamples that are not selected on observed parallax), adopting the\nslope of the $PL$-relation observed for \\C\\ in the LMC. This would\nthen be solution 10 from Table~1 ($\\rho = -1.41 \\pm 0.10$), solution 1\nfrom Table~2 ($\\rho = -1.89 \\pm 0.11$) and solution 1 from Table~3\ncorrected for the off-set in the corresponding solution in $V$ and $I$\nas discussed in Sect.~4.3 ($\\rho = -2.50 \\pm 0.17$). These zero points\nhave to be corrected for Malmquist bias. If the Malmquist bias would\nbe evaluated in magnitude space, this bias would amount to 0.0092,\n0.021 and 0.013 magnitude in $V,I,K$, respectively, for a disk\npopulation and the adopted values for ${\\sigma}_{\\rm H}$ of,\nrespectively, 0.10, 0.15 and 0.12 mag (Stobie et al. 1989). However,\nif evaluated using the reduced parallax method the Malmquist bias is\nsmaller (see Oudmaijer et al. 1999), and from the numerical\nsimulations (Table~6) we find a Malmquist bias of 0.007 in $V$, 0.003\nin $I$, and an unphysical negative value in $K$, probably due to the\nsmaller number of stars involved. For the Malmquist bias we will\nassume a (round number) of 0.01 mag in all three bands.\n\n\nAlso, we have increased the errors in the zero points to reflect the\nsensitivity to uncertainties in the photometry, reddening and\nperiod-colour relations (see Sect.~5.1). For adopted slopes of\n$-2.81$, $-3.05$ and $-3.27$, the finally adopted zero points of the\n$PL$-relations in $V$, $I$ and $K$ are, respectively, $\\rho = -1.40\n\\pm 0.11$, $-1.88 \\pm 0.12$ and $-2.49 \\pm 0.17$. For the\nWesenheit-index, after correcting for Malmquist bias and increasing\nthe error bar due to the uncertainties described in Sect.~5.1, we\nadopt a zero point of $-2.55 \\pm 0.11$ for a slope of $-3.411$. \\\\\n\nThe `traditional' solution above has certain advantages, like the fact\nthat the errors are smallest compared to solutions that do not include\nall stars, or, since the slope adopted is the one in the LMC, a\ndistance determination to the LMC is essentially a comparison of zero\npoints only (apart from systematic effects). On the other hand,\nalternative solutions can be presented which also have merits. These\nsolutions are based on a volume complete sample (at least in $V$ and\n$I$) to avoid Malmquist bias. Although small, its value does depend on\nthe distribution of stars, and the intrinsic spread in the\n$PL$-relation and selecting a volume complete sample avoids Malmquist\nbias outright. In $K$, no volume complete sample could be constructed\nand we used the full sample instead. The alternative solutions take\ninto account the theoretical prediction that the slope of the\n$PL$-relation may change at $\\log P \\sim 0.5$ for solar metallicities\n(Alibert et al. 1999). Where the two alternative solutions differ are\nin the adopted slopes for the Galactic $PL$-relations. One alternative\nsolution takes into account the, admittedly at the 1$\\sigma$ level of\nsignificance, evidence presented in Sects.~4.1-4.2 that the slope of\nthe Galactic $PL$-relations are shallower than the ones in the LMC,\nand in accordance we have adopted the theoretical slopes predicted by\nBono et al. (1999) for solar metallicities. The second alternative\nmethod adopts the slopes in Gieren et al. (1998), who derived\ndistances from the infrared version of the surface brightness\ntechnique to Galactic \\C, which yields steeper slopes than for the\nLMC.\n\nThese alternative solutions are presented in Tables~1-3 (solutions\n54-55, 28-28 and 19-20, respectively). The zero points in $K$ have to\nbe corrected for Malmquist bias (+0.01 mag) and for the off-sets in\nthe corresponding $V$ and $I$ solutions, and the errors in all three\nzero points are increased for reasons indicated above. For the\nadopted slopes of $-2.22$, $-2.35$ and $-3.05$, the zero points of the\n$PL$-relations in $V$, $I$ and $K$ are, respectively, $\\rho = -1.95\n\\pm 0.12$, $-2.47 \\pm 0.15$ and $-2.68 \\pm 0.18$. For the adopted\nslopes of $-3.04$, $-3.33$ and $-3.60$, the zero points of the\n$PL$-relations in $V$, $I$ and $K$ are, respectively, $\\rho = -1.30\n\\pm 0.13$, $-1.75 \\pm 0.14$ and $-2.30 \\pm 0.18$. \\\\\n\n\n\\subsection{$PL$-relation of LMC \\C}\n\nBefore proceeding we have to adopt $PL$-relations for the LMC \\C. In\n$V$, for a slope of $-2.81$, Caldwell \\& Laney (1991) find a zero\npoint of 17.23 $\\pm$ 0.02. Tanvir (1999), for the same slope, gives an\nobserved zero point of 17.451 $\\pm$ 0.043. Adopting a mean reddening\nto the LMC of $E(B-V)$ of 0.08 (Caldwell \\& Laney 1991) and a ratio of\ntotal-to-selective reddening of $R_{\\rm V} = A_{\\rm V}/E(B-V) = $ 3.27\n(Eq.~(5) for typical colors) we derive a de-reddened zero point of\n17.19 $\\pm$ 0.04. For the \\C\\ in the LMC we adopt the weighted mean of\nthese two values, or a zero point of 17.22 $\\pm$ 0.02 in $V$ for a\nslope of $-2.81$.\n\nIn $I$, for a slope of $-3.041$, Gieren et al. (1998) find a zero\npoint of 16.74 $\\pm$ 0.06 (the error is calculated by us, from their\ndata). Tanvir (1999), for a slope of $-3.078$, gives an observed zero\npoint of 16.904 $\\pm$ 0.031. Adopting $A_{\\rm I} = 0.69 A_{\\rm V} =\n0.18$ mag for the reddening in $V$ calculated as above, we derive a\nzero point of 16.72 $\\pm$ 0.03. For the default slope of $-3.05$ we\nadopt the weighted mean of these two values, or a de-reddened zero\npoint in the $I$ band for the \\C\\ in the LMC of 16.72 $\\pm$ 0.02.\n\nIn $K$, for a slope of $-3.267$, Gieren et al. (1998) find a zero\npoint of 16.03 $\\pm$ 0.05 (the error is calculated by us from their\ndata) for the \\C\\ in the LMC. This value is adopted by us.\n\nFor the Wesenheit-index, for a slope of $-3.411$, Tanvir (1999) finds\na zero point of 16.051 $\\pm$ 0.017. This value is adopted by us.\\\\\n\n\\subsection{Metallicity correction}\n\nWe will now consider the effect of metallicity on the zero point. For\ncomparison, FC applied a correction of +0.042 mag to the zero point in\nthe $V$-band, based on Laney \\& Stobie (1994). The theoretical models\nof Bono et al. (1999), and Alibert et al. (1999) provide\n$PL$-relations and from those the difference $\\Delta M = M$(Gal) $-\nM$(LMC) can be determined which will depend on the photometric band\nand period. We have determined this difference for two periods, namely\nfor $\\log P_0 = 0.77$ which we have determined to be the mean period\nof the volume complete sample of Galactic \\C\\ in \\HP\\, and for $\\log\nP_0 = 0.47$ which is the mean period of \\C\\ in the LMC (Alcock et\nal. 1999). The results for $\\Delta M$ are listed in Table~7 for the\nthree photometric bands. This illustrates the difference between the\ntwo theoretical models, for the Alibert et al. (1999) models predict\nessentially no dependence on metallicity, while the Bono et al. (1999)\nmodels predict a significant metallicity dependence, which mostly is\nin the sense that the metal-rich pulsators are fainter than the\nmetal-poor ones. This is at variance with various empirical estimates\nthat give the opposite result, and that, in the $V$-band, vary between\n$-0.24 \\pm 0.16$ (Kennicutt et al. 1998) and about $-0.4$ mag/dex\n(Kochanek 1997, Sasselov et al. 1997, Storm et\nal. 1999\\footnote{Recently, Storm (2000) suggested that this result\nmay not be confirmed from his latest analysis and that the correction\nmay have a positive sign instead.}). A mean of these four\ndeterminations is $-0.38 \\pm 0.09$ mag/dex, which for a difference in\nmetallicity of 0.4 dex, implies $\\Delta M = -0.15 \\pm 0.04$ in the\n$V$-band. In the $I$-band we assume the same value following Sasselov\net al. (1997) and Kochanek (1997), but the reader should realise that\nthis number is less well established than the correction in $V$, and\nin the $K$-band adopt $\\Delta M = -0.07$. Note however, that a\nmetallicity dependence as large as 0.4 mag in $V$ as suggested by\nSekiguchi \\& Fukugita (1998) can be excluded at the 6$\\sigma$ level\n(Laney 1999, 2000). In recent papers, Saio \\& Gautschy (1998) and\nSandage et al. (1999) found no significant metallicity dependence on\nthe bolometric $PL$-relation, and slopes of $-0.08$ mag/dex in $V$ and\n$-0.1$ mag/dex in $I$ (Sandage et al. 1999), which represents a\nshallower dependence than the values listed above, that are adopted in\nthe present study, and which therefore may be an extreme view.\\\\\n\n\\subsection{The distance to the LMC}\n\nIn Table~8 are listed the true distance moduli (DM) to the LMC for\n$V,I,K$, the three slopes (`traditional' meaning the observed slopes\nfor the \\C\\ in the LMC, `shallower' adopting the theoretical slopes\nfrom Bono et al. and `steeper' adopting the observed slopes for\nGalactic \\C\\ from Gieren et al. (1998) and the three metallicity\ncorrections (`0' means no correction, `+' means a longer distance\nscale as implied by the models from Bono et al., and `$-$' means a\nshorter distance scale as implied from empirical evidence). The error\nquoted includes the error in the zero point of both the Galactic and\nLMC Cepheids, and where appropriate, the error due to the metallicity\ncorrection, and for the solutions with either steeper or shallower\nslope, the uncertainty due to the difference in DM at $\\log P = 0.47$\nand 0.77.\n\nAlso included are the weighted mean DM, averaged over $V,I,K$ (with\ninternal error), and, for reference, the (unweighted) mean DM per\nphotometric band of all the solutions (with the one-sided range in the\nsolutions). Also included is the solution based on the\nWesenheit-index assuming the slope observed in the LMC, and no\nmetallicity correction. The DM range from 18.45 $\\pm$ 0.18 to 18.86\n$\\pm$ 0.12. Several important conclusions may be drawn:\n%\\begin{itemize}\n\n\\bigskip\n\n%\\item \n{\\bf (1)} For every combination, the $PL$-relation in $K$ gives the\nshortest distance, and the difference between the distance based on\n$V$ and $K$ can be as large as 0.24 mag (solutions 4, 5 in Table~8). \n\n%The two models with the largest discrepancy both have a `shallower' slope. \n%The two models with the best consistency between the distances based on \n%$V,I,K$ (solutions 3,9) both have a `negative' metallicity correction.\n\nThis systematic effect is worrying and merits investigation. It could\nhint to errors in the reddening, or dereddening procedure. It is\nillustrative to note that the (minimum, maximum, mean) extinction for\nthe whole sample is ($-0.21$, 3.4, 1.3) in $A_{\\rm V}$, ($-0.08$, 2.1,\n0.75) in $A_{\\rm I}$, and ($-0.05$, 0.26, 0.10) in $A_{\\rm K}$. This\nimplies that any uncertainty in reddening is less in $K$. In Sect.~5.1\nwe have estimated these uncertainties (about 0.04 in $V$, 0.03 in $I$\nand 0.01 mag in $K$) and added them as a random errors. Possibly\nthese are errors of a systematic nature instead. It is interesting to\nnote that application of the procedures outlined in Sect.~3.2 results\nin negative reddening in some cases.\n\nOne can raise the question how much bluer the period-colour-relations\nneed to be to give positive reddening for all stars. It turns out that\nEq.~(4) needs to be bluer by 0.065 mag, Eq.~(8) by 0.055 mag, and\nEq.~(11) by 0.075 mag. For the default slopes and using all stars, the\nzero points in $V,I,K$ would change to, respectively, $-1.620$ (from\n$-1.411$), $-1.970$ (from $-1.892$), and $-2.660$ (from $-2.607$).\n\nOn the other hand, the DM based on the Wesenheit-index, which avoids\nthe use of a $PC$-relation to estimate the individual reddenings, is\nin perfect agreement with the DM based both on the $PL$-relations in $V$\nand $I$. This suggests that the reddening is not the main reason for\nthe systematically shorter DM in the $K$-band. \n\nAs pointed out in Sect.~4.3 there may be a bias in the $K$-band zero\npoint due to the smaller number of \\C\\ with accurate intensity-mean\nmagnitudes. The correction for this bias was estimated by comparing,\nfor the same sample of stars with $K$-band data, the zero point of the\n$PL$-relations in $V$ and $I$ to those for the full samples in $V$ and\n$I$, and this correction is about 0.1 mag, in the sense that it makes\nthe DM based on $K$ shorter than they would be without this\ncorrection. This uncertainty can only be eliminated if more\nintensity-mean NIR magnitudes come available.\n\n%zero point based On the other hand this possible systematic effect can\n%not explain the large differences of up 0.23 mag between solutions\n%using different colours, which likely implies that one or both of the\n%other assumptions about the slope or metallicity correction is\n%incorrect. Alternatively, there is a major problem concerning the reddening.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%Ik heb the BV_0, VI_0, JK_0 zo verandert dat alle AV,I,K >0 worden\n%%Dit is een variant op solutions 50, 25, 17\n%%Nodig BV_0 -0.065, ZP wordt -1.620\n%% VI_0 -0.055 -1.970\n%% JK_0 -0.075 -2.660\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n%\\item \n{\\bf (2)} The uncertainty in the type of metallicity correction introduces\na range in DM of up to 0.20 mag in $V,I$, and 0.12 mag in $K$.\n\n%\\item \n{\\bf (3)} The uncertainty in the slope of the Galactic $PL$-relations\nintroduces a range in DM of about 0.16 mag in $V,I$, and about 0.05\nmag in $K$.\\\\\n\n%\\end{itemize}\n\n\\noindent\nTaking the case with the observed slopes of LMC Cepheids with no\nmetallicity correction as default, one may summarise the results as\nfollows. Based on the $PL$-relation in $V$ and $I$, and the\nWesenheit-index, the true DM to the LMC is 18.60 $\\pm$ 0.11 ($\\pm$\n0.08 slope) ($^{+0.08}_{-0.15}$ metallicity). Based on the\n$PL$-relation in $K$ it is 18.52 $\\pm$ 0.18 ($\\pm$ 0.03 slope) ($\\pm\n0.06$ metallicity) ($^{+0.10}_{-0}$ sample bias). The terms between\nparenthesis indicate the possible systematic uncertainties due to the\nslope of the Galactic $PL$-relations, the metallicity corrections, and\nin the $K$-band, due to the limited number of stars. Recent work by\nSandage et al. (1999) indicate that the effect of metallicity towards\nshorter distances may be smaller in $V$ and $I$ than indicated here.\nA more accurate determination is not possible without more definite\ninformation on the slope of the Galactic $PL$-relations and the\nmetallicity correction. \\\\\n\nOur prefered distance modulus is the one based on the $PL$-relation in\n$V$, $I$ and the Wesenheit index, and puts the LMC 0.10 mag in DM\ncloser than the value of 18.70 derived by FC. The difference is due to\nfour effects that all work in the same direction, namely, (1) FC apply\na metallicty correction of +0.042 mag, (2) the difference in the zero\npoint in the Galactic $PL$-relation in $V$ between FC and this study\nis +0.03 mag (+0.01 mag is due to Malmquist bias which FC did not take\ninto account, while +0.02 mag is due to the different sample and\nslightly different photometry in some cases), (3) the difference in\nthe DM based on $V$ compared to the mean of the DM based on $V$, $I$\nand the Wesenheit-index is +0.02 mag, and (4) the difference between\nFC and this study in the adopted zero point of the $PL$-relation in\n$V$ of the LMC Cepheids is +0.01 mag. \\\\\n\nWe finally note that the influence of the choice of slope and the\nmetallicity correction are (predicted to be) smallest in the $K$-band\nas well as the uncertainty in the extinction correction. If the 20-30\nclosest \\C\\ without published NIR photometry could have their NIR\nintensity-mean magnitudes determined, then the uncertainty due to the\nsmall number of stars could be eliminated and the zero point in $K$\ncould be determined with an error that is a factor of two smaller than\nis possible at present. \\\\\n\n\n\\begin{table}\n\\caption[]{Metallicity dependence of the absolute magnitude between\nGalaxy and LMC from recent theoretical models. }\n\\begin{tabular}{rrrrl} \\hline\n$\\log P_0$ & ${\\Delta M}_{\\rm V}$ & ${\\Delta M}_{\\rm I}$ & ${\\Delta M}_{\\rm K}$\n& Reference \\\\ \\hline\n0.77 & 0.139 & 0.145 & 0.073 & Bono et al. (1999)\\\\\n0.77 & 0.005 &$-0.007$ & 0.004 & Alibert et al. (1999)\\\\\n0.47 & $-0.032$ & 0.062 & 0.025 & Bono et al. (1999)\\\\\n0.47 & $-0.008$ &$-0.018$ &$-0.003$ & Alibert et al. (1999)\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\n\n\\begin{table*}\n\\caption[]{Distance Moduli to the LMC. Based on the $PL$-relations in\n$V,I,K$ and the Wesenheit-index, for different assumptions about the\nslope of the Galactic $PL$-relation, and metallicity correction.}\n\\begin{tabular}{crccccccc} \\hline\nSolution & Slope & Metallicity & $V$ & $I$ & $K$ & $W$ & Mean\\\\\n & & dependence & & & & & over $V,I,K$ \\\\ \\hline\n1& traditional & 0 & 18.62 $\\pm$ 0.11 & 18.60 $\\pm$ 0.12 & 18.52 $\\pm$ 0.18\n & 18.60 $\\pm$ 0.11 & 18.60 $\\pm$ 0.07 & \\\\\n2& traditional & + & 18.71 $\\pm$ 0.12 & 18.70 $\\pm$ 0.13 & 18.57 $\\pm$ 0.18\n & & 18.68 $\\pm$ 0.08 & \\\\ \n3& traditional & $-$ & 18.47 $\\pm$ 0.12 & 18.45 $\\pm$ 0.12 & 18.45 $\\pm$ 0.18\n & & 18.46 $\\pm$ 0.08 & \\\\\n4& shallower & 0 & 18.80 $\\pm$ 0.14 & 18.76 $\\pm$ 0.19 & 18.57 $\\pm$ 0.19\n & & 18.73 $\\pm$ 0.10 & \\\\\n5& shallower & + & 18.86 $\\pm$ 0.12 & 18.86 $\\pm$ 0.16 & 18.62 $\\pm$ 0.19\n & & 18.81 $\\pm$ 0.09 & \\\\\n6& shallower & $-$ & 18.65 $\\pm$ 0.14 & 18.61 $\\pm$ 0.18 & 18.50 $\\pm$ 0.19\n & & 18.60 $\\pm$ 0.10 & \\\\\n7& steeper & 0 & 18.66 $\\pm$ 0.13 & 18.64 $\\pm$ 0.15 & 18.53 $\\pm$ 0.19\n & & 18.63 $\\pm$ 0.09 & \\\\\n8& steeper & + & 18.72 $\\pm$ 0.18 & 18.75 $\\pm$ 0.16 & 18.58 $\\pm$ 0.20\n & & 18.70 $\\pm$ 0.10 & \\\\\n9& steeper & $-$ & 18.51 $\\pm$ 0.14 & 18.49 $\\pm$ 0.15 & 18.46 $\\pm$ 0.19\n & & 18.49 $\\pm$ 0.09 & \\\\ \\hline\nmean/range & & & 18.67 / 0.20 & 18.65 / 0.21 & 18.53 / 0.09 & & 18.63 \\\\ \n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\n\n\\subsection*{Acknowledgements}\nWe thank Pascal Fouqu\\'e, Michael Feast and Patricia Whitelock for\nproviding tabular material in Gieren et al. (1998), respectively Feast\n\\& Whitelock (1997) in electronic format. We thank Giuseppe Bono and\nSanti Cassisi in calculating and communicating additional\n$PL(C)$-relations to us. Frederic Pont and Frederic Arenou are\nthanked for lively and interesting discussions. This research has\nmade use of the SIMBAD database, operated at CDS, Strasbourg, France.\n\n\n\n\\section*{Appendix}\n\nIn this appendix we list the sample of 236 \\C\\ in the \\HP\\ catalog\nconsidered in this study. Listed in Table~A1 are the HIP number and\nvariable star name, the parallax and error in the parallax from the\n\\HP\\ catalog except for RY Sco and Y Lac (Falin \\& Mignard 1999), the\nintensity-mean $V$ and $B-V$ adopted, the $\\log$ of the fundamental\nperiod, and the assumed pulsation mode. The $V-I$ colours and $JHK$\nphotometry can be found in G99, as described in Sect.~2.\n\n%page 92 latex manual\n\\setcounter{table}{0}\n\\renewcommand{\\thetable}{A\\arabic{table}}\n\n\\begin{table*}\n\\caption[]{The sample of \\HP\\ \\C}\n\n%\\scriptsize\n\n\\begin{tabular}{rrrrrrrr} \\hline\nHIP & Name & $\\pi$ & ${\\sigma}_{\\pi}$ & $V$ & $(B-V)$ & $\\log\n P_0$ & mode \\\\\n & & (mas) & (mas) & & & & \\\\ \\hline\n 1162 & FM Cas & 0.10 & 1.27 & 9.127 &0.989 & 0.764 & 0 \\\\\n 1213 & SY Cas & 2.73 & 1.49 & 9.868 &0.992 & 0.610 & 0 \\\\\n 2347 & DL Cas & 2.32 & 1.09 & 8.969 &1.154 & 0.903 & 0 \\\\\n 3886 & XY Cas & -0.02 & 1.58 & 9.935 &1.147 & 0.653 & 0 \\\\\n 5138 & VW Cas & -2.12 & 3.61 & 10.697 &1.245 & 0.778 & 0 \\\\\n 5658 & UZ Cas & 4.37 & 3.64 & 11.338 &1.110 & 0.629 & 0 \\\\\n 5846 & BP Cas & -0.60 & 2.04 & 10.920 &1.550 & 0.798 & 0 \\\\\n 7192 & V636 Cas & 1.72 & 0.81 & 7.199 &1.365 & 0.923 & 0 \\\\\n 7548 & RW Cas & 0.69 & 1.68 & 9.217 &1.196 & 1.170 & 0 \\\\\n 8312 & BY Cas & -0.85 & 3.25 & 10.366 &1.309 & 0.662 & 1 \\\\\n 8614 & VV Cas & -4.78 & 4.18 & 10.724 &1.143 & 0.793 & 0 \\\\\n 9928 & VX Per & 1.08 & 1.48 & 9.312 &1.158 & 1.037 & 0 \\\\\n 11174 & V440 Per & 1.62 & 0.83 & 6.282 &0.873 & 1.039 & 1 \\\\\n 11420 & SZ Cas & 2.21 & 1.60 & 9.853 &1.419 & 1.135 & 0 \\\\\n 11767 & $\\alpha$ UMi & 7.56 & 0.48 & 1.982 &0.598 & 0.754 & 1 \\\\\n 12817 & DF Cas & -0.27 & 3.65 & 10.848 &1.181 & 0.584 & 0 \\\\\n 13367 & SU Cas & 2.31 & 0.58 & 5.970 &0.703 & 0.440 & 1 \\\\\n 19978 & SX Per & -1.59 & 2.96 & 11.158 &1.155 & 0.632 & 0 \\\\\n 20202 & AS Per & 0.56 & 1.84 & 9.723 &1.302 & 0.697 & 0 \\\\\n 21517 & SZ Tau & 3.12 & 0.82 & 6.531 &0.844 & 0.651 & 1 \\\\\n 22445 & SV Per & -3.32 & 1.54 & 9.020 &1.029 & 1.046 & 0 \\\\\n 23210 & AN Aur & -1.19 & 2.34 & 10.455 &1.218 & 1.012 & 0 \\\\\n 23360 & RX Aur & 1.32 & 1.02 & 7.655 &1.009 & 1.065 & 0 \\\\\n 23768 & CK Cam & -0.33 & 0.95 & 7.541 &0.990 & 0.518 & 0 \\\\\n 24105 & BK Aur & 0.47 & 1.38 & 9.427 &1.062 & 0.903 & 0 \\\\\n 24281 & SY Aur & 1.15 & 1.70 & 9.074 &1.000 & 1.006 & 0 \\\\\n 24500 & YZ Aur & 3.70 & 2.10 & 10.332 &1.375 & 1.260 & 0 \\\\\n 25642 & Y Aur & -0.40 & 1.47 & 9.607 &0.911 & 0.586 & 0 \\\\\n 26069 & $\\beta$ Dor & 3.14 & 0.59 & 3.731 &0.807 & 0.993 & 0 \\\\\n 27119 & ST Tau & 3.15 & 1.17 & 8.217 &0.847 & 0.606 & 0 \\\\\n 27183 & EU Tau & 0.86 & 1.38 & 8.093 &0.664 & 0.473 & 1 \\\\\n 28625 & RZ Gem & 1.90 & 1.97 & 10.007 &1.025 & 0.743 & 0 \\\\\n 28945 & AA Gem & -2.25 & 2.42 & 9.721 &1.061 & 1.053 & 0 \\\\\n 29022 & CS Ori & -0.54 & 3.36 & 11.381 &0.924 & 0.590 & 0 \\\\\n 29386 & GQ Ori & 4.77 & 1.13 & 8.965 &0.976 & 0.935 & 0 \\\\\n 30219 & SV Mon & -1.18 & 1.14 & 8.219 &1.048 & 1.183 & 0 \\\\\n 30286 & RS Ori & 2.02 & 1.45 & 8.412 &0.945 & 0.879 & 0 \\\\\n 30827 & RT Aur & 2.09 & 0.89 & 5.446 &0.595 & 0.572 & 0 \\\\\n 31306 & DX Gem & -2.58 & 2.49 & 10.746 &0.936 & 0.650 & 1 \\\\\n 31404 & W Gem & 0.86 & 1.16 & 6.950 &0.889 & 0.898 & 0 \\\\\n 31624 & CV Mon & 3.76 & 2.77 & 10.299 &1.297 & 0.731 & 0 \\\\\n 31905 & BE Mon & -0.28 & 2.12 & 10.578 &1.134 & 0.432 & 0 \\\\\n 32180 & AD Gem & -0.18 & 1.60 & 9.857 &0.694 & 0.578 & 0 \\\\\n 32516 & V508 Mon & -2.42 & 2.28 & 10.518 &0.898 & 0.616 & 0 \\\\\n 32854 & TX Mon & 0.00 & 2.47 & 10.960 &1.096 & 0.940 & 0 \\\\\n 33014 & EK Mon & -0.77 & 2.69 & 11.048 &1.195 & 0.598 & 0 \\\\\n 33520 & TZ Mon & 1.61 & 2.12 & 10.761 &1.116 & 0.871 & 0 \\\\\n 33791 & AC Mon & 0.90 & 1.94 & 10.067 &1.165 & 0.904 & 0 \\\\\n 33874 & V526 Mon & 3.43 & 1.12 & 8.597 &0.593 & 0.579 & 1 \\\\\n 34088 & $\\zeta$ Gem & 2.79 & 0.81 & 3.918 &0.798 & 1.007 & 0 \\\\\n 34421 & V465 Mon & 2.28 & 1.88 & 10.379 &0.762 & 0.586 & 1 \\\\\n 34527 & TV CMa & 0.90 & 1.97 & 10.582 &1.175 & 0.669 & 0 \\\\\n 34895 & RW CMa & 3.12 & 2.16 & 11.096 &1.225 & 0.758 & 0 \\\\\n 35212 & RY CMa & 0.96 & 1.09 & 8.110 &0.847 & 0.670 & 0 \\\\\n 35665 & RZ CMa & -1.95 & 1.51 & 9.697 &1.004 & 0.629 & 0 \\\\\n 35708 & TW CMa & 1.26 & 1.51 & 9.561 &0.970 & 0.845 & 0 \\\\\n 36125 & VZ CMa & 1.58 & 1.65 & 9.383 &0.957 & 0.495 & 0 \\\\\n 36617 & VW Pup & -5.65 & 2.83 & 11.365 &1.065 & 0.632 & 0 \\\\\n 36685 & X Pup & -0.05 & 1.10 & 8.460 &1.127 & 1.414 & 0 \\\\\n 37174 & MY Pup & 0.65 & 0.52 & 5.677 &0.631 & 0.913 & 1 \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\\setcounter{table}{0}\n\\begin{table*}\n\\caption[]{Continued}\n\n%\\scriptsize\n\n\\begin{tabular}{rrrrrrrr} \\hline\nHIP & Name & $\\pi$ & ${\\sigma}_{\\pi}$ & $V$ & $(B-V)$ & $\\log\n P_0$ & mode \\\\\n & & (mas) & (mas) & & & & \\\\ \\hline\n 37207 & VZ Pup & 1.49 & 1.47 & 9.621 &1.162 & 1.365 & 0 \\\\\n 37506 & EK Pup & 3.54 & 2.34 & 10.664 &0.816 & 0.571 & 1 \\\\\n 37511 & WW Pup & 2.07 & 1.91 & 10.554 &0.874 & 0.742 & 0 \\\\\n 37515 & WX Pup & -1.05 & 1.08 & 9.063 &0.968 & 0.951 & 0 \\\\\n 38063 & AD Pup & -4.05 & 1.74 & 9.863 &1.049 & 1.133 & 0 \\\\\n 38907 & AP Pup & 1.07 & 0.64 & 7.371 &0.838 & 0.706 & 0 \\\\\n 38944 & WY Pup & 0.11 & 2.09 & 10.569 &0.791 & 0.720 & 0 \\\\\n 38965 & AQ Pup & 8.85 & 4.03 & 8.669 &1.337 & 1.479 & 0 \\\\\n 39010 & LS Pup & 3.90 & 2.71 & 10.442 &1.231 & 1.151 & 0 \\\\\n 39144 & WZ Pup & -0.55 & 1.77 & 10.326 &0.789 & 0.701 & 0 \\\\\n 39666 & BN Pup & 4.88 & 1.72 & 9.882 &1.186 & 1.136 & 0 \\\\\n 39840 & LX Pup & 3.08 & 2.59 & 10.630 &1.032 & 1.142 & 0 \\\\\n 40078 & HL Pup & -10.42 & 4.30 & 10.740 &0.862 & 0.542 & 0 \\\\\n 40155 & AH Vel & 2.23 & 0.55 & 5.695 &0.579 & 0.782 & 1 \\\\\n 40178 & AT Pup & 1.20 & 0.74 & 7.957 &0.783 & 0.824 & 0 \\\\\n 40233 & RS Pup & 0.49 & 0.68 & 7.028 &1.434 & 1.617 & 0 \\\\\n 41588 & V Car & 0.34 & 0.58 & 7.362 &0.872 & 0.826 & 0 \\\\\n 42257 & RZ Vel & 1.35 & 0.63 & 7.079 &1.120 & 1.310 & 0 \\\\\n 42321 & T Vel & 0.48 & 0.72 & 8.024 &0.922 & 0.666 & 0 \\\\\n 42831 & SW Vel & 1.30 & 0.90 & 8.120 &1.162 & 1.370 & 0 \\\\\n 42926 & SX Vel & 1.54 & 0.79 & 8.251 &0.888 & 0.980 & 0 \\\\\n 42929 & ST Vel & -1.62 & 0.99 & 9.704 &1.195 & 0.768 & 0 \\\\\n 44847 & BG Vel & 1.33 & 0.65 & 7.635 &1.175 & 0.999 & 1 \\\\\n 45570 & DK Vel & -1.70 & 3.78 & 10.614 &0.774 & 0.546 & 1 \\\\\n 45949 & W Car & 1.16 & 0.63 & 7.589 &0.788 & 0.641 & 0 \\\\\n 46746 & DR Vel & -0.45 & 1.07 & 9.520 &1.518 & 1.049 & 0 \\\\\n 47177 & AE Vel & -0.64 & 1.33 & 10.262 &1.243 & 0.853 & 0 \\\\\n 47854 & $l$ Car & 2.16 & 0.47 & 3.724 &1.299 & 1.551 & 0 \\\\\n 48122 & FN Vel & 0.77 & 1.63 & 10.430 &0.912 & 0.726 & 0 \\\\\n 48663 & GX Car & 1.43 & 1.12 & 9.364 &1.043 & 0.857 & 0 \\\\\n 50244 & CN Car & 5.11 & 1.53 & 10.700 &1.089 & 0.693 & 0 \\\\\n 50655 & RY Vel & -1.15 & 0.83 & 8.397 &1.352 & 1.449 & 0 \\\\\n 50722 & AQ Car & 1.02 & 0.81 & 8.851 &0.928 & 0.990 & 0 \\\\\n 51142 & UW Car & -0.64 & 1.12 & 9.426 &0.971 & 0.728 & 0 \\\\\n 51262 & YZ Car & 1.79 & 1.03 & 8.714 &1.124 & 1.259 & 0 \\\\\n 51338 & UX Car & 0.00 & 0.87 & 8.308 &0.627 & 0.566 & 0 \\\\\n 51894 & XX Vel & 1.14 & 1.50 & 10.654 &1.162 & 0.844 & 0 \\\\\n 51909 & UZ Car & -0.70 & 1.00 & 9.323 &0.875 & 0.716 & 0 \\\\\n 52157 & HW Car & -0.71 & 1.06 & 9.163 &1.055 & 0.964 & 0 \\\\\n 52380 & EY Car & 3.46 & 1.62 & 10.318 &0.854 & 0.459 & 0 \\\\\n 52570 & SV Vel & -1.27 & 0.97 & 8.524 &1.054 & 1.149 & 0 \\\\\n 52661 & SX Car & 2.48 & 1.06 & 9.089 &0.887 & 0.687 & 0 \\\\\n 53083 & WW Car & 4.23 & 1.39 & 9.743 &0.890 & 0.670 & 0 \\\\\n 53397 & WZ Car & -0.41 & 1.14 & 9.247 &1.142 & 1.362 & 0 \\\\\n 53536 & XX Car & -0.63 & 0.95 & 9.322 &1.054 & 1.196 & 0 \\\\\n 53589 & U Car & -0.04 & 0.62 & 6.288 &1.183 & 1.589 & 0 \\\\\n 53593 & CY Car & -0.30 & 1.40 & 9.782 &0.953 & 0.630 & 0 \\\\\n 53867 & FN Car & -1.91 & 2.48 & 11.542 &1.101 & 0.661 & 0 \\\\\n 53945 & XY Car & -0.62 & 0.95 & 9.295 &1.214 & 1.095 & 0 \\\\\n 54101 & XZ Car & -0.30 & 0.96 & 8.601 &1.266 & 1.221 & 0 \\\\\n 54543 & ER Car & 1.36 & 0.69 & 6.824 &0.867 & 0.887 & 0 \\\\\n 54621 & GH Car & 0.43 & 1.03 & 9.177 &0.932 & 0.915 & 1 \\\\\n 54659 & V898 Cen & -0.32 & 0.73 & 8.000 &0.574 & 0.547 & 0 \\\\\n 54715 & IT Car & 1.00 & 0.82 & 8.097 &0.990 & 0.877 & 0 \\\\\n 54862 & GI Car & -0.41 & 1.10 & 8.323 &0.739 & 0.802 & 1 \\\\\n 54891 & FR Car & 0.35 & 1.29 & 9.661 &1.121 & 1.030 & 0 \\\\\n 55726 & AY Cen & -0.24 & 1.04 & 8.830 &1.009 & 0.725 & 0 \\\\\n 55736 & AZ Cen & -0.20 & 1.04 & 8.636 &0.653 & 0.660 & 1 \\\\\n 56176 & V419 Cen & 1.72 & 0.93 & 8.186 &0.758 & 0.898 & 1 \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\\setcounter{table}{0}\n\\begin{table*}\n\\caption[]{Continued}\n\n%\\scriptsize\n\n\\begin{tabular}{rrrrrrrr} \\hline\nHIP & Name & $\\pi$ & ${\\sigma}_{\\pi}$ & $V$ & $(B-V)$ & $\\log\n P_0$ & mode \\\\\n & & (mas) & (mas) & & & & \\\\ \\hline\n 57130 & KK Cen & -1.84 & 2.89 & 11.480 &1.282 & 1.086 & 0 \\\\\n 57260 & RT Mus & 1.13 & 0.99 & 9.022 &0.834 & 0.489 & 0 \\\\\n 57884 & BB Cen & 2.85 & 1.27 & 9.781 &1.150 & 1.066 & 0 \\\\\n 57978 & UU Mus & 3.03 & 1.43 & 10.073 &0.953 & 0.757 & 1 \\\\\n 59575 & AD Cru & 1.87 & 2.32 & 11.051 &1.279 & 0.806 & 0 \\\\\n 60259 & T Cru & 0.86 & 0.62 & 6.566 &0.922 & 0.828 & 0 \\\\\n 60455 & R Cru & 1.97 & 0.82 & 6.766 &0.772 & 0.765 & 0 \\\\\n 61136 & BG Cru & 1.94 & 0.57 & 5.487 &0.606 & 0.678 & 1 \\\\\n 61981 & R Mus & 1.69 & 0.59 & 6.298 &0.757 & 0.876 & 0 \\\\\n 62986 & S Cru & 1.34 & 0.71 & 6.600 &0.761 & 0.671 & 0 \\\\\n 63693 & V496 Cen & 1.61 & 1.53 & 9.966 &1.172 & 0.646 & 0 \\\\\n 64969 & V378 Cen & 0.96 & 1.02 & 8.460 &1.035 & 0.969 & 1 \\\\\n 65970 & V659 Cen & 0.75 & 1.28 & 6.598 &0.758 & 0.750 & 0 \\\\\n 66189 & VW Cen & -2.02 & 3.63 & 10.245 &1.345 & 1.177 & 0 \\\\\n 66383 & KN Cen & -1.38 & 2.82 & 9.870 &1.582 & 1.532 & 0 \\\\\n 66696 & XX Cen & 2.04 & 0.94 & 7.818 &0.983 & 1.039 & 0 \\\\\n 67566 & V381 Cen & 1.13 & 0.91 & 7.653 &0.792 & 0.706 & 0 \\\\\n 70203 & V339 Cen & 0.33 & 1.16 & 8.753 &1.191 & 0.976 & 0 \\\\\n 71116 & V Cen & 0.05 & 0.82 & 6.836 &0.875 & 0.740 & 0 \\\\\n 71492 & V737 Cen & 3.71 & 0.84 & 6.719 &0.999 & 0.849 & 0 \\\\\n 72264 & BP Cir & 0.13 & 0.88 & 7.560 &0.702 & 0.531 & 1 \\\\\n 72583 & AV Cir & 3.40 & 1.09 & 7.439 &0.910 & 0.640 & 1 \\\\\n 74448 & IQ Nor & -0.24 & 3.08 & 9.566 &1.314 & 0.916 & 0 \\\\\n 75018 & R TrA & 0.43 & 0.71 & 6.660 &0.722 & 0.530 & 0 \\\\\n 75430 & GH Lup & 2.65 & 0.86 & 7.635 &1.210 & 0.967 & 0 \\\\\n 76918 & U Nor & 2.52 & 1.28 & 9.238 &1.576 & 1.102 & 0 \\\\\n 78476 & S TrA & 1.59 & 0.72 & 6.397 &0.752 & 0.801 & 0 \\\\\n 78797 & RS Nor & -0.23 & 1.81 & 10.027 &1.287 & 0.792 & 0 \\\\\n 79625 & GU Nor & 4.45 & 2.06 & 10.411 &1.273 & 0.538 & 0 \\\\\n 79932 & S Nor & 1.19 & 0.75 & 6.426 &0.945 & 0.989 & 0 \\\\\n 82023 & V340 Ara & 0.06 & 2.12 & 10.164 &1.539 & 1.318 & 0 \\\\\n 82498 & KQ Sco & 0.07 & 2.31 & 9.807 &1.934 & 1.458 & 0 \\\\\n 83059 & RV Sco & 2.54 & 1.13 & 7.040 &0.955 & 0.783 & 0 \\\\\n 83674 & BF Oph & 1.17 & 1.01 & 7.337 &0.868 & 0.609 & 0 \\\\\n 85035 & V636 Sco & -0.45 & 0.89 & 6.654 &0.936 & 0.832 & 0 \\\\\n 85701 & V482 Sco & -0.45 & 1.16 & 7.965 &0.975 & 0.656 & 0 \\\\\n 86269 & V950 Sco & 2.46 & 1.04 & 7.302 &0.775 & 0.683 & 1 \\\\\n 87072 & X Sgr & 3.03 & 0.94 & 4.549 &0.739 & 0.846 & 0 \\\\\n 87173 & V500 Sco & 2.21 & 1.30 & 8.729 &1.276 & 0.969 & 0 \\\\\n 87345 & RY Sco & 0.96 & 2.70 & 8.004 &1.426 & 1.308 & 0 \\\\\n 87495 & Y Oph & 1.14 & 0.80 & 6.169 &1.377 & 1.234 & 0 \\\\\n 89013 & CR Ser & -3.04 & 2.08 & 10.842 &1.644 & 0.724 & 0 \\\\\n 89276 & AP Sgr & -0.95 & 0.92 & 6.955 &0.807 & 0.704 & 0 \\\\\n 89596 & WZ Sgr & -0.75 & 1.76 & 8.030 &1.392 & 1.339 & 0 \\\\\n 89968 & Y Sgr & 2.52 & 0.93 & 5.744 &0.856 & 0.761 & 0 \\\\\n 90110 & AY Sgr & -0.99 & 2.28 & 10.549 &1.457 & 0.817 & 0 \\\\\n 90241 & XX Sgr & 2.64 & 1.22 & 8.852 &1.107 & 0.808 & 0 \\\\\n 90791 & X Sct & 0.97 & 1.46 & 10.006 &1.140 & 0.623 & 0 \\\\\n 90836 & U Sgr & 0.27 & 0.92 & 6.695 &1.087 & 0.829 & 0 \\\\\n 91239 & EV Sct & 0.91 & 1.92 & 10.137 &1.160 & 0.643 & 1 \\\\\n 91366 & Y Sct & 0.00 & 1.69 & 9.628 &1.539 & 1.015 & 0 \\\\\n 91613 & CK Sct & 3.62 & 2.12 & 10.590 &1.566 & 0.870 & 0 \\\\\n 91697 & RU Sct & 0.89 & 1.61 & 9.466 &1.645 & 1.294 & 0 \\\\\n 91706 & TY Sct & 4.02 & 2.27 & 10.831 &1.657 & 1.043 & 0 \\\\\n 91738 & CM Sct & -3.72 & 2.35 & 11.106 &1.371 & 0.593 & 0 \\\\\n 91785 & Z Sct & 1.14 & 1.66 & 9.600 &1.330 & 1.111 & 0 \\\\\n 91867 & SS Sct & -1.07 & 1.17 & 8.211 &0.944 & 0.565 & 0 \\\\\n 92370 & YZ Sgr & 0.87 & 1.03 & 7.358 &1.032 & 0.980 & 0 \\\\\n 92491 & BB Sgr & 0.61 & 0.99 & 6.947 &0.987 & 0.822 & 0 \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\\setcounter{table}{0}\n\\begin{table*}\n\\caption[]{Continued}\n\n%\\scriptsize\n\n\\begin{tabular}{rrrrrrrr} \\hline\nHIP & Name & $\\pi$ & ${\\sigma}_{\\pi}$ & $V$ & $(B-V)$ & $\\log\n P_0$ & mode \\\\\n & & (mas) & (mas) & & & & \\\\ \\hline\n 93063 & V493 Aql & -2.77 & 2.43 & 11.083 &1.280 & 0.475 & 0 \\\\\n 93124 & FF Aql & 1.32 & 0.72 & 5.372 &0.756 & 0.806 & 1 \\\\\n 93399 & V336 Aql & 0.75 & 1.47 & 9.848 &1.312 & 0.864 & 0 \\\\\n 93681 & SZ Aql & 0.20 & 1.10 & 8.599 &1.389 & 1.234 & 0 \\\\\n 93990 & TT Aql & 0.41 & 0.96 & 7.141 &1.292 & 1.138 & 0 \\\\\n 94004 & V496 Aql & -3.81 & 1.05 & 7.751 &1.146 & 0.833 & 0 \\\\\n 94094 & FM Aql & 2.45 & 1.11 & 8.270 &1.277 & 0.786 & 0 \\\\\n 94402 & FN Aql & 1.53 & 1.18 & 8.382 &1.214 & 1.138 & 1 \\\\\n 94685 & V473 Lyr & 1.94 & 0.62 & 6.182 &0.632 & 0.433 & 2 \\\\\n 95118 & V600 Aql & 1.42 & 1.80 & 10.037 &1.462 & 0.860 & 0 \\\\\n 96458 & U Vul & 0.59 & 0.77 & 7.128 &1.275 & 0.903 & 0 \\\\\n 96596 & V924 Cyg & 0.83 & 1.64 & 10.710 &0.847 & 0.746 & 0 \\\\\n 97309 & BR Vul & -2.80 & 1.70 & 10.687 &1.474 & 0.716 & 0 \\\\\n 97439 & V1154 Cyg & 0.88 & 0.88 & 9.190 &0.925 & 0.692 & 0 \\\\\n 97717 & SV Vul & 0.79 & 0.74 & 7.220 &1.442 & 1.653 & 0 \\\\\n 97794 & V1162 Aql & 0.15 & 1.15 & 7.798 &0.879 & 0.888 & 1 \\\\\n 97804 & $\\eta$ Aql & 2.78 & 0.91 & 3.897 &0.789 & 0.856 & 0 \\\\\n 98085 & S Sge & 0.76 & 0.73 & 5.622 &0.805 & 0.923 & 0 \\\\\n 98212 & X Vul & -0.33 & 1.10 & 8.849 &1.389 & 0.801 & 0 \\\\\n 98376 & GH Cyg & 1.93 & 1.67 & 9.924 &1.266 & 0.893 & 0 \\\\\n 98852 & CD Cyg & 0.46 & 1.00 & 8.947 &1.266 & 1.232 & 0 \\\\\n 99276 & V402 Cyg & 1.19 & 1.18 & 9.873 &1.008 & 0.640 & 0 \\\\\n 99567 & MW Cyg & -1.63 & 1.30 & 9.489 &1.316 & 0.775 & 0 \\\\\n 99887 & V495 Cyg & -0.95 & 1.32 & 10.621 &1.623 & 0.827 & 0 \\\\\n101393 & SZ Cyg & 0.86 & 1.09 & 9.432 &1.477 & 1.179 & 0 \\\\\n102276 & X Cyg & 1.47 & 0.72 & 6.391 &1.130 & 1.214 & 0 \\\\\n102949 & T Vul & 1.95 & 0.60 & 5.754 &0.635 & 0.647 & 0 \\\\\n103241 & V520 Cyg & 1.51 & 1.73 & 10.851 &1.349 & 0.607 & 0 \\\\\n103433 & VX Cyg & 0.88 & 1.43 & 10.069 &1.704 & 1.304 & 0 \\\\\n103656 & TX Cyg & 0.50 & 1.09 & 9.511 &1.784 & 1.168 & 0 \\\\\n104002 & VY Cyg & -0.02 & 1.44 & 9.593 &1.215 & 0.895 & 0 \\\\\n104185 & DT Cyg & 1.72 & 0.62 & 5.774 &0.538 & 0.549 & 1 \\\\\n104564 & V459 Cyg & 0.51 & 1.50 & 10.601 &1.439 & 0.860 & 0 \\\\\n104877 & V386 Cyg & 2.22 & 1.17 & 9.635 &1.491 & 0.721 & 0 \\\\\n105369 & V532 Cyg & 0.84 & 0.94 & 9.086 &1.036 & 0.516 & 0 \\\\\n106754 & V538 Cyg & 0.10 & 1.52 & 10.456 &1.283 & 0.787 & 0 \\\\\n107899 & VZ Cyg & 2.84 & 1.17 & 8.959 &0.876 & 0.687 & 0 \\\\\n108426 & IR Cep & 1.38 & 0.61 & 7.784 &0.888 & 0.476 & 1 \\\\\n108427 & CP Cep & 1.54 & 1.52 & 10.590 &1.668 & 1.252 & 0 \\\\\n108630 & BG Lac & -0.35 & 1.31 & 8.883 &0.949 & 0.727 & 0 \\\\\n109340 & Y Lac & 0.45 & 1.70 & 9.146 &0.731 & 0.636 & 0 \\\\\n110964 & AK Cep & 0.22 & 2.52 & 11.180 &1.341 & 0.859 & 0 \\\\\n110968 & V411 Lac & 0.67 & 0.70 & 7.860 &0.741 & 0.464 & 0 \\\\\n110991 & $\\delta$ Cep & 3.32 & 0.58 & 3.954 &0.657 & 0.730 & 0 \\\\\n111972 & Z Lac & 2.04 & 0.89 & 8.415 &1.095 & 1.037 & 0 \\\\\n112026 & RR Lac & 0.94 & 0.95 & 8.848 &0.885 & 0.807 & 0 \\\\\n112430 & CR Cep & 1.67 & 1.06 & 9.656 &1.396 & 0.795 & 0 \\\\\n112626 & V Lac & 0.34 & 0.85 & 8.936 &0.873 & 0.697 & 0 \\\\\n112675 & X Lac & 0.57 & 0.79 & 8.407 &0.901 & 0.893 & 1 \\\\\n114160 & SW Cas & 1.07 & 1.37 & 9.705 &1.081 & 0.736 & 0 \\\\\n115390 & CH Cas & 0.21 & 1.68 & 10.973 &1.650 & 1.179 & 0 \\\\\n115925 & CY Cas & 2.76 & 3.21 & 11.641 &1.738 & 1.158 & 0 \\\\\n116556 & RS Cas & 2.43 & 1.24 & 9.932 &1.490 & 0.799 & 0 \\\\\n116684 & DW Cas & 1.19 & 1.95 & 11.112 &1.475 & 0.699 & 0 \\\\\n117154 & CD Cas & 1.91 & 1.58 & 10.738 &1.449 & 0.892 & 0 \\\\\n117690 & RY Cas & 0.02 & 1.38 & 9.927 &1.384 & 1.084 & 0 \\\\\n118122 & DD Cas & 0.57 & 1.14 & 9.876 &1.188 & 0.992 & 0 \\\\\n118174 & CF Cas & -3.20 & 2.16 & 11.136 &1.174 & 0.688 & 0 \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\n\\begin{thebibliography}{}\n\\bibitem[]{} Alcock C., Allsman R.A., Axelrod T.S., et al., 1995, AJ 109, 1653\n\\bibitem[]{} Alcock C., Allsman R.A., Alves D.R., et al., 1999, AJ 117, 920\n\\bibitem[]{} Alibert Y., Baraffe I., Hauschildt P., Allard F., 1999,\nA\\&A 344, 551\n\\bibitem[]{} Andrievsky S.M., Kovtyukh V.V., Bersier D., et al.,\n%Luck R.E.,Gorka V.P., Yushchenko A.V., Usenko I.A., \n1998, A\\&A 329, 599\n\\bibitem[]{} Antonello E., Poretti E., Reduzzi L., 1990, A\\&A 236, 138\n\\bibitem[]{} Arenou F., Grenon M., Gomez A., 1992, A\\&A 258, 104\n\\bibitem[]{} Arenou F., Lindegren L., Froeschl\\'e, M., et al., \n%G\\'omez A.E., Turon C., Perryman M.A.C., Wielen R., \n1995, A\\&A 304, 52\n\\bibitem[]{} Bauer F., Afonso C., Albert J.N., \net al., 1999, A\\&A 348, 175\n\\bibitem[]{} Berdnikov L.N., Turner D.G., 1995, Pis'ma Astr. J. 21, 803\n\\bibitem[]{} Bono G., Caputo F., Castellani V., Marconi M., 1999, ApJ 512, 711\n\\bibitem[]{} Brown A.G.A., Arenou F., van Leeuwen F., Lindegren L.,\nLuri X., 1997, in: ``Hipparcos, Venice 1997'', Ed. B. Patrick,\nESA-SP 402, p. 63\n\\bibitem[]{} Caldwell J.A.R., Coulson I.M., 1986, MNRAS 218, 223\n\\bibitem[]{} Caldwell J.A.R., Coulson I.M., 1987, AJ 93, 1090\n\\bibitem[]{} Caldwell J.A.R., Laney C.D., 1991, in: ``IAU symposium\n148: The Magellanic Clouds'', Eds. Haynes R., Milne D., Kluwer, p. 249\n\\bibitem[]{} ESA, 1989, ``The Hipparcos Mission, volume {\\sc ii}: The Input\nCatalogue'', ESA SP-1111, Vol. {\\sc ii}\n\\bibitem[]{} ESA, 1997, ``The Hipparcos and Tycho Catalogues'', ESA SP-1200 \n\\bibitem[]{} Falin J.L., Mignard F., 1999, A\\&AS 135, 231\n\\bibitem[]{} Feast M.W., 1999, PASP 111, 775\n\\bibitem[]{} Feast M.W., Catchpole R.M., 1997, MNRAS 286, L1 (FC)\n\\bibitem[]{} Feast M.W., Whitelock P.A., 1997, MNRAS 291, 683 \n\\bibitem[]{} Fernie J.D., Beattie B., Evans N.R., Seager S., 1995,\nIBVS 4148 (F95)\n\\bibitem[]{} Gibson B.K., Stetson P.B., Freedman W.L., et al., astro-ph/9908149\n\\bibitem[]{} Gieren W.P., Fouqu\\'e P., G\\'omez M., 1998, ApJ 496, 17\n\\bibitem[]{} Groenewegen M.A.T, 1999, A\\&AS 139, 245 (G99)\n\\bibitem[]{} Kennicutt R.C., Stetson P.B., Saha A., et al., 1998, ApJ 498, 181\n\\bibitem[]{} Kochanek C.S., 1997, ApJ 491, 13\n\\bibitem[]{} Koen C., 1992, MNRAS 256, 65 \n\\bibitem[]{} Koen C., Laney D., 1998, MNRAS 301, 582\n\\bibitem[]{} Laney C.D., 1999, in: ``IAU symposium 192: The Stellar\nContent of the Local Group'', eds. P. Whitelock, R. Cannon, p. 459\n\\bibitem[]{} Laney C.D., 2000, in: ``IAU Coll. 176: The impact of\nlarge-scale surveys on variable star research'', ed. TBD, p. TBD\n\\bibitem[]{} Laney C.D., Stobie R.S., 1993, MNRAS 263, 921\n\\bibitem[]{} Laney C.D., Stobie R.S., 1994, MNRAS 266, 441\n\\bibitem[]{} Lanoix P., Paturel G., Garnier R., 1999, MNRAS 308, 969 (L99)\n\\bibitem[]{} Luri X., Torra J., Figueras F., et al., \n%G'omez A.E., Goupil M.J., Beaulieu, \n1999, in: ``Harmonizing Distance scales in a post-Hipparcos\nEra'', eds. D. Egret, A. Heck, ASP Conf. Ser. 167, p. 33\n\\bibitem[]{} Lutz T.E., Kelker D.H., 1973, PASP 85, 573 \n\\bibitem[]{} Madore B., Freedman W.L., 1991, PASP 103, 933\n\\bibitem[]{} Mantegazza L., Poretti E., 1992, A\\&A 261, 137\n\\bibitem[]{} Moffett T.J., Barnes T.G., 1984, ApJS 55, 389 \n\\bibitem[]{} Oudmaijer R.D., Groenewegen M.A.T., Schrijver H., 1998, MNRAS\n294, L41\n\\bibitem[]{} Oudmaijer R.D., Groenewegen M.A.T., Schrijver H., 1999,\nA\\&A 341, L55\n\\bibitem[]{} Pont F., 1999, in: ``Harmonizing Distance scales in a\npost-Hipparcos Era'', eds. D. Egret, A. Heck, ASP Conf. Ser. 167, p. 113\n\\bibitem[]{} Robichon N., Arenou F., Mermilliod J.-C., Turon C. 1999, \nA\\&A 345, 471\n\\bibitem[]{} Sachkov M.E., 1997, IBVS 4522\n\\bibitem[]{} Saio H., Gautschy A., 1998, ApJ 498, 360\n\\bibitem[]{} Sandage A., 1994, ApJ 430, 1\n\\bibitem[]{} Sandage A., Bell R.A., Tripicco M.J., 1999, ApJ 522, 250\n\\bibitem[]{} Sasselov D.D., Beauliau J.P., Renault C., \net al., 1997, A\\&A 324, 471\n\\bibitem[]{} Sekiguchi M., Fukugita M., 1998, Observatory 118, 73\n\\bibitem[]{} Smith H. Jr. 1987a, A\\&A 171, 336 \n\\bibitem[]{} Smith H. Jr. 1987b, A\\&A 171, 342 \n\\bibitem[]{} Smith H. Jr. 1987c, A\\&A 181, 391 \n\\bibitem[]{} Stobie R.S., Ishida K., Peacock J.A., 1989, MNRAS 238, 709\n\\bibitem[]{} Storm J., Carney B.W., Fry A.M., 1999, in: ``Harmonizing\nDistance scales in a post-Hipparcos Era'', eds. D. Egret, A. Heck,\nASP Conf. Ser. 167, p. 320\n\\bibitem[]{} Storm J., 2000, in: ``IAU Coll. 176: The impact of\nlarge-scale surveys on variable star research'', ed. TBD, p. TBD\n\\bibitem[]{} Tanvir N.R., 1999, in: ``Harmonizing Distance scales in a\npost-Hipparcos Era'', eds. D. Egret, A. Heck, ASP Conf. Ser. 167, p. 84\n\\bibitem[]{} Turon Lacarrieu C., Cr\\'ez\\'e M., 1977, A\\&A 56, 273\n\\bibitem[]{} Van Hoolst T., Waelkens C., 1995, A\\&A 295, 361\n\\bibitem[]{} Van Leeuwen F., 1997, Space Sci. Rev. 81, 208\n\n\\end{thebibliography}{}\n\n\\end{document}"
}
] |
[
{
"name": "astro-ph0002325.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[]{} Alcock C., Allsman R.A., Axelrod T.S., et al., 1995, AJ 109, 1653\n\\bibitem[]{} Alcock C., Allsman R.A., Alves D.R., et al., 1999, AJ 117, 920\n\\bibitem[]{} Alibert Y., Baraffe I., Hauschildt P., Allard F., 1999,\nA\\&A 344, 551\n\\bibitem[]{} Andrievsky S.M., Kovtyukh V.V., Bersier D., et al.,\n%Luck R.E.,Gorka V.P., Yushchenko A.V., Usenko I.A., \n1998, A\\&A 329, 599\n\\bibitem[]{} Antonello E., Poretti E., Reduzzi L., 1990, A\\&A 236, 138\n\\bibitem[]{} Arenou F., Grenon M., Gomez A., 1992, A\\&A 258, 104\n\\bibitem[]{} Arenou F., Lindegren L., Froeschl\\'e, M., et al., \n%G\\'omez A.E., Turon C., Perryman M.A.C., Wielen R., \n1995, A\\&A 304, 52\n\\bibitem[]{} Bauer F., Afonso C., Albert J.N., \net al., 1999, A\\&A 348, 175\n\\bibitem[]{} Berdnikov L.N., Turner D.G., 1995, Pis'ma Astr. J. 21, 803\n\\bibitem[]{} Bono G., Caputo F., Castellani V., Marconi M., 1999, ApJ 512, 711\n\\bibitem[]{} Brown A.G.A., Arenou F., van Leeuwen F., Lindegren L.,\nLuri X., 1997, in: ``Hipparcos, Venice 1997'', Ed. B. Patrick,\nESA-SP 402, p. 63\n\\bibitem[]{} Caldwell J.A.R., Coulson I.M., 1986, MNRAS 218, 223\n\\bibitem[]{} Caldwell J.A.R., Coulson I.M., 1987, AJ 93, 1090\n\\bibitem[]{} Caldwell J.A.R., Laney C.D., 1991, in: ``IAU symposium\n148: The Magellanic Clouds'', Eds. Haynes R., Milne D., Kluwer, p. 249\n\\bibitem[]{} ESA, 1989, ``The Hipparcos Mission, volume {\\sc ii}: The Input\nCatalogue'', ESA SP-1111, Vol. {\\sc ii}\n\\bibitem[]{} ESA, 1997, ``The Hipparcos and Tycho Catalogues'', ESA SP-1200 \n\\bibitem[]{} Falin J.L., Mignard F., 1999, A\\&AS 135, 231\n\\bibitem[]{} Feast M.W., 1999, PASP 111, 775\n\\bibitem[]{} Feast M.W., Catchpole R.M., 1997, MNRAS 286, L1 (FC)\n\\bibitem[]{} Feast M.W., Whitelock P.A., 1997, MNRAS 291, 683 \n\\bibitem[]{} Fernie J.D., Beattie B., Evans N.R., Seager S., 1995,\nIBVS 4148 (F95)\n\\bibitem[]{} Gibson B.K., Stetson P.B., Freedman W.L., et al., astro-ph/9908149\n\\bibitem[]{} Gieren W.P., Fouqu\\'e P., G\\'omez M., 1998, ApJ 496, 17\n\\bibitem[]{} Groenewegen M.A.T, 1999, A\\&AS 139, 245 (G99)\n\\bibitem[]{} Kennicutt R.C., Stetson P.B., Saha A., et al., 1998, ApJ 498, 181\n\\bibitem[]{} Kochanek C.S., 1997, ApJ 491, 13\n\\bibitem[]{} Koen C., 1992, MNRAS 256, 65 \n\\bibitem[]{} Koen C., Laney D., 1998, MNRAS 301, 582\n\\bibitem[]{} Laney C.D., 1999, in: ``IAU symposium 192: The Stellar\nContent of the Local Group'', eds. P. Whitelock, R. Cannon, p. 459\n\\bibitem[]{} Laney C.D., 2000, in: ``IAU Coll. 176: The impact of\nlarge-scale surveys on variable star research'', ed. TBD, p. TBD\n\\bibitem[]{} Laney C.D., Stobie R.S., 1993, MNRAS 263, 921\n\\bibitem[]{} Laney C.D., Stobie R.S., 1994, MNRAS 266, 441\n\\bibitem[]{} Lanoix P., Paturel G., Garnier R., 1999, MNRAS 308, 969 (L99)\n\\bibitem[]{} Luri X., Torra J., Figueras F., et al., \n%G'omez A.E., Goupil M.J., Beaulieu, \n1999, in: ``Harmonizing Distance scales in a post-Hipparcos\nEra'', eds. D. Egret, A. Heck, ASP Conf. Ser. 167, p. 33\n\\bibitem[]{} Lutz T.E., Kelker D.H., 1973, PASP 85, 573 \n\\bibitem[]{} Madore B., Freedman W.L., 1991, PASP 103, 933\n\\bibitem[]{} Mantegazza L., Poretti E., 1992, A\\&A 261, 137\n\\bibitem[]{} Moffett T.J., Barnes T.G., 1984, ApJS 55, 389 \n\\bibitem[]{} Oudmaijer R.D., Groenewegen M.A.T., Schrijver H., 1998, MNRAS\n294, L41\n\\bibitem[]{} Oudmaijer R.D., Groenewegen M.A.T., Schrijver H., 1999,\nA\\&A 341, L55\n\\bibitem[]{} Pont F., 1999, in: ``Harmonizing Distance scales in a\npost-Hipparcos Era'', eds. D. Egret, A. Heck, ASP Conf. Ser. 167, p. 113\n\\bibitem[]{} Robichon N., Arenou F., Mermilliod J.-C., Turon C. 1999, \nA\\&A 345, 471\n\\bibitem[]{} Sachkov M.E., 1997, IBVS 4522\n\\bibitem[]{} Saio H., Gautschy A., 1998, ApJ 498, 360\n\\bibitem[]{} Sandage A., 1994, ApJ 430, 1\n\\bibitem[]{} Sandage A., Bell R.A., Tripicco M.J., 1999, ApJ 522, 250\n\\bibitem[]{} Sasselov D.D., Beauliau J.P., Renault C., \net al., 1997, A\\&A 324, 471\n\\bibitem[]{} Sekiguchi M., Fukugita M., 1998, Observatory 118, 73\n\\bibitem[]{} Smith H. Jr. 1987a, A\\&A 171, 336 \n\\bibitem[]{} Smith H. Jr. 1987b, A\\&A 171, 342 \n\\bibitem[]{} Smith H. Jr. 1987c, A\\&A 181, 391 \n\\bibitem[]{} Stobie R.S., Ishida K., Peacock J.A., 1989, MNRAS 238, 709\n\\bibitem[]{} Storm J., Carney B.W., Fry A.M., 1999, in: ``Harmonizing\nDistance scales in a post-Hipparcos Era'', eds. D. Egret, A. Heck,\nASP Conf. Ser. 167, p. 320\n\\bibitem[]{} Storm J., 2000, in: ``IAU Coll. 176: The impact of\nlarge-scale surveys on variable star research'', ed. TBD, p. TBD\n\\bibitem[]{} Tanvir N.R., 1999, in: ``Harmonizing Distance scales in a\npost-Hipparcos Era'', eds. D. Egret, A. Heck, ASP Conf. Ser. 167, p. 84\n\\bibitem[]{} Turon Lacarrieu C., Cr\\'ez\\'e M., 1977, A\\&A 56, 273\n\\bibitem[]{} Van Hoolst T., Waelkens C., 1995, A\\&A 295, 361\n\\bibitem[]{} Van Leeuwen F., 1997, Space Sci. Rev. 81, 208\n\n\\end{thebibliography}"
}
] |
astro-ph0002326
|
Study of Multi-muon Events from EAS with the L3 Detector at Shallow Depth Underground
|
[] |
%
|
[
{
"name": "taup99_proc_astroph.tex",
"string": "\\documentstyle[twoside,fleqn,espcrc2,graphicx,here]{article}\n\n% put your own definitions here:\n% \\newcommand{\\cZ}{\\cal{Z}}\n% \\newtheorem{def}{Definition}[section]\n% ...\n\\newcommand{\\ttbs}{\\char'134}\n\\newcommand{\\AmS}{{\\protect\\the\\textfont2\n A\\kern-.1667em\\lower.5ex\\hbox{M}\\kern-.125emS}}\n\\newcommand {\\Figref}[1]{Figure~\\ref{fig:#1}}\n\n% add words to TeX's hyphenation exception list\n\\hyphenation{author another created financial paper re-commend-ed}\n\n% declarations for front matter\n\\title{Study of Multi-muon Events from EAS with the L3 Detector\n at Shallow Depth Underground}\n\n\\author{D. Bourilkov\n \\address{Institute for Particle Physics (IPP), ETH Z\\\"urich,\n CH-8093 Z\\\"urich, Switzerland}%\n \\thanks{\\tt \\mbox{e-mail: Dimitri.Bourilkov@cern.ch}}\n (for the L3+C Collaboration)}\n \n\\begin{document}\n\\begin{titlepage}\n%\n\\begin{flushright} \n{\\large\nastro-ph/0002326 \\\\\n% ETHZ-IPP PR-00-xx \\\\\n% hep-ex/9806027 \\\\\nFebruary 16, 2000\n}\n\\end{flushright}\n\n\\vspace*{3.0cm}\n\n\\begin{center} {\\Large \\bf\n Study of Multi-muon Events from EAS with the L3 Detector\\\\\n\\vspace*{0.15cm}\n at Shallow Depth Underground}\n\n\\vspace*{2.0cm}\n {\\Large\n Dimitri Bourilkov\\footnote{\\tt e-mail: Dimitri.Bourilkov@cern.ch}\n (for the L3+C Collaboration)}\n\n\\vspace*{1.0cm}\n{\\large\n Institute for Particle Physics (IPP), ETH Z\\\"urich, \\\\\n CH-8093 Z\\\"urich, Switzerland\n}\n\n\\vspace*{1.0cm}\n{\\Large\nPresented at the 6th International Workshop on\\\\\n\\vspace*{0.11cm}\nTopics in Astroparticle and Underground Physics\\\\\n\\vspace*{0.24cm}\nTAUP99, September 6-10, 1999, Paris, France\n}\n\\vspace*{3.3cm}\n\\end{center}\n\n%\\date{June 4, 1999}\n%\\maketitle\n% \n%\n% The abstract\n%\n%\\begin{abstract}\n%\\end{abstract}\n\n\n\\vspace*{1.0cm}\n\n\\end{titlepage}\n\\clearpage\n\\renewcommand{\\thefootnote}{\\arabic{footnote}}\n\\setcounter{footnote}{0}\n\n\\begin{abstract}\nWe present first preliminary data from the L3+Cosmics\nexperiment and results from Monte Carlo simulations of multi-muon events\nas observed 30 m underground.\n\\end{abstract}\n\n% typeset front matter (including abstract)\n\\maketitle\n\n\\section{THE L3+COSMICS EXPERIMENT}\nThe muon component of extensive air showers (EAS), due to the long muon range\nin the Earth's atmosphere, carries a wealth of information about the\nshower development. Study of multi-muon events gives an insight into the\nprimary cosmic ray composition and the physics of high energy hadronic\ninteractions.\nThe L3 detector, situated 30 m underground, offers\ninteresting possibilities to detect and study such\nevents~\\cite{PL97}, which are\ncomplementary to the data collected in traditional cosmic ray\nexperiments.\nThe hadron component of EAS is absorbed, while the muon component is\ndetected with low threshold (typically, if we exclude access shafts,\n15 GeV) and high momentum and spatial resolution by the sophisticated\ntracking system of the L3 detector. The muon spectrum can be measured\nup to 2 TeV with high precision. The multi-muon event rate is high enough\nto make studies of the knee region possible with one year of data taking.\n\nThis year, 5 billion triggers were collected with the full L3+Cosmics\nsetup. The independent readout and data acquisition system allows us\nto take data in parallel with L3. The acceptance of the setup is\n200~$\\rm m^2 sr$. The angular resolution is better than 3.5 mrad for\nmuons above 100 GeV and zenith angles from 0 to $\\rm 50^{\\circ}$.\nThe momentum resolution is 5.0 \\% at\n45 GeV. It is calibrated with $\\rm Z \\rightarrow \\mu^+\\mu^-$ events from\nthe LEP calibration runs, where the muon momentum is known exactly.\n\n\\section{MONTE CARLO SIMULATIONS}\nThe simulation program ARROW~\\cite{DB91,DB99} is used to calculate the\nhadron, muon and neutrino flux at the detector level. The method\ncombines simulations for fixed energies and different primary nuclei\nwith a parametrization of the energy dependence and allows to do\nfast calculations for different geometries and energy thresholds.\nResults for the L3+C setup with sensitive area 200~$\\rm m^2 sr$\n\\begin{figure}[htb]\n%\\vspace{-9pt}\n%\\resizebox{8.1cm}{6.3cm}{\\includegraphics*[1.5cm,2.0cm][15cm,10cm]{nmu-week-int-300-two-proc.eps}}\n\\vspace{-0.3cm}\n\\resizebox{8.1cm}{6.8cm}{\\includegraphics*[1.5cm,2.0cm][15cm,10cm]{nmu-week-int-300-two-proc.eps}}\n\\caption{Integrated $\\mu$ multiplicity - number of expected events with\n $\\rm N(>N_{\\mu})$ for a week of data taking.\n Lower curve - protons,\n middle curve - iron S,\n upper curve - iron H (see text).\n The predicted rate agrees well with the experimental one.}\n\\label{fig:nmu2}\n\\end{figure}\nare shown in~\\Figref{nmu2}.\n%\n\\begin{figure*}[htb]\n\\vspace{9pt}\n\\resizebox{\\textwidth}{11cm}{\\includegraphics*[1.0cm,6.5cm][21cm,24cm]{l3cprel99-1.ps}}\n\\caption{Preliminary data from the 1999 run. No corrections for acceptance\nor efficiency are applied.}\n\\label{fig:l3c}\n\\end{figure*}\nThe primary composition is divided in heavy (Fe) and\nlight (p) components in two limiting hypotheses:\nFe S for constant heavy contribution $\\rm \\sim 30$\\% and\nFe H for heavy contribution rising from 30\\% below to 70\\%\nabove the knee. The events with up to 6 muons are dominated by\nproton induced showers and above 10 muons the iron takes over.\nTo distinguish between the two hypotheses with this method\nwe need to detect events with $\\sim 50$ muons and more.\n% or to analyze simultaneously the muon momentum measurements.\n\n\\section{DATA AND OUTLOOK}\nA first small subset of our data is shown in~\\Figref{l3c}.\nOnly part of the events with up to 6 muons are reconstructed currently.\nThe observed charge ratio $\\mu^+/\\mu^-$ from the raw data\nis flat in the region between 50 and 500 GeV.\n% according to the chosen large binning\n\nIn the year 2000 an EAS array will be mounted above L3+C in order\nto detect the primary energy and core position. \nThe experimental program includes studies of \nmuon families and the primary composition,\nsidereal anisotropies,\nhigh multiplicity events in coincidences with other experiments,\nthe moon shadow,\nsearches for point sources,\ngamma ray bursts\n% for solar flares\nand exotic events.\n\n\\vspace{-0.4cm}\n\\begin{thebibliography}{9}\n\\bibitem{PL97} P.~Le Coultre et al., ICRC Durban, 1997.\n\\bibitem{DB91} D.~Bourilkov, S.~Petrov and H.~Vankov, Jour. of Physics G, 17 (1991)1925.\n\\bibitem{DB99} D.~Bourilkov, astro-ph/9907078.\n\\end{thebibliography}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002326.extracted_bib",
"string": "\\begin{thebibliography}{9}\n\\bibitem{PL97} P.~Le Coultre et al., ICRC Durban, 1997.\n\\bibitem{DB91} D.~Bourilkov, S.~Petrov and H.~Vankov, Jour. of Physics G, 17 (1991)1925.\n\\bibitem{DB99} D.~Bourilkov, astro-ph/9907078.\n\\end{thebibliography}"
}
] |
astro-ph0002327
|
The 35-Day Evolution of the Hercules X-1 Pulse Profile:\\ Evidence For A Resolved Inner Disk Occultation of the Neutron Star
|
[
{
"author": "D. Matthew Scott \\altaffilmark{1,2}"
},
{
"author": "Denis A. Leahy \\altaffilmark{3}"
},
{
"author": "Robert B. Wilson \\altaffilmark{2}"
}
] |
{Ginga} and Rossi X-ray Timing Explorer (RXTE) observations have allowed an unprecedented view of the recurrent systematic pulse shape changes associated with the 35-day cycle of Hercules X-1, a phenomenon currently unique among the known accretion-powered pulsars. We present observations of the pulse shape evolution. An explanation for the pulse evolution in terms of a freely precessing neutron star is reviewed and shown to have several major difficulties in explaining the observed pulse evolution pattern. Instead, we propose a phenomenological model for the pulse evolution based upon an occultation of the pulse emitting region by the tilted, inner edge of a precessing accretion disk. The systematic and repeating pulse shape changes require a {resolved} occultation of the pulse emission region. The observed pulse profile motivates the need for a pulsar beam consisting of a composite coaxial pencil and fan beam but the observed evolution pattern requires the fan beam to be focused around the neutron star and beamed in the antipodal direction. The spectral hardness of the pencil beam component suggests an origin at the magnetic polar cap, with the relatively softer fan beam emission produced by backscattering from within the accretion column, qualitatively consistent with several theoretical models for X-ray emission from the accretion column of an accreting neutron star.
|
[
{
"name": "ms.tex",
"string": "%\n% Revised version of ApJ ms#50709 \n%\n%% Preamble\n%\n% Command Definitions\n%\n\\renewcommand{\\deg}{^\\circ}\n\\newcommand{\\Msun}{{\\rm M}_\\odot}\n\n%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[11pt,aaspp4]{article}\n\n%%% Body of document\n\\begin{document}\n\\title{The 35-Day Evolution of the Hercules X-1 Pulse Profile:\\\\\nEvidence For A Resolved Inner Disk Occultation of the Neutron Star}\n\n\\author{D. Matthew Scott \\altaffilmark{1,2}, Denis A. Leahy \\altaffilmark{3}, \nRobert B. Wilson \\altaffilmark{2}} \n \n\\altaffiltext{1}{Universities Space Research Association}\n\\altaffiltext{2}{Space Science Directorate, SD-50, NASA/Marshall Space Flight\nCenter, Huntsville, AL 35812}\n\\altaffiltext{3}{Dept. of Physics, University of Calgary,\nCalgary, Alberta, Canada T2N 1N4} \n\\authoremail{scott@gibson.msfc.nasa.gov,wilson@gibson.msfc.nasa.gov,\nleahy@iras.ucalgary.ca}\n\n\\begin{abstract}\n{\\it Ginga} and Rossi X-ray Timing Explorer (RXTE) observations have allowed \nan unprecedented view of the recurrent systematic pulse shape changes \nassociated with the 35-day cycle of Hercules X-1, a phenomenon currently unique \namong the known accretion-powered pulsars. We present observations of the \npulse shape evolution. An explanation for the pulse evolution \nin terms of a freely precessing neutron star is reviewed and shown to have \nseveral major difficulties in explaining the observed pulse evolution pattern. \nInstead, we propose a phenomenological model for the pulse evolution based upon \nan occultation of the pulse emitting region by the tilted, inner edge of a \nprecessing accretion disk. The systematic and repeating pulse shape changes \nrequire a {\\it resolved} occultation of the pulse emission region. \nThe observed pulse profile motivates the need for a pulsar beam consisting of \na composite coaxial pencil and fan beam but the observed evolution pattern \nrequires the fan beam to be focused around the neutron star and beamed in the \nantipodal direction. The spectral hardness of the pencil beam component \nsuggests an origin at the magnetic polar cap, with the relatively softer fan \nbeam emission produced by backscattering from within the accretion column, \nqualitatively consistent with several theoretical models for X-ray emission \nfrom the accretion column of an accreting neutron star. \n\\end{abstract}\n\n\\keywords{pulsars: individual(Her X-1) --- X-rays: stars}\n\n\\section{Introduction}\nHer X-1 is a 1.24 second period accretion-powered X-ray pulsar in a \n1.7 day circular orbit with a normal stellar companion, HZ Her. In addition \nto these basic periodicities this binary system has long been known to \ndisplay an unusual 35-day long cycle of High and Low X-ray flux states. \nWithin a single 35-day cycle are found a Main High and Short High X-ray\nflux state lasting roughly ten and five days each respectively and separated\nby ten day long Low states (see e.g. Scott \\& Leahy 1999). Pulsations are \ndetected during the High states but cease during the intervening Low states. \nThe High states are punctuated by deep X-ray eclipses every 1.7 days \nindicating a line-of-sight close to the binary plane. \n\nA phenomenon currently known to exist only in Her X-1 is a repeating,\nsystematic evolution of the pulse profile that occurs during the 35-day \ncycle. Observations with the Large Area Counters \non {\\it Ginga} and the Proportional Counter Array (PCA) on RXTE have allowed \nan unprecedented view of the evolution of the pulse profile in shape and \nenergy spectrum across both the Main and the Short High states. The \n{\\it Ginga} observations cover the energy \nrange 1-37 keV and sample five Main and two Short High states. They\nare described in detail in Deeter et al. (1991), Scott (1993) and \nDeeter et al. (1998). The bulk of the data consists of a Main-Short-Main High\nstate sequence in April-May-June of 1989. Lightcurves and softness ratios for \nthe 1988 and 1989 observations as well as some pulse profiles can be found in \nLeahy (1995a). The RXTE observations cover a consecutive Main and Short High \nstate in September-October of 1996 and a Short-Main-Short High state sequence \nin September-October 1997. The 1996 Observations with the PCA in the range \n2-60 keV are presented in Scott et al. (1997a). \n\nIn this paper, we present a simple phenomenological model for the pulse \nevolution based upon the occultation of the central X-ray source by the inner \nedge of a tilted, precessing, accretion disk. This choice is motivated by the \nobserved association of pulse shape changes with {\\it decreases} in overall \nX-ray flux near the end of the Main High state (see Scott 1993; Scott et al. \n1997a; Deeter et al. 1998; Joss et al. 1978 and Soong et al. 1990a) and the \nwell known ability of a tilted, twisted, counter-precessing accretion disk to \nphenomenologically account for much of the complex 35-day optical and X-ray \nbehavior displayed by the Her X-1/HZ Her system (Petterson 1975; \nPetterson 1977; Gerend \\& Boynton 1976; Crosa \\& Boynton 1980; \nBoynton, Crosa \\& Deeter 1980; Middleditch 1983). \nWe stress that most of the observed 35-day behavior has been associated with \nthe {\\it outer} portion of the accretion disk whereas we will demonstrate that\nthe pulse evolution must be an {\\it inner} disk phenomenon.\n\nPrevious attempts to model the pulse shape evolution have relied on a\ncombination of neutron star free precession and obscuration by the accretion \ndisk (Tr\\\"umper et. al. 1986; Kahabka 1987, 1989), obscuration \nby ``flaps'' of matter at the juncture of the accretion disk and pulsar \nmagnetosphere (Petterson et al. 1991) and obscuration of the pulsar by a \ntilted precessing disk (Bai 1981; Averitsev et al. 1992). None of these \nprevious models attempted to explain more than a few aspects of the pulse \nevolution. The model presented here refines the disk and pulsar beam geometry \nto qualitatively account for the observed pulse shape and its evolution during \nboth the Main and Short High states.\n\nA discussion of relevant aspects of the tilted, twisted, \ncounter-precessing disk is presented in section 2. A \nsummary of the main features observed in the pulse evolution during the\n35-day cycle is presented in section 3. Section 4 discusses the absolute pulse \nphase alignment of the Main and Short High state pulses. Section 5 discusses \nthe pulse evolution as a consequence of \nneutron free precession. Section 6 briefly discusses pulse evolution as\na consequence of changing mass accretion patterns onto the neutron star.\nSection 7 presents a pulse evolution model based \non an inner disk occultation and a simple X-ray beam configuration. In \nsection 8 we discuss some implications of this inner disk occultation \ninterpretation.\n\n\\section{A tilted, twisted and counter-precessing disk in Her X-1}\n \nHer X-1 exhibits a rich variety of phenomena that appear to be well\nexplained by an accretion disk that is tilted, counter-precessing and \ntwisted. We review some of the observational arguments for such a disk \n(see Priedhorsky \\& Holt 1987 for an earlier review) \nand include some relevant new observations and interpretation. The occurrence \nof two distinct X-ray High states within the 35-day cycle has \nlong been known. The Main High state was found soon after the discovery of \nHer X-1 (\\cite{gia73}). The dimmer Short High state was first recognized \nin Copernicus observations (Fabian et al. 1973) and later in {\\it Ariel 5} \nand {\\it Uhuru} observations (Cooke \\& Page 1975; Jones \\& Forman 1976). \nFew extensive observations of the Short High state were made until\n1989 with {\\it Ginga} (Deeter et al. 1998). In figure 1 we show the 1-37 keV \nlightcurve obtained with {\\it Ginga} in 1989 and for the August 1991 Main High \nstate. The August 1991 observation caught a turn-on to the Main High state \nwhich is confirmed by simultaneous monitoring at lower sensitivity with the \nBurst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray \nObservatory (CGRO). The regularity of occurrence of the Short High state\nten days after the end of the Main High state is now clearly demonstrated by\nthe ongoing monitoring of Her X-1 with the RXTE All Sky Monitor (ASM) \n(see figure 1; Scott \\& Leahy 1999; and Shakura et al. 1999).\n\nThe companion star HZ Her is strongly heated by X-rays emanating from the \nneutron star and shows little variation in total magnitude, averaged over an\norbital cycle, throughout the 35-day cycle (Gerend \\& Boynton 1976, \nDeeter et al. 1976). Optical pulsations produced by reprocessing of the \nprimary X-ray flux have been observed during both the High and Low states \n(Middleditch \\& Nelson 1976, Middleditch 1983). These observations show that \ntotal X-ray production at the neutron star is relatively constant, eliminating\ngross periodic changes in accretion rate as the cause of the High-Low cycle. \nThe strongest evidence for a tilted, counter-precessing disk in\nHer X-1 comes from the complex set of systematic changes in the optical\norbital photometric light curve over the 35-day cycle that can be explained\nby a combination of disk emission and disk shadowing/occultation of the\nheated face of HZ Her (Gerend \\& Boynton 1976).\n\nThe occurrence of two distinct X-ray High states within the 35-day cycle has \nbeen attributed to obscuration of the central X-ray source by a \ntilted, twisted, counter-precessing accretion disk (Petterson 1975; \nPetterson 1977). \nSuch a disk geometry can be idealized as a set of tilted, concentric rings\nin which the azimuth of the line-of-nodes of each successively smaller\nring shifts smoothly as one moves radially inwards (Petterson 1977).\nThe presence of {\\it two} High states per 35-day cycle is naturally explained \nwhen the observer's line-of-sight lies close to the binary plane. \nThe appearance of pulsations with significant cold matter absorption at\nthe onset of either High state (hereafter turn-on), is interpreted as the \nemergence of the pulsar from behind the tilted, outer rim of the accretion \ndisk. The flux decline observed at the end of each High state shows little to\nno absorption effects and begins as the line-of-sight to the pulsar is \napproached by the hot, tilted {\\it inner} edge of the precessing accretion \ndisk. This behavior is illustrated in figure 2 and compared to a succession \nof High states observed with {\\it Ginga} in 1989 and with an averaged 35-day\nlightcurve observed with the ASM on RXTE.\n\nThe direction of disk precession is apparently retrograde or\n``counter-precessing''. The evidence for this comes from X-ray and optical\nobservations and theoretical considerations. X-ray absorption dips are \nobserved in the Main High state just before eclipse that march toward earlier \norbital phase as the High state progresses and at a frequency near but slightly \nlower than the sum of the orbital and 35-day frequencies (Crosa \\& Boynton \n1980, Scott \\& Leahy 1999). The optical lightcurve of HZ Her exihibits a \nsystematic pattern of changes and a harmonic decomposition revealed that \nnearly all power is confined to a discrete set of frequencies composed of sums \nof the orbital and 35-day frequencies (Deeter et al. 1976). A uniformly \ncounter-precessing disk will repeat the same disk-star orientation at the sum \nof the orbital and 35-day frequencies as will any phenomena dependent on the \norientation. Prograde precession should cause phenomena to repeat at the \ndifference of the orbital and 35-day frequencies but no such phenomena are \nobserved. Theoretically, a tilted disk should also precess in a retrograde \nfashion (Katz 1973). \n\n\\subsection{The outer disk and early High state behavior} \n\nX-ray pulsations appear during the flux rise at the start of the High \nstates (i.e. the turn-on) accompanied by cold matter absorption in the X-ray \nspectrum (e.g. Parmar, Sanford \\& Fabian 1980). \nThe only Short High state turn-on that has been well observed \nto date is the May 1989 Short High state which is compared in figure 3\nto the August 1991 Main High state turn-on. \nThe turn-on's are nearly identical in form and both \nshow an increase in softness ratio characteristic of cold matter absorption. \nThe turn-on's are modeled in figure 3 by an X-ray point source emerging \nthrough an atmosphere with a gaussian density profile lying above the plane \nof a tilted, precessing disk. The disk angular velocity is $2\\pi/34.85$ \n$\\rm day^{-1}$, the scale height is $1/24$ the disk radius and the disk is \ntilted at $20\\deg$ with respect to the orbital plane of Her X-1. The optical \ndepth at the base of the disk atmosphere is 30. \nThe disk model is described in more detail in section 7. The two turn-on's \nlast about 3 hours in contrast to the eclipse egress which lasts only a few \nminutes (e.g. Leahy 1995b). The pulse profile exhibits no significant changes \nduring the turn-on but merely increases in flux in different energy bands\n(Deeter et al. 1998). The X-ray observations coupled with the optical \nobservations imply that the primary cause of the High-Low flux cycle is \nobscuration. \n\nThe flux after the beginning of the Main High state often shows a gradual \nincrease by 20-50\\% over the next 1-4 days. \nThe pulse profile is relatively constant in shape during this period. We\npropose that the X-ray flux rise is the result of viewing the neutron star \nthrough a hot dense lower corona lying just above the outer accretion disk \nsurface. As the elevation of the observer's line-of-sight increases \nwith respect to the nominal outer \ndisk plane the amount of obscuration will decrease. This effect should also be \npresent in the Short High state and in the system LMC X-4 where a tilted \nprecessing disk is also postulated to occur \n(Lang et al. 1981). The existence of another \nmuch larger and lower density scattering corona is indicated by the existence \nof Low state flux at 5\\% of the peak Main High state flux (e.g. Choi et al.\n1997; Mihara et al. 1991). A two layer disk corona has been discussed \ntheoretically by Schandl \\& Meyer (1994). The lower corona has a temperature \nof $10^6$ K while the upper corona has a temperature of $10^{7.5}$ K. The \nobserved $\\sim50\\% $ flux increase implies a column density of \n$1 \\times 10^{24}$ $\\rm cm^{-2}$ at the base of the lower corona for pure \nThompson scattering. From figure 2, the duration of the flux increase implies \na vertical angular thickness to the lower corona of $\\approx 4\\deg - 14\\deg$ \nwith respect to the nominal outer disk plane. \n\n\\subsection{The inner disk and late High state behavior} \n\nIf pure obscuration by a precessing, tilted, thin, and {\\it planar} disk \nwere the cause of the High-Low flux cycle then one might expect to \nobserve: 1) rapid flux cutoffs at the ends of the High states equivalent to\nthe High state turn-on's 2) identical pulse profiles during the Main and \nShort High states and 3) nearly identical fluxes during the Main and Short\nHigh states except for variations caused by geometric differences in coronal \nobscuration.\nIn contrast, both types of High state show gradual flux declines that last \nseveral days and without significant absorption effects. A tilted and \n{\\it twisted} disk can explain the gradual flux decline if the disk is twisted \nin the direction of precession such that the azimuthal angle between the outer \nand inner disk line of nodes is $>90\\deg$. In a tilted and twisted disk the \nline-of-nodes and tilt of individual contiguous disk rings varies smoothly\nas one moves from the outer to inner disk radii. The hot, inner region of\nthe disk gradually covers the X-ray emitting region during a transition\nto a Low state. We illustrate this type of disk model in figure 2 and compare \nit to the lightcurve observed with {\\it Ginga} and an average lightcurve from \nthe RXTE/ASM. A tilt of $\\theta_{tilt,outer}=20\\deg$ for the outermost ring \nis determined from the assumption of an observer elevation of \n$\\alpha_{obs} = 5\\deg$ and the observed 35-day phase separation of \n$\\Delta \\psi \\sim 0.58$ for the Main and Short High state turn-on's\n\\footnote{$\\theta_{tilt,outer} = \\frac{\\alpha_{obs}}\n{\\sin (\\pi (\\Delta \\psi - 0.5))}$}. The required \nouter disk tilt is independent of the outer disk thickness.\nWe note that the geometry of the disk model proposed in Schandl \\& Meyer \n(1994) is inconsistent with the observations since it predicts\ncold matter absorption at the start of the Main High state with a gradual flux\ndecline caused by a covering up of the neutron star by an inner disk corona \nand the same events, but in {\\it opposite} sequence, during the Short High \nstate (e.g. see their figure 12). However, the same sequence of events is \nobserved in both the Main and Short High states.\n\nThe overall spectral changes during the Main High state were further \nexplored by comparing the 20-50 keV pulsed flux average Main High state \nlightcurve observed with BATSE with a 2-12 keV flux average Main High\nstate observed with RXTE/ASM. Following the procedure described in Scott\n\\& Leahy (1999), the BATSE pulsed flux light curve over\nthe timespan MJD 49933 to MJD 50507, obtained from folded-on-board data \n(see Bildsten et al. 1997), was sorted into orbital phase ``0.2'' turn-on\nMain High states or ``0.7'' orbital phase turn-on's and averaged. Seven Main \nHigh states were used to construct the average 0.2 turn-on Main High state \nlightcurve and eight for the average 0.7 turn-on Main High state. Likewise, \nfor the 2-12 keV RXTE/ASM a similar sorting and folding was done to construct \naverage light curves for the timespan MJD 50146 to MJD 50947 with 12 and \n10 Main High states averaged to form, respectively, the average 0.2 turn-on \nand 0.7 turn-on Main High state lightcurves. During the flux decline at the \nend of the Main High state, the 20-50 keV pulsed flux dropped to the \nlevel of the background flux more than one day preceding a similar drop in \nthe 2-12 keV flux in both turn-on type Main High states. In figure 4 we \ncompare the softness ratio formed by the two lightcurves. The turn-on at \n35-day phase 0.0 shows a rapid increase in softness ratio consistent with \ndecreasing absorption. The pre-eclipse dips also show up as decreased softness \nconsistent with absorption. However, the softness ratio shows a large \n{\\it increase} during the flux decline near the end of the Main High state \nfollowed by a large decline. The softness ratio increase is incompatible with \neither absorption or an energy independent Thomson scattering of an unresolved \npoint source by a corona or disk atmosphere (as in the Schandl \\& Meyer 1994 \nmodel) as the sole cause of the flux decline. Therefore the flux decline at \nthe end of the Main High state cannot be the result of an occultation of a \n{\\it point} source by either a cold or a hot disk edge. \n\nThe peak Short High state X-ray flux is only 30\\% that of the peak Main High \nstate flux and exhibits a quite different pulse profile. Dramatic changes in \nthe pulse profile are observed during the last few days of the \nMain High state and throughout the Short High state (see Deeter et al. 1998 \nand next section). If an obscuring region causes the gradual flux decline \nand the density scale height was much larger than the linear size of the \npulse emitting region then minimal pulse shape changes would be observed\nas well as little difference in pulse profile between the Main and Short High \nstates. \n\nTwo possible explanations for the High state flux declines, pulse shape \nevolution and the low Short High state flux are 1) Systematic changes in the \nX-ray beaming direction are occurring in addition to those caused by neutron \nstar rotation and/or 2) The scale height of a precessing obscuring inner disk \nregion is indeed comparable in size to the pulse emitting region. If \nexplanation 1) is correct then we are observing a combination of an\nobscuration of a point source causing the flux declines and beaming changes\nthat cause both pulse shape changes and the Main and Short High state flux\ndifference. This possibility has been advocated by \nTr\\\"umper et al. (1986) and Kahabka (1989) using beam changes caused by free \nprecession of the neutron star coupled with obscuration by a precessing disk. \nIn 2) the flux declines, the Main and Short High state flux and pulse shape \ndifferences and the pulse shape changes are caused purely by progressive \ndisk occultation of an extended source.\nWe will discuss both these explanations in more detail after reviewing the \nphenomenology of the pulse evolution and phase alignment of the Main and Short \nHigh state pulses.\n\n\\section{Phenomenology of the pulse evolution in Her X-1}\n\nWe now review the salient features of the pulse profiles and their evolution \npresented in figures 5 and 6 and documented in Scott (1993) and Deeter et al. \n(1998). The early 1-37 keV Main High state pulse profile consists of a large \nmain pulse and a smaller interpulse superposed on an underlying weakly pulsed \ncomponent (see figure 5 for profiles and nomenclature of specific pulse \nfeatures). The main pulse consists of two unequal shoulders (or peaks) at \nenergies below 5 keV, but at higher energies a third central peak appears that \ngrows with energy and dominates the main pulse profile above $\\sim 20$ keV. \nThese energy dependent features of the pulse are well known (see e.g. \nSoong et al. 1990b).\nWe display a subset of the {\\it Ginga} observations in figure 6 showing the\nevolution of the pulse profile during the Main and Short High states displayed \nin figure 1. \nFrom {\\it Ginga} and other observations, we propose that the Main \nHigh state pulse profile evolution consists of three basic events listed in \norder of decreasing duration: \n1) A deepening and widening of a ``gap'' in the underlying component near the \npulse phase of the {\\it preinterpulse minima} \nthat begins early in the Main High state and continues until the \nend (i.e. pulse phase $\\sim0.3$ in figure 6, top panels). This phenomenon can \nalso be observed in {\\it Uhuru} and {\\it HEAO 1} pulse profiles \n(Joss et al. 1978; Soong et al. 1990a) and in recent RXTE observations \n(Scott et al. 1997a). The well known quasi-sinusoidal pulse profile that \n``appears'' near the end of Main High state may simply be the uncovering of \nthis already present gap due to the disappearance of the overlying main pulse. \nThe quasi-sinusoidal profile is the last pulsed feature to disappear before the \nHigh states end.\n2) The disappearance of the {\\it leading} and then the {\\it trailing shoulder}\nof the main pulse over a roughly two day period that starts six to seven days \nafter the Main High state turn-on. The main pulse shows relatively little\nchange before this point. The disappearance of the leading shoulder of the\nmain pulse near the end of the Main High state has been noted many\ntimes previously (e.g. Soong et al. 1990a; Joss et al. 1978; Kahabka 1989;\nSheffer et al. 1992; Scott 1993; Scott et al. 1997a; Deeter et al. 1998).\n3) A rapid decay and disappearance of the spectrally {\\it hard central peak} \nof the main pulse was observed with {\\it Ginga} over an $\\sim12$ hour period \nthat took place within the time span of the shoulder decay. A similar rapid\ndecay of the main pulse was observed by {\\it HEAO 1} but at lower resolution \n(Soong et al. 1990a).\nIn the context of the occultation model described below, this \npulse shape evolution pattern suggests the presence, respectively, \nof three pulse emitting regions of decreasing size each roughly centered on \nthe pulsar. \n\nTwo Short High states have been observed in enough detail to follow\nthe pulse evolution. These are the {\\it Ginga} observations shown in figure 1 \nand recent RXTE observations (see Scott et al. 1997). However with these two \nShort High state observations, combined with the fragmentary observations of \nother Short High states, we can describe the following evolution pattern.\nAs the Short High state commences, the pulse profile is quite different \nin shape and lower in flux by $\\sim70\\%$ relative to the Main High state\npulse. \nBoth {\\it Ginga} and {\\it Exosat} observations of the Short High state profile \nreveal a {\\it small hard peak} and a \nlarger {\\it soft peak} separated by $180\\deg$ in pulse phase and superposed \non a {\\it quasi-sinusoid} (see figure 6). During {\\it Exosat} observations, the\n{\\it small hard peak} was actually larger than the {\\it soft peak} at energies\nabove $\\sim13$ keV (Kahabka 1987, 1989). {\\it Ginga} observations also \nshowed the {\\it small hard peak} increasing in amplitude relative to the \n{\\it soft peak} with increasing energy, but not exceeding that of the \n{\\it soft peak}. The RXTE observation of the November 1996 Short High state \ndid not reveal the presence of the {\\it small hard peak}.\nThe {\\it Ginga} observations show the {\\it small hard peak} disappearing \nwithin one day of the turn-on as did the earlier {\\it Exosat} observation \n(Kahabka 1987). The {\\it Ginga} and RXTE observations showed that the \n{\\it soft peak} also declined in flux, but more slowly, and disappeared three \nto four days after turn-on. A narrowing in width occurred in both cases. \n\nThe Short High state {\\it soft peak} contains an even softer component on the \ntrailing side of the peak indicated by a spectral \nsoftening at approximately pulse phase $0.6$ (see Fig. 5). The very soft \ncomponent is apparent \nas long as the {\\it soft peak} is present. \nThe {\\it Exosat} pulse profiles presented by Kahabka (1987, 1989) \nalso show this very soft component on the trailing side of the {\\it soft peak}.\n\nThe amplitude of the {\\it quasi-sinusoid} first increases and \nthen decreases as the May 1989 Short High state progresses, and is \nabout $180\\deg$ out of phase compared with the Main High state \n{\\it quasi-sinusoid} (see section 4). A similar flux increase of the \n{\\it quasi-sinusoid} can be seen in the Short High state profiles displayed \nin figure 4.3 of Kahabka (1987). The overall flux stays relatively constant \nfor about four days following the Short High state turn-on, but this is \ndue to a flux {\\it increase\\/} in the {\\it quasi-sinusoid} just \nbalancing a flux {\\it decrease\\/} in the {\\it small hard peak} and the \n{\\it soft peak}. The overall flux of the {\\it quasi-sinusoid} is roughly\nhalf that of the Main High state {\\it quasi-sinusoid}. As in the \nMain High state, the gap that defines the {\\it quasi-sinusoid} shows a \ndecrease in width and depth at increasing energies. \n\nIn summary, the Main High state pulse evolution involves a decay preferentially\non the leading edge of the {\\it main pulse} and {\\it interpulse} that begins \nlate in the High state. In addition, the formation and continuous slow \nevolution of an underlying {\\it quasi-sinusoidal} profile may also be occurring.\nThe Short High state involves the narrowing, decay and disappearance at very\ndifferent rates of the two peaks in the profile superposed on an underlying \n{\\it quasi-sinusoid}. Evolution of the {\\it quasi-sinusoid} is much slower \nand involves only subtle changes in the profile. These changes are illustrated\nin figure 6. Overall, comparison of the {\\it Ginga} observations with other \nobservations of the pulse evolution are consistent with a repeating, stable\nand systematic pattern of change in the pulse profile. Future observations\nare needed to explore the details and stability of the pulse\nevolution during the Short High state and especially the Main High state flux \ndecline.\n\n\\section{Pulse Phase Alignment of the Main and Short High state pulses}\n\nThe overall pulse evolution pattern can only be completely understood if the \nproper phase alignment of the Main and Short High state pulse profiles \nis known. To properly align the Main and Short High state profiles two \nmethods might be tried: 1) extrapolating the pulse timing ephemeris between \nHigh states across the Low state where pulsations are unobservable or\n2) matching pulse features that are common to each profile. \n\nFigure 5 displays a Main High state pulse profile, a closeup of the \n{\\it interpulse} of the same Main High state profile, and a Short High state \nprofile. Both profiles are taken from an early point in their respective \nHigh states when the effects of the pulse profile evolution are minimal. \nThe two High state profiles were phase aligned using the pulse timing \nextrapolation given in Deeter et al. (1998), in which a pulse phase ephemeris\nis extrapolated from the April and June 1989 Main High states into\nthe June 1989 Short High state. \n\nAt first glance the Main and Short High state pulse profiles seem quite \ndifferent but there are actually a number of features common to each profile. \nThe bottom of each panel has a hardness ratio for the profile. Note that the \nhardness ratio of the Main High state profile shows a dip at pulse phase 0.6 \nand a spectral hardening near pulse phase 1.0. The Short High state profile \nalso possesses a similar soft dip and spectral hardening separated by 0.4 in \npulse phase. \n\nThe phase alignment suggested by the spectral features implies that the \nMain High state {\\it interpulse} and the Short High state peak {\\it soft peak} \nshould be matched together.\nExamination of figure 5 shows that these two features exhibit very similar \nshapes, fluxes and energy dependence. The primary differences between the\ntwo features may simply be due to the different backgrounds upon which each\nfeature rests, since the underlying {\\it quasi-sinusoid} is shifted by 0.5\nin phase between the two High states. \n\nThe spectral softening at pulse phase 0.6 in either High state profile is \napparent in all the High states observed by {\\it Ginga} with the exception of \nthe anomalous June 1989 Main High state. The spectral softening is also readily \napparent in both the Main and Short High state profiles of the {\\it Exosat} \nobservations (see Kahabka 1987, 1989). \nEnergy dependent differencing of the {\\it Ginga } pulse profiles was used to \nisolate this soft excess feature. A pulse profile in a high energy band \nwas scaled until a fit to the surrounding pulse in a lower energy band was \nobtained and then the difference was taken. This process revealed that the \nsoft excess feature is very similar in shape, flux and color in all the High \nstates which suggests that it is the {\\it same} feature in both the Main and \nShort High states (see Scott 1993). The presence of the same soft \nexcess feature in both the Main High state {\\it interpulse} and Short High \nstate {\\it soft peak} strongly supports the phase alignment of figure 5. \n\nThe phase alignment also suggests that the {\\it hard central peak} of the \nMain High state pulse profile and the {\\it small hard peak} of the Short High \nstate profile are corresponding features. There is a significant flux \ndifference between these two features but both hard peaks increase in width \nand amplitude at higher energies relative to the surrounding pulse. The width \nincrease of the {\\it small hard peak} is only marginally observable in \nfigure 5, but is readily apparent in Kahabka (1989) and in RXTE/PCA\nobservations. In the {\\it Exosat} observation of the Short High state shown \nby Kahabka (1989), the {\\it small hard peak} is actually larger than the \n{\\it soft peak} at higher energies. \n\nWe can now describe the following similarities and differences of\nfeatures in the Main and Short High state profiles based upon the phase\nalignment of figure 5. The Main High state interpulse and the Short High\nstate {\\it soft peak} are the {\\it same} feature, as is the soft excess feature \nwithin each profile. The Short High state {\\it small hard peak} is a greatly \nreduced version of the {\\it hard central peak} of the Main High state. The \nlarge soft two peaked component underlying the {\\it hard central peak} in the \nMain High state is absent in the Short High state profile. The \n{\\it quasi-sinusoidal} profile of the Short High state is reduced in flux by \nabout 50\\% compared to the Main High state {\\it quasi-sinusoid}\nand shifted in phase by roughly 0.5. The Short High state profile\ncan be viewed as a modified version of the Main High state profile rather\nthan a completely distinct pulse.\n\nThe initial appearance and probable phase alignment of the Short High state \npulse profile require an explanation of 1) The disappearance \nof the soft shoulders of the Main High state main pulse. 2) The large drop in \nflux of the Main High state hard central peak 3) The nearly equivalent \namplitudes of the Main High state interpulse \nand the Short High state soft peak. 4) The $\\sim50\\%$ drop in flux \nand $\\sim180\\deg$ phase difference between the two High state \nquasi-sinusoidal profiles. \n \n\\section{Free precession of the neutron star}\n\nForce-free precession of the neutron star with a fixed beam geometry\nhas been proposed as the cause for the pulse shape change\nbetween the Main and Short High states by Tr\\\"umper et al. (1986) and was\nlater elaborated in Kahabka (1987), \\\"Ogelman \\& Tr\\\"umper (1988) and Kahabka \n(1989). They noted that free precession alone cannot explain the overall \nHigh-Low cycle since the beams needed to model the observed Main High state \npulse are too wide to disappear from view and cause a Low state.\nFor example, the unpulsed and quasi-sinusoidal components of the profile \nmust be produced by unbeamed emission or very wide beams, so free precession \ncannot cause these pulse components to disappear at the end of a High state.\nA model based solely on free precession also has great difficulty \nexplaining the cold matter absorption seen during turn-on in both kinds of \nHigh states. Therefore, a periodic obscuration of the X-ray source by the \naccretion disk is also assumed to explain the disappearance of the pulses and \nthe overall High-Low cycle. A composite model with a precessing disk acting \nas an occulting body and a freely precessing neutron star in which both cause\npulse shape changes has been proposed by Kahabka (1989). The period and phase \nof both the precessing disk and the freely precessing neutron star must be \nclosely locked together to prevent longterm drift between the pulse evolution \npattern and the High-Low intensity cycle (for example, the leading edge decay \nof the {\\it main pulse} has only been observed at the end of the Main High \nstate). The observed random walk in the phase of the Main High state poses \nsome difficulties for phase locking since a freely precessing neutron star \nshould be a relatively good clock (see Boynton, Crosa \\& Deeter 1980; \nTr\\\"umper et al. 1986 and Baykal et al. 1993). \n\nA spinning body can exhibit periodic, force-free precession if two of its three \nprincipal axes of inertia are unequal (i.e. a symmetric top \nwith $I_1 = I_2 \\not= I_3$). A review of the basic equations of free \nprecession can be found in Bisnovatyi-Kogan, Mersov \\& Sheffer (1990).\nFree precession can cause major changes in the observed pulse profile \nthat repeat over the course of successive precession cycles. \nThe pulse profile at a given pulse phase changes due to the slow variation \nin the angle between the magnetic dipole axis and the observer's line-of-sight.\nBeams emanating from the magnetic polar caps or from any fixed location\non the neutron star (other than the figure axis) will appear to a distant \nobserver to ``wobble'' in rotational latitude over the precession cycle.\nEither end of the dipole axis, when facing the observer, will oscillate\nsinusoidally in latitude during one free precession cycle. \nThe observed free precession light curve is \nhighly dependent on the angle between the angular momentum axis and the\nobserver's line-of-sight and the emission beam geometry and will be symmetric \nabout the precession phases of the latitude extrema in the dipole motion.\nThe sensitivity to the beam profile depends mostly on the beam width. \nA narrow beam produces pulse components that can appear\nand disappear from view as the wobbling takes place while components \nfrom wider beams will merely show variations in amplitude.\n\nAnother potentially observable signature of free precession is a characteristic \nvariation in the pulse period over the free precession cycle \n(Bisnovatyi-Kogan, Mersov \\& Sheffer 1990; Bisnovatyi-Kogan \\& Kahabka \n1993). Measurement of this effect was initially a major motivation for \nobserving Her X-1 with {\\it Ginga}. We can estimate the size of the period \nchange expected between the Main and Short High state using equation 7 of \nBisnovatyi-Kogan \\& Kahabka (1993) to be $\\sim 5.0 \\times 10^{-7}$ s. \nHowever the known random walk in pulse frequency (see Bildsten et al. 1997;\nDeeter 1981) \nalso causes pulse period changes. The expected period change between the Main \nand Short High state is given by:\n\\begin{equation}\n\\left < \\Delta P^2 \\right >^{\\frac{1}{2}} = P^2_0 (St)^{\\frac{1}{2}}\n\\end{equation} \nand has a value of $\\sim 8.0 \\times 10^{-7}$ s for a noise strength\n$S = 1.8 \\pm 0.8 \\times 10^{-19}$ $\\rm Hz^2\\ s^{-1}$ and $t = 17.5$ days. \nThe expected period changes are thus comparable and would be difficult to \nseparate unless many Main-Short-Main High state pulse period measurements \ncould be made. Currently, the most observable potential manifestation of \nfree precession is the pulse evolution observed between and within the High \nstates.\n\nThe ability of free precession to account for the change in pulse profile \nbetween the Main and Short High states was tested by Kahabka (1987) using \n{\\it Exosat} observations.\nThe Main High state pulse profile was modeled using a gaussian pencil beam \nfor the {\\it hard central peak} and a coaxial gaussian fan beam for the \n{\\it soft leading} and {\\it trailing peaks}. The {\\it interpulse} is produced \nby an identical antipodal fan beam. The opening angle of the fan beam was \ndetermined to be about $45\\deg$. We show a sequence of pulse profiles evolving \nover the 35-day cycle using the parameters determined by Kahabka (1987, 1989) \nin figure 7. The pulses occur one day apart over the 35-day cycle and do not \ninclude the unpulsed or quasi-sinusoidal component. The Main High state must \nbe centered roughly about day zero with the Short High state occurring 18 days \nlater. From the figure several features can be noted: (1) The {\\it interpulse} \nand the {\\it soft two peak component} are always visible. (2) The \n{\\it interpulse} flux increases (or decreases) as the {\\it main pulse} flux \ndecreases (or increases). (3) No leading edge decay of either the {\\it main \npulse} or {\\it interpulse} occurs. (4) The pulse profile evolves smoothly and \nslowly over the 35-day cycle, with no rapid profile changes. (5) The decrease \nin pulsed intensity is only about 10\\%-20\\% between the Main and Short High \nstate. All of these features are inconsistent with the evolution actually \nobserved as described in section 3. Related criticisms of free precession have \nbeen made by Bisnovatyi-Kogan, Mersov \\& Sheffer (1990).\nIn Kahabka (1989), a precessing disk was assumed to cause the\nleading edge decay of the {\\it main pulse} during the termination of the Main \nHigh state with some contribution from free precession. However, this model \nhas difficulty in explaining the actual Short High state profile and \nthe subsequent disappearance of both peaks in the profile as noted in points\n(1) and (2) above.\n\nA freely precessing neutron star with approximately axisymmetric fan and \npencil beams has several general problems in explaining the observed \npulse evolution in Her X-1. (1) The pencil beam cannot disappear from view \nwithout the fan beam disappearing as well. The {\\it small hard peak} of the \nShort High state appears to be the same pulse component as the\n{\\it hard central peak} of the Main High state (see section 4), but without \nthe surrounding {\\it soft two peaked component} that is presumably produced \nby a fan beam.\n(2) The preferential decay of one side of a fan beam cannot occur due to\nfree precession. The two cuts across a fan beam, which result in a two-peaked\npulse component, should change in amplitude and width simultaneously as\nprecession occurs. (3) Rapid profile changes, such as those observed near the \nend of the Main High state or the beginning of the Short High state,\nare difficult to explain unless the beam profile has sharp edges. For example,\nthe flux of the {\\it hard central peak} dropped by more than 70\\% in 6.7 \nhours near the end of the April 1989 Main High state. If we assume that the \n{\\it hard central peak} is produced by a pencil beam and that the precessional \nmotion of the pulsar is responsible for its amplitude decrease, then we can \nestimate the {\\it latitudinal} width of the pencil beam. \nWe conservatively estimate that the {\\it hard central peak} flux drops to zero \nin approximately 12 hours. In this period, the beam axis moves approximately \nthrough an angle $4\\Phi \\Delta t/P_{35}$ away from the observer's \nline-of-sight. With $\\Phi\\approx 12.5\\deg$, this produces a latitudinal \nwidth over this portion of the beam of about $0.7\\deg$. We can also estimate \nthe {\\it longitudinal} width of this portion of the beam to be $\\sim40\\deg$ \nfrom the observed pulse shape as the beam sweeps {\\it across} our\nline-of-sight. The beam responsible for the {\\it hard central peak} would \nhave to be $\\sim 60$ times broader in longitude than in latitude, a quite\nimprobable situation. \n\nTo explain a rapid change in the pulse profile observed with {\\it HEAO 1} \nnear the end of a Main High state (Soong et al. 1987) with a free precession \nmodel, Shakura, Postnov \\& Prokhorov (1998) have invoked a temporary transition\nfrom a symmetric top to a triaxial neutron star caused by a ``quake'' \nduring the Main High state flux decline. The quake induces a rapid shift in the\nrotational latitude of the magnetic axis and thus induces rapid changes\nin the observed pulse profile. This explanation may work for one case of\nobserved rapid pulse profile change but the rapid decline of the pulse\nduring the Main High state now appears to be a normal and repeating phenomenon\nrather than an anomalous event (see Deeter et al. 1998). It seems rather \nimprobable that neutron star quakes could be arranged to regularly occur \nduring the 35-day phase of the Main High state flux decline but not to occur \nat other times. In addition, there appears to be no evidence for an expected \nphase shift caused by the quake based on {\\it Ginga} and RXTE observations. In \nconclusion, we find little evidence supporting neutron star free precession as \nthe cause of the pulse shape changes in Her X-1. \n\n\\section{Other causes of systematically recurring pulse evolution}\nIf the neutron star is not undergoing free precession then the precessional\nmotion of the inner disk becomes the primary candidate causing pulse\nevolution. Pulse shape changes might be caused by modulation of matter flow\nonto the magnetic field lines by a changing aspect between the magnetosphere \nand a tilted, precessing accretion disk. The cycle of High and Low states\ncan be attributed to obscuration by the precessing accretion disk while the\npulse shape evolution results from variations in the accretion column\nstructure induced by the changing pattern of matter entry onto the magnetic\nfield lines. \nAs a naive example of a possible variation, assume the accreting matter\nattaches directly to a dipole magnetic field at a radius $R_m$ and then\ntravels along the field lines onto the magnetic poles. The angular\nextent of the accretion cap will be given by $\\sin^2(\\theta_C) = R/R_m$ where\n$R$ is the radius of the neutron star (Lamb, Pethick \\& Pines 1973).\nAn increase in $R_m$ will cause a decrease in the accretion\ncolumn radius at the neutron star surface and concentrate the energy\nreleased by the accretion into a smaller area. A decrease in $R_m$ will\nhave the opposite effect.\nA full evaluation of the coupling between a tilted, precessing accretion disk,\nthe neutron star magnetosphere and the net effect on the pulsar beam involves\ncomplex physics that has not been undertaken as yet and is beyond the scope of\nthis discussion.\n\nIt seems plausible that some degree of systematic pulse evolution should be\ncaused by a changing disk orientation, but we argue that this is unlikely \nto be the {\\it primary} cause of the pulse shape changes observed in Her X-1.\nNonlinear changes in the flow rate and pattern could be responsible for\nrapid changes observed in the pulse profile, but these rapid changes\nmust be scheduled to occur just as the overall flux declines at the end\nof the Main High state and not at other times. \nThis mechanism should also cause both {\\it increases} and {\\it decreases} in \nthe pulse profile. In the visible High states only decreases in pulse features \nare ever observed.\\footnote{During the\nShort High state the {\\it small hard peak} and\nthe {\\it soft peak} disappear, but this is accompanied by a compensating\nsmall flux increase in the quasi-sinusoidal component that occurs\nearly in the Short High state. The flux of the quasi-sinusoid subsequently\ndeclines. The early flux increase of the quasi-sinusoid may simply be part of\nan overall increase in flux as the line-of-sight passes through a decreasing\ndensity of coronal disk material at the start of the High state.} The\nmost complicated pulses are apparent at the beginning of the High states\nwith a subsequent disappearance of features as the High state progresses.\nNature would have to conspire so that increases in the amplitude of pulse \nprofile components occur only during the Low state. \n\nPetterson et al. (1991) have qualitatively presented a time dependent\ndisk obscuration model for the pulse evolution that relies on obscuration \nprovided by ``flaps'' of matter at the points \nwhere a tilted accretion disk meets the neutron star's magnetosphere. These\n``flaps'' rotate at the pulse period and move in pulse phase as the tilted disk \nprecesses. It is not clear whether the physics of disk-magnetosphere coupling \nwill produce obscuring flaps of this type, but in any case the model has some \nqualitative problems when confronted by the observed pulse profiles. \nDuring the Short High state, the interpulse flux for \nthe ``flaps'' model is \nlarger than during the Main High state (compare Figs.~2b and 3b of \nPetterson et al. 1991). The {\\it Ginga} observations show that the soft peak\nflux is {\\it the same or smaller} during the Short High state than that of the \nMain High state interpulse with which it is identified (see figure 5). Similar \nbehavior in the {\\it Exosat} observations can also be seen in Fig.~1 of \nPetterson et al. (1991). During the Short High state the ``flaps'' model \npredicts that the main pulse flux should decrease due to increasing ``flap'' \nobscuration, while the interpulse flux should increase, contrary to the \n{\\it Ginga} observations. In the Main High state, the main pulse \nflux and the interpulse flux should also change in an opposing manner according\nto the ``flaps'' model, but both fluxes are observed to decrease. \n\n\\section{Pulse evolution resulting from a resolved occultation of the neutron \nstar by a tilted, precessing accretion disk}\n\nThe apparent stability and repeating nature of the pulse evolution may be\nthe result of a resolved occultation of the pulse emission\nregion by the inner edge of a tilted, precessing accretion disk.\nTwo different occultation sequences, and hence two different sets of pulse\nshape changes will occur, as the observer sees the inner \ndisk edge sweeping alternately `upwards' and `downwards' across the pulse \nemitting region and these events will be $\\sim 180\\deg$ apart in disk \nprecession phase. The pulse shape changes observed during both\nHigh state types require the ``scale height'' of the disk (or more generally\nthe ``occulter'')\nto be roughly the size of the dominant pulse emitting region i.e. a few neutron\nstar radii, which will then naturally produce pulse shape changes associated\nwith decreases in X-ray flux. To pursue the occultation idea further a simple \ngeometric model is developed and qualitatively compared to the observations.\nThe model proposed below is a considerably refined version of the model\noriginally proposed by Bai (1981).\n\nA disk occultation model requires at least two components. A model for the \ntilted and precessing disk itself is necessary, and a model for the pulsar \nemission geometry. In the simplest approximation, the pulsar beams do not \ndepend on the azimuth of the disk and the disk simply occults the pulse \nemitting region. This is probably not entirely true since the disk is coupled \nto the neutron star through the magnetosphere and the azimuthal progression of \na tilted disk may cause some changes in the accretion column and hence the \npulse shape. However, these complexities will be ignored for now and the \nbeams from the pulsar are assumed to be decoupled from the disk.\nWith the choice of a physical location for the beam emission region with \nrespect to the neutron star, the apparent spatial location of each beam \ncomponent as seen by the observer can be computed. Likewise, the occulting \ndisk may have also have a complex geometry due to interaction with the \nmagnetosphere, among other effects, but we will assume a simple planar disk \nshape. The sequence of pulse shape changes can be modeled by sweeping the \ndisk over the pulse emission region and comparing the predicted pulse shape \nchanges with the observations. \n\nThe least obscured pulse should occur early in the Main High state\nafter the pulsar emerges from behind the outer disk rim.\nThe main and interpulse profiles are clearly asymmetric about their maxima \nat this time but we will provisionally make several assumptions to simplify\nthe modeling process. We will first assume that the beam is axisymmetric, the \nmagnetic field is purely dipole and that identical beam emission regions exist \nat the ends of an axis that is close to but not necessarily identical with the \nmagnetic dipole axis. We attribute the {\\it hard central peak} of the main \npulse to a pencil beam directed along the beam axis and the softer flanking \nshoulders to a surrounding fan beam (similar to Kahabka 1987). The interpulse \nis produced as the edge of the fan beam emanating from the antipodal magnetic \npole grazes the observer's line-of-sight. \n\nWe assume gaussian intensity profiles for the beams since Kahabka (1987) has \nshown that the pulse profile of Her X-1 can be well fit with a small number of\ngaussian components and this is confirmed by fitting the Ginga profiles. A \nsimple gaussian beam model for both the fan and pencil beams is used and is \ngiven by:\n\\begin{equation}\nI(\\theta)=I_{pen}\\exp(-\\theta^2/\\sigma_{p}^2)+\nI_{fan}\\exp((\\theta_{cone}-\\theta)^2/\\sigma_{f}^2)+I_{D}+I_{E}+I_{Low}\n\\end{equation}\nwhere $\\theta$ is the angle from the beam axis, $I_{pen}$ and $I_{fan}$ are the \npencil and fan beam amplitudes and $\\sigma_{p}$ and $\\sigma_{f}$ are the beam \nwidths. The fan beam opening angle is given by $\\theta_{cone}$. Three\nconstant flux components are present, two due to magnetospheric emission \n($I_{D}$ and $I_{E}$) and one due to Low state coronal emission $I_{Low}$.\nValues for\nthe beam components are given in Table 1. The soft two shoulder component\nin the Main High state main pulse results from a cut of the line-of-sight \nacross the two edges of the fan beam ``cone'', while the interpulse results\nfrom a grazing cut along the edge of the ``cone''. The large difference in the \namplitudes of the main pulse and the interpulse require the line-of-sight to \nbe $\\sim20\\deg-40\\deg$ from the neutron star's rotational equator. Since \nprevious optical and X-ray observations show that the observer is offset by \n$5-10\\deg$ relative to the binary plane (Gerend \\& Boynton 1976; \nMiddleditch 1983; Deeter et al. 1991) the neutron star rotation axis must \nbe inclined by $\\sim10\\deg-50\\deg$ to the orbital axis. \n\nTo model the physical location of the primary pulsar beams requires some \nadditional assumptions. Theoretically, beam models have been divided into\nslab and column geometries depending on the physical mechanism assumed to\ndecelerate the infalling plasma. Column models assume that either a \nradiation pressure shock or a collisionless shock lies above the neutron star\nsurface and decelerates the flow. Brainerd \\& M\\'esz\\'aros (1991) have shown \nthat the radiation pressure for the luminosity of the Her X-1 is too weak to \nsignificantly decelerate the infalling plasma. It thus seems prudent \nto assume a slab geometry for the magnetic polar cap of Her X-1. \nIn the slab model the infalling plasma is decelerated at the neutron star \nsurface and the emitting region is a thin cap only a few meters in height \n(M\\'esz\\'aros \\& Nagel 1985). In more complex models, X-ray radiation\nemitted from the foot of the accretion column is backscattered as it rises\nthrough the accretion column (e.g. Brainerd \\& M\\'esz\\'aros 1991). Thus the \nbeam consists of direct emission from the polar cap and a backscattered \ncomponent. \n\nWe will first consider a simple pulsar model in which a single emitting point \nlying on the neutron star surface is chosen to approximate the {\\it beam} \nemission region. The {\\it pulse} emission region will have a width of \n$\\le 2 R_{ns}$, where $R_{ns}$ is the neutron star radius. An observer will \nsee the emitting point sweep \nout an ellipse as the neutron star rotates with the surface blocking the \nemitting point \nfor a portion of the rotation period. We will refer to this beam geometry as a \n``direct fan beam'' geometry. The beam pattern originating from the emitting\npoint consists of a pencil beam surrounded by a concentric fan beam as in\nequation 2 (see figure 8, top panels). This was the same beam pattern and \nemission geometry used in the free precession model in section 5. \n\nWe will also consider a second beam/emission model in which the fan beam \nemission is produced by backscattered radiation from the accretion column that \nis focused around the neutron star and beamed in the antipodal direction, \na ``reversed fan beam'' geometry. \nThis beaming configuration will produce a similar pulse profile but the \nspatial locations of the pulse components will be significantly altered \n(see figure 8, bottom panels). The fan beam components will now be observed \nto originate at some distance above the neutron star surface and \n$\\theta_{cone}>90\\deg$. The {\\it interpulse} will now be emitted by the same \nmagnetic pole that produces the {\\it hard central peak} while the \n{\\it soft shoulders} of the main pulse come from the opposite pole. A similar \nfan and pencil beam configuration has been discussed theoretically by Brainerd \n\\& M\\'esz\\'aros (1991). In their model, a fan beam is produced from magnetic \npolar cap radiation that is preferentially backscattered by the incoming \naccretion flow and then gravitationally focused around the neutron star. The \naccretion column is calculated to be optically thin to Thomson scattering \nwhile the fan beam photons are produced by cyclotron resonance scattering. \nOnly photons at energies less than or equal to the surface cyclotron frequency \nwill be scattered in the accretion column. Support for this pulse profile\ninterpretation is provided by the observed cyclotron absorption feature\nin Her X-1, which reaches a maximum absorption depth at the pulse phase of \nthe hard central peak and by the disappearance of the main pulse shoulders \nabove the $\\sim38$ keV cyclotron line energy (Soong et al. (1990b)).\n\nThe location of the reversed fan beam emission was modeled by assuming \nthe emission occurred from a point at a height of $1.5\\ R_{ns}$. This\nis the cyclotron scattering height of 10 keV photons for a surface\nfield strength corresponding to a cyclotron line energy of 40 keV,\na simple dipole field and a neutron mass of $1.4\\ \\Msun$. Softer photons\nwill scatter from higher up and harder photons from lower down so the\napparent emission region location is energy dependent. The pulses displayed\nin figure 8 approximately model the Main High state pulse profile observed \nin the {\\it Ginga} $9.3 - 14$ keV band. Gravitational lightbending of the \nphoton trajectories causes the photons to appear to be emitted from a region \nhigher above the neutron star surface than for the case when no lightbending\nis present. We illustrate this effect in figure 9 where trajectories \nare calculated using the equations taken from Brainerd \\& M\\'esz\\'aros \n(1991) and Riffert \\& M\\'esz\\'aros (1989). A reversed fan beam with an \nopening angle of $\\theta_{cone}=140 \\deg$ with respect to the accretion \ncolumn and a profile with a half width of $\\sigma_{f}=20 \\deg$ was used to \ncalculate the nonattenuated fan beam intensity since this was a good\napproximation to the beam pattern shown in figure 9. The location of the \nfan beam emitting point was calculated using a sinusoidal approximation to \nthe photon impact parameter for the case of lightbending in figure 9. \n \nThe disk is modeled as an infinite plane with a circular hole centered\non the neutron star. The circular hole has a radius $R_{inner}$ and\na gaussian density profile in the direction perpendicular to the disk plane \ncharacteristic of an \n$\\alpha-$disk of Shakura \\& Sunyaev (1973). The vertical disk density \nprofile is described by:\n\\begin{equation}\n\\rho(z)=\\rho_0 \\exp(-z^2/\\sigma_{d}^2)\n\\end{equation} \nwhere $z$ is the vertical distance above the inner disk midplane,\nand requires the specification of the free parameters $\\rho_0$, the \nmidplane density of the disk and $\\sigma_{d}$, the disk ``scale height''. \nTo model the occultation, the disk is assumed to be simply a linear\nedge with a minimum distance $R_{occ}$ from the neutron star as seen by the \nobserver. \n\nThe disk selectively obscures the pulse emitting region. \nWhen the observer's line of sight lies at an angle \n$\\theta_{occ}$ above the disk midplane the disk edge will appear to be \nat a distance \n$R_{occ}=R_{inner}\\sin(\\theta_{occ})$ from the neutron star.\nThe optical depth of the disk material will be caused by Thomson scattering\ndue to the complete ionization of hydrogen and helium in the inner disk\nregion. The optical depth will therefore follow the density distribution\nand is assumed to scale as:\n\\begin{equation}\n\\tau(z)=\\tau_{disk}\\exp(-z^2/\\sigma_d^2)\n\\end{equation}\nwhere $\\sigma_d$\nis the optical depth scale height, and $\\tau_{disk}$ is the optical\ndepth at $z$=0.0. \n\nThe total attenuation caused by the disk for any emitting point depends \nonly on its height above (or below) the disk midplane and the angle \n$\\theta_{occ}$.\nThe observer's line-of-sight to the emitting point will pass through a range of \nheights above the disk plane, so the total optical depth must be found by \nintegrating along this path. \nThe total optical depth is calculated using:\n\\begin{equation}\n\\tau(z_0)=0.5(\\tau_{mid}/{\\sin\\theta_{occ}})\\int_{z_0}^{\\infty}\n\\exp(-{z \\over\\sigma_d \\cos\\theta_{occ}} )^2({dz \\over \\cos\\theta_{occ} }) \n\\end{equation}\nwhere $z_0$ is the height above the disk midplane where the ray connecting\nthe observer and the emitting point intersects the inner disk edge.\nThe extinction to the emitting point is then given by:\n\\begin{equation} \nA(z_0)=e^{-\\tau(z_0)} \n\\end{equation}\nThe effect of the twisted disk is taken into account by having the optical\ndepth increase to infinity as $z_0$ becomes increasingly negative (see\nfigure 2).\n\nThe geometric orientation of the neutron star and the inner disk are determined\nby tilt and azimuth angles. The tilt is specified with\nrespect to an axis that will be identified as (but is not required to be) \nthe stellar binary axis. Reasonable values for the disk tilt lie in the range \nof $10-20\\deg$ in order to fit the overall High state light curve with a \ntilted, twisted, counter-precessing disk (see figure 2). If one assumes\nthe disk edge is cutting across the face of the neutron star at 35-day\nphases 0.23 and 0.58 (from observing the pulse evolution) then a tilt of\n$11 \\deg$ can be derived.\n\n\\subsection{Comparison with Observations}\n\n\\subsubsection{Direct Fan Beam}\n\nCan this simple model reproduce, qualitatively, the features observed in \nthe Main High state pulse evolution? Figure 8 (top panel)\n shows the approximate spatial \nlocations of the pencil beam and fan beam emission regions for the direct\nfan beam model. The neutron star rotation is prograde in figure 8 \nso a counter-precessing inner disk edge will sweep across the neutron star\nface from right-to-left in the figure. \nWe define case 1 disk orientation as illustrated in the top panel of figure\n8, that is, the disk covers the neutron star from top-to-bottom as well\nas right-to-left. \nCase 2 disk orientation is defined as the case that the disk covers\nthe neutron star face from right-to-left, bottom-to-top, as illustrated \nin the lower panel of figure 8. A straightforward consideration of the\ntwisted disk geometry shows that during a full 35-day precession period,\ncase 1 and case 2 both occur, separated by one-half a precession period.\n\nThe relatively long period during the \nMain High state when the pulse profile shows only small changes, simply means \nthat the line-of-sight to the pulsar is far from the obscuring inner disk edge. \nAs the disk edge approaches the pulsar, it is clear from figure 8 (top panel), \nthat in \nboth case 1 and case 2, the {\\it trailing} shoulder (Bb) of the main pulse will \ndisappear before the pencil beam (C) or the leading shoulder (Ba).\nIn case 2, the {\\it interpulse} (A) will disappear before \nthe pencil beam (C) and in case 1 they disappear at nearly the same time. \nNeither case reproduces the pulse evolution behavior observed in either \nHigh state.\n\nReorienting the neutron star spin axis about the line-of-sight \nwill alter the occultation sequences. If the upper spin pole in figure 8\nis tipped toward the right (toward the oncoming disk edge) \nthen case 1 will produce a pulse \nprofile sequence in which the order of disappearance will be 1) the \nleading and trailing soft shoulders (Ba and Bb), 2) the hard central peak (C),\n 3) the interpulse (A).\nCase 1 does not resemble the observed Main High state pulse evolution sequence. \nBut it can\ncan reproduce the Short High state sequence if the emergence from the \nturn-on only reveals the occultation {\\it after} the disappearance of \nthe two soft shoulders. \nIf case 1 gives the Short High state sequence then case 2 must give the Main \nHigh state sequence.\nHowever, in case 2 the trailing shoulder (Bb) disappears first, then\nthe hard central peak (C) will \ndisappear, both before the leading shoulder (Ba), contrary to the observations.\n\nOne can consider all the different possible combinations of neutron star spin\nand motions of the disk edge. This has been done and the results (of\nwhether a satisfactory occultation sequence is obtained) are summarized\nin Table 2. Only two of the eight possibilities result in occultation\nsequences in the correct order for both the Main and Short High states. One \nrequires a reverse neutron star spin in one case and a prograde disk \nprecession in the other case. \nIs a retrograde rotation of the neutron star or a\nprograde precession of the disk possible? The long term spinup trend observed \nin Her X-1 (Nagase 1989) and the frequency behavior of optical pulsations \nfrom the lobes of the companion star HZ Her (Middleditch \\& Nelson 1976) both\nstrongly argue for a prograde pulsar spin. Likewise, the preeclipse dip \nrecurrence period and the predominance of\ninteger combinations of the {\\it sum} of the orbital and 35-day frequency\nin the power density spectrum of the optical light curve \nstrongly indicate a {\\it counter}-precession for the accretion disk \n(Deeter et al. 1976; Crosa and Boynton 1980).\nThus we discard the direct fan beam model, since it cannot give the correct\noccultation sequence and keep prograde spin and retrograde precession.\n\nWe also note that those occultation sequences from the direct fan beam model,\neven though in the correct order, have a difficulty. For the Short High state \nthe observed sequence starts with a weak hard pulse (C) but has no evidence\nwhatsoever for any trace of the leading (Ba) or trailing (Bb) shoulders.\nThis is very hard to achieve in the direct fan beam model since the hard\npulse (C) and soft shoulders (Ba, Bb) are produced in directly adjacent \nlocations. \nThe above qualitative difficulties in matching the observed sequence of pulse \nprofile changes can be resolved using a ``reversed'' fan beam, as we show \nnext.\n\n\\subsubsection{Reversed Fan Beam}\n \nBoth the observed Main and Short High state pulse evolution \ncan be reproduced qualitatively \nif the neutron star is tilted as shown in the lower panels of figure 8.\nCase 1 (disk tilted as in the upper panel) \nreproduces the Main High state decay of the {\\it leading} soft \nshoulder (Ba) followed by the {\\it hard central peak} (C) \nand the {\\it trailing} soft shoulder (Bb). The Short High state \nevolution is produced by the case 2 disk orientation as shown in the lower\npanel of figure 8. The observed evolution requires complete occultation of the \nsoft shoulders (Ba, Bb) of the main pulse before the Short High state turn-on.\nThis can be readily accomplished since the shoulders (Ba, Bb) are from\nregions well separated from the location of the {\\it hard central peak} (C). \nThe shorter length of the Short High state and the required initial partial \noccultation of the pulse emitting region can be produced by the same offset \nof the observer's line-of-sight from the binary plane. In figure 10a and 10b,\na disk occultation and the resulting pulse profile changes are illustrated\nusing the model disk and beam profiles described earlier. The parameters\nused are displayed in table 1.\n\nThe Main High state pulse evolution is modeled in figure 10a. \nThe leading edge decay of both the fan beam and the interpulse occurs \nas the disk edge sweeps across the neutron star face. The actual timing of \nthe decay of the soft shoulders and the interpulse put important constraints\non the apparent tilt of the neutron star relative to the disk edge, which\nis also quite sensitive to the actual locations of the emitting\nregions. For the model shown in figure 10a, the interpulse decays away a\nbit early relative to the soft shoulders compared to the observations. In\naddition the decay of the trailing soft shoulder is delayed compared to\nthe observations since the model disk edge appears to be too sharp. \nHowever, making the disk edge fuzzier will tend to wash out the Short\nHigh state sequence, assuming a fixed inner disk ring tilt and radius.\nThis model predicts that the pencil beam ({\\it hard central peak}, C), \nshould show a trailing edge decay, but observing this effect requires a \nknown pulse ephemeris during this decay phase. Lastly, as the disk edge cuts \nacross the neutron star face, short term variations in the pulse profile\nshould occur in addition to the longer term systematic changes, due to \nvariations in the disk opacity as material is accreted onto the neutron star. \n\nThe Short High state pulse evolution is modeled in figure 10b.\nThe disk motion will cause the pencil beam ({\\it small hard peak}, C) to decay \naway first followed by the interpulse (A). The more edge-on view of the inner \ndisk plane at the start of the Short High state will lengthen the traversal of\nthe disk edge across the neutron star face relative to the Main High state\nand this is consistent with the slow disappearance \nof the interpulse ({\\it soft peak}, A) relative to the same event during the \nMain High state. In contrast to the Main High state, no significant leading \nedge decay of the pulse components is predicted during the Short High state and \nnone is observed. The Short High state must begin with the accretion disk\npartially obscuring the pulse emission region to account for both the\ndifferent pulse shape and the lower Short High state flux. The \nplacement of the inner disk edge at the turn-on is probably somewhat variable\ndue to changes in the total disk twist and elevation so this model predicts\nthat the Short High state pulse profile should be quite variable as well at \nthe start of the turn-on. Depending on the exact placement of the inner disk \nedge, the {\\it small hard peak} (C) may be larger, smaller, or completely \nattenuated compared to the interpulse in figure 6. \nLikewise, the disk edge may be advanced enough that the interpulse is gone as \nwell at the turn-on.\n\nThe evolution of the quasi-sinusoidal components is modeled by the occultation\nof emission regions D and E in figure 10.\nThe deepening of the pre-interpulse minima early in the Main High state \nand the persistence of the quasi-sinusoidal pulse after the disappearance \nof the main pulse suggests an occultation of an emission region much larger \nin size than the neutron star. Radiation scattered from the inflowing \nmagnetospheric material many neutron star radii above the surface may produce \nthis emission. If we assume \n1) the magnetospheric flow is optically thin to Thomson scattering as in \nthe Brainerd \\& M\\'esz\\'aros model and 2) that accretion onto a magnetic pole \noccurs over a range of magnetic azimuth less than $180\\deg$, then two equal and \nconstant flux pulse components may be produced by scattering in the accretion \nflows. The locus of scattering points illuminated by the hard pencil \nbeam (C) over a neutron star rotation period are indicated by D and E\nin the rightmost panels of figure 8. D and E are much further away from the\nneutron star than the emission components A, Ba, Bb and C (middle column \nof panels in figure 8): the small circle between D and E indicates the\nneutron star surface.\nSince the emission from E is due to the magnetospheric flow onto the \nthe opposite pole \non the neutron star from the flow producing the emission at D,\nthe instantaneous location of scattered emission on E will \nbe $180\\deg$ different in pulse phase from the instantaneous location of \nthe emission on D. D and E are still close enough to the neutron\nstar that light travel time delays are negligible.\nIn the absence of any occultation, the instantaneous\nscattering from D and E are visible at all pulse phases so the total\nemission from D and E appears unmodulated.\nA third, small, constant-flux contribution should also be present from \nthe much larger accretion disk corona that produces the Low state flux.\n\nThe Main and Short High state quasi-sinusoidal pulse evolution and the\npreinterpulse deepening can together be interpreted as an occultation of the \nX-ray illuminated, magnetospheric flow (regions D and E). \nBoth the upper and lower\nmagnetospheric flows will sweep out cones as the neutron star rotates, which\ncross the ``plane of the sky'' at pulse phases 0.25 and 0.75. \nFor the neutron star orientation show in figure 8 (lower panels),\na deepening is predicted in the pulse profile during the Main High state \nnear pulse phase 0.25 as the \nouter portion of the upper magnetospheric flow \nrotates behind the oncoming disk edge. \nThe {\\it widening} will continue as the \noccultation progresses but the {\\it deepening} will stop since the flux at \npulse phase 0.25 will then be produced mostly by the unocculted, \nantipodal, magnetospheric flow. \n\nNear the middle of the \nMain High state, a second deepening is predicted at pulse phase 0.75 as the \ndisk begins to occult the lower \nmagnetospheric flow. At the Short High state turn-on, the lower magnetospheric \nflow will already be occulted, accounting for\nthe $\\sim 50\\%$ drop in flux observed in the ``quasi-sinusoid''. \nThe constant flux produced by the upper magnetospheric flow will now be\npreferentially occulted near pulse phase 0.75 as the occultation\nprogresses, producing a dip there, and an $\\sim 180\\deg$ phase shift \nbetween the two High state ``quasi-sinusoids''. \nThe dip should widen as the Short High state progresses. \nThe initial increase and \nthen decrease of the overall quasi-sinusoidal flux occurs simply because the\nline-of-sight is moving away from the outer disk edge and through decreasing\naccretion disk coronal density as the inner disk occultation progresses.\n\nA comparison of the model in figure 10 with the observations readily shows\nthat while many features of the quasi-sinusoidal evolution can be\nmodeled, there is a problem with component E. At the end of the Main High\nstate, the quasi-sinusoid peaks at pulse phase 0.75, whereas component\nD is near minima, implying that it is out-of-phase by 0.5. The Short High\nstate provides no constraint on E since it is completely occulted. The\n``fix'' to the simple model needed to produce the asymmetry in the soft \nshoulder peaks should also affect the location of pulse component E and may \nsolve this problem. In any case, using two rotating rings to model the \nquasi-sinusoids is probably a gross simplification of the actual situation \nsince the interaction geometry of the accretion column with the disk should be \nquite complex. In addition, another weakly pulsed component may be present due\nto scattering or reemission from the inner disk edge. This may be the cause\nof the low energy sinusoid that appears to be in phase\nwith the higher energy quasi-sinusoid (see e.g. McCray et al. 1982). We note \nthat the pulse evolution of\nthe soft energy quasi-sinusoid ($<\\ 1$ kev) is at present unknown and that its \nobservation may provide valuable clues about the inner disk. \nRecent BeppoSAX observations of a Short High state flux decline\n(Oosterbroek et al. 2000) discovered an increase in relative absorption that \ncan be explained by assuming seperate scattering and absorption regions. This \nis in qualitative agreement with a gradual inner disk occultation of an extended\nscattering region associated with the accretion column. \n\nThe radius of the inner disk edge can be estimated from the duration\nof the Main High state occultation event. Let $R_d$ be the inner disk radius \nand $R_e$ the radius of the pulse emitting region. From the reversed beam \nmodel $R_e$ is about $\\sim 2 \\; R_{ns}$ for the region emitting the main pulse.\nThe velocity of the disk edge is given approximately by \n$V_d=R_d \\omega_d \\sin \\theta_t$ where $\\omega_d$ is the angular velocity\nof the disk precession (equal to ${2 \\pi \\over P_{35}}$) and $\\theta_t$\nis the tilt angle of the inner disk. The inner disk radius can now be\nestimated from:\n$$ R_d={2R_e \\over T_{occ} \\omega_d \\sin \\theta_t} $$\nwhere $T_{occ}$ is the duration of the occultation of the main \npulse emitting region. From the April 1989 Main High state, \n$T_{occ}\\approx 3$ days. The inner disk tilt angle is estimated to be \nbetween $10-20\\deg$. These parameter values produce an estimate of \n$R_d\\approx 20-40 \\; R_{ns} $. This is much smaller than the corotation\nradius of $157 R_{ns}$ where the orbital angular velocity equals that\nof the neutron star, \nassuming a 12 km neutron star radius and $M_{NS} = 1.3 \\Msun$. \n\nIn conclusion, the reverse fan beam model with prograde neutron star spin \nand retrograde disk precession naturally accounts for the major features\nof the observed Main and Short High state pulse evolution. It also\naccounts for a number of other features, as described above, e.g.\nthe $180\\deg$ phase shift between the two High state ``quasi-sinusoids''. \n\n\\section{Discussion}\n\nThe model proposed here for the pulse evolution cycle in Her X-1\nconsists of an occultation of the neutron star by the inner edge of a tilted\nand precessing disk. The leading edge decay of the main and interpulses during\nthe Main High state preclude a beam geometry consisting of a pencil beam\nsurrounded by a fan beam and emitting from the neutron star surface. However, \nreversing the fan beam so that is emitted\nin the antipodal direction with respect to the pencil beam and at some \ndistance above the stellar surface \nallows the leading edge decay to be\nreproduced by an occultation in a natural fashion. The observed Short High\nstate evolution pattern then arises naturally with this geometry. \n\nCyclotron resonant scattering in the accretion column \nis an attractive mechanism for producing a pencil beam surrounded\nby an reversed fan beam.\nThe energy of the cyclotron resonance is directly proportional to the\nlocal magnetic field strength and this decreases with altitude above the \nneutron star surface. When the energy of an upward traveling photon equals \nthe local cyclotron energy, scattering will occur. This creates a natural \nenergy \ndependent filtering process for photons emitted in the accretion cap and\ndivides the beam into three components. Hard photons (especially those\nabove the surface cyclotron frequency) will escape in a pencil beam. Softer\nphotons will be backscattered and gravitationally focused around the neutron\nstar in an antipodally directed fan beam. Finally, photons scattered from the\naccretion column isotropically will produce a constant pulse component. \nThe softest photons will scatter from the highest altitudes in the accretion \ncolumn. The neutron star rotation will cause \nthe highest altitude emission (D and E in figure 8) to rotate with pulse phase.\nThe occultation of this high altitude emission \nby the precessing disk edge creates gaps in the constant\nemission profile and therefore a ``quasi-sinusoidal'' profile. \nA hard pencil beam (C), a softer fan beam (Ba and Bb)\nand a quasi-sinusoidal component (D and E)\nqualitatively match the observed energy dependence in the Main High state \nprofile. This type of beam model may be applicable to other X-ray pulsars\nas well, for example Vela X-1, which displays a pulse profile consisting of\ntwo doubled peaked components at soft X-ray energies, possibly superposed on\na quasi-sinusoidal component, that fills in at harder X-rays in a way quite \nsimilar to the Her X-1 main pulse (White, Swank \\& Holt 1983). In the case of \nVela X-1, the observer's line-of-sight would have to be located much closer \nto the neutron star spin equator than in Her X-1. \n\nWhile an occultation model apparently has many attractive features, a \nroughly $45\\deg$ tilt is required between the neutron star spin axis and the \nbinary axis of the system. Is this plausible? A large tilt to the neutron star\nmay have originated in the supernova explosion that gave it birth. The accretion\nof matter from the companion will cause angular momentum to be\naccreted by the neutron star. Since the direction of the time averaged \naccreted angular momentum is along the binary axis of the system, the neutron \nstar's spin axis \nshould become coaligned with the binary axis. This event will take some time\nand the accreted angular momentum will spin up the neutron star. In fact,\nthe alignment timescale and the spin-up timescale should be comparable.\nThe measured spin-up time of Her X-1 is about $10^{5}$ years. This timescale\nis the same as that predicted for the entire X-ray emitting phase of\nHer X-1 (Savonije 1978). Therefore, if Her X-1 is currently tilted that tilt\nwill in all likelyhood be maintained throughout the rest of the X-ray\nemitting phase. However the important question is what is the {\\it current} \nratio of accreted angular momentum to that at the start of the X-ray \nemitting phase?\n\nHer X-1 may be near the start of the X-ray emitting phase.\nThe X-ray emitting phase ends when the accretion flow \nbecomes great enough to smother the neutron star and prevent pulsations.\nHistorical optical observations of HZ Her show that the X-ray heating and\nhence the mass accretion rate has ceased occasionally for years to \ndecade-long periods over the last hundred years (Jones, Forman \\& Liller 1973;\nHudec \\& Wenzel 1986). \nThe current state of mass transfer depends on\nthe X-ray heating of HZ Her and is inhibited by the X-radiation pressure.\nThus HZ Her must be close to, but not quite, filling its Roche lobe.\nThis state of affairs is more \nconsistent with Her X-1 being at the beginning rather than the end of its \nX-ray phase. If so, then a highly tilted neutron star can plausibly exist in \nthe Her X-1 system. Another point in favor of such an interpretation is the \n1.24 second pulse period of Her X-1. This period is typical of the radio pulsar \npopulation. A period longer than 3 seconds or much shorter than 1 second \nwould unequivocally show that Her X-1 has been spun down or spun up by a \nsignificant history of interaction with circumstellar matter. Finally,\na tilted neutron star should cause a persistent asymmetry in the optical\norbital lightcurve about orbital phase 0.5. No such asymmetry was reported\nby Deeter et al. (1976) but later studies of the orbital optical lightcurve\nwith more data indicate the presence of just such an asymmetry (e.g. \nVoloshina, Lyuti \\& Sheffer 1990; Thomas et al. 1983).\n\nThe properties required of the inner disk to fit the observed pulse evolution\nare a scale height comparable to the neutron star diameter and a small inner\nradius ($20-40 R_{ns}$). \nFor comparison, the corotation radius \nis $157R_{ns}$ for Her X-1.\nThe predicted magnetospheric radius, $R_m$, for disk accretion depends on \nassumptions on the boundary conditions. \nUsing the known parameters for Her X-1 (Leahy \\& Scott 1998), one obtains \n$R_m=3.5\\times10^8\\alpha^{-2/61}$ cm for the model of Kiraly \\& M\\'esz\\'aros (1988);\n$R_m=3.8\\times10^8\\gamma^{2/7}$ cm for the model of Lamb (1988); and\n$R_m=4.9\\times10^8$ K cm for the formula of Finger et al. (1996) \n(which has the special case of $K=0.47$ for the model of Ghosh \\&\nLamb, 1978).\nThe model of Aly (1980) for a highly conducting disk, gives \nonly a slightly smaller value for the disk inner radius: \n$R_m=3.0\\times10^8\\alpha^{2/7}\\cos(\\chi)^{4/7}$ cm (for $\\chi$ near $\\pi/2$,\nthe dependence on $\\chi$ is $\\sin(\\chi)^{40/69}$, so the minimum $R_m$ is\n$\\simeq1/3$ of this for $\\chi=0$).\nThe disk viscosity parameter is $\\alpha$, $\\gamma$ is defined in \nLamb (1988), K is a dimensionless parameter, which Finger et al. (1996) find\nto be $\\simeq 1$ for A0535+26, and $\\chi$ is the tilt of the dipole axis \nfrom the equatorial plane.\nIn all cases the predicted disk radius greatly exceeds the inner disk\nradius required by the occultation model.\n\nAnother observation relevant to the magnetospheric radius is the spinup rate of \nHer X-~1. \nIt is the smallest among the accretion-powered\npulsars and indicates the slowest rate of net angular momentum accretion.\nDuring the giant outbursts of Be-transients, an X-ray flux vs. spin-up rate \ncorrelation has been observed in which spin-up occurs at a rate consistent\nwith the fiducial torque (e.g. Finger et al. (1996); Bildsten et al. (1997); \nNelson et al. (1997); Scott et al. (1997)). \nThe formula for the fiducial accretion torque $N_f$ is given by \n$N_f=\\dot M(GM_{X}R_s)^{1/2}$ where $R_s$ is the magnetospheric radius\nfor spin-up, $\\dot M$ is the mass accretion rate and \n$M_{X}$ is the mass of the neutron star. This formula\nassumes all the angular momentum of the accreting matter at $R_s$ \nis given to the neutron star.\nThe known spin-up rate gives a value for $R_s=8.5$ km: clearly too small to\nbe physical. \nThe small disk radius from the occultation model is much larger than this.\nThis implies that the actual torque on the neutron star must\nbe smaller than the fiducial torque, to allow a magnetospheric radius\nas large as $20-40R_{ns}$. \nIn the Ghosh \\& Lamb (1978, 1979) model of an aligned rotator, \na residual portion of the magnetic field is not screened by\ncurrents near the magnetospheric radius and will interact with material orbiting\nbeyond the corotation radius. The interaction adds a negative torque component \nto the total torque.\nA smaller net torque will be exerted if the magnetospheric radius approaches the\ncorotation radius\\footnote{Note that Ghosh and Lamb prefer to call the \ncorotation radius the `centrifugal radius' and the magnetospheric radius the \n`corotation radius'.} of the neutron star. \nThus nearly any spin-up rate can be obtained within a small range of\nmagnetospheric radii near to but inside the corotation radius. So it is\nnot surprising that the predicted magnetospheric radius from the Ghosh and\nLamb model for Her X-1 is nearly equal to the corotation radius given above.\nHowever, it is well known that the Ghosh and Lamb model \nis not consistent with the spin behaviour of many X-ray pulsars (e.g.\nBildsten et al. 1997; Nelson et al. 1997). In summary, different models \ngive a magnetospheric radius from the spin-up rate of Her X-1 in a\nwide range between $R_{ns}$ and $R_c=157R_{ns}$.\n\nHow does one account\nfor an inner disk edge which is at $20-40R_{ns}$?\nIt is much smaller than the predicted neutron star magnetosphere radius, \nyet may be much larger than the radius predicted from simple spin-up. \nWe speculate on what may be the real physical origin of the \n$20-40R_{ns}$ disk inner edge.\nOne possibility is that the dipole magnetic\nfield is much smaller than that indicated by the observed X-ray cyclotron\nline so that the predicted magnetospheric radius is much smaller. \nThe magnetospheric radius decreases from $\\sim 200R_{ns}$ to $30R_{ns}$ if the\ndipole component of B is a factor of 25 less than deduced from the cyclotron\nline. The cyclotron line would be explained as arising in non-dipolar magnetic\nfields in the accretion region at the neutron star surface. An emission \nregion concentrated in a non-dipolar surface pocket of the field and producing\na pencil beam would likely be difficult to distinguish from a similar emission \nregion in the case of a pure dipole. Another explanation has been put forth by \nBaushev \\& Bisnovatyi-Kogan (1999) in which a magnetic field of \n$4-6 \\times 10^{10}$ G is estimated for Her X-1 from the observed cyclotron \nline energy by assuming a large anisotropy exists in the electron momentum \ndistributions parallel and perpendicular to the magnetic field lines. Whether \neither of these possibilities is viable will probably require much more \nresearch. \n\nAn alternative to a reduced dipole field is a stable, thin inner disk which \npenetrates far into the magnetosphere. However, this seems very unlikely: the \nmagnetosphere is very stiff due to the steep gradient of magnetic pressure \nand energy density (as $r^{-6}$) for a dipole field. Models which have the \ndisk penetrate as deeply as possible (e.g. Aly 1980), do not have an inner \nradius very much less than other models (tilting the magnetic axis gives a \nreduction at most by a factor 3 in the inner disk radius). So a disk \npenetrating far into the magnetosphere appears to be unfeasible.\n\nAnother possibility is that current models for determining the magnetospheric\nradius are inadequate. For example, Miller \\& Stone (1997) use \nmagnetohydrodynamic calculations to show that the Balbus-Hawley\ninstability and magnetic braking have dramatic effects on the magnetospheric\nboundary. They also result in outflowing winds along field lines opened up\nby reconnection. It is quite possible that the small inner disk in Her X-1\nis due to such effects. We note that mass outflows are quite likely as there \nis extended X-ray emission from a large corona in Her X-1. \n\nThe model described in this paper is phenomenological and highly idealized.\nThe purpose was to show that an inner disk occultation can explain the \nobservations and has reasonable physical grounds for support. Considerable\nrefinement of the model remains to be done. The decay of the soft shoulders\nof the main pulse occurs earlier in the Main High state than an axisymmetric\nbeam model predicts. The soft shoulders of the Main High state main pulse\nare unequal in amplitude. These problems might indicate an offset \nin the dipole axis.\n\nAn occultation of the neutron star by the inner accretion disk explains the \npulse evolution cycle of Her X-1 in a natural fashion. Many of the details\nof the observed evolution can be accounted for by invoking a reversed \nfan beam geometry around a neutron star significantly inclined to the\nbinary axis of the system. The leading edge decay \nof the main pulse and interpulse during the Main High state is properly\npredicted. During the Short High state, the rapid disappearance of the \nsmall hard peak as well as the slower decay of the soft peak are predicted.\nNote that the soft peak shows little decay of either the leading or trailing\nedge and this is also predicted by the occultation model. In summary,\nmost of the curious pulse shape changes observed during the Main and Short \nHigh states are tied together with a single simple occultation model.\nWe note that no previous model for the pulse shape changes, including\nfree precession, has been able to account for the observed details \nof the pulse evolution.\n\n\\begin{acknowledgements}\nDMS acknowledges John E. Deeter and Paul E. Boynton for useful discussions\nand Fumiaki Nagase and Takashi Aoki for assistance while visiting ISAS. \n\\end{acknowledgements}\n\n% References\n\\newpage\n\\begin{thebibliography}{}\n\\bibitem[Aly 1980]{aly80} Aly, J. 1980, \\aap, 86, 192\n\\bibitem[Averitsev et al. 1992]{ave92} Averitsev, M., Titarchuk, L.,\n\\& Sheffer, E. 1992, Sov.Astron., 36, 35\n\\bibitem[Bai 1981]{bai81} Bai, T. 1981, \\apj, 243, 244 \n\\bibitem[Baushev et al. 1999]{baushev99} Baushev, A. N. \\& Bisnovatyi-Kogan, \nG. S. 1999, Astronomy Reports, 43, 241\n\\bibitem[Baykal et al. 1993]{baykal93} Baykal, A., Boynton, P. E., \nDeeter, J. E., \\& Scott, D. M. 1993, \\mnras, 265, 347 \n\\bibitem[Bildsten et al. 1997]{bildsten97} Bildsten, L.,\nChakrabarty, D., Chiu, J. et al. 1997, \\apjs, 113, 367\n\\bibitem[Bisnovatyi-Kogan et al. 1990]{bis90} Bisnovatyi-Kogan, G.,\nMersov, G., \\& Sheffer, E. 1990, Astron. Zu., 67, 85\n\\bibitem[Bisnovatyi-Kogan \\& Kahabka]{bis93} Bisnovatyi-Kogan, G.,\n\\& Kahabka, P. 1993, \\aap, 267, L43\n\\bibitem[Boynton et al. 1980]{boy80} Boynton, P., Crosa, L., \\& \nDeeter, J. 1980, \\apj, 237, 169 \n\\bibitem[Brainerd \\& Meszaros 1991]{bra91} Brainerd, J., \\& M\\'esz\\'aros, P.\n 1991, \\apj, 369, 179\n\\bibitem[Choi et al. 1997]{cho97} Choi, C., Seon, K., Dotani, T.,\n \\& Nagase, F. 1997, \\apjl, 476, L81 \n\\bibitem[Cooke \\& Page 1975]{coo75} Cooke, B., \\& Page, C. 1975, Nature, \n 256, 712 \n\\bibitem[Crosa \\& Boynton 1980]{cro80} Crosa, L., \\& Boynton, P. E. 1980, \n \\apj, 235, 999\n\\bibitem[Deeter 1981]{dee81}Deeter, J. E., 1981, PhD Thesis, University\nof Washington\n\\bibitem[Deeter et al. 1976]{dee76} Deeter, J., Crosa, L., Gerend, D., \n\\& Boynton, P. 1976, \\apj, 206, 861\n\\bibitem[Deeter et al. 1991]{dee91} Deeter, J., Boynton, P., Miyamoto, \nS., et al. 1991, \\apj, 383, 324 \n\\bibitem[Deeter et al. 1998]{dee98} Deeter, J., Scott, D. M., Boynton, P.,\net al. 1998, \\apj, 502, 802\n\\bibitem[Fabian et al. 1973]{fab73} Fabian, A., Pringle, J., \\& \nRees, M. 1973, Nature, 244, 212 \n\\bibitem[Finger et al. 1996]{fin96} Finger, M., Wilson, R. B., \\& Harmon, B. \n1996, \\apj, 459, 288\n\\bibitem[Gerend \\& Boynton 1976]{ger76} Gerend, D., \\& Boynton, P. \n1976, \\apj, 209, 562\n\\bibitem[Ghosh \\& Lamb 1978]{gho78} Ghosh, P., \\& Lamb, F. 1978, \n\\apj, 223, L83\n\\bibitem[Ghosh \\& Lamb 1979]{gho79} Ghosh, P., \\& Lamb, F. 1979, \n\\apj, 232, 259\n\\bibitem[Giacconi et al. 1973]{gia73} Giacconi, R., Gursky, H., Kellogg, \nE. et al. 1973, \\apj, 184, 227\n\\bibitem[Hudec \\& Wenzel 1986]{hudec86}Hudec, R., \\& Wenzel, W. 1986,\n\\aap, 158, 396\n\\bibitem[Jones, Forman \\& Liller 1973]{jon73} Jones, C., Forman, W.,\n\\& Liller, W. 1973, \\apjl, 182, L109\n\\bibitem[Jones \\& Forman 1976]{jon76}Jones, C., \\& Forman, W.\n1976, \\apjl, 209, L131 \n\\bibitem[Joss et al. 1978]{jos78} Joss, P., Fechner, W., Forman, W.,\n\\& Jones, C. 1978, \\apj, 225, 994\n\\bibitem[Kahabka 1987]{kab87} Kahabka, P. 1987 Ph.D. Thesis, Tech. Univ. \nMunchen\n\\bibitem[Kahabka 1989]{kab89} Kahabka, P. 1989, in The 23rd ESLAB Symposium\non Two Topics in X-ray Astronomy, Vol. 1 X-ray Binaries, p447 \n\\bibitem[Katz 1973]{kat73} Katz, J. I. 1973, {\\rm Nature Phys. Sci.}, 246, 87\n\\bibitem[Kiraly \\& Meszaros 1988] {kir88} Kiraly, P., \\& M\\'esz\\'aros, P.\n1988, \\apj, 333, 719\n\\bibitem[Lamb et al. 1973] {lam73} Lamb, F., Pethick, C., \\& Pines, D.\n1973, \\apj, 184, 271\n\\bibitem[Lamb 1988] {lam88} Lamb, F. 1988, in Timing Neutron Stars (NATO\nASI Vol. 262, Kluwer, Dordrecht) p649\n\\bibitem[Lang et al. 1981] {lan81} Lang, F., Levine, A., Britz, M.,\net al. 1981, \\apj, 246, L21\n\\bibitem[Leahy 1995a]{lea95a} Leahy, D. A. 1995a, \\aap Supp., 113, 21\n\\bibitem[Leahy 1995b]{lea95b} Leahy, D. A. 1995b, \\apj, 450, 339\n\\bibitem[Leahy \\& Scott 1998]{lea98} Leahy, D. A., \\& Scott, D.M. 1998, \n\\apj, 503, L63\n\\bibitem[McCray et al. 1982]{mcray82} McCray, R., Shull, M., Boynton, P.,\nDeeter, J., Holt, S., \\& White, N. 1982, \\apj, 262, 301\n\\bibitem[Meszaros \\& Nagel 1985] {mes85} M\\'esz\\'aros, P., \\& Nagel, W.\n1985, \\apj, 299, 138 \n\\bibitem[Miller \\& Stone 1997] {mil97} Miller, K., \\& Stone, J. 1997\n \\apj, 489, 890 \n\\bibitem[Riffert \\& Meszaros 1988] {riff88} Riffert, H., \\& M\\'esz\\'aros, P.\n1988, \\apj, 325, 207 \n\\bibitem[Middleditch 1983]{mid83} Middleditch, J. 1983, \\apj, 275, 278\n\\bibitem[Middleditch \\& Nelson 1976]{mid76} Middleditch, J.,\n\\& Nelson, J. 1976, \\apj, 208, 567\n\\bibitem[Mihara et al. 1991]{mih91} Mihara, T., Ohashi, T., Makishima, K.,\net al. 1991, \\pasj, 43, 501 \n\\bibitem[Nagase 1989]{nag89} Nagase, F. 1989, \\pasj, 41, 1\n\\bibitem[Nelson et al. 1997]{nel97} Nelson, R., Bildsten, L.,\nChakrabarty, D., et al. 1997, \\apj, 488, 117\n\\bibitem[\\\"Ogelman \\& Tr\\\"umper 1988]{oge88} \\\"Ogelman, H., \\& Tr\\\"umper, J.\n1988, {\\it Mem. Soc. Astron. Ital.}, 59, 169\n\\bibitem[Oosterbroek et al. 2000]{ooster00} Oosterbroek, T., Parmar, A. N.,\nDal Fiume, D., Orlandini, M., Santangelo, A., Del Sordo, S., \\&\nSegreto, A. 2000, \\aap, 353, 575 \n\\bibitem[Parmar et al. 1980]{parm80} Parmar, A. N., Sanford, P. W., \\& Fabian,\nA. C. 1980, \\mnras, 192, 311\n\\bibitem[Petterson 1975]{pet75} Petterson, J. 1975, \\apj, 201, L61\n\\bibitem[Petterson 1977]{pet77} Petterson, J. 1977, \\apj, 218, 783\n\\bibitem[Petterson et al. 1991]{pet91} Petterson, J., \nRothschild, R. \\& Gruber, D. 1991, \\apj, 378, 696\n\\bibitem[Priedhorsky \\& Holt 1987]{pried87} Priedhorsky, W. C., \\& Holt, S. S.\n1987, Space Science Reviews, 45, 291\n\\bibitem[Savonije 1978]{sav78} Savonije, G. J. 1978, \\aap, 62, 317\n\\bibitem[Schandl \\& Meyer 1994]{sch94} Schandl, S., \\& Meyer, F. \n1994, \\aap, 289, 149\n\\bibitem[Scott 1993]{sco93} Scott, D. M. 1993, PhD Thesis, University \nof Washington\n\\bibitem[Scott et al. 1997a]{sco97a} Scott, D. M., Wilson, R. B., Finger, M. \n\\& Leahy, D. 1997, ``Proceedings of the Fourth Compton Symposium'',\neds. C. Dermer, M. Strickland \\& J. Kurfess, AIP Conference Proceedings 410,\nAmerican Institute of Physics, Woodbury, New York, 748\n\\bibitem[Scott \\& Leahy 1999]{sco99} Scott, D. M., \\& Leahy, D. A. 1999,\n\\apj, 510, 974\n\\bibitem[Scott et al. 1997b]{sco97b} Scott, D. M., Finger, M., Wilson, R. B., \nKoh, D., Prince, T., Vaughan, B., Chakrabarty, D. 1997, \\apj, 488, 831\n\\bibitem[Shakura \\& Sunyaev 1973]{sha73} Shakura, N., \\& Sunyaev, R. 1973, \n\\aap, 24, 337\n\\bibitem[Shakura et al 1998]{sha98} Shakura, N., Postnov, K., \\&\nProkhorov, M. 1998, \\aap, 331 , L37\n\\bibitem[Sheffer et al 1992]{she92} Sheffer, E., et al. 1992, Sov. Astron.\n36, 41 \n\\bibitem[Soong et al. 1987]{soo87} Soong, Y., Gruber, D., \n\\& Rothschild, R. 1987, \\apj, 319, L77\n\\bibitem[Soong et al. 1990a]{soo90a} Soong, Y., Gruber, D., Peterson, L., \n\\& Rothschild, R. 1990a, \\apj, 348, 634\n\\bibitem[Soong et al. 1990b]{soo90b} Soong, Y., Gruber, D., Peterson, L., \n\\& Rothschild, R. 1990b, \\apj, 348, 641\n\\bibitem[Thomas et al. 1983]{thom83} Thomas, H., Africano, J., \nDelgado, A., \\& Schmidt, H. 1983, \\aap, 126, 45 \n\\bibitem[Trumper et al. 1986]{tru86} Tr\\\"umper, J., Kahabka, P., \n\\\"Ogelman, H., et al. 1986, \\apj, 300, L63 \n\\bibitem[Voloshina, Lyuti \\& Sheffer 1990]{vol90} Voloshina, I. B., \nLyuti, V. M., \\& Sheffer, E. K. 1990, Sov. Astron Lett., 16(4)\n\\bibitem[White, Swank \\& Holt]{white1983} White, N. E., Swank, J. H., \\&\nHolt, S. S. 1983, \\apj, 270, 711\n\\end{thebibliography} \n\n% Figure Captions\n\\newpage\n\nFig. 1---Light curves (1--37 keV) for {\\it Ginga} LAC observations of\nHer X-1 in the April, May and June 1989 Main, Short and Main High states,\nrespectively. The 35-Day phase is calculated using $P_{35}=34.8534$ days \n($20.5P_{orb}$) and an epoch $T_{0}=48478.6 - 31 P_{35} = 47398.14$ MJD with \nphase 0.0 corresponding to the Main High state turn-on. Eclipse ingress and \negress are denoted by dashed vertical lines. Ticks and numbers at the top of \neach panel indicate the 35-day phase. Solid vertical lines mark predicted \nturn-on time. The bottommost plot also shows the 20-50 keV pulsed flux \nlightcurve obtained from BATSE monitoring of Her X-1, with the flux scale \nshown on the righthand side. \n\nFig. 2---{\\it (upper panel)} View of the disk as seen from the neutron star. \nThe outermost ring (filled diamonds) is tilted by $20\\deg$, the innermost \nring (hollow diamonds) by $11\\deg$ and leads in precession phase by \n$138.6\\deg$. \nThe elevation of the observer of Her X-1 ($-5\\deg$) is marked by the \nhorizontal dashed line.\n% For LMC X-4, the observer\n% would be placed at an elevation of $22\\deg$ above the binary plane.\nBold solid vertical lines mark turn-on's.\nThe observer sees Her X-1 emerge as a point source from the outer disk\nrim but an extended source at the inner disk rim.\n%After turn-on until roughly the point marked by the vertical dotted line,\n%coronal obscuration will be decreasing. The 35-day phase of partial blocking\n%of the X-ray emission region during the turn-off is marked by dashed sinusoids.\nThe vertical dotted line shows the approximate point where the disk cuts across\nthe neutron star face during the Main High state. \n{\\it (Middle panel)} The 1989 1--37 keV Her X-1 light curve observed with \n{\\it Ginga}. \n{\\it (Bottom panel)} Nineteen ``0.2 turn-on'' 35-day cycles of the 2--12 keV \nRXTE ASM light curve folded at a period of 20.5 $P_{orb}$. \n\nFig. 3---{\\it (upper left panel)} {\\it Ginga} observation of 1-37 keV count rate\nduring the May 1989 Short High state turn-on. Vertical dashed line marks \npredicted eclipse egress. Solid curve models flux of point source rising through\nouter disk edge (see text). Errors are plotted, unless smaller than plotted\npoint size. \n{\\it (lower left panel)} Same for August 1991 Main\nHigh state turn-on. {\\it (upper right panel)} Softness ratios of two sets of \nenergies during the May 1989 Short High state turn-on. Note that harder flux \nincreases first consistent with cold matter absorption. \n{\\it (lower right panel)} Same for August 1991 Main High state turn-on.\n\nFig. 4---The softness ratio for the average Main High state light curve. The \nhard color is the BATSE 20-50 kev pulsed flux and the soft color is the \nRXTE/ASM 2-12 keV flux. The {\\it top} panel shows the average softness ratio \nfor 0.2 turn-on Main High states, the {\\it bottom} panel for 0.7 turn-on \nMain High states. Turn-on is 35-day phase 0. Vertical dashed lines mark \neclipse ingress/egress boundaries. \n\nFig. 5---Sample {\\it Ginga} pulse profiles in five energy bands,\nafter subtracting background and correcting for collimator\ntransmission. The bands increase in energy from top to\nbottom: 1.0--4.6, 4.6--9.3, 9.3--14, 14--23, 23--37 keV. The bottommost\npanels display a hardness ratio (9.3--23 keV band divided by 1.0--4.6 keV\nband). Pulse features discussed in the text are labeled. \n{\\it (a)}---Leftmost panel set. Main High state observation on MJD 47643. \nTotal exposure time is 8713 seconds. \n{\\it Main pulse} occupies phase interval 0.75--1.25 and the {\\it interpulse} \noccupies phase interval 0.3--0.7. \n{\\it (b)}---Center panel set. Same profiles as in (a), but with close-up\nof interpulse. \n{\\it (c)}---Rightmost panel set. Short High state observation on MJD 47662,\nless than a day after Short High state turn-on. Total exposure time is 10118 \nseconds. At same scale as center panel set.\n\nFig. 6---Time evolution of the pulse profile. Upper right and upper\nleft panels show evolution during the April 1989 Main High state in\nenergy bands 1.0-4.6 keV and 9.3-14 keV. The flux of the smallest amplitude \npulse in each panel is correct while offsets of 50 counts/sec have been \nadded between pulses for clarity. The 35d phase of the pulses increase\nwith decreasing amplitude as: 0.05, 0.162, 0.216, 0.243, 0.245, 0.247,\n0.249, 0.250. \n{\\it Lower left} and {\\it lower right} panels.\nSame for the May 1989 Short High state but with offsets of 20 counts/sec\nadded. The 35d phase increases with decreasing amplitude as 0.590, 0.595,\n0.613, 0.641, 0.698.\n\nFig. 7---Sequence of pulse profiles resulting from a freely precessing neutron \nstar with an axisymmetric pencil and fan beam using the parameters determined \nby Kahabka (1987,1989). The pencil beam amplitude is three times the fan beam \namplitude and both beam components have half-widths of about $20\\deg$. One \nfull 35-day precession cycle is shown with successive pulses occuring one day \napart and spaced by one flux unit. On the right is the pulsed flux light curve \nover the precession cycle normalized to a maximum value of 10.\n\nFig. 8---Top left panel. Model pulse comprised of identical beam configurations\nat each pole consisting of a central pencil beam (C) and surrounding by a \nfan beam (B) with an opening angle of $40^\\circ$. Three constant components \nare present, two produced by isotropic emission high in the accretion column \n(D,E) and one from coronal emission. Top center. Emission locations of \npulse components A, B and C. Location of disk edge for 35-day phase 0.23 \nshown moving from right-to-left, top-to-bottom across figure (case 1). \nTop right. Larger view showing emission locations of pulse components\nD and E. Bottom left. Same as above but with reversed fan beam (opening \nangle of $140^\\circ$) and light bending taken into account. Bottom center. \nThe `A' and `B' components are now emitted when the accretion column is on \nthe ``back'' side of the neutron star with respect to the observer. \nLocation of disk edge for 35-day phase 0.58 shown moving from right-to-left, \nbottom-to-top across figure (case 2). \n\nFig. 9---Top panel. Photon trajectories for $10$ keV photons backscattered\nfrom a cyclotron resonance at a height of $1.5 R_{ns}$ above a $1.4\\ \\Msun$ \nneutron star. The scattering height assumes a surface magnetic field strength \ncorresponding to a $40$ keV cyclotron line and a simple dipole field. \nBottom panel. The photon impact parameter and apparent emission angle for\nthe case of no light bending (diamonds) and with light bending (triangles).\nDistance units in Schwarzschild radii.\n\nFig. 10a---Model of Main High state pulse evolution. Left panel sets shows\na sequence of pulse profiles corresponding to the figure 8b, reversed fan\nbeam case. Middle panel set shows closeup of pulse emission region and\ngradual covering by disk. Rightmost panel set shows larger view of same \nregion. 35-day phase is shown at far right. \n\nFig. 10b---Model of Short High state pulse evolution. Left panel sets shows\na sequence of pulse profiles corresponding to the figure 8b, reversed fan\nbeam case. Middle panel set shows closeup of pulse emission region and\ngradual covering by disk. Rightmost panel set shows larger view of same \nregion. 35-day phase is shown at far right. \n\n%%% Tables\n\n% Table 1\n\\newpage\n\n\\makeatletter\n\\def\\jnl@aj{AJ}\n\\ifx\\revtex@jnl\\jnl@aj\\let\\tablebreak=\\nl\\fi\n\\makeatother\n\n% From here on, the file contains tabular data as an author might\n% prepare it.\n\n\\begin{deluxetable}{lrrrcrrrr}\n\\tablewidth{33pc}\n\\tablecaption{Disk occultation model parameters}\n\\tablehead{\n\\colhead{Parameter} & \\colhead{Value} &\\colhead{Symbol} }\n\\startdata \n\nObserver inclination & $85 \\deg$ & \\nl\nLOS-rotation axis angle & $61 \\deg$ & \\nl\nMagnetic axis - spin axis angle & $48 \\deg$ & \\nl\nspin axis - binary axis angle & $52 \\deg$ & \\nl\nNS azimuth & $45.5 \\deg$ & \\nl\nPencil beam scale factor & 2.75 & $I_{pen}$ \\nl\nHalf-width of pencil beam & $18 \\deg$ & $\\sigma_{p}$ \\nl\nFan beam scale factor & 1 & $I_{fan}$ \\nl\nOpening angle of direct fan beam & $40 \\deg$ & $\\theta_{cone}$ \\nl\nOpening angle of reversed fan beam & $140 \\deg$ & $\\theta_{cone}$ \\nl\nHalf-width of fan beam & $20 \\deg$ & $\\sigma_{f}$ \\nl\nEffective height of fan beam emission point & $2 R_{ns}$ & \\nl\nInner disk radius & $30.5 R_{ns}$ & \\nl\nAccretion disk tilt & $11 \\deg$ & \\nl\nOptical depth at disk atmosphere base & 30 & $\\tau_{disk}$ \\nl\nDisk atmosphere e-folding length & $1 R_{ns}$ & $\\sigma_d$ \\nl\nQuasi-sinusoidal emission point height & $15 R_{ns}$ \\nl \nQuasi-sinusoidal scale factor (D=E) & 0.1 & $I_{D,E}$ \\nl\nLow state emission scale factor & 0.1 & $I_{Low}$ \\nl\n\n\\enddata\n\\end{deluxetable} \n\n% Table 2\n\\newpage\n\n\\makeatletter\n\\def\\jnl@aj{AJ}\n\\ifx\\revtex@jnl\\jnl@aj\\let\\tablebreak=\\nl\\fi\n\\makeatother\n\n% From here on, the file contains tabular data as an author might\n% prepare it.\n\n\\begin{deluxetable}{lrrrcrrrr}\n\\tablewidth{33pc}\n\\tablecaption{direct fan beam disk occultation scenarios}\n\\tablehead{\n\\colhead{Spin} & \\colhead{Tilt} & \\colhead{Precession} & \\colhead{Okay?} }\n\\startdata \n\nprograde & left & retrograde & no \\nl\nprograde & right & retrograde & no \\nl\nprograde & left & prograde & yes \\nl\nprograde & right & prograde & no \\nl\nretrograde & right & prograde & no \\nl\nretrograde & left & prograde & no \\nl\nretrograde & left & retrograde & no \\nl\nretrograde & right & retrograde & yes \\nl\n\n\\enddata\n\\end{deluxetable} \n \n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002327.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Aly 1980]{aly80} Aly, J. 1980, \\aap, 86, 192\n\\bibitem[Averitsev et al. 1992]{ave92} Averitsev, M., Titarchuk, L.,\n\\& Sheffer, E. 1992, Sov.Astron., 36, 35\n\\bibitem[Bai 1981]{bai81} Bai, T. 1981, \\apj, 243, 244 \n\\bibitem[Baushev et al. 1999]{baushev99} Baushev, A. N. \\& Bisnovatyi-Kogan, \nG. S. 1999, Astronomy Reports, 43, 241\n\\bibitem[Baykal et al. 1993]{baykal93} Baykal, A., Boynton, P. E., \nDeeter, J. E., \\& Scott, D. M. 1993, \\mnras, 265, 347 \n\\bibitem[Bildsten et al. 1997]{bildsten97} Bildsten, L.,\nChakrabarty, D., Chiu, J. et al. 1997, \\apjs, 113, 367\n\\bibitem[Bisnovatyi-Kogan et al. 1990]{bis90} Bisnovatyi-Kogan, G.,\nMersov, G., \\& Sheffer, E. 1990, Astron. Zu., 67, 85\n\\bibitem[Bisnovatyi-Kogan \\& Kahabka]{bis93} Bisnovatyi-Kogan, G.,\n\\& Kahabka, P. 1993, \\aap, 267, L43\n\\bibitem[Boynton et al. 1980]{boy80} Boynton, P., Crosa, L., \\& \nDeeter, J. 1980, \\apj, 237, 169 \n\\bibitem[Brainerd \\& Meszaros 1991]{bra91} Brainerd, J., \\& M\\'esz\\'aros, P.\n 1991, \\apj, 369, 179\n\\bibitem[Choi et al. 1997]{cho97} Choi, C., Seon, K., Dotani, T.,\n \\& Nagase, F. 1997, \\apjl, 476, L81 \n\\bibitem[Cooke \\& Page 1975]{coo75} Cooke, B., \\& Page, C. 1975, Nature, \n 256, 712 \n\\bibitem[Crosa \\& Boynton 1980]{cro80} Crosa, L., \\& Boynton, P. E. 1980, \n \\apj, 235, 999\n\\bibitem[Deeter 1981]{dee81}Deeter, J. E., 1981, PhD Thesis, University\nof Washington\n\\bibitem[Deeter et al. 1976]{dee76} Deeter, J., Crosa, L., Gerend, D., \n\\& Boynton, P. 1976, \\apj, 206, 861\n\\bibitem[Deeter et al. 1991]{dee91} Deeter, J., Boynton, P., Miyamoto, \nS., et al. 1991, \\apj, 383, 324 \n\\bibitem[Deeter et al. 1998]{dee98} Deeter, J., Scott, D. M., Boynton, P.,\net al. 1998, \\apj, 502, 802\n\\bibitem[Fabian et al. 1973]{fab73} Fabian, A., Pringle, J., \\& \nRees, M. 1973, Nature, 244, 212 \n\\bibitem[Finger et al. 1996]{fin96} Finger, M., Wilson, R. B., \\& Harmon, B. \n1996, \\apj, 459, 288\n\\bibitem[Gerend \\& Boynton 1976]{ger76} Gerend, D., \\& Boynton, P. \n1976, \\apj, 209, 562\n\\bibitem[Ghosh \\& Lamb 1978]{gho78} Ghosh, P., \\& Lamb, F. 1978, \n\\apj, 223, L83\n\\bibitem[Ghosh \\& Lamb 1979]{gho79} Ghosh, P., \\& Lamb, F. 1979, \n\\apj, 232, 259\n\\bibitem[Giacconi et al. 1973]{gia73} Giacconi, R., Gursky, H., Kellogg, \nE. et al. 1973, \\apj, 184, 227\n\\bibitem[Hudec \\& Wenzel 1986]{hudec86}Hudec, R., \\& Wenzel, W. 1986,\n\\aap, 158, 396\n\\bibitem[Jones, Forman \\& Liller 1973]{jon73} Jones, C., Forman, W.,\n\\& Liller, W. 1973, \\apjl, 182, L109\n\\bibitem[Jones \\& Forman 1976]{jon76}Jones, C., \\& Forman, W.\n1976, \\apjl, 209, L131 \n\\bibitem[Joss et al. 1978]{jos78} Joss, P., Fechner, W., Forman, W.,\n\\& Jones, C. 1978, \\apj, 225, 994\n\\bibitem[Kahabka 1987]{kab87} Kahabka, P. 1987 Ph.D. Thesis, Tech. Univ. \nMunchen\n\\bibitem[Kahabka 1989]{kab89} Kahabka, P. 1989, in The 23rd ESLAB Symposium\non Two Topics in X-ray Astronomy, Vol. 1 X-ray Binaries, p447 \n\\bibitem[Katz 1973]{kat73} Katz, J. I. 1973, {\\rm Nature Phys. Sci.}, 246, 87\n\\bibitem[Kiraly \\& Meszaros 1988] {kir88} Kiraly, P., \\& M\\'esz\\'aros, P.\n1988, \\apj, 333, 719\n\\bibitem[Lamb et al. 1973] {lam73} Lamb, F., Pethick, C., \\& Pines, D.\n1973, \\apj, 184, 271\n\\bibitem[Lamb 1988] {lam88} Lamb, F. 1988, in Timing Neutron Stars (NATO\nASI Vol. 262, Kluwer, Dordrecht) p649\n\\bibitem[Lang et al. 1981] {lan81} Lang, F., Levine, A., Britz, M.,\net al. 1981, \\apj, 246, L21\n\\bibitem[Leahy 1995a]{lea95a} Leahy, D. A. 1995a, \\aap Supp., 113, 21\n\\bibitem[Leahy 1995b]{lea95b} Leahy, D. A. 1995b, \\apj, 450, 339\n\\bibitem[Leahy \\& Scott 1998]{lea98} Leahy, D. A., \\& Scott, D.M. 1998, \n\\apj, 503, L63\n\\bibitem[McCray et al. 1982]{mcray82} McCray, R., Shull, M., Boynton, P.,\nDeeter, J., Holt, S., \\& White, N. 1982, \\apj, 262, 301\n\\bibitem[Meszaros \\& Nagel 1985] {mes85} M\\'esz\\'aros, P., \\& Nagel, W.\n1985, \\apj, 299, 138 \n\\bibitem[Miller \\& Stone 1997] {mil97} Miller, K., \\& Stone, J. 1997\n \\apj, 489, 890 \n\\bibitem[Riffert \\& Meszaros 1988] {riff88} Riffert, H., \\& M\\'esz\\'aros, P.\n1988, \\apj, 325, 207 \n\\bibitem[Middleditch 1983]{mid83} Middleditch, J. 1983, \\apj, 275, 278\n\\bibitem[Middleditch \\& Nelson 1976]{mid76} Middleditch, J.,\n\\& Nelson, J. 1976, \\apj, 208, 567\n\\bibitem[Mihara et al. 1991]{mih91} Mihara, T., Ohashi, T., Makishima, K.,\net al. 1991, \\pasj, 43, 501 \n\\bibitem[Nagase 1989]{nag89} Nagase, F. 1989, \\pasj, 41, 1\n\\bibitem[Nelson et al. 1997]{nel97} Nelson, R., Bildsten, L.,\nChakrabarty, D., et al. 1997, \\apj, 488, 117\n\\bibitem[\\\"Ogelman \\& Tr\\\"umper 1988]{oge88} \\\"Ogelman, H., \\& Tr\\\"umper, J.\n1988, {\\it Mem. Soc. Astron. Ital.}, 59, 169\n\\bibitem[Oosterbroek et al. 2000]{ooster00} Oosterbroek, T., Parmar, A. N.,\nDal Fiume, D., Orlandini, M., Santangelo, A., Del Sordo, S., \\&\nSegreto, A. 2000, \\aap, 353, 575 \n\\bibitem[Parmar et al. 1980]{parm80} Parmar, A. N., Sanford, P. W., \\& Fabian,\nA. C. 1980, \\mnras, 192, 311\n\\bibitem[Petterson 1975]{pet75} Petterson, J. 1975, \\apj, 201, L61\n\\bibitem[Petterson 1977]{pet77} Petterson, J. 1977, \\apj, 218, 783\n\\bibitem[Petterson et al. 1991]{pet91} Petterson, J., \nRothschild, R. \\& Gruber, D. 1991, \\apj, 378, 696\n\\bibitem[Priedhorsky \\& Holt 1987]{pried87} Priedhorsky, W. C., \\& Holt, S. S.\n1987, Space Science Reviews, 45, 291\n\\bibitem[Savonije 1978]{sav78} Savonije, G. J. 1978, \\aap, 62, 317\n\\bibitem[Schandl \\& Meyer 1994]{sch94} Schandl, S., \\& Meyer, F. \n1994, \\aap, 289, 149\n\\bibitem[Scott 1993]{sco93} Scott, D. M. 1993, PhD Thesis, University \nof Washington\n\\bibitem[Scott et al. 1997a]{sco97a} Scott, D. M., Wilson, R. B., Finger, M. \n\\& Leahy, D. 1997, ``Proceedings of the Fourth Compton Symposium'',\neds. C. Dermer, M. Strickland \\& J. Kurfess, AIP Conference Proceedings 410,\nAmerican Institute of Physics, Woodbury, New York, 748\n\\bibitem[Scott \\& Leahy 1999]{sco99} Scott, D. M., \\& Leahy, D. A. 1999,\n\\apj, 510, 974\n\\bibitem[Scott et al. 1997b]{sco97b} Scott, D. M., Finger, M., Wilson, R. B., \nKoh, D., Prince, T., Vaughan, B., Chakrabarty, D. 1997, \\apj, 488, 831\n\\bibitem[Shakura \\& Sunyaev 1973]{sha73} Shakura, N., \\& Sunyaev, R. 1973, \n\\aap, 24, 337\n\\bibitem[Shakura et al 1998]{sha98} Shakura, N., Postnov, K., \\&\nProkhorov, M. 1998, \\aap, 331 , L37\n\\bibitem[Sheffer et al 1992]{she92} Sheffer, E., et al. 1992, Sov. Astron.\n36, 41 \n\\bibitem[Soong et al. 1987]{soo87} Soong, Y., Gruber, D., \n\\& Rothschild, R. 1987, \\apj, 319, L77\n\\bibitem[Soong et al. 1990a]{soo90a} Soong, Y., Gruber, D., Peterson, L., \n\\& Rothschild, R. 1990a, \\apj, 348, 634\n\\bibitem[Soong et al. 1990b]{soo90b} Soong, Y., Gruber, D., Peterson, L., \n\\& Rothschild, R. 1990b, \\apj, 348, 641\n\\bibitem[Thomas et al. 1983]{thom83} Thomas, H., Africano, J., \nDelgado, A., \\& Schmidt, H. 1983, \\aap, 126, 45 \n\\bibitem[Trumper et al. 1986]{tru86} Tr\\\"umper, J., Kahabka, P., \n\\\"Ogelman, H., et al. 1986, \\apj, 300, L63 \n\\bibitem[Voloshina, Lyuti \\& Sheffer 1990]{vol90} Voloshina, I. B., \nLyuti, V. M., \\& Sheffer, E. K. 1990, Sov. Astron Lett., 16(4)\n\\bibitem[White, Swank \\& Holt]{white1983} White, N. E., Swank, J. H., \\&\nHolt, S. S. 1983, \\apj, 270, 711\n\\end{thebibliography}"
}
] |
astro-ph0002328
|
An analytic model for the epoch of halo creation
|
[
{
"author": "W.J.Percival"
},
{
"author": "$^{1,2}$ L.Miller$^1$ and J.A.Peacock$^2$"
},
{
"author": "$^1$ Dept. of Physics"
},
{
"author": "Nuclear \\& Astrophysics Laboratory"
},
{
"author": "Keble Road"
},
{
"author": "Oxford OX1 3RH"
},
{
"author": "U.K."
},
{
"author": "Royal Observatory"
},
{
"author": "Blackford Hill"
},
{
"author": "Edinburgh EH9 3HJ"
}
] |
In this paper we describe the Bayesian link between the cosmological mass function and the distribution of times at which isolated halos of a given mass exist. By assuming that clumps of dark matter undergo monotonic growth on the time-scales of interest, this distribution of times is also the distribution of `creation' times of the halos. This monotonic growth is an inevitable aspect of gravitational instability. The spherical top-hat collapse model is used to estimate the rate at which clumps of dark matter collapse. This gives the prior for the creation time given no information about halo mass. Applying Bayes' theorem then allows {\em any} mass function to be converted into a distribution of times at which halos of a given mass are created. This general result covers both Gaussian and non-Gaussian models. We also demonstrate how the mass function and the creation time distribution can be combined to give a joint density function, and discuss the relation between the time distribution of major merger events and the formula calculated. Finally, we determine the creation time of halos within three N-body simulations, and compare the link between the mass function and creation rate with the analytic theory.
|
[
{
"name": "paper.tex",
"string": "\\documentstyle[epsf,graphics,epsfig]{mn}\n\n\\newcommand{\\etal}{{\\it et~al.}}\n\\newcommand{\\msun}{\\thinspace\\hbox{$M_{\\odot}$}\\ }\n\n\\title[The epoch of halo creation] \n{An analytic model for the epoch of halo creation}\n\n\\author[W.J. Percival \\etal]{W.J.Percival,$^{1,2}$ L.Miller$^1$\n\tand J.A.Peacock$^2$\\\\\n $^1$ Dept. of Physics, University of Oxford, \n Nuclear \\& Astrophysics Laboratory, Keble Road, Oxford OX1 3RH, U.K.\\\\\n $^2$ Institute for Astronomy, University of Edinburgh, \n Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, U.K.\\\\}\n\n\\date{Submitted for publication in MNRAS}\n\\begin{document}\n\\maketitle\n\n\\begin{abstract}\nIn this paper we describe the Bayesian link between the cosmological\nmass function and the distribution of times at which isolated halos of\na given mass exist. By assuming that clumps of dark matter undergo\nmonotonic growth on the time-scales of interest, this distribution of\ntimes is also the distribution of `creation' times of the halos. This\nmonotonic growth is an inevitable aspect of gravitational\ninstability. The spherical top-hat collapse model is used to estimate\nthe rate at which clumps of dark matter collapse. This gives the prior\nfor the creation time given no information about halo mass. Applying\nBayes' theorem then allows {\\em any} mass function to be converted\ninto a distribution of times at which halos of a given mass are\ncreated. This general result covers both Gaussian and non-Gaussian\nmodels. We also demonstrate how the mass function and the creation\ntime distribution can be combined to give a joint density function,\nand discuss the relation between the time distribution of major merger\nevents and the formula calculated. Finally, we determine the creation\ntime of halos within three N-body simulations, and compare the link\nbetween the mass function and creation rate with the analytic theory.\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: halos -- formation, cosmology: theory -- dark matter\n\\end{keywords}\n\n\\section{Introduction} \\label{sec:intro}\n\nThe hierarchical build-up of self-gravitating dark matter is thought\nto drive evolution in the observable universe. The formation of clumps\nof dark matter precipitates the formation of galaxies by providing a\npotential well into which gas can fall and subsequently cool. Violent\nmergers between equally sized halos and their associated galaxies are\nthought to be important for starbursts and quasar activation. In order\nto model and understand the observable universe it is therefore\nessential to understand the build-up of the dark structure.\n\nThe most widely used analytic model for the distribution of mass in\nisolated halos at any epoch comes from Press-Schechter (PS) theory\n\\cite{ps}. By smoothing the initial field of density fluctuations on\ndifferent scales, information on the distribution of perturbation\nsizes can be obtained. Linking the time at which these perturbations\ncollapse to the initial overdensities using the simplified spherical\ntop-hat collapse model allows the distribution of mass in isolated\nhalos at any epoch to be determined \\cite{ps,peacock,bond}.\n\nIn Percival \\& Miller \\shortcite{ev1} (hereafter paper~I), we used the\ntenets of PS theory to model the related, but distinct problem of\ndetermining the distribution of times at which halos of a given mass\nare created. Here, `creation' is defined as the epoch at which\nnon-linear collapse is predicted. Two derivations were given, one of\nwhich directly used the trajectories invoked in PS theory\n\\cite{peacock,bond}, and one of which used Bayes' theorem to convert\nfrom the PS mass function to a time distribution. The second\nderivation required the prior for the creation time which was\ncalculated by examining the trajectories model.\n\nIn this paper we extend the Bayesian link between the mass function\nand the creation time distribution to cover any mass function. This is\nimportant, not only because it is known that standard PS theory is\nwrong in detail (e.g. Sheth \\& Tormen 1999), but especially because\nthe new extension applies to mass functions derived from more general\ndensity fields including non-Gaussian models (e.g. Matarrese, Verde \\&\nJimenez 2000).\n\nFirst, we adopt the assumption that all clumps monotonically increase\nin mass on the cosmological time scales of interest. This monotonic\ngrowth is an inevitable aspect of gravitational instability. Every\nepoch should now be thought of as a creation time for a given clump,\nand we need not make the distinction between the creation time\ndistribution and the distribution of times at which a given halo\nexists. \n\nIn order to convert from a mass function to a distribution in time we\nrequire the prior for the creation time. This is the rate at which\ncreation events occur, given no information about the halo mass. In\nthis work we use the spherical top-hat collapse (STHC) model to\nprovide a simple mechanism for determining the required rate. In\nSection~\\ref{sec:tophat} we derive the link between collapse time and\nthe overdensity at an early epoch for the STHC model within any\nFriedmann cosmology. Having determined that this relation is\nindependent of halo mass, this leads directly to an approximation to\nthe prior for the creation time, described in Section~\\ref{sec:time}.\nThis is the second major assumption adopted in this paper: that the\nprior for the creation time is well approximated by this simple model\nfor the break-away of structure from linear expansion. This means that\nfollowing the two simple assumptions detailed above, we are able to\nconvert any mass function to give the distribution of epochs at which\nhalos of a given mass are created.\n\nSimple models of cosmologically evolving phenomena often adopt an\nimportant mass range rather than a specific halo mass (e.g. paper~I,\nGranato \\etal\\ 1999). In order to use the work presented here in these\nmodels, the joint distribution of halos in mass and creation time is\nrequired. Although calculating the required joint probability is\nformally impossible because the equations cannot be properly\nnormalised, a formula with the correct shape can be determined and is\npresented in Section~\\ref{sec:joint}.\n\nSo far we have not made a distinction between the slow accretion of\nmass onto a halo and major mergers between halos. Such a distinction\nis important because only major mergers are thought to play a vital\nrole in starbursts and quasar activation (see paper~I). The time\ndistribution calculated in this paper determines when halos existed\n(or were created by any mechanism assuming monotonic clump growth)\nwhich is not necessarily equal to the distribution of merger\nevents. This is discussed in Section~\\ref{sec:mergers}.\n\nFinally, we compare the analytic link between the mass function and\nthe creation rate to the results from three numerical simulations of\nstructure formation in different cosmological models. An analytic fit\nto the mass function as described by Sheth \\& Tormen \\shortcite{sheth}\nis adopted and is converted into a creation rate using the STHC\nmodel. This model is compared with and shown to be in good agreement\nwith the numerical results.\n\n\\section{The Spherical Top-Hat Collapse Model} \\label{sec:tophat}\n\nIn this Section we analyse the STHC model which is the simplest model\nfor the way in which clumps of dark matter break free from linear\ngrowth and undergo non-linear collapse. We present the derivation of\nthe link between the initial overdensity and the collapse time $t_{\\rm\ncoll}$ in a form which clearly shows that this link is independent of\nthe mass of the overdensity. The derivation also demonstrates a method\nfor calculating this link within any Friedmann cosmology. Similar\nderivations have been previously discussed in a variety of subsets of\nthis space: for an Einstein-de Sitter model, a derivation is given by\nGunn \\& Gott \\shortcite{gunn}, for an open $\\Omega_V=0$ model by Lacey\n\\& Cole \\shortcite{lc93}, and for a flat $\\Omega_V\\neq0$ universe by\nEke Cole \\& Frenk \\shortcite{eke}. A summary of these results is given\nin Kitayama \\& Suto \\shortcite{kitayama2}. A numerical prescription\nfor the calculation of the overdensity in any cosmology has also been\ndeveloped \\cite{somerville99}.\n\nThese derivations all use the same basic idea which is adopted in this\nwork: the behaviour of two spheres of equal mass is compared within\nthe cosmological framework. One of the spheres evolves with the\nbackground density $\\rho_b(t)$, while the other is perturbed by a\nuniform excess density $\\Delta\\rho(t)$. In subsequent analysis, a\nsubscript `$b$' denotes that a quantity relates to the sphere with\nbackground density, and `$p$' to the perturbation.\n\nMatter is assumed to be an ideal fluid with no pressure and the\nuniverse is modelled as spherically symmetric around the\nperturbation. As a consequence of Birkhoff's theorem, the\ngravitational field of both the perturbation and the background is\ndescribed by a Robertson-Walker (RW) metric with curvature constant\n$K$, and RW scale factor $a(t)$. The behaviour of such perturbations\nis governed by Friedmann's equation which we will consider in the\nform:\n\\begin{equation}\n \\left(\\frac{da}{dt}\\right)^2+K=\\frac{2GM}{a}+(H_0^2\\Omega_V)a^2\n \\label{eq:friedmann1}\n\\end{equation}\nwhere $M$ is the mass inside the sphere. Note that in order to compare\nspheres with different behaviour, we do {\\em not} normalise the scale\nfactor $a(t)$ to equal the curvature scale (by dividing by\n$\\sqrt{|K|}$) so $K$ is allowed to take any real value.\n\nTo calculate the behaviour of the overdensity at an early time, we\nnote that a series solution for $a(t)$ in the limit $t\\to0$ can be\nobtained for Equation~\\ref{eq:friedmann1}. This is given by $a=\\alpha\nt^{2/3}+\\beta t^{4/3}+O(t^{6/3})$, where:\n\\begin{equation}\n \\alpha=\\left(\\frac{9GM}{2}\\right)^{1/3}, \\hspace{1cm}\n \\beta=\\frac{3K}{20}\\left(\\frac{6}{GM}\\right)^{1/3}.\n \\label{eq:ab}\n\\end{equation}\nUsing the fact that the spheres contain equal mass, the behaviour of\n$\\delta(t)\\equiv\\Delta\\rho(t)/\\rho_b(t)$ in the limit $t\\to0$ is given\nby:\n\\begin{eqnarray}\n \\lim_{t\\to0}\\left(\\frac{\\Delta\\rho(t)}{\\rho_b(t)}\\right)\n &=&\\lim_{t\\to0}\\left(\\frac{a_b(t)^3}{a_p(t)^3}-1\\right) \\nonumber \\\\\n &=&\\frac{3}{\\alpha}(\\beta_p-\\beta_b)t^{2/3}+O(t^{4/3}). \n \\label{eq:limits}\n\\end{eqnarray}\nDefining: \n\\begin{equation}\n \\epsilon=\\frac{K}{(GMH_0)^{2/3}}, \n\\end{equation}\nthe present day normalisation of Equation~\\ref{eq:friedmann1} gives\nthat for a sphere of uniform background density:\n\\begin{equation}\n \\epsilon_b=(\\Omega_M+\\Omega_V-1)\n \\left(\\frac{2}{\\Omega_M}\\right)^{2/3},\n \\label{eq:kbg}\n\\end{equation}\nWe can now combine Equations~\\ref{eq:ab},~\\ref{eq:limits}~\\&~\\ref{eq:kbg} \nto determine the behaviour of $\\delta(t)$ in the limit $t\\to0$ as a \nfunction of $\\epsilon_p$:\n\\begin{displaymath}\n \\lim_{t\\to0}\\delta(t)=\n \\frac{9}{20}\\left(\\frac{4}{3}\\right)^{1/3}\n\\end{displaymath}\n\\begin{displaymath}\n \\hspace{1cm}\n \\times\n \\left[(\\Omega_M+\\Omega_V-1)\n \\left(\\frac{2}{\\Omega_M}\\right)^{2/3}-\\epsilon_p\\right](H_0t)^{2/3} \n\\end{displaymath}\n\\begin{equation}\n \\hspace{1cm}\n +O[(H_0t)^{4/3}]\n \\label{eq:ktolimd}\n\\end{equation}\n\nIf the field of perturbations is linearly extrapolated to present day\nand normalised here, the approximation of Carroll, Press \\& Turner\n\\shortcite{carroll} for the ratio of the current linear amplitude to\nthe Einstein-de Sitter model can be used to extrapolate the limiting\nbehaviour of $\\delta$ to this epoch. The extrapolated limit,\n$\\delta_{\\rm lim}$, is related to $\\epsilon_p$ by:\n\\begin{displaymath}\n \\delta_{\\rm lim} \\simeq \\frac{3}{8}\\left(4\\Omega_M\\right)^{2/3}\n \\left[(\\Omega_M+\\Omega_V-1)\n \\left(\\frac{2}{\\Omega_M}\\right)^{2/3}\n -\\epsilon_p\\right]\n\\end{displaymath}\n\\begin{equation}\n \\hspace{3mm}\n \\times\n \\left[\\Omega^{4/7}_M-\\Omega_V+\n \\left(1+\\frac{1}{2}\\Omega_M\\right)\n \\left(1+\\frac{1}{70}\\Omega_V\\right)\\right]^{-1}.\n \\label{eq:ktodc}\n\\end{equation}\nA similar formula is possible if the field of fluctuations is\nnormalised at any other epoch. Note that $\\delta_{\\rm\nlim}\\propto(\\epsilon_p+{\\rm constant})$ and the time dependence of\n$\\delta_{\\rm lim}$ is given by that of $\\epsilon_p$.\n\nFor the perturbation, the radius of maximum expansion can be\ncalculated from Equation~\\ref{eq:friedmann1}: this radius corresponds\nto the first positive root of the equation $2GM+H_0^2\\Omega_Va^3-Ka=0$\ndenoted by $a_{\\rm max}$. This leads to a necessary and sufficient\ncondition for the perturbation to collapse: that such a (finite) root\nexists. Because of the symmetry in Equation~\\ref{eq:friedmann1}, this\nmodel predicts that the perturbation will collapse to a singularity at\na time equal to twice the time required to reach maximal expansion:\n\\begin{equation}\n H_0t_{\\rm coll}=2\\int^{a^*_{\\rm max}}_{0}\n \\left(\\frac{2}{a^*}+\\Omega_V(a^*)^2\n -\\epsilon_p\\right)^{-1/2}\\,da^*\n \\label{eq:ttok}\n\\end{equation}\nwhere we have changed from $a$ to $a^*=aH_0^{2/3}/(GM)^{1/3}$, and\n$a^*_{\\rm max}$ is the first positive root of the equation:\n\\begin{equation}\n 2+\\Omega_V(a^*)^3-\\epsilon_p a^*=0.\n \\label{eq:amax}\n\\end{equation}\nAlthough collapse to a singularity does not occur in practice, the\nvirialisation epoch is assumed to be similar to $t_{\\rm coll}$. \n\nFor perturbations that collapse, $\\delta_{\\rm lim}$ is called the\n`critical' density and is denoted $\\delta_c$. Equation~\\ref{eq:ktodc}\nthen gives $\\delta_c(\\epsilon_p)$.\nEquations~\\ref{eq:ttok}~\\&~\\ref{eq:amax} give $t_{\\rm\ncoll}(\\epsilon_p)$, and the combination of these three Equations gives\nthe required link between $\\delta_c$ and the collapse time. Note that\nthese Equations are independent of the perturbation mass, and\ntherefore so is the link between the initial overdensity and the\ncollapse time.\n\nIn practice we wish to use these Equations to calculate\n$\\delta_c(z_{\\rm coll},\\Omega_M,\\Omega_V)$ or $d\\delta_c(z_{\\rm\ncoll},\\Omega_M,\\Omega_V)/dt$ where $z_{\\rm coll}$ is the collapse\nredshift. Unfortunately this is not easy as\nEquations~\\ref{eq:ttok}~\\&~\\ref{eq:amax} cannot be inverted to give\n$\\epsilon_p(t_{\\rm coll})$. The procedure adopted is as follows: the\ncollapse time can be numerically determined from $z_{\\rm coll}$ using\nthe Friedmann equation for the background cosmology. $\\epsilon_p$ can\nbe determined numerically using\nEquations~\\ref{eq:ttok}~\\&~\\ref{eq:amax}, and $\\delta_c$ can be\ncalculated using Equation~\\ref{eq:ktodc}. $d\\delta_c/dt$ can be\ncalculated numerically from $\\delta_c(t_{\\rm coll})$ and is discussed\nfurther in the next Section.\n\nFor the subset of cosmological models with $\\Omega_V=0$, the above\nprocedure is simplified and analytic formula can be obtained for\n$\\delta_c$. In this case, Equation~\\ref{eq:ttok} reduces to:\n\\begin{equation}\n H_0t_{\\rm coll}=2\\int^{2/\\epsilon_p}_{0}\n \\left(\\frac{2}{a^*}-\\epsilon_p\\right)^{-1/2}\\,da^*.\n\\end{equation}\nMaking the substitution $\\tan(\\theta)=(2/a^*-\\epsilon_p)^{-1/2}$, this\nintegral can be solved to give:\n\\begin{equation}\n H_0t_{\\rm coll}=\\frac{2\\pi}{\\epsilon_p^{3/2}}.\n \\label{eq:nocstetot} \n\\end{equation}\n\nWe now show that these Equations provide the result of Gunn \\& Gott\n\\shortcite{gunn} for an Einstein-de Sitter cosmology. In this case,\nsubstituting Equation~\\ref{eq:nocstetot} into Equation~\\ref{eq:ktodc}\ngives that:\n\\begin{equation}\n \\delta_c(t_{\\rm coll}) = \\frac{3}{20}\n \\left(\\frac{8\\pi}{H_0t_{\\rm coll}}\\right)^{2/3}.\n\\end{equation}\nWe can now change from collapse time to collapse redshift to give:\n\\begin{eqnarray}\n \\delta_c(z_{\\rm coll})&=&\\frac{3}{20}(12\\pi)^{2/3}(1+z_{\\rm coll}) \n \\nonumber \\\\\n &\\simeq&1.69(1+z_{\\rm coll}),\n\\end{eqnarray}\nwhich is the equation of Gunn \\& Gott \\shortcite{gunn}.\n\n\\section{From a mass function to a time distribution} \\label{sec:time}\n\nIn this Section we show how to convert from a mass function to the\ndistribution of times at which isolated halos of a given mass\nexist. First, we make the assumption that the mass of any clump is a\nmonotonically increasing function of time so that the mass will\nincrease between any two epochs. This is true for Press-Schechter\ntheory (see paper~I). Note that this mass growth is not constrained to\nbe continuous and the mass is allowed to undergo instantaneous finite\nincreases, or `mass jumps'. Following this assumption, every epoch at\nwhich a halo exists should also be considered as a `creation' epoch:\nevery halo is a new isolated halo of some mass. The distribution of\n`creation events' is therefore the same as the distribution of times\nat which the halos exist. Note that by definition this only applies to\nisolated halos which have not been subsumed into larger objects.\n\nIn this paper we have called this epoch the `creation' time of a halo\nin order to avoid confusion with other authors definitions of the\n`formation' time of a halo. Note that this semantic change was not\nadopted in paper~I. The `formation' time of a halo was defined by\nLacey \\& Cole \\shortcite{lc93} as the latest time when the largest\nprogenitor of a halo has a mass less than half that of the final\nhalo. This definition makes sense if we are discussing a non-evolving\nquantity, say the existence of a galaxy halo, and wish to know when it\nwas formed given that it exists at present day. However, suppose we do\nnot know anything about the build-up of a halo before or after it has\nmass $M$ and only wish to know when it was likely to have\nexisted. This Lacey \\& Cole definition of `formation' cannot help us\nfor we do not know the time and mass from which to determine\nprogenitors: progenitors of what?\n\nIn order to calculate the probability density function (pdf) of the\ntimes at which halos exist, we consider the set of all possible times\nand all possible halo masses. This is the `sample space' of our\n`experiment'. The experiment consists of choosing a particle, or small\nmass element, and an `event' is given by any subset of the sample\nspace: for instance that the particle is part of a halo of mass\n$M_1<M<M_2$ created at time $t_1<t<t_2$, or that the particle inhabits\na halo of mass $M$, created at time $t$.\n\nDenoting a generic pdf by the function $f$, the mass function is given\nby $f(M|t)\\,dM$, the distribution of halo masses at a given\nepoch. This is equal to $Mn(M)/\\rho$ where $n(M)$ is the number\ndensity of halos. The pdf we wish to determine is given by\n$f(t|M)\\,dt$, the distribution of times at which halos of mass $M$\nwere created. Note that our assumption of monotonic mass growth means\nthat $t$ is the same variable in $f(M|t)\\,dM$ {\\em and}\n$f(t|M)\\,dt$. These pdfs are then related by the following formula,\nbased on Bayes' theorem:\n\\begin{equation}\n f(t|M)\\,dt=\\frac{f(M|t)\\,dM\\,f(t)\\,dt}\n {\\int_0^{\\infty}\\left[f(M|t)\\,dM\\,f(t)\\right]\\,dt},\n \\label{eq:bayes}\n\\end{equation}\nwhere $f(t)\\,dt$ is the normalised prior for time, or the distribution\nof creation events in time given no information about the mass of\nhalo. In paper~I we calculated the prior using the Brownian random\nwalks invoked in PS theory with a sharp $k$-space filter. In order not\nto bias the distribution of up-crossings within this model, we assumed\na uniform prior for $\\delta_c$. \n\nThe reason the prior is uniform in $\\delta_c$ follows from the STHC\nmodel. Within this model, it is the density $\\delta$ associated with a\nparticle that is important, and the barrier has to move from $\\delta$\nto $\\delta-d\\delta$ for `halo creation' to have occurred. Given that\nthe mass of all clumps monotonically increases, all particles will be\nassociated with creation events at any $\\delta_c$. Following these two\nobservations, any two equal width intervals in $\\delta_c$ should\ncontain equal `numbers' of halo creation events.\n\nThe derivation presented in the previous Section showed that for the\nSTHC model, the link between the critical overdensity and the collapse\ntime is independent of the perturbation mass. Therefore, given no\ninformation about the mass contained within a perturbation, the pdf\nfor the time at which the perturbation collapses should be assumed to\nbe proportional to the time derivative of $\\delta_c(t)$. This gives\nthe rate at which the collapse threshold $\\delta_c(t)$ crosses the\ninitial overdensities. This can be calculated numerically from the\nfollowing formula:\n\\begin{displaymath}\n \\frac{d\\delta_c}{dt}\\propto\\frac{d\\epsilon_p}{dt}=\n\\end{displaymath}\n\\begin{equation}\n \\left[\\frac{d}{d\\epsilon_p}\n \\left(\\int\\limits_0^{a^*_{\\rm max}(\\epsilon_p)}\n \\left(\\frac{2}{a^*}+\\Omega_V(a^*)^2-\\epsilon_p\\right)\n ^{-\\frac{1}{2}}da^*\\right)\\right]^{-1},\n\\end{equation}\nwhere $a^*_{\\rm max}$ is the first positive root of the equation\n$2+\\Omega_V(a^*)^3-\\epsilon_p a^*=0$. Note that for\ncosmologies with $\\Omega_V=0$, the above equation can be\nanalytically solved as for Equation~\\ref{eq:nocstetot}, and the\nderivative $d\\delta/dt$ is proportional to $t^{-5/3}$.\n\nUnfortunately, $d\\delta_c(t)/dt$ cannot be normalised so that it\nintegrates over all time to give unity. This means that we cannot\nsimply take a multiple of $d\\delta_c(t)/dt$ as the prior for the\ncollapse time. However, we can still use Equation~\\ref{eq:bayes} by\nmaking use of a mathematical trick and placing an arbitrary upper\nlimit on $t$, $t_u$, which can be removed later without affecting the\nresult. This gives that:\n\\begin{equation}\n f(t|M)\\,dt=\\lim_{t_u\\to\\infty}\\left[\\frac{f(M|t)\\,dM\\,f(t,t_u)\\,dt}\n {\\int_0^{t_u}\\left[f(M|t)\\,dM\\,f(t,t_u)\\right]\\,dt}\\right]\n \\label{eq:bayes2}\n\\end{equation}\n\nThe connection between the mass function and the creation rate of\nhalos presented in this Section is consistent with that of paper~I:\nthe prior for time used is exactly the same. We have merely shown that\nadopting the STHC model for the rate at which structures are created\nallows {\\em any} mass function to be converted to give the pdf of the\ntime at which a halo of a given mass is created.\n\n\\section{The relation with the multiplicity function}\n\nChanging variables from mass to a function of\n\\begin{equation}\n \\nu\\equiv\\frac{\\delta_c}{\\sigma_M}\n\\end{equation}\nalters the form of the standard PS mass function to one which is\ninvariant with respect to time. Here $\\sigma_M$ is the rms fluctuation\nof the initial density field smoothed with a top-hat filter on a scale\nrelated to mass $M$. Unless stated otherwise we change variables in\nthe mass function from M to $\\ln\\nu(M,t)$. The normalised pdf\n$f(\\ln\\nu|t)$ is called the multiplicity function and is related to\nthe mass function by:\n\\begin{equation}\n f(M|t)=Af(\\ln\\nu|t)\\left.\\frac{\\partial\\ln\\nu}{\\partial M}\\right|_t,\n \\label{eq:multiplicity_M}\n\\end{equation}\nwhere $A$ is a normalisation constant. Note that we have retained the\ncondition on time in $f(\\ln\\nu|t)$, to emphasise that we are still\nconcerned with the distribution of halos at a particular\nepoch. Although the multiplicity function has a form which is\ninvariant with respect to time, it still gives the distribution of\n$\\ln\\nu$ we would expect for halos given a particular time. This is\n{\\em not} the same as the the distribution of $\\ln\\nu$ we would obtain\nif we chose halos at random in both mass and time, or the distribution\nof $\\ln\\nu$ we would obtain if we chose halos only of a particular\nmass.\n\nIf the mass function can be written in a form which is independent of\ntime as described above, then under the same change of variables, the\ncreation rate becomes independent of halo mass. The resulting pdf\n$f(\\ln\\nu|M)$ is now only valid if we are examining the distribution\nof halos at fixed mass. Following the notation adopted above, this is\ngiven by:\n\\begin{equation}\n f(t|M)=Af(\\ln\\nu|M)\\left.\\frac{\\partial\\ln\\nu}{\\partial t}\\right|_M.\n \\label{eq:multiplicity_t}\n\\end{equation}\n\n\\section{The joint distribution of halos in mass and time} \\label{sec:joint}\n\nBecause the mass of each halo is assumed to monotonically increase\nwith time, within any interval of mass and time, an infinite number of\n`creation events' occur. This means that the joint probability of the\nexistence of a halo in {\\em both} mass and time cannot be properly\nnormalised.\n\nEquation~\\ref{eq:bayes2} gives the link between two pdfs, the mass\nfunction and the creation rate using a mathematical trick to cope with\nan un-normalised prior in time. The numerator of this equation is the\njoint distribution of halos in mass and time,\n$f(M,t)\\,dM\\,dt=f(M|t)\\,dM\\,f(t)\\,dt$. The denominator is not a\nfunction of time: it only normalises the resulting formula so\n$f(t|M)\\,dt$ integrates to unity. Following this argument, given a\nmass function, multiplying by $d\\delta_c(t)/dt$ creates a function\nwith {\\em both} the correct mass and time behaviour. This joint\ndistribution function (not a pdf) has the same mass dependence as\n$f(M|t)$ and the same time dependence as $f(t|M)$.\n\nAs an example we consider the fitting function of Sheth \\& Tormen\n\\shortcite{sheth} to the multiplicity function determined from the\nresults of N-body simulations for different cosmological parameters:\n\\begin{displaymath}\n \\frac{Mn(M)}{\\rho}\\,dM=f(M|t)\\,dM=f(\\ln\\nu|t)\\,d\\ln\\nu \n\\end{displaymath}\n\\begin{equation}\n \\hspace{10mm}\n = A\\sqrt{\\frac{2}{\\pi}}\\left(1+\\frac{1}{\\nu'^{2p}}\\right)\\nu'e^{-\\nu'^2/2}\n \\,d\\ln\\nu,\n \\label{eq:sheth}\n\\end{equation}\nwhere $\\nu'=a^{1/2}\\nu$ and $a$~\\&~$p$ are parameters. Note that Sheth\n\\& Tormen displayed this formula using a different notation to that\nadopted here, although parameters $a$ and $p$ are the same in both\ncases. $A$ is determined by requiring that the integral of\n$f(\\ln\\nu|t)$ over all $\\ln\\nu$ gives unity. Sheth \\& Tormen found\nbest fit parameters $a=0.707$ and $p=0.3$ for their simulations and\ngroup finding algorithm. The standard PS multiplicity function has\n$a=1$, $p=0$ and $A=1/2$. Unless stated otherwise, by standard PS\ntheory, we refer to the adoption of this multiplicity function\ncombined with top-hat filtering (to calculate $\\sigma_M^2$). In order\nto convert this function to provide a model of both the time and mass\nof halo creation events, all we need to do is to multiply by\n$d\\delta_c/dt$.\n\nFor standard PS theory, writing $\\nu$ explicitly in terms of\n$\\sigma_M^2$ and $\\delta_c$ we find that the joint distribution of the\nexistence of a halo in mass and time reduces to:\n\\begin{displaymath}\n f(M,t)\\,dM\\,dt= \\frac{\\delta_c}\n {(2\\pi)^{1/2}\\sigma_{M}^{3}}\n\\end{displaymath}\n\\begin{equation}\n \\hspace{10mm}\n \\times\n \\exp\\left(-\\frac{\\delta_c^{2}}{2\\sigma_M^2}\\right)\n \\left|\\frac{d\\sigma_M^2}{dM}\\right|\n \\left|\\frac{d\\delta_c}{dt}\\right|\\,dM\\,dt, \n \\label{eq:fmnt}\n\\end{equation}\nAlthough not normalised, such a formula integrated over any two areas\nof the mass-time plane will provide the correct relative number\ndensities.\n\nNote that this is {\\em not} the same formula as obtained by simply\nmultiplying the mass function with the creation time distribution at\nfixed mass. This would be inconsistent within a Bayesian framework and\nwould produce a joint density function which lacks the correct mass\nand time behaviour: the form of each conditional pdf is altered by the\nother. Care should therefore be taken when using the creation rate in\nmodels which also include the mass function.\n\n\\section{The relation with merger events} \\label{sec:mergers}\n\nSo far, we have only been concerned with the epoch at which a halo is\ncreated. However, there is an important distinction between major\nmergers and the slow accretion of mass when applying the results in\nmodels of certain cosmological phenomena. For instance, only violent\nmerger events are thought to be important for starbursts and quasar\nactivation. In paper~I, we showed that for standard PS theory with a\nsharp $k$-space filter, if mass jumps in a particular trajectory\ncorrespond to merger events, then the distribution of mergers is the\nsame as that of the build-up of matter from all types of creation\nevent. This is because the trajectories are Brownian random walks\nwhich have the special property that their form is independent of the\ninitial point.\n\nGiven only the mass function and the assumptions outlined above it is\nnot possible to determine how each clump increases in mass, only the\ndistribution of times at which it reaches a certain mass. More\ninformation about the build-up of individual clumps is required before\nthe distribution of major mergers can be determined. Such information\nis available in PS theory and follows from the argument that each\ntrajectory gives the history of the halo masses in which a particular\nsmall mass element resides.\n\n\\section{Description of the Numerical Simulations} \\label{sec:simulations}\n\nA direct approach to modelling structure formation is to simulate the\nevolution of the mass density of the Universe using a distribution of\nsoftened particles. We have run three such simulations using the Hydra\nN-body, hydrodynamics code \\cite{couchman} with $128^3$ dark matter\nparticles to model the build-up of halos for three different\ncosmological models, described in Table~\\ref{tab:cosmo}.\n\n\\begin{table}\n \\centering\n \\begin{tabular}{cccccc} \n model & $\\Omega_{M}$ & $\\Omega_V$ & $\\Gamma$ &\n $\\sigma_{8}$ & h \\\\ \\hline \t\n $\\Gamma$CDM & 1 & 0 & 0.25 & 0.64 & 0.5 \\\\\n OCDM & 0.3 & 0 & 0.15 & 0.85 & 0.5 \\\\\n $\\Lambda$CDM & 0.3 & 0.7 & 0.15 & 0.85 & 0.5 \\\\\n \\end{tabular}\n \\caption{Table showing the parameters of the different cosmological\n models adopted in the three N-body simulations.} \\label{tab:cosmo}\n\\end{table}\n\nIn order to determine the {\\em rate} at which halos are created within\nthese simulations, we output particle positions at a large number of\ntimes. For the $\\Gamma$CDM simulation, we output particle positions at\n362 different epochs, separated by approximately equal intervals in\ntime. For the OCDM simulation the number of outputs was 345 and for\nthe $\\Lambda$CDM simulation, 499. The box size chosen was\n100\\,$h^{-1}$Mpc for all three simulations which gave a particle mass\nof $2.6\\times10^{11}$\\,\\msun for $\\Gamma$CDM and\n$7.9\\times10^{10}$\\,\\msun for the other two simulations. Groups of\nparticles were found for each output using a standard\nfriends-of-friends algorithm with linking length set to $b=0.2$ times\nthe mean interparticle separation.\n\n\\section{Fitting to the Mass Function}\n\nThe multiplicity function averaged over all output times is presented\nfrom each of the simulations in Fig.~\\ref{fig:nbody_mult}. Here we\nhave only considered groups containing over 45 particles in order to\nlimit the number of false detections due to numerical effects. In\ncompiling the data in this way, we have assumed that converting from\nmass to $\\ln\\nu$ does indeed convert the form of the mass function\ninto one which is independent of epoch. This Figure has been produced\nin such a way as to be directly comparable with figure~2 of Sheth \\&\nTormen \\shortcite{sheth}. For comparison we also plot their best fit\nmodel and the predictions of standard PS theory.\n\n\\begin{figure}\n \\setlength{\\epsfysize}{13.4cm}\n \\centerline{\\epsfbox{nbody_mult.eps}} \\caption{The measured\n multiplicity function from each of the three simulations analysed\n for all groups containing over 45 particles (solid triangles plotted\n with Poisson error bars). See Section~\\ref{sec:simulations} for\n details of these simulations. In compiling these data in this way we\n have assumed that the transfer of variables from $M$ to $\\ln\\nu$\n where $\\nu\\equiv\\delta_c/\\sigma_M$ does make the distribution of\n masses independent of epoch as found by Sheth \\& Tormen\n \\protect\\shortcite{sheth}. For comparison we have also plotted the\n best fit model to their data (dashed line) and the predictions of\n standard PS theory (dotted line). The solid line shows the best fit\n model to our data allowing the parameters of the Sheth \\& Tormen\n \\protect\\shortcite{sheth} fitting function to vary.}\n\\label{fig:nbody_mult}\n\\end{figure}\n\nWe have also plotted the model of Sheth \\& Tormen \\shortcite{sheth}\n(Equation~\\ref{eq:sheth}) after allowing the parameters to vary to\nsimultaneously fit the data from all three simulations. We find\nslightly different best fit parameters to those of Sheth \\&\nTormen. Our best fit parameters are $a=0.774, p=0.274$, compared to\nstandard PS theory $a=1, p=0$ and Sheth \\& Tormen $a=0.707,\np=0.3$. Note that the difference between our best fit values and those\nof Sheth \\& Tormen could be explained by the different group finding\nalgorithms used.\n\n\\section{Comparison between the Analytic and Numerical Halo Creation Rates}\n\nAlthough we have argued that the monotonic increase in mass means that\nall epochs are `creation' times for a given halo, we cannot simply\ncompare the creation rate formulae with the distribution of halo\nnumbers at different epochs: each halo should only be counted once. To\ndetermine the distribution of creation times of halos of mass $M$, we\ntherefore sequentially analysed the FOF output from $z=50$ to present\nday. All halos of mass $>M$ were examined at each epoch to determine\nwhether they were `new'. The definition of `new' adopted was that at\nleast half of the particles in a halo were not included in any halo of\nmass $>M$ at a previous output time. The number of these halos in the\nrequired mass range was taken to be the minimum number which could\nhave been created between that output time and the previous one. In\norder not to miss creation events where a halo was created and\nsubsumed into a larger halo all within the time interval between two\noutputs, we analysed the progenitors of all new halos with mass\ngreater than the required range. Those with a progenitor distribution\nat the previous step which could sum to a halo of the required mass\nwere recorded as a possible halo of the required mass. In this way we\ndetermined the minimum and maximum mass which could have been created\nin each time interval between output from the simulation.\n\nIn Fig.~\\ref{fig:nbody_form} we plot the creation rate for halos\nwithin two narrow mass ranges. In order to obtain the maximum number\nof creation events, we have used relative low numbers of particles in\neach group. Data are plotted for groups of between $45-50$ and\n$100-110$ particles. These distributions are compared with the three\nmultiplicity functions plotted in Fig.~\\ref{fig:nbody_form}, converted\ninto creation rates by multiplying by $d\\delta/dt$ for halos of mass\nequivalent to 45 or 100 particles. These curves have been normalised\nto the low redshift data.\n\nAll of the models reproduce the decrease in creation events to present\nday seen in the simulations. As output from the simulation occured\nafter approximately equal intervals of time, the high redshift data\nsuffers as the intervals contain relatively more creation events. This\nmeans that we cannot precisely follow the build-up of the clumps, and\nthe difference between the maximum and minimum mass which could have\nbeen created in each bin is increased. This is particularly noticable\nin the OCDM simulation where halos are created at earlier times and we\nhave fewer outputs from the simulation.\n\nHowever, there is evidence that the solid line (calculated from the\nbest fit to the mass function) also fits the creation rate data the\nbest out of the three models plotted. As a rough guide to this, the\nroot mean square value between the plotted data points and the model\nis 3.4 for this curve, compared to 6.7 for standard PS theory, and 5.0\nfor the best fit model of Sheth \\& Tormen \\shortcite{sheth}. Note that\nthe form of the creation rate is strongly dependent on the parameter\n$a$ in Equation~\\ref{eq:sheth}, and only weakly dependent on parameter\n$p$. This is consistent with the importance of these parameters for\nthe mass function: parameter $a$ controls the position of the\nhigh-mass cut-off, whereas parameter $p$ controls the low-mass tail of\nthe distribution.\n\n\\begin{figure*}\n \\setlength{\\epsfysize}{13.2cm}\n \\centerline{\\epsfbox{nbody_create.eps}} \\caption{The creation rate\n of halos as determined from the three cosmological simulations\n (solid circles) for a) 45-50 particles in a halo and b) 100-110\n particles. These group sizes correspond to masses of aproximately a)\n $1.2\\times10^{13}\\msun$ for $\\Gamma$CDM and $3.6\\times10^{12}\\msun$\n for the two other cosmologies, and b) $2.6\\times10^{13}\\msun$ for\n $\\Gamma$CDM and $7.9\\times10^{12}\\msun$ for the two other\n cosmologies. The error bars show the binned minimum and maximum mass\n which could have been created in halos of the required masses in\n each time interval. Symbols are plotted half way between the\n two. Note that the errors bars do not include counting errors. For\n comparison we also plot the three models of the mass function\n multiplied by $d\\delta_c/dt$ with lines as in\n Fig.~\\ref{fig:nbody_mult}. The models have been normalised to the\n low redshift data.}\n\\label{fig:nbody_form}\n\\end{figure*}\n\n\\section{Conclusions}\n\nWe have demonstrated a simple method for linking any mass function to\nthe corresponding distribution of times at which isolated halos of a\ngiven mass are created. In order to provide this link we adopted the\nassumption that the time scales of interest are those over which the\nmass of every clump can be thought of as monotonically increasing. The\nprior for the collapse time was estimated using the STHC model which\nties in directly with PS theory, although the method does not use any\nof PS theory beyond that of the STHC model. We have presented a new\nderivation of the link between the collapse time and initial\noverdensity for this model which explicitly shows that this link is\nindependent of the halo mass and is applicable in any Friedmann\ncosmology. Multiplying the mass function by a function with no mass\ndependence and proportional to the time derivative of the critical\noverdensity then provides a joint density function with the correct\nbehaviour for the creation of a halo in mass {\\em and}\ntime. Integrating over the resulting joint density function will give\nthe correct relative number densities of halos within different mass\nand time intervals.\n\nWe have extended the analysis of N-body simulation results presented\nin paper~I to cover three simulations of the build-up of dark matter\nwithin different cosmological models. Rather than using PS theory, we\nhave demonstrated how a fit to the mass function may be converted to\ngive a creation rate. Out of the three functions we have compared to\nthe mass function data, the best fit model for these data when\nconverted to a creation rate also fits the creation rate data the\nbest. This gives us confidence that the formalism presented here is\nsound, and should give accurate results in more general situations, in\nparticular non-Gaussian models.\n\n\\section{Acknowledgements}\nWe are grateful for the use of the Hydra N-body code \\cite{couchman}\nkindly provided by the Hydra consortium.\n\n\\begin{thebibliography}{}\n \\bibitem[\\protect\\citename{Bond \\etal\\ }1991]{bond} \n Bond J.R., Cole S., Efstathiou G., Kaiser N., 1991, ApJ, 379, 440\n \\bibitem[\\protect\\citename{Carroll, Press \\& Turner }1992]{carroll} \n Carroll S.M., Press W.H., Turner E.L., 1992, ARA\\&A, 30, 499 \n \\bibitem[\\protect\\citename{Couchman, Thomas \\& Pearce }1995]{couchman} \n Couchman H. M. P., Thomas P.A., Pearce F.R., 1995, ApJ, 452, 797\n \\bibitem[\\protect\\citename{Eke, Cole \\& Frenk }1996]{eke} \n Eke V.R., Cole S., Frenk C.S., 1996, MNRAS, 282, 263\n \\bibitem[\\protect\\citename{Granato \\etal\\ }1999]{granato} \n Granato G.L., Silva L., Monaco P., Panuzzo P., Salucci P., \n De Zotti G., Danese L., 1999, MNRAS submitted, astro-ph/9911304\n \\bibitem[\\protect\\citename{Gunn \\& Gott }1972]{gunn} \n Gunn J.E., Gott J.R., 1972, ApJ, 176, 1\n \\bibitem[\\protect\\citename{Kitayama \\& Suto }1996]{kitayama2} \n Kitayama T., Suto Y., 1996, ApJ, 469, 480\n \\bibitem[\\protect\\citename{Lacey \\& Cole }1993]{lc93} \n Lacey C., Cole S., 1993, MNRAS, 262, 627 \n \\bibitem[\\protect\\citename{Matarrese, Verde \\& Jimenez }2000]{matarrese} \n Matarrese S., Verde L., Jimenez R., 2000, ApJ submitted, \n astro-ph/0001366\n \\bibitem[\\protect\\citename{Peacock \\& Heavens }1990]{peacock} \n Peacock J. A., Heavens A. F., 1990, MNRAS, 243, 133\n \\bibitem[\\protect\\citename{Percival \\& Miller }1999]{ev1} \n Percival W.J., Miller L., 1999, MNRAS, 309, 823\n \\bibitem[\\protect\\citename{Press \\& Schechter }1974]{ps} \n Press W., Schechter P., 1974, ApJ, 187, 425 \n \\bibitem[\\protect\\citename{Sheth \\& Tormen }1999]{sheth} \n Sheth R.K., Tormen G., 1999, MNRAS, 108, 119\n \\bibitem[\\protect\\citename{Somerville \\& Primack }1999]{somerville99} \n Somerville R.S., Primack J.R., 1999, MNRAS accepted, \n astro-ph/9802268\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002328.extracted_bib",
"string": "\\begin{thebibliography}{}\n \\bibitem[\\protect\\citename{Bond \\etal\\ }1991]{bond} \n Bond J.R., Cole S., Efstathiou G., Kaiser N., 1991, ApJ, 379, 440\n \\bibitem[\\protect\\citename{Carroll, Press \\& Turner }1992]{carroll} \n Carroll S.M., Press W.H., Turner E.L., 1992, ARA\\&A, 30, 499 \n \\bibitem[\\protect\\citename{Couchman, Thomas \\& Pearce }1995]{couchman} \n Couchman H. M. P., Thomas P.A., Pearce F.R., 1995, ApJ, 452, 797\n \\bibitem[\\protect\\citename{Eke, Cole \\& Frenk }1996]{eke} \n Eke V.R., Cole S., Frenk C.S., 1996, MNRAS, 282, 263\n \\bibitem[\\protect\\citename{Granato \\etal\\ }1999]{granato} \n Granato G.L., Silva L., Monaco P., Panuzzo P., Salucci P., \n De Zotti G., Danese L., 1999, MNRAS submitted, astro-ph/9911304\n \\bibitem[\\protect\\citename{Gunn \\& Gott }1972]{gunn} \n Gunn J.E., Gott J.R., 1972, ApJ, 176, 1\n \\bibitem[\\protect\\citename{Kitayama \\& Suto }1996]{kitayama2} \n Kitayama T., Suto Y., 1996, ApJ, 469, 480\n \\bibitem[\\protect\\citename{Lacey \\& Cole }1993]{lc93} \n Lacey C., Cole S., 1993, MNRAS, 262, 627 \n \\bibitem[\\protect\\citename{Matarrese, Verde \\& Jimenez }2000]{matarrese} \n Matarrese S., Verde L., Jimenez R., 2000, ApJ submitted, \n astro-ph/0001366\n \\bibitem[\\protect\\citename{Peacock \\& Heavens }1990]{peacock} \n Peacock J. A., Heavens A. F., 1990, MNRAS, 243, 133\n \\bibitem[\\protect\\citename{Percival \\& Miller }1999]{ev1} \n Percival W.J., Miller L., 1999, MNRAS, 309, 823\n \\bibitem[\\protect\\citename{Press \\& Schechter }1974]{ps} \n Press W., Schechter P., 1974, ApJ, 187, 425 \n \\bibitem[\\protect\\citename{Sheth \\& Tormen }1999]{sheth} \n Sheth R.K., Tormen G., 1999, MNRAS, 108, 119\n \\bibitem[\\protect\\citename{Somerville \\& Primack }1999]{somerville99} \n Somerville R.S., Primack J.R., 1999, MNRAS accepted, \n astro-ph/9802268\n\\end{thebibliography}"
}
] |
astro-ph0002329
|
Emission-Line Properties of 3CR Radio Galaxies III: \\ Origins and Implications of the Velocity Fields
|
[
{
"author": "Stefi A. Baum\\altaffilmark{1} \\& Patrick J. McCarthy\\altaffilmark{2,3}"
}
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We present the results of an analysis of the large scale velocity fields of the ionized gas associated with powerful radio galaxies. Long-slit spectra of 52 objects provide a sample of resolved velocities that span a wide range of redshifts, radio and emission-line luminosities. Line widths reaching 1000 km s$^{-1}$ and resolved velocity fields with amplitudes of up 1500 km s$^{-1}$ are found on scales from 10 to 100 kpc in the environments of radio galaxies at redshifts larger than 0.5. The global velocities and FWHM are of comparable amplitudes in the FRII sources, while the FRI sources have FWHM values that are larger than their resolved velocity fields. We find evidence for systematically larger line widths and velocity field amplitudes at $z > 0.6$. Several of the largest amplitude systems contain two galaxies with small projected separations. All of the $> 1000$ km s$^{-1}$ systems occur in objects at $z > 0.6$ and all have comparable radio and [OII] sizes. There is a weak correlation of off-nuclear line widths and velocity field with the ratio of the radio and emission-line sizes, but it is of low statistical significance and there is a very large dispersion. The change in properties at redshifts above $z \sim 0.6$ could reflect a difference in environments of the host galaxies, with the hosts inhabiting higher density regions with increasing redshift (e.g., Hill \& Lilly 1991). The mass of ionized gas and the apparent enclosed dynamical mass are correllated and both increase steeply with redshift and/or radio power. The origin of the velocities remains uncertain. The data do not require jet-gas interactions to explain the kinematics and superficially are slightly more consistent with gravitational origins for the bulk of the kinematics. If the line width reflects the underlying gravitational potential, the observed FWHM traces the velocity dispersion of the host galaxy or its surrounding group or cluster. The highest velocities seen then point to interesting environments for intermediate and high redshift radio galaxies. Turbulent interactions with the expanding radio source as the origin of the kinematics are certainly not ruled out. In the jet interaction scenario, the maximum velocities seen in the nebula can be used to constrain the density of the pre-shock gas to be roughly n$_{e} > 0.6$ cm$^{-3}$.
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"name": "sbaum.tex",
"string": "\\documentstyle[12pt,aasms]{article}\n%\\documentstyle[aaspp]{article}\n\\tightenlines\n\\begin{document}\n\\def\\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\\\n\\def\\simlt{\\lower.5ex\\hbox{\\ltsima}}\n\\def\\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def\\simgt{\\lower.5ex\\hbox{\\gtsima}}\n\\def\\etal{{\\it et al.~}}\n\\def\\minspt{$^{\\prime}_\\cdot$}\n\\def\\secspt{$^{\\prime\\prime}_\\cdot$}\n \n\\title { Emission-Line Properties of 3CR Radio Galaxies III: \\\\\n Origins and Implications of the Velocity Fields }\n\n\\author{ Stefi A. Baum\\altaffilmark{1} \\& Patrick J. McCarthy\\altaffilmark{2,3}}\n\n\\altaffiltext{1}{The Space Telescope Science Institute, \\\\\n 3700 San Martin Dr., Baltimore, MD 21218 }\n\n\\altaffiltext{2}{The Observatories of the Carnegie Institution of Washington, \\\\\n 813 Santa Barbara St., Pasadena, CA 91101}\n \n\\altaffiltext{3}{Guest Observer at the National Optical Astronomy\nObservatories, Cerro Tololo Interamerican Observatory,\nwhich is operated by the Associated Universities for Research in\nAstronomy, Inc., under contract with the National Science Foundation}\n\n\\begin{abstract}\n\n We present the results of an analysis of the large scale velocity\nfields of the ionized gas associated with powerful radio galaxies.\nLong-slit spectra of 52 objects provide a sample of resolved velocities\nthat span a wide range of redshifts, radio and emission-line luminosities.\nLine widths reaching 1000 km s$^{-1}$ and resolved velocity fields with\namplitudes of up 1500 km s$^{-1}$ are found on scales from 10 to 100\nkpc in the environments of radio galaxies at redshifts larger than 0.5.\nThe global velocities and FWHM are of comparable amplitudes in the FRII\nsources, while the FRI sources have FWHM values that are larger than\ntheir resolved velocity fields. We find evidence for systematically\nlarger line widths and velocity field amplitudes at $z > 0.6$. Several\nof the largest amplitude systems contain two galaxies with small\nprojected separations. All of the $> 1000$ km s$^{-1}$ systems occur in\nobjects at $z > 0.6$ and all have comparable radio and [OII] sizes. \nThere is a weak correlation of off-nuclear line widths \nand velocity field with the ratio of the radio and\nemission-line sizes, but it is of low statistical significance and\nthere is a very large dispersion. \nThe change in properties at redshifts above $z \\sim 0.6$ could reflect\na difference in environments of the host galaxies, with the hosts\ninhabiting higher density regions with increasing redshift\n(e.g., Hill \\& Lilly 1991). \nThe mass of ionized gas and the apparent enclosed dynamical mass are\ncorrellated and both increase steeply with redshift and/or radio power.\n\n\nThe origin of the velocities remains uncertain. The data do not\nrequire jet-gas interactions to explain the kinematics and \nsuperficially are slightly more consistent with gravitational\norigins for the bulk of the kinematics. If the line width reflects the underlying\ngravitational potential, the observed FWHM traces the velocity\ndispersion of the host galaxy or its surrounding group or cluster. \nThe highest velocities seen then\npoint to interesting environments for intermediate and high redshift\nradio galaxies. Turbulent interactions with the expanding\nradio source as the origin of the kinematics are certainly not ruled out.\nIn the jet interaction scenario, the maximum velocities\nseen in the nebula can be used to constrain the density of the pre-shock gas to be\nroughly n$_{\\rm e} > 0.6$ cm$^{-3}$.\n\n\\end{abstract}\n\n\\section {Introduction}\n\nWe report the results of an investigation of the kinematic, ionization\nand morphological properties of the emission-line nebulae in powerful\nradio galaxies. We have analyzed long slit optical spectroscopic and\nnarrow band imaging observations of large samples of low (Baum,\nHeckman, and van Breugel 1990). Tadhunter, Fosbury, \\& Quinn 1989) and\nintermediate to high redshift radio galaxies (McCarthy, Spinrad \\& van\nBreugel 1995; McCarthy, Baum, and Spinrad 1996). We utilize radio data\nfrom the literature. The combined data allow us to address questions\nconcerning as the nature and origin of the emission line gas, the\nsource of energy for the kinematic behavior of the gas, the\nrelationship of the gas and radio activity to the host galaxy, and the\nnature of changes in gaseous environment or host properties as a\nfunction of epoch, environment, radio power and source structure.\n\nPrevious such studies have focused primarily on narrow redshift ranges\nor specific source types (e.g., Baum, Heckman \\& van Breugel 1992;\nTadhunter et al. 1989, Gelderman \\& Whittle 1994; Villar-Martin et al.\n1998). The sample amassed here allows us to address the relevant\nissues over a much wider range of radio luminosity and redshift. In\nparticular, with this sample, we examine changes in the properties of\nthe nebulae and their relationship to the radio source and host galaxy\nover the range of redshifts where we currently believe that both the\nhost galaxies of powerful radio sources and their environments are\nevolving rapidly, $0.3 < z < 2$. Similarly, we examine the evidence\nfor increased interaction between the radio source and its gaseous\nenvironment as a function of extended radio power and redshift.\n\nIn the low redshift sample considered by Baum, Heckman, \\& van Breugel\n(1992), they concluded that the bulk of the emission line gas\nkinematics were dominated by gravitational motions. For that sample it\nproved straightforward to statistically separate gas kinematics\nattributable to radio jet-gas interactions from those determined by\nthe underlying gravitational potential of the host galaxy. If we are\nable to perform a similar separation at higher redshift, then we could\nuse the gas kinematics as a function of redshift as a tracer of the\nevolution of the gravitational potential of the underlying host\ngalaxies (the bright ellipticals) and their environments. Conversely,\nif we can show that the gas kinematics either in individual sources or\noverall, are due to interactions with the out-flowing radio jets, then\ncarefully follow-up studies of individual sources should lead to a\nbetter understanding of jet physics (e.g., Clark et al. 1998). Lastly,\nthe apparent increase in the number of close companion galaxies and\npossible clusters at $z > 0.5$ (e.g. Hill \\& Lilly 1991; Yates et al.\n1989; Ellingson, Green, \\& Yee 1991) offer the possibility that\nkinematics of the emission-line gas may probe tidal interactions and\ncluster potentials on 100 kpc scales.\n\nThe 3CR and 1Jy class sources that we consider here comprise a\nrepresentative sample of the most luminous radio sources at all\nredshifts less than 3. At redshifts greater than $\\sim 0.1$, they are\nprimarily of the double-lobed Fanaroff \\& Riley (1974) type II\nmorphologies and have luminosities that range from $10^{42} - 10^{45}$\nerg sec$^{-1}$. The emission-line regions are seen on scales of up to\n300 kpc and arise from low density gas in moderate to high ionization\nlevels. The luminosities of the emission-line regions range from\n$10^{41} - 10^{44}$ erg sec$^{-1}$ and scale roughly with the radio\nluminosity (e.g. Rawlings and Saunders 1991; Baum, Heckman and van\nBreugel 1989a,b; McCarthy 1993; Xu, Livio, and Baum 1999). The total\nmass of ionized gas is uncertain but reasonable estimates range up to a\nfew $\\times 10^8$M$_{\\odot}$. The source of the ionization is also\nuncertain and is probably a mix of collisional heating and\nphoto-ionization, with nuclear photo-ionization likely dominating the\ntotal line luminosities over a large range of radio power and redshift\n(e.g. Robinson et al. 1987; Baum and Heckman 1989a,b; Rawlings and\nSaunders 1991; Baum, Zirbel, and O'Dea 1995; Villar-Martin et al. 1997,\nTadhunter et al. 1998). The general alignment of the emission-line\nregions with the axes defined by the radio lobes in nearly all powerful\nFanaroff and Riley Class II type radio galaxies (e.g. Baum \\& Heckman\n1989a,b; McCarthy et al. 1987; de Vries et al. 1999) is taken as further\nsupport for the presence of central photo-ionization by an anisotropic\nUV source. The precise spatial coincidence between radio hot-spots and\njets with bright emission-line regions in some sources (e.g. de Vries\net al. 1999; Miley et al. 1992, Villar-Martin et al, 1998), and the\ncorrelation between lobe and emission-line asymmetries (McCarthy, van\nBreugel, \\& Kapahi 1991) argues that shock heating is also an important\nprocess (e.g. Bicknell \\& Koekemoer 1995; Best et al. 1999).\n\nIn section 2, we describe the definition of the sample, the origin of\nthe data, and the derived quantities which are used in the analysis.\nIn section 3, we describe the results of the statistical analysis of\nthe derived quantities. In section 4, we describe the correlation\nresults. In section 5, we discuss the implications of these results\nand finally in section 6 we summarize the results and their\nimplications.\n\n\\subsection {The sample }\n\nThe majority of the objects are drawn from the 3CR sample (Bennet 1962;\nSpinrad et al. 1985, Djorgovksi et al. 1988; Strom et al. 1990). At\nredshifts larger than $\\sim 0.2$ nearly all of the 3CR galaxies that\nare known to have emission lines with extents of more than $5^{''}$ are\nincluded in our sample. The source samples in Baum, Heckman, \\& van\nBreugel (1990, 1992) \\& McCarthy, Baum, \\& Spinrad (1996) were drawn\nfrom the emission-line imaging surveys of a 408 MHz radio flux limited\nsample of low redshift equatorial radio sources by Baum et al. (1988)\nand a sample of intermediate and high redshift 3CR galaxies imaged by\nMcCarthy et al. (1995). The latter sample becomes significantly\nincomplete for $1.2 < z < 1.6$, where the principal lines that show\nlarge spatial extents (e.g. [OIII]5007, [OII]3727, Ly$\\alpha$) are\neither unreachable or are in regions of very strong sky emission. In\nthe range $0.2 < z < 1.2$ our sample contains all of the 3CR galaxies\nwith large emission-line regions except 3CR 172, 3CR 275, 3CR 341, 3CR\n244.1, 3CR 284, 3CR 180. At larger redshifts we do not have adequate\n2-D spectra of the extended gas in 3C 437 ($z = 1.48$), 3C 256 ($z =\n1.82$), 3C 326.1 ($z = 1.82$), 3C 454.1 ($z = 1.84$), and 3C 257 ($z =\n2.4$). We have excluded the two Virgo sources (3C 272.1 \\& 3C 274) from our\nanalysis as their linear extents are smaller than the resolution element for\nnearly all of the other objects in the sample.\nIn addition to the 3CR sources, at low redshift our sample\nincludes three Parkes sources (PKS 0634-206, PKS 0745-191, and PKS\n1345+125) from the equatorial sample of Baum et al. (1988). Similarly,\nat $z > 2$ we have added three sources from the 408MHz MRC/1Jy survey\n(McCarthy et al. 1996). These three objects are thought to be\nrepresentative of the large Ly$\\alpha$ emission regions in the most\ndistant radio galaxies.\n\n\\section { The Data}\nWe use ground-based long slit spectra and emission line images of 3CR\nand 1 Jy class radio galaxies that were obtained at the Kitt Peak and\nCerro Tololo National Observatories, Lick Observatory, and Palomar\nObservatory. The details of the observations and the basic data are\npresented in Baum, Heckman, and van Breugel (1990), McCarthy, Spinrad\nand van Breugel (1995) and references t herein. To this data we added\nsimilar data from the literature (e.g. Heckman \\etal\\ 1989; Tadhunter\n\\etal\\ 1989; Clark et al. 1998) as well as published radio maps\n(notably the compilation by Leahy, Bridle, \\& Strom (1996) of radio\nsource maps for the 3CR) to assemble the data used to derive the\ncorrelations presented here.\n\n\n\n\\subsection {Measured quantities} \\begin{itemize}\n \\item FWHM - For each velocity field plotted in either Baum,\n Heckman, \\& van Breugel (1990) or McCarthy, Baum, \\& Spinrad\n(1995) we determined a characteristic extra-nuclear FWHM. We used the\nmaximum value of the FWHM, excluding both the nucleus and the regions\nwhere the uncertainties are large. We averaged over three spatial\nresolution elements at the location of the maximum FWHM in assigning a\ncharacteristic \nvelocity width to the rather low signal-to-noise plots of FWHM vs.\ndistance that are available for these objects. The tabulated values for\nthe FWHM and our estimate of the associated uncertainties are given in\ncolumns 11 of Table 1.\n\nThe non-zero size of the spatial resolution elements in each spectra\nintroduce a component of broadening to the lines that is not physical\nin origin. This is likely to be important in a number cases for which\nthere are large velocity gradients (e.g. 3C 330) and for objects at\nhigh redshift where the spatial resolution element ($\\sim 1.5\"$)\ncorresponds to scales of $\\sim 10$ kpc.\n\n\n \\item V$_{\\rm peak}$ and V$_{max}$. We determined the maximum\npeak-to-peak amplitude of the resolved velocity field (V$_{\\rm peak}$)\nfor each slit position and object combination. As with all of the\nmeasurements we averaged over a few spatial resolution elements and\ngave low weight to regions of the slit with large velocity\nuncertainties. Since many of the emission-line regions are distributed\nasymmetrically with respect to the nucleus, the peak-to-peak amplitude\nis often poorly defined. For this reason we define V$_{max}$ - the\nmaximum one-sided velocity offset with respect to the nucleus,\nregardless of its spatial location. Thus objects with large amplitude\nvelocity fields, but one-sided nebulae (e.g. 3C 356) are properly\ncompared with smaller amplitude, but symmetric, objects (e.g. 3C 300).\nSeveral of the objects were observed with more than one telescope and\ninstrument combination, or in more than one position angle. For these\nwe determined single values for the V$_{\\rm peak}$ and V$_{max}$\nvelocity amplitudes by choosing the data set with the highest\nresolution and signal to noise ratios. For objects with multiple\nposition angles we use the angle the revealed the large velocities and\nline widths. In the cases of 3C 458 and 3C 265 for which two spatially\noffset slit positions were used, we included separate measurements for\neach. V$_{\\rm peak}$ and V$_{max}$ are tabulated in columns 6 \\& 7 of\nTable 1.\n\n \\item R$_{\\rm Vmax}$ and D$_{\\rm [OII]}$. Several of the derived\nquantities depend on both the observed velocities, or line widths, and\na characteristic linear scale. We considered a number of different\nchoices for this scale length and adopted two. The first is the\nisophotal size of the emission line region in kpc (denoted D$_{\\rm\n[OII]}$ in column 8 of Table 1) as determined from emission-line images\n(Baum et al. 1988; McCarthy, Spinrad and van Breugel 1995). These were\nmeasured at a fixed rest-frame surface brightness level corresponding\nto f(H$\\alpha$)$ = 3.0 \\times 10^{-15}$ erg sec$^{-1}$ cm$^{-2}$ per\nsquare arcsecond. Images in [OIII], [OII] or Ly$\\alpha$ were converted\nto equivalent H$\\alpha$ surface brightnesses (McCarthy et al. 1995).\nThe depth reached by the slit spectra and the narrow-band imaging were\nnot always identical, particularly when considering that not all of the\nregion of detected emission in the spectra were of sufficient quality\nto allow for accurate velocity measurements. We also measured the\ndistance from the nucleus to the point of maximum velocity directly\nfrom the spectra. This distance, R$_{\\rm Vmax}$ is listed in column 9\nin Table 1 and is used in several of the plots and computations.\n\n\\item{} Radio source sizes, D$_{\\rm Rad}$ and l$_{\\rm Rad}$ - The\nlinear (lobe separation) sizes of the radio sources are given as D$_{\\rm\nrad}$ in Column 12 of Table 1. The angular sizes were either measured\ndirectly from the maps in Baum et al. (1988) or taken from the\ncompilation in McCarthy, van Breugel and Kapahi (1991), and were then\nconverted to kpc using H$_0 = 50$ km sec$^{-1}$ Mpc$^{-1}$ and q$_0 = 0.1$.\nAs discussed above, the emission-line regions are\noften one sided and a simple comparison between the maximum size of the\nradio source and emission-line region may not give a proper reflection\nof the degree of spatial coincidence between the radio and\nline-emitting material. We used the most recent maps to determine the\nangular size of the radio sources on the same side of the nucleus as\nthe gas whose velocity field we measure. Thus for sources with\nasymmetric emission-line regions we tabulate the length of one arm of\nthe radio source, while for more symmetric nebulae we tabulate the\ntotal size of the source. This emission-nebula dependent measure of\nthe radio source extent is given as l$_{\\rm rad}$ in Column 13 of\nTable 1. Sources with one sided nebulae and close coincidences between\nradio lobes and emission line regions (e.g. 3C 441) can now be\nrecognized by the rough equalities of the two sizes in columns 8 and\n13, in Table 1.\n\n\\end{itemize}\n\n\\subsection {Derived quantities}\n\n\\begin{itemize}\n\n\\item Gas mass, M$_{\\rm gas}$ (column 14, Table 1). We estimated the\ntotal mass of line-emitting gas for each object in our sample. The\nmasses were derived from the measured luminosities and characteristic\nscales determined from the emission-line images, and an assumed value\nof the ionization parameter of 1\\%. The filling factor, in units of\n$10^{-5}$, is given by, $f_{v5} = 41.3 \\times (U_{-2}\\times\nr_{10}/L_{44})^{0.5} $, where $U_{-2}$ is the ionization parameter in units of\n$10^{-2}$, $U =\nQ(ion)/4\\pi r^2n_ec$. The mass of gas, in units of $10^8$M$_{\\odot}$,\nis $ 1.4 \\times (L_{44}\\times_{10}^3\\times f_{v5})^{0.5}$, where\n$L_{44}$ is the equivalent [OII]3727 luminosity in units of $10^{44}$\nerg/sec and $r_{10}$ is the size of the emission-line nebulae in units\nof 10 kpc. These masses are highly uncertain as they, 1) make very\nsimplified assumptions about the geometry of the line-emitting gas (a\nsphere of radius $r_{10}$), 2) adopt the same value of $U_{-2}$ for all of\nthe sources and 3) make no correction for ionization fraction,\nabundances etc.\n\n\\item\n Dynamical Mass, M$_{\\rm dyn}$ (column 17, Table 1). To the extent\nthat the large scale velocity fields reflect the gravitational\npotential and are representative of the circular velocity, they can be\nused to infer an interior dynamical mass. We use the distance to the\npeak emission-line velocity, R$_{\\rm Vmax}$ and the maximum velocity to\ncompute the inferred enclosed mass in units of $10^8$M$_{\\odot}$ as\n$0.0022 \\times $R$_{\\rm Vmax} \\times$ V$_{\\rm max}^2 $ with $R_{\\rm\nVmax}$ in kpc and V in km/sec. This apparent or inferred dynamical\nmass only really measures mass if the kinematics are\ndominated by rotation in response to the gravitational field, and will\nhave an entirely different meaning if the gas kinematics are set via\nradio source - cloud interactions.\n\n\\end{itemize}\n\n\\section {Results }\n\n Our sample and the derived data are listed in Table 1. For each\n source we list a single set of measurements corresponding to the\nslit position angle with the largest velocities. For 3C 458 and 3C 265\nwe list two sets of measurements as they were taken at two different\nslit positions, one centered on the nucleus and a parallel slit\nposition offset from the nucleus. For a few objects we are not able to\nmeasure meaningful values for all of the quantities and these are left\nblank in the table.\n\nIn Figures 1-4 we plot various relations between the observed and\nderived parameters described above. In Table 2 we give the derived\ncorrelation coefficients corresponding to plots shown in Figures 1 - 4.\n\n{\\tiny\n\\begin{planotable}{lrllrrrrrrrrrrrr}\n\\tablewidth{0pt}\n\\tablecaption{Data Table}\n\\tablehead\n{\n\\colhead{Source} & % 01\n\\colhead{FR} & % 03\n\\colhead{PA} & % 04\n\\colhead{$z$} & % 05\n\\colhead{P$_{\\rm{408}}$} & % 06\n\\colhead{V$_{\\rm{peak}}$} & % 07\n\\colhead{V$_{\\rm{max}}$} & % 08\n\\colhead{D$_{\\rm{[OII]}}$} & % 09\n\\colhead{R$_{\\rm{Vmax}}$} & % 10\n\\colhead{L$_{\\rm{[OII]}}$} & % 11\n\\colhead{FWHM} & % 12\n\\colhead{D$_{\\rm{Rad}}$} & % 14\n\\colhead{l$_{\\rm{Rad}}$} & % 15\n\\colhead{M$_{\\rm{gas}}$} & % 16\n\\colhead{M${\\rm{dyn}}$} & % 17\n\\colhead{Ref} \\cr % 18\n\\colhead{1} & % 01\n\\colhead{2} & % 03\n\\colhead{3} & % 04\n\\colhead{4} & % 05\n\\colhead{5} & % 06\n\\colhead{6} & % 07\n\\colhead{7} & % 08\n\\colhead{8} & % 09\n\\colhead{9} & % 10\n\\colhead{10} & % 11\n\\colhead{11} & % 12\n\\colhead{12} & % 13\n\\colhead{13} & % 14\n\\colhead{14} & % 15\n\\colhead{15} & % 16\n\\colhead{16} \\cr % 17\n}\n\n\\startdata\n3CR 272.1 & I & 085 &0.003 & 23.7 &250 &125 & \\ \\ \\ 2 & \\ \\ \\ 0.6 & \\ \\ 39.1 & 150 $\\pm$ 050 & 14 & 14 & 4.6 & 9.3 & 1 \\cr\n3CR 274.0 & I & 000 &0.004 & 25.6 &370 &250 & 21 & 0.8 &40.2 & 219 $\\pm$ 100 & 52 & 52 & 6.7 & ... & 1 \\cr\n3CR 264.0 & I & 085 &0.021 & 25.4 &17 &8.5 & 4 & 0.3 &39.8 & 450 $\\pm$ 150 & 29 & 15 & 4.2 & 6.7 & 1 \\cr\n3CR 442.0 & I & 126 &0.026 & 25.6 &140 &70 & 7 & 2 &40.2 & 300 $\\pm$ 100 & 385 &192 & 5.8 & 9.3 & 1 \\cr\n3CR 078.0 & I & 120 &0.029 & 25.7 &30 &15 & 7 & 1.6 &40.4 & 480 $\\pm$ 050 & 141 & 71 & 5.7 & 7.9 & 1 \\cr\n3CR 088.0 & I & 150 &0.030 & 25.6 &60 &40 & 8 & 3 &40.5 & 350 $\\pm$ 100 & 189 & 95 & 6.1 & 9.0 & 1 \\cr\n3CR 353.0 & I & 160 &0.030 & 26.7 &100 &100 & 6 & 2 &40.2 & 400 $\\pm$ 200 & 223 &112 & 5.8 & 9.7 & 1 \\cr\n3CR 098.0 & I & 163 &0.031 & 26.0 &310 &210 & 23 & 8 &40.6 & 250 $\\pm$ 050 & 264 &133 & 6.9 & 10.9 & 1 \\cr\nPKS 0634 & II & 124 &0.056 & 26.5 &480 &260 & 60 & 14 &42.2 & 150 $\\pm$ 100 &1169 &117 & 0.0 & 11.3 & 1 \\cr\n3CR 405.0 & II & 160 &0.056 & 26.5 &105 &62 & 13 & 3 &41.9 & 350 $\\pm$ 050 & 187 & 94 & 6.5 & 9.4 & 1 \\cr\n3CR 403.0 & II & 020 &0.059 & 26.4 &480 &260 & 16 & 6 &40.7 & 200 $\\pm$ 100 & 333 &167 & 6.7 & 11.0 & 1 \\cr\n3CR 033.0 & II & 019 &0.059 & 26.7 &310 &220 & 17 & 4 &41.4 & 300 $\\pm$ 150 & 419 &211 & 6.6 & 10.6 & 1 \\cr\n3CR 192.0 & II & 145 &0.060 & 26.3 &340 &230 & 39 & 20 &41.1 & 150 $\\pm$ 100 & 305 &191 & 7.8 & 11.4 & 1 \\cr\n3CR 285.0 & II & 140 &0.079 & 26.2 &390 &260 & 21 & 5 &41.2 & 200 $\\pm$ 100 & 374 &187 & 6.7 & 10.9 & 1 \\cr\n3CR 227.0 & II & 121 &0.086 & 26.7 &260 &160 & 144 & 20 &42.0 & 250 $\\pm$ 100 & 501 &274 & 8.0 & 11.1 & 1 \\cr\n3CR 433.0 & II & 129 &0.102 & 27.1 &410 &410 & 31 & 8 &40.6 & 500 $\\pm$ 200 & 161 & 82 & 6.9 & 11.5 & 1,2 \\cr\nPKS 0745 & I & 112 &0.103 & 26.7 &75 &75 & 34 & 7 &42.5 & 355 $\\pm$ 100 & 31 & 16 & 8.0 & ... & 1 \\cr\nPKS 1345 & 0 & 060 &0.122 & 26.8 &165 &165 & 26 & 6 &42.2 & 550 $\\pm$ 200 & 0.3 & 0.3 & 7.1 & 10.5 & 1 \\cr\n3CR 381.0 & II & 155 &0.161 & 27.0 &480 &280 & 127 & 29 &42.3 & 200 $\\pm$ 200 & 257 &130 & 8.3 & 11.7 & 2 \\cr\n3CR 063.0 & II & 090 &0.175 & 27.2 &290 &280 & 63 & 10 &41.9 & 500 $\\pm$ 100 & 88 & 44 & 7.4 & 11.2 & 1 \\cr\n3CR 033.1 & II & 054 &0.181 & 27.1 &150 &100 & 58 & 16 &41.8 & 300 $\\pm$ 200 & 884 &327 & 7.7 & 10.6 & 2 \\cr\n3CR 196.1 & I & 052 &0.198 & 27.2 &50 &50 & 25 & 7.0 &41.5 & 400 $\\pm$ 100 & 17 & 17 & 7.0 & 9.6 & 1 \\cr\n3CR 079.0 & II & 322 &0.256 & 27.6 &530 &350 & 117 & 53 &42.4 & 200 $\\pm$ 200 & 454 &195 & 8.8 & 12.2 & 2 \\cr\n3CR 460.0 & II & 215 &0.268 & 27.1 &220 &120 & 38 & 16 &41.6 & 500 $\\pm$ 250 & 32 & 8 & 7.7 & 10.7 & 2 \\cr\n3CR 300.0 & II & 000 &0.270 & 27.6 &450 &380 & 72 & 54 &42.7 & 300 $\\pm$ 100 & 526 &164 & 8.9 & 12.2 & 2 \\cr\n3CR 458.0 & II & 040 &0.290 & 27.5 &280 &180 & 232 & 68 &42.4 & 325 $\\pm$ 100 &1099 &633 & 9.0 & 11.7 & 2 \\cr\n3CR 458.0 & II & 040 &0.290 & 27.5 &350 &300 & 232 & 68 &42.4 & 350 $\\pm$ 150 &1099 &633 & 9.0 & ... & 2 \\cr\n3CR 299.0 & II & 000 &0.367 & 27.7 &320 &320 & 88 & 39 &42.5 & 600 $\\pm$ 100 & 78 & 20 & 8.6 & 11.9 & 2 \\cr\n3CR 306.1 & II & 180 &0.441 & 27.9 &080 &060 & 51 & 15 &42.7 & 400 $\\pm$ 200 & 690 &350 & 7.9 & 10.1 & 2 \\cr\n3CR 435.0 & II & 229 &0.471 & 27.8 &250 &150 & 281 & 76 &42.7 & 300 $\\pm$ 100 & 94 & 94 & 9.1 & 11.6 & 2 \\cr\n3CR 330.0 & II & 230 &0.550 & 28.5 &650 &450 & 85 & 82 &43.5 & 450 $\\pm$ 200 & 517 &259 & 9.4 & 12.6 & 2 \\cr\n3CR 169.1 & II & 126 &0.633 & 27.9 &1500 &1400 & 73 & 61 &43.0 & 500 $\\pm$ 100 & 339 &178 & 9.1 & 13.4 & 2 \\cr\n3CR 337.0 & II & 090 &0.635 & 28.2 &320 &260 & 105 &132 &41.9 & 400 $\\pm$ 200 & 384 &161 & 9.4 & 12.3 & 2 \\cr\n3CR 034.0 & II & 000 &0.689 & 28.3 &150 &150 & 170 & 28 &43.9 & ... & 425 &425 & 8.7 & 11.1 & 2 \\cr\n3CR 441.0 & II & 144 &0.707 & 28.4 &1100 &1050 & 162 &138 &42.7 & 100 $\\pm$ 100 & 308 &112 & 9.6 & 13.5 & 2 \\cr\n3CR 277.2 & II & 055 &0.766 & 28.4 &950 &950 & 316 &131 &43.5 & 500 $\\pm$ 100 & 521 &193 & 9.8 & 13.4 & 2 \\cr\n3CR 340.0 & II & 090 &0.775 & 28.4 &110 &060 & 38 & 19 &42.9 & 450 $\\pm$ 100 & 436 &223 & 8.1 & 10.2 & 2 \\cr\n3CR 352.0 & II & 150 &0.806 & 28.5 &650 &350 & 60 & 58 &43.3 & 850 $\\pm$ 100 & 100 &100 & 9.1 & 12.2 & 2 \\cr\n3CR 265.0 & II & 115 &0.811 & 28.7 &680 &450 & 283 &105 &44.1 & 500 $\\pm$ 100 & 768&768 & 9.8 & 12.7 & 2 \\cr\n3CR 265.0 & II & 115 &0.811 & 28.7 &500 &500 & 283 &105 &44.1 & 500 $\\pm$ 100 & 768&768 & 9.8 & 12.8 & 2 \\cr\n3CR 280.0 & II & 090 &0.998 & 29.0 &550 &500 & 98 & 72 &44.0 & 700 $\\pm$ 100 & 135& 68 & 9.4 & 12.6 & 2 \\cr\n3CR 356.0 & II & 148 &1.079 & 28.8 &1500 &1500 & 85 & 73 &43.9 & 700 $\\pm$ 100 & 302&302 & 9.4 & 13.6 & 2 \\cr\n3CR 368.0 & II & 065 &1.132 & 28.9 &575 &550 & 91 & 43 &44.1 & 1400$\\pm$ 100 & 93& 93 & 9.0 & 12.4 & 2 \\cr\n3CR 267.0 & II & 090 &1.140 & 28.9 &380 &380 & 31 & 21 &43.3 & 750 $\\pm$ 250 & 416&192 & 8.3 & 11.8 & 2 \\cr\n3CR 324.0 & II & 090 &1.206 & 29.0 &725 &500 & 92 & 53 &44.0 & 1000$\\pm$ 200 & 107&107 & 9.2 & 12.5 & 2 \\cr\n3CR 266.0 & II & 180 &1.275 & 29.0 &550 &450 & 47 & 33 &43.9 & 900 $\\pm$ 200 & 45& 45 & 8.8 & 12.2 & 2 \\cr\n3CR 266.0 & II & 180 &1.275 & 29.0 &1350 &1350 & 47 & 0.1 &43.9 & ... & 45& 45 & 0.0 & ... & 2 \\cr\n3CR 294.0 & II & 180 &1.786 & 29.4 &1300 &1200 & 152 & 91 &44.4 & 1100$\\pm$ 200 & 173& 77 & 9.7 & 13.4 & 2 \\cr\nMRC 0457 & II & 065 &1.960 & 28.9 &600 &550 & 114 & 67 &44.4 & 1400$\\pm$ 300 & 200& 96 & 9.5 & 12.6 & 2 \\cr\nMRC 0406 & II & 128 &2.44 & 29.8 &1900 &1000 & 76 & 45 &44.5 & 1000$\\pm$ 300 & 89& 55 & 9.2 & 14.0 & 2 \\cr\nMRC 2104 & II & 021 &2.49 & 29.6 &490 &350 & 139 & 23 &44.4 & 800 $\\pm$ 200 & 269&134 & 8.6 & 11.8 & 2 \\cr\n\\end{planotable}\n% put tables here so they get put up front.\n}\n\\noindent {\\bf Notes to Table 1:} Velocities are in\nunits of km sec${-1}$, radio power is in units of erg sec$^{-1}$ Hz$^{-1}$,\nemission-line luminosities are in units of erg sec$^{-1}$, all length scales\nare in kpc, M$_{gass}$ and M$_{dyn}$ are in solar mass units. Luminosities\nand masses are shown as logarithms. \n\n\\noindent references: 1) Baum, Heckman \\& van Breugel (1990); 2) McCarthy, Baum, \\& \nSpinrad (1995).\n\n\n\n\n\n\n% put tables here so they get put up front.\n\n\n\\begin{table}[htb]\n\\begin{center}\n\\begin{tabular}{ll}\n\\multicolumn{2}{c} {Fits to Correlations } \\\\\n\\hline\nRelationship & Correlation \\cr\n & Coefficient \\cr\n(1) & (2) \\cr\n\\hline\nP$_{\\rm 408}$ vs $z$ & 0.98 \\cr\nR$_{\\rm Vmax}$ vs $z$& 0.82 \\cr\nM$_{\\rm gas}$ vs $z$ & 0.77 \\cr\nR$_{\\rm Vmax}$ vs V$_{\\rm max}$ & 0.76 \\cr\nV$_{\\rm max}$ vs M$_{\\rm gas}$ & 0.76 \\cr\nM$_{\\rm dyn}$ vs $z$& 0.75 \\cr\nP$_{\\rm 408}$ vs V$_{\\rm max}$ & 0.67 \\cr\nV$_{\\rm max}$ vs $z$ & 0.64 \\cr\nM$_{\\rm gas}$ vs M$_{\\rm dyn}$ & 0.64 \\cr\nP$_{\\rm 408}$ vs FWHM & 0.63 \\cr\nFWHM vs $z$& 0.62 \\cr\nl$_{\\rm Rad}/$R$_{\\rm Vmax}$ vs V$_{\\rm max}$ & 0.43$^{*}$ \\cr\nl$_{\\rm Rad}/$R$_{\\rm Vmax}$ vs FWHM & 0.41$^{*}$ \\cr\nD$_{\\rm Rad}$ vs D$_{\\rm [OII]}$ & 0.34 \\cr\nFWHM vs M$_{\\rm gas}$ & 0.32 \\cr\nD$_{\\rm rad}$ vs FWHM & 0.26$^{*}$ \\cr\nD$_{\\rm rad}$ vs V$_{\\rm max}$ & 0.26 \\cr\nV$_{\\rm max}$ vs FWHM & 0.20 \\cr\nD$_{\\rm rad}$ vs $z$& 0.10 \\cr\n\\hline\n\\end{tabular}\n\\end{center}\n\\caption{The results of a least squares linear fit to the relationships in\nlog-log space. Uncertainties are in parentheses. }\n\\end{table}\n~\n\n\\section {Correlation Results}\n\nBelow we describe the most relevant correlation results.\n\n\\subsection {Radio Power with Redshift} In our sample, as in most flux limited samples \nextending to significant redshifts, radio power and redshift are strongly correlated\nmaking the disentanglement of redshift versus radio power effects a\ndifficult challenge.\n\n\\subsection{Log Gas Mass versus log Redshift}\n\nThere is an apparent correlation of the ionized gas mass with redshift,\nwith ionized gas mass increasing roughly linearly (in a log-log plot)\nwith redshift (Figure 1a). Further, the plot shows that the FR1 and FR2 sources\nfollow the same correlation. If this correlation is real (and not just\na selection effect - see below), then there are two straightforward\npossible explanations for it. \\begin{itemize}\n\n\\item The mass of cold gas within the parent galaxies increases with\nredshift, such that cold gas was more abundant in radio galaxy hosts at\nearlier epochs. This is consistent with (1) increased bending in radio\nsources at high redshift (e.g., Barthel \\& Miley 1988); (2) the higher\nfraction of compact GHz Peaked Spectrum quasars at high redshift (e.g.,\nO'Dea 1998); (3) the alignment effect occurring preferentially at high\nredshift (e.g., McCarthy 1993).\n\n\\item The flux of ionizing radiation, and hence the measured mass of\nionized gas for radiation bounded nebulae, increases with radio power\n(redshift). \\end{itemize}\n\nHowever, some caution is needed in interpreting the data, as the\ncorrelation may owe at least in part, to an observational selection\neffect, since sources with small masses of ionized gas at high redshift\nwould not have been detected as extended emission line sources and so\nwould not have been included in follow up spectroscopic studies such as\nthis one. That is, the limiting surface brightness curve defines an\nexcluded region of the plot. However, despite this caveat, the sources\nin our sample do nevertheless show an order of magnitude or more\nvariation in observed gas mass such that at low redshifts, (or radio\npowers) we do not find sources with as high gas masses as we do at\nhigher redshift (power).\n\n\\subsection{ Dynamical Mass versus $z$}\n\nWe also find an apparent correlation of redshift (and radio power) and\nenclosed dynamical mass (Figure 1b). FR1s have systematically low dynamical masses\nat a given redshift, and we find that the highest dynamical mass\nobjects are double kinematic systems (see the correlation of redshift\nwith V$_{max}$ below), which are found preferentially at the highest z. The\nmaximum derived dynamical masses are comparable to the masses of\nclusters, as derived from x-ray and lensing studies (Squires\n\\etal\\ 1997; Allen, Fabian, \\& Kneib 1996; Miralda-Escud\\'e \\& Babul\n(1995)), at comparable distances from the cluster center (e.g., 100\nkpc). There are two ways to understand this correlation, assuming for\nthe moment that the velocities do measure the gravitational potential\nand not the radio source jet thrust.\n\n\\begin{itemize}\n\n\\item The mass of the host galaxy is larger at redshifts and radio\npowers. This seems somewhat unlikely given that radio galaxies live in\nthe most massive galaxies even at low redshifts, and that it is well\nknown (Ledlow \\& Owen 1996; de Vries et al 1998) that at present \nFR1s (and not FR2s) on average occupy higher mass\nsystems at a fix radio luminosity.\n\n\\item The ionized gas probes progressively larger scales at higher\nredshift, thereby enclosing greater and greater dynamical mass. This\ncould be due either to the presence of more cold gas in the host\ngalaxies at higher z (see above) or, to the increased UV ionizing flux\nput out by the more powerful radio galaxies at high redshift in our\nsample. \\end{itemize}\n\n\\subsection{ Dynamical mass versus M$_{gas}$}\nThere is a strong apparent correlation of inferred dynamical mass with gas mass,\nwith a slope near one half - that is dynamical mass proportional to the\nsquare root of the gas mass (Figure 2a). The correlation for FR1 and FR2 radio\ngalaxies is the same, with the FR1s occupying the low mass portion of\nthe relationship.\n\nIf the correlation is real (and the inferred dynamical mass is really\na measure of enclosed mass) it suggests that \\begin{itemize}\n\n\\item there is a constant fraction of gas to gravitational mass of\n$\\sim 0.1\\%$ and \\item the ionized gas mass measures gas mass and not\nionizing flux. \\end{itemize}\n\nWe tested for the possibility that this correlation is artificial, since\none of the quantities depends on R and the other on R$^3$ by plotting\n$R\\times V$ against the [OII] luminosity directly; \nthe correlation, though noisier, remains (see Figure 2c).\n\n\\subsection { V$_{max}$ vs. R$_{V_{max}}$ }\n\nThere is an apparent correlation of maximum velocity versus the radius\nin kpc at which that maximum velocity is measured, with a slope near\nunity, such that the larger the distance, the larger the velocity (Figure 2d).\nFR1s fit on the same relationship as FR2s. This can be most\nsimply interpreted in the following way. The velocities are\ngravitationally induced, all radio galaxies have basically the same\nintrinsic masses and environments, and the further out one probes \nthe gas velocity, the greater the velocity one measures since a larger\nmass is encircled. In the most powerful radio sources (or the highest\nredshift sources) - the larger luminosity or ionizing radiation (which\nis assumed to scale with radio luminosity) illuminates gas\nat larger radii from the galaxy nucleus, producing this result.\n\nInterestingly, we see from this plot that the maximum velocity which is\nmeasured is roughly $1500$ km sec$^{-1}$. What can this mean? Two\nalternate scenarios present themselves; \\begin{itemize}\n\n\\item If the velocities are gravitational in origin, than as mentioned\nabove, 1500 km sec$^{-1}$ is roughly the velocity predicted for gas in\nequilibrium within a very rich cluster at a distance of $\\sim 100$ kpc\nfrom the nucleus (e.g., Mazure \\etal\\ 1996). It appears, however, that\nmany of the v $> 800$ km sec$^{-1}$ systems are composites (i.e., two\ngalaxies); the maximum velocity would then be a measure of the peak\ngalaxy encounter velocity. Again, 1500 km sec$^{-1}$ is a sensible pair-wise \nencounter velocity.\nIt is interesting to consider whether pairs can produce such\nvelocities without obvious clusters at redshifts of $0.6 - 0.7$ (e.g.\n3C 169.1, 3C 277.2 where these high velocities are also seen). We\nreturn to this later in the discussion.\n\n\\item If the velocities are shock induced from the radio source and not\ngravitational, then the maximum of 1500 km sec$^{-1}$ may correspond\nto the maximum velocity achieved before the gas is heated to\ntemperatures such that the radiative cooling time is longer than\nthe source lifetime. Bicknell, Dopita and O'Dea (1997)\nassert that detailed fast radiative shock models fit the following\nrelationship: $t_{rad,6} \\sim 1.9 n^{-1} V_3^{2.9}$ where $V_3$ is\nthe shock velocity in units of 1000 km/sec, n is the preshock density.\nThus for V = 1500 km/sec and a radio\nlifetime = $10^7$ years, only clouds with densities\ngreater than $0.6$ cm$^{-3}$ will produce significant optical and near-UV line emission.\nAt higher\nshock velocities or lower preshock densities the heated gas will\nbe too hot and diffuse to cool within the radio source lifetime.\n\\end{itemize}\n\n\\subsection {FWHM and V$_{max}$ versus l$_{\\rm Rad}$/R$_{\\rm Vmax}$}\n\nThe plots of FWHM and V$_{max}$ versus l$_{\\rm Rad}$/R$_{\\rm Vmax}$ \n(Figures 4a and 4b) are helpful in disentangling the relationship\nbetween the radio source and the observed velocities; if the radio\nsource is responsible for inducing the turbulence in the gas then we\nmight expect that there would be a strong correlation between the FWHM\n(or V$_{max}$) and the ratio of radio source to emission line nebulae size. That is,\nwe might expect that when the radio source and the nebulae are\ncomparably sized, the gas will be be most kinematically disturbed.\n\nThere appears to be a weak correlation with a trend towards\nlarger line widths in objects with comparable radio and emission-line sizes. \nHowever, this is not a statistically robust\ncorrelation and there is a large ranges in FWHM and V$_{max}$ values for a\ngiven relative size. Interestingly, the FR1s follow the same\ncorrelation as the FR2s. Longair et al. (1999) report a significant correlation between\nsource size and off-nuclear line widths in a small sample of $z \\sim 1$ 3CR galaxies.\n\n\\subsection{ FWHM versus $z$} There is an apparent correlation of line width and\nredshift (and radio power), which warrants further examination.\nThe plot of FWHM versus $z$ (Figure 3a) is essentially flat for $0.01 < z < 0.6$\nand rises steeply (or jumps) for larger\nredshifts. The highest line widths are seen at z$>1$; for $z < 1$\nthe maximum line width is 500 km sec$^{-1}$ and the mean is $370 \\pm 150$ km\nsec$^{-1}$ while for $z > 1$, the maximum is 1500 km\nsec$^{-1}$ and the mean is $1000 \\pm 250$ km sec$^{-1}$. \nThe FR1 sources have relatively high mean line widths relative to FR2 sources\nat the same redshift with an FR1 mean of $\\sim 385 \\pm 95$ km sec$^{-1}$ and\nan FR2 mean of $\\sim 285 \\pm 130$ at z$<0.2$.\n\nThe change in properties at redshifts above $z \\sim 0.6$ could signal\na difference in environments of the host galaxies.\nAt low redshift FR2s are predominantly found in the field or\ngroups of galaxies (e.g., Prestage \\& Peacock 1988 ), while at higher\nredshifts they are believed to be found in environments with densities reaching\nthose of rich clusters\n(e.g., Hill \\& Lilly 1991). Thus, if the line width reflects the underlying\ngravitational potential, the observed FWHM may trace the velocity\ndispersion of the host galaxy or its surrounding group or cluster. The\nsystematically high FWHM of FR1 sources relative to FR2 sources at low\nredshifts is grossly consistent with this scenario, since FR1s\noccupy more massive galaxies at a given radio luminosity\nand inhabit denser environments at low redshifts than do FR2s (Ledlow\n\\& Owen 1996; Hill \\& Lilly 1991). \n\nIn the alternative scenario, where the FWHM reflects an interaction\nwith the radio source, this same plot can be interpreted as FWHM versus\nradio power. At higher powers the interaction is stronger and the\nturbulence induced in the gas greater. In is not clear how this scenario \nwould produce the sudden change in line widths at $z > 0.6$.\n\n\\subsection{ V$_{max}$ versus z} The V$_{max}$ versus $z$\nplot is similar to the FWHM versus $z$ plot and could reflect the same\nprocess involved in the change in line widths at large redshifts. \nSpecifically, if one excludes the FR1s, which have\nsystematically low velocities at a given redshift (see the subsection 4.9\nbelow for an explanation of the FR1\nbehavior) then the velocities are flat for $0.01 < z < 0.7$ \nat a mean of $\\sim 230 \\pm 240$ km sec$^{-1}$ and then the mean value jumps\ndramatically to $v \\sim 720 \\pm 400$ km sec$^{-1}$ for $z > 1$.\nThis is, again, most likely due to a change in environments of the host\ngalaxies, but may also reflect the importance of radio power in\ndetermining the overall gas kinematics. In the latter scenario, it is,\nhowever, difficult to understand why one would see a `jump' at\nintermediate redshifts as opposed to a continuous correlation of\nvelocity with radio power.\n\nSpecial consideration should be given to the highest V$_{max}$ systems. We\nnote that of the sources with V$_{max}$ greater than $\\sim 800$ km\nsec$^{-1}$ approximately six of these sources show double kinematic\nstructure. 3C 169.1, 3C 356 and MRC 2104-242 for example, are systems\nwith two fully detached emission line regions with velocity differences\nof several hundred km sec$^{-1}$ or more (see McCarthy, Baum, \\&\nSpinrad (1996) for velocity versus distance plots). These are likely\nto be instances where we are seeing gas in two distinct kinematic\nsystems, for example two independent galaxies, or gas in \"split-line\"\nsystems where the gas has been wrapped around two sides of expanding\nradio plasma interacting with out-flowing radio plasma (e.g. Clark et\nal. 1997; Capetti et al. 1999) We also note that the maximum values of V$_{\\rm max}$\nseen are roughly $\\sim 1200-1500$ km sec$^{-1}$. See also the\ndiscussion under 4.5 above.\n\n\\subsection { FWHM/V$_{max}$ versus P$_{408}$}\n\nThe FR1 sources cleanly separate from the FR2 sources on this plot of FWHM/V$_{max}$ versus P$_{408}$\n(Figure 3d).\nIn the mean the FR1s have appreciably higher ratios of FWHM to\nmaximum velocity than the FR2s (8:2) at the same radio power. As Figures \n3c and 3d show, FR1s have both larger line widths and lower maximum\nvelocities at a given redshift than do the FR2s. This is consistent\nwith the earlier results from Baum \\etal\\ (1992) that indicated that\nthe emission line gas in FR1 sources was dominated by turbulent\nmotions, while that in FR2s showed a stronger component of systematic\nmotions (e.g., rotation, outflow, or inflow). This plot also shows\nthat the ratio of turbulent to systematic motion shows no evolution\nwith radio power or redshift for the FR2s. This seems to suggest a\ncommon origin for both the turbulent and the systematic motions seen in\nthe gas.\n\n\\section {Discussion}\n\nAs is typically the case for flux limited samples, radio power and\nredshift are very tightly coupled in our sample, making the deconvolution\nof radio power and redshift affects difficult, at best.\nA crucial question we must, nevertheless,\nseek to address is whether the kinematics\nwe observe are due primarily to interactions between the gas and\nthe outflow from the central engine or whether they reflect the\nunderlying potential of the host galaxy. A similar question was addressed\nbefore for the emission line gas in Seyfert galaxies (Whittle 1992) and\nin nearby FR1 and FR2 radio galaxies (Baum \\etal\\ 1992). In both cases\nthe conclusion was that the bulk of the velocities observed were dictated\nby the underlying gravitational potential and not by jet-gas interactions,\nthough in both cases examples where that rule was violated and jet-gas\ninteractions were dominant, were noted. In the\nhigh redshift/high radio power sample we address in this paper where\nwe expect the outflow to be stronger and the gas environment to be\nricher, we might expect jet-gas interactions to be more dominant.\nLooking at the statistical data as a whole, however we find no evidence which\n{\\it requires} jet interaction as the source of the gas kinematics.\nAs is the case for their nearer by AGN brethren, the emission line kinematics\neven in the bulk of these high redshift/high power sources can be explained\nby gravity and not interaction, though as described below if the\nkinematics are gravitational in origin, the highest velocities seen\npoint to interesting environments for intermediate and high redshift\nradio galaxies.\n\nThe apparent correlations of radio power\nwith gas FWHM, V${\\rm peak}$ and R$_{\\rm Vmax}$ point towards the importance\nof jet-gas interactions. However, it is not possible to distinguish\nwith our sample, whether these correlations are primarily with redshift\nrather than radio power. Further, additional correlations\nwith radio power or source size might have been expected if jet-gas\ninteractions dominate the kinematics of the gas.\nFor instance, if jet-gas interactions are dominant,\none might have naively expected that either smaller radio sources, i.e., those\nwhich are trapped within the ISM of the host galaxy, or sources in which\nthe radio source and emission line nebulae were of localized on the same\nsize scales would evidence stronger jet-gas interactions.\nHowever, no correlations are seen\nbetween the size of the radio source and the FWHM or maximum velocity\nof the gas. Similarly, no substantial correlation is seen between\nthe FWHM or the maximum velocity of the radio source and the ratio of\nthe radio to nebular size. Lastly, our sample shows no correlation of radio size with\nradio power or redshift, or of radio size with nebular size,\nbut does show a substantial correlation of\nnebular size with redshift and/or radio power. Taken as a whole these\nfindings would seem to indicate that the properties of the emission line\nnebula are coupled with redshift or radio power but not with the\nproperties of the radio source.\n\nThus, the kinematics and correlations we see,\ncan {\\it most easily} (though not\nnecessarily correctly of course) be interpreted in terms of a gravitational\norigin for the kinematic properties of the gas.\nTo wit; we find that the FWHM, maximum velocity, radius at which\nmaximum velocity is seen, apparent dynamic mass and gas mass all correlate\nwith redshift (or radio power). In addition, we find that the\nmaximum velocity and radius of maximum velocity are themselves\ncorrelated, as are the inferred dynamical mass and the gas mass,\nand the maximum velocity and gas mass.\nA plausible scenario which encapsulates the observations follows.\n\n\\begin{itemize}\n\\item\nThe emission line nebulae are largely ionization (and not matter) bounded.\nThat is, there is an abundance of cold gas in the ISM of the radio galaxies\nand when there is more ionizing radiation, more of the cold gas, and\nto further distances in the ISM, is illuminated and heated.\n\n\\item\nThe UV ionizing flux of the central engine is correlated with radio\npower (hence redshift in our sample) such that at higher power (redshift)\nthere is a higher UV ionizing flux and hence emission line gas is found\nto greater radii.\n\n\\item The emission line gas\nkinematics (both the line widths and the absolute\nvelocities) are dominated by gravitational effects and therefor reflect the\nunderlying potential at the distance where the gas is found.\n\n\\end {itemize}\n\nIf we take this model at face value, for the moment, we can then use it to understand the\nnature of the environments of powerful radio galaxies as a function\nof redshift. Specifically, at high redshift, where the highest\nrotational velocities are seen, we would have to be seeing the gravitational\npotential of not only the radio galaxies, but a cluster or group\nwhich surrounded it. The velocity separations seen (1200-1500\nkm sec$^{-1}$)\napproach those of the richest clusters seen at lower redshift (e.g., Mazure\n\\etal\\ 1996). This either indicates that high redshift high power radio\ngalaxies are uniquely situated in the deepest potentials or it suggests that\nthe host galaxies of powerful radio galaxies at high redshift are\nin pre-virialized environments in which infall may still dominate\nthe kinematics.\n\nCompletely alternative models\nin which the kinematics are dominated by interactions with the\nradio source cannot be ruled out.\nDetailed studies show that such interactions are clearly occurring in some\nsources and so must play at least a part in determining some of the kinematics\nwe see. For instance, an\nalternative interpretation of the sources which exhibit two very high velocity\nemission systems is that we are observing split line systems created by\ninteractions of the cocoon of the expanding radio source with cold gas in\nthe galaxy atmosphere, such as appears to be the case in the low velocity\nsystems studied in detail such as Cygnus-A (3C405; Tadhunter et al. 1999) and 3C171 (Clark et al. 1998).\nIf the velocities are shock induced from the radio source and not\ngravitational, then the maximum of 1500 km sec$^{-1}$ must correspond\nto the maximum velocity achievable without heating the gas to\ntemperatures so hot that the radiative cooling time is greater than\nthe lifetime of the radio source. Applying the models of Bicknell, Dopita,\nand O'Dea (1998), this\nwould constrain the pre-shock particle densities of the shocked clouds\nwe see to be n$_e > 0.6$ cm$^{-3}$.\n\n\n\\section{Summary}\n\nWe report the results of a study of the kinematics and morphology\nof the emission line nebula in powerful 3CR radio galaxies from redshift\n$\\sim$ zero to $\\sim 4$ based on the data presented in\nBaum, Heckman and van Breugel (1990) and McCarthy, Baum, and Spinrad (1996)\nand additional data gathered on these and similar sources\nfrom the more general literature.\nThe 3CR is a well-defined radio-flux limited sample; radio power\n(AGN luminosity) is strongly correlated with redshift in this sample.\n\nWe investigate the correlation of the kinematic\nproperties of the gas with other inherent properties, such as\nredshift, radio and line luminosity, radio and emission line morphology\nand extent. We also investigate correlations with\nderived properties such as inferred mass of emission line gas and\napparent dynamical mass, where the apparent dynamical mass is defined to be\nthe mass required\nto gravitationally induce the observed kinematics.\nWe find that both the inferred mass in emission line gas and the\napparent dynamical mass appear to increase with redshift (or radio power).\n\nFor each source we define a maximum emission line velocity (V$_{\\rm max}$, the maximum\ndifference between gas velocity and the\nsystemic velocity of the galaxy, measured as the emission line velocity\nat the continuum peak) and the projected radius at which that maximum velocity\noccurs (R$_{\\rm Vmax}$). We find that across the full sample, the\nmaximum emission line velocity increases with R$_{\\rm Vmax}$ and with\nthe absolute size of the nebula.\nWe also find that the sources with the highest maximum velocities (1000-1500\nkm sec$^{-1}$) are those with two independent kinematic systems present.\n\nNo correlations are seen\nbetween the size of the radio source and the FWHM or maximum velocity\nof the gas. Similar to the above, no substantial correlation is seen between\nthe FWHM or the maximum velocity of the radio source and the ratio of\nthe radio to nebular size.\nLastly, our sample shows no correlation of radio size with\nradio power or redshift, or of radio size with nebular size,\nbut does show a substantial correlation of\nnebular size with redshift and/or radio power.\n\nThese results are consistent with (but do not necessitate) a\npicture in which the kinematics of the emission line gas are predominantly\ndictated by gravity and the line luminosity of the nebula is predominantly\ndetermined by the ionizing luminosity of the central engine. If the mass\nof cold gas increases with redshift,\nthen the increasingly powerful AGN present in the 3CR sample at higher\nredshift, will illuminate a larger ionized nebula.\nIf the velocities are predominantly gravitational, then\nthe most powerful sources which are at the highest redshifts\nin our sample, and show the highest\nemission line gas velocity, would have to be\nfound in very deep gravitational potentials, such as cluster\nenvironments. Alternatively, at the highest redshifts,\npowerful radio galaxies may be in environments which are in a relatively young\nevolutionary state where the kinematics are still dominated by infall.\nIn the gravitational interpretation, the very highest velocity systems,\nwith apparently disjoint multiple velocity systems in the nebula of a\ngiven source, are cases where two galaxies are merging or interacting,\nand gas systems associated with each galaxy are seen.\n\n\\section{Acknowledgments}\n\nWe thank the staffs of the Kitt Peak and Cerro Tololo sites of the National Optical Astronomy\nObservatories as well as those of the Lick and Palomar Observatories. At the time these\nobservations were being carried out, the Carnegie Institution had access to the Hale\n5m telescope under a cooperative agreement with the California Institute of Technology. \n\n\\begin{thebibliography}\n\n\\bibitem{}{ Allen, S. W., Fabian, A. C., Kneib, J. P., 1996, MNRAS, 279, 616 }\n\n%\\bibitem{}{ Antonucci, R. R. J., $\\&$ Miller, J. S. 1985, \\apj, 297, 621 }\n\n%\\bibitem{}{ Balick, B., $\\&$ Heckman, T. 1982, \\araa, 20, 431 }\n\n\\bibitem{}{Barthel, P. D., \\& Miley, G. K., 1988, Nature, 333, 319}\n\n%\\bibitem{}{Baum, S. A. 1987, Ph. D. Thesis, University of Maryland }\n\n\n\\bibitem{}{ Baum, S. A., Heckman, T., Bridle, A., van Breugel, W.,\n$\\&$ Miley, G. 1988, ApJS, 68, 643 }\n\n\\bibitem{}{ Baum, S. A., $\\&$ Heckman, T. 1989$a$, \\apj, 336, 681 }\n\n\\bibitem{}{ Baum, S. A., $\\&$ Heckman, T. 1989$b$, \\apj, 336, 702. }\n\n\\bibitem{}{ Baum, S. A., Heckman, T., $\\&$ van Breugel, W. 1992, ApJ, 389, 208 }\n\n\\bibitem{}{ Baum, S. A., Heckman, T., $\\&$ van Breugel, W. 1990, ApJS, 74, 389 }\n\n\\bibitem{}{ Baum, S. A., Zirbel, E. L., \\& O'Dea, C. P., 1995, ApJ, 451, 88}\n\n\\bibitem{}{ Best, P., Longair, M., \\& Rottgering, H. 1999, in \"The Hy-Redshift\nUniverse\", ASP Conf. Series, A. Bunker \\& W. van Breugel, eds. in press}\n\n\n\\bibitem{}{ Bennet, A. S. 1962, MNRAS, 68, 163 }\n\n\\bibitem{}{ Bicknell, G. \\& Koekemoer, A. 1995, in IAU Symp 175,\n``Extraglactic Radio Jets'', R. Ekers et al. eds., p 473.}\n\n\\bibitem{}{Bicknell, G., Dopita, M. A., \\& O'Dea, C. P., 1997, ApJ, 485, 112}\n\n%\\bibitem{}{ Bridle, A. H., Fomalont, E. B., Byrd, G. G., $\\&$ Valtonen, M. \n%1989, \\aj, 97, 674 }\n\n%\\bibitem{}{ Burns, J. O., Basart, J. P., De Young, D. S., \n% Ghiglia, D. C. 1984, \\apj 238, 515 }\n\n\\bibitem{}{ Capetti, A., Axon, D., Macchetto, F. D., Marconi, A.\nWinge, C. 1999, ApJ, 516, 187 }\n\n%\\bibitem{}{ Chambers, K., Miley, G., $\\&$ Joyce, R. 1988, \\apj, 329, L75 }\n\n\\bibitem{}{ Clark, N. E., Axon, D. J., Tadhunter, C. N., Robinson, A., O'Brien, P. 1998, ApJ, 494, 546 }\n\n%\\bibitem{}{ Djorgovski, S. 1985, PASP, 97, 1119 }\n\n%\\bibitem{}{ Djorgovski, S., Spinrad, H., Pedelty, J., Rudnick, L., $\\&$ \n%Stockton, A. 1987, \\aj, 93, 1307 }\n\n%\\\\bibitem{}{ Djorgovski, S., Spinrad, H., $\\&$ Dickinson, M. 1991, \\apj, \n% ( in prep.).\n\n\\bibitem{}{Djorgovski, S., Spinrad, H., McCarthy P., \n Dickinson, M., van Breugel, W., $\\&$ Strom, R. 1988, AJ, 96, 836 }\n\n%\\bibitem{}{ Eales, S. A., $\\&$ Rawlings, S. 1990, \\mnras, 243, 1p }\n\n%\\bibitem{}{ Eales, S. A., $\\&$ Rawlings, S. 1993, \\apj, 411, 67 }\n\n\\bibitem{}{ Ellingson, E., Green, R., \\& Yee, H. 1991, ApJ 371, 49}\n\n\\bibitem{}{ Fanaroff, B., Riley, J. M. 1974, MNRAS, 167, 31}\n\n%\\bibitem{}{ Fanti, R., Fanti, C., Schilizzi, R. T., Spencer, R. E., Rendong, \n%N., Parma, P., van Breugel, W., $\\&$ Venturi, T. 1990, A$\\&$A, 231, 333 }\n\n%\\bibitem{}{ Feretti, L., Gioia, I. M., Giovannini, G., Gregorini, L., $\\&$ \n%Padrielli, L. 1984, A$\\&$A, 139, 50 }\n\n%\\bibitem{}{ Fosbury, R. A. E. 1986, in Structure and Evolution of Active \n%Galactic Nuclei, eds. G. Givrincin, F. Mardirossian, M. Mezzetti, $\\&$\n% M. Ramonella (Dordrect: Reidel) p. 297 }\n\n%\\bibitem{}{ Fosbury, R. A. E. 1989, in Extranuclear Activity in \n%Galaxies, E. J. A. Meurs $\\&$ R. A. E. Fosbury, eds., European Southern \n%Observatory Conference{ and Workshop Proceedings, No. 32, p. 169 }\n\n\\bibitem{}{Gelderman, R. \\& Whittle, M. 1994, ApJS, 91, 491}\n\n%\\bibitem{}{ Heckman, T., Smith, E., Baum, S., van Breugel,W., Miley G.,\n%et al. 1986, \\apj, 4311, 526 }\n\n% \\\\bibitem{}{ Hammer, F., Le Fevre, O. $\\&$ Proust }\n\n%\\bibitem{}{ Hammer, F., $\\&$ Le Fevre, O. 1990, \\apj, 357, 38 }\n\n\\bibitem{}{ Heckman, T. M., Baum, S. A., van Breugel, W. J. M., \\& McCarthy, P.\n1989, ApJ, 338, 48}\n\n\\bibitem{}{ Hill, G. J., \\& Lilly, S. J., 1991, ApJ, 367, 1}\n\n%\\bibitem{}{ Hutchings, J. B., Johnson, I., $\\&$ Pike, R. \n%1988, \\apjs, 66, 361 }\n\n%\\bibitem{}{ Jannuzi, B., $\\&$ Elston, R. 1991, \\apj, 366, L69 }\n\n%\\bibitem{}{ Jenkins, C. J., Pooley, G. G., $\\&$ Riley, J. M. 1977, \n % MmRAS, 84, 61 }\n\n%\\bibitem{}{ Kristian, J. A., Sandage, A. R., $\\&$ Katem, B. 1974, \\apj, \n % 191, 43 }\n\n%\\bibitem{}{ Laing, R. A. 1981, \\mnras 195, 261 }\n\n%\\bibitem{}{ Laing, R. A., Longair, M. S., Riley, J. M., Kibblewhite, E. J. \n%1978, \\mnras, 183, 547 }\n\n%\\bibitem{}{ Laing, R. A., Riley, J., $\\&$ Longair, M. 1983, \\mnras, \n% 204, 151 }\n\n%\\bibitem{}{ Laing, R. A., Owen, F., $\\&$ Puschell, J. 1984, (unpublished) }\n\n%\\bibitem{}{ Leahy, J. P., $\\&$ Williams, A. G. 1984, \\mnras,\n % 210, 929 }\n\n\\bibitem{} {Ledlow, M. J., \\& Owen, F. N., 1996, AJ, 112, 9}\n\n%\\bibitem{}{ Le Fevre, O., Hammer, F., Nottale, L., $\\&$ Mathez, G. 1987, \n% Nature, 326, 268 }\n\n%\\bibitem{}{ Le Fevre, O., Hammer, F., Nottale, L., Mazure, A., \n% $\\&$ Christian, C. 1988b, \\apj, 324, L1 }\n\n%\\bibitem{}{ Le Fevre, O., Hammer, F., $\\&$ Jones, J. 1988a, \\apj, \n% 331, L73 }\n\n%\\bibitem{}{ Le Fevre, O. $\\&$ Hammer, F. 1988, \\apj 333, L37 }\n\n%\\bibitem{}{ Le Fevre, O., $\\&$ Hammer, F. 1990, \\apj 350, L1 }\n\n\\bibitem{}{ Leahy, J. P., Bridle, A., \\& Strom, R. G. 1995, \nin \"Extragalactic Radio Sources\", R. D. Ekers et al., eds., Kluwer, IAU Symp. 175, 157}\n\n%\\bibitem{}{ Leahy, J. P., Muxlow, T. $\\&$ Stephens, P. 1989, \\mnras 239, 40 }\n\n%\\bibitem{}{ Lilly, S. J., Longair, M., $\\&$ McLean, I. 1983, NATURE, 301, 488 }\n\n%\\bibitem{}{ Lilly, S. J., $\\&$ $\\&$ Longair, M. 1984, \\mnras, 211, 833 }\n\n%\\bibitem{}{ Longair, M., 1975, \\mnras 173, 309 }\n\n\\bibitem{}{ Longair, M., et al. 1999, in \"The Hy-Redshift Universe\", ASP conference series,\nin press.}\n\n%\\bibitem{}{ Longair, M. S. $\\&$ Riley, J. M. 1979, \\mnras, 188,625 }\n\n%\\bibitem{}{ Mackay, C. D. 1969, \\mnras, 145, 31 }\n%\n%\\bibitem{}{ Mackay, C. D. 1971, \\mnras, 151, 421 }\n\n%\\bibitem{}{ Mantovani, F., Saikia, D. J., Browne, I. A. W., Fanti, R., Muxlow, T.,\n % Padrielli, L. 1990, \\mnras 245, 427 }\n\n\\bibitem{}{Mazure, A. \\etal\\ 1996, A\\&A, 310, 31 }\n\n\\bibitem{}{McCarthy, P. 1993, Ann. Rev. A\\&Ap, 31, 639 }\n\n%\\bibitem{}{ McCarthy, P., Elston, R., \\& Eisenhardt, P. 1992, \\apj, 387, L29 }\n\n\\bibitem{}{ McCarthy, P. J., van Breugel, W. J. M., \nSpinrad, H., \\& Djorgovski, S. 1987, \\apj, 321, L29 }\n\n\n%\\bibitem{}{ McCarthy, P., van Breugel, W., \\& Spinrad, H. 1989, \\aj, 97, 36 }\n\n% \\bibitem{}{ McCarthy, P., Spinrad, H., van Breugel, W., Liebert, J.,\n% Dickinson, M., Djorgovski, S., $\\&$ Eisenhardt, P. 1990, ApJ, 365, 487 }\n\n\\bibitem{}{McCarthy, P., van Breugel, W., \\& Kapahi, V. 1991, ApJ, 371, 478 }\n\n\\bibitem{}{ McCarthy, P., Spinrad, H., \\& van Breugel, W., 1995, ApJS, 99, 27}\n\n\\bibitem{}{McCarthy, P. J., Baum, S. A., \\& Spinrad, H. 1996a, ApJS, 106, 281}\n\n\\bibitem{}{McCarthy, P. J., Kapahi, V. K., van Breugel, W., Persson, S. E.,\nAthreya, R., \\& Subrahmanya, C. R., 1996b, ApJS, 107, 19}\n\n\\bibitem{}{Miley, G. K., Chambers, K. C., van Breugel, W., Macchetto, F. 1992, ApJ, 401, L69 }\n\n\n%\\bibitem{}{ Miller, J. S., \\& Stone, R. P. S. 1987, Lick Observatory \n% Technical Bulletin, 48, 1 }\n\n\\bibitem{}{Miralde-Escud\\`e, J., \\& Babul, A., 1995, ApJ, 449, 18}\n\n\\bibitem{}{O'Dea, C. P., 1998, PASP, 110, 493}\n\n%\\bibitem{}{ Oke, J. B. 1974, \\apjs, 27, 21 }\n\n%\\bibitem{}{ Osterbrock, D. E., Koski, A. T., Phillips, M. M. 1986, \\apj, \n% 206, 898 }\n\n%\\bibitem{}{ Pedelty, J. A., Rudnick, L., McCarthy, P. J., \\& Spinrad, H. \n%1989a, \\aj, 97, 647 }\n\n%\\bibitem{}{ Pedelty, J. A., Rudnick, L., McCarthy, P. J., \\& Spinrad, H. 1989b, \n% \\aj, 98, 1232 }\n\n%\\bibitem{}{ Pearson, T. J., Perley, R. A., \\& Readhead, A. C. S., 1985, \n% \\aj, 90, 738 }\n\n%\\bibitem{}{ Perryman, M. A. C., Lilly, S. J., Longair, M. S., Downes, A. J. B. \n%1984, \\mnras, 209, 159 }\n\n%\\bibitem{}{ Pooley, G. G., $\\&$ Henbest, S. N. 1974, \\mnras, 169, 477 }\n\n\\bibitem{}{ Prestage, R. M., Peacock, J. A. 1988, MNRAS, 230, 131 }\n\n%\\bibitem{}{ Rigler, M., Lilly, S., Stockton, A., Hammer, F., \\& Le Fevre, O.\n%1992, \\apj, 385, 61 }\n\n\\bibitem{}{ Rawlings, S. \\& Saunders, R. 1991, Nature, 349, 138}\n\n\\bibitem{}{ Robinson, A., Binette, L., Fosbury, R. A. E., Tadhunter, C. N. 1987, MNRAS, 227, 97 }\n \n \n%\\bibitem{}{ Riley, J. M., \\& Pooley, G. G. 1975, \\mnras,\n% 80, 105 }\n\n%\\bibitem{}{ Riley, J. M., Longair, M. S., \\& \n%Gunn, J. E. 1980, \\mnras, 192, 233 }\n\n%\\bibitem{}{ Schilizzi, R., Kapahi, V. K., \\& Neff, S. 1982, J. of Astron. \n% $\\&$ Astrohpys., 3, 173 }\n\n%\\bibitem{}{ Smith, E. P. 1987, Ph. D. Thesis, University of Maryland }\n\n%\\bibitem{}{ Smith, E. P., \\& Heckman, T. 1989a, \\apjs, 69, 365 }\n\n%\\bibitem{}{ Smith, E. P., \\& Heckman, T. 1989b, \\apj, 341, 658 }\n\n%\\bibitem{}{ Smith, H. E., \\& Spinrad, H. 1980, PASP, 92, 553 }\n\n%\\bibitem{}{ Spangler, S., Myers, S. T., \\& Pogge, J., J. 1984, \\aj 89, 1478. }\n\n%\\bibitem{}{ Spencer, R. E., McDowell, J. C., Charleworth, M., Fanti, \n% C., Parma, P., $\\&$ Peacock, J. A. 1989, \\mnras 240, 657 }\n\n%\\bibitem{}{Spinrad, H., $\\&$ Djorgovski, S. 1984a, \\apj, 280, L9 }\n\n%\\bibitem{}{Spinrad, H., $\\&$ Djorgovski, S. 1984b, \\apj, 285, L49 }\n\n\\bibitem{}{Spinrad, H., Djorgovski, S., Marr, J., $\\&$ Aguilar L. A. 1985, \n PASP, 97, 932 }\n\n%\\bibitem{}{ Spinrad, H., Filippenko, A., Wyckoff, A., Stocke, J., Wagner, M.\n%$\\&$ Lawrie, D. 1985b, \\apj, 299, L7 }\n\n%\\bibitem{}{ Spinrad, H. 1986, PASP, 98, 269 }\n\n\\bibitem{}{Squires, G., Neumann, D. M., Kaiser, N., Arnaud, M., Babul, A., \nBoehringer, H., Fahlman, G., \\& Woods, D., 1997, ApJ, 482, 648}\n\n%\\bibitem{}{ Stone, R. P. S. 1977, \\apj, 218, 767 }\n\n\\bibitem{}{ Strom, R. G., Riley, J. M., Spinrad, H., van Breugel, W., Djorgovski, \nS., Liebert, J., $\\&$ McCarthy, P. 1990, A\\&A, 227, 19 }\n\n\n\\bibitem{}{Tadhunter, C. N., Fosbury, R. A. E., $\\&$ Quinn, P. J., 1989, MNRAS,\n240, 225}\n\n\\bibitem{}{ Tadhunter, C. N., Packham, C., Axon, D. J., Jackson, N. J., \nHough, J. H., Robinson, A., Young, S., Sparks, W. 1999 MRNAS, 307, 24 }\n\n\n\\bibitem{}{Tadhunter, C. N., Morganti, R.,\nRobinson, A., Dickson, R., Villar-Martin, M., \\& Fosbury, R. A. E. 1999, 298, 1035}\n\n\\bibitem{}{Villar-Martin, M., Tadhunter, C. N., Clark, N.,\n1997, A\\&A, 323, 21}\n\n\\bibitem{}{Villar-Martin, M., Tadhunter, C. N., Morganti, R.,\nClark, N., Killeen, N., \\& Axon, D. 1998, A\\&A, 332, 479}\n\n\\bibitem{}{Villar-Martin, M., Binette, L., \\& Fosbury, R. A. E. 1999, A\\&A, 346, 7}\n\n\\bibitem{}{de Vries, {\\it et al.} 1997, ApJS, 110, 191}\n\n\\bibitem{}{de Vries, W. H., O'Dea, C. P., Baum, S. A., Perlman, E., Lehnert, M. D.\n\\& Barthel, P. D. 1998, ApJ 503, 156}\n\n\\bibitem{}{Whittle, M., 1992, ApJ, 387, 109}\n\n\\bibitem{}{Xu, C., Livio, M. \\& Baum, S., 1999, AJ, 118, 1169}\n\n\n\n\\bibitem{}{Yates, M., Miller, L., \\& Peacock, J. 1989, MNRAS, 240, 129}\n\n\\end{thebibliography}\n\n% put tables here so they get put up front.\n\n\n\n\\begin{figure}\n\\epsfxsize=7in\n\\epsffile{sbaum.fig1.ps}\n\\caption{In each of the panels of this figure, and the three subsequent\nfigures, the filled symbols refer to FRII sources, while the open symbols\nrepresent FRI and transition sources. In the upper panels the mass of\nionized gas and the apparent dynamical mass are plotted against\nredshift. In the lower panels the derived mass of ionized gas is plotted\nagainst the maximum FWHM (left) and the maximum velocity (right). All of\nthe masses are shown in units of M$_{\\odot}$. } \n%\\label{figspectra}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize=7in\n\\epsffile{sbaum.fig2.ps}\n\\caption{In the upper left the apparent dynamical mass is plotted against the\nderived mass of ionized gas. See the discussion in the text of the degeneracy between\nthese derived quantities. The isophotal emission-line size is plotted against redshift\nin the upper right panel, while the maximum velocity is plotted against the radial\nposition of the fastest moving [OII] emission in the lower left. The lower right\npanel shows the run of R$_{Vmax} \\times V_{max}$ with emission-line luminosity. } \n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize=7in\n\\epsffile{sbaum.fig3.ps}\n\\caption{The upper left and right panels show the run of\nFWHM and V$_{Max}$ against redshift, while the lower panels\nshow the ratio of the FWHM to the maximum velocity (left) and\nmaximum (right) velocity against the 408MHz monochromatic radio power.\n} \n%\\label{figspectra}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize=7in\n\\epsffile{sbaum.fig4.ps}\n\\caption{Plotted are the off-nuclear FWHM (upper left) and the \nmaximum velocity (upper right) against the\nratio of the radio and emission line sizes. The lower left\nand right panels show the same quantities plotted against the\nfull linear size of the radio source.\n} \n%\\label{figspectra}\n\\end{figure}\n\\end{document}\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002329.extracted_bib",
"string": "\\begin{thebibliography}\n\n\\bibitem{}{ Allen, S. W., Fabian, A. C., Kneib, J. P., 1996, MNRAS, 279, 616 }\n\n%\\bibitem{}{ Antonucci, R. R. J., $\\&$ Miller, J. S. 1985, \\apj, 297, 621 }\n\n%\\bibitem{}{ Balick, B., $\\&$ Heckman, T. 1982, \\araa, 20, 431 }\n\n\\bibitem{}{Barthel, P. D., \\& Miley, G. K., 1988, Nature, 333, 319}\n\n%\\bibitem{}{Baum, S. A. 1987, Ph. D. Thesis, University of Maryland }\n\n\n\\bibitem{}{ Baum, S. A., Heckman, T., Bridle, A., van Breugel, W.,\n$\\&$ Miley, G. 1988, ApJS, 68, 643 }\n\n\\bibitem{}{ Baum, S. A., $\\&$ Heckman, T. 1989$a$, \\apj, 336, 681 }\n\n\\bibitem{}{ Baum, S. A., $\\&$ Heckman, T. 1989$b$, \\apj, 336, 702. }\n\n\\bibitem{}{ Baum, S. A., Heckman, T., $\\&$ van Breugel, W. 1992, ApJ, 389, 208 }\n\n\\bibitem{}{ Baum, S. A., Heckman, T., $\\&$ van Breugel, W. 1990, ApJS, 74, 389 }\n\n\\bibitem{}{ Baum, S. A., Zirbel, E. L., \\& O'Dea, C. P., 1995, ApJ, 451, 88}\n\n\\bibitem{}{ Best, P., Longair, M., \\& Rottgering, H. 1999, in \"The Hy-Redshift\nUniverse\", ASP Conf. Series, A. Bunker \\& W. van Breugel, eds. in press}\n\n\n\\bibitem{}{ Bennet, A. S. 1962, MNRAS, 68, 163 }\n\n\\bibitem{}{ Bicknell, G. \\& Koekemoer, A. 1995, in IAU Symp 175,\n``Extraglactic Radio Jets'', R. Ekers et al. eds., p 473.}\n\n\\bibitem{}{Bicknell, G., Dopita, M. A., \\& O'Dea, C. P., 1997, ApJ, 485, 112}\n\n%\\bibitem{}{ Bridle, A. H., Fomalont, E. B., Byrd, G. G., $\\&$ Valtonen, M. \n%1989, \\aj, 97, 674 }\n\n%\\bibitem{}{ Burns, J. O., Basart, J. P., De Young, D. S., \n% Ghiglia, D. C. 1984, \\apj 238, 515 }\n\n\\bibitem{}{ Capetti, A., Axon, D., Macchetto, F. D., Marconi, A.\nWinge, C. 1999, ApJ, 516, 187 }\n\n%\\bibitem{}{ Chambers, K., Miley, G., $\\&$ Joyce, R. 1988, \\apj, 329, L75 }\n\n\\bibitem{}{ Clark, N. E., Axon, D. J., Tadhunter, C. N., Robinson, A., O'Brien, P. 1998, ApJ, 494, 546 }\n\n%\\bibitem{}{ Djorgovski, S. 1985, PASP, 97, 1119 }\n\n%\\bibitem{}{ Djorgovski, S., Spinrad, H., Pedelty, J., Rudnick, L., $\\&$ \n%Stockton, A. 1987, \\aj, 93, 1307 }\n\n%\\\\bibitem{}{ Djorgovski, S., Spinrad, H., $\\&$ Dickinson, M. 1991, \\apj, \n% ( in prep.).\n\n\\bibitem{}{Djorgovski, S., Spinrad, H., McCarthy P., \n Dickinson, M., van Breugel, W., $\\&$ Strom, R. 1988, AJ, 96, 836 }\n\n%\\bibitem{}{ Eales, S. A., $\\&$ Rawlings, S. 1990, \\mnras, 243, 1p }\n\n%\\bibitem{}{ Eales, S. A., $\\&$ Rawlings, S. 1993, \\apj, 411, 67 }\n\n\\bibitem{}{ Ellingson, E., Green, R., \\& Yee, H. 1991, ApJ 371, 49}\n\n\\bibitem{}{ Fanaroff, B., Riley, J. M. 1974, MNRAS, 167, 31}\n\n%\\bibitem{}{ Fanti, R., Fanti, C., Schilizzi, R. T., Spencer, R. E., Rendong, \n%N., Parma, P., van Breugel, W., $\\&$ Venturi, T. 1990, A$\\&$A, 231, 333 }\n\n%\\bibitem{}{ Feretti, L., Gioia, I. M., Giovannini, G., Gregorini, L., $\\&$ \n%Padrielli, L. 1984, A$\\&$A, 139, 50 }\n\n%\\bibitem{}{ Fosbury, R. A. E. 1986, in Structure and Evolution of Active \n%Galactic Nuclei, eds. G. Givrincin, F. Mardirossian, M. Mezzetti, $\\&$\n% M. Ramonella (Dordrect: Reidel) p. 297 }\n\n%\\bibitem{}{ Fosbury, R. A. E. 1989, in Extranuclear Activity in \n%Galaxies, E. J. A. Meurs $\\&$ R. A. E. Fosbury, eds., European Southern \n%Observatory Conference{ and Workshop Proceedings, No. 32, p. 169 }\n\n\\bibitem{}{Gelderman, R. \\& Whittle, M. 1994, ApJS, 91, 491}\n\n%\\bibitem{}{ Heckman, T., Smith, E., Baum, S., van Breugel,W., Miley G.,\n%et al. 1986, \\apj, 4311, 526 }\n\n% \\\\bibitem{}{ Hammer, F., Le Fevre, O. $\\&$ Proust }\n\n%\\bibitem{}{ Hammer, F., $\\&$ Le Fevre, O. 1990, \\apj, 357, 38 }\n\n\\bibitem{}{ Heckman, T. M., Baum, S. A., van Breugel, W. J. M., \\& McCarthy, P.\n1989, ApJ, 338, 48}\n\n\\bibitem{}{ Hill, G. J., \\& Lilly, S. J., 1991, ApJ, 367, 1}\n\n%\\bibitem{}{ Hutchings, J. B., Johnson, I., $\\&$ Pike, R. \n%1988, \\apjs, 66, 361 }\n\n%\\bibitem{}{ Jannuzi, B., $\\&$ Elston, R. 1991, \\apj, 366, L69 }\n\n%\\bibitem{}{ Jenkins, C. J., Pooley, G. G., $\\&$ Riley, J. M. 1977, \n % MmRAS, 84, 61 }\n\n%\\bibitem{}{ Kristian, J. A., Sandage, A. R., $\\&$ Katem, B. 1974, \\apj, \n % 191, 43 }\n\n%\\bibitem{}{ Laing, R. A. 1981, \\mnras 195, 261 }\n\n%\\bibitem{}{ Laing, R. A., Longair, M. S., Riley, J. M., Kibblewhite, E. J. \n%1978, \\mnras, 183, 547 }\n\n%\\bibitem{}{ Laing, R. A., Riley, J., $\\&$ Longair, M. 1983, \\mnras, \n% 204, 151 }\n\n%\\bibitem{}{ Laing, R. A., Owen, F., $\\&$ Puschell, J. 1984, (unpublished) }\n\n%\\bibitem{}{ Leahy, J. P., $\\&$ Williams, A. G. 1984, \\mnras,\n % 210, 929 }\n\n\\bibitem{} {Ledlow, M. J., \\& Owen, F. N., 1996, AJ, 112, 9}\n\n%\\bibitem{}{ Le Fevre, O., Hammer, F., Nottale, L., $\\&$ Mathez, G. 1987, \n% Nature, 326, 268 }\n\n%\\bibitem{}{ Le Fevre, O., Hammer, F., Nottale, L., Mazure, A., \n% $\\&$ Christian, C. 1988b, \\apj, 324, L1 }\n\n%\\bibitem{}{ Le Fevre, O., Hammer, F., $\\&$ Jones, J. 1988a, \\apj, \n% 331, L73 }\n\n%\\bibitem{}{ Le Fevre, O. $\\&$ Hammer, F. 1988, \\apj 333, L37 }\n\n%\\bibitem{}{ Le Fevre, O., $\\&$ Hammer, F. 1990, \\apj 350, L1 }\n\n\\bibitem{}{ Leahy, J. P., Bridle, A., \\& Strom, R. G. 1995, \nin \"Extragalactic Radio Sources\", R. D. Ekers et al., eds., Kluwer, IAU Symp. 175, 157}\n\n%\\bibitem{}{ Leahy, J. P., Muxlow, T. $\\&$ Stephens, P. 1989, \\mnras 239, 40 }\n\n%\\bibitem{}{ Lilly, S. J., Longair, M., $\\&$ McLean, I. 1983, NATURE, 301, 488 }\n\n%\\bibitem{}{ Lilly, S. J., $\\&$ $\\&$ Longair, M. 1984, \\mnras, 211, 833 }\n\n%\\bibitem{}{ Longair, M., 1975, \\mnras 173, 309 }\n\n\\bibitem{}{ Longair, M., et al. 1999, in \"The Hy-Redshift Universe\", ASP conference series,\nin press.}\n\n%\\bibitem{}{ Longair, M. S. $\\&$ Riley, J. M. 1979, \\mnras, 188,625 }\n\n%\\bibitem{}{ Mackay, C. D. 1969, \\mnras, 145, 31 }\n%\n%\\bibitem{}{ Mackay, C. D. 1971, \\mnras, 151, 421 }\n\n%\\bibitem{}{ Mantovani, F., Saikia, D. J., Browne, I. A. W., Fanti, R., Muxlow, T.,\n % Padrielli, L. 1990, \\mnras 245, 427 }\n\n\\bibitem{}{Mazure, A. \\etal\\ 1996, A\\&A, 310, 31 }\n\n\\bibitem{}{McCarthy, P. 1993, Ann. Rev. A\\&Ap, 31, 639 }\n\n%\\bibitem{}{ McCarthy, P., Elston, R., \\& Eisenhardt, P. 1992, \\apj, 387, L29 }\n\n\\bibitem{}{ McCarthy, P. J., van Breugel, W. J. M., \nSpinrad, H., \\& Djorgovski, S. 1987, \\apj, 321, L29 }\n\n\n%\\bibitem{}{ McCarthy, P., van Breugel, W., \\& Spinrad, H. 1989, \\aj, 97, 36 }\n\n% \\bibitem{}{ McCarthy, P., Spinrad, H., van Breugel, W., Liebert, J.,\n% Dickinson, M., Djorgovski, S., $\\&$ Eisenhardt, P. 1990, ApJ, 365, 487 }\n\n\\bibitem{}{McCarthy, P., van Breugel, W., \\& Kapahi, V. 1991, ApJ, 371, 478 }\n\n\\bibitem{}{ McCarthy, P., Spinrad, H., \\& van Breugel, W., 1995, ApJS, 99, 27}\n\n\\bibitem{}{McCarthy, P. J., Baum, S. A., \\& Spinrad, H. 1996a, ApJS, 106, 281}\n\n\\bibitem{}{McCarthy, P. J., Kapahi, V. K., van Breugel, W., Persson, S. E.,\nAthreya, R., \\& Subrahmanya, C. R., 1996b, ApJS, 107, 19}\n\n\\bibitem{}{Miley, G. K., Chambers, K. C., van Breugel, W., Macchetto, F. 1992, ApJ, 401, L69 }\n\n\n%\\bibitem{}{ Miller, J. S., \\& Stone, R. P. S. 1987, Lick Observatory \n% Technical Bulletin, 48, 1 }\n\n\\bibitem{}{Miralde-Escud\\`e, J., \\& Babul, A., 1995, ApJ, 449, 18}\n\n\\bibitem{}{O'Dea, C. P., 1998, PASP, 110, 493}\n\n%\\bibitem{}{ Oke, J. B. 1974, \\apjs, 27, 21 }\n\n%\\bibitem{}{ Osterbrock, D. E., Koski, A. T., Phillips, M. M. 1986, \\apj, \n% 206, 898 }\n\n%\\bibitem{}{ Pedelty, J. A., Rudnick, L., McCarthy, P. J., \\& Spinrad, H. \n%1989a, \\aj, 97, 647 }\n\n%\\bibitem{}{ Pedelty, J. A., Rudnick, L., McCarthy, P. J., \\& Spinrad, H. 1989b, \n% \\aj, 98, 1232 }\n\n%\\bibitem{}{ Pearson, T. J., Perley, R. A., \\& Readhead, A. C. S., 1985, \n% \\aj, 90, 738 }\n\n%\\bibitem{}{ Perryman, M. A. C., Lilly, S. J., Longair, M. S., Downes, A. J. B. \n%1984, \\mnras, 209, 159 }\n\n%\\bibitem{}{ Pooley, G. G., $\\&$ Henbest, S. N. 1974, \\mnras, 169, 477 }\n\n\\bibitem{}{ Prestage, R. M., Peacock, J. A. 1988, MNRAS, 230, 131 }\n\n%\\bibitem{}{ Rigler, M., Lilly, S., Stockton, A., Hammer, F., \\& Le Fevre, O.\n%1992, \\apj, 385, 61 }\n\n\\bibitem{}{ Rawlings, S. \\& Saunders, R. 1991, Nature, 349, 138}\n\n\\bibitem{}{ Robinson, A., Binette, L., Fosbury, R. A. E., Tadhunter, C. N. 1987, MNRAS, 227, 97 }\n \n \n%\\bibitem{}{ Riley, J. M., \\& Pooley, G. G. 1975, \\mnras,\n% 80, 105 }\n\n%\\bibitem{}{ Riley, J. M., Longair, M. S., \\& \n%Gunn, J. E. 1980, \\mnras, 192, 233 }\n\n%\\bibitem{}{ Schilizzi, R., Kapahi, V. K., \\& Neff, S. 1982, J. of Astron. \n% $\\&$ Astrohpys., 3, 173 }\n\n%\\bibitem{}{ Smith, E. P. 1987, Ph. D. Thesis, University of Maryland }\n\n%\\bibitem{}{ Smith, E. P., \\& Heckman, T. 1989a, \\apjs, 69, 365 }\n\n%\\bibitem{}{ Smith, E. P., \\& Heckman, T. 1989b, \\apj, 341, 658 }\n\n%\\bibitem{}{ Smith, H. E., \\& Spinrad, H. 1980, PASP, 92, 553 }\n\n%\\bibitem{}{ Spangler, S., Myers, S. T., \\& Pogge, J., J. 1984, \\aj 89, 1478. }\n\n%\\bibitem{}{ Spencer, R. E., McDowell, J. C., Charleworth, M., Fanti, \n% C., Parma, P., $\\&$ Peacock, J. A. 1989, \\mnras 240, 657 }\n\n%\\bibitem{}{Spinrad, H., $\\&$ Djorgovski, S. 1984a, \\apj, 280, L9 }\n\n%\\bibitem{}{Spinrad, H., $\\&$ Djorgovski, S. 1984b, \\apj, 285, L49 }\n\n\\bibitem{}{Spinrad, H., Djorgovski, S., Marr, J., $\\&$ Aguilar L. A. 1985, \n PASP, 97, 932 }\n\n%\\bibitem{}{ Spinrad, H., Filippenko, A., Wyckoff, A., Stocke, J., Wagner, M.\n%$\\&$ Lawrie, D. 1985b, \\apj, 299, L7 }\n\n%\\bibitem{}{ Spinrad, H. 1986, PASP, 98, 269 }\n\n\\bibitem{}{Squires, G., Neumann, D. M., Kaiser, N., Arnaud, M., Babul, A., \nBoehringer, H., Fahlman, G., \\& Woods, D., 1997, ApJ, 482, 648}\n\n%\\bibitem{}{ Stone, R. P. S. 1977, \\apj, 218, 767 }\n\n\\bibitem{}{ Strom, R. G., Riley, J. M., Spinrad, H., van Breugel, W., Djorgovski, \nS., Liebert, J., $\\&$ McCarthy, P. 1990, A\\&A, 227, 19 }\n\n\n\\bibitem{}{Tadhunter, C. N., Fosbury, R. A. E., $\\&$ Quinn, P. J., 1989, MNRAS,\n240, 225}\n\n\\bibitem{}{ Tadhunter, C. N., Packham, C., Axon, D. J., Jackson, N. J., \nHough, J. H., Robinson, A., Young, S., Sparks, W. 1999 MRNAS, 307, 24 }\n\n\n\\bibitem{}{Tadhunter, C. N., Morganti, R.,\nRobinson, A., Dickson, R., Villar-Martin, M., \\& Fosbury, R. A. E. 1999, 298, 1035}\n\n\\bibitem{}{Villar-Martin, M., Tadhunter, C. N., Clark, N.,\n1997, A\\&A, 323, 21}\n\n\\bibitem{}{Villar-Martin, M., Tadhunter, C. N., Morganti, R.,\nClark, N., Killeen, N., \\& Axon, D. 1998, A\\&A, 332, 479}\n\n\\bibitem{}{Villar-Martin, M., Binette, L., \\& Fosbury, R. A. E. 1999, A\\&A, 346, 7}\n\n\\bibitem{}{de Vries, {\\it et al.} 1997, ApJS, 110, 191}\n\n\\bibitem{}{de Vries, W. H., O'Dea, C. P., Baum, S. A., Perlman, E., Lehnert, M. D.\n\\& Barthel, P. D. 1998, ApJ 503, 156}\n\n\\bibitem{}{Whittle, M., 1992, ApJ, 387, 109}\n\n\\bibitem{}{Xu, C., Livio, M. \\& Baum, S., 1999, AJ, 118, 1169}\n\n\n\n\\bibitem{}{Yates, M., Miller, L., \\& Peacock, J. 1989, MNRAS, 240, 129}\n\n\\end{thebibliography}"
}
] |
astro-ph0002330
|
New Dark Matter Physics: Clues from Halo Structure
|
[
{
"author": "Craig J. Hogan and Julianne J. Dalcanton"
}
] |
We examine the effect of primordial dark matter velocity dispersion and/or particle self-interactions on the structure and stability of galaxy halos, especially with respect to the formation of substructure and central density cusps. Primordial velocity dispersion is characterised by a ``phase density'' $Q\equiv \rho/\langle v^2\rangle^{3/2}$, which for relativistically-decoupled relics is determined by particle mass and spin and is insensitive to cosmological parameters. Finite $Q$ leads to small-scale filtering of the primordial power spectrum, which reduces substructure, and limits the maximum central density of halos, which eliminates central cusps. The relationship between $Q$ and halo observables is estimated. The primordial $Q$ may be preserved in the cores of halos and if so leads to a predicted relation, closely analogous to that in degenerate dwarf stars, between the central density and velocity dispersion. Classical polytrope solutions are used to model the structure of halos of collisional dark matter, and to show that self-interactions in halos today are probably not significant because they destabilize halo cores via heat conduction. Constraints on masses and self-interactions of dark matter particles are estimated from halo stability and other considerations.
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[
{
"name": "newdark14.tex",
"string": "%\\documentstyle{article}\n%\\documentstyle[preprint,aps,psfig]{revtex}\n\\documentstyle[aps,psfig]{revtex}\n\\begin{document}\n\\title{New Dark Matter Physics: Clues from Halo Structure}\n\\author{Craig J. Hogan and Julianne J. Dalcanton}\n\\address{Astronomy Department, \nUniversity of Washington,\nSeattle, Washington 98195-1580}\n\n\\maketitle\n\n\\begin{abstract}\nWe examine the effect of primordial dark matter\nvelocity dispersion and/or particle self-interactions on the structure and stability\nof galaxy halos, especially with respect to the formation of substructure\nand central density cusps. \nPrimordial velocity dispersion is characterised by a ``phase density''\n$Q\\equiv \\rho/\\langle v^2\\rangle^{3/2}$, which\n for relativistically-decoupled relics is determined by particle mass and\nspin and is insensitive to cosmological parameters. \nFinite $Q$\n leads to small-scale filtering of the primordial power spectrum, which \nreduces substructure, and limits the maximum central density of halos, which\neliminates central cusps. \nThe relationship between $Q$ and halo observables is estimated. The primordial\n$Q$ may be preserved in the cores of halos and if so leads to a predicted relation, closely\nanalogous to that in degenerate dwarf stars, between the central\ndensity and velocity dispersion. Classical\npolytrope solutions are used to model the structure of halos of collisional dark\nmatter, and to show that self-interactions in halos today are probably not significant\nbecause they destabilize halo cores\nvia heat conduction. Constraints on masses and self-interactions of dark matter \nparticles are estimated from halo stability and other considerations. \n\\end{abstract}\n\\newpage\n\n\\section{How Cold and How Collisionless is the Dark Matter?}\n\nThe successful concordance of predictions and observations of large scale structure and\nmicrowave anisotropy vindicates many assumptions of standard cosmology,\nin particular the hypothesis that the dark matter is composed of\nprimordial particles which are cold and collisionless\\cite{cdm}. \nAt the same time, \n there are hints of discrepancies observed in the small-scale structure within\ngalaxy haloes, which we explore as two related but separate issues,\nnamely the predictions of excessive substructure and sharp central cusps\nin dark matter halos.\n\n The first\n``substructure problem'' is that CDM predicts excessive relic\nsubstructure\\cite{ghigna,klypin}: \nmuch of the mass of a CDM halo is not smoothly distributed but\nis concentrated in many massive sublumps, like galaxies in \ngalaxy clusters. The model predicts that galaxy halos should contain many dwarf\ngalaxies which are not seen, and which would disrupt disks even if they are invisible.\nThe\nsubstructure problem appears to be caused by the ``bottom-up'' hierarchical clustering\npredicted by CDM power spectra; fluctuations on small scales collapse early and survive as\ndense condensations. Its\nabsence hints that the small scale power spectrum is filtered to suppress early collapse\non subgalactic scales. \n\n The second ``cusp problem'' is that\nCDM also predicts\\cite{dubinski,nfw,moore98,moore99a,moore99b} a universal, monotonic \nincrease of density towards the center of halos which is not seen in close studies of \ndark-matter-dominated galaxies\\cite{swaters,swaters2,carignan}\n(although the observational issue is far from settled\\cite{vandenbosch,dalcanton}). \nThe formation of central cusps has been observed for many years in simulations\nof collapse of cold matter in a wide variety of circumstances; it may be\nthought of \nas low-entropy material sinking to the center during \nhalo formation. Simulations suggest that dynamical ``pre-heating'' of CDM\nby hierarchical clustering is\nnot enough to prevent a cusp from forming--- that some material is always left with a low\nentropy and sinks to the center. If this is right, the central structure of halos might \nprovide clues to the primordial entropy which are insensitive to complicated\ndetails of nonlinear collapse. \n\n\n\nIt may be possible to explain these\ndiscrepancies in a CDM framework\\cite{frank}, for example by using various\n baryonic contrivances. It is also possible that the observations can\nbe interpreted more sympathetically for CDM; we explore this\npossibility in more detail in a separate paper\\cite{dalcanton}.\n However \nit is also possible\n that the problems with halo structure are \n giving specific quantitative clues about new properties of the dark matter particles.\nBy examining halo structure and stability,\nin this paper we make a quantitative assessment\nof the effects of modifications of the two main properties of\nCDM--- the addition of primordial velocity dispersion, and/or the addition of particle\nself-interactions. In particular we focus on aspects of halo structure which provide the\ncleanest ``laboratories'' for studying \ndark matter properties. The\nultimate goal of this exercise is to measure and constrain particle properties from halo\nstructure.\n\n\n Endowing the particles with non-zero primordial velocity dispersion\n produces two\nseparate effects: \na filter in the primordial power spectrum which limits small-scale substructure, \nand a phase packing or Liouville limit which produces halo cores.\nBoth effects depend on the same quantity, the \n``phase density'' which we choose to define using the \nmost observationally accessible units,\n $Q\\equiv\n \\rho/\\langle v^2\\rangle^{3/2}$,\nwhere $\\rho$ is the density and $\\langle v^2\\rangle$ is the velocity dispersion.\nThe definitions of these quantities depend on whether we are discussing\nfine-grained or coarse-grained $Q$.\\footnote{For a uniform monatomic ideal thermal gas, \n $Q$ is related in a straightforward way to\nthe usual thermodynamic entropy; for $N$\nparticles,\n$S=- kN[\\ln (Q)+{\\rm constant}].$} \nFor collisionless particles, the \nfine-grained $Q$ does not change but the coarse-grained $Q$ can decrease \nas the sheet occupied by particles folds up in phase space.\nThe coarse-grained $Q$ can be estimated directly from astronomical \nobservations, while the fine-grained $Q$ relates directly to \nmicrophysics of dark matter particles.\n For particles which decouple \nwhen still relativistic, the initial microscopic phase density $Q_0$,\nwhich for nondissipationless collisionless particles is \nthe maximum value for all time, can be related to the particle\nmass and type, with little reference to the cosmology. The most familiar \nexamples are the standard neutrinos, but we include in our discussion the \nmore general case which yields different numerical factors for\nbosons and for particles with a significant chemical potential.\n\nThe physics of both the filtering and the\nphase packing in the collisionless case closely parallels\nthat of massive neutrinos\\cite{gerstein,cowsik}, the standard form\nof\n ``hot'' dark matter. Dominant hot dark matter overdoes both of these\neffects--- the filtering scale is too large \nto agree with observations of galaxy formation (both in emission\nand quasar absorption) and the phase density is too low to agree with \nobservations of giant-galaxy halos\\cite{tremaine}. However one can introduce \nnew particles with a lower velocity dispersion (``warm'' dark\nmatter, \\cite{bond,bardeen,blumenthal,melott,primack,dodelson}),\nwhich is the option we consider here. \n\nAlthough warm\ndark matter has most often been invoked as a solution to fixing \napparent (and no longer problematic\\cite{peacock,cdm}) difficulties\nwith predictions of the CDM power spectrum for matching galaxy clustering data,\na \nspectrum filtered on smaller scales may also solve several other classic problems of CDM \non galactic and subgalactic scales\\cite{whiterees,navarrosteinmetz} which are sometimes\nattributed to baryonic effects. The main effect in warm models is that the first nonlinear\nobjects are larger and form later, suppressing substructure and increasing the angular\nmomentum of galaxies\\cite{sommerlarsen}.\nThis improves the predictions for dwarf galaxy populations\\cite{colin},\nbaryon-to-dark-matter ratio, disk size and angular momentum, and quiet flows on the scale\nof galaxy groups. If the filtering is confined to small scales the predictions are likely\nto remain acceptable for Lyman-$\\alpha$ absorption during the epoch of\ngalaxy formation at $z\\approx 3$\\cite{croft,dave,white}.\n\nLiouville's theorem tells us that dissipationless, collisionless particles can\nonly decrease their coarse-grained phase density, and \nwe conjecture that halo cores on small scales \napproximately preserve the primordial\nphase density. The\nuniversal character of the phase density allows us to make definite predictions for the\nscaling of core density and core radius with halo velocity dispersion. These relations are \nanalogous to those governing nonrelativistic degenerate-dwarf stars: more\ntightly bound (i.e. massive) halos should have smaller, denser cores. \n A survey\\cite{dalcanton} of \n available\nevidence on the phase density of \n dark matter cores on scales from dwarf spheroidal\ngalaxies to galaxy clusters shows that the phase density\nneeded to create the cores of rotating dwarf galaxies is much lower than that \napparently present in dwarf spheroidal\ngalaxies\\cite{aaronson,olszewski,faber,lake,gerhard,ralston,mateo}--- so at least\none of these populations is not probing primordial phase density. Translating\ninto masses of neutrino-like relics, the spheroidals prefer masses of about\n1 keV (unless the observed stars occupy only a small central portion of an\nimplausibly large, massive and high-dispersion halo), and the disks prefer about\n200 eV. \n \nThe larger phase density is also preferred from the point\nof view of filtering. If we take $\\Omega\\approx 0.3$\n(instead of 1 as in most of the original warm scenarios--- which reduces the scale for a\ngiven mass, because it lowers the temperature and therefore the number of the particles),\nthe filtering scale for 1 keV particles is at about $k=3{\\rm Mpc}^{-1}$--- small enough to \npreserve the successful large-scale predictions of CDM but also\nlarge enough to impact the substructure problem.\nGalaxy halo substructure therefore favors a primordial phase\ndensity corresponding to collisionless thermal relics with a mass of around\n1 keV. \nIn this scenario the densest dwarf spheroidals might well preserve the primordial\nphase density and in principle could allow a measurement of the particle mass.\\footnote{This\nraises another unresolved issue: whether the filtering actually prevents systems\nas small as dwarf spheroidals from forming at all. The predictions of \nwarm dark models are not yet worked out enough to answer this question.}\n(Conversely, a mass as large as 1 keV can only solve the core problem\nin disks with \nadditional nonlinear dynamical heating, so that the central matter no longer remains on \nthe lowest adiabat, or with the aid of baryonic effects\\cite{frank}.)\n\n To have the\nright mean density and phase density today, relativistically-decoupling\nparticles of this phase density must have\n separated out at least\nas early as\n the QCD era, when the number of degrees of freedom was much \nlarger than at classical weak decoupling. Their\ninteractions with normal Standard Model particles must therefore be ``weaker than weak,''\nruling out not only standard neutrinos but many other particle candidates.\nThe leading CDM particle\ncandidates, such as WIMPs and axions, form in standard scenarios with\nmuch higher phase densities, although more elaborate\nmechanisms are possible to endow these particles with the velocities\nto dilute $Q$. \nWe review briefly some of the available options for making low-$Q$ candidates,\nsuch as particles decaying out of equilibrium.\n\n A new wrinkle on this story comes if we endow the particles with \nself-interactions\\cite{carlson,delaix,atrio,spergel,mohapatra}.\nWe consider a simple parametrized model of particle self-interactions based on\nmassive intermediate particles of adjustable mass and coupling, and explore the \nconstraints on these parameters from halo structure. Self-interactions \nchange the filtering of the power spectrum early on, and if they are strong\nenough they \nqualititatively change the global structure and stability of halos.\n\nIn the interacting case, linear perturbations below\nthe Jeans scale oscillate as sound waves instead of damping by free streaming---\nanalogous to a baryon plasma rather than a neutrino gas.\nThis effect introduces a filter which is sharper in $k$ than that from streaming, and \nalso on a\nscale about ten times smaller than the streaming for the same rms particle velocity--- about\nright to reconcile the appropriate filtering\nscale with the $Q$ needed for phase-density-limited disk cores. These\nself-interactions could be so weak that the particles are effectively collisionless\ntoday as in standard CDM.\n\n On the other hand stronger self-interactions have major effects during the nonlinear\nstages of structure formation and on the structure of galaxy halos\\cite{spergel}. \n We\nconsider this possibility in some detail, using Lane-Emden polytropes as fiducial models\nfor collisional halos. Their structures are close analogs of\ndegenerate dwarf stars\nand we call them ``giant dwarfs''. We find that these structures are subject\nto an instability caused by heat conduction by particle diffusion.\\footnote{Degenerate dwarf\nstars are\nnot subject to this instability because they are supported without\na temperature gradient; the same stabilization could occur in halo cores only if\nthe dark matter is fermionic and degenerate (e.g., \\cite{fuller,shi}). The instability we\ndiscuss here is essentially what happens in a thermally-supported star with no nuclear\nreactions, except that the conduction is by particle diffusion rather than by radiation.\nThis effect may have already been observed\nnumerically.\\cite{hannestad}} Although a\nlittle of this might be interesting (e.g. leading to the formation of central black \nholes\\cite{ostriker} or to high-density, dwarf spheroidal galaxies), typical halos can\nonly be significantly collisional if they last for a Hubble time; for this to be the\ncase, the particle interactions must be so strong that diffusion is suppressed, which in\nturn requires a fluid behavior for all bound dark matter structures. This option is not very\nattractive from a phenomenological point of view\\cite{delaix,spergel}; for example, dwarf\ngalaxies or galaxies in clusters tend to sink like rocks instead of orbiting like\nsatellites, and the collapse of cores occurs most easily in those low-dispersion halos\nwhere we seek to stabilize them. \n\n \n\n\\section{Particle Properties and Phase Densities}\n\n \nWe adopt the hypothesis that some dark matter cores are real and due to dark matter\nrather than baryonic physics or observational artifacts. At present this interpretation\nis suggested rather than proven by observations. We\nalso conjecture that the heating which sets the finite central phase density is\nprimordial, part of the physics of the particle creation rather than some byproduct of\nhierarchical clustering. At present this is a conjecture suggested rather than proven by\nsimulations.\n\n In the clustering\nhierarchy, more higher-entropy material is created as time goes on, but numerical\nexperiments indicate that this heated material tends to \nend up in the outer halo.\nThis is the basic reason why CDM halos always have central cusps: there\nis always a little bit of material which remembers the low primordial entropy\nand sinks to the center. The halo center contains the lowest-entropy\nmaterial, which we conjecture is a relic of the original entropy\nof the particles---\n or equivalently, their original phase density, which is most directly related to \nmeasurable properties of halo dynamics. \nWe begin by relating the phase density to particle properties in\nsome simple models.\n \n\n\\subsection{Phase Density of Relativistically-Decoupled Relics}\n\nConsider particles of mass $m$ originating in equilibrium and\ndecoupling at\na temperature $T_D>>m $ or chemical potential $\\mu>>m $. The original\ndistribution function is\\cite{landau}\n\\begin{equation}\nf(\\vec p)=(e^{(E-\\mu)/T_D}\\pm 1)^{-1}\\approx (e^{(p-\\mu)/T_D}\\pm 1)^{-1}\n\\end{equation}\nwith $E^2=p^2+m^2$ and $\\pm$ applies to fermions and bosons\nrespectively. The number density and pressure of the particles are\\cite{kolb}\n\\begin{equation}\nn ={g\\over (2\\pi)^3}\\int fd^3p\n\\end{equation}\n\\begin{equation}\nP ={g\\over (2\\pi)^3}\\int {p^2\\over 3E} fd^3p\n\\end{equation}\nwhere $g$ is the number of spin degrees of freedom. Unless stated otherwise,\nwe adopt units with $\\hbar=c=1$.\n\nWith adiabatic expansion this distribution\nis preserved with momenta of\nparticles varying as $p\\propto R^{-1}$, so the density\nand pressure can be calculated at any subsequent time\\cite{peebles}.\nFor thermal relics $\\mu=0$, we can \nderive the density and pressure in the limit\nwhen the particles have cooled to be nonrelativistic:\n\\begin{equation}\nn={g T_0^3\\over (2\\pi)^3}\\int {d^3p \\over e^p\\pm 1}\n\\end{equation}\n\\begin{equation}\nP={g T_0^5\\over (2\\pi)^3 3m}\\int {p^2d^3p \\over e^p\\pm 1}\n\\end{equation}\nwhere the pseudo-temperature $T_0=T_D(R_D/R_0)$ records the expansion of\nany fluid element relative to its initial size and temperature\nat decoupling $R_D,T_D$. \n\nIt is useful to define a ``phase density'' $Q\\equiv\n \\rho/\\langle v^2\\rangle^{3/2}$ proportional\nto the inverse specific entropy for nonrelativistic matter, \nwhich is preserved under adiabatic expansion and contraction. For\nnondissipative particles $Q$ cannot increase, although it can decrease due to\nshocks (in the collisional case) or coarse-graining (in the collisionless case,\ne.g. in\n``violent relaxation'' and other forms of dynamical heating.) \nCombining the above expressions for density and pressure\nand using $\\langle v^2\\rangle=3P/nm$, we find\n\\begin{equation}\nQ_X =q_X g_X m_X^4.\n\\end{equation}\n The dimensionless coefficient for the thermal case is \n\\begin{equation}\nq_T={4\\pi \\over (2\\pi)^3}\n{ [\\int dp (p^2/e^p\\pm 1)]^{5/2} \\over\n[\\int dp (p^4/e^p\\pm 1)]^{3/2} }=0.0019625,\n\\end{equation}\nwhere the last equality holds for thermal fermions.\nAn analogous calculation for the degenerate fermion case \n($T=0, \\mu_D>>m_X$) yields the same expression for\n$Q $ but with a different coefficient,\n\\begin{equation}\nq_d={4\\pi \\over (2\\pi)^3}\n{ [\\int_0^1p^2 dp]^{5/2} \\over\n[\\int_0^1p^4 dp ]^{3/2} }=0.036335.\n\\end{equation}\nTo translate from $\\hbar=c=1$ into more conventional astronomers' units,\n\\begin{equation}\n(100 eV)^4/c^5= 12,808 {(M_\\odot/{\\rm kpc}^3)\\over ({\\rm km\\ s^{-1}})^{3}}\n=12.808 {(M_\\odot/{\\rm pc}^3)\\over (100\\ {\\rm km\\ s^{-1}})^{3}}\n\\end{equation}\nThe phase density in this situation depends on the particle properties but not\nat all on the cosmology; the decoupling temperature, the current\ntemperature and density do not enter. The numerical factors \njust depend on whether the particles are thermal or degenerate, bosons or fermions,\nwhich makes the quantity $Q$ a potentially precise tool for measuring particle\nproperties. \nMany scenarios envision thermal relics so we adopt this as a fiducial reference\nin quoting phase densities in $m^4$ units---bearing in mind that the actual\nmass may be different in cases such as degnerate sterile neutrinos\\cite{shi,fuller},\nand that \nfor the astrophysical effects discussed below, it is the phase density that\nmatters. \nFor a neutrino-like ($g=2$), thermal relic, \n\\begin{equation}\nQ_T= 5\\times 10^{-4} {(M_\\odot/{\\rm pc}^3)\\over ({\\rm km\\ s^{-1}})^{3}}\n(m_X/1{\\rm keV})^4.\n\\end{equation}\n\n\n\\subsection{Space Density of Thermal Relics}\n\nFor a standard, relativistically-decoupled\nthermal relic, the mean density of the particles can be estimated\\cite{kolb}\nfrom the\nnumber of particle degrees of freedom at the epoch $T_D$ of decoupling,\n$g_{*D}$; the ratio to the critical density is\n\\begin{equation}\n\\Omega_X =78.3 h^{-2} [g_{eff}/g_{*D}] (m_X/{\\rm 1 keV})\n=2.4 h_{70}^{-2} (m_X/{\\rm 1 keV}) (g_{eff}/1.5)(g_{*D}/100)^{-1} \n\\end{equation} \nwhere $g_{eff}$ is\nthe number of effective photon degrees of freedom of the particle \n($=1.5$ for a two-component fermion).\nFor standard neutrinos which decouple at around 1MeV, $g_{*D}=10.75$. \n\n \nCurrent observations suggest that the dark matter density \n$\\Omega_X\\approx 0.3$ to $0.5$, hence the mass density for a warm relic\nwith\n$m_X\\ge$ 200 eV clearly requires a much larger \n$g_{*D}$ than the standard value for neutrino decoupling. Above about 200 MeV, the \n activation of the extra gluon and quark degrees of freedom\n(24 and 15.75 respectively including $uds$ quarks)\ngive $g_{*D}\\approx 50$; activation of heavier modes of the Standard\nModel above $\\approx 200$GeV produces \n$g_{*d}\\approx 100$; this gives a reasonable match for\n$m_X\\approx 200$ eV and $\\Omega_X\\le 0.5$, as suggested\nby current evidence. Masses of the order of 1 keV can be accomodated\nby somewhat earlier decoupling ($\\approx$ TeV) and including many extra (e.g.,\nsupersymmetric or extra-dimensional) degrees of\nfreedom. Alternatively a degenerate particle can be introduced via mixing of a sterile\nneutrino, combined with a primordial chemical potential adjusted to give the right\ndensity\\cite{shi}.\n In any of these cases, the particle must interact\nwith Standard Model particles much more weakly than normal weak interactions,\nwhich decouple at $\\approx 1$ MeV. \n\n\nNote that warm dark matter particles have low \n densities compared with photons and other species at 1 MeV\n so they do not strongly affect \nnucleosynthesis. However, their effect is not entirely negligible since they \nare relativistic at early times and add considerably more to the mean total\ndensity in the radiation era than standard CDM particles. \nThey add the\nequivalent of $(T_X/T_\\nu)^3= 10.75/g_{*d}$\n of an effective extra neutrino species,\nwhich leads to a small increase in the predicted primordial helium abundance for a\ngiven \n$\\eta$. Because the phase density fixes\nthe mean density at which the particles become relativistic, \nit also fixes this effect on nucleosynthesis (independent of the \nother particle properties, thermal or degenerate etc.) This effect might eventually\nbecome detectable with increasingly precise measurements of cosmic abundances.\n\n \n\\subsection{Decaying WIMPs and Other Particle Candidates}\n\nThermally decoupled relics are \nthe simplest way to obtain the required finite\nphase density, but they are not the only way.\n Heavier particles can be produced with\n a kinetic temperature higher\nthan the radiation, accelerated by some nonthermal process.\nWeakly interacting massive particles, including\nthe favored Lightest Supersymmetric Particles, can\nreduce their phase density if they form via out-of-equilibrium\nparticle decay. A small density of heavy \nunstable particles (X1) can separate out in the standard way, then\n later decay into the present-day (truly stable) dark matter particles (X2).\nIn a supersymmetric scheme one can imagine for example a gravitino separating\nout and decaying into neutralino dark matter. \n\n\nIn the normal Lee-Weinberg scenario for WIMP generation, the \nparticle density is in approximate thermal equilibrium until\n $T\\approx m_{X}/20$. The particles thin out by annihilation until\ntheir relic density freezes out when the the annihilation rate matches the Hubble\nrate, \n$n_{X}\\langle \\sigma_{ann}v\\rangle\\approx H$. The density\ntoday is then \n\\begin{equation}\n\\Omega_{X}\\approx T_{\\gamma 0}^3 H_0^{-2}m_{Planck}^{-3}\\langle \\sigma_{ann}v\\rangle^{-1}\n\\approx(m_W/100{\\rm GeV})^2(m_W/m_X)^2\n\\end{equation}\nwhere we have used the typical weak annihilation cross section\n$\\sigma_{ann}\\approx \\alpha^2m_X^2/m_W^4$ determined by the mass\nof the $W$.\nThe kinetic temperature of the WIMPs freezes out at about\nthe same time as the abundance, so they are very cold today,\nwith typical velocities\n$v\\approx \\sqrt{20} T_0/m_X\\approx 10^{-14} (m_X/100 GeV)^{-1}$.\nThis of course endows them with small velocities and an enormous phase density.\n\nA smaller phase density can be produced if these particles\ndecay at some point into the particles present today. \nIf the secondary particles are much lighter than the first,\nthey can be generated with relativistic velocities at relatively\nlate times as we require.\nSuppose the primary $X1$ particles decay into secondary $X2$ \nparticles at a temperature $T_{decay}$. To produce particles with the\nvelocity $\\approx 0.4$ km/sec today (characteristic of a fiducial\n200 eV thermal relic phase density), or $v\\approx c$ at\n$T\\approx/300 {\\rm eV}$,\n\\begin{equation}\nm_{X1}\\approx m_{X2} T_{decay}/300 {\\rm eV}.\n\\end{equation}\nWe also want to get the right density of $X2$ particles. Suppose the \ndensity of $X1$ is determined by a Lee-Weinberg freezeout,\nsuch that $n_{X1}(T_\\gamma\\approx m_{X1}/20)\\sigma_{ann}v\\approx H$.\nIn order to have $\\rho_{X2}\\approx \\rho_{rad}/600$ at $z_{nr}\\approx 10^6$,\n$\\rho_{X1}\\approx \\rho_{rad}/600$ at $ T_{decay}$, and then\n\\begin{equation}\nm_{X2}^2T_{decay}\\approx{600\\times 20m_W^4\\over \\alpha^2m_{Planck}}\n\\approx (100{\\rm MeV})^3.\n\\end{equation}\nThus we obtain\n\\begin{equation}\nm_{X1}m_{X2}\\approx (30{\\rm GeV})^2.\n\\end{equation}\nA simple example would be a more or less standard 50 GeV WIMP primary\nwhich decays at $T_{decay}\\approx 1$keV into marginally \nrelativistic 20 GeV secondaries. Alternatively the primary could be \nheavier than this and the secondary lighter. Such scenarios have to be crafted\nto be consistent with various constraints, such as the long required\nlifetime for $X1$ (in the example just given, a week or so) and the decay width of the $Z$\n(which must not notice the existence of $X2$); although not compelling, \nthey are not all ruled out.\\footnote{It is also possible to \nreduce the scale of filtering of linear perturbations for a given phase density\n by arranging for the decay relatively late, and for the decay products to be\nnonrelativistic. This option seems even more contrived and we will not pursue \nit in detail here.}\n\nThe other perennial favorite dark matter candidate is the axion. \nThe usual scenario is to produce these by condensation, which if \nhomogeneous produces dark matter even colder than the WIMPs--- indeed,\nas bosons in a macroscopic coherent state. However, it is natural\nto contemplate modifications to this picture where the condensing fields\nare not uniform but have topological defects or Goldstone excitations,\nproduced by the usual Kibble mechanism during symmetry\nbreaking (e.g. \\cite{hoganrees,battye}). In this case the axions are produced with\nrelativistic velocities and could in principle lead to the desired velocity \ndispersion.\n\n \n\n \n\n\n\\section{Cores from Finite Primordial Phase Density}\n\nWe have shown several examples of how particle properties determine \nprimordial phase density. Here we explore how the phase density affects \nthe central structure of dark matter halos. \n\n\\subsection{Core Radius of an Isothermal Halo}\n\nConsider the evolution of classical dissipationless, collisionless particles in phase\nspace. Truly Cold Dark Matter is formed with zero velocity dispersion occupying a three\ndimensional subspace (determined by the Hubble flow $\\vec v= H\\vec r$) of six dimensional\nphase space. Subsequent nonlinear evolution wraps up the phase sheet so that a\ncoarse-grained average gives a higher entropy and a lower phase density. In general a small\namount of cold material remains which naturally sinks to the center of a system. There is\nin principle no limit to the central density; the phase sheet can pack an arbitrary number\nof phase wraps into a small volume.\n\nBy contrast, with warm dark matter the initial phase sheet has a finite thickness. The \nparticles do not radiate so the phase density can never exceed this initial value. In the \nnonlinear formation of a halo, the phase sheet evolves as an incompressible fluid in\nphase space. The outer\nparts of a halo form in the same way as CDM by wraps of the sheet whose thickness is\nnegligible, but in the central parts the finite thickness of the sheet prevents arbitrarily\nclose packing--- it reaches a ``phase packing'' limit. For a given velocity dispersion at\nany point in space, the primordial phase density of particles imposes an upper limit on\ntheir density\n$\\rho$, corresponding to \n adiabatic compression.\nThus warm dark matter halos cannot form the singular central cusps\npredicted by Cold Dark Matter but instead form cores with a maximum limiting \n density at small radius, determined by\nthe velocity dispersion.\n\n We estimate the structure of the halo \ncore\n by conjecturing that the matter in the central parts of the halo \nlies close to the primordial adiabat defined by $Q$. This\nwill be a good assumption for cores which form quietly without too much\ndynamical heating. Simulations indicate this to be the case in essentially all CDM\n halos, although in principle it could\nbe that warm matter typically experiences more additional\ndynamical heating than cold matter,\nin which case the core could be larger. This question can be resolved with \nwarm simulations, including a reasonable sampling of the particle distribution function\nduring nonlinear clustering\\cite{wadsley}; for the present we derive a rigorous upper\nlimit to the core density for a given velocity dispersion, and conjecture that this will\nbe close the actual central structure. \n\nA useful model for illustration and fitting is\na standard isothermal sphere model for the halo. The spherical case \nwith an isotropic distribution of velocities maximizes the central density \ncompatible with the phase\ndensity limit. \nThe conventional definition of core size in an isothermal\nsphere\\cite{binney} is the \n``King radius''\n\\begin{equation}\nr_0=\\sqrt{9\\sigma^2/ 4\\pi G \\rho_0}\n\\end{equation} \nwhere $\\sigma$ denotes the one-dimensional velocity dispersion,\nand $\\rho$ denotes the central density. Making the adiabatic\nassumption, $\\rho_0= Q (3\\sigma^2)^{3/2}$, we find\n\\begin{equation}\nr_0=\n\\sqrt{9 \\sqrt{2}/ 4\\pi 3^{3/2}}(QG v_{c\\infty})^{-1/2}=\n0.44 (QG v_{c\\infty})^{-1/2}\n\\end{equation} \nwhere $v_{c\\infty}=\\sqrt{2}\\sigma$\ndenotes the asymptotic circular velocity\nof the halo's flat rotation curve.\n(Note that aside from numerical factors this is the same mass-radius relation as\na degenerate dwarf star; the galaxy\ncore is bigger than a Chandrasekhar dwarf of the same specific binding energy by a\nfactor\n$(m_{proton}/m_X)^2$. The collisional case treated below is even closer to a scaled\nversion of a degenerate dwarf star.)\n\nFor the thermal and degenerate phase densities\nderived above, \n\\begin{equation}\nr_{0,thermal}= 5.5 {\\rm kpc} (m_X/100{\\rm eV})^{-2}\n(v_{c\\infty}/30{\\rm km s^{-1}})^{-1/2}\n\\end{equation}\n\\begin{equation}\nr_{0,degenerate}= 1.3 {\\rm kpc} (m_X/100{\\rm eV})^{-2}\n(v_{c\\infty}/30{\\rm km s^{-1}})^{-1/2},\n\\end{equation}\nwhere we have set $g=2$.\nThe circular velocity in the central\ncore displays the harmonic behavior $v_c\\propto r$; it reaches half of\nits asymptotic value at a radius $r_{1/2}\\approx 0.4 r_0$. \n\nInstead of fitting an isothermal sphere to an entire rotation curve, in some situations we\nmight opt to measure the central density directly by fitting the linear inner portion of\na rotation curve if it is well-resolved in the core:\n\\begin{equation}\nv_c/r=\\sqrt{4\\pi G\\rho/3}\n= 2.77 G^{1/2}Q^{1/2}v_{c\\infty}^{3/2}\n= 6.71 {\\rm km\\ s^{-1} \\ kpc^{-1}}(m_X/100{\\rm eV})^{2}\n(v_{c\\infty}/30{\\rm km s^{-1}})^{3/2}.\n\\end{equation}\n\n\n\\subsection{Comparison with galaxy and cluster data}\n\n\nIn a separate paper\\cite{dalcanton} we review the current \nrelevant data in more detail, including a consideration of interpretive\nambiguities. Here we offer a summary of the situation.\n\nThe relationship of core radius or central density with halo velocity\ndispersion is a simple prediction of the primordial phase density\nhypothesis, which can be in principle be tested on \na cosmic population of halos. In particular if\nphase packing is the explanation of dwarf galaxy cores, the dark matter cores of giant\ngalaxies and galaxy clusters are predicted to be much smaller than for dwarfs, \n unobservably hidden in a central region dominated by\nbaryons. There is currently at least one well-documented case of a galaxy cluster with a\nlarge core ($\\approx 30$kpc) as measured by a lensing fit\\cite{tyson}, which \n cannot be explained at all by phase packing with primordial phase density.\nOn the other hand more\nrepresentative samples of relaxed clusters do not show evidence\nof cores\\cite{dalcanton,williams}. \n\nThe favorite\n laboratories for finding evidence of dark matter cores are dwarf disk galaxies\nwhich display a central core even at radii where the baryonic contribution\n is negligible\\cite{carignan,swaters,swaters2}. Rotation curves allow a direct\nestimate of the enclosed density as a function of radius, right out to a fairly\nflat portion which allows an estimate of the dark matter velocity dispersion---\nall the information we need to estimate a phase density for a core. \nThree of the best-resolved cases\\cite{dalcanton} yield estimates \nof $Q\\approx 10^{-7}- 10^{-6} (M_\\odot/{\\rm pc}^3)/ ({\\rm km\\ s^{-1}})^{3}$.\nThe sensitive dependence of $Q$ on particle mass means that $m_X$ is \nreasonably well bounded even from just from a handful of such cases; a thermal value of \n$m_X\\ge$300 eV does not produce large enough cores to help at all (that is, one\nmust seek unrelated explanations of the data), while values $m_X\\le$100 eV produce\nsuch large cores that they conflict with observed rotation curves of normal giant\ngalaxies\\cite{tremaine} and LSB galaxies\\cite{pickering}. This is why we\nadopt a fiducial reference value of 200 eV for dwarf disk cores.\n\n\n Dwarf\nspheroidal galaxies do not have gas on \ncircular orbits so their dynamics is studied with stellar velocity\ndispersions\\cite{aaronson,olszewski,faber,mateo}. Here we have an estimate of the mean\ndensity in the volume encompassed by the stellar test particles, but we do not know the\nvelocity dispersion of the dark matter halo particles (which may larger than that of the\nstars if the latter occupy only\nthe harmonic central portion of a large dark matter core) so estimates \nof the phase density are subject to other assumptions and modeling \nconstraints\\cite{lake,gerhard}. If we assume that the stars are not much more\nconcentrated than the dark matter, we get the largest estimate\\footnote{This is the largest\nvalue of the mean phase density of material in the region enclosed by the stellar\nvelocity tracers;\nthere is no real observational upper limit for the maximum phase density. Without the\nrotation curve information, these systems are consistent with singular isothermal \nspheres or other cuspy profiles for the dark matter} of\nthe phase density, which in the largest case\\cite{dalcanton} is about\n$Q\\approx 2\\times 10^{-4} (M_\\odot/{\\rm pc}^3)/ ({\\rm km\\ s^{-1}})^{3}$ corresponding to a\nthermal relic of mass\n$m_X\\approx 800$eV. The apparent phase densities estimated for dwarf\nspheroidals are thus much larger than for dwarf disks, even at the same radius. \nThe mass-to-light ratio in the most extreme of these systems is about 100 in \nsolar units, an order of magnitude more than that found for purely baryonic, old\nstellar populations in elliptical galaxies\\cite{fukugita}, so there is little doubt\nthat they are dominated by dark matter. The CDM prediction is that there are other, more\nweakly bound halos in which gas was unable to cool and form \nstars, and which therefore have an even higher mass-to-light ratio.\n\n\n\\section{Filtering of Small-Scale Fluctuations}\nThe non-zero primordial velocity dispersion naturally leads to a filtering of the \nprimordial power spectrum.\nThe transfer function of Warm Dark Matter is almost\nthe same as Cold Dark Matter on large scales, but is\nfiltered by free-streaming on small scales. The \ncharacteristic wavenumber for filtering at any time is given\nby $k_X= H/\\langle v^2\\rangle^{1/2}$, the inverse\ndistance travelled by a particle at the rms velocity in\na Hubble time. The detailed shape of the transfer function \ndepends on the detailed evolution of the Boltzmann equation,\nand in particular whether the particles are free-streaming or\ncollisional.\n\nIn the current application,\nwe are concerned with $H$ during the radiation-dominated era\n($z\\ge 10^4$), so that $H^2=8\\pi G \\rho_{rel}/3\\propto (1+z)^4 $, where \n$\\rho_{rel }$ includes all relativistic degrees of freedom.\nFor constant $Q$, $\\langle v^2\\rangle^{1/2}= (\\rho_X/Q)^{1/3}\\propto\n(1+z)$ as long as the $X$ particles\nare nonrelativistic. For particles with a small velocity dispersion today,\nthe \ncomoving filtering scale\\cite{kolb} is thus approximately independent\nof redshift over a considerable interval of redshift (see Figure 1). \n The ``plateau'' scale is independent of $H_0$:\n\\begin{equation}\nk_{X,comov}= H_0 \\Omega_{rel}^{1/2} v_{X0}^{-1}\n=0.65\\ {\\rm Mpc^{-1}} (v_{X0}/1 {\\rm km\\ s^{-1}})^{-1}\n\\end{equation}\nwhere \n$\\Omega_{rel}= 4.3\\times 10^{-5}h^{-2}$ is the density in\nrelativistic species and \n $v_{X0}=(Q/\\bar\\rho_{X0})^{-1/3}$ is the rms velocity of\nthe particles at their present mean cosmic density\n$\\bar\\rho_{X0}$.\nFor the thermal case, in terms of particle\nmass, we have\n\\begin{equation}\nv_{X0,thermal}=0.93\\ {\\rm km\\ s^{-1}} h_{70}^{2/3} (m_X/ 100 {\\rm\neV})^{-4/3}(\\Omega_X/0.3)^{1/3}(g/2)^{-1/3},\n\\end{equation}\nand hence\n\\begin{equation}\n k_{X,comov}= 15 \\ {\\rm Mpc^{-1}} h_{70}^{-2/3} (m_X/ 1 {\\rm\nkeV})^{-4/3}(\\Omega_X/0.3)^{-1/3}(g/2)^{1/3}.\n\\end{equation}\n\n\nIn the case of free-streaming, relativistically-decoupled\nthermal particles, the transfer function has been computed\nprecisely\\cite{bardeen,sommerlarsen}; the characteristic\nwavenumber where the square of the transfer function falls to half \nthe CDM value is about $k_{1/2,stream}\\approx k_{X,comov}/5.5$. \nThe simple streaming case only works\nfor high phase densities $m_X\\ge 1$keV, that is, comparable to that\nobserved in dwarf spheroidals.\nFor example, to produce an acceptable number of galaxies at a dwarf galaxy scale\nwithout invoking disruption,\nPress-Schechter theory\\cite{kamionkowski} implies a spectral\ncutoff at about $k=3 h_{70} {\\rm Mpc}^{-1}$, \nrequiring a thermal relic mass of about 1100 eV. Hydrodynamic \nsimulations show that the same cutoff scale\npreserves the large scale success of CDM and probably improves the \nCDM situation on galaxy scales in ways mentioned previously\\cite{sommerlarsen}. \n Although the typical uncertainty\non the phenomenologically best filtering scale is at least a factor of two, \nit is clear that the smallest phase density compatible with standard streaming filtering\nis too large to have\na direct impact on the core problem in dwarf disk galaxies.\n\nOn the other hand the discrepancy is only a factor of a few in mass,\nless than an order of magnitude in linear damping scale. We have already mentioned two\n modifications which could reconcile these scales. It could be that warm\nmodels turn out to\n be sometimes more effective at producing smooth cores\nthan we have guessed from the minimal phase-packing constraint, due to more efficient\ndynamical heating than CDM; this would produce a\n nonlinear amplifier of the primordial velocities, probably with a large \nvariation depending on dynamical history (an especially good option if cores turn out to\nbe common in galaxy clusters.) Another\npossibility is that the primordial velocities are introduced relatively late\n(nonrelativistically) by particle decay.\n\nStill another possibility is a different relationship of\n$k_{1/2}$ and $k_X$ from the standard collisionless streaming behavior. For example, if the\nparticles are self-interacting, then the free streaming is suppressed and the relevant\nscale is the standard Jeans scale dividing growing behavior from\nacoustic oscillations, $4\\pi G\\rho_{total}-k_J^2c_S^2=0$. This comes out to\n$k_J=\\sqrt{3}H/c_S=\\sqrt{27/5}k_X$, 13 times shorter\nthan $k_{1/2,stream}$ at a fixed phase density. (An intuitive view of\nthe this numerical factor is that\nduring the long period when $k_X$ is flat, streaming particles continue\nto move and damp on larger scales, whereas the comoving Jeans scale just remains fixed,\nsharply dividing oscillating from growing behavior.)\nThe acoustic case is similar to the behavior of fluctuations in high-density,\nbaryon-dominated models, which have a sharp cutoff at the Jeans\nscale\\cite{peacock}.\nWe conclude that some particle self-interactions may be \ndesirable to reconcile the scale of the transfer function of primordial \nperturbations with the phase packing effect on disk cores.\n\n\\section{Collisional Dark Matter}\n\n\n We now turn to the case where the \n dark matter particles are not collisionless, but scatter off of each other\nvia a new intermediate force. Self-interactions of dark matter have\nbeen motivated from both an astrophysical and a particle physics point of\nview\\cite{carlson,delaix,atrio,spergel,mohapatra}. Our goal here is\nagain to relate the properties of the new particles to the potentially observable\nproperties of dark matter halos. In addition to the single parameter $Q$ considered for\nthe collisionless case, we can use halo properties to constrain\nfundamental parameters of the particles--- the masses of the dark matter particles \nand intermediate bosons carrying the interactions, as well as a coupling constant. \n\n Such\nself-interactions lead to modifications in several of the previous arguments.\n As we have seen, self-interactions can have\nobservable effects via the transfer function even if they are negligible today. \nStronger self-interactions also affect the structure and stability of halos;\ncollisional matter has a fluid character leading to \nequilibrium states of self-gravitating halos much like those of stars. \nThese systems are quite different from collisionless systems. Although entropy must \nincrease outwards for stability against convection (which naturally happens\ndue to shocks in the hierarchy), it cannot\nincrease too rapidly and remain hydrostatically stable; in particular, stable solutions\nhave a minimum nonneglible \ntemperature gradient, and the\nisothermal case is no longer a stable static solution as it is for collisionless matter.\nSince collisional matter conducts heat between fluid elements, these solutions\nare all unstable on some timescale. \n\n\\subsection{Particles and Interactions}\nWe now apply several simple physical arguments to constrain properties of \nthe dark matter candidate and its interactions. Some of these have been considered\npreviously\\cite{spergel}. The most important constraints are summarized in \nfigure 2. \n\n\nSuppose that the dark matter \n $X$ particles with mass $m_X$, which may be either\nfermions or bosons, interact\nvia massive bosons $Y$ whose mass $m_Y$ determines the\nrange of the interactions, and a coupling constant\n$e$. These may be considered analogous to strong interaction\nscatterings \nwhere we regard pions as Yukawa scalar intermediates, or electroweak\ninteractions with $W,Z$ as vector intermediates.\nThe interactions must be elastic scatterings to avoid \na net energy loss, although ``dissipative'' three-body\nencounters are permitted as long as the energy does not leave\nthe $XY$ subsystem nor travel far in space. \n For most purposes even\nthe sign of the interaction does not matter--- it may be attractive or\nrepulsive, as happens with vectors and like charges.\nThe $Y$ particles at tree level interact only with\n$X$, although the $X$ may (as is usual with dark matter candidates) be allowed some\nmuch weaker interactions with ordinary matter.\nIn this model the collision cross section\nfor strong scattering is about\n\\begin{equation}\n\\sigma\\approx m_Y^{-2} {\\rm min}\n\\left[e^4\\left({m_Y\\over m_X v^2}\\right)^2,\n\\ e^4 \\left({m_X\\over m_Y}\\right)^2,\n\\ 1\\right]\n\\end{equation}\nwhere the first case is coupling-limited (and depends\non the particle velocity and coupling strength, like electromagnetic\nscattering of electrons),\nthe second case holds for $m_Y>m_X$ (like neutrino\nneutral-current interactions) and the third is the\nrange-limited, strong interaction limit (like neutron scattering).\n\nThere are several simple constraints on the particle masses.\nIf the dark matter is collisional, \nthe rate of net annihilations of $X$ must be highly\nsuppressed compared to the scattering rate, or the \nmass of the halo would quickly radiate away as $Y$ particles.\nEither there is a primordial asymmetry\n(so the number of \n$\\bar X$ is negligible), or \n\\begin{equation}\nm_Y>2m_X,\n\\end{equation}\n suppressing\nwhat would otherwise be a rapid channel for $X$ to annihilate and\nradiate $Y$. (Recall that in this model, there is no direct route to annihilate\ninto anything else). In any case\nthe\n$Y$ must not be too light or the typical inelastic collisions will radiate them;\nfor particles with relative velocities $v\\approx 10^{-3}$ typical of dark matter in \ngalaxies, we must have \n\\begin{equation}\nm_Y> m_X v^{2}\\approx 10^{-6} m_X,\n\\end{equation}\nso that the energy of collisions is typically insufficient to \ncreate a real $Y$.\nIn addition, if attractive, the range of the interactions must be less than\nthe ``Bohr radius'' for these interactions, requiring\n\\begin{equation}\nm_Y>e^2m_X,\n\\end{equation}\n in order not to form bound ``atoms''.\nThe close analogy with $Y$ is the pion, which is just\nlight enough to allow a bound state of deuterium.\nBound states would be a disaster since they would behave like\nnuclear reactions in stars. \nSuch states would add an internal source of energy\nin the halos, creating winds or other energy flows which would \nunbind large amounts of matter. All of these constraints eliminate the upper\nleft region of figure 2, with details depending on the coupling strength and\nhalo velocity. \n\n\\subsection{Parameters for Collisional Behavior}\n\nThe properties of interacting particles define a characteristic column density,\n $m_X/\\sigma$; a slab of $X$ at this column is one mean free path thick.\nThis is the quantity that specifies the degree of collisional or collisionless behavior\nof a system. In order to connect the halo astrophysics with dark matter properties\nwe convert from units with $\\hbar=c=1$:\n\\begin{equation}\n(1\\ {\\rm GeV})^3= 4.6\\times 10^3\\ {\\rm g\\ cm^{-2}}\n=2.2\\times 10^7\\ {\\rm M_\\odot\\ pc^{-2}}\n\\end{equation}\nFor comparison, the average mass column density\nwithin radius $r_{kpc}{\\rm kpc}$ for a halo with a circular velocity\n$v_{30}\\times 30{\\rm km\\ sec^{-1}}$\n is \n\\begin{equation}\n\\Sigma_h= {v^2\\over \\pi Gr}= 0.014\\ v_{30}^2 r_{kpc}^{-1}\n{\\rm g\\ cm^{-2}}=(15{\\rm MeV})^3v_{30}^2 r_{kpc}^{-1}.\n\\end{equation}\nA halo therefore enters the strongly-collisional regime---\nqualitatively different from classical CDM--- if\n\\begin{equation}\nm_Y^4e^{-4}(15{\\rm MeV})^{-3}v_{30}^{-2} r_{kpc} < m_X<\\min[(15{\\rm MeV})^3v_{30}^2\nr_{kpc}^{-1}m_Y^{-2},\n 15{\\rm MeV}(e/v)^{4/3}(v_{30}^2 r_{kpc}^{-1})^{1/3}].\n\\end{equation}\nThis criterion is shown in figure 2 as the right boundary of the ``unstable cores''\nregion; indeed this marginally-collisional case maximizes the rate of thermal\nconduction instability, as discussed below.\n\nWe also compute\nthe criterion for non-streaming behavior in the early universe--- the amount of\nself-interaction needed to affect the transfer function as discussed above.\nIt is\nsignificantly less than that required for collisional behavior today:\n\\begin{equation}\n{\\sigma\\over m_X}\n\\approx H(t_{eq})/n_X(t_{eq})v_X(t_eq)m_X\n=\\Sigma_0^{-1}\\Omega_{rel}^{5/2}\\Omega_X^1 v_X(t_0),\n\\end{equation}\nwhere $eq$ refers to the epoch of equal densities in dark matter and relativistic\nspecies, and\n\\begin{equation}\n\\Sigma_0\\equiv c\\rho_{crit}/H_0=0.1213 h_{70}^{-1} {\\rm g\\ cm^{-2} }\n\\end{equation}\nis the characteristic cosmic column density today.\nUsing the units conversion above we have\n\\begin{equation}\n{\\sigma\\over m_X}\n\\approx(600 {\\rm MeV})^{-3}(v_{X0}/1 {\\rm km \\ s^{-1}})^{-1}\n(\\Omega_X/0.3)^{2}h_{70}^4,\n\\end{equation}\ncorresponding to a mass column for one expected scattering\nof $2\\times 10^4 {\\rm g\\\ncm^{-2}}$. \nParticles scattering off of each other more strongly than this no longer have streaming\nbehavior at high redshift but support acoustic oscillations, much like baryons but with\nonly their own pressure (that is, without the interaction with radiation pressure and\nwithout decoupling from it). We should bear in mind that a somewhat larger cross section\nis needed to avoid diffusive (``Silk'') damping, but even at this level of interaction\nthe scale of damping is is significantly reduced from the streaming case. \nThis criterion is shown in figure 2 as the right boundary of the\n``Jeans''\nregion (although some acoustic behavior before $t_{eq}$ occurs even to the right of this).\n\n\\subsection{Polytropes}\n\nThe equilibrium configurations of collisional dark matter correspond to those\nof classical self-gravitating fluids. The simplest cases to consider and\ngeneral enough for our level of precision are classical polytrope solutions---\n stable configurations of a classical,\nself-gravitating, ideal gas with a polytropic equation of state.\\cite{zeldovich}\nIn the absence of shocks or conduction, the pressure\nand density of a fluid element obey an equation of state $p=K_1\\rho^{\\gamma_1}$.\n For an adiabatic, classical, nonrelativistic, monatomic gas,\nor for nonrelativistic degenerate particles,\nthe adiabatic index\n$\\gamma_1=5/3$ and different values of $K_1$ correspond to different entropy.\nIf the \nentropy varies radially as a power-law,\n equilibrium \nself-gravitating configurations \nare given by\n classical Lane-Emden polytrope solutions. The radial variation of pressure and density\nobey\n$p(r)=K_2\\rho^{\\gamma_2}(r)$; the second index\n$\\gamma_2$ tracks the radial variation between different fluid elements\nin some particular configuration (that is, including variations\nin entropy).\nFor gas on the same adiabat everywhere, $\\gamma_1=\\gamma_2$;\nfor the case of nonrelativistic degenerate or adiabatic matter, $\\gamma_1=\\gamma_2=5/3$\n applies and is a good model of degenerate dwarfs. \nIf \nthe entropy is increasing with radius, as would be expected\nif assembled in a cosmological hierarchy, then $\\gamma_2< \n\\gamma_1$, conferring stability against convection.\n\nThe character of the solutions is well known\\cite{zeldovich}.\n As long as $\\gamma_2> 6/5$ the\nhalo structure is like a star, with a flat-density core in the center, falling off in the\nouter parts to vanishing density at a boundary. If it is rotating, the \nstructure is similar but rotationally flattened. \nThese solutions describe approximately the structure of stars,\nespecially degenerate dwarfs, and \nhalos of highly collisional dark \nmatter.\\footnote{It is worth commenting on some differences and similarities with \ncollisionless halos with finite phase density material. The polytrope solutions\nare for collisional matter with an isotropic pressure and local balance of pressure\ngradient and gravity. Collisionless particles can fill phase space more sparsely, but this\njust means that at a given mass density they must have a larger maximum velocity;\nthe collisional solution saturates the phase density limit and\n has the largest\nmass density for a given coarse-grained phase density. In this sense,\nonce one is solving the cusp problem with finite phase density,\nnothing further is gained by making the particles collisional.\nCollisionless particles allow anisotropy in the momentum\n distribution function, and therefore a wider\nrange of ellipsoidal figures, but cannot pack into tighter cores. \nFor the same reason, the inner phase-density-limited\n core is expected to be close to\nspherical except for rotational support, whether the particles are collisional or not.\nThe phase space is fully occupied and therefore the velocity\ndistribution is close to isotropic wherever the local entropy approaches \nthe primordial value.}\nIf $\\gamma_2<6/5$ \n(and in particular for the isothermal \ncase $\\gamma_2=1$) there is a dynamical instability \nand no stable solution; the system runs away on a gravitational\ntimescale, with the center collapsing and the outer layers \nblowing off. \n\n\n\n \n\n\\subsection{Giant Dwarfs}\n At zero entropy the equilibrium configuration is\nthe exactly soluble $\\gamma=5/3$ polytrope, which we adopt as\nan illustrative example. That is, we model a dwarf galaxy core\nas a degenerate dwarf star, the only difference being a \nparticle mass much smaller than a proton\n allowing a halo mass much bigger than a star. For total mass $M$\nand radius\n$R$, the Lane-Emden solution gives a central pressure \n $p_c=0.770\nGM^2/R^4$ and a central density $\\rho_c=5.99\\bar\\rho=1.43 M/R^3$.\nUsing the above relation for the equation of state we \nobtain the standard degenerate dwarf solution, which has\n\\begin{equation}\nR= 4.5 m_X^{-8/3} M^{-1/3} m_{Planck}^{2}\n=0.98{\\rm kpc}\\left({m_X\\over 100{\\rm eV}}\\right)^{-8/3}\n\\left({M\\over 10^{10}M_\\odot}\\right)^{-1/3},\n\\end{equation}\nwhere $m_{Planck}=\\sqrt{\\hbar c/G}$ and $M_\\odot=9.48\\times 10^{37}m_{Planck}$.\n This ``giant dwarf'' configuration is stable even at zero temperature up to\nthe Chandrasekhar limit for $X$ particles.\\footnote{Defined\nanalogously to the Chandrasekhar limit for standard dwarfs (with $Z=A$ because there is just\none kind of particle providing both mass and pressure, similar to a neutron star),\n\\begin{equation}\nM_{CX}= 3.15 {m_{Planck}^3\\over m_X^2}\n=4.95\\times 10^{14}M_\\odot(m_X/100{\\rm eV})^{-2}.\n\\end{equation} }\n\n \n\n\nSince the mass is not directly observable, it is more\nuseful to consider the velocity of a circular orbit at the surface,\n$v_c=(GM/R)^{1/2}$.\nWe then obtain the relation for a degenerate system,\n\\begin{equation}\nm_X= 4.5^{3/8} v_c^{-1/4} (r_cm_{Planck})^{-1/2} m_{Planck},\n\\end{equation}\nor in more conventional astrophysical units, \n\\begin{equation}\nm_X= 87 eV \\ (v_c/30{\\rm km/s})^{-1/4} (r_c/1 kpc)^{-1/2}. \n\\end{equation}\nNote that as in the collisionless case, no cosmological assumptions or \nparameters have entered into this expression.\n\n\nFor any adiabatic nonrelativistic matter the solution is similar.\nThe absolute\nscale of the giant dwarf, determined by $K_2$,\n is fixed by the phase density $Q$. In general there is a range of entropy but \nonce again the \n the lowest-entropy material (which is densest at a given pressure) \nsinks to the center of a halo\n and forms an approximately adiabatic core. The rest of the halo forms\na thermally-supported atmosphere\nabove it. Once again cores are the places to look for signs of a primordial\nceiling to phase density. \nHowever, as we see below the behavior changes if conduction or radiation are not\nnegligible. As we know, a thermally supported star which conducts heat\nand has no nuclear or other source of energy is \nunstable. \n\n\n\\subsection{Heat Conduction Time and Halo Stability}\nIf the collision rates are not very high we must consider\nheat and momentum transport between fluid elements\nby particle diffusion. The most\nserious consideration for radial stability is the transport of heat.\n In all\nstable thermally supported solutions the \ndense inner parts are hotter; if \nconduction is allowed, heat is transported outwards. The entropy\nof the central material decreases, \nthe interior is compressed to higher density and the outer\nlayers spread to infinity, a manifestation of the gravothermal catastrophe.\nWith conduction the inner gas falls in and\nthe outer gas drifts \nout on a diffusion timescale, attempting to approach\n a singular isothermal sphere. \n\nConsider the scenario\\cite{spergel} where the dark matter cross\nsection is small enough to remain essentially noninteracting on large scales,\npreserving the successes of CDM structure formation simulations,\nbut large enough to become collisional \n in the dense central regions of galaxies.\nAlthough this scenario was introduced to help solve the \ncusp problem, we will see that the conductive instability\n makes matters worse. If stable cores\nare to last for a Hubble time, the dark matter halos must either be effectively\ncollisionless (standard dark matter),\nor very strongly interacting, so that the inevitable conduction is\nslow (or made of degenerate fermions so there is no temperature gradient.)\n\n\nElementary kinetic theory\\cite{landau} yields an estimate\nfor the the conduction\nof heat by particle diffusion;\nthe ratio of energy flux to temperature\ngradient is the classical conduction coefficient $\\kappa\\approx\n\\sigma^{-1}\\sqrt{T/m}$. Assuming a halo in approximate virial\nequilibrium and profile $v(r)$, this yields a timescale for\nheat conduction,\n\\begin{equation}\nt_{cond}\\approx {v \\sigma\\over 2 Gm_X} {-d\\log r\\over d \\log v}\n\\end{equation}\nwhere $v$ is the typical particle velocity\n(which is about the virial velocity of the halo independent of the \nmass of the particles $m_X$). The first factor is essentially\nthe time it takes a particle to random walk a distance $r$,\n$t_{diffuse}\\approx {r^2 n \\sigma/v}$.\n The last factor\ncharacterizes the temperature and entropy gradient; dynamical stability\nprevents it from being very large, and in most\nof the matter it typically takes a value not much larger than unity.\\footnote{The conductive\n destabilization probably happens\nfaster than Spergel and Steinhardt estimated.\nThey used the Spitzer formula describing core collapse in\nglobular clusters, which takes about 300 times longer\nthan the two-particle relaxation time. However, the large factor\narises because in the globular cluster case the relaxation is\nentirely gravitational and is dominated by very long-range\ninteractions with distant stars. In the present situation the interactions are\nstrong and short-range, leading to significant exchange of\nboth energy and momemtum in each scattering. The transport of\nheat takes place on the same timescale as the diffusion of particles, with numerical\nfactors of the order of unity as in standard solutions of the Boltzmann\nequation for gases.} \n\n\nA halo with conduction therefore forms a kind of cooling flow, with the core collapsing and\nthe envelope expanding. If it is hydrostatically quasi-stable (that is, if the core\ncollapse is slow and regulated by the particle diffusion),\nwe can use the Lane-Emden solutions to set bounds on the numerical factor\n${d\\log r/ d \\log v}$ governing the instability. \nThe equation of state tells us that\n $v\\propto \\rho^{1/2n_2}$ where $n_2=(\\gamma_2 -1)^{-1}$. The largest value of $n_2$\nwhich corresponds to a quasi-stable solution is $n_2=5$. The density\nprofile is steeper than isothermal ($n_2=\\infty$), $\\rho\\propto r^{-2}$;\ntherefore $|{d\\log r/ d \\log v}|\\le n_2 \\le 5$. In the rough estimates here\nwe set these factors to unity.\\footnote{Another interesting limit is that\nof small but nonzero self-interactions. \nThe halo is essentially collisionless, but occasional scatterings still take\nplace. The collisionless isothermal sphere, singular or not, is then\nan approximate solution, but still subject to a slow secular instability from\nheat conduction.\nIt is also possible to set up situations where halos are evaporated by a hot\nexternal environment, heated from outside by collapse of the cosmic web.}\n\n\nConduction can be suppressed if the scattering is very frequent.\nFor nondegenerate $X$, stable\ncores require that \n the conduction time exceeds the Hubble time $H_0^{-1}$.\nFor stability over a Hubble time, the column density of a \nhalo with velocity $v$ must exceed ${m_X/ \\sigma}= Hv/G$; therefore\nthe particles must satisfy\n\\begin{equation}\n{m_X\\over \\sigma}\\ge\n1.0\\times 10^{-4} {\\rm g\\ cm^{-2}} h_{70} v_{stable,30}.\n\\end{equation}\nwhere $v_{stable,30}\\times 30{\\rm km s^{-1}}$ denotes the \nvelocity in the lowest-velocity stable halo.\nPerhaps surprisingly, the mass and radius of the halo\ndo not enter explicitly. \n\nThis condition constrains the\nparticles to be highly interactive.\nGalaxy halos have slow conduction compared to $H$ only \nabove a critical velocity dispersion \n$v_{crit}\\approx (G/H)(m_X/\\sigma)$.\nHalos below this threshold\nshould have collapsed cores, and above the threshold the\ncore radius/mass relation is determined as before by\n the giant dwarf sequence for the the particle's phase density.\nThe existence of stable bound 30 km/s halos of highly-collisional dark matter\nrequires\n\\begin{equation}\n{m_X\\over \\sigma}\\le \n(2.8 {\\rm MeV})^3 h_{70} v_{stable,30},\n\\end{equation}\nshown in figure 2 as the right boundary of the ``fluid'' region. \n\nThe ``thickness'' of a halo with velocity $v_{30}\\times 30{\\rm km s^{-1}}$,\nin units\nof particle pathlengths, is\n\\begin{equation}\n{\\Sigma_h\\sigma\\over m_X}\\approx\n10^2 v_{30}^2r_{kpc}^{-1}h_{70}^{-1}v_{stable,30}^{-1}\n\\end{equation}\nso it is clear that all dark-matter-dominated structures,\nfrom small galaxies to galaxy clusters\n($v_{30}\\approx 1- 30$, $r_{kpc}\\approx 0.1- 1000$), are highly \ncollisional and their dark matter behaves as a fluid.\n Even for very diffuse \nmatter at the mean cosmic density ($\\Omega_X=0.3$), the \nparticle mean free path is at most $12 v_{core,30}h_{70}^{-1}$Mpc,\nabout the same as the scale of nonlinear clustering,\nso all bound dark matter structures act like fluids.\n\n\nAre other data consistent with the idea \nthat essentially all dark matter acts like a fluid? This option\nhas been considered previously\\cite{delaix} and while it is perhaps\nnot definitively ruled out, it is not phenomenogically \ncompelling. Serious problems arise for example\nfrom satellite galaxies which are thought\\cite{johnston} to have had several \norbits without stopping and sinking as they would in a fluid,\nor from galaxies in clusters, at least some of which appear (from lens\nreconstruction mass maps) to have retained some of their dark matter halos. An\nintriguing possibility is that a small collision rate might contribute to \nenough instability to feed the formation of black holes\\cite{ostriker}. However\nthe rate of the instability is greatest in the lowest mass, lowest density \ngalaxy cores, a trend not conspicuous in the demography of central black holes of\ngalaxies\\cite{magorrian}.\\footnote{We have to take note of another possibility: perhaps the\ndwarf spheroidals, which have the lowest velocity dispersions of all galaxies and\nare also the densest, have already collapsed by heat conduction. In this way\nwe could use phase packing to give the cores of\nthe dwarf disk galaxies and still explain why the dwarf spheroidals \nhave such a large phase density. Note that this scheme also gives the right\nfiltering scale since the particles are collisional at early times. The \ndwarf spheroidals need\nnot of course collapse all the way to black holes,\nbut they may well have singular dark matter profiles.} \n\nWe conclude that dark matter self-interactions are likely to be negligible in galaxy halos,\nand that this places significant constraints on the particles.\nFigure 2 summarizes the constraints on the parameters $m_X,m_Y$ of\n this interacting-particle model\nfrom the various constraints considered here.\n\\section{Conclusions}\nWe have found that some halos might preserve in their inner structure\n observable clues to new dark matter physics, and that indeed\nsome current observations already hint that the dark matter might be warm rather\nthan cold. \nWe conclude with a summary:\n\n1. Halo cores can be created by a ``phase-packing limit''\ndepending on finite initial phase density. They\nmay provide a direct probe of\n primordial velocity dispersion in dissipationless dark\nmatter. \n\n2. For relativistically-decoupled thermal relics, the phase density depends on \nthe particle mass and spin but not on cosmological parameters.\n\n\n3. Rotation curves in a few dwarf disk galaxies indicate cores with \na phase density corresponding to that of a \n200 eV thermal relic or an rms velocity of about 0.4\nkm/sec at the current cosmic mean density. Velocity dispersions in \ndwarf spheroidal galaxies indicate a higher phase density, corresponding\nto a thermal relic mass of about 1 keV. At most one of these populations\ncan be tracing the primordial phase density.\n\n4. Thermal relics in this mass range can match the mean cosmic density with a plausible\nsuperweak decoupling from Standard Model particles before the QCD epoch. \n\n5. Other very different particles are consistent with the \nhalo data, provided they have the about the same mean density and phase density.\nExamples include WIMPs from particle decay and axions from defect decay.\n\n6. Cores due to phase packing limited by primoridial $Q_0$ predict \n a\nuniversal relation between core radius and halo velocity dispersion.\n The relation is not found in a straightforward interpretation of the data.\n\n7. Primordial velocity dispersion also suppresses halo substructure\n(and solves some other\ndifficulties with CDM) by filtering \nprimordial adiabatic perturbations. Estimates based on luminosity functions prefer\nfiltering on a scale of about\n$k\\approx 3 {\\rm Mpc}^{-1}$; \nfor collisionless particles, this scale\ncorresponds to a filter caused by\nstreaming of about a 1keV thermal relic.\n\n8. Weak self-interactions change from streaming to acoustic\nbehavior, reducing the damping scale and sharpening the filter.\n\n9. Stronger self-interactions\ndestabilize halos by thermal conduction, making the cusp \nproblem worse (unless\nthey are very strong--- too strong for satellite-galaxy kinematics---\n or particles are degenerate, eliminating the central temperature gradient).\n \n\n10. A simulation which samples a warm distribution function reasonably well is\nstrongly motivated, to determine whether primordial $Q$ is preserved in the centers\nof halos, or whether nonlinear effects can amplify dynamical heating in \nsuch models to explain cores on all scales. \n \n \n%\\newpage\n\n\\acknowledgements\nWe are grateful for useful discussions of these issues with\nF. van den Bosch, A. Dolgov,\nG. Fuller, B. Moore, J. Navarro, T. Quinn, J. Stadel,\nJ. Wadsley, and S. White.\nJD gratefully acknowledges the hospitality of the Institute\nfor Theoretical Physics at UC Santa Barbara, which is supported\nin part by the National Science Foundation under Grant No.\\ PHY94-07194.\nJD was partially supported by NSF Grant AST-990862. CJH thanks\nthe Max-Planck-Institute f\\\"ur\nAstrophysik, \n the Isaac Newton Institute for Mathematical\nSciences and the Ettore Majorana Centre for Scientific\nCulture for hospitality.\nHis work was supported at the University of Washington\nby NSF and NASA, and at the Max-Planck-Institute f\\\"ur\nAstrophysik by a Humboldt Research Award.\n\\begin{thebibliography}{}\n\\bibitem{aaronson}\nAaronson, M. 1983, ApJ 266, L11\n\\bibitem{atrio}\nAtrio-Barandela, F., and Davidson, S. 1997, Phys. Rev. D 55, 5886 \n\\bibitem{bardeen}\nBardeen, J. et al. 1986, Astrophys. J. 304, 15\n\\bibitem{battye}\nBattye, R. A. and Shellard, E. P.S. 1994, Nucl. Phys. B423, 260\n\\bibitem{binney}\nBinney, J. and Tremaine, S. 1987, {\\it Galactic Dynamics}, (Princeton:\nPrinceton University Press)\n\\bibitem{blumenthal}\nBlumenthal, G.\n Pagels, H. and Primack, J. R. 1982, Nature, 299, 37\n\\bibitem{bond}\nBond, J. R., Efstathiou, G., and Silk, J. 1980, Phys. Rev. Lett. 45, 1980\n\\bibitem{frank}\nvan den Bosch, F. et al. 1999, Astron. J., submitted (astro-ph/9911372)\n\\bibitem{bullock}\nBullock, J. S. et al. 2000, MNRAS in press, astro-ph/9908159\n\\bibitem{carignan}\nCarignan, C. 1985, Astrophys. J.S 58, 107\n\\bibitem{carlson}\nCarlson, E. D., Machacek, M. E. and Hall, L. J. 1992, Astrophys. J. 398, 43\n\\bibitem{colin}\n Colin, P., Avila-Reese, V., \nand\n Valenzuela, O. 2000,\nsubmitted to the Astrophysical Journal, astro- ph/ 0004115 \n\\bibitem{colombi}\nColombi, S., Dodelson, S., and Widrow, L. M.1996, Ap. J. 458, 1\n\\bibitem{cowsik}\nCowsik, R., and McClelland, J. 1972, Phys. Rev. Lett. 29, 669\n\\bibitem{croft}\nCroft, R. A. C. et al. 1999, Astrophys. J. 520, 1\n\\bibitem{dalcanton}\nDalcanton, J. and Hogan, C. J. 2000, submitted to Astrophys. J., astro-ph/0004381\n\\bibitem{dave}\nDave, R., Hernquist, L, Katz, N., Weinberg, D. H. 1999, Astrophys. J. 511, 521 \n\\bibitem{delaix}\nde Laix, A., Scherrer, R. J., and Schaefer, Astrophys. J. 452, 495\n\\bibitem{dodelson}\nDodelson, S. and Widrow, L. M. 1994, Phys. Rev. Lett. 72, 17\n\\bibitem{dubinski}\nDubinski, J. and Carlberg, R. 1991, Astrophys. J. 378, 496\n\\bibitem{faber}\nFaber, S. and Lin, D. 1983, Astrophys. J. 266, L21\n\\bibitem{fukugita}\nFukugita, M., Hogan, C. J., and Peebles, P. J. E. 1998,\nAstrophys. J. 503, 518\n\\bibitem{fuller}\nFuller, G., 1999, preprint\n\\bibitem{gerhard}\nGerhard, O. E. and Spergel, D. N. 1992, Astrophys. J. 389, L9\n\\bibitem{gerstein}\nGerstein, S. S. and Zeldovich, Ya. B. 1966, ZhETF Pis'ma Red. 4,174\n\\bibitem{ghigna}\nGhigna, S., Moore, B., Governato, F., Lake, G., Quinn, T., and Stadel, J.\n1999, Astrophys. J. submitted (astro-ph/9910166)\n\\bibitem{hannestad}\nHannestad, S., 1999, astro-ph/9912558\n%\\bibitem{hoganlens}\n%Hogan, C. J., 1999 Astrophys. J. 527, 42, astro-ph/9811290\n%\\bibitem{hoganwarm}\n%Hogan, C. J. 1999, astro-ph/9912549\n\\bibitem{hoganrees}\nHogan, C. J. and Rees, M. J. 1988, Phys. Lett. B205, 28\n\\bibitem{hogangoldstone}\nHogan, C. J. 1995, Phys. Rev. Lett. 74, 3105\n\\bibitem{johnston}\nJohnston, K. V., Majewski, S. R., Siegel, M. H., Reid, I. N.,\nand Kunkel, W. E. 1999, Astron. J. 118, 1719\n\\bibitem{kamionkowski}\nKamionkowski, M. and Liddle, A. R. 1999, astro-ph/9911103\n\\bibitem{klypin}\nKlypin, A., Kravtsov, A. V., Valenzuela, O., and Prada, F. 1999, Astrophys. J., 523, 32\n\\bibitem{kolb}\nKolb, E. W. and Turner, M. S. 1990, {\\it The Early Universe},\n(Redwood City: Addison-Wesley)\n\\bibitem{lake}\nLake, G. 1990, Astrophys. J. 356, L43\n\\bibitem{landau}\nLandau, L. D. and Lifschitz, E. M. 1958, {\\it Statistical Physics},\n(Reading: Addison-Wesley)\n\\bibitem{magorrian}\nMagorrian, J. et al. 1998, Astron. J. 115, 2285\n\\bibitem{mateo}\nMateo, M. 1998, Ann. Rev. Astr. Astrophys. 36, 435\n\\bibitem{melott} \n Melott, A. and Schramm, D. N. 1985 Astrophys. J. 298, 1 \n\\bibitem{mohapatra}\nMohapatra, R. N. and Teplitz, V. L. 2000, astro-ph/0001362\n\\bibitem{moore98}\nMoore, B., Governato, F., Quinn, T., Stadel, J., and Lake, G. 1998, Astrophys. J. 499, L5\n\\bibitem{moore99a}\nMoore, B., Ghigna, S., Governato, F., Lake, G., Quinn, T., Stadel, J.,\nand Tozzi, P. 1999, Astrophys. J. 524, L19\n\\bibitem{moore99b}\nMoore, B., Quinn, T., Governato, F., Stadel, J., and Lake, G. 1999,\nMNRAS, submitted (astro-ph/9903164)\n\\bibitem{navarrosteinmetz}\nNavarro, J. F. and Steinmetz, M. 1999, Astrophys. J., in press (astro-ph/9908114)\n\\bibitem{nfw}Navarro, J. F., Frenk, C. S. and White, S. D. M. 1996,\nMNRAS 462, 563\n\\bibitem{olszewski}\nOlszewski, E. and Aaronson, M. 1987, Astron. J. 94, 657\n\\bibitem{ostriker}\nOstriker, J. P., astro-ph/9912548, Phys. Rev. Lett., submitted\n\\bibitem{pagels}\nH. Pagels and J.R. Primack 1982, Phys. Rev. Lett., 48, 223\n\\bibitem{peacock}\nPeacock, J. A. 1999, {\\it Cosmological Physics}, (Cambridge: Cambridge University Press)\n\\bibitem{peebles}\nPeebles, P. J. E. 1993, {\\it Principles of Physical Cosmology},\n(Princeton: Princeton University Press)\n\\bibitem{pickering}\nPickering, T. E., van Gorkom, J. H., Impey, C. D., and Quillen, A. C. 1999,\nAstron. J. 118,765-776\n\\bibitem{cdm}\nPrimack, J. R. 1997, in Formation of Structure in the Universe, ed. A. Dekel\nand J. P. Ostriker, astro-ph/9707285\n\\bibitem{primack}\n Primack, J. R. and Blumenthal, G. in\nFormation and Evolution of Galaxies and Large Structures in the\nUniverse, J. Audouze and J. Tran Thanh Van, eds. (Reidel, Dordrecht,\n1983) pp. 163-183; reprinted in Beyond the Standard Model,\nJ.Tran Thanh Van, ed. (Editions Frontieres, 1983) pp. 445-464\n\\bibitem{ralston}\nRalston, J. P. and Smith, L. L. 1991, Astrophys. J. 367, 54\n\\bibitem{shi}\nShi, X., and Fuller, G. M. 1999, Phys. Rev. Lett. 82, 2832\n\\bibitem{sommerlarsen}\nSommer-Larsen, J., and Dolgov, A. 1999, astro-ph/9912166\n\\bibitem{spergel}\nSpergel, D. N. and Steinhardt, P. J. 1999, astro-ph/9909386\n\\bibitem{swaters}\nSwaters, R. 1999, Ph.D. thesis, Groningen\n\\bibitem{swaters2}\nSwaters, R. A., Madore, B. A., and Trewhella, M. 2000, Astrophys. J. in press, astro-ph/0001277\n\\bibitem{tremaine}\nTremaine, S. and Gunn, J. E. 1979, Phys. Rev. Lett. 42, 407\n\\bibitem{tyson}\nTyson, J. A., Kochanski, G. P., and Dell'Antonio, I. P. 1998,\nAstrophys. J. 498,L107\n\\bibitem{vandenbosch}\nvan den Bosch, F. C., Robertson, B. E., Dalcanton, J. J.,\n \\& de Blok, W. J. G. 2000, Astron. J. 119, 1579.\n\\bibitem{wadsley}\nWadsley, J. et al. 1999, in preparation\n\\bibitem{whiterees}\nWhite, S. D. M., and Rees, M. J. 1978, MNRAS 183, 341\n\\bibitem{white}\nWhite, M. and Croft, R. A. C. 2000, astro-ph/0001247\n\\bibitem{williams}\n Williams, L. L. R., Navarro, J. F., Bartelmann, M. 1999,\nAstrophys. J. 527,535\n\\bibitem{zeldovich}\nZeldovich, Ya. B. and Novikov, I.D. 1971,\n{\\it Relativistic Astrophysics}, vol. 1 (Chicago: University of Chicago press)\n\\end{thebibliography}\n\n\n\\begin{figure}[htbp]\n%\\vspace{1.5in}\n%\\centerline{\\psfig{file=3Jeans.eps}}\n%\\vspace{0.5in}\n\\caption{Characteristic masses and velocities as\n a function of inverse scale factor\n$(1+z)$, for a cosmological model with $\\Omega_X=0.3$,\n$\\Lambda=0.7$. \nMass and velocity are plotted in units with $H_0=\\bar\\rho=c=1$,\nor $M=0.3\\rho_{crit} c^3H_0^{-3}=1.56\\times 10^{21}h_{70}M_\\odot$.\nThe total rest mass of dark matter \nin a volume $H^{-3}$ is denoted by $Hx$; total mass-energy of all forms\nin the same volume is denoted by $H$. \nCharacteristic rms velocities and streaming masses (rest mass of $X$ in a volume\n$k_X^{-3}$) are also shown,\nfor dark matter with three different phase densities. The cases plotted correspond to\nrelativistically-decoupled thermal relics decoupling at three different effective degrees\nof freedom, corresponding to 1, 8, and 80 times that for a single standard massive\nneutrino--- ``hot'', ``warm'', and ``cool''. (For $h=0.7$, the corresponding masses are 13,\n108, and 1076 eV respectively, and the rms velocities at the present epoch are $1.3\\times\n10^{-5}$,\n$7.9\\times 10^{-7}$, and$3.6\\times 10^{-8}$, respectively).\nNote the\n long flat period with nearly constant comoving $k_X$ for the cool particles, during\nthe period when the universe\nis radiation-dominated but $X$ is nonrelativistic.\nThe difference between\nstreaming and collisional behavior during this period has a significant\neffect on the scale of filtering in the transfer function, with a sharper \ncutoff and a smaller scale (for fixed $k_X$) in the collisional Jeans limit.}\n\\end{figure}\n\n\n\\begin{figure}[htbp]\n%\\vspace{1.5in}\n%\\centerline{\\psfig{file=XY.eps}}\n%\\vspace{0.5in}\n\\caption{A sketch of the principal \nconstraints from halo structure arguments on the masses of collisional dark matter\nparticle $X$ and particle mediating its self-interactions, $Y$.\nThis plot assumes a coupling constant $e=0.1$. \nThe rightmost region is indistinguishable from standard collisionless\nCDM. The region labled ``Jeans'' \nis essentially collisionless today, but collisional before $t_{eq}$ and consistent\nwith other constraints; in this regime the particles are no longer\nfree-streaming, and the filtering scale and the\nshape of the transfer function are significantly modified by self-interactions. \nSomewhat stronger interactions lead to a conductive instability in halos; \nthe ``unstable cores'' constraint is ruled out if we require stability down to \nhalo velocities of 30 ${\\rm km \\ s^{-1}}$. \nThe leftmost region (``fluid'') produces halos which are \nso collisional they are stable against conduction for a Hubble time, \nbut is probably ruled out by the unusual fluid-dynamical behavior this\nwould cause in the trajectories of satellite galaxies and galaxies in clusters.\nThe upper constraint comes from suppression of the annihilation channel (by the inability\nto radiate $Y$); if\nthis does not apply (that is, if there there no $\\bar X$ around) then parallel,\nsomewhat higher constraints come from suppressing dissipation by $Y$ radiation, or\nfrom the prohibition against bound $X$ atoms.\n The bottom\nconstraint corresponds to a phase-packing limit for giant galaxies; this last \nconstraint on mass applies for relativistically-decoupled light relics only, and is\nten times higher if we use the limit from dwarf spheroidals.}\n\\end{figure}\n\n%\\centerline{\\psfig{file=figure1.ps}}\n%\\centerline{\\psfig{file=figure2.ps}}\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002330.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem{aaronson}\nAaronson, M. 1983, ApJ 266, L11\n\\bibitem{atrio}\nAtrio-Barandela, F., and Davidson, S. 1997, Phys. Rev. D 55, 5886 \n\\bibitem{bardeen}\nBardeen, J. et al. 1986, Astrophys. J. 304, 15\n\\bibitem{battye}\nBattye, R. A. and Shellard, E. P.S. 1994, Nucl. Phys. B423, 260\n\\bibitem{binney}\nBinney, J. and Tremaine, S. 1987, {\\it Galactic Dynamics}, (Princeton:\nPrinceton University Press)\n\\bibitem{blumenthal}\nBlumenthal, G.\n Pagels, H. and Primack, J. R. 1982, Nature, 299, 37\n\\bibitem{bond}\nBond, J. R., Efstathiou, G., and Silk, J. 1980, Phys. Rev. Lett. 45, 1980\n\\bibitem{frank}\nvan den Bosch, F. et al. 1999, Astron. J., submitted (astro-ph/9911372)\n\\bibitem{bullock}\nBullock, J. S. et al. 2000, MNRAS in press, astro-ph/9908159\n\\bibitem{carignan}\nCarignan, C. 1985, Astrophys. J.S 58, 107\n\\bibitem{carlson}\nCarlson, E. D., Machacek, M. E. and Hall, L. J. 1992, Astrophys. J. 398, 43\n\\bibitem{colin}\n Colin, P., Avila-Reese, V., \nand\n Valenzuela, O. 2000,\nsubmitted to the Astrophysical Journal, astro- ph/ 0004115 \n\\bibitem{colombi}\nColombi, S., Dodelson, S., and Widrow, L. M.1996, Ap. J. 458, 1\n\\bibitem{cowsik}\nCowsik, R., and McClelland, J. 1972, Phys. Rev. Lett. 29, 669\n\\bibitem{croft}\nCroft, R. A. C. et al. 1999, Astrophys. J. 520, 1\n\\bibitem{dalcanton}\nDalcanton, J. and Hogan, C. J. 2000, submitted to Astrophys. J., astro-ph/0004381\n\\bibitem{dave}\nDave, R., Hernquist, L, Katz, N., Weinberg, D. H. 1999, Astrophys. J. 511, 521 \n\\bibitem{delaix}\nde Laix, A., Scherrer, R. J., and Schaefer, Astrophys. J. 452, 495\n\\bibitem{dodelson}\nDodelson, S. and Widrow, L. M. 1994, Phys. Rev. Lett. 72, 17\n\\bibitem{dubinski}\nDubinski, J. and Carlberg, R. 1991, Astrophys. J. 378, 496\n\\bibitem{faber}\nFaber, S. and Lin, D. 1983, Astrophys. J. 266, L21\n\\bibitem{fukugita}\nFukugita, M., Hogan, C. J., and Peebles, P. J. E. 1998,\nAstrophys. J. 503, 518\n\\bibitem{fuller}\nFuller, G., 1999, preprint\n\\bibitem{gerhard}\nGerhard, O. E. and Spergel, D. N. 1992, Astrophys. J. 389, L9\n\\bibitem{gerstein}\nGerstein, S. S. and Zeldovich, Ya. B. 1966, ZhETF Pis'ma Red. 4,174\n\\bibitem{ghigna}\nGhigna, S., Moore, B., Governato, F., Lake, G., Quinn, T., and Stadel, J.\n1999, Astrophys. J. submitted (astro-ph/9910166)\n\\bibitem{hannestad}\nHannestad, S., 1999, astro-ph/9912558\n%\\bibitem{hoganlens}\n%Hogan, C. J., 1999 Astrophys. J. 527, 42, astro-ph/9811290\n%\\bibitem{hoganwarm}\n%Hogan, C. J. 1999, astro-ph/9912549\n\\bibitem{hoganrees}\nHogan, C. J. and Rees, M. J. 1988, Phys. Lett. B205, 28\n\\bibitem{hogangoldstone}\nHogan, C. J. 1995, Phys. Rev. Lett. 74, 3105\n\\bibitem{johnston}\nJohnston, K. V., Majewski, S. R., Siegel, M. H., Reid, I. N.,\nand Kunkel, W. E. 1999, Astron. J. 118, 1719\n\\bibitem{kamionkowski}\nKamionkowski, M. and Liddle, A. R. 1999, astro-ph/9911103\n\\bibitem{klypin}\nKlypin, A., Kravtsov, A. V., Valenzuela, O., and Prada, F. 1999, Astrophys. J., 523, 32\n\\bibitem{kolb}\nKolb, E. W. and Turner, M. S. 1990, {\\it The Early Universe},\n(Redwood City: Addison-Wesley)\n\\bibitem{lake}\nLake, G. 1990, Astrophys. J. 356, L43\n\\bibitem{landau}\nLandau, L. D. and Lifschitz, E. M. 1958, {\\it Statistical Physics},\n(Reading: Addison-Wesley)\n\\bibitem{magorrian}\nMagorrian, J. et al. 1998, Astron. J. 115, 2285\n\\bibitem{mateo}\nMateo, M. 1998, Ann. Rev. Astr. Astrophys. 36, 435\n\\bibitem{melott} \n Melott, A. and Schramm, D. N. 1985 Astrophys. J. 298, 1 \n\\bibitem{mohapatra}\nMohapatra, R. N. and Teplitz, V. L. 2000, astro-ph/0001362\n\\bibitem{moore98}\nMoore, B., Governato, F., Quinn, T., Stadel, J., and Lake, G. 1998, Astrophys. J. 499, L5\n\\bibitem{moore99a}\nMoore, B., Ghigna, S., Governato, F., Lake, G., Quinn, T., Stadel, J.,\nand Tozzi, P. 1999, Astrophys. J. 524, L19\n\\bibitem{moore99b}\nMoore, B., Quinn, T., Governato, F., Stadel, J., and Lake, G. 1999,\nMNRAS, submitted (astro-ph/9903164)\n\\bibitem{navarrosteinmetz}\nNavarro, J. F. and Steinmetz, M. 1999, Astrophys. J., in press (astro-ph/9908114)\n\\bibitem{nfw}Navarro, J. F., Frenk, C. S. and White, S. D. M. 1996,\nMNRAS 462, 563\n\\bibitem{olszewski}\nOlszewski, E. and Aaronson, M. 1987, Astron. J. 94, 657\n\\bibitem{ostriker}\nOstriker, J. P., astro-ph/9912548, Phys. Rev. Lett., submitted\n\\bibitem{pagels}\nH. Pagels and J.R. Primack 1982, Phys. Rev. Lett., 48, 223\n\\bibitem{peacock}\nPeacock, J. A. 1999, {\\it Cosmological Physics}, (Cambridge: Cambridge University Press)\n\\bibitem{peebles}\nPeebles, P. J. E. 1993, {\\it Principles of Physical Cosmology},\n(Princeton: Princeton University Press)\n\\bibitem{pickering}\nPickering, T. E., van Gorkom, J. H., Impey, C. D., and Quillen, A. C. 1999,\nAstron. J. 118,765-776\n\\bibitem{cdm}\nPrimack, J. R. 1997, in Formation of Structure in the Universe, ed. A. Dekel\nand J. P. Ostriker, astro-ph/9707285\n\\bibitem{primack}\n Primack, J. R. and Blumenthal, G. in\nFormation and Evolution of Galaxies and Large Structures in the\nUniverse, J. Audouze and J. Tran Thanh Van, eds. (Reidel, Dordrecht,\n1983) pp. 163-183; reprinted in Beyond the Standard Model,\nJ.Tran Thanh Van, ed. (Editions Frontieres, 1983) pp. 445-464\n\\bibitem{ralston}\nRalston, J. P. and Smith, L. L. 1991, Astrophys. J. 367, 54\n\\bibitem{shi}\nShi, X., and Fuller, G. M. 1999, Phys. Rev. Lett. 82, 2832\n\\bibitem{sommerlarsen}\nSommer-Larsen, J., and Dolgov, A. 1999, astro-ph/9912166\n\\bibitem{spergel}\nSpergel, D. N. and Steinhardt, P. J. 1999, astro-ph/9909386\n\\bibitem{swaters}\nSwaters, R. 1999, Ph.D. thesis, Groningen\n\\bibitem{swaters2}\nSwaters, R. A., Madore, B. A., and Trewhella, M. 2000, Astrophys. J. in press, astro-ph/0001277\n\\bibitem{tremaine}\nTremaine, S. and Gunn, J. E. 1979, Phys. Rev. Lett. 42, 407\n\\bibitem{tyson}\nTyson, J. A., Kochanski, G. P., and Dell'Antonio, I. P. 1998,\nAstrophys. J. 498,L107\n\\bibitem{vandenbosch}\nvan den Bosch, F. C., Robertson, B. E., Dalcanton, J. J.,\n \\& de Blok, W. J. G. 2000, Astron. J. 119, 1579.\n\\bibitem{wadsley}\nWadsley, J. et al. 1999, in preparation\n\\bibitem{whiterees}\nWhite, S. D. M., and Rees, M. J. 1978, MNRAS 183, 341\n\\bibitem{white}\nWhite, M. and Croft, R. A. C. 2000, astro-ph/0001247\n\\bibitem{williams}\n Williams, L. L. R., Navarro, J. F., Bartelmann, M. 1999,\nAstrophys. J. 527,535\n\\bibitem{zeldovich}\nZeldovich, Ya. B. and Novikov, I.D. 1971,\n{\\it Relativistic Astrophysics}, vol. 1 (Chicago: University of Chicago press)\n\\end{thebibliography}"
}
] |
astro-ph0002331
|
CO on Titan: More Evidence for a Well-Mixed Vertical Profile
|
[] |
We report new interferometric observations of the $\COjtwo$ rotational transition on Titan. We find that the spectrum is best fit by a uniform profile of 52 ppm, with estimated errors of 6 ppm (40 to 200 km) and 12 ppm (200 to 300 km).
|
[
{
"name": "gurwelltext.tex",
"string": "%\\documentstyle[12pt,aaspp4,psfig]{article}\n\\documentstyle[12pt,emulateapj,psfig]{article}\n%%----------------------------------------------------------------------------\n%% Mathematical constructs and notation\n%%\n\\def\\scinot#1#2{\\ {\\fam0 \\rm #1\\ \\times \\ 10^{#2}}}\n\\def\\tover#1#2{{\\strut\\displaystyle #1 \\over \\strut\\displaystyle #2}}\n%%----------------------------------------------------------------------------\n%% Substitutions I want\n%%\n\\def\\asec{\\ifmmode^{\\prime\\prime}\\else$\\null^{\\prime\\prime}$\\fi}\n\\def\\deg{\\ifmmode^\\circ\\else$\\null^\\circ\\ $\\fi}\n\\def\\eg{{\\rm e.g., }}\n\\def\\etal{{\\it et al.\\ }}\n\\def\\ie{{\\rm i.e., }}\n\\def\\sec{{\\fam0 ''\\hskip-5pt .\\hskip+2pt}}\n%%----------------------------------------------------------------------------\n%% Chemical species\n%%\n\\def\\CHfour{{\\fam0 CH_4}}\n\\def\\CO{{\\fam0 CO}}\n\\def\\COjone{{\\fam0 CO}\\ (1-0)}\n\\def\\COjtwo{{\\fam0 CO}\\ (2-1)}\n\\def\\COjthree{{\\fam0 CO}\\ (3-2)}\n\\def\\CeighteenO{{\\fam0 C^{18}O}}\n\\def\\twelveCO{{\\fam0 ^{12}CO}}\n\\def\\thirteenCO{{\\fam0 ^{13}CO}}\n\\def\\twelveCOjone{{\\fam0 ^{12}CO}\\ (1-0)}\n\\def\\twelveCOjtwo{{\\fam0 ^{12}CO}\\ (2-1)}\n\\def\\twelveCOjthree{{\\fam0 ^{12}CO}\\ (3-2)}\n\\def\\thirteenCOjone{{\\fam0 ^{13}CO}\\ (1-0)}\n\\def\\thirteenCOjtwo{{\\fam0 ^{13}CO}\\ (2-1)}\n\\def\\COtwo{{\\fam0 CO_2}}\n\\def\\thirteenCOtwo{{\\fam0 ^{13}CO_2}}\n\\def\\Htwo{{\\fam0 H_2}}\n\\def\\water{{\\fam0 H_2O}}\n\\def\\HtwoO{{\\fam0 H_2O}}\n\\def\\Ntwo{{\\fam0 N_2}}\n\\def\\Otwo{{\\fam0 O_2}}\n\\def\\SOtwo{{\\fam0 SO_2}}\n\\def\\CHthree{{\\fam0 CH_3}}\n\\def\\HCthreeN{{\\fam0 HC_3N} }\n%%----------------------------------------------------------------------------\n%% Units\n%%\n\\def\\cmmone{{\\fam0\\, cm^{-1}}}\n\\def\\cmmtwo{{\\fam0\\, cm^{-2}}}\n\\def\\cmmthree{{\\fam0\\, cm^{-3}}}\n\\def\\micron{{\\fam0\\, \\mu m}}\n\\def\\mmone{{\\fam0\\, m^{-1}}}\n\\def\\msmone{{\\fam0\\, m\\ s^{-1}}}\n\\def\\smone{{\\fam0\\, sec^{-1}}}\n\n%%----------------------------------------------------------------------------\n%% Formats for bibliography in the Icarus style\n%%\n\\def\\rppr#1#2#3#4#5#6{\\rm {#1}\\ #2.\\ #3.\\ {\\it #4}\\ \n {\\bf #5},\\ #6.\\par}\n\\def\\rbk#1#2#3#4{\\rm { #1}\\ #2.\\ {\\it #3}.\\ #4\\par}\n\n\n\\begin{document}\n\n\n\n\\received{ }\n\\accepted{ }\n\\journalid{ }{ }\n\\articleid{ }{ }\n\\slugcomment{ }\n\n\n\\lefthead{ }\n\\righthead{ }\n\n\\title{CO on Titan: More Evidence for a Well-Mixed \nVertical Profile}\n\n\\altaffiltext{1}{\\it phone: (617) 495-7292, FAX: (617) 495-7345, e-mail:\nmgurwell@cfa.harvard.edu}\n\n\\altaffiltext{2}{\\it phone: (626) 395-6186, FAX: (626) 585-1917, e-mail:\ndom@gps.caltech.edu}\n\n\\center{Mark A. Gurwell\\altaffilmark{1}}\n\\center{\\it Harvard--Smithsonian Center for Astrophysics, \\\\\n\t60 Garden St., Cambridge, MA 02138}\n\n\\centerline{and}\n\n\\center{Duane O. Muhleman\\altaffilmark{2}}\n\\center{\\it Division of Geological and Planetary Sciences, \nCalifornia Institute of Technology, Pasadena, \nCalifornia 91125}\n\n\n\\center{Submitted to Icarus: February 9, 2000}\n\n\\raggedright\n\n\\begin{abstract}\n\nWe report new interferometric observations of the $\\COjtwo$\nrotational transition on Titan. We find that the spectrum is best fit\nby a uniform profile of 52 ppm, with estimated errors of 6 ppm\n(40 to 200 km) and 12 ppm (200 to 300 km).\n\n\\end{abstract}\n\n\\parindent 20pt\n\\parskip 0pt\n\n\\section{Introduction}\n\nThe atmosphere of Titan exhibits a complex photochemistry, and many\nnitriles and hydrocarbons have been detected by Voyager spacecraft and\nfrom Earth. Until recently, however, only two oxygen-bearing species\nhad been detected on Titan: $\\COtwo$ (observed by Voyager 1;\n\\cite{samu1983}) and CO (observed from Earth; \\cite{lutz1983}).\n\nThe presence of oxygenated molecules is interesting because the\natmosphere of Titan is strongly reducing. The cold temperatures of\nthe lower stratosphere and the troposphere imply that $\\COtwo$\ncondenses out of the lower atmosphere and is continuously deposited on\nthe surface. To sustain the carbon dioxide abundance a source of\noxygen is needed, and it is generally assumed to be supplied in water\nfrom bombardment of the upper atmosphere by icy grains. In this model\nvaporized water is quickly photolyzed to produce OH, and OH reacts\nwith hydrocarbon radicals such as $\\CHthree$ to produce CO. CO in\nturn reacts with OH to produce $\\COtwo$ (\\cite{samu1983},\n\\cite{yung1984}, \\cite{toub1995}, \\cite{lara1996}). While $\\COtwo$ has\na short lifetime (order 10$^3$--10$^4$ years), the photochemical\nlifetime of $\\CO$ in the atmosphere of Titan is estimated to be very\nlong ($\\sim 10^9$ years; \\cite{yung1984}, \\cite{chas1991}).\n\nObservationally the missing piece of the oxygen chemistry has been\nthe source, water. Recently, water vapor was detected in the\nupper atmosphere of Titan by the Short Wavelength Spectrometer (SWS)\naboard the Infrared Satellite Observatory (\\cite{cous1998}). With\nobservations of the three major components of oxygen chemistry, it is\nnow possible to check the internal consistency of photochemical\nmodels, and to compare the oxygen chemistry and water infall rate of\nTitan with the other giant planets, particularly Saturn\n(\\cite{feuc1997}, \\cite{cous1998}).\n\nUnderstanding the oxygen chemistry relies on accurate knowledge of the\nabundance and distribution of each species. A longstanding discussion\nregarding the CO distribution in Titan's atmosphere, spanning more\nthan a decade, has been primarily directed toward determining if CO is\nwell-mixed (\\cite{mart1988}, \\cite{gurw1995}, \\cite{hida1998}). Since\nthe residence lifetime of CO is long compared to transport timescales,\nthe molecular weight of $\\CO$ is the same as for the dominant $\\Ntwo$\ngas, and the atmosphere is never cold enough for CO to condense,\ncarbon monoxide should be uniformly mixed in the Titan atmosphere to\nhigh altitudes.\n\nObservational data, however, give conflicting results. Table 1\nprovides data on the CO abundance as measured by ground-based\nobservers over the past 17 years. These observations have been\nsensitive to either the troposphere (near- and mid-IR) or the\nstratosphere (millimeter). The data in Table 1 show that no clear\nconsensus has emerged regarding the CO abundance, either in the\ntroposphere or the stratosphere.\n \nIn this Note, we present an analysis of new interferometric\nobservations of the $\\COjtwo$ line on Titan. The results of this\nstudy have important implications for our understanding of the oxygen\nbudget and photochemistry of the stratosphere of Titan.\n\n\\section{Observations and Data Reduction}\n\nObservations of the $\\COjtwo$ rotational transition (rest frequency\n$\\nu_0$=230.5380 GHz) on Titan were made on November 11 and 12, 1999\nwith the Owens Valley Radio Observatory Millimeter Array, located near\nBig Pine, California. The Titan ephemeris data was generated using\nthe Jet Propulsion Laboratory's Horizons on-line system\n(\\cite{gior1996}). Titan was approaching eastern elongation with\nrespect to Saturn, with a separation increasing from $\\sim$145$''$ to\nmore than 200$''$ over the two day period.\n\nThe interferometer was aligned in a fairly compact configuration,\nproviding a synthesized beam of roughly 2\\arcsec$\\times$2.5\\arcsec~ at\nthe observing frequency, while Titan's apparent surface diameter was\n0.86$''$ (at a distance of 8.2165 AU). Titan was observed on each\nnight over a period of about 7 hours, when it was above 30$\\deg$\nelevation. A single measurement on each baseline consisted of a three\nminute integration during which the complex visibility of the source\nwas recorded. Amplitude and phase gain variations were monitored\nthrough observations of 0235+164 approximately every 20 minutes, and\nantenna pointing was checked about every two hours using 3C84. The\ntotal integration time spent on Titan equaled 238 minutes on each\nnight.\n\nThe signal was detected for each antenna pair in two correlator\nsystems: a wide-band analog cross correlator ($\\sim$1 GHz bandwidth)\nand a digital spectrometer. The CO line is significantly wider than\nthis system bandwidth, and we utilized two local oscillator tunings to\nprovide better coverage of the line: on November 11 the digital\nspectrometer measured (in two secondary LO tunings) the line in the\nupper sideband from $\\Delta\\nu = -656$ MHz $\\rightarrow +32$ MHz, and\non November 12 from $\\Delta\\nu = -32$ MHz $\\rightarrow +656$ MHz.\nSpectra in the image sideband, approximately 3 GHz lower in frequency,\nwere also recorded. The sideband signals were isolated to better than\n20 dB using a phase-switching cycle. The combination of two first and\nsecond LO tunings allowed us to ultimately measure $\\pm$650 MHz of the\ncenter frequency of each sideband at 4 MHz resolution, and $\\pm$16 MHz\nat 0.5 MHz resolution in the line core. \n\nCalibration of the digital correlator passband was done through\nobservations of 3C273 and an internal correlated noise source. The\nrelative calibration of the sidebands was accurately measured from\nobservations of Uranus, 3C273, 3C84, and 0235+164 (to $\\leq 1$\\%),\nsince nearly all weather and instrumental effects impact each sideband\nin a similar manner. We note that the ability to isolate the\nastronomical signal sidebands and record independent spectra in each\nsideband represents a significant advantage for interferometric\nrelative to single-dish observations of CO on Titan because the\nemission line is significantly broader than the spectrometer\nbandwidth. In this case the most precise measure of the\nline-to-continuum (LTC) ratio is provided by separating the sidebands.\nThis relative sideband calibration then allows for the production of\nan accurate LTC spectrum, with one sideband sensing the continuum, and\nthe other the line.\n\nThe Titan signal strength was sufficient for the application of phase\nself-calibration (see \\cite{thom1986}) to remove atmospheric phase\nvariations, which cause decorrelation of the signal, on timescales\nshorter than the standard calibration cycle. After calibration, a\ncomplete spatially unresolved (e.g. ``zero-spacing'') spectrum for\neach day was obtained by fitting the observed complex visibilities for\neach channel with a model of the Titan visibility function, correcting\nfor the spatial sampling of the interferometer. The absolute flux\nscale was provided by scaling the continuum sideband intensity to\nequal the radiative transfer model flux of Titan at 227.5 GHz,\ncorrected for the date and time of the observations (see below). The\nsame scaling factor was applied to the emission line sideband,\npreserving the relative calibration.\n\nThe resulting combined spectrum of the $\\COjtwo$ line on Titan is\nshown in Figure 1. The data clearly shows the $\\COjtwo$ line is a\nstrong emission feature in the spectrum of Titan. The image sideband\nspectrum is essentially flat except for a weak emission line due to\nthe $\\HCthreeN~(25-24)$ rotational transition at 227.419 GHz. This is\nparticularly important because it shows that the sideband isolation\nprocedure was effective to well below the noise level of the spectrum.\n\n\\section{Modeling \\& Analysis}\n\nThe radiative transfer model used to analyze the new CO data is nearly\nidentical to the one discussed in Gurwell and Muhleman (1995), and we\nonly highlight important aspects.\n\nThe basic parameters of the Titan atmosphere were derived from revised\nVoyager 1 radio occultation results (\\cite{lind1983}, \\cite{lell1990},\n\\cite{cous1995}), including an atmospheric base at 2575 km from the\ncenter of Titan, with a surface pressure and temperature of 1460\nmillibar and 96.7 K. For the thermal profile of the atmosphere we\nused an equatorial profile determined by Coustenis and B\\'ezard (1995,\ntheir profile A) based upon the occultation results and Voyager 1/IRIS\nspectra (Fig.~2) combined with model J of Yelle (1991) for the upper\natmosphere; this same model was used by Hidayat \\etal (1998) to\nanalyze their results. This model is appropriate since the\nobservations reported here are unresolved (whole-disk) spectra, which\nare heavily weighted by emission from equatorial and low latitudes.\n\nThe millimeter continuum opacity on Titan is due to collision induced\ndipole absorption by $\\Ntwo-\\Ntwo$, $\\Ntwo-$Ar, and $\\Ntwo-$CH$_4$,\nand was modeled according to the results of Courtin (1988). The\nspectroscopic parameters for the $\\COjtwo$ line were taken from the\nJPL catalog (\\cite{pick1992}; see also http://spec.jpl.nasa.gov). The\nfull Voigt lineshape profile calculation using a fast computational\nmethod (\\cite{hui1978}), integrated in pressure over atmospheric\nlayers of constant temperature, was done using a collisional\nline-broadening coefficient for $\\COjtwo$ in $\\Ntwo$ of $\\gamma = 2.21\n(T/300 ~ {\\fam0 K})^{-0.74}$ MHz mbar$^{-1}$ (\\cite{semm1987}).\nRadiative transfer calculations at appropriate frequencies were\nperformed for a variety of radial steps, including limb-sounding\ngeometries, and integrated over the apparent disk to provide the model\nwhole-disk spectrum.\n\nThe contribution functions ($W(z) = e^{-\\tau}d\\tau/dz$) for several\nfrequency offsets from the $\\COjtwo$ line center are shown in Fig. 2,\nfor a single raypath at the disk center. This function describes the\nrelative contribution of different regions of the atmosphere to the\nemitted radiation at each frequency. The plotted functions assume a\nCO abundance of 50 ppm, constant with altitude. The $\\Delta\\nu=-3000$\nMHz contribution function corresponds to the middle of the continuum\n(lower) sideband, and is dominated by the collision induced opacity of\n$\\Ntwo$. The other functions correspond to the emission (upper)\nsideband, and are dominated by $\\COjtwo$ opacity. The full line\nsenses the atmosphere from 40 km (the tropopause) to 400 km. However,\nthe range from 200 to 400 km is sounded mostly in the inner 4 MHz of\nthe line core. At 4 MHz spectral resolution we are limited to sensing\nthe CO abundance from the tropopause to $\\sim$200 km. The 0.5 MHz\nspectrum of the line core pushes this upper bound to near 350 km\nin the absence of noise. Thermal noise on the spectral measurements\nin practice limit our sensitivity to $\\sim 300$ km.\n\n\\subsection{Best-fit Uniform CO Distribution}\n\nThe radiative transfer model was run for a series of uniform CO\ndistributions from $q$(CO)=10 to 90 ppm, in steps of 10 ppm.\nResulting spectra are shown in Fig.~1 (in steps of 20 ppm for\nclarity). The model spectra have been convolved to the measurement\nspectral resolution of the data in each panel. The model calculations\nshow that the continuum (lower) sideband emission is essentially\nunaffected by the CO distributions considered, and is an excellent\ncontinuum measurement. The model gives a flux at 227.5 GHz\nof 1.565 Jy for the geometry of the observations, equal to a\ndisk-average Rayleigh-Jeans brightness temperature of 71.4 K.\n\nEven by eye, the 50 ppm uniform model provides an exceptionally good\nfit to the data at both resolutions. The 50 ppm model gives an RMS\nresidual of 86.8 mJy for the 4 MHz data, with models of 40 and 60 ppm\ngiving RMS residuals that are factors of 1.4 and 1.1 times larger,\nrespectively. Given that a large number of channels are involved\n(324), even an 10\\% increase in RMS residuals is quite significant.\nThe 0.5 MHz spectrum is also consistent with this model. A rigorous\nleast-squares analysis for the best-fit uniform profile gives a formal\nsolution of 52$\\pm$2 ppm from 40 to 300 km.\n\n\\subsection{Best-fit Non-Uniform CO Distribution}\n\nAn iterative least-squares inversion algorithm (following\n\\cite{gurw1995}) based on the radiative transfer model was utilized to\nsolve for a best-fit non-uniform CO distribution. The logarithm of\nthe CO distribution was constrained to be a linear function of\naltitude. This constrained solution tests whether a gradient in the\nCO distribution is consistent with the observed spectrum.\n\nWe find that the best-fit non-uniform profile, with formal error, is\n48$\\pm$4 ppm at 40 km, rising to 60$\\pm$10 ppm at 300 km. The RMS\nresidual is 86.1 mJy, representing less than 1\\% improvement in the\nresidual over the best-fit uniform profile.\n\n\\subsection{Error Estimates and the Best-fit CO Distribution}\n\nThe formal errors quoted in the above sections are the direct results\nof the least-squares analyses, and therefore do not take into account\nerrors in the radiative transfer modeling or the calibration of the\nspectrum.\n\nTo test whether the continuum emission model is a serious source of\nerror (since the spectrum is calibrated by referencing to the\ncontinuum sideband data), we recomputed the continuum emission at\n227.5 GHz, scaling the collision induced dipole absorption calculated\nfrom the data of Courtin (1988) by factors of 0.5 and 2. The\ncalculated emission results were indistinguishable from the nominal\nmodel, which can be explained as the result of two factors. First,\nthe collision induced continuum absorption scales as the square of\npressure, and is therefore a very steep function of\naltitude. Therefore, increasing (or decreasing) the absorption\ncoefficient even by factors of two will only increase the peak of the\ncontribution function by a small fraction of a scale height. Second,\nthe peak of the contribution function is right at the tropopause,\nwhere the temperature gradient is near zero. The result is that the\nemission change is very small, and we estimate that this error is\nabout 1\\%. \n\nThe spectrum sidebands were calibrated assuming the QSO calibration\nsources had a spectral index of -0.5 (e.g. flux $\\propto \\nu^{-0.5}$).\nHowever, the spectral index of these types of sources vary over the\nrange of 0 to -1, and could lead to a calibration error of\napproximately 1\\% in the relative calibration over the 3 GHz\ndifference in the sidebands.\n\nAdding the calibration errors in quadrature, we find an error in the\nrelatively calibrated spectrum of about 1.4\\%. Using the uniform\ndistribution models discussed in section 3.1, we find that a 3\\% error\nin the relative calibration could lead to an error of roughly 10 ppm\nin a worst-case situation (we note that this does not include a\nrefitting of the {\\it lineshape}, which would tend to reduce this\nerror; hence this is a worst-case estimate). The calibration error is\nthen about 6 ppm using this scaling. For the uniform model solution,\nthe formal error is significantly smaller than this calibration error\nestimate, and we believe that the error of our measurement is\ntherefore about 6 ppm.\n\nNoting that the non-uniform solution only improves the RMS residuals by\n1\\% at best, and that the formal errors on the non-uniform solution\nencompass our uniform solution, we favor the uniform model for the CO\ndistribution, which is in agreement with the current understanding of\nthe chemistry of CO in the atmosphere of Titan. The high resolution data\nprovides the information on altitudes above 200 km, and as can be seen\nin Fig.~1 this data has a higher RMS noise (by a factor of $\\sim$2);\nthis increases our error estimate by a factor of about two over this\naltitude range. We therefore find that the $\\COjtwo$ spectrum is best fit\nby a uniform profile of 52 ppm, with estimated errors of 6 ppm\n(40 to 200 km) and 12 ppm (200 to 300 km).\n\n\\section{Discussion}\n\nThe results presented here are nearly identical to our previous\nestimate of the CO distribution based on observations of the $\\COjone$\ntransition (\\cite{gurw1995}) and consistent with the original\nmeasurement of tropospheric CO (\\cite{lutz1983}). Taken together,\nthese measurements suggest a vertical profile of CO that is constant\nwith altitude, at about 52 ppm, from the surface to at least 300 km.\n\nThese results are at odds with the recent measurements of Noll (1996),\nwho found a tropospheric abundance of 10 ppm, and Hidayat \\etal\n(1998), who found a stratospheric CO abundance of around 27 ppm (Table\n1). Noll (1996) explored the possibility that their simple reflecting\nlayer was not the surface, but a higher altitude 'haze' layer. If the\nreflecting layer was at 0.9 bar (14 km) the spectrum was best fit with\na CO abundance of 60 ppm. However, based on other evidence they found\nthis model less satisfactory than a surface reflecting layer. The\nresults of Hidayat \\etal come from an analysis of several lines of CO,\nincluding the $\\COjone$ and $\\COjtwo$ lines; the discrepancy between\ntheir results and ours does not appear to be due to differences in\nmodeling the atmosphere of Titan, but derives from differences in the\nmeasurement techniques and the resulting calibrated spectra\n(A.~Marten, personal communication). However, we do point out that\nthe interferometric method does offer advantages over single-dish\nobservations for measuring the very broad lines of CO from the\natmosphere of Titan.\n\nWe find the model of a uniform distribution of CO in the atmosphere of\nTitan provides a good fit to our data, but we cannot rule out a\ndifference between the tropospheric and stratospheric CO abundance,\nsince our data is insensitive to the lower atmosphere. A final\nconfirmation of the abundance of CO and its vertical distribution\nrequires further near- and mid-IR measurements of CO in the\ntroposphere.\n\n\\vskip 25pt\n\n\\center{\\bf Acknowledgements}\n\nThis work was supported in part by NASA grant NAG5-7946.\n\n\\begin{thebibliography}{ }\n\n\n\n\\bibitem[Chassefi\\`ere and Cabane 1991]{chas1991}\\rppr{\nChassefi\\`ere, D.~and M.~Cabane}{1991}{Stratospheric depletion of CO\non Titan} {Geophys.~Res.~Lett.}{18}{467-470}\n\n\\bibitem[Courtin 1988]{cour1988}\\rppr{Courtin, R.}{1988}{Pressure-induced\nabsorption coefficients for radiative transfer calculations in Titan's\natmosphere}{Icarus}{75}{245-254}\n \n\\bibitem[Coustenis and B\\'ezard 1995]{cous1995}\\rppr{Coustenis, A.,\nand B.~B\\'ezard}{1995}{Titan's atmosphere from Voyager infrared\nobservations ~ IV. Latitudinal variations of temperature and\ncomposition}{Icarus}{115}{126-140}\n\n\\bibitem[Coustenis \\etal 1998]{cous1998}\\rppr{Coustenis, A.,\nA.~Salama, E.~Lellouch, Th.~Encrenaz, G.L.~Bjoraker, S.E.~Samuelson,\nTh.~de Graauw, H.~Feuchtgruber, and M.F.~Kessler}{1998}{Evidence for\nwater vapor in Titan's atmosphere from ISO/SWS\ndata}{Astron.~Astrophys.}{336}{L85-L89}\n\n\\bibitem[Feuchtgruber \\etal 1997]{feuc1997}\\rppr{Feuchtgruber, H.,\nE.~Lellouch, Th.~de Graauw, B.~B\\'ezard, Th.~Encrenaz, and\nM.~Griffin}{1997}{External supply of oxygen tot he atmospheres of the\ngiant planets}{Nature}{389}{159-162}\n\n\\bibitem[Giorgini \\etal 1996]{gior1996}\\rppr{Giorgini, J.D.,\nD.K.~Yeomans, A.B.~Chamberlin, P.W.~Chodas, R.A.~Jacobson,\nM.S.~Keesey, J.H.~Lieske, S.J.~Ostro, E.M.~ Standish, and\nR.N.~Wimberly}{1996}{JPL's on-line solar system data\nservice}{B.A.A.S.}{28}{No.~3, 1158}\n\n\\bibitem[Gurwell and Muhleman 1995]{gurw1995}\\rppr{Gurwell, M.A., and\nD.O.~Muhleman}{1995}{CO on Titan: Evidence for a well-mixed vertical\nprofile}{Icarus}{117}{375-382}\n\n\\bibitem[Hidayat \\etal 1998]{hida1998}\\rppr{Hidayat, T., A.~Marten,\nB.~B\\'ezard, D.~Gautier, T.~Owen, H.E.~Matthews, and G.~Paubert}\n{1998}{Millimeter and submillimeter heterodyne observations of Titan:\nthe vertical profile of carbon monoxide in its stratosphere}\n{Icarus}{133}{109-133}\n\n\\bibitem[Hui \\etal 1978]{hui1978}\\rppr{Hui, A.K., B.H.~Armstrong, and\nA.A. Wray}{1978}{Rapid computation of the Voigt and complex error\nfunctions}{J.~Quant.~Spectrosc.~Radiat.~Transfer}{19}{509-516}\n \n\\bibitem[Lara \\etal 1996]{lara1996}\\rppr{Lara, L.M., E.~Lellouch,\nJ.J.~L\\'opez-Moreno, and R.~Rodrigo}{1996}{Vertical distribution of\nTitan's atmospheric neutral constituents}{J.~Geophys.~Res.}{101}\n{23261-23238}\n\n\\bibitem[Lellouch 1990]{lell1990}\\rppr{Lellouch, E.}{1990}{Atmospheric\nmodels of Titan and Triton}{Ann.~Geophysicae}{8}{653-660}\n \n\\bibitem[Lindal \\etal 1983]{lind1983}\\rppr{Lindal, G.F., G.E.~Wood,\nH.B.~Hotz, D.N.~Sweetnam, V.R.~Eshleman, and G.L.~Tyler}{1983}{The\natmosphere of Titan: An analysis of the Voyager 1 radio occultation\nmeasurements}{Icarus}{53}{348-363}\n \n\\bibitem[Lutz \\etal 1983]{lutz1983}\\rppr{Lutz, B.L., C.~de Bergh,\nand T.~Owen}{1983}{Titan: Discovery of carbon monoxide in its\natmosphere}{Science}{220}{1374-1375}\n \n\\bibitem[Marten \\etal 1988]{mart1988}\\rppr{Marten, A., D.~Gautier,\nL.~Tanguy, A.~Lecacheux, C.~Rosolen, and G.~Paubert}{1988}{Abundance\nof carbon monoxide in the stratosphere of Titan from millimeter\nheterodyne observations}{Icarus}{76}{558-562}\n \n\\bibitem[Muhleman \\etal 1984]{muhl1984}\\rppr{Muhleman,\nD.O., G.L.~Berge, and R.T.~Clancy}{1984}{Microwave measurements of\ncarbon monoxide on Titan}{Science}{223}{393-396}\n \n\\bibitem[Noll \\etal 1996]{noll1996}\\rppr{Noll, K.S., T.R.~Geballe,\nR.F.~Knacke, and Y.J.~Pendleton}{1996}{Titan's 5$\\micron$ spectral\nwindow: carbon monoxide and the albedo of the surface}\n{Icarus}{124}{625-631}\n\n\\bibitem[Paubert \\etal 1984]{paub1994}\\rppr{Paubert, G., D.~Gautier,\nand R.~Courtin}{1984}{The millimeter spectrum of Titan: Detectability\nof HCN, HC$_3$N, CH$_3$CN, and the CO abundance.}{Icarus}{60}{599-612}\n \n\\bibitem[Pickett \\etal 1992]{pick1992}\\rbk{Pickett, H.M.,\nR.L.~Poynter, and E.A.~Cohen}{1992} {Submillimeter, Millimeter and\nMicrowave Spectral Line Catalog}{JPL Publication 80--23, Rev. 3}\n \n\\bibitem[Samuelson \\etal 1983]{samu1983}\\rppr{Samuelson, R.E.,\nW.C.~Maguire, R.A.~Hanel, V.G.~Kunde, D.E.~Jennings, Y.L.~Yung,\nand A.C.~Aikin}{1983}{$\\COtwo$ on Titan} {J.~Geophys.~Res.}\n{88}{8709-8715}\n\n\\bibitem[Semmoud-Monnanteuil and Colmont 1987]{semm1987}\\rppr{\nSemmoud-Monnanteuil, N., and J.M.~Colmont}{1987}{Pressure broadening of\nmillimeter lines of carbon monoxide}{J.~Molec.~Spec.}{126}{210-219}\n\n\\bibitem[Thompson, Moran, and Swenson 1986]{thom1986}\\rbk{Thompson,\nA.R., J.M.~Moran, and G.W.~Swenson Jr.}{1986}{Interferometry and\nSynthesis in Radio Astronomy}{1st ed. Wiley, New York}\n\n\\bibitem[Toublanc \\etal 1995]{toub1995}\\rppr{Toublanc, D.,\nJ.P.~Parisot, J.~Brillet, D.~Gautier, F.~Raulin, and\nC.P.~McKay}{1995}{Photochemical modeling of Titan's\natmosphere}{Icarus}{113}{2-26}\n\n\\bibitem[Yelle 1991]{yell1991}\\rppr{Yelle, R.V.}{1991}{Non-LTE models\nof Titan's upper atmosphere}{Astrophys.~J.}{383}{380-400}\n \n\\bibitem[Yung \\etal 1984]{yung1984}\\rppr{Yung, Y.L., M.~Allen, and\nJ.P.~Pinto}{1984}{Photochemistry of the atmosphere of Titan:\nComparison between model and observations}\n{Astrophys.~J.~Suppl.~Ser.}{55}{465-506}\n\n\\end{thebibliography}\n\n\\vfill\n\n\\centerline{TABLE 1. Observations of CO in Titan's Atmosphere}\n\\label{tab:coobs}\n\\begin{center}\n\\begin{tabular}{cccl}\n\\hline\\noalign{\\smallskip}\n\nAltitude & Mixing ratio (ppm)$^a$ & Wavelength & ~~~Reference \\\\\n\n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n\nTroposphere & 48$^{+100}_{-32}$ & 1.57$\\micron$ & \\cite{lutz1983} \\\\\nStratosphere & 60$\\pm$40$^b$ & 2.6 mm & \\cite{muhl1984} \\\\\nStratosphere & 2$^{+2}_{-1}$ & 2.6 mm & \\cite{mart1988} \\\\\nStratosphere & 50$\\pm$10 & 2.6 mm & \\cite{gurw1995} \\\\\nTroposphere & 10$^{+10}_{-5}$ & 4.8$\\micron$ & \\cite{noll1996} \\\\\nStratosphere & 27$\\pm$5$^c$ & 2.6, 1.3, 0.9 mm & \\cite{hida1998} \\\\\n\n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n\nStratosphere & 52$\\pm$6 & 1.3 mm & this work \\\\\n\n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\n\\noalign{\\smallskip}\n\n\\multispan4 {$^a$Mixing ratio defined as N(CO)/N(Total), i.e.~{\\it\n not} referenced to $\\Ntwo$. \\hfill} \\\\\n\n\\noalign{\\smallskip}\n\n\\multispan4 {$^b$Reanalyzed by Paubert \\etal (1984): 75$^{+105}_{-45}$\nppm \\hfill}\\\\\n\n\\noalign{\\smallskip}\n\n\\multispan4 {$^c$Non-uniform model: 29$\\pm$5 ppm (60 km), 24$\\pm$5\nppm (175 km), 4.8$\\pm$2 ppm (350 km) \\hfill}\\\\\n\n\\end{tabular}\n\\end{center}\n\n%%%% Here come the Figure captions %%%%%\n\n\\vfill\n\n\\begin{center}\n{\\sc Figure Captions}\n\\end{center}\n\\figcaption{ Calibrated $\\COjtwo$ spectrum obtained November 11--12,\n1999 with the OVRO millimeter interferometer, and model spectra\ncalculated assuming uniform profiles of $q$(CO)=10, 30, 50, 70, and 90\nppm. The largest panel shows the full spectrum in both sidebands at 4\nMHz resolution. The continuum sideband is flat except for a weak,\nnarrow emission feature due to the $\\HCthreeN (25-24)$ rotational\ntransition near $\\Delta\\nu=-3119$ MHz. The larger inset concentrates\non the upper sideband data, containing the CO emission feature\n($\\pm$650 MHz of the line center) at 4 MHz resolution. The small\ninset provides the inner $\\pm$16 MHz of the line core at 0.5 MHz\nresolution. For each panel, the model spectra are convolved to the\nspectral resolution of the data.\n\\label{fig1}}\n\n\\figcaption{({\\it left}) Contribution functions for selected frequencies\nnear the $\\COjtwo$ line center for the Titan atmosphere, at normal\nincidence. These functions were calculated assuming a uniform \nprofile $q$(CO)=50 ppm. ~ ({\\it right}) The model atmospheric\ntemperature profile derived from Voyager 1 radio occultation\nmeasurements and IRIS spectra, and smoothly merged to fit a non-LTE\nmodel of the upper atmosphere (adopted from \\cite{cous1995}).\n\\label{fig2} }\n\n\\vfill\n\n\\newpage\n\n\\centerline{\\psfig{figure=gurwellfig1.ps,angle=0.,height=\\vsize}}\n\n\\newpage\n\n\\centerline{\\psfig{figure=gurwellfig2.ps,angle=0.,height=\\vsize}}\n\t\t\t \n\\end{document}\n"
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"name": "astro-ph0002331.extracted_bib",
"string": "\\begin{thebibliography}{ }\n\n\n\n\\bibitem[Chassefi\\`ere and Cabane 1991]{chas1991}\\rppr{\nChassefi\\`ere, D.~and M.~Cabane}{1991}{Stratospheric depletion of CO\non Titan} {Geophys.~Res.~Lett.}{18}{467-470}\n\n\\bibitem[Courtin 1988]{cour1988}\\rppr{Courtin, R.}{1988}{Pressure-induced\nabsorption coefficients for radiative transfer calculations in Titan's\natmosphere}{Icarus}{75}{245-254}\n \n\\bibitem[Coustenis and B\\'ezard 1995]{cous1995}\\rppr{Coustenis, A.,\nand B.~B\\'ezard}{1995}{Titan's atmosphere from Voyager infrared\nobservations ~ IV. Latitudinal variations of temperature and\ncomposition}{Icarus}{115}{126-140}\n\n\\bibitem[Coustenis \\etal 1998]{cous1998}\\rppr{Coustenis, A.,\nA.~Salama, E.~Lellouch, Th.~Encrenaz, G.L.~Bjoraker, S.E.~Samuelson,\nTh.~de Graauw, H.~Feuchtgruber, and M.F.~Kessler}{1998}{Evidence for\nwater vapor in Titan's atmosphere from ISO/SWS\ndata}{Astron.~Astrophys.}{336}{L85-L89}\n\n\\bibitem[Feuchtgruber \\etal 1997]{feuc1997}\\rppr{Feuchtgruber, H.,\nE.~Lellouch, Th.~de Graauw, B.~B\\'ezard, Th.~Encrenaz, and\nM.~Griffin}{1997}{External supply of oxygen tot he atmospheres of the\ngiant planets}{Nature}{389}{159-162}\n\n\\bibitem[Giorgini \\etal 1996]{gior1996}\\rppr{Giorgini, J.D.,\nD.K.~Yeomans, A.B.~Chamberlin, P.W.~Chodas, R.A.~Jacobson,\nM.S.~Keesey, J.H.~Lieske, S.J.~Ostro, E.M.~ Standish, and\nR.N.~Wimberly}{1996}{JPL's on-line solar system data\nservice}{B.A.A.S.}{28}{No.~3, 1158}\n\n\\bibitem[Gurwell and Muhleman 1995]{gurw1995}\\rppr{Gurwell, M.A., and\nD.O.~Muhleman}{1995}{CO on Titan: Evidence for a well-mixed vertical\nprofile}{Icarus}{117}{375-382}\n\n\\bibitem[Hidayat \\etal 1998]{hida1998}\\rppr{Hidayat, T., A.~Marten,\nB.~B\\'ezard, D.~Gautier, T.~Owen, H.E.~Matthews, and G.~Paubert}\n{1998}{Millimeter and submillimeter heterodyne observations of Titan:\nthe vertical profile of carbon monoxide in its stratosphere}\n{Icarus}{133}{109-133}\n\n\\bibitem[Hui \\etal 1978]{hui1978}\\rppr{Hui, A.K., B.H.~Armstrong, and\nA.A. Wray}{1978}{Rapid computation of the Voigt and complex error\nfunctions}{J.~Quant.~Spectrosc.~Radiat.~Transfer}{19}{509-516}\n \n\\bibitem[Lara \\etal 1996]{lara1996}\\rppr{Lara, L.M., E.~Lellouch,\nJ.J.~L\\'opez-Moreno, and R.~Rodrigo}{1996}{Vertical distribution of\nTitan's atmospheric neutral constituents}{J.~Geophys.~Res.}{101}\n{23261-23238}\n\n\\bibitem[Lellouch 1990]{lell1990}\\rppr{Lellouch, E.}{1990}{Atmospheric\nmodels of Titan and Triton}{Ann.~Geophysicae}{8}{653-660}\n \n\\bibitem[Lindal \\etal 1983]{lind1983}\\rppr{Lindal, G.F., G.E.~Wood,\nH.B.~Hotz, D.N.~Sweetnam, V.R.~Eshleman, and G.L.~Tyler}{1983}{The\natmosphere of Titan: An analysis of the Voyager 1 radio occultation\nmeasurements}{Icarus}{53}{348-363}\n \n\\bibitem[Lutz \\etal 1983]{lutz1983}\\rppr{Lutz, B.L., C.~de Bergh,\nand T.~Owen}{1983}{Titan: Discovery of carbon monoxide in its\natmosphere}{Science}{220}{1374-1375}\n \n\\bibitem[Marten \\etal 1988]{mart1988}\\rppr{Marten, A., D.~Gautier,\nL.~Tanguy, A.~Lecacheux, C.~Rosolen, and G.~Paubert}{1988}{Abundance\nof carbon monoxide in the stratosphere of Titan from millimeter\nheterodyne observations}{Icarus}{76}{558-562}\n \n\\bibitem[Muhleman \\etal 1984]{muhl1984}\\rppr{Muhleman,\nD.O., G.L.~Berge, and R.T.~Clancy}{1984}{Microwave measurements of\ncarbon monoxide on Titan}{Science}{223}{393-396}\n \n\\bibitem[Noll \\etal 1996]{noll1996}\\rppr{Noll, K.S., T.R.~Geballe,\nR.F.~Knacke, and Y.J.~Pendleton}{1996}{Titan's 5$\\micron$ spectral\nwindow: carbon monoxide and the albedo of the surface}\n{Icarus}{124}{625-631}\n\n\\bibitem[Paubert \\etal 1984]{paub1994}\\rppr{Paubert, G., D.~Gautier,\nand R.~Courtin}{1984}{The millimeter spectrum of Titan: Detectability\nof HCN, HC$_3$N, CH$_3$CN, and the CO abundance.}{Icarus}{60}{599-612}\n \n\\bibitem[Pickett \\etal 1992]{pick1992}\\rbk{Pickett, H.M.,\nR.L.~Poynter, and E.A.~Cohen}{1992} {Submillimeter, Millimeter and\nMicrowave Spectral Line Catalog}{JPL Publication 80--23, Rev. 3}\n \n\\bibitem[Samuelson \\etal 1983]{samu1983}\\rppr{Samuelson, R.E.,\nW.C.~Maguire, R.A.~Hanel, V.G.~Kunde, D.E.~Jennings, Y.L.~Yung,\nand A.C.~Aikin}{1983}{$\\COtwo$ on Titan} {J.~Geophys.~Res.}\n{88}{8709-8715}\n\n\\bibitem[Semmoud-Monnanteuil and Colmont 1987]{semm1987}\\rppr{\nSemmoud-Monnanteuil, N., and J.M.~Colmont}{1987}{Pressure broadening of\nmillimeter lines of carbon monoxide}{J.~Molec.~Spec.}{126}{210-219}\n\n\\bibitem[Thompson, Moran, and Swenson 1986]{thom1986}\\rbk{Thompson,\nA.R., J.M.~Moran, and G.W.~Swenson Jr.}{1986}{Interferometry and\nSynthesis in Radio Astronomy}{1st ed. Wiley, New York}\n\n\\bibitem[Toublanc \\etal 1995]{toub1995}\\rppr{Toublanc, D.,\nJ.P.~Parisot, J.~Brillet, D.~Gautier, F.~Raulin, and\nC.P.~McKay}{1995}{Photochemical modeling of Titan's\natmosphere}{Icarus}{113}{2-26}\n\n\\bibitem[Yelle 1991]{yell1991}\\rppr{Yelle, R.V.}{1991}{Non-LTE models\nof Titan's upper atmosphere}{Astrophys.~J.}{383}{380-400}\n \n\\bibitem[Yung \\etal 1984]{yung1984}\\rppr{Yung, Y.L., M.~Allen, and\nJ.P.~Pinto}{1984}{Photochemistry of the atmosphere of Titan:\nComparison between model and observations}\n{Astrophys.~J.~Suppl.~Ser.}{55}{465-506}\n\n\\end{thebibliography}"
}
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astro-ph0002332
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Probing black hole X-ray binaries with the Keck telescopes
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The advent of the large effective apertures of the Keck telescopes has resulted in the determination with unprecedented accuracy of the mass functions and mass ratios of faint ($R \approx 21$ mag) X-ray transients (GS~2000+25, GRO~J0422+32, Nova Oph 1977, Nova Vel 1993), as well as constraining the main-sequence companion star parameters and producing images of the accretion disks around the black holes.
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[
{
"name": "black2.tex",
"string": "% Article to demonstrate style for SPIE Proceedings\n% Special instructions are included in this file after the\n% symbol %>>>>\n% The following commands have been added in the LaTeX style \n% file (spie.sty) and will not be understood in other styles:\n% \\supit{}, \\authorinfo{}, \\skiplinehalf, \\keywords{}\n% The bibliography style file is called spiebib.bst, \n% which replaces the normal LaTeX style unstr.bst. \n% One departure from the specifications found in unstr.bst \n% is the addition of the `journal' field to the \\inproceedings \n% entry type, whose use is demonstrated in Ref. 5 (Hanson93c).\n\n\\documentstyle[spie]{article} \n%>>>> psfig.sty to include EPS figures; comment out if not needed\n\\input{psfig} \n\n\\title{Probing black hole X-ray binaries with the Keck telescopes}\n\n%>>>> The author is responsible for formatting the \n% author list and their institutions. Use \\skiplinehalf \n% to separate author list from addresses and between each address.\n% The correspondence between each author and his/her address can be \n% indicated with a superscript in italics, \n% which is easily obtained with \\supit{}.\n\n\\author{Emilios T. Harlaftis\\supit{a} and Alexei V. Filippenko\\supit{b} \n\\skiplinehalf \n\\supit{a}Institute of Astronomy and Astrophysics, National Observatory \\\\\nof Athens, P. O. Box 20048, Athens - 118 20, Greece\\\\\n\\supit{b}Department of Astronomy, University of California,\n Berkeley, CA 94720-3411, USA\\\\\n}\n\n%>>>> Further information about the authors, other than their \n% institution and addresses, should be included as a footnote, \n% which is facilitated by the \\authorinfo{} command.\n\n\\authorinfo{Further author information: (Send correspondence to \nE. T. Harlaftis)\\\\E. T. Harlaftis: E-mail: ehh@astro.noa.gr\\\\ \nA. V. Filippenko: E-mail: alex@astro.berkeley.edu}\n%% NB: when using amstex, you need to use @@ instead of @\n \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n%>>>> uncomment following for page numbers\n% \\pagestyle{plain} \n%>>>> uncomment following to start page numbering at 301 \\setcounter{page}{301} \n \n \\begin{document} \n \\maketitle \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n\\begin{abstract}\nThe advent of the large effective apertures of the Keck telescopes has\nresulted in the determination with unprecedented accuracy of the mass\nfunctions and mass ratios of faint ($R \\approx 21$ mag) X-ray\ntransients (GS~2000+25, GRO~J0422+32, Nova Oph 1977, Nova Vel 1993),\nas well as constraining the main-sequence companion star parameters and \nproducing images of the accretion disks around the black holes. \n\\end{abstract}\n\n%>>>> Please include a list of keywords after the abstract \n\n\\keywords{black hole physics, interacting binaries, novae, \nX-ray binaries, X-ray transients, \nNova Oph 1977, GS~2000+25, GRO~J0422+32, Nova Vel 1993} \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{INTRODUCTION}\n\\label{sect:intro} % \\label{} allows reference to this section\n\n\nZel'dovich and Novikov (1966) were the first to propose the technique\nwhich is still in use for ``weighing\" black holes. They suggested\nthat black holes could be detected indirectly from light emitted\nthrough the interaction with a donor star in an X-ray binary system.\nThe motion of the donor star around the black hole would produce a\nradial velocity sinusoidal curve which could be detected from the\nDoppler shifts of the photospheric absorption lines of the donor star.\nThe semi-amplitude ($K$) of the curve together with the binary period\n($P$) determine the mass function of the black hole (a lower limit to\nits mass), using Kepler's third law: $f_{x} = PK^3/(2\\pi G)$. Indeed,\nX-ray binaries were found in the late 1960s and the first black-hole\ncandidate, Cyg X-1, in 1971 (Oda et al. 1971). Efforts in measuring\nthe mass of Cyg X-1 were affected by uncertainties in\nthe evolution of the massive donor star, and with a low mass function\n($f_{x}=0.22\\pm0.01~M_{\\odot}$; Bolton 1975) this was not regarded as\nunequivocal evidence for a black hole (see Herrero et al. 1995 for\nthe most recent work).\n\n\\section{HUNTING FOR BLACK HOLES IN X-RAY NOVAE}\n \nIn the 1980s the observational effort was turned to X-ray novae (XRNs,\na sub-group of low-mass X-ray binaries). Unlike classical novae, XRNs\nare accretion-driven events that show disk outbursts with a typical\nrise of 8--10 mag in a few days and a subsequent decline over several\nmonths. After the XRN has subsided into quiescence, the accretion\ndisk does not dominate the observed flux, rendering the companion star\nvisible. The low-mass companion star allows the mass function of the\nblack hole, a good approximation of the mass in a high-inclination\nsystem, to be determined. In the 1990s, X-ray satellites found 6 XRNs\nwith identified companion stars in the optical (Nova Muscae 1991,\nCheng et al. 1992; Nova Persei 1992, Casares et al. 1995a and\nreferences therein; Nova Sco 1994, Bailyn et al. 1995; Nova Vel 1993,\nFilippenko et al. 1999; GRO J1719-24, e.g., Ballet et al. 1993;\nXTE~J1550-564, e.g., Smith et al. 1998).\n\nThe prototype target in the 1980s was A0620--00, but unfortunately its\nmass function was close to the maximum mass of a neutron star\n($f_{x}=3.2\\pm0.2~M_{\\odot}$; McClintock and Remillard 1986). It was\nnot until 1992 that a mass function of a candidate black hole in the XRN\n1989, GS~2023+338, was found to be much heavier than the maximum mass\nof a neutron star ($f_{x}=6.08\\pm0.06~M_{\\odot}$; Casares et\nal. 1992). Since then, efforts have been directed toward\nmeasuring actual masses, thus producing the first observed mass\ndistribution of black holes (Bailyn et al. 1998; Miller et al. 1998;\nfor the theoretical distribution see Fryer 1999). The determination\nof the masses of stellar remnants after supernova explosions is\nessential for an understanding of the late stages of evolution of\nmassive stars. Very recently, the first observational evidence for\nthe progenitor, a supernova or hypernova with a mass $> 30 M_{\\odot}$,\nthat produced the black hole of $7.0\\pm0.2 ~M_{\\odot}$ in GRO~J1655-40\nwas found with the Keck-I telescope (from high metal abundances that\nwere presumably deposited onto the surface of the companion F5IV-star\nby the supernova explosion; Israelian et al. 1999).\n\n \\begin{figure*}\n%>>>> following adds vertical space needed for figure; \n% uncomment if figure is to be pasted into manuscript\n%% \\vspace{7.5cm}\n \\begin{center}\n \\begin{tabular}{c}\n \\psfig{figure=j0422.ps,width=10cm} \n \\end{tabular}\n \\end{center}\n \\caption[example] \n%>>>> use \\label inside caption to get Fig. number with \\ref{}\n { \\label{fig:example}\t \n{\\it Bottom:} the radial velocity curve of the companion \nstar to the black hole GRO~J0422+32 as extracted from spectra near\nH$\\alpha$ with Keck-I/LRIS (Harlaftis et al. 1999). {\\it\nTop:} the radial velocity curve of the companion star to the black\nhole GRO~J0422+32 as extracted from 4.2-m WHT/ISIS near-infrared\nspectra (8450-8750~\\AA) (Casares et al. 1995a). The\nreduction in the individual measurement uncertainties is a factor of\nfour using Keck-I. The sinusoidal fit to the radial velocities gives\n$K = 338\\pm39$ km s$^{-1}$ with the WHT data and $K = 372\\pm10$ km\ns$^{-1}$ with the Keck data for the radial velocity semi-amplitude of\nthe companion star. This yields better accuracy in the estimate of\nthe lower limit of the black hole's mass, from $P K^3 /(2 \\pi G) =\n0.85\\pm0.30~M_{\\odot}$ to $1.13\\pm0.09~M_{\\odot}$ for the\nlow-inclination system GRO~J0422+32. WHT data courtesy of Jorge Casares.} \n \\end{figure*} \n\n\n\n\\section{RADIAL VELOCITY CURVES}\n\n\nUtilizing the Doppler effect produced by the shifting photospheric\nlines due to the orbital motion of the companion star around the black\nhole, but now with the 10-m Keck-I and Keck-II telescopes, Filippenko\nand his collaborators have produced the four\nmost accurate mass functions ($f_{x}=5.0\\pm0.1\n~M_{\\odot}$, $1.2 \\pm0.1~M_{\\odot}$, $4.7\\pm0.2~M_{\\odot}$,\n$3.2\\pm0.1~M_{\\odot}$, respectively for GS~2000+25, GRO~J0422+32, Nova\nOph 1977, Nova Vel 1993; Filippenko et al. 1995a, 1995b, 1997, 1999). \nFigures 1 and 2 show the great improvement\nthat the large aperture of Keck offers in comparison to 4-m-class\ntelescopes in extracting radial velocity curves of the motion of the\ndonor star around the black hole by cross-correlating main-sequence\ntemplate spectra with the observed spectra.\n\n\n\\section{THE MAIN SEQUENCE COMPANION STAR}\n\nThe line broadening function affecting the absorption lines of the\nobject spectra consists of the convolution of the instrumental profile\n(full width at half-maximum = 108 km s$^{-1}$) with the companion star's \nrotational broadening profile (of width $\\upsilon \\sin i$), \nwith further smearing due to changes in the orbital\nvelocity of the companion star during a given exposure. The exposure\ntime for each object spectrum ($T_{\\rm exp}~\\approx$ 25--40 min)\nresulted in orbital smearing of the lines up to $2\\pi K_{\\rm c} T_{\\rm\nexp}/P$, which can range up to 242 km s$^{-1}$; hence, the template\nspectra were subsequently smeared by the amount corresponding to the\norbital motion through convolution with a rectangular profile and the\nresulting template spectrum was further broadened from 2 to 150 km\ns$^{-1}$ by convolution with the Gray (1976) rotational profile. We\nscaled the blurred template spectrum by a factor $0 < f < 1$ to match\nthe absorption-line strengths in the Doppler-corrected average\nspectrum. Finally, the simulated template spectrum (i.e., smeared and\nbroadened) was subtracted from the Doppler-corrected average spectrum\nof Nova Oph 1977 and $\\chi^{2}$ was computed from a smoothed version\nof the residual spectrum. The minimum $\\chi^{2}$ gives the optimal\n$\\upsilon \\sin i$, $f$, and spectral type of the companion star (for\nmore details see Harlaftis et al. 1996, 1997, 1999).\n\n\n \\begin{figure*}\n%>>>> following adds vertical space needed for figure; \n% uncomment if figure is to be pasted into manuscript\n%% \\vspace{7.5cm}\n \\begin{center}\n \\begin{tabular}{c}\n \\psfig{figure=gs2000.ps,width=10cm} \n \\end{tabular}\n \\end{center}\n \\caption[example] \n%>>>> use \\label inside caption to get Fig. number with \\ref{}\n { \\label{fig:example} {\\it Bottom:} the radial velocity curve of\n the companion star to the black hole GS~2000+25 as extracted from\n spectra near H$\\alpha$ with Keck-I/LRIS in just 1 night (Harlaftis\n et al. 1996). {\\it Top:} the radial velocity curve of the\n companion star to the black hole GRO~J0422+32 as extracted from\n 4.2-m WHT/ISIS in 3 nights (Casares et al. 1995b). The sinusoidal\n fit to the radial velocities gives $K = 520\\pm16$ km s$^{-1}$ with\n the WHT data and $K = 520\\pm5$ km s$^{-1}$ with the Keck data for\n the radial velocity semi-amplitude of the companion star. This\n yields better accuracy in the estimate of the lower limit of the\n black hole's mass, from $PK^{3}/(2\\pi G) =\n 5.02\\pm0.46~M_{\\odot}$ to $5.01\\pm0.15~M_{\\odot}$ for the\n high-inclination system GS~2000+25. WHT data courtesy of Jorge\n Casares.} \\end{figure*}\n\nFigure 3 summarizes the procedure we follow to deconvolve the\nmain-sequence spectrum from the target spectrum. The spectrum of a\nM2~V template (BD~$+44^{\\circ}2051$) is shown at the bottom, binned to\n124 km s$^{-1}$ pixels (=4 pixels and similar to the instrumental\nresolution). This template was then treated so that its line profiles\nsimulate those of the GRO~J0422+32 spectra. The smearing in radial\nvelocity due to the orbital line broadening while exposing are applied to\nindividual copies of the M2 template, and these were subsequently\naveraged using weights identical to those corresponding to the\nGRO~J0422+32 spectra. Next, a rotational broadening profile\ncorresponding to $\\upsilon \\sin i = 50$ km s$^{-1}$ was applied; the\nresult is the second spectrum from the bottom in Figure 3. The\nspectrum above is the Doppler-corrected average of the GRO~J0422+32\ndata in the rest frame of the M2~V template. Finally, the residual\nspectrum is shown at the top after 0.61 times the simulated M2~V\ntemplate ($f = 0.61 \\pm 0.04$ for M2; Table 4) was subtracted from the\nDoppler-shifted average spectrum. The M-star absorption lines and TiO\nbands are evident in the Doppler-corrected average, and they are\nalmost completely removed by subtraction of the template spectrum\n(e.g., the Na~I~D line). Emission from He{\\small~I} $\\lambda$5876\nbecomes prominent after subtraction of the M2~V template and weak\nemission from He{\\small~I} $\\lambda$6678 is also present. Note that\nthere is no evidence for Li{\\small~I} $\\lambda$6708 absorption, to an\nequivalent width upper limit of 0.13~\\AA\\ ($1\\sigma$) relative \nto the original continuum, except in GS~2000+25 (see Mart\\'\\i n\net al. 1994 for lithium in X-ray binaries).\n\n \\begin{figure*}\n%>>>> following adds vertical space needed for figure; \n% uncomment if figure is to be pasted into manuscript\n%% \\vspace{7.5cm}\n \\begin{center}\n \\begin{tabular}{c}\n \\psfig{figure=average.ps,height=12cm,angle=-90} \n \\end{tabular}\n \\end{center}\n \\caption[example] \n%>>>> use \\label inside caption to get Fig. number with \\ref{}\n { \\label{fig:example}\t \n\nResults of the technique followed to extract $\\upsilon \\sin i$, $f$,\nand the spectral type of the companion star. From bottom to top: the M2~V\ntemplate BD +$44^{\\circ}2051$, the M2~V template convolved with a\ncomplex profile to simulate effects of orbital smearing and rotational\nbroadening ($\\upsilon \\sin i = 50$ km s$^{-1}$), the Doppler-shifted\naverage spectrum of GRO~J0422+32, and the residual spectrum of\nGRO~J0422+32 after subtraction of the M2~V template times $f =\n0.61$. The spectra are binned to 124 km s$^{-1}$ pixels. An offset of\n0.6 mJy was added to each successive spectrum for clarity. The\nresidual spectrum is dominated by the disk spectrum (e.g., broad\nH$\\alpha$ and He{\\small~I} lines in emission). Several other lines are\nalso marked, such as the characteristic Fe{\\small~I}+Ca{\\small~I}\nblend at 6495~\\AA\\ in G--M stars, as well as the Ca{\\small~I}\n6717~\\AA\\ and Fe{\\small~I} lines surrounding the absent Li{\\small~I}\nline at 6707.8~\\AA. }\n\\end{figure*}\n\n\n\\section{THE MASS RATIO OF THE BLACK HOLE BINARIES}\n\nDetermination of the mass ratio (from the rotational\nbroadening of the photospheric lines in the companion star) and the\ninclination (inferred from the ellipsoidal modulations of the\ncompanion star), when combined with the mass function, can fully\ndescribe the system's parameters and the masses of the binary\ncomponents. The mass ratio $q = M_{2}/M_{1}$ is found by measuring\nthe rotational broadening of the absorption lines of the companion,\n$\\upsilon \\sin i$, through the relation\n\n\\[ \\frac{\\upsilon \\sin i}{K_{c}} = \n0.46 \\left[ (1+q)^{2} ~q \\right] ^{1/3}, \\]\n\n\\noindent\nwhich is valid since the binary period is so short that the companion\nstar is tidally locked to the black hole. We determined mass ratios \nfor the first time for binaries as faint as 21 mag using the \n$\\chi^{2}$ optimization technique described in the\nprevious section to extract the rotational broadening of the\nabsorption lines of the donor star (Harlaftis et al. 1996, 1997, 1999).\nThe complete results of \nthe analysis of the Keck data are given in Table 1.\n\n\n\\begin{table} [h]\n\\caption{Keck-deduced parameters}\n\\renewcommand{\\arraystretch}{1.4}\n\\setlength\\tabcolsep{5pt}\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|}\n\\hline\\noalign{\\smallskip}\n&Oph 1977 & GRO~J0422+32 & GS~2000+25 & Vel 1993\\\\\n\\hline\n\\rule[-1ex]{0pt}{3.5ex} $K_{c}$ (km s$^{-1}$)&441$\\pm$6 &372$\\pm$10 &520$\\pm$5 &475$\\pm$6\\\\\n\\hline\n\\rule[-1ex]{0pt}{3.5ex} $f_{x}$ &4.65$\\pm$0.21 &1.13$\\pm$0.09 &5.01$\\pm$0.15 &3.17$\\pm$0.12\\\\\n\\hline\n\\rule[-1ex]{0pt}{3.5ex} Spectral type& K5V$\\pm$2&M2V$^{+2}_{-1}$ &K5V$^{+1}_{-2}$&K8V$\\pm$2\\\\\n\\hline\n\\rule[-1ex]{0pt}{3.5ex} $f$ \\% & 30$\\pm$3 & 61$\\pm$4 & 94$\\pm$5 &\\\\\n \\hline\n\\rule[-1ex]{0pt}{3.5ex} \n$\\upsilon \\sin$~i (km s$^{-1}$)& $50^{+17}_{-23}$&90$^{+22}_{-27}$&86$\\pm$8&\\\\\n\\hline\n\\rule[-1ex]{0pt}{3.5ex} $q$&0.014$^{+0.019}_{-0.012}$ & 0.116$^{+0.079}_{-0.071}$ & 0.042$\\pm$0.012 &\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\\section{THE ACCRETION DISK}\n\nThe accretion disk in its quiescent state has mainly been undetected\nso far by X-ray satellites but can be studied in the optical. \nDouble-peaked \nBalmer profiles are observed with ``S''-wave components either\nfrom the companion star (Nova Oph 1977) or the bright spot\n(GS~2000+25) and an H$\\alpha$ emissivity law is observed, \nsimilar to that seen in \ndwarf novae. An imaging technique, Doppler tomography, shows the\naccretion disks in GS~2000+25, Nova Oph 1977 and GRO~J0422+32 to be\npresent (Fig. 4). \nFurther, mass transfer from the donor star continues\nvigorously to the outer disk as evidenced by the ``bright spot,'' the\nimpact of the gas stream onto the outer accretion disk in GS~2000+25\n(Fig. 4; Harlaftis et al. 1996). \n\n \\begin{figure*}\n%>>>> following adds vertical space needed for figure; \n% uncomment if figure is to be pasted into manuscript\n% \\vspace{7.5cm}\n \\begin{center}\n \\begin{tabular}{c}\n \\psfig{figure=doppler.ps,height=12cm} \n \\end{tabular}\n \\end{center}\n \\caption[example] \n%>>>> use \\label inside caption to get Fig. number with \\ref{}\n { \\label{fig:example} The H$\\alpha$ Doppler image ({\\it top-right\n panel}) of the accretion disk surrounding the black hole GS~2000+25\n ({\\it bottom-right panel} for Nova Oph 1977), as reconstructed from\n 13 Keck-I/LRIS spectra which are also presented ({\\it top-left\n panel}; {\\it bottom-left panel} for the 12 spectra of Nova Oph\n 1977). By projecting the image in a particular direction, one\n obtains the H$\\alpha$ emission-line profile as a function of\n velocity; for example, projecting toward the top results in the\n profile at orbital phase 0.0, which has a blueshifted peak. The\n path in velocity coordinates of gas streaming from the dwarf K5\n secondary star is illustrated. The GS~2000+25 Doppler map shows a\n bright spot, at the upper left quadrant, which results from\n collision of the gas stream with the accretion disk around the\n black hole. The Nova Oph 1977 map also shows a trace of an ``S''-wave\n component which, however, is not resolved with clarity. The image\n was reconstructed by applying Doppler tomography, a maximum entropy\n technique, to the phase-resolved spectra, as described by Harlaftis\n et al. (1996, 1997, 1999). } \\end{figure*}\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%% References %%%%%\n\n%% edit the following to include your own references\n%% the entries must be in the order of citation in the manuscript text\n\n\\begin{thebibliography}{99} \n%% the last item specifies width of reference number column\n\n\\bibitem{}\nBailyn, C., et al. (1995) Nature, 378, 157\n\n\\bibitem{}\nBailyn, C. D., Jain, R. K., Coppi, P., Orosz, J. A. (1998) ApJ, 499, 367\n\n\\bibitem{}\nBallet, J., et al. (1993) IAUC No. 5874\n\n\\bibitem{}\nBolton, C. T. (1975) ApJ, 200, 269\n\n\\bibitem{}\nCasares, J., et al. (1992) Nature, 355, 614\n\n\\bibitem{}\nCasares, J., et al. (1995a) MNRAS, 276, 35 \n\n\\bibitem{}\nCasares, J., et al. (1995b) MNRAS, 277, L45\n\n\\bibitem{}\nCheng, F. H., et al. (1992) 397, 664\n\n%\\bibitem{}\n%Charles, P. A. (1999) ESO Workshop on {\\it Black Holes in\n%Binaries and Galactic Nuclei}, this Volume\n\n\\bibitem{}\nFilippenko, A. V., Matheson, T., Barth, A. J. (1995a) ApJ, 455, L139\n\n\n\\bibitem{}\nFilippenko, A. V., Matheson, T., Ho, L. C. (1995b) ApJ, 455, 614\n\n\\bibitem{}\nFilippenko, A. V., et al. (1997) PASP, 109, 461\n\n\\bibitem{}\nFilippenko, A. V., et al. (1999) PASP, 111, 969\n\n\\bibitem{}\nFryer, C. L. (1999) ApJ, 522, 413\n\n\\bibitem{}\nGray, D. F. (1976) The Observations and Analysis of Stellar Photospheres (New\n York: Wiley-Interscience), p. 373\n\n\\bibitem{}\nHarlaftis, E. T., Collier, S. J., Horne, K., Filippenko, A. V. (1999) A\\&A, 341, 491\n\n\\bibitem{}\nHarlaftis, E. T., Horne, K., Filippenko, A. V. (1996) PASP, 108, 762\n\n\\bibitem{}\nHarlaftis, E. T., Steeghs, D., Horne, K., Filippenko, A. V. (1997) AJ, 114, 1170\n\n\\bibitem{}\nHerrero, A., et al. (1995), A\\&A, 297, 556\n\n\\bibitem{}\nIsraelian, G., et al. (1999) Nature, 401, 142\n\n\\bibitem{}\nMcClintock, J. E., Remillard, R. A. (1986) ApJ, 308, 110 \n\n\\bibitem{}\nMart\\'\\i n, E., et al. (1994) ApJ, 435, 791\n\n\\bibitem{}\nMiller, J. C., Shahbaz, T., Nolan, L. A. (1998) MNRAS, 294, L25\n\n\\bibitem{}\nOda, M., et al. (1971) ApJ, 166, L10\n\n\\bibitem{}\nSmith, D. A., Marshall, F. E., Smith, E. A. (1998) IAUC No. 7008\n\n\\bibitem{}\nZel'dovich, Ya. B., Novikov, I. D. (1966) Sov. Physics -- Uspekhi, 8, 522\n\\end{thebibliography}\n\n \\end{document} \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002332.extracted_bib",
"string": "\\begin{thebibliography}{99} \n%% the last item specifies width of reference number column\n\n\\bibitem{}\nBailyn, C., et al. (1995) Nature, 378, 157\n\n\\bibitem{}\nBailyn, C. D., Jain, R. K., Coppi, P., Orosz, J. A. (1998) ApJ, 499, 367\n\n\\bibitem{}\nBallet, J., et al. (1993) IAUC No. 5874\n\n\\bibitem{}\nBolton, C. T. (1975) ApJ, 200, 269\n\n\\bibitem{}\nCasares, J., et al. (1992) Nature, 355, 614\n\n\\bibitem{}\nCasares, J., et al. (1995a) MNRAS, 276, 35 \n\n\\bibitem{}\nCasares, J., et al. (1995b) MNRAS, 277, L45\n\n\\bibitem{}\nCheng, F. H., et al. (1992) 397, 664\n\n%\\bibitem{}\n%Charles, P. A. (1999) ESO Workshop on {\\it Black Holes in\n%Binaries and Galactic Nuclei}, this Volume\n\n\\bibitem{}\nFilippenko, A. V., Matheson, T., Barth, A. J. (1995a) ApJ, 455, L139\n\n\n\\bibitem{}\nFilippenko, A. V., Matheson, T., Ho, L. C. (1995b) ApJ, 455, 614\n\n\\bibitem{}\nFilippenko, A. V., et al. (1997) PASP, 109, 461\n\n\\bibitem{}\nFilippenko, A. V., et al. (1999) PASP, 111, 969\n\n\\bibitem{}\nFryer, C. L. (1999) ApJ, 522, 413\n\n\\bibitem{}\nGray, D. F. (1976) The Observations and Analysis of Stellar Photospheres (New\n York: Wiley-Interscience), p. 373\n\n\\bibitem{}\nHarlaftis, E. T., Collier, S. J., Horne, K., Filippenko, A. V. (1999) A\\&A, 341, 491\n\n\\bibitem{}\nHarlaftis, E. T., Horne, K., Filippenko, A. V. (1996) PASP, 108, 762\n\n\\bibitem{}\nHarlaftis, E. T., Steeghs, D., Horne, K., Filippenko, A. V. (1997) AJ, 114, 1170\n\n\\bibitem{}\nHerrero, A., et al. (1995), A\\&A, 297, 556\n\n\\bibitem{}\nIsraelian, G., et al. (1999) Nature, 401, 142\n\n\\bibitem{}\nMcClintock, J. E., Remillard, R. A. (1986) ApJ, 308, 110 \n\n\\bibitem{}\nMart\\'\\i n, E., et al. (1994) ApJ, 435, 791\n\n\\bibitem{}\nMiller, J. C., Shahbaz, T., Nolan, L. A. (1998) MNRAS, 294, L25\n\n\\bibitem{}\nOda, M., et al. (1971) ApJ, 166, L10\n\n\\bibitem{}\nSmith, D. A., Marshall, F. E., Smith, E. A. (1998) IAUC No. 7008\n\n\\bibitem{}\nZel'dovich, Ya. B., Novikov, I. D. (1966) Sov. Physics -- Uspekhi, 8, 522\n\\end{thebibliography}"
}
] |
astro-ph0002333
|
{A Close-Separation Double Quasar Lensed by a Gas-Rich Galaxy} \footnote{Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract No. NAS5-26555.}
|
[
{
"author": "Michael~D.~Gregg\\altaffilmark{2,3}"
},
{
"author": "Lutz~Wisotzki\\altaffilmark{4,5}"
},
{
"author": "Robert~H.~Becker\\altaffilmark{2,3}"
},
{
"author": "Jos\\'e~Maza\\altaffilmark{6}"
},
{
"author": "Paul~L.~Schechter\\altaffilmark{5,7}"
},
{
"author": "Richard~L.~White\\altaffilmark{8}"
},
{
"author": "Michael~S.~Brotherton\\altaffilmark{9}"
},
{
"author": "and Joshua~N.~Winn\\altaffilmark{5,7}"
}
] |
In the course of a Cycle~8 snapshot imaging survey with STIS, we have discovered that the z=1.565 quasar HE~0512$-$3329 is a double with image separation 0\farcs644, differing in brightness by only 0.4~magnitudes. This system is almost certainly gravitationally lensed. Although separate spectra for the two images have not yet been obtained, the possibility that either component is a Galactic star is ruled out by a high signal-to-noise composite ground-based spectrum and separate photometry for the two components: the spectrum shows no trace of any zero redshift stellar absorption features belonging to a star with the temperature indicated by the broad band photometry. The optical spectrum shows strong absorption features of \MgII, \MgI, \FeII, \FeI, and \CaI, all at an identical intervening redshift of z=0.9313, probably due to the lensing object. The strength of \MgII\ and the presence of the other low-ionization absorption features is strong evidence for a damped \Lya\ system, likely the disk of a spiral galaxy. Point spread function fitting to remove the two quasar components from the STIS image leads to a tentative detection of a third object which may be the nucleus of the lensing galaxy. The brighter component is significantly redder than the fainter, due to either differential extinction or microlensing.
|
[
{
"name": "preprint.tex",
"string": "%\\documentclass {aastex}\n\\documentclass [preprint]{aastex}\n%\\usepackage{aasms4}\n\\newcommand{\\Lya}{Ly$\\alpha$}\n\\newcommand{\\MgII}{\\ion{Mg}{2}}\n\\newcommand{\\MgI}{\\ion{Mg}{1}}\n\\newcommand{\\CaI}{\\ion{Ca}{1}}\n\\newcommand{\\CaII}{\\ion{Ca}{2}}\n\\newcommand{\\CIII}{\\ion{C}{3}]}\n\\newcommand{\\CIV}{\\ion{C}{4}}\n\\newcommand{\\FeI}{\\ion{Fe}{1}}\n\\newcommand{\\FeII}{\\ion{Fe}{2}}\n\\def\\roma#1{\\ifmmode{#1}\\else{$#1$}\\fi} \n\\def\\extra#1{\\roma{\\phantom{\\rm#1}}}\n\\def\\kms{{\\rm km\\,s^{-1}\\,}} % km s-1\n\\def\\kmsmpc{\\roma{\\rm\\,km\\,s^{-1}\\,Mpc^{-1}}} % kmsMpc\n\\newcommand\\Ho{\\roma{\\,\\rm H_{\\circ}}} % Ho\n\\newcommand\\qo{\\roma{\\,\\rm q_{\\circ}}} % qo\n\n\\slugcomment{{\\em Astronomical Journal, in Press}} \n\n\\begin{document}\n\n\\title {{\\bf A Close-Separation Double Quasar Lensed by a Gas-Rich\nGalaxy} \\footnote{Based on observations with the NASA/ESA Hubble Space\nTelescope, obtained at the Space Telescope Science Institute, which is\noperated by the Association of Universities for Research in Astronomy,\nInc. under NASA contract No. NAS5-26555.}}\n\n\\author{Michael~D.~Gregg\\altaffilmark{2,3},\nLutz~Wisotzki\\altaffilmark{4,5},\nRobert~H.~Becker\\altaffilmark{2,3},\nJos\\'e~Maza\\altaffilmark{6},\nPaul~L.~Schechter\\altaffilmark{5,7},\nRichard~L.~White\\altaffilmark{8},\nMichael~S.~Brotherton\\altaffilmark{9}, \nand\nJoshua~N.~Winn\\altaffilmark{5,7}\n}\n%\\authoremail{gregg@igpp.llnl.gov}\n\n\\altaffiltext{2}{Physics Dept., University of California, Davis, CA\n95616; gregg,bob@igpp.llnl.gov}\n\\altaffiltext{3}{Institute for Geophysics and Planetary Physics,\nLawrence Livermore National Laboratory}\n\\altaffiltext{4}{Hamburger Sternwarte, Germany; lwisotzki@hs.uni-hamburg.de}\n%Gojenbergsweg 112, D-21029, Hamburg, Germany}\n\\altaffiltext{5}{Massachusetts Institute of Technology;\nschech@achernar.mit.edu, jnwinn@mit.edu}\n\\altaffiltext{6}{Universidad de Chile; jose@das.uchile.cl}\n\\altaffiltext{7}{Visiting Astronomer, Cerro Tololo Inter-American\nObservatory, National Optical Astronomy Observatories}\n\\altaffiltext{8}{Space Telescope Science Institute; rlw@stsci.edu}\n\\altaffiltext{9}{Kitt Peak National Observatory; mbrother@noao.edu}\n\n\n\\begin{abstract}\n\nIn the course of a Cycle~8 snapshot imaging survey with STIS, we have\ndiscovered that the z=1.565 quasar HE~0512$-$3329 is a double with\nimage separation 0\\farcs644, differing in brightness by only\n0.4~magnitudes. This system is almost certainly gravitationally\nlensed. Although separate spectra for the two images have not yet\nbeen obtained, the possibility that either component is a Galactic\nstar is ruled out by a high signal-to-noise composite ground-based\nspectrum and separate photometry for the two components: the spectrum\nshows no trace of any zero redshift stellar absorption features\nbelonging to a star with the temperature indicated by the broad band\nphotometry. The optical spectrum shows strong absorption features of\n\\MgII, \\MgI, \\FeII, \\FeI, and \\CaI, all at an identical intervening\nredshift of z=0.9313, probably due to the lensing object. The\nstrength of \\MgII\\ and the presence of the other low-ionization\nabsorption features is strong evidence for a damped \\Lya\\ system,\nlikely the disk of a spiral galaxy. Point spread function fitting to\nremove the two quasar components from the STIS image leads to a\ntentative detection of a third object which may be the nucleus of the\nlensing galaxy. The brighter component is significantly redder than\nthe fainter, due to either differential extinction or microlensing.\n\n\\end{abstract}\n\n\\keywords{gravitational lensing; quasars: individual}\n\n\\section {Introduction}\n\nThe study of gravitationally lensed quasars has become a powerful tool\nfor addressing a number of astrophysical questions. In particular,\nconcentrating on studying the lensing objects themselves provides a\nsample of distant galaxies selected by mass rather than by light\n(Kochanek et al.\\ 1999). Because the component separations scale with\nthe square root of the mass of the lens, sampling the low end of the\nlens mass function becomes difficult from the ground, particularly in\nthe optical/IR, for separations $\\lesssim 1\\arcsec$. This\nobservational bias leads to a preponderance of massive spheroidal\ngalaxies in the present sample of lenses and at least partly accounts\nfor the relative lack of known close-separation lenses, which are\npredicted to exist by theoretical models of the lensing phenomenon\n(e.g.\\ Maoz \\& Rix 1993; Rix et al.\\ 1994; Jain et al.\\ 1999). There\nare currently only seven systems with separations $\\leq 0\\farcs9$ out\nof 43 confirmed lensed quasars listed by Kochanek et al.\\ (1998).\n\nWe are now well into a Cycle~8 snapshot survey of up to 300 targets,\naimed specifically at finding close-separation lensed quasars using\nthe imaging capabilities of STIS (Kimble et al.\\ 1997; Woodgate et\nal.\\ 1998) on board the Hubble Space Telescope. The probability that\na quasar is lensed increases with redshift and apparent magnitude\n(Turner, Ostriker, \\& Gott 1984); the snapshot survey targets bright,\nhigh redshifts quasars selected using estimates for the probability of\nlensing by Kochanek (1998). The results of the full snapshot survey\nwill appear in time (Gregg et al.\\ 2000, in prep.); here we report the\ndiscovery of a close-separation gravitationally lensed quasar from\namong the first 80 snapshot targets.\n\n\\section {Observations}\n\n\\subsection {Discovery}\n\nThe quasar HE~0512$-$3329 was originally identified in the Hamburg/ESO\nsurvey for bright QSO's (Wisotzki et al.\\ 1996). With $B$ = 17.0 and z\n= 1.569 (Reimers, K\\\"{o}hler, \\& Wisotzki 1996), HE~0512$-$3329 had an\na priori probability of $\\sim 1.3\\%$ of being lensed, fairly typical\nfor the targets in our snapshot survey. The STIS snapshot sequence,\nobtained on 1999 August 26, consists of $3 \\times 40$s CR-split\nexposures in the clear 50CCD (CL) aperture and one additional 80s\nCR-split exposure in the longpass F28$\\times$50LP (LP) filter. The effective\nwavelength and full width half maximum of the CL band are 6167.6\\AA\\\nand 4410\\AA\\ and for the LP band are 7333\\AA\\ and 2721\\AA. The STIS\nimages reveal two point sources with a separation of 0\\farcs644. The\ndifference in brightness between the two components~A and B is $\\Delta\nCL = 0.35$ and $\\Delta LP = 0.49$; this small difference is\ncharacteristic of the more highly magnified lensed systems, which our\nselection technique is designed to favor.\n\nThe lensing hypothesis was strengthened by examining the discovery\nspectrum of HE~0512$-$3329 which shows a rather typical quasar energy\ndistribution having emission lines of \\CIV~1549 and \\CIII~1909 (see\nFigure~1 of Reimers et al.\\ 1996). If one of the two components were\na garden variety Galactic star, the strongest stellar absorption lines\nwould be easily identifiable (see below, \\S 2.3). A binary quasar is\na possible alternative explanation (Kochanek, Falco, \\& Mu\\~{n}oz\n1999), however, the discovery spectrum exhibits a strong absorption\nfeature consistent with \\MgII\\ at an intervening redshift of 0.93, and\na few weaker absorption lines of \\FeII\\ at the same redshift. These\nlow-ionization absorption features suggested that the duplicity is due\nto a lensing object at this redshift.\n\n\n\\subsection {Follow-up Spectroscopy at Keck Observatory}\n\nIn early 2000 January, we obtained a 9\\AA\\ resolution spectrum of\nHE~0512$-$3329 using the Low Resolution Imaging Spectrograph (LRIS,\nOke et al.\\ 1995) at Keck Observatory. The slit was oriented at the\nposition angle of the two quasar images on the sky, 17\\arcdeg. The\nseeing was 1\\arcsec, insufficient to resolve the components. From\nthis 300s exposure (Figure~1), we obtain a redshift of $1.565 \\pm\n0.001$ based on Gaussian fits to the \\CIV\\ and \\CIII\\ emission peaks.\nThe S/N of this new spectrum is 50 to 100 over most of its wavelength\nrange and confirms the presence of the strong intervening absorption,\nclearly resolving the \\MgII~2796.4, 2803.5 doublet and detecting the\nassociated \\MgI~2853 line. Also seen is a rich absorption system of\n\\FeII~2260.8, 2344.2, 2374.5, 2382.8, 2586.7, and 2600.2, and\n\\CaI~4227.9 belonging to the same intervening system; \\CaII~3933 and\n3969 fall in the atmospheric A band. The mean of the absorption\nredshifts is z = $0.9313 \\pm 0.0005$. The profile of the \\MgII\\\nemission line is asymmetric, which can be attributed to absorption by\n\\FeI~3721.0 or intervening \\MgII\\ local to the quasar. There is\nanother weak intervening \\MgII\\ absorption feature at z=1.1346.\n\n\\begin{figure}[p]\n\\plotone{fig1.ps}\n\\caption{Keck LRIS 9\\AA\\ resolution spectrum of HE~0512$-$3329\nobtained in January, 2000. The upper abscissa scale is the rest frame\nof the quasar with a redshift of 1.565; prominent emission line\nfeatures are marked above the spectrum. Lines associate with the\nintervening system at z=0.9313 are identified below the spectrum. The\nabsorption lines are probably due to the lensing galaxy and are\nunresolved at the instrumental resolution. There is a second rather\nweak intervening \\MgII\\ 2800 absorption system at z=1.1346, marked in\nparenthesis. The small difference in brightness of the two components\nand the lack of any visible stellar absorption features (dotted lines)\nin this high S/N composite spectrum argues strongly against component\nB being a foreground star.}\n\\end{figure}\n\nComponent~B is 70\\% the brightness of A. The lack of any discernible\nstellar absorption features in the Keck spectrum (Figure~1) argues\nstrongly against component~B being a foreground star. The RMS noise\nin the spectrum is at the level of 0.15\\AA\\ equivalent width. The\nstrongest features in late type stars have equivalent widths of a few\n\\AA ngstroms and would be detected easily in the Keck spectrum; for\ncomparison, the equivalent width of the intervening \\MgI\\ 2853\\AA\\\nfeature is 1.4\\AA. The only possible stellar contaminant is a\ncompletely featureless O-type subdwarf or white dwarf and such stars\nare extremely rare. If this were the case, however, the spectrum of\nHE~0512$-$3329 would be much bluer, unless either the QSO or the\nputative star has a large amount of intrinsic reddening.\n%Additionally, the equivalent widths of the \\CIV\\ and \\CIII\\ emission\n%lines in the composite spectrum are within $\\sim 10-15\\%$ of those for\n%ordinary quasars, as measured from the mean of $\\sim 500$ quasars from\n%the FIRST Bright Quasar Survey (White et al.\\ 2000).\n\n\\subsection {Photometry}\n\nWe have done point-spread function (PSF) fitting photometry on the\nSTIS images using IRAF/DAOPHOT. From observations of an unlensed\nquasar in our program, we obtain aperture corrections of $-0.222$ and\n$-0.303$ for the CL and LP bands, to go from the fitted 3 pixel radius\nto 0\\farcs5. To this we add an additional $-0.1$ magnitudes to correct\nto the ``true'' magnitude in an infinite aperture, as is standard\npractice with WFPC2 (Holtzman et al.\\ 1996). The resulting calibrated\nSTIS ``STmagnitudes'' and errors are listed in Table~1.\n\nThe $LP$ bandpass is completely contained within the $CL$. Because\nthey are similar in shape, the $LP$ flux can be scaled by the relative\nthroughputs and subtracted from the $CL$, producing an effective\n``shortpass'' measurement (Gregg \\& Minniti 1997; Gardner et al.\\\n2000) extending from 5500\\AA\\ to 2000\\AA, with effective wavelength of\n4424\\AA\\ and FWHM of 2569\\AA. The $SP-LP$ difference provides some\nwide-band color information (Table~1).\n\nIn 1999 December, we obtained VRI photometry of HE~0512$-$3329 using\nthe Mosaic~II CCD imager at the Blanco 4m telescope at Cerro\nTololo Inter-American Observatory\\footnote{Cerro Tololo Inter-American\nObservatory, NOAO, is operated by the Association of Universities for\nResearch in Astronomy, Inc. (AURA), under cooperative agreement with\nthe National Science Foundation.}. Although the seeing was $\\sim\n0\\farcs8 - 0\\farcs9$ and the two components are not cleanly resolved,\npoint-spread function (PSF) fitting using IRAF/DAOPHOT successfully\nseparated them, yielding positions in excellent agreement with the HST\nimages and photometry consistent with the STIS results. The separations\nobtained in V, R, and I are 0\\farcs654, 0\\farcs646, and 0\\farcs643,\nrespectively, compared to 0\\farcs644 obtained from the centroids of\nthe components in the STIS CL images.\n\nNo photometric standards were taken at CTIO, so we have calibrated the\nCTIO photometry using zeropoints determined by convolving the Keck\nspectrophotometry with Cousins VRI passbands. This procedure is\nitself calibrated using a model for the spectrum of Vega (Kurucz 1992)\nfor which we adopt $B = V = R = I = 0.0$. Slit losses limit the\nabsolute accuracy, but, fortuitously, the spectroscopy was obtained\nwhen the position angle of HE~0512$-$3329 was only 23\\arcdeg\\ from the\nparallactic angle. Because the effective slit width was somewhat\ngreater than the atmospheric dispersion between the red and blue\nextremes of the spectrum (Filippenko 1982), the colors obtained from\nthe composite spectrum are reasonably accurate and can be used to\nestablish the relative zeropoints of the VRI photometry. Also, we\nhave determined a zeropoint transformation between the effective STIS\nSP bandpass and Johnson B using the mean quasar spectrum (Brotherton\net al.\\ 2000) from the FIRST Bright Quasar Survey (FBQS; White et al.\\\n2000), redshifted to z=1.565. The resulting colors of HE~0512$-$3329\nare $B-V = 0.68, V-R = 0.46, V-I = 0.82$ for component~A, and $B-V =\n0.32, V-R = 0.37, V-I = 0.69$ for component~B (Table~1). Schlegel,\nFinkbeiner, \\& Davis (1998) estimate a Galactic extinction of $A_B =\n0.104$ for this line of sight; Burstein \\& Heiles (1982) give a much\nlower value of 0.010. The numbers in Table~1 have not been corrected\nfor Galactic extinction.\n\n\\begin {deluxetable}{lrrrrrrrrr}\n\\tabletypesize{\\small}\n\\tablewidth{0pc}\n\\tablecaption{HE 0512$-$3329}\n\\tablehead{\n\\colhead{Object} &\n\\colhead{R.A. (J2000)} &\n\\colhead{Dec.\\ (J2000)} &\n\\colhead{$CL$} &\n\\colhead{$LP$} &\n\\colhead{$SP$} &\n\\colhead{$B$} &\n\\colhead{$V$} &\n\\colhead{$R$} &\n\\colhead{$I$}\n%\n}\n\\startdata\nA & 05 14 10.7833 & $-33$ 26 22.504 & 17.94 & 18.53 & 19.47 &\n18.36 & 17.68 & 17.22 & 16.86 \\\\\nB & 05 14 10.7687 & $-33$ 26 23.121 & 18.28 & 19.03 & 19.46 &\n18.35 & 18.03 & 17.66 & 17.34 \\\\\n% B-V V-R R-I\n% 0.32 0.37 0.32\nB-A & -0\\farcs183 & 0\\farcs618 & 0.35 & 0.49 & -0.01 &\n-0.01 & 0.35 & 0.44 & 0.48 \\\\\nerrors & 0\\farcs003 & 0\\farcs003 & 0.02 & 0.02 & 0.02 &\n0.04 & 0.02 & 0.02 & 0.02 \\\\\n\\enddata\n\\tablecomments{Photometry is uncorrected for Galactic reddening; errors\nare statistical only.}\n\\end {deluxetable}\n\n\\begin {deluxetable}{lccrrr}\n\\tabletypesize{\\small}\n%\\singlespace\n\\tablewidth{0pc}\n\\tablecaption{Field Star Difference Photometry}\n\\tablehead{\n\\colhead{Object} &\n\\colhead{R.A. (J2000)} &\n\\colhead{Dec.\\ (J2000)} &\n\\colhead{$\\Delta V_i$} &\n\\colhead{$\\Delta R_i$} &\n\\colhead{$\\Delta I_i$}\n%\n}\n\\startdata\nStar 1 $-$ A & 5 14 08.98 & $-33$ 27 08.1 & -1.04 & -1.14 & -1.12 \\\\ % 16.512 \nStar 2 $-$ A & 5 14 11.62 & $-33$ 26 50.1 & 0.56 & 0.77 & 0.95 \\\\ % 18.110 \nStar 3 $-$ A & 5 14 14.83 & $-33$ 27 24.7 & 0.91 & 0.93 & 0.96 \\\\ % 18.458 \nStar 4 $-$ A & 5 14 18.74 & $-33$ 26 03.6 & -0.38 & -0.38 & -0.32 \\\\ % 17.172 \nStar 5 $-$ A & 5 14 19.06 & $-33$ 26 13.6 & 1.33 & 0.99 & 0.72 \\\\ % 18.876 \nStar 6 $-$ A & 5 14 08.63 & $-33$ 24 26.9 & -0.30 & -0.17 & -0.09 \\\\ % 17.252 \nStar 7 $-$ A & 5 14 08.51 & $-33$ 24 48.4 & 0.81 & 0.78 & 0.77 \\\\ % 18.354 \nStar 8 $-$ A & 5 13 57.75 & $-33$ 26 24.3 & 1.25 & 0.88 & 0.54 \\\\ % 18.799 \nStar 9 $-$ A & 5 14 05.42 & $-33$ 29 15.7 & -0.58 & -0.42 & -0.29 \\\\ % 16.970 \n\\enddata\n\\tablecomments{Numbers are instrumental magnitude differences $m_{star} - m_A$\nin the Cousins system; no color terms have been applied.}\n\\end {deluxetable}\n\nThe broad band colors of the two components clinch the case for\nHE~0512$-$3329 being a lensed quasar. By comparison with the Bruzual\net al.\\ stellar library, the $B-V$ color of component~B indicates a\nspectral type of F0, yet V-R and V-I are consistent with a much cooler\nobject, about F9/G0. Our simulations show that any star in this\nspectral range with the relative brightness of component~B would\ncontribute easily detectable absorption features, at $\\sim 10\\sigma$\nlevel or greater, to the composite spectrum at the indicated locations\nin Figure~1; \\CaII~H and K and the Balmer lines would be particularly\nconspicuous. The broad band colors of component~B are, in fact, more\nconsistent with a slightly reddened quasar than a star.\n\nFor future reference for monitoring variability of the lens\ncomponents, we list in Table~2 the instrumental magnitude differences,\n$m_i - m_{\\rm A}$, for nine field stars with $V \\approx 16$ to 18 in\nthe vicinity of HE~0512$-$3329. The astrometry has been derived from\nthe digitized sky survey and has an offset of $\\Delta R.A. =\n+0\\farcs55$ and $\\Delta Dec.\\ = +0\\farcs77$ relative to the STIS\nimages, but these positions are sufficient to unambiguously identify \nthe comparison stars.\n\n\\section{The Nature of the Lensing Object}\n\nThe presence of the strong intervening \\MgII\\ absorption and the many\nassociated low ionization lines are evidence that the lensing object\ncontains a damped \\Lya\\ absorption (DLA) system (Boisse et al.\\ 1998).\nA DLA system at a redshift $< 1$ is most likely to be the\nhydrogen-rich disk of a spiral galaxy. Dust in the galaxy may produce\ndifferential reddening in the two components of HE~0512$-$3329.\n\n\\subsection{Possible Detection of a Third Object}\n\nTo explore for the lensing galaxy and possible additional quasar\nimages, the STIS $CL$ images were combined using the {\\sc DRIZZLE}\npackage (Fruchter \\& Hook 1998) in IRAF/STSDAS. A sampling rate of\n0.5 times the original image scale and a {\\sc PIXFRAC} value of 0.6\nwere used. The subpixel image shifts were determined using the IRAF\ntask {\\sc XREGISTER}. The final combined $CL$ image is shown in the\nleft panel of Figure~2. The distance between centroids of the two\nimages is 0\\farcs644; at the probable lens redshift of 0.9313, this\nseparation is only $\\sim 4$ kpc, adopting \\Ho = 70 \\kmsmpc and \\qo =\n0.5. The mass associated with an Einstein ring of this scale is $\\sim\n3 \\times 10^{10}$ M$_\\odot$.\n\n\\begin{figure}[t]\n\\plotone{fig2.ps}\n\\caption{{\\bf Left:} STIS 50CCD ($CL$) image of HE~0512$-$3329.\nComponent~A is 0.35 magnitudes brighter than B in this passband. The\nseparation is 0\\farcs644. The orientation is given by the compass\npoints; the North arrow is 0\\farcs25 long. \\newline \n{\\bf Right:} Residuals\nafter PSF removal. The object immediately above and to the right of\nA, indicated by the white arrow, may be the nucleus of the lensing\ngalaxy. There is also excess low surface brightness flux around each\ncomponent.}\n\\end{figure}\n\nThe PSF removal was done using the {\\sc SCLEAN} task in IRAF/STSDAS.\nFor the PSF itself, we used the theoretical STIS PSF from the {\\bf\nTiny Tim} package and also the STIS PSF generated by the Hubble Deep\nField South project (Gardner et al.\\ 2000). They yield very similar\nresults. The residual image is shown in the right hand panel of\nFigure~2. There is an excess of counts just above and to the right of\ncomponent~A (white arrow in Figure~2). The RMS in the\nbackground-subtracted image is $\\sim \\pm 1.3$ counts while the peak in\nthe excess region is 8.7. The total flux is $\\sim 5.9$ magnitudes\nfainter than component~A, giving it $CL = 23.8$. Its FWHM is roughly\ntwice that of a point source, consistent with being nonstellar. We\ntentatively identify this object as the nucleus of the lensing galaxy.\nFor our adopted cosmology, this object has $M_V \\approx -19$, roughly\nthe nucleus of a roughly $L^*$ galaxy with a bulge-to-disk ratio of\n$\\sim 3$ and, for the above quoted Einstein ring mass, a M/L ratio of\n$\\sim 20$. At the intervening redshift of 0.9313, the the two lines\nof sight to the quasar pass 1.6 (A) and 2.7 (B) kpc from the position\nof the third object. \n\nThere is excess light of lower surface brightness between the two\nquasar images and immediately below component~A as well as to the\nright of component~B in Figure~2. Although the third object is not\ndetected with confidence in the LP image, the low surface brightness\nlight distribution is qualitatively reproduced in the redder passband.\nNo such excess light is seen when the same analysis is applied to an\nimage of an unlensed quasar from our snapshot program. Deeper images\nare needed to confirm the reality of this low surface brightness fuzz\nand, if real, determine whether it is due to the lens, the host\ngalaxy, or another object.\n\n\\subsection{Reddening Analysis}\n\nThe STIS and ground-based photometry are consistent in showing that\ncomponent~A is redder than B. Going from red to blue, the magnitude\ndifference between the two images decreases, becoming equal within the\nerrors in the concocted STIS $SP$ and transformed $B$ bands\n(Figure~3). Observed in the ultraviolet, component~B will be the\nbrighter. This trend can be attributed to differential reddening,\nwith extinction along the line of sight to component~A being greater.\nColor differences between the quasar images can also be arise from\nmicrolensing by stars in the lensing galaxy, producing differential\nmagnification of the quasar continuum (Wambsganss \\& Paczy\\'nski 1991)\nalong the two lines of sight. This effect has been observed in at\nleast one quasar, HE~1104$-$1805 (Wisotzki et al.\\ 1993). The\nfollowing reddening analysis is valid only if microlensing is\nnegligible in HE~0512$-$3329.\n\n\\begin{figure}[t]\n\\plotone{fig3.ps}\n\\caption{Trend of the broad band magnitudes of HE~0512$-$3329 for\ncomponents A, B, and the composite A+B. The VRI photometry is from\nthe ground-based CTIO imaging while the B magnitudes are derived from\nthe difference between the STIS CL and LP bands; both have been\nzeropointed using the Keck spectrophotometry in Figure~1 (see text for\ndetails). The brightness of the two images converges from red to\nblue. This can be attributed to differential extinction or\nmicrolensing, possibly both. These data have been corrected from\nTable~1 for Galactic absorption of $A_B = 0.104$}\n\\end{figure}\n\nTo quantify the amount of differential reddening, we have fitted an\nextinction model to the photometry results, following the procedure of\nFalco et al.\\ (1999). In this approach, it is assumed that the quasar\nis not variable, that the lensing magnification is not wavelength\ndependent, and that the extinction law does not vary with position in\nthe lensing galaxy and is well-approximated by a typical Galactic\nextinction curve with $R_V = A_V/E(B-V) = 3.1$. Correcting a sign\nerror in equation~3 of Falco et al., we have\n\\begin{equation}\n\\chi^2 = \\sum_{j=1}^{N_{\\lambda}}\\sum_{i=1}^{N_c} \\frac{\\{m_i(\\lambda_j) - m_{\\circ}(\\lambda_j)\n+ 2.5\\log(M_i) - E_i~R[\\lambda_j/(1+z)]\\}^2}{\\sigma_{ij}^{2}}\n\\end{equation}\nwhere $m_i$ are the observed magnitudes of each of the $N_c$\ncomponents in the $N_{\\lambda}$ photometric bands with effective\nwavelength $\\lambda_j$, $m_{\\circ}$ is the unlensed magnitude of the\nquasar, $M_i$ is magnification of each component, $E_i$ is the\nextinction of each component, z is the redshift of the lens, and\n$\\sigma_{ij}$ are the photometric errors. The summations are over the\n4 bandpasses, $B, V, R,$ and $I$, and two components, A and B.\n\nRelative magnifications and extinctions can be found by minimizing\n$\\chi^2$ while holding one magnification fixed at unity and one\nextinction at 0. As component~B is bluer and fainter, we fix its\nparameters at these values. The extinction law has been parametrized\nusing the equations of Cardelli, Clayton, \\& Mathis (1989). For this\nanalysis, we first corrected the photometry listed in Table~1 for\nGalactic extinction of $A_B = 0.104$ from Schlegel et al.\\ (1998).\n\nThe fit for the relative extinction results in the estimate of $A_V =\n0.34$ for component~A, in excess of the extinction at component~B; the\nunextincted, wavelength independent relative magnification of A is\n2.45 times that of B. The $\\chi^2$ of this fit is 0.66. For\ncomparison, a fit with both extinctions held to zero yields a relative\nmagnification of 1.35, roughly consistent with the brightness\ndifference between the two components in $V$ or $R$. The $\\chi^2$ for\nthis fit is 67, as might be expected given the varying magnitude\ndifference between the two components as a function of wavelength,\nwhich renders an achromatic magnification model a poor explanation of\nthe brightness variation with wavelength.\n\nThe separate extinctions to each component of HE~0512$-$3326 can be\nestimated by assuming that the unlensed quasar spectrum has typical\ncolors. After correcting for Galactic reddening using the Schlegel et\nal.\\ (1998) value, the difference in $B-V$ between the composite\nspectrum of HE~0512$-$3326 (Figure~1) and the FBQS mean spectrum is\n0.31. With $R_V = 3.1$, this is equivalent to $A_V = 0.97$. Knowing\nthe $V$ magnitudes and relative extinction, the separate extinctions\ncan be computed as $A_V^{\\rm A} = 1.10$ and $A_V^{\\rm B} = 0.76$,\nexcluding any grey component. Given the multitude of assumptions and\nthe bootstrapping from the spectrophotometry, these numbers must be\nconsidered provisional, but they do suggest that the extinction to\neach component is comparable and that both lines of sight intercept\nthe same or similar absorption systems. Spectroscopy of the two\ncomponents separately would allow a detailed study of the extinction\ncurve in the disk of the lensing galaxy and would also determine\nwhether microlensing could be contributing to the pattern of color\ndifferences.\n\n\\section {Conclusion}\n\nThe presently available data leave little doubt that HE~0512$-$3329 is\ngravitationally lensed. The spectroscopic evidence strongly suggests\nthat the lens is a spiral galaxy. Spatially resolved spectroscopy of\nthe two images of HE~0512$-$3329 is needed to confirm its nature;\nhowever, the presence of strong low-ionization lines in the composite\nspectrum indicates that at least one of the lines of sight is sure to\npass through a damped Ly$\\alpha$ system in the disk of the lens.\nUltraviolet spectroscopy of the A and B components can further be used\nto derive the extinction curve in the disk of the lens as well as\nabundances of heavy elements. This lensed quasar has been found among\nthe first 80 targets of an HST Cycle~8 snapshot program designed to\nsearch for such small separation systems. The program was renewed for\nup to 300 additional snapshots in Cycle~9. If close-separation\ntargets are found with this frequency for the duration of the survey,\nthe lensing statistics for small separation systems will be boosted by\na significant factor.\n\n\\acknowledgments\n\nMark Lacy is thanked for helpful discussions. The referee is credited\nwith constructive comments which improved this paper. We are grateful\nto Sune Toft for calling our attention to an error in our original\ncalculation of the differential reddening. Support for this work was\nprovided by NASA through grant number GO-8202 from the Space Telescope\nScience Institute, which is operated by AURA, Inc., under NASA\ncontract NAS5-26555. We also acknowledge support from NSF grant\nAST-98-02791. This work was performed under the auspices of the\nU.S. Department of Energy by University of California Lawrence\nLivermore National Laboratory under contract No.~W-7405-Eng-48.\nJ.N.W. thanks the Fannie and John Hertz Foundation for financial\nsupport.\n\n\\begin{references}\n\n\\reference{} Boisse, P., Le Brun, V., Bergeron, J., Deharveng, J.-M.,\n1998, A\\&A 333, 841\n\n\\reference{} Brotherton, M. S., Tran, H. D., Laurent-Muehleisen, S. A.,\nBecker, R. H., White, R. L., \\& Gregg, M. D. 2000, in preparation\n\n\\reference{} Bruzual, A. G., Persson, S. E., Gunn, J. E., Stryker,\nL. L. 1996, Stellar Atlas, from the STScI database,\nftp://ftp.stsci.edu/cdbs/cdbs2/grid/bpgs \n\n\\reference{} Burstein, D. \\& Heiles, C. 1982, AJ, 87, 1165\n\n\\reference{} Cardelli, J. A., Clayton, G. C., \\& Mathis, J. S. 1989, ApJ,\n345, 245\n\n\\reference{} Falco, E. E., Impey, C. D., Kochanek, C. S., Leh\\'ar, J.,\nMcLeod, B. A., Rix, H.-W., Keeton, C. R., Mu\\~noz, J. A., Peng,\nC. Y. 1999, ApJ, 523, 617\n\n\\reference{} Filippenko, A. V. 1982, PASP, 94, 715\n\n\\reference{} Fruchter, A. S. \\& Hook, R. N. 1998, astro-ph/9808087\n\n\\reference{} Gardner, J. P., et al.\\ 2000, astro-ph/9912167\n\n\\reference{} Gregg, M. D. \\& Minniti, D. 1997, PASP, 109, 1062\n\n\\reference{} Gregg, M. D., Wisotzki, L., Becker, R. H., Schechter,\nP. L., Maza, J. \\& White, R. L. 2000, in preparation\n\n\\reference{} Holtzman, J. A., et al.\\ 1995, PASP, 107, 156\n\n\\reference{} Jain, D., Panchapakesan, N., Mahajan, S., \\& Bhatia,\nV. B. 1999, astro-ph/9911004\n\n\\reference{} Kimble, R. A., et al.\\ 1997, ApJL, 492, L83\n\n\\reference{} Kochanek, C. 1998, private communication\n\n\\reference{} Kochanek, C. S., Falco, E. E., Impey, C., Lehar, J.,\nMcLeod, B. Rix, H.-W. 2000, cfa-www.harvard.edu/castles\n\n\\reference{} Kochanek, C. Falco, E. E., Impey, C. D., Leh\\'ar, J.,\nMcLeod, B. A., Rix, H.-W., Keeton, C. R., Mu\\~noz, J. A., Peng,\nC. Y. 1999, astro-ph/9910165\n\n\\reference{} Kochanek, C. S., Falco, E. E., \\& Mu\\~{n}oz, J. A. 1999 ApJ,\n510, 590\n\n\\reference{} Kurucz, R. L. 1992, private communication\n\n\\reference{} Maoz, D. \\& Rix, H.-W. 1993, ApJ, 416, 425\n\n\\reference{} Oke, J. B., Cohen, J. G., Carr, M., Cromer, J., Dingizan,\nA., Harris, F. H., Labrecque S., Lucinio, R., Schaal, W., Epps, H., \\&\nMiller, J. 1995, PASP, 107, 375\n\n\\reference{} Reimers, D., K\\\"ohler, T. \\& Wisotzki, L. 1996 A\\&AS,\n115, 235\n\n\\reference{} Rix, H.-W., et al.\\ 1994, ApJ, 435, 49\n\n\\reference{} Schlegel, D. J., Finkbeiner, D. P., \\& Davis, M. 1998, ApJ,\n500, 525\n\n\\reference{} Turner, E. L., Ostriker, J. P. \\& Gott~III, J. R. 1984, ApJ,\n284, 1\n\n\\reference{} Wambsganss, J. \\& Paczy\\'nski, B. 1991 AJ, 102, 864\n\n\\reference{} White, R. L., et al.\\ 2000, ApJS, in press\n\n\\reference{} Wisotzki, L., K\\\"ohler, T., Groote, D., \\& Reimers,\nD. 1996, A\\&AS, 115, 227\n\n\\reference{} Wisotzki, L., K\\\"ohler, T., Kayser, R., \\& Reimers,\nD. 1993, A\\&A 278, L15\n\n\\reference{} Woodgate, B. E., et al.\\ 1998, PASP, 110, 1183\n\n\\end{references}\n\n\\end{document}\n"
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astro-ph0002334
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Distance-Redshift in Inhomogeneous FLRW
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[
{
"author": "R. Kantowski"
}
] |
\vskip .2 truein We give distance--redshift relations in terms of elliptic integrals for three different mass distributions of the Friedmann-Lema\^\i tre-Robertson-Walker (FLRW) cosmology. These models are dynamically pressure free FLRW on large scales but, due to mass inhomogeneities, differ in their optical properties. They are the filled-beam model (standard FLRW), the empty-beam model (no mass density exists in the observing beams) and the 2/3 filled-beam model. For special $\OM$--\ $\OL$ values the elliptic integrals reduce to more familiar functions. These new expressions for distance-redshift significantly reduce computer evaluation times.
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{
"name": "Z2DL.tex",
"string": "%Revised MS# 51346 by R. Kantowski, J.K. Kao, and R. C. Thomas June, 27, 2000\n\n\\documentclass[preprint]{aastex}\n \n\\newcommand{\\be}{\\begin{equation}} \n\\newcommand{\\ee}{\\end{equation}}\n\n\\newcommand{\\bea}{\\begin{eqnarray}} \n\\newcommand{\\eea}{\\end{eqnarray}} \n\\newcommand{\\eg}{e.g., } \n\\newcommand{\\ie}{i.e., } \n\\newcommand{\\OM}{\\Omega_m} \n\\newcommand{\\OO}{\\Omega_0}\n\\newcommand{\\OL}{\\Omega_{\\Lambda}} \n\n\\newcommand{\\nn}{\\nonumber\\\\} \n\n\\newcommand{\\bO}{b_{\\Omega}}\n\\newcommand{\\bb}{\\hat b}\n\\newcommand{\\mz}{$m$-$z$\\ } \n\n\\begin{document}\n\\title{Distance-Redshift in Inhomogeneous FLRW} \n\\author{ R. Kantowski }\n\\affil{ University of Oklahoma, Department of Physics and\nAstronomy,\\\\ Norman, OK 73019, USA }\n\\email{kantowski@mail.nhn.ou.edu}\n\n\\author{ J. K. Kao}\n\\affil{ Tamkang University, Department of Physics,\\\\\nTamsui, Taipei, Taiwan 25137 R.O.C.}\n\\email{g3180011@tkgis.tku.edu.tw}\n\\author{ R. C. Thomas }\n\\affil{ University of Oklahoma, Department of Physics and\nAstronomy,\\\\ Norman, OK 73019, USA }\n\\email{thomas@mail.nhn.ou.edu}\n\n\\begin{abstract} \\vskip .2 truein We give distance--redshift relations \nin terms of elliptic integrals\nfor three different mass distributions of\nthe Friedmann-Lema\\^\\i tre-Robertson-Walker (FLRW) \ncosmology. These models are dynamically pressure free FLRW on large scales\nbut, due to mass inhomogeneities, differ in their optical properties. \nThey are the filled-beam model \n(standard FLRW), the empty-beam model (no mass density exists in the \nobserving beams) and the 2/3 filled-beam model. For special $\\OM$--\\ $\\OL$ values\nthe elliptic integrals reduce to more familiar functions. These new expressions \nfor distance-redshift significantly reduce computer evaluation times.\n\\end{abstract}\n\n\\keywords{cosmology: theory -- large-scale structure of universe}\n\n\\section{INTRODUCTION} \\label{sec-intro} \nAs limits on the global cosmological parameters $\\OM$ and $\\Lambda$ have been refined,\n\\cite{SB} and \\cite{PS1},\nthe optical inadequacy of the standard distance-redshift relation ($D$-$z$) of \nFLRW has become more apparent. The problem was first recognized long ago by \n\\cite{Zel}, \\cite{BB}, and \\cite{KR}\nbut the lack of relevant data limited its significance. Even though the average mass density \nparameter $\\OM$ (along with $H_0$ and $\\Lambda$) determines the large scale dynamic behavior \nof the pressure free universe, knowledge of the actual mass inhomogeneity is necessary to \naccurately determine these \nparameters from most observations. Most observations determine $\\OM$ and $\\Lambda$ by \n(indirectly) comparing theoretical $D$-$z$ curves to observed data. However, \n $D$-$z$ depends on more than the average mass density. It can depend significantly \non details of how the mass is distributed, \\ie on how inhomogeneous the mass is on\nthe scale of the widths of the observing beams. \nIf some significant fraction ($\\rho_I/\\rho_0 \\le 1$) \nof the total mass density is in the form of inhomogeneities and is excluded from \nthe lines of sight to the distant objects observed, a modified, \\ie a partially \nfilled-beam $D$-$z$ is required. \n\nThe necessity of taking into account the effect of inhomogeneities on \nobservations is relatively easy to understand. \nHomogeneous matter\ninside an observing beam of light gravitationally focuses\nthe beam much differently than does an equal-mass clump of externally lensing matter. \nThe simplest correction for this gravity-light effect requires the introduction \nof another parameter $\\nu,\\ \n0\\le\\nu\\le 2,$ which gives the fraction $\\rho_I/\\rho_0 =\\nu(\\nu+1)/6$ of the mass density\nof the universe removed from the observing beams as inhomogeneities. Using $\\nu$ \nrather than $\\rho_I/\\rho_0$ or some other parameter is dictated by the mathematics of \nspecial functions. \nA reduced mass density in an observing beam causes it to diverge relative\nto a standard FLRW beam. For an observed object in such a universe \nto have the standard FLRW \nangular size it would thus have to be moved to a smaller $z$; i.e., objects will appear\nless bright than in the standard FLRW universe.\nA reasonable application of this model to SNe Ia observations takes \n$\\rho_I$ as the galactic contribution to the total mass density $\\rho_0$ and the remaining \ncontribution as a smooth intergalactic medium. \nGalaxies are easily excluded from SNe Ia foregrounds by selection (intended or not)\nand if galaxy mass roughly follows light, including their mass in $\\rho_I$ is appropriate.\nIn the partially filled-beam model where the additional parameter $\\nu\\ne 0$ \nhas been introduced, \nonly lensing by mass clumps external to the beam has been neglected. \nTo compare individual observations to $D$-$z$ \nof this model requires only an occasional lensing correction; however, \ncomparison with the standard FLRW $D$-$z$ ($\\nu=0$) model requires a defocusing correction\nfor the partially empty-beam of every observation, as well as the \noccasional lensing correction. \nIf only weak and transparent lensing occurs (to the $z_{max}$ being observed)\nthe standard FLRW $D$-$z$ ($\\nu=0$) should give the mean $D$-$z$ curve. \n\\cite{WY} argues that by using flux-averaging the mean can be accurately obtained.\n\\cite{KRa} and \\cite{KRb} claims that determining cosmological parameters \n from data compared \nwith the partially filled Hubble curves given here is likely to be easier. \nBeyond selection effects, \nunknown lensing probabilities can be highly non-Gaussian and should make the mean more \ndifficult \nto observationally determine, \\ie should require more data if a \ngiven accuracy of the cosmic parameters is to be obtained, \\cite{BB,HW,HD}. \nThe down side for partially filled-beam models is that you must select against\nlensing and must determine the additional parameter $\\nu$.\n\nIn Sec.\\,\\ref{sec-lumdist} we outline the procedure required to obtain $D$-$z$\nfor partially filled-beam FLRW observations and how the result simplifies for the \nthree special cases of $\\nu =$ 0, 1, and 2. In Sec.\\,\\ref{sec-results} we give the \nnew results for these three special cases. Some concluding remarks are given in \nSec.\\,\\ref{sec-conclusions} and in the Appendix we discuss our Fortran \nimplementation of these results.\n\n\n\\section{The Luminosity Distance-redshift Relation} \\label{sec-lumdist} \n\nFor models being discussed here (and for most cosmological models), \nangular or apparent size distance \nis related to luminosity distance by $D_<(z)=D_{\\ell}(z)/(1+z)^2$. \nHence we need to give only one\nor the other, and we have chosen to give luminosity distances. \nThe $D_{\\ell}(z)$ which accounts\nfor a partially depleted mass density in the observing beam but neglects \nlensing by external masses\nis found by integrating the second order differential equation for the \ncross sectional area $A(z)$\n of an observing beam from source ($z=z_s$) to observer ($z=0$), see \\cite{KRa}\nfor some history of this equation:\n\\bea \n&&(1+z)^3\\sqrt{1+\\OM z+\\OL[(1+z)^{-2}-1]}\\times\\nonumber\\\\ &&\\hskip 1 in {d\\ \\over\ndz}(1+z)^3\\sqrt{1+\\OM z+ \\OL[(1+z)^{-2}-1]}\\,{d\\ \\over dz}\\sqrt{A(z)}\\nonumber\\\\ &&\\hskip 2.0 in\n+ {(3+\\nu)(2-\\nu)\\over 4}\\OM(1+z)^5\\sqrt{A(z)}=0. \\label{lame} \n\\eea\nThe required boundary conditions are:\n\\bea\n\\sqrt{A}|_s&=&0,\\nonumber\\\\ {d\\sqrt{A\\big|_s }\\over dz}&=& -\\sqrt{\\delta\\Omega} {c\\over\nH_s(1+z_s)}, \\label{Aboundary} \n\\eea \n where $\\delta\\Omega$ is the solid angle of the beam at the source\nand \nthe FLRW value of the Hubble parameter at $z_s$ is\nrelated to the current value $H_0$ at $z=0$ by: \n\\be\nH_s=H_0(1+z_s)\\ \\sqrt{1+\\OM\nz_s+\\OL[(1+z_s)^{-2}-1]}. \\label{Hs} \n\\ee\nThe luminosity distance is then simply related to the area $A\\big|_0$ of the beam \nat the observer by: \n\\be\nD_{\\ell}^2\\equiv {A\\big|_0 \\over \\delta\\Omega}(1+z_s)^2.\n\\label{Dl} \n\\ee\nEquation (\\ref{lame}) can be put into the form of a Lam\\'e equation\nand its solution has been given in terms of Heun \nfunctions in \\cite{KRa}. Solutions can also be given in terms of Lam\\'e functions \nbut neither Heun nor Lam\\'e functions are currently available \nin standard computer libraries. Consequently, such expressions are not particularly \nuseful for comparison with data, at this time. \nFor the special case where $\\Lambda=0$ the Lam\\'e functions reduce to \nassociated Legendre functions and these expressions are useful. Other special \ncases also exist as is pointed out in \\cite{KRa}. \n\n\n\nIn the next section we give useful expressions for \n$D_{\\ell}$ for three special cases where $\\Lambda$ is arbitrary but \nwhere the filling parameter $\\nu$ is restricted to values 0, 1, and 2. For these \nthree cases we can write $D_{\\ell}$ as an elliptic integral and hence we can\ngive $D_{\\ell}$ in terms of the three fundamental incomplete Legendre elliptic integrals\n$F(\\phi,{\\rm k}), E(\\phi,{\\rm k}),$ and $ \\Pi(\\phi,\\alpha^2,{\\rm k})$. These functions are universally\navailable and these new expressions significantly speed up the evaluation of \n$D_{\\ell}$\\ (see the Appendix). Distance-redshift for $\\OO=1$ \ncan be given in terms of hypergeometric functions, see (\\ref{2F1ansnu=0B1}) and (\\ref{2F1ansnu=2B1}), \nor associated Legendre functions, \nsee (\\ref{Pansnu=0B1}) and (\\ref{Pansnu=2B1}); however, we also give $D_{\\ell}$ as \nmore complicated expressions\ninvolving Legendre elliptic integrals, (\\ref{ansnu=0B1}) and (\\ref{ansnu=2B1}), \nbecause these \nexpressions evaluate more rapidly using currently available Fortran routines.\n\n\nIt is not at all clear that the solution of (\\ref{lame}) can be written as elliptic integrals\nfor the special cases of $\\nu=$ 0, 1 and 2. However, the steps required to arrive at this \nconclusion\ncan be found in \\cite{WE} under integral functions for Lam\\'e and Matthew equations\n(see especially Sec.\\,19.53). The authors have carried out the \nconversion directly for all three cases; however, the $\\nu=0$ and $2$ conversions can be reached \nby simpler means. The integral for $\\nu=0$, the standard FLRW filled-beam case, \nis given in (\\ref{nu=0}) and is well known.\nThe $\\nu=2$ (empty-beam) integral given in (\\ref{nu=2}) is easy to obtain because the \ncoefficient \nof $\\sqrt{A}$ vanishes in (\\ref{lame}). The first integral is trivial and the second\nis elliptic resulting in (\\ref{nu=2}).\nFor $\\nu=1$, the 66\\% \nfilled-beam model, the integral is given in (\\ref{ansnu=1A}); however, no simple way of getting this from \n (\\ref{lame}) seems to exist. \n\nIn Sec. \\ref{sec-results}. we outline results for all big bang models in the first \nquadrant of the $\\OM$--\\ $\\OL$ plane (see Fig. 1), hoping to facilitate their usage. \nLuminosity distances for the three large open domains are given in subsections A, and \nfor the boundaries of these domains in subsections B.\n\\section{Luminosity Distances as Legendre Elliptic Integrals} \\label{sec-results}\n\n\\centerline{\\bf I. $\\nu=0$, Completely Filled-Beam Observations (Standard FLRW)}\n{\\bf A. Three Open Big Bang Domains}\n\n\\cite{KSSE} and \\cite{KS} gave magnitude-redshift relations for standard pressure-free FLRW \nmodels as \ninverse Weierstrass functions and more recently \\cite{FB} gave\ncomoving distances and light travel times for these models using Legendre elliptic integrals. \nIn this section we give simpler and more useful results which are directly comparable with \n\\cite{ED} who used Jacobi elliptic functions. \nThe well known and often used integral form for luminosity distance in standard FLRW is:\n\\be \nD_{\\ell}(\\OM,\\OL,\\nu=0;z)= {c\\over H_0}{1+z \\over \\sqrt{|1-\\OO|}}\\ S_{\\kappa}\n\\left[ \\sqrt{|1-\\OO|} \n\\int_0^z{dz\\over \\sqrt{(1+z)^2(1+\\OM z)-z(z+2)\\OL}}\n\\right]\\label{nu=0}\n\\ee\nwhich we integrate using \\cite{BF} to obtain,\n\\be\nD_{\\ell}(\\OM,\\OL,\\nu=0;z)={c\\over H_0}{1+z \\over \\sqrt{|1-\\OO|}}\\ S_{\\kappa}\n\\Bigl[\\ \n-g\n\\Bigl\\{\nF(\\phi_z,{\\rm k})-F(\\phi_0,{\\rm k})\n\\Bigr\\}\n\\Bigr],\n\\label{ansnu=0}\n\\ee\nor equivalently using an addition formula for $F(\\phi,{\\rm k})$, \\ie \n$F(\\phi_z,{\\rm k})-F(\\phi_0,{\\rm k})$ = $F(\\Delta\\phi_z,{\\rm k})$ we get:\n\\be\nD_{\\ell}(\\OM,\\OL,\\nu=0;z)={c\\over H_0}{1+z \\over \\sqrt{|1-\\OO|}}\\ S_{\\kappa}\n\\Bigl[\\ \n-g\\\nF(\\Delta\\phi_z,{\\rm k})\n\\Bigr].\n\\label{Del_ansnu=0}\n\\ee\nThe parameter $\\kappa\\equiv$ ($\\OO-1$)/$|\\OO-1|$ is determined by the sign of the \n3-curvature and $S_{\\kappa}[\\ ]$ is \none of two functions:\n\\[\nS_{\\kappa}[\\ ]= \\left\\{\n\\begin{array}{l c l}\n{\\rm sinh}[\\ ] &:& \\kappa= -1, \\\\\n{\\rm sin}[\\ ] &:& \\kappa = +1.\n\\end{array}\n\\right.\n\\]\nConstants $g$ and ${\\rm k}$ depend on the cosmic parameters $\\OM\\ \\&\\ \\OL$, and $F(\\phi,{\\rm k})$ \nis the incomplete Legendre \nelliptic integral of the first kind.\\footnote{\n$F(\\phi,{\\rm k})\\equiv \\int_0^{\\phi} 1/\\sqrt{1-{\\rm k}^2\\sin^2\\phi}\\ d\\phi$}\nThe constants $g$ and ${\\rm k}$ depend on $\\OM\\ \\&\\ \\OL$\nonly through a combination called $b$ defined by:\n\\be\nb\\equiv -(27/2){\\OM^2\\OL\\over (1-\\OO)^3}, \\hskip .5 in -\\infty\\le b \\le \\infty,\n\\ee\n\\bea\nb<0 \\ \\Leftrightarrow \\kappa = -1,\\nonumber\\\\\nb>0 \\ \\Leftrightarrow \\kappa = +1.\\nonumber\n\\eea\nThe functions $\\phi_z$ and $\\Delta\\phi_z$ depend on the redshift $z$ and the cosmic parameters \n$\\OM\\ \\&\\ \\OL$ (not just on the combination $b$). Domains for the various $b$ \nvalues in the $\\OM$--\\ $\\OL$ plane are shown in Fig. 1.\n\n{\\bf 1.} For the two open domains defined by $b < 0$ and $2 < b$, quantities \n$g,{\\rm k},$ $\\phi_z$, and $\\Delta\\phi_z$ are conveniently written in \nterms of intermediate constants $v_{\\kappa},\\ y_1$ and $A$\ndefined by:\n\\be \nv_{\\kappa}\\equiv\\left[\\kappa(b-1)+\\sqrt{b(b-2)}\\right]^{1/3}, \\hskip .5in v_{\\kappa}\\ge 1.\n\\label{v}\n\\ee \n\\be\ny_1\\equiv{-1+\\kappa (v_{\\kappa}+v_{\\kappa}^{-1})\\over 3},\n\\label{y1kappa}\n\\ee\n\\be\nA=A(\\OM,\\OL)\\equiv \\sqrt{y_1(3y_1+2)}=\\sqrt{{v_{\\kappa}^2+v_{\\kappa}^{-2}+1\\over 3}}\\ge 1.\n\\label{A}\n\\ee\nParameters $g$ and ${\\rm k}$ are then given by:\n\\be\ng=g(\\OM,\\OL)= 1/\\sqrt{A(\\OM,\\OL)}=\n\\left[ {3\\over v_{\\kappa}^2+v_{\\kappa}^{-2}+1}\\right]^{1/4}\\le 1,\n\\ee\nand\n\\be\n{\\rm k}^2={\\rm k}^2(\\OM,\\OL)= {2A+\\kappa(1+3y_1)\\over 4A}= \n\\left[{1\\over 2}+{1\\over 4}g^2(v_{\\kappa}+v_{\\kappa}^{-1})\\right]\\le 1.\n\\ee\nFunctions $\\phi_z$, and $\\Delta\\phi_z$ are given by:\n\\be\n\\phi_z=\\phi(\\OM,\\OL;z)\n=\\cos^{-1}\n\\left[\n{(1+z)\\OM/|1-\\OO|+\\kappa y_1-A\n\\over\n(1+z)\\OM/|1-\\OO|+\\kappa y_1+A}\n\\right],\n\\label{phiA1}\n\\ee\nand\n\\be\n\\Delta\\phi_z=\\Delta\\phi(\\OM,\\OL;z)\n= 2\\ \\tan^{-1}\\left[{-z\\ \\sqrt{A}\\sqrt{|1-\\OO|}\\sqrt{1+z[1-(1-\\OO)\\OM^{-1}y_1]^{-1}}\n\\over\n1+z [1-(1-\\OO)\\OM^{-1}y_1]^{-1}+\\sqrt{(1+z)^2(1+\\OM z)-z(z+2)\\OL}}\n\\right].\n\\label{Del_phiA1}\n\\ee\n\n\n{\\bf 2.} For the domain $0 < b < 2$ ($\\Rightarrow \\kappa=1$) three intermediate parameter \n$y_1,\\ y_2$ and\n$y_3$ are \nconvenient to use, although none are really necessary. In \nthis domain of $b$, intermediate parameters $y_1,\\ y_2$ and $y_2$ are related to the cosmic parameters \n$\\OM \\&\\ \\OL$ through $b$ by:\n\\bea\ny_1&\\equiv& {1\\over 3}\n\\left(\n-1+{\\rm cos}\\left[{{\\rm cos}^{-1}(1-b)\\over 3}\\right]+\n\\sqrt{3}\\ {\\rm sin}\\left[{{\\rm cos}^{-1}(1-b)\\over 3}\\right]\\right), \\ \\ 0\\le y_1\\le 1/3,\n\\nonumber\\\\\ny_2&\\equiv& {1\\over 3}\n\\left(\n-1-2\\ {\\rm cos}\\left[{{\\rm cos}^{-1}(1-b)\\over 3}\\right]\\right), \\ \\ -1\\le y_2\\le -2/3,\n\\nonumber\\\\\ny_3&\\equiv& {1\\over 3}\n\\left(\n-1+{\\rm cos}\\left[{{\\rm cos}^{-1}(1-b)\\over 3}\\right]-\n\\sqrt{3}\\ {\\rm sin}\\left[{{\\rm cos}^{-1}(1-b)\\over 3}\\right]\\right), \\ \\ -2/3\\le y_3\\le 0.\n\\label{y123}\n\\eea\nThe following expressions are valid \n{\\bf only} in the lower right part of the $\\OM$--\\ $\\OL$ plane. \nIn the upper left domain where $b$ also satisfies $0\\le b \\le 2$,\nexpressions can be given, but\nthere a big bang \ndoesn't occur. The parameters $g$ and ${\\rm k}$ and functions $\\phi_z$ and $\\Delta\\phi_z$ \nneeded to evaluate (\\ref{ansnu=0}) and (\\ref{Del_ansnu=0}) are:\n\\be\ng=g(\\OM,\\OL)\\equiv {2\\over \\sqrt{y_1-y_2}},\n\\ee\n\\be\n{\\rm k}^2={\\rm k}^2(\\OM,\\OL)\\equiv { y_1-y_3\\over y_1-y_2 }\\le 1,\n\\label{k+}\n\\ee\n\\be\n\\phi_z=\\phi(\\OM,\\OL;z)={\\rm sin}^{-1}\n\\sqrt{\ny_1-y_2\n\\over\n(1+z)\\OM/|1-\\OO|+y_1\n}\n\\label{phiA2},\n\\ee\n\\bea\n\\Delta\\phi_z&=&\\Delta\\phi(\\OM,\\OL;z)\\nonumber\\\\\n&=& 2\\ \\tan^{-1}\\left[ {\n\\sqrt{y_1-y_2}\\ \\ \\left[\\sqrt{y_3-\\OM/(1-\\OO)}-\\sqrt{y_3-(1+z)\\OM/(1-\\OO)}\\right]\n\\over\n\\sqrt{[y_1-\\OM/(1-\\OO)][y_2-(1+z)\\OM/(1-\\OO)]}+\\sqrt{[y_1\\longleftrightarrow y_2]}\n}\n\\right],\n\\label{Del_phiA2}\n\\eea\nwhere $y_1\\longleftrightarrow y_2$ means repeat the previous term with $y_1$ \nand $y_2$ exchanged.\n\n{\\bf B. Boundaries} \n\n1. $\\OO\\equiv\\OM+\\OL=1$\n\nFor the spatially flat model ($\\ b\\rightarrow \\pm\\infty)$\n a much simpler expression involving hypergeometric functions results:\n\\bea \n&&D_{\\ell}(\\OM,\\OL=1-\\OM,\\nu=0;z)= {c\\over H_0}(1+z)\\int_0^z{dz\\over \\sqrt{1+\\OM z(3+3z+z^2)}}\n\\nonumber\\\\\n&& \\hskip .5in\n= {c\\over H_0}{2(1+z)\\over \\OM^{1/3}}\n\\Biggr[\n{}_2F_1\\left( \\frac16,\\frac23;\\frac76;1-\\OM\\right) \n\\nonumber\\\\\n&& \\hskip .5in\n- \n\\left({1\\over [1+\\OM z(3+3z+z^2)]^{1/6} }\\right)\\,{}_2F_1\\left( \\frac16,\\frac23;\\frac76;{1-\\OM\\over 1+\\OM z(3+3z+z^2)}\\right)\n\\Biggl].\n\\label{2F1ansnu=0B1}\n\\eea\nWhen $\\OM\\ne 1$ (\\ref{2F1ansnu=0B1}) can be expressed as associated Legendre functions, \n\\bea\n&&D_{\\ell}(\\OM,\\OL=1-\\OM,\\nu=0;z)= {c\\over H_0}{\n2^{1/6}\\Gamma\\left(1/6\\right)(1+z)\n\\over \n3 [\\OM^5(1-\\OM)]^{1/12}\n}\\nonumber\\\\\n&& \\hskip 1in\n\\times\\left[\n{\\rm P}^{-1/6}_{-1/6}\\left({1\\over \\sqrt{\\OM}}\\right)-\n{1\\over (1+z)^{(1/4)}}\\,{\\rm P}^{-1/6}_{-1/6}\\left(\\sqrt{{1+\\OM z(3+3z+z^2)}\\over \\OM(1+z)^3}\\right)\n\\right].\n\\label{Pansnu=0B1}\n\\eea\nIf (\\ref{Pansnu=0B1}) is given in terms of Legendre elliptic integrals the\nresult is more complicated:\n\\bea\nD_{\\ell}(\\OM,\\OL=1-\\OM,\\nu=0;z)\n&&={c\\over H_0}{1+z \\over (3)^{1/4}\\sqrt{\\OM}(\\OM^{-1}-1)^{1/6}}\n\\biggl[ \n-\\{F(\\phi_z,{\\rm k})-F(\\phi_0,{\\rm k})\\}\n\\biggr],\n\\nonumber\\\\\n&&={c\\over H_0}{1+z \\over (3)^{1/4}\\sqrt{\\OM}(\\OM^{-1}-1)^{1/6}}\n\\biggl[ \n-F(\\Delta\\phi_z,{\\rm k})\n\\biggr],\n\\label{ansnu=0B1}\n\\eea\nwhere\n\\be\n{\\rm k}^2=\\left[{1\\over 2}+{\\sqrt{3}\\over 4}\\right],\n\\label{kOO=1}\n\\ee\n\\be\n\\phi_z=\\phi(\\OM;z)=\\cos^{-1}\n\\left[\n 1+z + (1-\\sqrt{3})(\\OM^{-1}-1)^{1/3}\n\\over\n1+z + (1+\\sqrt{3})(\\OM^{-1}-1)^{1/3}\n\\right],\n\\label{phiOO=1}\n\\ee\nand\n\\be\n\\Delta\\phi_z=\\Delta\\phi(\\OM,\\OL;z)\n\\equiv2\\ \\tan^{-1}\\left[{-z\\ \\sqrt{\\sqrt{3}\\OM(1/\\OM-1)^{1/3}}\n\\sqrt{1+z[1+(1/\\OM-1)^{1/3}]^{-1}}\n\\over\n1+z [1+(1/\\OM-1)^{1/3}]^{-1}+\\sqrt{1+\\OM z(3+3z+z^2)}}\n\\right].\n\\label{Del_phiOO=1}\n\\ee\n\n2. $b=2$\n\nThis value of $b$ can be identified with ``critical\" values of the cosmic \nparameters, \\cite{FI}. We give a result good only for the lower $b=2$ curve, \nsee (\\ref{lower_b=con}). These models start with a big bang and \nexpand to the the finite Einstein radius \nat $t=\\infty$, see A3(vii-b) in the appendix of \\cite{MG}:\n\\bea\n&&D_{\\ell}(\\OM,\\OL(\\OM),\\nu=0;z)= {c\\over H_0} {1+z\\over\\sqrt{|1-\\OO|}}\n\\nonumber\\\\\n&& \n\\times \\sin\\left\\{ \\ln\\left(\n{\n\\left[\\sqrt{1/3-\\Omega_m/(1-\\Omega_0)} +1\\right]\n\\left[\\sqrt{1/3-(1+z)\\Omega_m/(1-\\Omega_0)} -1\\right]\n\\over\n\\left[\\sqrt{1/3-\\Omega_m/(1-\\Omega_0)} -1\\right]\n\\left[\\sqrt{1/3-(1+z)\\Omega_m/(1-\\Omega_0)} +1\\right]\n}\n\\right)\n\\right\\}.\n\\eea\n\n3. $\\OL=0$\n\nThis result is due to \\cite{MW}, we include it for completeness:\n\\be\nD_{\\ell}(\\OM,\\OL=0,\\nu=0;z) ={2c\\over H_0\\OM^2}\\left\\{\\OM\nz+(\\OM-2)\\left(\\sqrt{1+\\OM z}-1\\right)\\right\\}. \n\\label{Mattig} \n\\ee\n\n4. $\\OM=0$\n\nThese are massless big bang models, $\\OL<1$, discussed by \\cite{RH}:\n\n\\be\nD_{\\ell}(\\OM=0,\\OL,\\nu=0;z)={c (1+z)\\over H_0 \\OL}\n\\left\\{ 1+z-\\sqrt{\\OL+(1+z)^2(1-\\OL)}\\right\\}.\n\\label{OM=0}\n\\ee\n\n\\vskip .25 in\n\\centerline{\\bf II. $\\nu=1$,\\ 66\\% Filled-Beam Observations}\n{\\bf A. Four Open Big Bang Domains}\n\\bea \n&&D_{\\ell}(\\OM,\\OL,\\nu=1;z)=\n\\nonumber\\\\\n&&{c\\over H_0}2\\,(1+z){\\rm Sign}\\left[3-\\OM/(1-\\OO)\\right]\n\\sqrt{\\left|\n{\n\\left[3-\\OM(1+z)/(1-\\OO)\\right]\\left[3-\\OM/(1-\\OO)\\right]\n\\over \n(1-\\OO)[36+\\OM^2\\OL/(1-\\OO)^3]\n}\\right|\n}\n\\times \\nonumber\\\\\n&&\nS_{(\\OM,\\OL,z)}\n\\Biggl[\\ \\sqrt{|(1-\\OO)[36+\\OM^2\\OL/(1-\\OO)^3]|}\n\\times \\nonumber\\\\\n&&\nP\\,\\int_0^z{dz\\over2\\,\\left[ 3-\\OM(1+z)/(1-\\OO) \\right]\\sqrt{(1+z)^2(1+\\OM z)-z(z+2)\\OL}}\n\\Biggr],\n\\label{ansnu=1A}\n\\eea\nwhere \n\\[\nS_{(\\OM,\\OL,z)}[\\ ]= \\left\\{\n\\begin{array}{l c l}\n{\\rm cosh}[\\ ] &:& b<0\\,\\&\\,\\left[3-\\OM(1+z)/(1-\\OO)\\right]\\left[3-\\OM/(1-\\OO)\\right]<0, \\\\\n{\\rm sinh}[\\ ] &:& b<0\\,\\&\\,\\left[3-\\OM(1+z)/(1-\\OO)\\right]\\left[3-\\OM/(1-\\OO)\\right]>0, \\\\\n{\\rm sin}[\\ ] &:& 0<b<486, \\\\\n{\\rm sinh}[\\ ] &:& 486<b.\n\\end{array}\n\\right.\n\\]\nOnly the principal value of the integral (P) is needed and \nunlike the $\\nu=0$ case, this integral takes on different forms when evaluated using \nLegendre elliptic integrals, depending on the \nvalue of the parameter $b$. Parts of the analytic result (\\ref{ansnu=1A1})\nsometimes diverge even though the \ntotal expression remains finite.\nFor example when $b=486$, \\ie when \n$\\sqrt{36+\\OM^2\\OL/(1-\\OO)^3}=0$ or equivalently $y_1=3$, a limit must be taken. \nThe resulting $D_{\\ell}$ on this new \nboundary can be found in \nII.B.5 below. This new boundary splits the one open domain $2<b<\\infty$ into two \nparts, see Fig.\\,2. Consequently, the $\\OM$--\\ $\\OL$ plane is more complicated \nfor $\\nu=1$ than for either $\\nu=0$ or $\\nu=2$. \nSee A1 below for additional trouble points that occur. \n\n{\\bf 1.} For the three open domains defined by $b < 0, 2 < b<486$, and $486<b$ the luminosity distance $D_{\\ell}$ takes the form:\n\\bea\n&&D_{\\ell}(\\OM,\\OL,\\nu=1;z)=\n\\nonumber\\\\\n&&{c\\over H_0}2\\,(1+z){\\rm Sign}\\left[3-\\OM/(1-\\OO)\\right]\n\\sqrt{\\left|\n{\n\\left[3-\\OM(1+z)/(1-\\OO)\\right]\\left[3-\\OM/(1-\\OO)\\right]\n\\over \n(1-\\OO)[36+\\OM^2\\OL/(1-\\OO)^3]\n}\\right|\n}\n\\times \\nonumber\\\\\n&&\nS_{(\\OM,\\OL,z)}\n\\Biggl[\n{\\kappa\\ \\sqrt{|36+\\OM^2\\OL/(1-\\OO)^3|}\n\\over 2\\,\\sqrt{A}\\ [A+\\kappa(y_1-3)]}\n\\Biggl\\{\n\\left[F(\\phi_z,{\\rm k})-F(\\phi_0,{\\rm k})\\right]\n\\nonumber\\\\\n&&\n +{A-\\kappa(y_1-3)\\over 2\\kappa(y_1-3)}\n\\left[\n{\\rm P}\\,\\Pi(\\phi_z,\\hat{\\alpha}^2,{\\rm k})-{\\rm P}\\,\\Pi(\\phi_0,\\hat{\\alpha}^2,{\\rm k})\n\\right]\n\\Biggr\\}\n+f_b\n\\Biggr],\n\\label{ansnu=1A1}\n\\eea\n\nwhere $y_1,A,{\\rm k},$ and $\\phi_z$ are defined in (\\ref{y1kappa})-(\\ref{phiA1}) and the \nadditional constant $\\hat{\\alpha}^2$ is:\n\\be\n\\hat{\\alpha}^2\\equiv {(A+\\kappa(y_1-3))^2\\over 4A\\kappa(y_1-3)}.\n\\ee\n$\\Pi(\\phi,\\alpha^2,{\\rm k})$ is the incomplete Legendre elliptic integral of the third \nkind\\footnote{\n$\\Pi(\\phi,\\alpha^2,{\\rm k})\\equiv \\int_0^{\\phi} 1/\\left[(1-\\alpha^2\\sin^2\\phi)\n\\sqrt{1-{\\rm k}^2\\sin^2\\phi}\\ \\right]\\ d\\phi$. In arriving at the results for the two-thirds filled \nbeam model we discovered that equation 361.54 of \\cite{BF} has the two square-root terms \ninterchanged for the case $\\alpha^2/(\\alpha^2-1)> {\\rm k}^2$.} and P\\,$\\Pi(\\phi,\\alpha^2,{\\rm k})$\nis the principal part of that integral.\nThe function $f_b$ is one of,\n\\[ \nf_b = \\left\\{\n\\begin{array}{l c l}\n{1\\over 4}\\ln\\left|\\{[1+h(z)][1-h(0)]\\}/\\{[1+h(0)][1-h(z)]\\}\\right| &:& b<0\\ {\\rm or}\\ 486<b, \\\\\n{1\\over 2}\\left[\\tan^{-1}h(z)-\\tan^{-1}h(0)\\right]&:& 2<b<486, \n\\end{array}\n\\right. \n\\]\nwhere $h(z)$ is defined by:\n\\be\nh(z)\\equiv \n{\n\\sqrt{|36+\\OM^2\\OL/(1-\\OO)^3|}\n\\sqrt{(1+z)\\OM/|1-\\OO|+\\kappa y_1}\n\\over\n(3-y_1)\n\\sqrt{\n\\left[(1+z)\\OM/|1-\\OO|-\\kappa(1+y_1)/2\\right]^2\n-(1+y_1)(1-3y_1)/4\n}\n}.\n\\ee\nSome care has to be taken when using these expressions. Divergences in the function $f_b$ \nnecessarily occur and cancel divergences in $\\Pi(\\phi,\\alpha^2,{\\rm k})$.\nDivergences in $f_b$ \nalso occur which add to divergences in $\\Pi(\\phi,\\alpha^2,{\\rm k})$ and cancel \nzeros in the multiplicative factor $\\sqrt{\\left|\n\\left[3-\\OM(1+z)/(1-\\OO)\\right]\\left[3-\\OM/(1-\\OO)\\right]\\right|}$ of (\\ref{ansnu=1A1}).\nRedshift independent divergences occur when $\\OM/(1-\\OO)=3$ and\nwhen $\\OM(3-y_1)/(1-\\OO)=y_1(2y_1+5)$. These points are plotted in Figure 2. \nRedshift dependent divergences occur at $(1+z)=3(1-\\OO)/\\OM$ and at \n$(1+z)\\OM(3-y_1)/(1-\\OO)=y_1(5+2y_1)$. These points appear in the $\\OM$--\\ $\\OL$\nplane respectively to the left of the $\\OM/(1-\\OO)=3$ line and between the \n$\\OM(3-y_1)/(1-\\OO)=y_1(5+2y_1)$ and $b=486$ curves.\n\nComputer evaluation of (\\ref{ansnu=1A1}) can be speeded up by reducing the number of\nLegendre elliptic integrals that must be evaluated. As in (\\ref{Del_ansnu=0}) we can\nuse the addition formula for $F(\\phi,{\\rm k})$, \\ie\n$F(\\phi_z,{\\rm k})-F(\\phi_0,{\\rm k})=F(\\Delta\\phi_z,{\\rm k})$ and \nan addition formula for \n$\\Pi(\\phi,\\alpha^2,{\\rm k})$,\\footnote{This equation is 116.03 of \\cite{BF}, corrected\nfor two sign errors.}\n\\be\n\\Pi(\\phi_z,\\alpha^2,{\\rm k})-\\Pi(\\phi_0,\\alpha^2,{\\rm k})=\\Pi(\\Delta\\phi_z,\\alpha^2,{\\rm k})\n+\\frac12\\sqrt{{\\alpha^2\\over (\\alpha^2-1)(\\alpha^2-{\\rm k}^2)}}\n\\log\n\\left(\n{1+\n\\xi\n\\over\n1-\n\\xi\n}\n\\right),\n\\label{AddFormulaPiA1}\n\\ee\n\nwhere\n\\be\n\\xi\\equiv {\n\\sin\\phi_z\\sin\\phi_0\\sin\\Delta\\phi_z\\sqrt{\\alpha^2(\\alpha^2-1)(\\alpha^2-{\\rm k}^2)}\n\\over\n1-\\alpha^2\\sin^2\\Delta\\phi_z-\\alpha^2\\sin\\phi_z\\sin\\phi_0\\cos\\Delta\\phi_z\\sqrt{1-{\\rm k}^2\\sin^2\\Delta\\phi_z}\n},\n\\ee\nto cut the number of elliptic functions from four to two.\nWe were not able to simplify this expression enough to justify inclusion of a \nrewritten version of (\\ref{ansnu=1A1}). However, it was used in our Fortran \nimplementation (see Appendix).\n\n\n{\\bf 2.} For the open domain defined by $0 < b < 2$ the luminosity distance $D_{\\ell}$ has a somewhat simpler form:\n\\bea\n&&D_{\\ell}(\\OM,\\OL,\\nu=1;z)=\n{c\\over H_0}{2\\,(1+z)\\over \\sqrt{|1-\\OO|}}\n\\sqrt{\n{\n\\left[3-\\OM(1+z)/(1-\\OO)\\right]\\left[3-\\OM/(1-\\OO)\\right]\n\\over \n\\left[36+\\OM^2\\OL/(1-\\OO)^3\\right]\n}\n}\n\\times \\nonumber\\\\\n&&\n{\\rm sin}\n\\Biggl[\n{\n\\sqrt{36+\\OM^2\\OL/(1-\\OO)^3}\n\\over \n(3-y_1)\\sqrt{y_1-y_2}\n}\n\\Biggl\\{\n-\\Biggl[F(\\phi_z,{\\rm k})-F(\\phi_0,{\\rm k})\\Biggr]\n\\nonumber\\\\\n&&\\hskip .5in\n+\\left[\n\\Pi\\left(\\phi_z,{y_1-3\\over y_1-y_2},{\\rm k}\\right)-\\Pi\\left(\\phi_0,{y_1-3\\over y_1-y_2},{\\rm k}\\right)\\right]\n\\Biggr\\}\n\\Biggr].\n\\label{ansnu=1A2}\n\\eea\nThe constants $y_1,\\ y_2$ and ${\\rm k}$, and the function $\\phi_z$ are as defined in I.A.2 above\n[see (\\ref{y123})-(\\ref{phiA2})].\nJust as in the previous case, the number of Legendre elliptic functions in (\\ref{ansnu=1A2})\ncan be reduced from four to two\nby using the appropriate addition formulas. For $F(\\phi,{\\rm k})$ the formula is always \nthe same, see (\\ref{ansnu=0}) and (\\ref{Del_ansnu=0}),\nbut because $\\alpha^2$ is negative (\\ref{AddFormulaPiA1}) changes to: \n\\be\n\\Pi(\\phi_z,\\alpha^2,{\\rm k})-\\Pi(\\phi_0,\\alpha^2,{\\rm k})=\\Pi(\\Delta\\phi_z,\\alpha^2,{\\rm k})\n-\\frac12\\sqrt{{\\alpha^2\\over (1-\\alpha^2)(\\alpha^2-{\\rm k}^2)}}\n\\tan^{-1}\n\\left(\\xi\\right),\n\\label{AddFormulaPiA2}\n\\ee\nwhere\n\\be\n\\xi\\equiv {\n\\sin\\phi_z\\sin\\phi_0\\sin\\Delta\\phi_z\\sqrt{\\alpha^2(1-\\alpha^2)(\\alpha^2-{\\rm k}^2)}\n\\over\n1-\\alpha^2\\sin^2\\Delta\\phi_z-\\alpha^2\\sin\\phi_z\\sin\\phi_0\\cos\\Delta\\phi_z\\sqrt{1-{\\rm k}^2\\sin^2\\Delta\\phi_z}\n}.\n\\ee\nThis is 116.02 of \\cite{BF} with one sign error corrected.\n\n{\\bf B. Boundaries}\n\n1. $\\OO\\equiv\\OM+\\OL=1$\n\nFor these models $\\ b\\rightarrow \\pm\\infty$ and \n a much simpler expression results:\n\\bea \n&&D_{\\ell}(\\OM,\\OL=1-\\OM,\\nu=1;z)\n\\nonumber\\\\\n&& \\hskip .5in \n= {c\\over H_0}{2(1+z)^{3/2}\\over \\sqrt{1-\\OM}}\n{\\rm sinh}\\left[\n{\\sqrt{1-\\OM}\\over 2}\\int_0^z{ dz\\over (1+z) \\sqrt{1+\\OM z(3+3z+z^2)} }\\right],\n\\nonumber\\\\\n&& \\hskip .5in\n={c\\over H_0\\sqrt{1-\\OM}}(1+z)^2\n\\Biggl[\n\\left(\n{\n1+\\sqrt{1-\\OM}\n\\over\n\\sqrt{1+\\OM z(3+3z+z^2)} +\\sqrt{1-\\OM}\n}\n\\right)^{ 1/3 }\n\\nonumber\\\\\n&& \\hskip 2in\n-\\left(\n{\n1-\\sqrt{1-\\OM}\n\\over\n\\sqrt{1+\\OM z(3+3z+z^2)} -\\sqrt{1-\\OM}\n}\n\\right)^{ 1/3}\n\\Biggr].\n\\label{ansnu=1FB}\n\\eea\nThis result can be given in terms of Legendre elliptic integrals $F(\\phi,{\\rm k})$\nand $\\Pi(\\phi,\\alpha^2,{\\rm k})$; \nhowever, the authors can think of no useful purpose in doing so.\n\n2. $b=2$\n\nSee the description for the $\\nu=0$ case in section I.B.2 including (\\ref{lower_b=con}) for this\n``critical\" value of $b$: \n\\bea \n&&D_{\\ell}(\\OM,\\OL(\\OM),\\nu=1;z)={c\\over H_0}{(1+z)\\sqrt{3/2}\\over \\sqrt{|1-\\OO|}\\,(11)}\n\\Biggl\\{\n\\nonumber\\\\\n&&\n\\sqrt{8}\n\\left[\n\\sqrt{1-3\\,{\\OM\\over 1-\\OO}}-\n\\sqrt{1-3\\,{\\OM(1+z)\\over 1-\\OO}}\\\n\\right]\n\\cos\\left({4\\over \\sqrt{6}}\\log\\,(h_z)\\right)\n\\nonumber\\\\\n&&\n+\\left[\n8+\\sqrt{\\left(1-3\\,{\\OM\\over 1-\\OO}\\right)\\left(1-3\\,{(1+z)\\OM\\over 1-\\OO}\\right)}\\\n\\right]\n\\sin\\left(\n{4\\over \\sqrt{6}}\\log\\,(h_z)\n\\right)\n\\Biggr\\},\n\\label{ansnu=1B2}\n\\eea\nwhere $h_z$ is defined by:\n\\be\nh_z=\\left(\n{\n1+\\sqrt{1/3-\\OM/(1-\\OO)}\n\\over\n1+\\sqrt{1/3-(1+z)\\OM/(1-\\OO)}\n}\n\\right)\n\\sqrt{\n{\n2/3+(1+z)\\OM/(1-\\OO)\n\\over\n2/3+\\OM/(1-\\OO)\n}\n}.\n\\ee\n3. $\\OL=0$\n\nThis result was first given by \\cite{DC2},\n\\be\nD_{\\ell}(\\OM,\\OL=0,\\nu=1;z) = {c\\over H_0}{4\\over\n3\\OM^2}\\left[\\left({3\\over 2}\\OM-1+{1\\over 2}\\OM z \\right)\\sqrt{1+\\OM z} - \\left({3\\over 2}\\OM-1\\right)\\right].\n\\label{DC2} \n\\ee\n\n4. $\\OM=0$\n\nThis result is exactly the same as the $\\nu=0$ result (\\ref{OM=0}). If there is no mass\nin the universe then removing 33\\% of no mass from the beam changes nothing.\n\n5. $b=486$\n\nThis result is equivalent to the $b\\rightarrow 486$ limit of (\\ref{ansnu=1A1})\nbut is simpler to use.\nBecause $\\OL(\\OM)$ is double valued for $b=$ constant $\\ge 2$ , two expressions \nmust be given to draw the $b=486$\ncurve, see Fig. 2.\nFor the upper part of the curve:\n\\be\n\\OL(\\OM)=1-\\OM+3\\sqrt{2/b}\\ \\OM\\ \\cosh\\left[{\\cosh^{-1}\n\\left[\\sqrt{b/2}\\ (\\OM^{-1}-1)\\right]\\over 3}\\right],\n\\ee\nwhere \n$0\\le \\OM\\le 1/(1-\\sqrt{2/b})$.\nIn this expression hyperbolic cosine analytically \nbecomes cosine for $\\OM\\ge 1/(1+\\sqrt{2/b})$. \nFor the lower part of the curve:\n\\be\n\\OL(\\OM)=1-\\OM+3\\sqrt{2/b}\\ \\OM\\ \\cos\\left[{\\cos^{-1}\n\\left[\\sqrt{b/2}\\ (1-\\OM^{-1})\\right]+\\pi\\over 3}\\right],\n\\label{lower_b=con}\n\\ee\nwhere \n$1\\le \\OM\\le 1/(1-\\sqrt{2/b})$.\nThe simplified result is:\n\\bea\n&&D_{\\ell}(\\OM,\\OL(\\OM),\\nu=1;z)\n={c\\over H_0}{(1+z)\\over \\sqrt{|1-\\OO|}(33)^{(3/4)}}\n\\sqrt{\n\\left[3-{\\OM(1+z)\\over (1-\\OO)}\\right]\\left[3-{\\OM\\over (1-\\OO)}\\right] \n}\n\\times \n\\nonumber\\\\\n&&\n\\Biggl\\{\nF\\left(\\phi_0,{\\rm {\\sqrt{33}+5\\over 2\\sqrt{33}}}\\right)-F\\left(\\phi_z,{\\rm {\\sqrt{33}+5\\over 2\\sqrt{33}}}\\right)\n-2\\left[E\\left(\\phi_0,{\\rm {\\sqrt{33}+5\\over 2\\sqrt{33}}}\\right)-E\\left(\\phi_z,{\\rm {\\sqrt{33}+5\\over 2\\sqrt{33}}}\\right)\\right]\n\\nonumber\\\\\n&&\n+2\\,(33)^{(1/4)}\n\\Biggl[\n{\\sqrt{8+\\left[2+\\OM/(1-\\OO)\\right]^2}\n\\over\n\\sqrt{3-\\OM/(1-\\OO)}\\left[3+\\sqrt{33}-\\OM/(1-\\OO)\\right]\n}\n\\nonumber\\\\\n&&\n-\\,{\\sqrt{8+\\left[2+(1+z)\\OM/(1-\\OO)\\right]^2}\n\\over\n\\sqrt{3-(1+z)\\OM/(1-\\OO)}\\left[3+\\sqrt{33}-(1+z)\\OM/(1-\\OO)\\right]\n}\n\\Biggr]\n\\Biggr\\}.\n\\label{ansnu=1B486}\n\\eea\nThe arguments of the elliptic functions, $\\phi_z$ and $\\phi_0$, can be calculated\nfrom (\\ref{phiA1}) using $y_1=3$ and $A=\\sqrt{33}$. To reduce the number of \nelliptic functions needed to evaluate (\\ref{ansnu=1B486}), addition formulas for \n$F(\\phi,{\\rm k})$ and $E(\\phi,{\\rm k})$ can be used \n[see (\\ref{Del_ansnu=0}), (\\ref{AddFormulaE}), and (\\ref{AddFormulaE_A1})]. \nThe value of $\\Delta\\phi_z$ is given by (\\ref{Del_phiA1}).\n\n\\vskip .25 in\n\\centerline{\\bf III. $\\nu=2$, Empty-Beam Observations}\n{\\bf A. Three Open Big Bang Domains}\n\\bea \nD_{\\ell}(\\OM,\\OL,\\nu=2;z)&=&{c\\over H_0}(1+z)^2\n\\int_0^z{dz\\over(1+z)^2\\sqrt{(1+z)^2(1+\\OM z)-z(z+2)\\OL}}.\n\\label{nu=2}\n\\eea\nLike the $\\nu=1$ case this integral takes on different forms when evaluated in terms of \nLegendre elliptic integrals, depending on the \nvalue of the parameter $b$. \n \n{\\bf 1.} For the two open domains defined by $b < 0$ and $2 < b$ the luminosity distance $D_{\\ell}$ takes the form:\n\\bea \nD_{\\ell}(\\OM,\\OL,\\nu=2;z)&=&{c\\over H_0}{(1+z)^2\\over \\OL}\n\\Biggl\\{\n\\nonumber\\\\\n&&\n\\hskip -1.75in\n-(A+\\kappa y_1)\n\\Biggl[\n{\n\\sqrt{(1+z)^2(1+\\OM z)-z(z+2)\\OL}\n\\over \n(1+z)[(1+z)\\OM/|1-\\OO|+A+\\kappa y_1]\n}\n-{1\\over \\OM/|1-\\OO|+A+\\kappa y_1}\n\\Biggr]\n\\nonumber\\\\\n&&\n\\hskip -1.75in -\n{\n(A-\\kappa y_1)\\sqrt{|1-\\OO|}\n\\over\n2\\sqrt{A}\n}\n\\Biggl[\nF(\\phi_z,{\\rm k})-F(\\phi_0,{\\rm k})\n\\Biggr]\n+\\sqrt{A}\\sqrt{|1-\\OO|}\n\\Biggl[\nE(\\phi_z,{\\rm k})-E(\\phi_0,{\\rm k})\n\\Biggr]\n\\Biggr\\}\n\\label{ansnu=2A1}\n\\eea\nwhere $y_1,A,{\\rm k},$ and $\\phi_z$ are defined in (\\ref{y1kappa})-(\\ref{phiA1}).\\footnote{\n$E(\\phi,{\\rm k})\\equiv \\int_0^{\\phi} \\sqrt{1-{\\rm k}^2\\sin^2\\phi}\\ d\\phi$}\nJust as with the result for the $\\nu=1$ case, \\ie (\\ref{ansnu=1A1}), the number of \nLegendre elliptic integrals required to evaluate (\\ref{ansnu=2A1}) can be reduced from\nfour to two by using addition formulas 116.01 of \\cite{BF}. The addition formula\nfor $E(\\phi,{\\rm k})$ is:\n\\be\nE(\\phi_z,{\\rm k})-E(\\phi_0,{\\rm k})=E(\\Delta\\phi_z,{\\rm k})\n-{\\rm k}^2\\sin\\phi_z\\sin\\phi_0\\sin\\Delta\\phi_z.\n\\label{AddFormulaE}\n\\ee\nFor this case \n\\bea\n&&-{\\rm k}^2\\sin\\phi_z\\sin\\phi_0\\sin\\Delta\\phi_z=\n-{2\\left[2A+\\kappa(1+3y_1)\\right]\\over\\left[(1+z)\\OM/(1-\\OO)-y_1-\\kappa A\\right]}\n\\nonumber\\\\\n&&\\times\n{ \\sqrt{ \\left[(1+z)\\OM/(1-\\OO)-y_1\\right]\\left[ \\OM/(1-\\OO)-y_1\\right] }\\over\n\\left[\\OM/(1-\\OO)-y_1-\\kappa A\\right] \n\\left[\\tan(\\Delta\\phi_z/2)+1/\\tan(\\Delta\\phi_z/2)\\right]\n},\n\\label{AddFormulaE_A1}\n\\eea\nwhere an expression for $\\tan(\\Delta\\phi_z/2)$ is given by (\\ref{Del_phiA1}). \n \n{\\bf 2.} For the domain $0 < b < 2$ the luminosity distance $D_{\\ell}$ takes the form:\n\\bea \n&&D_{\\ell}(\\OM,\\OL,\\nu=2;z)=\n\\nonumber\\\\\n&&\n\\hskip .25in\n{c\\over H_0}{(1+z)^2\\over \\OL}\n\\Biggl\\{\n-y_3\n\\Biggl[\n{\n\\sqrt{(1+z)^2(1+\\OM z)-z(z+2)\\OL}\n\\over \n(1+z)[(1+z)\\OM/|1-\\OO|+y_3]\n}\n-{1\\over \\OM/|1-\\OO|+y_3}\n\\Biggr]\n\\nonumber\\\\\n&&\n\\hskip .25in -\n{y_2\\sqrt{|1-\\OO|}\n\\over\n\\sqrt{y_1-y_2}\n}\n\\Biggl[\nF(\\phi_z,{\\rm k})-F(\\phi_0,{\\rm k})\n\\Biggr]-\n\\sqrt{y_1-y_2}\\sqrt{|1-\\OO|}\n\\Biggl[\nE(\\phi_z,{\\rm k})-E(\\phi_0,{\\rm k})\n\\Biggr]\n\\Biggr\\},\n\\label{ansnu=2A2}\n\\eea\nwhere the constants $y_1,\\ y_2,\\ y_3$ and ${\\rm k}$ are defined in (\\ref{y123})-(\\ref{k+})\nbut the function $\\phi_z$ is now defined as \n\\bea\n\\phi_z=\\phi(\\OM,\\OL;z)\n&=&\\sin^{-1}\\sqrt{\n{\n(1+z)\\OM/|1-\\OO|+y_2\n\\over\n(1+z)\\OM/|1-\\OO|+y_3\n}\n}.\n\\label{phi++}\n\\eea\nFor this case the value of $\\Delta\\phi_z$ needed to reduce the number of elliptic integrals is\nthe NEGATIVE of that given by (\\ref{Del_phiA2}) for the $\\nu=0$ case.\nWhen the addition formula (\\ref{AddFormulaE}) is used, an\nadditional term is contributed to (\\ref{ansnu=2A2}) which can be evaluated using,\n\\bea\n&&-{\\rm k}^2\\sin\\phi_z\\sin\\phi_0\\sin\\Delta\\phi_z=\n{\\OM(y_1-y_3)|1-\\OO|^{(-3/2)}(y_1-y_2)^{(-1/2)}\\over [(1+z)\\OM^2/(1-\\OO)^2-(2+z)y_1\\OM/(1-\\OO)-2y_1(1+y_1)]}\n\\nonumber\\\\\n&&\n\\times\n\\left\\{{[y_2-\\OM/(1-\\OO)]\\sqrt{(1+z)^2(1+\\OM z)-z(z+2)\\OL}\\over [y_3-(1+z)\\OM/(1-\\OO)]}-\n{[y_2-(1+z)\\OM/(1-\\OO)]\\over [y_3-\\OM/(1-\\OO)]}\\right\\}.\n\\eea\n{\\bf B. Boundaries} \n\n1. $\\OO\\equiv\\OM+\\OL=1$\n\nThis case is the $\\ b\\rightarrow \\pm\\infty$ limit of (\\ref{nu=2}) and \n a simpler expression containing hypergeometric functions results:\n\\bea \n&&D_{\\ell}(\\OM,\\OL=1-\\OM,\\nu=2;z)\n\\nonumber\\\\\n&& \n\\hskip .5in\n={c\\over H_0}(1+z)^2\n\\Biggl\\{\n1-{1\\over (1+z)\\sqrt{1+\\OM z(3+3z+z^2)}}\n\\nonumber\\\\\n&& \n\\hskip 1in\n+\n\\frac35\\ \\OM^{1/3}\\Biggl[\n\\left( \n{1 \\over[1+\\OM z(3+3z+z^2)]^{5/6} }\\right)\\,\n{}_2F_1\\left( \\frac56,\\frac13;\\frac{11}6;{1-\\OM\\over 1+\\OM z(3+3z+z^2)}\\right)\n\\nonumber\\\\\n&& \n\\hskip 2in\n-{}_2F_1\\left( \\frac56,\\frac13;\\frac{11}6;1-\\OM\\right) \n\\Biggr]\n\\Biggr\\}.\n\\label{2F1ansnu=2B1}\n\\eea\nWhen $\\OM\\ne 1$, (\\ref{2F1ansnu=2B1}) can be expressed in terms of \nassociated Legendre functions as,\n\\bea \n&&D_{\\ell}(\\OM,\\OL=1-\\OM,\\nu=2;z)=\n\\nonumber\\\\\n&& \n\\hskip .5in{c\\over H_0}(1+z)^2\n\\Biggl\\{\n1-{1\\over (1+z)\\sqrt{1+\\OM z(3+3z+z^2)}}\n+\n{\\Gamma\\left(5/6\\right)\\over 2^{1/6}}\n\\left[{\\OM\\over \n1-\\OM}\n\\right]^{5/12}\n\\nonumber\\\\\n&& \n\\times\n\\left[\n{(1+z)^{1/4}\\over \n\\sqrt{1+\\OM z(3+3z+z^2)}}\n{\\rm P}^{-5/6}_{1/6}\\left(\\sqrt{{1+\\OM z(3+3z+z^2)}\\over \\OM(1+z)^3}\\right)\n-{\\rm P}^{-5/6}_{1/6}\\left({1\\over \\sqrt{\\OM}}\\right)\n\\right]\n\\Biggr\\}\n.\n\\label{Pansnu=2B1}\n\\eea\nWhen $\\OM\\ne 1$, (\\ref{2F1ansnu=2B1}) can also be expressed in terms of \nLegendre elliptic integrals as,\n\\bea \nD_{\\ell}(\\OM,\\OL=1-\\OM,\\nu=2;z)&=&{c\\over H_0}{(1+z)^2\\over 1- \\OM}\n\\Biggl\\{\n\\nonumber\\\\\n&&\n\\hskip -2.5in\n-(\\sqrt{3}+1)\\left(\\OM^{-1}-1\\right)^{1/3}\n\\Biggl[\n{\n\\sqrt{1+\\OM z(3+3z+z^2)}\n\\over \n(1+z)[1+z+(\\sqrt{3}+1)\\left(\\OM^{-1}-1\\right)^{1/3}]\n}\n-{1\\over 1+(\\sqrt{3}+1)\\left(\\OM^{-1}-1\\right)^{1/3}}\n\\Biggr]\n\\nonumber\\\\\n&&\n\\hskip -1.5in -\n{1\\over (\\sqrt{3}+1)(3)^{1/4}}\n\\sqrt{\\OM}\\left(\\OM^{-1}-1\\right)^{1/6}\n\\Biggl[\nF(\\phi_z,{\\rm k})-F(\\phi_0,{\\rm k})\n\\Biggr]\n\\nonumber\\\\\n&&\n\\hskip -1.0in +\n(3)^{1/4}\\sqrt{\\OM}\\left(\\OM^{-1}-1\\right)^{1/6}\n\\Biggl[\nE(\\phi_z,{\\rm k})-E(\\phi_0,{\\rm k})\n\\Biggr]\n\\Biggr\\},\n\\label{ansnu=2B1}\n\\eea\nwhere the constant ${\\rm k}$ is given by (\\ref{kOO=1}) and the functions $\\phi_z$ \nand $\\Delta\\phi_z$ are given respectively by (\\ref{phiOO=1}) and (\\ref{Del_phiOO=1}). \nFor this case the additional term needed to use the addition formula (\\ref{AddFormulaE}) \nin (\\ref{ansnu=2B1}) is:\n\\bea\n&&-{\\rm k}^2\\sin\\phi_z\\sin\\phi_0\\sin\\Delta\\phi_z\n\\nonumber\\\\\n&&\n={\nz\\ 2(3)^{3/4}\\left(2+\\sqrt{3}\\,\\right)\\sqrt{1-\\OM}\n\\over \n\\left[1+z+\\left(1+\\sqrt{3}\\,\\right)\\left(\\OM^{-1}-1\\right)^{1/3}\\right]\n\\left[1+\\left(1+\\sqrt{3}\\,\\right)\\left(\\OM^{-1}-1\\right)^{1/3}\\right]\n}\n\\nonumber\\\\\n&&\n\\times\n{\n\\left\\{z+ \\left[1+\\left(\\OM^{-1}-1\\right)^{1/3}\\right]\\left[1+\\sqrt{1+\\OM z(3+3z+z^2)}\\right]\\right\\}\n\\over\n\\left\\{2+3\\,z\\,\\OM+z^2\\,\\OM\\left[1+\\left(1+\\sqrt{3}\\,\\right)\\left(\\OM^{-1}-1\\right)^{1/3}\\right]\n+2\\sqrt{1+\\OM z(3+3z+z^2)}\\right\\}\n}.\n\\label{AddFormulaE_B1}\n\\eea\n2. $b=2$\n\nSee the description for the $\\nu=0$ case in section I.B.2 including (\\ref{lower_b=con}) for this\n``critical\" value of $b$: \n\\bea \n&&D_{\\ell}(\\OM,\\OL(\\OM),\\nu=2;z)\n\\nonumber\\\\\n&&={c\\over H_0}{9\\,\\OM\\,(1+z)^2 \\over 2|1-\\OO|^{3/2}}\n\\Biggl\\{\n{1\\over (1+z)}\\sqrt{\\frac13-{(1+z)\\OM\\over 1-\\OO}} -\\sqrt{\\frac13-{\\OM\\over 1-\\OO}} \n\\nonumber\\\\\n&&\n+{\\OM\\over 1-\\OO}\n\\log\\left[\n{\n1+\\sqrt{1/3-(1+z)\\OM/(1-\\OO)}\n\\over\n1+\\sqrt{1/3-\\OM/(1-\\OO)}\n}\n\\sqrt\n{\n{\n2/3+\\OM/(1-\\OO)\n\\over\n2/3+(1+z)\\OM/(1-\\OO)\n}\n}\n\\right]\n\\Biggr\\}.\n\\eea\n\n3. $\\OL=0$\n\nThis result was first given by \\cite{DC1},\n\\bea\n&&D_{\\ell}(\\OM,\\OL=0,\\nu=2;z) \\nonumber\\\\ &&\\hskip .5 in ={c\\over H_0}{\\OM(1+z)^2\\over\n4(1-\\OM)^{3/2}}\\Biggl[{3\\OM\\over 2(1-\\OM)} \\ln\\left\\{ \\left({1+\\sqrt{1-\\OM}\\over1-\\sqrt{1-\\OM}\n}\\right) \\left({\\sqrt{1+\\OM z}-\\sqrt{1-\\OM} \\over \\sqrt{1+\\OM z}+\\sqrt{1-\\OM} }\\right)\n\\right\\}\\nonumber\\\\ &&\\hskip .5 in +{3\\over\\sqrt{1-\\OM}}\\left({\\sqrt{1+\\OM z}\\over 1+z} -1\\right)\n+{2\\sqrt{1-\\OM}\\over \\OM}\\left( 1 - {\\sqrt{1+\\OM z}\\over (1+z)^2}\\right)\\Biggr]\\,, \n \\label{DC1}\n\\eea \nand can be rewritten using the identity \n\\be\n\\sinh^{-1}\\sqrt{{1-\\OM\\over \\OM(1+z)}} =\n{1\\over2} \\ln\\left({\\sqrt{1+\\OM z}+\\sqrt{1-\\OM} \\over \\sqrt{1+\\OM z}-\\sqrt{1-\\OM} }\\right)\\,. \n\\ee\n When $\\OM > 1$ equation (\\ref{DC1})\nis analytically continued using $\\sqrt{1-\\OM} \\longrightarrow \\pm i \\sqrt{\\OM-1}$, which\nsimplifies by using, $\\sinh^{-1}(i x) = i \\sin^{-1}(x)$ to give a form containing only real\nvariables. The $\\OM = 1$ result for all $\\nu$ was given by \\cite{DV}: \n\\be\nD_{\\ell}(\\OM=1,\\OL=0,\\nu;z) = {c\\over H_0}{1\\over\n(\\nu+{1\\over2})}\\left[(1+z)^{({\\nu\\over2}+1)}- (1+z)^{(-{\\nu\\over2}+{1\\over 2})}\\right].\n\\label{Dash} \n\\ee\n4. $\\OM=0$\n\nThis result is exactly the same as the $\\nu=0$ and $\\nu=1$ result (\\ref{OM=0}). If there is no mass\nin the universe then removing 100\\% of no mass from the beam removes nothing.\n\n\\section{Conclusions} \\label{sec-conclusions}\n\nWe have given useful forms for the luminosity distance in three currently relevant \ncosmologies. They are all dynamically FLRW cosmologies in the large but \ndiffer in how gravitating\nmatter effects optical observations. The models are labeled by an additional \nparameter $\\nu$ ($\\nu$ = 0, 1, and 2) beyond the familiar $H_0,\\Omega_m,$ and $\\Lambda$. The \n$\\nu=0$ model is standard FLRW where all matter is homogeneous and transparent \non the scale \nof the observing beam widths. This model is called the `filled-beam' model.\nThe \n$\\nu=2$ model assumes the opposite; all matter is inhomogeneous and excluded \nfrom the observing beams. \nThis extreme case is called the `empty-beam' model. \nThe \n$\\nu=1$ model assumes that 1/3 of the mass density of the universe is excluded \nfrom observing beams and hence it is the `two-thirds filled-beam' model.\nThese three cases were singled out because their distance-redshift relations\ncan be given in terms of incomplete elliptic integrals; functions which are universally \navailable in computer libraries and very efficiently evaluated.\\footnote{\nThe results appearing in Section \\ref{sec-results} have been coded \nand are posted at http://www.nhn.ou.edu$\\sim$thomas/z2dl.html.\nThis code is discussed in the Appendix and compared to the numerical \nintegration times of \\cite{KHS}.} \nFor the $\\nu=1$ and 2 cases, somewhat simpler expressions than what we have given exist, but \nonly for complex arguments of the elliptic integrals. We chose to give \nexpressions whose arguments are real and which \ncan be rapidly evaluated.\nResults are available \nfor all $0\\le\\nu\\le 2$ but only in terms of the less familiar and unavailable \nHeun functions, \\cite{KRa}. We have extended the flat space, $\\OO=1$, results given \nhere to arbitrary filling parameter $\\nu$. These new results will be available shortly. \nRelated results have been independantly found by \\cite{DM}.\nA calculation similar to the $\\nu=1$ case given here is that \nof the age of the Universe as a \nfunction of redshift and can be found in \\cite{TK}.\n\n\n\n\\acknowledgements\nR. Kantowski wishes to thank VP for Research, E. Smith, for funds\nto support J.K. Kao's visit to OU during the summer of 1998 when the first elliptic \nintegral results were obtained. R. C. Thomas thanks P. Helbig for \ndiscussions of his code, see\n\\cite{KHS}, and E. Baron for benchmarking discussions. \n\n\\appendix\n\\section{Appendix} \n\\label{sec-appendix}\n\nOne expected practical use of the results given in this paper is to\nspeedup distance evaluations for the $\\nu=$ 0,1,2 partially filled beam FLRW models.\n We have implemented and made publicly available a Fortran 90 version \nof this work called Z2DL (see http://www.nhn.ou.edu$\\sim$thomas/z2dl.html \nfor Z2DL with documentation and extensive\nCPU-time benchmark results).\nZ2DL uses Carlson elliptic integrals (see \\cite{PTVF}\nand references therein)\nand results in a fast distance calculator. \nWe have benchmarked Z2DL by comparing it with the commonly used and \nfast numerical integration \nroutine ANGSIZ (see \\cite{KHS}). For a given\n($\\OM,\\OL$), the total CPU-time required to convert $5\\times 10^5$ redshifts (equally\nspaced between z=0 and z=5) to luminosity distance using Z2DL and ANGSIZ \nseparately were\nrecorded. By calculating the ratio of ANGSIZ CPU-time to Z2DL CPU-time \non a grid of points in ($\\OM,\\OL$) we have generated three speedup surfaces,\none for each value of $\\nu=$ 0,1,2 (see Fig. 3 for the $\\nu=0$ surface). The results \nfor all three comparisons are given as contour plots at the web site.\nUsing an IBM AIX 375 MHz Power III\napproximately 7 hours was required to generate each\n($\\OM,\\OL$) grid of 30 x 30 points (minus models without a big bang).\n\nFor the purpose of a clearer presentation, we omitted speedup points along\nthe $\\OM=0$ and $\\OL=0$ lines. Along these boundaries\nspeedup factors are greater than 100. The large open domains of the \n $\\Omega_m$-$\\OL$ plane, \\ie subsection `A' cases, \nconstitute the majority of\nmodels in the grid and also those with the least impressive speedup.\nHowever, even for these cases, the improvement is substantial: typically \n17-20 for $\\nu=0$ (standard filled beam FLRW), 6-8 for $\\nu=1$ (66\\%\nfilled beam FLRW), and 11-13 for $\\nu=2$ (empty beam FLRW).\n\nTo gauge the level of agreement between distances computed by\nANGSIZ and Z2DL, a finer grid of ($\\OM,\\OL$) with 3000 x 3000 points\n(between 0 and 3 in both directions, also excluding models without a\nbig bang) was used. For each ($\\OM,\\OL$), both routines were used to\ncompute luminosity distance for z=1. Most often the results agree to within\none part in $10^6$. Cases where disagreements greater than one part in\n$10^3$ occur are near the upper b=2 line (see Fig. 1). We found that \nANGSIZ was giving less accurate distances near this boundary of non-big bang models\nas ANGSIZ documentation explains.\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[Bertotti(1966)]{BB} Bertotti, B. 1966, Proc. Roy. Soc. London, A, 294, 195\n\n\\bibitem[Byrd \\& Friedman(1971)]{BF} Byrd, P. F. \\& Friedman, M. D. 1971,\n Handbook of Elliptic Integrals for Engineers \\& Scientists \n(New York : Springer-Verlag)\n\n\\bibitem[Damianski et al.(2000)]{DM} Damianski, M., de Ritis, R., Marino, A. A., \\&\nPiedipalumbo, E., astro-ph/0004376\n \n\\bibitem[Dashevskii \\& Slysh(1966)]{DV} Dashevskii, V. M., \\& Slysh, V. I. 1966,\n\\sovast--AJ, 9, 671\n\n\\bibitem[Dyer \\& Roeder(1972)]{DC1} Dyer, C. C., \\& Roeder, R. C. 1972, \\apjl, 174, L115\n\n\\bibitem[Dyer \\& Roeder(1973)]{DC2} Dyer, C. C., \\& Roeder, R. C. 1973, \\apjl, 180, L31\n\n\\bibitem[Edwards(1972)]{ED} Edwards, D. 1972, \\mnras, 159, 51\n\n\\bibitem[Feige(1992)]{FB} Feige, B. 1992, Astron. Nachr., 313, 139\n\n\\bibitem[Felten \\& Isaacman(1986)]{FI} Felton, J. E. \\& Isaacman, R. 1986, \nRev. Mod. Phys., 58, 689\n\n\\bibitem[Holz \\& Wald(1998)]{HW} Holz, D. E., \\& Wald, R. M. 1998, \\prd, 58, 063501 \n\n\\bibitem[Holz(1998)]{HD} Holz, D. E. 1998, \\apjl, 506, L1 \n\n\\bibitem[Kantowski(1969)]{KR} Kantowski, R. 1969, \\apj, 155, 89 \n\n\\bibitem[Kantowski(1998a)]{KRa} Kantowski, R. 1998a, \\apj, 507, 483 \n\n\\bibitem[Kantowski(1998b)]{KRb} Kantowski, R. 1998b, in Sources and Detection of Dark Matter in the Universe, \nedited by D.B. Cline (Amsterdam: Elsevier Press).\n\n\\bibitem[Kaufman \\& Schucking(1971)]{KSSE} Kaufman, S. E. \\& Schucking, E. L. 1971, \\aj, 76, 583\n\n\\bibitem[Kaufman(1971)]{KS} Kaufman, S. E. 1971, \\aj, 76, 751\n\n\\bibitem[Kayser et al.(1997)]{KHS} Kayser, R., Helbig, P., \\& Schramm, T. 1997, \\aap, 318, 680\n\n\\bibitem[Lema\\^\\i tre(1931)]{LA} Lema\\^\\i tre, A. G. 1931, \\mnras, 91, 483\n\n\\bibitem[Mattig(1958)]{MW} Mattig, W. 1958, Astro. Nach. 284, 109\n\n\\bibitem[McVittie(1965)]{MG} McVittie, G. C. 1965, General Relativity and Cosmology,\n(Urbana: The University of Illinois Press)\n\n\\bibitem[Perlmutter et al.(1999)]{PS1} Perlmutter, S. et al. 1999, \\apj, 517, 565\n\n\\bibitem[Press et al.(1994)]{PTVF} Press, W., Teukolsky, S., Vetterling, W., \\& Flannery, B. 1994, \nNumerical Recipes (Cambridge: University Press) \n\n\n\\bibitem[Robertson(1933)]{RH}Robertson, H. P. 1933, Rev. Mod. Phys. 5, 62\n\n\n\\bibitem[Schmidt et al.(1998)]{SB} Schmidt, B. P. et al. 1998, \\apj, 507, 46 \n\n\\bibitem[Thomas \\& Kantowski(2000)]{TK} Thomas, R. C. \\& Kantowski, R. 2000, astro-ph/0002334\n\n\\bibitem[Wang(1999)]{WY} Wang, Y. 1999, astro-ph/9907405\n\n\\bibitem[Whittaker \\& Watson(1927)]{WE} Whittaker, E. T., \\& Watson, G. N. 1927,\n A Course in Modern Analysis (Cambridge: Cambridge University Press) \n\n\\bibitem[Zel'dovich(1964)]{Zel} Zel'dovich, Ya. B. 1964, \\sovast--AJ, 8, 13\n\\end{thebibliography}\n\n\n\\clearpage\n\n\n\\figcaption[fig1_3.eps]{The $\\Omega_m$-$\\OL$ plane showing various $b$ domains \nthat require different expressions for distance-redshift $D_{\\ell}$ for all\nthree cases: $\\nu=0,1,2$ \\ie filled-beam, 66\\% filled-beam, and empty-beam. \n\\label{fig1_3}}\n\n\\figcaption[fig2_3.eps]{Additional domains in the $\\Omega_m$-$\\OL$ plane \nfor $\\nu=1$, \\ie for 66\\% filled-beam observations, where complications due \nto divergent terms occur in the analytic results. \nFor $\\OM$--\\ $\\OL$ values on the dashed and\ndot-dashed lines, define respectively by $\\OL=1-\\OM4/3$ \nand $\\OM(3-y_1)/(1-\\OO)=y_1(2y_1+5)$, expression (\\ref{ansnu=1A1}) must be evaluated \nby taking a numerical limit. For points to the left of the straight dashed line and points \nbetween the dot-dashed and $b=486$ curves, a single value of $z$ exits for which \n(\\ref{ansnu=1A1}) also diverges. These $z$ values are defined respectively\nby $(z+1)=3(1-\\OO)/\\OM$ and \n$(1+z)\\OM(3-y_1)/(1-\\OO)=y_1(5+2y_1)$. For $\\OM,\\OL$, and $z$ satisfying either\nequation a limiting process must be used to evaluate \n$D_{\\ell}$ via (\\ref{ansnu=1A1}), see the Appendix. \nFor points on the divergent $b=486$ curve an analytic limit \nwas obtained in (\\ref{ansnu=1B486}).\n\\label{fig2_3}}\n\n\\figcaption[fig3_3.eps]{Contour plot of the $\\Omega_m$-$\\OL$ plane showing speedup \nfactors for Z2DL over ANGSIZ when $\\nu=0$ (standard filled beam FLRW cosmology). \nSpeedup factors for the other\ntwo cases considered in this paper, $\\nu=1,2$ \\ie the 66\\% filled-beam and empty-beam \ncan be found at the web site. \n\\label{fig3_3}}\n\n\\plotone{fig1_3.eps}\n\\eject\n\\plotone{fig2_3.eps}\n\\eject\n\\plotone{fig3_3.eps}\n\n\n\n\\end{document}\n\n"
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{
"name": "astro-ph0002334.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Bertotti(1966)]{BB} Bertotti, B. 1966, Proc. Roy. Soc. London, A, 294, 195\n\n\\bibitem[Byrd \\& Friedman(1971)]{BF} Byrd, P. F. \\& Friedman, M. D. 1971,\n Handbook of Elliptic Integrals for Engineers \\& Scientists \n(New York : Springer-Verlag)\n\n\\bibitem[Damianski et al.(2000)]{DM} Damianski, M., de Ritis, R., Marino, A. A., \\&\nPiedipalumbo, E., astro-ph/0004376\n \n\\bibitem[Dashevskii \\& Slysh(1966)]{DV} Dashevskii, V. M., \\& Slysh, V. I. 1966,\n\\sovast--AJ, 9, 671\n\n\\bibitem[Dyer \\& Roeder(1972)]{DC1} Dyer, C. C., \\& Roeder, R. C. 1972, \\apjl, 174, L115\n\n\\bibitem[Dyer \\& Roeder(1973)]{DC2} Dyer, C. C., \\& Roeder, R. C. 1973, \\apjl, 180, L31\n\n\\bibitem[Edwards(1972)]{ED} Edwards, D. 1972, \\mnras, 159, 51\n\n\\bibitem[Feige(1992)]{FB} Feige, B. 1992, Astron. Nachr., 313, 139\n\n\\bibitem[Felten \\& Isaacman(1986)]{FI} Felton, J. E. \\& Isaacman, R. 1986, \nRev. Mod. Phys., 58, 689\n\n\\bibitem[Holz \\& Wald(1998)]{HW} Holz, D. E., \\& Wald, R. M. 1998, \\prd, 58, 063501 \n\n\\bibitem[Holz(1998)]{HD} Holz, D. E. 1998, \\apjl, 506, L1 \n\n\\bibitem[Kantowski(1969)]{KR} Kantowski, R. 1969, \\apj, 155, 89 \n\n\\bibitem[Kantowski(1998a)]{KRa} Kantowski, R. 1998a, \\apj, 507, 483 \n\n\\bibitem[Kantowski(1998b)]{KRb} Kantowski, R. 1998b, in Sources and Detection of Dark Matter in the Universe, \nedited by D.B. Cline (Amsterdam: Elsevier Press).\n\n\\bibitem[Kaufman \\& Schucking(1971)]{KSSE} Kaufman, S. E. \\& Schucking, E. L. 1971, \\aj, 76, 583\n\n\\bibitem[Kaufman(1971)]{KS} Kaufman, S. E. 1971, \\aj, 76, 751\n\n\\bibitem[Kayser et al.(1997)]{KHS} Kayser, R., Helbig, P., \\& Schramm, T. 1997, \\aap, 318, 680\n\n\\bibitem[Lema\\^\\i tre(1931)]{LA} Lema\\^\\i tre, A. G. 1931, \\mnras, 91, 483\n\n\\bibitem[Mattig(1958)]{MW} Mattig, W. 1958, Astro. Nach. 284, 109\n\n\\bibitem[McVittie(1965)]{MG} McVittie, G. C. 1965, General Relativity and Cosmology,\n(Urbana: The University of Illinois Press)\n\n\\bibitem[Perlmutter et al.(1999)]{PS1} Perlmutter, S. et al. 1999, \\apj, 517, 565\n\n\\bibitem[Press et al.(1994)]{PTVF} Press, W., Teukolsky, S., Vetterling, W., \\& Flannery, B. 1994, \nNumerical Recipes (Cambridge: University Press) \n\n\n\\bibitem[Robertson(1933)]{RH}Robertson, H. P. 1933, Rev. Mod. Phys. 5, 62\n\n\n\\bibitem[Schmidt et al.(1998)]{SB} Schmidt, B. P. et al. 1998, \\apj, 507, 46 \n\n\\bibitem[Thomas \\& Kantowski(2000)]{TK} Thomas, R. C. \\& Kantowski, R. 2000, astro-ph/0002334\n\n\\bibitem[Wang(1999)]{WY} Wang, Y. 1999, astro-ph/9907405\n\n\\bibitem[Whittaker \\& Watson(1927)]{WE} Whittaker, E. T., \\& Watson, G. N. 1927,\n A Course in Modern Analysis (Cambridge: Cambridge University Press) \n\n\\bibitem[Zel'dovich(1964)]{Zel} Zel'dovich, Ya. B. 1964, \\sovast--AJ, 8, 13\n\\end{thebibliography}"
}
] |
astro-ph0002335
|
Discovery of an Obscured Broad Line Region in the High Redshift Radio Galaxy MRC~2025-218
|
[
{
"author": "James E. Larkin$^1$"
},
{
"author": "Ian S. McLean$^1$"
},
{
"author": "James R. Graham$^2$"
},
{
"author": "E. E. Becklin$^1$"
},
{
"author": "Donald F. Figer$^3$"
},
{
"author": "Andrea M. Gilbert$^2$"
},
{
"author": "N. A. Levenson$^{2,4}$"
},
{
"author": "Harry I. Teplitz$^{5,6}$"
},
{
"author": "Mavourneen K. Wilcox$^1$ \\& Tiffany M. Glassman$^1$"
}
] |
This paper presents infrared spectra taken with the newly commissioned NIRSPEC spectrograph on the Keck II Telescope of the High Redshift Radio Galaxy MRC~2025-218 (z=2.63) These observations represent the deepest infrared spectra of a radio galaxy to date and have allowed for the detection of H$\beta$, [OIII] (4959/5007), [OI] (6300), H$\alpha$, [NII] (6548/6583) and [SII] (6716/6713). The H$\alpha$ emission is very broad (FWHM = 9300 km/s) and luminous (2.6$\times$10$^{44}$ ergs/s) and it is very comparable to the line widths and strengths of radio loud quasars at the same redshift. This strongly supports AGN unification models linking radio galaxies and quasars, although we discuss some of the outstanding differences. The [OIII] (5007) line is extremely strong and has extended emission with large relative velocities to the nucleus. We also derive that if the extended emission is due to star formation, each knot has a star formation rate comparable to a Lyman Break Galaxy at the same redshift.
|
[
{
"name": "Larkin.tex",
"string": "\\documentstyle[emulateapj,epsf]{article}\n\n\\lefthead{Larkin et al.}\n\\righthead{Obscured Broad Line in MRC2025}\n\\begin{document}\n \n\\title{Discovery of an Obscured Broad Line Region in the High Redshift\nRadio Galaxy MRC~2025-218}\n\n\\author{James E. Larkin$^1$, Ian S. McLean$^1$, James R. Graham$^2$,\nE. E. Becklin$^1$, Donald F. Figer$^3$, Andrea M. Gilbert$^2$,\nN. A. Levenson$^{2,4}$, Harry I. Teplitz$^{5,6}$,\nMavourneen K. Wilcox$^1$ \\& Tiffany M. Glassman$^1$ }\n\n\\affil{$^1$Dept. of Physics and Astronomy, University of California,\nLos Angeles,\n$^2$Dept. of Astronomy, University of California, Berkeley,\n$^3$Space Telescope Science Institute,\n$^4$Dept. of Physics and Astronomy, John's Hopkins University,\n$^5$LASP, Goddard Space Flight Center,\n$^6$NOAO Research Associate}\n\\authoremail{larkin@astro.ucla.edu}\n\n\\begin{abstract}\nThis paper presents infrared spectra taken with the newly commissioned\nNIRSPEC spectrograph on the Keck II Telescope of the High Redshift\nRadio Galaxy MRC~2025-218 (z=2.63) These observations represent the\ndeepest infrared spectra of a radio galaxy to date and have allowed\nfor the detection of H$\\beta$, [OIII] (4959/5007), [OI] (6300), H$\\alpha$,\n[NII] (6548/6583) and [SII] (6716/6713). The H$\\alpha$ emission is very\nbroad (FWHM = 9300 km/s) and luminous (2.6$\\times$10$^{44}$ ergs/s)\nand it is very comparable to the line widths and strengths of radio\nloud quasars at the same redshift. This strongly supports AGN\nunification models linking radio galaxies and quasars, although we\ndiscuss some of the outstanding differences. The [OIII] (5007) line is\nextremely strong and has extended emission with large relative\nvelocities to the nucleus. We also derive that if the extended\nemission is due to star formation, each knot has a star formation rate\ncomparable to a Lyman Break Galaxy at the same redshift.\n\n\\end{abstract}\n\n\\keywords{galaxies: active --- galaxies: structure --- galaxies: quasars\n--- galaxies: kinematics and dynamics --- infrared: galaxies}\n\n\\section{Introduction}\n\nDeep radio surveys have proven to be one of the best methods for\nfinding high redshift galaxies. Most evidence suggests that these\npowerful radio sources are the precursors of local giant ellipticals\n(e.g. Pentericci, et al. 1999). Many have irregular and complex\nmorphologies suggestive of mergers and they are often surrounded by an\noverdensity of compact sources; presumably sub-galactic clumps\n(e.g. van Breugel et al. 1998). At both low and high redshifts, radio\ngalaxies usually have strong optical emission lines, especially OIII\nat 5007~\\AA. It is strongly debated, however, if the emission lines\narise by the same mechanism as the radio jets. Several authors\n(e.g. Rawlings \\& Saunders 1992, Eales \\& Rawlings 1993, and Evans\n1998) have demonstated a strong correlation between radio luminosity\nand [OIII] luminosity, but as Evans showed, there is a strong selection\neffect based on the detection limits as a function of distance and\nthis may explain much of the correlation. Since the galaxies are\noften disturbed, star formation, large scale shocks and a central AGN\nare all possible sources of the line emission. Active galaxy\nunification models suggest that radio galaxies are quasars with\nobscured broad line regions (e.g. Antonucci 1993). Eales \\& Rawlings\n(1993, 1996) and Evans (1998) have been successful at using infrared\nspectrographs on 4-meter class telescopes to measure a few of the\nbrightest lines in small samples of radio galaxies in the redshift\nrange 2.2 to 2.6 and they find line ratios most consistent with\nSeyfert 2 (obscured AGN) nuclei. Independent of our current efforts,\na team has also successfully used the ISAAC instrument on the VLT to\nobserve high redshift radio galaxies (HzRGs) including\nMRC~2025-218 (McCarthy, personal communication).\n\nAn additional unexplained phenomenon is that at high redshifts\n(z$>$0.6) the radio, optical continuum, infrared continuum and\nemission line structures tend to be closely aligned (Chambers, Miley,\n\\& van Bruegel 1987, and McCarthy et al. 1987). This is probably not\nseen in lower redshift targets because the central activity tends to\nbe a smaller fraction of the total luminosity than in high redshift\nsources. Among the proposed explanations are that the emission\nlines arise from shock induced star formation (De Young 1989, Rees\n1989) or that it is scattered light originating from the central\nnucleus (Fabian 1991). This is a crucial question in our\nunderstanding of how and when most star formation occured in giant\nelliptical galaxies and in clusters in general.\n\nMRC~2025-218 (z=2.630) has a compact near infrared and optical continuum\nmorphology (van Breugel et al. 1998), but extended Ly$\\alpha$ emission\n(5$^{\\prime \\prime}$) aligned with its radio axis (McCarthy et\nal. 1992). The extended UV emission has significant (8.3$\\pm$2.3 \\%)\nlinear polarization perpendicular to the UV axis (Cimatti et al. 1996)\nsuggesting that scattering plays a significant role. McCarthy et\nal. also found three extremely red galaxies (ERO's: R-K $>$ 6 mag)\nwithin 20$^{\\prime \\prime}$ of the radio galaxy. This is a large\noverdensity of such objects and strongly suggests an association\nbetween the ERO's and the active galaxy. In this paper we present\ninfrared spectra taken with a long slit oriented close to the radio\naxis and including one of the ERO's. The ERO spectra will be\ndescribed in a future paper. For all calculations we have assumed a\ncosmology with $\\Lambda$=0, q$_0$=0.1 and H$_0$=75 km s$^{-1}$\nMpc$^{-1}$. For a redshift of 2.63 this yields a luminosity distance\nof 2.1$\\times$10$^4$ Mpc and an angular scale of 7.7 kpc per\narcsecond.\n\n%--------------------------------------------------------------------\n\\section{Observations and Data Reduction}\n\nThe field of MRC~2025-218 was observed on 4 Jun, 1999 (UT) with the\nnear infrared spectrograph NIRSPEC (McLean, et al. 1998 and McLean, et\nal. 2000) on the Keck II Telescope during its commissioning. First\nthe field was imaged in the K-band with the slitviewing camera which\nis a HgCdTe PICNIC detector (256$^2$ pixels) sensitive from 1 to 2.5\nmicrons. Figure 1 shows the reduced image of the field with a total\nintegration time of 540 seconds and a FWHM of 0\\farcs54. As shown in\nthe figure, the slit (42$^{\\prime \\prime}$ long and 0\\farcs57 wide)\nwas placed on both the radio galaxy and the extremely red galaxy\ndubbed ERO-A by McCarthy et al. (1992). This corresponded to a slit\nposition angle of -7 degrees.\n\n{\\plotfiddle{larkin_fig1.ps}{2.8in}{0}{40}{40}{0}{-55}}\n{\\footnotesize Figure 1. - K band image of the MRC 2025-218 field.}\n\\medskip\n\nFor spectroscopy, the telescope was repeatedly moved roughly 20\narcseconds to center the objects first in the upper portion of the\nslit then the lower portion. Four 300 second exposures were taken in\nboth the H-band ($\\sim$1.6$\\mu$m) and K-band ($\\sim$2.2$\\mu$m)\nyielding an effective integration time on MRC~2025-215 of 20 minutes\nin each band. For guiding, NIRSPEC's optical guide camera was used to\nactively track a bright star roughly 2 arcminutes from MRC~2025-218.\n\nArc lamp and flat lamp spectra were taken at each setting prior to\nchanging mechanism setups. The 7.6 magnitude A0 star PPM~272233 was\nalso observed at the same settings in order to remove telluric\nabsorption effects from the atmosphere. The calibrator star was\nreduced first. For each band the spectral pair was subtracted and\ndivided by a reduced flat field lamp spectra. Bad pixels were then\nidentified and removed by medianing the four nearest neighbors. The\nspectra were spatially rectified using a quadratic polynomial at each\nrow, then spectrally rectified with a quadratic at each column. The\nnegative spectrum of the star was then shifted and subtracted from the\npositive spectrum producing a combined spectrum with residual\natmospheric lines removed. The stellar spectrum was extracted by\naveraging the central 3 pixels along the 2-d spectrum. A synthetic\nblack body spectrum was divided into the stellar spectrum and residual\nhydrogen absorption lines from the Brackett series were interpolated\nover. The spectra of the radio galaxy were reduced in a similar way\nexcept they were divided by the reduced calibration star spectrum\ninstead of a black body. For extraction of the galaxy spectra, a 6\npixel spatial aperture (1\\farcs14) was used. Spectrophotometry was\nobtained by determining the equivalent widths of the emission lines\nwithin a 1\\farcs5 aperture in the spectra and comparing this to the\nbroad band fluxes of the galaxy in a 1\\farcs5 circular aperture in the\nslit viewing camera images.\n\n{\\plotfiddle{larkin_fig2.ps}{2.9in}{270}{38}{38}{-15}{230}}\n{\\footnotesize Figure 2. - H band spectrum of MRC 2025-218. It is\ndominated by [OIII] at rest wavelength 5007~\\AA. Also present is the\nother member of this doublet ([OIII], 4959~\\AA) and a weak H$\\beta$\nemission line.}\n\\medskip\n\n%--------------------------------------------------------------------\n\\section{Results}\n\nFigure 2 shows the H-band spectrum of MRC~2025-218. By far the most\ndominant line is [OIII] (5007 \\AA) redshifted to 1.82 $\\mu$m. This line\nis highlighted in figure 3 where the complete position velocity map of\nthis line is presented. Panel (a) of figure 3 is stretched to\nhighlight the spectrally double nature of the nuclear emission\n($\\Delta$v $\\sim$ 200 km sec$^{-1}$). Panel (b) shows three faint\nemission knots at large angular separations (1$^{\\prime\n\\prime}$-2$^{\\prime \\prime}$) and/or high kinematic velocities\n($\\sim$400 km s$^{-1}$) Although faint, these structures repeat in the\nindividual spectra that cover the [OIII] line. Two knots appear at\nessentially 0 km sec$^{-1}$ relative velocity, but 1\\farcs8 North and\n2\\farcs4 South of the Nucleus. A high speed clump appears 1$^{\\prime\n\\prime}$ North of the nucleus and at a redshifted relative velocity of\n410 km sec$^{-1}$. This high speed clump is also the brightest within\nour slit with a flux of roughly 1$\\times$10$^{-16}$ ergs s$^{-1}$\ncm$^{-2}$. Also detected in the H-band spectrum is the other member of\nthe [OIII] doublet at 4959 \\AA, and H$\\beta$. The ratio of\n[OIII]~/~H$\\beta$ is extremely large at 17$\\pm$7. The H$\\beta$ line has\na total nuclear flux of only\n5~$\\times$~10$^{-17}$~ergs~cm$^{-2}$~s$^{-1}$. Table 1 gives all\ndetected fluxes and line widths.\n\nFigure 4 shows the K-band spectrum which is dominated by a broad\nH$\\alpha$ emission line. The spectrum has had a median filter passed\nover it to improve the appearance of the fainter lines. The H$\\alpha$\nis well modeled by a pair of Gaussians having line widths of\n9300$\\pm$900 km/s and 730$\\pm$100 km/s. The narrow component is\nconsistent with the Ly$\\alpha$ line width of 700 km/s found by\nVillar-Martin et al. 1999. After subtracting away the two H$\\alpha$\ncomponents, the middle graph in figure 4 shows the strong [NII]\n(6548/6583 \\AA) emission lines as well as weaker features from [OI]\n(6300 \\AA) and [SII](6716/6731 \\AA). The line fluxes and widths are\nalso given in table 1.\n\n{\\plotfiddle{larkin_fig3.ps}{1.9in}{270}{40}{40}{-30}{190}} {\\footnotesize\nFigure 3. - Position velocity plots for OIII (5007). Panel (a) is\nstretched to show the double nuclear peak. Panel (b) highlights three\nextended emission regions circled in white. The OIII line is highly\ndisturbed with several different kinematic and spatial components\nincluding a kinematically split nucleus and a high velocity (400 km/s)\nknot located 2'' off nucleus. Nearby OH lines from the Earth's\natmosphere are labeled.}\n\\medskip\n\n\\smallskip\n{\\centering\n\\footnotesize \\begin{tabular}{lccc}\n\\multicolumn{4}{c}{\\bf TABLE 1} \\\\\n\\multicolumn{4}{c}{\\bf Emission Line Strengths} \\\\\n\\hline\n\\hline\n\\multicolumn{1}{c}{} & Rest & Flux & Line Width \\\\\n\\multicolumn{1}{c}{Line} & $\\lambda$(\\AA) & ($\\times 10^{-16}$\nergs s$^{-1}$ cm$^{-2}$) & (km s$^{-1}$) \\\\\n\\hline\nSII & 6731 & 0.4$\\pm$0.3 & 200$\\pm$100 \\\\\nSII & 6716 & 0.6$\\pm$0.3 & 200$\\pm$100 \\\\\nNII & 6583 & 1.3$\\pm$0.3 & 880$\\pm$100 \\\\\nNII & 6548 & 1.3$\\pm$0.3 & 880$\\pm$100 \\\\\nH$\\alpha$(narrow) & 6563 & 2.7$\\pm$0.4 & 730$\\pm$100 \\\\\nH$\\alpha$(broad) & 6563 & 18$\\pm$2 & 9300$\\pm$900 \\\\\nOI & 6300 & 0.8$\\pm$0.3 & 800$\\pm$400 \\\\\nOIII & 5007 & 8.4$\\pm$1.6 & 600$\\pm$200 \\\\\nOIII & 4959 & 2.1$\\pm$0.4 & 600$\\pm$200 \\\\\nH$\\beta$ & 4861 & 0.5$\\pm$0.3 & 600$\\pm$200 \\\\\n\\hline\n\\end{tabular} }\n\n%--------------------------------------------------------------------\n\\section{Discussion}\n\n\\subsection{ Nuclear Spectrum}\n\nThe nuclear spectrum of the HzRG MRC~2025-218 is clearly dominated by\nemission lines from a central AGN. The broad H$\\alpha$ line width is\n9300 km/s which is only seen in type I AGN (unobscured broad line\nregions). This line width is very close to the mean H$\\beta$ line\nwidth of 9870$\\pm$950 km/s of radio loud quasars in the redshift range\n2.0 to 2.5 by McIntosh et al., 1999. The ratio of\n[OIII]/H$\\beta$ is 17 which is also only seen in AGN and ratios of\n[NII]/H$\\alpha$ and [OI]/H$\\alpha$ are also consistent with AGN\nexcitation (Osterbrock, 1989).\n\nFrom the H$\\alpha$/H$\\beta$ narrow line ratio of 5.4 we derive an\noptical extinction A$_V$=1.4 mag. In this calculation we've assumed an\nintrinsic ratio of H$\\alpha$/H$\\beta$ = 3.1 as seen in local AGN\n(Osterbrock, 1989), and the interstellar extinction law of Cardelli et\nal. (1989). This must be treated as an upper limit, however, since\nradio loud objects may have elevated H$\\alpha$ due to collisional\nexcitation (e.g. Baker et al. 1994). If the broad line ratio of\nH$\\alpha$/H$\\beta$ were similar to the narrow line ratio, then broad\nH$\\beta$ should have marginally been detected in our H-band spectrum.\nWe therefore feel safe in the assumption that the extinction to the\nbroad line region is similar to the value for the narrow line region\n(1.4 mag), but not necessarily significantly greater. This extinction\nis also sufficient to explain the lack of broad Ly$\\alpha$ detections\nin McCarthy et al. (1990) and Villar-Martin et al. (1999b). Without\nextinction our broad line emission would predict a Ly$\\alpha$ broad\nline flux of 2.6$\\times$10$^{-15}$~ergs~s$^{-1}$~cm$^{-2}$ in the\nVillar-Martin slit which would have been easily detected but with\nA$_V$=1.4 mag this is reduced to less than 3$\\times$10$^{-16}$\nergs~s$^{-1}$~cm$^{-2}$ which would have been marginably detected at\nbest.\n\n{\\plotfiddle{larkin_fig4.ps}{4in}{0}{40}{40}{0}{0}}\n{\\footnotesize Figure 4. - The K band spectrum of MRC 2025-218 is\ndominated by a very wide (9300 km s$^{-1}$) strong emission line of\nH$\\alpha$. The upper graph is the reduced spectrum overlayed with the\nH$\\alpha$ profiles. The dashed line is the x-axis for this graph. The\nmiddle graph has had the continuum and H$\\alpha$ emission lines\nsubtracted to emphasize the weaker lines of NII. The bottom graph is\nthe residuals after subtracting gaussians for each emission line.}\n\\medskip\n\nGiven the similarities in line width with radio loud quasars we now\ntry to determine if the extinction could explain the observed\ndifferences between MRC~2025-218 and radio loud quasars. If we\ncorrect the H$\\alpha$ flux for A$_V$=1.4 mag (the upper limit to the\nnarrow line extinction), then the broad line flux becomes\n5.2$\\times$10$^{-15}$ ergs~s$^{-1}$~cm$^{-2}$ or a broad line\nH$\\alpha$ luminosity of 2.6$\\times$10$^{44}$ ergs s$^{-1}$. We used\nthe sample of quasars of McIntosh et al. (1999) to derive a mean\nH$\\alpha$ luminosity of 6.11$\\times$10$^{44}$ ergs s$^{-1}$ based on\nthe mean H$\\beta$ equivalent width of their sample, no extinction and\nan intrinsic ratio of 3.1 between H$\\alpha$ and H$\\beta$. The one\nsigma dispersion in this value is only 10\\% in their sample. Our\nextinction corrected H$\\alpha$ luminosity is then weaker than their\nmean by a factor of 2.6 suggesting the central engines are very\nsimilar. If we go a step further and assume that the intrinsic\nluminosities are the same, then the broad line extinction would need\nto be A$_V$=3.5 mag instead of A$_V$=1.4 mag as derived above for the\nnarrow line region.\n\nA remaining difference between MRC~2025-218 and the quasars in the\nMcIntosh sample is the H-band magnitude. MRC~2025-218 has a broad band\nmagnitude of H=19.1 while the mean quasar H-band magnitude is\n15.16. After correcting for the different redshifts (quasar mean\nz=2.2) then MRC~2025-218 is 3.2 magnitudes fainter than the quasars at\na rest wavelength of 4550 \\AA. If the broad band flux of MRC~2025-218\nis dominated by the AGN then it would require A$_V$=4.2~mag to make it equal\nto the quasar sample. This is surprisingly close to the value of 3.5 mag\nrequired to match the broad H$\\alpha$ fluxes. The\nassumption that the AGN dominates the broad band flux in a radio\ngalaxy, however, is not obvious and may be in conflict with the\nempirically determined K magnitude versus redshift relation observed\nin both low redshift and high redshift objects (Eales et\nal. 1997). MRC~2025-218 is consistent with the K vs. Z relation both\nwith and without taking the line emission into account.\n\nVillar-Martin et al. (1999) find that MRC~2025-218 has large ratios\nof [NV]/HeII and [NV]/[CIV] and suggest that the most likely explanation\nis that N is overabundant. They held out the possibility, however,\nthat contamination from a broad line region was enhancing this line\nin comparison to their other radio galaxies. But they argued against\nthis due to the lack of any broad lines including [CIII]. From our\nbroad H$\\alpha$ detection, however, we clearly see that the broad line\nregion is only partially obscured and the strong NV emission is probably\nnot indicative of high metalicity. This is further corroborated by\nthe relatively low ratios of [NII]/H$\\alpha$(narrow).\n\n\\subsection{Spectral Shape and Extended Emission}\n\nThe double spectral peak found in [OIII] could be due to a high velocity\n(200 km s$^{-1}$) cloud of gas or possibly a double active\nnucleus. The unsmoothed H$\\alpha$ narrow line is quite noisy but also\nshows a double profile with a separation of 200 km s$^{-1}$. Due to\nthe noise, however, we are not confident in the second H$\\alpha$ peak.\nIf the second peak were due to a star forming region it would be\nunlikely that the [OIII] line would be double as well since the\nOIII/H$\\beta$ ratio should be much lower for a starburst.\n\nThe off nucleus knots seen in [OIII] are difficult to\nunderstand. Extended OIII has been observed in other radio galaxies\naligned to the radio axis (Armus et al. 1998) but no line ratios have\nbeen determined for this gas. If we assume that the emission is from\nstarbursts then our brightest knot (1$\\times$10$^{-16}$ ergs s$^{-1}$\ncm$^{-2}$) would have an [OIII]/H$\\alpha$ ratio less than 1.0. This\nwould make the H$\\alpha$ flux greater than\n1$\\times$10$^{-16}$~ergs~s$^{-1}$~cm$^{-2}$ and a luminosity more than\n5$\\times$10$^{42}$ ergs s$^{-1}$. Assuming the relationship of\nKennicutt (1983) that the star formation rate is equal to L(H$\\alpha$)\ndivided by 1.12$\\times10^{41}$ ergs/s we derive a star formation rate\nof 45 M$_{\\odot}$ yr$^{-1}$. This is comparable to the rates seen in\nPettini et al. (1998) where they studied 5 star forming galaxies in\nthe redshift range 2.2 to 3.3. This is also close to the estimated\nstar formation rate of the Lyman Break Galaxy MS1512-cB58. As\ncalculated in Teplitz et al. (2000) cB58 has a SFR of 620 M$_{\\odot}$\nyr$^{-1}$ but after removing a factor of 30 for gravitational lensing\nthis becomes 21 M$_{\\odot}$ yr$^{-1}$.\n\n%-----------------------------------------------------------------\n\\section{Conclusions}\n\nWe have obtained the most sensitive infrared spectra ever taken of a\nhigh redshift radio galaxy. The galaxy has very strong emission lines\nwith ratios and line widths consistent with an obscured quasar. The\nnarrow line region appears to be partially obscured with A$_V$ around\n1.4 mag, but from comparisons with high redshift quasars, we estimate\nthat the extinction to the broad line region is between 3 and 5\nmagnitudes. Since other radio galaxies in the same redshift range\ndon't show broad emission lines, we suggest that MRC~2025-218 is\nfurther along in its evolution towards an unobscured quasar. We\ncannot rule out any of the proposed mechanisms for the production of\nthe aligned emission. But based on the [OIII] line strength if the\nmajority of the emission is due to star formation, we find that the\nstar formation rate is comparable to that of Lyman Break Galaxies at\nsimilar redshifts. We urge even deeper observations of this and other\nsimilar radio galaxies in order to measure additional extended line\nemission.\n\n\\acknowledgments\n\nIt is a pleasure to acknowledge the hard work of past and present\nmembers of the NIRSPEC instrument team at UCLA: Maryanne Angliongto,\nOddvar Bendiksen, George Brims, Leah Buchholz, John Canfield, Kim\nChin, Jonah Hare, Fred Lacayanga, Samuel B. Larson, Tim Liu, Nick\nMagnone, Gunnar Skulason, Michael Specncer, Jason Weiss and Woon\nWong. In addition, we thank the Keck Director Fred Chaffee, CARA\ninstrument specialist Thomas A. Bida, and all the CARA staff involved\nin the commissioning of NIRSPEC. We also want to thank\nLee Armus for many useful discussions. We are also grateful for a\nvery careful review from our anonymous referee. Data presented herein\nwere obtained at the W.M. Keck Observatory which was made possible by\nthe generous financial support of the W.M. Keck Foundation.\n\n\\begin{references}\n\\reference{asm} Antonucci, R. 1993, ARA\\&A, 31, 473\n\\reference{asm} Armus, L., Soifer, B. T., Murphy, T. W., Neugebauer, G., Evans,\nA. S., \\& Matthews, K. 1998, \\apj, 495, 276\n\\reference{bak} Baker, A. C., Carswell, R. F., Bailey, J. A., Espey, B. R.,\nSmith, M. G., \\& Ward, M. J. 1994, MNRAS, 270, 575\nA. S., \\& Matthews, K. 1998, \\apj, 495, 276\n\\reference{bit} Binney, J. \\& Tremaine, S. 1987, \\it Galactic Dynamics \\rm,\n(Princeton: Princeton University Press\n\\reference{crd} Cardelli, J. A., Clayton, G. C. \\& Mathis, J. S. 1989,\n\\apj, 345, 245\n\\reference{cmm} Chambers, K. C., Miley, G. K., van Breugel, W. J. M., Bremer,\nM. A. R., Huang, J. S., \\& Trentham, N. A. 1996, \\apjs, 106, 215\n\\reference{cim} Cimatti, A., Dey, A., van Breugel, W., Antonucci, R.\n\\& Spinrad, H. 1996, \\apj, 465, 145\n\\reference{deY} De Young, D. S. 1989, \\apj, 342, L59\n\\reference{evans} Evans, A. S. 1998, \\apj, 498, 553\n\\reference{fab} Fabian, A. 1991, MNRAS, 238, 41\n\\reference{grah} Graham, J. R., Carico, D. P., Matthews, K., Neugebauer, G.,\nSoifer, B. T. \\& Wilson, T. D. 1990, \\apjl, 354, L5\n\\reference{ken} Kennicutt, R. 1983, \\apj, 272, 54\n\\reference{mpw} McCarthy, P. J., Persson, S. E., \\& West, S. C. 1992\n\\apj, 386, 52\n\\reference{mkv} McCarthy, P. J., Kapahi, V., van Breugel, W. \\&\nSubrahmanya, C. 1990, \\aj, 100, 1014\n\\reference{mci} McIntosh, D. H., Rieke, M. J., Rix, H.-W., Foltz, C. B.\n\\& Weymann, R. J. 1999, \\apj, 514, 40\n\\reference{mclean} McLean, I. S., et al. 1998, SPIE, 3354, 566\n\\reference{mclean} McLean, I. S., et al. 2000, PASP, in preparation\n\\reference{oster} Osterbrock, D.E. 1989, \\it Astrophysics of Gaseous Nebulae\nand Active Galactic Nuclei \\rm (Mill Valley: University Science Books)\n\\reference{prm} Pentericci, L., Rottgering, H. J., A., Miley, G. K.,\nMcCarthy, P., Spinrad, H., van Breugel, W. J. M., \\& Macchetto, F. 1999,\nA\\&A, 341, 329\n\\reference{pet} Pettini, M., Kellogg, M. Steidel, C. C., Dickinson, M.,\nAdelberger, K. L. \\& Giavalisco, M. 1998, \\apj, 508, 539\n\\reference{ree} Rees, M. J. 1989, MNRAS, 239, 1\n\\reference{tep} Teplitz, H. I. 2000, \\apjl, submitted\n\\reference{van} van Breugel, W. J. M., Stanford, S. A., Spinrad, H., Stern,\nD., \\& Graham, J. R. 1998, \\apj, 502, 614\n\\reference{vima} Villar-Martin, M., Binette, L. \\& Fosbury, R. A. E.\n1999a, 346, 7\n\\reference{vim} Villar-Martin, M., Fosbury, R. A. E., Binette, L., \nTadhunter, C. N., \\& Rocca-Volmerange, B. 1999b, accepted for A\\&A\n\\end{references}\n\n\\end{document}\n\n"
}
] |
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astro-ph0002336
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Constraints on Cosmological Parameters from Future \\ Galaxy Cluster Surveys
|
[
{
"author": "Zolt\\'an Haiman\\altaffilmark{1,2,3}"
},
{
"author": "Joseph J. Mohr\\altaffilmark{4,5,6} \\& Gilbert P. Holder\\altaffilmark{6}"
}
] |
We study the expected redshift evolution of galaxy cluster abundance between $0\lsim z \lsim 3$ in different cosmologies, including the effects of the cosmic equation of state parameter $w\equiv p/\rho$. Using the halo mass function obtained in recent large scale numerical simulations, we model the expected cluster yields in a 12~deg$^{2}$ Sunyaev-Zel'dovich Effect (SZE) survey and a deep 10$^{4}$~deg$^{2}$ X-ray survey over a wide range of cosmological parameters. We quantify the statistical differences among cosmologies using both the total number and redshift distribution of clusters. Provided that the local cluster abundance is known to a few percent accuracy, we find only mild degeneracies between $w$ and either $\Omega_m$ or $h$. As a result, both surveys will provide improved constraints on $\Omega_m$ and $w$. The $\Omega_m$--$w$ degeneracy from both surveys is complementary to those found either in studies of CMB anisotropies or of high--redshift Supernovae (SNe). As a result, combining these surveys together with either CMB or SNe studies can reduce the statistical uncertainty on both $w$ and $\Omega_m$ to levels below what could be obtained by combining only the latter two data sets. Our results indicate a formal statistical uncertainty of $\approx 3\%$ (68$\%$ confidence) on both $\Omega_m$ and $w$ when the SZE survey is combined with either the CMB or SN data; the large number of clusters in the X--ray survey further suppresses the degeneracy between $w$ and both $\Omega_m$ and $h$. Systematics and internal evolution of cluster structure at the present pose uncertainties above these levels. We briefly discuss and quantify the relevant systematic errors. By focusing on clusters with measured temperatures in the X--ray survey, we reduce our sensitivity to systematics such as non-standard evolution of internal cluster structure.
|
[
{
"name": "msrev.tex",
"string": "\\documentclass{article}\n\\usepackage{graphicx,emulateapj}\n\n\\submitted{Submitted to ApJ, Feb. 17, 200; Resubmitted, Nov. 28, 2000}\n\n%\\def\\myputfigure#1#2#3#4#5%\n%{\\hskip0.03\\textwidth\\vskip#5pt\n%\\makebox[0pt]{\\hskip#2in\n%\\includegraphics[width=#3\\textwidth]{#1}}\\vskip#4pt\\hfill}\n\n\\def\\myputfigure#1#2#3#4#5%\n{\\vskip#5pt\\makebox[0pt]{\\hskip#2in\n\\includegraphics[width=#3\\textwidth]{#1}}\\vskip#4pt\\hfill}\n\n\\def\\gsim{\\;\\rlap{\\lower 2.5pt\n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$>$}\\;}\n\\def\\lsim{\\;\\rlap{\\lower 2.5pt\n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$<$}\\;}\n\\def\\msun{{\\rm\\,M_\\odot}}\n\\def\\yr{{\\rm\\,yr}}\n\\def\\au{{\\rm\\,AU}}\n\\def\\del{{\\partial}}\n\\def\\gm{{\\rm\\,g}}\n\\def\\cm{{\\rm\\,cm}}\n\\def\\sec{{\\rm\\,s}}\n\\def\\erg{{\\rm\\,erg}}\n\\def\\kev{{\\rm\\,keV}}\n\\def\\ev{{\\rm\\,eV}}\n\\def\\K{{\\rm\\,K}}\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\lta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar''218$}}\n \\raise 2.0pt\\hbox{$\\mathchar''13C$}}}\n\\def\\gta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar''218$}}\n \\raise 2.0pt\\hbox{$\\mathchar''13E$}}}\n\\newcommand{\\beq}{\\begin{equation}}\n\\newcommand{\\eeq}{\\end{equation}}\n\n\n\\lefthead{HAIMAN, MOHR \\& HOLDER}\n\\righthead{COSMOLOGICAL PARAMETERS FROM GALAXY CLUSTER SURVEYS}\n\n\\begin{document}\n\n\\title{Constraints on Cosmological Parameters from Future \\\\\nGalaxy Cluster Surveys}\n\\author{Zolt\\'an Haiman\\altaffilmark{1,2,3}, Joseph J. \nMohr\\altaffilmark{4,5,6} \n\\& Gilbert P. Holder\\altaffilmark{6}}\n\\altaffiltext{1}{Hubble Fellow}\n\\altaffiltext{2}{Princeton University Observatory, Princeton, NJ}\n\\altaffiltext{3}{NASA/Fermilab Astrophysics Center, Fermi National \nAccelerator Laboratory, Batavia, IL}\n\\altaffiltext{4}{Chandra Fellow}\n\\altaffiltext{5}{Departments of Astronomy and Physics, University of \nIllinois, 1202 W. Green St, Urbana, IL 61801}\n\\altaffiltext{6}{Department of Astronomy and Astrophysics, University of \nChicago, 5640 S. Ellis Ave, Chicago, IL 60637}\n\n\\authoremail{zoltan@astro.princeton.edu}\n\\authoremail{jmohr@uiuc.edu}\n\n\n\\begin{abstract}\nWe study the expected redshift evolution of galaxy cluster abundance between\n$0\\lsim z \\lsim 3$ in different cosmologies, including the effects of the\ncosmic equation of state parameter $w\\equiv p/\\rho$. Using the halo mass\nfunction obtained in recent large scale numerical simulations, we model the\nexpected cluster yields in a 12~deg$^{2}$ Sunyaev-Zel'dovich Effect (SZE)\nsurvey and a deep 10$^{4}$~deg$^{2}$ X-ray survey over a wide range of\ncosmological parameters. We quantify the statistical differences among\ncosmologies using both the total number and redshift distribution of clusters.\nProvided that the local cluster abundance is known to a few percent accuracy,\nwe find only mild degeneracies between $w$ and either $\\Omega_m$ or $h$. As a\nresult, both surveys will provide improved constraints on $\\Omega_m$ and $w$.\nThe $\\Omega_m$--$w$ degeneracy from both surveys is complementary to those\nfound either in studies of CMB anisotropies or of high--redshift Supernovae\n(SNe). As a result, combining these surveys together with either CMB or SNe\nstudies can reduce the statistical uncertainty on both $w$ and $\\Omega_m$ to\nlevels below what could be obtained by combining only the latter two data sets.\nOur results indicate a formal statistical uncertainty of $\\approx 3\\%$ (68$\\%$\nconfidence) on both $\\Omega_m$ and $w$ when the SZE survey is combined with\neither the CMB or SN data; the large number of clusters in the X--ray survey\nfurther suppresses the degeneracy between $w$ and both $\\Omega_m$ and $h$.\nSystematics and internal evolution of cluster structure at the present pose\nuncertainties above these levels. We briefly discuss and quantify the relevant\nsystematic errors. By focusing on clusters with measured temperatures in the\nX--ray survey, we reduce our sensitivity to systematics such as non-standard\nevolution of internal cluster structure.\n\n\\end{abstract}\n\\keywords{cosmology: theory -- cosmology: observation}\n\n\\section{Introduction}\n\nIt has long been realized that clusters of galaxies provide a uniquely useful\nprobe of the fundamental cosmological parameters. The formation of the\nlarge--scale dark matter (DM) potential wells of clusters is likely independent\nof complex gas dynamical processes, star formation, and feedback, and involve\nonly gravitational physics. As a result, the abundance of clusters $N_{\\rm\ntot}$ and their distribution in redshift $dN/dz$ should be determined purely by\nthe geometry of the universe and the power spectrum of initial density\nfluctuations. Exploiting this relation, the observed abundance of nearby\nclusters has been used to constrain the amplitude $\\sigma_{\\rm 8}$ of the power\nspectrum on cluster scales to an accuracy of $\\sim 25\\%$\n(e.g. \\cite{white93,viana96}). The value of $\\sigma_{\\rm 8}$ in these studies\ndepends on the assumed underlying cosmology, especially on the density\nparameters $\\Omega_m$ and $\\Omega_\\Lambda$. Subsequent works\n(\\cite{bahcall98,blanchard98,viana99}) have shown that the redshift--evolution\nof the observed cluster abundance places useful constrains on these two\ncosmological parameters.\n\nIn the above studies, the equation of state for the $\\Lambda$--component has\nbeen implicitly assumed to be $p=w\\rho$ with $w=-1$. The recent suggestion\nthat $w$ might be different from $-1$, or even redshift dependent\n(\\cite{turner97,caldwell98}) has inspired several studies of cosmologies with a\ncomponent of dark energy. From a particle physics point of view, such $w>-1$\ncan arise in a number of theories (see\n\\cite{freese87,ratra88,turner97,caldwell98} and references therein). It is\ntherefore of considerable interest to search for possible astrophysical\nsignatures of the equation of state, especially those that distinguish $w=-1$\nfrom $w>-1$. Wang et al. (2000) has summarized current astrophysical\nconstraints that suggest $-1 \\leq w \\lsim -0.2$; while recent observations of\nType Ia SNe suggest the stronger constraint $w \\lsim -0.6$ (\\cite{ptw99}).\n\nThe galaxy cluster abundance provides a natural test of models that include a\ndark energy component with $w\\ne -1$, because $w$ directly affects the linear\ngrowth of fluctuations $D_z$, as well as the cosmological volume element\n$dV/dzd\\Omega$. Furthermore, because of the dependence of the angular diameter\ndistance $d_A$ on $w$, the experimental detection limits for individual\nclusters, e.g., from the Sunyaev--Zel'dovich effect (SZE) decrement or the\nX--ray luminosity, depend on $w$. Wang \\& Steinhardt (1998, hereafter WS98)\nstudied the constraints on $w$ from a combination of measurements of the\ncluster abundance and Cosmic Microwave Background (CMB) anisotropies. Their\nwork has shown that the slope of the comoving abundance $dN/dz$ between $0<z<1$\ndepends sensitively on $w$, an effect that can break the degeneracies between\n$w$ and combinations of other parameters $(h,\\Omega,n)$ in the CMB anisotropy\nalone.\n\nHere we consider in greater detail the constraints on $w$, and other\ncosmological parameters, from cluster abundance evolution. Our main goals are:\n(1) to quantify the statistical accuracy to which $w\\neq -1$ models can be\ndistinguished from standard $\\Lambda$ Cold Dark Matter (CDM) cosmologies using\ncluster abundance evolution; (2) to assess these accuracies in two specific\ncluster surveys: a deep SZE survey (\\cite{carlstrom99}) and a large solid angle\nX--ray survey, and (3) to contrast constraints from cluster abundance to those\nfrom CMB anisotropy measurements and from luminosity distances to\nhigh--redshift Supernovae (\\cite{schmidt98,perlmutter99}).\n\nOur work differs from the analysis of WS98 in several ways. We examine the\nsurface density of clusters $dN/dzd\\Omega$, rather than the comoving number\ndensity $n(z)$. This is important from an observational point of view, because\nthe former, directly measurable quantity inevitably includes the additional\ncosmology-dependence from the volume element $dV/dzd\\Omega$. We incorporate\nthe cosmology--dependent mass--limits expected from both types of surveys.\nBecause the SZE survey has a nearly $z$--independent sensitivity, we find that\nhigh--redshift clusters at $z>1$ yield useful constraints, in addition to those\nstudied by WS98 in the range $0<z<1$. Finally, we quantify the statistical\nsignificance of differences in the models by applying a combination of a\nKolmogorov--Smirnov (KS) and a Poisson test to $dN/dzd\\Omega$, and obtain\nconstraints using a grid of models for a wide range of cosmological parameters.\n\nThis paper is organized as follows. In \\S~\\ref{sec:surveys}, we describe the\nmain features of the proposed SZE and X-ray surveys relevant to this work. In\n\\S~\\ref{sec:models} we briefly summarize our modeling methods and assumptions.\nIn \\S~\\ref{sec:sensitivity}, we quantify the effect of individual variations of\n$w$ and of other parameters on cluster abundance and evolution. In\n\\S~\\ref{sec:wconstraints}, we obtain the constraints on these parameters by\nconsidering a grid of different cosmological models. In\n\\S~\\ref{sec:discussion}, we discuss our results and the implications of this\nwork. Finally, in \\S~\\ref{sec:conclusions}, we summarize our conclusions.\n\n\\section{Cluster Surveys}\n\\label{sec:surveys}\n\nThe observational samples available for studies of cluster abundance evolution\nwill improve enormously over the coming decade. The present samples of tens of\nintermediate redshift clusters (e.g., \\cite{gioia90,vikhlinin98}) will be\nreplaced by samples of thousands of intermediate redshift and hundreds of high\nredshift ($z>1$) clusters. At a minimum, the analysis of the European Space\nAgency {\\it X--ray Multi--mirror Mission (XMM)} archive for serendipitously\ndetected clusters will yield hundreds, and perhaps thousands of new clusters\nwith emission weighted mean temperature measurements (\\cite{romer00}).\nDedicated X-ray and SZE surveys could likely surpass the {\\it XMM} sample in\nareal coverage, number of detected clusters or redshift depth. The imminent\nimprovement of distant cluster data motivates us to estimate the cosmological\npower of these future surveys. Note that in practice, the only survey details\nwe utilize in our analyses are the virial mass of the least massive, detectable\ncluster (as a function of redshift and cosmological parameters), and the solid\nangle of the survey. We include here a brief description of two representative\nsurveys.\n\n\\subsection{A Sunyaev--Zel'dovich Effect Survey}\n\\label{subsec:SZ}\n\nThe SZE survey we consider is that proposed by Carlstrom and collaborators\n(\\cite{carlstrom99}). This interferometric survey is particularly promising,\nbecause it will detect clusters more massive than $\\sim2\\times10^{14}M_\\odot$,\nnearly independent of their redshift. Combined, this low mass threshold and\nits redshift independence produce a cluster sample which extends, depending on\ncosmology, to redshifts $z\\sim3$. The proposed survey will cover 12~deg$^2$ in\na year; it will be carried out using ten 2.5~m telescopes and an 8~GHz\nbandwidth digital correlator operating at cm wavelengths (\\cite{mohr99}). The\ndetection limit as a function of redshift and cosmology $M_{\\rm\nmin}(z,\\Omega_m,h)$ for this survey has been studied using mock observations of\nsimulated galaxy clusters (\\cite{holder00}), and we draw on those results here.\n\nOptical and near infrared followup observations will be required to\ndetermine the redshifts of SZE clusters. Given the relatively small\nsolid angle of the survey, it will be straightforward to obtain deep,\nmultiband imaging. We expect that the spectroscopic followup will\nrequire access to a multiobject spectrograph on a 10~m class\ntelescope. The ongoing development of infrared spectrographs may\ngreatly enhance our ability to effectively measure redshifts for the\nmost distant clusters detected in the SZE survey.\n\n\\subsection{A Deep, Large Solid Angle X--ray Survey}\n\\label{subsec:COSMEX}\n\nWe also consider the cosmological sensitivity of a large solid angle, deep\nX-ray imaging survey. The characteristics of our survey are similar to those\nof a proposed Small Explorer class mission, called the Cosmology Explorer,\nspear-headed by G. Ricker and D. Lamb. The survey depth is\n$3.6\\times10^6$~cm$^2$s at 1.5~keV, and the coverage is 10$^4$~deg$^2$\n(approximately half the available unobscured sky). We assume that the imaging\ncharacteristics of the survey are sufficient to allow separation of the $10\\%$\nclusters from the $90\\%$ AGNs and galactic stars. We focus on clusters which\nproduce 500 detected source counts in the 0.5:6.0~keV band, sufficient to\nreliably estimate the emission weighted mean temperature in a survey of this\ndepth (the external and internal backgrounds sum to $\\sim1.4$~cts/arcmin$^2$).\n\nTo compute the number of photons detected from a cluster of a particular flux,\nwe assume the clusters emit Raymond--Smith spectra (\\cite{raymond77}) with\n$1\\over3$ solar abundance, and we model the effects of Galactic absorption\nusing a constant column density of $n_H=4\\times10^{20}$~cm$^{-2}$. The\nmetallicity and Galactic absorption we've chosen are representative for a\ncluster studied in regions of high Galactic latitude; when analyzing a real\ncluster one would, of course, use the Galactic $n_{H}$ appropriate at the\nlocation of the cluster. Cluster metallicities vary, but for the 0.5:6~keV\nband, line emission contributes very little flux for clusters with temperatures\nabove 2~keV. For example, if the cluster metallicity were doubled to $2\\over3$\nsolar, the conversion between flux and the observed counts in the\n0.5:6~keV band for this particular survey would vary by $\\sim1.4$\\% and\n$\\sim0.1$\\% for Raymond-Smith spectral models with temperatures $kT=2$~keV and\n10~keV, respectively. We assume that the detectors have a quantum efficiency\nsimilar to the ACIS detectors (\\cite{bautz98,chartas98}) on the {\\it Chandra\nX-ray Observatory}, and the energy dependence of the mirror effective area\nmimics that of the mirror modules on ABRIXAS (\\cite{friedrich98}).\n\nThe X-ray survey could be combined with the Sloan Digital Sky Survey\n(SDSS) to obtain redshifts for the clusters -- the redshift\ndistribution of the clusters which produce 500 photons in the survey\ndescribed above is well sampled at the SDSS photometric redshift\nlimit.\n\n\\subsection{Determining the Survey Limiting Mass $M_{\\rm min}$}\n\\label{subsec:mlim}\n\nFor our analysis, the most important aspect of both surveys is the\nlimiting halo mass $M_{\\rm min} (z,\\Omega_m,w,h)$, as a function of\nredshift and cosmological parameters. More specifically, we seek the\nrelation between the detection limit of the survey, and the\ncorresponding limiting ``virial mass''. In our modeling below, we\nwill be using the mass function of dark halos obtained in large scale\ncosmological simulations (\\cite{jenkins00}). In these simulations,\nhalos are identified as those regions whose mean spherical overdensity\nexceeds the fixed value $\\delta\\rho/\\rho_b=180$ (with respect to the\nbackground density $\\rho_b$, and irrespective of cosmology; see\ndiscussion below). In what follows, we adopt the same definition for\nthe mass of dark halos associated with galaxy clusters.\n\nIn the X-ray survey, $M_{\\rm min}$ follows from the cluster X-ray\nluminosity -- virial mass relation and the details of the survey. We\nadopt the relation between virial mass and temperature obtained in\nhydrodynamical simulations by Bryan \\& Norman (1998),\n\\begin{equation}\nM_{\\rm vir}=a\\frac{T^{3/2}}{E(z)\\sqrt{\\Delta_c(z)}},\n\\label{eq:mt}\n\\end{equation}\nwhere $H(z)=H_0 E(z)$ is the Hubble parameter at redshift $z$, $a=1.08$ is a\nnormalization determined from the hydrodynamical simulations, and $\\Delta_c$ is\nthe enclosed overdensity (relative to the critical density) which defines the\ncluster virial region. The normalization $a$ is found to be relatively\ninsensitive to cosmological parameters, and the redshift evolution of\nEquation~\\ref{eq:mt} appears to be consistent with the hydrodynamical\nsimulations in those models where it has been tested (\\cite{bryan98}). Here we\nassume that Equation~\\ref{eq:mt} holds in all cosmologies with the same value\nof $a$ (see $\\S$\\ref{subsec:systematics} for a discussion of the effects of\nerrors in the mass-temperature relation), and use the fitting formulae for\n$\\Delta_c$ provided by WS98, which includes the case $w\\ne -1$. Finally, we\nconvert $M_{\\rm vir}$ from Equation~\\ref{eq:mt} to the mass $M_{180}$ enclosed\nwithin the spherical overdensity of $\\delta\\rho/\\rho=180$ (with respect to the\nbackground density), assuming that the halo profile is well described by the\nNFW model with concentration $c=5$ (Navarro, Frenk \\& White 1997, hereafter\nNFW).\n\nWe next utilize Equation~\\ref{eq:mt}, together with the relation between\nbolometric luminosity and temperature found by Arnaud \\& Evrard (1999), to find\nthe limiting mass of a cluster that produces 500 photons in the 0.5:6.0~keV\nband in a survey exposure. For these calculations we assume that the\nluminosity-temperature relation does not evolve with redshift, consistent with\nthe currently available observations (\\cite{mushotzky97}; relaxing this\nassumption is discussed below in \\S~\\ref{sec:discussion}).\n\nFor an interferometric SZE survey, the relevant observable is the\ncluster visibility $V$, which is the Fourier transform of the\ncluster SZE brightness distribution on the sky as seen by the\ninterferometer. The visibility is proportional to the total SZE flux\ndecrement $S_\\nu$,\n\\begin{equation}\nV\\propto S_\\nu (M,z) \\propto f_{ICM}\\frac{M\\langle T_e\\rangle_n}{d_A^2(z)} \n\\label{eq:MlimSZ}\n\\end{equation}\nwhere $\\left<T_e\\right>_n$ is the electron density weighted mean temperature,\n$M$ is the virial mass, $f_{ICM}$ is the intracluster medium mass fraction and\n$d_A$ is the angular diameter distance. We normalize this relation using mock\nobservations of numerical cluster simulations (see \\cite{mohr97} and\n\\cite{mohr99a}) carried out in three different cosmological models, including\nnoise characteristics appropriate to the proposed SZE array (see\n\\cite{holder00} for more details). The ICM mass fraction is set to\n$f_{ICM}=0.12$ in all three cosmological models. This mass fraction is\nconsistent with analyses of X-ray emission from well defined samples if\n$H_{0}=65$~km~s$^{-1}$~Mpc$^{-1}$, our fiducial value. Note that we use the\nsame $f_{ICM}=0.12$ in all our cosmological models rather than varying it with\nthe $H_{0}$ scaling appropriate for analyses of cluster X-ray emission. In the\ndiscussion which follows, this choice allows us to focus solely on the\ncosmological discriminatory power of cluster surveys; naturally, in\ninterpreting a real cluster survey one would likely allow $f_{ICM}$ to vary\nwith $H_{0}$.\n\n\\myputfigure{fig01.eps}{3.2}{0.50}{-25}{-00}\n\\figcaption{Limiting cluster virial masses ($M_{180}$) for detection in the \nX--ray survey (upper pair of curves) and in the SZE survey (lower pair\nof curves). The solid curves show the mass limit in our fiducial flat\n$\\Lambda$CDM model, with $w=-1$, $\\Omega_m=0.3$, and $h=0.65$, and the\ndotted curves show the masses in the same model except with $w=-0.5$.\n\\label{fig:mlim}}\n\\vspace{\\baselineskip} \n\nNote that for a flux limited survey, the limiting mass in\nequation~\\ref{eq:MlimSZ} is sensitive to cosmology through its\ndependence on $d_A$ and the definition of the virial mass $M$. We\nadopt the simulation--normalized value of $M^{*}_{\\rm min}(z)$ in our\nfiducial cosmology as a template, and then we rescale this relation to\ndetermine $M_{\\rm min}(z)$ in the model of interest using the relation\n\\begin{equation}\nM_{\\rm min}(z)=\nM^*_{min}(z)\\frac{h^{*}}{h}\\left[\\frac{hd_A(z)}{h^{*}d^*_A(z)}\\right]^{6/5}\n\\label{eq:Mscale}\n\\end{equation}\nHere the superscript $^*$ refers to quantities in the $\\Lambda$CDM\nreference cosmology, and we have used the scaling of virial mass with\ntemperature (Eqn.~\\ref{eq:mt}): $M\\propto \\left<T_e\\right>_n^{3/2}$.\nWe tested this scaling by comparing it to mock observations in\nsimulations of two different cosmologies (open CDM and standard CDM),\nand found that agreement was better than $\\sim 10\\%$ in the redshift\nrange $0<z<3$. Finally, in the numerical simulations used to\ncalibrate Equation~\\ref{eq:MlimSZ}, the halo mass was defined to be\nthe total mass enclosed within a region whose mean spherical interior\ndensity is 200 times the critical density. As in the X--ray case, we\nconvert $M_{\\rm min}(z)$ from Equation~\\ref{eq:Mscale} to the desired\nmass $M_{180}$ by assuming that the halo profile follows NFW with \nconcentration $c=5$.\n\nThe mass limits we derive for both surveys are shown in the redshift\nrange $0<z<3$ in Figure~\\ref{fig:mlim}, both for $\\Lambda$CDM and for\na $w=-0.5$ universe. The SZE mass limit is nearly independent of\nredshift, and changes little with cosmology. As a result, the cluster\nsample can extend to $z\\approx 3$. In comparison, the X--ray mass\nlimit is a stronger function of $w$, and it rises rapidly with\nredshift. For the X-ray survey considered here the number of detected\nclusters beyond $z\\approx 1$ is negligible.\n\nThese mass limits incorporate some simplifying assumptions that have\nnot been tested in detail (although we consider small variations of\nthe mass limits below). Our goal is to capture the scaling with\ncosmological parameters and redshift as best as presently possible.\nHowever, we emphasize that further theoretical studies of the\nsensitivities of these scalings to, for example, energy injection\nduring galaxy formation will be critical to interpreting the survey\ndata. In the case of the X--ray survey, the cluster sample will have\nmeasured temperatures, allowing the limiting mass to be estimated\nindependent of the cluster luminosity. In the case of the SZE survey, deep X-ray\nfollowup or multifrequency SZE followup observations should yield\ndirect measurements of the limiting mass.\n\n\\section{Estimating the Cluster Survey Yield}\n\\label{sec:models}\n\nTo derive cosmological constraints from the observed number\nand redshift distribution of galaxy clusters, the fundamental quantity\nwe need to predict is the comoving cluster mass function. The\nPress--Schechter formalism (\\cite{press74}; hereafter PS), which\ndirectly predicts this quantity in any cosmology, has been shown to be\nin reasonably good agreement (i.e. to within a factor of two)\nwith results of N--body simulations, in cosmologies and halo\nmass ranges where it has been tested (\\cite{lacey94,gross98,lee99}).\nNumerical simulations have only recently reached the large size\nrequired to accurately determine the mass function of the rarest, most\nmassive objects, such as galaxy clusters with $M>10^{15}M_{\\odot}$.\n\nIn this paper, we adopt the halo mass function found in a series of recent\nlarge--scale cosmological simulations by Jenkins et al.~2000. The results of\nthese simulations are particularly well--suited for the present application.\nThe large simulated volumes allow a statistically accurate determination of the\nhalo mass function; for halo masses of interest here, to better than $\\lsim\n30\\%$. In addition, the mass function is computed in three different\ncosmologies at a range of redshifts, and found to obey a simple 'universal'\nfitting formula. Although this does not guarantee that the same scaling holds\nin other, untested cosmologies, we make this simplifying assumption in the\npresent paper. In the future, the validity of this assumption has to be tested\nby studying the numerical mass function across a wider range of cosmologies.\n\nGenerally, the simulation mass function predicts a significantly larger\nabundance of massive clusters than does the PS formula. For sake of\ndefiniteness, we note that in the simulations, halos are identified as those\nregions whose mean spherical overdensity exceeds the fixed value\n$\\delta\\rho/\\rho_b=180$ with respect to the background density $\\rho_b$. This\nis somewhat different from the typical halo definition within the context of\nthe PS formalism, where the overdensity, relative to the critical density, is\ntaken to be that of a collapsing spherical top--hat at virialization.\n\nFollowing Jenkins et al.~2000, we assume that the comoving number\ndensity $(dn/dM)dM$ of clusters at redshift $z$ with mass $M\\pm dM/2$\nis given by the formula,\n\\beq\n\\frac{dn}{dM}(z,M)=\n0.315 \n\\frac{\\rho_0}{M} \n\\frac{1}{\\sigma_M}\n\\frac{d\\sigma_M}{dM}\n\\exp\\left[-\\left|0.61-\\log(D_z\\sigma_M)\\right|^{3.8}\\right],\n\\label{eq:dndm}\n\\eeq\nwhere $\\sigma_M$ is the r.m.s. density fluctuation, computed on\nmass--scale $M$ from the present--day linear power spectrum\n(\\cite{eisenstein98}), $D_z$ is the linear growth function, and\n$\\rho_0$ is the present--day mass density. The directly observable\nquantity, i.e. the average number of clusters with mass above $M_{\\rm\nmin}$ at redshift $z\\pm dz/2$ observed in a solid angle $d\\Omega$ is\nthen simply given by\n\\beq\n\\frac{dN}{dzd\\Omega}\\left(z\\right) =\n\\left[\n\\frac{dV}{dzd\\Omega}\\left(z\\right)\n\\int_{M_{\\rm min}(z)}^\\infty dM \\frac{dn}{dM} \n\\right]\n\\label{eq:dNdzdom}\n\\eeq \nwhere $dV/dzd\\Omega$ is the cosmological volume element, and $M_{\\rm\nmin}(z)$ is the limiting mass as discussed in section\n\\ref{subsec:mlim}. Equations \\ref{eq:dndm} and \\ref{eq:dNdzdom}\ndepend on the cosmological parameters through $\\rho_0$, $D_z$, and\n$dV/dzd\\Omega$, in addition to the mild dependence of $\\sigma_M$ on\nthese parameters through the power spectrum (although the dependence\non the power--spectrum is more pronounced in the X--ray survey, where\nthe limiting mass varies strongly with redshift). Note that the\ncomoving abundance $dn/dM$ is exponentially sensitive to the growth\nfunction $D_z$. We use convenient expressions for $dV/dzd\\Omega$ and\n$D_z$ in open and flat $\\Omega_\\Lambda$ cosmologies available in the\nliterature (\\cite{peebles80,carroll92,eisenstein96}). In the case of\ncosmologies with $w\\neq -1$, we have evaluated $dV/dzd\\Omega$\nnumerically, but used the fitting formulae for $D_z$ obtained by WS98,\nwhich are accurate to better than 0.3\\% for the cases of constant\n$w$'s considered here. \n\n\\subsection{Normalizing to Local Cluster Abundance}\n\\label{subsec:normalize}\n\nTo compute $dN/dzd\\Omega$ from equation~\\ref{eq:dNdzdom}, we must\nchoose a normalization for the density fluctuations $\\sigma_M$. This\nis commonly expressed by $\\sigma_8$; the present epoch, linearly\nextrapolated {\\it rms} variation in the density field filtered on\nscales of $8h^{-1}$~Mpc. To be consistent in our analysis, we choose\nthe normalization for each cosmology by fixing the local cluster\nabundance above a given mass $M_{\\rm nm}=10^{14} h^{-1}~M_\\odot$. In\nall models considered, we set the local abundance to be\n$1.03\\times10^{-5}~(h/0.65)^3~{\\rm Mpc^{-3}}$, the value derived in\nour fiducial $\\Lambda$CDM model (see below). We have chosen to\nnormalize using the local cluster abundance (upto a factor $h^3$)\nabove mass $M_{\\rm nm}$ rather than above a particular emission\nweighted mean temperature $kT_{\\rm nm}$, because this removes the\nsomewhat uncertain cosmological sensitivity of the virial mass\ntemperature ($M-T_x$) relation from the normalization process;\nspherical tophat calculations suggest a significant offset in the\n$M-T_x$ normalization of the open and flat $\\Omega_m=0.3$ models which\nhydrodynamical simulations do not seem to reproduce\n(\\cite{evrard96,bryan98,viana99}).\n\nAn alternative approach to the above is to regard $\\sigma_8$ a\n``free--parameter'', on equal footing with the other parameters we let\nfloat below. This possibility will be discussed further in \\S~6. Here\nwe note that our normalization approach is sensible, because the\nnumber density of nearby clusters can be measured to within a factor\nof $h^3$, and the masses of nearby clusters can be measured directly\nthrough several independent means; these include the assumption of\nhydrostatic equilibrium and using X-ray images and intracluster medium\n(ICM) temperature profiles, weak lensing, or galaxy dynamical mass\nestimates. The only cosmological sensitivity of these mass estimators\nis their dependence on the Hubble parameter $h$; we include this $h$\ndependence when normalizing our cosmological models. Note that\nprevious derivations of $\\sigma_8$ (e.g. Viana \\& Liddle 1993; Pen\n1998) in various cosmologies from the local cluster abundance $N(>kT)$\nabove a fixed threshold temperature $kT_{\\rm min}\\sim 7$keV yielded a\nconstraint with the approximate scaling $\\sigma_8\\Omega_m^{1/2}\n\\approx 0.5$. We find a similar relation when varying $\\Omega_m$\naway from our fiducial cosmology; however, we note that if a $\\sim 5$\ntimes smaller threshold temperature were used, the constrained\ncombination would be quite different, $\\sigma_8\\Omega_m\\sim$constant.\nSince our adopted normalization is based on mass, rather than\ntemperature, in general, we find still different scalings. As an\nexample, when $h=0.65$ and $w=-1$ are kept fixed, our normalization\nprocedure translates into $\\sigma_8(\\Omega_m/0.3)^{0.85}\\approx 0.9$.\n\n\\subsection{Fiducial Cosmological Model}\n\nThe parameters we choose for of our fiducial cosmological model are\n$(\\Omega_\\Lambda,\\Omega_{\\rm m},h,\\sigma_{8},n)=(0.7,0.3,0.65,0.9,1)$.\nThis flat $\\Lambda$CDM model is motivated as a ``best--fit'' model\nthat produces a local cluster abundance consistent with observations\n(\\cite{viana99}), and satisfies the current constraints from CMB\nanisotropy (\\cite{lange00}, see also \\cite{white00}), high--$z$ SNe, and\nother observations (Bahcall et al. 1999). We have assumed a baryon\ndensity of $\\Omega_b h^2=0.02$, consistent with recent D/H\nmeasurements (e.g. Burles \\& Tytler 1998). Note that the power\nspectrum index $n$ is not important for the analysis presented here,\nbecause we normalize on cluster scales $\\sigma_{8}$, and we find that\nthis minimizes the effect of varying $n$ on the density fluctuations\nrelevant to cluster formation.\n\n\\section{Exploring the Cosmological Sensitivity}\n\\label{sec:sensitivity}\n\nIn this section, we describe how variations of the individual\nparameters $\\Omega$, $w$, and $h$, as well as the cosmological\ndependence of the limiting mass $M_{\\rm min}$, affect the cluster\nabundance and redshift distribution. This will be useful in\nunderstanding the results of the next section, when a full grid of\ndifferent cosmologies is considered. We then describe our method of\nquantifying the statistical significance of differences between the\ndistributions $dN/dz$ in a pair of different cosmologies.\n\n\\subsection{Single Parameter Variations}\n\\label{subsec:parameters}\n\nThe surface density of clusters more massive than $M_{\\rm min}$\ndepends on the assumed cosmology mainly through the growth function\n$D(z)$ and volume element $dV/dzd\\Omega$, as well as through the\ncosmology--dependence of the limiting mass $M_{\\rm min}$ itself. In\nthe approach described in section \\ref{sec:models}, once a cosmology\nis specified, the normalization of the power spectrum $\\sigma_{8}$ is\nfound by keeping the abundance of clusters at $z=0$ constant. We\ntherefore consider only three ``free'' parameters, $w$, $h$,\n$\\Omega_m$, specifying the cosmology. We assume the universe to be\neither flat ($\\Omega_Q=1-\\Omega_m$), or open with $\\Omega_Q=0$.\n\n\\myputfigure{fig02.eps}{3.2}{0.49}{-25}{-00} \n\\figcaption{Effect of changing $\\Omega_m$ when all other parameters are held\nfixed. The four panels show (clockwise from upper left) the surface\ndensity of clusters at redshift $z$; the linear growth function; the\nvolume element in units of ${\\rm Mpc^3~sr^{-1}~redshift^{-1}}$; and\nthe comoving cluster abundance. The solid curve shows our fiducial\nflat $\\Lambda$CDM model, with $w=-1$, $\\Omega_m=0.3$, and $h=0.65$.\nAlso shown are models with $\\Omega=0.27$ (dotted curve); $\\Omega=0.33$\n(short--dashed curve); and OCDM models with $\\Omega =0.27,0.30,0.33$\n(long--dashed curves, top to bottom).\n\\label{fig:clust_om}}\n\n\\myputfigure{fig03.eps}{3.2}{0.49}{-25}{-00}\n\\figcaption{Effect of changing $w$ when all other parameters are held \nfixed. The solid curve shows our fiducial flat $\\Lambda$CDM model,\nwith $w=-1$, $\\Omega_m=0.3$, and $h=0.65$. The dotted curve is the\nsame model with $w=-0.6$, the short--dashed curve with $w=-0.2$, and\nthe long--dashed curve is an open CDM model with $\\Omega_m=0.3$.\n\\label{fig:clust_w}}\n\n\\subsubsection{Changing $\\Omega_m$}\n\nThe effects of changing $\\Omega_m$ are demonstrated in\nFigure~\\ref{fig:clust_om}. The curves correspond to a flat $\\Lambda$CDM\nuniverse with ($h=0.65,w=-1$), and $\\Omega_m=0.27$ (dotted), $\\Omega_m=0.30$\n(solid), and $\\Omega_m=0.33$ (short--dashed). In addition, the long--dashed\ncurves show the same three models (top to bottom), assuming open CDM with\n$\\Omega_\\Lambda=0$. The top left panel shows the total number of clusters in a\n12 square degree field, detectable down to the constant SZE decrement $S_{\\rm\nmin}$. As discussed in section \\ref{subsec:mlim} above, a constant $S_{\\rm\nmin}$ implies a redshift and cosmology--dependent limiting mass $M_{\\rm min}$.\nIn the SZE case, we find that if we had not included this effect, the\nsensitivity to $\\Omega_m$ would have been somewhat stronger. Several\nconclusions can be drawn from Figure~\\ref{fig:clust_om}. Overall, the top left\npanel shows that a decrease in $\\Omega_m$ increases the number of clusters (and\nvice versa) at all redshifts. Note that the dependence is strong, for\ninstance, a $10\\%$ decrease in $\\Omega_m$ increases the total number of\nclusters by $\\sim30\\%$ in either $\\Lambda$CDM or OCDM cosmologies. As\nemphasized by Bahcall \\& Fan (1998), Viana \\& Liddle (1999) and others, this\nmakes it possible to estimate an upper limit on $\\Omega_m$ using current,\nsparse data on cluster abundances (i.e. only a few high--$z$ clusters). A\nsecond important feature seen in the top left panel is that the shape of the\nredshift distribution is not changed significantly, a conclusion that holds\nboth in $\\Lambda$CDM and OCDM. Finally, the remaining three panels reveal that\nthe effects of $\\Omega_m$ arise mainly from the changes in the comoving\nabundance (bottom left panel). In flat $\\Lambda$CDM, $\\Omega_m$ has relatively\nlittle effect on the volume or the growth function, and the comoving abundance\nis determined by the value of $\\sigma_8$ that keeps the the local abundance\nconstant at $z=0$ (we find $\\sigma_8$=0.83 for $\\Omega_m=0.33$ and\n$\\sigma_8=1.00$ for $\\Omega_m=0.27$). In addition, we find that the change in\nthe shape of the underlying power spectrum with $\\Omega_m$ enhances the\ndifferences caused by $\\Omega_m$ (when we artificially keep the power spectrum\nat its $\\Omega_m=0.3$ shape, we find $\\sigma_8$=0.84 for $\\Omega_m=0.33$). We\nalso note that the volume element and the comoving abundance act in the same\ndirection: a lower $\\Omega_m$ increases both the comoving abundance and the\nvolume element. In OCDM, the growth function has a larger effect, and relative\nto $\\Lambda$CDM, the redshift distribution is much flatter.\n\n\\myputfigure{fig04.eps}{3.2}{0.49}{-25}{-00}\n\\figcaption{Effect of changing $h$ when all other parameters are held fixed.\nThe $\\Lambda$CDM model of Figure~\\ref{fig:clust_w} is shown (solid\ncurve) together with models with $h=0.55$ (dotted curve); $h=0.80$\n(short--dashed curve); and OCDM models with $h=0.55,0.65,0.80$\n(long--dashed curves, top to bottom).\n\\label{fig:clust_h}}\n\n\\subsubsection{Changing $w$} \n\nThe effects of changing $w$ are demonstrated in Figure~\\ref{fig:clust_w}. The\nfigure shows models with ($\\Omega_m=0.3,h=0.65$) and with three different\n$w$'s: $w=-1$ (solid curve), $w=-0.6$ (dotted curve), and $w=-0.2$\n(short--dashed curve). In addition, we show the result from an open CDM model\nwith ($\\Omega=0.3,h=0.65$; long--dashed curve). The figure reveals that\nincreasing $w$ above $w=-1$ causes the slope of the redshift distribution above\n$z\\approx 0.5$ to flatten, increasing the number of high--$z$ clusters.\nFurthermore, ``opening'' the universe has an effect similar to increasing $w$.\nThe other three panels demonstrate the reason for these scalings. The top\nright panel shows that the growth function is flatter in higher $w$ models,\nsignificantly increasing the comoving number density of high--redshift clusters\n(bottom left panel). The volume element (bottom right panel) has the opposite\nbehavior, in the sense the volume in higher--$w$ models is smaller, which tends\nto balance the increase in the comoving abundance caused by the growth function\nin the range $0<z\\lsim 0.5$; but for higher redshifts, the growth function\n``wins''. An important conclusion seen from Figure~\\ref{fig:clust_w} is that\nboth the total number of clusters as well as the shape of their redshift\ndistribution, significantly depends on $w$. We also note that in the SZE case,\nour sensitivity to $w$ has been enhanced by the cosmological dependence of the\nmass limit (opposite to what we found for the $\\Omega_m$--sensitivity, which we\nfound was weakened by the same effect).\n\n\\subsubsection{Changing $h$}\n\nFigure~\\ref{fig:clust_h} demonstrates the effects of changing $h$. Three\n$\\Lambda$CDM models are shown with ($\\Omega_m=0.30,w=-1$), and $h=0.55$ (dotted\ncurve), $h=0.65$ (solid curve), and $h=0.80$ (short--dashed curves). The\nlong--dashed curves correspond to OCDM models with the same parameters (top to\nbottom). Comparing the top right panel with that of Figure~\\ref{fig:clust_om},\nthe qualitative behavior of $dN/dz$ under changes in $h$ and $\\Omega_m$ are\nsimilar: decreasing $h$ increases the total number of clusters, but does not\nconsiderably change their redshift distribution. However, the sensitivity to\n$h$ is significantly less: the total number of clusters is seen to increase by\n$\\sim 25\\%$ only when $h$ is decreased by the same percentage. Note that the\ngrowth function is not effected by $h$, and the $h$ sensitivity is driven by\nour normalization process, which fixes the abundance at $z=0$\n(see~\\S~\\ref{subsec:normalize}). Since the volume scales as $\\propto h^{-3}$,\nwe fix the comoving abundance to be proportional to $\\propto h^{3}$. As a\nresult, $dN/dzd\\Omega$ is nearly independent of $h$. In fact, the entire\n$h$--dependence is attributable to the small change caused by $h$ in the shape\nof the power spectrum (for a pure power--law spectrum, there would be no\n$h$--dependence, and the three curves for the flat universe in the top left\npanel of Figure~\\ref{fig:clust_h} would look identical).\n\n\\myputfigure{fig05.eps}{3.2}{0.49}{-25}{-00} \n\\figcaption{Effect of changing $w$ (upper panels) or $\\Omega_m$ (lower panels)\nwhen all other parameters are held fixed, including the mass limit. The types\nof the curves correspond to the different models in the SZE survey, as shown in\nFigures~\\ref{fig:clust_om}~\\&~\\ref{fig:clust_w}.\n\\label{fig:clust_mlim}}\n\n\\subsubsection{Abundances in the X--ray Survey}\n\nThe evolution of the cluster abundance, and its sensitivity to $\\Omega_m$ and\n$w$ in the X--ray survey are shown in Figure~\\ref{fig:clust_x}. Because of the\nmuch larger solid angle surveyed, the numbers of clusters is significantly\nlarger than in the SZE case, despite the higher limiting mass\n(cf. Fig~\\ref{fig:mlim}). Nevertheless, the general trends that can be\nidentified in the X--ray sample are similar to those in the SZE case. Raising\n$w$ increases the total number of clusters, and flattens their redshift\ndistribution. As in the SZE survey, raising $\\Omega_m$ decreases the total\nnumber of clusters.\n\n\\subsection{Effects of the Limiting Mass Function}\n\nFinally, we examine the extent to which the above conclusions depend on the\ncosmology and redshift--dependence of the limiting mass $M_{\\rm min}$. \n\n\\myputfigure{fig06.eps}{3.1}{0.51}{-25}{-00} \n\\figcaption{Effect of changing $w$ (upper panels) or $\\Omega_m$ (lower panels)\nwhen all other parameters are held fixed in the X--ray survey. Note the much\nlarger numbers of clusters in comparison to the SZE survey. In the top panel,\nthe curves correspond to $w=-1$ (solid), $w=-0.6$ (dotted) and $w=-0.2$\n(dashed). In the bottom panel, the curves correspond to $\\Omega_m=0.3$\n(solid), $\\Omega_m=0.27$ (dotted) and $\\Omega_m=0.33$ (dashed).\n\\vspace{\\baselineskip}\n\\label{fig:clust_x}}\n\n\\subsubsection{The SZE Survey}\n\nWe first compute cluster abundances above the fixed mass $M_{\\rm\nmin}=10^{14}h^{-1}{\\rm M_\\odot}$, characteristic of the SZE survey detection\nthreshold in the range of cosmologies and redshifts considered here. The\nresults are shown in Figure~\\ref{fig:clust_mlim}: the bottom panels show the\nsurface density and comoving abundance when $\\Omega_m$ is changed (the models\nare the same as in Figure~\\ref{fig:clust_om}), and the top panels show the same\nquantities under changes in $w$ (the cosmological models are the same as in\nFigure~\\ref{fig:clust_w}). A comparison between Figures~\\ref{fig:clust_mlim}\nand \\ref{fig:clust_w} gives an idea of the importance of the mass limit. The\ngeneral trend seen in Figure~\\ref{fig:clust_w} remains true, i.e. increasing\n$w$ flattens the redshift distribution at high--$z$. However, when a constant\n$M_{\\rm min}$ is assumed, the ``pivot point'' moves to slightly higher\nredshift, and the total number of clusters becomes less sensitive to $w$.\nSimilar conclusions can be drawn from a comparison of Figure~\\ref{fig:clust_om}\nwith the bottom two panels of Figure~\\ref{fig:clust_mlim}: under changes in\n$\\Omega_m$ the general trends are once again similar, but the differences\nbetween the different models are amplified when a constant $M_{\\rm min}$ is\nused. In summary, we conclude that in the SZE case (1) the variation of the\nmass limit with redshift and cosmology has a secondary importance, and (2) it\nweakens the $\\Omega_m$ dependence, but strengthens the $w$ dependence.\n\n\\subsubsection{The X--ray Survey}\n\nIn comparison to the SZE survey, the X--ray mass limit is not only higher, but\nis also significantly more dependent on cosmology (cf. Fig~\\ref{fig:mlim}). On\nthe other hand, the X--ray sample goes out only to the relatively low redshift\n$z=1$, where the growth functions in the different cosmologies diverge\nrelatively little. This suggests that in the X--ray case the mass limit is\nmore important than in the SZE survey. In order to separate the effects of the\nchanging mass limit from the change in the growth function and the volume\nelement, in Figure~\\ref{fig:clust_xnoM} we show the sensitivity of $dN/dz$ to\nchanges in $\\Omega_m$ and $w$, without including the effects from the mass\nlimit. The same models are shown as in Figure~\\ref{fig:clust_x}, except we\nhave artificially kept the mass limit at its value in the fiducial cosmology.\nThe figure reveals that essentially all of the $w$--sensitivity seen in\nFigure~\\ref{fig:clust_x} is caused by the changing mass limit; when $M_{\\rm\nmin}$ is kept fixed, the cluster abundances change very little. On the other\nhand, comparing the bottom panels of Figures~\\ref{fig:clust_x}\nand~\\ref{fig:clust_xnoM} shows that including the scaling of the mass limit\nsomewhat reduces the $\\Omega_m$ dependence, just as in the SZE case.\n\n\\myputfigure{fig07.eps}{3.1}{0.51}{-25}{-00} \n\\figcaption{Effect of changing $w$ (upper panels) or $\\Omega_m$ (lower panels)\nwhen all other parameters are held fixed in an X--ray survey, and the survey\nmass limit is held fixed at its fiducial value, irrespective of cosmology. A\ncomparison with Figure~\\ref{fig:clust_x} shows that nearly all of the\n$w$--sensitivity is accounted for by the cosmology--dependence of the limiting\nmass. On the other hand, the $\\Omega_m$--sensitivity is caused mostly by the\ngrowth function.\n\\vspace{\\baselineskip}\n\\label{fig:clust_xnoM}}\n\n\\begin{figure*}[htb]\n\\vskip-0.2in\n\\hbox to \\hsize{\\hfil\\hskip-0.2in\\vbox to 3.3in{\n\\epsfysize=3.3in\n\\epsfbox{fig08.eps}\\vfil}\\hfil}\\vskip-0.4in\n\\caption{\\footnotesize Contours of 1, 2, and 3$\\sigma$ likelihood for different\nmodels when they are compared to a fiducial flat $\\Lambda$CDM model with\n$\\Omega_m=0.3$ and $h=0.65$, using the SZE survey. The three panels show three\ndifferent cross--sections of constant total probability at fixed values of $h$\n(0.55,0.65, and 0.80) in the investigated 3--dimensional $\\Omega_m,w,h$\nparameter space.}\n\\label{fig:slices}\n\\vskip-0.2in\n\\end{figure*}\n\n\\subsection{Overview of Cosmological Sensitivity}\n\nIn summary, we conclude that changes in $w$ modify both the normalization and\nthe shape of the redshift distribution of clusters, while changes in $\\Omega_m$\nor $h$ effect essentially only the overall amplitude. This suggests that\nchanges in $w$ can not be fully degenerate with changes in either $\\Omega_m$ or\n$h$ (or a combination), making it possible to measure $w$ from cluster\nabundances alone. These conclusions hold either for clusters above a fixed\ndetection threshold in and SZE or X-ray survey, or for a sample of clusters\nabove a fixed mass. We find that the sensitivity to $\\Omega_m$ arises mostly\nthrough the growth function, both in the SZE and X--ray surveys. This\nsensitivity is slightly weakened by the scaling of the limiting mass $M_{\\rm\nmin}$ with $\\Omega_m$. We find that the $w$ sensitivity is also dominated by\nthe growth function in the SZE survey, which goes out to relatively high\nredshifts; but the sensitivity to $w$ is enhanced by the $w$--dependence of\n$M_{\\rm min}$. In comparison, in the X--ray survey, which only probes\nrelatively low redshifts, nearly all of the $w$--sensitivity is caused by the\ncosmology--dependence of the limiting mass, rather than the growth function.\n\n\\begin{figure*}[b]\n\\vskip-0.3in\n\\hbox to \\hsize{\\hfil\\hskip-0.30in\\vbox to 3.3in{\n\\epsfysize=3.3in\n\\epsfbox{fig09.eps}\\vfil}\\hfil}\\vskip-0.40in\n\\caption{\\footnotesize Contours of 1, 2, and 3$\\sigma$ likelihood for models\nwhen they are compared to a fiducial flat $\\Lambda$CDM model, as in\nFigure~\\ref{fig:slices}, but for the X--ray survey.}\n\\label{fig:slicex}\n\\end{figure*}\n\n\\section{Constraints on Cosmological Parameters}\n\\label{sec:wconstraints}\n\nWe derive cosmological constraints by considering a 3--dimensional\ngrid of models in $\\Omega_m,h$, and $w$. As described above, we first\nfind $\\sigma_8$ in each model, so that all models are normalized to\nproduce the same local cluster abundance at $z=0$. We then compute\n$dN/dzd\\Omega$ in these models for $0.2 \\leq \\Omega_m \\leq 0.5$, $0.5\n\\leq h \\leq 0.9$, and $-1 \\leq w \\leq -0.2$. The range for $w$\ncorresponds to that allowed by current astrophysical observations\n(\\cite{wang00}); although recent observations of Type Ia SNe suggest\nthe stronger constraint $w \\lsim -0.6$ (\\cite{ptw99}).\n\n\\subsection{Comparing $dN/dz$ in Two Different Cosmologies}\n\\label{subsec:probabilities}\n\nThe main goal of this paper is to quantify the accuracy to which $w$ can be\nmeasured in future SZE and X--ray surveys. To do this, we must answer the\nfollowing question: given a hypothetical sample of $N_{\\rm tot}$ clusters (with\nmeasured redshifts) obeying the distribution $dN_A/dz$ of the test model (A)\ncosmology, what is the probability $P_{\\rm tot}(A,B)$ that the same sample of\nclusters is detected in the fiducial (B) cosmology, with distribution\n$dN_B/dz$? We have seen in section \\ref{subsec:parameters} that the overall\namplitude, and the shape of $dN/dz$ are both important. Motivated by this, we\ndefine\n\\beq\nP_{\\rm tot}(A,B) = P_{0}(A,B) \\times P_z(A,B)\n\\label{eq:probs}\n\\eeq \nwhere $P_{0}(A,B)$ is the probability of detecting $N_{A, \\rm tot}$\nclusters when the mean number is $N_{B, \\rm tot}$, and $P_z(A,B)$ is\nthe probability of measuring the redshift distribution of model (A) if\nthe true parent distribution is that of model (B). We assume $P_{0}$\nis given by the Poisson distribution, and we use the\nKolmogorov--Smirnov (KS) test to compute $P_z(A,B)$ (\\cite{press92}).\nThe main advantage of this approach, when compared to the usual\n$\\chi^2$ tests, is that we do not need to bin the data in redshift.\n\nFor reference, it is useful to quote here some examples for the\nprobabilities, taking ($\\Omega_m=0.3,h=0.65,w=-1$) as the fiducial (B)\nmodel. For example, closest to this model in Figure \\ref{fig:clust_w}\nis the one with $w=-0.6$. For this case, we find $P_0=0.25$ and\n$P_z=0.1$ for a total probability of $P_{\\rm tot}=0.025$. In other\nwords, the two cosmologies could be distinguished at a likelihood of\n$1.2\\sigma$ using only the total number of clusters, at $1.6\\sigma$\nusing only the shape of the redshift distribution, and at the\n$2.3\\sigma$ level using both pieces of information. In this case, the\ndistinction is made primarily by the different redshift distributions,\nrather than the total number of detected clusters. Taking the\n$\\Omega_m=0.33$ $\\Lambda$CDM cosmology from Figure \\ref{fig:clust_om}\nas another example for model (A), we find $P_0=0.0075$ (=$2.7\\sigma$),\n$P_z=0.78$ (=$0.3\\sigma$), and a total probability of $P_{\\rm\ntot}=0.0058$ (=$2.8\\sigma$). Not surprisingly, the shape of the\nredshift distribution does not add significantly to the statistical\ndifference between these two models, which differ primarily by the\ntotal number of clusters.\n\n\\subsection{Expectations from the Sunyaev--Zel'dovich Survey}\n\\label{subsec:wSZ}\n\nFigure~\\ref{fig:slices} shows contours of 1, 2, and 3$\\sigma$ for the\ntotal probability $P_{\\rm tot}$ for models when compared to the\nfiducial flat $\\Lambda$CDM model. For reference, we note that the\ntotal number of clusters in the SZE survey in our fiducial model is\n$\\approx 100$, located between $0<z<3$. The three panels show three\ndifferent cross--sections of the investigated 3--dimensional\n$\\Omega_m,h,w$ parameter space, taken at constant values of $h=$ 0.55,\n0.65, and 0.80, spanning the range of values preferred by other\nobservations. The most striking feature in this figure is the\ndirection of the contours, which turn upwards in the $w,\\Omega_m$\nplane, and become narrower for larger values of $w$. We find that the\ntrough of maximum probability for fixed $h=0.65$ is well described by\n\\beq \n(\\Omega_m - 0.3) (w+1)^{-5/2} = 0.1,\n\\label{eq:degen}\n\\eeq with further constant shifts in $\\Omega_m$ caused by changing $h$. The\n$\\pm 3\\sigma$ width enclosed by the contours around this relation is relatively\nnarrow in $\\Omega_m$ ($\\pm 10\\%$). In a $\\Lambda$CDM case, even when a large\nrange of values is considered for $h$ ($0.45 < h < 0.90$), the constraint $0.26\n\\lsim \\Omega_m \\lsim 0.36$ follows; when $w\\ne -1$ is considered, the allowed\nrange widens to $0.27 \\lsim \\Omega_m \\lsim 0.41$. On the other hand, a wide\nrange of $w$'s is seen to be consistent with $w=-1$: the largest value shown,\n$w\\approx -0.2$ is approximately $3\\sigma$ away from $w=-1$, and $w=-0.6$ is\nallowed at $1\\sigma$. Note that $h$ is not well determined, i.e. the contours\nlook similar for all three values of $h$, and 1$\\sigma$ models exist for any\nvalue of $h$ in the range $0.5\\lsim h \\lsim 0.9$. This is not surprising, as\nFigure~\\ref{fig:clust_h} shows $dN/dzd\\Omega$ is insensitive to the value of\n$h$, with only a mild $h$--dependence through the non--power law shape of the\npower spectrum.\n\n\\subsection{Expectations from the X--ray Survey}\n\\label{subsec:wCOSMEX}\n\nThe total number of clusters in the X--ray survey in our fiducial model is\n$\\approx 1000$, ten times that in the SZE survey; all X--ray clusters are\nlocated between $0<z<1$. Figure~\\ref{fig:slicex} contains expectations for the\nX-ray survey; we show contours of 1, 2, and 3$\\sigma$ probabilities relative to\nthe fiducial $\\Lambda$CDM model. The qualitative features are similar to that\nin the SZE case, but owing to the larger number of clusters, the constraints\nare significantly stronger and the contours are narrower. However, the\ncontours extend further along the $w$ axis, and the largest value of $w$\nallowed at a probability better than $3\\sigma$ is $w>-0.2$ (assuming that the\nvalues of $\\Omega_m$ and $h$ are not known). Although the contours are narrower\nthan in the SZE case, assuming that $h$ and $w$ are unknown, the allowed range\nof $\\Omega_m$ is similar to that in the SZE case, $0.26\\lsim \\Omega_m \\lsim\n0.42$. Note that because of the shape and direction of the likelihood\ncontours, a knowledge of $h$ would not significantly improve this constraint\n(although if $h$ is found to be low, then the lower limit in $\\Omega_m$ would\nincrease). Finally, assuming that both $h$ and $\\Omega_m$ are known to high\naccuracy ($\\approx 3\\%$), the allowed $3\\sigma$ range on $w$ could be reduced\nto $-1\\leq w\\lsim -0.85$.\n\n\\section{Results and Discussion}\n\\label{sec:discussion}\n\n\\subsection{Total Number vs. the Redshift Distribution}\n\\label{subsec:shape}\n\nOur main results are presented in Figures~\\ref{fig:slices} and\n\\ref{fig:slicex}, which show the probabilities of various models relative to a\nfiducial $\\Lambda$CDM model in the SZE and X--ray surveys. As demonstrated by\nthese figures, the cluster data determine a combination of $\\Omega_m$ and $w$.\nIn the absence of external constraints on $\\Omega_{m}$ and $h$, $w$ as large as\n$-0.2$ differs from $w=-1$ by $3\\sigma$; while $w=-0.6$ would be $1\\sigma$ away\nfrom our fiducial $\\Lambda$CDM cosmology. Owing to the larger number of\nclusters in the X--ray survey, the constrained combination of $\\Omega_m$ and\n$w$ is significantly narrower than in the SZE survey; the direction of the\ncontours is also somewhat different. As a result, analysis of the X--ray \nsurvey could distinguish\na $w\\approx -0.85$ model from $\\Lambda$CDM at $3\\sigma$ significance, provided\n$\\Omega_m$ is known to an accuracy of $\\sim3\\%$ from other studies.\n\nIt is interesting to ask whether these constraints arise mainly from the total\nnumber of detected clusters, or from their redshift distribution. To address\nthis issue, in Figure~\\ref{fig:sep} we show separate likelihood contours for\nthe probability $P_0$ (total number of clusters, left panels), and for the\nprobability $P_z$ (shape of redshift distribution, right panels). In the SZE\ncase, the contours of likelihood from the shape information alone are broad,\nand adding these constraints to the Poisson--probability plays almost no role\nin the range $w\\lsim -0.7$ (the contours of $P_{\\rm tot}$ and $P_0$ are very\nsimilar). However, at larger $w$, the shape becomes increasingly\nimportant. Adding in this information significantly reduces the allowed region\nrelative to the Poisson--probability alone at $w\\gsim -0.7$. It is the\ncombination of the $P_0$ and $P_z$ contours that allows ruling out $w\\gsim\n-0.2$ at the $3\\sigma$ level. Note that the difference in shapes arises mostly\nfrom the high--redshift ($z\\gsim 1$) clusters (cf. Fig.~\\ref{fig:clust_w}).\n\nIn the X--ray case (bottom panels in Fig.~\\ref{fig:sep}), the situation is\ndifferent, because the contours of $P_0$ and $P_z$ are both much narrower. As\na result, the contours for the combined likelihood are somewhat reduced, but\nthey still reach to $w\\approx -0.2$ (at $\\sim 2\\sigma$). Note that as in the\nSZE survey, the redshift distribution (of clusters primarily in the $0<z<1$\nrange) plays an important role. As Figures~\\ref{fig:clust_h} and\n~\\ref{fig:clust_om} show, the total number of clusters can be adjusted by\nchanging $\\Omega_m$ and $h$. In terms of the total number of clusters, $w$ is\ntherefore degenerate both with $\\Omega_m$ and $h$: raising $w$ lowers the total\nnumber, but this can always be offset by a change in $\\Omega_m$ and/or $h$.\nThe bottom left panel in Fig.~\\ref{fig:sep} reveals that based on $P_0$ alone,\n$w=-0.2$ (and $\\Omega_m=0.43$) can not be distinguished from $\\Lambda$CDM even\nat the $1\\sigma$ level. On the other hand, the middle panel in\nFig.~\\ref{fig:slicex} shows that when the shape information is added, $w \\lsim\n-0.2$ follows to $2\\sigma$ significance.\n\n\\myputfigure{fig10.eps}{3.35}{0.50}{-35}{-00}\n\\figcaption{Likelihood contours of 1, 2, and 3$\\sigma$ probabilites as in\nFigures \\ref{fig:slices} and \\ref{fig:slicex}, but when only the total number\nof clusters (left panels), or only the redshift distributions (right panels)\nare used to compute the likelihoods between two models.\n\\vspace{\\baselineskip}\n\\label{fig:sep}}\n\n\\subsection{Discussion of Possible Systematic Uncertainties}\n\\label{subsec:systematics}\n\nOur results imply that the cluster abundances in the SZE and X--ray surveys can\nprovide useful constraints on cosmological parameters, based on statistical\ndifferences expected among different cosmologies. The purpose of this section\nis to summarize and quantify the various systematic uncertainties that can\naffect these constraints.\n\n\\vspace{\\baselineskip} {\\it Knowledge of the Limiting Mass $M_{\\rm min}$}. Our\nconclusions above are dependent on the chosen limiting mass, which is a\nfunction of both redshift and cosmology. From the discussion in\n\\S~\\ref{subsec:parameters} we have seen that the limiting mass plays a\nsecondary role in the SZE survey, where the bulk of the constraint comes from\nthe growth function. In comparison, we find that $M_{\\rm min}$ plays an\nimportant role in the X--ray survey. To demonstrate the importance of\nthe mass limit explicitly, in Figure~\\ref{fig:slicex-noM} we show the\nlikelihood contours in the $\\Omega_m - w$ plane when the variations of the\nlimiting mass with cosmology are not taken into account. Not surprisingly,\nthis makes the contours somewhat narrower, but nearly parallel to $w$ -- this\nis consistent with our finding in Figure \\ref{fig:clust_xnoM} that the mass\nlimit accounts for nearly all of the $w$--dependence, but it reduces the\n$\\Omega_m$ dependence. Figure~\\ref{fig:slicex-noM} demonstrates the need to\naccurately know the limiting mass $M_{\\rm min}$, and its cosmological scaling, in\nthe X--ray survey.\n\n\\myputfigure{fig11.eps}{3.2}{0.48}{-35}{-00} \n\\figcaption{Likelihood contours for a fixed $h=0.65$ in the X--ray survey, as\nin the middle panel of Figure~\\ref{fig:slicex}, but zooming in for clarity.\nThe added (nearly horizontal) contours shows the allowed region when variations\nof the limiting mass with cosmology are not taken into\naccount.\n\\label{fig:slicex-noM}}\n\\vspace{\\baselineskip}\n\nBecause our proposed cluster sample will have measured X--ray temperatures, the\nuncertainty in our knowledge of the limiting mass will likely be dominated by\nthe theoretical uncertainties of the $M-T$ relation. In order to quantify the\neffect of such errors, we have performed a set of simple modifications to our\nmodeling of the constraints from the X--ray survey. In all cases, we adopt the\nsame $M-T$ relations as we did before (cf. eq.~\\ref{eq:mt}). However, in the\nfiducial model, we use a limiting mass that is altered by either $\\pm 5\\%$ or\n$\\pm 10\\%$ from the mass inferred from this $M-T$ relation. This mimics a\nsituation where the theoretical $M-T$ relation we apply is either 5\\% or 10\\%\naway from the relation in the real universe. In a second set of calculations,\nwe mimic a situation where the slope of the $M-T$ relation is incorrectly\nmodeled; i.e. we alter this slope in the fiducial model to $\\alpha=1.5 \\pm\n0.05$. The deviations to the likelihood contours caused by these offsets are\ndemonstrated in Figure~\\ref{fig:slicex-mlim}, which shows the effects of the\noffset in the $M-T$ normalization, and in Figure~\\ref{fig:slicex-slope}, which\nshows the effects of the offsets in the slope. As the figures reveal, the\ncontours shift relatively little under these changes. We conclude that the\nresults we derive are robust, as long as we can predict the $M-T$ relation to\nwithin $\\sim 10\\%$.\n\n\\begin{figure*}[hbt]\n\\vskip-0.2in\n\\hbox to \\hsize{\\hfil\\hskip-0.25in\\vbox to 5.6in{\n\\epsfysize=5.6in\n\\epsfbox{fig12.eps}\n\\vfil}\\hfil}\\vskip-0.4in\n\\caption{\\footnotesize The middle panels show the likelihood contours for a\nfixed $h=0.65$ in the X--ray survey, as in Figure~\\ref{fig:slicex}. The upper\nand lower panels show the deviations in the contours caused by either a $\\pm\n5\\%$ or a $\\pm 10\\%$ offset in the $M-T$ normalization.}\n\\label{fig:slicex-mlim}\n\\vskip-0.2in\n\\end{figure*}\n \n\\begin{figure*}[hbt]\n\\vskip-0.2in\n\\hbox to \\hsize{\\hfil\\hskip-0.2in\\vbox to 3.3in{\n\\epsfysize=3.3in\n\\epsfbox{fig13.eps}\n\\vfil}\\hfil}\\vskip-0.4in\n\\caption{\\footnotesize The middle panels show the likelihood contours for a\nfixed $h=0.65$ in the X--ray survey, as in Figure~\\ref{fig:slicex}. The other\ntwo panels show the deviations caused by an offset in the slope $M\\propto\nT^\\alpha$.}\n\\label{fig:slicex-slope}\n\\vskip-0.2in\n\\end{figure*}\n\n\\begin{figure*}[b]\n\\vskip-0.4in\n\\hbox to \\hsize{\\hfil\\hskip-0.2in\\vbox to 3.3in{\\epsfysize=3.3in\n\\epsfbox{fig14.eps} \\vfil}\\hfil}\\vskip-0.4in\n\\caption{\\footnotesize The middle panel shows the likelihood contours for a\nfixed $h=0.65$ in the X--ray survey, as in Figure~\\ref{fig:slicex}. The left\nand right panels show the deviations in the contours caused by a $\\pm 2\\%$\noffset in the local cluster abundance determination.}\n\\label{fig:slicex-ncom}\n\\end{figure*}\n\nIn our approach, we have attempted to utilize the whole observed cluster\nsample, down to the detection threshold: we had to therefore include the above\ncosmological dependencies. In principle, measured cluster velocity dispersions\nand X--ray temperatures (both of which are cosmology independent) could be\nutilized to improve the constraints, i.e. by selecting sub--samples that\nmaximize the differences between models. Further work is needed to clarify the\nfeasibility of this approach, as well as to quantify the accuracy to which the\ndependence of $M_{\\rm min}$ on $\\Omega_m$, $h$, $w$, and $z$ can be predicted.\n\n\\vspace{\\baselineskip} {\\it Evolution of Internal Cluster Structure}. Further\nwork is also required to test the cluster structural evolution models we\nuse. For the X--ray survey, we have assumed that the cluster\nluminosity--temperature relation does not evolve, consistent with current\nobservations (\\cite{mushotzky97}), and in the SZE survey, we have adopted the\nstructural evolution found in state of the art hydrodynamical simulations.\nBecause of the sensitivity of the survey yields to the limiting mass, cluster\nstructural evolution which changes the observability of high redshift clusters\ncan introduce systematic errors in cosmological constraints: for example, both\nlow $\\Omega_m$ cosmologies and positive evolution of the cluster\nluminosity--temperature relation increase the cluster yield in an X-ray survey.\nSZE surveys are generally less sensitive to evolution than X--ray surveys,\nbecause the X--ray luminosity is heavily dependent on the core structure (e.g.,\nthe presence or absence of cooling instabilities), whereas the SZE visibility\ndepends on the integral of the ICM pressure over the entire cluster\n(Eqn.~\\ref{eq:MlimSZ}). We are testing these assertions with a new suite of\nhydrodynamical simulations in scenarios where galaxy formation at high redshift\npreheats the intergalactic gas before it collapses to form clusters\n(\\cite{bialek00}; Mohr et al. in prep). However, most importantly, we\nemphasize that because of the sensitivity of X--ray surveys to evolution, we\nhave only used those clusters which produce enough photons to measure an\nemission weighted mean temperature. In this case, one can directly extract the\nminimum temperature $T_{lim}(z)$ of detected clusters as a function of\nredshift. Correctly interpreting such a survey requires mapping $T_{lim}(z)\\to\nM_{lim}(z)$ using the mass-temperature relation; the evolution of the\nmass-temperature relation is less sensitive to the details of preheating than\nthe luminosity-temperature relation. Thus, in a survey constructed in this\nmanner, it should be possible to disentangle the cosmological effects from\nthose caused by the evolution of cluster structure.\n\n\\vspace{\\baselineskip} {\\it Cluster Mass Function}. In our treatment, we have\nrelied on the mass function inferred from large scale numerical simulations of\nJenkins et al. (2000). Although we do not expect the results presented here to\nchange qualitatively, changes in $dN/dM$ by upto the quoted accuracy of $\\sim\n30\\%$ could affect the exact shape of the likelihood contours shown in\nFigures~\\ref{fig:slices} and \\ref{fig:slicex}. It is important to test the\nscaling of the mass function with cosmological parameters in future\nsimulations. We have further ignored the effects of galaxy formation and\nfeedback on the limiting mass. In principle, the relation between the cluster\nSZE decrement and virial mass in the lowest mass clusters could be affected by\nthese processes. In addition, the dependence of both the SZE decrement and the\nX--ray flux likely exhibits a non--negligible intrinsic scatter. The SZE\ndecrement to virial mass relation is found to have a small scatter in numerical\nsimulations (Metzler 1998), and to cause a negligible increase in the total\ncluster yields (Holder et al. 1999). However, the presence of scatter could\neffectively lower the limiting masses in our treatment of the X--ray survey.\n\n\\vspace{\\baselineskip} {\\it Local Cluster Abundance}. Perhaps the most\ncritical assumption is that the local cluster abundance is known to high\naccuracy. We have used this assumption to determine $\\sigma_8$, i.e. to\neliminate one free parameter -- effectively assigning ``infinite weight'' to\nthe cluster abundance near $z=0$. This approach is appropriate for several\nreasons. The cosmological parameters make little difference to the cluster\nabundance at $z\\approx 0$, other than the volume being proportional to\n$h^{-3}$. Similarly, the study of local cluster masses is cosmologically\nindependent (upto a factor of $h$). In a $10^4$ square degree survey, we find\nthat the total number of clusters between $0<z<0.1$, down to a limiting mass of\n$2\\times 10^{14}h^{-1}~{\\rm M_\\odot}$ is $\\approx 2500$; with a random error of\nonly $\\pm 2\\%$. We have experimented with our models, assuming that the\nnormalization at $z=0$ is incorrectly determined by a fraction of 2\\%. In\nFigure~\\ref{fig:slicex-ncom}, we show the shift in the usual likelihood contour\nin the X--ray survey, caused by errors in the local abundance at this level.\nAs the figure shows, the shift is relatively small (by about the width of the\n$1\\sigma$ region). In similar calculations with errors of $\\pm 4\\%$, we find\nshifts that are approximately twice as significant. We conclude that for our\nnormalization procedure to be valid, the local cluster abundance has to be\nknown to an accuracy of about $\\lsim 10\\%$.\n\nAlthough such an accuracy can be achieved by only $\\sim 600$ nearby clusters\n(which can be provided, for example, by an analysis of the SDSS data or perhaps\nthe 2MASS survey), it is interesting to consider a different approach, where\n$\\sigma_8$ is treated as another free parameter in addition to $\\Omega_m, h,$\nand $w$. The result of such a calculation over a 4--dimensional grid is\ndisplayed in Figure~\\ref{fig:slicex-nosig}. This figure shows the likelihood\ncontours along the slice $h=0.65$ through this parameter space, but in\nprojection along the $\\sigma_8$ axis; to be compared directly with the middle\npanel of Figure~\\ref{fig:slicex}. Allowing $\\sigma_8$ to vary results in a\nrange of values $0.70 < \\sigma_8 < 0.97$, and considerably expands the allowed\nlikelihood region. The shape of the contours stay nearly unchanged, but their\nwidths along the $\\Omega_m$ direction expand by approximately a factor of $\\sim\n4$, and their lengths along the $w$ direction increase by about a factor of 2.\nWe conclude that our constraints would be significantly weakened without the\nlocal normalization (but would still be potentially useful when combined with\nother data; see below).\n\n\\vspace{\\baselineskip} {\\it More General Cosmologies}. In section\n\\ref{sec:wconstraints}, we restricted our range of models to flat CDM models.\nWe find that the redshift distribution of clusters in open CDM models typically\nresembles that in models with high $w$. This is demonstrated in\nFigure~\\ref{fig:clust_w}: both in the $w=-0.2$ and the OCDM model, the redshift\ndistributions are flatter and extend to higher $z$ than in $\\Lambda$CDM. We\nfind that OCDM models with suitably adjusted values of $\\Omega_m$ and $h$ are\ntypically difficult to distinguish from those with $w\\gsim -0.5$, but the flat\nshape of $dN/dzd\\Omega$ makes OCDM easily distinguishable from $\\Lambda$CDM.\nNote that open CDM models appear inconsistent with the recent CMB anisotropy\ndata from the Boomerang and Maxima experiments\n(e.g. \\cite{lange00,white00,bond00}). A broader study of different\ncosmological models, including those with both dark energy and curvature,\ntime--dependent $w$, and those with non--Gaussian initial conditions could\nreveal new degeneracies, and will be studied elsewhere.\n\n\\myputfigure{fig15.eps}{3.25}{0.49}{-35}{-00} \n\\figcaption{Likelihood contours for a fixed $h=0.65$ in the X--ray survey, as\nin Figure~\\ref{fig:slicex}; however, we here considered $\\sigma_8$ as a free\nparameter, rather than fixing its value based on the local \nabundance. For the range of $\\Omega$ and $w$ shown, models with\na likelihood better than 3$\\sigma$ take on values between \n$0.7<\\sigma_8<0.97$. \\vspace{\\baselineskip}\n\\label{fig:slicex-nosig}}\n\n\\subsection{Clusters versus CMB Anisotropy and High-$z$ SNe}\n\\label{subsec:cmb}\n\nA useful generic feature of the likelihood contours presented here is their\ndifference from those expected in CMB anisotropy or Supernovae data. Two\ndifferent cosmologies produce the same location (spherical harmonic index\n$\\ell_{\\rm peak}$) for the first Doppler peak for the CMB temperature\nanisotropy, provided they have the same comoving distance to the surface of\nlast scattering (cf. \\cite{wang98,white98,huey99}). Note that this is only the\nmost prominent constraint that can be obtained from the CMB data, with\nconsiderable more information once the location and height of the second and\nhigher Doppler peaks are measured. Similarly; the apparent magnitudes of the\nobserved SNe constrain the luminosity distance $d_L(z)$ to $0\\leq z\\lsim 1$\n(\\cite{schmidt98,perlmutter99}). In general, both of these types of\nobservations will determine a combination of cosmological parameters that is\ndifferent from the cluster constraints derived here.\n\n\\myputfigure{fig16.eps}{3.25}{0.47}{-35}{-00} \n\\figcaption{Likelihood contours for a fixed $h=0.65$ as in\nFigure~\\ref{fig:slicex}, but zooming in for clarity. Also shown are\ncombinations of $w$ and $\\Omega_m$ that keep the spherical harmonic index\n$\\ell$ of the first Doppler peak in the CMB anisotropy data constant to within\n$\\pm 1\\%$ (dashed lines); and combinations that keep the luminosity distance to\nredshift $z=1$ constant to the same accuracy.\\vspace{\\baselineskip}\n\\label{fig:slicex-zoom}}\n\nIn Figure~\\ref{fig:slicex-zoom}, we zoom in on the relevant region of the\n$\\Omega_m-w$ plane in the X--ray survey, and compare the cluster constraints to\nthose expected from CMB anisotropy or high--$z$ SNe. The three dashed curves\ncorrespond to the CMB constraints: the middle curve shows a combination of\n$\\Omega_m$ and $w$ that produces the constant $\\ell_{\\rm peak}\\approx 243$\nobtained in our fiducial $\\Lambda$CDM model (using the fitting formulae from\nWhite 1998 for the physical scale $k_{\\rm peak}$); the other two dotted curves\nbracket a $\\pm 1\\%$ range around this value. Similarly, the dotted curves\ncorrespond to the constraints from SNe. The middle curve shows a line of\nconstant $d_L$ at $z=1$ that agrees with the $\\Lambda$CDM model; the two other\ncurves produce a $d_L$ that differs from the fiducial value by $\\pm 1\\%$. As\nthe figures show, the lines of CMB and SNe parameter degeneracies run somewhat\nunfavorably parallel to each other; however, both of those degeneracies are\nmuch more complementary to the direction of the parameter degeneracy in cluster\nabundance studies. In particular, the maximum allowed value of $w$, using both\nthe CMB or SNe data, is $w\\approx -0.8$; while this is reduced to $w\\approx\n-0.95$ when the cluster constraints are added. Note that in\nFigure~\\ref{fig:slicex-zoom}, we have assumed a fixed value of $h=0.65$;\nhowever, we find that relaxing this assumption does not significantly change\nthe above conclusion. The CMB and SNe constraints depend more sensitively on\n$h$ than the cluster constraints do: as a result, the confidence regions do not\noverlap significantly even in the three--dimensional ($w,\\Omega_m,h$) space.\n\nThe high complementarity of the cluster constraint to those from the other two\nmethods can be understood based on the discussions in\n$\\S$~\\ref{subsec:parameters}. To remain consistent with the CMB and SNe Ia\nconstraints, an increase in $w$ must be coupled with a decrease in\n$\\Omega_{m}$; however, both increasing $w$ and lowering $\\Omega_m$ raises the\nnumber of detected clusters. To keep the total number of clusters constant, an\nincrease in $w$ must be balanced by an increase in $\\Omega_m$. Note that this\nstatement is true both for the SZE and the X--ray surveys. Combining the\ncluster constraints with the CMB and SNe Ia constraints will therefore likely\nresult in improved estimates of the cosmological parameters, and we do not\nexpect this conclusion to rely on the details of the two surveys considered\nhere.\n\n\\section{Conclusions}\n\\label{sec:conclusions}\n\nWe studied the expected evolution of galaxy cluster abundance from $0\\lsim z\n\\lsim 3$ in different cosmologies, including the effects of variations in the\ncosmic equation of state parameter $w\\equiv p/\\rho$. By considering a range of\ncosmological models, we quantified the accuracy to which $\\Omega_m$, $w$, and\n$h$ can be determined in the future, using a 12~deg$^{2}$ Sunyaev-Zel'dovich\nEffect survey and a deep 10$^{4}$~deg$^{2}$ X-ray survey. In our analysis, we\nhave assumed that the local cluster abundance is known accurately: we find that\nin practice, an accuracy of $\\sim 5\\%$ is sufficient for our results to be\nvalid.\n\nWe find that raising $w$ significantly flattens the redshift--distribution,\nwhich can not be mimicked by variations in either $\\Omega_m$, $h$, which affect\nessentially only the normalization of the redshift distribution. As a result,\nboth surveys will be able to improve present constraints on $w$. In the\n$\\Omega_m-w$ plane, both the SZE and X--ray surveys yield constraints that are\nhighly complementary to those obtained from the CMB anisotropy and high--$z$\nSNe. Note that the SZE and X--ray surveys are themselves somewhat\ncomplementary. In combination with these data, the SZE survey can determine\nboth $w$ and $\\Omega_m$ to an accuracy of $\\approx 10\\%$ at $3\\sigma$\nsignificance. Further improvements will be possible from the X--ray survey.\nThe large number of clusters further alleviates the degeneracy between $w$ and\nboth $\\Omega_m$ and $h$, and, as a result, the X--ray sample can determine $w$\nto $\\approx 10\\%$ and $\\Omega_m$ to $\\approx 5\\%$ accuracy, in combination with\neither the CMB or the SN data.\n\nOur work focuses primarily on the statistics of cluster surveys. We have\nprovided an estimate of the scale of various systematic uncertainties. Further\nwork is needed to clarify the role of these uncertainties, arising especially\nfrom the analytic estimates of the scaling of the mass limits with cosmology,\nthe dependence of the cluster mass function on cosmology, and our neglect of\nissues such as galaxy formation in the lowest mass clusters. However, our\nfindings suggest that, in a flat universe, the cluster data lead to tight\nconstraints on a combination of $\\Omega_m$ and $w$, especially valuable because\nof their high complementarity to those obtained from the CMB anisotropy or\nHubble diagrams using SNe as standard candles.\n\n\\acknowledgements\n\nWe thank L. Hui for useful discussions, D. Eisenstein, M. Turner, D. Spergel\nand the anonymous referee for useful comments, and J. Carlstrom and the COSMEX\nteam for providing access to instrument characteristics required to estimate\nthe yields from their planned surveys. ZH is supported by the DOE and the NASA\ngrant NAG 5-7092 at Fermilab, and by NASA through the Hubble Fellowship grant\nHF-01119.01-99A, awarded by the Space Telescope Science Institute, which is\noperated by the Association of Universities for Research in Astronomy, Inc.,\nfor NASA under contract NAS 5-26555. JJM is supported by Chandra Fellowship\ngrant PF8-1003, awarded through the Chandra Science Center. The Chandra\nScience Center is operated by the Smithsonian Astrophysical Observatory for\nNASA under contract NAS8-39073.\n\n\\begin{thebibliography}{99}\n\n\\bibitem[Arnaud \\& Evrard 1999]{arnaud99} Arnaud, M. \\& Evrard, A.E. 1999, \\mnras, 305, 631\n\n\\bibitem[Bahcall et al. 1999]{bahcall99} Bahcall, N.A., Ostriker, J. P., Perlmutter, S., \\& Steinhardt, P. J. 1999, Science, 284, 1481\n\n\\bibitem[Bahcall \\& Fan 1998]{bahcall98} Bahcall, N.A. \\& Fan, X. 1998, \\apj, 504, 1\n\n\\bibitem[Bautz et al. 1998]{bautz98} Bautz, M.W., Pivovaroff, M., Baganoff, G., Isobe, T., Jones, S.E., Kissel, S.E., Lamarr, B., Manning, H.L., Prigozhin, G.Y., Ricker, G.R., Nousek, J.A., Grant, C.E., Nishikida, D., Scholze, F., Thornagel, R., \\& Ulm, G. 1998, SPIE Proceeding, 3444, 210\n\n\\bibitem[Bialek, Evrard \\& Mohr 2000]{bialek00} Bialek, J., Evrard, \nA.E. \\& Mohr, J.J. 2000, \\apj, submitted (astro-ph/0010584)\n\n\\bibitem[Blanchard \\& Bartlett 1998]{blanchard98} Blanchard, A. \\& Bartlett, J.G. 1998, \\astap, 332, L49\n\n\\bibitem[Bond \\& Myers 1996]{bond96} Bond, J. R., \\& Myers, S. T. 1996, \\apjs,\n103, 41\n\n\\bibitem[Bond et al. 2000]{bond00} Bond, J. R., et al. 2000, in Proc. IAU\nSymposium 201, PASP, in press (astro-ph/0011378)\n\n\\bibitem[Bryan \\& Norman 1998]{bryan98} Bryan, G.L. \\& Norman, M.L. 1998, \\apj,\n495, 80\n\n\\bibitem[Burles \\& Tytler 1998]{burles98} Burles, S., \\& Tytler, D. 1998, \\apj, 499, 699\n\n\\bibitem[Caldwell, Dave \\& Steinhardt 1998]{caldwell98} Caldwell, R.R., Dave, R. \\& Steinhardt, P.J. 1998, \\apss, 261, 303\n\n\\bibitem[Carlstrom et al. 1999]{carlstrom99} Carlstrom, J.E., Joy, M.K., Grego, L., Holder, G.P., Holzapfel, W.L., Mohr, J.J., Patel, S. \\& Reese, E.D. 1999, {\\it Physica Scripta}, 60, in press (astro-ph/9905255)\n\n\\bibitem[Carroll, Press \\& Turner 1992]{carroll92} Carroll, S., Press, W. \\& Turner, E. 1992, \\araa, 30, 499\n\n\\bibitem[Chartas et al. 1998]{chartas98} Chartas, G., Garmire, G., Nousek, J., Koch, S., Kissel, S., Prigozhin, G., \\& Bautz, M. 1998, SPIE Proceedings, 3444, 258\n\n\\bibitem[Eisenstein 1996]{eisenstein96} Eisenstein, D.J. 1996, PhD dissertation, Harvard University\n\n\\bibitem[Eisenstein \\& Hu 1998]{eisenstein98} Eisenstein, D.J. \\& Hu, W. 1998, \\apj, 504, L57\n\n\\bibitem[Evrard, Metzler \\& Navarro 1996]{evrard96} Evrard, A.E., Metzler, C.A. \\& Navarro, J.F. 1996, \\apj, 469, 494\n\n\\bibitem[Freese, Adams \\& Frieman 1987]{freese87} Freese, K., Adams, F. C., \\& Frieman, J. A. 1987, Nucl. Phys. B, 287, 797\n\n\\bibitem[Friedrich et al. 1998]{friedrich98} Friedrich, P., Brauninger, H., Burkert, W., Dohring, T., Egger, R., Hasinger, G., Oppitz, A., Predehl, P. \\& Trumper, J. 1998, SPIE Proceedings, 3444, 369\n\n\\bibitem[Gioia et al. 1990]{gioia90} Gioia, I.M., Maccacaro, T., Schild, R.E., Wolter, A., Stocke, J.T., Morris, S.L. \\& Henry, J.P. 1990, \\apjs, 72, 567\n\n\\bibitem[Gross et al 1998]{gross98} Gross, M.A.K., Zomerville, R.S., Primack, J.R., Holtzman, J. \\& Klypin, A. 1998, \\mnras, 301, 81\n\n\\bibitem[Holder et al. 2000]{holder00} Holder, G.P., Mohr, J.J., Carlstrom, J.E., Evrard, A.E. \\& Leitch, E.M. 2000, \\apj, submitted (astro-ph/9912364)\n\n\\bibitem[Huey et al. 1999]{huey99} Huey, G., Wang, L., Dave, R., Caldwell, R. R., \\& Steinhardt, P. J. 1999, \\prd, 59 \n\n\\bibitem[Jenkins et al. 2000]{jenkins00} Jenkins, A. et al. 2000, MNRAS, submitted, astro-ph/0005260\n\n%\\bibitem[Lacey \\& Cole 1993]{lacey93} Lacey, C. \\& Cole, S. 1993, \\mnras, 262, 627\n\n\\bibitem[Lacey \\& Cole 1994]{lacey94} Lacey, C. \\& Cole, S. 1994, \\mnras, 271, 676\n\n\\bibitem[Lange et al. 2000]{lange00} Lange, A. E., et al. 2000, \\prd, submitted, astro-ph/0005004\n\n\\bibitem[Lee \\& Shandarin 1999]{lee99} Lee, J. \\& Shandarin, S.F. 1999, \\apj, 517, L5\n\n\\bibitem[Metzler 1998]{metzler98} Metzler, C. A. 1998, \\apj, submitted, (astro-ph/9812295)\n\n\\bibitem[Mohr \\& Evrard 1997]{mohr97} Mohr, J.J. \\& Evrard, A.E. 1997, \\apj, 491, 13\n\n\\bibitem[Mohr, Mathiesen \\& Evrard 1999]{mohr99a} Mohr, J.J., Mathiesen, B. \\& Evrard, A.E. 1999, \\apj, 517, 627\n\n\\bibitem[Mohr et al. 1999]{mohr99} Mohr, J.J., Carlstrom, J.E., Holder, G.P., Holzapfel, W.L., Joy, M.K., Leitch, E.M. \\& Reese, E.D. 1999, Proceedings of the VLT Opening Symposium, Antofagasto, Chile, in press (astro-ph/9905256)\n\n\\bibitem[Mushotzky \\& Scharf 1997]{mushotzky97} Mushotzky, R.F. \\& Scharf, C.A. 1997, \\apj, 482, 13\n\n\\bibitem[Navarro, Frenk, \\& White 1997]{nfw97} Navarro, J. F., Frenk, C. S., \\& White, S. D. M. 1997, ApJ, 490, 493 (NFW)\n\n\\bibitem[Peebles 1980]{peebles80} Peebles, P.J.E., 1980, {\\it The Large Scale Structure of the Universe}, Princeton University Press: Princeton\n\n\\bibitem[Pen 1998]{pen80} Pen, U.-L. 1998, \\apj, 498, 60\n\n\\bibitem[Perlmutter, Turner \\& White 1999]{ptw99} Perlmutter, S., Turner, M. S., \\& White, M. 1999, \\prl, 83, 670\n\n\\bibitem[Perlmutter et al. 1999]{perlmutter99} Perlmutter, S. et al. 1999, \\apj, 517, 565\n\n\\bibitem[Press \\& Schechter 1974]{press74} Press, W.H. \\& Schechter, P. 1974, \\apj, 193, 437\n\n\\bibitem[Press et al. 1992]{press92} Press, W.H., Teukolsky, S.A., Vetterling, W.T. \\& Flannery, B.P., 1992, {\\it Numerical Recipes in C: The Art of Scientific Computing}, 2nd Edition, Cambridge University Press: Cambridge\n\n\\bibitem[Ratra \\& Peebles 1988]{ratra88} Ratra, B., \\& Peebles, P. J. E. 1988, \\prd, 37, 3406\n\n\\bibitem[Raymond \\& Smith 1977]{raymond77} Raymond, J.C. \\& Smith, B.W. 1977, \\apjs, 35, 419\n\n\\bibitem[Romer et al. 2000]{romer00} Romer, A.K., Viana, P.T.P., Liddle, A.R. \\& Mann, R.G. 2000, \\apj, submitted (astro-ph/9911499)\n\n\\bibitem[Schmidt et al. 1998]{schmidt98} Schmidt, B.P. et al. 1998, \\apj, 507, 46\n\n\\bibitem[Turner \\& White 1997]{turner97} Turner, M. S., \\& White, M. 1997, \\prd, 56, 4439\n\n\\bibitem[Viana \\& Liddle 1996]{viana96} Viana, P.T.P. \\& Liddle, A.R. 1996, \\mnras, 281, 323\n\n\\bibitem[Viana \\& Liddle 1999]{viana99} Viana, P.T.P. \\& Liddle, A.R. 1999, \\mnras, 303, 535\n\n\\bibitem[Vikhlinin et al. 1998]{vikhlinin98} Vikhlinin, A., McNamara, B.R., Forman, W., Jones, C., Quintana, H. \\& Hornstrup, A. 1998, \\apj, 503, 77\n\n\\bibitem[Wang \\& Steinhardt 1998]{wang98} Wang, L., \\& Steinhardt, P. J. 1998, ApJ, 508, 483\n\n\\bibitem[Wang et al. 2000]{wang00} Wang, L., Calwell, R. R., Ostriker, J. P., \\& Steinhardt, P. J. 2000, \\apj, in press, (astro-ph/9901388)\n\n\\bibitem[White, Efstathiou \\& Frenk 1993]{white93} White, S.D.M., Efstathiou, \nG., Frenk, C.S. 1993, \\mnras, 262, 1023\n\n\\bibitem[White 1998]{white98} White, M. 1998, \\apj, 506, 495\n\n\\bibitem[White, Scott \\& Pierpaoli 2000]{white00} White, M., Scott, D., \\& Pierpaoli, E. 2000, \\apj, in press, astro-ph/0004385\n\n\\end{thebibliography}\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002336.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem[Arnaud \\& Evrard 1999]{arnaud99} Arnaud, M. \\& Evrard, A.E. 1999, \\mnras, 305, 631\n\n\\bibitem[Bahcall et al. 1999]{bahcall99} Bahcall, N.A., Ostriker, J. P., Perlmutter, S., \\& Steinhardt, P. J. 1999, Science, 284, 1481\n\n\\bibitem[Bahcall \\& Fan 1998]{bahcall98} Bahcall, N.A. \\& Fan, X. 1998, \\apj, 504, 1\n\n\\bibitem[Bautz et al. 1998]{bautz98} Bautz, M.W., Pivovaroff, M., Baganoff, G., Isobe, T., Jones, S.E., Kissel, S.E., Lamarr, B., Manning, H.L., Prigozhin, G.Y., Ricker, G.R., Nousek, J.A., Grant, C.E., Nishikida, D., Scholze, F., Thornagel, R., \\& Ulm, G. 1998, SPIE Proceeding, 3444, 210\n\n\\bibitem[Bialek, Evrard \\& Mohr 2000]{bialek00} Bialek, J., Evrard, \nA.E. \\& Mohr, J.J. 2000, \\apj, submitted (astro-ph/0010584)\n\n\\bibitem[Blanchard \\& Bartlett 1998]{blanchard98} Blanchard, A. \\& Bartlett, J.G. 1998, \\astap, 332, L49\n\n\\bibitem[Bond \\& Myers 1996]{bond96} Bond, J. R., \\& Myers, S. T. 1996, \\apjs,\n103, 41\n\n\\bibitem[Bond et al. 2000]{bond00} Bond, J. R., et al. 2000, in Proc. IAU\nSymposium 201, PASP, in press (astro-ph/0011378)\n\n\\bibitem[Bryan \\& Norman 1998]{bryan98} Bryan, G.L. \\& Norman, M.L. 1998, \\apj,\n495, 80\n\n\\bibitem[Burles \\& Tytler 1998]{burles98} Burles, S., \\& Tytler, D. 1998, \\apj, 499, 699\n\n\\bibitem[Caldwell, Dave \\& Steinhardt 1998]{caldwell98} Caldwell, R.R., Dave, R. \\& Steinhardt, P.J. 1998, \\apss, 261, 303\n\n\\bibitem[Carlstrom et al. 1999]{carlstrom99} Carlstrom, J.E., Joy, M.K., Grego, L., Holder, G.P., Holzapfel, W.L., Mohr, J.J., Patel, S. \\& Reese, E.D. 1999, {\\it Physica Scripta}, 60, in press (astro-ph/9905255)\n\n\\bibitem[Carroll, Press \\& Turner 1992]{carroll92} Carroll, S., Press, W. \\& Turner, E. 1992, \\araa, 30, 499\n\n\\bibitem[Chartas et al. 1998]{chartas98} Chartas, G., Garmire, G., Nousek, J., Koch, S., Kissel, S., Prigozhin, G., \\& Bautz, M. 1998, SPIE Proceedings, 3444, 258\n\n\\bibitem[Eisenstein 1996]{eisenstein96} Eisenstein, D.J. 1996, PhD dissertation, Harvard University\n\n\\bibitem[Eisenstein \\& Hu 1998]{eisenstein98} Eisenstein, D.J. \\& Hu, W. 1998, \\apj, 504, L57\n\n\\bibitem[Evrard, Metzler \\& Navarro 1996]{evrard96} Evrard, A.E., Metzler, C.A. \\& Navarro, J.F. 1996, \\apj, 469, 494\n\n\\bibitem[Freese, Adams \\& Frieman 1987]{freese87} Freese, K., Adams, F. C., \\& Frieman, J. A. 1987, Nucl. Phys. B, 287, 797\n\n\\bibitem[Friedrich et al. 1998]{friedrich98} Friedrich, P., Brauninger, H., Burkert, W., Dohring, T., Egger, R., Hasinger, G., Oppitz, A., Predehl, P. \\& Trumper, J. 1998, SPIE Proceedings, 3444, 369\n\n\\bibitem[Gioia et al. 1990]{gioia90} Gioia, I.M., Maccacaro, T., Schild, R.E., Wolter, A., Stocke, J.T., Morris, S.L. \\& Henry, J.P. 1990, \\apjs, 72, 567\n\n\\bibitem[Gross et al 1998]{gross98} Gross, M.A.K., Zomerville, R.S., Primack, J.R., Holtzman, J. \\& Klypin, A. 1998, \\mnras, 301, 81\n\n\\bibitem[Holder et al. 2000]{holder00} Holder, G.P., Mohr, J.J., Carlstrom, J.E., Evrard, A.E. \\& Leitch, E.M. 2000, \\apj, submitted (astro-ph/9912364)\n\n\\bibitem[Huey et al. 1999]{huey99} Huey, G., Wang, L., Dave, R., Caldwell, R. R., \\& Steinhardt, P. J. 1999, \\prd, 59 \n\n\\bibitem[Jenkins et al. 2000]{jenkins00} Jenkins, A. et al. 2000, MNRAS, submitted, astro-ph/0005260\n\n%\\bibitem[Lacey \\& Cole 1993]{lacey93} Lacey, C. \\& Cole, S. 1993, \\mnras, 262, 627\n\n\\bibitem[Lacey \\& Cole 1994]{lacey94} Lacey, C. \\& Cole, S. 1994, \\mnras, 271, 676\n\n\\bibitem[Lange et al. 2000]{lange00} Lange, A. E., et al. 2000, \\prd, submitted, astro-ph/0005004\n\n\\bibitem[Lee \\& Shandarin 1999]{lee99} Lee, J. \\& Shandarin, S.F. 1999, \\apj, 517, L5\n\n\\bibitem[Metzler 1998]{metzler98} Metzler, C. A. 1998, \\apj, submitted, (astro-ph/9812295)\n\n\\bibitem[Mohr \\& Evrard 1997]{mohr97} Mohr, J.J. \\& Evrard, A.E. 1997, \\apj, 491, 13\n\n\\bibitem[Mohr, Mathiesen \\& Evrard 1999]{mohr99a} Mohr, J.J., Mathiesen, B. \\& Evrard, A.E. 1999, \\apj, 517, 627\n\n\\bibitem[Mohr et al. 1999]{mohr99} Mohr, J.J., Carlstrom, J.E., Holder, G.P., Holzapfel, W.L., Joy, M.K., Leitch, E.M. \\& Reese, E.D. 1999, Proceedings of the VLT Opening Symposium, Antofagasto, Chile, in press (astro-ph/9905256)\n\n\\bibitem[Mushotzky \\& Scharf 1997]{mushotzky97} Mushotzky, R.F. \\& Scharf, C.A. 1997, \\apj, 482, 13\n\n\\bibitem[Navarro, Frenk, \\& White 1997]{nfw97} Navarro, J. F., Frenk, C. S., \\& White, S. D. M. 1997, ApJ, 490, 493 (NFW)\n\n\\bibitem[Peebles 1980]{peebles80} Peebles, P.J.E., 1980, {\\it The Large Scale Structure of the Universe}, Princeton University Press: Princeton\n\n\\bibitem[Pen 1998]{pen80} Pen, U.-L. 1998, \\apj, 498, 60\n\n\\bibitem[Perlmutter, Turner \\& White 1999]{ptw99} Perlmutter, S., Turner, M. S., \\& White, M. 1999, \\prl, 83, 670\n\n\\bibitem[Perlmutter et al. 1999]{perlmutter99} Perlmutter, S. et al. 1999, \\apj, 517, 565\n\n\\bibitem[Press \\& Schechter 1974]{press74} Press, W.H. \\& Schechter, P. 1974, \\apj, 193, 437\n\n\\bibitem[Press et al. 1992]{press92} Press, W.H., Teukolsky, S.A., Vetterling, W.T. \\& Flannery, B.P., 1992, {\\it Numerical Recipes in C: The Art of Scientific Computing}, 2nd Edition, Cambridge University Press: Cambridge\n\n\\bibitem[Ratra \\& Peebles 1988]{ratra88} Ratra, B., \\& Peebles, P. J. E. 1988, \\prd, 37, 3406\n\n\\bibitem[Raymond \\& Smith 1977]{raymond77} Raymond, J.C. \\& Smith, B.W. 1977, \\apjs, 35, 419\n\n\\bibitem[Romer et al. 2000]{romer00} Romer, A.K., Viana, P.T.P., Liddle, A.R. \\& Mann, R.G. 2000, \\apj, submitted (astro-ph/9911499)\n\n\\bibitem[Schmidt et al. 1998]{schmidt98} Schmidt, B.P. et al. 1998, \\apj, 507, 46\n\n\\bibitem[Turner \\& White 1997]{turner97} Turner, M. S., \\& White, M. 1997, \\prd, 56, 4439\n\n\\bibitem[Viana \\& Liddle 1996]{viana96} Viana, P.T.P. \\& Liddle, A.R. 1996, \\mnras, 281, 323\n\n\\bibitem[Viana \\& Liddle 1999]{viana99} Viana, P.T.P. \\& Liddle, A.R. 1999, \\mnras, 303, 535\n\n\\bibitem[Vikhlinin et al. 1998]{vikhlinin98} Vikhlinin, A., McNamara, B.R., Forman, W., Jones, C., Quintana, H. \\& Hornstrup, A. 1998, \\apj, 503, 77\n\n\\bibitem[Wang \\& Steinhardt 1998]{wang98} Wang, L., \\& Steinhardt, P. J. 1998, ApJ, 508, 483\n\n\\bibitem[Wang et al. 2000]{wang00} Wang, L., Calwell, R. R., Ostriker, J. P., \\& Steinhardt, P. J. 2000, \\apj, in press, (astro-ph/9901388)\n\n\\bibitem[White, Efstathiou \\& Frenk 1993]{white93} White, S.D.M., Efstathiou, \nG., Frenk, C.S. 1993, \\mnras, 262, 1023\n\n\\bibitem[White 1998]{white98} White, M. 1998, \\apj, 506, 495\n\n\\bibitem[White, Scott \\& Pierpaoli 2000]{white00} White, M., Scott, D., \\& Pierpaoli, E. 2000, \\apj, in press, astro-ph/0004385\n\n\\end{thebibliography}"
}
] |
astro-ph0002337
|
NUCLEOSYNTHESIS IN CHANDRASEKHAR MASS MODELS FOR TYPE IA SUPERNOVAE AND CONSTRAINTS ON PROGENITOR SYSTEMS AND BURNING FRONT PROPAGATION
|
[
{
"author": "Franziska Brachwitz$^2$"
},
{
"author": "Ken'ichi Nomoto$^{1,4,5}$"
},
{
"author": "Nobuhiro Kishimoto$^1$"
},
{
"author": "Hideyuki Umeda$^{4,5}$"
},
{
"author": "W. Raphael Hix$^{3,5}$"
},
{
"author": "Friedrich-K. Thielemann$^{2,3,5}$"
}
] |
The major uncertainties involved in the Chandrasekhar mass models for Type Ia supernovae (SNe Ia) are related to the companion star of their accreting white dwarf progenitor (which determines the accretion rate and consequently the carbon ignition density) and the flame speed after the carbon ignition. We calculate explosive nucleosynthesis in relatively slow deflagrations with a variety of deflagration speeds and ignition densities to put new constraints on the above key quantities. The abundance of the Fe-group, in particular of neutron-rich species like $^{48}$Ca, $^{50}$Ti, $^{54}$Cr, $^{54,58}$Fe, and $^{58}$Ni, is highly sensitive to the electron captures taking place in the central layers. The yields obtained from such a slow central deflagration, and from a fast deflagration or delayed detonation in the outer layers, are combined and put to comparison with solar isotopic abundances. To avoid excessively large ratios of $^{54}$Cr/$^{56}$Fe and $^{50}$Ti/$^{56}$Fe, the central density of the "average" white dwarf progenitor at ignition should be as low as \ltsim 2 \e9 \gmc. To avoid the overproduction of $^{58}$Ni and $^{54}$Fe, either the flame speed should not exceed a few \% of the sound speed in the central low $Y_e$ layers, or the metallicity of the average progenitors has to be lower than solar. Such low central densities can be realized by a rapid accretion as fast as $\dot M$ \gtsim 1 $\times$ 10$^{-7}$M$_\odot$ yr$^{-1}$. In order to reproduce the solar abundance of $^{48}$Ca, one also needs progenitor systems that undergo ignition at higher densities. Even the smallest laminar flame speeds after the low-density ignitions would not produce sufficient amount of this isotope. We also found that the total amount of $^{56}$Ni, the Si-Ca/Fe ratio, and the abundance of some elements like Mn and Cr (originating from incomplete Si-burning), depend on the density of the deflagration-detonation transition in delayed detonations. Our nucleosynthesis results favor transition densities slightly below 2.2$\times 10^7$~g cm$^{-3}$.
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"name": "msn.tex",
"string": "%\\documentstyle[11pt,aasms4]{article}\n\\documentclass{article} \n\\usepackage[twocolumn]{emulateapj}\n\\usepackage{epsf,psfig}\n% local macros\n\\def\\ergs{ergs s$^{-1}$ }\n\\def\\gmc{g cm$^{-3}$}\n\\def\\kms{km s$^{-1}$}\n\\def\\rhoc{$\\rho_{\\rm c}$}\n\\def\\ms{M$_\\odot$}\n\\def\\mr{$M_r$}\n\\def\\ni{$^{56}$Ni}\n\\def\\ye{$Y_{\\rm e}$} \n\\def\\mdot{$\\dot M$}\n\\def\\msy{M$_\\odot$ yr$^{-1}$}\n\\def\\e#1{$\\times$ $10^{#1}$ }\n\\def\\ee#1{$10^{#1}$ }\n\\def\\ll#1{$L_{\\rm #1}$}\n\\def\\mm#1{$M_{\\rm #1}$}\n\\def\\vv#1{$v_{\\rm #1}$}\n\\def\\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\n\\def\\ltsim{\\lower.5ex\\hbox{\\ltsima}}\n\\def\\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def\\gtsim{\\lower.5ex\\hbox{\\gtsima}}\n\\def\\etal{et al. }\n%\\def\\etal{{\\sl et al.} }\n\\def\\afoe{$\\times$ 10$^{51}$ ergs }\n\\renewcommand{\\thefootnote}{\\fnsymbol{footnote}}\n\n\\begin{document}\n\n\\submitted{Published in the Astrophysical Journal Supplement Series,\n1999, v.125, pp.439-462}\n\n\\title{NUCLEOSYNTHESIS IN CHANDRASEKHAR MASS MODELS FOR TYPE IA\nSUPERNOVAE AND CONSTRAINTS ON PROGENITOR SYSTEMS AND BURNING FRONT PROPAGATION}\n\n\\author{\\footnote[1]{Present Address: \nDepartment of Physics, Nihon University, Tokyo 101-8308, Japan\n}Koichi Iwamoto$^{1,4,5}$, Franziska Brachwitz$^2$, \nKen'ichi Nomoto$^{1,4,5}$, Nobuhiro Kishimoto$^1$, \\\\\nHideyuki Umeda$^{4,5}$, \nW. Raphael Hix$^{3,5}$, Friedrich-K. Thielemann$^{2,3,5}$}\n\\affil{$^1$ Department of Astronomy, University of Tokyo, Tokyo 113-0033, Japan}\n\\affil{$^2$ Department of Physics and Astronomy, Universitty of Basel,\nCH-4056 Basel, Switzerland}\n\\affil{$^3$ Oak Ridge National Laboratory, Oak Ridge, TN 37831-4576, USA}\n\\affil{$^4$ Research Center for the Early Universe, School of \nScience, University of Tokyo, Tokyo 113-0033, Japan}\n\\affil{$^5$ Institute for Theoretical Physics, Santa Barbara, CA 93106-4030,\nUSA}\n\n\n\\begin{abstract}\n\n\tThe major uncertainties involved in the Chandrasekhar mass\nmodels for Type Ia supernovae (SNe Ia) are related to the companion\nstar of their accreting white dwarf progenitor (which determines\nthe accretion rate and consequently the carbon ignition density) and the \nflame speed after the carbon ignition. We calculate explosive\nnucleosynthesis in relatively slow deflagrations with a variety of\ndeflagration speeds and ignition densities to put new constraints on\nthe above key quantities. The abundance of the Fe-group, in\nparticular of neutron-rich species like $^{48}$Ca, $^{50}$Ti,\n$^{54}$Cr, $^{54,58}$Fe, and $^{58}$Ni, is highly sensitive to the\nelectron captures taking place in the central layers. The\nyields obtained from such a slow central deflagration, and from a fast\ndeflagration or delayed detonation in the outer layers, are combined\nand put to comparison with solar isotopic abundances. To avoid\nexcessively large ratios of $^{54}$Cr/$^{56}$Fe and\n$^{50}$Ti/$^{56}$Fe, the central density of the \"average\" white dwarf\nprogenitor at ignition should be as low as \\ltsim 2 \\e9 \\gmc. To\navoid the overproduction of $^{58}$Ni and $^{54}$Fe, either the flame\nspeed should not exceed a few \\% of the sound speed in the central low\n$Y_e$ layers, or the metallicity of the average progenitors has to be\nlower than solar. Such low central densities can be realized by a\nrapid accretion as fast as $\\dot M$ \\gtsim 1 $\\times$\n10$^{-7}$M$_\\odot$ yr$^{-1}$. In order to reproduce the solar\nabundance of $^{48}$Ca, one also needs progenitor systems that undergo\nignition at higher densities. Even the smallest laminar flame speeds\nafter the low-density ignitions would not produce sufficient amount of\nthis isotope. We also found that the total amount of $^{56}$Ni, the\nSi-Ca/Fe ratio, and the abundance of some elements like Mn and Cr\n(originating from incomplete Si-burning), depend on the density of the\ndeflagration-detonation transition in delayed detonations. Our\nnucleosynthesis results favor transition densities slightly below\n2.2$\\times 10^7$~g cm$^{-3}$.\n\n\n\\end{abstract}\n\n\\section {Introduction}\n\n\tThere are strong observational and theoretical indications\nthat Type Ia supernovae (SNe Ia) are thermonuclear explosions of\naccreting white dwarfs (e.g., Wheeler et al. 1995; Nomoto, Iwamoto \\&\nKishimoto 1997; Branch 1998). Theoretically, both the Chandrasekhar\nmass white dwarf models and sub-Chandrasekhar mass models have been\nconsidered (see, e.g., Arnett 1996; Nomoto \\etal 1994, 1996a, 1997b,\n1997c; Canal, Ruiz-Lapuente, \\& Isern 1997 for reviews of recent\nprogress). Though these white dwarf models can account for the basic\nobservational features of SNe Ia, the exact binary evolution that\nleads to SNe Ia has not been identified yet. Various evolutionary\nscenarios have been proposed, which include (1) a double degenerate\nscenario, i.e., the merging of two C+O white dwarfs in a binary system\nwith a combined mass exceeding the Chandrasekhar mass limit (e.g.,\nIben \\& Tutukov 1984; Webbink 1984) and (2) a single degenerate\nscenario, i.e., accretion of hydrogen or helium via mass transfer from\na binary companion at a relatively high rate (e.g., Nomoto 1982a). In\nthe case of helium accretion at low rates, He detonates at the base of\nthe accreted layer before the system reaches the Chandrasekhar mass\n(Nomoto 1982b; Woosley \\& Weaver 1986, 1994a; Livne \\& Arnett 1995).\nCurrently, the issues of the Chandrasekhar mass versus\nsub-Chandrasekhar mass models and the double degenerate versus single\ndegenerate scenarios are still debated (see, e.g., Renzini 1996 and\nBranch et al. 1995 for recent reviews), but they are being confronted\nwith an increasing number of observational constraints.\n\n\tThe observational search for the double degenerate scenario\nled to the discovery of a few binary white dwarfs systems, but with\ncombined mass being smaller than the Chandrasekhar mass (Renzini\n1996). Theoretically, it has been suggested that the merging of\ndouble white dwarf systems leads to accretion-induced collapse rather\nthan to SNe Ia (Nomoto \\& Iben 1985; Saio \\& Nomoto 1985, 1998). The\nChandrasekhar versus sub-Chandrasekhar mass issue has recently\nexperienced some progress. Photometric and spectroscopic features of\nSNe Ia in early phases clearly indicate that Chandrasekhar mass models\ngive a much more consistent picture than the sub-Chandrasekhar mass\nmodels of helium detonations (e.g., H\\\"oflich \\& Khokhlov 1996; Nugent\n\\etal 1997). This leaves us with the most likely progenitor system, a\nsingle degenerate system with hydrogen accretion from the companion\nstar, leading to a Chandrasekhar-mass white dwarf. However, the\nChandrasekhar mass model W7 (Nomoto, Thielemann, \\& Yokoi 1984;\nThielemann, Nomoto, \\& Yokoi 1986), widely used in galactic chemical\nevolution calculations, may require improvements in terms of the\nFe-group composition because it predicts significantly higher\n$^{58}$Ni/$^{56}$Fe ratios than solar. The direct determination of Ni\nabundances in late time SN Ia spectra is therefore important\n(Ruiz-Lapuente 1997; Liu, Jeffery, \\& Schultz 1997; Mazzali et\nal. 1998). The recent findings of supersoft X-ray sources, being\npotential progenitors of SN Ia events with high accretion rates,\ncausing ignition at low densities (van den Heuvel \\etal 1992;\nRappaport, Di Stefano, \\& Smith 1994; Di Stefano \\etal 1997), leave\nhope for Chandrasekhar-mass models, which meet all these requirements,\nalso for late time spectra.\n\n\tThe presupernova evolution of an accreting white dwarf depends\non the accretion rate $\\dot M$, the composition of the material\ntransferred from the companion star, and the initial mass of the white\ndwarf (e.g., Nomoto 1982a; Nomoto \\& Kondo 1991). Chandrasekhar mass\nwhite dwarfs can be obtained with a relatively high mass transfer rate\nof hydrogen of the order $\\dot M$ $\\approx$ 4 \\e{-8} -- \\ee{-5}\nM$_\\odot$ yr$^{-1}$. At $\\dot M > 4 \\times 10^{-6}$ M$_\\odot$\nyr$^{-1}$, the accreting white dwarf blows off a strong wind, which\nreduces $\\dot M$ to an effective accretion rate below \\ee{-6}\n$M_\\odot$ yr$^{-1}$ (Hachisu, Kato, \\& Nomoto 1996, 1999a). This\navoids the formation of an extended envelope in the accreting white\ndwarf. (Nomoto , Nariai, \\& Sugimoto 1979). At such rates hydrogen\nand helium burn steadily or with weak flashes, leading to a white\ndwarf with a growing C+O mass.\n\n\tFor the Chandrasekhar mass white dwarf model, carbon ignition\nin the central region leads to a thermonuclear runway. The ignition\ndensity depends on the stellar structure as a function of previous\naccretion history. High accretion rates lead to higher central\ntemperatures, i.e. favoring lower ignition densities. A flame front\nthen propagates at a subsonic speed $v_{\\rm def}$ as a {\\sl\ndeflagration wave} owing to heat transport across the front (Nomoto et\nal. 1984). The major and yet not fully solved questions are related to\nthe propagation of the burning front. Timmes \\& Woosley (1992) have\nanalyzed the propagation speed of laminar burning fronts in one\ndimension as a function of density and fuel composition. However, the\npropagation in three dimensions is influenced by instabilities that\ncan enhance the effective radial flame speed beyond its laminar value.\n\n\tThe flame front is subject to various types of instabilities,\nnamely, thermal instabilities (Bychkov \\& Liberman 1995a), the\nLandau-Darrius (L-D) instability (Landau \\& Lifshitz 1987), the\nRayleigh-Taylor (R-T) instability, and the Kevin-Helmholtz (K-H)\ninstability (Niemeyer, Woosley, \\& Hillebrandt 1996). The turbulent\nburning regime associated with the R-T bubbles on global scales has\nbeen studied (Livne 1993; Arnett \\& Livne 1994a; Khokhlov 1995;\nNiemeyer \\& Hillebrandt 1995a; Niemeyer et al. 1996), but there remain\nmany uncertainties, related partially to numerical resolution but also\nto the role and spectrum of turbulent length scales (Hillebrandt \\&\nNiemeyer 1997). With the present uncertainties, it is essential to\nperform parameterized sets of calculations that explore the possible\nrange of effective radial flame speeds.\n\n\tIn the deflagration wave, electron captures enhance the\nneutron excess. The amount of electron capture depends on both $v_{\\rm\ndef}$ (influencing the time duration of matter at high temperatures,\nand with it the availability of free protons for electron capture and\nthe high-energy tail of the electron energy distribution) and the\ncentral density of the white dwarf $\\rho_9 = \\rho_{\\rm c}$/10$^9$ g\ncm$^{-3}$ (increasing the electron chemical potential). The resultant\nnucleosynthesis in slow deflagrations (see, e.g., Khokhlov 1991b) has\nsome distinct features compared with faster deflagrations like W7\n(Nomoto \\etal 1984; Thielemann \\etal 1986), thus providing important\nconstraints on these two parameters. The constraint on the central\ndensity is equivalent to a constraint on the accretion rate, as\ndiscussed above. After an initial deflagration in the central layers,\nthe deflagration is accelerated as in W7, or assumed to turn into a\ndetonation at lower densities, as in the delayed detonation models\n(Khokhlov 1991a; Woosley \\& Weaver 1994a). For the latter, the\nuncertain transition density $\\rho_{\\rm tr}$ would result in a variety\nof total masses of $^{56}$Ni and expansion velocities of the outer\nlayers.\n\n\tTo obtain constraints on the three parameters ($\\rho_{\\rm\nign}$, $v_{\\rm def}$, and $\\rho_{\\rm tr}$), we performed explosive\nnucleosynthesis calculations for slow deflagrations followed by a\ndelayed detonation or a fast deflagration. These calculations assumed\nspherical symmetry and therefore might not be fully adequate for a\nrealistic and consistent approach, but we expect that they lead at\nleast to some clues how abundance features relate to the spherical\naverage of these quantities in realistic models. Initially slower\ndeflagrations cause an earlier expansion of the outer layers with\nrespect to the arrival of the burning front (as information of the\ncentral ignition propagates with sound speed; Nomoto, Sugimoto, \\& Neo\n1976) and lead to low densities for the outer deflagration and\ndetonation layers. In such a case, even a detonation does not lead to\na pure Fe-group composition, as expected in central detonations, and\nintermediate mass elements from Si to Ca are produced at a wide range\nof expansion velocities. Therefore, if the deflagration-detonation\ntransition (DDT) density is well tuned, delayed detonations can meet\nthese observational requirements as well as fast deflagration\n(Kirshner \\etal 1993). Compared with the earlier delayed detonation\nmodels by Khokhlov (1991b), we adopt a larger and more detailed\nnuclear reaction network that alos includes electron screening. In\ncomparison to the fast deflagration models by Woosley (1997b), we use\ninitial models with lower central densities and smaller flame speeds,\nto concentrate on our main aim, which is to find the \"average\" SN Ia\nconditions responsible for their nucleosynthesis contribution to\ngalactic evolution, i.e., especially the Fe-group composition.\n\n\tFrom the very early days of explosive nucleosynthesis\ncalculations, when no direct connection to astrophysical sites was\npossible yet, it was noticed (Trimble 1975) that the solar Fe-group\ncomposition could be reproduced with a superposition of matter from\nexplosive Si burning with about 90\\% originating from a $Y_e$ = 0.499\nsource and 10\\% from a $Y_e$ = 0.46 source. As it has been shown that\nSN II ejecta with $Y_e <$ 0.498 could cause serious problems in\ncomparison with observations (Thielemann, Nomoto, \\& Hashimoto 1996),\nSNe Ia have to be identified with this second source and the\nappropriate conditions which lead to the best agreement with solar\nabundances. For this reason we present detailed yields of delayed\ndetonation models as well as fast deflagration models and compare them\nwith solar abundances for a number of \"training sets\" of ignition\ndensities, flame speeds, and DDT densities.\n\n\tThese nucleosynthesis constraints can provide clues to the\nexplosion mechanism (i.e., the speed of the burning front) and the\nignition density (i.e., the accretion rate from the binary companion)\nfor the \"average\" or dominating SN Ia contributions during galactic\nchemical evolution. This is the purpose of the present paper. We have\nto be aware that there are some systematic variations that manifest\nthemselves in light curves (i.e., the brighter one is slower; Phillips\net al. 1990; Hamuy \\etal 1995) and might lead to a variation in\nnucleosynthesis as well (H\\\"oflich \\& Khokhlov 1996, H\\\"oflich,\nWheeler \\& Thielemann 1998). It is further of importance to explore\nmetallicity effects, which might have an influence on the evolution of\nthe progenitor systems, with respect to the initial mass function\n(IMF) and composition of white dwarfs as well as the binary accretion\nhistory (e.g., Yoshii, Tsujimoto, \\& Nomoto 1996; H\\\"oflich et\nal. 1998; Umeda et al. 1999; H\\\"oflich et al. 1999). Only the latter\nwill clarify whether the nature of SNe Ia at high redshifts is the\nsame as for nearby SNe Ia, which enters the determination of the\ncosmological parameters $H_0$ and $q_0$ (e.g., Branch \\& Tammann 1992;\nRiess, Press, \\& Kirshner 1995; Riess et al. 1999; Perlmutter \\etal\n1997, 1999). Observable spectral features could possibly help to\nidentify the metallicity due to slight changes in nucleosynthesis\n(H\\\"oflich et al. 1998; Hatano et al. 1999; Lentz et al. 1999).\n\n\tAfter a description of our model calculations in \\S2,\nincluding initial models, the hydrodynamic treatment, and a discussion\nof the input physics, we present in \\S3 detailed nucleosynthesis\nresults from slow deflagrations and delayed detonations in comparison\nwith the carbon deflagration model W7. In \\S4, the integrated\nabundances of SNe Ia models are combined with those of SNe II to\ncompare with solar abundances. Finally, we discuss constraints on\npossible evolutionary scenarios and give conclusions in \\S5. Very\npreliminary accounts of the present investigations on nucleosynthesis\nin slow deflagrations and delayed detonations have been given in\nNomoto et al. (1997c) and Thielemann et al. (1997).\n\n\\section {Initial Models, Explosion Hydrodynamics, and Input Physics}\n\n\\subsection{Initial Models}\n\n\tWe adopt two models with central densities of $\\rho_9$ = 1.37\n(C) and 2.12 (W) at the onset of thermonuclear runaway, i.e., at the\nstage when the timescale of the temperature rise in the center becomes\nshorter than the dynamical timescale. Here C and W imply that these\nare the same models as calculated for C6 and W7, respectively (Nomoto\n\\etal 1984). The initial white dwarfs of these models, before the\nonset of H-accretion, have a mass of $M$ = 1.0 \\ms, a central\ntemperature of $T_c$ = 1.0 \\e7 K, and compositions of $X(^{12}$C) =\n0.475, $X(^{16}$O) = 0.50, $X(^{22}$Ne) = 0.025.\n\n\tThe outer layers of the mass grid extend to the steady\nhydrogen burning shell as an outer boundary. The temperature and\ndensity at the burning shell are determined from the boundary\ncondition that the accreted matter is processed into helium with the\nmass accretion rate \\mdot. These values increase from initally 8 \\e7\nK and 1 \\e4 \\gmc~ to 1 \\e8 K and 1 \\e6 \\gmc~ at the point of central\ncarbon ignition. The accretion rate for case C is due to steady and\nstable hydrogen burning corresponding to the C+O core increase during\nan asymptotic giant branch evolution (see Nomoto 1982a). The rate for\ncase W is kept constant up to the point of carbon ignition at the\ncenter. The exact values are given by equations (1) and (2), where $M$\nindicates the mass of the accreting white dwarf.\n\n\\begin{eqnarray}\n {\\dot M}({\\rm C})& = &8.5 \\times 10^{-7} (M/{\\rm M}_\\odot - 0.52)\n {\\rm M}_\\odot {\\rm y}^{-1}\\\\\n {\\dot M}({\\rm W})& = & 4 \\times 10^{-8} {\\rm M}_\\odot {\\rm y}^{-1}.\n\\end{eqnarray}\n\n\tDuring the accretion phase the white dwarf mass $M$ increases\nwith time and the central temperature increases as a result of heat\ninflow from the H-burning shell as well as compressional heating.\nCooling is due mostly to plasmon neutrino losses and neutrino\nbremsstrahlung. Cooling due to Urca shells and the convective Urca\nprocess is not taken into account. This has no effect on case C, but\ncould delay the ignition in case W to higher densities (e.g.,\nPaczynski 1973; Iben 1982; Nomoto \\& Iben 1985; Barkat \\& Wheeler\n1990). When the central density \\rhoc~ reaches 1.5 \\e9 \\gmc~ (C) or\n2.5 \\e9 \\gmc~ (W), carbon is ignited in the center, where the nuclear\nenergy generation rate exceeds the neutrino losses. When the central\ntemperature increases owing to carbon ignition, a convective core\ndevelops. The convective energy transport is calculated in the\nframework of the time-dependent mixing length theory (Unno 1968). At\n$T_{\\rm c} \\sim$ 8 \\e8 K convection can no longer transport energy in\nour model and the central region undergoes a thermonuclear runaway\nwith \\rhoc~ = 1.37 \\e9 \\gmc~ (C) or 2.12 \\e9 \\gmc~ (W).\n\n\\subsection {Slow Deflagrations}\n\n\tWe know the absolute lower limit for the deflagration speed\nafter central ignition from the one-dimensional analysis of laminar\nflame fronts (Timmes \\& Woosley 1992), being close to 1\\% of the local\nsound speed $v_s$. On the other hand, any hydrodynamic instability can\nenhance the speed. Our parametrized \"fast\" deflagration studies, which\nreached 10\\%-30\\% of the sound speed and produced the model W7 (Nomoto\n\\etal 1984; Thielemann \\etal 1986), however, resulted in problematic\nFe-group nucleosynthesis (see also discussion below). The flame speed\nfound in multidimensional hydrodynamic simulations is still subject\nto large uncertainties, ranging from $v_{\\rm def}/v_{\\rm s} \\sim$\n0.015 (Niemeyer \\& Hillebrandt 1995a) to $v_{\\rm def}/v_{\\rm s} \\sim$\n0.1 (Niemeyer et al. 1996). Therefore, it is important to investigate\nhow the nucleosynthesis outcome depends on the flame speed. In order\nto contrast our \"fast\" deflagration model W7, we study \"slow\"\ndeflagrations here and choose the following parameter ranges: After\nthe central thermonuclear runaway, we assume that a slow (S)\ndeflagration propagates with speeds $v_{\\rm def}/v_{\\rm s}$ = 0.015\n(WS15, CS15), 0.03 (WS30, CS30), and 0.05 (CS50) and consider also\nextreme cases of fully and initially laminar flame fronts (WLAM, WSL). \nThe location of the deflagration wave in radial mass coordinate \\mr\\\nand the changes in temperature and density are shown in Figure\n\\ref{defr} as a function of time. Behind the deflagration wave, the\ntemperature rises quickly to values as high as $T$ = 9 $\\times$ \\ee9 K\nand the material experiences nuclear statistical equilibrium (NSE).\nAs the flame front propagates outward, the white dwarf expands slowly\nwhich reduces the central density \\rhoc. The decrease in \\rhoc~ for\nthese slow deflagrations is significantly slower than in W7.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 1 Here:\n%% tmr2.epsi and rmr2.epsi %\n%\\vskip 0.5cm\n\n\\placefigure{defr}\n\n\\subsection {Transition from Deflagration to Detonation}\n\n\tIf the deflagration speed continues to be much slower than in\nW7, the white dwarf undergoes a large amplitude pulsation, as first\nfound by Nomoto \\etal (1976). In this {\\sl pulsating deflagration}\nmodel, the white dwarf expands and nuclear burning is quenched when\nthe total energy of the star is still negative. In the following\ncontraction more material burns, resulting in a positive total energy\n$E$. Eventually the white dwarf is completely disrupted. The model\nby Nomoto \\etal (1976) resulted in $E$ = 5 \\e{49} ergs and a \\ni~ mass\nof \\mm{Ni}~ $\\sim$ 0.15 M$_\\odot$. Such a pulsating deflagration\nproduces explosion energies too small to account for typical SNe Ia\nbut might be responsible for rare events such as SN 1991bg.\n\n\tIn order to produce sufficient amounts of radioactive\n$^{56}$Ni ($\\sim$ 0.6 $M_\\odot$) to power SNe Ia light curves by a\ndeflagration wave, the flame speed must be accelerated. The degree to\nwhich the flame speed is increased depends on the effect of R-T\ninstabilities during the pulsation (Woosley 1997a). The deflagration\nmight induce a detonation when reaching the low-density layers. In\nthe {\\sl delayed detonation} model (Khokhlov 1991a; Woosley \\& Weaver\n1994b), the deflagration wave is assumed to be transformed into a\ndetonation at a specific density during the first expansion phase. In\nthe {\\sl pulsating} delayed detonation model (Khokhlov 1991b), the\ntransition into a detonation is assumed to occur close to the maximum\ncompression after recontraction, as a result of mixing.\n\n\tPhysical mechanisms by which such deflagration-to-detonation\ntransitions (DDTs) occur have been studied by Arnett \\& Livne (1994b),\nNiemeyer \\& Woosley (1997), Khokhlov, Oran, \\& Wheeler (1997), and\nNiemeyer \\& Kerstein (1997): (1) When a sufficiently shallow\ntemperature gradient is formed in the fuel, a deflagration propagates\nas a result of successive spontaneous ignitions. Such an over-driven\ndeflagration propagates supersonically. (2) If a sufficiently large\namount of fuel has such a shallow temperature gradient, the\ndeflagration may induce a detonation wave. The critical masses for\nthe formation of a detonation are quite sensitive to the carbon mass\nfraction $X({\\rm C})$, e.g., $\\sim$ \\ee{-19} \\ms~ and $\\sim$ \\ee{-14}\n\\ms~ at $\\rho \\sim$ $3\\times$ \\ee7 \\gmc~ for $X({\\rm C})$=1.0 or 0.5,\nrespectively. (Niemeyer \\& Woosley 1997). (3) Such a shallow\ntemperature gradient region in the fuel may be formed if the fuel is\nefficiently heated by turbulent mixing with ashes. Such a mixing and\nheat exchange may occur when the turbulent velocity associated with\nthe flame destroys the flame (Niemeyer \\& Woosley 1997; Khokhlov et\nal. 1997). Note that whether the DDT occurs by this mechanism is\ncontroversial (Niemeyer 1999), and thus the exact density of the DDT\nis still debated (Niemeyer \\& Kerstein 1997). Therefore,\nnucleosynthesis constraints on the DDT density are important to\nobtain.\n\n\tMotivated by the discussion above we transform the slow\ndeflagrations WS15 and CS15 artificially into detonations when the\ndensity ahead of the flame decreases to 3.0, 2.2, and 1.7 \\e7 \\gmc~\n(DD3, DD2, and DD1, respectively, where 3, 2, and 1 indicate\n$\\rho_7$=$\\rho/10^7$~g~cm$^{-1}$ at the DDT). Then the carbon\ndetonation propagates through the layers with $\\rho < $ \\ee8 \\gmc.\nFigures \\ref{dens} and \\ref{vexp} show the density distribution and\nexpansion velocity after the passage of the slow deflagration and the\nsubsequent delayed detonation. The explosion energy $E$ and the mass\nof synthesized \\ni~ of these WSDD/CSDD models as well as W7 and W70\nare summarized in Table 1. Here W70 is the same hydrodynamical model\nas W7 except for the initial mass fractions of $X(^{22}$Ne) = 0.0,\n$X(^{12}$C) = 0.50, $X(^{16}$O) = 0.50. This corresponds to zero\ninitial metallicity because $^{22}$Ne originates from the initial CNO\nelements.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 2 Here:\n%%%% tt2.epsi and rt2.epsi %%%%\n\n%:To the Editor: Please Place Figure 3 Here:\n%%%% velomass.epsi %%%%\n%\\vskip 0.5cm\n\n\tThe increase of the $^{56}$Ni mass from W7 to W70 is due to\nthe fact that the composition in W70 corresponds to a $Y_e$=0.5 or a\nproton/neutron ratio of 1, i.e., symmetric matter. In mass zones that\nare not affected by electron capture but which undergo complete\nSi burning, $^{56}$Ni is then the dominant nucleus, without competition\nby more neutron-rich species. Detonations in lower density matter do\nnot necessarily lead to complete Si burning. Therefore, the amount of\n$^{56}$Ni is smallest in DD1 models and largest in DD3 models. The\nsmall difference between WS and CS DD-models is again a $Y_e$\neffect. CS models have a smaller central density, which leads in the\ncentral regions to a smaller number of electron captures and larger\n$Y_e$ values, resulting again in more symmetric matter.\n\n\\subsection{Input Physics}\n\n\tThe methods for performing these calculations were the same as\nused in Shigeyama \\etal (1992) and Yamaoka \\etal (1992). We apply an\nimplicit Lagrangian hydrodynamics code (Nomoto \\etal 1984) for the\nslow deflagration and a Lagrangian PPM hydro code, as used in\nShigeyama \\etal (1992), for the detonation phase. Both codes use the\nsame mass grid of 200 radial zones for the white dwarf. The nuclear\nreaction network and the reaction rate library utilized are the same\nas described in Thielemann et al. (1996), i.e., thermonuclear rates\nusing the Hauser-Feshbach formalism (Thielemann, Arnould, \\& Truran\n1987), experimental charged particle rates from Caughlan \\& Fowler\n(1988), neutron induced rates from Bao \\& K\\\"appeler (1987), and\nextensions towards the proton and neutron drip lines from van Wormer\n\\etal (1994) and Rauscher \\etal (1994) with Coulomb enhancement\nfactors from Ichimaru (1993). Electron capture rates were adopted from\nFuller, Fowler, \\& Newman (1980, 1982, 1985). For nuclei beyond\n$A$=60, only ground state decay properties were used. We consulted the\nanalysis of Aufderheide \\etal (1994) so that the influence of a\nnucleus with a significant impact on $Y_e$ (either via decay or\nelectron capture) was neglected in either of the conditions\nexperienced in our calculations. It might, however, require a further\nstudy to test against the sensitivity of these electron capture rates.\nThe present set of Fuller, Fowler \\& Newman (1982) is based on\nestimates for average properties of the Gamow-Teller giant resonance\nrather than on more secure shell model calculations for fp-shell\nnuclei in the Fe-group (Dean et al. 1998).\n\n\tOne of the problems of nucleosynthesis calculations which\nfollow a thermonuclear evolution on long timescales through\nhigh-temperature regimes is the lack of accuracy. This lack of\naccuracy is due to the fact that in such situations, where actually a\nnuclear statistical equilibrium should exist, the cancellation of huge\nopposing rate flows is only attained up to machine accuracy (i.e.,\n$\\approx 10^{-12}-10^{-13}\\times$ the term size). In a similar way the\nterm $1/\\Delta t$, appearing in the diagonal of the Jacobi matrix of\nthe multidimensional Newton-Raphson iteration (Hix \\& Thielemann\n1999b), can become numerically negligible in comparison to reaction\nrate terms in the same sum, which leads to numerically singular\nmatrices. For that reason, we have adopted here the accurate\nsolution, i.e., we followed the nuclear evolution with a screened NSE\nnetwork containing 299 species during periods when temperatures beyond\n$T$=$6\\times 10^9$~K are attained (see Hix \\& Thielemann 1996, 1999a).\nThis takes into account the changes in binding energy or reaction\nQ-values due to screening. Weak reaction rates (electron captures and\nbeta-decays), which are not in an equilibrium and occur on longer\ntimescales, were included by using the NSE abundances. In this way we\ncould track accurately the evolution of the electron fraction $Y_e$.\n\n\\section {Explosive Nucleosynthesis}\n\n\\subsection {Slow Deflagration}\n\n\tIn the present study we follow the approach discussed above by\nvarying the ignition density and the initial deflagration velocity and\ntest specifically the effect on the Fe-group composition in the\ncentral part. Figure \\ref{rhoT} shows the maximum densities and\ntemperatures for the inner mass zones experiencing complete and\nincomplete Si burning in the models WS15, WS30, CS15, and W7 as a\ncomparison. It can be recognized that WS15 and WS30 experience\ndensities similar to that of W7, which is due to the common ignition\ndensities of initial model W, with WS15 attaining the highest\ntemperatures. CS15, based on initial model C, is shifted to smaller\ndensities.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 4 Here:\n%%%% fig4.epsi %%%%\n%\\vskip 0.5cm\n\n\tDuring the burning the central region undergoes electron\ncaptures on free protons and iron peak nuclei. The central densities,\nsimilar to W7 for both WS models but combined with higher\ntemperatures, result in more energetic Fermi distributions of\nelectrons and larger abundances of free protons. This leads to larger\namounts of electron captures on free protons and nuclei and smaller\ncentral $Y_e$ values. Figure \\ref{yemr} shows the final $Y_e$ during\ncharged-particle freeze-out and before long-term decay of unstable\nburning products. Table 2 lists this value of $Y_{\\rm e}$ in the\ncenter, $Y_{\\rm e,c}$, together with nucleosynthesis information,\nwhich will be discussed later. In summary, $Y_{\\rm e,c}$ is lower for\nhigher central densities and slower deflagrations, the latter leading\nalso to higher central temperatures. Figure \\ref{yemr} and Table 2\nalso list two models WSL and WLAM that experience (partially or\nentirely) deflagration velocities as small as the laminar speed, which\napparently do not follow this logic anymore. All models are discussed\nin detail in the following paragraphs.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 5 Here:\n%%%% yeall.epsi %%%%\n%\\vskip 0.5cm\n\n\tWS15, corresponding to a slow deflagration with a\nburning-front propagation of 1.5\\% of the sound speed, reaches higher\ncentral temperatures than WS30. The case WS30, corresponding to a\nburning-front propagation of 3\\% of the sound speed, has similar\ndensities, but slightly lower temperatures for each radial mass zone\nin comparison to WS15 (also for a shorter duration). Besides the\ndifferent central value, both models also have a different central\n$Y_e$ gradient (see Fig. \\ref{yemr}). The WS15 curve, with lower\ncentral values, reaches $Y_e$=0.4985 (inherited from the progenitor\nwhite dwarf after He burning) at smaller radii than WS30. A smaller\ndeflagration speed causes a later arrival of the burning front at a\ngiven mass coordinate. Thus, matter at this mass coordinate has a\nlonger time to preexpand between the arrival of the central\ninformation with sound speed and the arrival of the burning\nfront. Therefore, burning occurs there at a lower density (and\ntemperature) with smaller average electron energies, causing less\nelectron capture. This means that a smaller propagation speed produces\na smaller central $Y_e$, but reaches $Y_e$ = 0.4985 also at smaller\nradii, i.e., produces a steeper $Y_e$ gradient. W7, with a different\ndescription of the burning-front velocity, but on average a larger\nspeed, led to a higher central $Y_e$ and a flatter $Y_e$ gradient.\n\n\tCS15 and CS30, which also corresponds to a burning front\npropagation with 1.5\\% or 3\\% of sound speed, behave in a fashion very\nsimilar to WS15 and WS30 but are characterized by a smaller central\nignition density. Because of a smaller ignition density the central\n$Y_e$ values are larger. Otherwise the $Y_e$-gradients are the same\nfor CS15 and WS15 as well as CS30 and WS30, each pair having the same\nburning-front speed. CS50, a case with 5\\% of sound speed, has a more\nextended region of decreased $Y_e$ out to larger masses (coming close\nto the behavior of W7), but because of the lower ignition density and\nlower central temperatures the central $Y_{\\rm e,c}$ is larger again.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 6 Here:\n%%%% yetime.epsi %%%%\n\n%:To the Editor: Please Place Figure 7 Here:\n%%%% trholam.epsi %%%%\n%\\vskip 0.5cm\n\n\tWSL is an additional case and corresponds to a calculation\nwith an initially laminar flame speed (out to 0.05~M${_\\odot}$, see\nFig. \\ref{yemr}), before an artificial acceleration is induced via\nturbulent mixing of ashes. WSLAM starts in exactly the same manner;\nhowever, the front stays laminar, i.e., only the minimum flame speed\nis permitted. According to the previous discussion one would expect an\neven steeper $Y_e$-gradient, and thus a lower central $Y_e$, owing to\nhigher temperatures during a longer duration time. The steeper\ngradient can be seen outside 0.06 \\ms~for WSL, where the front starts\nto accelerate beyond the laminar speed. Inside the range of 0.06 \\ms\nthe $Y_e$ is almost constant and larger than e.g., in WS15, which\nexperienced the same ignition density and larger flame speeds. There\nare two reasons for this behavior in the very central zones:\n\n1. Initially during the burning, the lowest central $Y_e$-values of\n$\\sim$~0.432 are obtained as expected, but this value is -- in\ncontrast to all other cases encountered previously -- smaller (more\nneutron-rich) than the Fe-group nuclei in the valley of stability (see\nthe most neutron-rich entries in Table 2, i.e., $^{50}$Ti, $^{54}$Cr,\n$^{58}$Fe, and $^{64}$Ni with $Z/A$ values of 0.44, 0.444, 0.448, and\n0.438). This leads to counterbalancing $\\beta^-$-decays which win\nagainst electron captures as densities and temperatures (slowly)\ndecrease while matter is still in an NSE. This causes an increase in\n$Y_e$ to the displayed values before charged-particle freeze-out (see\nFig. \\ref{yetim}).\n\n2. During the laminar front propagation, the large amount of central\nelectron captures leads to neutrino losses which reduce the local\nenergy release to a point where the expansion is very small (see the\ntime dependence of $\\rho$ and $T$ in Fig. \\ref{rttim}). This keeps\ntemperatures and densities high for a prolonged period, and matter\nstays in an NSE (the differences between WSL and WLAM emerge when the\nburning front is accelerated in WSL beyond the laminar speed). This\nNSE distribution of nuclei - with a total $Y_e$ more neutron-rich than\nstable Fe-group nuclei - permits $\\beta^-$-decay of short-lived nuclei\ntoward a total $Y_e$ corresponding to neutron-rich, stable Fe-group\nmuclei (beyond 0.44) as long as temperatures are high enough to ensure\nan NSE. This results in the surprising fact that a burning front that\nstays laminar (WLAM) causes a higher $Y_e$ after charged-particle\nfreeze-out than WSL (see changes in Fig. \\ref{yetim} after 20~s).\nThus, a very small $Y_e$, which produces e.g., large amounts of\n$^{48}$Ca ($Z/A$=0.417), can only be attained in models with a higher\nignition density, causing large amounts of electron capture, but with\nnonlaminar burning fronts that permit a fast expansion rather than\nkeeping matter in NSE for a long time.\n\n\tWith the exception of the laminar burning-front models just\ndiscussed, which show a different behavior in Figure \\ref{yemr}, we\ncan summarize the major options for slow deflagrations to change $Y_e$\nvalues in the central part of SNe Ia explosions: (1) the burning-front\nspeed determines the $Y_e$ gradient, and the slowest speeds lead to\nthe smallest central values; (2) lower central ignition densities\ncause larger $Y_e$ values, with the gradient, however, depending only\non the propagation speed. These features hold true as long as $Y_e$\nvalues in explosive burning do not drop below 0.44, when competing\n$\\beta^-$-decays have also to be taken into account. While the\ncorrect conditions occurring in SNe Ia might be still forthcoming from\ndetailed multidimensional hydrodynamic calculations, this parameter\nstudy shows how nucleosynthesis results can give important clues to\n$v_{\\rm def}$ and $\\rho_{\\rm c,ign}$.\n\nFigures \\ref{xi15c}ab, \\ref{xi30c}ab, \\ref{xiw7c}ab, and\n\\ref{xiwslc}ab show abundance plots (mostly of Fe-group nuclei) for\nthe central parts of CS15, WS15, CS30, WS30, CS50, W7, WSL, and WLAM\nwhere electron capture plays an important role. We see that $Y_e$\nvalues of 0.47-0.485 lead to dominant abundances of $^{54}$Fe and\n$^{58}$Ni; values between 0.46 and 0.47 produce dominantly $^{56}$Fe;\nvalues in the range of 0.45 and below are responsible for $^{58}$Fe,\n$^{54}$Cr, $^{50}$Ti, and $^{62,64}$Ni; and values below 0.43-0.42 are\nresponsible for $^{48}$Ca. Figure \\ref{yemr} clearly indicates that\nbecause of the flat $Y_e$-gradient of W7, the total amount of matter\nexperiencing the range of $Y_e$=0.47-0.485 is much larger than in\ncases with slower deflagration speeds and larger $Y_e$-gradients. WS15\nand CS15 have similar total amounts of $^{54}$Fe and $^{58}$Ni, but at\nslightly different locations (see the $Y_e$-range in Fig. \\ref{yemr}\nand the different mass scales in Figs. \\ref{xi15c}a and \\ref{xi15c}b).\nWS30 and CS30 contain a larger amount of $^{54}$Fe and $^{58}$Ni,\nowing to the flatter $Y_e$-gradient. CS50 comes close to the original\nW7 model.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 8 Here:\n%%%% xics15_central.epsi and xiws15_central.epsi %%%%\n\n%:To the Editor: Please Place Figure 9 Here:\n%%%% xics30_central.epsi and xiws30_central.epsi %%%%\n\n%:To the Editor: Please Place Figure 10 Here:\n%%%% xics50_central.epsi and xiw7_central.epsi %%%%\n\n%:To the Editor: Please Place Figure 11 Here:\n%%%% xiwsl_central.epsi and xiwlam_central.epsi %%%%\n%\\vskip 0.5cm\n\n\\subsection{Fe-Group Composition in Slow Deflagrations}\n\n\tOne of the motivations for the present exercise is to get\nconstraints from comparison with solar Fe-group abundances. This can\nprovide a better understanding of the burning-front propagation and\ntest how the otherwise quite compelling features of the widely used\nmodel W7 can be improved. Figure \\ref{w7sol} shows the ratio of\nabundances produced in W7 to solar abundances. These are the results\nof recalculations of the original W7 with the present reaction rate\nlibrary and an increased accuracy in mass conservation in comparison\nto earlier studies due to the screened NSE treatment at high\ntemperatures discussed in \\S2.4. Displayed are abundance ratios after\nthe decay of unstable nuclei, normalized to unity for $^{56}$Fe. If\nSN Ia events are a relatively homogeneous class, the comparison of\nnucleosynthesis products with solar abundances is actually meaningful\nwithout averaging over a complete sample.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 12 Here:\n%%%% ysolw7.epsi %%%%\n%\\vskip 0.5cm\n\n\tIt is immediately obvious from Figure \\ref{w7sol} that the\nproduction of Fe-group nuclei in comparison to their solar values is a\nfactor of 2-3 larger than the production of intermediate nuclei from\nSi to Ca. When considering that SNe Ia produce about 0.8M$_\\odot$ of\nFe-group nuclei in comparison to $\\approx$0.1M$_\\odot$ from SNe II,\nand that the Ia/(II+Ibc) ratio is about 0.15-0.27 in our galaxy (van\nden Bergh \\& Tammann 1991; Cappelaro et al. 1997), SNe Ia are\nresponsible for more than 55\\% of Fe-group nuclei. Thus, even if an\nisotope has no contribution from SNe II, this implies that the\nisotopic ratios among the Fe-group in the SNe Ia ejecta should not\nexceed the solar ratios by a factor of \\(\\sim 2\\), in order to result\nin solar ratios for SNe II + SNe Ia. If we assume on the other hand\nthat an (Fe-group) isotope is made by SNe II in solar proportions,\nthen it has also to be made in solar proportions in SNe Ia to obtain\nthe solar mix for the sum of both contributions. An overproduction by\nSNe II would even ask for an underproduction in SNe Ia. If we are\nconservative and neglect the latter case, an overproduction of a\nfactor 1-2 in SNe Ia would be permitted. Multiplying this with an\naverage uncertainty factor of 2 would permit overproductions of 2-4,\ndependent on the fact whether an SNe II contribution is existing or\nnot. In general we do not know this at present, and we take an\noverproduction factor in SNe Ia of \\(\\sim 3\\) as an alarm sign for\nnucleosynthesis constraints. In this respect, we notice in Figure 12\nthe overproduction of $^{54}$Cr and $^{58}$Ni by a factor of \\(\\sim\n4-5\\). Here $^{54}$Cr is an $N=Z+6$ nucleus originating from the very\ncentral regions with low $Y_e$, while $^{58}$Ni (and $^{54}$Fe) are\nnuclei with $N=Z+2$ measuring the bulk neutron excess of the material\naffected by the deflagration wave in the intermediate $Y_e$ range\n$\\sim 0.48$ (see also Table 2). Outside of 0.3M$_\\odot$ in the\nexploding white dwarf, where electron capture is not effective, the\nneutron excess is only determined by the $^{22}$Ne ($N=Z+2$) admixture\nto $^{12}$C and $^{16}$O in the original composition, stemming from\n$^{14}$N in He burning, which in turn originated from all CNO-nuclei\nin H burning. The $Y_e$ or neutron-excess $\\eta$ outside 0.3M$_\\odot$\nis thus a measure of the metal abundance (nuclei heavier than He) and\nthe galactic age of the white dwarf. The quoted calculations were\nperformed with $X(^{22}{\\rm Ne}) = 0.025$, which corresponds to $\\eta$\nof \\(\\sim\\) 30 \\% higher than the solar metallicity, thus\noverestimating the average value for \"old\" white dwarfs undergoing a\nSN Ia event.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 13 Here:\n%%%% ysolw70.epsi %%%%\n%\\vskip 0.5cm\n\n\tUsing an averaged metallicity of SN Ia progenitor systems less\nthan solar would reduce the overproduction of these nuclei. This is\nshown in Figures \\ref{w70sol} for a deflagration model like W7 but\nwith zero metallicity (W70). Figures \\ref{w7full}a and 14b give the\ncomparison of the abundance distributions. Bravo et al. (1992) have\nperformed a similar test. As the total SNe Ia contribution in our\ngalaxy is given by an integral over time or metallicity up to the\nformation of the solar system, one expects average metallicities of\n0.5-0.6 times solar. This brings the $^{54}$Fe/$^{56}$Fe,\n$^{57}$Fe/$^{56}$Fe, $^{58}$Ni/$^{56}$Fe, and $^{62}$Ni/$^{56}$Fe\nratios within a factor of 2-3 of solar, respectively, which\ncorresponds to the present uncertainty range of thermonuclear reaction\nrates and the minimum $\\approx$50\\% contribution of SNe Ia to the Fe\ngroup. It does not reduce the $^{54}$Cr abundance sufficiently, which\noriginates solely from the central layers, where $Y_e$ is the smallest\nand entirely due to electron captures rather than the metallicity in\nterms of $^{22}$Ne. An interesting aspect of the change in\nmetallicity, leading to reductions of $^{54}$Fe and $^{58}$Ni, is the\nvarying amount of early Fe ($^{54}$Fe before $^{56}$Ni decay) and late\nNi ($^{58}$Ni after $^{56}$Ni decay) in SN Ia ejecta, leading to\nfeatures that can be analyzed in observed spectra (see H\\\"oflich et\nal. 1998). This analysis covers one uncertainty regarding the\ninitial composition. Another one would be a variation of the initial\n$^{12}$C/$^{16}$O ratio, depending strongly on the initial white dwarf\nmass and metallicity. This has also been addressed recently by Umeda\net al. (1999) and H\\\"oflich et al.~(1999). Thus, while the metallicity\nand initial composition are one set of parameters, the ignition\ndensity and burning-front velocity represent another set, as outlined\nin \\S 2. A burning front with a smaller velocity could reduce the\namount of material in the $Y_e$ range 0.47-0.485, where $^{54}$Fe,\n$^{58}$Ni, and $^{62}$Ni are produced in large amounts (see e.g.,\nTable 2).\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 14 Here:\n%%%% xiw7_full.epsi and xiw70_full.epsi %%%%\n%\\vskip 0.5cm\n\n\tIn Figures \\ref{s15solw7}a and 15b, \\ref{s30solw7}a and 16b,\n\\ref{s50solw7}, and \\ref{slsolw7}a and 18b the ratios to solar\nabundances (normalized to $^{56}$Fe) are displayed. Here the results\nof the central slow deflagration studies have been merged with (fast\ndeflagration) W7 compositions for the outer layers, where $Y_e$ is\ngiven by the initial $^{22}$Ne and not by electron captures. Thus,\nthese are not yet full delayed detonation models (which will be\ndiscussed in the next subsection), but more preliminary approximations\nto test the central Fe-group results. In comparison to Figure\n\\ref{w7sol} we see that in all cases the $^{58}$Ni problem is strongly\nreduced and would be fully resolved when using also smaller\nmetallicities (see W7 vs. W70). This is due to the steeper $Y_e$\ngradient which produces less matter in the intermediate $Y_e$ range\n0.47-0.485. The smaller propagation speed has, however, also the\nconsequence that $Y_e$ dips deeper in the central layers of WS15 and\nWS30 than in W7. Such $Y_e$'s lead to the overproduction of $^{50}$Ti\nand $^{54}$Cr. This is not the case for CS15 and CS30, due to the\nlower ignition density.\n\n\tAnother interesting point surfaces, which was also addressed\npreliminarily in Thielemann et al. (1996) and also Meyer, Krishnan, \\&\nClayton (1996) and Woosley (1997b). If one takes the results of\npresently existing and still crude SNe II nucleosynthesis calculations\nfrom initiated explosions as well as the results of W7, it turns out\nthat for some intermediate mass and all Fe-group elements the most\nneutron-rich nuclei are drastically underproduced. The central $Y_e$\nvalues of slow deflagration models comes close to conditions, where\nthese nuclei are produced in a normal freeze-out. This has the effect\nthat nuclei like $^{50}$Ti, $^{54}$Cr, $^{58}$Fe and partially\n$^{64}$Ni or $^{48}$Ca are produced for $Y_e$ values below 0.46 (or\n$\\eta=1-2Y_e=0.1$). Whether this leads after integration over all mass\nzones just to solar abundances or to a strong overproduction will be\ntested here (see also Table 2). Khokhlov et al. (1992) undertook\nalready a preliminary assessment of this question but did not consider\nall of these nuclei in their calculations. Woosley (1997b) tested\nmodels with higher ignition densities and burning-front velocities,\nwhether such elements can be produced. Here we take again the\nphilosophy to obtain constraints for the \"average\" case of SNe Ia, to\ntest on the one hand whether they can produce such isotopes at all,\nand if so, whether constraints can be set for the conditions in order\nto avoid overproductions beyond the often mentioned factor of 3.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 15 Here:\n%%%% ysolcs15w7.epsi and ysolws15w7.epsi %%%%\n\n%:To the Editor: Please Place Figure 16 Here:\n%%%% ysolcs30w7.epsi and ysolws30w7.epsi %%%%\n\n%:To the Editor: Please Place Figure 17 Here:\n%%%% ysolcs50w7.epsi %%%%\n\n%:To the Editor: Please Place Figure 18 Here:\n%%%% ysolwslw7.epsi and ysolwlamw7.epsi %%%%\n%\\vskip 0.5cm\n\n\tIt is a well-known fact that SNe Ia are not identical (see\ne.g., Hamuy et al. 1995) and that therefore a continuous superposition\nof such models has to be responsible for the solar Fe-group\ncomposition. On the other hand, we also know that the majority of SNe\nIa come from a narrow window of conditions (Branch 1998), i.e., the\nnotion of an average SN Ia event makes sense. If Fe-group elements\nare produced by SNe Ia to $\\sim$ 55 \\% and Ia's were the only sources\nof the neutron-rich Fe-group nuclei, we must conclude that an\noverproduction of a factor of 3 is permitted and that a larger\noverproduction has to be avoided for the average event. We see that\nfor the cases discussed before (CS15, WS15, CS30, WS30) $^{54}$Fe and\n$^{58}$Ni can be produced within the permitted uncertainty limits\n($^{58}$Ni however having a tendency for overpoduction). These are the\nnuclei with intermediate $Y_e$ (0.47-0.485), which measure the $Y_e$\ngradient via the amount of mass contained in that interval. CS50,\nwhich has a larger burning-front speed and a flatter slope, starts to\noverproduce these nuclei.\n\n\tThe more neutron-rich Fe-group nuclei depend more on the\ncentral layers, which experience lower $Y_e$-values. $^{54}$Cr is\nproduced within permitted limits in CS15 and CS30 but is overproduced\nin WS15 and WS30 owing to the higher ignition densities and central\n$Y_e$ values that are too low. $^{50}$Ti is produced close to solar\nvalues for CS15, underproduced by CS30, well produced for WS30, and\nclearly overproduced in WS15, preferring the central $Y_e$ values of\nCS15 and WS30, which are similar. $^{64}$Ni is essentially only made\nin large quantities for such low-$Y_e$ conditions as in WS15. Close to\nsolar values cannot be attained for $^{48}$Ca in any of these models,\nand its production would require lower $Y_e$ values. An attempt to do\nthis was a purely laminar, i.e., the slowest possible, burning\nfront. The display in Figure \\ref{slsolw7}a and 18b makes clear that\nthis is not possible, as discussed in \\S3.1. The main reason is that\nsuch conditions produce nuclei which are unstable against\n$\\beta^-$-decay. In intermediate phases sufficiently low $Y_e$ values\nare attained as a result of electron captures. NSE or\nQuasi-statistical equilibrium (QSE) redistributes abundances according\nto the then obtained smaller $Y_e$ values. $\\beta^-$-decay of the\nshort-lived neutron-rich isotopes leads to an increase in $Y_e$ during\nthe expansion, when the densities and temperatures (and therefore the\nelectron capture rates) decrease, before freeze-out from charged\nparticle reactions and NSE/QSE (see Fig. \\ref{yetim}). Thus, to\nproduce a nucleus like $^{48}$Ca in sufficient amounts, only very\nhigh-density ignitions (followed by a fast expansion to avoid the\ninfluence of $\\beta^-$-decays) of progenitor systems, which barely\navoid an accretion induced collapse (AIC), might be responsible (see,\ne.g., Nomoto \\& Kondo 1991; Woosley 1997b).\n\n\tFrom this exercise we see that not all of these neutron-rich\nnuclei can be made in similar proportions for one set of deflagration\nparameters unless a detailed fine-tuning of $v_{\\rm def}(r)$ and\n$Y_e(r)$ is performed or multidimensional propagation of the burning\nfront produces exactly a superposition of conditions as needed to fit\nall abundance constraints. In general CS15 and CS30 seem to be better\nmodels than WS15 and WS30 in terms of avoiding a large overproduction\nof neutron-rich elements. The burning-front speed in the central\nlayers seems to be constrained to values below 5\\% of the sound speed\nin order to avoid the overproduction of $^{58}$Ni (see CS50 and Figure\n\\ref{s50solw7} as well as Table 2 with comparable problems found for\nW7 and W70). If on the other hand there were no other sites than SNe\nIa to produce isotopes like $^{50}$Ti, $^{54}$Cr, $^{58}$Fe, $^{64}$Ni\nor $^{48}$Ca, we would have to overproduce in comparison to solar by\nabout a factor of 2, and some features of the models WS15, WS30 and\neven higher density events were needed, which can fill in the\nremaining deficiencies. Thus, one would need the majority of events\nsimilar to CS15 or CS30 and a smaller number of higher density\nignitions to produce the more neutron-rich nuclei. This could\nguarantee on the one hand some overproduction, which (in combination\nwith SNe II) would permit solar abundances in total, and avoid on the\nother hand not-permitted overproduction.\n\n\\subsection {Delayed Detonation}\n\n\tThe final aim, after constraining the central slow\ndeflagration part of SNe Ia, is to find also composition constraints\nfor the deflagration detonation transition (DDT). As discussed in \\S\n2.3, we chose transition densities of 3.0, 2.2, and 1.7$\\times\n10^7$~g~cm$^{-3}$ for the given models WS15 and CS15, which turn them\ninto WS15DD3, WS15DD2, WS15DD1 or CS15DD2 and CS15DD1. Figures\n\\ref{wdd12} - \\ref{cdd12} show the abundance distributions of slow\ndeflagrations combined with delayed detonation models against the\nexpansion velocity and $M_r$ of DD models. The central regions of\nthese models have been shown before in Figures \\ref{xi15c} and\n\\ref{xi30c}, thus the abundance distributions of neutron-rich species\nsuch as $^{54}$Cr, $^{50}$Ti, $^{58}$Fe, and $^{62}$Ni are not\nrepeated here.\n\n\tAs the deflagration wave propagates outward, the white dwarf\ngradually expands to undergo less electron capture and thus mostly\n\\ni~ is synthesized. Eventually, the deflagration enters the region\nof incomplete Si burning and explosive O-Ne-C-burning, where the\ntransition to a detonation occurs. For comparison the abundance\ndistributions of W7 and W70 were shown in Fugure \\ref{w7full}. The\ntotal masses of $^{56}$Ni($^{56}$Fe) produced in these combined models\nhave been summarized in Table 1.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 19 Here:\n%%%% xiws15dd1_full.epsi and xiws15dd2_full.epsi %%%%\n\n%:To the Editor: Please Place Figure 20 Here:\n%%%% xiws15dd3_full.epsi %%%%\n\n%:To the Editor: Please Place Figure 21 Here:\n%%%% xics15dd1_full.epsi and xics15dd2_full.epsi %%%%\n%\\vskip 0.5cm\n\n\tThese theoretical abundance distributions can be compared with\nthe observed expansion velocities of several elements as estimated\nfrom supernova spectra. It is seen that WDD2 and WDD1 produce two\nSi-S-Ar peaks at low velocity ($\\sim$ 4,000 \\kms) and high velocities\n(10,000 - 15,000 km s$^{-1}$). The intermediate mass elements at low\nvelocities are important to observe at late times in order to\ndistinguish between models. In particular, the minimum velocity of Ca\nin WDD models is $\\sim$ 4,000 \\kms, which would be higher for a faster\ndeflagration.\n\n\tThe Ca velocities should be compared with the observed minimum\nvelocities of Ca indicated by the red edge of the Ca II H and K\nabsorption blend (Fisher \\etal 1995). The lowest velocities of O and\nMg also provide interesting constraints. For example, SNe 1990N,\n1992A, and 1991T show O in the wide velocity range from $\\approx$\n10,000 to 20,000 \\kms\\ (Leibundgut \\etal 1991a; Jeffery \\etal 1992;\nMazzali \\etal 1993; Kirshner \\etal 1993). For W7 and WDDs, the\nminimum O velocity is 12,000 - 15,000 \\kms. The observed O velocity\nas low as 10,000 \\kms~ may indicate a mixing of O in the velocity\nspace.\n\n\tMeikle \\etal (1996) have observed a P Cyg-like feature at\n$\\sim$ 1.05/1.08 $\\mu$m in SN 1994D and 1991T. They note that, if\nthis feature is due to He, He in SN 1994D is likely to be formed in an\nalpha-rich freeze-out and mixed out to the high-velocity layers\n($\\sim$ 12,000 \\kms). The maximum velocity of He is 5,000 - 6,000\n\\kms~ in WDDs, being slower than $\\sim$ 9,000 \\kms~ in W7, so that\nmore extensive mixing of He would be required for WDDs than in W7.\n(Note that $^4$He is plotted neither in Fig. \\ref{w7full} nor in Figs. \n\\ref{wdd12} - \\ref{cdd12}, but its location can be easily identified\nwith the region where the $^{58}$Ni abundance forms a plateau up to\nthe point where it turns over to $^{54}$Fe on the same level. This is\nthe transition from alpha-rich freeze-out to incomplete Si burning.)\nAlternatively, if the feature is due to Mg, the Mg velocity is\nconfined to 12,500 - 16,000 \\kms~ in SN 1994D, which is consistent\nwith W7 (13,000 - 15,000 \\kms). For WDDs, on the other hand, the\nminimum velocities of Mg are 14,500 \\kms~ (WDD1), 16,500 \\kms~ (WDD2),\nand 18,000 \\kms~ (WDD3), and the latter two models seem to have too\nhigh velocities.\n\n\tMixing of ejected material in velocity space could occur\nconvectively during the propagation of the deflagration wave (Livne\n1993). Nonspherical explosions induced by delayed detonations could\nalso produce nonspherical abundance distribution, i.e., elemental\nmixing in the velocity space. From the calculated synthetic spectra\nand their comparison with the observations, more advanced methods\n(Harkness 1991) do not favor mixing opposite to initial suggestion by\nBranch \\etal (1985).\n\n\\section {Yields of SNe Ia and Galactic Chemical Evolution}\n\n\\subsection{Features of SN Ia Nucleosynthesis}\n\n\tComplete isotopic compositions of WDD and CDD models are given\nin Table 3. Table 3 assumes full decay of all unstable species. We\nprovide separately in Table 4 abundances of long-lived radioactive\nnuclei, of importance either for gamma-ray detection, extinct\nradioactivities, or chemical evolution. The abundances are compared\nwith solar abundances in Figures \\ref{csdsol} - \\ref{wsd3sol}, which\nare normalized to $^{56}$Fe. These Figures complement the earlier\nFigures \\ref{s15solw7} - \\ref{slsolw7}, where the fast deflagration W7\nwas utilized in the outer layers rather than delayed detonation\nmodels. The major conclusions on the Fe-group composition remain the\nsame as discussed before, in \\S 3.1, owing to the fact that they are\ngiven by the central slow deflagrations. What can be studied here is\nthe additional variation in the ratio of Fe-group to intermediate mass\nnuclei, which depends on the deflagration-detonation transition. Of\ncourse the variation in $^{56}$Fe (originating from $^{56}$Ni) in the\nouter detonation layers also influences the ratio of neutron-rich\nFe-group isotopes (from central locations) to $^{56}$Fe. Table 3\nincludes besides all DD-models (CDD1 short for CS15DD1 etc.) also W7\nand W70 updated with the latest reaction rate set and improved\naccuracy by using a screened NSE treatment for long duration times at\ntemperatures beyond $6\\times 10^9$~K (Hix \\& Thielemann 1996). The\nratios to solar abundances for W7 and W70 were shown in Figures\n\\ref{w7sol} and \\ref{w70sol}. The essential features due to the DDT,\nas displayed in Figures \\ref{csdsol} - \\ref{wsd3sol} and in Table 3\ncan be summarized as follows:\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 22 Here:\n%%%% ysolcs15dd1.epsi and ysolcs15dd2.epsi %%%%\n\n%:To the Editor: Please Place Figure 23 Here:\n%%%% ysolws15ss1.epsi and ysolws15dd2.epsi %%%%\n\n%:To the Editor: Please Place Figure 24 Here:\n%%%% ysolws15dd3.epsi %%%%\n%\\vskip 0.5cm\n\n1. The synthesized amount of Fe and thus the ratio between the\nintermediate mass elements and Fe, Si-Ca/Fe, is sensitive to the\ntransition density from deflagration to detonation, as was already\nshown in Table 1. Among the WDD models, WS15DD2 produces only about\n25\\% more \\ni~ than W7 ($\\sim$ 0.6 \\ms) but more Si-Ca than W7 by 40\\%\n(Fig. \\ref{wsdsol}b), since more oxygen is burned in the outer layers.\nTherefore, the Si-Ca/Fe ratios are moved up to a certain extent.\nWS15DD1 has even larger Si-Ca/Fe ratios, which are close to solar\nratios (Fig. \\ref{wsdsol}a). This is not indicated for SNe Ia, owing\nto observations of low-metallicity stars reflecting the average SN II\nbehavior (a reasoning outlined below in more detail). However, direct\nobservations of the Si-Ca/Fe ratio in SNe Ia remnants (Tycho, SN 1006,\netc.) are highly important and needed in order to distinguish between\nthe models (Hughes et al. 1995; Miyata et al. 1998; Hwang, Hughes \\&\nPetre 1998).\n\n2. Neutron-rich species such as $^{54}$Cr and $^{50}$Ti are mostly\nproduced in the slow deflagration phase. The degree of their\noverproduction with respect to $^{56}$Fe depends also on the mass of\n$^{56}$Ni produced in the outer detonation layers, as seen in Figure\n\\ref{wsd3sol}. This also explains why in Table 2 the entries for the\nsame central models (WS15, CS15 etc.) change for neutron-rich species,\nalthough the central part from which these neutron-rich species\noriginate is unaffected by the detonation. The reason is that the\nratios in comparison to $^{56}$Fe are taken.\n\n3. There are some Fe-group contributions from alpha-rich freeze-out\nand incomplete Si-burning layers that depend on the DDT. Figures\n\\ref{wdd12} - \\ref{cdd12} show that the mass region experiencing\nincomplete Si burning (indicated by the $^{54}$Fe plataeu) decreases\nin the sequence DD1-DD3. The region indicated by the $^{58}$Ni plateau\nexperiences alpha-rich freeze-out (the He abundance is not shown here)\nand increases in the sequence DD1-DD3. $^{52}$Fe (decaying to the\ndominant Cr isotope $^{52}$Cr) and $^{55}$Co (decaying to the only\nstable Mn isotope $^{55}$Mn) are typical features of incomplete Si\nburning. $^{59}$Cu (decaying to the only stable Co isotope $^{59}$Co)\nis a typical feature of an alpha-rich freeze-out. For these reasons\nwe see the strongest $^{52}$Cr and $^{55}$Mn overabundances in DD1 and\nthe strongest appearance of $^{59}$Co (while still underabundant) in\nDD3.\n\n\\subsection{The Role of SN Ia and SN II Contributions}\n\n\tThe chemical evolution of galaxies is dominated by its main\ncontributors SNe II, SNe Ia, and planetary nebulae. The latter do not\ncontribute to the element abundances in the range O through Ni\n(although a few specific minor isotopes can be produced in the\ns-process). Thus for the aspects considered here, we have to explain\ngalactic evolution and also solar abundances by the combined action of\nSNe II and Ia. The ratio of Fe-group elements to Si-Ca in SNe Ia is of\nspecific importance, in order to see how the overabundance of O-Ca/Fe\n(in comparison to solar) in SNe II can be compensated. Combined\nnucleosynthesis products of SNe Ia and SNe II with varying ratios can\nbe compared to solar abundances. An important aspect for such an\nundertaking is, however, to test the individual components against\nexisting observations first, before trying to attain a good solar mix\n(with possibly wrong predictions for the individual SN I and SN II\ncomponents).\n\n\tAlthough we do not have a good quantitative measure from SN Ia\nobservations for the Fe-group to Si-Ca ratio, the fast deflagration\nmodel W7 seems to give a good overall agreement via synthetic spectra\ncalculations with observed Ia spectra (see Branch 1998 for a\nreview). W7 has specific deficiencies in the global isotopic Fe-group\ncomposition from the inner layers, as discussed before, e.g., with\nrespect to $^{58}$Ni and $^{54}$Cr, but this does not affect the\nelement ratios too strongly.\n\n\tA similar or even worse situation is found for the\nquantitative analysis of SN II spectra. However, an independent tool\nexists that measures the integrated SN II yields: observed surface\nabundances of low-metallicity stars, which witness the abundances of\nthe interstellar medium at their point of formation during early\ngalactic evolution, when only SNe II contributed. For metallicities in\nthe range $-2<$[Fe/H]$<-1$ we expect the integrated (mass averaged)\nproperties of SNe II (see e.g., Nakamura et al. 1999). Here [x/y] is\ndefined as log$_{10}$[(x/y)/(x/y)$_\\odot$]. Such abundance features\nwere reproduced with nucleosynthesis products of SNe II as a function\nof stellar mass, taken from the calculations by Nomoto \\& Hashimoto\n(1988), Hashimoto \\etal (1996), and Thielemann \\etal (1996) as\nsummarized in Hashimoto (1995), Tsujimoto \\etal (1995), and Nomoto et\nal. (1997a). SNe II yields, integrated from $m_l$ = 10 \\ms~ to $m_u$ =\n50 \\ms~ with a Salpeter IMF, are also given in Table 3. The upper\nmass bound $m_u$ is chosen to reproduce [O/Fe] = +0.4, which is\nconsistent with the observations of low metallicity stars for [Fe/H]\n$<$ -- 1. Such observations in low-metallicity stars give also the\nbest constraints on average Fe-group abundances of SNe II, which are\npoorly known theoretically owing to the still existing lack of\nself-consistent core collapse supernova models. The representation of\nthe Fe-group (beyond Ti) closest to the low metallicity observations\nseems to be the one of our 20\\ms~star (see Figure 5b in Thielemann\n\\etal 1996 and note that the observed Co abundance has come down to\nabout -0.1, i.e., it shows a better agreement with the dashed line).\n\n\tA possible deviation from solar ratios has to be made up by an\nopposite behavior of SNe Ia setting in at about [Fe/H]=$-$1 in order\nto attain solar values at [Fe/H]=0. Fe-group elements for which\ninformation is available are Ti, Sc, Cr, Mn, Co, Ni (Magain 1987,\n1989; Gratton \\& Sneden 1988, 1991; Gratton 1989; Zhao \\& Magain 1990;\nNissen et al. 1994). They lead to typical uncertainties of 0.1 dex and\none finds average SN II values of 0.25, 0, -0.1, -0.3, -0.1, -0.1.\nTaken the typical uncertainty of 0.1 dex, this leaves Ti and Mn as\nelements with clear signatures for a SN II behavior different from\nsolar, which asks for the opposite SN Ia behavior. Cu and Zn start\nhaving strong s-process contributions. We avoid their discussion\nbecause of these complications and because they are not a clear\nindication for the required SN Ia signature.\n\n\tTi is dominated by the isotope $^{48}$Ti (see Table 3), i.e.,\nwe have to relate the element ratio Ti/Fe to $^{48}$Ti/$^{56}$Fe. We\nsee that for all models that underproduce Si-Ca (as needed for SNe\nIa), i.e., the DD2, DD3 and W7 models, $^{48}$Ti is also underproduced\nby similar amounts. This agrees with the observational trend that Ti\nis dominantly produced by SNe II and can be understood from the\n$^{48}$Cr abundances (decaying to the main Ti isoptope\n$^{48}$Ti). $^{48}$Ti is only produced in a strong alpha-rich\nfreeze-out as it occurs in SNe II. The small region of a weak\nalpha-rich freeze-out, indicated in Figure \\ref{rhoT}, is not\nsufficient.\n\n\tThe tendency is not so clear for Mn. The only stable Mn\nisotope is $^{55}$Mn, typically produced from unstable $^{55}$Co. This\nisotope results (1) from incomplete Si burning with a relatively high\n$Y_e$ (e.g., 0.4985; see its production in SNe II in Fig. 1 in\nThielemann et al. 1996 and the present Figs \\ref{wdd12} - \\ref{cdd12}\nin the incomplete Si-burning regions) or (2 from a somewhat reduced\n$Y_e$ (around 0.49) in complete Si burning (see Figs. \\ref{xi15c} -\n\\ref{xi30c}). This can be understood within the framework of\nquasi-equilibrium groups in Si burning, in our case the Si and the Fe\ngroup. Incomplete burning leads to a small total abundance in the Fe\ngroup in comparison to the Si group. Hix \\& Thielemann (1996) found\nthat in such a case the composition in the Fe group is typically more\nneutron-rich than expected from the global $Y_e$. Hence, $^{55}$Co\nwith a $Z/A$=0.49 is in incomplete burning also produced for\nconditions with a global $Y_e$ of 0.4985. Both locations (in complete\nand incomplete burning) can be nicely seen in Figure \\ref{w7full},\nwith the additional $Y_e$ information taken from Figure \\ref{yemr}. As\ndiscussed before, the same is found in the central parts in Figures\n\\ref{xi15c} - \\ref{xi30c} and globally in Figures \\ref{wdd12} -\n\\ref{cdd12}. The problem is, however, that with the exception of the\nDD1 models and W7, all DD models underproduce Mn/Fe in comparison to\nsolar, opposite to what is required from average SN II yields inferred\nfrom low-metallicity observations. It appears that the dominant source\nfor Mn is the incomplete Si-burning region, which is most extended in\nthe DD1 models.\n\n\t$^{52}$Cr is the dominant nucleus of the Cr isotopes. DD2\nshows a slight overabundance, DD1 a stronger overabundance. $^{52}$Cr\noriginating from $^{52}$Fe is also a nucleus dominated by incomplete\nSi burning and therefore this behavior is understandable. The light\nunderabundance in SNe II can thus be compensated by SNe Ia. Co from\nSNe II is slightly underproduced. All our calculations show an\nunderabundance in SN Ia models. It seems that the alpha-rich\nfreeze-out nucleus $^{59}$Cu (decaying to the only stable Co isotope\n$^{59}$Co) is never produced sufficiently. However, there exists the\nsame problem in SNe II (Nakamura et al. 1999) and possibly other\n(nuclear?) sources might be the origin of this behavior. $^{58}$Ni\noriginates from neutron-rich central regions and partially from\nalpha-rich freeze-out (where also $^{62}$Ni is produced via $^{62}$Zn\ndecay). We have worked hard on our models to avoid an overproduction. \nThus a slight underproduction in SNe II can easily be compensated.\nOne should also have a look at Bravo et al. (1993) and Matteucci et\nal. (1993), who performed chemical evolution calculations and\naddressed some of these questions with the then existing observational\nand model constraints.\n\n\tWe finally want to return to neutron-rich Fe-group isotopes\nand point to a different witness of galactic evolution. While\ntypically astronomical observations can give information only about\nelement abundances (with a few exceptions from molecular lines in\nstars), there exists one source of isotopic information, the so-called\nisotopic anomalies in meteorites. They are usually contained in\n\"inclusions\" of primitive meteorites consisting of minerals with much\nhigher melting temperatures than the surrounding matter. This gives\nsome indication that they originate from unprocessed \"star dust\" that\nsurvived temperatures in the early solar system and can give direct\nclues about its stellar origin. This is essentially proven for some\nSiC grains, graphites and diamonds (e.g., Zinner, Tang, \\& Andrews\n1989; Zinner 1995; Travaglio et al. 1999).\n\n\tThe nuclei $^{48}$Ca, $^{50}$Ti, $^{54}$Cr, and $^{58}$Fe,\nwhich play a crucial role in the central layers of SN Ia explosions,\ncan also be found in isotopic anomalies (Lee 1988; V\\\"olkening \\&\nPapanastassiou 1989, 1990; Loss \\& Lugmair 1990). They occur, however,\nonly in Ca-Al-rich inclusions whose history is less clear and some\nchemical processing in the early solar nebula has probably happened.\nNevertheless, it is interesting to investigate whether these observed\nanomalies can lead to any indication of their origin. Harper et\nal. (1990) found a correlation with the r-process nucleus $^{96}$Zn.\nThis would have pointed toward a SN II origin if the r-process\noriginates from SNe II. On the other hand, Ireland (1994) found a\nprobe where no correlation with r-process anomalies existed. Thus, no\nvery clear indication for their SN II or SN Ia origin (or both?) \npresently exists. In the present paper, however, we applied the\nworking hypothesis that their source is given by SN Ia ejecta, which\nis also indicated by the $Y_e$-constraints from SN II abundance\nobservations (Thielemann et al. 1996). In case of an additional SN II\ncontribution, even more stringent limits would exist.\n\n\\subsection{Ratios of SN Ia to SN II Events in the Galaxy}\n\n\tWe have full results for nucleosynthesis products of SNe Ia\nfrom the four models, WS15DD1-3, CS15DD1-2, W7, and W70, and the\nresults are shown in Figures \\ref{csdsol} - \\ref{wsd3sol} and\n\\ref{w7sol} - \\ref{w70sol}. CS30 and 50 as well as WS30 were\ncalculated only for the central slow deflagration layers and not full\ndelayed detonation models. This, as it affects the composition within\nthe Fe group, might not be a sufficient quantitative basis with\nrespect to relative abundances within the Fe group. But as the central\ndeflagration speeds have minor influence on the total abundance of\n$^{56}$Ni ($^{56}$Fe), the different DD models are probably sufficient\nto determine the best Si-Ca/Fe ratios. The observational data by\nGratton \\& Sneden (1991) and Nissen et al. (1994) for [x/Fe] at low\nmetallicities ($-2<$[Fe/H]$-<1$), x standing for elements from O\nthrough Ca, show an enhancement of the alpha elements (O through Ca)\nby a factor of 2-3 (0.3 to 0.5 dex in [x/Fe]) in comparison to\nFe. This is the clear fingerprint of the exclusive contribution of SNe\nII in early galactic evolution. It has long been the aim of chemical\nevolution calculations to explain this behavior, among the most recent\nones being Tsujimoto et al. (1995), Timmes, Woosley, \\& Weaver (1995),\nPagel \\& Tautvaisine (1995, 1997), and Kobayashi et al. (1998).\n\n\tTsujimoto et al. (1995) tried to determine the ratio of SN Ia\nto SNe Ib+II events in the Galaxy by aiming for a best fit to an\noveral solar abundance pattern from O to Ni. They made use of the\nmass-averaged SN II yields from 10 to 50 M$_\\odot$ as shown in Table 3\nand earlier results for W7. With the aid of a chemical evolution model\nthey obtained a ratio $N_{\\rm Ia}/N_{\\rm II}=0.12$ of the total number\nof SNe Ia to SNe II (+Ib) that occurred in our Galaxy. This resulted\nfrom an overal best fit to the observed abundances and is consistent\nwith the fact that the observed estimate of the SNe Ia frequency is as\nlow as 10 \\% of the total supernova rate. The observational\nconstraints for this ratio range from values around 0.15 (van den\nBergh \\& Tammann 1991) to more recent determinations of 0.27 with\nerrors of almost a factor of 2 (Cappelaro et al. 1997).\n\n\tRather than performing a full galactic evolution model, we\nwant to concentrate on a typical abundance ratio, Si/Fe, and its\ncontribution from SNe II and Ia. The averaged SNe II yields from our\ntheoretical models summarized in Table 3 correspond to a\n[Si/Fe]=0.347. The results of the 20 M$_\\odot$ model of Thielemann et\nal. (1996) would correspond to [Si/Fe]=0.304, which is close to the\nvalue of Gratton \\& Sneden (1991) and Ryan, Norris, \\& Beers (1996) of\n0.3. One should, however, be aware of the typical uncertainties of\n0.1~dex. Varying the SN Ia models among the above given list (W7,\nW70, DD1, DD2, and DD3) and making use of Si and Fe from the averaged\nSNe II ejecta or the 20 M$_\\odot$ star, leads also to a required\nIa/Ib+II ratio in order to obtain the solar mix of Si/Fe with both\ncontributions. This ratio is derived in the following way:\n\n\\begin{eqnarray}\n \\left({M({\\rm Si})\\over M({\\rm Fe})}\\right)_\\odot & = \n &{N_{\\rm Ia} M_{\\rm Ia}({\\rm Si}) + N_{\\rm II} M_{\\rm II}({\\rm Si})}\\over \n {N_{\\rm Ia} M_{\\rm Ia}({\\rm Fe}) + N_{\\rm II} M_{\\rm II}({\\rm Fe})},\\\\\n {N_{\\rm Ia}\\over N_{\\rm II}}& = \n & {{M_{\\rm II}({\\rm Si}) - M({\\rm Si})/M({\\rm Fe})_\\odot M_{\\rm II}\n({\\rm Fe})} \\over {M({\\rm Si})/M({\\rm Fe})_\\odot M_{\\rm Ia}({\\rm Fe}) \n- M_{\\rm Ia}({\\rm Si})}}. \n\\end{eqnarray}\n\n\tThe results for the obtained ratios are shown in Table 5. It\nis immediatey obvious that the DD1 models do not result in a physical\nsolution. With their Si-Ca/Fe ratios being almost solar, they cannot\ncompensate for the SNe II contribution, which have larger than solar\nvalues. There is a clear need for SNe Ia to produce ejecta with\nSi-Ca/Fe less than solar. Otherwise all models seem to be covered by\nthe error bars for the Ia/(Ib+II) ratios laid out by van den Bergh \\&\nTammann (1991) and Cappelaro et al. (1997). The DD3 values, especially\nfor the 20~M$_\\odot$ Si/Fe ratios being closest to the low-metallicity\n[Si/Fe], might somewhat indicate the lower limit. It should be noted\nthat although the Si/Fe ratios in the DD1 - DD3 models show a\nmonotonous behavior (i.e., decline), this does not lead to a\nmonotonous variation in Ia/(Ib+II) ratios, owing to the form of\nequation (4), where differences and not the Si/Fe ratios enter. This\nresults in negative values for DD1 (due to a negative denominator) and\ngoes through a maximum (when the denominator starts to be positive but\nis small) before decreasing to the DD3 values with an increasing\ndenominator. This is due to the fact that Si masses decrease with the\nDD1 - DD3 sequence, while Fe increases.\n\n\n\tWith a low SN Ia frequency of Ia/(II+Ib)=0.15 and W7\nabundances, $^{56}$Fe from SNe Ia amounts to about 55\\% of total\n$^{56}$Fe (see the discussion in \\S 3.2). Larger values would increase\nthis contribution. When assuming that SNe II do not produce\nneutron-rich species like $^{54}$Cr and $^{50}$Ti at all, we permitted\nfor the abundance ratios between such nuclei and $^{56}$Fe an\noverproduction factor of $\\sim$ 4. With the larger SN Ia frequencies\nof Table 5 and Cappelaro et al. (1997) such permitted overproductions\nwould need to be further reduced and more stringent limits would\napply.\n\n\\section{Summary and Outlook}\n\n\tFrom the very early days of explosive nucleosynthesis\ncalculations, when no direct connection to astrophysical sites was\npossible yet, it was noticed (Trimble 1975) that the solar Fe-group\ncomposition could be reproduced with a superposition of matter from\nexplosive Si burning with about 90\\% originating from a $Y_e$=0.499\nsource and 10\\% from a $Y_e$=0.46 source. We have discussed in some\ndetail in the present paper that the central part of SNe Ia could be\nthis second source, while Thielemann et al. (1996) have shown that SN\nII ejecta with $Y_e$$<$0.498 could cause serious problems.\n\n\tNew results by Hachisu \\etal (1999a, 1999b; see also Li \\& van\nden Heuvel 1997), which include wind losses in the interaction of\nbinary systems, come to the conclusion that the majority of SNe Ia\nprogenitor systems experience hydrogen accretion on white dwarfs at a\nrate that has them grow toward the Chandrasekhar mass through steady\nH- and He-burning. This leads to the single degenerate Chandrasekhar\nmass scenario (SD/Ch). Binary systems with steady H-burning on\naccreting white dwarfs and effective accretion rates as high as $\\dot\nM >$ 1 $\\times$ 10$^{-7}$ M$_\\odot$ yr$^{-1}$ might correspond to\nobserved supersoft X-ray sources. This also would lead to low central\nignition densities of the Chandrasekhar mass white dwarf at the\nthermonuclear runaway ($<$ 2 \\e9 \\gmc), which correspond to the C\nseries of the models discussed in the present paper. A small fraction\ncan deviate from steady H burning and would experience weak hydrogen\nflashes near the end of the accretion history. Such cases would\ncorrespond to our W series of models and even higher ignition\ndensities. Kobayashi et al. (1998) discussed metallicity effects and\ntheir influence on the delay time for the appearance of SNe Ia in\ngalactic evolution.\n\n\tOur nucleosynthesis results of the present paper are quite\nconsistent with these scenarios and favor case C. The reason is that\ntoo high ignition densities lead to a high degree of electron captures\nand small $Y_e$ values, which would cause an overproduction of\n$^{54}$Cr and $^{50}$Ti in excess of what is permitted for SNe Ia in a\nsolar mix. We have to make two reservations here. New shell model\ncalculations (Dean et al. 1998; Caurier et al. 1999) indicate that the\nelectron capture rates could be substantially reduced in comparison to\nthe rates by Fuller et al. (1980,1982,1985) employed here. The\napplication of these new capture rates might also permit models of our\nW series without serious deviations from the allowed central $Y_e$\nvalues. In addition, such conclusions deal only with the dominant or\naverage SN Ia events. If more neutron-rich nuclei like $^{48}$Ca are\nalso the result of SN Ia nucleosynthesis, an occasional event with a\nsignificantly higher ignition density is required, a fact also\nconsistent with the above scenario.\n \n\tOur nucleosynthesis results imply that for the dominant events\nthe central density of the Chandrasekhar mass white dwarf at\nthermonuclear runaway must be as low as or lower than \\ltsim 2 \\e9\n\\gmc, though the exact constraint depends somewhat on the flame speed. \nHere is the point where nucleosynthesis predictions can also be of\nhelp for providing constraints to the supernova modeling and the\nburning-front velocity. A carbon deflagration wave, propagating as\nslow as $v_{\\rm def}/v_{\\rm s} \\sim 0.015$ or even slightly slower,\nwould be the ideal choice for the neutron-rich species such as\n$^{54}$Cr and $^{50}$Ti; see cases CS15 and WS30. The latter case\nmakes also clear that slightly larger ignition densities than 1.5 \\e9\n\\gmc~(case C) are permitted if the flame speed is increased\nappropriately. An acceleration of the flame speed in the outer part\nof the central layers is permitted to about 3\\% of the sound speed or\nslightly more, but should clearly stay below 5\\%. For such fast\nburning fronts the $Y_e$-gradient becomes very flat and too much\nmaterial in the range $Y_e$ = 0.47-0.485 is produced. This leads to\ndominant abundances of $^{54}$Fe and $^{58}$Ni, a feature that was\nalready prominent in W7, and causes an excessive overproduction of\n$^{58}$Ni in galactic evolution. Our calculations were performed with\na constant fraction of the sound speed. An acceleration of the\nburning front is expected (Khokhlov 1995; Niemeyer \\& Woosley 1997)\nand future investigations should include such a time dependence, which\nis in agreement with the findings discussed above.\n\n\tFinally, nucleosynthesis can also give clues about the\ndeflagration-detonation transition (DDT). The most obvious consequence\nof choosing different transition densities is the amount of $^{56}$Ni\nproduced in a SN Ia event. H\\\"oflich and Khokhlov (1996) find from\nlight curve modeling and spectra that the typical $^{56}$Ni mass\nshould be in the range 0.5-0.7~M$_\\odot$. This agrees with W7. Among\nthe DD models it would ask for a value somewhere between DD1 and DD2\n(closer to DD2). Here 3, 2, and 1 stand for DDTs when densities ahead\nof the flame decrease to 3.0, 2.2, and 1.7 \\e7 \\gmc~. DD1 is excluded\nfor other reasons. The amount of Si-Ca in comparison to Fe is too\nlarge in DD1 models in order to compensate for the well-known\noverproduction of Si-Ca in SNe II during galactic evolution. Si/Fe\nratios in SN Ia models require specific Ia/(II+Ib) ratios in order to\nobtain a solar mix combined with SN II contributions (see Table 5).\nDD2 seems to be closest to the present observational constraints for\nthis ratio by Cappelaro et al. (1997).\n\n\tSmall DDT densities favor larger amounts of matter that\nexperience incomplete Si burning. Low-metallicity constraints require\nan overproduction of Mn (and Cr) in SNe Ia. These elements are mostly\nmade as $^{55}$Co and $^{52}$Fe (decaying to Mn and Cr), which are\nfavorably produced in incomplete Si burning and would also require a\nDDT between DD1 and DD2. (One should, however, realize that a fast\ndeflagration could possibly simulate this as well - see the Mn\noverproduction in Figure 12 - and on the other hand that these numbers\nwould have to be rescaled or reinterpreted in multi-D calculations.)\nThus, combining all requirements on the DDT from total Ni yields,\nSi/Fe and Ia/(II+Ib) ratios, as well as specific elements favored in\nincomplete Si-burning, we would argue for a DDT density slightly below\n2.2 \\e7 \\gmc~, i.e., results between DD1 and DD2. One should, however,\nbe careful with these constraints based on spherically symmetric\napproximations of the burning front. Full three-dimensional\ncalculations could possibly produce the required ratio of matter from\nincomplete Si burning and complete Si burning with alpha-rich\nfreeze-out in a different realization.\n\n\tMore extended calculations that make use of the conclusions\npresented here, including a time dependence of $v_{\\rm def}/v_{\\rm\nsound}$, the best choice for the DDT density, and a detailed galactic\nevolution model, replacing our comparisons of only the global yields,\nwill be the next step to undertake. That would also have to include\nfurther tests of the metallicity of the exploding object, a topic\nwhich has gained in importance with the cosmological interpretation of\nhigh-redshift SNe Ia. For this reason we repeat here in Figure\n25a-25c some of the Figures 19-21 with a continuation to smaller mass\nfractions and purely plotted as a function of velocity, in order to\nmagnify the behavior of the outer layers. The differences in\nvelocities between CDD and WDD models are negligibly small in these\nplots.\n\n%\\vskip 0.5cm\n%:To the Editor: Please Place Figure 25 Here:\n% XIVELCDD1.PS, XIVELCDD2.PS XIVELCDD3.PS %\n%\\vskip 0.5cm\n\nAs mentioned before, the $^{54}$Fe (in the outer layers not affected\nby electron captures but only by the neutron excess due to the initial\nmetallicity) ranging in velocities up to 15,000 - 19,000 km s$^{-1}$\nin the models DD1-DD3, is a strong indicator of metallicity (see Fig.\n14). The minima in S, Ar, and Ca, if observed in spectra, with\npositions between 16,000 and 21,000 km s$^{-1}$ in the DD1-DD3 models,\ncould give further clues on the deflagration-detonation\ntransition. And finally, any unburned intermediate mass elements at\nhigher velocities would give a clear indication of the metallicity of\nthe accreted matter. Our calculations and plots include only initial\ncompositions of $^{12}$C, $^{16}$O, and $^{22}$Ne. Solar abundances of\nCa, Ar, S, Si, or Fe would correspond to mass fractions of $1.2\\times\n10^{-4}$, $1.6 \\times 10^{-4}$, $7.6\\times 10^{-4}$, $1.3\\times\n10^{-3}$, or $2.3\\times 10^{-3}$.\n\nThus, any future investigations of very early time spectra, leading to\nabundance observations at high velocities, would provide strong\nconstraints on the SNe Ia mechanism and the relation to the\nmetallicity of the individual SNe Ia explosion.\n\n%\\vfill\\eject\n\\section*{Acknowledgments}\n\nThis work has been supported in part by the grant-in-Aid for\nScientific Research (05242102, 06233101) and COE research (07CE2002)\nof the Ministry of Education, Science and Culture in Japan, a\nfellowship of the Japan Society for the Promotion of Science for\nJapanese Junior Scientists (6728), the Swiss Nationalfonds\n(20-47252.96 and 2000-53798.98), the US National Science Foundation\n(grant PHY94-07194), and the DOE (contract DE-AC05-96OR22464). Part of\nthe computations were carried out on a Fujitsu VPP-500 at the\nInstitute of Physical and Chemical Research (RIKEN) and the Institute\nof Space and Astronautical Science (ISAS), and a Fujitsu VPP-300 at\nthe National Astronomical Observatory in Japan (NAO, Tokyo). We want\nto thank all participants of the NATO workshop on Thermonuclear\nSupernovae in Aiguablava, where the idea to the present research\nbegan. Some of us (K.I., K.N., W.R.H., and F.K.T.) thank the ITP at\nthe University of California, Santa Barbara, for hospitality and\ninspiration during the supernova program. The paper was completed\nduring the SNe Ia workshop at the Aspen Center for Physics (June\n1999).\n\n\\begin{thebibliography}{widest citation in source list}\n\n\\bibitem[]{}Arnett, W.D. 1996, Nucleosynthesis and Supernovae\n(Princeton: Princeton Univ. Press)\n\n\\bibitem[]{}Arnett, W.D., \\& Livne, E. 1994a, ApJ, 427, 314\n\n\\bibitem[]{}Arnett, W.D., \\& Livne, E. 1994b, ApJ, 427, 330\n\n\\bibitem[]{} Aufderheide, M., Fushiki, I., Woosley, S.E., Hartmann, D. \n1994, ApJS, 91, 389\n\n\\bibitem[]{} Bao, Z.~Y., K\\\"appeler, F. 1987, At. Data Nucl. Data\nTables, 36, 411\n\n\\bibitem[]{}Barkat, Z., \\& Wheeler, J.C. 1990, ApJ, 355, 602\n\n\\bibitem[]{}Branch, D., 1998, ARA\\&A, 36, 17\n\n\\bibitem[]{}Branch, D., Doggett, J.B., Nomoto, K., \\& Thielemann,\nF.-K. 1985, ApJ, 294, 619\n\n\\bibitem[]{}Branch, D., Livio, M., Yungelson, L.R., Boffi, F.R., \\&\nBaron, E. 1995, PASP, 107, 717\n\n\\bibitem[]{} Branch, D., Tammann, G.A. 1992, ARA\\&A 30, 359\n\n\\bibitem[]{}Bravo, E., Isern, J., \\& Canal, R. 1993, A\\&A, 269, 187\n\n\\bibitem[]{} Bravo, E., Isern, J., Canal, R., \\& Labay, J. 1992, A\\&A,\n257, 534\n\n\\bibitem[]{}Bychkov, V.V., \\& Liberman, M.A., 1995a, ApJ, 451, 711\n\n\\bibitem[]{}Canal, R., Ruiz-Lapuente, P., \\& Isern, J. 1997, in\nThermonuclear Supernovae, ed. P. Ruiz-Lapuente, R. Canal, \\& J. Isern,\n(Dordrecht:Kluwer), 257\n\n\\bibitem[]{}Cappellaro, E., Turatto, M., Tsvvetkov, D.Yu., Bartunov,\nO.S., Pollas, C., Evans, R., \\& Hamuy, M. 1997, A\\&A, 322, 431\n\n\\bibitem[]{} Caughlan, G.R., \\& Fowler, W.A. 1988, At. Data Nucl. Data\nTables, 40, 283\n\n\\bibitem[]{} Caurier, E., Langanke, K., Martinez-Pinedo, G., Nowacki,\nF. 1999, Phys. Rev. C, submitted\n\n\\bibitem[]{} Dean, D.J., Langanke, K., Chatterjee, L., Radha, P.B., \\&\nStrayer, M.R. 1998, Phys. Rev. C, 58, 536\n\n\\bibitem[]{}Di Stefano, R., Nelson, L.A., Lee, W., Wood, H.,\n Rappaport, S. 1997, in Thermonuclear Supernovae,\n ed. P. Ruiz-Lapuente, R. Canal, \\& J. Isern, (Dordrecht:Kluwer), 147\n\n\\bibitem[]{}Fisher, A., Branch, D., H\\\"oflich, P., \\& Khokhlov,\nA. 1995, ApJ, 447, L73\n\n\\bibitem[]{} Fuller, G.M., Fowler, W.A., \\& Newman, M. 1980, ApJS, 42,\n 447\n\n\\bibitem[]{} Fuller, G.M., Fowler, W.A., \\& Newman, M. 1982, ApJS, 48,\n 279\n\n\\bibitem[]{} Fuller, G.M., Fowler, W.A., \\& Newman, M. 1985, ApJ, 293,\n 1\n\n\\bibitem[]{} Gratton, R.G. 1989, A\\&A, 208, 171\n\n\\bibitem[]{} Gratton, R.G., \\& Sneden, C. 1988, A\\&A, 204, 193\n\n\\bibitem[]{} Gratton, R.G., \\& Sneden, C. 1991, A\\&A, 241, 501\n\n\\bibitem[]{}Hachisu, I., Kato, M., \\& Nomoto, K. 1996, ApJ, 470, L97\n\n\\bibitem[]{}Hachisu, I., Kato, M., \\& Nomoto, K. 1999a, ApJ, 522, 487\n\n\\bibitem[]{}Hachisu, I., Kato, M., Nomoto, K., \\& Umeda, H. 1999b,\nApJ, 519, 314\n\n\\bibitem[]{}Hamuy, M., Phillips, M.M., Maza, J., Suntzeff, R.A., \\&\nAviles, R. 1995, AJ, 109, 1\n\n\\bibitem[]{}Harkness, R.P. 1991, in SN 1987A and Other Supernovae, ed. \nI.J., Danziger \\& K. Kj\\\"ar (Garching:ESO), 447\n\n\\bibitem[]{} Harper, C.L., Nyquist, L.H., Shih, C.-Y., Wiesmann,\nH. 1990, in Nuclei in the Cosmos, ed. H. Oberhummer, W. Hillebrandt\n(Garching, MPI f\\\"ur Physik und Astrophysik), MPA/P4, 138\n\n\\bibitem[]{} Hartmann, D., Woosley, S.E., \\& El Eid, M.F. 1985, ApJ,\n297, 837\n\n\\bibitem[]{}Hashimoto, M., Nomoto, K., \\& Thielemann, F.-K. 1989,\nA\\&A, 210, L5\n\n\\bibitem[]{}Hashimoto, M. 1995, Prog. Theor. Phys., 94, 663\n\n\\bibitem[]{}Hashimoto, M., Nomoto, K., Tsujimoto, T., \\& Thielemann,\nF.-K. 1996, in IAU Colloq. 145, Supernovae and Supernova Remnants, ed. \nR. McCray \\& Z. Wang (Cambridge:Cambridge University Press), 157\n \n\\bibitem[]{}Hatano, K., Branch, D., Fisher, A., Baron, E., \\&\nFilippenko, A.V. 1999, ApJ Lett., submitted\n\n\\bibitem[]{}Hillebrandt, W., \\& Niemeyer, J.C. 1997, in Thermonuclear\n Supernovae, ed. P. Ruiz-Lapuente, R. Canal, \\& J. Isern,\n (Dordrecht:Kluwer), 337\n\n\\bibitem[]{} Hix, W.R., \\& Thielemann F.-K. 1996, ApJ, 460, 869\n\n\\bibitem[]{} Hix, W.R., \\& Thielemann F.-K. 1999a, ApJ, 511, 862\n\n\\bibitem[]{} Hix, W.R., \\& Thielemann F.-K. 1999b, J. Climate\n Appl. Meteor., in press\n\n\\bibitem[]{}H\\\"oflich, P., Dominguez, I., Thielemann, F.-K., \\&\nWheeler, J.C. 1999, in Proc.\\ 42nd Int.\\ Astrophys.\\ Colloq.\\\n(ESA-SP-429;ESA:Noordwijk), 243\n \n\\bibitem[]{}H\\\"oflich, P., \\& Khokhlov, A. 1996, ApJ, 457, 500\n\n\\bibitem[]{}H\\\"oflich, P., Wheeler, J.C., \\& Thielemann, F.-K. 1998,\n ApJ, 495, 617\n\n\\bibitem[]{}Hughes, J.P., et al. 1995, ApJ, 444, L81\n\n\\bibitem[]{}Hwang, U., Hughes, J.P., \\& Petre, R. 1998, ApJ, 497, 833\n\n\\bibitem[]{}Iben, I.,Jr. 1982, ApJ, 253, 248\n\n\\bibitem[]{} Iben, I.,Jr., \\& Tutukov, A.V. 1984, ApJS, 54, 335\n\n\\bibitem[] {} Ichimaru, S. 1993, Rev. Mod. Phys., 65, 255\n\n\\bibitem[] {} Ireland, T.R. 1994, ApJ, 434, L79\n\n\\bibitem[]{}Jeffery, D., Leibundgut, B., Kirshner, R.P., Benetti, S.,\nBranch, D., \\& Sonneborn, G. 1992, ApJ, 397, 304\n\n\\bibitem[]{}Khokhlov, A.M. 1991a, A\\&A, 245, 114\n\n\\bibitem[]{}Khokhlov, A.M. 1991b, A\\&A, 245, L25\n\n\\bibitem[]{}Khokhlov, A.M. 1995, ApJ, 449, 695\n\n\\bibitem[] {} Khokhlov, A.M., M\\\"uller, E., \\& H\\\"oflich, P. 1992, A\n\\& A, 253, L9\n\n\\bibitem[] {} Khokhlov, A.M., Oran, E.S., \\& Wheeler, J.C. 1997, ApJ,\n478, 678\n\n\\bibitem[]{}Kirshner, R.P., \\etal 1993, ApJ, 415, 589\n\n\\bibitem[] {} Kobayashi, C., Tsujimoto, T., Nomoto, K., Hachisu, I.,\n\\& Kato, M. 1998, ApJ, 503, L155\n\n\\bibitem[]{}Landau, L.D., \\& Lifshitz, E.M. 1987, Fluid Mechanics\n(Oxford:Pergamon)\n\n\\bibitem[] {} Lee, T. 1988, in Meteorites and the Early Solar System,\ned. J.F. Kerridge, \\& M.S. Matthews (Tuscon:Univ. Arizona Press), 1063\n\n\\bibitem[]{}Leibundgut, B., Kirshner R.P., Filippenko, A.V., Shields,\nJ.C., Foltz, C.B., Phillips, M.M., \\& Sonneborn, G. 1991a, ApJ, 371,\nL23\n\n\\bibitem[] {} Lentz, E.J., Baron, E., Branch, D., Hauschildt, P.H., \\&\nNugent, P.E., 1999, ApJ, in press\n\n\\bibitem[]{} Li, X.D., \\& van den Heuvel, E.P.J. 1997, A\\&A, 322, L9\n\n\\bibitem[]{}Liu, W.H., Jeffery, D.J., \\& Schultz, D.R. 1997, ApJ, 483,\n L107\n\n\\bibitem[]{}Livne, E. 1993, ApJ, 406, L17\n\n\\bibitem[]{}Livne, E., \\& Arnett, W.D. 1995, ApJ, 452, 62\n\n\\bibitem[] {} Loss, R.D., Lugmair, G.W. 1990, ApJ, 360, L59\n\n\\bibitem[] {} Magain, P. 1987, A\\&A, 179, 176\n\n\\bibitem[] {} Magain, P. 1989, A\\&A, 209, 211\n\n\\bibitem[]{} Matteucci, F., Raiteri, C.M., Busso, M., Gallino, R., \\&\nGratton, R. 1993, A\\&A, 272, 421\n\n\\bibitem[]{} Mazzali, P., Cappelaro, E., Danziger, I.J., Turatto, M.,\n\\& Benetti, S. 1998, ApJ, 499, L49\n\n\\bibitem[]{}Mazzali, P., Lucy, L.B., Danziger, I.J., Gouiffes, C.,\nCappellaro, E.R., \\& Turatto, M. 1993, A\\&A, 269, 423\n\n\\bibitem[]{}Meikle, W.P.W., \\etal 1996, MNRAS, 281, 263\n\n\\bibitem[]{} Meyer, B.S., Krishnan, T.D., \\& Clayton, D.D. 1996, ApJ,\n462, 825\n\n\\bibitem[]{}Miyata, E., Tsunemi, H., Kohmura, T., Suzuki, S., \\&\nKumagai, S. 1998, PASJ, 50, 257\n\n\\bibitem[]{}Nakamura, T., Umeda, H., Nomoto, K., Thielemann, F.-K., \\&\nBurrows, A. 1999, ApJ, 517, 193\n\n\\bibitem[]{}Niemeyer, J.C. 1999, ApJ, 523, L57\n\n\\bibitem[]{}Niemeyer, J.C., \\& Hillebrandt W. 1995a, ApJ, 452, 769\n\n\\bibitem[]{}Niemeyer, J.C., Hillebrandt W., \\& Woosley, S.E. 1996,\nApJ, 471, 903\n\n\\bibitem[]{}Niemeyer, J.C., \\& Kerstein, A.R. 1997, NewA, 2, 239\n\n\\bibitem[]{}Niemeyer, J.C., \\& Woosley, S.E. 1997, ApJ, 475, 740\n\n\\bibitem[] {} Nissen, P.E., Gustafsson, B., Edvardsson, B., \\&\n Gilmore, G. 1994, A\\&A, 285, 440\n\n\\bibitem[]{}Nomoto, K. 1982a, ApJ, 253, 798\n \n\\bibitem[]{}Nomoto, K. 1982b, ApJ, 257, 780\n\n\\bibitem[]{}Nomoto, K., \\& Hashimoto, M. 1988, Phys. Rep., 163, 13\n\n\\bibitem[]{}Nomoto, K., \\& Iben, I.,Jr. 1985, ApJ, 297, 531\n\n\\bibitem[]{}Nomoto, K., Iwamoto, K., \\& Kishimoto, N. 1997, Science, 276, 1378\n\n\\bibitem[] {} Nomoto, K., Hashimoto, M., Tsujimoto, T., Thielemann,\nF.-K., Kishimoto, N., Kubo, Y., \\& Nakasato, N. 1997a, Nucl. Phys. A,\n161, 79c\n\n\\bibitem[]{} Nomoto, K., Iwamoto, K., Nakasato, N., Thielemann., F.K.,\nBrachwitz, F., Tsujimoto, T., Kubo. Y., \\& Kishimoto, N. 1997b,\nNucl. Phys. A, 621, 467c\n\n\\bibitem[]{} Nomoto, K., et al. 1997c, in Thermonuclear Supernovae,\ned. P. Ruiz-Lapuente, R. Canal, \\& J. Isern, (Dordrecht:Kluwer), 349\n\n\\bibitem[]{}Nomoto, K., \\& Kondo, Y. 1991, ApJ, 367, L19\n\n\\bibitem[]{}Nomoto, K., Nariai, K., \\& Sugimoto, D. 1979, PASJ, 31, 287\n\n\\bibitem[]{}Nomoto, K., Sugimoto, D., \\& Neo, S. 1976, Ap\\&SS, 39, L37\n\n\\bibitem[]{}Nomoto, K., Thielemann, F.-K., \\& Yokoi, K. 1984, ApJ,\n286, 644\n\n\\bibitem[]{}Nomoto, K., Yamaoka, H., Shigeyama, T., Kumagai, S., \\&\nTsujimoto, T. 1994, in Les Houches, Session LIV, Supernovae,\ned. S. Bludman, R.Mochovitch, \\& Zinn-Justin(Amsterdam:Elsevier), 199\n\n\\bibitem[]{}Nomoto, K., Yamaoka, H., Shigeyama, T., \\& Iwamoto, K.\n1996a, in IAU Colloq. 145, Supernovae and Supernova Remnants,\ned. R. McCray \\& Z. Wang (Cambridge:Cambridge University Press), 49\n\n\\bibitem[]{}Nugent, P., Baron, E., Branch, D., Fisher, A., \\&\nHauschildt, P.H. 1997, ApJ, 485, 812\n\n\\bibitem[]{}Paczy\\'nski, B. 1973, Acta Astron, 23, 1\n\n\\bibitem[Pagel \\& Trautvaisiene (1995)] {pagel95} Pagel, B.E.J., \\&\n Trautvaisiene, G. 1995, MNRAS, 276, 505\n\n\\bibitem[Pagel \\& Trautvaisiene (1997)] {pagel97} Pagel, B.E.J., \\&\n Trautvaisiene, G. 1997, MNRAS, 288, 108\n\n\\bibitem[]{}Perlmutter, S., et al. 1997, ApJ, 483, 565\n\n\\bibitem[]{}Perlmutter, S., et al. 1999, ApJ, 517, 565\n\n\\bibitem[]{}Phillips, M.M., Hamuy, M., Maza, J., Ruiz, M.T., Carney,\nB.W., \\& Graham, J.A. 1990, PASP, 102, 299\n\n\\bibitem[]{}Rappaport, S., Di Stefano, R., \\& Smith, J.D., 1994 ApJ,\n 426, 692\n\n\\bibitem[Rauscher et~al. (1994)]{rauscher94} Rauscher, T., Applegate,\nJ.H., Cowan, J.J., Thielemann, F.-K., \\& Wiescher, M. 1994, ApJ, 429,\n499\n\n\\bibitem[]{}Renzini, A. 1996, in IAU Colloq. 145, Supernovae and\nSupernova Remnants, ed. R. McCray \\& Z. Wang (Cambridge:Cambridge\nUniversity Press), 77\n\n\\bibitem[]{}Riess, A.G., Press, W.H., \\& Kirshner, R.P. 1995, ApJ,\n438, L17\n\n\\bibitem[]{}Riess, A.G., et al. 1999, AJ, 117, 707\n\n\\bibitem[]{}Ruiz-Lapuente, P. 1997, in Thermonuclear Supernovae,\ned. P. Ruiz-Lapuente, R. Canal, \\& J. Isern, (Dordrecht:Kluwer), 681\n\n\\bibitem[Ryan et al. (1996)] {ryan96} Ryan, S.G., Norris, J.E., \\&\n Beers, T.C. 1996, ApJ, 471, 254\n\n\\bibitem[Saio \\& Nomoto 1985]{sanom1985} Saio, H., \\& Nomoto, K. 1985,\nA\\&A, 150, L21\n\n\\bibitem[Saio \\& Nomoto 1985]{sanom1998} Saio, H., \\& Nomoto, K. 1998,\nApJ, 500, 388\n\n\\bibitem[]{}Shigeyama, T., Nomoto, K., Yamaoka, H., \\& Thielemann,\nF.-K. 1992, ApJ, 386, L13\n\n\\bibitem[Thielemann et al. (1987)]{thielemann87} Thielemann, F.-K.,\nArnould, M., \\& Truran, J.~W. 1987, in Advances in Nuclear\nAstrophysics, ed. E.~Vangioni-Flam (Gif sur Yvette:Editions\nFronti\\`ere), 525\n\n\\bibitem[]{}Thielemann, F.-K., Nomoto, K., \\& Hashimoto, M. 1996, ApJ,\n460, 408\n\n\\bibitem[]{}Thielemann, F.-K., Nomoto, K., Iwamoto, K., \\& Brachwitz,\nF. 1997, in Thermonuclear Supernovae, ed. P. Ruiz-Lapuente, R. Canal,\n\\& J. Isern (Dordrecht:Kluwer), 485\n\n\\bibitem[]{}Thielemann, F.-K., Nomoto, K., \\& Yokoi, K. 1986, A\\&A,\n158, 17\n\n\\bibitem[]{}Timmes, F., \\& Woosley, S.E. 1992, ApJ, 396, 649\n\n\\bibitem[Timmes et al. (1995)] {timmes95} Timmes, F., Woosley, S.E.,\n \\& Weaver, T.A. 1995, ApJS, 98, 617\n\n\\bibitem[]{}Travaglio, C., Gallino, R., Amarari, S., Zinner, E.,\nWoosley, S.E., \\& Lewis, R. 1999, ApJ, 510, 325\n\n\\bibitem[Trimble (1975)] {trimble75} Trimble, V. 1975,\nRev. Mod. Phys., 47, 877\n\n\\bibitem[]{}Tsujimoto, T., Nomoto, K., Yoshii, Y., Hashimoto, M.,\nYanagida, S., \\& Thielemann, F.-K. 1995, MNRAS, 277, 945\n\n\\bibitem[]{}Umeda, H., Nomoto, K., Yamaoka, H, \\& Wanajo, S. 1999,\nApJ, 513, 861\n\n\\bibitem[]{} Unno, W. 1968, PASJ, 19, 140\n\n\\bibitem[]{}van den Bergh, S., \\& Tammann, G. 1991, ARA\\&A, 29, 363\n\n\\bibitem[]{}van den Heuvel, E.P.J., Bhattacharya, D., Nomoto, K., \\&\nRappaport, S.A. 1992, A\\&A, 262, 97\n\n\\bibitem[van Wormer et~al. (1994)]{wormer94} van Wormer, L., G\\\"orres,\nJ., Iliadis, C., Wiescher, M., \\& Thielemann, F.-K. 1994, ApJ, 432,\n267\n\n\\bibitem[]{} V\\\"olkening, J. \\& Papanastassiou, D.A. 1989, ApJ, 347,\nL43\n\n\\bibitem[]{} V\\\"olkening, J. \\& Papanastassiou, D.A. 1990, Lunar and\nPlanetary Science XXI(Houston:Lunar.Planet.Inst.), No 1276\n\n\\bibitem[Webbink 1984]{webb1984}\nWebbink, R.F. 1984, ApJ, 277, 355\n\n\\bibitem[]{}Wheeler, J.C., Harkness, R.P., Khokhlov, A.M., \\&\nH\\\"oflich, P. 1995, Phys. Rep., 53, 221\n\n\\bibitem[]{}Woosley, S.E. 1997a, in Thermonuclear Supernovae,\ned. P. Ruiz-Lapuente, R. Canal, \\& J. Isern (Dordrecht:Kluwer), 313\n\n\\bibitem[]{}Woosley, S.E. 1997b, ApJ, 476, 801\n\n\\bibitem[]{}Woosley, S.E., \\& Weaver, T.A. 1986, ARA\\&A, 24, 205\n\n\\bibitem[]{}Woosley, S.E., \\& Weaver, T.A. 1994a, ApJ, 423, 371\n\n\\bibitem[]{}Woosley, S.E., \\& Weaver, T.A. 1994b, in Les Houches,\nSession LIV, Supernovae, ed. S.A.Bludman, R.Mochovitch, \\&\nJ.Zinn-Justin(Amsterdam:Elsevier), 63\n\n\\bibitem[]{}Yamaoka, H., Shigeyama, T., Nomoto, K., \\& Thielemann,\nF.-K. 1992, ApJ, 393, L55\n\n\\bibitem[]{}Yoshii, Y., Tsujimoto, T., \\& Nomoto, K. 1996, ApJ, 462,\n266\n\n\\bibitem[Zhao \\& Magain (1990)] {zhaomag90} Zhao, G., \\& Magain,\nP. 1990, A\\&A 238, 242\n\n\\bibitem[]{} Zinner, E. 1995, in Nuclei in the Cosmos III,\ned. M. Busso, R. Gallino, \\& C.M. Raiteri (New York:AIP Press), 567\n\n\\bibitem[]{} Zinner, E., Tang, M., \\& Anders, E. 1989,\nGeochim. Cosmochim. Acta, 53, 3273\n\n\\end{thebibliography}\n\n\\newpage\n\n\\epsfverbosetrue\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\vspace*{-9.5cm}\n\\epsfbox[-47 61 351 755]{tmr2.epsi}\n%%\\centerline{\\psfig{figure=tmr2.epsi,h=-2cm, width=6cm}}\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\vspace{-3cm}\n\\epsfbox[-47 61 351 755]{rmr2.epsi}\n%%\\centerline{\\psfig{figure=rmr2.epsi,width=6cm}}\n\\vspace{10cm}\n\\caption{\nTemperatures and densities for the deflagration wave (WS15) and\ndelayed detonation (DD1) as a function of radial mass coordinate\n\\mr. The labels indicate different instances in time, 1-6 correspond\nto the deflagration phase, 7-11 to the propagation of the detonation after\nthe deflagration-detonation transition. \\label{defr}}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\vspace*{-9.5cm}\n\\epsfbox[-47 61 351 747]{tt2.epsi}\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\vspace{-3cm}\n\\epsfbox[-47 61 351 747]{rt2.epsi}\n\\vspace{10cm}\n\\caption{\nThe distribution of temperatures and densities as a\nfunction of time during the passage of the slow deflagration (WS15)\nand the subsequent delayed detonation (DD1). The labeled numbers\nindicate different mass zones. The prominent spike, occurring for\nlabels $\\ge$ 5, shows the action of the detonation and its fast\npropagation (small time differences between different mass zones).\n\\label{dens}}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-890 300 -530 926]{velomass.epsi}\n\\vspace{8cm}\n\\caption{\nThe distribution of expansion velocities after the passage\nof the slow deflagration and the subsequent delayed detonation. \n\\label{vexp}}\n\\end{figure}\n\n\n\\newpage\n\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-42 665 195 749]{fig4.epsi}\n\\vspace{6cm}\n\\caption{\nMaximum densities $\\rho_{\\rm max}$ and temperatures\n$T_{\\rm 9,max}$ during Si-burning of the central layers obtained during\nthe propagation of the burning front. The model W7 is compared to\nthree slow deflagrations which start (for a density of 2.1$\\times\n10^9$g cm$^{-3}$) with burning front velocities of 1.5\\% (slow\ndeflagration WS15) and 3\\% (WS30) of the sound speed and for an\nignition density of 1.37$\\times 10^9$g cm$^{-3}$ with a burning front\nvelocity of 1.5\\% of sound (CS15). The crosses (C-det) correspond to\ncarbon detonations of sub-Chandrasekhar mass models. They will not be\ndiscussed here, but it is obvious that the smaller temperatures and\ndensities lead to negligible amounts of electron\ncaptures. \\label{rhoT}}\n\\end{figure}\n\n\n\\vspace{2cm}\n\\begin{figure}[hb]\n\\epsfxsize=7.5cm\n\\epsfysize=6cm\n\\epsfbox[-900 100 -450 403]{yeall.epsi}\n\\vspace{1cm}\n\\caption{$Y_e$, the total proton to nucleon ratio and thus a measure of \nelectron captures on free protons and nuclei, after freeze-out of\nnuclear reactions as a function of radial mass for different\nmodels. In general it can be recognized that small burning front\nvelocities lead to steep $Y_e$-gradient which flatten with increasing\nvelocities (see the series of models CS15, CS30, and CS50 or WS15,\nWS30, and W7). Lower central ignition densities shift the curves up\n(C vs. W), but the gradient is the same for the same propagation\nspeed. This only changes when the $Y_e$ attained via electron captures\nduring explosive burning is smaller than for stable Fe-group\nnuclei. Then, $\\beta^-$-decay during the expansion to smaller\ntemperatures and densities will reverse this effect (see models WSL\nand WLAM discussed in more detail in the text).\n\\label{yemr}}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-865 76 -451 573]{yetime.epsi}\n\\vspace{1cm}\n\\caption{\n$Y_e(t)$ for the central mass zones in CS, WS, WSL, WSLAM and W7 \nmodels. We see that $Y_e$ attains the lowest values for the highest ignition\ndensities and slowest burning front speeds. This tendency continues for the\nextreme cases of laminar burning front models, but the slow expansion in\nthese models permits fast $\\beta^-$-decays of short-lived nuclei in\nNSE or QSE equilibria before charged-particle freeze-out.\n\\label{yetim}}\n\\end{figure}\n\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-900 40 -495 614]{trholam.epsi}\n\\caption{\n$\\rho(t)$ and $T(t)$ for the central mass zones in WSL and WSLAM\nmodels. The bifurctaion between WSL and WLAM marks the point where the\nburning front was accelerated beyond the laminar speed in WSL,\nresulting in a faster expansion.\n\\label{rttim}}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-900 86 -495 583]{xics15_central.epsi}\n\\end{figure}\n\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-900 81 -495 614]{xiws15_central.epsi}\n\\vspace{1cm}\n\\caption{ Abundance plots (mostly of Fe-group nuclei) for the cases\nCS15 and WS15. Shown are the locations of the nuclei overproduced in\nW7, $^{54}$Fe and $^{58}$Ni, corresponding to $Y_e$ values of\n0.47-0.485. Due to the $Y_e$-gradients which are steeper than for W7,\nthe amount of matter in a given $Y_e$-range is reduced, but also\nsmaller central values are attained, giving rise to more neutron-rich\nnuclei. A $Y_e$ of about 0.46$\\approx$26/56 (which was also attained\nin W7) causes no problems and leads to a large abundance of stable\n$^{56}$Fe (not from $^{56}$Ni decay). Values in the range of 0.44 to\n0.46 result also in $^{50}$Ti, $^{54}$Cr, $^{58}$Fe, and $^{62,64}$Ni. \n$^{48}$Ca with Z/A$\\approx$0.42 is only produced if $Y_e$ approaches\nvalues smaller than 0.44 (see Hartmann et al. 1985). \\label{xi15c}\n}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-900 86 -495 583]{xics30_central.epsi}\n\\end{figure}\n\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-900 81 -495 614]{xiws30_central.epsi}\n\\vspace{1cm}\n\\caption{ Abundance plots (mostly of Fe-group nuclei) for the cases\nSame as \\ref{xi15c} for the\ncases CS30 and WS30. \\label{xi30c}}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-900 86 -495 583]{xics50_central.epsi}\n\\end{figure}\n\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-900 81 -495 614]{xiw7_central.epsi}\n\\vspace{1cm}\n\\caption{ \nSame as \\ref{xi15c} for the cases CS50 and W7. \nOne sees that the low $Y_e$ region becomes more extended with increasing\nburning front velocities, while the central values increase somewhat.\n$^{55}$Co and $^{52}$Fe are not plotted here for W7 but are are\nshown in Figure \\ref{w7full}.\n\\label{xiw7c}} \n\\end{figure}\n\n\\newpage\n\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-900 86 -495 583]{xiwsl_central.epsi}\n\\end{figure}\n\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=6cm\n\\epsfbox[-900 81 -495 614]{xiwlam_central.epsi}\n\\vspace{1cm}\n\\caption{ \nSame as \\ref{xi15c} for the\ncases WSL and WLAM. WLAM has an almost constant $Y_e$(\\mr) with values\nclose to those of WSL at 0.05 M$_\\odot$ (see also Figure\n\\ref{yemr}). \\label{xiwslc}}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}[ht]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-950 -100 -472 520]{ysolw7.epsi}\n\\vspace{-1.5cm}\n\\caption{ \nRatio of abundances to solar predicted in model W7 (this\nis a recalculation of the 1986 model [Thielemann, Nomoto \\& Yokoi\n1986] with presently available updated reaction rates and a screened\nNSE treatment for temperatures beyond $6\\times 10^9$K, as described in\nHix \\& Thielemann 1996). Isotopes of one element are connected by\nlines. The ordinate is normalized to $^{56}$Fe. Intermediate mass\nelements exist, but are underproduced by a factor of 2-3 in comparison\nto Fe-group elements. Among the Fe-group, $^{54}$Cr and $^{58}$Ni are\noverproduced by a factor of 4, which exceeds the permitted factor of\n\\(\\sim 3\\).\\label{w7sol}}\n\\end{figure}\n\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-950 -100 -472 520]{ysolw70.epsi}\n\\vspace{-2cm}\n\\caption{Same as Figure \\ref{w7sol}, i.e. a deflagration model\ntreated exactly like W7, but with an initial composition corresponding\nto zero metallicity (50\\% mass fractions of $^{12}$C and $^{16}$O\nwithout $^{22}$Ne admixture, i.e. $Y_e$=0.5). The production of\nneutron-rich species $^{54}$Fe, $^{58}$Ni, and $^{62}$Ni are smaller\nthan the original W7 model. Noticeable is also the almost complete\nabsence of intermediate odd-Z elements which are produced in explosive\noxygen burning for a $Y_e$ smaller than 0.5. The even-Z intermediate\nmass elements are also effected. They are not set off by a constant\nfactor in comparison to $^{56}$Fe, as seen in Figure \\ref{w7sol} for\nW7, but increase with mass. The increasing deviation between $N=Z$ and\na line in the nuclear chart with $Y_e$$<$0.5, with increasing nuclear\nmass, does not occur. \\label{w70sol}}\n\\end{figure}\n\n\\newpage\n\n% Figure 14: XIW7_FULL.PS and XIW70_FULL.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{xiw7_full.epsi}\n\\vspace{1.5cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{xiw70_full.epsi}\n\\vspace{1.5cm}\n\\caption{Composition of W7 and W70. The major changes are given in the mass\nzones outside the central 0.3\\ms, where $Y_e$ is enherited from the initial\nmetallicity in form of $^{22}$Ne and not due to electron captures.\nThis has effects on the Fe-group composition in the alpha-rich freeze-out\nregion (on $^{58,57}$Ni and $^{52}$Fe, the latter two decaying to \n$^{57}$Fe and $^{52}$Cr) and the incomplete Si-burning region\n($^{58,57}$Ni, $^{55}$Co, and $^{54,52}$Fe, the unstable species decaying\nto $^{57}$Fe, $^{55}$Mn, and $^{52}$Cr). \n$^{58,57}$Ni, $^{55}$Co, and $^{54}$Fe decrease below the plot limits\nin the incomplete burning region while $^{52}$Fe (N=Z) increases.\n\\label{w7full}}\n\\end{figure}\n\n\\newpage\n\n% Figure 15: YSOLCS15W7.PS and YSOLWS15W7.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolcs15w7.epsi}\n\\vspace{2cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolws15w7.epsi}\n\\vspace{2cm}\n\\caption{Comparison to solar for SN Ia compositions which are made up of\nthe slow deflagrations CS15 and WS15 in the central layers and a W7\ncomposition in the outer layers. This is mainly a test for the\nFe-group composition, especially $^{50}$Ti, $^{54}$Cr, $^{58}$Fe,\nand $^{64}$Ni. \\label{s15solw7}}\n\\end{figure}\n\n\\newpage\n\n% Figure 16: YSOLCS30W7.PS and YSOLWS30W7.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolcs30w7.epsi}\n\\vspace{2cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolws30w7.epsi}\n\\vspace{2cm}\n\\caption{Comparison to solar for a SN Ia composition made up from\nCS30 and WS30 in the central layers and W7 in the outer layers. \nThe neutron-rich species decline in comparison with CS15 and WS15.\n\\label{s30solw7}}\n\\end{figure}\n\n\\newpage\n\n% Figure 17: YSOLCS50W7.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\vspace{3cm}\n\\epsfbox[-900 320 -512 770]{ysolcs50w7.epsi}\n\\vspace{6cm}\n\\caption{Comparison to solar for CS50 with a W7 composition in\nthe outer layers. A further decrease of (very) neutron-rich species is visible,\nbut $^{54}$Fe and $^{58}$Ni, originating from intermediate $Y_e$ regions,\nincrease to excessive values due to the flatter $Y_e$-gradient of faster\ndeflagrations (see Figure \\ref{yemr}).\n\\label{s50solw7}}\n\\end{figure}\n\n\\newpage\n\n% Figure 18: YSOLWSLW7.PS and YSOLWLAMW7.PS \n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolwslw7.epsi}\n\\vspace{2cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolwlamw7.epsi}\n\\vspace{2cm}\n\\caption{Comparison to solar for WSL and WLAM with a W7 composition in\nthe outer layers. Excessive ratios for neutron-rich species are observed\ndue to extended low $Y_e$-regions out to 0.06 M$_\\odot$ (see Figure\n\\ref{yemr}).\n\\label{slsolw7}}\n\\end{figure}\n\n\\newpage\n\n% Figure 19: XIWS15DD1_FULL.PS and XIWS15DD2_FULL.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{xiws15dd1_full.epsi}\n\\vspace{2cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{xiws15dd2_full.epsi}\n\\vspace{2cm}\n\\caption{Composition of WS15DD1 and WS15DD2 against the expansion\nvelocity and $M(r)$. \\label{wdd12}}\n\\end{figure}\n\n\\newpage\n\n% Figure 20: XIWS15DD3_FULL.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\vspace{3cm}\n\\epsfbox[-900 320 -512 770]{xiws15dd3_full.epsi}\n\\vspace{6cm}\n\\caption{Composition of WS15DD3.\nIn the series DD1-DD3 we\nsee a decrease in the total amount of intermediate mass elements (Si-Ca), an\nincrease in $^{56}$Ni, and a change of the ratio between matter experiencing\nan alpha-rich freeze-out (indicated by the $^{58}$Ni-plateau) and\nincomplete Si-burning ($^{54}$Fe-plateau). \n \\label{wdd13}}\n\n\\end{figure}\n\n\\newpage\n\n% Figure 21: XICS15DD1_FULL.PS and XICS15DD2_FULL.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{xics15dd1_full.epsi}\n\\vspace{2cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{xics15dd2_full.epsi}\n\\vspace{2cm}\n\\caption{Composition of CS15DD1 and CS15DD2. \nThe outer layers affected by the detonation behave almost identical to the\nWSDD series.\n \\label{cdd12}}\n\\end{figure}\n\n\\newpage\n\n% Figure 22: YSOLCS15DD1_NEU.PS and YSOLCS15DD2_NEU.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolcs15dd1.epsi}\n\\vspace{2cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolcs15dd2.epsi}\n\\vspace{2cm}\n\\caption{Comparison to solar for CS15DD1 and CS15DD2. A decrease\nof the Si-Ca/Fe ratio is observable, a decrease of e.g. $^{55}$Mn and\n$^{52}$Cr (dominated by incomplete Si-burning), and an increase of\n$^{62}$Ni (decaying from $^{62}$Zn) and $^{59}$Co (alpha-rich\nfreeze-out). \n\\label{csdsol}}\n\n\\end{figure}\n\n\\newpage\n\n% Figure 23: YSOLWS15DD1_NEU.PS and YSOLWS15DD2_NEU.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolws15dd1.epsi}\n\\vspace{2cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsfbox[-900 120 -512 570]{ysolws15dd2.epsi}\n\\vspace{2cm}\n\\caption{Comparison to solar for WS15DD1 and WS15DD2. \\label{wsdsol}}\n\n\\end{figure}\n\n\\newpage\n\n% Figure 24: YSOLWS15DD3_NEU.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\vspace{3cm}\n\\epsfbox[-900 320 -512 770]{ysolws15dd3.ps}\n\\vspace{6cm}\n\\caption{Comparison to solar for WS15DD3. In this series DD1-DD3\nwe see similar changes as shown in Figure \\ref{csdsol}. Differences in\nthe neutron-rich species $^{50}$Ti, $^{54}$Cr, $^{58}$Fe, and\n$^{62}$Ni are due to the differences between the W and C series in the\ncentral slow deflagration layers (higher ignition densities).\n\\label{wsd3sol}}\n\\end{figure}\n\n\\newpage\n\n% Figure 25: XIVELCDD1.PS XIVELCDD2.PS XIVELCDD3.PS\n\\begin{figure}[hb]\n\\epsfxsize=7cm\n\\epsfysize=5cm\n\\vspace*{-3cm}\n\\epsfbox[-1000 120 -502 770]{xivelcdd1.ps}\n\\epsfxsize=7cm\n\\epsfysize=5cm\n\\vspace{-2cm}\n\\epsfbox[-1000 120 -502 770]{xivelcdd2.ps}\n\\epsfxsize=7cm\n\\epsfysize=5cm\n\\vspace{-2cm}\n\\epsfbox[-1000 120 -502 770]{xivelcdd3.ps}\n\\vspace{0.5cm}\n\\caption{Mass fractions in the models CS15DD1-DD3 as a function of expansion\nvelocity, which reveals more easily the outer layers affected by the\ndeflagration-detonation transition and the quenching of nuclear\nburning up to unburned matter in the very outer layers. Intermediate\nmass elements beyond Mg are essentially unburned for velocities larger\nthan 20000-30000 km s$^{-1}$ and would be found in their solar values\nscaled with the appropriate metallcity. The initial composition of the\nwhite dwarf for the present calculation consists only of $^{12}$C,\n$^{16}$O, and $^{22}$Ne (according to the CNO metallicity of the\naccreted matter).\n\\label{xivel}}\n\n\\end{figure}\n\n\\newpage\n\n\n%\\begin{table}\n\\begin{table}\n\\centerline{Table 1: Masses of $^{56}$Ni in SN Ia Models Investigated}\n\\vskip 0.2cm\n\\label{tabdd}\n\\begin{center}\n\\begin{tabular}{crrrr}\n\\hline\nModel & Mass & Energy & $^{56}$Ni Mass \\\\\n\\hline\nW7 & 1.38 \\ms\\ & 1.3\\afoe & 0.59 \\ms\\ \\\\\nW70 & 1.38 \\ms\\ & 1.3\\afoe & 0.64 \\ms\\ \\\\\nWS15DD1 & 1.38 \\ms\\ & 1.33\\afoe & 0.56 \\ms\\ \\\\\nWS15DD2 & 1.38 \\ms\\ & 1.40\\afoe & 0.69 \\ms\\ \\\\\nWS15DD3 & 1.38 \\ms\\ & 1.43\\afoe & 0.77 \\ms\\ \\\\\nCS15DD1 & 1.38 \\ms\\ & 1.34\\afoe & 0.56 \\ms\\ \\\\\nCS15DD2 & 1.38 \\ms\\ & 1.44\\afoe & 0.74 \\ms\\ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\n%\\begin{table}[h]\n\\begin{table}\n\\centerline{Table 2: Nucleosynthesis of Neutron-rich Species ($X_i/X(^{56}$Fe)/Solar Ratio)}\n\\vskip 0.2cm\n\\label{tabsd}\n\\begin{center}\n\\begin{tabular}{crrrrrrrrrr}\n\\hline\nModel & $\\rho_9$ & $v_{\\rm def}$/$v_{\\rm s}$ & $Y_{\\rm e,c}$\n& $^{50}$Ti & $^{54}$Cr & $^{58}$Fe & $^{64}$Ni & $^{62}$Ni & \n$^{54}$Fe & $^{58}$Ni \\\\\n\\noalign{\\hrule}\nWSL & 2.12 & $\\sim$0.01 & 0.442 & 39 & 74 & 15 & 7 & 5 & 1.2 & 2.1 \\\\\nWLAM & 2.12 & $\\sim$0.01 & 0.447 & 22 & 47 & 9 & 1.6 & 5 & 1.8 & 3.8 \\\\\nWS15W7 & 2.12 & 0.015 & 0.440 & 4 & 7 & 1.7 & 0.7 & 2.1 & 1.3 & 2.7 \\\\\nWS15DD1 & 2.12 & 0.015 & 0.440 & 4 & 7 & 1.8 & 0.7 & 1.1 & 1.9 & 1.3 \\\\ \nWS15DD2 & 2.12 & 0.015 & 0.440 & 3.1 & 6 & 1.5 & 0.6 & 2.4 & 1.3 & 1.5 \\\\\nWS15DD3 & 2.12 & 0.015 & 0.440 & 2.8 & 5 & 1.3 & 0.5 & 3.2 & 1.0 & 1.5 \\\\\nWS30W7 & 2.12 & 0.03 & 0.445 & 1.3 & 4 & 1.5 & 0.1 & 2.5 & 1.3 & 2.6 \\\\\nCS15W7 & 1.37 & 0.015 & 0.449 & 0.5 & 2 & 0.9 & 0.01 & 1.9 & 1.3 & 2.7 \\\\\nCS15DD1 & 1.37 & 0.015 & 0.449 & 0.2 & 1.1 & 0.5 & 0.01 & 0.5 & 2.0 & 1.4 \\\\\nCS15DD2 & 1.37 & 0.015 & 0.449 & 0.6 & 2.7 & 1.3 & 0.01 & 2.8 & 1.2 & 1.4 \\\\\nCS30W7 & 1.37 & 0.03 & 0.455 & 0.07 & 0.5 & 0.3 & 0.002 & 2.0 & 1.4 & 2.7 \\\\\nCS50W7 & 1.37 & 0.05 & 0.459 & 0.003 & 0.04 & 0.04 & 0.0004 & 1.8 & 1.8 & 3.2 \\\\\nW7 & 2.12 & up to 0.3 & 0.446 & 1.1 & 3.8 & 1.6 & 0.05 & 2.3 & 2.4 & 4.3 \\\\\nW70 & 2.12 & up to 0.3 & 0.446 & 0.97 & 3.4 & 1.4 & 0.04 & 1.3 & 1.7 & 3.0 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n%\\small \n%\\begin{table}[t]\n\\begin{table}\n\\centerline{Table 3: Nucleosynthesis products of SN II and Ia models\n}\n\\vskip 0.2cm\n\\label{tabmas}\n\\begin{center}\n\\begin{tabular}{lcccccccc}\n\\hline \\hline\n& \\multicolumn{7}{c}{Synthesized mass (M$_\\odot$)} \\\\\n\\cline{2-9} \n& \\multicolumn{1}{c}{Type II} & \\multicolumn{7}{c}{Type Ia} \\\\\nSpecies & 10$-$50M$_\\odot$ & W7 & W70 & WDD1 & WDD2 & WDD3 & CDD1 & CDD2 \\\\\n\\hline \n%\n%\n$^{12}$C & 7.93E-02 & 4.83E-02 & 5.08E-02 & 5.42E-03 & 8.99E-03 & 1.66E-02 & 9.93E-03 & 5.08E-03 \\\\\n$^{13}$C & 3.80E-09 & 1.40E-06 & 1.56E-09 & 5.06E-07 & 3.30E-07 & 3.17E-07 & 8.46E-07 & 4.16E-07 \\\\\n$^{14}$N & 1.56E-03 & 1.16E-06 & 3.31E-08 & 2.84E-04 & 2.69E-04 & 1.82E-04 & 9.06E-05 & 9.03E-05 \\\\\n$^{15}$N & 1.66E-08 & 1.32E-09 & 4.13E-07 & 9.99E-07 & 5.32E-07 & 1.21E-07 & 2.53E-07 & 2.47E-07 \\\\\n$^{16}$O & 1.80 & 1.43E-01 & 1.33E-01 & 8.82E-02 & 6.58E-02 & 5.58E-02 & 9.34E-02 & 5.83E-02 \\\\\n$^{17}$O & 9.88E-08 & 3.54E-08 & 3.33E-10 & 3.77E-06 & 4.58E-06 & 3.60E-06 & 9.55E-07 & 1.01E-06 \\\\\n$^{18}$O & 4.61E-03 & 8.25E-10 & 2.69E-10 & 6.88E-07 & 6.35E-07 & 2.39E-07 & 2.08E-07 & 1.92E-07 \\\\\n$^{19}$F & 1.16E-09 & 5.67E-10 & 1.37E-10 & 1.70E-09 & 4.50E-10 & 2.30E-10 & 5.83E-10 & 4.24E-10 \\\\\n$^{20}$Ne & 2.12E-01 & 2.02E-03 & 2.29E-03 & 1.29E-03 & 6.22E-04 & 4.55E-04 & 1.16E-03 & 6.05E-04 \\\\\n$^{21}$Ne & 1.08E-03 & 8.46E-06 & 2.81E-08 & 1.16E-05 & 1.39E-06 & 1.72E-06 & 3.63E-06 & 1.99E-06 \\\\\n$^{22}$Ne & 1.83E-02 & 2.49E-03 & 2.15E-08 & 1.51E-04 & 4.21E-04 & 8.25E-04 & 4.41E-04 & 2.11E-04 \\\\\n$^{23}$Na & 6.51E-03 & 6.32E-05 & 1.41E-05 & 8.77E-05 & 2.61E-05 & 3.01E-05 & 5.10E-05 & 3.50E-05 \\\\\n$^{24}$Mg & 8.83E-02 & 8.50E-03 & 1.58E-02 & 7.55E-03 & 4.47E-03 & 2.62E-03 & 7.72E-03 & 4.20E-03 \\\\\n$^{25}$Mg & 1.44E-02 & 4.05E-05 & 1.64E-07 & 8.23E-05 & 2.66E-05 & 2.68E-05 & 4.85E-05 & 3.25E-05 \\\\\n$^{26}$Mg & 2.01E-02 & 3.18E-05 & 1.87E-07 & 6.25E-05 & 2.59E-05 & 1.41E-05 & 4.96E-05 & 2.97E-05 \\\\\n$^{27}$Al & 1.48E-02 & 9.86E-04 & 1.13E-04 & 4.38E-04 & 2.47E-04 & 1.41E-04 & 4.45E-04 & 2.35E-04 \\\\\n$^{28}$Si & 1.05E-01 & 1.54E-01 & 1.42E-01 & 2.72E-01 & 2.06E-01 & 1.58E-01 & 2.77E-01 & 1.98E-01 \\\\\n$^{29}$Si & 8.99E-03 & 9.08E-04 & 5.79E-05 & 5.47E-04 & 3.40E-04 & 2.13E-04 & 5.52E-04 & 3.22E-04 \\\\\n$^{30}$Si & 8.05E-03 & 1.69E-03 & 7.12E-05 & 1.03E-03 & 6.41E-04 & 3.88E-04 & 1.05E-03 & 6.14E-04 \\\\\n$^{31}$P & 1.21E-03 & 3.57E-04 & 9.12E-05 & 2.38E-04 & 1.60E-04 & 1.07E-04 & 2.40E-04 & 1.52E-04 \\\\\n$^{32}$S & 3.84E-02 & 8.46E-02 & 9.14E-02 & 1.60E-01 & 1.22E-01 & 9.37E-02 & 1.63E-01 & 1.17E-01 \\\\\n$^{33}$S & 1.78E-04 & 4.24E-04 & 6.07E-05 & 2.74E-04 & 1.92E-04 & 1.34E-04 & 2.71E-04 & 1.79E-04 \\\\\n$^{34}$S & 2.62E-03 & 1.98E-03 & 1.74E-05 & 2.76E-03 & 2.04E-03 & 1.46E-03 & 2.77E-03 & 1.90E-03 \\\\\n$^{36}$S & 1.78E-06 & 4.18E-07 & 3.41E-11 & 2.23E-07 & 1.31E-07 & 7.44E-08 & 2.22E-07 & 1.25E-07 \\\\\n$^{35}$Cl & 1.01E-04 & 1.37E-04 & 1.06E-05 & 9.28E-05 & 7.07E-05 & 5.33E-05 & 9.03E-05 & 6.56E-05 \\\\\n$^{37}$Cl & 1.88E-05 & 3.67E-05 & 5.56E-06 & 2.94E-05 & 2.26E-05 & 1.71E-05 & 2.86E-05 & 2.11E-05 \\\\\n$^{36}$Ar & 6.62E-03 & 1.47E-02 & 1.91E-02 & 3.11E-02 & 2.41E-02 & 1.87E-02 & 3.18E-02 & 2.34E-02 \\\\\n$^{38}$Ar & 1.37E-03 & 9.50E-04 & 6.60E-07 & 1.23E-03 & 9.90E-04 & 7.44E-04 & 1.20E-03 & 9.26E-04 \\\\\n$^{40}$Ar & 2.27E-08 & 1.87E-08 & 3.42E-12 & 7.81E-09 & 5.19E-09 & 3.56E-09 & 7.56E-09 & 4.82E-09 \\\\\n%\n%\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\newpage\n\n%\\begin{table}[p]\n\\begin{table}\n\\centerline{Continued form TABLE 3.}\n\\vskip 0.2cm\n\\begin{center}\n\\begin{tabular}{lcccccccc}\n\\hline \\hline\n& \\multicolumn{7}{c}{Synthesized mass (M$_\\odot$)} \\\\\n\\cline{2-9} \n& \\multicolumn{1}{c}{Type II} & \\multicolumn{7}{c}{Type Ia} \\\\\nSpecies & 10$-$50M$_\\odot$ & W7 & W70 & WDD1 & WDD2 & WDD3 & CDD1 & CDD2 \\\\\n\\hline \n%\n%\n$^{39}$K & 6.23E-05 & 7.23E-05 & 1.67E-06 & 6.76E-05 & 5.67E-05 & 4.52E-05 & 6.39E-05 & 5.34E-05 \\\\\n$^{41}$K & 5.07E-06 & 6.11E-06 & 4.83E-07 & 5.43E-06 & 4.52E-06 & 3.62E-06 & 5.20E-06 & 4.25E-06 \\\\\n$^{40}$Ca & 5.77E-03 & 1.19E-02 & 1.81E-02 & 3.10E-02 & 2.43E-02 & 1.88E-02 & 3.18E-02 & 2.38E-02 \\\\\n$^{42}$Ca & 4.23E-05 & 2.82E-05 & 1.06E-08 & 3.09E-05 & 2.55E-05 & 1.93E-05 & 2.97E-05 & 2.36E-05 \\\\\n$^{43}$Ca & 1.08E-06 & 9.64E-08 & 6.17E-08 & 6.60E-08 & 2.22E-07 & 4.18E-07 & 5.15E-08 & 2.96E-07 \\\\\n$^{44}$Ca & 5.53E-05 & 8.02E-06 & 1.38E-05 & 1.44E-05 & 2.95E-05 & 4.66E-05 & 1.37E-05 & 3.62E-05 \\\\\n$^{46}$Ca & 1.43E-10 & 4.16E-09 & 1.01E-09 & 5.01E-09 & 4.73E-09 & 4.47E-09 & 8.79E-10 & 1.18E-09 \\\\\n$^{48}$Ca & 5.33E-14 & 2.60E-09 & 2.47E-09 & 1.63E-06 & 1.64E-06 & 1.55E-06 & 3.54E-11 & 4.93E-10 \\\\\n$^{45}$Sc & 2.29E-07 & 2.21E-07 & 3.85E-08 & 2.49E-07 & 2.09E-07 & 1.76E-07 & 2.47E-07 & 2.02E-07 \\\\\n$^{46}$Ti & 7.48E-06 & 1.33E-05 & 3.49E-07 & 1.34E-05 & 1.12E-05 & 8.58E-06 & 1.27E-05 & 1.05E-05 \\\\\n$^{47}$Ti & 2.11E-06 & 5.10E-07 & 4.08E-07 & 5.65E-07 & 1.56E-06 & 2.57E-06 & 4.93E-07 & 1.95E-06 \\\\\n$^{48}$Ti & 1.16E-04 & 2.05E-04 & 3.13E-04 & 7.10E-04 & 6.11E-04 & 5.23E-04 & 7.32E-04 & 6.20E-04 \\\\\n$^{49}$Ti & 5.98E-06 & 1.71E-05 & 2.94E-06 & 5.27E-05 & 4.39E-05 & 3.59E-05 & 5.22E-05 & 4.17E-05 \\\\\n$^{50}$Ti & 3.81E-10 & 1.07E-04 & 1.04E-04 & 3.52E-04 & 3.51E-04 & 3.51E-04 & 2.08E-05 & 7.28E-05 \\\\\n$^{50}$V & 7.25E-10 & 1.55E-08 & 1.22E-08 & 9.74E-09 & 9.33E-09 & 9.07E-09 & 4.94E-09 & 1.20E-08 \\\\\n$^{51}$V & 1.00E-05 & 7.49E-05 & 4.27E-05 & 1.33E-04 & 1.16E-04 & 1.02E-04 & 1.11E-04 & 1.09E-04 \\\\\n$^{50}$Cr & 4.64E-05 & 2.73E-04 & 6.65E-05 & 4.44E-04 & 3.53E-04 & 2.84E-04 & 4.49E-04 & 3.36E-04 \\\\\n$^{52}$Cr & 1.15E-03 & 6.36E-03 & 7.73E-03 & 1.68E-02 & 1.37E-02 & 1.13E-02 & 1.65E-02 & 1.40E-02 \\\\\n$^{53}$Cr & 1.19E-04 & 9.22E-04 & 5.66E-04 & 1.66E-03 & 1.38E-03 & 1.17E-03 & 1.59E-03 & 1.33E-03 \\\\\n$^{54}$Cr & 2.33E-08 & 9.24E-04 & 9.04E-04 & 1.60E-03 & 1.60E-03 & 1.60E-03 & 2.31E-04 & 8.02E-04 \\\\\n$^{55}$Mn & 3.86E-04 & 8.87E-03 & 6.66E-03 & 8.48E-03 & 7.05E-03 & 6.16E-03 & 8.10E-03 & 6.77E-03 \\\\\n$^{54}$Fe & 3.62E-03 & 9.55E-02 & 7.30E-02 & 7.08E-02 & 5.91E-02 & 5.15E-02 & 7.20E-02 & 5.64E-02 \\\\\n$^{56}$Fe & 8.44E-02 & 6.26E-01 & 6.80E-01 & 5.87E-01 & 7.13E-01 & 7.95E-01 & 5.65E-01 & 7.57E-01 \\\\\n$^{57}$Fe & 2.72E-03 & 2.45E-02 & 1.92E-02 & 1.08E-02 & 1.67E-02 & 2.06E-02 & 1.01E-02 & 1.80E-02 \\\\\n$^{58}$Fe & 7.22E-09 & 3.03E-03 & 2.96E-03 & 3.23E-03 & 3.23E-03 & 3.24E-03 & 8.63E-04 & 3.06E-03 \\\\\n$^{59}$Co & 7.27E-05 & 1.04E-03 & 9.68E-04 & 3.95E-04 & 6.25E-04 & 7.75E-04 & 2.91E-04 & 6.35E-04 \\\\\n$^{58}$Ni & 3.63E-03 & 1.10E-01 & 8.34E-02 & 3.14E-02 & 4.29E-02 & 4.97E-02 & 3.15E-02 & 4.47E-02 \\\\\n$^{60}$Ni & 1.75E-03 & 1.24E-02 & 1.47E-02 & 5.08E-03 & 1.15E-02 & 1.67E-02 & 2.81E-03 & 1.21E-02 \\\\\n$^{61}$Ni & 8.35E-05 & 2.35E-04 & 2.15E-04 & 7.00E-05 & 3.58E-04 & 5.92E-04 & 4.00E-05 & 4.27E-04 \\\\\n%\n%\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\newpage\n\n%\\begin{table}[p]\n\\begin{table}\n\\centerline{Continued form TABLE 3.}\n\\vskip 0.2cm\n\\begin{center}\n\\begin{tabular}{lcccccccc}\n\\hline \\hline\n& \\multicolumn{7}{c}{Synthesized mass (M$_\\odot$)} \\\\\n\\cline{2-9} \n& \\multicolumn{1}{c}{Type II} & \\multicolumn{7}{c}{Type Ia} \\\\\nSpecies & 10$-$50M$_\\odot$ & W7 & W70 & WDD1 & WDD2 & WDD3 & CDD1 & CDD2 \\\\\n\\hline \n%\n$^{62}$Ni & 5.09E-04 & 3.07E-03 & 1.85E-03 & 1.37E-03 & 3.69E-03 & 5.46E-03 & 6.51E-04 & 4.60E-03 \\\\\n$^{64}$Ni & 3.20E-14 & 1.70E-05 & 1.65E-05 & 2.32E-04 & 2.31E-04 & 2.32E-04 & 2.47E-06 & 9.29E-06 \\\\\n$^{63}$Cu & 8.37E-07 & 2.32E-06 & 3.00E-06 & 2.77E-06 & 4.88E-06 & 5.92E-06 & 6.14E-07 & 3.97E-06 \\\\\n$^{65}$Cu & 4.07E-07 & 6.84E-07 & 8.33E-07 & 7.08E-07 & 2.04E-06 & 3.38E-06 & 1.14E-07 & 2.05E-06 \\\\\n$^{64}$Zn & 1.03E-05 & 1.06E-05 & 7.01E-05 & 3.71E-06 & 3.10E-05 & 5.76E-05 & 1.87E-06 & 3.96E-05 \\\\\n$^{66}$Zn & 8.61E-06 & 1.76E-05 & 6.26E-06 & 2.16E-05 & 6.42E-05 & 1.04E-04 & 2.84E-06 & 6.11E-05 \\\\\n$^{67}$Zn & 1.52E-08 & 1.58E-08 & 7.28E-09 & 6.35E-07 & 6.55E-07 & 6.27E-07 & 1.69E-09 & 4.01E-08 \\\\\n$^{68}$Zn & 3.92E-09 & 1.74E-08 & 1.13E-08 & 7.44E-08 & 8.81E-08 & 9.42E-08 & 3.08E-09 & 3.03E-08 \\\\\n%\n%\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n%\\begin{table}[p]\n\\begin{table}\n\\centerline{Table 4: Major Radioactive Species in SN Ia Models}\n\\vskip 0.2cm\n\\begin{center}\n\\begin{tabular}{lccccccc}\n\\hline \\hline\n& \\multicolumn{7}{c}{Synthesized mass (M$_\\odot$)} \\\\\n\\cline{2-8} \n& \\multicolumn{7}{c}{Type Ia} \\\\\nSpecies & W7 & W70 & WDD1 & WDD2 & WDD3 & CDD1 & CDD2 \\\\\n\\hline \n%\n%\n$^{22}$Na & 1.73E-08 & 1.08E-08 & 2.66E-08 & 1.33E-08 & 3.04E-08 & 1.68E-08 & 9.\n64E-09\\\\\n$^{26}$Al & 4.93E-07 & 2.92E-08 & 4.61E-07 & 1.88E-07 & 1.64E-07 & 3.81E-07 & 2.32E-07\\\\\n$^{36}$Cl & 2.58E-06 & 3.97E-10 & 1.25E-06 & 7.85E-07 & 4.89E-07 & 1.23E-06 & 7.35E-07\\\\\n$^{39}$Ar & 1.20E-08 & 2.00E-13 & 6.04E-09 & 4.44E-09 & 3.29E-09 & 5.99E-09 & 4.12E-09\\\\\n$^{40}$K & 8.44E-08 & 5.46E-12 & 3.29E-08 & 2.35E-08 & 1.73E-08 & 3.13E-08 & 2.15E-08\\\\\n$^{41}$Ca & 6.09E-06 & 4.83E-07 & 5.42E-06 & 4.52E-06 & 3.62E-06 & 5.20E-06 & 4.25E-06\\\\\n$^{44}$Ti & 7.94E-06 & 1.38E-05 & 1.44E-05 & 2.95E-05 & 4.65E-05 & 1.36E-05 & 3.62E-05\\\\\n$^{48}$V & 4.95E-08 & 1.61E-08 & 6.52E-08 & 5.38E-08 & 4.11E-08 & 6.33E-08 & 5.03E-08\\\\\n$^{49}$V & 1.52E-07 & 3.23E-08 & 1.18E-07 & 1.03E-07 & 8.63E-08 & 9.99E-08 & 8.88E-08\\\\\n$^{53}$Mn & 2.77E-04 & 2.48E-04 & 1.58E-04 & 1.54E-04 & 1.50E-04 & 8.47E-05 & 9.69E-05\\\\\n$^{60}$Fe & 7.52E-07 & 7.19E-07 & 7.33E-05 & 7.33E-05 & 7.36E-05 & 6.23E-08 & 2.74E-07\\\\\n$^{56}$Co & 1.44E-04 & 1.26E-04 & 6.04E-05 & 5.51E-05 & 5.20E-05 & 6.18E-05 & 5.24E-05\\\\\n$^{57}$Co & 1.48E-03 & 1.42E-03 & 6.43E-04 & 6.42E-04 & 6.36E-04 & 4.50E-04 & 4.47E-04\\\\\n$^{60}$Co & 4.22E-07 & 4.13E-07 & 3.76E-07 & 3.81E-07 & 3.78E-07 & 1.09E-07 & 4.23E-07\\\\\n$^{56}$Ni & 5.86E-01 & 6.41E-01 & 5.64E-01 & 6.90E-01 & 7.73E-01 & 5.55E-01 & 7.37E-01\\\\\n$^{57}$Ni & 2.27E-02 & 1.75E-02 & 9.95E-03 & 1.59E-02 & 1.98E-02 & 9.57E-03 & 1.74E-02\\\\\n$^{59}$Ni & 6.71E-04 & 6.39E-04 & 2.54E-04 & 2.53E-04 & 2.51E-04 & 2.03E-04 & 1.90E-04\\\\\n$^{63}$Ni & 8.00E-07 & 7.81E-07 & 1.69E-06 & 1.74E-06 & 1.73E-06 & 1.98E-07 & 8.31E-07\\\\\n%\n%\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\\newpage\n%\\begin{table}\n\\begin{table}\n\\centerline{Table 5: $N_{\\rm Ia}/N_{\\rm II}$ Ratios obtained for different Models of SN Ia}\n\\vskip 0.2cm\n\\label{tabIaII}\n\\begin{center}\n\\begin{tabular}{crrrrr}\n\\hline\n%\n%\nSN II Model & W7 & W70 & DD1 & DD2 & DD3 \\\\\n\\hline\n20~M$_\\odot$ & 0.214 & 0.176 & 1.08 & 0.187 & 0.146 \\\\\n10-50~M$_\\odot$ & 0.295 & 0.243 & 1.48 & 0.257 & 0.201 \\\\\n%\n%\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\end{document}\n\n\n\n\n"
}
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{
"name": "astro-ph0002337.extracted_bib",
"string": "\\begin{thebibliography}{widest citation in source list}\n\n\\bibitem[]{}Arnett, W.D. 1996, Nucleosynthesis and Supernovae\n(Princeton: Princeton Univ. Press)\n\n\\bibitem[]{}Arnett, W.D., \\& Livne, E. 1994a, ApJ, 427, 314\n\n\\bibitem[]{}Arnett, W.D., \\& Livne, E. 1994b, ApJ, 427, 330\n\n\\bibitem[]{} Aufderheide, M., Fushiki, I., Woosley, S.E., Hartmann, D. \n1994, ApJS, 91, 389\n\n\\bibitem[]{} Bao, Z.~Y., K\\\"appeler, F. 1987, At. Data Nucl. Data\nTables, 36, 411\n\n\\bibitem[]{}Barkat, Z., \\& Wheeler, J.C. 1990, ApJ, 355, 602\n\n\\bibitem[]{}Branch, D., 1998, ARA\\&A, 36, 17\n\n\\bibitem[]{}Branch, D., Doggett, J.B., Nomoto, K., \\& Thielemann,\nF.-K. 1985, ApJ, 294, 619\n\n\\bibitem[]{}Branch, D., Livio, M., Yungelson, L.R., Boffi, F.R., \\&\nBaron, E. 1995, PASP, 107, 717\n\n\\bibitem[]{} Branch, D., Tammann, G.A. 1992, ARA\\&A 30, 359\n\n\\bibitem[]{}Bravo, E., Isern, J., \\& Canal, R. 1993, A\\&A, 269, 187\n\n\\bibitem[]{} Bravo, E., Isern, J., Canal, R., \\& Labay, J. 1992, A\\&A,\n257, 534\n\n\\bibitem[]{}Bychkov, V.V., \\& Liberman, M.A., 1995a, ApJ, 451, 711\n\n\\bibitem[]{}Canal, R., Ruiz-Lapuente, P., \\& Isern, J. 1997, in\nThermonuclear Supernovae, ed. P. Ruiz-Lapuente, R. Canal, \\& J. Isern,\n(Dordrecht:Kluwer), 257\n\n\\bibitem[]{}Cappellaro, E., Turatto, M., Tsvvetkov, D.Yu., Bartunov,\nO.S., Pollas, C., Evans, R., \\& Hamuy, M. 1997, A\\&A, 322, 431\n\n\\bibitem[]{} Caughlan, G.R., \\& Fowler, W.A. 1988, At. Data Nucl. Data\nTables, 40, 283\n\n\\bibitem[]{} Caurier, E., Langanke, K., Martinez-Pinedo, G., Nowacki,\nF. 1999, Phys. Rev. C, submitted\n\n\\bibitem[]{} Dean, D.J., Langanke, K., Chatterjee, L., Radha, P.B., \\&\nStrayer, M.R. 1998, Phys. Rev. C, 58, 536\n\n\\bibitem[]{}Di Stefano, R., Nelson, L.A., Lee, W., Wood, H.,\n Rappaport, S. 1997, in Thermonuclear Supernovae,\n ed. P. Ruiz-Lapuente, R. Canal, \\& J. Isern, (Dordrecht:Kluwer), 147\n\n\\bibitem[]{}Fisher, A., Branch, D., H\\\"oflich, P., \\& Khokhlov,\nA. 1995, ApJ, 447, L73\n\n\\bibitem[]{} Fuller, G.M., Fowler, W.A., \\& Newman, M. 1980, ApJS, 42,\n 447\n\n\\bibitem[]{} Fuller, G.M., Fowler, W.A., \\& Newman, M. 1982, ApJS, 48,\n 279\n\n\\bibitem[]{} Fuller, G.M., Fowler, W.A., \\& Newman, M. 1985, ApJ, 293,\n 1\n\n\\bibitem[]{} Gratton, R.G. 1989, A\\&A, 208, 171\n\n\\bibitem[]{} Gratton, R.G., \\& Sneden, C. 1988, A\\&A, 204, 193\n\n\\bibitem[]{} Gratton, R.G., \\& Sneden, C. 1991, A\\&A, 241, 501\n\n\\bibitem[]{}Hachisu, I., Kato, M., \\& Nomoto, K. 1996, ApJ, 470, L97\n\n\\bibitem[]{}Hachisu, I., Kato, M., \\& Nomoto, K. 1999a, ApJ, 522, 487\n\n\\bibitem[]{}Hachisu, I., Kato, M., Nomoto, K., \\& Umeda, H. 1999b,\nApJ, 519, 314\n\n\\bibitem[]{}Hamuy, M., Phillips, M.M., Maza, J., Suntzeff, R.A., \\&\nAviles, R. 1995, AJ, 109, 1\n\n\\bibitem[]{}Harkness, R.P. 1991, in SN 1987A and Other Supernovae, ed. \nI.J., Danziger \\& K. Kj\\\"ar (Garching:ESO), 447\n\n\\bibitem[]{} Harper, C.L., Nyquist, L.H., Shih, C.-Y., Wiesmann,\nH. 1990, in Nuclei in the Cosmos, ed. H. Oberhummer, W. Hillebrandt\n(Garching, MPI f\\\"ur Physik und Astrophysik), MPA/P4, 138\n\n\\bibitem[]{} Hartmann, D., Woosley, S.E., \\& El Eid, M.F. 1985, ApJ,\n297, 837\n\n\\bibitem[]{}Hashimoto, M., Nomoto, K., \\& Thielemann, F.-K. 1989,\nA\\&A, 210, L5\n\n\\bibitem[]{}Hashimoto, M. 1995, Prog. Theor. Phys., 94, 663\n\n\\bibitem[]{}Hashimoto, M., Nomoto, K., Tsujimoto, T., \\& Thielemann,\nF.-K. 1996, in IAU Colloq. 145, Supernovae and Supernova Remnants, ed. \nR. McCray \\& Z. Wang (Cambridge:Cambridge University Press), 157\n \n\\bibitem[]{}Hatano, K., Branch, D., Fisher, A., Baron, E., \\&\nFilippenko, A.V. 1999, ApJ Lett., submitted\n\n\\bibitem[]{}Hillebrandt, W., \\& Niemeyer, J.C. 1997, in Thermonuclear\n Supernovae, ed. P. Ruiz-Lapuente, R. Canal, \\& J. Isern,\n (Dordrecht:Kluwer), 337\n\n\\bibitem[]{} Hix, W.R., \\& Thielemann F.-K. 1996, ApJ, 460, 869\n\n\\bibitem[]{} Hix, W.R., \\& Thielemann F.-K. 1999a, ApJ, 511, 862\n\n\\bibitem[]{} Hix, W.R., \\& Thielemann F.-K. 1999b, J. Climate\n Appl. Meteor., in press\n\n\\bibitem[]{}H\\\"oflich, P., Dominguez, I., Thielemann, F.-K., \\&\nWheeler, J.C. 1999, in Proc.\\ 42nd Int.\\ Astrophys.\\ Colloq.\\\n(ESA-SP-429;ESA:Noordwijk), 243\n \n\\bibitem[]{}H\\\"oflich, P., \\& Khokhlov, A. 1996, ApJ, 457, 500\n\n\\bibitem[]{}H\\\"oflich, P., Wheeler, J.C., \\& Thielemann, F.-K. 1998,\n ApJ, 495, 617\n\n\\bibitem[]{}Hughes, J.P., et al. 1995, ApJ, 444, L81\n\n\\bibitem[]{}Hwang, U., Hughes, J.P., \\& Petre, R. 1998, ApJ, 497, 833\n\n\\bibitem[]{}Iben, I.,Jr. 1982, ApJ, 253, 248\n\n\\bibitem[]{} Iben, I.,Jr., \\& Tutukov, A.V. 1984, ApJS, 54, 335\n\n\\bibitem[] {} Ichimaru, S. 1993, Rev. Mod. Phys., 65, 255\n\n\\bibitem[] {} Ireland, T.R. 1994, ApJ, 434, L79\n\n\\bibitem[]{}Jeffery, D., Leibundgut, B., Kirshner, R.P., Benetti, S.,\nBranch, D., \\& Sonneborn, G. 1992, ApJ, 397, 304\n\n\\bibitem[]{}Khokhlov, A.M. 1991a, A\\&A, 245, 114\n\n\\bibitem[]{}Khokhlov, A.M. 1991b, A\\&A, 245, L25\n\n\\bibitem[]{}Khokhlov, A.M. 1995, ApJ, 449, 695\n\n\\bibitem[] {} Khokhlov, A.M., M\\\"uller, E., \\& H\\\"oflich, P. 1992, A\n\\& A, 253, L9\n\n\\bibitem[] {} Khokhlov, A.M., Oran, E.S., \\& Wheeler, J.C. 1997, ApJ,\n478, 678\n\n\\bibitem[]{}Kirshner, R.P., \\etal 1993, ApJ, 415, 589\n\n\\bibitem[] {} Kobayashi, C., Tsujimoto, T., Nomoto, K., Hachisu, I.,\n\\& Kato, M. 1998, ApJ, 503, L155\n\n\\bibitem[]{}Landau, L.D., \\& Lifshitz, E.M. 1987, Fluid Mechanics\n(Oxford:Pergamon)\n\n\\bibitem[] {} Lee, T. 1988, in Meteorites and the Early Solar System,\ned. J.F. Kerridge, \\& M.S. Matthews (Tuscon:Univ. Arizona Press), 1063\n\n\\bibitem[]{}Leibundgut, B., Kirshner R.P., Filippenko, A.V., Shields,\nJ.C., Foltz, C.B., Phillips, M.M., \\& Sonneborn, G. 1991a, ApJ, 371,\nL23\n\n\\bibitem[] {} Lentz, E.J., Baron, E., Branch, D., Hauschildt, P.H., \\&\nNugent, P.E., 1999, ApJ, in press\n\n\\bibitem[]{} Li, X.D., \\& van den Heuvel, E.P.J. 1997, A\\&A, 322, L9\n\n\\bibitem[]{}Liu, W.H., Jeffery, D.J., \\& Schultz, D.R. 1997, ApJ, 483,\n L107\n\n\\bibitem[]{}Livne, E. 1993, ApJ, 406, L17\n\n\\bibitem[]{}Livne, E., \\& Arnett, W.D. 1995, ApJ, 452, 62\n\n\\bibitem[] {} Loss, R.D., Lugmair, G.W. 1990, ApJ, 360, L59\n\n\\bibitem[] {} Magain, P. 1987, A\\&A, 179, 176\n\n\\bibitem[] {} Magain, P. 1989, A\\&A, 209, 211\n\n\\bibitem[]{} Matteucci, F., Raiteri, C.M., Busso, M., Gallino, R., \\&\nGratton, R. 1993, A\\&A, 272, 421\n\n\\bibitem[]{} Mazzali, P., Cappelaro, E., Danziger, I.J., Turatto, M.,\n\\& Benetti, S. 1998, ApJ, 499, L49\n\n\\bibitem[]{}Mazzali, P., Lucy, L.B., Danziger, I.J., Gouiffes, C.,\nCappellaro, E.R., \\& Turatto, M. 1993, A\\&A, 269, 423\n\n\\bibitem[]{}Meikle, W.P.W., \\etal 1996, MNRAS, 281, 263\n\n\\bibitem[]{} Meyer, B.S., Krishnan, T.D., \\& Clayton, D.D. 1996, ApJ,\n462, 825\n\n\\bibitem[]{}Miyata, E., Tsunemi, H., Kohmura, T., Suzuki, S., \\&\nKumagai, S. 1998, PASJ, 50, 257\n\n\\bibitem[]{}Nakamura, T., Umeda, H., Nomoto, K., Thielemann, F.-K., \\&\nBurrows, A. 1999, ApJ, 517, 193\n\n\\bibitem[]{}Niemeyer, J.C. 1999, ApJ, 523, L57\n\n\\bibitem[]{}Niemeyer, J.C., \\& Hillebrandt W. 1995a, ApJ, 452, 769\n\n\\bibitem[]{}Niemeyer, J.C., Hillebrandt W., \\& Woosley, S.E. 1996,\nApJ, 471, 903\n\n\\bibitem[]{}Niemeyer, J.C., \\& Kerstein, A.R. 1997, NewA, 2, 239\n\n\\bibitem[]{}Niemeyer, J.C., \\& Woosley, S.E. 1997, ApJ, 475, 740\n\n\\bibitem[] {} Nissen, P.E., Gustafsson, B., Edvardsson, B., \\&\n Gilmore, G. 1994, A\\&A, 285, 440\n\n\\bibitem[]{}Nomoto, K. 1982a, ApJ, 253, 798\n \n\\bibitem[]{}Nomoto, K. 1982b, ApJ, 257, 780\n\n\\bibitem[]{}Nomoto, K., \\& Hashimoto, M. 1988, Phys. Rep., 163, 13\n\n\\bibitem[]{}Nomoto, K., \\& Iben, I.,Jr. 1985, ApJ, 297, 531\n\n\\bibitem[]{}Nomoto, K., Iwamoto, K., \\& Kishimoto, N. 1997, Science, 276, 1378\n\n\\bibitem[] {} Nomoto, K., Hashimoto, M., Tsujimoto, T., Thielemann,\nF.-K., Kishimoto, N., Kubo, Y., \\& Nakasato, N. 1997a, Nucl. Phys. A,\n161, 79c\n\n\\bibitem[]{} Nomoto, K., Iwamoto, K., Nakasato, N., Thielemann., F.K.,\nBrachwitz, F., Tsujimoto, T., Kubo. Y., \\& Kishimoto, N. 1997b,\nNucl. Phys. A, 621, 467c\n\n\\bibitem[]{} Nomoto, K., et al. 1997c, in Thermonuclear Supernovae,\ned. P. Ruiz-Lapuente, R. Canal, \\& J. Isern, (Dordrecht:Kluwer), 349\n\n\\bibitem[]{}Nomoto, K., \\& Kondo, Y. 1991, ApJ, 367, L19\n\n\\bibitem[]{}Nomoto, K., Nariai, K., \\& Sugimoto, D. 1979, PASJ, 31, 287\n\n\\bibitem[]{}Nomoto, K., Sugimoto, D., \\& Neo, S. 1976, Ap\\&SS, 39, L37\n\n\\bibitem[]{}Nomoto, K., Thielemann, F.-K., \\& Yokoi, K. 1984, ApJ,\n286, 644\n\n\\bibitem[]{}Nomoto, K., Yamaoka, H., Shigeyama, T., Kumagai, S., \\&\nTsujimoto, T. 1994, in Les Houches, Session LIV, Supernovae,\ned. S. Bludman, R.Mochovitch, \\& Zinn-Justin(Amsterdam:Elsevier), 199\n\n\\bibitem[]{}Nomoto, K., Yamaoka, H., Shigeyama, T., \\& Iwamoto, K.\n1996a, in IAU Colloq. 145, Supernovae and Supernova Remnants,\ned. R. McCray \\& Z. Wang (Cambridge:Cambridge University Press), 49\n\n\\bibitem[]{}Nugent, P., Baron, E., Branch, D., Fisher, A., \\&\nHauschildt, P.H. 1997, ApJ, 485, 812\n\n\\bibitem[]{}Paczy\\'nski, B. 1973, Acta Astron, 23, 1\n\n\\bibitem[Pagel \\& Trautvaisiene (1995)] {pagel95} Pagel, B.E.J., \\&\n Trautvaisiene, G. 1995, MNRAS, 276, 505\n\n\\bibitem[Pagel \\& Trautvaisiene (1997)] {pagel97} Pagel, B.E.J., \\&\n Trautvaisiene, G. 1997, MNRAS, 288, 108\n\n\\bibitem[]{}Perlmutter, S., et al. 1997, ApJ, 483, 565\n\n\\bibitem[]{}Perlmutter, S., et al. 1999, ApJ, 517, 565\n\n\\bibitem[]{}Phillips, M.M., Hamuy, M., Maza, J., Ruiz, M.T., Carney,\nB.W., \\& Graham, J.A. 1990, PASP, 102, 299\n\n\\bibitem[]{}Rappaport, S., Di Stefano, R., \\& Smith, J.D., 1994 ApJ,\n 426, 692\n\n\\bibitem[Rauscher et~al. (1994)]{rauscher94} Rauscher, T., Applegate,\nJ.H., Cowan, J.J., Thielemann, F.-K., \\& Wiescher, M. 1994, ApJ, 429,\n499\n\n\\bibitem[]{}Renzini, A. 1996, in IAU Colloq. 145, Supernovae and\nSupernova Remnants, ed. R. McCray \\& Z. Wang (Cambridge:Cambridge\nUniversity Press), 77\n\n\\bibitem[]{}Riess, A.G., Press, W.H., \\& Kirshner, R.P. 1995, ApJ,\n438, L17\n\n\\bibitem[]{}Riess, A.G., et al. 1999, AJ, 117, 707\n\n\\bibitem[]{}Ruiz-Lapuente, P. 1997, in Thermonuclear Supernovae,\ned. P. Ruiz-Lapuente, R. Canal, \\& J. Isern, (Dordrecht:Kluwer), 681\n\n\\bibitem[Ryan et al. (1996)] {ryan96} Ryan, S.G., Norris, J.E., \\&\n Beers, T.C. 1996, ApJ, 471, 254\n\n\\bibitem[Saio \\& Nomoto 1985]{sanom1985} Saio, H., \\& Nomoto, K. 1985,\nA\\&A, 150, L21\n\n\\bibitem[Saio \\& Nomoto 1985]{sanom1998} Saio, H., \\& Nomoto, K. 1998,\nApJ, 500, 388\n\n\\bibitem[]{}Shigeyama, T., Nomoto, K., Yamaoka, H., \\& Thielemann,\nF.-K. 1992, ApJ, 386, L13\n\n\\bibitem[Thielemann et al. (1987)]{thielemann87} Thielemann, F.-K.,\nArnould, M., \\& Truran, J.~W. 1987, in Advances in Nuclear\nAstrophysics, ed. E.~Vangioni-Flam (Gif sur Yvette:Editions\nFronti\\`ere), 525\n\n\\bibitem[]{}Thielemann, F.-K., Nomoto, K., \\& Hashimoto, M. 1996, ApJ,\n460, 408\n\n\\bibitem[]{}Thielemann, F.-K., Nomoto, K., Iwamoto, K., \\& Brachwitz,\nF. 1997, in Thermonuclear Supernovae, ed. P. Ruiz-Lapuente, R. Canal,\n\\& J. Isern (Dordrecht:Kluwer), 485\n\n\\bibitem[]{}Thielemann, F.-K., Nomoto, K., \\& Yokoi, K. 1986, A\\&A,\n158, 17\n\n\\bibitem[]{}Timmes, F., \\& Woosley, S.E. 1992, ApJ, 396, 649\n\n\\bibitem[Timmes et al. (1995)] {timmes95} Timmes, F., Woosley, S.E.,\n \\& Weaver, T.A. 1995, ApJS, 98, 617\n\n\\bibitem[]{}Travaglio, C., Gallino, R., Amarari, S., Zinner, E.,\nWoosley, S.E., \\& Lewis, R. 1999, ApJ, 510, 325\n\n\\bibitem[Trimble (1975)] {trimble75} Trimble, V. 1975,\nRev. Mod. Phys., 47, 877\n\n\\bibitem[]{}Tsujimoto, T., Nomoto, K., Yoshii, Y., Hashimoto, M.,\nYanagida, S., \\& Thielemann, F.-K. 1995, MNRAS, 277, 945\n\n\\bibitem[]{}Umeda, H., Nomoto, K., Yamaoka, H, \\& Wanajo, S. 1999,\nApJ, 513, 861\n\n\\bibitem[]{} Unno, W. 1968, PASJ, 19, 140\n\n\\bibitem[]{}van den Bergh, S., \\& Tammann, G. 1991, ARA\\&A, 29, 363\n\n\\bibitem[]{}van den Heuvel, E.P.J., Bhattacharya, D., Nomoto, K., \\&\nRappaport, S.A. 1992, A\\&A, 262, 97\n\n\\bibitem[van Wormer et~al. (1994)]{wormer94} van Wormer, L., G\\\"orres,\nJ., Iliadis, C., Wiescher, M., \\& Thielemann, F.-K. 1994, ApJ, 432,\n267\n\n\\bibitem[]{} V\\\"olkening, J. \\& Papanastassiou, D.A. 1989, ApJ, 347,\nL43\n\n\\bibitem[]{} V\\\"olkening, J. \\& Papanastassiou, D.A. 1990, Lunar and\nPlanetary Science XXI(Houston:Lunar.Planet.Inst.), No 1276\n\n\\bibitem[Webbink 1984]{webb1984}\nWebbink, R.F. 1984, ApJ, 277, 355\n\n\\bibitem[]{}Wheeler, J.C., Harkness, R.P., Khokhlov, A.M., \\&\nH\\\"oflich, P. 1995, Phys. Rep., 53, 221\n\n\\bibitem[]{}Woosley, S.E. 1997a, in Thermonuclear Supernovae,\ned. P. Ruiz-Lapuente, R. Canal, \\& J. Isern (Dordrecht:Kluwer), 313\n\n\\bibitem[]{}Woosley, S.E. 1997b, ApJ, 476, 801\n\n\\bibitem[]{}Woosley, S.E., \\& Weaver, T.A. 1986, ARA\\&A, 24, 205\n\n\\bibitem[]{}Woosley, S.E., \\& Weaver, T.A. 1994a, ApJ, 423, 371\n\n\\bibitem[]{}Woosley, S.E., \\& Weaver, T.A. 1994b, in Les Houches,\nSession LIV, Supernovae, ed. S.A.Bludman, R.Mochovitch, \\&\nJ.Zinn-Justin(Amsterdam:Elsevier), 63\n\n\\bibitem[]{}Yamaoka, H., Shigeyama, T., Nomoto, K., \\& Thielemann,\nF.-K. 1992, ApJ, 393, L55\n\n\\bibitem[]{}Yoshii, Y., Tsujimoto, T., \\& Nomoto, K. 1996, ApJ, 462,\n266\n\n\\bibitem[Zhao \\& Magain (1990)] {zhaomag90} Zhao, G., \\& Magain,\nP. 1990, A\\&A 238, 242\n\n\\bibitem[]{} Zinner, E. 1995, in Nuclei in the Cosmos III,\ned. M. Busso, R. Gallino, \\& C.M. Raiteri (New York:AIP Press), 567\n\n\\bibitem[]{} Zinner, E., Tang, M., \\& Anders, E. 1989,\nGeochim. Cosmochim. Acta, 53, 3273\n\n\\end{thebibliography}"
}
] |
astro-ph0002338
|
Discovery of a Color-Selected Quasar at $z = 5.50$\altaffilmark{1}
|
[
{
"author": "Daniel Stern\\altaffilmark{2}"
},
{
"author": "Hyron Spinrad\\altaffilmark{3}"
},
{
"author": "Peter Eisenhardt\\altaffilmark{2}"
},
{
"author": "Andrew J.~Bunker\\altaffilmark{4}"
},
{
"author": "Steve Dawson\\altaffilmark{3}"
},
{
"author": "S.~A.~Stanford\\altaffilmark{5}"
},
{
"author": "\\& Richard Elston\\altaffilmark{6}"
}
] |
We present observations of \rd300, a quasar at $z = 5.50$ discovered from deep, multi-color, ground-based observations covering 74 arcmin$^2$. This is the most distant quasar or AGN currently known. The object was targeted as an $R$-band dropout, with $R_{AB} > 26.3$ (3$\sigma$ limit in a 3\arcsec\ diameter region), $I_{AB} = 23.8$, and $z_{AB} = 23.4$. The Keck/LRIS spectrum shows broad \lya/\nv\ emission and sharp absorption decrements from the highly-redshifted hydrogen forests. The fractional continuum depression due to the \lya\ forest is $D_A = 0.90$. \rd300\ is the least luminous, high-redshift quasar known ($M_B \approx -22.7$).
|
[
{
"name": "rd300.tex",
"string": "\n%% --------------------------------------------------------------------\n%% Thu Feb 17 12:56:15 2000\n%% This file was generated automagically from the files\n%% rd300.bbl and rd300.tex using\n%% nat2jour.pl\n%% All citations have been inlined and dependencies on the natbib\n%% package have been removed so that this file (together with\n%% rd300-aas.bbl) should be suitable for submission to journals with\n%% the citation styles of ApJ or MNRAS.\n%% --------------------------------------------------------------------\n\n\\documentstyle[11pt,aaspp4,flushrt]{article}\n%\\documentstyle[11pt,emulateapj,flushrt]{article}\n%\\citestyle{aa}\n\n\\slugcomment{\\it to appear in The Astrophysical Journal Letters}\n\\lefthead{Stern et al.}\n\\righthead{Quasar at $z = 5.50$}\n\n%GOOD AASTEX DEFINITIONS\n\\def\\cf{{c.f.,}}\n\\def\\ie{{i.e.,}}\n\\def\\eg{{e.g.,}}\n\\def\\etal{{et al.~}}\n\n\\def\\rd300{RD~J030117+002025}\n\n\\def\\deg{\\ifmmode {^{\\circ}}\\else {$^\\circ$}\\fi}\n\\def\\hr{$^{h}$}\n\\def\\min{$^{m}$}\n\\def\\secper{\\ifmmode \\rlap.{^{s}}\\else $\\rlap{.}{^{s}} $\\fi}\n\\def\\ew{equivalent width}\n\n\\def\\kms{\\ifmmode {\\rm\\,km\\,s^{-1}}\\else\n ${\\rm\\,km\\,s^{-1}}$\\fi}\n\\def\\kmsMpc{\\ifmmode {\\rm\\,km\\,s^{-1}\\,Mpc^{-1}}\\else\n ${\\rm\\,km\\,s^{-1}\\,Mpc^{-1}}$\\fi}\n\\def\\ergAcm2{\\ifmmode {\\rm\\,ergs\\,cm^{-2}\\,{\\rm \\AA}^{-1}}\\else\n ${\\rm\\,ergs\\,cm^{-2}\\,\\AA^{-1}}$\\fi}\n\\def\\ergcm2s{\\ifmmode {\\rm\\,ergs\\,cm^{-2}\\,s^{-1}}\\else\n ${\\rm\\,ergs\\,cm^{-2}\\,s^{-1}}$\\fi}\n\\def\\ergsHz{\\ifmmode {\\rm\\,ergs\\,s^{-1}\\,Hz^{-1}}\\else\n ${\\rm\\,ergs\\,s^{-1}\\,Hz^{-1}}$\\fi}\n\\def\\ergs{\\ifmmode {\\rm\\,ergs\\,s^{-1}}\\else\n ${\\rm\\,ergs\\,s^{-1}}$\\fi}\n\\def\\ergsA{\\ifmmode {\\rm\\,ergs\\,s^{-1}\\,\\AA^{-1}}\\else\n ${\\rm\\,ergs\\,s^{-1}\\,\\AA^{-1}}$\\fi}\n\\def\\WHz{\\ifmmode {\\rm\\,W\\,Hz^{-1}}\\else\n ${\\rm\\,W\\,Hz^{-1}}$\\fi}\n\\def\\WHzsr{\\ifmmode {\\rm\\,W\\,Hz^{-1}\\,sr^{-1}}\\else\n ${\\rm\\,W\\,Hz^{-1}\\,sr^{-1}}$\\fi}\n\\def\\ergscmHz{\\ifmmode {\\rm\\,ergs\\,cm^{-2}\\,Hz^{-1}}\\else\n ${\\rm\\,ergs\\,cm^{-2}\\,Hz^{-1}}$\\fi}\n\\def\\Msun{M_\\odot}\n\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\n\\def\\hone{\\ion{H}{1}}\n\\def\\htwo{\\ion{H}{2}}\n\n\\def\\lyb{Ly$\\beta$}\n\\def\\ovi{\\ion{O}{6} $\\lambda$1035}\n\\def\\lya{Ly$\\alpha$}\n\\def\\nv{\\ion{N}{5} $\\lambda$1240}\n\\def\\siii{\\ion{Si}{2} $\\lambda$1260}\n\\def\\siivoiv{\\ion{Si}{4}/\\ion{O}{4}] $\\lambda$1403}\n\\def\\civ{\\ion{C}{4} $\\lambda$1549}\n\\def\\alii{\\ion{Al}{2} $\\lambda$1670}\n\\def\\oii{[\\ion{O}{2}] $\\lambda$3727}\n\\def\\oiipair{[\\ion{O}{2}] $\\lambda \\lambda$3726,3729}\n\\def\\hbeta{H$\\beta$}\n\\def\\oiii{[\\ion{O}{3}] $\\lambda$5007}\n\\def\\oiiipair{[\\ion{O}{3}] $\\lambda \\lambda$4959,5007}\n\\def\\halpha{H$\\alpha$}\n\n\\def\\loxytwo{L_{\\rm [OII]}}\n\\def\\soxytwo{\\sigma_{\\rm [OII]}}\n\\def\\woxytwo{W_{\\rm [OII]}}\n\\def\\lmm{lines mm$^{-1}$}\n\n%END OF GOOD AASTEX DEFINITIONS\n\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n%\\journalid{337}{15 January 1989}\n%\\articleid{11}{14}\n\n\\begin{document}\n\n\\title{Discovery of a Color-Selected Quasar at $z =\n5.50$\\altaffilmark{1}}\n\n\\author{Daniel Stern\\altaffilmark{2}, Hyron Spinrad\\altaffilmark{3},\nPeter Eisenhardt\\altaffilmark{2}, \\\\ Andrew J.~Bunker\\altaffilmark{4},\nSteve Dawson\\altaffilmark{3}, S.~A.~Stanford\\altaffilmark{5},\n\\& Richard Elston\\altaffilmark{6}}\n\n\\altaffiltext{1}{Based on observations at the W.M. Keck Observatory,\nKitt Peak National Observatory, and Palomar Observatory. Keck\nObservatory is operated as a scientific partnership among the\nUniversity of California, the California Institute of Technology, and\nthe National Aeronautics and Space Administration. The Observatory was\nmade possible by the generous financial support of the W.M. Keck\nFoundation.}\n\n\\altaffiltext{2}{Jet Propulsion Laboratory, California\nInstitute of Technology, Mail Stop 169-327, Pasadena, CA 91109}\n\n\\altaffiltext{3}{Department of Astronomy, University of California,\nBerkeley, CA 94720}\n\n\\altaffiltext{4}{Institute of Astronomy, Madingley Road,\nCambridge, CB3 OHA, England}\n\n\\altaffiltext{5}{Physics Department, University of California, Davis,\nCA 95616, and Lawrence Livermore National Laboratory}\n\n\\altaffiltext{6}{Department of Astronomy, The University of Florida,\nP.O. Box 112055, Gainesville, FL 32611}\n\n\\begin{abstract}\n\nWe present observations of \\rd300, a quasar at $z = 5.50$ discovered\nfrom deep, multi-color, ground-based observations covering 74\narcmin$^2$. This is the most distant quasar or AGN currently known.\nThe object was targeted as an $R$-band dropout, with $R_{\\rm AB} >\n26.3$ (3$\\sigma$ limit in a 3\\arcsec\\ diameter region), $I_{\\rm AB} =\n23.8$, and $z_{\\rm AB} = 23.4$. The Keck/LRIS spectrum shows broad\n\\lya/\\nv\\ emission and sharp absorption decrements from the\nhighly-redshifted hydrogen forests. The fractional continuum\ndepression due to the \\lya\\ forest is $D_A = 0.90$. \\rd300\\ is\nthe least luminous, high-redshift quasar known ($M_B \\approx -22.7$).\n\n\\end{abstract}\n\n\\keywords{quasars: general -- quasars: individual (\\rd300) -- early \nuniverse } \n\n\n\\section{Introduction}\n\nThe past few years have witnessed a watershed in our direct\nobservations of the high-redshift Universe. A decade ago, only a\nhandful of galaxies were identified past a redshift of 3. These\nsources represented the rare beast in the cosmos: high-redshift radio\ngalaxies, or galaxies associated with extremely distant, luminous\nquasars. New techniques and instruments allow us now to \nroutinely identify normal, star-forming galaxies at these same epochs\n\\markcite{Steidel:96a}(\\eg Steidel {et~al.} 1996). \\markcite{Stern:99e}Stern \\& Spinrad (1999) review modern search\ntechniques for distant galaxies. Improved computing power and\nambitious, large-area surveys also have pushed the frontier of distant\nquasar studies \\markcite{Djorgovski:99, Fan:99}(\\eg Djorgovski {et~al.} 1999; Fan {et~al.} 1999). Now we are \nregularly identifying objects which have collapsed only $\\sim 1$ Gyr\nafter the Big Bang. Such observations tell us about the earliest\nphases of galaxy and structure formation and probe the conditions of\nthe early Universe.\n\nThe identification of high-redshift quasars is especially important\nfor several reasons. First, quasars at early cosmic epoch require the\nrapid formation of a supermassive black hole. Assuming black holes are\nnot primordial, this requires the condensation of a large cloud of\nhydrogen, presumably embedded within a dark matter halo. Additionally,\nthe presence of metal lines in quasars demand a previous generation of\nstars (two generations for nitrogen). High-redshift quasars thus\nconstrain models of galaxy and structure formation\n\\markcite{Loeb:93, Eisenstein:95}(\\eg Loeb 1993; Eisenstein \\& Loeb 1995). Also, quasars provide valuable\nprobes of the intervening intergalactic medium \\markcite{Rauch:98}(\\eg Rauch 1998)\nand the intergalactic ionizing background. For example, the absence of\na smooth depression in quasar continua short-ward of the \\lya\\ emission\nstrongly constrains the amount of neutral hydrogen in the intergalactic\nmedium \\markcite{Gunn:65}(Gunn \\& Peterson 1965). \\markcite{Songaila:99}Songaila {et~al.} (1999) find no Gunn-Peterson\ntrough out to redshift 5 from deep spectroscopic observations of\nSDSSp~J033829.31+002156.3 at $z = 5.00$ \\markcite{Fan:99}(Fan {et~al.} 1999).\n\nIn this Letter, we report the discovery of a quasar at $z = 5.50$, the\nmost distant quasar identified to date. The previous most distant\nquasar was SDSSp~J120441.73$-$002149.6 at $z = 5.03$ \\markcite{Fan:00}(Fan {et~al.} 2000).\nAt $z = 5.50$, an $H_0 = 50 \\kmsMpc, \\Lambda = 0, \\Omega = 1$ (0.1)\nuniverse is 790 Myr (1.51 Gyr) old, corresponding to a look-back time\nof 94.0\\%\\ (90.9\\%) of the age of the universe. For the lambda\ncosmology supported by recent studies of distant supernovae, $H_0 = 65\n\\kmsMpc, \\Lambda = 0.7, \\Omega_{\\rm m} = 0.3$, the universe is 1.11 Gyr\nold at $z=5.50$, corresponding to a look-back time of 92.4\\%\\ of the\nage of the universe.\n\n\n\\section{Observations and Target Selection}\n\n\\rd300\\ was identified from deep $RIz$-band imaging using a slightly\nredder version of the `dropout' color selection techniques which have\nproved successful at identifying high-redshift galaxies\n\\markcite{Steidel:96a, Dey:98, Spinrad:98}(\\eg Steidel {et~al.} 1996; Dey {et~al.} 1998; Spinrad {et~al.} 1998) and quasars\n\\markcite{Kennefick:95, Djorgovski:99, Fan:99, Stern:00b}(\\eg Kennefick, Djorgovski, \\& de~Calvalho 1995; Djorgovski {et~al.} 1999; Fan {et~al.} 1999; Stern {et~al.} 2000b). The\nselection criteria rely upon absorption from the \\lya\\ and\n\\lyb\\ forests attenuating the rest-frame ultraviolet continua. At $z\n\\simeq 5$, such objects will disappear from the $R$-band. Long-ward of\nthe redshifted \\lya, both quasars and star-forming galaxies display\nrelatively flat (in $f_\\nu$) continua. In concept, our survey is\nsimilar to established quasar surveys relying upon the digitized\nPalomar Sky Survey \\markcite{Djorgovski:99}(\\eg Djorgovski {et~al.} 1999) or Sloan Digital Sky\nSurvey \\markcite{Fan:99}(\\eg Fan {et~al.} 1999). In practice, we probe a much smaller\narea of sky (eventually a few $\\times$ 100 arcmin$^2$) to much fainter\nmagnitudes. Our survey is designed to study the high-redshift,\n``normal'' galaxy population, but is also sensitive to (low-luminosity)\nhigh-redshift quasars.\n\nThe $Iz$ imaging was obtained using the Kitt Peak National Observatory\n150\\arcsec\\ Mayall telescope with its Prime Focus CCD imager (PFCCD)\nequipped with a thinned AR coated $2048 \\times 2048$ Tektronics CCD.\nThis configuration gives a $14.3 \\times 14.3$ arcminute field of view\nwith 0\\farcs43 pixels. The CCD was operated using ``short scan'', where\nthe CCD was mechanically displaced while its charge is shifted in the\nopposite direction to reduce fringing at $I$ and $z$ to very low\nlevels. Two hours of Mould $I$-band ($\\lambda_c = 8200$ \\AA; $\\Delta\n\\lambda = 1820$ \\AA) data were obtained on UT 1995 August 31. The\n$z$-band (RG850, long-pass filter) data were obtained during UT 1997\nNovember $4 - 6$, and the summed image represents 3.3 hours of\nintegration. The combined, processed $I$ and $z$ images reach limiting\nmagnitudes of 25.7 and 24.8 mag, respectively (3$\\sigma$ limits in\n3\\arcsec\\ diameter apertures; AB magnitudes are used throughout this\nLetter) and have 0\\farcs9 and 1\\farcs2 seeing, respectively. These\nimages comprise one field in the $BRIzJK$ \\markcite{Elston:00}Elston, Eisenhardt, \\& Stanford (2000) field\ngalaxy survey.\n\nOn UT 1999 November $11 - 12$, we used the COSMIC camera\n\\markcite{Kells:98}(Kells {et~al.} 1998) on the 200\\arcsec\\ Hale telescope at Palomar\nObservatory to obtain extremely deep (4.4~hour) Kron-Cousins $R$-band\n($\\lambda_c = 6200$ \\AA; $\\Delta \\lambda = 800$ \\AA) imaging of the same\nfield, with the purpose of identifying high-redshift candidates.\nCOSMIC uses a $2048 \\times 2048$ pixel SITe (formerly Tektronix)\nthinned CCD with 0\\farcs2846 pixels, yielding a $9.7 \\times 9.7$ arcmin\nfield-of-view. Our combined, processed $R$-band image has 1\\farcs2\nseeing and reaches a depth of 26.3 mag (3$\\sigma$ limit in\n3\\arcsec\\ diameter aperture).\n\nHigh-redshift candidates for spectroscopy, designated RD for $R$-drop,\nwere identified on the basis of a strong $R-I$ color index and\nrelatively flat $I-z$ color. No morphological criteria were\nimplemented as the primary goal of this program is to study ``normal,''\nstar-forming galaxies at high redshift. Candidates were then screened\nby eye, yielding a total of six good targets over the central 74\narcmin$^2$ field. Fig.~\\ref{fig_findingchart} presents a finding chart\nfor \\rd300, the brightest of our candidates and the subject of this\nLetter. Other candidates will be discussed in a future publication.\n\n\n% FIGURE 1\n\n\\begin{figure}[!t]\n\\begin{center}\n\\plotfiddle{fig1.ps}{3.7in}{0}{70}{70}{-225}{-55}\n%\\scalebox{0.5}{\\rotatebox{-90}{\\includegraphics{qso_opt/fig1.eps}}}\n\\end{center}\n\n\\caption{Finding chart for \\rd300, a quasar at $z = 5.50$, from the\nKPNO $I$-band imaging. The field is 2\\arcmin $\\times$ 2\\arcmin,\ncentered at $\\alpha = 03^{\\rm h} 01^{\\rm m} 17.01^{\\rm s}, \\delta =\n+00\\deg 20\\arcmin 25\\farcs96$ (J2000). North is at the top and east is\nto the left. The quasar is unresolved in this 0\\farcs9 seeing image.}\n\n\\label{fig_findingchart}\n\\end{figure}\n\n\nWe obtained spectra of several $R$-band dropouts through 1\\farcs5 wide,\n13\\arcsec\\ $-$ 44\\arcsec\\ long slitlets using the Low-Resolution\nImaging Spectrometer \\markcite{Oke:95}(LRIS; Oke {et~al.} 1995) on the Keck~II telescope\non UT 2000 January 10 and 11. Observations were obtained at a position\nangle of $-$111.6\\deg\\ (east of north) with the 150 lines mm$^{-1}$\ngrating ($\\lambda_{\\rm blaze} = 7500$ \\AA; $\\Delta \\lambda_{\\rm FWHM}\n\\approx 17$ \\AA). The spectra sample the wavelength range 4000 \\AA\\ to\n1$\\mu$m. Seeing was $\\approx$ 1\\farcs1 during both nights and\nconditions were photometric. We performed $\\approx$ 3\\arcsec\\ spatial\noffsets between each 1800~s exposure in order to facilitate removal of\nfringing at long wavelength ($\\lambda \\simgt 7200$ \\AA).\n\nAll data reductions were performed using IRAF and followed standard\nslit spectroscopy procedures. We calculated the dispersion using a\nHgNeArKr lamp spectrum observed immediately subsequent to the science\nobservations (RMS variations of 0.6 \\AA), and employed telluric\nemission lines to adjust the wavelength zero-point. The spectra were\nflux-calibrated using observations of Feige~67 and Feige~110\n\\markcite{Massey:90}(Massey \\& Gronwall 1990). We corrected for foreground Galactic extinction\nusing a reddening of $E_{\\rm B-V} = 0.03$ determined from the dust maps\nof \\markcite{Schlegel:98}Schlegel, Finkbeiner, \\& Davis (1998). The final composite spectrum of \\rd300,\npresented in Fig.~\\ref{fig_spectrum}, represents 4.5~hours of\nintegration.\n\n\n% FIGURE 2\n\n\\begin{figure}[!t]\n\\begin{center}\n\\plotfiddle{fig2.eps}{3.4in}{-90}{50}{50}{-200}{285}\n%\\scalebox{0.5}{\\rotatebox{-90}{\\includegraphics{qso_opt/fig1.eps}}}\n\\end{center}\n\n\\caption{Spectrum of \\rd300\\ at $z = 5.50$, obtained with LRIS on the\nKeck~II telescope. The total exposure time is 4.5~hours, and the\nspectrum was extracted using a 1\\farcs5 $\\times$ 1\\farcs5 aperture.\nThe spectrum has been smoothed using a 15 \\AA\\ boxcar filter. Vertical\ndotted lines indicate the expected wavelength of common spectroscopic\nfeatures in quasars; not all are detected.}\n\n\\label{fig_spectrum}\n\\end{figure}\n\n\n\\section{Results and Discussion}\n\nThough of moderate signal-to-noise ratio, the spectrum of \\rd300\\ has\nthe unambiguous signature of an extremely distant quasar. The broad\nemission with a sharp absorption at 7900 \\AA\\ is consistent with\n\\lya/\\nv\\ emission attenuated by the nearly opaque \\lya\\ forest at $z =\n5.50$. An additional discontinuity is visible at 6690 \\AA, associated\nwith the \\lyb\\ forest. The \\lya\\ forest absorption and poor detection of\nthe long-wavelength \\siivoiv\\ emission make centroiding on the emission\nfeatures ill-advised; the redshift is instead determined from the sharp\nforest decrements. We estimate $z = 5.50 \\pm 0.02$. This and other\nproperties of \\rd300\\ are given in Table~1.\n\nThe spectral character of \\rd300\\ is slightly atypical of high-redshift\nquasars, though it undoubtedly resides within the diverse category of\nquasars. The \\lya/\\ion{N}{5} complex is unusually broad and\ndistinguishing the emission lines is impractical. Many of the highest\nredshift quasars share similar spectroscopic shapes, \\eg\\\nSDSSp~J033829.31+002156.3 at $z = 5.00$, SDSSp~J021102.72$-$000910.3 at\n$z = 4.90$ \\markcite{Fan:99}(Fan {et~al.} 1999), and GB~1428+4217 at $z = 4.72$\n\\markcite{Hook:98}(Hook \\& McMahon 1998).\n\nThe strong continuum absorption associated with the \\lya\\ forest is the\ndominant spectroscopic feature of \\rd300. A robust determination of\n$D_A$, the standard parameter for describing the \\lya\\ forest decrement\n\\markcite{Oke:82}(Oke \\& Korycansky 1982), requires knowledge of the continuum spectral slope\nlong-ward of \\lya. We estimate $D_A$ by assuming the standard quasar\npower law spectral index of $-0.5$ for the continuum long-ward of\n\\lya\\ \\markcite{Richstone:80, Schneider:92}(\\eg Richstone \\& Schmidt 1980; Schneider {et~al.} 1992), with the amplitude\ndetermined over the wavelength interval $\\lambda \\lambda 8400 - 9000$\n\\AA\\ (between the \\nv\\ and \\siivoiv\\ emission complexes). We derive\n$D_A = 0.90 \\pm 0.02$. We derive $D_B = 0.95 \\pm 0.04$ for the\nstrength of the Ly$\\beta$ forest. The $D_A$ value is comparable to\nthose measured for distant galaxies in the Hubble Deep Field at similar\nredshifts \\markcite{Weymann:98, Spinrad:98}(Weymann {et~al.} 1998; Spinrad {et~al.} 1998) and models of the \\lya\\ forest\n\\markcite{Madau:95, Zhang:97}(Madau 1995; Zhang {et~al.} 1997).\n\nAt $z = 5.50$, the features used to describe continuum properties are\nredshifted to challenging wavelengths. We estimate $AB_{\\rm 1450(1 +\nz)}$ using the continuum modeled above. Consistent with previous work\nin this field, $M_B$ is calculated for an Einstein-de~Sitter universe\nwith $H_0 = 50 \\kmsMpc, q_0 = 0.5$ and the standard quasar power\nlaw index of $-0.5$. We find $M_B \\approx -22.7$; see\n\\markcite{Stern:00a}Stern {et~al.} (2000a) for details of how we calculate $M_B$.\n\nComparison with the 1.4~GHz FIRST survey \\markcite{Becker:95}(Becker, White, \\& Helfand 1995) reveals no\nradio source within 30\\arcsec\\ of the quasar to a limiting flux density\nof $f_{\\rm 1.4 GHz} \\simeq 1$ mJy (5$\\sigma$).\n\nHow unusual is it to find a quasar as distant and luminous as \\rd300\\\nin a $\\simeq 100$ arcmin$^2$ field? This is difficult to answer as\n\\rd300\\ is the least luminous $z > 4$ quasar known. The previously\nknown high-redshift ($z > 4$) quasars of lowest luminosity are\nPC~0027+0521 \\markcite{Schneider:94}($z = 4.21, M_B = -24.0$; Schneider, Schmidt, \\& Gunn 1994), which\nwas discovered serendipitously, and the X-ray selected quasar\nRX~J105225.9+571905 \\markcite{Schneider:98}($z = 4.45, M_B = -23.9$; Schneider {et~al.} 1998).\nThese luminosities are comparable to the lower luminosity objects in\nthe $z \\simlt 1$ Bright Quasar Survey \\markcite{Schmidt:83}(Schmidt \\& Green 1983). Most\nhigh-redshift quasar luminosity functions \\markcite{Schmidt:95b}(\\eg Schmidt, Schneider, \\& Gunn 1995)\nhave been derived from samples of quasars $\\approx 100$ times as\nluminous as \\rd300. To calculate the expected surface density of\nhigh-redshift, faint quasars, we follow the methodology\noutlined in \\markcite{Kennefick:95}Kennefick {et~al.} (1995) and \\markcite{Boyle:98}Boyle \\& Terlevich (1998): we adopt the\n\\markcite{Boyle:91}Boyle {et~al.} (1991) $z = 2$ quasar luminosity function (for $q_0 = 0.5$),\nscaled down in density using the evolution predicted by\n\\markcite{Schmidt:95b}Schmidt {et~al.} (1995), namely, that the quasar space density falls\noff by a factor of 2.7 per unit redshift beyond $z = 3$. The predicted\nsurface density of $R$-drop ($4.3 \\simlt z \\simlt 5.8$) quasars with\n$M_B \\leq -22.5$ is $\\simeq 2 \\times 10^{-3}$ arcmin$^{-2}$, implying\n$\\approx 0.15$ such quasars should have been uncovered in our survey.\n\nIt is dangerous, yet enticing, to draw conclusions from a single\nobject. The discovery of the quasar \\rd300\\ at $z = 5.50$ in the\nmodest sky coverage of our survey is suggestive of less dramatic\nevolution in the quasar luminosity function at faint magnitudes and\nhigh redshift. Such a change would have significant cosmological\nimplications, including changing the budget of high-energy, ionizing\nphotons in the early Universe. We also note that the low\nsignal-to-noise ratio data are suggestive of strong hydrogen absorption\nnear the quasar redshift. Is this due to a neutral hydrogen cloud near\nthe quasar, at odds with the proximity effect? Or are we\nseeing the first glimpses of an object radiating prior to the\nreionization epoch, with neutral intergalactic hydrogen absorbing the\nrest-frame UV photons? Higher resolution, higher signal-to-noise ratio\ndata will be essential for answering these questions.\n\n% OR ARE WE JUST PLAIN LUCKY, cf. McCarthy etal. (1988)?\n\n\\acknowledgements\n\nWe are indebted to the expertise of the staffs of Kitt Peak, Palomar,\nand Keck Observatories for their help in obtaining the data presented\nherein, and to the efforts of Bev Oke and Judy Cohen in designing,\nbuilding, and supporting LRIS. We especially thank Barbara Schaeffer,\nGreg Wirth, and Jerome at Keck~II for their assistance during the\nJanuary 2000 observing run. We are grateful to Carlos DeBreuck and\nRichard McMahon for carefully reading the manuscript and to the\nreferee, Ray Weymann, for prompt and helpful comments. Portions of\nthis work were carried out by the Jet Propulsion Laboratory, California\nInstitute of Technology, under a contract with NASA. Portions of this\nwork was performed under the auspices of the U.S. Department of Energy\nby University of California Lawrence Livermore National Laboratory\nunder contract No. W-7405-Eng-48. This work has been supported by the\nfollowing grants: NSF grant AST~95$-$28536 (HS), the Cambridge\nInstitute of Astronomy PPARC observational rolling grant\nref.~no.~PPA/G/O/1997/00793 (AJB), and NSF CAREER grant AST~9875448\n(RE).\n\n\n%\\bibliographystyle{apj}\n%% \\bibliography\n\\begin{thebibliography}{}\n\n\\bibitem[Becker, White, \\& Helfand 1995]{Becker:95}\nBecker, R.~H., White, R.~L., \\& Helfand, D.~J. 1995, \\apj, 450, 559\n\n\\bibitem[Boyle, Jones, Shanks, Marano, Zitelli, \\& Zamorani 1991]{Boyle:91}\nBoyle, B.~J., Jones, L.~R., Shanks, T., Marano, B., Zitelli, V., \\& Zamorani, G. 1991, in {\\it The Space Distribution of Quasars}, ed. D.~Crampton, Vol.~21 (San Francisco: ASP Conference Series), 191\n\n\\bibitem[Boyle \\& Terlevich 1998]{Boyle:98}\nBoyle, B.~J. \\& Terlevich, R.~J. 1998, \\mnras, 293, L49\n\n\\bibitem[Dey, Spinrad, Stern, Graham, \\& Chaffee 1998]{Dey:98}\nDey, A., Spinrad, H., Stern, D., Graham, J.~R., \\& Chaffee, F. 1998, \\apj, 498, L93\n\n\\bibitem[Djorgovski, Gal, Odewahn, de~Calvalho, Brunner, Longo, \\& Scaramella 1999]{Djorgovski:99}\nDjorgovski, S.~G., Gal, R.~R., Odewahn, S.~C., de~Calvalho, R.~R., Brunner, R., Longo, G., \\& Scaramella, R. 1999, in {\\it Wide Field Surveys in Cosmology}, ed. Y.~Mellier \\& S.~Colombi (Gif sur Yvette: Editions Fronti\\`eres), 89\n\n\\bibitem[Eisenstein \\& Loeb 1995]{Eisenstein:95}\nEisenstein, D.~J. \\& Loeb, A. 1995, \\apj, 443, 11\n\n\\bibitem[Elston, Eisenhardt, \\& Stanford 2000]{Elston:00}\nElston, R., Eisenhardt, P., \\& Stanford, S.~A. 2000, in preparation\n\n\\bibitem[Fan {et~al.} 1999]{Fan:99}\nFan, X. {et~al.} 1999, \\aj, 118, 1\n\n\\bibitem[Fan {et~al.} 2000]{Fan:00}\n---. 2000, \\aj, 119, 1\n\n\\bibitem[Gunn \\& Peterson 1965]{Gunn:65}\nGunn, J.~E. \\& Peterson, B.~A. 1965, \\apj, 142, 1633\n\n\\bibitem[Hook \\& McMahon 1998]{Hook:98}\nHook, I.~M. \\& McMahon, R.~G. 1998, \\mnras, 294, L7\n\n\\bibitem[Kells, Dressler, Sivaramakrishnan, Carr, Koch, Epps, Hilyard, \\& Pardeilhan 1998]{Kells:98}\nKells, W., Dressler, A., Sivaramakrishnan, A., Carr, D., Koch, E., Epps, H., Hilyard, D., \\& Pardeilhan, G. 1998, \\pasp, 110, 1487\n\n\\bibitem[Kennefick, Djorgovski, \\& de~Calvalho 1995]{Kennefick:95}\nKennefick, J.~D., Djorgovski, S.~G., \\& de~Calvalho, R.~R. 1995, \\aj, 110, 2553\n\n\\bibitem[Loeb 1993]{Loeb:93}\nLoeb, A. 1993, \\apj, 403, 542\n\n\\bibitem[Madau 1995]{Madau:95}\nMadau, P. 1995, \\apj, 441, 18\n\n\\bibitem[Massey \\& Gronwall 1990]{Massey:90}\nMassey, P. \\& Gronwall, C. 1990, \\apj, 358, 344\n\n\\bibitem[Oke \\& Korycansky 1982]{Oke:82}\nOke, J.~B. \\& Korycansky, D.~G. 1982, \\apj, 255, 11\n\n\\bibitem[Oke {et~al.} 1995]{Oke:95}\nOke, J.~B. {et~al.} 1995, \\pasp, 107, 375\n\n\\bibitem[Rauch 1998]{Rauch:98}\nRauch, M. 1998, \\araa, 36, 267\n\n\\bibitem[Richstone \\& Schmidt 1980]{Richstone:80}\nRichstone, D.~O. \\& Schmidt, M. 1980, \\apj, 235, 361\n\n\\bibitem[Schlegel, Finkbeiner, \\& Davis 1998]{Schlegel:98}\nSchlegel, D., Finkbeiner, D., \\& Davis, M. 1998, \\apj, 500, 525\n\n\\bibitem[Schmidt \\& Green 1983]{Schmidt:83}\nSchmidt, M. \\& Green, R.~F. 1983, \\apj, 269, 352\n\n\\bibitem[Schmidt, Schneider, \\& Gunn 1995]{Schmidt:95b}\nSchmidt, M., Schneider, D.~P., \\& Gunn, J.~E. 1995, \\aj, 110, 68\n\n\\bibitem[Schneider, Schmidt, \\& Gunn 1994]{Schneider:94}\nSchneider, D.~P., Schmidt, M., \\& Gunn, J.~E. 1994, \\aj, 107, 1245\n\n\\bibitem[Schneider, Schmidt, Hasinger, Lehmann, Gunn, Giacconi, Tr\\\"umper, \\& Zamorani 1998]{Schneider:98}\nSchneider, D.~P., Schmidt, M., Hasinger, G., Lehmann, I., Gunn, J.~E., Giacconi, R., Tr\\\"umper, J., \\& Zamorani, G. 1998, \\aj, 115, 1230\n\n\\bibitem[Schneider, van Gorkom, Schmidt, \\& Gunn 1992]{Schneider:92}\nSchneider, D.~P., van Gorkom, J.~H., Schmidt, M., \\& Gunn, J.~E. 1992, \\aj, 103, 1451\n\n\\bibitem[Songaila, Hu, Cowie, \\& McMahon 1999]{Songaila:99}\nSongaila, A., Hu, E.~M., Cowie, L.~L., \\& McMahon, R.~G. 1999, \\apj, 525, L5\n\n\\bibitem[Spinrad, Stern, Bunker, Dey, Lanzetta, Yahil, Pascarelle, \\& Fern\\`andez-Soto 1998]{Spinrad:98}\nSpinrad, H., Stern, D., Bunker, A.~J., Dey, A., Lanzetta, K., Yahil, A., Pascarelle, S., \\& Fern\\`andez-Soto, A. 1998, \\aj, 116, 2617\n\n\\bibitem[Steidel, Giavalisco, Dickinson, \\& Adelberger 1996]{Steidel:96a}\nSteidel, C.~S., Giavalisco, M., Dickinson, M., \\& Adelberger, K.~L. 1996, \\aj, 112, 352\n\n\\bibitem[Stern, Djorgovski, Perley, de~Carvalho, \\& Wall 2000a]{Stern:00a}\nStern, D., Djorgovski, S.~G., Perley, R., de~Carvalho, R., \\& Wall, J. 2000a, \\aj, in press (April; astro-ph/0001394)\n\n\\bibitem[Stern, Odewahn, Gal, Djorgovski, de~Carvalho, van Breugel, \\& Spinrad 2000b]{Stern:00b}\nStern, D., Odewahn, S.~C., Gal, R., Djorgovski, S.~G., de~Carvalho, R., van Breugel, W., \\& Spinrad, H. 2000b, \\aj, in preparation\n\n\\bibitem[Stern \\& Spinrad 1999]{Stern:99e}\nStern, D. \\& Spinrad, H. 1999, \\pasp, 111, 1475\n\n\\bibitem[Weymann, Stern, Bunker, Spinrad, Chaffee, Thompson, \\& Storrie-Lombardi 1998]{Weymann:98}\nWeymann, R., Stern, D., Bunker, A.~J., Spinrad, H., Chaffee, F., Thompson, R., \\& Storrie-Lombardi, L. 1998, \\apj, 505, L95\n\n\\bibitem[Zhang, Anninos, Norman, \\& Meiksin 1997]{Zhang:97}\nZhang, Y., Anninos, P., Norman, M.~L., \\& Meiksin, A. 1997, \\apj, 485, 496\n\n\\end{thebibliography}\n\n\\eject\n\n% TABLE 1\n\\begin{deluxetable}{lclc}\n%\\tablewidth{0pt}\n\\tablecaption{Properties of \\rd300}\n\\tablehead{\n\\colhead{Parameter} &\n\\colhead{Value} &\n\\colhead{Parameter} &\n\\colhead{Value}}\n\\startdata\n$\\alpha$ (J2000) & $03^{\\rm h} 01^{\\rm m} 17.01^{\\rm s}$ & $z$ & $5.50 \\pm 0.02$ \\nl\n$\\delta $ (J2000) & $+00\\deg 20\\arcmin 25\\farcs96$ & $AB_{\\rm 1450 (1 + z)}$ (mag) & 24.1 \\nl\n$R_{\\rm AB}$ (mag) & $> 26.3$ & $M_B$ (mag) & $-22.7$ \\nl\n$I_{\\rm AB}$ (mag) & 23.8 & $W_{\\rm Ly\\alpha/NV}^{\\rm obs}$ (\\AA) & $\\simeq 300$\\nl\n$z_{\\rm AB}$ (mag) & 23.4 & $D_A$ & $0.90 \\pm 0.02$ \\nl\n\t\t & & $D_B$ & $0.95 \\pm 0.04$ \\nl\n\\enddata\n\n\\tablecomments{$R$-band magnitude is 3$\\sigma$ limit is a 3\\arcsec\\\ndiameter aperture.}\n\n\\label{table1}\n\\end{deluxetable}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002338.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Becker, White, \\& Helfand 1995]{Becker:95}\nBecker, R.~H., White, R.~L., \\& Helfand, D.~J. 1995, \\apj, 450, 559\n\n\\bibitem[Boyle, Jones, Shanks, Marano, Zitelli, \\& Zamorani 1991]{Boyle:91}\nBoyle, B.~J., Jones, L.~R., Shanks, T., Marano, B., Zitelli, V., \\& Zamorani, G. 1991, in {\\it The Space Distribution of Quasars}, ed. D.~Crampton, Vol.~21 (San Francisco: ASP Conference Series), 191\n\n\\bibitem[Boyle \\& Terlevich 1998]{Boyle:98}\nBoyle, B.~J. \\& Terlevich, R.~J. 1998, \\mnras, 293, L49\n\n\\bibitem[Dey, Spinrad, Stern, Graham, \\& Chaffee 1998]{Dey:98}\nDey, A., Spinrad, H., Stern, D., Graham, J.~R., \\& Chaffee, F. 1998, \\apj, 498, L93\n\n\\bibitem[Djorgovski, Gal, Odewahn, de~Calvalho, Brunner, Longo, \\& Scaramella 1999]{Djorgovski:99}\nDjorgovski, S.~G., Gal, R.~R., Odewahn, S.~C., de~Calvalho, R.~R., Brunner, R., Longo, G., \\& Scaramella, R. 1999, in {\\it Wide Field Surveys in Cosmology}, ed. Y.~Mellier \\& S.~Colombi (Gif sur Yvette: Editions Fronti\\`eres), 89\n\n\\bibitem[Eisenstein \\& Loeb 1995]{Eisenstein:95}\nEisenstein, D.~J. \\& Loeb, A. 1995, \\apj, 443, 11\n\n\\bibitem[Elston, Eisenhardt, \\& Stanford 2000]{Elston:00}\nElston, R., Eisenhardt, P., \\& Stanford, S.~A. 2000, in preparation\n\n\\bibitem[Fan {et~al.} 1999]{Fan:99}\nFan, X. {et~al.} 1999, \\aj, 118, 1\n\n\\bibitem[Fan {et~al.} 2000]{Fan:00}\n---. 2000, \\aj, 119, 1\n\n\\bibitem[Gunn \\& Peterson 1965]{Gunn:65}\nGunn, J.~E. \\& Peterson, B.~A. 1965, \\apj, 142, 1633\n\n\\bibitem[Hook \\& McMahon 1998]{Hook:98}\nHook, I.~M. \\& McMahon, R.~G. 1998, \\mnras, 294, L7\n\n\\bibitem[Kells, Dressler, Sivaramakrishnan, Carr, Koch, Epps, Hilyard, \\& Pardeilhan 1998]{Kells:98}\nKells, W., Dressler, A., Sivaramakrishnan, A., Carr, D., Koch, E., Epps, H., Hilyard, D., \\& Pardeilhan, G. 1998, \\pasp, 110, 1487\n\n\\bibitem[Kennefick, Djorgovski, \\& de~Calvalho 1995]{Kennefick:95}\nKennefick, J.~D., Djorgovski, S.~G., \\& de~Calvalho, R.~R. 1995, \\aj, 110, 2553\n\n\\bibitem[Loeb 1993]{Loeb:93}\nLoeb, A. 1993, \\apj, 403, 542\n\n\\bibitem[Madau 1995]{Madau:95}\nMadau, P. 1995, \\apj, 441, 18\n\n\\bibitem[Massey \\& Gronwall 1990]{Massey:90}\nMassey, P. \\& Gronwall, C. 1990, \\apj, 358, 344\n\n\\bibitem[Oke \\& Korycansky 1982]{Oke:82}\nOke, J.~B. \\& Korycansky, D.~G. 1982, \\apj, 255, 11\n\n\\bibitem[Oke {et~al.} 1995]{Oke:95}\nOke, J.~B. {et~al.} 1995, \\pasp, 107, 375\n\n\\bibitem[Rauch 1998]{Rauch:98}\nRauch, M. 1998, \\araa, 36, 267\n\n\\bibitem[Richstone \\& Schmidt 1980]{Richstone:80}\nRichstone, D.~O. \\& Schmidt, M. 1980, \\apj, 235, 361\n\n\\bibitem[Schlegel, Finkbeiner, \\& Davis 1998]{Schlegel:98}\nSchlegel, D., Finkbeiner, D., \\& Davis, M. 1998, \\apj, 500, 525\n\n\\bibitem[Schmidt \\& Green 1983]{Schmidt:83}\nSchmidt, M. \\& Green, R.~F. 1983, \\apj, 269, 352\n\n\\bibitem[Schmidt, Schneider, \\& Gunn 1995]{Schmidt:95b}\nSchmidt, M., Schneider, D.~P., \\& Gunn, J.~E. 1995, \\aj, 110, 68\n\n\\bibitem[Schneider, Schmidt, \\& Gunn 1994]{Schneider:94}\nSchneider, D.~P., Schmidt, M., \\& Gunn, J.~E. 1994, \\aj, 107, 1245\n\n\\bibitem[Schneider, Schmidt, Hasinger, Lehmann, Gunn, Giacconi, Tr\\\"umper, \\& Zamorani 1998]{Schneider:98}\nSchneider, D.~P., Schmidt, M., Hasinger, G., Lehmann, I., Gunn, J.~E., Giacconi, R., Tr\\\"umper, J., \\& Zamorani, G. 1998, \\aj, 115, 1230\n\n\\bibitem[Schneider, van Gorkom, Schmidt, \\& Gunn 1992]{Schneider:92}\nSchneider, D.~P., van Gorkom, J.~H., Schmidt, M., \\& Gunn, J.~E. 1992, \\aj, 103, 1451\n\n\\bibitem[Songaila, Hu, Cowie, \\& McMahon 1999]{Songaila:99}\nSongaila, A., Hu, E.~M., Cowie, L.~L., \\& McMahon, R.~G. 1999, \\apj, 525, L5\n\n\\bibitem[Spinrad, Stern, Bunker, Dey, Lanzetta, Yahil, Pascarelle, \\& Fern\\`andez-Soto 1998]{Spinrad:98}\nSpinrad, H., Stern, D., Bunker, A.~J., Dey, A., Lanzetta, K., Yahil, A., Pascarelle, S., \\& Fern\\`andez-Soto, A. 1998, \\aj, 116, 2617\n\n\\bibitem[Steidel, Giavalisco, Dickinson, \\& Adelberger 1996]{Steidel:96a}\nSteidel, C.~S., Giavalisco, M., Dickinson, M., \\& Adelberger, K.~L. 1996, \\aj, 112, 352\n\n\\bibitem[Stern, Djorgovski, Perley, de~Carvalho, \\& Wall 2000a]{Stern:00a}\nStern, D., Djorgovski, S.~G., Perley, R., de~Carvalho, R., \\& Wall, J. 2000a, \\aj, in press (April; astro-ph/0001394)\n\n\\bibitem[Stern, Odewahn, Gal, Djorgovski, de~Carvalho, van Breugel, \\& Spinrad 2000b]{Stern:00b}\nStern, D., Odewahn, S.~C., Gal, R., Djorgovski, S.~G., de~Carvalho, R., van Breugel, W., \\& Spinrad, H. 2000b, \\aj, in preparation\n\n\\bibitem[Stern \\& Spinrad 1999]{Stern:99e}\nStern, D. \\& Spinrad, H. 1999, \\pasp, 111, 1475\n\n\\bibitem[Weymann, Stern, Bunker, Spinrad, Chaffee, Thompson, \\& Storrie-Lombardi 1998]{Weymann:98}\nWeymann, R., Stern, D., Bunker, A.~J., Spinrad, H., Chaffee, F., Thompson, R., \\& Storrie-Lombardi, L. 1998, \\apj, 505, L95\n\n\\bibitem[Zhang, Anninos, Norman, \\& Meiksin 1997]{Zhang:97}\nZhang, Y., Anninos, P., Norman, M.~L., \\& Meiksin, A. 1997, \\apj, 485, 496\n\n\\end{thebibliography}"
}
] |
astro-ph0002339
|
RUNAWAY OF LINE-DRIVEN WINDS TOWARDS CRITICAL AND OVERLOADED SOLUTIONS
|
[
{
"author": "Achim Feldmeier"
}
] |
Line-driven winds from hot stars and accretion disks are thought to adopt a unique, critical solution which corresponds to maximum mass loss rate and a particular velocity law. We show that in the presence of negative velocity gradients, radiative-acoustic (Abbott) waves can drive shallow wind solutions towards larger velocities and mass loss rates. Perturbations introduced downstream from the wind critical point lead to convergence towards the critical solution. By contrast, low-lying perturbations cause evolution towards a mass-overloaded solution, developing a broad deceleration region in the wind. Such a wind differs fundamentally from the critical solution. For sufficiently deep-seated perturbations, overloaded solutions become time-dependent and develop shocks and shells.
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[
{
"name": "paper.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[art8,aaspp4,flushrt,tighten,psfig]{article}\n\n\\slugcomment{Astrophysical Journal Letters, in press}\n\n\\lefthead{Feldmeier \\& Shlosman}\n\\righthead{Wind evolution towards critical and overloaded solutions}\n\n\n\\newcommand{\\pa}{\\partial}\n\\newcommand{\\cri}{_{\\rm c}}\n\\newcommand{\\ter}{_{\\rm t}}\n\\newcommand{\\Abb}{_{\\rm A}}\n\\newcommand{\\Abbcri}{_{\\rm Ac}}\n\\newcommand{\\Abbter}{_{\\rm At}}\n\n\\begin{document}\n\n\\title{RUNAWAY OF LINE-DRIVEN WINDS TOWARDS CRITICAL AND OVERLOADED\nSOLUTIONS}\n\n\\author{Achim Feldmeier}\n\n\\affil{Imperial College, Prince Consort Road, London SW7 2BZ, England\n\\\\ email: {\\tt a.feldmeier@ic.ac.uk}}\n\n\\and\n\n\\author{Isaac Shlosman}\n\n\\affil{University of Kentucky, Lexington, KY 40506, U.S.A. \\\\ email:\n{\\tt shlosman@pa.uky.edu}}\n\n\n\\begin{abstract}\n\nLine-driven winds from hot stars and accretion disks are thought to\nadopt a unique, critical solution which corresponds to maximum mass\nloss rate and a particular velocity law. We show that in the\npresence of negative velocity gradients, radiative-acoustic (Abbott)\nwaves can drive shallow wind solutions towards larger velocities and\nmass loss rates. Perturbations introduced downstream from the wind\ncritical point lead to convergence towards the critical solution. By\ncontrast, low-lying perturbations cause evolution towards a\nmass-overloaded solution, developing a broad deceleration region in\nthe wind. Such a wind differs fundamentally from the critical\nsolution. For sufficiently deep-seated perturbations, overloaded\nsolutions become time-dependent and develop shocks and shells.\n\n\\end{abstract}\n\n\\keywords{accretion disks --- galaxies: active --- cataclysmic\nvariables --- hydrodynamics --- stars: mass loss --- stars: winds}\n\\twocolumn\n \n\\section{Introduction}\n\nAtmospheres of hot luminous stars and accretion disks in active\ngalactic nuclei and cataclysmic variables form extensive outflows due\nto super-Eddington radiation fluxes in UV resonance and subordinate\nlines. An understanding of these winds is hampered by the pathological\ndependence of the driving force on the flow velocity gradient. Castor,\nAbbott, \\& Klein (1975; CAK hereafter) found that line-driven winds\n(hereafter LDWs) from O~stars should adopt a unique, critical state\nwhich corresponds to maximum mass loss rate. The equation of motion\nfor a 1-D, spherically symmetric, polytropic outflow subject to a\nSobolev line force allows for two infinite families of so-called\nshallow and steep solutions. However, none of these families can\nprovide for a {\\it global} solution alone. Shallow solutions do not\nreach infinity, while steep solutions do not extend into the subsonic\nregime including the photosphere. The critical wind starts then as the\nfastest shallow solution and switches at the critical point in a\ncontinuous and differentiable manner to the slowest steep\nsolution. Hence the critical point and not the sonic point determines\nthe bottleneck in the wind. This description in principle applies\nequally to winds from stars and accretion disks.\n\nA physical interpretation of the CAK critical point was given by\nAbbott (1980), who derived a new type of radiative-acoustic waves\n(hereafter Abbott waves). These waves can propagate inward, in the\nstellar rest frame, only from below the CAK critical point. Above the\ncritical point, they are advected outwards. Hence, the CAK critical\npoint serves as an information barrier, much as the sonic or Alfv\\'en\npoints in thermal and hydromagnetic winds. Abbott's analysis was\nchallenged by Owocki \\& Rybicki (1986) who found for a pure absorption\nLDW the signal speed to be the sound speed and not the much faster\nAbbott speed. As noted already by these authors, this should be a\nconsequence of assuming pure line absorption, which does not allow for\nany radiatively modified, inward wave mode. Meanwhile there is ample\nevidence for Abbott waves in time-dependent wind simulations (Owocki\n\\& Puls 1999).\n\nShallow solutions fail to reach infinity because they cannot perform\nthe required spherical expansion work, implying that the flow starts\nto decelerate. Since this usually occurs very far out in the wind, the\nlocal wind speed is much larger than the local escape speed, and the\nwind escapes to infinity. Thus, a simple generalization of the CAK\nmodel allowing for flow deceleration renders shallow solutions\nglobally admissible. This raises a fundamental question of why the\nwind would adopt the critical solution at all, and attain the critical\nmass loss rate and velocity law, as proposed by CAK.\n\nIn this Letter we analyze a physical mechanism which drives shallow\nsolutions towards the critical one, and discuss under what conditions\nthis evolutions does not terminate at the CAK solution, but continues\ninto the realm of overloaded solutions. We find that simulations so\nfar were affected by numerical runaway towards the critical solution,\nby not accounting for Abbott waves in the Courant time step.\n\n\n\\section{Abbott waves}\n\nAbbott waves are readily derived by bringing the wind equations into\ncharacteristic form. We consider a 1-D planar wind of velocity\n$v(z,t)$ and density $\\rho(z,t)$, assuming zero sound speed. The\ncontinuity and Euler equation are,\n %\n\\begin{equation}\n \\label{continuity}\n {\\pa \\rho \\over \\pa t} + v {\\pa \\rho \\over \\pa z} + \\rho {\\pa v\n \\over \\pa z} = 0,\\\\\n\\end{equation}\n\\begin{equation}\n\\label{euler} \nE \\equiv {\\pa v \\over \\pa t} + v\\, {\\pa v \\over \\pa z} + g(z) -\n C \\, F(z) \\left({\\pa v / \\pa z \\over \\rho}\\right)^\\alpha = 0.\n \\end{equation}\n %\n Here, $g(z)$ and $F(z)$ are gravity and radiative flux,\nrespectively. The CAK line force is given by $g_{\\rm l} \\equiv C \\,\nF(z) \\, (v' / \\rho)^\\alpha$ (with $v' \\equiv \\partial v/\\partial z$),\nwith constant $C$ and exponent $0<\\alpha <1$. The unique, stationary\nCAK wind, $v\\cri(z), \\rho\\cri(z)$, is found by requiring a critical\npoint at some $z\\cri$. The number of solutions for $vv'(z)$ changes\nfrom 2 to 1 at $z\\cri$ (which is a saddle point), hence $\\partial\nE/\\partial (vv')\\cri=0$ holds. Writing $C$ in terms of critical point\nquantities, the Euler equation becomes,\n \n $${\\pa v \\over \\pa t} + v\\, {\\pa v \\over \\pa z} + g(z) - $$\n% \n\\begin{equation}\n\\alpha^{-\\alpha} (1-\\alpha)^{-(1-\\alpha)} \\, {F(z) \\over F(z\\cri)} \\;\ng(z\\cri)^{1-\\alpha} (\\rho\\cri v\\cri)^\\alpha \\left({\\pa v / \\pa z \\over\n\\rho}\\right)^\\alpha =0.\n \\end{equation}\n %\n \\noindent Note that for stationary planar winds, $\\rho v$ is\nconstant. If, in addition, $g$ and $F$ are taken constant with height,\nand $\\rho\\cri v\\cri \\, v'/\\rho$ is replaced by $vv'/\\dot m$, with\nnormalized mass loss rate $\\dot m \\equiv \\rho v/\\rho\\cri v\\cri$, one\nfinds that $E$ does no longer depend explicitly on $z$ for stationary\nsolutions. Hence, $vv'$ is independent of $z$, too. This implies that\n$z\\cri$ is ill-defined, and every point of the CAK solution is a\ncritical point. CAK removed this degeneracy by introducing gas\npressure terms. Here we take a different approach and assume\n$g=z/(1+z^2)$. A situation with roughly constant radiative flux and\ngravity showing a maximum at finite height could be encountered above\nisothermal disks around compact objects (cf. Feldmeier \\& Shlosman 1999). The\ncritical point is determined by the regularity condition, $dE/dz\\cri=0$, hence\n$z\\cri=1$ and the critical point coincides with the gravity maximum. For\nsimplicity also we chose $\\alpha=1/2$ from now on, which is reasonably\nclose to realistic values $\\alpha \\le 2/3$ (Puls et al.~1999). None of\nour results should depend qualitatively on the assumptions made so\nfar. The Euler equation is\n %\n \\begin{equation}\n \\label{euler2} \n {\\pa v \\over \\pa t} + v\\, {\\pa v \\over \\pa z} + g(z) -\n 2\\sqrt{g\\cri \\rho\\cri v\\cri} \\; \\sqrt{\\pa v / \\pa z \\over \\rho} =0,\n \\end{equation}\n %\n \\noindent where $g\\cri \\equiv g(z\\cri)$. The stationary solutions for\nwind acceleration are given by\n %\n \\begin{equation}\n \\label{windsol}\n vv'(z) = {g\\cri \\over \\dot m} \\, \\left( 1 \\pm \\sqrt{1- {\\dot mg(z)\n\\over g\\cri}}\\right)^2,\n \\end{equation}\n %\n \\noindent where plus and minus signs refer to steep and shallow\nsolutions, respectively. For $\\dot m \\le 1$, shallow and steep\nsolutions are globally, i.e., everywhere, defined. For $\\dot m>1$,\nsolutions are called {\\it overloaded}, and become imaginary in a\nneighborhood of the gravity maximum. These winds carry too large mass\nloss rates and eventually stagnate.\n\nNext we put the Euler equation into quasi-linear form, which does {\\it\nnot} mean to linearize it. Differentiating $E$ with respect to $z$\n(Courant \\& Hilbert 1962; Abbott 1980) and introducing $f\\equiv \\pa\nv/\\pa z$, eqs.~(\\ref{continuity}, \\ref{euler2}) become,\n %\n \\begin{eqnarray}\n \\label{characon}\n &&\\left[{\\pa \\over \\pa t} + v \\, {\\pa \\over \\pa z}\\right] \\rho \\;+\\;\n \\rho f = 0,\\\\\n \\label{charaeul}\n &&\\left[{\\pa \\over \\pa t} + (v+v\\Abb) \\, {\\pa \\over \\pa\n z} \\right] {f \\over \\rho} \\;+\\; {1\\over \\rho}\\, {\\pa g \\over \\pa z} =\n 0,\n \\end{eqnarray}\n %\n \\noindent with inward Abbott speed in the rest frame, $v\\Abb \\equiv\n-\\sqrt{g\\cri v/\\dot m v'}$. In the WKB approximation, individual\nspatial and temporal variations are much larger than the inhomogeneous\nterm $g'/\\rho$ in eq.~(\\ref{charaeul}), and the latter can be\nneglected. Consequently, $v'/\\rho$ is a Riemann invariant propagating\nat characteristic speed $v+v\\Abb$. Perturbations of $v'/\\rho$\ncorrespond to the amplitude of a wave propagating at phase speed\n$v+v\\Abb$. Note that $v'/\\rho$ is proportional to the Sobolev line\noptical depth, indicating that this wave is a true radiative mode.\n\nThe second characteristic is determined by the continuity equation\n(\\ref{characon}). In the advection operator in square brackets, $v$\nhas to be read as $v+0$ in the zero-sound speed limit. This outwards\npropagating invariant corresponds to a sound wave, with amplitude\n$\\rho$ scaling with gas pressure.\n\nAt the critical point, $\\dot m=1$ and $vv'(z\\cri)=g(z\\cri)$ after\neq.~(\\ref{windsol}), hence $v\\Abbcri=-v\\cri$ (where we introduced\n$v\\Abbcri \\equiv v\\Abb(z\\cri)$). Abbott waves stagnate at the critical\npoint, in analogy with sound waves at the sonic point. For shallow\nsolutions, $\\dot m<1$ and $vv'<v\\cri v\\cri'$ from eq.~(\\ref{windsol}),\nhence $v+v\\Abb <0$. Shallow LDW solutions are therefore the\nsubcritical analog to solar wind breezes.\n\nBecause in the rest frame, the inward Abbott mode can propagate at\nlarger absolute speeds than the outward sound mode, Abbott waves can\ndetermine the Courant time step in time-explicit hydrodynamic\nsimulations. Violating the Courant step results in numerical\ninstability. Despite this fact, Abbott waves along shallow solutions\nwere never considered in the literature.\n\n\n\\section{Wind convergence towards the critical solution}\n\\label{acceleration}\n\nWe turn our attention to a physical mechanism which can drive LDWs\naway from shallow solutions, and towards the critical one. Starting\nfrom an arbitrary shallow solution as initial condition, we explicitly\nintroduce perturbations at some fixed location in the wind and study\ntheir evolution. In order to keep {\\it unperturbed} shallow solutions\nstable in numerical simulations, we fix one outer boundary condition,\naccording to inward propagating Abbott waves. Either a constant mass\nloss rate at the outer boundary or non-reflecting boundary conditions\n(Hedstrom 1977) serve this aim. At the inner, subcritical boundary, we\nalso fix one boundary condition, according to incoming sound waves.\nNon-reflecting boundary conditions and $\\rho=const$ give similar\nresults.\n\nWind convergence towards the critical solution is then triggered by\nnegative flow velocity gradients. Allowing for $v'<0$ turns the inward\nAbbott mode of phase speed $v+v\\Abb <0$ in the rest frame into an\noutwards propagating mode. This is readily seen for a line force which\nis zero for negative $v'$, i.e., when all photons are absorbed at a\nresonance location between the photosphere and the wind point. The\nEuler equation simplifies to that for an ordinary gas, with\ncharacteristic speed $v-0 >0$ in the zero sound speed limit. At the\nother extreme, for a purely local line force where the unattenuated\nstellar or disk radiation field reaches the wind point, $g_{\\rm l}\n\\propto \\sqrt{|v'|}$. Here the Abbott phase speed is found to be\n$v+v\\Abb$, with $v\\Abb = +\\sqrt{ -g\\cri v/\\dot m v'}$ for $v'<0$.\n\nConsider then a sawtooth-like velocity perturbation (sinusoidal\nperturbation lead to similar results). Slopes $v'>0$ propagate\ninwards, slopes $v'<0$ propagate outwards. Hence, as a kinematical\nconsequence, a sawtooth which is initially symmetric with respect to\nthe underlying stationary velocity law evolves towards larger\nvelocities. This is demonstrated in Figure~1 where, in course of time,\na periodic sawtooth perturbation is introduced at $z=2$. The line\nforce is assumed to be $\\propto \\sqrt{|v'|}$, and the initial shallow\nsolution has $\\dot m=0.8$. The figure shows 2${1 \\over 2}$\nperturbation cycles. For upward pointing kinks the slopes propagate\napart and a flat velocity law develops between them. At each time\nstep $dt$, a new increment $dv = 4dt\\, \\delta v/T$ ($\\delta v$ and $T$\nbeing the amplitude and period of the sawtooth) is added at $z=2$,\nhence the flattening velocity law does not show up in region A of\nFigure~1. Overall, the wind speed at the perturbation site evolves\ntowards larger values during these phases. On the other hand, for\ndownward pointing kinks of the sawtooth, $-\\delta v$, the two\napproaching slopes merge, and the wind speed evolves back towards its\nunperturbed value after each decrement $-dv = -4dt\\, \\delta v/T$. The\nwind velocity hardly evolves during these phases, cf.~region B of\nFigure~1. Over a full perturbation cycle, the wind speed clearly\nincreases. \n\n\\begin{figure}[ht]\n\\vbox to3.6in{\\rule{0pt}{3.6in}} \n\\special{psfile=fig1.ps angle=0 hoffset=-40 voffset=-30 vscale=55\nhscale=55} \n\\caption{{\\it Upper panel\\/}: Evolution of a shallow wind\nduring 2$1 \\over 2$ periods of a sawtooth perturbation of amplitude\n10\\% being introduced at $z=2$. Regions `A' and `B' correspond to\nphases where upward and downward pointing kinks, respectively, are\nintroduced into the flow. {\\it Lower panel\\/}: stable Abbott wave\nexcitation in the critical wind, at 35\\% perturbation amplitude.}\n\\end{figure} \n\nEssentially any perturbation which introduces negative $v'$ will\naccelerate the wind. The amplitude of the perturbation is rather\nirrelevant since, with decreasing perturbation wavelength, negative\n$v'$ occur at ever smaller amplitudes. However, in more realistic\nwinds, dissipative effects may smear out short-scale perturbations \nbefore they can grow. Details of the physical mechanism will be\ndiscussed elsewhere.\n\n{\\it If} the perturbation lies downstream from the critical point, the\nwind converges to the critical solution. Namely, as soon as the\nperturbation site comes to lie on the supercritical part of the CAK\nsolution during its evolution, positive velocity slopes propagate {\\it\noutwards}, and combine with negative slopes to a full wave train. No\ninformation is propagated upstream. This unconditional stability of\nthe outer CAK solution is shown in the lower panel of Fig.~1.\n\n\n\\section{Wind convergence towards overloaded solutions}\n\\label{overloaded}\n\nWind runaway towards larger speeds as caused by perturbations\nintroduced {\\it upstream} from the critical point does not terminate\nat the critical CAK solution. For low-lying perturbations,\ncommunication with the wind base is still possible once the\nsubcritical branch of the CAK solution is reached. The wind gets\nfurther accelerated into the domain of mass-overloaded solutions\n(where $vv'> v\\cri v'\\cri$ and hence $v> v\\cri$ for $z<z\\cri$\naccording to eq.~\\ref{windsol}), until a generalized critical point\ndevelops, which prevents inward propagation of Abbott waves and\nadjustment of the mass loss rate. Such generalized critical points are\ngiven by `termination' points, $z\\ter$, of overloaded solutions, where\nthe velocity becomes imaginary. At $z\\ter$, the number of real\nsolutions $vv'(r)$ changes from 2 (shallow and steep) to 0. Hence,\ntermination points are defined by the same condition as the CAK\ncritical point (at which the number of solutions changes from 2 via 1\nto 2), $\\pa E/\\pa (vv')\\ter=0$. From the stationary version of\neq.~(\\ref{euler2}), $v\\Abbter =-v\\ter$, hence Abbott waves stagnate at\ntermination points, and the latter are generalized critical points.\n\nThe fact that perturbations with negative $v'$ accelerate the wind\neither to the critical or an overloaded state can be casted into\nblack-hole conjecture (Penrose 1965): a LDW avoids a `naked' base, and\nencloses it with a critical surface.\n\nSince to each $z\\ter$ there corresponds a unique, supercritical mass\nloss rate, the latter is determined by the perturbation {\\it location}\nalone. Using $v\\Abbter=-v\\ter$, one finds $\\dot m\\ter= g\\cri/g\\ter >1$\nfor a planar wind with constant radiative flux.\n\nAt a termination point, $vv'$ jumps to the decelerating branch, $vv'\n<0$. Beyond a well-defined location above the gravity maximum, the\nsuper-CAK mass loss rate can again be lifted by the line force, and\n$vv'$ jumps back to the accelerating branch. Hence, two stationary\nkinks occur in the velocity law. Figure~2 shows a hydrodynamic\nsimulation of the evolution towards an overloaded solution.\nSawtooth-type velocity perturbations were introduced at $z=0.8$.\nCorrespondingly, $\\dot m=1.025$ for the overloaded solution, using\n$g=z/(1+z^2)$.\n\n\\begin{figure}[ht]\n\\plotone{fig2.ps} \n\\caption{Wind evolution towards a stationary, overloaded\nsolution showing an extended decelerating region. A periodic sawtooth\nperturbation is introduced into a shallow solution at $z=0.8$,\nupstream from the critical point at $z\\cri=1$. }\n\\end{figure} \n\n\nFuture work has to clarify whether LDWs show deep-seated\nperturbations. It seems however unlikely that they would occur at a\nunique location. Hence, overloaded winds should be non-stationary and\nshow a {\\it range} of supercritical mass loss rates.\n\nMore fundamentally, time-dependent overloaded solutions occur already\nfor single, unique perturbation sites, once the latter lie below a\ncertain height. For the present wind model, this is at $z \\approx\n0.66$. The overloading is then so severe and the decelerating region\nso broad that negative wind speeds result (cf.~Poe, Owocki, \\& Castor\n1990). The corresponding mass loss rates are still only a few percent\nlarger than the CAK value. The gas which falls back towards the\nphotosphere collides with outflowing gas, and a time-dependent\nsituation develops. Within each perturbation period, a shock forms in\nthe velocity law, supplemented by a dense shell. These shocks and\nshells propagate outwards (Feldmeier \\& Shlosman 2000).\n\nAlthough strong perturbations introducing negative velocity gradients\ncan appear already in O~star winds, accretion disk winds are the prime\nsuspects. The reason for this is that accretion processes and their radiation\nfields in cataclysmic variables and galactic nuclei are intrinsically\nvariable on a range of timescales (Frank, King, \\& Raine 1992), and\nthat disk LDWs are driven by a combination of uncorrelated, local and\ncentral radiation fluxes.\n \n\\section{Summary}\n\nWe find that shallow solutions to line-driven winds are subcritical\nwith respect to Abbott waves (sub-abbottic). These waves cause\nshallow solutions to evolve towards larger speeds and mass loss rates\nbecause of the asymmetry of the line force with regard to positive and\nnegative velocity gradients and because perturbations with opposite signs of\n$dv/dz$ propagate in opposite directions. Steep velocity slopes\npropagate towards the wind base, steepen the inner wind and lift\nit to higher mass loss rates. In the presence of enduring wind\nperturbations, this proceeds until a critical point forms and\nAbbott waves can no longer penetrate inwards.\n\nThe resulting solution does not necessarily correspond to the CAK\nwind. For perturbations which originate below the critical point, the\ndeveloping Abbott wave barrier is found to be the termination point of\na mass-overloaded solution. The velocity law acquires a kink at the\ntermination point, where the wind starts to decelerate. Whether the\nwind converges to a critical or overloaded solution depends entirely\non the {\\it location} of perturbations, and not, e.g., on boundary\nconditions at the wind base.\n\nIf Abbott waves are not accounted for in the Courant time step of\nhydrodynamic simulations, we find that {\\it numerical} runaway can\ndrive the solution towards the critical CAK wind. A detailed\ndiscussion of this will be given elsewhere.\n\nFuture work has to clarify whether and where perturbations causing\nlocal flow deceleration, $dv/dz<0$, can occur in LDWs. Overloaded\nwinds may be detected observationally. While their mass loss rates\nshould still be close to CAK values, broad regions of decelerating\nflow could be identified in P~Cygni line profiles. Furthermore, shocks\noccurring in overloaded solutions with infalling gas may contribute to\nthe X-ray emission from LDWs, besides shocks from the line-driven\ninstability (Lucy 1982; Owocki et al.~1988). Note that the present wind\nrunaway occurs already in the lowest order Sobolev approximation,\nand is therefore, unrelated to the line-driven instability which\ndepends on velocity curvature terms (Feldmeier 1998).\n\n\n\\acknowledgments\n\nWe thank R.~Buchler, J.~Drew, R.~Kudritzki, C.~Norman, S.~Owocki, and\nJ.~Puls for intense blackboard discussions, and the referee, Stan\nOwocki, for suggestions improving the manuscript. This work was\nsupported in part by PPA/G/S/1997/00285, NAG 5-3841, WKU-522762-98-6\nand HST~GO-08123.01-97A.\n\n\\clearpage\n\n\\begin{references}\n\n\\reference{} Abbott, D. C. 1980, ApJ, 242, 1183\n\n\\reference{} Castor, J. I., Abbott, D. C., \\& Klein, R. I. 1975, ApJ,\n 195, 157 (CAK)\n\n\\reference{} Courant, R., \\& Hilbert, D. 1962, Methods of Mathematical\n Physics, New York: Interscience\n\n\\reference{} Feldmeier, A. 1998, A\\&A, 332, 245\n\n\\reference{} Feldmeier, A., \\& Shlosman, I. 1999, ApJ, 526, 344\n \n\\reference{} Feldmeier, A., \\& Shlosman, I. 2000, ApJ, in preparation\n\n\\reference{} Frank, J., King, A., \\& Raine, D. 1992, Accretion Power\n in Astrophysics, Cambridge Univ. Press\n\n\\reference{} Hedstrom, G. W. 1979, J. Comp. Phys., 30, 222\n\n\\reference{} Lucy, L. B. 1982, ApJ, 255, 286\n\n\\reference{} Owocki, S. P., \\& Rybicki, G. B. 1986, ApJ, 309, 127\n\n\\reference{} Owocki, S. P., Castor, J. I., \\& Rybicki, G. B. 1988,\n ApJ, 335, 914\n\n\\reference{} Owocki, S. P., \\& Puls, J. 1999, ApJ, 510, 355\n\n\\reference{} Penrose, R. 1965, Phys. Rev. Lett., 14, 57\n\n\\reference{} Poe, C. H., Owocki, S. P., \\& Castor, J. I. 1990, ApJ,\n 358, 199\n\n\\reference{} Puls, J., Springmann, U., \\& Lennon, M., A\\&AS, 141, 23\n\n\\end{references}\n\n \n\\end{document}\n\n"
}
] |
[] |
astro-ph0002340
|
The Toronto Red-Sequence Cluster Survey: First Results
|
[
{
"author": "Michael D. Gladders and H.K.C. Yee"
}
] |
The Toronto Red-Sequence Cluster Survey (TRCS) is a new galaxy cluster survey designed to provide a large sample of optically selected $0.1 < z < 1.4$ clusters. The planned survey data is 100 square degrees of two color ($R$ and $z'$) imaging, with a 5$\sigma$ depth $\sim$2 mag past $M^*$ at $z=1$. The primary scientific drivers of the survey are a derivation of $\Omega_{m}$ and $\sigma_8$ (from $N(M,z)$ for clusters) and a study of cluster galaxy evolution with a complete sample. This paper gives a brief outline of the TRCS survey parameters and sketches the methods by which we intend to pursue the main scientific goals, including an explicit calculation of the expected survey completeness limits. Some preliminary results from the first set of data ($\sim$ 6 deg$^2$) are also given. These preliminary results provide new examples of rich $z\sim1$ clusters, strong cluster lensing, and a possible filament at $z\sim1$.
|
[
{
"name": "gladders.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Gladders \\& Yee}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{The Toronto Red-Sequence Cluster Survey: First Results}\n \\author{Michael D. Gladders and H.K.C. Yee}\n\\affil{Department of Astronomy, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 3H8, Canada}\n\n\\begin{abstract}\n The Toronto Red-Sequence Cluster Survey (TRCS) is a new galaxy\n cluster survey designed to provide a large sample of optically\n selected $0.1 < z < 1.4$ clusters. The planned survey data is 100\n square degrees of two color ($R$ and $z'$) imaging, with a 5$\\sigma$\n depth $\\sim$2 mag past $M^*$ at $z=1$. The primary scientific\n drivers of the survey are a derivation of $\\Omega_{m}$ and $\\sigma_8$ \n (from $N(M,z)$ for clusters) and a study of cluster galaxy\n evolution with a complete sample. This paper gives a brief outline\n of the TRCS survey parameters and sketches the methods by which we\n intend to pursue the main scientific goals, including an explicit\n calculation of the expected survey completeness limits. Some\n preliminary results from the first set of data ($\\sim$ 6\n deg$^2$) are also given. These preliminary results provide new\n examples of rich $z\\sim1$ clusters, strong cluster lensing, and a\n possible filament at $z\\sim1$.\n\\end{abstract}\n\n\\section{The TRCS}\n\\paragraph{}\nThe Toronto Red-Sequence Cluster Survey (TRCS) is a major new\nobservational effort designed to identify and characterize a large\nsample of galaxy clusters to redshifts as high as $z\\sim1.4$. When\ncompleted, the TRCS will be the largest imaging survey ever completed\non 4m telescopes, and will provide a large and homogeneous sample of\ngalaxy clusters for detailed follow-up study. The basic survey is\nenvisioned as 100 deg$^2$ of 2 filter ($R$ and $z'$) imaging, to a\ndepth which is $\\sim$2 mag past $M^*$ at $z=1$ in both filters. The\ndesign of the survey is based on a new method for identifying galaxy\nclusters (Gladders \\& Yee 2000a) developed specifically for the TRCS.\nIn brief, this method searches for clustering in the 5-D space of: x-y\npositions, $R-z'$ color, $z'$ mag, and morphology in the form of a\nconcentration index. The x-y positions provide the surface density\nenhancement. A color slice in the color-mag plane provides separation\nin $z$ space via the {\\it red sequence} of early-type galaxies in\nclusters (Figure 1) and increases the S/N of density enhancements.\nMorphology allows us to key onto early-type galaxies, the primary\npopulation in cluster centers.\n\n\\begin{figure}\n\\plotone{gladders1.eps}\n\\caption{\nModeled cluster CMDs to z=1.4 (left panel, solid lines), from Kodama\n\\& Arimoto (1997). Diamonds indicate simulated field galaxies for a 1\narcmin$^2$ FOV. The *s show M$^{*}$ for each redshift. The TRCS\nphotometric completeness limits are shown (dashed line). We also show\nreal CMDs (right) for CL1322+3114 at $z=0.75$ and k-corrected to\n$z=1$. These data are from HST images degraded to TRCS seeing and\ndepth. Cluster image objects (*) and field image objects ($\\diamond$)\nare shown. Note the visibility of the cluster red sequence.}\n\\end{figure}\n \n\\subsection{Scientific Goals}\n\\paragraph{}\nThe TRCS is being driven by two major scientific goals. The first is\nbased on the theoretical prediction that the evolution of the\nmass-spectrum of galaxy clusters with redshift, $N(M,z)$, should be a\nstrong function of two cosmological parameters, $\\Omega_{m}$ and\n$\\sigma_8$ (Figure 2). The goal is to use the clusters identified in\nthe survey to measure $N(M,z)$ directly from the survey data. Redshift\ncan be estimated from the color of red sequence (e.g., L\\'{o}pez-Cruz\n\\& Yee 2000), and the mass of each cluster can be estimated from its\nrichness, as measured by the parameter $B_{gc}$ (e.g., Yee \\&\nL\\'{o}pez-Cruz 1999). The second major scientific goal is a study of\nthe cluster galaxy populations, which can be done using the TRCS for\nthe first time with a complete sample. The definition of a complete,\nor volume limited, sample is derived from extensive simulations of the\nsurvey selection functions.\n\n\\begin{figure}[htp]\n\\plotfiddle{gladders2.eps}{3cm}{0.0}{50}{40}{-165}{-40}\n\\caption{The expected cumulative counts of clusters per~deg$^2$ for two\ncosmologies, for Abell Richness Class (ARC) 1 and 2. The 100\\%\ncompleteness redshift for ARC 1 is $\\sim1.1$, and $\\sim1.3$ for the\nricher, rarer ARC 2 clusters.}\n\\end{figure}\n \n\n\\subsection{Survey Completeness and Selection Functions}\n\\paragraph{}\nAny detailed understanding of the cosmological or galaxy evolution\nresults deriving from the TRCS requires a good understanding of the\nsurvey selection functions. Specifically, we wish to know how well the\ncluster-finding algorithm finds clusters of various sorts (as\ndescribed by various parameters). To this end, we have constructed a\nnumber of cluster and field simulations (Gladders \\& Yee 2000b) to\ndirectly test the algorithm. A large suite of possible clusters have\nbeen tested; the parameters describing the clusters are given in Table\n1. The results of this process demonstrate that the TRCS should be\ncomplete for all reasonable clusters of Abell Richness Class $\\geq$ 1\nclusters ($\\sigma_{v}\\geq750$ km s$^{-1}$) to at least $z=1.1$.\n\\begin{table}\n\\begin{tabular}{lll}\n\\hline\nParameter & Model Values & Notes \\\\\\hline\nLF $R$-band $M^*$ & -22.5, -22.25, -22.0 & $\\alpha=-1.0$\\\\\nAbell Richness counts & 35,44,56,72,93,120& Richness Classes 0-2 \\\\\nNFW core scale radius & 0.1,0.2,0.3,0.4,0.5 & in $h^{-1}$ Mpc\\\\\nellipticity &0.0,0.2,0.4,0.6,0.8 & measured at 1 $h^{-1}$ Mpc \\\\ \nblue fraction & 0.1,0.5,0.65,0.8,0.9 & \\\\\nred sequence age & 9,10,11,11.5 & lower limit of SF in Gyr \\\\\nscatter in formation ages& 0.5,1.0,max & tophat width in Gyr \\\\\ncluster redshift&0--1.4&\\\\\\hline\n\\end{tabular}\n\\caption{Cluster model parameters used to test the cluster finding \nalgorithm as applied to the TRCS.}\n\\end{table}\n\n\\section{Some First Results}\nThe first run for the TRCS occurred at CFHT in May, 1999. A total of\n21 pointings were acquired with the CFH12K camera, with each pointing\ncovering 0.272 deg$^2$. The bulk of the images have seeing better than\n0\\farcs7, with some as good 0\\farcs5. At the time of writing, the\ntotal TRCS dataset consists of about 35 deg$^2$ of data. However, the\nresults presented below are based on only the first 6 deg$^2$. Figure\n3 shows a rich ($B_{gc}\\sim2000$), compact cluster at photometric\nredshift of $z\\sim0.95$ (left panel). The cluster appears to be\nembedded in a large\n\\begin{figure}[htp]\n\\plotfiddle{gladders3.eps}{3.65cm}{0.0}{48}{48}{-140}{-12}\n\\caption{The image on the left shows the core of the cluster (A) and a possibly associated\ngroup (B). The central and right panels show the surface density of\ngalaxies in a {\\it much larger region} (roughly 20'x30') with and\nwithout a color cut.}\n\\end{figure}\n\\noindent \nfilamentary structure ($\\sim$10 h$^{-1}$ Mpc long) traced out by\nred galaxies (center panel). The excess is undetectable without a\ncolor cut (right panel). The efficacy of color information in\nisolating high-$z$ structures is obvious.\n\n\\paragraph{}\nFigure 4 shows the cores of several other rich clusters, one of which\nappears to have a gravitational arc. The success of the TRCS\nin finding rich, high-z cluster candidates in the few\ndegrees searched so far implies that the total survey will contain\nseveral hundred $z\\geq0.8$ cluster candidates, a preliminary result\nwhich is supportive of a low-density, high normalization cosmological\nmodel. \n\n\\begin{figure}\n\\plottwo{gladders4.eps}{gladders5.eps}\n\\caption{\nTwo rich cluster candidates with estimated redshifts of 0.45 and 0.85\n(left to right). Though not readily visible here, the cluster at 0.85\nappears to have a gravitational arc, consistent with its richness of\n$B_{gc}\\sim2500$. Large color images of these clusters can be found at\n\\texttt{http://www.astro.utoronto.ca/$\\sim$gladders/TRCS/trcs1.html}}\n\\end{figure} \n\n\\section{Secondary Projects}\nThe TRCS dataset is also well suited for a number of other detailed\nstudies. For example, preliminary work has already revealed a\nsignificant population of extremely red ($R-z' \\geq 3.5$) point\nsources. Such objects are likely L and T dwarfs, with some\ncontamination by $z\\geq5.5$ QSOs. Other studies are possible using the\nsurvey data, e.g. studies of cluster lensing (strong and weak), cosmic\nshear, halo structure, low surface brightness galaxies and early-type\ngalaxy correlations.\n\n\\references{\n\\reference Gladders, M.D., \\& Yee, H.K.C. 2000a, in prep.\n\\reference Gladders, M.D., \\& Yee, H.K.C. 2000b, in prep.\n\\reference Kodama, T., \\& Arimoto, N. 1997, 320, 41\n\\reference L\\'{o}pez-Cruz, O., \\& Yee, H.K.C. 2000, (to be submitted to ApJ)\n\\reference Yee, H.K.C., \\& L\\'{o}pez-Cruz, O. 1999, AJ, 117, 1985\n\n}\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[] |
astro-ph0002341
|
Variable stars in the field of the globular cluster E3
|
[
{
"author": "B. J. Mochejska"
},
{
"author": "J. Kaluzny"
}
] |
We present the results of a search for variable stars in the faint sparse globular cluster E3. We have found two variable stars: an SX Phe variable (V1) and a W UMa eclipsing binary (V2). We have applied period-luminosity and period-color-luminosity relations to the variables to obtain their distance moduli. V1 seems to be a blue straggler belonging to E3, based on its distance modulus and location on the CMD. V2 is probably located behind the cluster, in the Milky Way halo. We also present $V/B-V$ and $V/V-I$ color magnitude diagrams of E3.
|
[
{
"name": "mochejska.tex",
"string": "\\documentstyle[11pt,aaspp4]{article}\n\\begin{document}\n\n\\title{Variable stars in the field of the globular cluster E3}\n\n\\author{B. J. Mochejska, J. Kaluzny}\n\\affil{Copernicus Astronomical Center, 00-716 Warszawa, Bartycka 18}\n\\affil{\\tt e-mail: mochejsk@camk.edu.pl, jka@camk.edu.pl} \n\\author{I. Thompson}\n\\affil{Carnegie Institution of Washington, 813 Santa Barbara Street,\nPasadena, CA 91101, USA}\n\\affil{\\tt e-mail: ian@ociw.edu}\n\\begin{abstract}\nWe present the results of a search for variable stars in the faint\nsparse globular cluster E3. We have found two variable stars: an SX\nPhe variable (V1) and a W UMa eclipsing binary (V2). We have applied\nperiod-luminosity and period-color-luminosity relations to the\nvariables to obtain their distance moduli. V1 seems to be a blue\nstraggler belonging to E3, based on its distance modulus and location\non the CMD. V2 is probably located behind the cluster, in the Milky\nWay halo. We also present $V/B-V$ and $V/V-I$ color magnitude\ndiagrams of E3.\n\\end{abstract}\n\n\\section{Introduction}\n\nWe present the results of a search for variable stars in the faint\nsparse globular cluster E3, located at $\\alpha_{2000}=9^h20^m59^s$,\n$\\delta_{2000}=-77\\arcdeg16\\arcmin57\\arcsec$. The cluster was\ndiscovered on the ESO B Schmidt Survey of the Southern Sky by Lauberts\n(1976). The first $BV$ photometry of the cluster was presented by van\nden Bergh, Demers \\& Kunkel (1980). Numerous candidates for blue\nstragglers were identified. The photoelectric photometry of Frogel \\&\nTwarog (1983) confirmed this finding. A subsequent study by Hesser et\nal. (1984) using $UBV$ photoelectric and photographic observations\nshowed a sparsely populated subgiant branch in the color-magnitude\ndiagram. The first CCD photometry for E3 in the $BV$ bands, obtained\nwith the CTIO 4m telescope, was published by McClure et\nal. (1985). These observations suggested the presence of a second\nsequence of stars $\\sim0.75$ mag. above the cluster main sequence,\ninterpreted as evidence for a significant population of binary stars\nin E3. The cluster was further studied by Gratton \\& Ortolani (1987),\nwho provided new $BV$ CCD photometry from the 2.2m telescope at ESO.\n\n\\begin{figure}[t]\n\\plotfiddle{mochejska.fig1.ps}{10cm}{0}{80}{80}{-180}{-10}\n\\caption{Finding chart for the variables in E3. North is up and east\nis to the left.}\n\\label{fig:map}\n\\end{figure}\n\n\\section{Observations and Data Reduction}\n\nThe data for this project was obtained with the Las Campanas\nObservatory 1.0m Swope telescope during two separate runs: from April\n11 to 21, 1996 and from May 16 to 27, 1996. For the first few nights\nof the April run the telescope was equipped with the TEK1 1024x1024\nCCD camera giving a pixel scale of $0.70\\arcsec/pixel$. On the night\nof April 14 the camera was switched to the TEK3 2048x2048 CCD with a\npixel scale of $0.61\\arcsec/pixel$. During the May run the FORD\n2048x2048 CCD camera with a pixel scale of $0.41\\arcsec/pixel$ was\nused.\n\nThe main observing target on both runs was the M4 globular cluster.\nSeveral exposures of E3 were taken at the beginning of most nights. A\ntotal of 121 long ($400\\div900\\;sec$) exposures were taken in the $V$\nfilter (33, 42 and 46 with TEK1, TEK3 and FORD, respectively), six\nshort ($35\\div120\\;sec$) exposures in $V$ (2 with TEK1, 4 with FORD),\ntwo $600\\;sec$ exposures in $I$ (TEK1) and two $480\\;sec$ exposures in $B$\n(TEK1).\n\nThe preliminary processing of the CCD frames was done with the\nstandard routines in the IRAF-CCDPROC package.\\footnote{IRAF is\ndistributed by the National Optical Astronomy Observatories, which are\noperated by the Association of Universities for Research in Astronomy,\nInc., under cooperative agreement with the NSF} The images from the\nTEK3 camera were clipped to a size of 1024x1024 pixels$^2$ to cover\nroughly the same field as the TEK1 images. Due to the high degree of\npsf variability on the images taken with the FORD camera, only the\ncentral 800x800 pixel$^2$ sections were used.\n\n\\begin{figure}[!t]\n\\plotfiddle{mochejska.fig2.ps}{2.3cm}{0}{80}{80}{-250}{-510}\n\\caption{Phased $V$ filter light curves of the two variables in E3.}\n\\label{fig:var}\n\\end{figure}\n\nPhotometry was extracted using the {\\it Daophot/Allstar} package\n(Stetson 1987). A PSF varying linearly with the position on the frame\nwas used. The PSF was modeled with a Moffat function. Stars were\nidentified using the FIND subroutine and aperture photometry was measured\nwith the PHOT subroutine. Approximately 40 bright isolated stars were\ninitially chosen by {\\it Daophot} for the construction of the PSF. Of\nthose the stars with profile errors greater than twice the average\nwere rejected and the PSF was recomputed. This procedure was repeated\nuntil no such stars were left on the list. The PSF was then further\nrefined on frames with all but the PSF stars subtracted.\nThis procedure was applied twice. The PSF obtained in the above\nmethod was then used by {\\it Allstar} in profile photometry.\n\nThe image where the most stars were identified was chosen as the\ntemplate. The template star list was then transformed to the $(X,Y)$\ncoordinate system of each of the frames and used as input to {\\it\nAllstar} in the fixed-position mode. The output profile photometry was\ntransformed to the common instrumental system of the template image\nand then combined into a database. The databases were created for the\nlong ($400-900\\;sec$) exposures in the $V$ filter only.\n\n\\section{Variable stars}\n\nWe have followed the procedure for selecting variables given in\nKaluzny et al. (1998), where it is described in detail. From the 1541\nstars in the $V$ database 11 variable star candidates were selected.\nAfter the rejection of stars with noisy and/or chaotic light curves we\nwere left with two variables. Their periods were refined using the\nanalysis of variance method, as described by Schwarzenberg-Czerny\n(1989). These two variables were confirmed with ISIS - the image\nsubtraction package (Alard \\& Lupton 1998, Alard 1999). No other\nvariables were detected using this method.\n\nIn Figure \\ref{fig:var} we present the phased $V$ light curves of the\ntwo variables. Table \\ref{tab:var} lists the parameters of these \nvariables: name, period, $V$ magnitude ($\\langle V\\rangle$ for the \npulsating variable, $V_{max}$ for the eclipsing binary), the $B-V$ and\n$V-I$ colors. The variables are indicated by open circles on the finding\nchart in Figure \\ref{fig:map}.\n\nV1 is a pulsating variable, most likely of the SX Phe type, judging\nfrom its short period (0.0853 days) and the shape of its light\ncurve. V2 is an eclipsing binary with a period of 0.4490 days. Its\nlight curve shows an absence of the constant light phase, indicating\nthat it is a W UMa type variable.\n\nWe have used the period-luminosity calibration for SX Phe stars derived\nby McNamara (1997) to estimate the distance modulus to V1:\n\\[M_V=-3.725 \\log P - 1.933\\]\nAdopting a value of reddening E(B-V)=0.30 (Harris 1996) we obtain a\ndistance modulus $(m_V-M_V)_0=14.46$. This value is in agreement with\nthe distance moduli found in literature: 14.55 - van den Bergh et\nal. (1980), 14.4 - Frogel \\& Twarog (1983), 14.2 - Gratton \\& Ortolani\n(1987), indicating that V1 is located at the same distance as the\ncluster.\n\nThe following period-color-luminosity calibrations for W UMa type\neclipsing binaries derived by Rucinski (2000) were applied to V2:\n\\[M_V^{BV} = -4.44 \\log P + 3.03 (B-V)_0 + 0.12\\]\n\\[M_V^{VI} = -4.43 \\log P + 3.63 (V-I)_0 - 0.31\\]\n\nThe fact that $B-V$ and $V-I$ colors were determined at random phase\nshould not influence the outcome substantially, as in the case of\ncontact binaries the color does not change significantly throughout\nthe cycle. Using a value of $E(V-I)=1.28 E(B-V)$ (Schlegel et\nal. 1997) we obtained a distance modulus of 15.42 mag. from the first\ncalibration and 14.83 mag. from the second. The variable appears to\nbe located behind the cluster, in the Milky Way halo.\n\n\\begin{table}\n\\caption[]{\\sc Variables in E3\\\\}\n\\begin{tabular}{cccccl}\n\\hline\\hline\nName& $P$ (days) & $V$ & $B-V$ & $V-I$ & Comments\\\\ \n\\hline\nV1 & 0.0853 & 17.48 & 0.60 & 0.86 & SX Phe\\\\\nV2 & 0.4490 & 18.17 & 0.66 & 0.96 & W UMa \\\\\n\\hline\n\\end{tabular}\n\\label{tab:var}\n\\end{table}\n\n\\section{Color-magnitude diagrams}\nTo construct the color-magnitude diagrams we combined pairs of long\nexposures in the $BVI$ filters. \nThe transformation from instrumental magnitudes to the standard system \nwas derived from the observations of the Landolt fields (Landolt 1992).\nThe following relations were adopted:\n\\begin{eqnarray*}\nv = V - 0.0189 \\times (B-V) + const\\\\\nb - v = 0.9359 \\times (B-V) + const\\\\\nv = V - 0.0182 \\times (V-I) + const\\\\\nv - i = 0.9843 \\times (V-I) + const\n\\end{eqnarray*}\n\nWe have compared our $BV$ photometry with that of McClure et al. (1985).\nThe average differences in $V$ magnitude and $B-V$ color were computed\nfor 6 selected stars in the range $15.5\\leq V\\leq 19.25$ and were found to\nbe $\\Delta V=0.02\\pm0.014$ and $\\Delta (B-V)=0.04\\pm0.080$.\n\n\\begin{figure}[tb]\n\\vspace{7cm}\n\\special{psfile=mochejska.fig3a.ps hoffset=-5 voffset=-60 vscale=40 hscale=40 angle=0}\n\\special{psfile=mochejska.fig3b.ps hoffset=235 voffset=-60 vscale=40 hscale=40 angle=0}\n\\caption{The $V/B-V$ and $V/V-I$ color-magnitude diagrams of the inner\n$2\\arcmin$ of the E3 globular cluster. Variable V1 is denoted by an open\ncircle and V2 by an open square.}\n\\label{fig:cmd}\n\\end{figure}\n\nThe colors and magnitudes for variable stars were determined following\na different procedure. For variable V1 its average magnitude $\\langle\nV\\rangle$ was used to place it on the CMDs. V2 was plotted with its\nmagnitude outside of the eclipses $V_{max}$. To derive the colors we\nused the single $B$ and $I$ exposures and interpolated the $V$\nmagnitudes from the nearest exposures in $V$ to those epochs. The\nfinal values of $B-V$ and $V-I$ were taken as the average of two color\ndeterminations, with the average scatter of 0.04 mag.\n\nThe resultant $V/B-V$ and $V/V-I$ color-magnitude diagrams are shown\nin Figure \\ref{fig:cmd}, with the variable V1 denoted by an open\ncircle and V2 by an open square. Only stars within $2\\arcmin$ of the\ncluster center are plotted. Both variables are located among candidate \nblue stragglers, although V2 appears to be located behind the cluster,\nbased on the distance modulus determination in the previous section.\n\nThe cluster main sequence is apparent in both diagrams. It exhibits\nconsiderable scatter and there is some indication of a second sequence\nrunning above it, although not as clear as in Figure 3 of McClure et\nal. (1985). This would indicate that E3 could possess a significant\npopulation of binary stars. This is in agreement with the idea\nproposed by van den Bergh et al. (1980) that severe tidal stripping\nhad depleted the cluster in single stars, leading to an increased\nbinary frequency. \n\nA gap in the main sequence near the turnoff, at $V\\sim19.5$ is visible\nin both CMDs. This has been previously noted by McClure et al. (1985)\nand shown to be more of a visual effect, as no significant\ndiscontinuities are present in the cumulative luminosity function for\nstars on the main sequence (Figure 6 therein). This result is\nconfirmed by our analysis.\n\nThe subgiant and lower giant branches are also discernible in the\ndiagrams, although they show substantial scatter. This is regarded as\na real feature of the cluster, as commented in literature\n(i.e. Hesser et al. 1984). A number of stars blueward of the turnoff\nare present, possibly blue stragglers belonging to the cluster, as\nfirst noted by van den Bergh et al. (1980).\n\n\\section{Conclusions}\n\nOur variability search in E3 resulted in the discovery of two variable\nstars: an SX Phe variable (V1) and a W UMa eclipsing binary (V2). We\nhave applied period-luminosity and period-color-luminosity relations\nto the variables to obtain their distance moduli. V1 seems to be a\nblue straggler belonging to E3, based on its distance modulus and\nlocation on the CMD. V2 is probably located behind the cluster.\n\n\\acknowledgments{We would like to thank Krzysztof Z. Stanek for his\nerror scaling, database manipulation and period finding programs and\nGrzegorz Pojma{\\'n}ski for $lc$ - the light curve analysis utility,\nincorporating the analysis of variance algorithm. BJM and JK were\nsupported by the polish KBN grant 2P03D003.17 and by NSF grant\nAST-9819787.}\n\n\\begin{references}\n\\reference{} Alard, C. 1999, preprint (astro-ph/9903111)\n\\reference{} Alard, C., Lupton, R.~H. 1998, ApJ, 503, 325\n\\reference{} Frogel, J.A., Twarog, B.A. 1983, ApJ, 274, 270\n\\reference{} Gratton, R.G., Ortolani, S. 1987, A\\&AS, 67, 373\n\\reference{} Harris, W.~E. 1996, AJ, 112, 1487\n\\reference{} Hesser,J.~E., McClure, R.~D., Hawarden, T.~G., Cannon, R.~D., \n von Rudloff, R., Kruger, B., Egles, D. 1984, PASP, 96, 406\n\\reference{} Kaluzny, J., Stanek, K.~Z., Krockenberger, M., Sasselov, D.~D.,\n Tonry, J.~L., \\& Mateo, M. 1998, AJ, 115, 1016\n\\reference{} Landolt, A. 1992, AJ, 104, 340\n\\reference{} Lauberts, A. 1976, A\\&A, 52, 309\n\\reference{} McClure, R.~D., Hesser, J.~E., Stetson, P.~B., Stryker, L.~L.\n 1985, PASP, 97, 665\n\\reference{} McNamara, D.~H. 1997, PASP, 109, 1221\n\\reference{} Rucinski, S.~M. 2000, preprint (astro-ph/0001152)\n\\reference{} Schlegel, D. J., Finkbeiner, D. P., Davis, M. 1997, AAS,\n 191, 8704\n\\reference{} Schwarzenberg-Czerny, A. 1989, MNRAS 253, 198\n\\reference{} Stetson, P.~B. 1987, PASP, 99, 191\n\\reference{} van den Bergh, S., Demers, S., Kunkel, W.~E. 1980, ApJ, 239,\n 112\n\\end{references}\n\n\\end{document}\n\n\n"
}
] |
[] |
astro-ph0002342
|
The discovery of a low mass, pre-main-sequence stellar association around $\gamma$-Velorum
|
[
{
"author": "M. Pozzo"
},
{
"author": "R.D.~Jeffries"
},
{
"author": "T.~Naylor"
},
{
"author": "E. J.~Totten\\thanks{Visiting astronomer at the Cerro Tololo Interamerican Observatory}"
},
{
"author": "S.~Harmer\\thanks{Nuffield Foundation Undergraduate Research Bursar (NUF-URB98)}"
},
{
"author": "Department of Physics"
},
{
"author": "Keele"
},
{
"author": "Staffordshire"
},
{
"author": "ST5 5BG"
},
{
"author": "UK"
}
] |
We report the serendipitous discovery of a population of low mass, pre-main sequence stars (PMS) in the direction of the Wolf-Rayet/O-star binary system $\gamma^{2}$ Vel and the Vela OB2 association. We argue that $\gamma^{2}$ Vel and the low mass stars are truly associated, are approximately coeval and that both are at distances between 360-490\,pc, disagreeing at the 2$\sigma$ level with the recent Hipparcos parallax of $\gamma^{2}$ Vel, but consistent with older distance estimates. Our results clearly have implications for the physical parameters of the $\gamma^{2}$ Vel system, but also offer an exciting opportunity to investigate the influence of high mass stars on the mass function and circumstellar disc lifetimes of their lower mass PMS siblings. %A PMS low-mass star association around $\gamma$-Velorum has been %serendipitously discovered thanks to the analysis of ROSAT X-Ray %observations. The spatial distribution of these objects suggests that %they are physically associated with the Wolf-Rayet star. This is the %natural scenario where to study what influence a very bright star can %have on a low-mass star association.
|
[
{
"name": "gamvel.tex",
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Pozzo et al.]\n {M. Pozzo, \n R.D.~Jeffries, T.~Naylor, E. J.~Totten\\thanks{Visiting astronomer at the\n Cerro Tololo Interamerican Observatory}, \n S.~Harmer\\thanks{Nuffield Foundation \nUndergraduate Research Bursar (NUF-URB98)}, \nM.~Kenyon\\thanks{Present address, University College, Gower St., London\n WC1E 6BT}\\\\\n Department of Physics, Keele University, Keele, Staffordshire, ST5 5BG, UK}\n\\date{Accepted 0000 Received 0000}\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\pubyear{0000}\n\n\\include{latex_macros}\n\\begin{document}\n\n\n\\label{firstpage}\n\\maketitle\n\n\\begin{abstract}\nWe report the serendipitous discovery of a population of low mass,\npre-main sequence stars (PMS) in the direction of the Wolf-Rayet/O-star\nbinary system $\\gamma^{2}$ Vel and the Vela OB2 association. We argue\nthat $\\gamma^{2}$ Vel and the low mass stars are truly associated, are\napproximately coeval and that both are at distances between\n360-490\\,pc, disagreeing at the 2$\\sigma$ level with the recent Hipparcos\nparallax of $\\gamma^{2}$ Vel, but consistent with older distance estimates. \nOur results clearly have implications\nfor the physical parameters of the $\\gamma^{2}$ Vel system, but also\noffer an exciting opportunity to investigate the influence of high mass\nstars on the mass function and circumstellar disc lifetimes of their\nlower mass PMS siblings.\n\n\n%A PMS low-mass star association around $\\gamma$-Velorum has been\n%serendipitously discovered thanks to the analysis of ROSAT X-Ray\n%observations. The spatial distribution of these objects suggests that\n%they are physically associated with the Wolf-Rayet star. This is the\n%natural scenario where to study what influence a very bright star can\n%have on a low-mass star association.\n\n\\end{abstract}\n\n\\begin{keywords}\n stars: pre-main-sequence -- X-rays: stars -- stars: Wolf-Rayet.\n\\end{keywords}\n\n\n\n\\section{Introduction}\n\nAs little as 15 years ago it was believed that high mass stars formed\nmainly in OB associations and that low mass stars formed mainly in T\nassociations. In the last few years it has become increasingly\nrecognized that the majority of low mass stars in the solar\nneighbourhood are in fact likely to have formed in OB\nassociations. The mass function in OB associations may\nmatch popular log-normal parameterisations of the general field population \nsuch as those proposed by Miller \\& Scalo (1979), with many low\nmass stars formed for every O/B star. The main reason for\nthis shift in paradigm is the discovery of numerous low mass pre-main\nsequence (PMS) stars in young OB associations by virtue of their high levels\nof X-ray activity (see for example Walter et al. 1994, 1999; Naylor \\&\nFabian 1999, Preibisch \\& Zinnecker 1999 and references\ntherein). Recently, some evidence has been found that these X-ray\nselected groups can be quite small, concentrated around just one or two\nhigh mass stars, which are themselves part of larger\nassociations. Examples include\n$\\beta$ Cru (Feigelson \\& Lawson 1997), $\\sigma$ Ori (Walter,\nWolk \\& Sherry 1998) and $\\eta$ Cha (Mamajek, Lawson \\& Feigelson\n1999).\n\n\nThe investigation of these low mass PMS stars is of prime importance in\nestablishing the form of the {\\em initial} mass function. Although OB\nassociations are by definition unbound, they are young enough that\ndynamical effects such as mass segregation and preferential evaporation\nwill not have occurred; and they are usually free of the heavy,\nvariable extinction that plagues observations of active star forming\nregions. If the majority of low mass stars are born in OB associations\nit is crucial to establish the influence that high mass\nneighbours have on the formation and evolution of their lower mass\nsiblings. The winds and ionizing radiation of hot\nstars could influence the mass function and circumstellar disc\nlifetimes of the lower mass stars, with implications for angular\nmomentum evolution and planet formation. These ideas have gained\ncurrency with the discovery of evaporating discs around PMS stars\nin the Orion nebula (McCaughrean \\& O'Dell 1996) and theoretical\nstudies showing that discs could be ionized and evaporated by\nthe UV radiation fields of O stars (Johnstone, Hollenbach \\& Bally\n1998). In more extreme circumstances, nearby supernova explosions have\nbeen invoked both as a means of terminating low mass star formation (Walter\net al. 1994) or triggering it (Preibisch \\& Zinnecker 1999).\n\nIn this paper we report the discovery, by X-ray selection, of a low mass\nstellar population that seems likely to be associated with the nearest\nexample of a Wolf-Rayet (WR) star, $\\gamma^{2}$ Velorum\n(HD 68273, HIP 39953, WR11). Like about\nhalf of the $\\simeq 200$ galactic WR stars known, it is a binary\nsystem (WC8+O8) with an orbital period of 78.5 days and a massive,\ninteracting stellar wind. There is currently some controversy\nconcerning the distance to $\\gamma^{2}$ Vel, which impacts upon the\ndeduced luminosities, masses and mass loss rates from the system. It is\nimportant to get these parameters right because, as the nearest WR,\n$\\gamma^{2}$ Vel is an extreme test of stellar evolution models and\ncalibrates the absolute magnitudes of WR stars. The Hipparcos\nparallax yields a distance of $258^{+41}_{-31}$\\,pc to $\\gamma^{2}$ Vel\n(Schaerer, Schmutz \\& Grenon 1997, van der Hucht et al. 1997), in\nmarked contrast to previous distance estimates which place it at\n350-450\\,pc. The larger distance is in better agreement with the mean\ndistance to the Vela OB2 association ($410\\pm12$\\,pc), of which\n$\\gamma^{2}$ Vel is the most massive proper-motion member (de Zeeuw et\nal. 1999). \n\nThe presence of a low mass stellar association in the extreme\nenvironment around $\\gamma^{2}$ Velorum offers an excellent empirical\ntest of the possible influence of winds and ionizing radiation on low mass \nstars and their discs. Additionally it gives us a chance to measure the\ndistance to $\\gamma^{2}$ Vel by matching PMS isochrones to the low mass\nstars.\n\n\\section{X-Ray observations}\n\n\\begin{figure}\n\\vspace*{8.0cm}\n\\special{psfile=fig1.eps \nhscale=46 vscale=46 hoffset=0 voffset=0}\n\\caption{{\\em ROSAT} PSPC X-ray image of the region around $\\gamma^{2}$\nVel. The greyscale is such that black represents $\\geq 1$ photon per\n5x5 arcsec pixel and the brightest source in the centre of the image is\n$\\gamma^{2}$ Vel. Another 108 significant X-ray sources have been found in this\nimage. The solid outline shows the location of our optical CCD survey.}\n\\end{figure}\n\n\nWe suspected the presence of a low mass association around $\\gamma^{2}$\nVel from the large surrounding population of X-ray point sources seen\nin {\\em ROSAT} images, taken for a programme\nto investigate its interacting stellar winds (see Willis, Schild \\&\nStevens 1995 and Fig.1).\nThe X-ray observations of the WR were retrieved from the\n{\\em ROSAT} public archive and consisted of 10 Position Sensitive\nProportional Counter (PSPC) datasets and 2 datasets taken with the High\nResolution Imager. In this initial paper we discuss only the more\nsensitive PSPC results, which contain the vast majority of the X-ray point sources.\n\nWe used the Starlink-distributed \n{\\sc asterix} data reduction package in our X-ray analysis (Allan \\& Vallance 1995).\nThe 10 PSPC datasets were sorted into 1$^{\\circ}\\times1^{\\circ}$ images, selecting\npulse height channels 11 to 240 (approximately 0.1-2.4\\,keV photons) \nand excluding times with anomalously high background rates. \nThe images were centered on\n$\\gamma^{2}$ Vel (the brightest source in each dataset) and then\nsummed. The resulting image has dimensions of $720 \\times 720$\n5 arcsecond pixels and an effective on-axis exposure time of\n25.3 ks. We used the Point Source Searching (PSS - Allan 1992)\nalgorithm to search for sources by\nCash-statistic maximisation. By assuming the background to be zero we\nobtained a preliminary list \nof 104 X-ray sources which were masked out of the image. The masked\nimage was then patched and smoothed with a 75 arcsec FWHM gaussian to\ncreate a background map. We then executed the PSS algorithm again and\nfound 109 sources above a pseudo-gaussian significance level of\n4.5$\\sigma$, which corresponds roughly to 1 spurious detection in the\nX-ray image. The positions of the X-ray sources were corrected for errors in the\nsatellite aspect solution by comparing the optical and X-ray positions\nof $\\gamma^{2}$ Vel and four other bright stars from the CDS SIMBAD\ndatabase. We applied shifts of\n4.5 arcsec in RA and 13.8 arcsec in Dec to the X-ray positions.\n\n\\section{Optical photometry}\n\n\\begin{figure}\n\\vspace*{15.0cm}\n\\special{psfile=fig2a.eps \nhscale=82 vscale=82 hoffset=-135 voffset=-115}\n\\caption{(Top) CMD for the region around $\\gamma^{2}$ Vel. The solid\nlines in this and the plot below are isochrones at 1, 5 and 10\\,Myr\ncalculated from the models of D'Antona \\& Mazzitelli (1997). The dashed\nbox indicates the region from which PMS stars were selected for\nFig.3. (Bottom) The location of the X-ray source correlations in the\nCMD. Eleven spurious correlations are expected and are expected to lie\nin the clump at $V\\simeq 19$, $V-I\\simeq1$.}\n\\end{figure}\n\n\nCCD photometry of the X-ray field was obtained on 8 February 1999 with\nthe 0.9-m telescope at the Cerro Tololo\nInter-American Observatory. A Tek 2048x2048 CCD was\nused to give a 13.5x13.5 arcmin$^{2}$ field of view. \nEight overlapping fields around $\\gamma^{2}$-Vel were\nsurveyed in {\\it BVI} with short (20,10,10s) and long (200,100,100s) \nexposures, together with five fields from Landolt (1992) to determine \nzeropoints, colour terms and extinction coefficients. Several standards\nwith $V-I_{c}>2.5$ were observed. Figure~1\nillustrates the location of the fields around $\\gamma^{2}$\\,Vel. The external\naccuracy of our photometry was determined to be \naround 0.02 mag on the $BVI_{\\rm c}$ system.\n\nPhotometry was performed for each of the eight fields using an optimal\naperture algorithm (Naylor 1998; Totten et al. in preparation), and the results\ncombined to give an optical catalogue of sources. \nAstrometry was performed by comparison with star positions\nin version A2.0 of the USNO catalogue (Monet 1998) and we estimate\npositional accuracies of around 0.3 arcsec. The final catalogue\ncontains 20617 individual objects with their magnitudes, colours and\npositions. Figure 2a shows the $V$ versus $V-I_{\\rm c}$ \ncolour-magnitude diagram (CMD). The location of a possible\nPMS low-mass star association is clearly visible above the bulk of the\nbackground contamination. To this optical catalogue, we added the\npositions of bright ($V<11$)\nstars found in this region from the SIMBAD database.\n\nTo establish an appropriate cross-correlation radius to use between\nthe X-ray and optical source lists we modelled the cumulative number of\nX-ray sources that were correlated with an optical source with $V<19$\n(see Jeffries, Thurston \\& Pye 1997 for details). Assuming a uniform spread of\noptical sources, we determined that there were 77 correlations (from 83\nX-ray sources inside the CCD survey) within\n10 arcsec of X-ray positions, that 66\nof these would be true counterparts to X-ray\nsources, 11 would be spurious correlations and \nthat the $1\\sigma$ X-ray error circle was 3.7 arcsecs.\nFigure~2b shows 75 sources that have an optical counterpart within 10 arcsecs (another\ntwo are bright stars without $V-I$ colours).\nClearly the X-ray emitting population coincides with the proposed PMS\npopulation in the CMD. Indeed, if we were to consider just a subset of the\noptical catalogue consisting of a broad strip containing all these PMS\nsources, we would only expect 1 of these correlations to be spurious.\n\n\nWe have calculated the X-ray properties of this population and these\nalong with the HRI observations will be reported in a subsequent\npublication. Briefly, the X-ray to bolometric flux ratio of these\nobjects lies in the range $10^{-5}$ to $10^{-2}$, broadly what we would\nexpect from a population of young PMS stars. The cut-off in the\nPMS X-ray correlations at $V\\simeq18$ is almost certainly due to the X-ray\nsensitivity. To be detected in X-rays, fainter objects would have to\nhave higher than feasible X-ray to bolometric flux ratios. However, it is\nclear that the PMS sequence we have found extends down to the limits of\nour optical survey at $V\\sim20.5$.\n\n\n\\section{Discussion}\n\\begin{figure}\n\\vspace*{15.0cm}\n\\special{psfile=fig3.eps \nhscale=83 vscale=83 hoffset=-30 voffset=-40}\n\\caption{(Top) The spatial distribution of PMS stars (from inside the\ndashed box in Fig.2) around $\\gamma^{2}$ Vel. A clumping towards\n$\\gamma^{2}$ Vel (marked with a cross) is apparent.\n(Bottom) The relative spatial density of these PMS sources as a\nfunction of distance from $\\gamma^{2}$ Vel. This plot is normalized\nusing a background population to account for non-uniform coverage in\nthe CCD survey.}\n\\end{figure}\n\n\n\n\nThe appearance of Fig.2 should leave the reader in no doubt that we\nhave found a young and exceptionally rich population of low mass active\nstars in the {\\em direction} of $\\gamma^{2}$ Vel. The central question to\nbe answered is whether these sources are physically close to\n$\\gamma^{2}$ Vel and/or whether they are background members of the Vela OB2\nassociation. We can tackle this problem in a number of ways.\n\n\\subsection{Are the PMS stars and $\\gamma^{2}$ Vel aligned?}\n\nFigure 3a shows the spatial distribution of\nPMS stars selected from the CMD \nin a strip enclosing the bulk of the X-ray sources (marked with\na dashed box in Fig.2). This box was chosen to avoid background\ncontamination. We determined the radial distribution of these stars,\ncentred on $\\gamma^{2}$ Vel. The\ndistribution is normalized using the radial distribution of background\nstars with a similar $V$\nmagnitude range, but a colour range of 0.8$<V-I_{\\rm c}<$1.7, \nunder the assumption that the background\nstars are uniformly distributed. \nThe resulting radial distribution is shown in Fig. 3b, which exhibits\na small but significant (at the $3\\sigma$ level) peak within 5 arcmin\nof the centre of the CCD\nsurvey and $\\gamma^{2}$ Vel. The point closest to $\\gamma^{2}$ Vel is\nmissing because the 30 arcsec\nregion immediately surrounding $\\gamma^{2}$ Vel is swamped by its light\nand no accurate photometry was obtained there.\nIn a similar fashion\nwe can show that the X-ray sources are also marginally concentrated\ntoward the centre of the field even after correction for the PSPC\nvignetting function. \n\nThere is thus some evidence that the PMS stars and\n$\\gamma^{2}$ Vel are spatially correlated, although this does not rule\nout a chance alignment of $\\gamma^{2}$ Vel with a background cluster of\nlow mass stars in Vela OB2. In particular, it is possible that\nany concentration we see could be associated with $\\gamma^{1}$ Vel, a\nB2III, single lined spectroscopic binary which is a\ncommon proper motion companion to $\\gamma^{2}$ Vel. $\\gamma^{1}$ Vel\nis also a likely member of the Vela OB2 association, has a\nspectroscopic parallax of $\\simeq450$\\,pc and is located only 41\narcsecs at a PA of 220$^{\\circ}$ from $\\gamma^{2}$ Vel.\n\n\n\\subsection{Are the PMS stars and $\\gamma^{2}$ Vel at the same\ndistance?}\n\nThe isochrones plotted in Fig.2 come from the D'Antona \\& Mazzitelli\n(1997) low mass evolutionary models. We have converted from bolometric\nluminosity and effective temperature to magnitude and colour using\nempirical bolometric corrections as a function of colour and a\ncolour-effective temperature relationship derived by forcing the well\nstudied low mass stars in the Pleiades cluster to fit a\n125\\,Myr isochrone (see Jeffries \\& Tolley 1998). \nThe assumed distance and reddening are those appropriate for\nthe Vela OB2 association of 410\\,pc and $E(V-I)\\simeq 0.06$. It is\nclear that if the PMS stars are at the mean distance of the Vela OB2\nassociation they appear to be about $4\\pm2$\\,Myr old (taking into\naccount the likely presence of unresolved binary systems). If however,\nthe PMS association were at the Hipparcos distance to $\\gamma^{2}$ Vel,\nthe isochrones would be shifted upwards by 1 magnitude. In that case we\nwould deduce that the PMS population had an age $>10$\\,Myr. The age of\n$\\gamma^{2}$ Vel, based upon the mass of the O star ($\\sim\n30$M$_{\\odot}$) at the Hipparcos distance, is less\nthan 5\\,Myr (Schaerer et al. 1997; de Marco \\& Schmutz 1999). Thus if\nthe Hipparcos distance is adopted, the PMS stars and $\\gamma^{2}$ Vel\ncannot be at the same distance {\\em and} coeval. \nHowever, {\\em if} $\\gamma^{2}$ Vel were at the mean distance of\nthe Vela OB2 association, it would be more massive (see below), \nslightly younger and could easily be coeval with the PMS population.\nAn age range of 2-6\\,Myr would be compatible with distances between 490\nand 360\\,pc.\n\n\n\\subsection{How far away is $\\gamma^{2}$ Vel?}\n\nThe evidence that $\\gamma^{2}$ Vel is as close as 258\\,pc from the\nHipparcos parallax should be treated with some caution. de Zeeuw et\nal. (1999) examine the high mass membership of the Vela OB2 association\non the basis of both proper motions and parallaxes. The association is\nwell defined by proper motions and has an angular radius of about 6\ndegrees. The {\\em mean} parallax from 93 members corresponds to\n$410\\pm12$\\,pc. The parallax dispersion can be quite well modelled as a\ngaussian with a $\\sigma=0.68$ mas, such that $\\sim95\\%$ of the members appear to\nlie between 260\\,pc and 900\\,pc. The dispersion is reasonably\nconsistent with the errors on the individual points and not\ninconsistent with the idea that all the stars are at nearly {\\em the\nsame} distance. Indeed, if we were to assume that the front to back\nsize of Vela OB2 were similar to its diameter on the sky, then all the\nstars should be contained within $\\pm40$\\,pc. We would therefore\ninterpret the parallax to $\\gamma^{2}$ Vel simply as a $\\sim2\\sigma$\ndeviation and that its distance was $410\\pm40$\\,pc.\n\nThe companionship of $\\gamma^{1}$ Vel is also evidence for a distance\ncloser to the mean Vela OB2 distance. Although these objects have a\ncommon proper motion, they were too close together on the sky for Hipparcos\nto obtain independent parallaxes. The distance to\n$\\gamma^{1}$ Vel from its spectral type and photometry is almost\ncertainly 400-500\\,pc (e.g. Abt et al. 1976; Hern\\'{a}ndez \\& Sahade 1980).\nThe idea that $\\gamma^{2}$ Vel is a foreground object randomly placed\nwithin 1 arcminute of another bright member of the Vela OB2 association\nhas a probability of only $\\sim10^{-3}$. There is also reasonable\nevidence that the radial velocities of the two systems are\nsimilar. Hern\\'{a}ndez \\& Sahade (1980) quote $9.7\\pm 1.0$\\kms\\ for\n$\\gamma^{1}$ Vel and Niemel\\\"{a} \\& Sahade (1980) give $12\\pm1$\\kms\\ for\n$\\gamma^{2}$ Vel, although it is likely that the accuracy of the latter\nresult is exaggerated (Schmutz et al. 1997). \n\n\\subsection{Can the PMS stars be at a range of distances?}\n\nPreibisch \\& Zinnecker (1999) observed a very similar PMS\nCMD in the Upper Sco OB association, with a similar vertical scatter\nof about $\\pm 0.6$ mag about the isochrones. They showed that if one\ntakes into account unresolved binaries, photometric errors and allowed\na $\\sim10\\%$ range in distance, that the scatter around the PMS\nisochrones was exactly as expected for a coeval population at $\\sim5$\\,Myr. \nWe therefore similarly conclude\nthat the CMD in Fig. 2 shows no evidence for a \nlarge spread in {\\em either} the age or distance\nof the PMS population we have found. In particular, we can rule out any\ndistance modulus spread in a coeval population that is larger than a few tenths\nof a magnitude, or any age spread in a co-spatial population of more than a Myr\nor so (for a mean age of $\\sim4$\\,Myr). Thus unless there is a\nconspiracy to place older stars closer to us, the PMS association seems\nlikely to have a relatively narrow spread around an age and distance that are\nincompatible with the deduced age for $\\gamma^{2}$ Vel and its\nHipparcos distance.\n\n\\subsection{Is a larger distance to $\\gamma^{2}$ Vel consistent with\nits physical properties?}\n\nOur findings challenge the conclusions of several recent papers which\nuse the Hipparcos parallax of $\\gamma^{2}$ Vel and its error to derive:\nthe absolute magnitude of the system and its components; system masses\nfrom the interferometric binary separation of Hanbury-Brown (1970); the\nO star luminosity, mass and age from stellar evolution models and hence\nthe orbital inclination and further mass estimates from radial velocity\ncurves (see van der Hucht et al. 1997; Schaerer et al. 1997, Schmutz\net al. 1997, de Marco \\& Schmutz 1999). A distance as large as 410\\,pc\nfor $\\gamma^{2}$ Vel significantly changes the system parameters\ndeduced in these papers. The system luminosity increases by a factor\n2.5. The effective temperature and luminosity deduced for the O star\nwould then give it a mass $>40$\\msun\\ and an age $<3$\\,Myr, compared\nwith the values of 30\\msun\\ and 3.6\\,Myr quoted by de Marco \\& Schmutz\n(1999). At this larger distance, an age of 2-3\\,Myr could be compatible\nwith the low mass PMS stars we have found. The absolute magnitude of\nthe O star would decrease to $-6.0\\pm0.3$ (van der Hucht et al. 1997),\nwhich argues for a supergiant rather than a giant classification. Van\nder Hucht et al. comment that this would be in better agreement with\npublished spectra of Conti \\& Smith (1972) and Niemel\\\"{a} \\& Sahade\n(1980). As the mass ratio from the radial velocity curves is fixed,\nthe WR mass increases by a similar fraction. The total system mass,\nbased on a binary separation of $4.3\\pm0.5$ mas, increases from\n$30\\pm10$\\msun\\ to $120\\pm40$\\msun\\ (now comfortably exceeding the\nminimum mass from radial velocity curves -- Niemel\\\"{a} \\& Sahade 1980)\nand the binary inclination is reduced to around $50^{\\circ}$ to explain\nthe radial velocity curves.\n\n\n\\section{Conclusions}\n\nFrom our discussion there seem to be two possible scenarios. (1) That\nthe PMS stars are approximately at the same distance and age as\n$\\gamma^{2}$ Vel, and that this distance places $\\gamma^{2}$ Vel within\nthe Vela OB2 association at 360-490\\,pc. (2) That the PMS stars are\npart of the Vela OB2 association, possibly surrounding $\\gamma^{1}$\nVel, but that $\\gamma^{2}$ Vel is an isolated foreground object with no\nsurrounding low mass stars at a similar age. We believe that (1) is\n{\\em far} more plausible than (2) because of the dispersion in the Vela\nOB2 Hipparcos parallaxes and the likely association of $\\gamma^{1}$ and\n$\\gamma^{2}$ Vel. Recently, the idea that $\\gamma^{2}$ Vel could form\nin isolation without accompanying low mass stars has also been\nchallenged by the near IR detection of a K-type PMS companion only 4.7\narcsec distant (Tokovinin et al. 1999).\n\nIf the low mass PMS stars we have found are truly in the vicinity of\n$\\gamma^{2}$ Vel, they represent an exciting opportunity to explore the\ninfluence of adjacent high mass loss stars and ionizing UV radiation\nfields on the mass function and circumstellar disc lifetimes of low\nmass stars. It will be interesting to compare the frequencies of\nT-Tauri discs around these stars with the frequencies found in\nT associations and OB associations with similar ages.\nThe PMS stars in Fig.2 have masses, found from the D'Antona\n\\& Mazzitelli (1997) models, down to (an age dependent) mass of \nabout 0.15\\msun. The mass function will be addressed when we\nhave a better census of the association membership.\n\n\n\\section*{ACKNOWLEDGMENTS}\n\nThis research has made use of {\\em ROSAT} data obtained from the\nLeicester Database Archive Service at the Department of Physics and\nAstronomy, Leicester University, UK. The Cerro Tololo Interamerican\nObservatory is operated by the Association of Universities for Research\nin Astronomy, Inc., under contract to the US National Science\nFoundation. TN was supported by a UK Particle and Physics and\nAstronomy Research Council (PPARC) Advanced Fellowship. SH was\nsupported by a Nuffield Foundation Undergraduate Research Bursary\n(NUF-URB98). EJT is a PPARC postdoctoral research associate. MK was\nsupported by an undergraduate research bursary from Keele University.\nComputational work for this paper was performed on the Keele node of\nthe Starlink network funded by PPARC.\n\n\n\\begin{thebibliography}{}\n \\bibitem{Abt1976} Abt H. A., Landolt A. U., Levy S. G., Mochnacki S.,\n1976, AJ, 81, 541\n \\bibitem{Allan1992} Allan D. J., 1992, ASTERIX User note number 004,\nStarlink, Rutherford Appleton Laboratory, UK\n \\bibitem{Allan1995} Allan, D. J., Vallance, R. J., 1995, STARLINK User note\nnumber 98.6 , Rutherford Appleton Laboratory, UK \n \\bibitem{Conti1972} Conti P. S., Smith L. F., 1972, ApJ, 172, 623\n \\bibitem{D'Antona1997} D'Antona F., Mazzitelli I., 1997, Mem.\\ Soc.\\\nAstron.\\ Ital., 68, 807\n \\bibitem{Demarco1999} De Marco O., Schmutz W., 1999, A\\&A, 345, 163 \n \\bibitem{Zeeuw1999} de Zeeuw P. T., Hoogerwerf R., de Bruijne J. H. J.,\nBrown A. G. A., Blaauw A., 1999, AJ, 117, 354\n \\bibitem{Eggen1980} Eggen O. J., ApJ, 238, 627\n \\bibitem{Feigelson1997} Feigelson, E., Lawson, W. A., 1997, AJ, 113, 2130\n \\bibitem{Hanbury1970} Hanbury Brown R., Davis, J., Herbison-Evans, D.,\nAllen, L. R., 1970, MNRAS, 148, 103\n \\bibitem{Hernandez1980} Hern\\'{a}ndez C. A., Sahade J., 1980, PASP, 92, 819\n \\bibitem{Jeffries1998} Jeffries R. D., Tolley A. J., 1998, MNRAS, 300,\n331\n \\bibitem{Jeffries1997} Jeffries R. D., Thurston M. R., Pye J. P., 1997,\nMNRAS, 287, 350\n \\bibitem{Johnstone1998} Johnstone D., Hollenbach D., Bally J., 1998, ApJ,\n499, 758\n \\bibitem{Landolt1992} Landolt A. U., 1992, AJ, 104, 340\n \\bibitem{McCaughrean1996} McCaughrean, M. J., O'Dell, R. C., 1996, AJ,\n111, 1977\n \\bibitem{Mamajek1999} Mamajek E. E., Lawson W. A., Feigelson E. D., 1999,\nApJ, 516, L77\n \\bibitem{Miller1979} Miller G. E., Scalo J. M., 1979, ApJS 41, 513 \n \\bibitem{Monet1998} Monet D. G., 1998, AAS, 193, 12003.\n \\bibitem{Naylor1998} Naylor T., 1998, MNRAS, 296, 339\n \\bibitem{Naylor1999} Naylor T., Fabian A. C., 1999, MNRAS, 302, 714 \n \\bibitem{Niemela1980} Niemel\\\"{a} V. S., Sahade J., 1980, ApJ, 238, 244\n \\bibitem{Preibisch1999} Preibisch T., Zinnecker H., 1999, AJ, 117, 2381 \n \\bibitem{Shaerer1997} Schaerer D., Schmutz W., Grenon M., 1997, ApJ, 484,\nL153\n \\bibitem{Schmutz1997} Schmutz W. et al., 1997, A\\&A, 328, 219\n \\bibitem{Tokovinin1999} Tokovinin A. A., Chalabaev A., Shatsky N. I.,\nBeuzit J. L., 1999, A\\&A, 346, 481\n \\bibitem{Hucht1997} van der Hucht K. A., et al., 1997, New Astronomy, 2,\n245 \n \\bibitem{Walter1994} Walter F. M., Vrba, F. J., Mathieu R. D., Brown,\nA., Myers P. C., 1994, AJ, 107, 692\n \\bibitem{Walter1999} Walter, F. M., Alcal\\'{a}, J. M., Neuh\\\"{a}user,\nR., Sterzik, M., Wolk, S. J., 1999, in Mannings, V., Boss, A., Russell,\nS., eds, Protostars and Planets IV, University of Arizona press, in press\n \\bibitem{Willis1995} Willis A. J., Schild H., Stevens I. R., 1995, A\\&A,\n298, 549\n\\bibitem{Walter98} Walter, F. M., Wolk, S. J., Sherry, W., 1998, in\nDonahue, R. A., Bookbinder, J. A., eds, Cool Stars, Stellar Systems and\nthe Sun, Tenth Cambridge Workshop, ASP Conference series Vol. 154, San\nFrancisco, p.1793\n\\end{thebibliography}\n\n\\label{lastpage}\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n"
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In preparation}\n%\n% JOURNAL ABBREVIATIONS\n%\n\\newcommand{\\aanda} {Astr.\\ Astro\\-phys.\\nolinebreak\\ }\n\\newcommand{\\aasupp} {Astr.\\ Astro\\-phys.\\nolinebreak\\ Suppl.\\nolinebreak\\ }\n\\newcommand{\\aj} {Astron.\\nolinebreak\\ J.\\nolinebreak\\ }\n\\newcommand{\\annrev} {Ann.\\ Rev.\\ Astr.\\ Astro\\-phys.\\nolinebreak\\ }\n\\newcommand{\\acta} {Acta Astron.\\nolinebreak\\ }\n\\newcommand{\\apj} {Astro\\-phys.\\nolinebreak\\ J.\\nolinebreak\\ }\n\\newcommand{\\apjs} {Astro\\-phys.\\nolinebreak\\ J.\\ Suppl.\\nolinebreak\\ }\n\\newcommand{\\apjsupp}{\\apjs}\n\\newcommand{\\aplett} {Astro\\-phys.\\nolinebreak\\ Lett.\\nolinebreak\\ }\n\\newcommand{\\gafd} {Geo\\-phys.~Astro\\-phys.\\ Fluid Dyn.\\nolinebreak\\ }\n\\newcommand{\\ibvs} {Inf.\\ Bull.\\ var.\\ Stars\\nolinebreak\\ }\n\\newcommand{\\jgr} {J.\\ Geo\\-phys.~Res.\\nolinebreak\\ } \n\\newcommand{\\jpp} {J.\\ Plasma Phys.\\nolinebreak\\ }\n\\newcommand{\\mn} {Mon.\\ Not.\\ R.\\ astr.\\nolinebreak\\ Soc.\\nolinebreak\\ }\n\\newcommand{\\pf} {Phys.\\nolinebreak\\ Fluids\\nolinebreak\\ }\n\\newcommand{\\pasp} {Publ.\\ astr.\\ Soc.\\ Pacif.\\nolinebreak\\ }\n\\newcommand{\\sovast} {Soviet astr.\\nolinebreak\\ }\n\\newcommand{\\procasa}{Proc.\\ Astr.\\ Soc.\\ Australia\\nolinebreak\\ }\n\\newcommand{\\solp} {Solar Phys.\\nolinebreak\\ }\n%\n% MATH MACROS\n%\n\\newcommand{\\deriv}[2]{\\mbox{${{\\displaystyle d#1}\\over\n {\\displaystyle d#2}}$}} \n\\newcommand{\\sderiv}[2]{\\mbox{${{\\displaystyle d^2#1}\\over\n {\\displaystyle d#2^2}}$}} \n\\newcommand{\\pderiv}[2]{\\mbox{${{\\displaystyle\\partial#1}\\over\n {\\displaystyle\\partial#2}}$}} \n\\newcommand{\\spderiv}[2]{\\mbox{${{\\displaystyle\\partial^2#1}\\over\n {\\displaystyle\\partial#2^2}}$}} \n\\newcommand{\\half}{\\mbox{$\\frac{1}{2}$}}\n\\newcommand{\\twiddles}{\\mbox{$\\sim $}}\n\\newcommand{\\varomega}{\\varpi}\n\\newcommand{\\twid}{\\mbox{$\\sim $}}\n\\newcommand{\\bvec}[1]{\\mbox{\\boldmath ${#1}$}}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bd}{\\begin{displaymath}}\n\\newcommand{\\ed}{\\end{displaymath}}\n\n\n\n\n\n\n\n\n\n\n\n\n"
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[
{
"name": "astro-ph0002342.extracted_bib",
"string": "\\begin{thebibliography}{}\n \\bibitem{Abt1976} Abt H. A., Landolt A. U., Levy S. G., Mochnacki S.,\n1976, AJ, 81, 541\n \\bibitem{Allan1992} Allan D. J., 1992, ASTERIX User note number 004,\nStarlink, Rutherford Appleton Laboratory, UK\n \\bibitem{Allan1995} Allan, D. J., Vallance, R. J., 1995, STARLINK User note\nnumber 98.6 , Rutherford Appleton Laboratory, UK \n \\bibitem{Conti1972} Conti P. S., Smith L. F., 1972, ApJ, 172, 623\n \\bibitem{D'Antona1997} D'Antona F., Mazzitelli I., 1997, Mem.\\ Soc.\\\nAstron.\\ Ital., 68, 807\n \\bibitem{Demarco1999} De Marco O., Schmutz W., 1999, A\\&A, 345, 163 \n \\bibitem{Zeeuw1999} de Zeeuw P. T., Hoogerwerf R., de Bruijne J. H. J.,\nBrown A. G. A., Blaauw A., 1999, AJ, 117, 354\n \\bibitem{Eggen1980} Eggen O. J., ApJ, 238, 627\n \\bibitem{Feigelson1997} Feigelson, E., Lawson, W. A., 1997, AJ, 113, 2130\n \\bibitem{Hanbury1970} Hanbury Brown R., Davis, J., Herbison-Evans, D.,\nAllen, L. R., 1970, MNRAS, 148, 103\n \\bibitem{Hernandez1980} Hern\\'{a}ndez C. A., Sahade J., 1980, PASP, 92, 819\n \\bibitem{Jeffries1998} Jeffries R. D., Tolley A. J., 1998, MNRAS, 300,\n331\n \\bibitem{Jeffries1997} Jeffries R. D., Thurston M. R., Pye J. P., 1997,\nMNRAS, 287, 350\n \\bibitem{Johnstone1998} Johnstone D., Hollenbach D., Bally J., 1998, ApJ,\n499, 758\n \\bibitem{Landolt1992} Landolt A. U., 1992, AJ, 104, 340\n \\bibitem{McCaughrean1996} McCaughrean, M. J., O'Dell, R. C., 1996, AJ,\n111, 1977\n \\bibitem{Mamajek1999} Mamajek E. E., Lawson W. A., Feigelson E. D., 1999,\nApJ, 516, L77\n \\bibitem{Miller1979} Miller G. E., Scalo J. M., 1979, ApJS 41, 513 \n \\bibitem{Monet1998} Monet D. G., 1998, AAS, 193, 12003.\n \\bibitem{Naylor1998} Naylor T., 1998, MNRAS, 296, 339\n \\bibitem{Naylor1999} Naylor T., Fabian A. C., 1999, MNRAS, 302, 714 \n \\bibitem{Niemela1980} Niemel\\\"{a} V. S., Sahade J., 1980, ApJ, 238, 244\n \\bibitem{Preibisch1999} Preibisch T., Zinnecker H., 1999, AJ, 117, 2381 \n \\bibitem{Shaerer1997} Schaerer D., Schmutz W., Grenon M., 1997, ApJ, 484,\nL153\n \\bibitem{Schmutz1997} Schmutz W. et al., 1997, A\\&A, 328, 219\n \\bibitem{Tokovinin1999} Tokovinin A. A., Chalabaev A., Shatsky N. I.,\nBeuzit J. L., 1999, A\\&A, 346, 481\n \\bibitem{Hucht1997} van der Hucht K. A., et al., 1997, New Astronomy, 2,\n245 \n \\bibitem{Walter1994} Walter F. M., Vrba, F. J., Mathieu R. D., Brown,\nA., Myers P. C., 1994, AJ, 107, 692\n \\bibitem{Walter1999} Walter, F. M., Alcal\\'{a}, J. M., Neuh\\\"{a}user,\nR., Sterzik, M., Wolk, S. J., 1999, in Mannings, V., Boss, A., Russell,\nS., eds, Protostars and Planets IV, University of Arizona press, in press\n \\bibitem{Willis1995} Willis A. J., Schild H., Stevens I. R., 1995, A\\&A,\n298, 549\n\\bibitem{Walter98} Walter, F. M., Wolk, S. J., Sherry, W., 1998, in\nDonahue, R. A., Bookbinder, J. A., eds, Cool Stars, Stellar Systems and\nthe Sun, Tenth Cambridge Workshop, ASP Conference series Vol. 154, San\nFrancisco, p.1793\n\\end{thebibliography}"
}
] |
astro-ph0002343
|
Subaru Observations for the $K$-Band Luminosity Distribution \\ of Galaxies in Clusters near to 3C 324 at $z \sim$ 1.2
|
[
{
"author": "Masaru {\\sc Kajisawa}"
},
{
"author": "Toru {\\sc Yamada}"
},
{
"author": "Ichi {\\sc Tanaka}"
},
{
"author": "%"
},
{
"author": "Toshinori {\\sc Maihara}"
},
{
"author": "Fumihide {\\sc Iwamuro}"
},
{
"author": "Hiroshi {\\sc Terada}"
},
{
"author": "Miwa {\\sc Goto}"
},
{
"author": "Kentaro {\\sc Motohara}"
},
{
"author": "Hirohisa {\\sc Tanabe}"
},
{
"author": "Tomoyuki {\\sc Taguchi}"
},
{
"author": "Ryuji {\\sc Hata}"
},
{
"author": "{Kyoto 606-8502}"
},
{
"author": "Masanori {\\sc Iye}"
},
{
"author": "Masatoshi {\\sc Imanishi}"
},
{
"author": "Yoshihiro {\\sc Chikada}"
},
{
"author": "{National Astronomical Observatory, 2-21-1, Osawa, Mitaka, Tokyo 181-8588}"
},
{
"author": "Chris {\\sc Simpson}"
},
{
"author": "Toshiyuki {\\sc Sasaki}"
},
{
"author": "George {\\sc Kosugi}"
},
{
"author": "Tomonori {\\sc Usuda}"
},
{
"author": "Tomio {\\sc Kanzawa} and Tomio {\\sc Kurakami}"
},
{
"author": "{Subaru Telescope, National Astronomical Observatory of Japan,}"
},
{
"author": "{650 North Aohoku Place, Hilo, HI 96720, U.S.A. }"
},
{
"author": "\\vspace{0.5cm}"
}
] |
[
{
"name": "text.tex",
"string": "\\documentstyle[PASJadd,epsbox]{PASJ95}\n%\n% PASJ LaTex \n%\n%\\draft\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\markboth{M.\\ Kajisawa et al.}\n{$K$-band Luminosity Distribution in Clusters at $z\\sim1.2$}\n\n\\newcommand{\\vol}{52}\n\\newcommand{\\no}{1}\n\\newcommand{\\lett}{}\n\\newcommand{\\spage}{\\bf ??}\n\\newcommand{\\rdate}{1999 September 3}\n\\newcommand{\\adate}{1999 December 22}\n\n\\begin{document}\n%\\setcounter{page}{1}\n\n\\title{Subaru Observations for the $K$-Band Luminosity Distribution \\\\\nof Galaxies in Clusters near to 3C 324 at $z \\sim$ 1.2}\n\n\\author{Masaru {\\sc Kajisawa}, Toru {\\sc Yamada}, Ichi {\\sc Tanaka} \\\\\n{\\it Astronomical Institute, Tohoku University, Aoba-ku, Sendai 980-8578} \\\\\n{\\it E-mail(MK): kajisawa@astr.tohoku.ac.jp } \\\\\n%\n \\\\\nToshinori {\\sc Maihara}, Fumihide {\\sc Iwamuro}, Hiroshi {\\sc Terada}, Miwa {\\sc Goto},\\\\\nKentaro {\\sc Motohara}, Hirohisa {\\sc Tanabe}, Tomoyuki {\\sc Taguchi}, Ryuji {\\sc Hata} \\\\\n{\\it Department of Physics, Faculty of Science, Kyoto University, Sakyo-ku,} \\\\\n{\\it Kyoto 606-8502} \\\\\n%\n \\\\\nMasanori {\\sc Iye}, Masatoshi {\\sc Imanishi}, Yoshihiro {\\sc Chikada} \\\\\n{\\it National Astronomical Observatory, 2-21-1, Osawa, Mitaka, Tokyo 181-8588}\\\\\n%\n \\\\\nChris {\\sc Simpson}, Toshiyuki {\\sc Sasaki}, George {\\sc Kosugi}, Tomonori {\\sc Usuda}, \\\\\nTomio {\\sc Kanzawa} and Tomio {\\sc Kurakami} \\\\\n{\\it Subaru Telescope, National Astronomical Observatory of Japan,} \\\\\n{\\it 650 North Aohoku Place, Hilo, HI 96720, U.S.A. }\\\\\n\\vspace{0.5cm}\n }\n\n\\abst{\n We investigate the $K$-band luminosity distribution of galaxies\nin the region of clusters at $z\\sim1.2$ near to the radio galaxy 3C\n324. The imaging data were obtained during the commissioning period of\nthe Subaru telescope. There is a significant excess of the surface\nnumber density of the galaxies with $K =$ 17--20 mag in the region\nwithin $\\sim$ 40'' from 3C 324. At this bright end, the measured\nluminosity distribution shows a drop, which can be represented by the\nexponential cut off of the Schechter-function formula; the best-fitted\nvalue of the characteristic magnitude, $K^{*}$, is $\\sim\n18.4\\pm0.8$. This measurement follows the evolutionary trend of the\n$K^*$ of the rich clusters observed at an intermediate redshift, which is\nconsistent with passive evolution models with a formation redshift $z_f\n\\gtsim 2$. At $K \\gtsim 20$ mag, however, the excess of the galaxy\nsurface density in the region of the clusters decreases abruptly,\nwhich may imply that the luminosity function of the cluster galaxies\nhas a negative slope at the faint end. This may imply strong\nluminosity segregation between the inner and outer parts of the clusters,\nor some deficit of faint galaxies in the cluster central region of the\ncluster. \n}\n%\n\\kword{galaxies: evolution --- galaxies: formation --- galaxies: luminosity function, mass function}\n%\n\n\\maketitle\n\\thispagestyle{headings}\n%\\clearpage\n\\section{Introduction}\n\n The luminosity function (LF) is one of the basic probes for studying\ngalaxy formation. Particularly, the near-infrared $K$-band LF can be\nused as a tracer of the galaxy mass distribution since the\nnear-infrared light of a quiescent galaxy is dominated by low-mass\nstars, and can be an approximate measure of the total stellar mass.\nHierarchical structure formation models can be directly tested by\nobserving the evolution of near-infrared LF over a significant\nredshift range (e.g., Kauffmann et al. 1993). \n\n Near-infrared observations also have some practical advantages when one\ninvestigates the LF of galaxies at high redshift; it provides a\nrelatively uniform and unbiased measure of the galaxy luminosity\ndistribution, since the galaxy luminosity in the $K$-band is much less\nsensitive to the on-going star-formation activity, the scale of which\nmay vary from galaxy to galaxy; also, the $K$-correction factor is\nrelatively small and nearly independent of the Hubble type, even at\nlarge redshifts. \n\n Observing the near-infrared LF in high-redshift-rich clusters may\nconstrain the history of the evolution of the galaxy mass distribution\nin the highest density environment in the Universe. De Propris et\nal. (1999) recently investigated the evolution of the $K$-band LF of\ngalaxies in rich clusters at $z=$0.1--0.9. The measured LF can be\nfitted by the Schechter function, and the behavior of the\ncharacteristic magnitude, $K^*$, along redshift is consistent with those\npredicted by the passive-evolution models with a single starburst at\n$z=2-3$. Combining these results with the mild evolution of the\nmass-to-light ratio of the cluster elliptical galaxies, they concluded\nthat the assembly of galaxies at the bright end of the LF was largely\ncompleted by $ z\\approx 1$. \n\n Pushing these studies toward higher redshift constrains the\nformation history of galaxies in clusters more strongly. In\na general field environment, Kauffmann and Charlot (1998) claimed a\ndeficit of red giant elliptical galaxies at $z \\gtsim\n1$. Franceschini et al. (1998) also argued that the number density of\nbright elliptical galaxies significantly decreases above $z \\sim\n1.3$. Although there is still much debate on these subjects (e.g.,\nTotani, Yoshii 1998), it would be interesting to also study the $K$-band LF of\ngalaxies in rich clusters at $z \\gtsim 1$. Observing rich\nclusters has an advantage, because the galaxies are at a single distance\nand the LF can be evaluated by measuring the galaxy surface-density\nexcess of the cluster region over the non-cluster region, while it is\nstill a time-consuming task to spectroscopically measure the distances\nto each individual galaxy in the field. The disadvantage is that the\nuncertainty of the field correction could seriously affect the\nresults, especially at the faintest end where the galaxy counts may be\ndominated by the foreground/background galaxies. \n\n Recently, more than several clusters and cluster candidates at $z\n\\gtsim 1$ have been discovered (Dickinson 1995; Yamada et al. 1997;\nStanford et al. 1997; Hall, Green 1998; Ben\\'\\i tez et al. 1999;\nRosati et al. 1999). Most of these objects have been selected or identified\nby the surface density excess of the quiescent old galaxy\npopulation. Near-infrared luminosity distributions of the galaxies in\nthese high-redshift clusters, however, have so far not been studied\nintensively. \n\n In this paper, we present the $K$-band luminosity distribution of the\ngalaxies in the clusters at $z \\sim 1.2$ near to the radio galaxy 3C 324\nusing the images obtained with the Subaru telescope. These clusters\nare recognized by Kristian et al. (1974) and by Spinrad and Djorgovski\n(1984), and firmly identified by Dickinson (1995). The clusters have been\nspectroscopically confirmed, and the surface-density excess was\nrevealed to be due to the superposition of two systems at $z=1.15$\nand $z=1.21$ (Dickinson 1997a, b). The extended X-ray emission, whose\nluminosity is comparable to that of the Coma cluster, has been detected\ntoward the direction of 3C 324 (Dickinson 1997a), which indicates that\nat least one of the two systems, probably the $z=1.21$ one in which 3C\n324 exists, is a fairly collapsed massive system. Smail and Dickinson\n(1995) detected a weak shear pattern in the field that may be produced\nby a cluster associated with 3C 324. \n%\n We describe the observation and the data reduction briefly in section\n2. In section 3, we present the obtained $K$-band luminosity function\nand the surface number density distribution. Our conclusions and the\ndiscussions are given in the last section. \n\n\\section{Observations and Data Reduction}\n\n The 3C 324 field was observed at the $K^\\prime$ band with the Subaru\ntelescope equipped with the Cooled Infrared Spectrograph and Camera\nfor OHS (CISCO, Motohara et al. 1998) on 1999 March 31 and April 1,\nduring the telescope commissioning period. The detector used was\na 1024 $\\times$ 1024 HgCdTe array with a pixel scale of 0.\\hspace{-2pt}''116,\nwhich provides a field of view of $\\sim$ 2' $\\times$ 2'.\n A number of dis-registered images with short exposures\n(20 s for each frame) were taken in a circular dither pattern\nwith a 10'' radius; a series of twelve frames were taken at one\nplace and the telescope was then moved to the next position. The total\nnet exposure time was 3000 s. The weather condition was stable during the\nobservations, and the seeing was $\\sim$0.\\hspace{-2pt}''8 on March 31 (1600\ns) and between 0.\\hspace{-2pt}''3 and 0.\\hspace{-2pt}''5 on April 1\n(1400 s). \n\n The data were reduced using the IRAF software package.\nThere was a variation in the bias level\nof CISCO during the observations and the residual pattern is not flat\nand makes a 10--20$\\%$ discontinuity of the background level in each\nframe at the boundary of the quadrants of the array at the central\ncolumn of the detector. In the first and the second frames of the\nseries of the twelve exposures taken at one position, the residual is\nmuch smaller than those in the following other frames. We thus made\nthe `template' bias\nframe, which was to be scaled and subtracted from all frames, by\nsubtracting the first frame of the seriese averaged over the\nobservations from the average of the third to twelfth frames. \n%\n Flat fielding was performed using the frame constructed from our own data\nby median stacking of the bias-subtracted images after masking out the\ntentatively detected objects. As a check, we compared our\nflat-fielding frame with that constructed from many other frames taken\nwith CISCO by the time of the observations (made by the CISCO team),\nand found that their difference was less than 5\\%. We indeed performed\nthe same analysis using this general flat-fielding frame, and found no\nsystematic difference in the results. \n%\n After the flat-fielding, by fitting the\nbackground with the 10th-order surface function after masking the\ndetected objects, we subtracted the sky background and the\nremaining slight distortion near to the central column due to the bias\nvariation and a small pattern of an unfocused image, which was probably\ncaused by a piece of dust on the camera window, and appeared in the\ntop-left quadrant of the frame during our observations.\nSince the fitted surface was smooth and had a small\ngradient over the frame, except for the regions of the dust pattern and\nnear to the central column, source detection and photometry were little\naffected by this procedure. As a further check, we also performed the\nmedian-sky (prepared from the disregistered data frames) subtraction\nbefore removing the spurious patterns by the surface fitting, and found\nlittle difference in the results. \n%\n The resultant frames were convolved with the Gaussian kernel in order\nto match the FWHM of the stellar images to the worst one (0.\\hspace{-2pt}''8).\n They were then co-registered and normalized to be median\nstacked. \n%\n\n The flux densities of the detected sources were calibrated to those\nin the $K$-band by using a star in the list of UKIRT Faint Standards,\nFS 27 ($K-K^\\prime = -0.01$), observed just after the 3C 324 field at\na similar zenith distance. Since the true-color term of the\ntelescope and the instrument has not been defined at this stage, and we\ndo not have infrared colors of the objects, no color correction was\napplied. Using the model spectra and the transmission curve of\nthe CISCO $K^\\prime$ filter, we evaluated $K-K^\\prime \\sim -0.1$ for\nan old passively evolving galaxy at $z=1.2$. Many foreground galaxies\nmay have bluer infrared spectra and the color correction may be\nsmaller than this. We checked the stability of the results presented\nbelow by artificially shifting the magnitude zero point by 0.1--0.2 mag,\nand confirmed that they are little affected by the procedure. \n\n We used the SExtractor software (Bertin, Arnouts 1996) to detect\nthe objects in our image. A detection threshold of $\\mu_K =$ 22.4 mag\narcsec$^{-2}$ over 20 connected pixels was used. Photometry was made\nwith 3'' diameter apertures. We removed the bright objects\nwith $K < 18$, whose light profile is consistent with the stellar ones from\nthe final galaxy catalog. We did not make any star/galaxy separation\nat the fainter magnitude, but the contribution of the stars was small\nat $K > 18$ and at most $\\sim 5--10 \\%$ (De Propris et al. 1999). \nA total of 146 sources were cataloged. \n%\n\n Figure 1 shows the distribution of the detected objects on the\nsky. The position angle of the frame is 218$^\\circ$. We show the\nobjects with $K < 20$ mag by the filled circles and those with $K >\n20$ by the open ones. In order to evaluate the completeness of the\nobject detection, we performed a simulation using the IRAF ARTDATA\npackage. An artificial galaxy with a given apparent magnitude is\ngenerated and added on the observed frame at random coordinates, and\nthe source-detection procedure with the same threshold was performed\nto check whether the artificial object can be detected or not. By\nrepeating this procedure, we estimated the probability that a galaxy\nwith a given magnitude is detected. Each artificial galaxy has a\nlight profile with parameters randomly selected from the range of\nhalf-light radius between 0.\\hspace{-2pt}''1 and 0.\\hspace{-2pt}''8\n(corresponds to 0.9--6.9\nkpc at $z=1.2$ for $H_0=50$ km s$^{-1}$ Mpc$^{-1}$ and $q_0=0.5$) and\nthat of the axial ratio between 0.3 and 1.0. While the range of the\nradius was chosen to represent typical galaxies at $z=1.2$, it covered the\nsize of the typical field galaxies. Yan et al. (1998) showed that the\nsize of galaxies with $H=$ 19--23 mag (roughly corresponding to\n$K=$ 18--22 mag) is between 0.\\hspace{-2pt}''2 and\n0.\\hspace{-2pt}''6. The seeing effect was\ntaken into account by convolving the model-galaxy image with the\nGaussian kernel. The result is shown in figure 2. They are\nequally-weighted averaged values for the model galaxies with various\nsizes and axial ratios. The detection completeness was $\\sim 90$\\% at\n$K= 21$ mag and still $\\sim 70$\\% at $K=21.5$ mag; we use the\naverage value for the disk and de Vaucouleurs profiles in the rest of\nthis paper. \n\n The detection completeness is low for the low surface brightness\ngalaxies. It may become $\\sim 70$\\% and $\\sim 50$\\% at $K=21$ and 21.5\nmag, respectively, if we assume an effective radius between\n0.\\hspace{-2pt}''7 and\n0.\\hspace{-2pt}''8. This, however, certainly underestimates the true\ncompleteness value, since the faint galaxies have generally smaller\nsizes of $\\sim$ 0.\\hspace{-2pt}''3--0.\\hspace{-2pt}''4 at $H=22$ mag\n(Yan et al. 1998). \n \n\\section{Results}\n\n Figure 3 shows the differential number counts of galaxies\ndetected on the entire field of the CISCO $K^\\prime$-band image. The\ncounts were made by 0.5 mag step with one magnitude bin. For\na comparison, those obtained in the general fields taken from various\nliteratures are also shown. The corrected counts of the frame are\nfairly consistent with those of the Hawaii Deep Survey (Cowie et\nal. 1994) and in Moustakas et al. (1997) at $K \\gtsim 22$ mag, where\nthe galaxy counts may be dominated by the foreground/background\ngalaxies. Bershady et al. (1998) gives systematically higher counts\nthan others, which may be due to the large-scale structures in the galaxy\ndistribution and the small area of the observed regions. \n\n In figure 4, we show the galaxy surface-density profile in the frame\nas a function of the distance from 3C 324 for those objects with $K\n=$17--20 mag. The dashed line shows the averaged field surface density\nobtained from the literature shown in figure 3. There is a\nconspicuous surface-density excess of galaxies within $\\sim$ 40''\nfrom 3C 324. The radius corresponds to $\\sim 0.35$ Mpc at $z \\sim\n1.2$. This result is consistent with those presented in figure 3 of\nDickinson (1997b). Dickinson (1997b) also revealed that the galaxies\nwithin 30'' radius from 3C 324 show strong peaks at $z=1.21$ and\n1.15 in the redshift distribution. In the following discussion we do\nnot distinguish the two systems at $z \\sim 1.2$, since the detailed\nredshift distribution of the galaxies or the relative population of\nthem is still unknown. Namely, we discuss the average properties of\nthe two clusters. Since their redshifts are close, it little affects\nthe discussion about the absolute luminosity and the color\ndistributions. In fact, it is a common technique to combine a few\nclusters at similar redshifts to reduce the statistical fluctuation of\nthe galaxy counts. \n\n We tentatively divide the observed field into the ``cluster\" region,\nwhich is the region within 40'' radius from 3C 324 (shown by the\nlarge circle in Figure 1), and the adjacent ``outer\" region, which is\nthe remaining region of the frame. The area of the cluster and the\nouter regions are 1.433 arcmin$^2$ and 1.981 arcmin$^2$, respectively, and 71\ngalaxies are in the cluster region. In figure 5, we show the\ndifferential number counts for the two regions separately as well as\nthe average counts in the literature shown in figure 3, approximated\nby the straight line fitted at $K > 17$ mag. In fitting the average\nfield counts, we put weights by the errors of the values in order to\nminimize the effect of the uncertainties in the incompleteness correction\nfor the data in the literature. \n%\n Here we plotted the density normalized for the area of the cluster\nregion so that the readers can see the true numbers of galaxies\ndetected on our frame in each magnitude bin. As expected from figure\n4, the excess of the galaxy surface density of the cluster region is\nclearly seen at $K \\sim$ 17--20 mag. On the other hand, the counts of\nthe outer region are similar to the general field counts over the\nentire magnitude range, and are likely to be dominated by the\nforeground/background field galaxies. \n\n At $K \\sim$ 20--21 mag, the excess of the surface number density of the\ncluster region decreases very rapidly, and the density even becomes\nconsistent with those of the field at $K =21$ mag. The slope of the\ncounts between $K=19$ mag and 21 mag in the cluster region becomes\nfairly flat while the counts of the outer region keeps rising with a\nsimilar slope as in the general fields. \n\n The decline of the counts could be due to detection\nincompleteness at the crowded region. To check this, we show the\nevaluated detection completeness as a function of the radius from\n3C 324 (figure 6). It can be seen that the detection completeness for\nthe galaxies with $K=$ 20--22 mag only marginally decreases toward 3C\n324, except for the innermost bin within 10'' radius where the\neffect of the host of 3C 324, which is the brightest cluster galaxy in\nthe system at $z=1.21$, becomes large and an $\\sim 20\\%$ decrease of the\ncompleteness is seen. \n \n Figure 7 shows the obtained luminosity distribution of the galaxies\nin the ``cluster\" region. For the field correction, the average counts\nshown in figure 5 are used. It shows some cut-off at the bright end,\nand also drops abruptly toward the fainter magnitude at $K \\sim 20$\nmag. We fitted the Schechter function, $\\Phi\n(L) = \\phi^* ( {L \\over {L^*}} )^\\alpha exp (- {L \\over {L^*}} )$, \n (Schechter 1976), to the bright end of the luminosity distribution\nusing the data points in the range of 17-20 mag in order to compare\nthe results with those obtained in a similar manner for the\nlower redshift clusters in De Propris et al. (1999) (but there is a\ndiscripancy in that we treat\nthe differential number counts here, while De Propris et al. (1999)\ninvestigated the cumulative ones). The faint-end slope of the\nSchechter function, \n $\\alpha$ = $-0.9$, is assumed as in De Propris et al. (1999). Although\nthe fitting is far from perfect, the drop toward the brightest end can\nbe represented by the exponential cut off, as in the Schechter\nfunction. The characteristic magnitude derived in this procedure is\n$K^{*} =$ 18.4 $\\pm$ 0.8 mag. \n\n The apparent rapid drop in the luminosity distribution at $K=$ 20--21\nmag seems to be conspicuous. If we assume $\\alpha=-0.9$, the expected\nnumber of the {\\it cluster} galaxies per magnitude is $\\sim$ 9.1 at $K\n= 21$ mag, while the observed count between $K=20.5$ and 21.5 mag is\nnegative after a field correction. The detection completeness is\nstill $\\sim$ 95--70\\% at this depth, and may not be much affected by the\nuncertainties in the incompleteness correction. The expected average\nnumber of field galaxies is 22.8 per magnitude at $K = 21$ mag,\nwhile the observed count is 18 and to be 21.6 after the incompleteness\ncorrection. If this behavior is due to a fluctuation of the\nforeground/background galaxy counts, there must be a sudden deficit\nof about ten galaxies per magnitude just below $\\sim 20$ mag and just\ninside the 40'' radius from 3C 324. \n%\n If we assume that there are 9.1 cluster galaxies in the region, the\ncorresponding number of `observed' field galaxies is 12.5. If the\nnumber density of the field galaxies follows Poisson statistics,\nthe confidence level of the lower limit (12.5 galaxies) is 99.5\\% for\n$n=23$. If we assume the presence of 12 and 6 cluster galaxies (9$\\pm$3\ngalaxies), the corresponding number of field galaxies is 9.6 and\n15.6, respectively, and the confidence level is 99.98\\% and 95.0\\%. \n%\n If we assume that the sum of the cluster and field galaxy counts\napproximately follow Poisson statistics, the expected number of\ngalaxies per magnitude at $K=21$ mag is 31.9 for $\\alpha = -0.9$. The\nconfidence level for the lower limit (21.6) is then 97.7\\%. Thus, in fact, the\nformal significance of the deficit of cluster galaxies is not very\nlarge. In the real universe, the distribution of galaxies is more\ninhomogeneous and the significance may be even lower. However, there\nis also no reason that such a relatively rare deficit occurs just in the\n`cluster' region where the brighter galaxies are strongly\nclustered. We therefore argue that the absence of any number count excess \nat $K = 21$ relative to the expected field galaxy counts is instead an\nintrinsic property of the cluster. We can\ninvestigate this further by using the color information for the\ngalaxies. Indeed, we found four galaxies in the `cluster' region whose\n$B-R$ and $R-K$ colors are consistent with those of the galaxies at\n$z=1.2$ or higher redshift (Kajisawa et al. 2000),\nalthough we do not see how many of them indeed belong to the\nclusters and how many are background galaxies. The true number of\ncluster galaxies can only be determined by future complete\nspectroscopic surveys or more accurate photometric refshift\nmeasurements. \n\n How stable are these results in spite of the non-negligible\nuncertainty of the applied field correction ? The galaxy counts of the\n``outer\" region of the frame may provide another representative field\ncorrection. Although there is a disadvantage that the statistical\nuncertainty is large especially at the bright end, due to the small\nnumber of the objects, there is an advantage that the\nforeground/background galaxies in the outer region share similar\nlarge-scale structures with those in the adjacent cluster\nregion. Furthermore, they also share any possible systematic errors in\nour data reduction and analysis. At the bright end, $17 < K < 20$, the\ncounts in the outer region are 10--50 $\\%$ smaller than the average\nfield counts. This does not change the resultant luminosity\ndistribution of the cluster galaxies very much, since the number of\ncluster galaxies is much larger than both the number densities of the\nouter region and the average field. On the other hand, at $20 < K <\n21.5$, where the deficit of the cluster galaxies is observed, the\nnumber density of the outer region is very similar to that of the\naverage field (figure 5). Thus, the resultant luminosity distribution\ndoes not change very much at $K \\ltsim 21.5$ if we use the counts in\nthe outer region on the same frame instead of the average field counts\nfor the field correction. \n\n We also examined the surface density profile of faint galaxies\nwith $K=$ 20--22 mag (figure 8). The raw counts as well as those\ncorrected using the results shown in figure 6 are plotted. The surface\ndensity within 40'' radius from 3C 324 is even consistent with\nthose of the field, either the average one or the counts in the\n``outer\" region in the same frame. We show the expected surface-density\nprofile within 40'' radius scaled from the excess counts at\n$K=$ 17--20 mag assuming the slope of the faint end of LF, ($\\alpha$=0,\n$-0.9$, $-1.4$), and the characteristic magnitude, $K^* = 18.4$ mag. The\ncase of $\\alpha=-1.4$ cannot be compatible with the observed\ndata. Even for the case of $\\alpha=-0.9$, the observed points are\nsystematically smaller than the expected counts, although the trend is\nsomewhat marginal. The observed data seems to be more consistent with the\ncase of $\\alpha=0$, or even that of no surface density excess. \n\n It is difficult to constrain the further faint end of the LF below $K\n\\sim 22$ mag, since the galaxy counts are dominated by the\nforeground/background galaxies, even in the ``cluster\" region, and the\nuncertainty of the incompleteness correction may also greatly affect the\nresults. We note, however, that the surface density of the\ndetected objects in the cluster region is systematically higher than\nthat of the outer region at $K =$ 21.5--23 mag. Some excess of the\ncluster galaxies could exist at this magnitude range. \n\n\n\\section{Conclusion and Discussions}\n\n We presented the luminosity distribution and the surface-density\ndistribution for the $K$-band selected galaxies in the region of the\nclusters at $z=1.15$ and 1.21 near to the radio galaxy 3C 324. While the\nbright end of the luminosity distribution can be represented by the\nSchechter-function-like exponential cut off with a characteristic\nmagnitude of $K^* \\sim 18.4$ mag, a rapid decrease in the\nsurface-density excess compared to the average field counts is also seen at\nthe faint end below $K \\sim 20$ mag, $\\sim 1.5$ magnitude fainter than\n$K^*$. \n\n Figure 9 compares the obtained value of $K^{*}$ with those of the\nlower-redshift clusters studied by De Propris et al. (1999). Various\nlines in the figure show the behavior expected for the no-evolution\nand the passive-evolution models with various cosmological parameters\ncalculated by using GISSEL96 (Bruzual, Charlot 1993). Following De\nPropris et al., we used a 0.1 Gyr burst model with a Salpeter IMF and\nwith solar metallicity. It can be seen that our result follows the\ntrend of the intermediate-redshift clusters that is consistent with\nthe passive evolution models with star-formation epoch of $z \\gtsim\n2$. At $K \\ltsim$ 20 mag, the dominant population in the clusters of\n3C 324 seems to be old quiescent galaxies which were formed at\nleast $\\sim 1$ Gyr ago from the observed epoch. \n\n The faint-end slope of the optical and near-infrared LF of the nearby\nand intermediate-redshift clusters has been studied extensively\n(Sandage et al. 1985; Thompson, Gregory 1993; Driver et al. 1994;\nKashikawa et al. 1995; Biviano et al. 1995; Secker, Harris 1996;\nMetcalfe et al. 1994; Barger et al. 1996; Smith et al.\n1997; Wilson et al. 1997; Driver et al. 1998). Through\nnear-infrared observations, Barger et al. (1996) give\n$\\alpha=-1$ for the $K$-band LF of the $z\\sim 0.31$ clusters. There\nis no such deficit as seen in the 3C 324 clusters at the magnitude\nrange between $M_K^*$ and $M_K^* + 3$. Wilson et al. (1997) also give\n$\\alpha=-1$ and $-1.3$ for the $I$-band LF of the two clusters at\n$z\\sim 0.2$, respectively. Although there are some unevenness within a\nfactor of two, no rapid drop is seen between $m_I^*$ and $m_I^*+4$. \n\n There is evidence that the optical LF of the clusters may be bimodal\nand better fitted by the combination of a Gaussian distribution for\nthe bright (giant) galaxies and the Schechter function for the faint\n(dwarf) galaxies rather than by the single Schechter function (Sandage\net al. 1985; Thompson, Gregory 1993; Kashikawa et al. 1995; Biviano\net al. 1995; Secker, Harris 1996; Metcalfe et al. 1994). Indeed,\nboth the $B$-band and $R$-band LFs of the Coma cluster show some\n`gap' at $\\sim 1$ mag fainter than the peak magnitude of the bright\npopulation (Biviano et al. 1995; Secker, Harris 1996). In the $R$\nband, the characteristic magnitude of the `faint' population is $\\sim\n1$--$1.5$ mag fainter than the peak magnitude of the `bright' one\n(Secker, Harris 1996). The shape of the $H$-band luminosity function of\nthe Coma cluster (De Propris et al. 1998) is also consistent with\nthese results. \n\n On the other hand, a deficit of the galaxies is seen at $\\sim$\n1.5--2.5 mag fainter than the $K^*$ in the 3C 324 clusters. Although\nthere is still an uncertainty of $\\sim 1$ mag in the value of the $K^*$,\nthe deficit of the galaxy seems to occur at the magnitude range where\nthe dwarf population already begins to dominate in the Coma cluster.\nHow can we interpret this deficit of the faint galaxies at $K \\sim 21$\nin the 3C 324 clusters if it is not just a statistical fluctuation of\nthe foreground/background galaxies and an intrinsic property of the\ncluster? \n\n It may be due to luminosity segregation between the inner and outer\nradius from 3C 324. The physical diameter of the ``cluster region\" (R\n$<$ 40'') studied in this paper is $\\sim 0.7$ Mpc, and thus should be\nconsidered to be a central part of the cluster. Driver et\nal. (1998) have shown that the dwarf galaxies ($M_R > M_R^*+3$) are less\nconcentrated than the luminous galaxies in the clusters with\nBautz--Morgan type III, namely, irregular less-concentrated\nsystems. The rich clusters at high redshift may still be dynamically\nyoung and share the properties of irregular clusters seen in the local\nuniverse. If the faint galaxies in the 3C 324 clusters are more\npopulous in the outskirt region, or distributed rather flat over the\nscale of a few Mpc, the excess of the surface density can be easily hidden\nby the numerous foreground/background galaxies. \n\n Another possibility is the intrinsic deficiency of the faint galaxy\npopulation in the cluster(s). There is a model involving a late formation of\ndwarf galaxies. Kepner et al. (1997) have shown that the UV background\nradiation of $J_\\nu$ = 10$^{-21}$ erg s$^{-1}$ cm$^{-2}$ Hz$^{-1}$ at\nthe Lyman limit at $z=3$ and evolves as $(1+z)^4$ can prevent a\nbaryonic collapse in the dark-matter halo with a circular velocity of\n$\\ltsim 30$ km s$^{-1}$ by $z\\sim1.5$, although the Hubble Deep\nField observation did not prove the presence of many `bursting dwarf'\npopulations (Ferguson, Babul 1998). The circular velocity, $\\sim 30$\nkm s$^{-1}$, corresponds to the dynamical mass of $\\sim 10^9 M_\\odot$,\nor may be $L \\sim 0.01$ $L^*$ and much less luminous than the\n$K \\sim 21$ mag object ($\\sim 0.1$ $L^*$). In a rich cluster environment\nat a high redshift, however, the limiting mass could be larger, since\nthere may be large extra contribution of UV radiation by the massive\nstars rapidly formed in the primordial giant elliptical galaxies,\nwhich constitute the bright end of the LF at the observed epoch, in\naddition to the general background field, which may be due to quasars.\n\n The results presented in the paper are just for one region and the\nsuperposition of the two distinct systems could make the situation\nmore complex. Clearly, it is important to extend the study of the LF\nto other high-redshift clusters as well as to constrain more firmly\nthe faint-end of the LF in the intermediate-redshift clusters. \\\\\n\\vspace{0.5cm}\n\n%*********** ACKNOWLEDGES\nWe would like to thank the referee, Mark Dickinson for his invaluable\ncomments. The present result is indebted to all the members of the Subaru\nObservatory, NAOJ, Japan. This research was supported by grants-in-aid\nfor scientific research of the Japanese Ministry of Education,\nScience, Sports and Culture (08740181, 09740168). This work was also\nsupported by the Foundation for the Promotion of Astronomy of Japan. \nThe Image Reduction and Analysis Facility (IRAF) used in this paper is\ndistributed by National Optical Astronomy Observatories, operated by\nthe Association of Universities for Research in Astronomy, Inc., under\ncontact to the National Science Foundation. \n\n\n%\\clearpage\n\n\\section*{References}\n\\small\n\n\\re\nBarger A. J., \nArag\\'on-Salamanca A., Ellis R. S., Couch W. J., Smail I., Sharples R. \nM. 1996, MNRAS 279, 1 \n\n\\re\nBen\\'\\i tez N., Broadhurst T., Rosati P., Courbin F., Squires G.,\nLidman C., Magain P. 1999, ApJ 527, 31\n\n\\re\nBershady M. \nA., Lowenthal J. D., Koo D. C. 1998, ApJ 505 50 \n\n\\re\nBertin E., Arnouts S. 1996, A\\&AS 117, 393 \n\n\\re\nBiviano A., Durret F., \nGerbal D., Le Fevre O., Lobo C., Mazure A., Slezak E. 1995, A\\&AS \n297, 610 \n\n\\re\nBruzual A. G., Charlot S. 1993, ApJ 405, 538 \n\n\\re\nCowie L. L., Gardner J. \nP., Hu E. M., Songaila A., Hodapp K. W., Wainscoat R. J. 1994, ApJ \n434, 114 \n\n\\re\nDe Propris R., Eisenhardt P. R., Stanford S. \nA., Dickinson M. 1998, ApJ 503, L45 \n\n\\re\nDe Propris R., Stanford \nS. A., Eisenhardt P. R., Dickinson M., Elston R. 1999, AJ\nsubmitted (astro-ph/9905137)\n\n\\re\nDickinson M. 1995, ASP Conf. \nSer. 86, 283 \n\n\\re\nDickinson M. 1997a, in HST and the High Redshift Universe, ed\nN. R. Tanvir, A. Arag\\'on-Salamanca, J.V. Wall (World\nScientific, Singapore) p207\n\n\\re\nDickinson M. 1997b, in The Early \nUniverse with the VLT, ed J. Bergeron (Springer, Berlin)\np274\n\n\\re\nDriver S. P., Phillipps \nS., Davies J. I., Morgan I., Disney M. J. 1994, MNRAS 268, 393 \n\n\\re\nDriver S. \nP., Couch W. J., Phillipps S. 1998, MNRAS 301, 369 \n\n\\re\nFerguson H. C., Babul A. 1998, MNRAS 296, 585 \n\n\\re\nFranceschini A., \nSilva L., Fasano G., Granato L., Bressan A., Arnouts S., Danese L.\n1998, ApJ 506, 600 \n\n\\re\nHall P. B., Green R. \nF. 1998, ApJ 507, 558 \n\n\\re\nKashikawa N., \nShimasaku K., Yagi M., Yasuda N., Doi M., Okamura S., \nSekiguchi M. 1995, ApJ 452, L99 \n\n\\re\nKauffmann G., \nCharlot S. 1998, MNRAS 297, L23 \n\n\\re\nKauffmann G., White S. D. M., Guiderdoni B. 1993, MNRAS 264, 201 \n\n\\re\nKepner J. V., Babul A., Spergel D. N. 1997, ApJ 487, 61\n\n\\re\nKristian J., \nSandage A., Katem B. 1974, ApJ 191, 43 \n\n\\re\nMcLeod B. A., Bernstein \nG. M., Rieke M. J., Tollestrup E. V., Fazio G. G. 1995, ApJS 96, 117 \n\n\\re\nMetcalfe N., \nGodwin J. G., Peach J. V. 1994, MNRAS 267, 431 \n\n\\re\nMinezaki T., Kobayashi Y., Yoshii Y., Peterson B. A. 1998, ApJ \n494, 111 \n\n\\re\nMotohara K., Maihara T., Iwamuro F., Oya S., Imanishi M., Terada H., \nGoto M., Iwai J., et al. 1998, Proc. SPIE 3354, 659 \n\n\\re\nMoustakas L. A., \nDavis M., Graham J. R., Silk J., Peterson B. A., Yoshii Y. 1997, \nApJ 475, 445 \n\n\\re\nRosati P., Stanford S. A., \nEisenhardt P. R., Elston R., Spinrad H., Stern D., Dey A. 1999, \nAJ 118, 76\n\n\\re\nSandage \nA., Binggeli B., Tammann G. A. 1985, AJ 90, 1759 \n\n\\re\nSecker J., Harris \nW. E. 1996, ApJ 469, 623 \n\n\\re\nSchechter P. 1976, ApJ \n203, 297 \n\n\\re\nSmail I., \nDickinson M. 1995, ApJ 455, L99 \n\n\\re\nSmith R. M., \nDriver S. P., Phillipps S. 1997, MNRAS 287, 415 \n\n\\re\nSpinrad H., \nDjorgovski S. 1984, ApJ 280, L9 \n\n\\re\nStanford S. A., Elston R., Eisenhardt P. R., Spinrad H., Stern D., Dey A. 1997, AJ 114, 2232\n\n\\re\nThompson L. A., \nGregory S. A. 1993, AJ 106, 2197 \n\n\\re\nTotani T., Yoshii \nY. 1998, ApJ 501, L177 \n\n%Whitmore, B. \n%C., Gilmore, D. M. \\& Jones, C. 1993, \\apj, 407, 489 \n\n\\re\nWilson G. \n, Smail I., Ellis R. S., Couch W. J. 1997, MNRAS 284, 915 \n\n\\re\nYamada T., Tanaka I., \nArag\\'on-Salamanca A., Kodama T., Ohta K., Arimoto N. 1997, ApJ \n487, L125 \n\n\\re\nYan L., McCarthy P. J., Storrie-Lombardi L. J., Weymann R. J. 1998,\nApJ 503, L19 \n\n\n\n\\clearpage\n\n% Fig.1\n\\begin{figure*}[p]\n\\begin{center}\n \\epsfile{file=fig1.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 1.\\ Distribution of the 146 detected objects on\nthe sky. The position\nangle of the figure is 218$^\\circ$. 3C 324 is shown by the filled\nsquare. The objects with $K < 20$ are shown by the filled circles and\nthose with $K > 20$ by the open circles. The large circle indicates\nthe ``cluster\" region within 40'' from 3C 324. \n\\end{figure*}\n\n\\begin{figure*}[p]\n\\begin{center}\n \\epsfile{file=fig2.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 2.\\ Detection completeness as a function of the\napparent magnitude derived from the simulation (see text). Each\nsymbol represents the adopted profiles of the artificial galaxies; de\nVaucouleurs profile (open circle), exponential profile (open square),\naverage of both profiles (shaded pentagon), respectively.\n\\end{figure*}\n\n\\begin{figure*}[p]\n\\begin{center}\n \\epsfile{file=fig3.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 3.\\ $K$-band number counts of the galaxies in the 3C 324 region.\n The observed counts (shaded triangles) as well as the\nincompleteness-corrected counts (shaded circles) are shown. The galaxy\ncounts in the general field taken from literatures are also plotted. \n\\end{figure*}\n\n\\begin{figure*}[p]\n\\begin{center}\n \\epsfile{file=fig4.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 4.\\ Surface number density profile of the galaxies with 17 $< K <$ 20\nas a function of the radius from 3C 324. The dashed line represents the\naveraged surface number densities in the field shown in figure 2. The\nerror-bars represent the square root of the number of detected\ngalaxies. \n\\end{figure*}\n\n\\begin{figure*}[p]\n\\begin{center}\n \\epsfile{file=fig5.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 5.\\ Corrected (shaded symbol) and raw (open symbol) $K$-band number\ncounts of the ``cluster\" and the ``outer\" regions. The filled\ntriangles show the approximate average field counts. The number\ndensity is normalized by the area of the ``cluster'' region. \n\\end{figure*}\n\n\n\\begin{figure*}[p]\n\\begin{center}\n \\epsfile{file=fig6.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 6.\\ Detection completeness as a function of the distance from the 3C 324 for the galaxies with $20 < K < 22$. \n%The error-bars represents the square root of the number of the artificial galaxies detected in each region.\n\\end{figure*}\n\n\\begin{figure*}[p]\n\\begin{center}\n \\epsfile{file=fig7.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 7.\\\nLuminosity function of the cluster region. The solid line is the Schechter function fitted to the points between $K=17$ and 20 mag. Note that the observed values at $K=20.5$ and 21.0 are negative.\n\\end{figure*}\n\n\\begin{figure*}[p]\n\\begin{center}\n \\epsfile{file=fig8.ps,scale=0.6}\n \\end{center}\n\\footnotesize Fig.\\ 8.\\\nRaw (filled circles) and the corrected (open circles) surface\nnumber density profile of the galaxies with 20 $< K <$ 22 in function\nof the radius from 3C 324. The dashed line represents the averaged\nsurface number densities in the field shown in figure 2. For a \ncomparison, we also show the expected profiles derived from the counts\nat $K=$ 17--20 mag assuming the Schecter function and various values of\nthe faint-end slope (squares). \n\\end{figure*}\n\n\\begin{figure*}[p]\n\\begin{center}\n \\epsfile{file=fig9.ps,scale=0.7}\n \\end{center}\n\\footnotesize Fig.\\ 9.\\\n$K^{*}$-$z$ Hubble diagram for the clusters at $z=0.1-0.9$ studied\nby De Propris et al. (1999) and the 3C 324 cluster. Lines represent\ngalaxy models calculated using GISELL96 (see text) under the various\nset of the cosmological parameters, $\\Omega_0$ and $\\Lambda_0$.\nH$_{0} =$ 65 km s$^{-1}$ Mpc$^{-1}$ is adopted. \n\\end{figure*}\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n"
}
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astro-ph0002344
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Color--Magnitude Sequence in the Clusters at $z$ $\sim$ 1.2 \\ near the Radio Galaxy 3C 324
|
[
{
"author": "Masaru {\\sc Kajisawa}"
},
{
"author": "Toru {\\sc Yamada}"
},
{
"author": "Ichi {\\sc Tanaka}"
},
{
"author": "%"
},
{
"author": "Toshinori {\\sc Maihara}"
},
{
"author": "Fumihide {\\sc Iwamuro}"
},
{
"author": "Hiroshi {\\sc Terada}"
},
{
"author": "Miwa {\\sc Goto}"
},
{
"author": "Kentaro {\\sc Motohara}"
},
{
"author": "Hirohisa {\\sc Tanabe}"
},
{
"author": "Tomoyuki {\\sc Taguchi}"
},
{
"author": "Ryuji {\\sc Hata}"
},
{
"author": "Masanori {\\sc Iye}"
},
{
"author": "Masatoshi {\\sc Imanishi}"
},
{
"author": "Yoshihiro {\\sc Chikada}"
},
{
"author": "Michitoshi {\\sc Yoshida}"
},
{
"author": "{National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo 181-8588}"
},
{
"author": "Chris {\\sc Simpson}"
},
{
"author": "Toshiyuki {\\sc Sasaki}"
},
{
"author": "George {\\sc Kosugi}"
},
{
"author": "Tomonori {\\sc Usuda}"
},
{
"author": "and"
},
{
"author": "Kazuhiro {\\sc Sekiguchi}"
},
{
"author": "{Subaru Telescope, National Astronomical Observatory of Japan,}"
},
{
"author": "{650 North Aohoku Place, Hilo, HI 96720, U.S.A. }"
},
{
"author": "\\vspace{0.5cm}"
}
] |
[
{
"name": "text.tex",
"string": "\\documentstyle[PASJadd,epsbox]{PASJ95}\n%\n% PASJ LaTex \n%\n%\\draft\n\n\\markboth{M.\\ Kajisawa et al.}\n{C-M Sequence in the Clusters at $z\\sim1.2$}\n\n\\newcommand{\\vol}{52}\n\\newcommand{\\no}{1}\n\\newcommand{\\lett}{}\n\\newcommand{\\spage}{\\bf ??}\n\\newcommand{\\rdate}{1999 November 26}\n\\newcommand{\\adate}{1999 December 22}\n\n\\font\\yfsm=cmb10\n\n\\begin{document}\n%\\setcounter{page}{1}\n\n\\title{Color--Magnitude Sequence in the Clusters at $z$ $\\sim$ 1.2 \\\\\nnear the Radio Galaxy 3C 324} \n\n\\author{Masaru {\\sc Kajisawa}, Toru {\\sc Yamada}, Ichi {\\sc Tanaka} \\\\\n{\\it Astronomical Institute, Tohoku University, Aoba-ku, Sendai, Miyagi 980-8578} \\\\\n{\\it E-mail(MK): kajisawa@astr.tohoku.ac.jp } \\\\\n%\n \\\\\nToshinori {\\sc Maihara}, Fumihide {\\sc Iwamuro}, Hiroshi {\\sc Terada},\nMiwa {\\sc Goto}, \\\\\nKentaro {\\sc Motohara}, \nHirohisa {\\sc Tanabe}, Tomoyuki {\\sc Taguchi}, Ryuji {\\sc Hata} \\\\\n{\\it Department of Physics, Faculty of Science, Kyoto University,}\n{\\it Sakyo-ku, Kyoto 606-8502} \\\\\n%\n \\\\\nMasanori {\\sc Iye}, Masatoshi {\\sc Imanishi}, Yoshihiro {\\sc Chikada},\nMichitoshi {\\sc Yoshida} \\\\\n{\\it National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo\n 181-8588} \\\\\n%\n \\\\\nChris {\\sc Simpson}, Toshiyuki {\\sc Sasaki}, George {\\sc Kosugi},\nTomonori {\\sc Usuda}\\\\\nand\\\\\nKazuhiro {\\sc Sekiguchi} \\\\\n{\\it Subaru Telescope, National Astronomical Observatory of Japan,} \\\\\n{\\it 650 North Aohoku Place, Hilo, HI 96720, U.S.A. }\\\\\n\\vspace{0.5cm}\n }\n\n\\abst{\n We have investigated the optical and near-infrared colors of\n$K'$-selected galaxies in clusters at $z \\sim 1.2$ near to the radio\ngalaxy 3C 324 using images obtained with the Subaru telescope and\narchival HST data. The distribution of colors of\nthe galaxies in the cluster region is found to be fairly broad, and \nit may imply \nsignificant scatter in their star-formation histories,\nalthough the effect of contamination of field galaxies is uncertain.\nThe red sequence of galaxies whose $R-K$ colors are consistent with\npassive evolution models for old galaxies is \nfound to be truncated at $K' \\sim 20$ mag, and there are few fainter\ngalaxies with similar red colors in the cluster region.\nWe find that the bulge-dominated galaxies selected by quantitative\nmorphological classification form a broad sequence in the\ncolor--magnitude diagram, whose slope is much steeper than that\nexpected from metallicity variations within a passively evolving\ncoeval galaxy population. We argue that the observed color--magnitude\nsequence can be explained by metallicity and age variations, and the\nfainter galaxies with $K' > 20$ mag may be 1--2 Gyr younger than the\nbrighter galaxies. Some spatial segregation of the\ncolor and $K'$-band luminosity is seen in the sky distribution; the\nredder and the brighter objects tend to be located near 3C 324.}\n%\n\\kword{galaxies: clusters of --- galaxies: evolution --- galaxies: formation}\n%\n\n\\maketitle\n\\thispagestyle{headings}\n\n%\\vspace{0.5cm}\n%\\clearpage\n\\section{Introduction}\n By tracing the average properties of galaxies in rich clusters and\ntheir progenitors from low to high redshift, we can study how galaxies\nin similar environments evolve with cosmic time, and obtain insights\ninto the phenomenon of galaxy formation. In nearby and\nintermediate-redshift clusters, the majority of bright galaxies are\nknown to form a tight and conspicuous red sequence in the color--magnitude\ndiagram (e.g., Visvanathan, Sandage 1977; Bower et al. 1992). This\ncolor--magnitude (hereafter C--M) relation seen in nearby clusters\nextends over a range of at least 4-magnitudes (Garilli et al. 1996)\nand possibly 5--6 mag (e.g., De Propris et al. 1998) from the brightest\ncluster galaxies; the slope of the relation does not vary from\ncluster to cluster. Bower et al. (1992) showed that the small\ndispersion of the C--M relation for early-type galaxies in the Coma and\nVirgo clusters places a strong constraint on their age or coevality by\nassuming a simple star-formation history; they found that the\nearly-type galaxies in these clusters are older than $\\sim$ 10 Gyr, if\nan age spread of $\\sim 1$ Gyr is assumed (see Bower et al. 1998 for\nmore general discussion). Arag\\'on-Salamanca et al. (1993) then found\na systematic evolution in the colors of the reddest cluster members\nwhich they interpreted as being passive evolution of old galaxies formed at\n$z \\gtsim 2$. Ellis et al. (1997) and Stanford et al. (1998)\ninvestigated {\\it morphologically selected} early-type galaxies in\nintermediate-redshift clusters, and found that the well-defined C--M\nsequence with small scatter holds there. Gladders et al. (1998) also\nfound that the evolution of the slope of the C--M sequence is\nconsistent with the predictions of passive evolution. These\nconclusions from studies of the C--M relation are complemented by those\nfrom Fundamental Plane analysis (e.g., van Dokkum et al. 1996,\n1998). The C--M relation is more favorably interpreted as being a metallicity\nsequence, rather than an age sequence, since otherwise the slope should\nbe much steeper than observed even at an intermediate redshift (Kodama,\nArimoto 1997), although some age difference between bright and\nfaint galaxies has been pointed out by some authors based on the\nobserved differences in the absorption-line strength (e.g., Terlevich et\nal. 1999).\n\n On the other hand, there are many observational indications that the\nstar-formation activity in more distant clusters is higher than that\nin local clusters. It is known that the fraction of blue galaxies in\nclusters increases rapidly with the redshift at intermediate-redshift\n(Butcher, Oemler 1978, 1984; Rakos, Schombert 1995). Rakos and\nSchombert showed that the fraction of blue galaxies becomes $\\sim$\n80\\% at $z =$ 0.9. Through spectroscopic studies of\nintermediate-redshift clusters, it is also known that a significant\nfraction of galaxies have emission-lines and/or post-starburst\nsignatures (e.g., Dressler, Gunn 1992; Postman et al. 1998;\nDressler et al. 1999; Poggianti et al. 1999). Postman et al. (1998)\ninvestigated two clusters at $z \\sim$ 0.9 spectroscopically, and found\nthat about half of the galaxies show high levels of star formation\nactivity. It is expected from these results that a more active evolution\nof galaxies may be observed in clusters at higher redshift.\n\n Recently, a number of clusters and cluster candidates at $z$ $\\gtsim$\n1 have been discovered (Dickinson 1995; Yamada et al. 1997; Stanford\net al. 1997; Hall, Green 1998; Ben\\'\\i tez et al. 1999; Tanaka et\nal. 1999; Rosati et al. 1999). By observing high-redshift clusters,\nany differences in the star-formation history can be seen more clearly.\nTanaka et al. (1999) investigated the colors of galaxies in the\ncluster 1335.8+2820 at $z \\sim$ 1.1, and showed that the optical and\nnear-infrared color distributions of the galaxies in this cluster are\nwide, which may be attributed to variations in the star-formation\nactivity. They found that the fraction of galaxies which show some\nUV excess over the expected colors for passive evolution is more than\n75\\% in this cluster. Stanford et al. (1997) investigated the\nNIR-selected cluster CIG J0848+4453 at $z =$ 1.27, and also showed that\nthose galaxies whose $RJK$ colors are consistent with passively evolving\nelliptical models have relatively blue $B-K$ colors, which indicates\nthat some star-formation activity is occurring in the old galaxies in\nthe cluster core. It is therefore interesting to expand the detailed\ncolor analysis to other clusters at $z$ $\\gtsim$ 1, and to see whether\nthese results apply generally to high-redshift clusters.\n\n In this paper, we consider the optical and near-infrared (NIR)\ncolors of $K'$-selected galaxies in those clusters at $z \\sim$ 1.2 near\nto the radio galaxy 3C 324 (Dickinson 1997a,b; Kajisawa, Yamada 1999;\nKajisawa et al. 2000, hereafter as Paper I) using images\nobtained with the Subaru telescope\nand archival data from the Hubble Space Telescope (HST).\n\n An excess of galaxy surface density in this region was recognized by\nKristian et al. (1974) and by Spinrad and Djorgovski (1984), and firmly\nidentified by Dickinson (1995). In Dickinson's (1997b) spectroscopic\nstudy, the surface-density excess was revealed to be due to the\nsuperposition of two clusters or rich groups at $z=1.15$ and\n$z=1.21$. Extended X-ray emission with a luminosity comparable to\nthat of the Coma cluster has been detected in the direction of 3C 324\n(Dickinson 1997a), which suggests that at least one of the two systems\nis a fairly collapsed massive system. Smail and Dickinson (1995)\ndetected a weak shear pattern in the field that may be produced by a\ncluster. In the following discussion, we do not distinguish the two\nsystems at $z \\sim 1.2$, since a detailed redshift distribution of\nthe galaxies or the relative population of them is still not\navailable. We thus discuss the average properties of the two\nclusters. Since their redshifts are close, it has little effect on our\ndiscussion about the luminosity and color distributions.\n\n Using a $K'$-selected sample provides such advantages as (i)\nthe selection bias at large redshift is small, and thus a direct comparison\nwith lower-redshift clusters is possible (Arag\\'on-Salamanca et\nal. 1993) and (ii) the sample selection is less affected by the\nstar-formation activity. Furthermore, the rest-frame mid-UV color provided\nby the HST data enables us to detect even a small amount of recent\nstar-formation (e.g., Ellis et al. 1997; Smail et al. 1998). We\ndescribe the observations and data reduction briefly in section 2. In\nsection 3, we present the color-magnitude and two-color diagrams. Our\nconclusions and discussions are given in the last section.\n\n In a previous Paper I,\nwe studied the $K$-band luminosity distribution of the galaxies in\nthese clusters near to 3C 324 using the same $K'$-band data, which\nis closely related to the results presented here. In summary,\nPaper I showed that the shape of the bright end ($K \\ltsim 20$) of\nthe luminosity function is similar to those of lower-redshift clusters;\nalso the measured value of the characteristic magnitude, $K^*$, follows\nthe evolutionary trend of intermediate-redshift clusters, which is\nconsistent with passive evolution models with $z_{\\rm form} \\gtsim 2$. At\nthe faint end, however, the excess galaxy surface density within 40''\n of 3C 324 decreases abruptly at $K \\sim 20$, which may indicate\na strong luminosity segregation with distance from 3C 324 or a real\ndeficit in the faint galaxy population in the clusters. Kajisawa and\nYamada (1999) also presented results from a study of the colors and\nmorphologies of an {\\it optically selected} sample of cluster galaxies\nusing the same HST data.\n\n\\section{Observations and Data Reduction}\n\\subsection{$K'$-Band Image}\n\n $K'$-band imaging of the 3C 324 field was carried out with the Cooled\nInfrared Spectrograph and Camera for OHS (CISCO, Motohara et al. 1998)\nmounted on the Subaru Telescope on 1999 April 1 and 2 (UT),\nduring the telescope commissioning period. The detector is a 1024\n$\\times$ 1024 HAWAII HgCdTe array with a pixel scale of 0.\\hspace{-2pt}''116,\nwhich provides a field of view of $\\sim$ 2' $\\times$ 2'. The presently \nimages studied are common to those analyzed in\nPaper I. See Paper I for details concerning the data reduction.\nThe seeing size of the resultant frame is 0.\\hspace{-2pt}''8 arcsec as measured from\nthe FWHM of the stellar images.\n\n A flux calibration was performed by observing one the UKIRT Faint\nStandard FS 27 immediately after the 3C 324 field at a similar zenith\ndistance. We used the empirical relation $K' - K = 0.2 (H - K)$\n(Wainscoat, Cowie 1992) in order to derive the $K'$ mag of\nFS 27 from its $H$ and $K$ mag.\n\n Source detection was performed with the SExtractor image analysis\npackage (Bertin, Arnouts 1996). We used a detection threshold of\n$\\mu_{K'} =$ 22.4 mag arcsec$^{-2}$ over 20 connected pixels. We\nremoved from the final catalog those bright objects with $K' <$ 18, which\nappeared unresolved. Although we did not make any star/galaxy separation at $K'\n> 18$, the contamination by stars in the catalogue is small at $K'\n> 18$ (at most $\\sim$ 5 -- 10\\%; De Propris et al. 1999). In total,\n146 sources were cataloged. We used a 3'' diameter aperture to\nmeasure the $K'$ mag of the objects and a 1.\\hspace{-2pt}''6 one to\nderive the colors.\n\n\\subsection{Optical Images}\n\n To investigate the colors of the $K'$-selected galaxies, we analyzed\nthe archival HST/WFPC2 F702W and F450W images of the 3C 324 field\n(PI: M.Dickinson; PIDs 5465 and 6553, respectively). The total\nexposure times were 64800 sec for the F702W image and 17300 sec for\nthe F450W image.\n\n After combining the separate exposures with cosmic-ray rejection, we\naligned the F702W and the F450W images to the $K'$ image using\npoint sources common to the frames. The optical images were\n then convolved with a Gaussian kernel to match the FWHM of the stellar\nimages in the $K'$ frame. Photometry of each $K'$-selected object\nwas performed using apertures with identical positions and size\n(1.\\hspace{-2pt}''6 diameter) regarding the $K'$ image in each optical\nframe. We used the STMAG system for these optical magnitudes, and\nhereafter refer them as $R_{\\rm F702W}$ and $B_{\\rm F450W}$ (STMAG\nis defined as $m_{\\rm ST} = -21.10-2.5 {\\rm log} f_\\lambda$ where\n$f_\\lambda$ is expressed in erg cm$^{-2}$ s$^{-1}$ \\AA $^{-1}$; \nHST Data Handbook Vol.1). Due to the limitation of the WFPC2\nfield of view (figure 10), the number of $K'$-selected galaxies for\nwhich $R_{\\rm F702W}$ and $B_{\\rm F450W}$ mag were measured is 139.\n\n\n\\section{Results}\n\n\\subsection{Color--Magnitude Diagram}\n\n Figure 1 shows the C--M diagram ($K'$ vs $R_{\\rm F702W}-K'$) of the\ndetected galaxies. We have divided the observed frame into the\n`cluster' region (within 40'' of 3C 324) and the `outer' region\n(the remainder of the frame); note that a clear excess of galaxies\nwith $K$ $\\ltsim$ 20 mag in the `cluster' region has been recognized\nat $\\sim 10 \\sigma$ significance (Dickinson 1995; Paper I). \nThe areas of the `cluster' and the `outer' regions are\n1.193 arcmin$^{2}$ \nand 1.877 arcmin$^{2}$, respectively, and the galaxies in each region\nare plotted with different symbols in the figure. The error bars are\nbased on the 1$\\sigma$ background fluctuation within a 1.\\hspace{-2pt}''6\naperture. The dotted line represents the $\\sim$ 70\\% completeness\nlevel of $K'$ = 21.5 (Paper I). The dashed line shows $R_{\\rm F702W}\n= $ 28 mag, which corresponds to the $\\sim$ 3$\\sigma$ detection limit\nin this band. Most of the $K'$-selected galaxies, except for a few\nextremely red objects, have $R_{\\rm F702W}$ magnitudes brighter than this\nlimit.\n\n In figure 1, the red envelope of the galaxies with $R_{F702W} - K'\n\\sim$ 6 can be seen, and those objects with $K' \\ltsim$ 21 mag and\n$R_{\\rm F702W} - K' >$ 4.5 are dominated by the galaxies in the `cluster'\nregion, despite the area of the outer region being 1.6-times larger\nthan that of the cluster region. In the magnitude range 17 $< K' <$\n21, there are 6$\\pm$2, 8$\\pm$1, and 5$\\pm$3 cluster galaxies with\n$R_{\\rm F702W}-K' >$ 5.5, 4.5 $< R_{\\rm F702W}-K' <$ 5.5, and $R_{\\rm\nF702W}-K' <$\n4.5, respectively, after applying a field correction using the `outer'\nregion. The quoted uncertainties are based on Poisson statistics.\nThus, about one-third of the cluster galaxies with $K' <$ 21 mag have\n$R_{\\rm F702W}-K' >$ 5.5 and their stellar populations are expected to be\nfairly old ($\\gtsim$ 2 Gyr); a more detailed comparison with the\ngalaxy evolutionary models is presented below.\n\n We confirm the existence of the `red finger', a sequence of galaxies\nwith $R_{\\rm F702W}-K' \\sim$ 6 and $K' \\sim$ 18--19 mag, which was\nidentified by Dickinson (1995). The observed colors of these galaxies\nare consistent with Dickinson's result if we consider $R_{\\rm F702W} - R$\nand $K' - K$ color differences. Kodama et al. (1998) derived the slope\nand zero point of this `red finger' using the data of Dickinson\n(1995), and showed that the sequence is consistent with a metallicity\nsequence at $z \\sim 1.2$ for passively evolving galaxies. This red\nsequence of galaxies in the cluster region, however, seems to be\ntruncated at $K'$ $\\sim$ 20. Although there are a few red objects in the\nouter region, there is no such object in the cluster region fainter\nthan this magnitude. This is {\\it not} due to incompleteness; at $K'\n\\sim 21$ the catalog is still $\\sim 90$\\% complete (Paper I).\nTo emphasize this point, figure 2 shows the number counts of the\n`red sequence' galaxies with 5.7 $< R_{\\rm F702W} - K' <$ 6.3, which\ncorresponds to the color range adopted in Kodama et al. (1998),\ntogether with the detection completeness in the $K'$-band evaluated in\nPaper I.\n\n Another important aspect of the C--M diagram in figure 1 is that the\ncolor distribution of galaxies in the cluster region is fairly wide:\nin addition to the `red sequence' galaxies, there are many galaxies\nwith bluer $R_{\\rm F702W} - K'$ colors in the cluster region. There seems\nto exist an even more significant surface density excess within the\n`cluster' region in the range 4.5 $< R_{\\rm F702W} - K' <$ 5.5 ($\\sim 8\n\\pm 1$ cluster galaxies) compared with those in the $R_{\\rm F702W} - K' >\n5.5$ range ($\\sim 6 \\pm 2$ cluster galaxies). At $R_{\\rm F702W} - K' <$\n4.5, a marginal excess of cluster-region galaxies can also be seen\n(5$\\pm$3 cluster galaxies). The galaxies with bluer $R_{\\rm F702W} - K'$\ncolors tend to be fainter at $K'$. The median magnitude of the\ngalaxies with $4.5 < R_{\\rm F702W} - K' < 5.5$ is $K' \\sim 20$, while that\nof the redder ones is $K' \\sim 19$.\n\n\\subsection{Two Color Diagram}\n\n The wide spread in the optical-NIR colors may be due to age differences\nand/or ongoing star formation as well as to contamination by\nforeground/background galaxies. To investigate the causes of the large\nscatter in the C--M diagram, we show a $B_{\\rm F450W}-R_{\\rm F702W}$ vs\n$R_{\\rm F702W}-K'$ two-color diagram for the galaxies with $K' < 22$ in\nfigures 3 and 4. The shaded and open symbols in figure 3 represent the\ngalaxies in the `cluster' and the `outer' regions, respectively.\nThe arrows show that the objects are fainter than the 3 $\\sigma$ upper\nlimit of $B_{\\rm F450W}$ = 26.\n\n In figure 4, we add the model colors of galaxies with various\nstar-formation histories observed at $z =$ 1.2, using the GISSEL96 code\n(Bruzual, Charlot 1993), and adopting the Salpeter initial mass\nfunction. We examined the star formation models with a 1 Gyr single burst,\nexponentially decaying star-formation rates with timescales $\\tau =$\n0.5 and 1 Gyr, and a constant star formation rate (SFR). We also\ninvestigated a 1 Gyr single burst model with a metallicity of 0.2-times\nthe solar value, and confirmed that the differences between it and the\nsolar-metallicity model are seen along the `age direction', as\nexpected from the ``age--metallicity degeneracy''. The colors of the\nmodels of old-population plus ongoing starburst are also\nplotted; to produce these we have added the constant SFR models with\nan age of 0.1 Gyr and mass fractions from 0.02\\% to 0.5\\% to the old\nsingle-burst models. It can be seen that these models may be mimicked by\nthe exponentially decaying models. Note that these models have much\nredder colors than those for spiral galaxies, which are\ncharacterized by $\\tau >$ 2 Gyr (Bruzual, Charlot 1993).\n\n It is found from figure 4 that the colors of the galaxies in the red\nsequence, $R_{\\rm F702W} - K' > 5.5$, are consistent with those of the\nmodels whose age is 3--4 Gyr, irrespective of the existence of a small\namount of ongoing star formation.\n\n On the other hand, many of the galaxies with $4.5 < R_{\\rm F702W} -K' <\n5.5$ are more consistent with the models with a younger age, 1--3 Gyr,\nand are insensitive to the amount of star-formation activity, if we assume\nthey are at the same redshift and neglect possible reddening by dust.\nThe bluer $R_{\\rm F702W} - K'$ colors must be due, at least in part, to a\nyounger age, since the $B_{\\rm F450W}-R_{\\rm F702W}$ color would be $\\sim$\n0.5--1 mag bluer than observed if the bluer $R_{\\rm F702W} - K'$ colors\nwere purely due to star-formation activity. In fact, the bluer\n$R_{\\rm F702W} - K'$ colors must be {\\it predominantly} due to\na youthfulness effect for objects with $B_{\\rm F450W}-R_{\\rm F702W} \\gtsim 0$,\nwhich are less affected by star formation. Note that the effect of\nmetallicity on the age estimation is small in this range. Although there may be\neffects of dust extinction, the reddening arrow (Cardelli et\nal. 1989) in figure 4 is almost parallel to the lines of constant age.\nThere are also some galaxies in the color range $B_{\\rm F450W} -\nR_{\\rm F702W}\n\\ltsim$ 0 and $R_{\\rm F702W} - K' \\sim$ 4, which may be consistent with\n$\\sim$ 1 Gyr-old galaxies at $z =$ 1.2 or galaxies with strong\nstar-formation, although the contamination by foreground/background\ngalaxies is expected to be large in this color range. From these\nresults, both the ages and star formation histories of the 3C 324\ncluster galaxies appear to have significant scatter.\n\n In figure 4, we have further divided the $K'$-selected galaxies into\ntwo samples with $K' <$ 20 (circles) and 20 $< K' <$ 22\n(squares). As inferred from figure 2, there are few `red sequence'\ngalaxies with $K' >$ 20 mag. On the other hand, most galaxies with\n$R_{\\rm F702W} - K' \\sim$ 4.5 whose colors are consistent with those at $z\n\\sim 1.2$ have $K' >$ 20. The population with $R_{\\rm F702W} - K' \\sim$\n4.5--5.5 is a mixture of the bright and faint samples. There may be a\ntrend that galaxies with younger ages or stronger star-formation\nactivity are fainter in the $K'$-band. Postman et al. (1998)\ninvestigated two clusters at $z \\sim$ 0.9, and showed the existence of\na correlation between the `color age' and luminosity (their figures 18\nand 19). The 3C 324 clusters may have a similar property.\n\n The arguments about the star-formation histories of the galaxies\npresented above are based on the assumption that many of these red\ngalaxies are indeed at $z=1.2$. In order to further understand the\nproperties of\nthe cluster galaxies, we filtered the sample to be less\ncontaminated by the foreground galaxies. Most of the galaxies with\n$R_{\\rm F702W} - K'$ bluer than the passive evolution models at $z =$ 1.2\nat a given $B_{\\rm F450W} - R_{\\rm F702W}$ color are considered to be in the\nforeground. We tentatively divided the two-color diagram into two color\ndomains of `$z=1.2$' and `foreground' using as a boundary the 1 Gyr\nburst model with 0.2 solar metallicity. The galaxies in the `$z=1.2$'\ncolor domain are expected to be dominated by the cluster members,\nalthough some of them may be dusty foreground galaxies or relatively\nyoung galaxies at a higher redshift. As a further check, we compared the\nnumber counts of galaxies in the `foreground' color domain located in\nthe `cluster' region with the general field counts derived by\naveraging the number counts taken from the literature (see Paper\nI) in figure 5. They are fairly consistent down to $K\n\\sim 21.5$, where our detection incompleteness becomes as large as\n$\\sim 30 \\%$.\n\n At $K \\gtsim 20$, even the total number counts of the `cluster'\nregion are slightly lower than the average field counts. At the same\ntime, there are not as many galaxies in the `cluster' region with $K >\n20$ in the `$z = 1.2$' color domain, as expected for a luminosity\nfunction with a steep faint-end slope, $\\alpha \\ltsim -1$. For\nexample, there are four galaxies in the`$z=1.2$' color domain between\n$20.5 < K' < 21.5$, while the expected number is 9.1 for $\\alpha=-0.9$\n(Paper I). The apparent deficiency of the surface density excess\nin the `cluster' region discussed in Paper I may thus be at\nleast partly due to the intrinsically small number of cluster\ngalaxies, although it is still highly uncertain how many of the four\ngalaxies are in the background and how many cluster galaxies may have\nbeen missed by the color selection: complete spectroscopic surveys or\nmore accurate photometric redshift measurements are needed to\ndetermine the precise number of cluster galaxies at faint magnitude\nlevels.\n\n\\subsection{Properties of the Color-Selected Galaxies}\n\n Using the criteria described above, we investigated the properties of\nthe `color-selected' cluster galaxy candidates. First, we applied a\nquantitative morphological classification to those galaxies in the\n`$z=1.2$' color domain, using the WFPC2 $R_{\\rm F702W}$ image. The\nclassification was performed using the central concentration index,\n$C$, and the asymmetry index, $A$, to separate early-type (bulge\ndominated), late-type (disk dominated), and irregular galaxies\n(Abraham et al. 1996). Our procedure for measuring the $C$ and $A$ indices\nfollowed Abraham et al. (1996), except that we adopted the centering\nalgorithm of Conselice et al. (1999). Early-type galaxies show a\nstrong central concentration, while late-type galaxies have a lower\nconcentration. Irregular galaxies have a high asymmetry.\n\n We divided the galaxies in the `$z=1.2$' color domain into several\n$R_{\\rm F702W}$ magnitude bins. Since the $C$ and $A$ indices depend on\nobject brightness, even if the intrinsic light profiles are identical,\nthe boundaries between morphological types in the log $C$--log $A$\nplane should be determined separately for each magnitude bin. The\nboundaries are determined with the help of simulated galaxy images\nproduced with the IRAF ARTDATA package. For this purpose, we\nconstructed artificial galaxies with pure de Vaucouleurs (bulge) or\npure exponential (disk) profiles with a similar range of half-light\nradii as the observed galaxies. The $C$ and $A$ indices of these\nartificial galaxies were measured in an identical manner to the real\nones. As a result of this simulation, we divided the morphological\nclasses as shown in figure 6. Although the artificial galaxies have no\nintrinsic irregularity, their apparent asymmetry arises from the\naddition of noise, we adopted the 90\\% completeness limit as the\nboundary of the irregular galaxies in each magnitude bin. We set the\nboundary between the bulge and disk-dominated galaxies so that the\nfractions of correctly classified galaxies in each sample would be equal.\nThe resultant completeness of this bulge/disk classification is $\\sim\n90\\%$ for the $R_{\\rm F702W}$ = 24--25 mag bin and $\\sim 70\\%$ for the\n27--28 mag bin. The resultant classification for the observed galaxies\nwithin the `$z=1.2$' color domain is shown in figure 7.\n \n In figure 8, we show the F702W-band montage of those galaxies\nhaving `$z=1.2$' colors. The top three rows are for those galaxies\nclassified as `bulge-dominated', the middle three rows are the\n`disk-dominated' galaxies, and the bottom three rows are the\n`irregular' galaxies. Our morphological classification seems to work\nwell. Each of the three rows for each morphological type represents a\nrange of $R_{\\rm F702W}-K'$ color. It can be seen that about half of\nthe bulge-dominated galaxies have relatively blue colors\n($R_{F702W}-K' < 5.5$).\nOn the other hand, there are several red ($R_{\\rm F702W}-K' > 5.5$)\ndisk-dominated galaxies; this may imply that star-formation activity has\nceased in these objects, or it may be an effect of dust reddening,\nalthough there may also be some contamination by `bulge-dominated' or\nbackground galaxies. The relatively large number of `irregular'\ngalaxies may indicate that galaxy interactions occur frequently in the\n3C 324 clusters.\n\n Dickinson (1997b) presented a montage of the spectroscopically\nconfirmed cluster members at $z =$ 1.15 and $z =$ 1.21 using the same\n$R_{\\rm F702W}$-band image. Although he did not identify \nthings such as the coordinates, we visually compared our reduced\nimage with his figure 3 and confirmed that not only some red galaxies,\nbut also some blue galaxies in figure 8 are really cluster members. Of\nthe fifteen spectroscopically confirmed cluster members (excluding 3C\n324 itself) in figure 3 of Dickinson (1997b), we identified seven red\n($R-K > 5.5$) galaxies and three bluer galaxies within the `$z=1.2$'\ncolor domain from their morphology and environment. We also found that\nthree spectroscopically confirmed cluster galaxies lie in the\nforeground color domain near to the boundary ($B_{\\rm F450W}-R_{\\rm\nF702W} \\sim\n-0.6$, $R_{\\rm F702W}-K' \\sim 3.8$). It may not be surprising that some\nblue-cluster galaxies were missed in our color selection, since the\nboundary of the color domain is for the ideal model galaxies and there\nmay be an effect of dust reddening in the UV flux.\n\n Figure 9 shows the C--M diagram for the galaxies in the `$z=1.2$'\ncolor domain with their morphological classifications. A morphological\nclassification was not assigned for a few faint galaxies whose surface\nbrightness in the $R_{\\rm F702W}$-band was too low.\n\n We compare the colors and magnitudes of the bulge-dominated galaxies\nwith the metallicity-sequence model for early-type galaxies calibrated\nwith the Coma cluster C--M relation (Kodama, Arimoto 1997) using the\nKodama and Arimoto population synthesis model (solid line). The model\ngalaxies are formed coevally at $z_{\\rm f} =4.5$ and then evolve passively.\nClearly, the observed colors of the bulge-dominated galaxies are not\ncompatible with the model prediction, and the fainter objects are $\\sim\n1$ mag bluer than the model prediction. In fact, the bulge-dominated\ngalaxies in the `cluster' region seem to form a rather broad sequence\nwith a much steeper slope from $R_{\\rm F702W}-K' \\sim 6$ and $K' \\sim 18$\nto $R_{\\rm F702W}-K' \\sim 4.5$ and $K' \\sim 21$.\n\n In figure 10, we show the sky distribution of the galaxies in the `$z\n= 1.2$' color domain. The distribution of the galaxies seems to have\nan irregular structure and some spatial segregation between\nbright and faint sample can be seen; the redder and brighter galaxies tend\nto be located around 3C 324, while the bluer or fainter galaxies have a\nmore diffuse distribution. While the surface densities of the\ncolor-selected galaxies with $K < 20$ are 12.6 arcmin$^{-2}$ and 2.1\narcmin$^{-2}$ in the cluster region and the outer region,\nrespectively, the densities of the fainter galaxies are 7.5\narcmin$^{-2}$ and 5.9 arcmin$^{-2}$. Similarly, while the surface\ndensities for the red ($R_{\\rm F702W}-K' > 5.5$) galaxies are 6.7\narcmin$^{-2}$ and 2.1 arcmin$^{-2}$, those for the bluer galaxies are\n12.6 arcmin$^{-2}$ and 6.4 arcmin$^{-2}$. The color segregation\ntherefore seems to be weaker than the luminosity segregation.\n\n\\section{Discussion}\n\n We have presented the color distribution of the $K'$-band selected\ngalaxies in the region of the clusters at $z=1.2$ near to the radio\ngalaxy 3C 324. While the `red finger', a sequence of galaxies with\n$R_{\\rm F702W}-K' \\sim$ 6 and $K' \\sim$ 18--19 whose colors are consistent\nwith ages $\\gtsim 3$ Gyr (or $z_{\\rm f} > 4.5$; see Kodama et al. 1998) was\nrecognized in the color-magnitude diagram, we also found that this\nsequence is truncated at $K' \\sim 20$ mag; also, few galaxies in the\n`cluster' region with fainter magnitudes have similar red colors.\nGarilli et al. (1996) presented optical C--M diagrams ($g-r$ vs $r$)\nfor 67 low-redshift Abell and EMSS clusters, where most of these\nclusters show a red sequence extending over more than 4 magnitudes. De\nPropris et al. (1998) presented a C--M diagram ($B-R$ vs $H$) for the\nComa cluster, where the C--M relation for early type galaxies ranges\nover more than 5 mag. Compared with these low-redshift clusters,\nthe `red sequence' of the 3C 324 clusters is clearly truncated.\n\n We investigated the significance of this truncation, assuming that the\nred sequence population has a $K$-band luminosity distribution whose shape\nis identical to the cluster population as a whole. We assumed a\nfaint-end slope of $\\alpha = -0.9$, and adopted a characteristic magnitude\nof $K^*=18.4$ (Paper I). The normalization was determined from the\nobserved number of red sequence galaxies with $17 < K < 20$, and the\nexpected number of red galaxies with $20 < K < 21$ was estimated,\ntaking incompleteness into account. The estimated number of red\ngalaxies with $5.7 < R_{\\rm F702W}-K' < 6.3$ and $20 < K <21$ is 3.63 in\nthe cluster region and 4.85 for the entire region, while the observed\nnumbers are 0 and 1, respectively.\n \n We also investigated the $B_{\\rm F450W}-R_{\\rm F702W}$ vs $R_{\\rm F702W}-K'$\ntwo-color diagram and compared the observed colors with models of\nvarious star-formation histories, assuming that the galaxies are\nindeed at $z=1.2$. We found that the large scatter in $R_{\\rm F702W}-K'$\nis due to variations in both the age and star-formation activity, and\nthat the\nobjects with bluer $R_{\\rm F702W}-K'$ colors have younger ages than the\n`red finger' objects, provided that they are not dominated by\nforeground/background galaxies.\n\n For moderately red objects with $4.5 < R_{\\rm F702W}-K' < 5.5$ and\n$B_{\\rm F450W}-R_{\\rm F702W} > 0$, the bluer $R_{\\rm F702W}-K'$ color\nis found to\nbe mainly due to younger ages. There is a trend that galaxies with\nfainter $K'$ mag have bluer colors. Because the near-infrared\n$K'$ magnitude can be an approximate measure of the total stellar mass\nfor quiescent galaxies, it may imply that the relatively low-mass\ngalaxies are, on average, younger than the massive galaxies in the 3C\n324 clusters.\n\n The `bulge-dominated' galaxies within the cluster region seem to form\na broad color-magnitude sequence whose slope is much steeper than\npredicted by coeval passive-evolution models. From the above\ndiscussion, this can be interpreted as an effect of the age sequence\nin addition to the metallicity sequence, provided that the galaxies\nreally are cluster members. For a comparison, in figure 9, we also plot the\n`metallicity plus age' sequence model, using the Kodama and Arimoto\ncode. In this model, the zero point is the same as the pure\nmetallicity-sequence model discussed in the previous section at\n$R_{\\rm F702W}-K'$ = 6 ($z_{\\rm f} = 4.5$, $\\sim 3$ Gyr old), and the fainter\ngalaxies are 0.5 Gyr younger per 1 $M_{V}$-magnitude (at\n$z=0.02$). The mean metallicity at each magnitude is adjusted so that\nthe model sequence coincides with the Coma cluster C--M relation, when\nit is evolved passively to $z = 0.02$. It can be seen that this model\nwell reproduces the sequence of the `bulge-dominated' cluster-region\ngalaxies. The age difference may thus be as much as $\\sim 2$ Gyr\nbetween galaxies with $K'=18$ and $K'=21$.\n \n Is this picture consistent with the well-defined C--M sequence\nobserved in intermediate-redshift clusters? The C--M relation of\nmorphologically selected early-type galaxies in clusters at $z\n=$ 0.2--0.8 is known to extend over a range of at least 3--4 magnitudes\nwith a scatter smaller than 0.1 mag (e.g., Ellis et al. 1997; Stanford\net al. 1998). This is very different from the C--M sequence observed at\n$z=1.2$. However, if the relatively large scatter and steep slope of\nthe C--M relation for the bulge-dominated galaxies in the 3C 324\nclusters are caused by an age difference and the evolution is passive after\n$z=1.2$, the younger (bluer) galaxies would change their color and\nluminosity more rapidly than the old (red) galaxies, and may\nbecome as red as and even fainter within a relatively short time. The\nC--M relation would then become tighter and would extend over a larger\nmagnitude range, with a shallower slope. Note that the effect of an\nadditional small amount of star formation at $z = 1.2$ with a standard\nIMF is negligible at intermediate-z, if the star formation ceases\nimmediately after $z =$ 1.2, because the brightness of these component\ndeclines rapidly as massive stars die and the main sequence burns\ndown.\n\n For example, we compared the color and luminosity evolution of the 1\nGyr burst models with different ages, using the GISSEL96 code. One\nmodel is 3 Gyr old at $z = 1.2$ (formation redshift $z_{\\rm f} \\sim 5$,\n$H_{0} =$ 50 km s$^{-1}$ Mpc$^{-1}$, $q_{0}$ = 0.5) and its\noptical--NIR color is $R_{\\rm F702W} - K' \\sim 6$, which roughly\ncorresponds to the `red sequence' population. The other is 1.5 Gyr old\nat $z = 1.2$ ($z_{\\rm f} \\sim 2$) and its $R_{\\rm F702W} - K' \\sim 5$, which\nrepresents the bluer galaxies. At $z \\sim 0.7$, the difference in\n$R_{\\rm F702W} - K'$ color between these two models is only $\\Delta\n(R_{\\rm F702W}-K') \\sim 0.1$, and the difference in $B_{\\rm F450W} -\nR_{\\rm F702W}$ color, which is more sensitive to a small amount of star\nformation, becomes $\\sim 0.1 $ by $z \\sim$ 0.5. The fading of the\nyounger model galaxy in the $K'$ band is about 0.5 mag greater than\nthat of the old model galaxy at $z \\ltsim$ 0.9; if we assume that the\nyounger galaxy is about 1 magnitude fainter at $z = 1.2$, it becomes\nabout 1.5 magnitude fainter at an intermediate redshift. From these\nresults, the bluer `bulge-dominated' population in the 3C 324 clusters\nis expected to form a fainter part of the tight C--M relation at\nintermediate-redshift, which may at least partially explain the\nobserved apparent truncation of the red sequence at $z=1.2$.\n\n In Paper I, we showed that the excess of the surface density in\nthe cluster region drops abruptly at $K \\sim$ 20 mag. One possible\ninterpretation is that there may be an intrinsic deficit of faint\ngalaxies in the clusters. Despite the existence of color selected\ngalaxies with $K > 20$ mag in the cluster region, this possibility\ncannot be completely ruled out, since the number of these objects may\nnot be large enough (subsection 3.2). There is, however, another possible\nexplanation, that there is a difference in the spatial distribution\nbetween bright and faint galaxies, and that the apparent deficit of the\nsurface-density excess is due to the more uniform distribution of the\nfaint cluster galaxies. Indeed, such luminosity segregation is also\nseen in the spatial distribution of the color-selected galaxies that\nmay be at $z \\gtsim 1.2$, as shown in figure 10 (subsection 3.3). This\ntendency is insensitive to subtle changes of the boundary between the\n`$z=1.2$' and `foreground' color domains in figure 4. There are\nseveral possible origins for such a luminosity segregation. Within the\nframework of the theory of biased galaxy formation with cold dark\nmatter, luminosity segregation is naturally predicted (Valls-Gabaud et\nal. 1989). In biased CDM theory, the most massive and oldest galaxies\ncorrespond to the highest peaks of the initial density fluctuations, and\nare concentrated more strongly at the early formation epoch.\nAlternatively, merger events may play important roles (e.g.,\nFusco-Femiano, Menci 1998); since galaxy merging may occur more\nfrequently at the dense cluster core, massive galaxies can be formed\nefficiently in the central region.\n\n The difference in the sky distribution between those galaxies with\ndifferent colors and magnitudes may be the result of the superposition\nof two systems, namely those at $z =$ 1.21 and 1.15, that may\ncontain different galaxy populations. Postman et al. (1998) indeed\nshow such an example. The cluster Cl 0023+0423 at $z =$ 0.84 was\nrevealed to consist of two poor clusters or groups of galaxies; they\nfound that there are few luminous galaxies in one system, while\nluminous red galaxies exist in the other system. The 3C 324 clusters\nmay be in similar situation to Cl 0023+0423. Although they are not\nassociated with each other in the real space in the case of the 3C324\nclusters, there may be a large variety of galaxy populations among the\nhigh-redshift clusters or groups. \n\n Finally, we note a rather speculative feature about the galaxy\nspatial distribution. The large-scale distribution of those galaxies\nwith a `$z =$ 1.2' color domain in the field extends in an east--west\ndirection centered at 3C 324, and is aligned with the radio axis of 3C\n324. This may imply a possible relationship between the past radio\njet activity of 3C 324 and galaxy formation (e.g., West 1994).\\\\\n\\vspace{0.5cm}\n\n%*********** ACKNOWLEDGES\nWe wish to thank Alfonso Arag\\'on-Salamanca, the referee of this\npaper, for his invaluable comments. \nThe present result is indebted to all the members of the Subaru\nObservatory, NAOJ, Japan. We thank Nobuo Arimoto for kindly providing\nthe Kodama and Arimoto evolutionary synthesis models. This research\nwas supported by grants-in-aid for scientific research of the\nMinistry of Education, Science, Sports and Culture (08740181,\n09740168). This work was also supported by the Foundation for the\nPromotion of Astronomy. This work is based in part on\nobservations with the NASA/ESA Hubble Space Telescope, obtained from\nthe data archive at the Space Telescope Science Institute, which is\noperated by AURA, Inc.\\ under NASA contract NAS5--26555. The Image\nReduction and Analysis Facility (IRAF) used in this paper is\ndistributed by National Optical Astronomy Observatories, operated by\nthe Association of Universities for Research in Astronomy, Inc., under\ncontact to the National Science Foundation. \n\n\n%\\clearpage\n\n\\section*{References}\n\\small\n\n\\re\nAbraham R. G., van Den Bergh S., Glazebrook K., Ellis R. S., Santiago\nB. X., Surma P., Griffiths R. E. 1996, ApJS 107, 1\n\n\\re\nArag\\'on-Salamanca A., Ellis R. S., Couch W. J., Carter D. 1993, MNRAS 262, 764\n\n\\re\nBen\\'\\i tez N., Broadhurst T., Rosati P., Courbin F., Squires G.,\nLidman C., Magain P. 1999, ApJ 527, 31\n\n\\re\nBertin E., Arnouts S. 1996, A\\&AS 117, 393 \n\n\\re\nBower R. G., Kodama T., Terlevich A. 1998, MNRAS 299, 1193\n\n\\re\nBower R. G., Lucey J. R., Ellis R. S. 1992, MNRAS 254, 601\n\n\\re\nBruzual A. G., Charlot S. 1993, ApJ 405, 538\n\n\\re\nButcher H., Oemler A. Jr 1978, ApJ 219, 18 \n\n\\re\nButcher H., Oemler A. Jr 1984, ApJ 285, 426 \n\n\\re\nCardelli J. A., Clayton G. C., Mathis J. S. 1989, ApJ 345, 245\n\\re\nConselice C. J., Bershady M. A., Jangren A. 1999, ApJ in press ({\\it\nastro-ph}/9907399)\n\n\\re\nDe Propris R., Eisenhardt P. R., Stanford S. A., Dickinson M. 1998,\nApJ 503, L45\n\n\\re\nDe Propris R., Stanford S. A., Eisenhardt P. R., Dickinson M., Elston\nR. 1999, AJ 118, 719\n\n\\re\nDickinson, M. 1995, ASP Conf. Ser. 86, 283\n\n\\re\nDickinson M. 1997a, in HST and the High Redshift Universe, ed\nN. R. Tanvir, A. Arag\\'on-Salamanca, J.V. Wall (World\nScientific, Singapore) p.207\n\n\\re\nDickinson, M. 1997b, in The Early Universe with the VLT, ed J. Bergeron \n(Springer, Berlin) p274\n\n\\re\nDressler A., Gunn J. E. 1992, ApJS 78, 1 \n\n\\re\nDressler A., Smail I., Poggianti B. M., Butcher H., Couch W. J., Ellis\nR. S., Oemler A. Jr 1999, ApJS 122, 51\n\n\\re\nEllis R. S., Smail I., Dressler A., Couch W. J., Oemler A. Jr,\nButcher H., Sharples R. M. 1997, ApJ 483, 582\n\n\\re\nFusco-Femiano R., Menci N. 1998, ApJ 498, 95\n\n\\re\nGarilli B., Bottini D., Maccagni D., Carrasco L., Recillas E. 1996,\nApJS 105, 191\n\n\\re\nGladders M. D., L\\'opez-Cruz O., Yee H. K. C., Kodama T. 1998, ApJ 501,\n571\n\n\\re\nHall P. B., Green R. F. 1998, ApJ 507, 558\n\n\\re\nHST Data Handbook, Ver3.1 1998, http://www.stsci.edu/documents/data-handbook.html\n\n\\re\nKajisawa M., Yamada T. 1999, PASJ 51, 719\n\n\\re\nKajisawa M., Yamada T., Tanaka I., Maihara T., Iwamuro F., Terada H.,\nGoto M., Motohara K. et al. 2000, PASJ in press (Paper I)\n\n\\re\nKodama T., Arimoto N. 1997, A\\&A 320, 41\n\n\\re\nKodama T., Arimoto N., Barger A. J., Arag\\'on-Salamanca A. 1998, A\\&A\n334, 99\n\n\\re\nKristian J., \nSandage A., Katem B. 1974, ApJ 191, 43 \n\n\\re\nMotohara K., Maihara T., Iwamuro F., Oya S., Imanishi M., Terada H., \nGoto M., Iwai J., et al. 1998, Proc. SPIE 3354, 659 \n\n\\re\nPoggianti B. M., Smail I., Dressler A., Couch W. J., Barger A. J., Butcher H., \nEllis R. S., Oemler A. Jr 1999, ApJ 518, 576\n\n\\re\nPostman M., Lubin L. M., Oke, J. B. 1998, AJ 116, 560\n\n\\re\nRakos K. D., Schombert J. M. 1995, ApJ 439, 47\n\n\\re\nRosati P., Stanford S. A., Eisenhardt P. R., Elston R., Spinrad H.,\nStern D., Dey A. 1999, AJ 118, 76\n\n\\re\nSmail I., Dickinson M. 1995, ApJ 455, L99\n\n\\re \nSmail I., Edge A. C., Ellis R. S., Blandford R. D. 1998, MNRAS 293,\n124\n\n\\re\nSpinrad H., \nDjorgovski S. 1984, ApJ 280, L9 \n\n\\re\nStanford S. A., Eisenhardt P. R., Dickinson M. 1998, ApJ 492, 461\n\n\\re \nStanford S. A., Elston R., Eisenhardt P. R., Spinrad H., Stern D.,\nDey A. 1997, AJ 114, 2232\n\n\\re\nTanaka I., Yamada T., Arag\\'on-Salamanca A., Kodama T., Miyaji T., Ohta\nK., Arimoto N. 1999, ApJ in press ({\\it astro-ph}/9907437)\n\n\\re\nTerlevich A. I., Kuntschner H., Bower R. G., Caldwell N., Sharples\nR. M. 1999, MNRAS in press ({\\it astro-ph}/9907072)\n\n\\re\nValls-Gabaud D., Alimi J.-M., Blanchard A. 1989, Nature 341, 215\n\n\\re\nvan Dokkum P. G., Franx M. 1996, MNRAS 281, 985\n\n\\re\nvan Dokkum P. G., Franx M., Kelson D. D., Illingworth G. D. 1998, ApJ \n504, L17\n\n\\re\nVisvanathan N., Sandage A. 1977, ApJ 216, 214\n\n\\re\nWainscoat R. J., Cowie L. L. 1992, AJ 103, 332\n\n\\re\nWest M. J. 1994, MNRAS 268, 79 \n\n\\re\nYamada T., Tanaka I., Arag\\'on-Salamanca A., Kodama T., Ohta K.,\nArimoto N. 1997, ApJ 487, L125\n\n\n\\clearpage\n\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig1.ps,scale=0.75}\n \\end{center}\n\\footnotesize Fig.\\ 1.\\ \n$R_{\\rm F702W} - K'$ vs $K'$ color--magnitude diagram for the galaxies in\nthe region of 3C 324. The shaded and open circles represent galaxies in\nthe `cluster' region within 40'' of 3C 324, and the adjacent\n`outer' region, respectively. 3C 324 is plotted with the solid\nsquare. The dotted line represents $K' =$ 21.5 mag, and the dashed\nline shows $R_{\\rm F702W} =$ 28 mag (see text).\n\\end{figure*}\n\n%\\begin{fv}{2}{18pc}%\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig2.ps,scale=0.6}\n \\end{center}\n\\footnotesize Fig.\\ 2.\\ \nNumber counts of the `red sequence' galaxies with 5.7 $< R_{\\rm F702W} -\nK' <$ 6.3, except for those objects not detected in the $R_{\\rm F702W}$-band\nimage. The hatched region represents those galaxies within 40 arcsec\nradius of 3C 324. Detection completeness in the $K'$ image is also\nshown.\n\\end{figure*}\n\n%\\begin{fv}{3}{18pc}%\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig3.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 3.\\ \n$R_{\\rm F702W} - K'$ vs $B_{\\rm F450W} - R_{\\rm F702W}$ two-color\ndiagram for the\ngalaxies with $K' <$ 22. The meaning of the symbols is similar to\nthose in figure 1.\n\\end{figure*}\n\n%\\begin{fv}{4}{18pc}%\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig4.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 4.\\ \nSame two-color diagram as figure 3, but the galaxies are divided\ninto brighter and fainter samples (circles for $K' <$ 20, and\nsquares for $K' >$ 20), and the models for the galaxies at $z = 1.2$\nwith various star-formation histories are plotted along the age\nsequence. Tracks of the models of 1 Gyr-burst (solid line for solar\nmetallicity and dot-dashed line for 0.2 solar), $\\tau =$ 0.5 Gyr\n(long-dashed line), $\\tau =$ 1 Gyr (short-dashed line), and constant\nSFR (thin dashed line) are shown. The crosses represent the ages of 2,\n3, 4 Gyr. The dotted lines represent the track of old (1 Gyr burst)\n$+$ ongoing starburst (constant SFR) with mass fractions of 0.02,\n0.05, 0.1, 0.2, 0.5\\% (from right to left). We show the effect of\nreddening by the large arrow using the galactic extinction curve given\nin Cardelli et al. (1989) for $E(B-V) =0.3$.\n\\end{figure*}\n\n%\\begin{fv}{5}{18pc}%\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig5.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 5.\\ \n$K$-band number counts of galaxies in the `cluster' region. The hatched\nregion represents those of the galaxies within the `foreground' color\nrange in figure 4. The dash-dotted line shows the averaged general field\ncounts derived from the literature (Paper I). No color\ncorrection is applied in converting the $K'$-band magnitude to\n$K$-band one. \n\\end{figure*}\n\n\n%\\begin{fv}{6}{18pc}%\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig6.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 6.\\ \nlog $C$--log $A$ morphological classification for the artificial\ngalaxies on the WFPC2 image shown in each magnitude bin. Each symbol\nrepresents the light profile of artificial galaxies. The dotted lines show\nthe boundary between `bulge', `disk', and `irregular' galaxies (see\ntext).\n\\end{figure*}\n\n%\\begin{fv}{7}{18pc}%\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig7.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 7.\\ \nMorphological classification of the real galaxies within the\n`$z=1.2$' color range on the WFPC2 image.\n\\end{figure*}\n\n%\\begin{fv}{8}{18pc}%\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig8.ps,scale=1.0}\n \\end{center}\n\\footnotesize Fig.\\ 8.\\ \nHST WFPC2 $R_{\\rm F702W}$-band images of the galaxies in figure 7. The top\nthree rows: `bulge-dominated' galaxies. Middle: `disk-dominated'\ngalaxies. Bottom: irregular galaxies. In each morphological block,\neach row represents galaxy color; $R_{\\rm F702W} - K' > 5.5$ (top), 4.5 $<\nR_{\\rm F702W} - K' < 5.5$ (middle), and $R_{\\rm F702W} - K' <$ 4.5 (bottom).\n\\end{figure*}\n\n%\\begin{fv}{9}{18pc}%\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig9.ps,scale=0.7}\n \\end{center}\n\\footnotesize Fig.\\ 9.\\ \n$R_{\\rm F702W} - K'$ vs $K'$ color-magnitude diagram for those galaxies\nwithin the `$z = 1.2$' color range in figure 4. The shape of each\nsymbol represents the morphology classified in figure 7. The solid\nline represents the metallicity-sequence C-M relation model for the\nComa cluster (Kodama, Arimoto 1997), which would be observed at\n$z=1.2$, assuming passive evolution. The dotted line shows a similar\nmodel with a 1--3 Gyr age difference along the sequence (see text).\n\\end{figure*}\n\n%\\begin{fv}{10}{18pc}%\n\\begin{figure*}[p]\n \\begin{center}\n \\epsfile{file=fig10.ps,scale=0.65}\n \\end{center}\n\\footnotesize Fig.\\ 10.\\ \nSpatial distribution of the galaxies within the `$z = 1.2$' color\nrange. The meaning of the shape of each symbol is the same as in figure\n9. The size of each symbol represents $K' < 20$ (large), $K' > 20$\n(small), respectively. The pattern of each symbol represents\n$R_{\\rm F702W} - K'$ color, $R_{\\rm F702W} - K'> 5.5$ (filled), $4.5 <\nR_{\\rm F702W} - K' < 5.5$ (hatched), $R_{\\rm F702W} - K' < 4.5$ (dotted). 3C\n324 is plotted with a diamond. The upper light solid line shows the\nboundary of the optical WFPC2 images. The large solid circle\nrepresents a 40-arcsec radius from 3C324.\n\\end{figure*}\n\n\n\\end{document}\n\n\u001f\n"
}
] |
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astro-ph0002345
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X-ray absorption lines in the Seyfert 1 galaxy NGC~5548 discovered with Chandra-LETGS
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[
{
"author": "J.S. Kaastra \\inst{1}"
},
{
"author": "R. Mewe \\inst{1}"
},
{
"author": "D.A. Liedahl \\inst{2}"
},
{
"author": "S. Komossa \\inst{3}"
},
{
"author": "A.C. Brinkman \\inst{1}"
}
] |
We present for the first time a high-resolution X-ray spectrum of a Seyfert galaxy. The Chandra-LETGS spectrum of NGC~5548 shows strong, narrow absorption lines from highly ionised species (the H-like and He-like ions of C, N, O, Ne, Na, Mg, Si, as well as \ion{Fe}{xiv} -- \ion{Fe}{xxi}). The lines are blueshifted by a few hundred km/s. The corresponding continuum absorption edges are weak or absent. The absorbing medium can be modelled by an outflowing, thin and warm shell in photoionization equilibrium. The absorption lines are similar to lower ionization absorption lines observed in the UV, although these UV lines originate from a different location or phase of the absorbing medium. Redshifted with respect to the absorption lines, emission from the \ion{O}{viii} Ly$\alpha$ line as well as the \ion{O}{vii} triplet is visible. The flux of these lines is consistent with emission from the absorbing medium. The \ion{O}{vii} triplet intensity ratios demonstrate that photoionization dominates and yield an upper limit to the electron density of $7\times 10^{16}$~m$^{-3}$. \keywords{Galaxies: individual: NGC~5548 -- Galaxies: Seyfert -- quasars: absorption lines -- -- X-rays: galaxies }
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[
{
"name": "paper.tex",
"string": "% aa.dem\n% AA vers. 4.01, LaTeX class for Astronomy & Astrophysics\n% demonstration file\n% (c) Springer-Verlag HD\n%-----------------------------------------------------------------------\n%\n%\\documentclass[referee]{aa} % for a referee version\n%\n\\documentclass{aa}\n\n\\usepackage{graphicx,times}\n\\def\\simlt {\\lower.5ex\\hbox{$\\; \\buildrel < \\over \\sim \\;$}} \n\\def\\simgt{\\lower.5ex\\hbox{$\\; \\buildrel > \\over \\sim \\;$}} \n\\def\\msun {\\hbox{M$_{\\odot}$}} \n\\def\\mdot {$\\mathaccent 95 m$} \n\\def\\Mdot {$\\mathaccent95 M$} \n\\def\\ism {interstellar medium}\n\\def\\deg {$^\\circ$} \n\\def\\arcmin {$^\\prime$} \n\\def\\arcsec{$^{\\prime\\prime}$} \n\\def\\etal {{et al.}}\n\n\\begin{document}\n\\thesaurus{11 % A&A Section 11: Galaxies\n (11.09.1 NGC~5548; % Galaxies: individual\n 11.19.1 % Galaxies: Seyfert\n 11.17.1 % quasars: absorption lines\n 13.25.2)} % X-rays: galaxies\n\n \\title{X-ray absorption lines in the Seyfert 1 galaxy NGC~5548 discovered\n with Chandra-LETGS}\n\n\\author{ J.S. Kaastra \\inst{1}\n \\and\n R. Mewe \\inst{1}\n \\and\n D.A. Liedahl \\inst{2}\n \\and\n S. Komossa \\inst{3}\n \\and\n A.C. Brinkman \\inst{1}\n }\n \n\\offprints{J.S. Kaastra}\n\\mail{J.Kaastra@sron.nl}\n\n\\institute{ SRON Laboratory for Space Research\n Sorbonnelaan 2, 3584 CA Utrecht, The Nether\\-lands \n \\and\n Physics Department,\n Lawrence Livermore National Laboratory, \n P.O. Box 808, L-11, Livermore, CA 94550, USA\n \\and\n Max Planck Institut f\\\"ur Extraterrestrische Physik,\n Postfach 1603, D-85740 Garching, Germany}\n\n\\date{Received 1-Feb-2000 / Accepted 4-Feb-2000 }\n\n\n\\maketitle\n\n\\begin{abstract}\n\nWe present for the first time a high-resolution X-ray spectrum of a Seyfert\ngalaxy. The Chandra-LETGS spectrum of NGC~5548 shows strong, narrow absorption\nlines from highly ionised species (the H-like and He-like ions of C, N, O, Ne,\nNa, Mg, Si, as well as \\ion{Fe}{xiv} -- \\ion{Fe}{xxi}). The lines are\nblueshifted by a few hundred km/s. The corresponding continuum absorption edges\nare weak or absent. The absorbing medium can be modelled by an outflowing, thin\nand warm shell in photoionization equilibrium. The absorption lines are similar\nto lower ionization absorption lines observed in the UV, although these UV lines\noriginate from a different location or phase of the absorbing medium.\nRedshifted with respect to the absorption lines, emission from the \\ion{O}{viii}\nLy$\\alpha$ line as well as the \\ion{O}{vii} triplet is visible. The flux of\nthese lines is consistent with emission from the absorbing medium. The\n\\ion{O}{vii} triplet intensity ratios demonstrate that photoionization dominates\nand yield an upper limit to the electron density of $7\\times 10^{16}$~m$^{-3}$.\n\n\\keywords{Galaxies: individual: NGC~5548 --\nGalaxies: Seyfert -- quasars: absorption lines --\n-- X-rays: galaxies }\n\\end{abstract}\n\n\\section{Introduction}\n\nLow to medium energy resolution X-ray spectra of AGN such as obtained by the\nRosat or ASCA observatories showed the presence of warm absorbing material (see\nreferences in Kaastra \\cite{kaastra}). This was deduced from broad band fits to\nthe continuum, showing a flux deficit at wavelengths shorter than the expected\nedges of ions such as \\ion{O}{vii} and \\ion{O}{viii}. The relation of this warm\nX-ray absorber to the medium that produces narrow UV absorption lines in\n\\ion{C}{iv} or \\ion{N}{v} is not clear, mainly due to a lack of sufficient\nconstraints in the X-ray band.\n%\nA major drawback of all previous X-ray studies of AGN has been the low spectral\nresolution, making it hard to disentangle any emission line features from the\nsurrounding absorption edges, and prohibiting the measurements of Doppler shifts\nor broadening. With the Chandra spectrometers it is now possible for the first\ntime to obtain high-resolution X-ray spectra of AGN.\n\n\\section{Observations}\n\nThe present Chandra observations were obtained on December 11/12, 1999, with an\neffective exposure time of 86400~s. The detector used was the High Resolution\nCamera (HRC-S) in combination with the Low Energy Transmission Grating (LETG).\nThe spectral resolution of the instrument is about 0.06~\\AA\\ and almost constant\nover the entire wavelength range (1.5--180~\\AA). Event selection and background\nsubtraction were done using the same standard processing as used for the\nfirst-light observation of Capella (Brinkman et al. \\cite{brinkman}). The\nwavelength scale is currently known to be accurate to within 15~m\\AA. The\nefficiency calibration has not yet been finished, and our efficiency estimates\nare based upon preflight estimates for wavelengths below 60~\\AA\\ and on inflight\ncalibration based upon data from Sirius~B for longer wavelengths. We estimate\nthat the current effective area is accurate to about 20--30~\\%, that it may show\nlarge scale systematic variations within those limits, but it does not show\nsignificant small scale variations.\n\nThe observed count spectrum was corrected for higher spectral order\ncontamination by subtracting at longer wavelengths the properly scaled observed\ncount spectrum at shorter wavelengths. The spectrum was then converted to flux\nunits by dividing it by the effective area, and by correcting for the galactic\nabsorption of $1.65\\times 10^{24}$~m$^{-2}$ (Nandra et al. \\cite{nandra}), as\nwell as for the cosmological redshift, for which we took the value of 0.01676\n(Crenshaw et al. \\cite{crenshaw}).\n%\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics[angle=-90]{fig1.ps}}\n\\caption{Chandra LETGS X-ray spectrum of NGC~5548,\ncorrected for order contamination, redshift and galactic\nabsorption.}\n\\label{fig:fig1}\n\\end{figure}\n%\nThe spectrum in the 5--38~\\AA\\ range is shown in Fig.~\\ref{fig:fig1}. The\ncontinuum is rather smooth; the reality of the large-scale structures cannot be\nassessed completely at this moment given our current understanding of the\nefficiency calibration of the instrument. Nevertheless, there is no indication\nfor the presence of strong \\ion{O}{vii} or \\ion{O}{viii} K-shell absorption\nedges at 16.77 and 14.23~\\AA, respectively. A more detailed discussion of the\nspectrum, including the long-wavelength part will be given in a forthcoming\npaper, when the full efficiency calibration of the instrument is available.\n\n\\subsection{Absorption lines}\n\nThe most striking feature of the spectrum is the presence of narrow absorption\nlines, including the Lyman $\\alpha$ and $\\beta$ transitions of H-like C, N, O,\nNe and Mg, as well as the 2--1 resonance absorption line of He-like O and Ne.\nWe have searched the wavelength range of Fig.~\\ref{fig:fig1} systematically for\nabsorption and emission lines, and found the lines listed in\nTable~\\ref{tab:data}. In addition we provide data for some weaker features for\nwhich the equivalent widths (or their upper limits) help to constrain models.\nWe give expected wavelength $\\lambda_0$, the measured wavelength difference\n$\\Delta\\lambda\\equiv \\lambda_0-\\lambda_{\\mathrm obs}/(1+z)$ (thereby accounting\nfor the cosmological redshift $z$), the equivalent line width $W$ (determined\nfrom a gaussian fit to the line profile), and the proposed line identification.\nA negative sign before an equivalent width indicates an emission line.\n%\n\\begin{table}[!h]\n\\caption{Absorption and emission lines identified in NGC~5548.\nLines possibly blended by lines from other ions are indicated\nby an asterisk.}\n\\label{tab:data}\n\\centerline{\n\\begin{tabular}{|rrrl|}\n\\hline\n%$\\lambda_0$ & $\\Delta\\lambda$ & W & Identification \\\\\n%(\\AA) & (m\\AA) & (m\\AA) & \\\\\n$\\lambda_0$ (\\AA)& $\\Delta\\lambda$ (m\\AA) & W (m\\AA)& Identification \\\\\n\\hline \n 5.217 & 57$\\pm$ 25 & 19$\\pm$ 15 & Si XIV 1s - 3p (Ly$\\beta$) \\\\\n 6.182 & 12$\\pm$ 16 & 18$\\pm$ 7 & Si XIV 1s - 2p (Ly$\\alpha$) \\\\\n 8.421 & 1$\\pm$ 11 & 24$\\pm$ 8 & Mg XII 1s - 2p (Ly$\\alpha$) \\\\\n 9.169 & -9$\\pm$ 29 & 14$\\pm$ 9 & Mg XI 1s$^2$ - 1s2p $^1$P$_1$ (r)\\\\\n 9.314 & -19$\\pm$ 0 & -9$\\pm$ 11 & Mg XI 1s$^2$ - 1s2s $^3$S$_1$ (f)\\\\\n10.025 & -16$\\pm$ 15 & 21$\\pm$ 10 & Na XI 1s - 2p (Ly$\\alpha$) \\\\\n11.003 & 8$\\pm$ 13 & 21$\\pm$ 10 & Na X 1s$^2$ - 1s2p $^1$P$_1$ (r) \\\\\n12.134 & 0$\\pm$ 7 & 38$\\pm$ 9 & Ne X 1s - 2p (Ly$\\alpha$) * \\\\\n12.274 & 13$\\pm$ 21 & 26$\\pm$ 9 & Fe XVII 2p-4d * \\\\\n12.292 & -5$\\pm$ 21 & 26$\\pm$ 9 & Fe XXI 2p-3d * \\\\\n12.844 & -27$\\pm$ 23 & 16$\\pm$ 11 & Fe XX 2p-3d blend \\\\\n12.904 & -4$\\pm$ 12 & 25$\\pm$ 11 & Fe XX 2p-3d \\\\\n13.447 & 21$\\pm$ 8 & 46$\\pm$ 9 & Ne IX 1s$^2$ - 1s2p $^1$P$_1$ (r) * \\\\\n13.522 & 26$\\pm$ 12 & 25$\\pm$ 11 & Fe XIX 2p-3d blend \\\\\n13.698 & 24$\\pm$ 32 & -18$\\pm$ 13 & Ne IX 1s$^2$ - 1s2s $^3$S$_1$ (f) \\\\\n13.826 & 59$\\pm$ 11 & 26$\\pm$ 10 & Fe XVII 2p-3p \\\\\n14.207 & 0$\\pm$ 14 & 22$\\pm$ 10 & Fe XVIII 2p-3d blend\\\\\n15.014 & 5$\\pm$ 12 & 19$\\pm$ 10 & Fe XVII 2p-3d \\\\\n15.176 & 64$\\pm$ 13 & 25$\\pm$ 9 & O VIII 1s - 4p (Ly$\\gamma$) \\\\\n15.265 & -39$\\pm$ 13 & 25$\\pm$ 9 & Fe XVII 2p-3d \\\\\n16.006 & 7$\\pm$ 10 & 40$\\pm$ 9 & O VIII 1s - 3p (Ly$\\beta$) \\\\\n16.612 & 10$\\pm$ 11 & -45$\\pm$ 15 & No id \\\\\n17.396 & -19$\\pm$ 28 & 20$\\pm$ 10 & O VII 1s$^2$ - 1s5p $^1$P$_1$ \\\\\n17.768 & -25$\\pm$ 17 & 22$\\pm$ 10 & O VII 1s$^2$ - 1s4p $^1$P$_1$ \\\\\n18.627 & -7$\\pm$ 17 & 21$\\pm$ 10 & O VII 1s$^2$ - 1s3p $^1$P$_1$ \\\\\n18.969 & -22$\\pm$ 7 & 55$\\pm$ 10 & O VIII 1s - 2p (Ly$\\alpha$) \\\\\n21.602 & -40$\\pm$ 10 & 53$\\pm$ 12 & O VII 1s$^2$ - 1s2p $^1$P$_1$ (r) \\\\\n21.602 & 70$\\pm$ 15 & -33$\\pm$ 16 & O VII 1s$^2$ - 1s2p $^1$P$_1$ (r) \\\\\n21.804 & 25$\\pm$ 17 & -33$\\pm$ 19 & O VII 1s$^2$ - 1s2p $^3$P$_{1,2}$(i) \\\\\n22.101 & 11$\\pm$ 11 & -64$\\pm$ 19 & O VII 1s$^2$ - 1s2s $^3$S$_1$ (f) \\\\\n24.781 & -4$\\pm$ 12 & 54$\\pm$ 14 & N VII 1s - 2p (Ly$\\alpha$) \\\\\n28.466 & -25$\\pm$ 11 & 36$\\pm$ 12 & C VI 1s - 3p (Ly$\\beta$) \\\\\n33.736 & -36$\\pm$ 10 & 99$\\pm$ 17 & C VI 1s - 2p (Ly$\\alpha$) \\\\\n38.950 & -88$\\pm$ 25 & 35$\\pm$ 22 & Fe XV 3s$^2$-3s5p \\\\\n39.146 & 25$\\pm$ 25 & 164$\\pm$ 61 & No id \\\\\n40.268 & -46$\\pm$ 45 & 216$\\pm$ 82 & C V 1s$^2$ - 1s2p $^1$P$_1$ (r) \\\\\n50.350 & -11$\\pm$ 32 & 47$\\pm$ 30 & Fe XVI 3s-4p \\\\\n52.911 & -36$\\pm$ 12 & 73$\\pm$ 21 & Fe XV 3s$^2$-3s4p \\\\\n58.963 & -9$\\pm$ 52 & 48$\\pm$ 40 & Fe XIV 3p-4d \\\\\n\\hline\\noalign{\\smallskip}\n\\end{tabular}\n}\n\\end{table}\n%\nThe presence of these aborption lines can be seen as evidence for a warm,\nabsorbing medium in NGC~5548 along the line of sight towards the nucleus. The\nabsorption can be very strong: the core of the \\ion{C}{vi} Ly$\\alpha$ line for\nexample absorbs some 90~\\% of the continuum, and this is just a lower limit,\nsince the true line profile is smeared out by the instrument. That the optical\ndepth in some lines is considerable is evidenced by two facts: firstly, the\nequivalent width ratio of the Ly$\\beta$ to Ly$\\alpha$ lines of \\ion{C}{vi} and\n\\ion{O}{viii} is much larger than the ratio of their oscillator strengths (0.079\nto 0.417). Secondly, we see absorption features of sodium, despite the fact\nthat the sodium abundance is 20 times smaller than, e.g., the magnesium\nabundance. All this can be explained if the line cores of the more abundant\nelements are strongly saturated.\n\n\\subsection{Column densities}\n\nUsing the observed equivalent width $W$ of the absorption lines, it is possible\nto derive the absorbing column density, assuming a gaussian velocity\ndistribution (standard deviation $\\sigma_{\\rm v}$) of the absorbing ions and\nneglecting the scattered line emission contribution:\n\\begin{equation}\n\\label{eqn:w}\nW = {\\lambda \\sigma_{\\rm v}\\over c} \\int\\limits_{-\\infty}^{\\infty}\n[1-\\exp (-\\tau_0\\mathrm{e}^{\\displaystyle -y^2/2})]\n{\\mathrm d}y,\n\\end{equation}\nwith $\\tau_0$ the optical depth of the line at the line center,\ngiven by\n\\begin{equation}\n\\label{eqn:tau}\n\\tau_0 = 0.106 f N_{20} \\lambda / \\sigma_{\\rm v,100}.\n\\end{equation}\nHere $f$ is the oscillator strength, $\\lambda$ the wavelength in \\AA,\n$\\sigma_{\\rm v,100}$ the velocity dispersion in units of 100~km/s and $N_{20}$ the\ncolumn density of the ion in units of $10^{20}$~m$^{-2}$. Given a value for\n$\\sigma_{\\rm v}$ and the measured equivalent width, these equations yield the\ncolumn density. For some ions we have more than one absorption line identified,\nand this allows us to constrain $\\sigma_{\\rm v}$. From the \\ion{O}{vii},\n\\ion{O}{viii} and \\ion{C}{vi} ions we obtain $\\sigma_{\\rm v}$=140$\\pm$30~km/s.\nUsing this value, we derive the column densities of Table~\\ref{tab:col}.\n%\n\\begin{table}[!h]\n\\caption{Derived column densities}\n\\label{tab:col}\n\\centerline{\n\\begin{tabular}{|lrr|lrr|}\n\\hline\nion & log $N$ & log $N$ & ion & log $N$ & log $N$ \\\\\n & observed & model & & observed & model \\\\\n & (m$^{-2}$) & (m$^{-2}$) & & (m$^{-2}$)& (m$^{-2}$) \\\\\n\\hline\n\\ion{C}{vi} & 21.2$\\pm$0.3 & 21.2 & \\ion{Si}{xiv} & 22.6$\\pm$1.6 & 19.8 \\\\\n\\ion{N}{vii} & 21.1$\\pm$0.5 & 21.0 & \\ion{Fe}{xiv} & 19.9$\\pm$0.7 & 20.1 \\\\\n\\ion{O}{vii} & 21.2$\\pm$0.3 & 21.3 & \\ion{Fe}{xv} & 20.3$\\pm$0.2 & 20.1 \\\\\n\\ion{O}{viii} & 22.1$\\pm$0.3 & 22.1 & \\ion{Fe}{xvi} & 20.4$\\pm$0.5 & 19.6 \\\\\n\\ion{Ne}{ix} & $<$22.8$\\pm$1.2 & 21.1 & \\ion{Fe}{xvii} & 20.5$\\pm$0.3 & 20.5 \\\\\n\\ion{Ne}{x} & $<$22.6$\\pm$1.1 & 21.2 & \\ion{Fe}{xviii}& 20.3$\\pm$0.5 & 20.4 \\\\\n\\ion{Na}{x} & 20.9$\\pm$0.8 & - & \\ion{Fe}{xix} & 20.6$\\pm$0.7 & 20.0 \\\\\n\\ion{Na}{xi} & 21.4$\\pm$1.0 & - & \\ion{Fe}{xx} & 20.9$\\pm$0.5 & 19.3 \\\\\n\\ion{Mg}{xi} & 20.8$\\pm$0.7 & 20.8 & \\ion{Fe}{xxi} &$<$20.9$\\pm$0.7 & 18.2 \\\\\n\\ion{Mg}{xii} & 22.3$\\pm$1.3 & 20.4 & & & \\\\\n\\hline\\noalign{\\smallskip}\n\\end{tabular}\n}\n\\end{table}\n%\nWe give the column density $N$ in logarithmic units. The reason is the\nrelatively large inferred optical depth of some lines, e.g. 70 for the\n\\ion{O}{viii} Ly$\\alpha$ line. This makes the line core saturated and hence\nsignificant changes in the column density lead to minor changes in the\nequivalent width.\n\nOne of the most striking features of the spectrum is the absence of the oxygen\ncontinuum absorption edges that were deduced from low resolution X-ray spectra\nsuch as those acquired with Rosat (Nandra et al. \\cite{nandra}), ASCA (Fabian\net al. \\cite{fabian}) or BeppoSAX (Nicastro et al. \\cite{nicastro}). The\nabsence is, however, consistent with the column densities derived above from the\nline absorption. We predict a jump of 11~\\% at the \\ion{O}{viii} edge\n(14.23~\\AA) and 4~\\% at the \\ion{O}{vii} edge (16.77~\\AA), all within a factor\nof 2. We can measure any jumps near the edges with an accuracy of about 10~\\%\nof the continuum, but we find no evidence for an absorption edge; the data even\nsuggest a small emission edge (radiative recombination continuum) of\n10$\\pm$10~\\%.\n\nThe column densities of the other ions for which we have absorption measurements\ndo not lead to significant absorption edges, except for \\ion{Ne}{ix} and\n\\ion{Ne}{x}, which should be at the low side of their column density range in\norder to avoid significant continuum absorption. Note that the \\ion{Ne}{x}\nLy$\\alpha$ line has some blending from \\ion{Fe}{xvii} 4d-2p; taking that into\naccount leads to a somewhat smaller column density.\n\nWe have made a set of runs using the XSTAR photoionization code (Kallman \\&\nKrolik \\cite{kallman}), using solar abundances and the spectral shape as given\nby Mathur et al. (\\cite{mathur}), normalised to 13\nphotons~m$^{-2}$s$^{-1}$\\AA$^{-1}$ at 20~\\AA. We obtained a good overall\nagreement with our measured column densities using a hydrogen column density of\n$3\\times 10^{25}$~m$^{-2}$ and $\\xi=100\\pm 25$ (in units of 10$^{-9}$~W\\,m).\nThis column density is comparable to the value derived from earlier ASCA\nobservations (Fabian et al. \\cite{fabian}). However, our ionization parameter\nis significantly larger, having most of the oxygen as \\ion{O}{viii} or\n\\ion{O}{ix}. The plasma temperature of the absorber implied by the XSTAR model\nis $2\\times 10^{5}$~K. The low temperatures imply that thermal contributions to\nline broadening ($\\sigma_{\\rm v}$) are negligible.\n\n\\subsection{Velocity fields}\n\nThe absorption lines appear to be blueshifted: the average blueshift of the C,\nN and O lines is 280$\\pm$70~km/s. There is some evidence that the lines are\nbroadened in proportion to their wavelengths, indicative of Doppler broadening.\nSubtracting the instrumental line width ($\\sigma$=0.023~\\AA) yields for the\nintrinsic line broadening a width ($\\sigma$) of 270$\\pm$100~km/s, somewhat\nlarger than the width of 140~km/s derived from line ratios (previous section).\nThis could indicate that the absorber consists of a few narrow components\n($\\sigma\\sim$140~km/s), with different mean velocities and $\\sigma\\sim$270~km/s\nfor the ensemble. As an illustration we show the velocity profile of six of the\nstrongest absorption lines in Fig.~\\ref{fig:fig2}. On the blue side, the line\nprofiles extend out to about 2000~km/s. There is no clear evidence for the\npresence of an underlying broad emission component for these lines, although for\n\\ion{O}{viii} and \\ion{C}{vi} there appears to be an excess at the red side of\nthe absorption line.\n%\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics[angle=-90]{fig2.ps}}\n\\caption{Line profile for six absorption lines. The intensity is scaled\nto 1 in the $\\pm$(5000--10000)~km/s range. Bin size is 0.02~\\AA.}\n\\label{fig:fig2}\n\\end{figure}\n\n\\subsection{Emission lines}\n\nThe LETGS spectrum of NGC~5548 shows only a few emission lines. Except for a\nclear detection of the He-like triplet of \\ion{O}{vii}, we only identified the\nforbidden lines of the same triplets of \\ion{Ne}{ix} and \\ion{Mg}{xi}; these are\nmarginally detected. Here we focus upon the \\ion{O}{vii} triplet\n(Fig.~\\ref{fig:fig3}). The forbidden ($f$) and intercombination ($i$) line are\nnot blue-shifted like the absorption lines but have a marginally significant\nredshift of 200$\\pm$130~km/s. The ratio $i/f$ can be used as a density\ndiagnostic if the coupling between the upper levels ($2^3$S and $2^3$P) of $f$\nand $i$ is determined by electron collisions and not by the external radiation\nfield from the central source. For a photon flux of\n50~photons\\,m$^{-2}$s$^{-1}$\\AA$^{-1}$ at 1600 \\AA\\ and the atomic parameters\ntaken from Porquet \\& Dubau (\\cite{porquet}) we estimate that this is the case\nas long as $n_{\\mathrm e} > 4\\times 10^{14}$~m$^{-3}$. The ratio $i/f$ does\ndepend only weakly upon the type of ionization balance: Collisional ionization\nequilibrium (CIE) or photoionization equilibrium (PIE) (Mewe \\cite{mewe} and\nPorquet \\& Dubau \\cite{porquet}). From the observed value $i/f$ of\n0.45$\\pm$0.29 we derive an upper limit to the electron density $n_{\\mathrm e}$\nof $7\\times 10^{16}$~m$^{-3}$. The observed ratio $G=(i+f)/r$ is 3.2$\\pm$1.5,\nalthough this value might be somewhat smaller due to overlap of the $r$\nabsorption component. For CIE plasmas, $G$ should be of order 1, while for PIE\nplasmas, values larger than about 4 can be expected (Liedahl \\cite{liedahl},\nPorquet \\& Dubau \\cite{porquet}). Thus, the \\ion{O}{vii} triplet probably\noriginates from a photoionized plasma.\n%\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics[angle=-90]{fig3.ps}}\n\\caption{Spectrum near the \\ion{O}{vii} triplet (data with error bars) plus\na simple model fit (continuum plus gaussian lines) for the main absorption\nand emission components discussed in the text.}\n\\label{fig:fig3}\n\\end{figure}\n%\nDoes the emission from the triplet arise from the same medium that absorbs the\ncontinuum? Assuming that the absorber has the shape of a thin, spherical shell,\nwe calculate on the basis of recombination and the absorber parameters derived\nin section 2.2 emission line intensities that agree within the error bars with\nthe measured intensities. The upper limit for $n_{\\mathrm e}$ found from the\n$i/f$ ratio then implies a lower limit for the thickness of the shell of\n$5\\times 10^{8}$~m, and a distance from the central source of at least $8\\times\n10^{13}$~m. Thus, both the absorption and emission of the \\ion{O}{vii}\nresonance line, as well as the emission from $i$ and $f$ may originate in the\nsame expanding shell.\n\n\\section{Discussion}\n\nFor the first time we see narrow absorption lines in the X-ray spectrum of an\nAGN. However narrow absorption lines in Seyfert galaxies have been seen before\nin the UV band. Shull and Sachs (\\cite{shull}) discovered narrow absorption\nfeatures in the \\ion{C}{iv} and \\ion{N}{v} lines. This was confirmed by Mathur\net al. (\\cite{mathur}) and studied in more detail by Mathur et al.\n(\\cite{mathur99}) and Crenshaw et al. (\\cite{crenshaw}). These last authors\nfind at least 5 narrow absorption components in the \\ion{C}{iv}~1550~\\AA\\, and\n\\ion{N}{v}~1240~\\AA\\, lines. These components are broadened by\n$\\sigma_v$=20--80~km/s, somewhat smaller than we find. The rms width of the\nensemble of UV absorption lines is 160~km/s for \\ion{C}{iv} and 260~km/s for\n\\ion{N}{v}, consistent with the effective line width of 270$\\pm$100~km/s that we\nfind from our Chandra data. Also, the average blueshift of the UV absorption\nlines ($-390$~km/s for \\ion{C}{iv} and $-490$~km/s for \\ion{N}{v}) is only\nslightly larger than what we find for the C, N and O lines ($-280\\pm 70$~km/s).\nNote that our wavelength scale has residual uncertainties of 100--300~km/s for\nmost of our lines.\n\nHowever, the column density of the lithium-like ions \\ion{C}{iv} and \\ion{N}{v}\nas derived by Crenshaw et al. is 100 times smaller than the column density of\nthe corresponding hydrogen-like ions that we find. The difference may be\nattributed to either time variability (low column density during the UV\nobservations), a high degree of ionization (hydrogenic ions dominating) or a\nstratified absorber (with UV and X-ray absorption lines originating from\ndifferent zones). We favour this last possibility. This is supported by the\nfact that our simulations with XSTAR imply \\ion{C}{iv} and \\ion{N}{v} columns\nthat are 100 times smaller than the measured values by Crenshaw et al.\n\nCrenshaw \\& Kraemer (\\cite{crenshawk}) find that the weakest of the five\ndynamical components (their number 1) in the UV absorption lines has the highest\noutflow velocity ($-1056$~km/s). Based upon the \\ion{N}{v} to \\ion{C}{iv}\nratio, they argue that this component has the highest ionization parameter and\ncould produce the oxygen continuum absorption edges as implied by the ASCA data.\nOur modelling with XSTAR also predicts column densities of \\ion{N}{v} and\n\\ion{C}{iv} close to the measured values for component 1. But the outflow\nvelocity of the X-ray absorber that we find is significantly smaller than the\nvelocity of UV component 1. However, Mathur et al. (\\cite{mathur99}) identify\ncomponent 3 ($-540$~km/s) as the most likely counterpart to the X-ray warm\nabsorber. We conclude that the detailed relation between UV and X-ray absorbers\nis still an open issue.\n\n\\begin{acknowledgements}\nThe Laboratory for Space Research Utrecht is supported\nfinancially by NWO, the Netherlands Organization for Scientific\nResearch. Work at LLNL was performed under the auspices of the\nU.S. Department of Energy, Contract No. W-7405-Eng-48.\n\n\\end{acknowledgements}\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[2000]{brinkman}\nBrinkman, A.C., Gunsing, C.J.T., Kaastra, J.S., et al., 2000, ApJ 530, L111\n\\bibitem[1999]{crenshaw}\nCrenshaw, D.M., Kraemer, S.B., Boggess, A., et al., 1999, ApJ 516, 750\n\\bibitem[1999]{crenshawk}\nCrenshaw, D.M., Kraemer, S.B., 1999, ApJ 521, 572\n\\bibitem[1994]{fabian}\nFabian, A.C., Nandra, K., Brandt, W.N., et al., 1994, in: New Horizon\nof X-ray Astronomy, p. 573, eds. Makino, F. \\& Ohashi, T., Univ. Ac. Press.\n\\bibitem[1999]{kaastra}\nKaastra, J.S., 1999, in: X-ray spectroscopy in astrophysics, p. 269,\neds. van Paradijs, J. \\& Bleeker, J.A.M., Springer.\n\\bibitem[1999]{kallman}\nKallman, T.R., Krolik, J.H., 1999, XSTAR photoionzation code, \nftp://legacy.gsfc.nasa.gov/software/plasma\\_codes/xstar/\n\\bibitem[1999]{liedahl}\nLiedahl, D.A., 1999, in: X-ray spectroscopy in astrophysics, p. 189,\neds. van Paradijs, J. \\& Bleeker, J.A.M., Springer.\n\\bibitem[1995]{mathur}\nMathur, S., Elvis, M., Wilkes, B., 1995, ApJ 452, 230\n\\bibitem[1999]{mathur99}\nMathur, S., Elvis, M., Wilkes, B., 1999, ApJ 519, 605\n\\bibitem[1999]{mewe}\nMewe, R., 1999, in: X-ray spectroscopy in astrophysics, p. 109,\neds. van Paradijs, J. \\& Bleeker, J.A.M., Springer.\n\\bibitem[1993]{nandra}\nNandra, K., Fabian, A.C., George, I.M., et al., 1993, MNRAS 260, 504\n\\bibitem[2000]{nicastro}\nNicastro, F., de Rosa, A., Feroci, M., et al., 2000, ApJ, in press\n\\bibitem[2000]{porquet}\nPorquet, D., Dubau, J., 2000, A\\&A, in press\n\\bibitem[1993]{shull}\nShull, J.M., Sachs, E.R., 1993, ApJ 416, 536\n\n\\end{thebibliography}\n\n\\end{document}\n\n"
}
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[
{
"name": "astro-ph0002345.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[2000]{brinkman}\nBrinkman, A.C., Gunsing, C.J.T., Kaastra, J.S., et al., 2000, ApJ 530, L111\n\\bibitem[1999]{crenshaw}\nCrenshaw, D.M., Kraemer, S.B., Boggess, A., et al., 1999, ApJ 516, 750\n\\bibitem[1999]{crenshawk}\nCrenshaw, D.M., Kraemer, S.B., 1999, ApJ 521, 572\n\\bibitem[1994]{fabian}\nFabian, A.C., Nandra, K., Brandt, W.N., et al., 1994, in: New Horizon\nof X-ray Astronomy, p. 573, eds. Makino, F. \\& Ohashi, T., Univ. Ac. Press.\n\\bibitem[1999]{kaastra}\nKaastra, J.S., 1999, in: X-ray spectroscopy in astrophysics, p. 269,\neds. van Paradijs, J. \\& Bleeker, J.A.M., Springer.\n\\bibitem[1999]{kallman}\nKallman, T.R., Krolik, J.H., 1999, XSTAR photoionzation code, \nftp://legacy.gsfc.nasa.gov/software/plasma\\_codes/xstar/\n\\bibitem[1999]{liedahl}\nLiedahl, D.A., 1999, in: X-ray spectroscopy in astrophysics, p. 189,\neds. van Paradijs, J. \\& Bleeker, J.A.M., Springer.\n\\bibitem[1995]{mathur}\nMathur, S., Elvis, M., Wilkes, B., 1995, ApJ 452, 230\n\\bibitem[1999]{mathur99}\nMathur, S., Elvis, M., Wilkes, B., 1999, ApJ 519, 605\n\\bibitem[1999]{mewe}\nMewe, R., 1999, in: X-ray spectroscopy in astrophysics, p. 109,\neds. van Paradijs, J. \\& Bleeker, J.A.M., Springer.\n\\bibitem[1993]{nandra}\nNandra, K., Fabian, A.C., George, I.M., et al., 1993, MNRAS 260, 504\n\\bibitem[2000]{nicastro}\nNicastro, F., de Rosa, A., Feroci, M., et al., 2000, ApJ, in press\n\\bibitem[2000]{porquet}\nPorquet, D., Dubau, J., 2000, A\\&A, in press\n\\bibitem[1993]{shull}\nShull, J.M., Sachs, E.R., 1993, ApJ 416, 536\n\n\\end{thebibliography}"
}
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astro-ph0002346
|
Cyclotron lines in X-ray pulsars as a probe of relativistic plasmas in superstrong magnetic fields
|
[
{
"author": "D. Dal Fiume\\mrka"
},
{
"author": "Filippo Frontera\\mrkb"
},
{
"author": "Nicola Masetti\\mrka"
},
{
"author": "Mauro Orlandini\\mrka"
},
{
"author": "Eliana Palazzi\\mrka"
},
{
"author": "Stefano Del Sordo\\mrkc"
},
{
"author": "Andrea Santangelo\\mrkc"
},
{
"author": "Alberto Segreto\\mrkc"
},
{
"author": "Tim Oosterbroek\\mrkd"
},
{
"author": "Arvind N. Parmar\\mrkd"
}
] |
The systematic search for the presence of cyclotron lines in the spectra of accreting X-ray pulsars is being carried on with the BeppoSAX satellite since the beginning of the mission. These highly successful observations allowed the detection of cyclotron lines in many of the accreting X-ray pulsars observed. Some correlations between the different measured parameters were found. We present these correlations and discuss them in the framework of the current theoretical scenario for the X--ray emission from these sources.
|
[
{
"name": "cyc_compton.tex",
"string": "\\documentstyle[epsfig,graphics]{aipproc}\n\\input pstricks\n\\input ulem.sty\n\\input times.sty\n\\begin{document}\n\\def\\A{\\mbox{ASCA\\ }} \\def\\B{\\mbox{BeppoSAX\\ }} \\def\\ind{\\mbox{~~~}}\n\\def\\asm{\\mbox{RXTE/ASM\\ }} \\def\\exo{\\mbox{EXOSAT\\ }}\n\\def\\etal{{et al. }}\n\\newcommand{\\lx}{\\mbox{L$_X$}} \\newcommand{\\ergs}{\\mbox{erg s$^{-1}$}}\n\\newcommand{\\ergcm}{\\mbox{erg cm$^{-2}$ s$^{-1}$}}\n\\newcommand{\\mrka}{\\mbox{$^{1}$}}\n\\newcommand{\\mrkb}{\\mbox{$^{2}$}}\n\\newcommand{\\mrkc}{\\mbox{$^{3}$}}\n\\newcommand{\\mrkd}{\\mbox{$^{4}$}}\n\\newcommand{\\mrke}{\\mbox{$^{5}$}}\n\\newcommand{\\mrkf}{\\mbox{$^{6}$}}\n\n\\title{\nCyclotron lines in X-ray pulsars as a probe of\nrelativistic plasmas in superstrong magnetic fields}\n\n\\bigskip\\medskip\n\n\\author{\nD. Dal Fiume\\mrka, Filippo Frontera\\mrkb,\nNicola Masetti\\mrka, Mauro Orlandini\\mrka, Eliana Palazzi\\mrka,\nStefano Del Sordo\\mrkc, Andrea Santangelo\\mrkc, Alberto Segreto\\mrkc,\nTim Oosterbroek\\mrkd, Arvind N. Parmar\\mrkd}\n\n\\address\n{ \\mrka Istituto TESRE/CNR, via Gobetti 101, 40129 Bologna, Italy \\\\\n\\mrkb Istituto TeSRE and Dipartimento di Fisica, Universit\\'a di\nFerrara, via Paradiso 1, 44100 Ferrara, Italy\\\\\n\\mrkc IFCAI/CNR, via U. La Malfa 153, 90146 Palermo, Italy\\\\\n\\mrkd Space Science Department, ESA, ESTEC, Noordwjik, The\nNetherlands\n}\n\n\\maketitle\n\\begin{abstract}\nThe systematic search for the presence of cyclotron lines in the spectra\nof accreting X-ray pulsars is being carried on with the BeppoSAX\nsatellite since the beginning of the mission. These highly successful\nobservations allowed the detection of cyclotron lines in many of\nthe accreting X-ray pulsars observed. Some correlations between\nthe different measured parameters were found. We present these\ncorrelations and discuss them in the framework of the current\ntheoretical scenario for the X--ray emission from these sources.\n\\end{abstract}\n\n\\section*{Introduction}\n\nAccreting magnetized neutron stars are an ideal cosmic\nlaboratory for high energy relativistic physics. Cyclotron resonance\nfeatures are the signature of the presence of a superstrong magnetic field,\nfollowing the first discovery in Her X-1 (Tr\\\"umper et al.\n\\cite{trump}). These features are due to the discrete Landau energy levels\nfor motion of free electrons perpendicular to the field in presence\nof a locally uniform superstrong magnetic field. A slight deviation\nfrom a pure harmonic relationship in the spacing of the different levels\nis expected due to relativistic effects\n($\\frac{\\omega_n}{m_e} =((1+2n\\frac{B}{B_{\\rm crit}}\n\\sin^2\\theta)^\\frac{1}{2} -1)/\\sin^2 \\theta$, e.g. Araya and Harding \n\\cite{araya}).\nTherefore the detection of these features in the emitted X--ray spectra\nis in principle a direct measure of the field intensity.\\\\\nAs the number of sensitive measurements in the hard X--ray interval (above\n$\\sim$ 10 keV) is continuously growing, a sample is available to search\nfor possible correlations between the observed parameters.\nA detailed modeling is difficult and a parametrized shape of the\ncontinuum still is not available from theoretical models, but\nsubstantial advances in our understanding of the radiation transport in\nstrongly magnetized atmospheres were done in the last decade (e.g.\nAlexander et al. \\cite{alex1}, Alexander and M\\'esz\\'aros \\cite{alex2},\nAraya and Harding \\cite{araya}, Isenberg et al. \\cite{isenba,isenbb},\nNelson et al. \\cite{nelson}).\nSome of these new results focused on the properties of the cyclotron\nresonance features observed in the spectra of accreting X--ray pulsars. \nIn this report we discuss the current status of the measurements of\ncyclotron lines, with emphasis on the possible correlations between\nobservable parameters.\n\n\\section*{The data}\n\nThe \\B satellite has observed all the bright persistent\nand three bright transient (recurrent) accreting X--ray pulsars.\nApart from the case of X Persei (Di Salvo et al. \\cite{robba}), a source\nwith a luminosity substantially lower\nthan the other sources in the sample, the spectra observed by \\B can be\nempirically described using the classical power--law--plus--cutoff spectral\nfunction by White et al. \\cite{white}. The sensitive broad band \\B\nobservations also allowed the detailed characterization of low energy\ncomponents below a few keV\n(like in Her X--1, Dal Fiume et al. \\cite{herx1}, and in 4U1626--67,\nOrlandini et al. \\cite{1626}) and the detection of absorption\nfeatures in the hard X--ray range of the spectra, interpreted as cyclotron\nresonance features.\n\nA summary of the properties of the broad band spectra and of the\ncyclotron lines as measured with \\B is reported in Dal Fiume et al.\n\\cite{ddf}.\nFrom these measurements we obtained evidence of a correlation between\nthe centroid energy of the feature and its width. This correlation is\npresented and discussed elsewhere (Dal Fiume et al. \\cite{ddf,ddf98}).\n\n\\subsection*{Transparency in the line}\nA straightforward parameter to be obtained from observations is the\ntransparency in the line, defined as the ratio between the transmitted\nobserved flux and the integrated flux from the continuum without the\nabsorption feature. This ratio likely depends on the harmonic\nnumber of the feature we are observing (e.g. Wang et al. \\cite{wang})\nand on the physical\nparameters of the specific accretion column. From an observational\npoint of view, this ratio is strongly affected by the modelization of\nthe ``continuum'' shape, that is by the spectral shape used to\ndescribe the differential broad band photon number spectrum. In Figure 1\nwe report the observed transparencies obtained dividing the observed\nby the expected flux, both integrated in a $\\pm 2\\sigma$ interval around\nthe line\ncentroid (here $\\sigma$ is the Gaussian width of the measured cyclotron\nfeature). To further emphasize the uncertainty in this estimate, we\nadded a 10\\% error to the data. The purely statistical uncertainties are\nsubstantially smaller.\n\\begin{figure}[h]\n\\centerline{\n\\psfig{file=opacities_10pcent.eps,angle=270,width=0.98\\textwidth}}\n\\caption{Transparency in the observed cyclotron resonance features\nwith \\B. The error bars are {\\it NOT} statistical, but rather indicate\nthe uncertainty in the determination of the shape and intensity of the\nexpected continuum flux (with no line absorption).}\n\\end{figure}\n\\begin{figure}[h]\n\\centerline{\n\\psfig{file=ratio_10pcent.eps,angle=270,width=0.98\\textwidth}}\n\\caption{Ratio between the measured photon flux in two energy band\nversus the cyclotron line energy\nwith \\B. The error bars are {\\it NOT} statistical, but rather indicate\nthe uncertainty in the determination of the shape and intensity of the\nmeasured photon flux.}\n\\end{figure}\nThis measured transparency is related to a simple physical parameter,\nthe opacity to photons with energy approximately equal to the cyclotron\nresonance energy. However the emerging integral flux and the shape of\nthe line itself are non trivially related to the radiation transport in\nthis energy interval, a rather difficult problem to be solved.\\\\\nFrom the phenomenological point of view, one can observe that the\nmeasured transparencies cluster around 0.5--0.6, with the notable\nexception of Cen X--3.\n\n\\subsection*{Magnetic field intensity and spectral hardness}\nThe influence of the magnetic field intensity on the broad band spectral\nshape is debated. Early attempts to estimate a possible dependence of\nelectron temperature, and therefore of broad band spectral shape, on the\nmagnetic field intensity were done by Harding et al \\cite{hard84}.\nActually they conclude that {\\it ``the equilibrium atmospheres have\ntemperatures and optical depths that are very sensitive to the strength\nof the surface magnetic field''}. If this is the case and if the broad\nband spectral hardness is related, as one could naively assume, to\nthe temperature of the atmosphere, some correlation between this\nhardness and the cyclotron line energy should appear in data.\n\nThis seems to be the case shown in Figure 2. Here we report the ratio\nbetween photon fluxes in two ``hard'' bands (the flux in 20--100 keV\ndivided by the flux in 7--15 keV) versus the cyclotron line centroid.\nThe ratio between the two fluxes is affected by the\nchoice of the continuum, as in Figure 1. We therefore also in this case\nadded 10\\% error bars that indicate this uncertainty. The\nstatistical errors are substantially smaller.\\\\\nThe number of sources in this plot is still very limited and therefore\none cannot\nexclude that this apparent correlation is merely due to the limited size\nof the sample. Nevertheless the apparent correlation is in the right\ndirection, i.e. harder spectra are observed for higher field\nintensities.\\\\\nWe parenthetically add that no cyclotron resonance feature was observed\nin the pulse--phase averaged spectra of the two hardest sources of this\nclass observed\nwith \\B (GX1+4 Israel et al. \\cite{israel} and GS1843+00 Piraino et al.\n\\cite{piraino}). If this correlation proves to be correct, this may\nsuggest that cyclotron resonance features in these two sources should be\nsearched at the upper limit of the \\B energy band or beyond.\n\n\\subsection*{Conclusions}\nIn conclusion, even if no complete, parametric theoretical approach to\nmodel the observed spectra of accreting X--ray pulsars is still\navailable, some quantitative measures of parameters of hot plasmas in\nsuperstrong magnetic fields are possible.\\\\\nModeling the transparency in the cyclotron resonance feature is a\ncomplex problem. Further information will be extracted\nfrom maps of this transparency as a function of pulse phase. \\\\\nThe correlation between\nspectral hardness and field intensity is in agreement\nwith theoretical models. This correlation, if confirmed, can be used as\na rough estimate of the magnetic field intensity from the measured\nspectral hardness.\n\n\\acknowledgments\nThis research is supported by Agenzia Spaziale Italiana (ASI) and \nConsiglio Nazionale delle Ricerche (CNR) of Italy. \\B is a joint\nprogram of ASI and of the Netherlands Agency for Aerospace Programs (NIVR).\n\n\\begin{references}\n\n\\bibitem{trump}Tr\\\"umper, J. \\etal 1978 {\\it Ap. J. Letters}, {\\bf 219},\nL105\n%\n\\bibitem{araya}Araya, R. A. and Harding, A. K. 1999 {\\it Ap. J}, {\\bf\n517}, 334\n%\n\\bibitem{alex1}\nAlexander, S. G. et al. 1996 {\\it Ap. J.}, {\\bf 459}, 666\n%\n\\bibitem{alex2}\nAlexander, S. G. and M\\'esz\\'aros, P. 1991 {\\it Ap. J.}, {\\bf 373}, 565\n%\n\\bibitem{isenba} Isenberg, M. \\etal 1998a, {\\it Ap. J.}, {\\bf 493}, 154\n%\n\\bibitem{isenbb} Isenberg, M. \\etal 1998b, {\\it Ap. J.}, {\\bf 505}, 688\n%\n\\bibitem{nelson}\nNelson, R. W. et al. 1995 {\\it Ap. J. Letters}, {\\bf 438}, L99\n%\n\\bibitem{robba}Di Salvo, T. 1998 {\\it Ap. J.}, {\\bf 509}, 897\n%\n\\bibitem{white}White, N. E. \\etal 1983 {\\it Ap. J.}, {\\bf 270}, 711\n%\n\\bibitem{herx1}Dal Fiume, D. \\etal 1998 {\\it Astron. Astrophys}, {\\bf\n329}, L41 \n%\n\\bibitem{1626}Orlandini, M. \\etal 1998 {\\it Ap. J. Letters}, {\\bf 500},\nL165\n%\n\\bibitem{ddf}Dal Fiume, D. \\etal 1999 {\\it Adv. Sp. Res.}, in press ({\\it\nastro-ph/9906086})\n%\n\\bibitem{ddf98}Dal Fiume, D. \\etal 1998 {\\it Nucl. Physics B}, {\\bf 69},\n145\n%\n\\bibitem{wang}Wang, J. C. L. \\etal 1993 {\\it Ap. J.}. {\\bf 414}, 815\n%\n\\bibitem{hard84}Harding, A. K. \\etal 1984 {\\it Ap. J.}, {\\bf 278}, 369\n%\n\\bibitem{israel}Israel, G. L. \\etal 1998 {\\it Nucl. Phys. B}, {\\bf 69},\n141\n%\n\\bibitem{piraino}\nPiraino, S. \\etal 2000 {\\it Astron. Astrophys.}, submitted\n%\n\\end{references}\n\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002346.extracted_bib",
"string": "\\bibitem{trump}Tr\\\"umper, J. \\etal 1978 {\\it Ap. J. Letters}, {\\bf 219},\nL105\n%\n\n\\bibitem{araya}Araya, R. A. and Harding, A. K. 1999 {\\it Ap. J}, {\\bf\n517}, 334\n%\n\n\\bibitem{alex1}\nAlexander, S. G. et al. 1996 {\\it Ap. J.}, {\\bf 459}, 666\n%\n\n\\bibitem{alex2}\nAlexander, S. G. and M\\'esz\\'aros, P. 1991 {\\it Ap. J.}, {\\bf 373}, 565\n%\n\n\\bibitem{isenba} Isenberg, M. \\etal 1998a, {\\it Ap. J.}, {\\bf 493}, 154\n%\n\n\\bibitem{isenbb} Isenberg, M. \\etal 1998b, {\\it Ap. J.}, {\\bf 505}, 688\n%\n\n\\bibitem{nelson}\nNelson, R. W. et al. 1995 {\\it Ap. J. Letters}, {\\bf 438}, L99\n%\n\n\\bibitem{robba}Di Salvo, T. 1998 {\\it Ap. J.}, {\\bf 509}, 897\n%\n\n\\bibitem{white}White, N. E. \\etal 1983 {\\it Ap. J.}, {\\bf 270}, 711\n%\n\n\\bibitem{herx1}Dal Fiume, D. \\etal 1998 {\\it Astron. Astrophys}, {\\bf\n329}, L41 \n%\n\n\\bibitem{1626}Orlandini, M. \\etal 1998 {\\it Ap. J. Letters}, {\\bf 500},\nL165\n%\n\n\\bibitem{ddf}Dal Fiume, D. \\etal 1999 {\\it Adv. Sp. Res.}, in press ({\\it\nastro-ph/9906086})\n%\n\n\\bibitem{ddf98}Dal Fiume, D. \\etal 1998 {\\it Nucl. Physics B}, {\\bf 69},\n145\n%\n\n\\bibitem{wang}Wang, J. C. L. \\etal 1993 {\\it Ap. J.}. {\\bf 414}, 815\n%\n\n\\bibitem{hard84}Harding, A. K. \\etal 1984 {\\it Ap. J.}, {\\bf 278}, 369\n%\n\n\\bibitem{israel}Israel, G. L. \\etal 1998 {\\it Nucl. Phys. B}, {\\bf 69},\n141\n%\n\n\\bibitem{piraino}\nPiraino, S. \\etal 2000 {\\it Astron. Astrophys.}, submitted\n%\n"
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astro-ph0002347
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Observations of synchrotron radiation across a wide range of wavelengths provide clear evidence that electrons are accelerated to relativistic energies in supernova remnants (SNRs). However, a viable mechanism for the pre--acceleration of such electrons to mildly relativistic energies has not yet been established. In this paper an electromagnetic particle--in--cell (PIC) code is used to simulate acceleration of electrons from background energies to tens of keV at perpendicular collisionless shocks associated with SNRs. Free energy for electron energization is provided by ions reflected from the shock front, with speeds greater than the upstream electron thermal speed. The PIC simulation results contain several new features, including: the acceleration, rather than heating, of electrons via the Buneman instability; the acceleration of electrons to speeds exceeding those of the shock--reflected ions producing the instability; and strong acceleration of electrons perpendicular to the magnetic field. Electron energization takes place through a variety of resonant and non--resonant processes, of which the strongest involves stochastic wave--particle interactions. In SNRs the diffusive shock process could then supply the final step required for the production of fully relativistic electrons. The mechanisms identified in this paper thus provide a possible solution to the electron pre--acceleration problem.
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"name": "Dieck.tex",
"string": "% This is the astro-ph version of Dieckmann et al. A&A 2000\n\\documentclass[12pt]{article}\n\n\\def\\ref#1{\\noindent \\parshape=2 0pt 400pt 20pt 380pt #1}\n\n\\begin{document}\n\n\\centerline{\\Large Electron acceleration due to high frequency}\n \n\\centerline{\\Large instabilities at supernova remnant shocks}\n\n\\vskip 0.5cm\n\n\\centerline{\\large M. E. Dieckmann,$^{\\rm a,}$\\footnote{Present address:\nInstitutet f\\\"or teknik och naturvetenskap, Link\\\"opings Universitet, Campus \nNorrk\\\"oping, S--601 74 Norrk\\\"oping, Sweden} K. G. \nMcClements,$^{\\rm b,}$\\footnote{Corresponding author. E--mail: \nk.g.mcclements@ukaea.org.co.uk} S. C. Chapman,$^{\\rm a}$}\n\n\\centerline{\\large R. O. Dendy,$^{\\rm b,a}$ and L. O'C. Drury$^{\\rm c}$}\n\n\\vskip 0.3cm\n\n\\centerline{$^{\\rm a}$ Space and Astrophysics Group, Department of Physics, \nUniversity of Warwick,} \n\n\\centerline{Coventry, CV4 7AL, UK} \n\n\\vskip 0.3cm\n \n\\centerline{$^{\\rm b}$ EURATOM/UKAEA Fusion Association, Culham Science \nCentre, Abingdon,} \n\n\\centerline{Oxfordshire OX14 3DB, UK}\n \n\\vskip 0.3cm\n\n\\centerline{$^{\\rm c}$ Dublin Institute for Advanced Studies, 5 Merrion Square,\nDublin 2, Ireland}\n\n\\vskip 0.3cm\n\n\\centerline{To appear in {\\it Astronomy and Astrophysics} (accepted: February \n15 2000)} \n\n \\begin{abstract}\n\n Observations of synchrotron radiation across a wide range of\n wavelengths provide clear evidence that electrons are accelerated to\n relativistic energies in supernova remnants (SNRs). However, a viable\n mechanism for the pre--acceleration of such electrons to mildly \n relativistic energies has not yet been\n established. In this paper an electromagnetic particle--in--cell \n (PIC) code is used to simulate acceleration of electrons from\n background energies to tens of keV \n at perpendicular collisionless shocks associated\n with SNRs. Free energy for electron energization is provided by ions \n reflected from the shock front, with speeds greater \n than the upstream electron thermal speed. The PIC simulation\n results contain several new features, including:\n the acceleration, rather than heating, of electrons via the Buneman\n instability; the acceleration of electrons to speeds exceeding those\n of the shock--reflected ions producing the instability;\n and strong acceleration of electrons perpendicular to the\n magnetic field. Electron energization takes place through a\n variety of resonant and non--resonant processes, of which the\n strongest involves stochastic wave--particle interactions. In SNRs\n the diffusive shock process could then\n supply the final step required for the production\n of fully relativistic electrons. The mechanisms identified in this\n paper thus provide a possible solution to the electron\n pre--acceleration problem.\n\n \\end{abstract}\n\n\\section{Introduction}\n\nThe detection of radio synchrotron emission from shell--type supernova\nremnants (SNRs) is a clear indication that electrons of typically GeV\nenergy are being accelerated in such objects. There is now convincing\nevidence that synchrotron emission from some remnants extends to\nX--ray wavelengths (Pohl \\& Esposito 1998): this implies the presence\nof electrons with energies of order 10$^{14}$eV. The prime example of\nthis is the remnant of SN1006, recent observations of which using the\nASCA (Koyama et al. 1995) and ROSAT (Willingale et al. 1996)\nspacecraft show that X--ray emission from the bright rim has a hard,\napproximately power--law spectrum. In contrast, emission from the\ncentre is softer, with a strong atomic line component. The sharp edges and\nstrong limb brightening observed at both X--ray and radio wavelengths\nindicate that: the acceleration site is the strong outer\nshock bounding the remnant; the acceleration is continuous; and\nthe local diffusion coefficient of electrons near the shock front\nis substantially reduced relative to that in the general interstellar\nmedium (Achterberg et al. 1994). The possibility that the X--ray\nemission from SN1006 is thermal bremsstrahlung has been\nexamined by Laming (1998), and found to be less tenable than the\nsynchrotron interpretation. \n\nThere is thus extensive observational evidence that the strong\ncollisionless shocks bounding shell--type SNRs accelerate electrons to\nrelativistic energies. The standard interpretation of extragalactic\nradio jet observations is also based on the premise that the\nrelativistic electrons responsible for observed synchrotron emission\nare produced by shocks, although in this case the shock parameters are\nmuch less certain. Heliospheric shocks, on the other hand, do not\ngenerally appear to be associated with strong electron acceleration,\nperhaps because the Mach numbers of such shocks are much lower than\nthose of SNRs and extragalactic radio jets, although Anderson et al. (1979)\nhave published data showing that keV electrons \nare produced in the vicinity of the perpendicular bow shock \nof the Earth.\n\nWhile diffusive shock acceleration (Axford et al. 1977; Krymsky 1977; Bell \n1978; Blandford \\& Ostriker 1978) provides an efficient \nmeans of generating highly energetic electrons from an already mildly \nrelativistic threshold, and can operate at oblique shocks as well as \nparallel ones (Kirk \\& Heavens 1989),\nthe ``injection'' or ``pre--acceleration'' question \nremains very open: by what mechanisms can electrons be accelerated from \nbackground (sub--relativistic) energies to mildly relativistic energies\n(Levinson 1996)? In \nthis paper, we investigate one of the possible answers, which has attractive \n``bootstrap'' characteristics. Specifically, we suggest that waves are excited\nby collective instability of the non--Maxwellian population of ions reflected \nfrom a perpendicular shock front, and that these waves damp on\nthermal electrons, thereby accelerating them. Such a process was first\nproposed as a candidate acceleration mechanism for cosmic ray\nelectrons by Galeev (1984). This model was developed\nfurther by Galeev et al. (1995), with the added ingredient\nof macroscopic electric fields implied by the need to maintain\nquasi--neutrality in a plasma with an escaping population of\nelectrons. McClements et al. (1997) carried out a\nprimarily analytical study of electron acceleration by ion--excited\nwaves at quasi--perpendicular shocks, which was necessarily restricted to\nquantifying linear r\\'egimes of wave excitation and particle\nacceleration, in relation to inferred shock parameters. \n\nInstabilities driven by shock--reflected ions at\nSNR shocks have also been invoked by\nPapadopoulos (1988) and Cargill \\& Papadopoulos\n(1988) as mechanisms for electron heating, rather than\nelectron acceleration. On the basis of a simple analytical\ncalculation, Papadopoulos predicted that strong electron\nheating would occur at quasi--perpendicular shocks with ``superhigh''\nMach numbers (specifically, shocks with fast magnetoacoustic Mach numbers $M_F\n> 30$--40) through the combined effects of Buneman\n(two--stream) and ion acoustic instabilities. In this model the\nBuneman instability, driven by the relative streaming of\nshock--reflected ions and upstream electrons, heats the electrons to a\ntemperature $T_e$ much greater than the ion temperature $T_i$: in\nthese circumstances, the ion acoustic instability can be driven\nunstable if there is a supersonic streaming between the electrons and\neither reflected or non--reflected (``background'') ions. Using a hybrid\ncode, in which ions were treated as particles and electrons as a\nmassless fluid, Cargill \\& Papadopoulos (1988) found that\nthe electron heating predicted by Papadopoulos (1988)\ncould occur in a self--consistently computed shock structure. However,\nas Cargill \\& Papadopoulos point out in the last paragraph of their\n1988 paper, the use of a fluid model for the electrons means that\nhybrid codes cannot be used to investigate electron\nacceleration. Recently, Bessho \\& Ohsawa (1999) have used a\nparticle--in--cell (PIC) code to investigate acceleration of electrons\nfrom tens of keV to highly relativistic energies at oblique shocks in \nwhich the electron gyrofrequency $\\Omega_e$ exceeds the electron plasma\nfrequency $\\omega_{pe}$. \n\nAn improved theoretical understanding of electron acceleration at shocks\nis desirable not only for intrinsic interest, but also to enable \nobservations of synchrotron and inverse Compton emission to be\nrelated quantitatively to shock parameters. However, almost all work on\nparticle acceleration has concentrated on ions. There are several\nreasons for this. First, upstream momentum and energy fluxes are dominated by\nions, and the shock structure problem therefore reduces essentially to\nthat of isotropizing the ion distribution. Second, much of our\nunderstanding is based on the use of hybrid codes, in which electrons\nare represented as a fluid: such codes cannot provide information on\nelectron acceleration. However, the very fact that electron dynamics does not\nappear to be important for shock structure allows us to separate the\ntwo problems: prescribing the ion parameters using the results of\nhybrid code simulations, we can examine in detail physical processes\noccurring on electron timescales. This is the approach followed in\nthis paper. We describe the results of a fully nonlinear \ninvestigation, carried out by large scale numerical simulation using a \nPIC code and backed up by analytical and numerical studies, \nof the underlying plasma physics mechanisms. We consider the case\n$\\omega_{pe} > \\Omega_e$, which is qualitatively distinct from the\nstrongly--magnetized r\\'egime investigated by Bessho \\& Ohsawa (1999). \nOur primary goal is finding a mechanism capable of producing mildly\nrelativistic electrons: once they have attained rigidities comparable to\nthose of shock--heated protons, they can undergo resonant scattering,\nand subsequent acceleration to relativistic energies can then proceed\nvia the diffusive shock mechanism. Our approach enables us\nto test earlier predictions of both electron acceleration (Galeev\n1984; Galeev et al. 1995; McClements et al. 1997) and electron heating \n(Papadopoulos 1988; \nPapadoulos \\& Cargill 1988) at very high Mach number astrophysical\nshocks. Simulation results are presented for a range of reflected ion\nspeeds in Sect. 2; plasma instabilities occurring in the\nsimulations, and other processes likely to play a role in electron\nacceleration and heating at SNR shocks, are identified\nin Sect. 3; and the results of these investigations are discussed\nin Sect. 4. \n\n\\section{Particle--in--cell code simulations}\n\nTo investigate wave excitation and particle acceleration in the vicinity of\na perpendicular SNR shock we use an electromagnetic \nrelativistic PIC code described by Devine (1995). The\nparticle--in--cell principle (Denavit \\& Kruer 1980) relies\non self--consistent evolution of electromagnetic fields and macroparticles\nin sequential stages. Relativistic \nelectromagnetic PIC codes have been used previously to simulate acceleration \nprocesses in astrophysical plasmas (e.g. McClements et al. \n1993; Bessho \\& Ohsawa 1999). A distinctive feature of the code used\nin the present study is the fact that the energy density of\nelectromagnetic or electrostatic fluctuations can be readily\ndetermined as a function of frequency $\\omega$, wavevector $k$ or time $t$:\nthis greatly facilitates the identification of any wave modes excited\nin a particular simulation. \n\nThe code has one space dimension $(x)$ and three velocity dimensions \n$(v_x,v_y,v_z)$. To model a plasma containing shock--reflected proton\nbeams, we construct a simulation box with 350 grid cells in the\n$x$--direction and with the local\nmagnetic field {\\bf B} oriented in the $y$--direction. McClements et\nal. (1997) pointed out that, at any given point in the\nshock foot, there are in fact two proton beams, one propagating away from the\nshock, the other towards it. For simplicity, we assume in our PIC\nmodel that the two beams propagate with equal speeds $u_{b\\perp}$ in\nopposite directions perpendicular to the magnetic field, and that\nboth background ions and electrons have zero net drift: thus, the simulated\nplasma has zero current. Strictly speaking, this is unrealistic,\nsince, in self--consistent models of perpendicular\nshocks, the magnetic field magnitude has a finite gradient along the\nshock normal direction, and a finite current is then required by\nAmp\\`ere's law (Woods 1969). We will discuss this\napproximation in Sect. 4. The frame of reference in each simulation is\nthe upstream plasma frame: time evolution in the simulation can thus\nbe interpreted as spatial variation in the shock foot, with $t=0$ in\nthe simulation corresponding to the interface between the undisturbed\nupstream plasma and the foot. The size of the foot $L_{\\rm foot}$ lies\napproximately in the range $(0.3 - 0.7)v_s/\\Omega_i$, where $v_s$ is\nthe shock speed and $\\Omega_i$ is the upstream ion gyrofrequency (McClements\net al. 1997). Thus, if the simulation is to be confined to the\nfoot, the duration of the simulation should be no greater than\n$$ t_{\\rm max} = {L_{\\rm foot}\\over v_s} \\simeq (88 - 205){2\\pi\\over\n\\Omega_e}, \\eqno (1) $$ \nwhere $\\Omega_e$ is the electron gyrofrequency (the true proton/electron mass\nratio, 1836, was used in the simulations).\nThe simulations reported here lasted for either 70 or 135 electron\ncyclotron periods $2\\pi/\\Omega_e$. \n\nThe proton beams were assumed to be initially Maxwellian with thermal\nspeed $\\delta u_{\\perp} = 3 \\times 10^5\\,$ms$^{-1}$ ($\\delta u_{\\perp}$ being\ndefined such that the equivalent temperature in energy units is \n$m_p\\delta u_{\\perp}^2$, where $m_p$ is the proton mass), and a\nrange of perpendicular drift speeds $u_{b\\perp} = 3.25v_{e0}$, $3.5v_{e0}$,\n$5v_{e0}$ and $6v_{e0}$, where $v_{e0}$ is the electron thermal speed,\ndefined in the same way as $\\delta u_{\\perp}$ and initially set equal\nto $3.75 \\times 10^6\\,$ms$^{-1}$ (this corresponds to an electron\ntemperature $T_e \\simeq 9.3 \\times 10^5\\,\\hbox{K} \\simeq\n80\\,\\hbox{eV}$). The value chosen for the total beam number\ndensity, $0.33n_e$, is consistent with the highest values of this\nparameter found in hybrid simulations of quasi--perpendicular shocks with\nAlv\\'enic Mach numbers $M_A$ ranging up to about 60 (Quest\n1986). Cargill \\& Papadopoulos (1988) used\n$M_A = 50$ in their hybrid simulation of an SNR shock (it\nwas computationally difficult to simulate shocks with higher $M_A$). \nThe density of each beam $n_b$ is, accordingly, one sixth of the\nelectron density $n_e$, so that the background proton density $n_i$\nrequired by charge balance is\n$0.67n_e$ (the background proton thermal speed $v_i$ was\nset equal to $1.9 \\times 10^5\\,$ms$^{-1}$). \nThe electron plasma frequency $\\omega_{pe}/2\\pi$ and\ngyrofrequency $\\Omega_e/2\\pi$ in our simulations were set equal to $10^5$Hz and\n$10^4$Hz, respectively, corresponding to $n_e \\simeq 1.2 \\times\n10^8\\,$m$^{-3}$ and magnetic field $B \\simeq 3.6 \\times 10^{-7}\\,$T.\nThe ratio $\\omega_{pe}/\\Omega_e$ is typically of order $10^2$ or\nhigher in HII regions of the interstellar medium. We have\nchosen a relatively low value of this ratio in order to study and\ncompare the effects of instabilities occurring on both the\n$\\omega_{pe}^{-1}$ and $\\Omega_e^{-1}$ timescales. \n\nThe electrons, background protons and each proton beam were represented,\nrespectively, by 3200, 800 and 7200 particles per cell. The use of a\nrelatively small number of background protons per cell is\njustified by the fact that instabilities driven by the proton beams have much\nhigher frequencies than noise fluctuations associated with the\nbackground protons: large numbers of electrons and beam protons in\neach cell ensure a level of noise energy well below the wave energy\nproduced by the instabilities. In what follows we measure time in electron\ncyclotron periods, using the notation $\\tilde{t}=\\Omega_e t/2\\pi$. We\nalso define $\\tilde{k}=kv_{e0}/\\Omega_e$\n(only waves propagating in the $x$--direction are represented), a \nnormalized frequency $\\tilde{\\omega} = \\omega/\\Omega_e$, and \n$r = kv_{\\perp}/\\Omega_{e}$, $v_{\\perp}$ being electron \nvelocity perpendicular to the magnetic field.\n\nIn every simulation, transfer of energy from beam protons to electrons\nwas observed, but the power flux between the two species increased\ndramatically when $u_{b\\perp}$ was raised from $3.5v_{e0}$ to\n$5v_{e0}$. Figure 1 is a time evolution plot of perpendicular kinetic\nenergy ${\\cal E}_{\\perp e} = \\sum_j m_ev_{\\perp j}^2/2$, where $m_e$\nis electron mass and the summation is over all electrons in the\nsimulation box. Since the total electron number is constant, ${\\cal\nE}_{\\perp e}$ can be regarded as a measure of the effective\nperpendicular electron \ntemperature (although it should be stressed at the outset that the\nelectrons do not always have a Maxwellian distribution). The energy is\nnormalized to its initial value, which was identical in the four simulations.\nWhen $u_{b\\perp} = 3.25v_{e0}$ and $3.5v_{e0}$ (upper plot)\nthe energy increases by approximately an order of magnitude in around\n60--100 electron cyclotron periods; when $u_{b\\perp} =\n5v_{e0}$ and $6v_{e0}$ (lower plot) the energy increases by a factor of\nabout 40 within $\\tilde{t} \\simeq 15-30$. The perpendicular energies of\nthe other two particle populations, again normalized to the initial\nelectron energy, are\nplotted versus time for the case of $u_{b\\perp} = 6v_{e0}$ in\nFig. 2. In the case of the beam protons (upper plot), both bulk motion\nenergy and thermal energy are included. During the simulation the\nbeam proton energy drops by less than 1\\%, while the background proton\nenergy (lower plot) rises by no more than about 10\\% (in the other\nsimulations the perpendicular energies of the two ion species changed\nby even smaller amounts). In absolute terms the energy gained\nby background protons is very small compared to that lost by beam protons,\nwith almost all the energy being transferred to electrons: we will\ndemonstrate that the beam protons excite an instability which couples\nthem efficiently to electrons. \n \nIn all the cases studied, electrons were energized in the direction \nperpendicular to the magnetic field. The upper plot in Fig. 3 shows, in\nmore detail than Fig. 1, the time evolution of ${\\cal E}_{\\perp e}$\n(once again normalized to its initial\nvalue) in the first 25 electron cyclotron periods of the simulation\nwith $u_{b\\perp} = 6 v_{e0}$. The lower plot shows the time evolution\nof $\\langle \\varepsilon_0\nE_x(x,t)^2/2 \\rangle$, where $\\varepsilon_0$ is the permittivity of free\nspace, $E_x(x,t)$ is the $x$--component of the electric field, and the \nbrackets $\\langle \\rangle$ denote a spatial average over the simulation box. \nIn general, $E_x$ is the dominant field component:\nsince propagation in the $x$--direction only is represented, it \nfollows that the waves excited are predominately electrostatic. Henceforth,\nthe term ``electric field'' refers to the $x$--component. The field\nhas a single value in each simulation box cell: the electrostatic\nfield energy density $\\langle \\varepsilon_0\nE_x(x,t)^2/2 \\rangle$ is calculated by summing $\\varepsilon_0\nE_x(x,t)^2/2$ over the box and dividing by the number of cells.\nThe energy density plotted in the lower frame of Fig. 3 is \nnormalized to the perpendicular electron energy density at $\\tilde{t} = 0$.\nThe electron energy grows rapidly in two main phases, at \n$\\tilde{t} \\simeq 5$ and $\\tilde{t} \\simeq 14$, and \nthen continues to grow at a slower rate. The \nfield energy is greatly enhanced at times when the particle kinetic \nenergy is growing rapidly: this suggests strongly that the \nfields are involved in particle acceleration. In the case of the wave\nenergy burst at $\\tilde{t} \\simeq 5$, the field energy grows to a\nlevel comparable to the electron kinetic energy at that time. The\nenergy of the burst occurring at $\\tilde{t} \\simeq 14$, on the other\nhand, is much lower than that of the electrons.\nFigure 4 shows the time evolution of ${\\cal E}_{\\perp e}$ and field\nenergy in the simulation with $u_{b\\perp} = 3.25 v_{e0}$. The upper\nplot shows ${\\cal E}_{\\perp e}$ growing on a timescale comparable to \nthe transit time of the simulation box through\nthe shock foot. The lower plot shows that electrostatic field activity \nis again correlated with electron acceleration. Figure 4 resembles the\nsecond of the two periods of wave growth in Fig. 3 (at\n$\\tilde{t} \\simeq 14$), in that the wave energy is small compared to the\nelectron kinetic energy. \n\nWe now consider the distribution of wave amplitudes in wavenumber\nspace. Figure 5 shows the time evolution of this distribution\nin the simulation with $u_{b\\perp} = 6 v_{e0}$. The grey scale\nshows the base 10 logarithm of the wave amplitude \nobtained by Fourier transforming in space the electric field of \none of two counter--propagating waves excited by the ion beams. \nThe start of the burst\nin wave energy in the lower plot of Fig. 3 at $\\tilde{t} \\simeq 3$ can\nbe identified with the burst at $\\tilde{k} \\simeq 1.8$ in Fig. 5. \nThis reaches an amplitude of 35 Vm$^{-1}$, generating a harmonic at \n$\\tilde{k} \\simeq 3.6$. When the peak amplitude is reached there is an\nincrease in wave energy at $\\tilde{k} < 1$. The frequency of this low \n$\\tilde{k}$ noise is close to the upper hybrid frequency\n$\\omega_{uh} = (\\omega_{pe}^2 +\n\\Omega_e^2)^{1/2}$. Its appearance correlates with the maximum\nof the first wave burst at $\\tilde{t} \\simeq 5$ in the lower plot of\nFig. 3, and with the \nstrong increase of electron kinetic energy in the upper plot,\nsuggesting that it arises from a redistribution of\nwave energy and changes in the electron distribution. After $\\tilde{t}\n\\simeq 8$, when the initial wave burst has disappeared, a more\nbroadband perturbation is generated at $\\tilde{k} \\simeq 1.3$, the\nmean $\\tilde{k}$ decreasing with time. At $\\tilde{t}=14$ the wave\namplitude peaks at about 16$\\,$Vm$^{-1}$: this is considerably lower\nthan the peak electric field of 35$\\,$Vm$^{-1}$ in the first burst, but\nnevertheless strong enough to generate two harmonics (at $\\tilde{k}\n\\simeq 2.6$ and $\\tilde{k} \\simeq 3.9$). \n\nThe corresponding plot for the simulation with $u_{b\\perp} =\n3.25v_{e0}$ is shown in Fig. 6. In this case instability occurs at\ndiscrete, regularly--spaced values of $\\tilde{k}$. Waves with\nrelatively high $\\tilde{k}$ ($\\simeq 4$) are the first to be driven\nunstable: during the course of the simulation, the instability shifts\nto lower discrete wavenumbers. Broadband noise develops \nat $\\tilde{k} < 1$, as in Fig. 5, but at a later time in the\nsimulation ($\\tilde{t} \\simeq 35$). This appears to be associated with\na more gradual evolution of the electron distribution than that which\noccurs in the simulation with $u_{b\\perp}=6v_{e0}$. The difference in temporal\nbehaviour between Figs. 5 and 6 will be discussed later in this paper.\nFigures 5 and 6 show that in both simulations the plasma eventually\nstabilizes, on a timescale which depends on the beam velocity. \n\nThe dependence of wave amplitude on $\\tilde{k}$ and $\\tilde{t}$ when\n$u_{b\\perp}=5v_{e0}$ is qualitatively similar to Fig. 5: after an \nintense burst early in the simulation, a wave with slowly--varying\namplitude is observed to cascade down in $\\tilde{k}$ as time\nprogresses. The growth rate of the first wave burst is 20\\% higher in\nthe simulation with $u_{b\\perp} = 6v_{e0}$ than it is in the\nsimulation with $u_{b\\perp} = 5v_{e0}$. In the former case, as\nmentioned above, the peak amplitude of \nthe second burst is 16$\\,$Vm$^{-1}$, at \n$\\tilde{k} = 1.25$ and $\\tilde{t} = 14$; the corresponding figures\nfor the simulation with $u_{b\\perp} = 5v_{e0}$ are 12$\\,$Vm$^{-1}$,\n$\\tilde{k}=1.88$ and $\\tilde{t} = 12$. The wave amplitude distribution in the\nsimulation with $u_{b\\perp}=3.5v_{e0}$ is similar to Fig. 6: bursts of\nwave activity occur at discrete $\\tilde{k}$, with the high $\\tilde{k}$\nmodes being driven unstable first. \n\nIn principle, it is also possible to determine the time evolution of wave \namplitude as a function of $\\tilde{\\omega}$ and $\\tilde{k}$. However, in order\nto obtain good frequency resolution it is necessary to average the\namplitude over times longer than the electron acceleration timescale.\nElectrostatic waves in the electron cyclotron range propagating\nperpendicular to the magnetic field include, for example, electron\nBernstein waves, whose dispersion relation depends on the electron\ndistribution. Since this is rapidly evolving, it can be difficult \nto interpret observed distributions of wave amplitude in\n$\\tilde{\\omega}$ and $\\tilde{k}$. \nHowever, we have found that the most strongly--growing waves in the\nsimulations invariably have $\\tilde{\\omega} \\simeq\n\\tilde{k}u_{b\\perp}/v_{e0}$: one can thus obtain the frequencies of\nthe high intensity modes in Figs. 5 and 6 by multiplying $\\tilde{k}$\nby $u_{b\\perp}/v_{e0}$. By this means, it is straightforward to verify\nthat the modes excited early in both simulations have $\\tilde{\\omega}\n\\simeq 10$, and hence $\\omega \\simeq \\omega_{pe}$. \n\n\\section{Analysis of simulation results}\n\nShort--lived bursts of narrowband wave activity, correlated with\nrapid increases in electron kinetic energy, occur for all four values\nof $u_{b\\perp}/v_{e0}$ considered above.\nThese bursts appear throughout the simulations \nwith $u_{b\\perp} = 3.25 v_{e0}$ and $u_{b\\perp} = 3.5 v_{e0}$; in the\ncase of $u_{b\\perp} = 5v_{e0}$ and $u_{b\\perp} = 6v_{e0}$, they appear\nonly at early times. In every case, the instability cascades to longer\nwavelengths in the course of the simulation. In order to compare the simulation\nresults with those given by linear instability analysis (described in\nthe next subsection), we determine\ngrowth rates for the first wave that interacts significantly with the\nelectrons: in such cases one may assume \nthat the electrons are still represented by a single Maxwellian velocity \ndistribution with thermal speed $v_{e0}$. \nThe simulations provide the wavenumber $\\tilde{k}$ of the unstable\nwave modes and the electric field amplitude $E$. The real frequencies \n$\\tilde{\\omega}$ of the unstable wave modes are assumed to be equal to \n$\\tilde{k}u_{b\\perp}/v_{e0}$. The normalized growth rate \n$\\gamma/\\Omega_e$ is estimated by fitting an exponential to the plot\nof wave amplitude versus time during the period of most rapid growth\nin each simulation. \n\nThe results of this analysis are shown in Table 1. The symbol $E_m$ denotes\nthe maximum value of $E$ during each simulation. In three of the four \nsimulations there is a period of wave growth which can be described accurately\nas exponential. In each case, the growth rate falls to zero, and\nthe wave decays: an example of this behaviour, for the case of\n$u_{b\\perp} = 6v_{e0}$, is shown in Fig. 7, where wave amplitude (defined \nas in Figs. 5 and 6) at $\\tilde{k} = 1.8$ is plotted versus normalized time. \nA possible reason for wave collapse (observed in all four simulations) will be\ndiscussed later in this paper. In the case of $u_{b\\perp} = 3.25v_{e0}$, the \nmode referred to in Table 1 ($\\tilde{k} \\simeq 3.6$) is the second to be \ndestabilized in that simulation. It appears to grow linearly \nrather than exponentially: for this reason, no figure is given for\nits growth rate. The first mode to be destabilized in this simulation, \nwith $\\tilde{k} \\simeq 3.9$, does not grow to a large amplitude (compared to\nthe noise level), and so it is difficult to determine its growth\nrate. Later in the paper we will present evidence of wave--wave\ninteraction between the second mode excited ($\\tilde{k} \\simeq 3.6$) and the \nthird mode excited ($\\tilde{k} \\simeq 3.3$), which may help to\nexplain the linear growth of the latter. \n\n\\vskip 0.5cm\n%\\vfill\\eject\n\n\\noindent {\\bf Table 1.} Parameters of highest intensity wave mode in\neach simulation. \n\n\\vskip 0.2cm\n\n\\noindent \\begin{tabular}{lllll}\n\n\\hline\n\n$u_{b\\perp}/v_{e0}$ & $\\tilde{k}$ & $\\tilde{\\omega}$ & $\\gamma/\\Omega_e$ & \n$E_m$ (Vm$^{-1}$) \\\\\n\n\\hline \n\n$6.0$ & 1.8 & 10.8 & 0.24 & 35 \\\\\n\n$5.0$ & 2.15 & 10.7 & 0.2 & 23 \\\\\n\n$3.5$ & 3.3 & 11.6 & 0.05 & 2.5 \\\\\n\n$3.25$ & 3.6 & 11.7 & -- & 1.6 \\\\\n\n\\hline\n\n\\end{tabular}\n\n\\vskip 0.5cm\n\nLet us now examine whether the growth rates derived from the PIC simulations\nin Table 1 and Fig. 7 can be reproduced using linear\nstability theory. \n\n\\subsection{Linear stability analysis} \n\nThe appropriate dispersion relation for electrostatic,\nperpendicular--propagating waves with frequencies in the electron\ncyclotron range and above, excited by an ion beam with a Maxwellian\ndistribution in $v_{\\perp}$, is (Melrose 1986) \n$$ 1-{\\omega_{pi}^2\\over \\omega^2} + \n{2\\omega_{pb}^2\\left[1+\\zeta_b Z(\\zeta_b)\n \\right]\\over k^2\\delta u_{\\perp}^2}\n- {\\omega_{pe}^2\\over \\omega}{e^{-\\lambda_e}\\over \n \\lambda_e}\\sum_{\\ell = -\\infty}^{\\infty}{\\ell^2I_{\\ell}\\over \n \\omega - \\ell\\Omega_e} = 0 \\,, \\eqno (2) $$\nwhere: $\\omega_{pi}$, $\\omega_{pb}$ are the background and beam ion plasma\nfrequencies; $Z$ is the plasma dispersion function, with argument\n$\\zeta_b \\equiv (\\omega-ku_{b\\perp})/k\\delta u_{\\perp}$; and $I_{\\ell}$ \nis the modified Bessel function of the first kind of order $\\ell$ with\nargument $\\lambda_e \\equiv T_ek^2/(m_e\\Omega_e^2)$. Both species of\nion, having a much longer cyclotron period than the electrons, can be\ntreated as unmagnetized particles on the timescales of interest here.\nStrictly speaking, there should be a term in Eq. (2) for each of the\ntwo proton beams, but since they have mean perpendicular speeds\nof opposite sign, and $\\omega \\simeq ku_{b\\perp}$ is a prerequisite\nfor wave--particle interaction, we need only consider one of them. \n\nSolutions of Eq. (2) for complex $\\omega$ in terms of real $k$ can be\nreadily obtained numerically, and compared with the simulation results\nin Table 1. In Figs. 8 and 9 $\\tilde{\\gamma} \\equiv\n\\rm{Im}(\\tilde{\\omega})$ is plotted versus $\\tilde{k}$ for parameters\ncorresponding to the initial conditions of the simulations with\n$u_{b\\perp} = 6v_{e0}$ and $u_{b\\perp} = 3.25v_{e0}$. In the former\ncase it can be seen that strong instability drive occurs at $\\tilde{k}\n\\simeq 1.8$ with maximum growth rate $\\tilde{\\gamma} \\simeq 0.25$, as\nobserved early in the simulation (Fig. 5 and Table 1). The unstable real\nfrequencies range from $\\tilde{\\omega} \\simeq 8$ to $\\tilde{\\omega}\n\\simeq 10.8$, and are thus clustered around the dimensionless electron\nplasma frequency ($\\tilde{\\omega} = 10$). The main instability appears to\nbe essentially unaffected by cyclotronic effects: the growth rate does\nnot depend on how close the frequency is to a cyclotron\nharmonic. There are, however, two much weaker instabilities at $\\tilde{k} <\n1$, which are narrowband in both $\\tilde{k}$ and $\\tilde{\\omega}$, the\nreal frequencies lying just below the second and third cyclotron\nharmonics. In Fig. 9 instability occurs at $\\tilde{k} \\sim\n3-4$, the corresponding real\nfrequencies again clustering around $\\omega_{pe}$. In this case,\nhowever, the instability is modulated by cyclotronic effects, as\nin the simulation. Instability again occurs at $\\tilde{k} < 1$, with\nreal frequency $\\tilde{\\omega} \\simeq 1.8$.\n\nThe mode appearing early in the simulation with $u_{b\\perp} = 6v_{e0}$\narises from a two--stream instability\n(Buneman 1958). This can be driven by ions drifting relative to\nelectrons in an unmagnetized plasma: it can also occur in a\nmagnetized plasma, with ions drifting across the field, if\n$\\omega_{pe}/\\Omega_e$ is sufficiently large, and the instability\ndrive is sufficiently strong. Electrons as well as ions are then\neffectively unmagnetized and the appropriate dispersion relation is\n(Melrose 1986) \n$$ 1 - {\\omega_{pi}^2\\over \\omega^2} +\n{2\\omega_{pb}^2\\left[1+\\zeta Z(\\zeta_b)\n \\right]\\over k^2\\delta u_{\\perp}^2}\n + {2\\omega_{pe}^2\\left[1+\\zeta Z(\\zeta_e)\n \\right]\\over k^2v_{e0}^2} = 0 \\,, \\eqno (3) $$ \nwhere $\\zeta_e \\equiv \\omega/kv_{e0}$. In the frequency r\\'egime of\ninterest here ($\\omega \\simeq \\omega_{pe}$), it can be shown easily \nthat the background ion term in Eq. (3) can be neglected. Letting the\nthermal speeds of the two remaining species tend to zero, Eq. (3) reduces to\n$$ 1-{\\omega_{pb}^2\\over (\\omega-ku_{b\\perp})^2}\n -{\\omega_{pe}^2\\over \\omega^2} = 0 \\,. \\eqno (4) $$\nThis differs slightly from the original two--stream dispersion relation\nanalysed by Buneman (1958) in that the ions, rather\nthan the electrons, have a finite drift speed. Buneman's equation\nbecomes identical to Eq. (4) under the transformation $\\omega\n\\rightarrow ku_{b\\perp} - \\omega$: using this, we can infer\nfrom Buneman's analysis that Eq. (4) has a root $\\omega = \\omega_0\n+i\\gamma$, where real frequency $\\omega_0$ and growth rate $\\gamma$\nare given approximately by \n$$ \\omega_0 \\simeq ku_{b\\perp} -\n\\omega_{pb}^{2/3}\\omega_{pe}^{1/3} \\cos^{4/3}\\theta, \\eqno (5) $$ \n$$ \\gamma \\simeq \\omega_{pb}^{2/3}\\omega_{pe}^{1/3}\n\\cos^{1/3}\\theta\\sin \\theta, \\eqno (6) $$ \n$\\theta$ being a parameter whose value depends on\n$(ku_{b\\perp} - \\omega_{pe})/\\omega_{pb}^{2/3}\n\\omega_{pe}^{1/3}$ (Buneman 1958): it is straightforward to\nverify that the strongest wave growth occurs when $\\theta = \\pi/3$,\nwhich corresponds to \n$ku_{b\\perp} = \\omega_{pe}$. If $ku_{b\\perp} \\gg \n\\omega_{pb}^{2/3}\\omega_{pe}^{1/3} \\cos^{4/3}\\theta$, it follows from\nEq. (5) that $\\omega \\simeq ku_{b\\perp}$ and so the strongest\ndrive occurs at $\\omega \\simeq \\omega_{pe}$. However, since $\\theta$\ncan have a range of values, the instability has finite bandwidth, extending to\nfrequencies significantly below $\\omega_{pe}$. Solving the full\nBuneman dispersion relation [Eq. (4)] with $u_{b\\perp} = 6v_{e0}$,\nwe obtain results which are almost identical to those\nobtained from the magnetized dispersion relation [Eq. (2)], except, of\ncourse, that the cyclotronic features at $\\tilde{k} < 1$ in Fig. 8 do\nnot appear. Even in the case of $u_{b\\perp} = 3.25v_{e0}$, Eq. (4)\nyields instability at about the same wavenumbers and frequencies as\nEq. (2) [although the growth rates are somewhat higher in the case of\nEq. (4)]. The essential\ndifference between Figs. 8 and 9 is that the lower beam speed in the\nlatter yields lower growth rates: when $\\tilde{\\gamma}$ is\nsufficiently small, the gyromotion of an electron in one wave growth\nperiod cannot be neglected, and the instability is modified by\ncyclotronic effects. However, the instability remains Buneman--like in\ncharacter. \n\nFurther analysis of Eq. (2) indicates that the instability\ngrowth rate is a slowly--decreasing function of $\\delta\nu_{\\perp}/u_{b\\perp}$: in the case of $u_{b\\perp} = 6v_{e0}$, for\nexample, the maximum growth rate is around $0.06\\Omega_e$ when $\\delta\nu_{\\perp}/u_{b\\perp} = 0.3$. The Buneman instability is thus robust,\nin the sense that its occurrence is not critically dependent on the\nvelocity--space width of the reflected ion distribution. In any event,\nthe values of $\\delta u_{\\perp}/u_{b\\perp}$ used in our PIC simulations\nare broadly consistent with reflected beam ion distributions occurring\nin the hybrid simulations of Cargill \\& Papadopoulos (1988). \n\nThe instabilities at $\\tilde{k} < 1$ in Figs. 8 and 9 arise\nfrom the interaction of a beam mode ($\\omega \\simeq ku_{b\\perp}$) with\nelectron Bernstein modes. The existence of such instabilities can be\ninferred analytically by taking the limit of Eq. (2) for cold beam and\nbackground protons: \n$$1-{\\omega_{pi}^2\\over \\omega^2} - {\\omega_{pb}^2\\over (\\omega-ku_{b\\perp})^2}\n-{\\omega_{pe}^2\\over \\omega}{e^{-\\lambda_e}\\over \n\\lambda_e}\\sum_{\\ell = -\\infty}^{\\infty}{\\ell^2I_{\\ell}\\over \n\\omega - \\ell\\Omega_e} = 0 \\,. \\eqno (7) $$\nIn the absence of the proton beam term, Bernstein mode solutions of\nEq. (7) have frequencies which approach \n$\\ell\\Omega_e$ ($\\ell = 1,2,3,...$) as $k \\to \\infty$ and\n$(\\ell+1)\\Omega_e$ as $k \\to 0$ (the long wavelength limit\nis different for frequencies equal to or greater than the upper hybrid\nfrequency $\\omega_{uh}$, which in the case of the simulations presented\nin Sect. 2 is about 10$\\Omega_e$). When $n_b \\ne 0$, approximate\nanalytical solutions of Eq. (7) can be obtained by setting \n$\\omega = ku_{b\\perp} + i\\gamma$ and solving perturbatively for\n$\\gamma$ in certain limits. For example, letting $\\lambda_e \\to 0$ and\nassuming that $\\omega$ does not lie close to a harmonic of $\\Omega_e$, \nwe obtain\n$${\\gamma\\over \\Omega_e} \\simeq \\left({m_e\\over m_p}\\right)^{1/2}\n\\left({n_b\\over n_e}\\right)^{1/2}\\left({\\omega^2\\over \\Omega_e^2} - 1\n\\right)^{1/2}\\,. \\eqno (8) $$ \nInstability, corresponding to real $\\gamma$, thus requires $\\omega > \\Omega_e$.\nFor $\\omega$ \nsufficiently close to $\\ell\\Omega_e$, the electron term in Eq. (7) is \ndominated by the $\\ell$--th harmonic, and instead of Eq. (8) we obtain \n$${\\gamma\\over \\Omega_e} \\simeq {\\omega\\over \\Omega_e}\\left({m_e\\over \nm_i}\\right)^{1/2}\\left({n_b\\over n_e}\\right)^{1/2}{\\lambda_e e^{\\lambda_e}\\over\n\\left(\\ell I_{\\ell}\\right)^{1/2}}\\left(1 - {\\ell\\Omega_e\\over \\omega}\n\\right)^{1/2}. \\eqno (9) $$ \nNumerical solutions of Eq. (2) for $\\omega \\sim \\Omega_e$ are broadly\nconsistent with Eqs. (8) and (9). In both these cases\nthe growth rate scales as $(m_e/m_p)^{1/2}$: in contrast, the Buneman\ngrowth rate [Eq. (6)] scales as $(m_e/m_p)^{1/3}$. This helps to\nexplain the fact that in Figs. 8 and 9 the Buneman instability is\nstronger than the lower frequency Bernstein instability. \nIt should also be noted that most astrophysical plasmas have a higher\nratio of electron plasma frequency to gyrofrequency that that assumed\nin the simulations ($\\omega_{pe}/\\Omega_e = 10$). Normalized to\n$\\Omega_e$, the Buneman growth rate scales as $\\omega_{pe}/\\Omega_e$,\nand so the instability is less likely to be modified by\ncyclotronic effects when $\\omega_{pe}/\\Omega_e > 10$. The electron\nBernstein modes exist because $T_e$ is finite: thus,\nthe transition from Buneman to electron Bernstein instability depends\non the value of $v_{e0}$. If the initial electron temperature in the\nsimulations had been lower than 80$\\,$eV, the Buneman instability\nwould, again, have been affected to a lesser extent by cyclotronic\neffects. \n\n\\subsection{Nonlinear effects}\n\nFigure 1 shows strong increases in electron kinetic energy\nperpendicular to the magnetic field in all four simulations. There is\na strong correlation between acceleration and wave excitation via the\nBuneman instability (Figs. 3 and 4). Although such waves can energize\nelectrons via Landau damping (Papadopoulos 1988), one\nwould expect this process to be of limited effectiveness when, as in\nthe present case, the\nwaves are propagating perpendicular to the magnetic field and have a\ngrowth rate which is comparable to or less than $\\Omega_e$.\nIt is likely therefore that the very strong electron acceleration observed in\nthe simulations is due at least in part to nonlinear processes. \n\nAs noted previously, the second mode to be excited in the simulation\nwith $u_{b\\perp}=3.25v_{e0}$ does not undergo an \nexponential growth phase. Figure 10 shows the time evolving wave \namplitudes of this mode, at $\\tilde{k} = 3.6$ (upper plot), and the third\nmode to be excited, at $\\tilde{k}=3.3$ (lower plot). The\namplitude at $\\tilde{k}=3.6$ grows linearly up to $\\tilde{t} \\simeq\n27$, and then collapses. The amplitude at $\\tilde{k}=3.3$ grows exponentially\nfrom $\\tilde{t} \\simeq 7$ to $\\tilde{t} \\simeq 14$, with\n$\\gamma/\\Omega_e \\simeq 0.04$: this is close to the\ngrowth rate at $\\tilde{k}=3.3$ found by linear stability analysis\n(Fig. 9). The amplitude remains constant \nuntil $\\tilde{t} \\simeq 27$, and then grows linearly until \n$\\tilde{t} \\simeq 35$. The linear growth of the wave at $\\tilde{k} =\n3.3$ thus correlates strongly with the collapse of the wave at \n$\\tilde{k} = 3.6$: this suggests wave--wave coupling.\nThe linear growth of the wave at $\\tilde{k} = 3.6$ may, in\nturn, be correlated with the decay of the first mode to be excited, at \n$\\tilde{k} \\simeq 3.9$\n(see Fig. 6): the latter has the highest growth rate of waves in this\nrange, according to linear stability analysis (Fig. 9).\n\nWe now consider specific nonlinear processes which may be occurring\nin the simulations. Karney (1978) examined the nonlinear\ninteraction of large amplitude electrostatic lower hybrid waves with\nions. The particle motion is described by a normalized Hamiltonian \n$$h = \\frac{1}{2}{({p}_{x}+y)}^{2} + \\frac{1}{2} {{p}_{y}}^{2}\n-\\alpha\\sin{(y-\\mu t)}, \\eqno (10)$$\nwhere: $\\hat{\\bf y}$, $\\hat{\\bf z}$ are, respectively, the wave\npropagation and magnetic field directions; the canonical momentum\ncomponents $p_x$, $p_y$ are normalized to $m\\Omega/k$, where $m$ and\n$\\Omega$ are particle mass and gyrofrequency; the position variable\n$y$ is normalized to $1/k$; $\\mu$ is wave frequency in units of\n$\\Omega$; and $\\alpha$ is given by \n$$\\alpha = \\frac{E/B}{\\Omega/k}, \\eqno (11)$$ \n$E$ being the wave electric field amplitude. The first two terms in\nthe Hamiltonian describe the motion of the particle in the magnetic\nfield; the third term arises from the electrostatic wave. The system\ncan be regarded as consisting of two harmonic oscillators: one \nassociated with the particle gyromotion around $B$, the other with the\nwave. These oscillators are coupled by the parameter $\\alpha$, the\nvalue of which determines the extent to which the system phase space \nis regular or stochastic. Karney (1978) solved the Hamiltonian equations \ncorresponding to Eq. (10) for a range of initial conditions, plotting \nnormalized Larmor radius $r = kv_{\\perp}/\\Omega$ versus wave phase\nangle $\\phi$ at the particle's position, for successive transits of\nthe particle through a particular gyrophase angle. Particle\ntrajectories were thus represented as discrete sets of points in\n$(r,\\phi)$ space. For sufficiently small values of $\\alpha$, all particles \nhave regular orbits, represented by smooth curves in\n$(r,\\phi)$ space, spanning all values of $\\phi$ and with only\nsmall variations in $r$. When $\\alpha$ exceeds a certain threshold\n$\\alpha_0$, ``islands'' appear in $(r,\\phi)$ space, within which\nparticle trajectories are confined. Further increases in $\\alpha$ lead\nto the formation of more islands, which cause the phase space to become\nstochastic: at sufficiently large $\\alpha > \\alpha_c$, the system\nphase space is completely stochastic, with no regular orbits remaining. The\ninitial electron distributions in our simulations decrease \nmonotonically in $v_{\\perp}$: in such cases stochasticity in\nphase space tends to favour particle diffusion to larger velocities,\ni.e. acceleration. \n\nKarney (1978) obtained the following analytical estimate for $\\alpha_0$:\n$$\\alpha_0 = \\left | \\frac{r(\\omega/\\Omega - \\ell)}{\\ell (d/dr) \nJ_{\\ell}(r)} \\right |, \\eqno (12)$$\nwhere $\\ell\\Omega$ is the cyclotron harmonic closest to $\\omega$ and\n$J_{\\ell}$ is the Bessel function of order $\\ell$.\nKarney's analysis does not explicitly involve a \nparticular type of wave or particle, or a specific particle\ndistribution function. The results can thus be applied to the case of\nelectrons interacting with electrostatic waves excited by the Buneman\ninstability, in which case $m = m_e$ and $\\Omega=\\Omega_e$.\nCombining Eqs. (11) and (12) and using the identity\n$$\\frac{d}{dr}J_{\\ell}(r) = \\frac{\\ell}{r}J_{\\ell}(r) -\nJ_{\\ell+1}(r), \\eqno(13)$$ \nwe infer that the critical electric field $E=E_i$ for island formation\nin $(r,\\phi)$ space is\n$$E_i = \\frac{v_{\\perp}B_{0}|\\mu -\\ell|}{\\ell|\n\\frac{\\ell}{r}J_{\\ell}(r) - J_{\\ell+1}(r)|}. \\eqno (14)$$\nIn general, it is not possible to determine analytically an expression\nfor the electric field amplitude $E=E_c$ corresponding to\n$\\alpha=\\alpha_c$, above which the phase space becomes completely\nstochastic. Karney obtained an empirical expression for $\\alpha_c$,\nbased on numerical calculations with particular values of $\\mu$ and\n$r$, which may not be applicable to the simulation results discussed\nhere. However, island formation is a first step in the destruction of\nregularity in the system phase space, and $E_i$ can be regarded as an\napproximate threshold for stochasticity: electric field amplitudes\nwhich are significantly higher than $E_i$ will convert regular\norbits at a particular $v_{\\perp}$ into stochastic ones.\n \nIn the cases $u_{b\\perp} = 5v_{e0}$ and $6v_{e0}$, linear\nstability analysis indicates that wave growth occurs across a range of\nfrequencies $\\omega \\sim \\omega_{pe}$, which includes cyclotron\nharmonics: in such cases $\\mu = \\ell$, and any non--zero wave amplitude\n$E$ will cause islands to be formed. In the case of the lower two beam\nspeeds, the unstable frequencies lie between cyclotron harmonics, and $E_i$ is\nthus always finite. Table 2 lists the values of $E_i$ derived from\nEq. (14) that are required for comparison with the highest\nintensity wave mode excited in each simulation. The actual peak\nelectric fields of these waves are given in Table 1. \n\n\\vskip 4.0cm\n\n\\noindent {\\bf Table 2.} Values calculated for $E_i$ using the \nwave parameters given in Table 1.\n\n\\vskip 0.2cm\n\n\\noindent \\begin{tabular}{llllll}\n\n\\hline \n\n$v_{\\perp}/v_{e0}$ & closest $\\ell$ & $(\\mu-\\ell)$ & $kv_{\\perp}/\\Omega_e$ &\n$E_i$ (Vm$^{-1}$) \\\\\n\n\\hline \n\n6.0 & 11 & 0.2 & 10.8 & 1.8 \\\\\n\n5.0 & 11 & 0.3 & 10.7 & 2.3 \\\\\n\n3.5 & 12 & 0.4 & 11.6 & 2.1 \\\\\n\n3.25 & 12 & 0.3 & 11.7 & 1.4 \\\\\n\n\\hline\n\n\\end{tabular}\n\n\\vskip 0.5cm\n\nComparing Tables 1 and 2, we see that waves are excited \nwith amplitudes exceeding $E_i$ in all\nfour cases. For the simulation with $u_{b\\perp}=3.25v_{e0}$, \n$E/E_i \\simeq 1.1$. This ratio rises to 1.2 for\n$u_{b\\perp} = 3.5v_{e0}$, 10 for $u_{b\\perp} = 5v_{e0}$, and 19 for\n$u_{b\\perp} = 6v_{e0}$. In the latter two cases, as we have seen,\nwaves are excited with $\\omega = \\ell\\Omega_e$, for which island\nformation occurs regardless of the value of $E$. The fact that $E_m/E_i\n\\gg 1$ at higher values of $u_{b\\perp}$ indicates that the phase\nspace in these simulations is characterized by strong\nstochasticity. The waves rapidly collapse, however, soon after the\nonset of strong electron acceleration. \nIn the other two simulations, the peak amplitudes\nare only just sufficient for island formation to occur, and it is\nlikely that little stochasticity occurs in the system phase space. \nThe waves excited in these simulations decay more gradually than those\nproduced at higher $u_{b\\perp}$. \n\nWe now consider possible explanations for two of the results noted above:\nthe sharp rise in wave amplitude when the beam speed is raised from\n$3.5v_{e0}$ to $5v_{e0}$; and wave collapse, which occurs in all four\nsimulations but is particularly rapid in the two simulations with\nhigher $u_{b\\perp}$. \nAs far as the dependence of wave amplitude on $u_{b\\perp}$ is\nconcerned, the first point to note is that the unstable waves all\nsatisfy $\\omega \\simeq u_{b\\perp}k$. In each simulation the total\nnumber of computational particles is, of course, finite, \nthe Maxwellian electron velocity distribution being initialized up to\n$v_{\\perp} \\simeq 5v_{e0}$.\nThus, the beams with $u_{b\\perp} = 5v_{e0}$ and $6v_{e0}$\nexcite waves with phase velocities exceeding the velocity of any\nelectron in the simulation: this is not so in the simulations with \n$u_{b\\perp}=3.25v_{e0}$ and $3.5v_{e0}$. The minimum electron velocity \nrequired for wave--particle interactions is the phase\nvelocity of the wave: thus, only the slow beams\ncan excite waves capable of interacting with electrons at the start of\nthe simulations. The wave--particle interaction results in\nelectron acceleration, the energy for this being drawn from the\nwave. This energy loss may account for the relatively low peak\nelectric field amplitudes of waves excited by the slow beams. \n\nThe waves generated by the fast beams, on the other hand, cannot initially \ninteract resonantly with the electron population, and so their amplitudes can\ngrow to levels much higher than $E_i$. Sufficiently high wave\namplitudes can activate a second acceleration mechanism, which arises\nfrom particle trapping in the wave electric field (Karney\n1978): electrons with an initially monotonic\ndecreasing distribution are re--distributed uniformly within the trap,\nthe result being a net increase in kinetic energy. The wave can trap\nelectrons with perpendicular velocities differing from the wave's\nphase velocity by up to $v_{\\rm tr}$, where \n$$v_{\\rm tr} = \\sqrt{\\frac{eE}{mk}}. \\eqno (15) $$\nFor $u_{b\\perp} = 5v_{e0}$, the maximum electric field is 23$\\,$Vm$^{-1}$\nand the wavenumber $k$ is $5.7 \\times 10^{-3} \\times\n2\\pi\\,$m$^{-1}$. In this case \n$v_{\\rm tr} = 1.1 \\times 10^7\\,$ms$^{-1}\\,\\simeq 2.8v_{e0}$.\nFor $u_{b\\perp} = 6v_{e0}$, the maximum field is 35$\\,$Vm$^{-1}$\nand $k = 4.8 \\times 10^{-3} \\times 2\\pi\\,$m$^{-1}$, so that\n$v_{\\rm tr} = 1.4 \\times 10^7\\,$ms$^{-1}\\, \\simeq 3.8v_{e0}$.\nThe waves excited in the simulations with higher beam speeds can thus\ntrap electrons deep within the electron thermal population: a large\nnumber of electrons can then be pre--accelerated to velocities\ncomparable to the wave's phase velocity, with further acceleration\ntaking place via the stochastic mechanism discussed previously. A two--stage\nprocess of this type \nwas proposed by Karney (1978). Whereas the first burst of\nwave activity in Fig. 3 contained more energy than the electron\npopulation, the energy in the second burst was much lower than the\nperpendicular electron kinetic energy by that stage of the simulation.\nThis may have been due to the first burst resulting in trapped electrons\npopulating the region of phase space at $v_{\\perp} \\simeq u_{b\\perp}$,\nvia the trapping mechanism. The perpendicular electron velocity\ndistribution would then be considerably broader than it was initially,\nwith an effective thermal speed $v_e > v_{e0}$. The beam distribution,\non the other hand, did not change significantly during the simulation\n(see Fig. 2), and so $u_{b\\perp}/v_e < u_{b\\perp}/v_{e0}$. \nThe situation would then be similar to that of the simulations\nwith lower beam speeds, in which electrons can immediately absorb\nenergy from waves with $\\omega \\simeq ku_{b\\perp}$, and one would expect \nany subsequent wave burst to have a peak energy much lower than that\nof the electron population, as observed.\n\nWith regard to the second observation, wave collapse, it is\ninteresting to note that in every case the wave amplitude falls to a level well\nbelow $E_i$: intuitively, one would have expected the waves to cease\ninteracting with electrons, and hence to reach a steady--state level, when\ntheir amplitudes had fallen below $E_i$. The collapse may be\nassociated with changes in the dispersion characteristics of the wave\nmode resulting from strong particle acceleration. Karney (1978)\njustified his Hamiltonian approach by considering only stochastic\nregions of phase space, at particle speeds (and hence wave phase\nspeeds) greatly exceeding $v_{e0}$. The stochastic regions thus lie in the \nhigh velocity tail of the initial Maxwellian electron distribution,\nand most electrons are not initially affected by the wave--particle\ninteraction. However, in the simulations with $u_{b\\perp} = 5\nv_{e0}$, $6v_{e0}$ the reduction in $u_{b\\perp}/v_e$ noted above\nmeans that perpendicular electron speeds are no longer small compared\nto the wave phase speed, and we find that there is a transition from the pure\nBuneman instability shown in Fig. 8 to the more complicated\ninstability shown in Fig. 9: the latter, as we have discussed, has a\nBuneman--like envelope, but also has cyclotronic features, and in fact\nlinear stability analysis shows that the variation of $\\omega$ with $k$ in\nthis case is characteristic of the beam/electron Bernstein mode\ndiscussed in Subsect. 3.1. As $u_{b\\perp}/v_e$ falls, the maximum\ngrowth rate drops considerably, but remains positive if \nthe electrons retain a Maxwellian distribution. However, as we now\ndemonstrate, the electron distributions occurring in the simulations\nare often far from Maxwellian. \n\n\\subsection{Particle distributions}\n\nFrom the simulation results we have evaluated the distribution\nof perpendicular electron speeds $f(v_{\\perp})$, defined such that \n$$ \\int_0^{\\infty}f(v_{\\perp})dv_{\\perp} = N_e\\,, \\eqno (16) $$\nwhere $N_e$ is the total number of electrons in the simulation. \nWith this definition, a Maxwellian velocity distribution is of the form \n$v_{\\perp}e^{-v_{\\perp}^2/2v_e^2}$, decreasing monotonically\nfor $v_{\\perp} > v_e$. One advantage of plotting a distribution in this\nway is that the thermal speed of a Maxwellian can be readily\nidentified graphically, being the speed at which\n$df/dv_{\\perp} = 0$. In Fig. 11 $f(v_{\\perp})$ is plotted for \n$\\tilde{t}=0$, $45$, $90$ and $135$ in the simulations with\n$u_{b\\perp} = 3.25v_{e0}$ (dash--dotted curves) and $u_{b\\perp}\n= 3.5v_{e0}$ (solid curves). The two curves are identical for\n$\\tilde{t}=0$, since the same initial electron temperature is used in\nall four simulations. At\n$\\tilde{t} = 45$ the proton beams have generated hot electron tails,\npeaking at $v_{\\perp} \\simeq 4v_{e0}$ ($u_{b\\perp} = 3.25v_{e0}$) and \n$v_{\\perp} \\simeq 6v_{e0}$ ($u_{b\\perp} = 3.5v_{e0}$). The maximum\nelectron speeds in the two cases are $7v_{e0}$ ($u_{b\\perp} =\n3.25v_{e0}$) and $10v_{e0}$ ($u_{b\\perp} = 3.5v_{e0}$). At $\\tilde{t}\n= 90$ the slower beam has produced a local maximum in $f(v_{\\perp})$ \nat $5v_{e0}$, and a high velocity cutoff at $10v_{e0}$. The local\nmaximum has become less pronounced at $\\tilde{t} = 135$.\nIn the case of $u_{b\\perp} = 3.5v_{e0}$ a local maximum can be seen at \n$\\tilde{t} = 45$: by $\\tilde{t} = 90$, however, the distribution is\nmonotonic decreasing above a speed only slighly higher than the\ninitial thermal speed. By the end of this simulation\n$f(v_{\\perp})$ extends up to 12$v_{e0}$.\n\nIn Fig. 12 $f(v_{\\perp})$ is shown for $\\tilde{t}=0$, $20$, $40$ and\n$70$ in the simulations with $u_{b\\perp} = 5v_{e0}$ (dash--dotted\ncurves) and $u_{b\\perp} = 6v_{e0}$ (solid curves). At $\\tilde{t}=20$\nthe two distributions have local maxima at $v_{\\perp} \\gg v_{e0}$,\nas in the second frame of Fig. 11: for $u_{b\\perp} = 5v_{e0}$ the\ndistribution peaks locally at $v_{\\perp} \\simeq 10v_{e0}$ and \nfalls to zero at $v_{\\perp} \\simeq 18v_{e0}$. The corresponding\nfigures at the same stage of the simulation with $u_{b\\perp} =\n6v_{e0}$ are $12v_{e0}$ and $22v_{e0}$. By $\\tilde{t}=40$, the local\nmaxima still exist and, indeed, the bumps--on--tail containing these\nmaxima actually comprise most of the electron population in both\ncases. By this time the high velocity tails extend to \n$v_{\\perp} \\simeq 25 - 30v_{e0}$. Local maxima close to the original thermal\nspeeds $v_{e0}$ still exist, but these have disappeared by $\\tilde{t}\n= 70$. The strong wave bursts in these simulations \noccur before $\\tilde{t}=20$: after this time, a weaker, more broadband\ninstability occurs at lower $\\tilde{k}$, but still with $\\tilde{\\omega}\n\\simeq \\tilde{k}u_{b\\perp}/v_{e0}$. To model this instability,\nwe can approximate the solid curve at $\\tilde{t}=20$ in Fig. 12 by\nsuperposing two Maxwellians, with thermal velocities $v_{ec}=v_{e0}$,\n$v_{eh} = 10v_{e0}$ and densities $n_{ec} = 0.38n_e$,\n$n_{eh} = 0.62n_e$. The solid curve in Fig. 13 shows the true distribution \nat $\\tilde{t}=20$; the\ndashed curve shows the bi--Maxwellian fit to this distribution. The\nmatch is not exact, but is close enough to suggest that we can\nmodel wave excitation at this stage of the simulation by\nsolving a modified version of the dispersion relation\n[Eq. (2)], with the parameters of the dashed curve defining the\nelectron distribution. Results indicate an electron Bernstein\ninstability with maximum growth rate \n$\\gamma \\simeq 0.08\\Omega_e$ at $\\tilde{k} \\simeq 1.4$,\n$\\tilde{\\omega} \\simeq 8.2\\Omega_e$: the wavenumbers are \nconsistent with those of fluctuations appearing at\n$\\tilde{t} \\ge 20$ in Fig. 5. \n\nThe electron distributions at $\\tilde{t} = 70$ in the simulations with\n$u_{b\\perp}=5v_{e0}$ and $u_{b\\perp} = 6v_{e0}$ (Fig. 12) can both be\napproximated by single Maxwellians, respectively with $v_e \\simeq\n8v_{e0}$ and $v_e \\simeq 12v_{e0}$. The proton beam--excited Buneman\ninstability can thus produce electron distributions whose\nperpendicular thermal speeds exceed the velocities of the ion\nbeams which produced them. The fastest--moving electrons have\n$v_{\\perp} \\gg u_{b\\perp}$. This phenomenon, observed in all four\nsimulations, is further strong evidence for nonlinear processes\nplaying a role in electron acceleration: in the quasi--linear limit,\nunmagnetized electrons of a particular speed $v_0$ can only interact with waves\nwhose phase speed equals $v_0$, and the range of wave phase speeds is\ndetermined in turn by the ion beam speeds. In the case of $u_{b\\perp}\n= 6v_{e0}$, the final electron temperature is about 11.5$\\,$keV: this\nis easily sufficient to account for thermal X--ray emission observed\nfrom SNRs such as Cas A (Papadopoulos 1988). Individual \nelectron energies up to several tens of keV were obtained in the\nsimulations. \n\n\\section{Conclusions and Discussion}\n\nUsing particle--in--cell (PIC) simulations and linear stability theory, we have\nshown that electrostatic waves in the electron plasma range, excited\nby ions reflected from a high Mach number perpendicular shock, can\neffectively channel the free energy of the shock into\nelectrons. Such shocks are known to be associated with SNRs, and the\nprocesses investigated in this paper may thus help to account for both\nX--ray thermal bremsstrahlung and the creation of ``seed'' electron\npopulations for diffusive shock acceleration to MeV and GeV energies\nin such objects. The simulation results provide confirmation of a proposal by\nPapadopoulos (1978) and Cargill \\& Papadopoulos (1978)\nthat streaming between reflected ions and upstream electrons can give\nrise to a strong Buneman instability. Whereas these authors\nassumed that the sole effect of the Buneman instability would be electron\nheating, the PIC simulations show acceleration -- the development of strongly\nnon--Maxwellian, anisotropic features in electron velocity\ndistributions. The maximum electron velocities are considerably higher\nthan those expected on the basis of quasi--linear theory: this implies\nthat nonlinear wave--particle interactions are contributing to the\nacceleration. When the beam speed is greater than about four times the\ninitial electron thermal speed, thermalization of the electron\npopulation is observed after saturation of the Buneman instability,\nthe final electron temperature being of the order of 10--12$\\,$keV. \n\nIt is possible that the acceleration process identified in this paper\nmay be relevant to oblique shocks as well as strictly perpendicular \nones. A necessary requirement is the presence of \nreflected ion beams, which have been observed (Sckopke et al. 1983) \nupstream of both quasi--parallel and quasi--perpendicular regions of\nthe Earth's bow shock (the term ``quasi--perpendicular'' is conventionally\nused to describe a shock at which the angle $\\theta_{Bn}$ between the shock\nnormal and the upstream magnetic field is greater than 45$^{\\circ}$). \nLeroy et al. (1982) used a hybrid code to simulate ion reflection at shocks \nwith a range of values of $\\theta_{Bn}$, finding very similar results for \n$\\theta_{Bn} = 80^{\\circ}$ and $\\theta_{Bn} = 90^{\\circ}$. They inferred from \nthis that hybrid simulations which use strictly perpendicular geometry may be\ncompared with observational data of quasi--perpendicular shocks.\nAdditional necessary requirements \nfor electron acceleration via the Buneman instability are that the \nprojection of the reflected ion beam velocity onto the plane perpendicular to \nthe upstream field exceed the upstream electron thermal speed, and that the\nplasma be weakly magnetized, in the sense that $\\omega_{pe} > \\Omega_e$. When \nthese conditions are satisfied locally, the Buneman instability\nwill occur. Whether this instability is sufficient to produce significant\nelectron energization at oblique shocks as well as perpendicular and nearly\nperpendicular ones remains to be demonstrated, however. In the simulations \npresented in this paper, acceleration occurred on timescales shorter than an \nion cyclotron period. It was not necessary to represent the shock foot \nstructure, since this has dimensions of the order of a reflected ion Larmor \nradius, and for this reason $\\theta_{Bn}$ is not explicitly a parameter in our \nmodel. Leroy et al. (1982) have noted, however, that extrapolations of results\nobtained for nearly perpendicular shocks ($80^{\\circ} \\le \\theta_{Bn}\n\\le 90^{\\circ}$) to more oblique shocks should be\ntreated with caution, since the physical processes governing the shock\nstructure can be expected to change as $\\theta_{Bn}$ is reduced.\n\nThe simulation results and our analysis of them suggest that the\ndamping of waves in the electron plasma range\nat perpendicular SNR shocks could \nprovide a solution to the cosmic ray electron injection problem. Although \nwave--particle interactions at such shocks have been invoked \npreviously in this context (Galeev 1984; Papadopoulos \n1988; Cargill \\& Papadopoulos 1988; Galeev et al. \n1995; McClements et al. 1997), the simulation\nresults presented here contain several new features. These include:\nthe acceleration, rather than heating, of electrons via the Buneman\ninstability; the acceleration of electrons to speeds exceeding those\nof the shock--reflected ions producing the instability; and strong acceleration\nof electrons perpendicular to the magnetic field. The wave--particle \nmechanisms proposed by Galeev (1984) and McClements et\nal. (1997) gave rise to electron acceleration primarily\nalong the magnetic field. Diffusive shock\nacceleration, which is probably essential for the production of \nultra--relativistic electrons, can occur when the electrons\nhave magnetic rigidities comparable to those of ions flowing\ninto the shock. Since, however, the diffusive shock mechanism requires \nelectrons to be rapidly scattered, its efficacy \ndoes not depend sensitively on the initial pitch angle distribution.\nThe geometry of the simulations described here ({\\bf B} \nperpendicular to the one space dimension) excludes the \npossibility of acceleration by electrostatic waves along the parallel \ndirection. The present model is complementary to those of Galeev (1984), \nGaleev et al. (1995) and McClements et al. (1997), in that it provides an \nalternative means of energizing electrons at perpendicular shocks. At a \nreal SNR shock, perpendicular acceleration via the Buneman \ninstability and parallel acceleration via wave excitation at $\\omega < \n\\Omega_e$ are both likely to occur. PIC simulations in two space \ndimensions would make it possible to assess quantitatively the \nrelative contributions of these two types of instability to electron \nenergization under a range of conditions. \n \nWe discuss finally our neglect of the finite plasma current present in\nthe foot region of perpendicular shocks. This approximation does not\nappear to have introduced unrealistic elements into our simulation\nresults, except insofar as the absence of a finite drift between the\nelectrons and background protons removes a possible source of drive\nfor the ion acoustic instability, invoked as one of the electron\nheating mechanisms in the model of Papadopoulos\n(1988). However, if the background protons and electrons flowing\ninto the shock foot are approximately isothermal, it seems\nunlikely that any instability excited by their relative streaming\ncould result in a significant transfer of energy from one species\nto the other. Another possibility is that ion acoustic instability\ncould result from the streaming of beam protons relative to\nelectrons. This would require, however, the electron temperature to be\nextremely large compared to the beam proton temperature (ion Landau\ndamping strongly suppresses the instability when the temperatures are\nequal): even in the\nsimulation which produced an effective electron temperature of 80\ntimes the initial temperature, this condition was not satisfied. Thus,\nthe simulation parameters were such that the ion acoustic instability\ncould not occur. It is interesting to note, however, that the curve\ncorresponding to $u_{b\\perp} = 6v_{e0}$ in the lower frame of Fig. 1 bears\na certain resemblance to a curve in Fig. 5 of Papadopoulos' 1988\npaper (Fig. 5), showing schematically the predicted variation of\nelectron temperature with distance in\na quasi--perpendicular shock foot: in both cases, there is a very rapid rise\nin the total electron energy, resulting from strong Buneman instability,\nfollowed by a more gradual rise, which coincides in the simulations\nwith the excitation of electron\nBernstein modes. The latter may play a role in the simulations which is \nsimilar to that of the ion acoustic mode in the model of Papadopoulos. \n\n\\vskip 0.5cm\n\n\\noindent {\\bf Acknowledgements.} This work was supported by the \nCommission of the European Communitities, under TMR Network Contract \nERB--CHRXCT98-- 0168, by the UK Department of Trade and Industry, and by\nEURATOM. S. C. Chapman was supported by a PPARC lecturer fellowship.\n\n\\vskip 1.0cm\n\n\\centerline{REFERENCES}\n\n\\vskip 0.5cm\n\n\\ref{Achterberg A., Blandford R.D., Reynolds S.P., 1994, A\\&A 281, 220}\n\n\\ref{Anderson K.A., Lin R.P., Martel F., Lin C.S., Parks G.K., Reme H., 1979, \nGeophys. Res. Lett. 6, 401}\n\n\\ref{Axford W.I., Leer E., Skadron G., 1977, in: Proceedings of the 15th \nInternational Cosmic Ray Conference, Christov C.Y. (ed.), Central Research \nInstitute for Physics, Budapest, vol. 11, 132} \n\n\\ref{Bell A.R., 1978, MNRAS 182, 147} \n\n\\ref{Bessho N., Ohsawa Y., 1999, Phys. Plasmas 6, 3076}\n \n\\ref{Blandford R.D., Ostriker J.P., 1978, ApJ 221, L29} \n\n\\ref{Buneman O., 1958, Phys. Rev. Lett. 1, 8} \n\n\\ref{Cargill P.J., Papadopoulos K., 1988, ApJ 329, L29} \n\n\\ref{Denavit J., Kruer W.L., 1980, Comments Plasma Phys. Cont. Fusion 6, 35}\n\n\\ref{Devine P., 1995, Ph.D. Thesis, University of Sussex}\n\n\\ref{Galeev A.A., 1984, Sov. Phys. JETP 59, 965}\n\n\\ref{Galeev A.A., Malkov M.A., V\\\"olk H.J., 1995, J. Plasma Phys. 54, 59}\n\n\\ref{Karney C.F.F., 1978, Phys. Fluids 21, 1584} \n\n\\ref{Kirk J.G., Heavens A.F., 1989, MNRAS 239, 995} \n\n\\ref{Koyama K., Petre R., Gotthelf E.V, Hwang, U., Matsuura M., Ozaki M., Holt \nS.S., 1995, Nature 378 255}\n\n\\ref{Krymsky G.F., 1977, Dokl. Akad. Nauk. SSSR 234, 1306}\n\n\\ref{Laming J.M., 1998, ApJ 499, 309}\n\n\\ref{Leroy M.M., Winske D., Goodrich C.C., Wu C.S., Papadopoulos, K., 1982, J. \nGeophys. Res. 87, 5081}\n\n\\ref{Levinson A., 1996, MNRAS 278, 1018}\n\n\\ref{McClements K.G., Bingham R., Su J.J., Dawson J.M., Spicer D.S., 1993, \nApJ 409, 465}\n\n\\ref{McClements K.G., Dendy R.O., Bingham R., Kirk J.G., Drury L.O'C., 1997, \nMNRAS 291, 241}\n\n\\ref{Melrose D.B., 1986, Instabilities in Space and Laboratory Plasmas, \nCambridge University Press}\n\n\\ref{Papadopoulos K., 1988, Ap\\&SS 144, 535}\n\n\\ref{Pohl M., Esposito J.A., 1998, ApJ 507, 327}\n\n\\ref{Quest K.B., 1986, J. Geophys. Res. 91, 8805}\n\n\\ref{Sckopke N., Paschmann G., Bame S.J., Gosling J.T., Russell C.T., 1983, J. \nGeophys. Res. 88, 6121} \n\n\\ref{Willingale R., West R.G., Pye J.P., Stewart G.C., 1996 MNRAS 278, 479}\n\n\\ref{Woods L.C., 1969, J. Plasma Phys. 3, 435}\n\n\\newpage\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,9.0)\n\\put(0.3,2.0){\\special{psfile=figure1.ps angle=0 hscale=35 vscale=35}}\n\\put(4.4,7.9){$u_{b\\perp} = 3.25v_{e0}$}\n\\put(2.9,8.6){$3.5v_{e0}$}\n\\put(4.1,5.4){$5v_{e0}$}\n\\put(3.0,6.17){$6v_{e0}$}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Total electron perpendicular kinetic\nenergy, normalized to its initial value, versus simulation time in\nelectron cyclotron periods $2\\pi/\\Omega_e$, for several values of\n$u_{b\\perp}/v_{e0}$. Energy transfer to electrons is much more rapid at\n$u_{b\\perp} = 5v_{e0}$ and $u_{b\\perp} = 6v_{e0}$ than it is at lower\nbeam speeds.}}% \n\\label{energy1}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,10.0)\n\\put(0.3,2.0){\\special{psfile=figure2.ps angle=0 hscale=35 vscale=35}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Normalized beam proton (upper plot) and\nbackground proton (lower plot) perpendicular kinetic energies (both\nnormalized to initial electron thermal energy) versus simulation time for the\nsimulation with $u_{b\\perp} = 6v_{e0}$. The beam proton energy drops\nby less than 1\\%; the background proton energy increases by\napproximately 10\\%.}}% \n\\label{energy2}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,8.0)\n\\put(0.3,0.5){\\special{psfile=figure3.ps angle=0 hscale=35 vscale=35}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Time evolution of perpendicular electron\nkinetic energy (upper plot) and electrostatic field energy (lower\nplot) in the simulation with $u_{b\\perp} = 6v_{e0}$.}}%\n\\label{waves}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,8.0)\n\\put(0.3,0.0){\\special{psfile=figure4.ps angle=0 hscale=35 vscale=35}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Time evolution of perpendicular electron\nkinetic energy (upper plot) and electrostatic field energy (lower\nplot) in the simulation with $u_{b\\perp} = 3.25v_{e0}$.}}%\n\\label{dispersion}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,8.0)\n\\put(0.3,0.0){\\special{psfile=figure5.ps angle=0 hscale=35 vscale=35}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Base 10 logarithm of electric field\namplitude (Vm$^{-1}$) versus $\\tilde{k}$ and $\\tilde{t}$\nin the simulation with $u_{b\\perp} = 6v_{e0}$.}}%\n\\label{phasespace}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,8.0)\n\\put(0.3,0.0){\\special{psfile=figure6.ps angle=0 hscale=35 vscale=35}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Base 10 logarithm of electric field\namplitude (Vm$^{-1}$) versus $\\tilde{k}$ and $\\tilde{t}$\nin the simulation with $u_{b\\perp} = 3.25v_{e0}$.}}% \n\\label{distribution}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,11.7)\n\\put(-0.7,1.0){\\special{psfile=figure7.ps angle=0 hscale=45 vscale=45}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Time evolution of electric field\namplitude (Vm$^{-1}$) at $\\tilde{k}=1.8$ after the onset of\ninstability in the simulation with $u_{b\\perp} = 6v_{e0}$. The horizontal\nline is $E_i$ for this wave; the diagonal line shows an exponential fit to the\ngrowth rate with $\\gamma/\\Omega_e = 0.24$.}}\n\\label{amplitude6.0}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,10.0)\n\\put(0.1,9.5){\\special{psfile=figure8.ps angle=-90 hscale=35 vscale=35}}\n\\put(0.4,6.3){\\large $\\tilde{\\gamma}$}\n\\put(4.5,2.2){\\large $\\tilde{k}$}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Predicted linear growth rates of waves\nwith $\\omega > \\Omega_e$ when the beam\nspeed is $6v_{e0}$. The other dispersion relation parameters\ncorrespond to the initial conditions of all four simulations.}} \n\\label{hotbeam1}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,10.0)\n\\put(0.1,9.0){\\special{psfile=figure9.ps angle=-90 hscale=35 vscale=35}}\n\\put(0.4,6.8){\\large $\\tilde{\\gamma}$}\n\\put(4.5,2.2){\\large $\\tilde{k}$}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Predicted linear growth rates of waves\nwith $\\omega > \\Omega_e$ when the beam speed is $3.25v_{e0}$.}}\n\\label{hotbeam2}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,11.7)\n\\put(-0.7,1.0){\\special{psfile=figure10.ps angle=0 hscale=45 vscale=45}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Time evolution of electric field\namplitude (Vm$^{-1}$) at $\\tilde{k} = 3.6$ (upper plot) and $\\tilde{k}\n= 3.3$ (lower plot) after the onset of instability in the simulation\nwith $u_{b\\perp} = 3.25v_{e0}$. The vertical lines indicate a period\nin which there is an anti--correlation between the two wave\namplitudes.}} \n\\label{amplitude3.25}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,11.7)\n\\put(-0.7,0.0){\\special{psfile=figure11.ps angle=0 hscale=45 vscale=45}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Normalized perpendicular electron\nspeed distributions at various times in the simulations with $u_{b\\perp} =\n3.25v_{e0}$ (dash--dotted lines) and $u_{b\\perp} = 3.5v_{e0}$ (solid\nlines).}}\n\\label{phase1}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,10.7)\n\\put(-0.7,0.0){\\special{psfile=figure12.ps angle=0 hscale=45 vscale=45}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Normalized perpendicular electron\nspeed distributions at various times in the simulations with $u_{b\\perp} =\n5v_{e0}$ (dash--dotted lines) and $u_{b\\perp} = 6v_{e0}$ (solid\nlines).}}\n\\label{phase2}\n\\end{figure}\n\n\\begin{figure}\n\\setlength{\\unitlength}{1cm}\n\\begin{picture}(0.0,10.7)\n\\put(0.0,1.0){\\special{psfile=figure13.ps angle=0 hscale=40 vscale=40}}\n\\end{picture}\n\\parbox[b]{8.6cm}{\\caption[]{Normalized perpendicular electron\nspeed distribution at $\\tilde{t}=20$ in the simulation with $u_{b\\perp}\n=6{v}_{e0}$. The solid curve is the distribution sampled in the\nsimulation; the dashed curve shows a bi--Maxwellian fit.}}\n\\label{fit}\n\\end{figure}\n\n\\end{document}\n\n"
}
] |
[] |
|
astro-ph0002348
|
ASCA and BeppoSAX observations of the peculiar X--ray source 4U1700+24/HD154791
|
[
{
"author": "D. Dal~Fiume\\mrka"
},
{
"author": "N. Masetti\\mrka"
},
{
"author": "C. Bartolini\\mrkb"
},
{
"author": "S. Del Sordo\\mrkc"
},
{
"author": "F. Frontera\\mrkd"
},
{
"author": "A. Guarnieri\\mrkb"
},
{
"author": "M. Orlandini\\mrka"
},
{
"author": "E. Palazzi\\mrka"
},
{
"author": "A. Parmar\\mrke"
},
{
"author": "A. Piccioni\\mrkb"
},
{
"author": "A. Santangelo\\mrkc"
},
{
"author": "A. Segreto\\mrkc"
}
] |
The X-ray source 4U1700+24/HD154791 is one of the few galactic sources whose counterpart is an evolved M star \cite{ddf,garcia,gaudenzi}. In X-rays the source shows extreme erratic variability and a complex and variable spectrum. While this strongly suggests accretion onto a compact object, no clear diagnosis of binarity was done up to now. We report on \A and \B X--ray broad band observations of this source and on ground optical observations from the Loiano 1.5 m telescope.
|
[
{
"name": "1700_compton5.tex",
"string": "\\documentstyle[epsfig,graphics]{aipproc}\n\\input pstricks\n\\input ulem.sty\n\\input times.sty\n\\begin{document}\n\\def\\A{\\mbox{ASCA\\ }} \\def\\B{\\mbox{BeppoSAX\\ }} \\def\\ind{\\mbox{~~~}}\n\\def\\asm{\\mbox{RXTE/ASM\\ }} \\def\\exo{\\mbox{EXOSAT\\ }}\n\\def\\src{4U1700+24/HD154791 } \\def\\ssrc{4U1700+24 } \\def\\etal{{ et al. }}\n\\newcommand{\\lx}{\\mbox{L$_X$ }} \\newcommand{\\ergs}{\\mbox{erg s$^{-1}$ }}\n\\newcommand{\\ergcm}{\\mbox{erg cm$^{-2}$ s$^{-1}$ }}\n\\newcommand{\\mrka}{\\mbox{$^{1}$}}\n\\newcommand{\\mrkb}{\\mbox{$^{2}$}}\n\\newcommand{\\mrkc}{\\mbox{$^{3}$}}\n\\newcommand{\\mrkd}{\\mbox{$^{4}$}}\n\\newcommand{\\mrke}{\\mbox{$^{5}$}}\n\n\\title{\nASCA and BeppoSAX observations\nof the peculiar X--ray source 4U1700+24/HD154791}\n\n\\bigskip\\medskip\n\n\\author\n{D. Dal~Fiume\\mrka , N. Masetti\\mrka , C. Bartolini\\mrkb ,\nS. Del Sordo\\mrkc , F. Frontera\\mrkd , A. Guarnieri\\mrkb ,\nM. Orlandini\\mrka , E. Palazzi\\mrka , A. Parmar\\mrke ,\nA. Piccioni\\mrkb , A. Santangelo\\mrkc , A. Segreto\\mrkc }\n\n\\address\n{ \\mrka Istituto TESRE/CNR, via Gobetti 101, 40129 Bologna, Italy \\\\\n\\mrkb Dipartimento di Astronomia, Universit\\'a di Bologna, via\nRanzani 1, 40127 Bologna, Italy\\\\\n\\mrkc IFCAI/CNR, via U. La Malfa 153, 90146 Palermo, Italy\\\\\n\\mrkd Istituto TeSRE and Dipartimento di Fisica, Universit\\'a di\nFerrara, via Paradiso 1, 44100 Ferrara, Italy\\\\\n\\mrke Space Science Department, ESA, ESTEC, Noordwjik, The\nNetherlands}\n\n\\maketitle\n\\begin{abstract}\nThe X-ray source 4U1700+24/HD154791 is one of the few galactic sources\nwhose counterpart is an evolved M star \\cite{ddf,garcia,gaudenzi}.\nIn X-rays the source shows extreme erratic variability and a complex and\nvariable spectrum. While this strongly suggests accretion onto a compact\nobject, no clear diagnosis of binarity was done up to now.\nWe report on \\A and \\B X--ray broad band observations of this source and on\nground optical observations from the Loiano 1.5 m telescope.\n\\end{abstract}\n\\section{Introduction}\n\nIn optical astronomy the identification of a binary system comes in most\ncases from the\nobservation of photometric and/or radial velocity variations.\nAs not all X-ray binaries have known optical\ncounterparts, a further effective criterium in galactic X--ray\nastronomy for the identification of a binary system\nwith an accreting compact object was often based on the observed\nX--ray luminosity. For X--ray binaries harbouring a neutron star or\npossibly a black hole, luminosities \\lx of the order of\n10$^{34}$ -- 10$^{35}$ \\ergs are easily reached.\nThe diagnosis of the presence of a neutron star in most cases is\ndirectly confirmed by the observation of\npulsations or thermonuclear bursts, apart from bright persistent Low\nMass X--Ray Binaries (LMXRBs).\nX--ray binaries harbouring white dwarfs also show some distinctive\nfeatures. As an example in polars and intermediate polars optical and\nUV observations often reveal the distinctive\nsignatures of the presence of a white dwarf in the system. Orbital\nperiods and light curves also add unambiguous and reliable evidence of\nthe presence of white dwarfs in this class of X--ray binaries.\\\\\nFor a number of X--ray sources the identification of a class or even the\ndiagnosis of binarity is rather difficult, especially when the observed\nX--ray luminosity is $\\leq 10^{33}$ \\ergs.\\\\ \\src belongs to this class.\nThe optical counterpart was identified by Garcia et al. \\cite{garcia}\nas a late\ntype giant on the basis of the positional coincidence with a HEAO1--A3\nerror box. The optical spectrum of this giant looks quite normal\n\\cite{ddf,garcia}, even if Gaudenzi and Polcaro \\cite{gaudenzi}\nfind some interesting and variable features in its\nspectrum. Variable UV line emission was detected \\cite{ddf,garcia}\nin different IUE pointings, showing at last some\nunusual features in the emission from this otherwise normal giant. These\nhigh excitation lines are likely linked to the same mechanism that\nproduces the observed X--ray emission.\nIn spite of various attempts, no evidence of a binary orbit was obtained\nfrom radial velocity analysis of optical spectra.\\\\\nThe X--ray source shows extreme erratic variability, but no pulsations\nwere detected. The rapid (10--1000 s) time variability is strongly\nsuggestive of turbulent accretion, often observed in X--ray binaries.\nThe X--ray spectrum is rather energetic and was measured\nup to 10 keV.\nThe X--ray luminosity \\lx $\\sim 10^{33}$ \\ergs at an assumed\ndistance of 730 pc \\cite{garcia} may be marginally consistent\nwith coronal emission, even if an evolved giant is not expected to be a\nstrong X-ray emitter.\nTherefore the picture emerging from observations gives only hints in\nfavour of a binary system, given that no ``classical'' feature to be\nassociated to the presence of a compact object was found.\\\\\nWe have observed this source for $\\sim$15 years both with X--ray satellites\n(EXOSAT, \\A and \\B) and with ground optical observations from the Loiano\n1.5 m and 0.6 m telescopes of the Bologna Astronomical Observatory.\nHere we report on the \\A and \\B observations, performed respectively on\nMarch 8, 1995 and on March 27, 1998. We also report on photometric\noptical UBVRI monitoring.\n\n\n\\section{Observations}\n\nIn Figure 1 we show the observed 1.5--9 keV count rate from the GIS2 and GIS3\ninstruments on board \\A and the 1.5--10 keV observed count\nrate from the MECS2 and MECS3 instruments on board \\B.\nA clear increase of the \\ssrc count rate was detected in November 1997\nby RXTE/ASM ({\\em http://space.mit.edu/XTE/ASM\\_lc.html} ).\nThe \\B observation was performed approximately five months after this\nevent, when the source had already recovered its quiescent flux.\nThe substantial erratic variability already detected with \\exo \\cite{ddf}\nis clearly present also in both observations. The source\nflux in the \\B observation is significantly lower than that in the \\A\nobservation.\n\\begin{figure}[h]\n\\centerline{\n\\psfig{file=gis23_250n.eps,width=0.48\\textwidth}\\ \\psfig{file=sax_250n.eps,width=0.48\\textwidth}\n}\n\\caption{Count rate time series from the \\A and \\B observations}\n\\end{figure}\nThe erratic source variability is clearly visible in the Power Spectral\nDensity (PSD) shown in Figure 2, calculated on the time series of GIS2\nand GIS3 count rate binned on 0.1 s. The spectra were calculated for\nruns with typical duration of 3000s. The PSD shown in Figure 2 is\nobtained by averaging the spectra of different runs and by summing\nadjacent frequencies with a logarithmic rebinning.\n\\begin{figure}\n\\centerline{\n\\psfig{file=gis23_psd_n.ps,width=0.9\\textwidth,height=10truecm}\n}\n\\caption{Power Spectral Density from ASCA observation}\n\\end{figure}\nThe observed X--ray source luminosity (2--10 keV) was $L_X =\n1.7\\times10^{33}$ \\ergs in the \\A observation and $L_X=6\\times 10^{32}$\n\\ergs in the \\B observation assuming a distance of $\\sim$700 pc\n\\cite{garcia}.\\\\\nThe X--ray energy spectrum cannot be fitted by simple single component\nmodels. The high energy ($>$2 keV) spectrum can be fitted by an absorbed\nthermal continuum, but the extrapolation of such a model at lower\nenergies lies significantly below the measured spectrum, both in \\A\nand in \\B observations.\\\\\nFor a thermal model, similar to that used in the\nlow luminosity source $\\gamma$ Cas (a suspected Be/white dwarf binary\n\\cite{kubo,owens}), the addition of a complex\nabsorber (e.g. a partial absorber) is\nneeded to model the low energy part of the spectrum. The lack of Fe\nemission line however requires a very low Fe abundance.\\\\\nAs an example the count rate spectra from the \\A and \\B\nobservations fitted\nwith an optically thin thermal bremsstrahlung continuum with partial\nabsorber ({\\it ``bremss'' } and {\\it ``pcfabs'' } models in XSPEC)\nare shown in Figure 3.\nThe \\B spectrum is softer than that observed with \\A, and very\nsimilar to that observed with \\exo \\cite{ddf} at almost\nexactly the same flux level of the \\B observation.\n\\begin{figure}\n\\centerline{\n\\psfig{file=ascabrems_n.eps,width=0.5\\textwidth,height=8truecm}\\ \\psfig{file=saxbrems_n.eps,width=0.5\\textwidth,height=8truecm}\n}\n\\caption{\nLeft: fit to \\A data. Partial covering fraction: 0.75$\\pm$0.01. Temperature\nkT=6.25 $\\pm$ 0.2. Reduced $\\chi^{2}_{dof}$: 1.55\nRight: fit to \\B data. Partial covering fraction: 0.72$\\pm$0.04. Temperature\nkT=3.6 $\\pm$ 0.3. Reduced $\\chi^{2}_{dof}$: 0.9\n}\n\\end{figure}\nOptical observations were performed at the Loiano 1.5 m telescope of the\nBologna Astronomical Observatory during the last 15 years.\nHD154791, the optical counterpart of the X--ray source, is a M2--M3 giant\n\\cite{garcia,gaudenzi} with a rather normal optical\nspectrum. A simple comparison with M1--M3 III templates shows\na close match with the M2 template of HD104216.\nIn Figure 4 we report the long term UBVRI photometry of HD154791.\nNo clear long term trend is visible. Some variability is present, in\nparticular in the U measurements, that may be intrinsic to the source.\nThe long-term spectral/photometric monitoring of the source is\ncontinuing.\n\n\\begin{figure}\n\\centerline{\\psfig{file=ubvri_n_n.eps,height=7.8cm,width=0.9\\textwidth}}\n\\centerline{ }\n\\caption{UBVRI long term variability of HD154791}\n\\end{figure}\n\n\\section{Discussion}\nThe observations we report still cannot be used to perform a\n``classical'' diagnosis of binarity. We nevertheless note some\ninteresting similarities with other low luminosity X--ray sources. In\nparticular some interesting similarities can be found with the X--ray\nemission from $\\gamma$ Cas.\nThe power spectrum is strikingly similar and the energy spectrum shows a\nsimilar shape, even if no iron line is detected in \\ssrc.\n\nHowever this close resemblance of the properties of the X--ray emission\ndoes not help to determine the presence of a compact object in a binary\nsystem, as for $\\gamma$ Cas itself the diagnosis of binarity is not\ncompletely assessed. In fact Owens \\etal \\cite{owens} favour the\nhypothesis of a WD binary,\nbut a completely different point of view is based on recent UV/X--ray\nobservations of $\\gamma$ Cas \\cite{smith}. Smith \\etal support the\nhypothesis that the X--ray\nemission of $\\gamma$ Cas comes from continuous flaring from the Be star.\nThis hypothesis cannot be easily adapted to the case of \\src, as the\nmuch colder M giant star should not be expected to have strong and\npersistent X--ray flaring activity. If this is the case, i.e. the\nobserved X--ray emission from \\ssrc is coronal, HD154791 should\nbe an exception in its own class.\nIf the similarity of the properties of the X--ray emission from \\ssrc\nand $\\gamma$ Cas comes from a common origin, we suggest that the WD\nbinary hypothesis is much more comfortable and more easily met.\n\n{\\bf Acknowledgements}.\nThis research is supported by the Agenzia Spaziale Italiana (ASI) and the\nConsiglio Nazionale delle Ricerche (CNR) of Italy. \\B is a joint\nprogram of ASI and of the Netherlands Agency for Aerospace Programs (NIVR).\nThe \\A observation was performed as part of the joint ESA/Japan scientific\nprogram. CB, AG and AP acknowledge a grant from ``Progetti di ricerca\nex-quota 60\\%'' of Bologna University.\n\n\\begin{references}\n\n\\bibitem{ddf}Dal Fiume, D. \\etal 1990 {\\it Il Nuovo Cimento C}, {\\bf 13}, 481\n%\n\\bibitem{garcia} Garcia, M. \\etal 1983, {\\it ApJ}, {\\bf 267}, 291\n%\n\\bibitem{gaudenzi}\nGaudenzi, S. F., Polcaro, V. F. 1999 {\\it Astron. Astrophys.}, {\\bf\n347}, 473\n%\n\\bibitem{kubo}\nKubo, S. \\etal 1998 {\\it PASJ}, {\\bf 50}, 417\n%\n\\bibitem{owens}\nOwens, A. \\etal 1999 {\\it Astron. Astrophys}, {\\bf 348}, 170\n%\n\\bibitem{smith}\nSmith, M. A. \\etal 1998 {\\it ApJ}, {\\bf 503}, 877.\n\\end{references}\n\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002348.extracted_bib",
"string": "\\bibitem{ddf}Dal Fiume, D. \\etal 1990 {\\it Il Nuovo Cimento C}, {\\bf 13}, 481\n%\n\n\\bibitem{garcia} Garcia, M. \\etal 1983, {\\it ApJ}, {\\bf 267}, 291\n%\n\n\\bibitem{gaudenzi}\nGaudenzi, S. F., Polcaro, V. F. 1999 {\\it Astron. Astrophys.}, {\\bf\n347}, 473\n%\n\n\\bibitem{kubo}\nKubo, S. \\etal 1998 {\\it PASJ}, {\\bf 50}, 417\n%\n\n\\bibitem{owens}\nOwens, A. \\etal 1999 {\\it Astron. Astrophys}, {\\bf 348}, 170\n%\n\n\\bibitem{smith}\nSmith, M. A. \\etal 1998 {\\it ApJ}, {\\bf 503}, 877.\n"
}
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astro-ph0002349
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Mode identification from line-profile variations
|
[
{
"author": "C. Aerts\\altaffilmark{1} \\& L. Eyer"
}
] |
We review the current status of different mode-identification techniques based on observed line-profile variations. Three basic methods are currently available to identify the non-radial pulsation modes. These three methods are described, together with their different variants. We further present applications to real data, focusing especially on $\delta\,$Scuti stars. After having discussed all the methods and their applications, we present an inventory in which we compare the properties of the different methods. Finally, we end with future prospects, both on the theoretical and observational side.
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[
{
"name": "aerts.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\n\\markboth{Aerts \\& Eyer}{Mode identification from line-profile variations}\n\\pagestyle{myheadings}\n\n\\setcounter{page}{1}\n\n\\newcommand{\\ds}{\\displaystyle}\n\n\\begin{document}\n\\title{Mode identification from line-profile variations}\n\\author{C. Aerts\\altaffilmark{1} \\& L. Eyer}\n\\affil{Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Belgium\\\\\nconny@ster.kuleuven.ac.be; laurent@ster.kuleuven.ac.be}\n\\altaffiltext{1}{Postdoctoral Fellow, Fund for Scientific Research, Flanders}\n\n\\begin{abstract}\nWe review the current status of different mode-identification techniques based\non observed line-profile variations. Three basic methods are currently\navailable to identify the non-radial pulsation modes. These three methods are\ndescribed, together with their different variants. We further present\napplications to real data, focusing especially on $\\delta\\,$Scuti stars.\nAfter having discussed all the methods and their applications, we present an\ninventory in which we compare the properties of the different methods. Finally,\nwe end with future prospects, both on the theoretical and observational side.\n\\end{abstract}\n\n\\keywords{Stars: oscillations, Stars: variables: $\\delta\\,$Scuti, \nStars: variables: $\\gamma\\,$Dor, Line: profiles}\n\n\\section{Introduction}\n\nIntrinsic variable stars are an important diagnostic to test stellar models,\nwhich provide in turn valuable clues to our understanding of stellar and\ngalactic evolution. Variable stars pulsate in so-called {\\it non-radial\npulsation modes}. Since the early seventies, ample observational evidence of\nthe presence of such non-radial pulsations has become available. From then on,\ndetailed observational and theoretical studies of non-radial pulsations have\nbeen conducted. It has become clear that by understanding the pulsations in\nfull detail, one can probe the internal structure of the stars and hence\nconfront the results with stellar evolution theories, i.e., one can apply {\\it\nasteroseismology}. \n\nThe non-radial pulsations lead to periodic variations of physical quantities,\nsuch as surface brightness, radial velocity, temperature, etc. By comparing\nthe observed variations with those predicted by theory, it is in principle\npossible to determine the most important parameters that characterise the\npulsation. One specific aspect of studying pulsations therefore is to know\nwhat kind of modes are active in pulsating variables, i.e., the aspect of {\\it\nmode identification}. Specifically, mode-identification techniques try to\nassign values to the spherical wavenumbers $(\\ell,m)$: the degree and azimuthal\nnumber of the spherical harmonic $Y_{\\ell}^m$ that describes the non-radial\npulsation. The identification of non-radial pulsation modes from observational\ndata of variable stars is important, since it is a first step towards\nasteroseismology. Indeed, the amount of astrophysical information that can be\nderived from the study of non-radial pulsations depends directly on the number\nof modes that can be successfully identified.\n\nInspired by this potential of identifying the non-radial pulsation modes, the\nstudy of {\\it mode-identification techniques} has become an extended topic by\nitself in variable star research. We have been involved in the development and\nthe application of such mode-identification methods. In this review, we focus\non the different identification techniques that are currently used to identify\nnon-radial pulsations from line-profile variations.\n\nThe introduction of high-resolution spectrographs with sensitive detectors has\nhad an enormous impact on the field of mode identification. Spectroscopic data\nusually offer a very detailed picture of the pulsation velocity field. On the\nother hand, they require large telescopes and sophisticated instrumentation.\nBefore accurate detectors were available, identifications had to be obtained\nfrom photometric observations. These kind of data are suitable to study\nlong-period pulsations because they can be obtained with small telescopes,\nwhich are available on longer time scales. For a review on photometric studies\nof $\\delta\\,$Scuti stars we refer to Poretti and to Garrido (these\nproceedings).\n\nThe plan of our paper is as follows. We first briefly give a (non-mathematical)\nintroduction into the domain of non-radial pulsations. Next, we explain how a\ntheoretical line profile can be calculated for a non-radially\npulsating star. The following section is devoted to the description of the\ndifferent identification techniques: line-profile fitting, Doppler Imaging, and\nthe moment method. We briefly review the main characteristics of each method in\nSection\\,5 and we finally end with some future prospects in this\nfield of research. In particular, we point out the importance of the\nidentification of pulsation modes in $\\gamma\\,$Dor stars.\n\n\\section{Non-radial pulsations}\nWith a radial pulsation the physical parameters throughout a star vary\nperiodically along the radial direction and spherical symmetry is preserved\nduring a pulsation cycle. The differential equation describing the radial\ndisplacement is of the Sturm-Liouville type and thus allows eigensolutions that\ncorrespond to an infinitely countable amount of eigenfrequencies. The smallest\nfrequency corresponds to the fundamental radial pulsation mode. The period of\nthis mode is inversely proportional to the square root of the mean density of\nthe star. Radial pulsations are characterised by the radial wavenumber $n$: the\nnumber of nodes of the eigenfunction between the center and the surface of the\nstar.\n \nIf transverse motions occur in addition to radial motions, one uses the term\nnon-radial pulsations. The pulsation modes are then not only characterised by\na radial wavenumber $n$, but also by non-radial wavenumbers $\\ell$ and $m$. The\nlatter numbers \ncorrespond to the degree and the azimuthal number of the spherical\nharmonic $Y_{\\ell}^m$ that represents the dependence of the mode on the angular\nvariables $\\theta$ and $\\varphi$ for a star with a spherically symmetric\nequilibrium configuration (see Equation\\,(\\ref{nrp}) below). The degree $\\ell$\nrepresents the number of nodal lines, while the azimuthal number $m$ denotes\nthe number of such lines that pass through the rotation axis of the star.\nFor stars that\nare not spherically symmetric, the expansion of the eigenfunctions in terms of\nspherical harmonics is no longer obvious.\n\nA distinction is made between $p$-modes, $g$-modes, and $r$-modes. In $p$-modes, the\nrestoring force is the pressure force; radial modes can be viewed as a special\ncase of non-radial $p$-modes. In $g$-modes, the restoring force is the buoyancy\nforce; such modes have periods that are longer than the period of the radial\nfundamental mode. Finally, $r$-modes or toroidal modes are characterised by\npurely transverse motions; such modes only attain finite periods in rotating\nstars.\n\nIn the case of spheroidal modes in the approximation of a non-rotating star,\nthe pulsation velocity expressed in a system of spherical coordinates\n$(r,\\theta,\\varphi)$ centered at the centre of the star and with polar axis\nalong the symmetry axis of pulsation, is given by\n\\begin{equation}\n\\label{nrp}\n\\ds{\\vec{v}_{\\rm puls}=\n\\left(v_r,v_{\\theta},v_{\\varphi}\\right)=N_{\\ell}^mv_{\\rm p}\n\\left(1,K\\frac{\\partial}{\\partial\\theta},\\frac{K}{\\sin\\theta}\n\\frac{\\partial}{\\partial\\varphi}\\right)Y_{\\ell}^m(\\theta,\\varphi)\n\\exp{\\left({\\rm i}\\omega t\\right)}\n}\n\\end{equation}\n(e.g., see Smeyers 1984, Unno et al.\\ 1989).\nIn this expression, $N_{\\ell}^m$ is the normalisation factor for the\n$Y_{\\ell}^m(\\theta,\\varphi)$ over the visible hemisphere of the star, $v_{\\rm\np}$ is the pulsation amplitude, $\\omega$ is the pulsation frequency, \nand $K$ is the ratio of the horizontal to the vertical velocity amplitude. The\nlatter can be found from the boundary conditions: $K=GM/(\\omega^2R^3)$. \nThe sign of the azimuthal number $m$ describes how the mode progresses with\nrespect to the rotation of the star. We here adopt the convention that positive\n$m$-values represent waves that travel opposite to the rotation (retrograde\nmodes), while negative $m$-values are associated with modes that travel in the\ndirection of the rotation (prograde modes). Modes with $m=0$ are axisymmetric\nmodes, while those with $\\ell=|m|$ are called sectoral modes. In all other\ncases ($\\ell\\neq |m|$ and $m\\neq 0$) one speaks of tesseral modes.\n\nA caveat for many analyses on non-radial pulsations is that the theoretical\nframework that is used only applies in the slow-rotation approximation, i.e.,\nin the case where the effects of the Coriolis force and of the centrifugal\nforces can be neglected in deriving an expression for the components of the\npulsation velocity. We emphasize that it is not allowed to describe an\noscillation mode for a rotating star in terms of a single spherical harmonic,\nand so to ascribe a single set of wavenumbers ($\\ell,m$) to a mode. The\nCoriolis force, for instance, introduces a transverse velocity field that is of\nthe same order of magnitude as the pulsation velocity for a non-rotating star\nif the ratio $\\Omega/\\omega$ of the rotation frequency to the pulsation\nfrequency approaches unity. In particular, we have studied the effect of the\nCoriolis force on line-profile variations in the \ncase of $p$-modes (Aerts \\& Waelkens\n1993) and we have found that the line profiles can be largely influenced for\nsome stellar parameters. A comparable study for $g$-modes was presented\nby Lee \\& Saio (1990). For stars having $\\Omega/\\omega\\approx 1$ or larger,\nthe centrifugal forces also become important. Including the latter enormously\nincreases the complexity of the mathematical treatment of the problem, because\ndeviations from spherical symmetry have to be taken into account. It is clear\nthat $\\Omega/\\omega$-values, which are too large to be neglected if the aim is\nto obtain an accurate description of the pulsation, are met in several stars\ndiscussed in the literature. A re-evaluation of observed line profiles in rapid\nrotators is therefore necessary in some cases.\n\n\\section{Line-profile variations}\n\nThe velocity field caused by the non-radial pulsation(s) leads, through Doppler\ndisplacement, to periodic variations in the profiles of spectral lines.\nTheoretical line-profile variations can be calculated in the following way.\nConsider a system of spherical coordinates $(r,\\theta,\\varphi)$ with the polar\naxis coinciding with the direction to the observer. The velocity field due to\nthe rotation and the pulsation leads to a Doppler shift at a point\n$(R,\\theta,\\varphi)$ on the visible surface of the star. The local\ncontribution of a point $(R,\\theta,\\varphi)$ to the line profile is\nproportional to the projected intensity of that\npoint. We approximate this projected intensity as follows.\nWe divide the stellar surface into a number of \ninfinitesimal surface elements, which, for computational purposes, have \nfinite dimensions. Next, we assume that\nthe intensity $I_{\\lambda}(\\theta,\\varphi)$ \nis the same for all points of the considered surface element.\nThe projected intensity of the surface element\nsurrounding the point $(R,\\theta,\\varphi)$ then\nis the product of the intensity $I_{\\lambda}(\\theta,\\varphi)$ \nand the projection on the line\nof sight of the surface element around the considered point:\n\\begin{equation}\nI_{\\lambda}(\\theta,\\varphi)R^2\\sin\\theta\\cos\\theta\\ d\\theta\\ d\\varphi.\n\\end{equation}\n\nBecause of variations of the intensity over the stellar surface, and of the\ntemperature dependence of an absorption line, the contributions of the\ndifferent points on the visible stellar surface to the line profile have a\ndifferent amplitude. \nIn first instance, however, one assumes that \nthe perturbations of the intensity and of the\nsurface affect the line profile only slightly. These effects are therefore\nneglected and it is assumed that\n\\mbox{$\\delta I_{\\lambda}(\\theta,\\varphi)=0$} during the pulsation. \nThe time dependence of the intensity is important when the spectral \nline\nis sensitive to the temperature and when the temperature differs for different\npoints on the stellar surface. This time dependence is also neglected in most\ncalculations.\n\nThe most important effect that then changes the projected intensity over the\nvisible surface is the limb darkening. Usually, the intensity is assumed to be\nisotropic in the $\\varphi$ coordinate and \nthe $\\theta$-dependence of the\nintensity is described by a limb-darkening law of the form\n\\begin{equation}\n\\label{randverduistering}\nh_{\\lambda}(\\theta)=1-u_{\\lambda}+u_{\\lambda}\\cos\\theta,\n\\end{equation}\nwhere $u_{\\lambda}\\in [0,1]$ is called the limb-darkening coefficient; it\ndepends on the considered wavelength range. Wade \\& Rucinski (1985) have\ntabulated limb-darkening coefficients in terms of temperature, gravity\nand wavelength.\nThe projected intensity of a surface element centered around the point\n$P(R,\\theta,\\varphi)$ with size $R^2\\sin\\theta\\ d\\theta\\ d\\varphi$ then is\n\\begin{equation}\n\\label{energie}\nI_0h_{\\lambda}(\\theta)R^2\\sin\\theta\\cos\\theta\\ d\\theta\\ d\\varphi,\n\\end{equation}\nwhere $I_0$ is the intensity at $\\theta=0$.\n\nIn order to take into account intrinsic broadening effects, the local line\nprofile is convolved with an intrinsic profile, which we take to be Gaussian\nwith variance ${\\sigma}^2$, where $\\sigma^2$ depends on the spectral line\nconsidered. Generalisations to an intrinsic Voigt profile or a profile derived\nfrom a stellar atmosphere model are easily performed.\n\nLet us represent by $p(\\lambda)$ the line profile and by ${\\lambda}_{ij}$ the\nDoppler-corrected wavelength for a point on the star with coordinates\n$({\\theta}_i,{\\varphi}_j)$, i.e.,\n\\begin{equation}\n\\ds{\\frac{{\\lambda}_{ij}-{\\lambda}_0}{{\\lambda}_0}=\n\\frac{\\lambda ({\\theta}_i,{\\varphi}_j)-{\\lambda}_0}{{\\lambda}_0}=\n\\frac{\\triangle \\lambda({\\theta}_i,{\\varphi}_j)}{{\\lambda}_0}=\n\\frac{v({\\theta}_i,{\\varphi}_j)}{c}}\n\\end{equation}\nwith $v({\\theta}_i,{\\varphi}_j)$ the component of the \nsum of the pulsation and rotation velocity\nof the considered point in the line of sight. An explicit expression for\n$v({\\theta}_i,{\\varphi}_j)$ can be found in e.g., Aerts et al.\\ (1992). The\nline profile can then be approximated as\n\\begin{equation}\n\\label{conv}\n\\ds{p(\\lambda)=\\sum_{i,j}\n\\frac{I_0h_{\\lambda}({\\theta}_i)}\n{\\sqrt{2\\pi}\\sigma}\n\\exp{\n\\left(\n{-\n\\frac{(\\lambda_{ij}-\\lambda)^2}{2\\sigma^2}\n}\n\\right)\n} R^2\\sin\\theta_i\\cos\\theta_i\\triangle\\theta_i\\triangle\\varphi_j},\n\\end{equation}\nwhere the sum is taken over the visible stellar surface\n($\\theta\\in[0^{\\circ},90^{\\circ}], \\varphi\\in[0^{\\circ},360^{\\circ}[$).\n\\begin{figure}\n\\mbox{\\epsfxsize=.3\\textwidth\\epsfysize=0.9\\textwidth\\epsfbox[0 0 250 500]\n{aerts1.ps}}\n\\mbox{\\epsfxsize=.3\\textwidth\\epsfysize=0.9\\textwidth\\epsfbox[0 0 250 500]\n{aerts2.ps}}\n\\mbox{\\epsfxsize=.3\\textwidth\\epsfysize=0.9\\textwidth\\epsfbox[0 0 250 500]\n{aerts3.ps}}\n\\caption{Theoretically determined line-profile variations calculated by means of\nthe basic formalism given in Section\\,3. We used an $\\ell=2$ mode and \nrespectively\n$m=0$ (left panel), $m=-1$ (middle panel), and $m=-2$ (right panel). The other\nvelocity parameters are: $v_{\\rm p}=5\\,$km/s, $v\\sin\\,i=30\\,$km/s, \n$\\sigma=4\\,$km/s, and $i=55^{\\circ}$. The phase of each profile increases from \n0.0 (lowest profile) to 1.0 (highest profile) in steps of 0.05. }\n\\end{figure}\n\nWe show in Figures\\,1 and 2 sets of theoretically calculated profiles for\n$\\ell=2$ and $\\ell=6$ modes. The profiles in Figure\\,1 are for prograde modes, \nthose in\nFigure\\,2 for retrograde modes. The other velocity parameters are \n$v_{\\rm p}=5\\,$km/s, $v\\sin\\,i=30\\,$km/s, $\\sigma=4\\,$km/s, and $i=55^{\\circ}$.\nOther studies in which theoretical profiles are given are published by Kambe \\&\nOsaki (1988) and by Schrijvers et al.\\ (1997).\n\n\\begin{figure}\n\\mbox{\\epsfxsize=.3\\textwidth\\epsfysize=0.9\\textwidth\\epsfbox[0 0 250 500]\n{aerts4.ps}}\n\\mbox{\\epsfxsize=.3\\textwidth\\epsfysize=0.9\\textwidth\\epsfbox[0 0 250 500]\n{aerts5.ps}}\n\\mbox{\\epsfxsize=.3\\textwidth\\epsfysize=0.9\\textwidth\\epsfbox[0 0 250 500]\n{aerts6.ps}}\n\\caption{The same as in Figure\\,1, but for \n$\\ell=6$ with $m=+2$ (left panel), \n$m=+4$ (middle panel), and $m=+6$ (right panel).}\n\\end{figure}\n\nIdeally, the calculation for the line profile described above should be\ngeneralised in order to take into account the following additional\ntime-dependent effects: a variable surface normal, a variable intensity through\nnon-adiabatic temperature variations, a variable intrinsic profile, Coriolis\nand centrifugal correction terms to the pulsation velocity expression. The most\nup-to-date code that takes into account some of these effects is written by\nTownsend (1997). He used Lee et al.\\ 's (1992) formalism to take into account\nrotation effects. This formalism incorporates the Coriolis force for all\nvalues of $\\Omega/\\omega$, but neglects the centrifugal forces, which are $\\sim\n\\Omega^2$. A variable surface normal is taken into account, but the intensity\nvariations are still assumed to be adiabatic according to the approximation\npresented by Buta \\& Smith (1979). This user-friendly code published by\nTownsend (1997) is available upon request from the author.\n\n\\section{Identification techniques}\n\nIn this section, we describe the different methods that are used to identify\nmodes. It is clear that the velocity expression based on the non-radial\npulsation model presented above contains many free parameters, even in the\nsimple formulation in which rotational and non-adiabatic effects are neglected.\nEspecially the infinity of candidate modes is a problem when constructing\nidentification techniques and it often keeps the predictive power of the\nmethods low. This is in particular the case for the methods that are based on a\ntrial-and-error principle. We point out that quantitative methods are better to\nobtain a reliable mode identification. This need for quantitative methods has\nbecome apparent since more and more detailed spectroscopic analyses have\nrevealed that multimode pulsations are often present. Below, we treat three\nmethods, more or less in the order of their appearance in the literature.\n\nIn describing the methods, we assume that the pulsation frequencies have been\ndetermined from the observables of the variable stars. For a description of the\ndifferent methods used to derive the modal frequencies, we refer to the review\nof Mantegazza: Mode detection from line-profile variations (these proceedings).\nWe pay special attention to describe applications to $\\delta\\,$Scuti stars in\nthis paper. For a review on identification methods applied to OB-type variables\nwe refer to Aerts (1994).\n\n\n\\subsection{Objective line-profile fitting}\n\nSince Osaki (1971) computed theoretical line profiles for various non-radial\npulsations, the identification of modes from spectroscopic observations has\nbecome possible. The identification of non-radial pulsation modes from\nline-profile variations was first achieved by line-profile fitting on a\ntrial-and-error basis. The idea is to compare the observed line-profile\nvariations with those predicted by theoretical calculations. This technique\nwas the first one in use to identify modes from spectroscopic observations.\n\\begin{figure}\n%\\mbox{\\epsfxsize=.9\\textwidth\\epsfysize=.9\\textwidth\\epsfbox[50 200 570 700]\n\\mbox{\\epsfxsize=1.07\\textwidth\\epsfysize=1.07\\textwidth\\epsfbox[75 200 570 700]\n{aerts7.ps}}\n\\caption{Observed (dots) and theoretical line-profile variations of the\n$\\delta\\,$Scuti star $\\rho\\,$Puppis. The full line is a model for a radial\npulsation while the dashed line is a model for which only rotational broadening\nappears. V stands for the projected rotation velocity, M for the intrinsic\nbroadening, and A for the amplitude of the pulsation; these three velocities\nare indicated next to each panel and are expressed in km/s. Figure taken with\npermission from Campos \\& Smith (1980b).}\n\\end{figure}\n\\begin{figure}\n\\mbox{\\epsfxsize=1.\\textwidth\\epsfysize=1.\\textwidth\\epsfbox[150 20 570 520]\n{aerts8.ps}}\n\\caption{Line-profile variations of the $\\delta\\,$Scuti\nstar $\\rho\\,$Puppis observed with the CAT/CES of ESO by Mathias et al.\\ (1997).\n The quality of these data are much better than those\npresented in Figure\\,3. They have revealed the presence of\nadditional small-amplitude modes, besides the main radial mode.}\n\\end{figure}\n\nPioneering work in the field of line-profile fitting was done by M. Smith and\nhis collaborators. They obtained line profiles for various types of pulsating\nstars. We show in Figure\\,3 their observed line profiles,\nrepresented as dots, of the $\\delta\\,$Scuti star $\\rho\\,$Puppis (Campos \\&\nSmith 1980b). The theoretical profiles that are presented by the full line\nare constructed with a radial mode. The dashed curves represent rotationally\nbroadened lines, i.e., lines for a non-pulsating star. These dashed lines show\nthat the line profiles of $\\rho\\,$Puppis are indeed variable in time because of\nthe pulsation of the star. The representation by the full line is rather\nfaithful and the authors concluded that the star pulsates radially. Later on,\nit was found by means of the moment method applied to more recent spectra (see\nFigure\\,4 and Section\\,4.3) that the main mode is indeed\nradial, but that at least one, and probably two, additional small-amplitude\nmodes are present in $\\rho\\,$Puppis (Mathias et al.\\ 1997), a conclusion\nthat would have been very hard to obtain by means of the fitting technique.\n\nIn the seventies and early eighties, the fitting technique by trial-and-error\nwas very popular, simply because it was the only one available. Besides\napplications in the case of $\\delta\\,$Scuti stars (Campos \\& Smith 1980b, Smith\n1982), the technique was also applied to line-profile variations of\n$\\beta\\,$Cephei stars (Smith 1977, 1983; Campos \\& Smith 1980a), Be stars\n(e.g., Vogt \\& Penrod 1983, Baade 1984), and the so-called 53\\,Per stars (Smith\n1977, Smith et al.\\ 1984). Smith (1982) describes mode-typing for 9\n$\\delta\\,$Scuti stars by means of line-profile fitting. Most of the results\nthat he obtained are still valid today as far as the main modes of the stars\nare concerned.\n\nAs already mentioned, the main disadvantage of the trial-and-error line-profile\nfitting is the large number of free parameters that appear in the velocity\nexpression due to the non-radial pulsation. In principle, the complete free\nparameter space has to be scanned before a decision on the best mode can be\nobtained. This was not yet possible some 15 years ago, because it was\ncomputationally too demanding. For this reason, only a limited number of\ncombinations were tried out, with the result that the identification technique was not very\nobjective. Moreover, the non-radial pulsation model can be quite successful in\nreproducing the line profiles observed on a short time scale \nfor different sets of input parameters, i.e., the\nfitting technique does not necessarily lead to a unique solution. We also\npoint out (see Aerts et al.\\ 1992, Aerts \\& Waelkens 1993) that the apparent\nquality of some fits is suspect in the sense that in early modeling, one\nneglected temperature variations and rotational effects, which obviously must\naffect the profiles in some cases (Lee et al.\\ 1992).\n\nOther problems that appeared in early applications of the line-profile-fitting\ntechnique are caused by the often very limited time base of the data, because\nof which it was sometimes necessary to assume that modes temporarily disappear\nin order to re-obtain good fits for new data that span a longer time scale.\nAlso, the values found for the intrinsic profile sometimes had to be varied\nfrom one night to another in order to obtain reliable fits. In the case of\nrapidly rotating stars, one usually assumed equator-on geometries and\nhigh-degree sectoral modes because these are the ones that best reproduce the\nobserved moving bump phenomenon. Finally, it was mentioned, but most often not\ntaken into account for applications to rapid rotators, that one used an\nexpression for the pulsation velocity that is related to one spherical\nharmonic. This is, however, only valid in the case of a non-rotating star. All\nthe abovementioned assumptions were introduced in an {\\it ad hoc} fashion and\ncast doubt on the reliability of the model.\n\nNowadays, it is possible to identify the pulsation mode by performing\nline-profile fitting in an objective way. This can be achieved by calculating a\nkind of overall standard deviation per wavelength pixel between theoretically\ndetermined and observed profiles for a large grid of possible wavenumbers and\nvelocity parameters. In order to do so, one needs a large homogeneous data set\nof high-resolution profiles that are well-spread over the period that appears\nin the line-profile variability. The theoretical limitations of the model have\nalso mostly been overcome by now, as explained in Section\\,3.\n\nA plus point of objective line-profile fitting is that both the wavenumbers\n($\\ell,m)$ and all the other velocity parameters are derived. In this way, the\ncomplete motion due to pulsation can be reconstructed once the best fit is\nselected. \n\nTHE major drawback of objective line-profile fitting is that it is still\nlimited to a monoperiodic pulsation. Indeed, it is in practice impossible to\nconsider combinations of all kinds of different modes to fit the data without\nany restriction on the parameters. It is nevertheless useful to use fitting for\nmultiperiodic stars, once estimates of the spherical wavenumbers and the\nvelocity parameters are at hand from other methods such as those presented in the\nfollowing two sections.\n\n\n\\subsection{Doppler Imaging}\n\nIn recent spectroscopic studies, a lot of attention has been paid to the\nline-profile variations of rapidly rotating OB stars. This has been in\nparticular the case since it was recognised that the line profiles of rapid\nrotators allow a Doppler Imaging of the stellar surface (Vogt et al.\\\n1987), so that a mapping of the velocity over this surface is possible (Baade\n1987).\n\n\\begin{figure}\n\\mbox{\\epsfxsize=0.9\\textwidth\\epsfysize=0.9\\textwidth\\epsfbox[30 170 550 730]\n{aerts9.ps}}\n\\caption{Grey-scale representation of the observed line-profile variations of\n$\\varepsilon\\,$Per. The spectra are residuals with respect to the global\naverage line profile, shown as full line in the lower panel. The dashed line is\nthe nightly average profile. Darker shades indicate a depression relative to\nthe mean line while bright regions correspond to places where the profile is\nshallower than the mean. Figure taken from Gies \\& Kullavanijaya (1988) with\npermission.}\n\\end{figure}\n\nGies \\& Kullavanijaya (1988) first presented an objective criterion based on\nDoppler Imaging to determine the periods and pulsation parameters of the modes\nin the rapidly rotating line-profile variable B\\,0.7\\,III star\n$\\varepsilon\\,$Per. In Figure\\,5 we show a grey-scale representation of the\nresidual line-profile variations (with respect to the global symmetric line\nprofile) of $\\varepsilon\\,$Per obtained on 26 November 1996. Black denotes\nlocal deficiencies of the flux and white local increments. Gies \\& Kullavanijaya\nnoted that emission patterns that move through the line profile during the\npulsation cycle are easily detected and visualised in such a representation.\nThis way of presenting data has since then become very popular. Fourier\nanalysis of the line-profile variations at each wavelength point yields the\nperiods of the variations by frequency peaks in the resulting periodogram.\n\nSubsequently, the azimuthal number $m$ is obtained by considering the number of\nphase changes $\\triangle$(Phase) \nat each signal frequency versus the line position. These observed\nphase changes are shown in Figure\\,6 in the case of the four\nfrequencies detected by Gies \\& Kullavanijaya in their line-profile variations\nof $\\varepsilon\\,$Per. The basic idea behind the estimation of $m$ is the\nfollowing. Let us {\\bf assume} that sectoral modes are excited, that we are\ndealing with an equator-on view and that the bump motion is caused by the large\nrotation of the star. Since each of the three components of $\\vec{v}_{\\rm puls}$\nis proportional to $\\exp{\\left({\\rm i}(\\omega t + m\\varphi)\\right)}$,\nthe phase decreases by $m/2$ cycles between the blue and the red wing of the\nprofile. In this way, an upper limit of $m$ is given by 2$\\triangle$(Phase).\nOn the other hand,\n\\begin{equation}\n\\ds{\\frac{d{\\rm Phase}/d\\varphi}{dV_{\\rm rot}/d\\varphi}=\n\\frac{m/2\\pi}{V_{\\rm eq}\\sin\\,i\\sin\\theta\\cos\\varphi}},\n\\end{equation}\nwhere $V_{\\rm rot}$ is the component of the rotation velocity in the\nline-of-sight and $V_{\\rm eq}$ stands for the equatorial rotation speed.\nIn this way,\n\\begin{equation}\n2\\pi (V_{\\rm eq}\\sin\\,i)\n\\ds{\\frac{d({\\rm Phase})}{dV_{\\rm rot}}}\n\\end{equation}\nis a lower limit for $m$. By calculating both limits, one obtains an estimate\nof the azimuthal number of the mode.\n\n\\begin{figure}\n%\\mbox{\\epsfxsize=0.9\\textwidth\\epsfysize=0.9\\textwidth\\epsfbox[300 130 570 600]\n\\begin{center}\n\\mbox{\\epsfxsize=0.78\\textwidth\\epsfysize=0.78\\textwidth\\epsfbox[300 135 565 577] \n{aerts10.ps}} \n\\end{center}\n\\caption{\nThe phase of the power spectrum of the line-profile variations of\n$\\varepsilon\\,$Per as a function across the line profile. Each plot corresponds\nto the phases at the peak frequencies S3, S4, S5, S6 that were found in the\nprofile variations. An estimate of the azimuthal number $m$ is derived from\nthese phase changes (see text for an explanation). Figure taken from Gies \\&\nKullavanijaya (1988) with permission.}\n\\end{figure}\n\\begin{table}\n\\caption{The limits for the azimuthal number $m$ for the star\n$\\varepsilon\\,$Per as derived by Gies \\&\nKullavanijaya (1988)}\n\\begin{center}\n\\tabcolsep=8pt\n\\begin{tabular}{cccc}\n\\tableline\n{Signal}&{Lower Limit}&{Upper limit}&{Adopted}\\\\\n\\tableline\nS3 & -3.93 & -2.98 & -3 \\\\\nS4 & -4.42 & -3.60 & -4 \\\\\nS5 & -5.15 & -4.46 & -5 \\\\\nS6 & -6.90 & -5.20 & -6\n\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\nIn Table\\,1 we list the limiting values for the azimuthal number $m$ obtained\nby Gies \\& Kullavanijaya (1988) from the observed phase changes shown in\nFigure\\,6. Additional frequencies and interpretations of the line-profile\nvariability of $\\varepsilon\\,$Per \nare available by now (see e.g., Gies et al.\\ 1999), but we do not\nwant to describe the details here since the $\\varepsilon\\,$Per case was only\ngiven as an example of the method.\n\nA major disadvantage of the Doppler Imaging method as proposed by Gies \\&\nKullavanijaya (1988) is that equator-on-viewed sectoral modes are assumed\nwithout a real physical argument. For this and also other reasons, a number of\ngeneralisations of the method have been proposed in the literature. Merryfield\n\\& Kennelly (1993) propose to use the Doppler Imaging principle to obtain the\nwavenumbers by considering a two-dimensional Fourier transform, which leads to\npower diagrams as a function of the frequency and as a function of \nwhat they call the\n``apparent'' azimuthal number \\it{\\^m}\\rm. They propose that\n\\it{\\^m}\\rm\\ may be \nan estimate of the degree rather than the azimuthal number in\nthe case of tesseral modes. This finding was unambiguously proven \nfor the first time for all\nconsidered modes by Telting \\& Schrijvers (1997), who performed an extensive\nsimulation study to evaluate the Doppler Imaging method as an identification\nmethod. They also found that the phase variation for the first harmonic of the\nfrequency contains information on the azimuthal number $m$. So far, Schrijvers \n\\& Telting applied their method to (new) $\\beta\\,$Cep stars \n(for an overview of their applications, see Schrijvers 1999).\n\nKennelly \\& collaborators (Kennelly et al.\\ 1992a: $\\tau\\,$Peg; 1992b:\n$\\gamma\\,$Boo; 1996: $\\theta^2\\,$Tau; 1998a: $\\varepsilon\\,$Cep) \nare the only ones\nso far who have actually used the Doppler Imaging principle to obtain the\nwavenumbers for a group of rapidly rotating $\\delta\\,$Scuti stars. Hereto, they\ngathered numerous high-quality spectra and they considered a two-dimensional\nFourier transform. Their latest technique consists of the following two steps:\n\\begin{itemize}\n\\item\nperform a DDLPV: Doppler Deconvolution of line-profile variations. First, one\nderives the intrinsic profile $\\psi(v)$ from the deconvolution\n${\\overline\\phi} (v) = R(v) \\ast\n\\psi(v)$, where ${\\overline\\phi} (v)$ is the time-averaged line profile and\n$R(v)$ the rotationally broadened profile. As first guess for $\\psi$, the\nsynthetic spectrum from a model atmosphere is taken. Subsequently, the observed\ntime-dependent pulsationally broadened components $\\phi(v,t)$ of the spectra\nare modeled from the deconvolution $\\phi(v,t) = B(v,t) \\ast \\psi(v)$. As\ninitial guess for $\\phi$ they take the rotational broadening $R$.\n\nIn Figure\\,7 we show the result of the DDLPV technique applied by\nKennelly et al.\\ (1998a) to their line-profile variations of the $\\delta\\,$Scuti\nstar $\\varepsilon\\,$Cep.\n\\item\nperform FDI: Fourier Doppler Imaging, by remapping the time-variable component\nof $B(v,t)$ from velocity to Doppler space $B(\\phi,t)$ by means of\n$\\phi_i=\\sin^{-1} (v_i/v\\sin\\,i)$. Next, the two-dimensional Fourier transform\nof $B(\\phi,t)$, and the corresponding amplitude spectrum, is computed.\n\\end{itemize}\nWe refer to Kennelly et al.\\ (1998b) for more details, but we point out here\nthat $\\overline{\\phi}(v)$ also contains a broadening component due to the\npulsation which is not taken into account by the authors. \n\n\\begin{figure}[t]\n\\mbox{\\epsfxsize=0.9\\textwidth\\epsfysize=0.7\\textwidth\\epsfbox[-10 -10 530 230] \n{aerts11.ps}} \n\\caption{Time series of broadening functions of $\\varepsilon\\,$Cep \nusing the DDLPV \ntechnique (see text for an explanation). The profiles are plotted as a function \nof Doppler shift and time. Patterns of variation owing to the pulsations of the \nstar can be seen as bumps which travel through the profiles. Figure taken from \nKennelly et al. (1998a) with permission.} \n\\end{figure}\n\nThe only assumption\nthat Kennelly et al.\\ (1998a)\n use is that the rotation causes the bump motion (i.e., $v \\ll \nv\\sin\\,i$) and that an accurate estimate of the rotational velocity is known.\nWe show in Figure\\,8 the two-dimensional amplitude spectrum of \n$\\varepsilon\\,$Cep,\nobtained from Fourier Doppler Imaging of the time-variable component of the\nbroadening function in Doppler space and time. The measured frequencies are\nindicated as crosses (Kennelly et al.\\ 1998a).\n\\begin{figure}\n\\mbox{\\epsfxsize=0.9\\textwidth\\epsfysize=0.7\\textwidth\\epsfbox[-10 -10 530 530]\n{aerts12.ps}}\n\\caption{The two-dimensional Fourier amplitude spectrum and frequency analysis\nof $\\varepsilon\\,$Cep. \nThe spectrum was computed using the Fourier Doppler Imaging technique (see text\nfor an explanation). The window function for the spectrum is illustrated as an\ninset. The frequencies identified by the two-dimensional frequency analysis are\nindicated as crosses. Figure taken from Kennelly et al.\\ (1998a) with\npermission.}\n\\end{figure}\n\nThe Doppler Imaging technique is not really suited to analyse data sets that\ncontain very few spectra per night. In this sense, its applicability is limited\nto short-period pulsators (i.e., $p$-mode pulsators) for which one usually\nfocuses on one or a few stars per night during an observing mission with a\ntime base of typically a week. The observing strategy with long-term\nspectroscopy, which is necessary to analyse the line-profile variations of\n$g$-mode pulsators, is totally different. In this case one takes a large sample\nof stars which are each measured between two and five times per night during\nweeks that are in their turn separated by months (for an example of a long-term\nspectroscopic project, see Aerts et al.\\ 1999a). Grey-scale representations and\nidentification methods as the ones shown in Figure\\,5 and\nFigure\\,6 become meaningless in this case, the more so because most\n$g$-mode pulsators found up to now are slow rotators.\n\nTHE major problem with the Doppler Imaging technique, in whatever form, is that\nthe spherical wavenumbers are estimated from diagnostics that are not\nimmediately interpretable in terms of the physics involved in the pulsational\ndisplacement. Indeed, the underlying mathematical basis for this method is\nlacking. A first effort to link the physical quantities directly to the\namplitude and phase in Fourier space was undertaken by Hao (1998). This effort\ndid not lead to new results compared with those already obtained by Telting \\&\nSchrijvers (1997) from their simulation study and does not give any information\non the velocity parameters other than the degree of the pulsation. In fact,\nonly one, and in the best case the two, wavenumber(s) is (are) estimated as\nreal number(s) from the observed phase changes. A real value of $\\ell$ and $m$\nhas, however, no physical meaning. Moreover, no information can be derived,\nfor example, for\nthe amplitude of the pulsation and for the inclination angle. On the\nother hand, multiperiodicity is easily taken into account, contrary to the\nother methods. We therefore advise to combine Doppler Imaging with line-profile\nfitting once the best estimates of $(\\ell,m$) for each of the modes are\nobtained. We finally recall that the method is only applicable to rapid\nrotators because of the basic assumption that the rotation carries bumps across\nthe profiles. For the same reason it is also unsuitable to detect axisymmetric\nmodes ($m=0)$ and low-degree tesseral modes.\n\n\\subsection{The moment method}\nAs an alternative to the line-profile-fitting technique, Balona\n%(1986a,b;\\linebreak[3]1987;\\linebreak[3]1990) proposed a new method to identify\n(1986a, b; 1987; 1990) proposed a new method to identify\nthe modes from line-profile variations:~{\\it the moment method}. This method is\nbased on the time variations of the first few moments of a line profile. We\nhave extended this method and applied it for the first time to line-profile\nvariations of a real star, namely the monoperiodic $\\beta\\,$Cephei star\n$\\delta\\,$Ceti (Aerts et al.\\ 1992). In the meantime, this method turned out to\nbe the best identification technique for slow rotators. \nWe here briefly sketch the basic ideas of\nthe moment method in our formulation (see Aerts 1996 for the latest version).\n\nSince a line profile is a convolution (see Equation\\,(\\ref{conv})) of an\nintrinsic profile (here denoted by $g(v)$) and the intensity in the direction\nof the observer integrated over the visible surface (denoted by $f(v)$), the\n$n$th moment of a line profile $(f\\ast g)(v)$ is defined as\n\\begin{equation}\n\\label{defmom}\n<v^n>_{f\\ast g}\\equiv {\\displaystyle{\\int_{-\\infty}^{+\\infty}}v^n f(v)\\ast\ng(v)\\,dv \\over\n\\displaystyle{\\int_{-\\infty}^{+\\infty}}f(v)\\ast g(v)\\,dv},\n\\end{equation}\nwhere $v$ is the total velocity component in the line of sight. In principle,\nall the moments are needed to give a complete description of the line profile,\nbut we have shown that the first three moments contain enough information to\naccurately describe the profiles (Aerts et al.\\ 1992, De Pauw et al.\\ 1993).\nNote that normalised moments are considered such that they are only slightly\ninfluenced by temperature variations and by uncertainties in the intrinsic\nprofile.\n\nWe have shown that, in the slow-rotation approximation, the first three moments\nof a monoperiodic pulsation with frequency $\\omega$ are given by~:\n\\begin{equation}\n\\label{mono1}\n<v>_{_{f\\ast g}}=v_{\\rm p}A(\\ell,m,i)\\sin[(\\omega-m\\Omega)t+\\psi],\n\\end{equation}\n\\begin{equation}\n\\label{mono2}\n\\renewcommand{\\arraystretch}{1.5}\\begin{array}{ll}\n<v^2>_{_{f\\ast g}}=\\!\\!\\!&v_{\\rm p}^2C(\\ell,m,i)\n{\\sin[2(\\omega-m\\Omega)t+2\\psi+\\frac{3\\pi}{2}]}\\\\ &+v_{\\rm\np}v_{_{\\Omega}}D(\\ell,m,i){\\sin[{(}\\omega-m\\Omega)t+\\psi+\\frac{3\\pi}{2}]}\\\\\n&+v_{\\rm p}^2E(\\ell,m,i)+\\sigma^2+b_2v_{_{\\Omega}}^2,\\end{array}\n\\end{equation}\n\\begin{equation}\n\\label{mono3}\n\\renewcommand{\\arraystretch}{2}\\begin{array}{ll}\n<v^3>_{_{f\\ast g}}=\\!\\!\\!&v_{\\rm p}^3F(\\ell,m,i)\n\\sin[3(\\omega-m\\Omega)t+3\\psi]\\\\\n&+v_{\\rm\np}^2v_{_{\\Omega}}G(\\ell,m,i){\\sin[2{(}\\omega-m\\Omega)t+2\\psi+\\frac{3\\pi}{2}]}\\\\\n&+\\left[v_{\\rm p}^3R(\\ell,m,i)+v_{\\rm p}v_{_{\\Omega}}^2S(\\ell,m,i)+v_{\\rm\np}\\sigma^2T(\\ell,m,i{)}\n\\right]\\\\&\\times \\, {\\sin}[{(}\\omega-m\\Omega)t+\\psi]\n\\end{array}\\end{equation}\n(Aerts et al.\\ 1992). In these expressions, $\\psi$ is a phase constant\ndepending on the reference epoch, $i$ is the inclination angle between the\nrotation axis and the line of sight, $v_{_{\\Omega}}$ is the projected rotation\nvelocity (a uniform rotation is assumed), $b_2$ is a constant depending on the\nlimb-darkening function, $\\sigma$ again represents the width of the Gaussian\nintrinsic profile as in Section\\,3, and the functions $A,C,D,E,F,G,R,S,T$\ndepend on the kind of mode and on the inclination. They contain the complete\nphysics of the pulsation. For an explicit expression of these functions, we\nrefer to Aerts et al.\\ (1992), but we point out here that these functions are\nthe same for positive and negative azimuthal numbers because the slow-rotation\napproximation is used. It is then impossible in this description to decide\nfrom the moments how a mode travels with respect to the rotation.\n\n\\begin{figure}\n\\mbox{\\epsfxsize=0.9\\textwidth\\epsfysize=0.9\\textwidth\\epsfbox[50 20 700 560]\n{aerts13.ps}}\n\\caption{The three observed (dots) velocity moments of the \nCa\\,I\\,$\\lambda\\lambda\\,6122.21$\\AA\\ line of $\\rho\\,$Puppis. The first, second,\nand third moments are expressed in respectively km/s, (km/s)$^2$, and\n(km/s)$^3$. The full line is a\nfit for a monoperiodic pulsation model for the frequency $f=7.098168\\,$c/d. We\nrefer to Mathias et al.\\ (1997) for a complete description of the data.}\n\\end{figure}\n\nBy means of an example, we show in Figure\\,9 the first three moments of the\nCa\\,I\\,$\\lambda\\lambda\\,6122.21$\\AA\\ line observed for the $\\delta\\,$Scuti star\n$\\rho\\,$Puppis. The observed moments are fitted with a monoperiodic pulsation\nmodel for the frequency $f=7.098168\\,$c/d (for a full description of the data,\nsee Mathias et al.\\ 1997). It is noted from the middle panel of this figure\nthat the second moment of $\\rho\\,$Puppis is dominated by the frequency\n$2\\omega$, a situation that is typical in the case of an axisymmetric mode (see\nAerts et al.\\ 1992). The top panel of the figure shows that $<v^3>$ is\ndominated by the frequency $\\omega$. This is a general characteristic of the\nthird moment since the term varying with $\\omega$ is influenced by all\nvelocities together, i.e., by the rotation, the pulsation, and the intrinsic\nprofile, while this is not the case for the other two terms (see\nExpression\\,(\\ref{mono3})).\n\nThe periodograms of the three moments can immediately be interpreted in terms\nof the periods that are present, while the corresponding phase diagrams of the\nmoments are interpretable in terms of all the non-radial pulsation parameters.\nThe basic idea is to compare the observed variations of the moments with\ntheoretically calculated expressions for these variations for various\npulsation modes, and so to determine the mode that best corresponds to the\nobservations. This is achieved through the construction of a so-called\ndiscriminant, which is based on the amplitudes of the moments:\n\\renewcommand{\\arraystretch}{2.5}\n\\begin{equation}\n\\begin{array}{ll}\n\\label{discr}\n\\Gamma_{\\ell}^m&(v_{\\rm p},i,v_{_{\\Omega}},\\sigma)\\equiv\n\\Biggl[\n\\biggl|AA-v_{\\rm p}|A(\\ell,m,i)|f_{AA}\\biggr|^2\\\\\n&+\\biggl(\\biggl|CC-v_{\\rm p}^2|C(\\ell,m,i)|\\biggr|^{1/2}f_{CC}\\biggr)^2\\\\\n&+\\biggl(\\biggl|DD-v_{\\rm p}v_{_{\\Omega}}|D(\\ell,m,i)|\\biggr|^{1/2}f_{DD}\n\\biggr)^2\\\\\n&+\\biggl(\\biggl|EE-v_{\\rm\np}^2|E(\\ell,m,i)|-\\sigma^2-b_2v_{_{\\Omega}}^2\\biggr|^{1/2} f_{EE}\\biggr)^2\\\\\n&+\\biggl(\\biggl|FF-v_{\\rm p}^3|F(\\ell,m,i)|\\biggr|^{1/3}f_{FF}\\biggr)^2\\\\\n&+\\biggl(\\biggl|GG-v_{\\rm p}^2v_{_{\\Omega}}|G(\\ell,m,i)|\\biggr|^{1/3}\nf_{GG}\\biggr)^2\\\\ &+\\biggl(\\biggl|RST-v_{\\rm p}^3|R(\\ell,m,i)| -v_{\\rm\np}v_{_{\\Omega}}^2|S(\\ell,m,i)|\\\\ &\\ \\ \\ \\ \\ \\ -v_{\\rm\np}\\sigma^2|T(\\ell,m,i)|\\biggr|^{1/3}f_{RST}\\biggr)^2\n\\Biggr]^{1/2}.\n\\end{array}\n\\end{equation} \nThe functions $f_{AA},\\ldots,f_{RST}$ are weights given according to the\nquality of the fits to the moments. We refer to Aerts (1996) for their\ncalculation and for a more detailed description and an evaluation \nof the discriminant.\n\nTo define a criterion for mode identification, we proceed as follows. The\nfunction $\\Gamma_{\\ell}^m(v_{\\rm p},i,v_{_{\\Omega}},\\sigma)$ is minimised for\neach set of values $(\\ell,m)$~:\n\\begin{equation}\n\\gamma_{\\ell}^m \\equiv \\ds{\\min_{v_{\\rm p},i,v_{_{\\Omega}},\\sigma} \n\\Gamma_{\\ell}^m(v_{\\rm p},i,v_{_{\\Omega}},\\sigma)}.\n\\end{equation}\nThe ``best solution'' for $\\ell$ and $m$ is defined as the one for which\n$\\gamma_{\\ell}^m$ attains the lowest value; it then also provides values for\n$v_{\\rm p}, i, v_{_{\\Omega}}$ and $\\sigma$.\n\nOur discriminant was thoroughly tested (Aerts 1996) and turned out to be more\naccurate compared to the one presented by Balona (1990), which is based on the\nfirst two moments only. As with line-profile fitting, both the wavenumbers\n($\\ell,m)$ and all the other velocity parameters are derived. The moment\nmethod is particularly suited to identify lower-degree modes ($\\ell\\leq\\,6$) in\nslow rotators. In this sense, it is completely complementary to the Doppler\nImaging method. The reason for this limitation is that it uses integrated line\nprofiles, because of which high-degree modes are almost completely canceled\nout in the moment variations. The\ncode that calculates the minima of the discriminant as presented here is\nwritten in the statistical package GAUSS and is available upon request from the\nfirst author of this paper.\n\nWe recall that the discriminant is unable to find the sign of $m$, because the\ntheoretical expressions for the moments have only been determined in the case\nthat the Coriolis force can be neglected. A generalisation that includes the\nCoriolis force, and thus is able to derive the sign of $m$, has been done as\nwell (Aerts, unpublished).\n\nA generalisation of the moment method to multiperiodic pulsations has been\nproposed (Mathias et al.\\ 1994a). From our study and the one by Aerts et al.\\\n(1994b) it is clear that the moment method is less accurate for multiperiodic\nstars, but still better than any other alternative in the case of slow\nrotation. The biggest problem in the treatment of multiperiodic variations is\nthe appearance of long beat periods due to the interaction of the different\nmodes. This effect requires many observations, well-spread over the total\nbeat period. A second theoretical problem is that a discriminant constructed to\nidentify all the present modes at the same time is numerically too involved to\nbe of any practical use. We are thus obliged to identify each mode separately\nby means of the discriminant given in Expression\\,(\\ref{discr}). In this way,\nall the information present in the beat-terms is lost.\n\nAn application of the discriminant to the moments of $\\rho\\,$Puppis shown in\nFigure\\,9 is given in Table\\,2.\n\\renewcommand{\\arraystretch}{1.1}\n\\begin{table}\n\\caption{The minima of the discriminant for the main mode ($f=7.098\\,$c/d) \nof $\\rho\\,$Pup}\n\\begin{center}\n\\begin{tabular}{ccccccc}\n\\tableline\n$\\ell$ & $|m|$ & $\\gamma_{\\ell}^m$ & $v_{\\rm p}$ & $i$ & $v\\sin\\,i$ &\n$\\sigma$\\\\\n\\tableline\n0&0&0.08&5.6&--&15.3&6.5\\\\\n1&1&0.13&10.0&$38^{\\circ}$&14.8&5.9\\\\ \n2&1&0.17&12.1&$64^{\\circ}$&16.4&2.2\\\\\n1&0&0.18&5.0&$7^{\\circ}$&19.6&1.7\\\\ \n2&2&0.23&15.0&$53^{\\circ}$&10.3&4.8\\\\\n$\\vdots$&$\\vdots$&$\\vdots$&$\\vdots$&$\\vdots$&$\\vdots$&$\\vdots$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\nClearly, the main mode of $\\rho\\,$Puppis is a radial one with a pulsation\nvelocity amplitude of some 6\\,km/s. As already mentioned in\nSection\\,4.1, we found evidence of two additional frequencies in\nour data: 7.82\\,c/d \\& 6.31\\,c/d (Mathias et al.\\ 1997). Their amplitudes are\ntoo low to achieve an unambiguous mode identification. They are not found in\nphotometry so far.\n\nUp to now, the moment method in the given formulation has mainly been applied\nto $\\beta\\,$Cephei stars (see e.g., Aerts et al.\\ 1992, Mathias et al.\\\n1994a,b, Aerts et al.\\ 1994a,b) but also to two $\\delta\\,$Scuti stars (20\\,CVn:\nMathias \\& Aerts 1996, $\\rho\\,$Puppis: Mathias et al.\\ 1997). Previous\nattempts to identify modes in $\\delta\\,$Scuti stars with Balona's (1990)\nversion of the moment method are presented by Mantegazza et al.\\ (FG\\,Vir:\n1994) and by Mantegazza \\& Poretti (X\\,Caeli: 1996). We have recently obtained\na large data set of high-quality line-profile variations of 20\\,CVn to check\nour findings presented in the 1996 paper, which were based on only very few\nspectra. We will proceed with the reduction and analysis process of the new\ndata sets in the forthcoming months (Mathias et al., in preparation).\n\nTHE major limitation of the moment method is the fact that no confidence\nintervals for the minima of the discriminant and the corresponding velocity\nparameters $v_{\\rm p}, i, v_{_{\\Omega}}, \\sigma$ are available. Therefore, the\ncompeting modes as listed in Table\\,2 are difficult to compare with each other.\nThe standard error of the minimum and of the estimates for $v_{\\rm p}, i,\nv_{_{\\Omega}}$ and $\\sigma$ is caused by observational noise, by limitations of\nthe model describing the line-profile variations due to non-radial pulsation,\nand also by numerical inaccuracies occurring in the determination of the\nmoments, of the amplitudes of the moments, and of the minima of the\ndiscriminant. Unfortunately, no method is found up to now to determine these\nuncertainties. We are currently elaborating on a statistically founded method\nto try and estimate these standard errors. If we succeed in doing so, then the\nmajor drawback of this method will be overcome. Again, line-profile fitting\nfor the best solutions found by the discriminant is helpful to check the result\nof the mode identification.\n\\vspace{-1.0em}\n\n\\section{Comparison between the methods}\n\n\\renewcommand{\\arraystretch}{1.1}\n\\begin{table}[b!]\n\\vspace{-1em}\n\\caption{The main properties of each of the three identification methods\nbased on observed line-profile variations. LPF, DI, and MM stand for\nrespectively line-profile fitting, Doppler Imaging, and the moment method.}\n\\begin{center}\n\\tabcolsep=10pt\n\\begin{tabular}{rccc}\n\\tableline\n& LPF & DI & MM\\\\\\tableline\nDeduced parameters & $\\ell, m$, ampl & $\\ell, m ? $ & $\\ell, m$, ampl\\\\\n& vsini, $\\sigma, i$ & &vsini, $\\sigma, i$\\\\\\tableline\nLimitations & no & v/vsini$\\leq\\,20\\%$ & $\\ell\\leq\\,6$ \n\\\\\\tableline\nMultiperiodicity & no & easy & possible \\\\\\tableline\nUnderlying physics & yes & no & yes \\\\\\tableline\nStandard errors & no & no & not yet \\\\\\tableline\nComputation time & long & short & in between \\\\\\tableline\nAdditional modeling & no & necessary & as check \n\\\\\\tableline\n%\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nWe have already mentioned the main advantages and disadvantages for each of the\nthree methods described above. We briefly review them in Table\\,3. The\nmethods are complementary in the sense that one is suited for slow rotators\nwith low-degree modes (moment method), another for rapid rotators with\nhigh-degree modes (Doppler Imaging) and the third (line-profile variation\nfitting) is very useful (moment method)/necessary (Doppler Imaging) \nas a check of the results obtained with the other two methods.\n\n\\section{Conclusions and future developments}\n\nIn this review, we have discussed the different mode-identification techniques\nthat are currently used to study the non-radial pulsations in pulsating stars\nfrom observations of line-profile variations. Three basic methods are\npresented, are compared to each other and applications to real observations of\n$\\delta\\,$Scuti stars are described.\n\nLine-profile variations offer a very detailed picture of the various aspects of\nthe pulsation velocity field. On the other hand, photometric observations are\neasier to obtain on a long time-basis and are as such often superior for\na very accurate determination of the pulsation frequencies, especially in the\ncase of lower-degree modes. High-degree modes hardly show up in photometry and\ncan only be found from high-quality line-profile variation data. An example of \nadditional modes being seen in spectra compared to photometry is presented by De\nMey et al.\\ (1998). They have analysed high-quality line profiles of the\nmultiperiodic \n$\\delta\\,$Scuti primary of the double-lined spectroscopic binary $\\theta\\,$Tuc.\nThe dominant frequency is the same in the photometric and spectroscopic data,\nbut the second frequency that shows up in the spectra was never found before in\nphotometry. This example confirms that \nthe gathering of simultaneous photometry and spectroscopy is the best strategy\nto find a complete and accurate identification of all the appearing modes\nin multiperiodic stars.\n\nFuture possible improvements from a theoretical point of view concern on the\none hand the development of mathematical expressions for the phase and\namplitude in Fourier space in such a way that these quantities can be\nimmediately interpreted in terms of the physical parameters of the pulsational\nvelocity field. We also briefly mention that a new method of ``Doppler\nMapping'' was recently presented by Berdyugina et al.\\ (2000). They apply a\nspectral inversion technique to obtain maps of the surface corotating with the\ndominant pulsation mode. From these maps, they determine the pulsation degree\nand study the latitudinal distribution of the pulsation field. The method\nstill needs to be further explored. Secondly, the inclusion of temperature\nvariations during the pulsation cycle is still not accurately done, since an\nadiabatic pulsation is assumed while it is to be expected that non-adiabatic\neffects are important in the outer region of the atmosphere where the observed\nspectral lines are formed. Finally, the inclusion of centrifugal forces may be\nan improvement for the most rapid rotators. The latter is only necessary for\nstars rotating close to their break-up velocity.\n\nFrom an observational point of view, large progress can be expected in the near\nfuture now that better and better detectors become available. For the\nshort-period $\\delta\\,$Scuti stars, the major problem in obtaining high\ntemporal and spatial resolution profiles is that the ratio of the integration\ntime to the main pulsation period is rather high. This was one of the reasons\nwhy the application of the moment method to the stars FG\\,Vir and X\\,Caeli was\nnot very successful. The abovementioned ratio in these cases was respectively\n13\\% and 8\\%, while it amounts to only 1\\% for our profiles of $\\rho\\,$Puppis\nshown in Figure\\,4. For such high ratios, the pulsational motion is averaged\nout over a part of the cycle and this prevents unambiguous identifications,\nespecially for multiperiodic stars.\n\nAn interesting new technique for the interpretation of \nline-profile variations is by working\nwith cross-correlation functions instead of real spectra. Such a technique can\nbe performed by means of current spectrographs such as ELODIE attached to the\n1.93m telescope in the Haute-Provence Observatory. Our analysis of 20\\,CVn\n(Mathias \\& Aerts 1996) was already based on cross-correlation profiles and has\nshown that they perfectly contain the pulsational motion on the condition that\nthe correlation is based on a suitable set of selected spectral lines. \nBy using a cross-correlation function, one can significantly decrease the\nintegration time and still obtain a high S/N ratio. At the same time, one can\nobserve optically fainter stars with success. More accurate versions of\nELODIE-type spectrographs are CORALIE, attached to the Swiss 1.2m telescope and\nFEROS, attached to the ESO 1.5m telescope, both situated at La Silla in Chile.\n\nFinally, we would like to point out that mode identification from line-profile\nvariations will become an important tool to obtain some information on the\nnature of the excited modes in stars belonging to the new class of\n$\\gamma\\,$Dor stars. For reviews on this new group of pulsating stars we refer\nto Krisciunas (1998) and to Zerbi (these proceedings). Since the multiperiodic\nvariations detected in them have periods roughly a factor 20 longer than the\nperiod of the radial fundamental mode for such stars, high-order $g$-modes are\nbelieved to be the cause of the variability. However, there is yet no pulsation\nmechanism that can explain the onset and the maintenance of the pulsations in\nthese stars.\n\nHandler \\& Krisciunas have given subsequent updated lists of {\\it bona fide}\nmembers of the group, which currently constitutes 13 members. We have recently\ntaken the first steps towards the discovery of cool \n$g$-mode pulsators by searching\nfor $\\gamma\\,$Dor stars in an unbiased sample of 39 new variable A2--F8 stars\ndiscovered by means of the Hipparcos mission (Aerts et al.\\ 1999b). We have\nreported the discovery of 14 new $\\gamma\\,$Doradus variables among this\nunbiased sample. We primarily focussed on the limited group of new variables\nfor which both Hipparcos and Geneva data are available, mainly because the\nlatter allow an accurate determination of the effective temperature. It is very\nlikely, however, that our more extended list of 200 unclassified variable\nA2--F8 stars of which no Geneva data are at our disposal contains more objects\nof this type. This seems to be confirmed by a recent analysis by Handler\n(1999).\n\nIn 1996, we also started a search for new $\\gamma\\,$Dor stars by means of\nground-based Geneva photometry. Our search has resulted so far in the discovery\nof three new and some five suspected $\\gamma\\,$Dor stars (Eyer \\& Aerts, \n2000). In order to firmly establish the $\\gamma\\,$Dor nature of all\nthese new candidates we have started a long-term spectroscopic campaign with\nCORALIE in the course of 1997, which is still ongoing. We found line-profile\nvariability from our high-resolution spectra for almost all candidates. Some of\nthem, however, turn out to be binaries (Eyer \\& Aerts, in preparation).\n\nLine-profile studies of $\\gamma\\,$Dor stars are still scarce. Examples in which\na large amount of spectra have been obtained and analysed are given by Balona\net al.\\ (1996, $\\gamma\\,$Dor) and by Aerts \\& Krisciunas (1996, 9\\,Aur). The\nlatter study is based on cross-correlations obtained with the (by now\nunmounted) spectrograph CORAVEL and showed convincingly that such correlation\nfunctions indeed contain a sufficient amount of information to characterise the\npulsational behaviour.\n\n\nIt is clear that a combination of long-term photometry and spectroscopy is\nessential and the only way to study the multiperiodic variability in the\n$\\gamma\\,$Dor stars. The best observing strategy is the same as the one for the\nslowly pulsating B stars (Aerts et al.\\ 1999a), which are also multiperiodic\n$g$-mode pulsators. At present, we do not yet have a sufficient amount of line\nprofiles for our targets, but we will continue our monitoring of $\\gamma\\,$Dor\nstars with CORALIE during the forthcoming years. This will eventually lead to\nmode identifications, by applying the moment method.\n\n\\begin{references} \n\\reference\nAerts, C. 1994, In Pulsation, Rotation and Mass Loss in Early-Type Stars,\nL.A. Balona, H.F. Henrichs, J.M. LeContel, \nKluwer Academisch Publishers, 75\n\\reference \nAerts, C. 1996, \\astap, 314, 115 \n\\reference\nAerts, C., De Cat, P., Peeters, E., et al. 1999a, \\astap, 343, 872\n\\reference\nAerts, C., Eyer, L., Kestens, E. 1999b, \\astap, 337, 790\n\\reference \nAerts, C., De Pauw, M., Waelkens, C. 1992, \\astap, 266, 294 \n\\reference\nAerts, C., Krisciunas, K. 1996, \\mnras, 278, 877\n\\reference\nAerts, C., Mathias, P., Gillet, D., Waelkens, C. 1994a, \\astap, 286, 109\n\\reference\nAerts, C., Waelkens, C. 1993, \\astap, 273, 135 \n\\reference\nAerts, C., Waelkens, C., De Pauw, M. 1994b, \\astap, 286, 136 \n\\reference \nBaade, D. 1984, \\astap, 135, 101\n\\reference\nBaade, D. 1987, In Physics of Be stars, A. Slettebak, T.P. Snow, \nCambridge University Press, 361\n\\reference \nBalona, L.A. 1986a, \\mnras, 219, 111\n\\reference \nBalona, L.A. 1986b, \\mnras, 220, 647\n\\reference\nBalona, L.A. 1987, \\mnras, 224, 41\n\\reference \nBalona, L.A. 1990, In Progress of Seismology of the Sun and\n Stars, Y. Osaki, H. Shibahashi, Lecture Notes in Physics, 367, 443\n\\reference\nBalona, L.A., B\\\"ohm, T., Foing, B.H., et al. 1996, \\mnras, 281, 1315\n\\reference\nBerdyugina, S.V., Korhonen, H., Schrijvers, C., Telting, J.H., 2000, In The Be\nphenomenon in early-type stars, M.A. Smith, H.F. Henrichs, ASP Conference\nSeries, in press\n\\reference\nButa, R.J., Smith, M.A. 1979, \\apj, 232, 213\n\\reference \nCampos, A.J., Smith, M.A. 1980a, \\apj, 238, 250\n\\reference \nCampos, A.J., Smith, M.A. 1980b, \\apj, 238, 667\n\\reference\nDe Mey, K., Daems, K., Sterken, C. 1998, \\astap, 336, 527\n\\reference \nDe Pauw, M., Aerts, C., Waelkens, C. 1993, \\astap, 280, 493 \n\\reference\nEyer, L., Aerts, C., 2000, submitted to A\\&A\n\\reference\nGies, D. R., Kambe, E., Josephs, T. S., et al., 1999, \\apj, 525, 420\n\\reference \nGies, D.R., Kullavanijaya, A. 1988, \\apj, 326, 813\n\\reference\nHandler, G., 1999, \\mnras, 309, 19\n\\reference\nHao, J. 1998, \\apj, 500, 440\n\\reference \nKambe, E., Osaki, Y. 1988, \\pasj, 40, 313\n\\reference\nKennelly, E.J., Brown, T.M., Foing, B.H., et al. 1998a, \nIn Precise Stellar Radial\nVelocities, J.B. Hearnshaw, C.D. Scarfe, ASP Conference Series, 110, 53\n\\reference\nKennelly, E.J., Brown, T.M., Kotak, R., et al. 1998b, \\apj, 495, 440\n\\reference\nKennelly, E.J., Yang, S., Walker, G.A.H. 1992b, \\pasp, 104, 15\n\\reference\nKennelly, E.J., Walker, G.A.H., Catala, C., et al. 1996, \\astap, 313, 571\n\\reference\nKennelly, E.J., Walker, G.A.H., Merryfield, W.J. 1992a, \\apj, 400, L71\n\\reference\nKrisciunas, K. 1998, In New Eyes to See Inside the Sun and Stars, F.L.\nDeubner, J. Christensen-Dalsgaard, D.W. Kurtz, Kluwer Academic Publishers, 339\n\\reference\nLee, U., Saio, H. 1990, \\apj, 349, 570\n\\reference \nLee, U., Jeffery, C.S., Saio, H. 1992, \\mnras, 254, 185\n\\reference\nMantegazza, L., Poretti, E. 1996, \\astap, 312, 855\n\\reference\nMantegazza, L., Poretti, E., Bossi, M. 1994, \\astap, 287, 95\n\\reference\nMathias, P., Aerts, C. 1996, \\astap, 312, 905\n\\reference \nMathias, P., Aerts, C., De Pauw, M., Gillet, D., Waelkens, C. 1994a, \n\\astap, 283, 813\n\\reference\nMathias, P., Aerts, C., Gillet, D., Waelkens, C. 1994b, \\astap, 289, 875\n\\reference\nMathias, P., Gillet, D., Aerts, C., Breitfellner, M.G. 1997, \\astap, 327, 1077\n\\reference Merryfield, W.J., Kennelly, E.J. 1993, In New Perspectives on\nStellar Pulsation and Pulsating Variable Stars, J.M. Nemec, J.M. Matthews, \nCambridge University Press, 148\n\\reference\nOsaki, Y. 1971, \\pasj, 23, 485\n\\reference Schrijvers, C. 1999, PhD Thesis, University of Amsterdam, The\nNetherlands \n\\reference\nSchrijvers, C., Telting, J.H., Aerts, C., et al. 1997, A\\&AS 121, 343\n\\reference\nSmeyers, P. 1984, In Theoretical problems in stellar oscillations, \nProc. $25^{th}$ Li\\`{e}ge International Astrophysical Colloquium, 68\n\\reference\nSmith, M. 1977, \\apj, 215, 574\n\\reference\nSmith, M. 1982, \\apj, 254, 242\n\\reference\nSmith, M. 1983, \\apj, 265, 338\n\\reference\nSmith, M.A., Fitch, W.S., Africano, J.L., et al. 1984, \\apj, 282, 226\n\\reference\nTelting, J.H., Schrijvers, C. 1997, \\astap, 317, 723\n\\reference\nTownsend, R.H.D. 1997, \\mnras, 284, 839\n\\reference\nUnno, W., Osaki, Y., Ando, H., Saio, H., Shibahashi, H. 1989, \nNonradial oscillations of stars, $2^{nd}$ edition, University of Tokyo Press\n\\reference \nVogt, S.S., Penrod, G.D. 1983, \\apj, 275, 661\n\\reference\nVogt, S.S., Penrod, G.D., Hatzes, A.P. 1987, \\apj, 496, 127\n\\reference\nWade, R.A., Rucinski, S.M. 1985, A\\&AS, 60, 471\n\n\n\\end{references}\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002350
|
The black hole mass -- galaxy age relation
|
[
{
"author": "M.R. Merrifield$^1$"
},
{
"author": "Duncan A. Forbes$^{2,3}$ and A.I.~Terlevich$^2$"
},
{
"author": "$^1$School of Physics and Astronomy"
},
{
"author": "Nottingham NG7 2RD"
},
{
"author": "$^2$School of Physics and Astronomy"
},
{
"author": "Birmingham B15 2TT"
},
{
"author": "$^3$Astrophysics \\& Supercomputing"
},
{
"author": "Hawthorn VIC 3122"
},
{
"author": "Australia"
}
] |
We present evidence that there is a significant correlation between the fraction of a galaxy's mass that lies in its central black hole and the age of the galaxy's stellar population. Since the absorption line indices that are used to estimate the age are luminosity weighted, they essentially measure the time since the last significant episode of star formation in the galaxy. The existence of this correlation is consistent with several theories of galaxy formation, including the currently-favoured hierarchical picture of galaxy evolution, which predicts just such a relation between black hole mass and the time since the last burst of merger-induced star formation. It is not consistent with models in which the massive black hole is primordial, and hence uncoupled from the stellar properties of the galaxy.
|
[
{
"name": "bhmn.tex",
"string": "\\documentstyle[epsfig]{mn}\n%\\documentstyle[epsfig, referee]{mn}\n\n\\begin{document}\n\n\\title[Black hole mass -- galaxy age relation]{The black hole mass -- galaxy age\nrelation}\n\n\\author[Merrifield, Forbes \\& Terlevich]{\n M.R. Merrifield$^1$, \n Duncan A. Forbes$^{2,3}$ and A.I.~Terlevich$^2$\\\\\n $^1$School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD\\\\\n $^2$School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT\\\\\n $^3$Astrophysics \\& Supercomputing, Swinburne University, Hawthorn VIC 3122, \n Australia}\n\n\n\\date{Received:\\ \\ \\ Accepted: }\n \n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}%\n\n\\maketitle\n\n\\label{firstpage}\n\n\\begin{abstract}\nWe present evidence that there is a significant correlation between\nthe fraction of a galaxy's mass that lies in its central black hole\nand the age of the galaxy's stellar population. Since the absorption\nline indices that are used to estimate the age are luminosity\nweighted, they essentially measure the time since the last significant\nepisode of star formation in the galaxy. The existence of this\ncorrelation is consistent with several theories of galaxy formation,\nincluding the currently-favoured hierarchical picture of galaxy\nevolution, which predicts just such a relation between black hole mass\nand the time since the last burst of merger-induced star formation.\nIt is not consistent with models in which the massive black hole is\nprimordial, and hence uncoupled from the stellar properties of the\ngalaxy.\n\n\n\\end{abstract}\n\n\\begin{keywords}\nGalaxies: formation, nuclei -- quasars: general -- black hole physics\n\\end{keywords}\n\n\\section{Introduction}\n\nThe existence of active galactic nuclei has long been taken as\nevidence for the existence of massive black holes in the centres of\nsome galaxies (Lynden-Bell 1969). However, it is only relatively\nrecently that high spatial resolution studies of the kinematics of\ngalactic nuclei have revealed that essentially all galaxies harbour\nlarge central masses [see Ho (1999) for a review of the evidence].\nThe existence of these observations also means that there are now\nenough data to study the demographics of massive black holes, in order\nto seek clues to their origins.\n\nThe first significant discovery in this regard is that there is a\ncorrelation between the mass of the black hole, $M_{\\rm BH}$, and the\nmass of the host galaxy's spheroidal component,\n\\footnote{The term\n``spheroidal component'' refers to the whole system in the case of\nelliptical galaxies, but just the bulge in systems with significant\ndisk components.} \n$M_{\\rm sph}$. Although there is a variety of\npossible biasses in measuring this correlation, it seems broadly to be\nthe case that there is a linear relationship, such that $M_{\\rm BH}\n\\sim 0.005 M_{\\rm sph}$ (Magorrian et al.\\ 1998).\n\nAlthough this correlation is reasonably strong, there is still\nconsiderable scatter in the relation, such that there is more than a\nfactor of ten variation in the inferred value of $M_{\\rm BH}$ for\ngalaxies of given spheroid mass (Magorrian et al.\\ 1998). Some of\nthis scatter can probably be attributed to the uncertainties in\ncalculating black hole masses from relatively poor kinematic data and\nsimplified dynamical models (van der Marel 1997). However, there are\nalso astrophysical reasons why one might expect significant dispersion\nin this relation. For example, consider the simplest possible scenario\nin which galaxies form and evolve in near isolation. If the central\nblack holes in these galaxies accrete mass fairly steadily from their\nhosts, then the mass of a black hole simply reflects the age of its\nhost.\n\nUnder the currently-favoured hierarchical paradigm for galaxy\nformation, in which larger galaxies are formed from the merging of\nsmaller galaxies (White \\& Rees 1978), the simple linear correlation\nbetween galaxy mass and black hole mass is readily explained. Each\ntime two galaxies merge to form a larger system, their black holes\nrapidly spiral to the centre of the new galaxy due to dynamical\nfriction. The black holes then merge, creating a\nproportionately-larger black hole. However, a galaxy formed by this\nprocess of repeated mergers cannot be characterized by a single age,\nso the above explanation for the scatter in black hole masses must be\nmodified somewhat. One measure of such a galaxy's age is the time\nsince it last underwent a major merger, and Kauffmann \\& Haehnelt\n(2000) have shown that this timescale is a key factor in explaining\nthe scatter in black hole masses. If the last merger happened long\nago, then it will have occurred between relatively unevolved galaxies\nin which there would have been a large amount of cold gas. If the\nblack hole accretes some fixed fraction of this gas, then galaxies in\nwhich the last merger occurred longer ago will contain more massive\nblack holes.\n\nThis picture, in which black holes acquire much of their mass through\naccretion of material from their host galaxies, seems quite credible.\nHowever, it is not the only possible scenario. Stiavelli (1998) has\nargued that galaxies with essentially identical properties could be\nformed around pre-existing massive black holes. In this case, the\nspread in black hole masses would simply reflect the stochastic nature\nof whatever physics was responsible for the formation of the\nprimordial black holes.\n\nIn this Letter, we investigate whether we can attribute the observed\nscatter in black hole masses to an astrophysical cause, and hence\nwhether we can discriminate between the above scenarios.\nSpecifically, we investigate whether the masses of black holes\ncorrelate with the ages of their host galaxies as determined by\nstellar absorption line diagnostics. \n%Since these age indicators\n%measure a luminosity-weighted mean age, they provide an estimate of\n%the time since the last significant burst of star formation. Thus,\n%the presence of a correlation between this measure of age and black\n%hole mass would provide direct evidence for a scenario in which black\n%hole growth is coupled to the major galaxy mergers that induce bursts\n%of star formation.\n\n\n\\section{Analysis}\n\n\\subsection{Black hole mass determinations}\n\nThere are now several compilations of central black hole mass\nestimates in nearby galaxies (e.g.\\ Ho 1999). The difficulty in using\nsuch compilations for quantitative studies is that they contain data\nobtained using a variety of heterogeneous techniques. Thus, not only are\nthere likely to be systematic errors in the derived masses, but the\nnature of these errors will vary within the compilation.\n\nTo minimize the impact of such uncertainties, we have chosen to\nconsider a sample containing only objects from a single study where\nthe analysis has been performed in a consistent fashion. Although it\ncould not be argued that such a sample is necessarily free of\nsystematic errors, one might reasonably hope that the consistent\nanalysis should produce relatively consistent results. For example,\nif one galaxy is found to have a more massive black hole than another\noptically-identical galaxy within a single sample, then it is likely\nthat the two systems are intrinsically different; one cannot say the\nsame if one compares two galaxies from different samples that have\nbeen analyzed using different techniques.\n\nThe largest consistently-analyzed sample available is that published\nby Magorrian et al.\\ (1998). Their study of galaxies' stellar\nkinematics presented estimates for the masses of the central black\nholes and spheroidal components of 32 galaxies. The only exceptional\ngalaxy in this dataset is NGC~1399. The luminosity distribution of\nthis galaxy has a very large diffuse envelope, making it one of the\nmost extreme known examples of a cD galaxy (Schombert 1986). It is\ntherefore almost impossible to disentangle the mass of this extensive\ngalaxy from the mass of the cluster that surrounds it. In fact, it is\ninteresting to note that this galaxy lies well above Magorrian et\nal.'s (1998) mean relation between $M_{\\rm BH}$ and $M_{\\rm sph}$.\nHowever, if one adds to $M_{\\rm sph}$ an estimate for the total mass\nin the cD envelope (which was excluded from the original mass\nestimate), it is straightforward to place NGC~1399 right on the mean\nrelation. Unfortunately, it is difficult to justify this ad hoc\ncorrection when one is trying to carry out a consistent analysis.\nGiven the undesirability of such a posteriori manipulation, and the\nfact that such extreme cD systems are likely to have evolved by very\ndifferent mechanisms from regular ellipticals, NGC~1399 has been\nexcluded from the sample, leaving a dataset of 31 galaxies. We\nshould, however, note that the presence of this galaxy in the sample\nmakes no difference to the statistical significance of the conclusions\npresented below.\n\n\n\\subsection{Age determinations}\n\nAs with the black hole mass estimates, it is important that the galaxy\nage estimates be made in as consistent a manner as possible. We have\ntherefore used values from the recent catalogue of Terlevich \\& Forbes\n(2000), which is compiled from a relatively homogeneous dataset of\nhigh-quality absorption line measurements for galaxies (e.g. H$\\beta$,\nH$\\gamma$, [MgFe]). Using the stellar population model of Worthey\n(1994), these line indices can be used to break the age/metallicity\ndegeneracy, thus giving separate age and metallicity estimates. \n\nFor a few galaxies not in the Terlevich \\& Forbes (2000) catalogue,\nthe same line indices have been measured by Trager et al.\\ (1998)\nusing data of comparable quality. Combining these measurements with\nthe Terlevich \\& Forbes dataset, one can obtain consistent age\nestimates for 23 of the galaxies in the current sample.\n\nThe line index measurements come from the galaxies' central regions\nand are luminosity weighted. They are therefore dominated by the last\nmajor burst of star formation. Thus, the age estimate probably\nreflects the time since the galaxy's last major merger event,\nwhich will have induced significant amounts of star formation [see\nalso Forbes, Ponman \\& Brown (1998)].\n\n\n\n\\begin{figure}\n\\centering \\epsfig{figure=bhfig1.ps, width=8cm}\n\\caption{ \nFraction of galaxies' masses in their central black holes as\na function of the ages inferred for their stellar components.\nThe names of the galaxies are labelled. The horizontal\nline shows the nominal mean value for black hole masses (Magorrian\net al.\\ 1998).}\n\\end{figure}\n\n\\subsection{The black hole mass -- galaxy age relation}\n\nFigure~1 shows the fraction of each galaxy's spheroidal component mass\nthat resides in its central black hole as a function of the age\ninferred for the galaxy's stellar population. There is clearly a\nlarge amount of scatter in this plot; indeed, since there are sizeable\nuncertainties in both the black hole mass determinations and the age\nestimates, one could not expect to see a tight correlation. However,\nthere is a definite trend in the sense that older galaxies of a given\ntotal mass contain more massive black holes: the four youngest\ngalaxies all have black holes whose masses lie below the mean of\n$M_{\\rm BH} = 0.005 M_{\\rm sph}$, while three of the four oldest\ngalaxies lie above this line. More quantitatively, a Spearman rank\ntest rejects the possibility that $M_{\\rm BH}/M_{\\rm sph}$ and $t$\nare uncorrelated at $>99\\%$ confidence. The robust nature of a rank\ntest means that the significance of this correlation does not hang on\nthe outlying points -- the same confidence level is reached if, for\nexample, NGC~7332 is excluded from the analysis.\n\n\n\\section{Discussion}\n\nAlthough there does appear to be a significant correlation between\nmeasured black hole mass and galaxy age estimate, it is not\nnecessarily astrophysical in origin. We must first consider the\npossibility that it arises from some systematic error in the analysis.\nHowever, the kinematic data from which the black hole masses were\ninferred are completely independent from the line index data that\nprovide the age estimates. Since the line index data were not\nselected with this project in mind, and the black hole mass estimates\nplayed no role in the choice of sample, the selection process\ncannot have induced the correlation that is seen in Fig.~1. Further,\nthe independent nature of the data sets used to measure the two\nordinates means that there can be nothing in this analysis that might\npreferentially over-estimate the black hole masses in old galaxies,\nor underestimate the masses in young systems.\n\nIt should also be borne in mind that the absolute calibrations of the\nblack hole masses and galaxy ages are significantly uncertain. In the\ncase of the absorption line indices, for example, the age estimates\nare derived from spectral synthesis modelling, which remains a\nsomewhat uncertain process, so the absolute values of the ages of two\ngalaxies may be quite ill-determined. However, the fact that one is\nolder than the other can be determined relatively reliably by this\nmodelling process, so the approximate ordering of galaxy ages can be\ndetermined quite robustly. Since the Spearman rank test described\nabove depends only on this ordering, the statistical significance of\nthe correlation is not dependent on the details of the adopted\ncalibration.\n\nIt would thus appear that there is an underlying astrophysical\ncorrelation between the fraction of a galaxy's mass in its central\nblack hole and the age of its most recently formed stellar component.\nHence, in addition to the established correlation between black hole\nmass, $M_{\\rm BH}$ and galaxy mass, $M_{\\rm sph}$, there seems to be a\n``second parameter'' correlation with the age of the youngest stellar\ncomponent. At any given value of $M_{\\rm sph}$, different age\ngalaxies will have different values of $M_{\\rm BH}$, so this secondary\ncorrelation must go some way toward explaining the scatter in the\nprimary relation. \n\nWe have sought to quantify the contribution of this second parameter\nto the scatter in the relation between $M_{\\rm sph}$ and $M_{\\rm BH}$\nby calculating\n\\begin{equation}\n\\log(M_{\\rm BH}/M_{\\rm sph})^* = \\log(M_{\\rm BH}/M_{\\rm sph}) - \n\\log(t/10\\,{\\rm Gyr}).\n\\end{equation}\nThis process corrects the mass ratio for the effects of age by\nsubtracting the simplest possible linear fit to the correlation in\nFig.~1. As one would expect, this correction reduces the scatter in\nthe relation: for the data in this sample, the dispersion in\n$\\log(M_{\\rm BH}/M_{\\rm sph})$ is 0.42 dex while that in $\\log(M_{\\rm\nBH}/M_{\\rm sph})^*$ is only 0.31 dex. Clearly, even the corrected mass\nratio still contains considerable scatter. However, given the large\nuncertainties in the individual black hole mass and galaxy age\ndeterminations, it would be very surprising if the dispersion were\nreduced below a factor of two ($\\sim 0.3$ dex).\n\nThe simplest explanation for the existence of the second parameter\ncorrelation is that a single physical process couples the growth of\nthe central black hole to the triggering of star formation in a\ngalaxy. As outlined in the Introduction, the hierachical picture of\ngalaxy and black hole evolution described by Kauffmann \\& Haehnelt\n(2000) suggests that galaxy mergers lie behind both processes. Where\nthe last major merger occurred long ago, it will have taken place in a\ngas-rich environment that will provide ample fuel to augment the mass\nof the black hole. Since the last major episode of star formation\nwill also be triggered in the merger, such galaxies will contain old\nstellar populations and massive black holes. Conversely, galaxies\nformed in more recent mergers will contain under-massive black holes\nand younger stellar populations.\n\nAlthough the correlation between black hole mass and galaxy age is\npredicted by the hierarchical merging models, it should be borne in\nmind that such a correlation is a fairly generic prediction of any\nmodel in which the black hole mass grows over time. Even if galaxies\nform monolithically, those that form first -- and hence contain the\noldest stellar populations -- will have had time to grow the largest\nblack holes. The models that do not fit easily with this correlation\nare those in which the black holes and stellar components form at\nentirely different times -- it would be hard to explain the observed\ncorrelation if, for example, the central black holes were entirely\nprimordial.\n\nThe study of black hole demographics is maturing rapidly, and, as we\nhope we have shown, it is already possible to detect phenomena beyond\nthe basic relation between $M_{\\rm BH}$ and $M_{\\rm sph}$. In the\nnear future, larger sets of both the kinematic and line-strength data\nwill become available, and more sophisticated modelling techniques\nwill be developed to refine the estimates for black hole masses and\ngalaxy ages. With these tools, it will become possible to address\nsubtler questions, such as whether a galaxy's environment plays a\nsignificant role in its black hole growth rate. Such analyses will\nprovide key tests for theories of black hole formation within the\nbroader context of galaxy evolution.\n\n\\section*{Acknowledgments}\n\nIt is a pleasure to thank the referee, Bob Mann, for a range of\nhelpful suggestions.\n\n\n\\begin{thebibliography}{99}\n\\bibitem{b8} Forbes, D.A., Ponman, T.J., Brown, R.J.N., 1998, ApJ, 508, L43\n\\bibitem{b2} Ho, L., 1999, in ``Observational evidence for black holes\nin the Universe,'' ed. S. K. Chakrabarti (Dordrecht: Kluwer)\n\\bibitem{b5} Kauffmann, G., \\& Haehnelt, 2000, MNRAS, submitted\n%(astro-ph/9906493) \n\\bibitem{b6} White, S.D.M., \\& Rees, M.J., 1978, MNRAS, 183, 341\n\\bibitem{b1} Lynden-Bell, D, 1969, Nat., 223, 690\n\\bibitem{b4} Magorrian, J., et al., 1998, AJ, 115, 2285\n\\bibitem{b11} Terlevich , A.I., Forbes, D.A., 2000, in preparation\n\\bibitem{b9} Trager, S.C., Worthey, G., Faber, S.M., Burstein, D., \nGonzalez, J.J., 1998, ApJS, 116, 1\n\\bibitem{b3} van der Marel, R.P., 1997, in Galaxy Interactions at Low and\nHigh redshift, Proc. IAU Symposium 186 (Kluwer, Dordrecht)\n\\bibitem{b10} Worthey, G., 1994, ApJS, 95, 107\n\n\n\\end{thebibliography}\n\\label{lastpage}\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002350.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{b8} Forbes, D.A., Ponman, T.J., Brown, R.J.N., 1998, ApJ, 508, L43\n\\bibitem{b2} Ho, L., 1999, in ``Observational evidence for black holes\nin the Universe,'' ed. S. K. Chakrabarti (Dordrecht: Kluwer)\n\\bibitem{b5} Kauffmann, G., \\& Haehnelt, 2000, MNRAS, submitted\n%(astro-ph/9906493) \n\\bibitem{b6} White, S.D.M., \\& Rees, M.J., 1978, MNRAS, 183, 341\n\\bibitem{b1} Lynden-Bell, D, 1969, Nat., 223, 690\n\\bibitem{b4} Magorrian, J., et al., 1998, AJ, 115, 2285\n\\bibitem{b11} Terlevich , A.I., Forbes, D.A., 2000, in preparation\n\\bibitem{b9} Trager, S.C., Worthey, G., Faber, S.M., Burstein, D., \nGonzalez, J.J., 1998, ApJS, 116, 1\n\\bibitem{b3} van der Marel, R.P., 1997, in Galaxy Interactions at Low and\nHigh redshift, Proc. IAU Symposium 186 (Kluwer, Dordrecht)\n\\bibitem{b10} Worthey, G., 1994, ApJS, 95, 107\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002351
|
Transport Phenomena and Light Element Abundances in the Sun and Solar Type Stars
|
[
{
"author": "Sylvie Vauclair"
}
] |
The observations of light elements in the Sun and Solar type stars give special clues for understanding the hydrodynamical processes at work in stellar interiors. In the Sun $^7$Li is depleted by 140 while $^3$He has not increased by more than $\cong~10\%$ in 3 Gyrs. Meanwhile the inversion of helioseismic modes lead to a precision on the sound velocity of about $.1\%$. The mixing processes below the solar convection zone are constrained by these observations. Lithium is depleted in most Pop~I solar type stars. In halo stars however, the lithium abundance seems constant in the ``spite plateau" with no observed dispersion, which is difficult to reconcile with the theory of diffusion processes. In the present paper, the various relevant observations will be discussed. It will be shown that the $\displaystyle \mu $-gradients induced by element settling may help solving the ``lithium paradox".
|
[
{
"name": "vauclair.tex",
"string": "\\documentstyle[11pt,newpasp,twoside]{article}\n\\markboth{Sylvie Vauclair}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{Transport Phenomena and Light Element Abundances in the Sun and Solar Type Stars}\n \\author{Sylvie Vauclair}\n\\affil{Laboratoire d'Astrophysique, 14 av. Ed. Belin, 31400-Toulouse, France }\n\n\\begin{abstract}\n\n The observations of light elements in the Sun and Solar type stars give special clues for\nunderstanding the hydrodynamical processes at work in stellar interiors. In the Sun $^7$Li\nis depleted by 140 while $^3$He has not increased by more than $\\cong~10\\%$ in 3 Gyrs.\nMeanwhile the inversion of helioseismic modes lead to a precision on the sound velocity of\nabout $.1\\%$. The mixing processes below the solar convection zone are constrained\nby these observations. \nLithium is depleted in most Pop~I solar type stars. \nIn halo stars however, the lithium abundance seems constant in the ``spite\nplateau\" with no observed dispersion, which is difficult to reconcile with the theory of\ndiffusion processes. \nIn the present paper, the various relevant observations will be\ndiscussed. It will be\nshown that the $\\displaystyle \\mu $-gradients induced \nby element settling may help solving the ``lithium\nparadox\".\n\n\n\\end{abstract}\n\n\\section{Introduction}\nElement diffusion and mixing processes in stellar interiors are now widely constrained,\nfirst by detailed observations of abundances, second by helio and asteroseismology.\nIn most cases however, pure microscopic diffusion in stars would lead to abundance\nvariations much larger than those observed : mild macroscopic motions in stellar radiative\nzones are definitely needed to account for the observations. This gives strong constraints\non the kind of mixing processes allowed. Other constraints come from the consequences of the\nnuclear reactions occuring in stellar interiors : in some cases stellar mixing from the\natmosphere down to the regions of nuclear processing is needed to explain the observed\nelement abundances. This is the case, for example, to account for the depletion of lithium\nin the Sun and solar type stars. \n\nLithium observations in main-sequence population I field stars and galactic clusters show a\nlarge abundance dispersion which has been extensively studied in the literature (see\n reviews by Deliyannis 2000, Charbonnel 2000, Michaud 2000 and Pinsonneault 2000). \nThe lithium abundance\ndecreases for decreasing effective temperature below 5500K and the depletion increases with\nincreasing age. This is generally attributed to the deepening of the convective zone,\nassociated with some mild mixing process connecting the bottom of the convective zone\nwith the nuclear destruction region.\n\nLithium is also depleted in F-type\nstars (the so-called ``Boesgaard dip\"). Several possible reasons have been invoked to explain\nthis feature, most related to mixing and nuclear destruction.\nElement segregation has been proved negligible here as it would lead to\nunobserved variations of metal abundances (Turcotte et al 1998)\nand beryllium (Boesgaard 2000).\n\nOn the other hand, observations of lithium in main-sequence population~II field stars show\nremarkably constant abundances, with a very small dispersion (e.g. Bonifacio and Molaro\n1997)\nWhy is lithium destroyed in Pop~I stars while it does not seem destroyed in Pop~II stars?\n\nFor the same effective temperatures, the convective zone is smaller in Pop~II stars than in\nPop~I stars because of their smaller metallicity. Meanwhile they have a smaller rotation\nvelocity on the average. This could explain why the lithium destruction induced by nuclear\nreactions is smaller in these stars than in Pop~I stars.\nHowever the element segregation is more important for smaller\ndensities and smaller rotation, so that this process should lead to a visible lithium\ndepletion, which is not observed (Vauclair and Charbonnel 1995 and 1998).\nThis represents the so-called\n``lithium paradox\". Here we suggest that the influence of\n$\\displaystyle \\mu $-gradients on the rotation-induced mixing may help solving this paradox.\n\n\\section{Competition between rotation induced mixing and element diffusion}\n\nIn rotating stars, the equipotentials of ``effective gravity'' (including the centrifugal\nacceleration) have\nellipsoidal shapes while the energy transport still occurs in a spherically\nsymetrical way. The resulting thermal imbalance must be compensated\nby macroscopic motions: the so-called ``meridional circulation''\n(Von Zeipel 1924). The stellar regions outside the convective\nzones cannot be in complete radiative equilibrium. They\nare subject to entropy variations given by~:\n\\begin{eqnarray}\n\\rho T \\left( {\\partial S \\over \\partial t} + {\\bf u} \\cdot {\\bf \\nabla} S\\right)\n & = & - {\\bf \\nabla} \\cdot {\\bf F} +\n\\rho \\varepsilon _{n} \\nonumber \\\\\n& = & \\rho \\varepsilon _{\\Omega} \\ (\\not= 0)\n\\end{eqnarray}\nwhere $\\displaystyle {\\bf F}$ represents the heat flux, $\\displaystyle \\varepsilon _{n}$ the\nnuclear\nenergy production and $\\displaystyle \\varepsilon _{\\Omega}$ an energy generation\nrate which results from sources and sinks of energy along the\n equipotentials.\n\nThe vertical component of the meridional velocity $\\displaystyle u_{r}$ is computed\nas a function of $\\displaystyle \\varepsilon _{\\Omega}$ in the stationary\nregime (from eq. 1):\n\n\\begin{equation}\nu_{r} = \\left( {P \\over C_{p}\\rho T }\\right)\n{\\varepsilon _{\\Omega} \\over g }\n\\end{equation}\nwhich, for a perfect gas, reduces to:\n\\begin{equation}\nu_{r} =\n{\\varepsilon _{\\Omega} \\over g} \\\n{{\\bf \\nabla} _{{\\rm ad}}\n \\over{\\bf \\nabla}_{{\\rm ad}} - {\\bf \\nabla} + \\nabla_{\\mu }}\n\\end{equation}\nwhere $\\displaystyle g$ represents the local gravity,\n$\\displaystyle {\\bf \\nabla}_{{\\rm ad}}$ and\n$\\displaystyle {\\bf \\nabla}$ the usual adiabatic and real ratios\n$\\displaystyle \\left( {d \\ln T\\over d \\ln P }\\right)$\nand $\\displaystyle \\nabla_{\\mu }$ the mean molecular weight\ncontribution\n$\\displaystyle \\left( {d \\ln \\mu \\over d \\ln P}\n\\right)$.\n\n\nThe expression of $\\displaystyle \\varepsilon _{\\Omega}$ is\ncomputed by expanding the right-hand-side of eq.~(1) on a level surface\nand writing that its mean value vanishes.\n\nMestel (1953, 1957 and 1965)\npointed out that, in the presence of vertical $\\displaystyle \\mu $-gradients,\n$\\displaystyle \\varepsilon _{\\Omega}$ contains two kinds of terms : those related\nto the resulting horizontal variations of $\\displaystyle \\mu $:\nthe so-called ``$\\displaystyle \\mu $-induced currents''\n$\\displaystyle E_{\\mu }$\nand those independent of\n$\\displaystyle \\mu $, the so-called ``$\\displaystyle \\Omega $-induced currents''\n$\\displaystyle E_{\\Omega}$ .\nThe expression of $\\displaystyle \\varepsilon _{\\Omega}$ obtained\nin this case has been\nderived in detail by Maeder and Zahn (1998), who took into account several effects which\nwere not\nincluded in the previous computations: more general equations\nof state instead of perfect gas law, presence of a thermal\nflux induced by horizontal turbulence,\nnon-stationary cases.\n\n\nVauclair (1999) discussed more simple expressions, valid only for negligible differential\nrotation. In this case\n$\\displaystyle \\mu $-currents are opposite\nto $\\displaystyle \\Omega$-currents in most of the star \nand $\\displaystyle \\varepsilon _{\\Omega}$ may be written :\n\n\\begin{equation}\n\\varepsilon _{\\Omega} =\n\\left( {L \\over M}\\right)\n\\left( E_{\\Omega} + E_{\\mu }\\right) P_{2}\n(\\cos \\theta)\n\\end{equation}\nwith:\n\\begin{eqnarray}{}\nE_{\\Omega} & = & {8 \\over 3}\n\\left({\\Omega^{2}r^{3} \\over GM }\\right)\n\\left( 1 - {\\Omega^{2} \\over 2\\pi G\\overline \\rho }\n\\right) \\\\\nE_{\\mu } & = & {\\rho _{m} \\over \\overline \\rho }\n\\left\\{\n{ r \\over 3 } \\\n{d \\over dr }\n\\left[\n\\left(\nH_{T}\n{d \\Lambda \\over dr}\\right)\n- (\\chi_{\\mu } + \\chi_{T} + 1) \\Lambda \\right]\n- {2 H_{T} \\Lambda \\over r } \\right\\}\n\\end{eqnarray}\n\nHere $\\displaystyle \\overline \\rho $ represents\nthe density average on the level surface\n$\\displaystyle (\\simeq \\rho )$ while\n$\\displaystyle \\rho _{m}$ is the mean density inside\nthe sphere of radius $\\displaystyle r$;\n$\\displaystyle H_{T}$ is the\ntemperature scale height;\n$\\displaystyle \\Lambda$ represents the\nhorizontal $\\displaystyle \\mu $ fluctuations\n$\\displaystyle {\\tilde{ \\mu}\\over \\overline \\mu } $;\n$\\displaystyle \\chi _{\\mu }$ and\n$\\displaystyle \\chi _{T}$ represent the\nderivatives:\n\\begin{equation}\n\\chi_{\\mu } =\n\\left(\n{\\partial \\ln \\chi \\over \\partial \\ln \\mu }\\right)_{P,T}\n\\quad ; \\quad\n\\chi_{T} =\n\\left( {\\partial \\ln \\chi \\over \\partial \\ln T }\\right)_{P, \\mu }\n\\end{equation}\n\n\nVertical $\\displaystyle \\mu $-gradients may occur in\nstars due to two different processes : first the nuclear reactions which occur in the\nstellar cores, second the helium settling which occurs in the outer layers.\nThe importance of the first process\nin reducing or even suppressing the meridional motions has been demonstrated\nseveral times in the literature (e.g. Huppert and\nSpiegel 1977). The second process on the other hand has not been extensively studied.\nWe claim here that it may play a crucial role for understanding the lithium problem in Pop~I\nand Pop\n~II stars.\n\n\n\\section{Application to Pop~II stars}\n\nComputations of $\\displaystyle \\mu $-currents induced by the helium settling in halo stars\nhave been performed by Vauclair 1999 and Th\\'eado and Vauclair 2000 a and b.\nWe found that, for\nslow rotation, $\\displaystyle \\mu $-currents cancel\n$\\displaystyle \\Omega$-currents for very small concentration gradients,\ncorresponding to $\\displaystyle \\mu $-gradients\nof order $\\displaystyle 10^{-15}$~cm$^{-1}$.\n\nLet us summarize the situation of a slowly rotating star\nin which element settling leads to an increase of the\n$\\displaystyle \\mu $-gradient below the outer convection\nzone.\nAt the beginning, the star is homogeneous and meridional\ncirculation can occur, leading to upward flows in the polar\nregions and downward flows in the equatorial parts\n(except in the very outer layers where the Gratton-\\\"Opik\nterm becomes important, which we do not discuss here).\nThe $\\displaystyle \\mu $-currents, opposite to the\nclassical $\\displaystyle \\Omega$-currents, are first\nnegligible. The $\\displaystyle \\mu $-gradients\nincreasing with time because of helium settling, the order\nof magnitude of the $\\displaystyle \\mu $-currents also\nincreases until it reaches \nthe value for which the circulation vanishes.\n\nThis does not occur all at once:\nas the $\\displaystyle \\mu $-gradient decreases\nwith depth below the convective zone, we expect that the meridional\ncirculation freezes out step by step (see figure 1 of Th\\'eado\nand Vauclair 2000a). An equilibrium situation\nmay be reached, in which the temperature and mean molecular\nweight gradients along the level surfaces are such that\n$\\displaystyle \\Omega$-currents and\n$\\displaystyle \\mu $-currents cancel each other.\n\nOnce it is reached, this equilibrium situation is quite robust. Suppose that some\nmechanism leads to a decrease of the\n $\\displaystyle \\mu $-gradient: then $\\displaystyle \\vert E_{\\mu }\\vert$ becomes smaller\nthan $\\displaystyle \\vert E_{\\Omega }\\vert $ and the circulation\ntends to be restablished in the $\\displaystyle \\vert E_{\\Omega }\\vert $\ndirection, thereby restoring the original $\\displaystyle \\mu $ gradient.\nSuppose now that the\n $\\displaystyle \\mu $-gradient is increased.\nThen $\\displaystyle \\vert E_{\\mu }\\vert$ becomes larger than\n$\\displaystyle \\vert E_{\\Omega }\\vert $ and the circulation begins in\nthe $\\displaystyle E_{\\mu }$ direction.\nHere again the original gradient is restored.\n\nWhen the meridional circulation is frozen below the convective zone, helium settling could \nproceed further; however, due to the increase of the diffusion time scale with depth,\nthis would modify the $\\displaystyle \\mu $-gradient. We may thus expect that\n$\\displaystyle \\mu $-currents would take place and restore the original equilibrium\ngradient, thereby strongly reducing the microscopic diffusion\n(Th\\'eado and Vauclair 2000b).\nThis self-regulating process could be the reason for the low dispersion of the\nlithium abundance in the lithium plateau of halo stars.\n\n\\section{Discussion : Pop I versus Pop II stars}\n\nThere are many observations in stars which give evidences of mixing processes\noccuring below the outer convective zones as, for example, the lithium depletion\nobserved in the Sun and in galactic clusters. The process we have described\nabove should not apply in all these stars. The reason could be related to the\nrapid rotation of young stars on the ZAMS and to their subsequent\n rotational braking.\n\n\nThe abundance determinations in the solar photosphere show that lithium\nhas been depleted by a factor of about 140 compared to the protosolar\nvalue while beryllium has not been\ndepleted by more than a factor 2, and maybe much less, as discussed by Balachandran and\nBell (1997).\nThese values represent strong constraints on the mixing processes in the solar interior.\n\nObservations of the $^3$He/$^4$He ratio in the solar\nwind\nand in the lunar rocks (Geiss 1993,\nGeiss and Gloecker 1998) show that this ratio may not\nhave increased by more than $\\cong~10\\%$ since 3 Gyr in the Sun.\nWhile the occurence of some mild mixing below\nthe solar convective zone is needed to explain\nthe lithium depletion ,\nthe $^3$He/$^4$He\nobservations put a strict constraint on its efficiency. The only way to obtain such a result\nis to postulate a mild mixing, which would be efficient down to the lithium nuclear burning\nregion but not too far below, to preserve the original $^3$He abundance. The efficiency of\nthis mixing should also decrease with time, as the $^3$He peak itself builts up during the\nsolar life.\n\nIt is interesting to compute the minimum\nenhancement of the $^3$He/$^4$He ratio implied by the lithium observed\ndepletion.\nVauclair and Richard 1998 showed that it is\npossible to deplete lithium by a factor larger than $100$ as observed\nand\nnot increase $^3$He/$^4$He by more than 5 percent since the solar\norigin. In this case beryllium is only depleted by about 10 percent.\n\nSuch a confined mixing zone is also needed from helioseismology~:\nalthough the introduction of pure element settling in the solar models considerably\nimproves the consistency with the seismic Sun, some discrepancies do remain, particularly\nbelow the\nconvective zone where a \"spike\" appears in the sound velocity (Richard et al 1996,\nTurck-Chi\\`eze et al. 1998). It has been shown that this behavior may be due to the helium\ngradient which would be too strong in case of pure settling. Mild macroscopic motions below\nthe convective zone slightly decrease this gradient and helps reducing the discrepancy\n(Richard et al 1996, Corbard et al 1998, Brun et al 1998).\nThe helium profiles directly obtained from\nhelioseismology (Basu 1998, Antia and Chitre 1998) show indeed a helium gradient smoother\nthan the gradient obtained with pure settling.\n\nThe constraints implied by both the helioseismic inversions and\nabundance determinations in the Sun converge towards the existence of a\nsmall mild mixing region below the convective zone, which would extend\ndown to a depth of the order of one scale height.\nThe implied mixing region must be very mild, with diffusion\ncoefficients of $10^3$ - $10^4$ only.\nIt must also be completely deconnected\nfrom the solar core. No mixing can indeed be allowed down to the nuclear\nenergy production region as it would lead to a sound velocity\nincompatible with helioseismology. In particular the mixing processes\ninvoked by Morel and Schatzman 1996 to decrease the neutrino fluxes are excluded by\nhelioseismology (Richard and Vauclair 1997).\n\nMixing processes localized at the boundary between convective and radiative regions include\novershooting and regions of large differential rotation like the ``tachocline\" below the\nsolar convective zone. Up to now, overshooting was generally treated in the models simply as\na continuation of the convective zone on a fraction of a pressure scale height. Recent\nparametrisations use a diffusion coefficient which decreases exponentially with decreasing\nradius (Freytag et al 1996). The tachocline, which represents in the present Sun the small\nboundary between the region of large differential rotation (in the convective zone) and the\nregion of solid rotation (in the radiative zone below) is also treated as a mixed layer with\nan exponentially decreasing diffusion coefficient (Brun et al 1998, Richard 1999). Results\nare encouraging, although more sophisticated numerical simulation including 2-D abundance\nvariations would be needed to go further.\n\nIn any case, the self-regulating process that we have discussed for halo stars in section~3\nwould not apply below the convective zone in the Sun and solar type stars because of the\ndifferential rotation which takes place there. Such a differential rotation would not be\nexpected in halo stars if we suppose that they always rotated slowly and thus did not suffer\nlarge transport of angular momentum. The different behavior for the lithium abundance in\nPop~I and Pop~II stars could thus be directly related to their rotation history.\n\n\n\n\\begin{references}\n\n\\reference Antia, H.M., Chitre, S.M., 1998, {\\it A\\&A} {\\bf 339}, 239\n\\reference Balachandran, S.C., Bell, R.A., 1997, {\\it American Astronomical Society Meeting}\n{\\bf 191}, 7408\n\\reference Basu, S., 1998, {\\it M.N.R.A.S.} {\\bf 298}, 719\n\\reference Boesgaard, A.M., 2000, to be published in {\\it The 11th Cambridge Workshop on\ncool stars, stellar systems and the sun,\nChallenges for the New Millenium}\n\\reference Bonifacio P., Molaro P., 1997, MNRAS, 285, 847\n\\reference Brun, A.,S., Turck-Chieze, S., Morel, P., 1998, {\\it ApJ}\n{\\bf 506}, 113\n\\reference Charbonnel, C., 2000, this meeting\n\\reference Corbard,T., Berthomieu, G., Provost, P., Morel, P., 1998, {\\it A\\&A} {\\bf 330},\n1149\n\\reference Deliyannis, C., 2000, this meeting\n\\reference Freytag,B., Ludwig,H., Steffen M., 1996, {\\it A\\&A}\n{\\bf 313}, 497\n\\reference Geiss, J.: 1993, {\\it Origin and Evolution of the Elements},\ned. Prantzos, Vangioni-Flam \\& Cass\\'e (Cambridge Univ.\nPress), {\\bf 90}\n\\reference Geiss, J., Gloecker, G., 1998, {\\it Space Science Reviews} {\\bf 84}, 239\n\\reference Huppert, H.E., Spiegel, E.A., 1977, {\\it ApJ} {\\bf 213}, 157\n\\reference Maeder A., Zahn J.-P., 1998, {\\it A\\&A} {\\bf 334}, 1000\n\\reference Mestel L., 1953, {\\it M.N.R.A.S.} {\\bf 113}, 716\n\\reference Mestel L., 1957, {\\it ApJ} {\\bf 126}, 550\n\\reference Mestel L., 1965, Stellar Structure, in Stars and StellarSystems, vol 8, ed. G.P.\nKuiper, B.M. Middlehurst, Univ. Chicago Press, 465\n\\reference Michaud, G., 2000, this meeting\n\\reference Pinsonneault, M., 2000, this meeting\n\\reference Richard, O., 1999, {\\it PhD thesis} , University of Toulouse\n\\reference Richard, O., Vauclair, S., Charbonnel, C., Dziembowski,\nW.A., 1996, {\\it A\\&A} {\\bf 312}, 1000\n\\reference Richard, O., Vauclair, S., 1997, {\\it A\\&A} {\\bf 322}, 671\n\\reference Th\\'eado, S., Vauclair, S., 2000 a, this meeting\n\\reference Theado, S., Vauclair, S., 2000 b, preprint\n\\reference Turck-Chieze, S., Basu, S., Berthomieu, G., Bonnano, A., Brun, A.S.,\nChristensen-Dalsgaard, J., Gabriel, M., Morel, P., Provost, J., Turcotte, S., The Golf Team,\n1998, in {\\it Structure and Dynamics of the Interior of the Sun and Sun-like Stars} ESA\nPublications Division, SP-418, 555\n\\reference Turcotte, S., Richer, J., Michaud, G. Iglesias,\nC.A., Rogers, F.J., 1998, {\\it ApJ} {\\bf 504}, 539\n\\reference Vauclair, S., 1999, {\\it A\\&A} {\\bf 351}, 973\n\\reference Vauclair, S., Charbonnel, C., 1995, {\\it A\\&A} {\\bf 295}, 715\n\\reference Vauclair, S., Charbonnel, C., 1998, {\\it ApJ} {\\bf 502}, 372\n\\reference Vauclair, S., Richard, O.: 1998, in {\\it Structure and Dynamics of the Interior\nof the Sun and Sun-like Stars} ESA Publications Division, SP-418, 427\n\\reference Von Zeipel H., 1924, {\\it M.N.R.A.S.} {\\bf 84}, 665\n\n\n\\end{references}\n\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002352
|
Self-regulated hydrodynamical process in halo stars : a possible explanation of the lithium plateau
|
[
{
"author": "Sylvie Th\\'eado and Sylvie Vauclair"
}
] |
It has been known for a long time (Mestel~1953) that the meridional circulation velocity in stars, in the presence of $\displaystyle \mu $-gradients, is the sum of two terms, one due to the classical thermal imbalance ($\displaystyle \Omega$-currents) and the other one due to the induced horizontal $\displaystyle \mu $-gradients ($\displaystyle \mu $-induced currents, or $\displaystyle \mu $-currents in short). In the most general cases, $\displaystyle \mu $-currents are opposite to $\displaystyle \Omega$-currents. Vauclair (1999) has shown that such processes can, in specific cases, lead to a quasi-equilibrium stage in which both the circulation and the helium settling is frozen. Here we present computations of the circulation currents in halo star models, along the whole evolutionary sequences for four stellar masses with a metallicity of [Fe/H] = -2. We show that such a self-regulated process can account for the constancy of the lithium abundances and the small dispersion in the Spite plateau.
|
[
{
"name": "theado_papier.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Th\\'eado and Vauclair}{Self-regulated hydrodynamical process\n in halo stars}\n\\pagestyle{myheadings}\n\n\\begin{document}\n\\title{Self-regulated hydrodynamical process\n in halo stars : a possible explanation of the lithium plateau}\n\\author{Sylvie Th\\'eado and Sylvie Vauclair}\n\\affil{Laboratoire d'Astrophysique, 14 av. Ed. Belin, 31400 Toulouse,\n France}\n\n\\begin{abstract}\nIt has been known for a long time (Mestel~1953) that the meridional\ncirculation velocity in stars, in the presence of \n$\\displaystyle \\mu $-gradients, is the sum of two terms, one due to\nthe classical thermal imbalance ($\\displaystyle \\Omega$-currents)\nand the other one due to the induced horizontal\n$\\displaystyle \\mu $-gradients ($\\displaystyle \\mu $-induced\ncurrents, or $\\displaystyle \\mu $-currents in short). In the most\ngeneral cases, $\\displaystyle \\mu $-currents are opposite to\n$\\displaystyle \\Omega$-currents. Vauclair (1999) has shown that\nsuch processes can, in specific cases, lead to a quasi-equilibrium\nstage in which both the circulation and the helium settling is frozen.\nHere we present computations of the circulation currents in halo star\nmodels, along the whole evolutionary sequences for four stellar masses\nwith a metallicity of [Fe/H] = -2. We show that such a self-regulated\nprocess can account for the constancy of the lithium abundances and the\nsmall dispersion in the Spite plateau.\n\\end{abstract}\n\n>From spectroscopic observations, the lithium abundance in main\nsequence Pop~II field stars with effective temperatures larger than\n5500~K is remarkably constant, with a very low dispersion if any (Spite\n\\& Spite 1982; Spite et al. 1996; Bonifacio \\& Molaro 1997; Molaro 1999), while \nlarge lithium abundance dispersions do occur for Pop I\nstars.\nWe claim that the reason for this behavior may be due to the\nself-regulating process in slowly rotating stars as described by\nVauclair (1999).\n\nIn rotating stars, the equipotentials of ``effective gravity''\n(including the centrifugal acceleration) have\nellipsoidal shapes while the energy transport still occurs in a\nspherically\nsymetrical way. The resulting thermal imbalance must be compensated\nby macroscopic motions: the so-called ``meridional circulation''(Von Zeipel 1924;\nMestel 1953;\nMaeder \\& Zahn 1998). \n\nIn the presence of vertical $\\displaystyle \\mu $-gradients,\nthe circulation velocity is the sum of two terms, one which does not\ndepend on $\\displaystyle \\mu $ (the so-called ``$\\displaystyle \\Omega\n$ currents'') and one which gathers the $\\displaystyle \\mu $\ndependent terms\n(the ``$\\displaystyle \\mu $ currents'').\n\nIn the present paper, we have computed the $\\displaystyle\n\\Omega$-currents and\nthe $\\displaystyle \\mu $-currents along the evolutionary track of a .75 solar mass halo\nstars.\nAll the parameters included in the computations are the same as for the solar models\n(Richard 1999). The horizontal $\\displaystyle \\mu $ gradients \nare derived using Zahn (1992) theory of anisotropic turbulence (see\nVauclair (1999 and 2000) for details).\nThe lithium variations with time are then computed within the same framework. \n\n\\begin{figure}\n\\plotfiddle{figure1a.eps}{6.0cm}{0}{40}{40}{-220}{-90}\n\\plotfiddle{figure1b.eps}{0cm}{0}{30}{40}{20}{-65}\n\\caption{\\small{Computations of the $\\Omega$-currents and $\\mu $-currents\n and lithium abundance variation with time \nin a $0.75 M_{\\odot}$ halo stars with [Fe/H]=-2.}}\n\\end{figure}\n\nThe $\\displaystyle \\mu $-currents increase with time below the convective zone because of\nhelium settling (it also increases in the\ncore because of nuclear reactions).\nAn equilibrium situation soon occurs below the convection zone, for\nwhich the two currents become equal. Then, the circulation freezes out\nas well as the gravitational settling. Lithium decreases very slowly and remains constant\nwhen the whole star\nis ``frozen''. The depletion is not larger than $25\\%$.\nThis can explain the very small dispersion observed in the Spite plateau.\n\nThere are many observations in stars which give evidences of mixing\nprocesses\noccuring below the outer convection zones as, for example, the lithium\ndepletion\nobserved in the Sun and in galactic clusters. The process we have\ndescribed\nhere should not apply in all these stars. The reason could be related to\nthe\nrapid rotation of young stars on the ZAMS and to their subsequent\n rotational braking and differential rotation, which is not supposed\nhere to take place in halo stars.\n\n\n\\begin{references}\n\\reference Bonifacio, P., \\& Molaro, P. 1997, \\mnras, 285, 847\n\\reference Maeder, A., \\& Zahn, J.-P. 1998, \\aap, 334, 1000\n\\reference Mestel, L. 1953, Mon. Not. R. Astron. Soc., 113,\n716\n\\reference Molaro, P. 1999, preprint\n\\reference Richard, O. 1999, phD Thesis, University of Toulouse\n\\reference Spite, M., \\& Spite F. 1982, \\aap, 115, 357\n\\reference Spite, F., Francois, P., Nissen, P.E., \\& Spite, M. 1996,\n\\apj, 408, 262\n\\reference Vauclair, S. 1999, \\aap, 351, 973\n\\reference Vauclair, S. 2000, this conference\n\\reference Von Zeipel, H. 1924, \\mnras, 84, 665\n\\reference Zahn, J.-P. 1992, \\aap, 265, 115\n\\end{references}\n\n\\end{document}\n\n"
}
] |
[] |
astro-ph0002353
|
Lithium abundances in main-sequence F stars and sub-giants
|
[
{
"author": "Jose Dias do Nascimento Jr"
},
{
"author": "Sylvie Th\\'eado and Sylvie Vauclair"
}
] |
The application to main-sequence stars of the rotation-in-duced mixing theory in the presence of $\displaystyle \mu $-gradients leads to partial mixing in the lithium destruction region, not visible in the atmosphere. The induced lithium depletion becomes visible in the sub-giant phase as soon as the convective zone deepens enough. This may explain why the observed `` lithium dilution " is smoother and the final dilution factor larger than obtained in standard models, while the lithium abundance variations are very small on the main sequence.
|
[
{
"name": "dias_paper.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Dias do Nascimento, Th\\'eado and Vauclair}{Self-regulated hydrodynamical process\n in halo stars}\n\\pagestyle{myheadings}\n\n\\begin{document}\n\\title{ Lithium abundances in main-sequence F stars and sub-giants }\n\\author{Jose Dias do Nascimento Jr, Sylvie Th\\'eado and Sylvie Vauclair}\n\\affil{Laboratoire d'Astrophysique, 14 av. Ed. Belin, 31400 Toulouse,\n France}\n\n\\begin{abstract}\nThe application to main-sequence stars of the rotation-in-duced mixing\ntheory in the presence of $\\displaystyle \\mu $-gradients \nleads to partial mixing in the\nlithium destruction region, not visible in the atmosphere. The induced\nlithium depletion becomes visible in the sub-giant phase as soon as the\nconvective zone deepens enough. This may explain why the observed ``\nlithium dilution \" is smoother and the final dilution factor larger than\nobtained in standard models, while the lithium abundance variations are very small on the\nmain sequence.\n\\end{abstract}\n\nThe observations of lithium in main-sequence stars on the hot side of the \n``Boesgaard dip\" \nshow a very small dispersion for normal stars while a light depletion \n(by a factor 3) is observed in Am stars (Burckhart and\nCoupry 2000).\nOn the other hand, on the sub-giant branch, these stars present a lithium depletion\nlarger than that predicted by the standard model (do Nascimento et al. 1999). \nThese observations \nsuggest that, while on the main sequence, the stars suffer in their\ninternal layers a lithium destruction larger\nthan the standard one : this extra-destruction, which must not appear at the surface in the\nmain-sequence phase, is then dredged up during the subsequent evolution on the sub-giant\nbranch (Vauclair 1991)\n\nIt has been suggested several times \nthat the process responsible for this extra-depletion could be the result of\nrotation-induced mixing.\nComputations including such macroscopic motions as described by Zahn 1992 and\nMaeder \\& Zahn 1998 have recently been performed by Charbonnel and Talon 1999 and 2000.\nThey show that the observations on the sub-giant branch can nicely be reproduced by such\nrotation-induced mixing.\nIn their computationsi however, the effect of the microscopic diffusion of lithium was not\nintroduced on the main-sequence, for the reason that in these stars the radiative\nacceleration may balance the lithium gravitational settling. \nFor helium, on the contrary, the radiative\nacceleration is negligible : helium settling was then introduced but not taken into account\nwhile computing the meridional circulation velocity.\n\nAs shown by Mestel 1953, Maeder and Zahn 1998, Vauclair 1999, (see also Vauclair 2000 and\nTh\\'eado and Vauclair 2000),\nin the presence of vertical $\\displaystyle \\mu $-gradients,\nthe circulation velocity is the sum of two terms which leed to motions in the opposite\ndirection, one which does not\ndepend on $\\displaystyle \\mu $ (the so-called ``$\\displaystyle \\Omega\n$ currents'') and one which gathers the $\\displaystyle \\mu $\ndependent terms\n(the ``$\\displaystyle \\mu $ currents'').\nIn case of helium gravitational settling, a ``$\\displaystyle \\mu $ gradient'' builts up\nwhich soon counteracts the standard meridional circulation and an equilibrium situation \nmay be reached, which could account for the fact that lithium is preserved on the main\nsequence, while extra-mixing occurs below the ``frozen layer\".\n\n\n\\begin{figure}\n\\plotfiddle{diasfig1a.eps}{5.0cm}{0}{30}{30}{-200}{-60}\n\\plotfiddle{diasfig1b.eps}{0cm}{0}{30}{30}{10}{-35}\n\\caption{\\small {computations of the $\\Omega$-currents and $\\mu $-currents in a $1.5\nM_{\\odot}$ star\n with a rotation velocity of 40 km.s-1\nand lithium evolution on the sub-giant branch \nobtained in this case, compared to the observations}}\n\\end{figure}\n\nIn the present paper, we have computed the \nevolution of a $1.5 M_{\\odot}$ star taking into account the same effects as discussed in\nTh\\'eado and Vauclair 2000. \nWe show that, when the opposite currents are taken into account, the layer just below the\nconvection zone freezes out while mixing proceeds below. While evolving out of the\nmain-sequence, dilution induced by the deepening of the convective zone leeds to a larger\ndepletion than predicted by the standard model, reproducing the upper envelope of the\nobservations. More computations are underway to extend these results to other masses and\nrotation parameters.\n\n\n\\begin{references}\n\\reference Burkhart, C., Coupry, M.F. 2000, preprint\n\\reference Charbonnel, C., Talon, S. 1999, {\\it A\\&A} {\\bf 351}, 635\n\\reference Charbonnel, C., Talon, S. 2000, this conference\n\\reference Dias do Nascimento Jr., J.D., Charbonnel, C., L\\`ebre, A., \nde Laverny, P., de Medeiros, J.R., 1999, preprint \n\\reference Maeder, A., \\& Zahn, J.-P. 1998, \\aap, 334, 1000\n\\reference Mestel L., 1953, {\\it M.N.R.A.S.} {\\bf 113}, 716\n\\reference Th\\'eado and Vauclair 2000, this conference\n\\reference Vauclair, S. 1991, in {\\it IAU Symp. 145, Evolution of Stars : the Photospheric\nAbundance Connection ( Michaud, G., Tutukov, A. eds.) p. 327}\n\\reference Vauclair, S. 1999, \\aap, 351, 973\n\\reference Vauclair, S. 2000, this conference\n\\reference Zahn, J.-P. 1992, \\aap, 265, 115\n\\end{references}\n\n\\end{document}\n\n"
}
] |
[] |
astro-ph0002354
|
X-ray flares on zero-age- and pre-main sequence stars in Taurus-Auriga-Perseus
|
[
{
"author": "B. Stelzer\\inst {1}"
},
{
"author": "R. Neuh\\\"auser\\inst {1}"
},
{
"author": "V. Hambaryan\\inst {2}"
}
] |
We present the results of a systematic search for X-ray flares on young stars observed during {\em ROSAT} PSPC observations of the Taurus-Auriga-Perseus sky region. All pointed PSPC observations currently available from the {\em ROSAT} Public Data Archive with known pre-main sequence T Tauri Stars or young Pleiads or Hyads in the field of view are analyzed. A study of the activity of late-type stars of different ages provides information on the evolution of their coronal activity, which may be linked to their angular momentum. We develop a criterion for the detection of flares based on the shape of the X-ray lightcurve. Applying our detection method to all 104 PSPC pointings from the archive we find 52 flares. Among them 15 are detected on T Tauri Stars, 20 on Pleiads, and 17 on Hyads. Only the 38 events which can definitely be attributed to late-type stars (i.e. stars of spectral type G and later) are considered in the statistical analysis of the properties of flaring stars. We investigate the influence of stellar parameters such as age, rotation and multiplicity on individual flare parameters and flare frequency. From the total exposure time falling to the share of each sample and the duration of the individual flares we compute a flare rate. We take into account that the detection sensitivity for large X-ray flares depends on the S/N and hence on the stellar distance. The values we derive for the flare rates are $0.86 \pm 0.16$\% for T Tauri Stars, $0.67 \pm 0.13$\% for Pleiads and $0.32 \pm 0.17$\% for Hyads. The flare rate of classical T Tauri Stars may be somewhat higher than that of weak-line T Tauri Stars ($F_{c} = 1.09 \pm 0.39$\% versus $F_{w} = 0.65 \pm 0.16$\%). Hardness ratios are used to track the heating that takes place during stellar flares. Hardness ratios are evaluated for three distinct phases of the flare: the rise, the decay, and the quiescent (pre- and post-flare) stage. In most cases the hardness increases during the flares as compared to the quiescent state. During both quiescence and flare phase TTSs display the largest hardness ratios, and the Hyades stars show the softest spectrum. \keywords{stars: flare -- X-rays: stars -- stars: late-type}
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[
{
"name": "h1477_tabs.tex",
"string": "\\documentclass{aa}\n\\usepackage{times}\n\\usepackage{graphics}\n\\usepackage{xspace}\n\\usepackage{epsfig}\n\\usepackage{rotating}\n\\usepackage{dcolumn}\n\\usepackage{longtable}\n\n% This is AABIB.STY, a LaTeX style for use with BibTeX style AABIB.BST\n% and the LaTeX package of Astrononomy and Astrophysics.\n% Adapted from RRBIB.STY which was adapted from ASTRON.STY by Sake Hogeveen.\n% Rob Rutten, Sterrekundig Instituut Utrecht, January 1991.\n%\n% It defines two forms of citation: \n% the \\cite command produces: author year \n% the \\cite* command produces: author (year)\n\n\\makeatletter\n\\@ifundefined{chapter}{\\def\\thebibliography#1{\n\\section*{References} %AA put back into\n%% \\@mkboth %RR taken out\n%% {REFERENCES}{REFERENCES}} %RR taken out\n \\list\n {\\relax}{\\setlength{\\labelsep}{0em}\n \\setlength{\\itemindent}{-\\bibhang}\n \\setlength{\\itemsep}{\\parskip} %RR instead of 0pt\n \\setlength{\\parsep}{0pt}\n \\setlength{\\leftmargin}{\\bibhang}}\n \\def\\newblock{\\hskip .11em plus .33em minus .07em}\n \\sloppy\\clubpenalty4000\\widowpenalty4000\n \\sfcode`\\.=1000\\relax}}%\n{\\def\\thebibliography#1{\n%% \\chapter*{Bibliography\\@mkboth %RR taken out\n%% {BIBLIOGRAPHY}{BIBLIOGRAPHY}} %RR taken out\n \\list\n {\\relax}{\\setlength{\\labelsep}{0em}\n \\setlength{\\itemindent}{-\\bibhang}\n \\setlength{\\itemsep}{\\parskip} %RR instead op 0pt\n \\setlength{\\parsep}{0pt}\n \\setlength{\\leftmargin}{\\bibhang}}\n \\def\\newblock{\\hskip .11em plus .33em minus .07em}\n \\sloppy\\clubpenalty4000\\widowpenalty4000\n \\sfcode`\\.=1000\\relax}}\n\n\\newlength{\\bibhang}\n\\setlength{\\bibhang}{1.4em} %AA 1.4em %RR 4x instead of 1.4em\n\n\\let\\@internalcite\\cite\n\\def\\cite{\\@ifstar{\\citey}{\\citefull}}\n\\def\\citefull{\\def\\astroncite##1##2{##1\\ ##2}\\@internalcite}\n\\def\\citey{\\def\\astroncite##1##2{##1\\ (##2)}\\@internalcite}\n\\def\\citeyear{\\def\\astroncite##1##2{##2}\\@internalcite}\n\\def\\citename{\\def\\astroncite##1##2{##1}\\@internalcite}\n\\def\\@citex[#1]#2{\\if@filesw\\immediate\\write\\@auxout{\\string\\citation{#2}}\\fi\n \\def\\@citea{}\\@cite{\\@for\\@citeb:=#2\\do\n {\\@citea\\def\\@citea{; }\\@ifundefined %RR?? %RR comma instead of ;\n {b@\\@citeb}{{\\bf ??}\\@warning %RR extra ?\n {Citation `\\@citeb' on page \\thepage \\space undefined}}%\n{\\csname b@\\@citeb\\endcsname}}}{#1}}\n\n\\def\\@cite#1#2{#1\\if@tempswa #2\\fi} %RR parentheses and comma out\n\\def\\@biblabel#1{}\n\n\\def\\astroncite#1#2{#1\\ #2}\n\\makeatother\n\n\n\\newcommand{\\myrule}{\\rule[-0.1cm]{0.cm}{0.5cm}}\n\\newcommand{\\newrule}{\\rule[-0.05cm]{0.cm}{0.4cm}}\n\\newcommand{\\widerule}{\\rule[-0.05cm]{0.cm}{0.7cm}}\n\\newcommand{\\negrule}{\\rule{-0.3cm}{0.0cm}}\n\\newcommand{\\Rsun}{\\ensuremath{R_\\odot}}\n\n\\setlongtables\n\n\n\\begin{document}\n\n\\thesaurus{06(%\n08.06.1; %stars: flare\n13.25.5; %X-rays: stars\n08.12.1)} %stars: late-type\n\n\\title{X-ray flares on zero-age- and pre-main sequence stars in Taurus-Auriga-Perseus}\n\n\\author{B. Stelzer\\inst {1}, R. Neuh\\\"auser\\inst {1} \\and V. Hambaryan\\inst {2}} \n\n\\institute{Max-Planck-Institut f\\\"ur extraterrestrische Physik,\n Giessenbachstr.~1,\n D-85740 Garching,\n Germany \\and\n Astrophysikalisches Institut Potsdam,\n An der Sternwarte 16,\n D-14482 Potsdam,\n Germany} \n\n\\offprints{B. Stelzer}\n\\mail{B. Stelzer, stelzer@xray.mpe.mpg.de}\n\\titlerunning{X-ray flares in Taurus-Auriga-Perseus}\n\n\\date{Received $<$6 April 1999$>$ / Accepted $<$3 February 2000$>$ } \n\\maketitle\n \n\\begin{abstract}\n\nWe present the results of a systematic search for X-ray flares \non young stars observed during \n{\\em ROSAT} PSPC observations of the Taurus-Auriga-Perseus sky region. \nAll pointed PSPC observations currently available from the \n{\\em ROSAT} Public Data Archive \nwith known pre-main sequence T Tauri Stars or young Pleiads\nor Hyads in the field of view are analyzed. A study of the activity\nof late-type stars \nof different ages provides information on the evolution of their\ncoronal activity, which may be linked to their angular momentum.\n\nWe develop a criterion for the detection of flares based on the \nshape of the X-ray lightcurve. Applying our detection method to all \n104 PSPC pointings from the archive we find 52 flares. \nAmong them 15 are detected on T Tauri Stars,\n20 on Pleiads, and 17 on Hyads. \nOnly the 38 events which can definitely be attributed to late-type\nstars (i.e. stars of spectral type G and later) are considered in the\nstatistical analysis of the properties of flaring stars. We \ninvestigate the influence of stellar parameters such as age, rotation and\nmultiplicity on individual flare parameters and flare frequency. \n\nFrom the total exposure time \nfalling to the share of each sample and the duration of the individual\nflares we compute a flare rate. \nWe take into account that the detection sensitivity for\nlarge X-ray flares depends on the S/N and hence on the stellar distance.\nThe values we derive for the flare rates are \n$0.86 \\pm 0.16$\\% for T Tauri Stars, \n$0.67 \\pm 0.13$\\% for Pleiads and $0.32 \\pm 0.17$\\% for Hyads.\nThe flare rate of classical T Tauri Stars \nmay be somewhat higher than that of weak-line T Tauri Stars \n($F_{\\rm c} = 1.09 \\pm 0.39$\\% versus\n$F_{\\rm w} = 0.65 \\pm 0.16$\\%).\n\nHardness ratios are used to track the heating\nthat takes place during stellar flares. Hardness ratios are evaluated for \nthree distinct phases of the flare: \nthe rise, the decay, and the quiescent (pre- and post-flare) stage.\nIn most cases the hardness increases\nduring the flares as compared to the quiescent state. \nDuring both quiescence and flare phase TTSs \ndisplay the largest hardness ratios, and\nthe Hyades stars show the softest spectrum.\n\n\n\n\\keywords{stars: flare -- X-rays: stars -- stars: late-type}\n\\end{abstract}\n\n\n\\section{Introduction}\\label{sect:intro}\n\nThe Taurus-Auriga-Perseus region offers the opportunity to study \nthe X-ray emission of young stars at several evolutionary stages. The \nyoungest stars observed \nby {\\em ROSAT} in this portion of the sky are the T Tauri Stars (TTSs) of\nthe Taurus-Auriga and Perseus star forming regions, \nlate-type pre-main sequence (PMS) stars of $M \\leq 3 {\\rm M}_\\odot$ \nwith an estimated age of $10^5-10^7\\,{\\rm yrs}$. \nTwo young star clusters, the Pleiades and Hyades, are also located \nin this region of the sky at \nage of $10^8\\,{\\rm yrs}$ and $6~10^8\\,{\\rm yrs}$, respectively.\nThey consist mostly of zero-age main-sequence (ZAMS) stars, \nexcept for some higher mass post-main sequence stars and\nbrown dwarfs, which are not studied here. \n\nFrom the early observations by the {\\em Einstein} satellite \nit was concluded that the X-ray emission of young \nstars arises in an optically thin, hot plasma at temperatures above\n$10^6\\,{\\rm K}$\n(\\cite{Feigelson81.1}). The emission region has been associated with the\nstellar corona where the X-rays are produced --- more or less \nanalogous to the solar X-ray emission --- through a stellar \n$\\alpha$-$\\Omega$-dynamo. \nThe dynamo is driven by the combination of rotation and \nconvective motions. \nCorrelations between\nthe X-ray emission of late-type stars and the stellar rotation \nsupport the notion that \ndynamo-generated magnetic fields are responsible for heating the coronae\n(\\cite{Pallavicini81.1}). \nBut successful direct measurements of the magnetic fields of TTSs \nhave been performed only recently (see e.g. \\cite{Guenther99.2}).\nThe details of the heating mechanism are still not well understood.\n\nThe correlation between stellar rotation and X-ray emission of\nlate-type stars suggests that the rotational evolution of young stars \ndetermines the development of stellar activity.\nThe rotational evolution of low-mass PMS stars partly depends on the\ncircumstellar environment. While classical TTSs (hereafter cTTSs) are\nsurrounded by a circumstellar disk, inferred from IR dust emission \n(\\cite{Bertout88.1}, \\cite{Strom89.1}, and \\cite{Beckwith90.1}) and \nmore recently from direct imaging (e.g. \\cite{McCaughrean96.1}), \nweak-line TTSs (wTTSs) lack such a disk, or at least the disk is not\noptically thick. \nOwing to contraction wTTSs spin up as they approach the main\nsequence. For cTTSs, on the other hand, coupling between the \ndisk and the star may prevent spin-up (\\cite{Bouvier93.1}).\nThe period observed on the ZAMS depends on the time the star has spent\nin the cTTS phase.\nAfter the main-sequence is reached, the rotation rate decreases again \n(see \\cite{Bouvier97.1}).\nAs a consequence of their slower rotation, stars on the\nZAMS and main sequence (MS) should on average show less X-ray activity \nthan PMS stars. \n\nEarlier investigations of X-ray observations of young late-type stars\nwere mostly concerned with the quiescent emission \n(see \\cite{Neuhaeuser95.1}, \\cite{Stauffer94.1}, \\cite{Gagne95.1}, \n\\cite{Hodgkin95.1}, \\cite{Micela96.1}, 1999, \\cite{Pye94.1}, and\n\\cite{Stern94.1}).\nIn contrast to these studies we focus on the occurrence of X-ray flares.\nFurthermore we discuss a larger sample than most of the previous \nstudies by using {\\em all} currently available observations from the\n{\\em ROSAT} Public Data Archive that contain any TTS, Pleiad or Hyad\nin the field of view.\n\nX-ray flares may be used as a diagnostics of stellar activity.\nThey are thought to originate in magnetic loops.\nIn contrast to findings from quasi-static loop\nmodeling, the only direct determination of the size of a flaring\nregion (\\cite{Schmitt99.1}) shows that the emitting region is\nvery compact.\nIn the loops which confine the coronal plasma \nmagnetic reconnection suddenly frees large\namounts of energy which is dissipated into heat and thus leads to a\ntemporary enhancement of the X-ray emission. \nThe decay of the lightcurve is accompanied\nby a corresponding (exponential) decay of the temperature and emission\nmeasure, which are obtained from \none- or two-temperature \nspectral models for an optically thin, thermal plasma \n(\\cite{Raymond77.1}, \\cite{Mewe85.1}, 1986).\n\nThe most powerful X-ray flares have been observed on the\nyoungest objects, notably a flare on the infrared \nClass I protostar YLW~15 in \n$\\rho$ Oph which has been presented by \\citey{Grosso97.1}.\nX-ray flares on TTSs observed so far (see \\cite{Montmerle83.1},\n\\cite{Preibisch93.1}, \\cite{Strom94.1}, \n\\cite{Preibisch95.1}, \\cite{Gagne95.1}, \\cite{Skinner97.1}, \\cite{Tsuboi98.1})\nexceed the maximum emission observed\nfrom solar flares by a factor of $10^3$ and more. Some extreme\nevents have shown X-ray luminosities of \n$\\sim L_{\\rm x} = 10^{33}\\,{\\rm erg/s}$.\nAlthough some of the strongest X-ray flares ever observed were detected\non TTSs \nto date no systematic search for TTS flares was undertaken. \n\nThis paper is devoted to a study of the relation between X-ray flare \nactivity and other stellar parameters, such as age, rotation rate, and\nmultiplicity.\nFor this purpose \nwe perform a statistical investigation of {\\em ROSAT} observations. \nWe develop a method for the flare\ndetection based on our conception of the typical shape of a flare \nlightcurve,\nwhere the term `typical shape' refers to the characteristics of\nthe X-ray lightcurve described above, i.e. a significant\nrise and subsequent decay of the lightcurve to the previous emission\nlevel. \nThe database and source detection is\ndescribed in Sect.~\\ref{sect:data}. \nIn Sect.~\\ref{sect:lcs} we describe how the lightcurves are\ngenerated. Our flare detection algorithm is explained \nin Sect.~\\ref{sect:detect}, where\nwe also present all flare parameters derived from the X-ray lightcurves. \nThen we describe the influence of observational restrictions on the data \nanalysis and how the related biases can be overcome \n(Sect.~\\ref{sect:bias}).\nIn Sect.~\\ref{sect:statcomp} we compare the flare characteristics of \ndifferent samples of flaring\nstars selected by their age, rotation rate, and multiplicity. We\npresent luminosity functions for TTSs, Pleiads, \nand Hyads during flare and quiescence.\nLuminosity functions of the non-active state of these stars\nhave been presented before (see e.g. \\cite{Pye94.1}, \\cite{Hodgkin95.1}, \n\\cite{Neuhaeuser97.3})\nand some of the flares discussed here have been discussed \nby \\citey{Gagne95.1}, \\citey{Strom94.1}, and \\citey{Preibisch93.1}. \nHowever,\n this is the first statistical evaluation of flare luminosities. \nFlare rates comparing stellar subgroups with different properties\n(such as age, $v\\,\\sin{i}$, and stellar multiplicity)\nare compiled in Sect.~\\ref{sect:rate}. \nBecause of lack of sufficient statistics for a \ndetailed spectral analysis, hardness ratios are used to describe the\nspectral properties of the flares.\nIn Sect.~\\ref{sect:hr} we present the observed relations between \nhardness ratios measured during different activity phases and between\nhardness and X-ray luminosity.\nFinally, we discuss and summarize \nour results in Sect.~\\ref{sect:discussion} and Sect.~\\ref{sect:conclusions}.\n\n\n\n\n\\section{Database and data reduction}\\label{sect:data}\n\nIn this section we introduce the stellar sample \nand explain the analysis of the raw data. \nDetails about our membership lists for TTSs,\nPleiads, and Hyads are given below\n(Sect.~\\ref{subsect:member}). We have retrieved all pointed\n{\\em ROSAT} PSPC observations from the archive \nthat contain at least one of the stars from these lists in their field.\nThe observations are listed in Table~\\ref{tab:pids}. \nAfter performing source detection on all of these pointings, we have \ncross correlated the membership lists with the detected X-ray sources and\nidentified individual TTSs, Pleiads, and Hyads in the X-ray image.\nThe process of source detection and identification is described in \nSect.~\\ref{subsect:soudet}.\n\n\n\n\\subsection{The stellar sample}\\label{subsect:member}\n\nThe analysis presented here is \nconfined to the Taurus-Auriga-Perseus region.\nThis portion of the sky includes the Taurus-Auriga complex, the MBM\\,12\ncloud, and \nthe Perseus molecular clouds with the reflection nebula NGC\\,1333 \nand the young cluster IC\\,348. Two open clusters containing mostly\nZAMS stars are found nearby the above mentioned star forming\nregions, the Pleiades and the Hyades.\nThe choice of this specific sky region thus\nenables us to compare the X-ray emission of young stars at different ages.\n\n\\begin{figure}\n\\begin{center}\n\\resizebox{8cm}{!}{\\includegraphics{./fig1.eps}}\n\\caption{Sky map of the Tau-Aur-Per region showing the pointing positions of\nthe {\\em ROSAT} PSPC observations. On display are all PSPC pointings\nselected from the {\\em ROSAT} Public Data Archive which contain at least\none TTS, Pleiad, or Hyad from the membership lists given in the text. In\naddition all stars from the membership lists are plotted.}\n\\label{fig:skymap}\n\\end{center}\n\\end{figure}\n\nOur sample of low-mass PMS stars \nin and around Taurus consists of all TTSs\nwhich are either on or very close to the Taurus star forming clouds\nor off the clouds at locations where they can still be linked with the \nTaurus clouds (see e.g. \\cite{Neuhaeuser97.2}).\nWe restrict our Taurus sample to objects between \n$\\alpha _{2000} = 2h$ and $5h$\nand $\\delta _{2000} = - 10^{\\circ}$ and $40 ^{\\circ}$.\nThe TTSs in Taurus comprise those \nlisted in the Herbig-Bell catalog (\\cite{Herbig88.1}; HBC), \nin \\citey{Neuhaeuser95.1} or in \\citey{Kenyon95.1}.\nIn addition we include TTSs newly identified either as\ncounterparts to previously unidentified {\\em ROSAT} sources\n(\\cite{Strom94.1}, \\cite{Wichmann96.1}, \\cite{Magazzu97.1},\n\\cite{Neuhaeuser97.2}, \\cite{Zickgraf98.1}, \n\\cite{Li98.1}, \\cite{Briceno98.1})\nor by other means \n(\\cite{Torres95.1}, \\cite{Oppenheimer97.1}, \\cite{Briceno98.1}, \n\\cite{Reid99.1}, \\cite{Gizis99.1}).\nTTSs in the molecular cloud MBM\\,12 (see \\cite{Hearty00.1}) \nare also in the examined sky region.\n\nIn addition to TTSs from Tau-Aur we include those from the Perseus molecular\ncloud complex, mainly IC\\,348 and\nNGC\\,1333, in our analysis.\nOur list of TTSs in IC\\,348 comprises X-ray detections \nidentified with H$\\alpha$ emission\nstars or with proper motion members (Tables~4~and~5 in\n\\cite{Preibisch96.1}), and emission line stars from \\citey{Herbig98.1},\nand \\citey{Luhman99.1}. TTS members of NGC\\,1333 are listed in \n\\citey{Preibisch97.3}. \n\nAll objects with low lithium strength are excluded,\nbecause it is dubious whether they are young.\nWe accept only those objects as PMS stars \nwhich show more lithium than Pleiades stars of the same spectral type,\ni.e. we exclude all those with $W_{\\lambda}$(Li) lower than $0.2$\\,\\AA~for \nF- and G-type stars and lower than $0.3$\\,\\AA~for K-type stars.\nWhen applying this criterion, we always use the spectrum\nwith the best resolution and best S/N, i.e. the high-resolution\nspectra from Wichmann et al. (in preparation). \nIf no high-resolution spectra are \navailable, we use the medium-resolution spectra from \\citey{Martin99.1},\n\\citey{Neuhaeuser97.2}, or \\citey{Magazzu97.1}.\n\nMembers of the Pleiades and Hyades clusters are \nselected from the Open Cluster database \ncompiled by C. Prosser and collegues \n(available at http://cfa-www.harvard.edu/ $\\sim$stauffer/opencl/index.html). \nThe tables collected in Prosser's database \nprovide a summary of membership classification based on different methods,\nsuch as photometry, spectra, radial velocity and H$\\alpha$ emission. In \naddition a final membership determination is given \nwhich we use to define our membership lists.\n\nFig.~\\ref{fig:skymap} shows a sky map with the positions \nof the selected PSPC observations.\n\n\n\n\\subsection{Source detection and identification}\\label{subsect:soudet}\n\nSource detection is performed on all observations given \nin Table~\\ref{tab:pids} and shown in Fig.~\\ref{fig:skymap} \nusing a combined local and map source detection algorithm based on a\nmaximum likelihood method (\\cite{Cruddace88.1}). All detections with\n$ML \\geq 7.4$ (corresponding to $\\sim 3.5$\\,Gaussian $\\sigma$ \ndetermined as best choice by \\cite{Neuhaeuser95.1}) \nare written to a source list, which is subsequently cross-correlated \nwith the membership lists introduced above. \nThe maximum distance $\\Delta$ between\noptical and X-ray position to be allowed in this identification process\ndepends on the off-axis angle of the source because the\npositional accuracy of the PSPC is worse at larger distances from the\ncenter due to broader point spread function (PSF). From distributions of \nthe normalized cumulative number of identifications versus offset $\\Delta$ \nfor different off-axis ranges we have determined the optimum\ncross-correlation radius for all detector positions (similar to\n\\cite{Neuhaeuser95.1}). A detailed\ndescription of this process together with a table providing $\\Delta$ for\ndifferent off-axis ranges will be given in Stelzer et al. (in preparation).\n\nObservations which are characterized by strong background variations \n(200020, 200008-0, and 200442), as well as observations consisting of two \nvery short intervals separated by a gap of $> 100\\,{\\rm h}$ \n(200068-0, 200914) are omitted from the flare detection and flare \nanalysis. Furthermore, \nwe neglect observations with a total duration of less than 1000\\,s.\nAll observations which have been ignored in the analysis presented in this \npaper are marked with an asterisk in Table~\\ref{tab:pids}.\n\n\\begin{table}\n\\caption{Complete list of {\\em ROSAT} PSPC pointings available from the\n{\\em ROSAT} Public Data Archive in October 1998, which include at least one\nTTS, Pleiad or Hyad from our membership lists (see text) in the field of\nview. All observations {\\em not} marked by an asterisk have been analyzed\nin this work. The total exposure time is given in Column~3. The \nremaining columns give the number of detected and\nundetected TTSs, Pleiads and Hyads \n(D -- detection, N -- non-detection). If more than one star\nwas identified with an X-ray source all identifications are\nlisted. For multiple systems each component is counted as one entry.}\n\\label{tab:pids}\n\\scriptsize\n\\begin{tabular}{rlrr@{~/~}rr@{~/~}rr@{~/~}r} \\\\ \\hline\nNo. & {\\em ROSAT} & exp\\,(s) & \\multicolumn{2}{c}{TTS} &\n\\multicolumn{2}{c}{Pleids} & \\multicolumn{2}{c}{Hyads} \\\\ \n & Pointing ID & & D & N & D & N & D & N \\\\ \\hline\n 1 & 180185p & 8897 & 16 & 7\n & 0 & 0 & 0 & 0 \\\\ \n 2 & 200001p--1 & 1520 & 0 & 2\n & 0 & 0 & 0 & 0 \\\\ \n 3 & 200001p-0 & 4486 & 23 & 12\n & 0 & 0 & 0 & 0 \\\\ \n 4 & 200001p-1 & 25591 & 26 & 9\n & 0 & 0 & 0 & 0 \\\\ \n 5 & 200008p--2$^*$ & 696 & 0 & 6\n & 2 & 162 & 0 & 0 \\\\ \n 6 & 200008p--4$^*$ & 121 & 0 & 5\n & 0 & 220 & 0 & 0 \\\\ \n 7 & 200008p--5$^*$ & 722 & 0 & 4\n & 1 & 110 & 0 & 2 \\\\ \n 8 & 200008p-0$^*$ & 5936 & 2 & 4\n & 86 & 165 & 1 & 0 \\\\ \n 9 & 200008p-2 & 7049 & 4 & 3\n & 88 & 161 & 1 & 0 \\\\ \n 10 & 200020p$^*$ & 39879 & 0 & 2\n & 0 & 0 & 13 & 8 \\\\ \n 11 & 200068p--1 & 1307 & 3 & 2\n & 49 & 184 & 0 & 0 \\\\ \n 12 & 200068p-0$^*$ & 12849 & 3 & 2\n & 93 & 155 & 1 & 0 \\\\ \n 13 & 200068p-1 & 27071 & 3 & 2\n & 101 & 145 & 1 & 0 \\\\ \n 14 & 200073p & 2376 & 0 & 1\n & 0 & 0 & 6 & 3 \\\\ \n 15 & 200082p-1$^*$ & 814 & 0 & 0\n & 0 & 0 & 0 & 2 \\\\ \n 16 & 200083p & 2799 & 0 & 0\n & 0 & 0 & 16 & 5 \\\\ \n 17 & 200107p--1 & 27692 & 0 & 0\n & 0 & 0 & 2 & 1 \\\\ \n 18 & 200107p-0 & 3923 & 0 & 0\n & 0 & 0 & 2 & 1 \\\\ \n 19 & 200402p & 10469 & 3 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 20 & 200441p & 10987 & 0 & 3\n & 0 & 0 & 15 & 8 \\\\ \n 21 & 200442p & 19948 & 2 & 0\n & 0 & 0 & 6 & 4 \\\\ \n 22 & 200443p & 20074 & 15 & 8\n & 0 & 0 & 12 & 2 \\\\ \n 23 & 200444p & 14593 & 0 & 1\n & 0 & 0 & 2 & 5 \\\\ \n 24 & 200547p & 28359 & 0 & 3\n & 0 & 0 & 0 & 0 \\\\ \n 25 & 200553p & 10961 & 0 & 0\n & 0 & 0 & 8 & 3 \\\\ \n 26 & 200556p & 22456 & 5 & 0\n & 67 & 81 & 3 & 0 \\\\ \n 27 & 200557p & 27648 & 7 & 0\n & 94 & 96 & 0 & 0 \\\\ \n 28 & 200576p & 1521 & 0 & 0\n & 0 & 0 & 12 & 2 \\\\ \n 29 & 200677p$^*$ & 650 & 3 & 13\n & 0 & 0 & 3 & 0 \\\\ \n 30 & 200694p & 1987 & 17 & 13\n & 0 & 0 & 1 & 1 \\\\ \n 31 & 200694p-1 & 5395 & 16 & 12\n & 0 & 0 & 2 & 0 \\\\ \n 32 & 200775p & 4096 & 0 & 2\n & 0 & 0 & 3 & 9 \\\\ \n 33 & 200776p & 22995 & 0 & 1\n & 0 & 0 & 10 & 5 \\\\ \n 34 & 200777p & 16296 & 0 & 1\n & 0 & 0 & 13 & 8 \\\\ \n 35 & 200778p & 1900 & 0 & 1\n & 0 & 0 & 15 & 11 \\\\ \n 36 & 200911p & 17460 & 0 & 0\n & 0 & 0 & 7 & 4 \\\\ \n 37 & 200911p-1 & 13755 & 0 & 0\n & 0 & 0 & 7 & 4 \\\\ \n 38 & 200912p & 1656 & 0 & 2\n & 0 & 0 & 3 & 6 \\\\ \n 39 & 200912p-1 & 23710 & 1 & 1\n & 0 & 0 & 5 & 4 \\\\ \n 40 & 200913p & 25341 & 2 & 0\n & 0 & 0 & 7 & 2 \\\\ \n 41 & 200914p$^*$ & 4098 & 0 & 0\n & 0 & 0 & 1 & 1 \\\\ \n 42 & 200915p & 3504 & 0 & 0\n & 0 & 0 & 2 & 2 \\\\ \n 43 & 200942p & 7367 & 0 & 0\n & 0 & 0 & 4 & 6 \\\\ \n 44 & 200945p & 4099 & 0 & 0\n & 0 & 0 & 7 & 4 \\\\ \n 45 & 200949p & 6098 & 17 & 3\n & 0 & 0 & 0 & 0 \\\\ \n 46 & 200980p & 10649 & 0 & 0\n & 0 & 0 & 3 & 3 \\\\ \n 47 & 200980p-1 & 4014 & 0 & 0\n & 0 & 0 & 3 & 3 \\\\ \n 48 & 200981p & 4491 & 2 & 1\n & 0 & 0 & 8 & 7 \\\\ \n 49 & 200982p & 7724 & 0 & 0\n & 0 & 0 & 10 & 3 \\\\ \n 50 & 201012p & 7492 & 2 & 1\n & 0 & 0 & 0 & 0 \\\\ \n 51 & 201013p & 4826 & 3 & 2\n & 0 & 0 & 0 & 0 \\\\ \n 52 & 201013p-1 & 4484 & 2 & 4\n & 0 & 0 & 0 & 0 \\\\ \n 53 & 201014p & 9910 & 1 & 1\n & 0 & 0 & 1 & 1 \\\\ \n 54 & 201015p & 10058 & 0 & 1\n & 0 & 0 & 1 & 1 \\\\ \n 55 & 201016p & 10576 & 6 & 6\n & 0 & 0 & 0 & 0 \\\\ \n 56 & 201017p & 8452 & 7 & 9\n & 0 & 0 & 0 & 0 \\\\ \n 57 & 201023p & 3058 & 0 & 0\n & 0 & 0 & 0 & 3 \\\\ \n 58 & 201025p & 5448 & 11 & 17\n & 0 & 0 & 0 & 0 \\\\ \n 59 & 201097p & 10287 & 0 & 0\n & 0 & 0 & 1 & 0 \\\\ \n 60 & 201278p & 1358 & 4 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 61 & 201278p-1 & 4028 & 4 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 62 & 201305p & 23643 & 94 & 96\n & 0 & 0 & 0 & 0 \\\\ \n 63 & 201312p & 2800 & 8 & 26\n & 0 & 0 & 0 & 0 \\\\ \n 64 & 201313p & 4027 & 22 & 12\n & 0 & 0 & 7 & 6 \\\\ \n 65 & 201314p & 2691 & 0 & 0\n & 0 & 0 & 12 & 4 \\\\ \n 66 & 201314p-1 & 1397 & 0 & 0\n & 0 & 0 & 9 & 6 \\\\ \\hline\n\\end{tabular}\n\\end{table}\n\n\\setcounter{table}{0}\n\n\\begin{table}\n\\caption{{\\em continued}}\n\\scriptsize\n\\begin{tabular}{rlrr@{/}rr@{/}rr@{/}r} \\\\ \\hline\nNo. & {\\em ROSAT} & exp\\,(s) & \\multicolumn{2}{c}{T} & \\multicolumn{2}{c}{P} & \\multicolumn{2}{c}{H} \\\\ \n & Pointing ID & & D & N & D & N & D & N \\\\ \\hline\n 67 & 201315p$^*$ & 645 & 4 & 1\n & 0 & 0 & 1 & 9 \\\\ \n 68 & 201315p-1 & 1544 & 5 & 0\n & 0 & 0 & 4 & 7 \\\\ \n 69 & 201315p-2 & 2298 & 5 & 0\n & 0 & 0 & 4 & 6 \\\\ \n 70 & 201316p & 4156 & 1 & 1\n & 0 & 0 & 3 & 3 \\\\ \n 71 & 201317p & 1731 & 0 & 0\n & 0 & 0 & 1 & 1 \\\\ \n 72 & 201319p & 1811 & 4 & 0\n & 0 & 0 & 3 & 1 \\\\ \n 73 & 201368p & 16594 & 0 & 1\n & 0 & 0 & 17 & 9 \\\\ \n 74 & 201369p & 15538 & 0 & 0\n & 0 & 0 & 24 & 4 \\\\ \n 75 & 201370p & 4975 & 0 & 1\n & 0 & 0 & 5 & 4 \\\\ \n 76 & 201370p-1 & 13652 & 1 & 0\n & 0 & 0 & 5 & 2 \\\\ \n 77 & 201484p & 7673 & 1 & 10\n & 0 & 0 & 0 & 0 \\\\ \n 78 & 201485p & 2429 & 0 & 3\n & 0 & 0 & 0 & 0 \\\\ \n 79 & 201485p-1 & 1904 & 1 & 2\n & 0 & 0 & 0 & 0 \\\\ \n 80 & 201504p & 109534 & 2 & 0\n & 0 & 0 & 4 & 0 \\\\ \n 81 & 201519p & 5889 & 2 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 82 & 201532p & 10183 & 9 & 6\n & 0 & 0 & 1 & 0 \\\\ \n 83 & 201533p & 10799 & 4 & 6\n & 0 & 0 & 0 & 0 \\\\ \n 84 & 201534p & 6213 & 0 & 1\n & 0 & 0 & 3 & 1 \\\\ \n 85 & 201598p & 5652 & 7 & 14\n & 0 & 0 & 0 & 0 \\\\ \n 86 & 201599p & 6175 & 6 & 15\n & 0 & 0 & 0 & 0 \\\\ \n 87 & 201600p & 5747 & 6 & 15\n & 0 & 0 & 0 & 0 \\\\ \n 88 & 201601p & 5817 & 5 & 16\n & 0 & 0 & 0 & 0 \\\\ \n 89 & 201602p & 5582 & 8 & 13\n & 0 & 0 & 0 & 0 \\\\ \n 90 & 201747p & 19600 & 0 & 1\n & 0 & 0 & 16 & 2 \\\\ \n 91 & 201748p & 16999 & 0 & 0\n & 0 & 0 & 2 & 3 \\\\ \n 92 & 201749p$^*$ & 924 & 0 & 0\n & 0 & 0 & 3 & 1 \\\\ \n 93 & 201749p-1 & 1540 & 0 & 0\n & 0 & 0 & 3 & 1 \\\\ \n 94 & 300178p & 710 & 0 & 7\n & 0 & 0 & 0 & 0 \\\\ \n 95 & 400312p & 10735 & 0 & 0\n & 0 & 0 & 1 & 0 \\\\ \n 96 & 700044p & 4611 & 5 & 0\n & 0 & 0 & 6 & 4 \\\\ \n 97 & 700063p & 1701 & 0 & 0\n & 0 & 0 & 1 & 0 \\\\ \n 98 & 700825p & 1435 & 0 & 0\n & 0 & 0 & 0 & 2 \\\\ \n 99 & 700825p-1 & 15744 & 0 & 0\n & 0 & 0 & 1 & 1 \\\\ \n 100 & 700913p & 2096 & 0 & 0\n & 0 & 0 & 1 & 0 \\\\ \n 101 & 700916p & 7161 & 0 & 0\n & 0 & 0 & 1 & 0 \\\\ \n 102 & 700919p & 2004 & 0 & 0\n & 0 & 0 & 1 & 0 \\\\ \n 103 & 700945p & 2516 & 0 & 0\n & 0 & 0 & 1 & 0 \\\\ \n 104 & 701055p & 9039 & 0 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 105 & 701253p & 5417 & 0 & 0\n & 0 & 0 & 0 & 2 \\\\ \n 106 & 800051p-0 & 1470 & 1 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 107 & 800051p-1 & 3347 & 1 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 108 & 800051p-2 & 3303 & 1 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 109 & 800083p & 10220 & 1 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 110 & 800104p & 7524 & 1 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 111 & 800193p & 21969 & 0 & 0\n & 0 & 0 & 3 & 3 \\\\ \n 112 & 900138p & 24899 & 6 & 0\n & 0 & 0 & 0 & 0 \\\\ \n 113 & 900154p & 28791 & 0 & 2\n & 0 & 0 & 0 & 0 \\\\ \n 114 & 900193p & 9128 & 3 & 22\n & 0 & 0 & 0 & 0 \\\\ \n 115 & 900353p & 7718 & 18 & 11\n & 0 & 0 & 12 & 4 \\\\ \n 116 & 900371p & 4227 & 1 & 0\n & 0 & 0 & 2 & 0 \\\\ \n 117 & 900371p-1 & 7718 & 0 & 0\n & 0 & 0 & 2 & 0 \\\\ \\hline\n\\end{tabular}\n\\end{table}\n\n\n\n\n\\section{Lightcurves}\\label{sect:lcs}\n\nUsing the arrival time information of the photons counted within a \npre-defined source circle lightcurves are generated for each of the \n{\\em ROSAT} sources \nthat have been identified with a TTS, Pleiad or Hyad \nfrom the membership lists. \n\nFor the source extraction radius we have used the \n99\\% quantile of the Point Spread Function (PSF) at 1\\,keV, \ni.e. the radius containing 99\\% of the 1\\,keV \nphotons at the respective off-axis angle. In contrast to the\nstandard EXSAS source radius of 2.5 FWHM, which becomes unreasonably \nlarge for off-axis sources \ndue to the extended wings of the PSF, this\nchoice of extraction radius limits the source size. \nClose to the detector center, some bright sources slightly overshine the\nnominal 99\\% quantile of the PSF probably due to small deviations from the\nassumed 1\\,keV spectrum. We have therefore checked all images\nfor such bright sources and determined a larger source radius for these\ncases based on visual inspection.\nIn crowded regions, where the \nPSF of several sources overlap, \nthe measured counts are upper limits to the actual emission of the sources.\nNone of the overlapping sources showed a flare, however, \nsuch that no further attention is drawn to the overestimation of the count\nrate in these cases.\n\nThe events measured within the circular source region are \nbinned into 400\\,s intervals. \nSince the typical duration of a flare is less than one hour,\nsignificantly longer integration times would lead to a loss of \ninformation about the structure of the lightcurve, while for shorter\nbin lengths the lightcurves are dominated by the low statistics.\nFurthermore, \nthe choice of 400\\,s integration time guarantees that no additional\nvariability is introduced by the telescope motion (wobble).\n\nDue to the earth eclipses the data stream is interrupted at\nperiodical time intervals. Depending on the phase used\nfor the time integration, at the beginning and/or end of each data segment\nthe 400\\,s intervals are only partly exposed. For the flare detection only bins\nwith full 400\\,s of exposure are used.\nTo gain independence of the\nbinning we generate lightcurves with different phasing of the 400\\,s \nintervals: First, in order to divide the given observing time into as \nmany 400\\,s exposures as possible, a lightcurve is binned in such a way that\na new 400\\,s interval starts after each observation gap. Thus, data are\nlost only at the end of each data segment, because the last bin remains\nuncomplete. Secondly, lightcurves are built by simply splitting the total \nobserving time into 400\\,s intervals beginning from the start of \nthe observation regardless of data gaps. \nIn this case data are rejected at the beginning {\\em and} \nend of each data segment. \n\nThe number of background counts falling in the source circle is determined\nfrom the smoothed background image which is created by cutting out the \ndetected sources and then performing a spline fit to the resulting image. \nThis method of background acquisition is of advantage in\ncrowded fields where an annulus around the source position -- the most widely \nused method for estimating the background -- likely is contaminated by \nother sources. The background count rate is found by dividing the\nnumber of background counts in the source circle \nthrough the exposure time extracted from the standard {\\em ROSAT} exposure map.\nTo take account of possible time variations in the background count rate, the\nbackground is determined separately for each data segment and subtracted \nfrom the measured count rate in the respective data interval. \n(When referring to `data segments'\nwe mean parts of the lightcurve that are separated from each other by gaps of\nat least 0.5\\,h.) \n\n\n\n\n\\section{Flare detection}\\label{sect:detect}\n\n\n\\subsection{The method}\\label{subsect:method_det}\n\nOne of the major elements of a flare by customary definition is \na significant increase in count rate,\nafter which the initial level of intensity is reached again. Therefore,\nour flare detection is based on the deviation of the count rate from the\n (previously determined) mean quiescent level of the source. \nTo ensure that the quiescent count rate contains no contribution from \nflares, in the first step, we determine mean count rates for all data\nsegments of each lightcurve and define the quiescent level as the lowest mean \nmeasured in any of these data segments.\n\nWe define a flare as an event which is characterized by two or more \nconsecutive time bins that constitute a sequence of either rising or falling \ncount rates, corresponding to rise and decay phase of the flare. \nIn addition, to ensure the significance of our\nflare detections, we define the upper standard deviation of the quiescent\nlevel as a point of reference and require that\n(a) all bins which are part of the flare\nare characterized by count rates higher than this level, and that (b)\nthe sum of the deviations of all these bins is more than 5\\,$\\sigma$ from \nthis level. \nA rise immediately followed by a\ndecay is counted as {\\em one} flare. \nSince the shape of a lightcurve is influenced to some degree by the binning\nused, we accept only flares that are detected in lightcurves with both\nbin phasings (see Sect.~\\ref{sect:lcs}). \n\nDetections of more than one flare in a single lightcurve are possible. \nTo estimate the contribution of each event properly,\nafter detection the decay of the first flare in each lightcurve \nis modeled by an exponential function, and a new lightcurve is generated\nby subtracting the fit function from the data. Having removed the\nfirst flare, we search for further flares in the reduced, \n`flare-subtracted' lightcurve using the same criteria as before. \nThis procedure is repeated until no additional flares are detected. \n\nSince many of the investigated sources are highly variable X-ray emitters\non timescales shorter than resolvable by our method, the\nmean count rate used until now in some cases is not a \ngood estimate for the quiescent emission. With the knowledge \nobtained about the times at which flares have occurred\nwe therefore redetermine the \nquiescent count rate taking the mean from the remaining data \nafter removal of\nall flare contributions. Using this new mean count rate we repeat the \nflare detection procedure.\n\n\n\n\\subsection{Flare Parameters}\\label{subsect:flarepar}\n\nWith the detection procedure described in the previous subsection \nwe have found 52 flares. We have always identified the nearest optical\nposition with the X-ray source. In one flare, however, two \npossible optical counterparts, DD\\,Tau and CZ\\,Tau, are closeby (at\n6$^{\\prime\\prime}$ and 24$^{\\prime\\prime}$ respectively), so that we can\nnot be sure which star flared. \nFifteen events were observed on TTSs, 20 on \nPleiads, and 17 on Hyads. On two TTSs (RXJ\\,0437.5+1851 and T\\,Tau) \nand two Hyads (VA\\,334 and VB\\,141) two flares occurred in the\nsame observation. VB\\,141 showed a third event during a\ndifferent {\\em ROSAT} exposure.\n\nHyades stars above $2\\,{\\rm M}_\\odot$, that have already\nevolved off the main-sequence, are not considered\nin the statistical analysis if they showed a flare. Brown dwarfs in \nthe Hyades and Pleiades are not on the main-sequence per definition, but\nthey are also too faint for X-ray detection (\\cite{Neuhaeuser99.1}). \nThus we discuss only the ZAMS from the Pleiades and Hyades.\n\nA complete list of all TTSs, Pleiads, and Hyads\non which at least one flare was detected \nis given in Table~\\ref{tab:opt_par}. Column~1 gives the\ndesignation of the flaring star. Column~2 is the distance estimate\nused for the count-to-energy-conversion. For TTSs \nin Taurus-Auriga we adopt a \nvalue of $140\\,{\\rm pc}$ (\\cite{Elias78.1}, \\cite{Wichmann98.1}), while\nthe TTSs in MBM\\,12 are located at $65\\,{\\rm pc}$ (\\cite{Hearty00.1}), and\nthose in Perseus are located at $350\\,{\\rm pc}$ (NGC\\,1333;\n\\cite{Herbig88.1}) and $300\\,{\\rm pc}$ (IC\\,348; \\cite{Cernicharo85.1}).\nPleiads are assumed to be at a distance of $116\\,{\\rm pc}$, the value\nderived by \\citey{Mermilliod97.1}. Finally, we use the individual\nHipparcos parallaxes for Hyades stars if available, and otherwise the mean\nvalue of $46\\,{\\rm pc}$ (\\cite{Perryman98.1}). We give\nspectral type, $v\\,\\sin{i}$, multiplicity, and binary separation \nof the stars and their respective references in columns~3 -- 9. For TTSs \nadditional columns specify whether the star is a cTTS or a wTTS.\n\n\\begin{figure*}\n\\begin{center}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig2.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig3.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig4.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig5.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig6.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig7.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig8.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig9.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig10.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig11.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig12.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig13.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig14.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n}\n\\caption{PSPC lightcurves for flares on TTSs in Taurus-Auriga and Perseus\ndetected by the procedure described in\nSect.~\\ref{subsect:method_det}. Identification of the X-ray source and {\\em\nROSAT} observation request number (in brackets) are given for each source. Binsize is 400\\,s, 1\\,$\\sigma$ uncertainties. The dashed line represents the quiescent count rate. Solid lines are exponential fits to the data points belonging to the flare down to the quiescent emission. Background count rates are shown as upper limits when the background subtracted count rate is below zero.}\n\\label{fig:lcs_TTS}\n\\end{center}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{center}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig15.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig16.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig17.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig18.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig19.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig20.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig21.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig22.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig23.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig24.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig25.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig26.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig27.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig28.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig29.ps}}}\n}\n\\caption{PSPC lightcurves for flares on members of the Pleiades cluster\ndetected by the procedure described in\nSect~\\ref{subsect:method_det}. Identification of the X-ray source and {\\em\nROSAT} observation request number (in brackets) are given for each source. Binsize is 400\\,s, 1\\,$\\sigma$ uncertainties. The dashed line represents the quiescent count rate. Solid lines are exponential fits to the data points belonging to the flare down to the quiescent emission. Background count rates are shown as upper limits when the background subtracted count rate is below zero.}\n\\label{fig:lcs_Ple}\n\\end{center}\n\\end{figure*}\n\n\\addtocounter{figure}{-1}\n\n\\begin{figure*}\n\\begin{center}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig30.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig31.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig32.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig33.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig34.ps}}}\n}\n\n\\caption{{\\em continued}}\n\\end{center}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{center}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig35.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig36.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig37.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig38.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig39.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig40.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig41.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig42.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig43.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig44.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig45.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig46.ps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig47.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig48.ps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.5cm}{!}{\\includegraphics{./fig49.ps}}}\n}\n\\caption{PSPC lightcurves for flares on members of the Hyades cluster\ndetected by the procedure described in\nSect~\\ref{subsect:method_det}. Identification of the X-ray source and {\\em\nROSAT} observation request number (in brackets) are given for each source. Binsize is 400\\,s, 1\\,$\\sigma$ uncertainties. The dashed line represents the quiescent count rate. Solid lines are exponential fits to the data points belonging to the flare down to the quiescent emission. Background count rates are shown as upper limits when the background subtracted count rate is below zero.}\n\\label{fig:lcs_Hya}\n\\end{center}\n\\end{figure*}\n\n\nThe lightcurves of all flares have been \nanalyzed by fitting an exponential to the decay of each flare. \nIn Figs.~\\ref{fig:lcs_TTS},~\\ref{fig:lcs_Ple},~and~\\ref{fig:lcs_Hya} the fit \nfunction and measured mean quiescent count rate are displayed together with the data. \nIn Tables~\\ref{tab:det_flares_TTS},~\\ref{tab:det_flares_Ple}~and~\\ref{tab:det_flares_Hya} we give the result\nof the modeling. Column~1 and column~2 contain the stellar identification \nof the X-ray source and the {\\em ROSAT} observation request number (ROR). \nThe mean quiescent \ncount rate is given in column~3, the maximum count rate inferred from the \nexponential fit to the lightcurve in column~4, and the decay \ntimescale $\\tau_{\\rm dec}$ from the fit in column~5. \nFor flares with poor data sampling\nwe did not determine the errors of $\\tau_{\\rm dec}$.\nColumn~6 is the estimated rise time of the flare. Due to data gaps \nin most cases no reasonable estimate can be given.\nLuminosities are listed in columns~7~and~8:\nquiescent luminosity $L_{\\rm qui}$, and \nmaximum luminosity during the flare $L_{\\rm max}$.\nWe assume that all stars in the system contribute the same level of\n X-ray emission during quiescence, but that only one component flares at\nany one time. Therefore, \nfor all multiple stars the observed quiescent count rate from \ncolumn~3 has been divided by the number of components \nbefore the conversion to luminosity and energy.\n\nFor the conversion from count rates to luminosities we have used \nthe mean {\\em ROSAT} PSPC energy-conversion-factor (ECF) \nfrom \\citey{Neuhaeuser95.1}, \ni.e. $ECF=1.1 \\cdot 10^{11}\\,{\\rm cts\\,cm^2/erg}$ and the distances given \nin Table~\\ref{tab:opt_par}.\nIn order to eliminate uncertainties in the distance estimate we have \ncomputed ratios of luminosity (given in column~9). \nHere, $L_{\\rm F}$ denotes the luminosity emitted during the \nflare, i.e. $L_{\\rm F} = L_{\\rm max} - L_{\\rm qui}$. \nThe total emitted energy during quiescence $E_{\\rm qui}$ (column~10) \nand during the flare alone $E_{\\rm F}$ (column~11) \nare inferred from the integration of the lightcurve \nbetween $t_{\\rm max}$ and $t_{\\rm max} + \\tau$. \nThe last column gives the reference for flares that have been \npublished previously.\nIn the last two rows of\nTables~\\ref{tab:det_flares_TTS},~\\ref{tab:det_flares_Ple}~and~\\ref{tab:det_flares_Hya}\nwe have listed the mean and median for each of the given parameters, except\n$\\tau_{\\rm ris}$ which is not well constrained. The means and medians \nhave been \ncomputed with the ASURV Kaplan-Meier estimator (see \\cite{Feigelson85.1}), \ntaking account of upper/lower limits. Lower limits of $L_{\\rm max}$ \noccur when there is doubt\nabout whether the maximum emission of the flare has been observed (due to\na data gap near the observed maximum). Upper limits for $\\tau_{\\rm dec}$\noccur when the decay is not observed because of a data gap between\nmaximum and post-flare quiescent count rate. Both luminosity and decay\ntimescale determine the flare energy, but the limits of\nthese two parameters carry opposite signs. We therefore consider all values\nof $E_{\\rm F}$ uncertain where $\\tau_{\\rm dec}$ or \n$L_{\\rm max}$ are a limit (indicated by colons in Tables~\\ref{tab:det_flares_TTS},~\\ref{tab:det_flares_Ple}~and~\\ref{tab:det_flares_Hya}) and have not included them in the \ncomputation of the mean and median.\n\n\n\\begin{table*}\n\\caption{Properties of stars in Tau-Aur-Per which flared during at\nleast one {\\em ROSAT} PSPC observation. Spectral types marked with\nan asterisk are determined from $B-V$ or $R-I$ given in the Open Cluster\ndatabase using the conversion given by\n\\protect\\citey{Schmidt-Kaler82.1}. The meaning of the flags in column\n`Multiplicity' is: B for binary, SB1 for single-lined spectroscopic binary,\nand SB2 for double-lined spectroscopic binary. \nFor one flare on TTSs it is not\nclear whether it belongs to DD\\,Tau, a cTTS, or CZ\\,Tau, a wTTS, because\nthe spatial resolution of the PSPC is too low to resolve these stars.\nDD\\,Tau and CZ\\,Tau both are binaries. Only flares on stars of spectral type G and later are\nanalysed in the remainder of this paper.}\\label{tab:opt_par}\n\\begin{tabular}{lrlrrrlrrcr}\\hline\nDesignation & Distance & \\multicolumn{2}{c}{Sp.Type (Ref)} &\n \\multicolumn{2}{c}{vsini (Ref)} & Mult & \\multicolumn{2}{c}{Binary sep} & \\multicolumn{2}{c}{TTS} \\\\ \n & \\multicolumn{1}{c}{[pc]} & & & \\multicolumn{2}{c}{[km/s]} & & [$^{\\prime\\prime}$] & & \\multicolumn{2}{c}{Type} \\\\ \\hline\n\\multicolumn{11}{c}{\\bf T Tauri Stars} \\\\ \\hline\n LkH$\\alpha$270 & 350.0 & K7M0 & (1) &\t & & &\t & & C & (1) \\\\ \n BPTau & 140.0 & K7 & (1) &\t 10.0 & (17) & &\t & & C & (1) \\\\ \n V410x-ray7 & 140.0 & M1 & (2) &\t & & &\t & & W & (2) \\\\ \n HD283572 & 140.0 & G5 I & (1) &\t 75.6 & (18) & &\t & & W & (1) \\\\ \n DDTau/CZTau & 140.0 & M1/M1.5 & (1) &\t & & B/B &\t 0.57/0.33 & (27) & C/W & (1) \\\\ \n L1551-51 & 140.0 & K7 & (1) &\t 27.0 & (1) & & & & W & (1) \\\\ \n RXJ0437.5+1851\\,B & 140.0 & M0.5 & (3) &\t 10.5 & (3) & B &\t 4.30 & (28) & W & (3) \\\\ \n LkCa19 & 140.0 & K0 & (1) &\t 18.6 & (17) & &\t & & W & (1) \\\\ \n LH$\\alpha$92 & 300.0 & K0 & (5) &\t & & &\t & & C & (1) \\\\ \n RXJ0422.1+1934 & 140.0 & M4.5 & (4) &\t & & B &\t 12.0 & (28) & C & (4) \\\\ \n TTau & 140.0 & K0 & (1) &\t 20.7 & (17) & B &\t 0.71 & (29) & C & (1) \\\\ \n RXJ0255.4+2005 & 65.0 & K6 & (6) &\t 10.0 & (6) & &\t & & W & (6) \\\\ \n LkH$\\alpha$325 & 350.0 & K7M0 & (1) &\t & & B &\t 11.0 & (30) & W & (1) \\\\ \\hline\n\\multicolumn{11}{c}{\\bf Pleiads} \\\\ \\hline\n hii1384 & 116.0 & A4V & (7) &\t 215.0 & (19) & & & & - & \\\\ \n hii2147 & 116.0 & G9 & (8) &\t 6.9 & (20) & SB2 & & (31) & - & \\\\ \n hii1100 & 116.0 & K3 & (8) &\t 5.4 & (20) & B & 0.78 & (32) & - & \\\\ \n hii303 & 116.0 & K1.4$^*$ & (9) & 17.4 & (20) & B & 1.81 & (32) & - & \\\\ \n hii298 & 116.0 & K1.4$^*$ & (9) & 6.6 & (20) & B & 5.69 & (32) & - & \\\\ \n hcg307 & 116.0 & & &\t 13.0 & (21) & & & & - & \\\\ \n hcg144 & 116.0 & & &\t & & & & & - & \\\\ \n hii2244 & 116.0 & K2.5 & (10) &\t 50.0 & (22) & &\t & & - & \\\\ \n hcg422 & 116.0 & & &\t & & &\t & & - & \\\\ \n hii1516 & 116.0 & K7$^*$ & (11) & 105.0 & (20) & &\t & & - & \\\\ \n hcg143 & 116.0 & M2$^*$ & (11) &\t & & &\t & & - & \\\\ \n sk702 & 116.0 & & &\t & & &\t & & - & \\\\ \n hii174 & 116.0 & K0.8$^*$ & (9) & 28.0 & (23) & & & & - & \\\\ \n hii191 & 116.0 & K7.7 & (12) &\t 9.1 & (20) & &\t & & - & \\\\ \n hcg97 & 116.0 & & &\t & & &\t & & - & \\\\ \n hii1653 & 116.0 & K6 & (8) &\t 21.0 & (8) & &\t & & - & \\\\ \n hii345 & 116.0 & G8 & (10) &\t 18.9 & (20) & &\t & & - & \\\\ \n hcg181 & 116.0 & M1.5$^*$ & (11) &\t & & &\t & & - & \\\\ \n hii253 & 116.0 & G1 & (10) &\t 37.0 & (23) & &\t & & - & \\\\ \n hii212 & 116.0 & M0.0 & (12) &\t 10.0 & (8) & &\t & & - & \\\\ \\hline\n\\multicolumn{11}{c}{\\bf Hyads} \\\\ \\hline\n V471Tau & 46.8 & K1.2$^*$ & (13) &\t & & &\t & & - & \\\\ \n VB50 & 44.9 & G1V & (14) &\t & & SB? & & (33) & - & \\\\ \n VA677 & 57.0 & K & (15) &\t 24.0 & (24) & SB2 & & (24) & - & \\\\ \n LP357-4 & 46.3 & M3 & (15) &\t & & &\t & & - & \\\\ \n VA275 & 46.3 & M2-3 & (15) &\t 10.0 & (25) & & & & - & \\\\ \n VB141 & 47.9 & A8$^*$ & (16) & & & &\t & & - & \\\\ \n VA334 & 41.0 & M0 & (15) &\t 6.0 & (24) & & & & - & \\\\ \n VB169 & 46.5 & A6.6$^*$ & (16) &\t & & &\t & & - & \\\\ \n VA673 & 46.3 & M1 & (15) &\t & & SB & & (34) & - & \\\\ \n VB190 & 46.3 & K & (15) &\t 8.5 & (24) & SB &\t & (32) & - & \\\\ \n VB85 & 41.2 & F5V & (14) &\t 55.0 & (26) & & & (35) & - & \\\\ \n VB45 & 47.2 & Am & (14) &\t 12.0 & (26) & SB1 & & (26) & - & \\\\ \\hline\n\\end{tabular}\n\n{\\bf Catalogues: } VB - \\cite{Bueren52.1}, VA - \\cite{Altena69.1}, LP - \\cite{Luyten81.1}, hii - \\cite{Hertzsprung47.1}, hcg - \\cite{Haro82.2}, sk - \\cite{Stauffer91.1}\n\n{\\bf References: } (1) - Herbig \\& Bell 1988, (2) - Strom \\& Strom 1994,\n(3) - Wichmann et al. (in preparation), (4) - Mart\\'\\i n \\& Magazz\\`u 1999, (5) - Herbig\n1998, (6) - Hearty et al. 2000, (7) - Mendoza 1956, (8) - Stauffer \\& Hartmann 1987,\n(9) - Johnson \\& Mitchell 1958, (10) - Soderblom et al. 1993a, (11) -\nStauffer 1982, Stauffer 1984, (12) - Prosser et al. 1991, (13) -\npriv. comm. between J. Stauffer and E. Weis according to the Open Cluster\ndata base, (14) - Morgan \\& Hiltner 1965, (15) - Pesch 1968, (16) - Morel \\& Magnenat\n1978, (17) - Hartmann \\& Stauffer 1989, (18) - Walter et al. 1987, (19) - Anderson\net al. 1966, (20) - Queloz et al. 1998, (21) - Jones et al. 1996, (22) -\nStauffer et al. 1984, (23) - Soderblom et al. 1993b, (24) - Stauffer et\nal. 1997, (25) - Stauffer et al. 1987, (26) - Kraft 1965, (27) - Leinert et\nal. 1993, (28) - K\\\"ohler \\& Leinert 1998, (29) - Ghez et al. 1993, (30) -\nCohen \\& Kuhi 1979, (31) - Raboud \\& Mermilliod 1998, (32) - Bouvier et al\n1997, (33) - Griffin et al. 1985, (34) - Stefanik \\& Latham 1992, (35) -\nZiskin 1993\n\n\\end{table*}\n\n\n\\begin{sidewaystable*}\n\\caption{Parameters derived from the lightcurves of flares on T Tauri\nStars detected in the {\\em ROSAT} PSPC observations from Table~1 (see\nSect.~\\ref{subsect:flarepar} for an explanation). The last column gives\nthe reference for flares that have been presented elsewhere in the\nliterature: [a] \\protect\\citey{Strom94.1},\n[b] \\protect\\citey{Preibisch93.1}, but newly reduced here. In the last two\nrows we give the mean (determined by taking account of lower/upper limits)\nand the median for each parameter.}\n\\label{tab:det_flares_TTS}\n\\newcolumntype{d}[1]{D{.}{.}{#1}}\n%\\begin{tabular}{llccr@{}d{2}@{}crrcr@{}d{3}@{}rcrc}\\hline\n\\begin{tabular}{llccr@{}d{2}@{}crrrr@{}d{3}@{}rcrc}\\hline\nDesig. & \\newrule ROR & $I_{\\rm qui}$ & $I_{\\rm max}$ &\n \\multicolumn{3}{c}{$\\tau_{\\rm dec}$} & \\multicolumn{1}{c}{$\\tau_{\\rm\n ris}$} & \\multicolumn{1}{c}{$L_{\\rm qui}$} &\n \\multicolumn{1}{c}{$L_{\\rm max}$} & \\multicolumn{3}{c}{$L_{\\rm\n F}/L_{\\rm qui}$} & $E_{\\rm qui}$ & \\multicolumn{1}{c}{$E_{\\rm\n F}$} & Notes \\\\\n & \\newrule & [cps] & [cps] & \\multicolumn{3}{c}{[h]} & \\multicolumn{1}{c}{[h]} & \\multicolumn{1}{c}{[erg/s]} & \\multicolumn{1}{c}{[erg/s]} & & & & [erg] & \\multicolumn{1}{c}{[erg]} & \\\\ \\hline\n LkH$\\alpha$270 \t &\t \\newrule \t 180185 \t &\t 0.061\t $\\pm$\t 0.008\t &\t 0.256\t $\\pm$\t 0.008\t &\t$<$ &\t 8.85\t &\t $\t \t \t \t \t \t $\t &\t $\t <\t 7.84\t $\t &\t 8.13e+30\t &\t$>$ 3.41e+31\t &\t$>$ &\t 3.197\t &\t \t \t &\t 2.59e+35\t &\t 5.23e+35:\t &\t \\\\ \n BPTau \t &\t \\newrule \t 200001-0 \t &\t 0.037\t $\\pm$\t 0.004\t &\t 0.247\t $\\pm$\t 0.034\t &\t &\t 2.67\t &\t $\t ^{+\t 0.96\t }_{-\t 0.92\t } \t $\t &\t $\t >\t 0.22\t $\t &\t 7.89e+29\t &\t 5.27e+30\t &\t &\t 5.676\t &\t $\\pm$\t 1.110\t &\t 7.58e+33\t &\t 2.73e+34\t &\t \\\\ \n V410x-ray7 \t &\t \\newrule \t 200001-0 \t &\t 0.050\t $\\pm$\t 0.011\t &\t 0.114\t $\\pm$\t 0.018\t &\t &\t 0.80\t &\t $\t ^{+\t 7.22\t }_{-\t 0.53\t } \t $\t &\t $\t >\t 0.00\t $\t &\t 1.07e+30\t &\t $>$ 2.43e+30\t &\t$>$ &\t 1.280\t &\t \t \t &\t 3.07e+33\t &\t $>$ 2.52e+33:\t &\t \\\\ \n HD283572 \t &\t \\newrule \t 200001-1 \t &\t 0.296\t $\\pm$\t 0.069\t &\t 1.762\t $\\pm$\t 0.101\t &\t &\t 1.78\t &\t $\t ^{+\t 0.18\t }_{-\t 0.19\t } \t $\t &\t $\t <\t 1.56\t $\t &\t 6.31e+30\t &\t 3.76e+31\t &\t &\t 4.953\t &\t $\\pm$\t 1.226\t &\t 4.04e+34\t &\t 1.27e+35\t &\t [a] \\\\ \n DDTau/CZTau \t &\t \\newrule \t 200001-1 \t &\t 0.004\t $\\pm$\t 0.005\t &\t 0.113\t $\\pm$\t 0.013\t &\t &\t 1.19\t &\t $\t ^{+\t 0.28\t }_{-\t 0.27\t } \t $\t &\t $\t <\t 2.99\t $\t &\t 2.13e+28\t &\t $>$ 2.41e+30\t &\t$>$ &\t 112.000\t &\t \t \t &\t 9.14e+31\t &\t$>$ 6.24e+33:\t &\t [a] \\\\ \n L1551-51 \t &\t \\newrule \t 200443 \t &\t 0.031\t $\\pm$\t 0.015\t &\t 0.188\t $\\pm$\t 0.027\t &\t$<$ &\t 8.83\t &\t $\t \t \t \t \t \t $\t &\t $\t >\t 0.48\t $\t &\t 6.61e+29\t &\t 4.01e+30\t &\t &\t 5.065\t &\t $\\pm$\t 2.645\t &\t 2.10e+34\t &\t $>$ 6.74e+34:\t &\t \\\\ \n RXJ0437.5+1851 \t &\t \\newrule \t 200913 \t &\t 0.103\t $\\pm$\t 0.027\t &\t 0.259\t $\\pm$\t 0.037\t &\t &\t 0.49\t &\t $\t ^{+\t 0.27\t }_{-\t 0.18\t } \t $\t &\t $\t >\t 0.00\t $\t &\t 1.10e+30\t &\t 5.52e+30\t &\t &\t 4.029\t &\t $\\pm$\t 1.304\t &\t 1.94e+33\t &\t 3.75e+33\t &\t \\\\ \n RXJ0437.5+1851 \t &\t \\newrule \t 200913 \t &\t 0.103\t $\\pm$\t 0.027\t &\t 0.242\t $\\pm$\t 0.027\t &\t &\t 0.94\t &\t $\t \t \t \t \t \t $\t &\t $\t >\t 0.11\t $\t &\t 1.10e+30\t &\t 5.16e+30\t &\t &\t 3.699\t &\t $\\pm$\t 1.133\t &\t 3.72e+33\t &\t 6.35e+33\t &\t \\\\ \n LkCa19 \t &\t \\newrule \t 201278-1 \t &\t 0.218\t $\\pm$\t 0.010\t &\t 0.382\t $\\pm$\t 0.040\t &\t &\t 0.22\t &\t $\t ^{+\t 0.22\t }_{-\t 0.09\t } \t $\t &\t $\t <\t 1.36\t $\t &\t 4.65e+30\t &\t 8.15e+30\t &\t &\t 0.752\t &\t $\\pm$\t 0.192\t &\t 3.68e+33\t &\t 1.72e+33\t &\t \\\\ \n LH$\\alpha$92 \t &\t \\newrule \t 201305 \t &\t 0.009\t $\\pm$\t 0.009\t &\t 0.699\t $\\pm$\t 0.029\t &\t &\t 1.55\t &\t $\t ^{+\t 0.11\t }_{-\t 0.12\t } \t $\t &\t $\t <\t 1.50\t $\t &\t 8.81e+29\t &\t 6.84e+31\t &\t &\t 76.667\t &\t $\\pm$\t 76.741\t &\t 4.92e+33\t &\t 2.38e+35\t &\t[b] \\\\ \n RXJ0422.1+1934 \t &\t \\newrule \t 700044 \t &\t 0.062\t $\\pm$\t 0.016\t &\t 0.240\t $\\pm$\t 0.016\t &\t$<$ &\t 2.15\t &\t $\t \t \t \t \t \t $\t &\t $\t >\t 0.43\t $\t &\t 6.61e+29\t &\t $>$ 5.12e+30\t &\t$>$ &\t 6.742\t &\t \t \t &\t 5.12e+33\t &\t 1.86e+34:\t &\t \\\\ \n TTau \t &\t \\newrule \t 700044 \t &\t 0.033\t $\\pm$\t 0.008\t &\t 0.139\t $\\pm$\t 0.008\t &\t &\t 0.38\t &\t $\t \t \t \t \t \t $\t &\t $\t >\t 0.00\t $\t &\t 3.52e+29\t &\t $>$ 2.96e+30\t &\t$>$ &\t 7.424\t &\t \t \t &\t 4.81e+32\t &\t $>$ 1.94e+33:\t &\t \\\\ \n TTau \t &\t \\newrule \t 700044 \t &\t 0.033\t $\\pm$\t 0.008\t &\t 0.092\t $\\pm$\t 0.018\t &\t &\t 0.61\t &\t $\t ^{+\t 5.46\t }_{-\t 0.41\t } \t $\t &\t $\t >\t 0.85\t $\t &\t 3.52e+29\t &\t $>$ 1.96e+30\t &\t$>$ &\t 4.576\t &\t \t \t &\t 7.73e+32\t &\t $>$ 1.74e+33:\t &\t \\\\ \n RXJ0255.4+2005 \t &\t \\newrule \t 900138 \t &\t 0.043\t $\\pm$\t 0.025\t &\t 0.232\t $\\pm$\t 0.032\t &\t &\t 1.62\t &\t $\t ^{+\t 0.29\t }_{-\t 0.30\t } \t $\t &\t $\t <\t 1.37\t $\t &\t 1.98e+29\t &\t 1.07e+30\t &\t &\t 4.395\t &\t $\\pm$\t 2.724\t &\t 1.15e+33\t &\t 3.19e+33\t &\t \\\\ \n LkH$\\alpha$325 \t &\t \\newrule \t 900193 \t & 0.170\t $\\pm$\t 0.013\t &\t 0.566\t $\\pm$\t 0.038\t &\t & 0.47\t &\t $\t ^{+\t 0.19\t }_{-\t 0.16\t } \t $ &\t $\t >\t 0.22\t $\t &\t 1.13e+31 & 7.54e+31\t &\t &\t 5.659\t &\t $\\pm$\t 0.627\t & 1.92e+34\t &\t 5.59e+34\t & \\\\ \\hline\nMEAN & \\newrule & $0.084 \\pm 0.021$ & $0.369 \\pm 0.105$ &\n \\multicolumn{3}{c}{$1.049 \\pm 0.194$} & & 2.51e+30 & 2.84e+31 & &\n \\multicolumn{2}{c}{$35.501 \\pm 13.161$} & 2.48e+34 & 5.79e+34 & \\\\\nMEDIAN & \\newrule & 0.047 & 0.241 & \\multicolumn{3}{c}{0.792} & & 8.35e+29\n & 6.15e+30 & & \\multicolumn{2}{c}{$5.192$} & 3.70e+33 & 6.35e+33 & \\\\ \\hline \n\\end{tabular}\n\\end{sidewaystable*}\n\n\n\\begin{sidewaystable*}\n\\caption{Parameters derived from the lightcurves of flares detected on\nmembers of the Pleiades cluster in the {\\em ROSAT} PSPC observations from\nTable~1. The last column gives the reference for flares that\nhave been presented elsewhere in the literature: [a]\n\\protect\\citey{Gagne95.1}, but newly reduced here. In the last two \nrows we give the mean (determined by taking account\nof lower/upper limits) and the median for each parameter.}\n\\label{tab:det_flares_Ple}\n\\newcolumntype{d}[1]{D{.}{.}{#1}}\n\\begin{tabular}{llccr@{}d{2}@{}crrrr@{}d{3}@{}rcrc}\\hline\nDesig. & \\newrule ROR & $I_{\\rm qui}$ & $I_{\\rm max}$ &\n \\multicolumn{3}{c}{$\\tau_{\\rm dec}$} & \\multicolumn{1}{c}{$\\tau_{\\rm ris}$} & \\multicolumn{1}{c}{$L_{\\rm qui}$} & \\multicolumn{1}{c}{$L_{\\rm max}$} & \\multicolumn{3}{c}{$L_{\\rm F}/L_{\\rm qui}$} & $E_{\\rm qui}$ & \\multicolumn{1}{c}{$E_{\\rm F}$} & Notes \\\\\n & \\newrule & [cps] & [cps] & \\multicolumn{3}{c}{[h]} & \\multicolumn{1}{c}{[h]} & \\multicolumn{1}{c}{[erg/s]} & \\multicolumn{1}{c}{[erg/s]} & & & & [erg] & [erg] & \\\\ \\hline\n hii2147 \t &\t \\newrule \t 200008-2 \t &\t 0.130\t $\\pm$\t 0.017\t &\t 1.041\t $\\pm$\t 0.017\t &\t &\t 0.52\t &\t $\t \t \t \t \t \t $\t &\t $\t <\t 3.13\t $\t &\t 9.52e+29\t &\t 1.52e+31\t &\t &\t 15.015\t &\t $\\pm$\t 1.985\t &\t 1.78e+33\t &\t 1.59e+34\t &\t \\\\ \n hii1384 \t &\t \\newrule \t 200008-2 \t &\t 0.063\t $\\pm$\t 0.010\t &\t 0.211\t $\\pm$\t 0.027\t &\t &\t 0.34\t &\t $\t ^{+\t 3.03\t }_{-\t 0.19\t } \t $\t &\t $\t >\t 0.22\t $\t &\t 9.22e+29\t &\t 3.09e+30\t &\t &\t 2.349\t &\t $\\pm$\t 0.590\t &\t 1.13e+33\t &\t 1.66e+33\t &\t \\\\ \n hii298 \t &\t \\newrule \t 200068-1 \t &\t 0.052\t $\\pm$\t 0.024\t &\t 0.180\t $\\pm$\t 0.032\t &\t &\t 1.28\t &\t $\t ^{+\t 0.82\t }_{-\t 0.54\t } \t $\t &\t $\t >\t 0.00\t $\t &\t 3.81e+29\t &\t $>$ 2.64e+30\t &\t$>$ &\t 5.923\t &\t \t \t &\t 1.75e+33\t &\t $>$ 5.43e+33:\t &\t \\\\ \n hii303 \t &\t \\newrule \t 200068-1 \t &\t 0.085\t $\\pm$\t 0.027\t &\t 0.236\t $\\pm$\t 0.039\t &\t &\t 1.17\t &\t $\t ^{+\t 0.81\t }_{-\t 1.01\t } \t $\t &\t $\t \t 3.12\t $\t &\t 6.22e+29\t &\t 3.45e+30\t &\t &\t 4.553\t &\t $\\pm$\t 1.742\t &\t 2.62e+33\t &\t 5.92e+33\t &\t \\\\ \n hcg307 \t &\t \\newrule \t 200068-1 \t &\t 0.004\t $\\pm$\t 0.007\t &\t 0.163\t $\\pm$\t 0.025\t &\t &\t 0.50\t &\t $\t ^{+\t 0.23\t }_{-\t 0.24\t } \t $\t &\t $\t \t 0.22\t $\t &\t 5.86e+28\t &\t 2.39e+30\t &\t &\t 39.750\t &\t $\\pm$\t 69.865\t &\t 1.05e+32\t &\t 2.64e+33\t &\t \\\\ \n hii1100 \t &\t \\newrule \t 200068-1 \t &\t 0.019\t $\\pm$\t 0.009\t &\t 0.107\t $\\pm$\t 0.023\t &\t &\t 0.83\t &\t $\t ^{+\t 0.69\t }_{-\t 0.49\t } \t $\t &\t $\t \t 1.48\t $\t &\t 1.39e+29\t &\t 1.57e+30\t &\t &\t 10.263\t &\t $\\pm$\t 5.452\t &\t 4.16e+32\t &\t 2.43e+33\t &\t [a] \\\\ \n hcg144 \t &\t \\newrule \t 200068-1 \t &\t 0.018\t $\\pm$\t 0.016\t &\t 0.407\t $\\pm$\t 0.046\t &\t &\t 0.56\t &\t $\t ^{+\t 0.14\t }_{-\t 0.13\t } \t $\t &\t $\t \t 4.58\t $\t &\t 2.64e+29\t &\t $>$ 5.96e+30\t &\t$>$ &\t 21.611\t &\t \t \t &\t 5.31e+32\t &\t $>$ 7.24e+33:\t &\t \\\\ \n hii2244 \t &\t \\newrule \t 200556 \t &\t 0.029\t $\\pm$\t 0.013\t &\t 0.149\t $\\pm$\t 0.013\t &\t &\t 3.49\t &\t $\t \t \t \t \t \t $\t &\t $\t <\t 1.64\t $\t &\t 4.25e+29\t &\t $>$ 2.18e+30\t &\t$>$ &\t 4.138\t &\t \t \t &\t 5.33e+33\t &\t $>$ 1.39e+34:\t &\t \\\\ \n hcg422 \t &\t \\newrule \t 200556 \t &\t 0.003\t $\\pm$\t 0.004\t &\t 0.041\t $\\pm$\t 0.009\t &\t$<$ &\t 1.56\t &\t $\t \t \t \t \t \t $\t &\t $\t \t 1.61\t $\t &\t 4.39e+28\t &\t 6.00e+29\t &\t &\t 12.667\t &\t $\\pm$\t 17.205\t &\t 2.47e+32\t &\t $<$ 1.97e+33:\t &\t \\\\ \n hii1516 \t &\t \\newrule \t 200556 \t &\t 0.028\t $\\pm$\t 0.019\t &\t 0.714\t $\\pm$\t 0.071\t &\t &\t 1.22\t &\t $\t ^{+\t 0.15\t }_{-\t 0.16\t } \t $\t &\t $\t <\t 1.64\t $\t &\t 4.10e+29\t &\t $>$ 1.05e+31\t &\t$>$ &\t 24.500\t &\t \t \t &\t 1.80e+33\t &\t $>$ 2.78e+34:\t &\t [a] \\\\ \n hcg97 \t &\t \\newrule \t 200557 \t &\t 0.003\t $\\pm$\t 0.005\t &\t 0.063\t $\\pm$\t 0.015\t &\t &\t 0.88\t &\t $\t ^{+\t 0.50\t }_{-\t 0.39\t } \t $\t &\t $\t \t 1.44\t $\t &\t 4.39e+28\t &\t 9.22e+29\t &\t &\t 20.000\t &\t $\\pm$\t 33.747\t &\t 1.39e+32\t &\t 1.77e+33\t &\t [a] \\\\ \n hii1653 \t &\t \\newrule \t 200557 \t &\t 0.034\t $\\pm$\t 0.019\t &\t 0.176\t $\\pm$\t 0.039\t &\t &\t 0.40\t &\t $\t ^{+\t 1.21\t }_{-\t 0.22\t } \t $\t &\t $\t <\t 1.16\t $\t &\t 4.98e+29\t &\t 2.58e+30\t &\t &\t 4.176\t &\t $\\pm$\t 2.660\t &\t 7.17e+32\t &\t 1.91e+33\t &\t \\\\ \n hii174 \t &\t \\newrule \t 200557 \t &\t 0.038\t $\\pm$\t 0.014\t &\t 0.153\t $\\pm$\t 0.023\t &\t &\t 1.12\t &\t $\t ^{+\t 0.30\t }_{-\t 0.28\t } \t $\t &\t $\t <\t 3.31\t $\t &\t 5.56e+29\t &\t 2.24e+30\t &\t &\t 3.026\t &\t $\\pm$\t 1.321\t &\t 2.24e+33\t &\t 4.28e+33\t &\t [a] \\\\ \n hii191 \t &\t \\newrule \t 200557 \t &\t 0.004\t $\\pm$\t 0.004\t &\t 0.119\t $\\pm$\t 0.021\t &\t &\t 0.99\t &\t $\t ^{+\t 0.21\t }_{-\t 0.19\t } \t $\t &\t $\t <\t 1.70\t $\t &\t 5.86e+28\t &\t 1.74e+30\t &\t &\t 28.750\t &\t $\\pm$\t 29.243\t &\t 2.09e+32\t &\t 3.79e+33\t &\t [a] \\\\ \n hii253 \t &\t \\newrule \t 200557 \t &\t 0.107\t $\\pm$\t 0.025\t &\t 0.213\t $\\pm$\t 0.030\t &\t &\t 1.44\t &\t $\t ^{+\t 0.70\t }_{-\t 0.56\t } \t $\t &\t $\t >\t 0.00\t $\t &\t 1.57e+30\t &\t $>$ 3.12e+30\t &\t$>$ &\t 0.991\t &\t \t \t &\t 8.12e+33\t &\t $>$ 5.07e+33:\t &\t \\\\ \n hii212 \t &\t \\newrule \t 200557 \t &\t 0.005\t $\\pm$\t 0.005\t &\t 0.053\t $\\pm$\t 0.014\t &\t &\t 1.07\t &\t $\t ^{+\t 0.68\t }_{-\t 0.50\t } \t $\t &\t $\t <\t 1.44\t $\t &\t 7.32e+28\t &\t$>$ 7.76e+29\t &\t$>$ &\t 9.600\t &\t \t \t &\t 2.82e+32\t &\t $>$ 1.72e+33:\t &\t [a] \\\\ \n hii345 \t &\t \\newrule \t 200557 \t &\t 0.055\t $\\pm$\t 0.013\t &\t 0.176\t $\\pm$\t 0.027\t &\t &\t 0.63\t &\t $\t ^{+\t 0.39\t }_{-\t 0.48\t } \t $\t &\t $\t <\t 1.32\t $\t &\t 8.05e+29\t &\t 2.58e+30\t &\t &\t 2.200\t &\t $\\pm$\t 0.753\t &\t 1.83e+33\t &\t 2.53e+33\t &\t [a] \\\\ \n hcg181 \t &\t \\newrule \t 200557 \t &\t 0.009\t $\\pm$\t 0.007\t &\t 0.128\t $\\pm$\t 0.021\t &\t &\t 0.70\t &\t $\t ^{+\t 0.32\t }_{-\t 0.30\t } \t $\t &\t $\t \t 0.33\t $\t &\t 1.32e+29\t &\t 1.87e+30\t &\t &\t 13.222\t &\t $\\pm$\t 10.574\t &\t 3.32e+32\t &\t 2.77e+33\t &\t [a] \\\\ \n sk702 \t &\t \\newrule \t 200557 \t &\t 0.010\t $\\pm$\t 0.009\t &\t 0.138\t $\\pm$\t 0.009\t &\t &\t 0.10\t &\t $\t \t \t \t \t \t $\t &\t $\t \t 1.27\t $\t &\t 1.46e+29\t &\t 2.02e+30\t &\t &\t 12.800\t &\t $\\pm$\t 11.590\t &\t 5.27e+31\t &\t 4.39e+32\t &\t \\\\ \n hcg143 \t &\t \\newrule \t 200557 \t & 0.011\t $\\pm$\t 0.009\t &\t 0.217\t $\\pm$\t 0.030\t &\t & 0.36\t &\t $\t ^{+\t 0.23\t }_{-\t 0.14\t } \t $ &\t $\t \t 0.11\t $\t &\t 1.61e+29\t & 3.18e+30\t &\t &\t 18.727\t &\t $\\pm$\t 15.585\t & 2.09e+32\t &\t 2.47e+33\t &\t [a] \\\\ \\hline\nMEAN & \\newrule & $0.035 \\pm 0.008$ & $0.234 \\pm 0.052$ &\n \\multicolumn{3}{c}{$0.919 \\pm 0.156$} & & 4.13 e+29 & 5.33e+30 & &\n \\multicolumn{2}{c}{$16.792 \\pm 3.059$} & 1.49e+33 & 3.73e+33 & \\\\\nMEDIAN & \\newrule & 0.019 & 0.163 & \\multicolumn{3}{c}{0.762} & & 2.64e+29\n & 2.51e+30 & & \\multicolumn{2}{c}{$12.996$} & 5.31e+32 & 2.50e+33 & \\\\ \\hline\n\\end{tabular}\n\\end{sidewaystable*}\n\n\n\\begin{sidewaystable*}\n\\caption{Parameters derived from the lightcurves of flares detected on\nmembers of the Hyades cluster in the {\\em ROSAT} PSPC observations from\nTable~1. No analysis of flares on Hyads are reported in the literature. In \nthe last two rows we give the mean (determined by taking account of\nlower/upper limits) and the median for each parameter.}\n\\label{tab:det_flares_Hya}\n\\newcolumntype{d}[1]{D{.}{.}{#1}}\n\\begin{tabular}{llccr@{}d{2}@{}rrrrr@{}d{3}@{}rcrc}\\hline\nDesig. & \\newrule ROR & $I_{\\rm qui}$ & $I_{\\rm max}$ &\n \\multicolumn{3}{c}{$\\tau_{\\rm dec}$} & \\multicolumn{1}{c}{$\\tau_{\\rm ris}$} & \\multicolumn{1}{c}{$L_{\\rm qui}$} & \\multicolumn{1}{c}{$L_{\\rm max}$} & \\multicolumn{3}{c}{$L_{\\rm F}/L_{\\rm qui}$} & $E_{\\rm qui}$ & \\multicolumn{1}{c}{$E_{\\rm F}$} & Notes \\\\\n & \\newrule & [cps] & [cps] & \\multicolumn{3}{c}{[h]} & \\multicolumn{1}{c}{[h]} & \\multicolumn{1}{c}{[erg/s]} & \\multicolumn{1}{c}{[erg/s]} & & & & [erg] & \\multicolumn{1}{c}{[erg]} & \\\\ \\hline\n V471Tau \t &\t \\newrule \t 200107-0 \t &\t 0.796\t $\\pm$\t 0.062\t &\t 1.135\t $\\pm$\t 0.062\t &\t &\t 0.10\t &\t $\t \t \t \t \t \t $\t &\t $\t <\t 5.87\t $\t &\t 1.90e+30\t &\t 2.70e+30\t &\t &\t 0.426\t &\t $\\pm$\t 0.115\t &\t 6.83e+32\t &\t 1.75e+32\t &\t \\\\ \n VB50 \t &\t \\newrule \t 200441 \t &\t 0.379\t $\\pm$\t 0.082\t &\t 0.975\t $\\pm$\t 0.101\t &\t &\t 0.47\t &\t $\t ^{+\t 0.17\t }_{-\t 0.14\t } \t $\t &\t $\t \t 0.22\t $\t &\t 4.16e+29\t &\t 2.14e+30\t &\t &\t 4.145\t &\t $\\pm$\t 1.065\t &\t 7.03e+32\t &\t 1.41e+33\t &\t \\\\ \n VA677 \t &\t \\newrule \t 200553 \t &\t 0.333\t $\\pm$\t 0.071\t &\t 0.493\t $\\pm$\t 0.080\t &\t &\t 2.38\t &\t $\t ^{+\t 1.68\t }_{-\t 0.87\t } \t $\t &\t $\t <\t 327.6\t $\t &\t 5.89e+29\t &\t $>$ 1.74e+30\t &\t$>$ &\t 1.961\t &\t \t \t &\t 5.04e+33\t &\t $>$ 3.07e+33:\t &\t \\\\ \n LP357-4 \t &\t \\newrule \t 200556 \t &\t 0.152\t $\\pm$\t 0.029\t &\t 0.345\t $\\pm$\t 0.034\t &\t &\t 3.75\t &\t $\t ^{+\t 1.75\t }_{-\t 1.15\t } \t $\t &\t $\t >\t 0.22\t $\t &\t 3.54e+29\t &\t 8.05e+29\t &\t &\t 1.270\t &\t $\\pm$\t 0.381\t &\t 4.79e+33\t &\t 3.83e+33\t &\t \\\\ \n VA275 \t &\t \\newrule \t 200776 \t &\t 0.055\t $\\pm$\t 0.028\t &\t 0.474\t $\\pm$\t 0.028\t &\t$<$ &\t 0.42\t &\t $\t \t \t \t \t \t $\t &\t $\t <\t 0.22\t $\t &\t 1.28e+29\t &\t 1.11e+30\t &\t &\t 7.618\t &\t $\\pm$\t 3.945\t &\t 1.94e+32\t &\t $<$ 9.30e+32:\t &\t \\\\ \n VB141 \t &\t \\newrule \t 200777 \t &\t 0.747\t $\\pm$\t 0.055\t &\t 1.040\t $\\pm$\t 0.078\t &\t &\t 1.44\t &\t $\t ^{+\t 0.76\t }_{-\t 0.53\t } \t $\t &\t $\t <\t 1.20\t $\t &\t 1.86e+30\t &\t $>$ 2.60e+30\t &\t$>$ &\t 0.392\t &\t \t \t &\t 9.67e+33\t &\t $>$ 2.39e+33:\t &\t \\\\ \n VA334 \t &\t \\newrule \t 200777 \t &\t 0.137\t $\\pm$\t 0.021\t &\t 0.329\t $\\pm$\t 0.021\t &\t$<$ &\t 1.39\t &\t $\t \t \t \t \t \t $\t &\t $\t \t 0.33\t $\t &\t 2.51e+29\t &\t $>$ 6.02e+29\t &\t$>$ &\t 1.401\t &\t \t \t &\t 1.25e+33\t &\t 1.11e+33:\t &\t \\\\ \n VB141 \t &\t \\newrule \t 200777 \t &\t 0.747\t $\\pm$\t 0.055\t &\t 1.003\t $\\pm$\t 0.075\t &\t &\t 0.75\t &\t $\t ^{+\t 0.95\t }_{-\t 0.37\t } \t $\t &\t $\t <\t 1.32\t $\t &\t 1.86e+30\t &\t 2.50e+30\t &\t &\t 0.343\t &\t $\\pm$\t 0.127\t &\t 5.03e+33\t &\t 1.09e+33\t &\t \\\\ \n VA334 \t &\t \\newrule \t 200777 \t &\t 0.137\t $\\pm$\t 0.021\t &\t 0.309\t $\\pm$\t 0.021\t &\t &\t 0.75\t &\t $\t \t \t \t \t \t $\t &\t $\t <\t 1.64\t $\t &\t 2.51e+29\t &\t 5.65e+29\t &\t &\t 1.255\t &\t $\\pm$\t 0.290\t &\t 6.76e+32\t &\t 5.41e+32\t &\t \\\\ \n VA677 \t &\t \\newrule \t 200911 \t &\t 0.282\t $\\pm$\t 0.056\t &\t 0.896\t $\\pm$\t 0.083\t &\t &\t 0.46\t &\t $\t ^{+\t 0.26\t }_{-\t 0.16\t } \t $\t &\t $\t <\t 1.61\t $\t &\t 4.98e+29\t &\t 3.17e+30\t &\t &\t 5.355\t &\t $\\pm$\t 1.232\t &\t 8.25e+32\t &\t 2.26e+33\t &\t \\\\ \n VA677 \t &\t \\newrule \t 200945 \t &\t 0.238\t $\\pm$\t 0.036\t &\t 0.474\t $\\pm$\t 0.073\t &\t &\t 0.22\t &\t $\t ^{+\t 0.34\t }_{-\t 0.11\t } \t $\t &\t $\t <\t 4.59\t $\t &\t 4.21e+29\t &\t $>$ 1.68e+30\t &\t$>$ &\t 2.983\t &\t \t \t &\t 3.33e+32\t &\t $>$ 4.26e+32:\t &\t \\\\ \n VB169 \t &\t \\newrule \t 201097 \t &\t 0.110\t $\\pm$\t 0.025\t &\t 0.251\t $\\pm$\t 0.025\t &\t &\t 0.18\t &\t $\t \t \t \t \t \t $\t &\t $\t <\t 1.67\t $\t &\t 2.59e+29\t &\t 5.90e+29\t &\t &\t 1.282\t &\t $\\pm$\t 0.434\t &\t 1.68e+32\t &\t 1.35e+32\t &\t \\\\ \n VA673 \t &\t \\newrule \t 201313 \t &\t 0.409\t $\\pm$\t 0.022\t &\t 0.975\t $\\pm$\t 0.066\t &\t &\t 1.78\t &\t $\t ^{+\t 0.48\t }_{-\t 0.35\t } \t $\t &\t $\t >\t 0.13\t $\t &\t 4.77e+29\t &\t $>$ 2.27e+30\t &\t$>$ &\t 3.768\t &\t \t \t &\t 3.06e+33\t &\t $>$ 5.35e+33:\t &\t \\\\ \n VB190 \t &\t \\newrule \t 201368 \t &\t 0.165\t $\\pm$\t 0.061\t &\t 0.472\t $\\pm$\t 0.061\t &\t &\t 0.20\t &\t $\t \t \t \t \t \t $\t &\t $\t <\t 20.52\t $\t &\t 1.92e+29\t &\t 1.10e+30\t &\t &\t 4.721\t &\t $\\pm$\t 1.931\t &\t 1.39e+32\t &\t 3.33e+32\t &\t \\\\ \n VB141 \t &\t \\newrule \t 201368 \t &\t 0.985\t $\\pm$\t 0.136\t &\t 6.897\t $\\pm$\t 0.183\t &\t &\t 1.21\t &\t $\t ^{+\t 0.16\t }_{-\t 0.18\t } \t $\t &\t $\t <\t 1.14\t $\t &\t 2.46e+30\t &\t 1.72e+31\t &\t &\t 6.002\t &\t $\\pm$\t 0.860\t &\t 1.07e+34\t &\t 4.08e+34\t &\t \\\\ \n VB85 \t &\t \\newrule \t 201368 \t &\t 0.209\t $\\pm$\t 0.027\t &\t 0.396\t $\\pm$\t 0.027\t &\t$<$ &\t 1.91\t &\t $\t \t \t \t \t \t $\t &\t $\t >\t 0.55\t $\t &\t 3.86e+29\t &\t $>$ 7.31e+29\t &\t$>$ &\t 0.895\t &\t \t \t &\t 2.65e+33\t &\t 1.50e+33:\t &\t \\\\ \n VB45 \t &\t \\newrule \t 201369 \t & 0.034\t $\\pm$\t 0.020\t &\t 0.167\t $\\pm$\t 0.020\t & &\t 0.37\t &\t $\t \t \t \t \t $\t &\t $\t <\t 0.98\t $\t &\t 4.12e+28 &\t $>$ 4.05e+29\t &\t$>$ &\t 8.824\t &\t \t &\t 5.49e+31\t &\t $>$ 2.72e+32:\t & \\\\ \\hline\nMEAN & \\newrule & $0.348 \\pm 0.069$ & $0.978 \\pm 0.367$ &\n \\multicolumn{3}{c}{$0.902 \\pm 0.234$} & & 7.26e+29 & 4.24e+30 & &\n \\multicolumn{2}{c}{$4.433 \\pm 0.767$} & 2.71e+33 & 5.62e+33 \\\\\nMEDIAN & \\newrule & 0.223 & 0.473 & \\multicolumn{3}{c}{0.463} & & 4.01e+29\n & 2.34e+30 & & \\multicolumn{2}{c}{$4.468$} & 7.64e+32 & 8.17e+32 \\\\ \\hline\n\\end{tabular}\n\\end{sidewaystable*}\n\n\n\n\n\\section{Observational selection effects}\\label{sect:bias}\n\nIt is the purpose of this paper to compare the flare activity of\ndifferent stars, and thus some attention has to be drawn to observational \nselection effects. In this section, \nwe will discuss how observational restrictions\ninfluence the search for flares. At several points during the data\nanalysis, we are confronted with the problem of finding a\nrepresentation of the data which is free from these biases.\n\nThe major difficulty with the statistical evaluation of flares on different\nstars is that\nthe sensitivity of the flare detection process depends on the measured\n(quiescent) count rate, which determines the signal-to-noise (S/N), \nand hence on the distance to the star. The \nobservational bias consists in the fact \nthat for bright stars ($L_{\\rm qui}$ large) the minimum luminosity \n$L_{\\rm F}$ of a detectable flare is higher than for a faint star. \nThe result is, among others, that at first hand it can not be decided\nwhether any observed correlation between $L_{\\rm qui}$ and $L_{\\rm F}$\nis real or produced by this effect.\nIn Fig.~\\ref{fig:Lf_Lq} we have plotted the flare luminosity \n$L_{\\rm F}$ against the quiescent luminosity $L_{\\rm qui}$.\n\nThe contribution of the observational bias to this correlation \ncan be estimated as follows:\nFor each quiescent count rate $I_{\\rm qui}$ we can determine the minimum\nstrength $L_{\\rm F}/L_{\\rm qui}$ needed for a flare to be detected, if we\nassume that a flare is found whenever there is a rise in count rate of at \nleast 3\\,$\\sigma$ within one 400\\,s time bin. (In our actual flare search we\nwere even more conservative; see Sect.~\\ref{sect:detect}.) \nHypothetical events of that kind obey\na detection threshold curve for $L_{\\rm F}/L_{\\rm qui}$ as shown in \nFig.~\\ref{fig:det_accuracy}. \nAs mentioned above, the minimum flare luminosity needed for detection of \na flare becomes\nlarger with increasing quiescent brightness. In contrast, \nthe required luminosity ratio, i.e. the relative strength of the events,\ndecreases when $I_{\\rm qui}$ increases. \nNote also, that the curve in Fig.~\\ref{fig:det_accuracy}\nis distance independent. But the relation between $L_{\\rm qui}$ and\nthe corresponding minimum $L_{\\rm F}$ of a detectable flare differs for \nstars at different distances. In Fig.~\\ref{fig:Lf_Lq} we have overplotted\nthe theoretical threshold for detection of a flare on a star\nat 140\\,pc distance. Note, that the slope of the data \nin Fig.~\\ref{fig:Lf_Lq} is somewhat steeper than the increase of the threshold \nimposed by the S/N. This seems to indicate an intrinsic correlation between\nquiescent and flare luminosity. We have subtracted the theoretical threshold \nvalue for $L_{\\rm F}$ from the observed flare luminosity for each of the\nstars from Fig.~\\ref{fig:Lf_Lq}. Correlation tests for the difference\nbetween\nthreshold and observed value for $L_{\\rm F}$,\n$(L_{\\rm F,theo} - L_{\\rm F,obs})$, with \n$L_{\\rm qui}$ show that the correlation is of low\nsignificance, $\\alpha$=0.05.\nThe data points below the theoretical curve are all Pleiads or Hyads. They \ndo not contradict the threshold curve,\nsince Pleiades and Hyades stars are closer than\n140\\,pc and therefore have a lower flare detection threshold.\n\n\\begin{figure}\n\\begin{center}\n\\resizebox{9cm}{!}{\\includegraphics{./fig50.eps}}\n\\caption{Correlation between quiescent and flare luminosity. \nTTSs, Pleiads, and Hyads are represented by different plotting symbols: TTS\n-- circles, Pleiads -- triangles, Hyads -- crosses. The solid\ncurve is the minimum flare strength needed for detection of a flare with\ngiven $L_{\\rm qui}$ if the star is at a distance of 140\\,pc. The data\npoints below that curve represent no contradiction to the calculated\nthreshold because the detection threshold increases with stellar distance,\ni.e. apparent brightness of the stars, and\ntherefore Pleiads and Hyads may show flares with smaller $L_{\\rm F}$ for\ngiven $L_{\\rm qui}$.}\n\\label{fig:Lf_Lq}\n\\end{center}\n\\end{figure}\n\\begin{figure}\n\\begin{center}\n\\resizebox{8.5cm}{!}{\\includegraphics{./fig51.eps}}\n\\caption{Relative flare strength, $L_{\\rm F}/L_{\\rm qui}$,\nas a function of the quiescent count rate\n$I_{\\rm qui}$ in double logarithmic scale. \nAssuming that the flare is characterized by a rise\nin count rate of 3\\,$\\sigma$ above the mean during a single 400\\,s time\nbin, the solid curve gives the minimum values of $L_{\\rm F}/L_{\\rm qui}$\nfor which a flare will be detected on stars with given $I_{\\rm qui}$. The\nobserved values consistently lie above this line. The meaning of the\nplotting symbols is the same as in Fig.~\\ref{fig:Lf_Lq}. For clarity we\nhave omitted error bars.}\n\\label{fig:det_accuracy}\n\\end{center}\n\\end{figure}\n\n\n\n\n\\section{Statistical comparison of the flaring stars}\\label{sect:statcomp}\n\nWe present now a statistical analysis of the X-ray flares from\nTables~\\ref{tab:det_flares_TTS},~\\ref{tab:det_flares_Ple}~and~\\ref{tab:det_flares_Hya}. \nA detailed discussion of the (quiescent) X-ray \nproperties of all detected and undetected \nstars is postponed to a later paper (Stelzer et al., in preparation).\n\nIn this section, different\nflare parameters will be checked for dependence on age, circumstellar\nenvironment, and rotation rate \n(Sect.~\\ref{subsect:lumfunct},~\\ref{subsect:cw},~\\ref{subsect:corrvsini}.)\nto see whether any of these properties has an effect on the\ncharacteristic luminosity and time scales of coronal activity.\nFor the statistical comparison of the flaring stars the \nASURV package version 1.2 (\\cite{Feigelson85.1}) was used. \n\nFirst we compare the flaring populations of TTSs, Pleiads, and Hyads\nconcerning their effective temperatures.\nWe have converted spectral types to effective temperatures\nusing the conversion given in \\citey{Kenyon95.1}\nfor PMS stars earlier than M0, and \\citey{Luhman99.1} for PMS M-type stars\nintermediate between dwarfs and giants. For Pleiades and Hyades stars\nwe have used the conversion of \n\\citey{Schmidt-Kaler82.1}.\nWe have applied two-sample tests to each pair of $T_{\\rm\neff}$-distributions\nto reveal possible differences between flaring stars of the three\ngroups. Henceforth, we denote the probability that the distributions\nare similar by $\\alpha$. In all but one of the comparisons we found\n$\\alpha > 0.2$, and therefore no significant differences in $T_{\\rm eff}$.\nThe exception is the logrank test between TTSs and Hyads where\n$\\alpha = 0.03$.\n\nMost flares occurred on G, K and M stars. However, some events were observed \non A and F stars. Stars of intermediate spectral type, \nlacking both a convection-driven dynamo and a strong stellar wind, \nseem to have no efficient mechanism to\ngenerate X-ray flares. Therefore, it is often assumed that X-ray emission \napparently seen on A or B stars, can be attributed to an (unknown) late-type \ncompanion (see e.g. \\cite{Stauffer94.1}, \\cite{Gagne94.1}, \n\\cite{Panzera99.1}). \nThe same arguments can be applied to explain X-ray\nflares on these stars. \nIn any case, the emission mechanism of early-type stars is\ndifferent from that of late-type stars. \nFrom the sharp onset of rotation-activity relations in dwarf stars\n\\citey{Walter83.1} has argued that the onset of solar-like dynamo\nactivity occurs abruptly at about spectral type F5.\nTo ensure that no stars with X-ray generation mechanisms other than\nstellar dynamos are included, \nwe have excluded the stars of spectral type F and earlier \nfrom the statistical analysis presented in this paper,\ni.e. we have restricted the flare sample to events on G, K, and M stars.\nThis limitation provides samples which have similar\n$T_{\\rm eff}$ distributions, i.e. $\\alpha > 0.2$ also for the\ntwo-sample test between TTSs and Hyads (see Table~\\ref{tab:teff} for the\ndetailed results). This justifies to \ncombine all flaring late-type stars for the statistical analysis.\nIn the following the stellar sample is restricted to G, K, and M stars.\nIf not explicitly mentioned the two flares on known white-dwarf systems \n(on V471\\,Tau and VA\\,673) are excluded from the sample, \nsince the white dwarf could be responsible for the X-ray event instead of\nits late-type companion. \n\\begin{table}\n\\caption{Results of two-sample tests between each pair of stellar samples \n(TTSs,\nPleiads, and Hyads) with respect to the effective temperature $T_{\\rm eff}$\nof the flaring star. Only flares on G, K, or M stars have been admitted. The analysis was performed with the ASURV package. Next\nto the mean and median of $T_{\\rm eff}$ we give the probability that the \nnull hypothesis of two distributions being the same is true derived\nfrom Gehan's generalized Wilcoxon test and the logrank test. The values suggest that there is no\nsignificant difference between the spectral types of the flaring TTSs,\nPleiads, and Hyads and justify to combine G, K, and M stars for the\ncomparison of flares from these different stellar groups.}\n\\label{tab:teff}\n\\begin{center}\n\\begin{tabular}{lccccc} \\hline\n\\multicolumn{6}{c}{$\\lg{T_{\\rm eff}}$} \\\\ \\hline\nSample & Sample & MEAN & MED. & Prob. & Prob. \\\\\nName & Size & & & GW (HV) & logrank \\\\ \\hline\n& & & & 0.395 & 0.525 \\\\\nTTSs & 15 & 3.63 $\\pm$ 0.08 & 3.600 & & \\\\\nPleiads & 14 & 3.66 $\\pm$ 0.07 & 3.675 & & \\\\ \\hline\n& & & & 0.897 & 0.972 \\\\\nTTSs & 15 & (see above) & & & \\\\\nHyads & 11 & 3.63 $\\pm$ 0.07 & 3.595 & & \\\\ \\hline\n& & & & 0.212 & 0.401 \\\\\nPleiads & 14 & (see above) & & & \\\\\nHyads & 11 & (see above) & & & \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\n\\subsection{Flare frequency of MS stars and spectral type}\\label{subsect:sptypes}\n\nIt is interesting to ask whether the depth of the\nconvection zone has any influence on the occurrence of surface\nflares. Since the relative size of the convection zone increases for later\nspectral types, the\ndistribution of flares onto stars of different spectral types may help to \nsolve this question. \nWhat we really want to check\nis whether the flare frequency depends on stellar mass, which corresponds\nto spectral type on the MS. Because PMS stars still evolve through the \nHertzsprung-Russell diagram (HRD),\ni.e. change their spectral type, we exclude the TTSs from this part of the\nanalysis. Flaring Pleiades and Hyades stars \nare combined to increase the sample size.\n\nWe have studied the spectral type distribution of flares \nby comparing the number of flares on stars of a certain spectral type\nto the total number of detected stars of that spectral type. \nThe detection sensitivity for\nflares of a given strength $L_{\\rm F}/L_{\\rm qui}$ is different for each\nstar because it depends on the level of quiescent emission $I_{\\rm qui}$ \n(see Sect.~\\ref{sect:bias}). $I_{\\rm qui}$,\ndepends on the spectral type of the star. For this reason, a \nsimple comparison between numbers of flares and numbers of detected stars\nof each spectral type would be misleading.\nThe observational bias can, however, be eliminated if the \nnumbers (of flares and detections) are evaluated above a certain \nthreshold $L_{\\rm F}/L_{\\rm qui}$. \nWe compare the number of flares with measured luminosity ratio above \na critical value $({L_{\\rm F}/L_{\\rm qui}})_{\\rm crit}$ \nto the number of detected stars \nfor which $I_{\\rm qui}$ exceeds the minimum value needed for detection\nof a flare of that critical strength. We have compiled these numbers \nfor a reasonable range of values \n$L_{\\rm F}/L_{\\rm qui}$, and show the result \nin Fig.~\\ref{fig:detsens_spt}. Plotted are the number of flares exceeding\n$L_{\\rm F}/L_{\\rm qui}$ divided by the number of detected stars that are\nbright enough for detection of flares with that value of \n$L_{\\rm F}/L_{\\rm qui}$.\nG stars clearly show the smallest rate of events throughout all of\nthe observed range of flare strengths. \n\\begin{figure}\n\\begin{center}\n\\resizebox{9cm}{!}{\\includegraphics{./fig52.eps}}\n\\caption{Fraction of flares among detected stars above a given threshold\n$L_{\\rm F}/L_{\\rm qui}$ for different spectral types. Shown are G\nstars (dashed line), K stars (solid line) and M stars (dotted\nline). Pleiades and Hyades stars have been combined. TTSs are not\nconsidered since they are on the PMS where the relation between the stellar\ninterior structure and the X-ray emission might be different. \nThroughout the examined range of $L_{\\rm F}/L_{\\rm qui}$ the number\nof flares per detected stars is lowest for spectral type G.}\n\\label{fig:detsens_spt}\n\\end{center}\n\\end{figure}\n\n\n\n\\subsection{Age of flaring stars (Luminosity functions)}\\label{subsect:lumfunct}\n\nTo study how the flare activity of young late-type stars \nevolves with stellar age \nwe have computed luminosity distribution functions (LDF) and performed \ntwo-sample tests for three subsamples of stars: TTSs, Pleiads, and Hyads. \n\nMaximum likelihood distributions for TTSs, Pleiads, and Hyads are presented \nin Fig.~\\ref{fig:lumfunct} for both flare luminosity $L_{\\rm F}$ \nand mean luminosity during the {\\em quiescent} part of flare observations \n$L_{\\rm qui}$. Note, that Fig.~\\ref{fig:lumfunct} (b) contains no\nupper limits because only stars which have shown a flare are included, and \n$L_{\\rm qui}$ during flare observations can be extracted from the \nlightcurves.\nThe flare luminosity in Fig.~\\ref{fig:lumfunct}\\,(a) includes\nupper limits. Since $L_{\\rm F} = L_{\\rm max} - L_{\\rm qui}$, upper\nlimits for $L_{\\rm max}$ (see\nTable~\\ref{tab:det_flares_TTS},~\\ref{tab:det_flares_Ple},\nand~\\ref{tab:det_flares_Hya}) translate to upper limits for $L_{\\rm F}$.\nLDFs for all non-flaring stars (detections and non-detections) will be\nshown elsewhere (Stelzer et al., in preparation).\n\\begin{figure}\n\\begin{center}\n\\rotatebox{270}{\\resizebox{7cm}{!}{\\includegraphics{./fig53.ps}}}\n\\rotatebox{270}{\\resizebox{7cm}{!}{\\includegraphics{./fig54.ps}}}\n\\caption{Luminosity functions for the flaring TTSs, Pleiads, and Hyads\nduring the X-ray flare {\\bf (a)} and during quiescence {\\bf (b)}. \nStars of spectral type earlier than G or unknown spectral type, and known\nwhite-dwarf systems are excluded. Note that the quiescent distribution of the Hyades stars is consistent with that of the Pleiads, due to the selection of flaring stars only (see discussion in the text).}\n\\label{fig:lumfunct}\n\\end{center}\n\\end{figure}\n\n\\begin{table}\n\\caption{Results of two-sample tests for the flare luminosity $L_{\\rm F}$\nand quiescent luminosity of flare observations $L_{\\rm qui}$. \nThe number of\nupper limits to the luminosity are listed in brackets in column `Sample\nSize'. See Table~\\ref{tab:teff} for the meaning of the remaining columns.\nAll distributions of $L_{\\rm F}$ are significantly different from\neach other. Flaring Pleiads and Hyads have similar $L_{\\rm qui}$ distributions.}\n\\label{tab:L_gkm_2s}\n\\begin{tabular}{lrrrr}\\hline\nSample Names & \\multicolumn{2}{c}{Sample sizes} & Prob. GW & Prob logrank \\\\ \\hline\n\\multicolumn{5}{c}{Flare luminosity $L_{\\rm F}$} \\\\ \\hline\nTTSs - Pleiads & 15(6) & 14(5) & $0.021$ & $0.017$ \\\\\nTTSs - Hyads & 15(6) & 9(3) & $0.001$ & $0.000$ \\\\\nPleiads - Hyads & 14(5) & 9(3) & $0.007$ & $0.010$ \\\\ \\hline\n\\multicolumn{5}{c}{Quiescent luminosity of flaring stars $L_{\\rm qui}$} \\\\ \\hline\nTTSs - Pleiads & 15(0) & 14(0) & $0.025$ & $0.010$ \\\\\nTTSs - Hyads & 15(0) & 9(0) & $0.007$ & $0.001$ \\\\\nPleiads - Hyads & 14(0) & 9(0) & $0.615$ & $0.243$ \\\\ \\hline\n\\end{tabular}\n\\end{table}\n\n\\begin{table}\n\\caption{Mean and median flare and quiescent luminosity of flaring TTSs,\nPleiads, and Hyads. The sample of cTTSs was to small to compute the median\nof $L_{\\rm F}$.}\n\\label{tab:L_gkm_mean}\n\\begin{tabular}{lrlcc}\\hline\nSample Name & \\multicolumn{2}{c}{Sample Size} & Mean & Median \\\\ \\hline\n\\multicolumn{5}{c}{Flare Luminosity $\\lg{L_{\\rm F}}$} \\\\ \\hline\nTTSs & 15 & (6) & $31.05 \\pm 0.19$ & $30.65$ \\\\\nPleiads & 14 & (5) & $30.51 \\pm 0.12$ & $30.30$ \\\\\nHyads & 9 & (3) & $30.06 \\pm 0.11$ & $29.99$ \\\\ \\hline\ncTTSs & 6 & (4) & $31.44 \\pm 0.32$ & $-$ \\\\\nwTTSs & 8 & (1) & $30.81 \\pm 0.22$ & $30.58$ \\\\ \\hline\n\\multicolumn{5}{c}{Quiescent Luminosity of Flaring Stars $\\lg{L_{\\rm qui}}$} \\\\ \\hline\nTTSs & 15 & (0) & $29.98 \\pm 0.17$ & $29.92$ \\\\\nPleiads & 14 & (0) & $29.52 \\pm 0.11$ & $29.61$ \\\\\nHyads & 9 & (0) & $29.50 \\pm 0.07$ & $29.47$ \\\\ \\hline\ncTTSs & 6 & (0) & $29.94 \\pm 0.19$ & $29.82$ \\\\\nwTTSs & 8 & (0) & $30.22 \\pm 0.19$ & $30.04$ \\\\ \\hline\n\\end{tabular}\n\\end{table}\n\nTwo-sample tests were applied to each pair of LDFs to search for \ndifferences.\nThe results are given in Table~\\ref{tab:L_gkm_2s} (for $L_{\\rm F}$\nand $L_{\\rm qui}$). \nThe null hypothesis of two samples being the same \nis rejected for all pairs of flare luminosity distributions \nat significance levels $\\alpha < 0.05$. The quiescent luminosity of\n{\\em flaring} TTSs\nis different from both the quiescent luminosity of {\\em flaring} Pleiads and {\\em flaring} Hyads. Usually the quiescent \nluminosity functions of Pleiades and Hyades stars are also \nfound to be distinct (see e.g. \\cite{Caillault96.1}). However, \nwe find no difference ($\\alpha > 0.61$) \nbetween the quiescence luminosities\nof the flaring stars in these two clusters.\nUsing the relation between $I_{\\rm qui}$ and the \nthreshold for $L_{\\rm F}/L_{\\rm qui}$ (see Fig.~\\ref{fig:det_accuracy}) we\nhave determined that \nmore than 90\\% of the detected Hyades stars are bright enough for\ndetection of a flare whose strength $L_{\\rm F}/L_{\\rm qui}$ is equal to \nthe mean observed for flares on late-type \nHyads, i.e. $L_{\\rm F}/L_{\\rm qui}=4.527$. The fact that mostly \n{\\em X-ray bright} \nHyades stars display flaring activity is therefore not a selection effect. \nInstead, flaring Hyads indeed are overluminous compared to the\nnon-flaring Hyades stars detected by the {\\em ROSAT} PSPC.\n\nThe mean luminosities of TTSs, Pleiads, and Hyads and their standard deviations\nderived with inclusion of upper limits are given in Table~\\ref{tab:L_gkm_mean}.\n\n\n\\subsection{Flaring cTTSs and wTTSs}\\label{subsect:cw}\n\nSo far we have not distinguished between cTTSs and wTTSs, because\nit is a matter of debate whether all cTTSs are younger than wTTSs.\nHowever, they are clearly distinguished by their circumstellar environment.\nThe disks of cTTSs may influence flare activity.\nWe have, therefore, compared cTTSs and wTTSs with respect to several flare\nparameters (see Table~\\ref{tab:cw_2s} for the results). \nSignificant differences are found in the flare luminosity \n$L_{\\rm F}$ and relative strength of the flare $L_{\\rm F}/L_{\\rm qui}$.\nThe decay timescale does not depend on the type of TTS.\nThe values given in \nTable~\\ref{tab:cw_2s} have been derived from all flares on TTSs except\nthe one on DD\\,Tau\\,/\\,CZ\\,Tau. \nDD\\,Tau is a cTTS binary and CZ\\,Tau a wTTS binary.\nThe four stars are not resolved in the PSPC\nimage. It is therefore \nimpossible to classify this flare concerning the type of TTS.\nWe have performed two further series of two-sample tests \nin which the event is included. In one of these series of tests the flare\nis attributed to DD\\,Tau, and the other time to \nCZ\\,Tau. The significance of the results did not change.\n\nThe mean flare and quiescent luminosities of cTTSs and wTTSs are given\nin Table~\\ref{tab:L_gkm_mean}. cTTSs, although characterized by lower\nquiescent emission, show stronger flares than wTTSs.\n\n\\begin{table}\n\\caption{Results of two-sample tests for differences between cTTSs and \nwTTSs with respect to the flare parameters \n$L_{\\rm qui}$, $L_{\\rm F}$, $\\tau_{\\rm dec}$, and $L_{\\rm F} / L_{\\rm qui}$. \nThe flare on the unresolved stars DD\\,Tau/CZ\\,Tau is not\nconsidered here, since it is not clear whether the event should be\nattributed to the wTTS (CZ\\,Tau) or to the cTTS (DD\\,Tau).\nThe meaning of columns~2--5 is the same as in Table~\\ref{tab:L_gkm_2s}.}\n\\label{tab:cw_2s}\n\\begin{tabular}{lrrcc} \\hline\nParameter & \\multicolumn{2}{c}{Sample Size} & Prob. GW & Prob logrank \\\\ \n & cTTSs & wTTSs & & \\\\ \\hline\n$\\lg{L_{\\rm F}}$ & 6(4) & 8(1) & 0.053 & 0.046 \\\\\n$\\lg{L_{\\rm qui}}$ & 6(0) & 8(0) & 0.206 & 0.264 \\\\\n$\\tau_{\\rm dec}$ & 6(2) & 8(1) & 0.714 & 0.752 \\\\\n$L_{\\rm F}/L_{\\rm qui}$ & 6(4) & 8(1) & 0.007 & 0.002 \\\\ \\hline\n\\end{tabular}\n\\end{table}\n\n\n\n\\subsection{$v\\,\\sin{i}$ of the flaring stars}\\label{subsect:corrvsini}\n\nStellar rotation is one of the necessary conditions for magnetic\nactivity. We have, therefore, examined the influence of the stellar rotation\nrate on the characteristics of X-ray flares. \nThe relation between flare parameters and projected rotational \nvelocity, $v\\,\\sin{i}$, is shown in Fig.~\\ref{fig:lx_vsini}.\n\\begin{figure}\n\\begin{center}\n\\resizebox{9cm}{!}{\\includegraphics{./fig55.eps}}\n\\resizebox{9cm}{!}{\\includegraphics{./fig56.eps}}\n\\caption{X-ray luminosities versus projected rotational\nvelocity $v\\,\\sin{i}$ in double logarithmic scale: {\\em top} - flare luminosity $L_{\\rm F}$, {\\em bottom} -\nluminosity ratio $L_{\\rm F}/L_{\\rm qui}$. While $L_{\\rm F}$ and\n$v\\,\\sin{i}$ may show a weak positive correlation, $L_{\\rm F}/L_{\\rm qui}$ does not depend on the rotation.}\n\\label{fig:lx_vsini}\n\\end{center}\n\\end{figure}\nThe statistical significance for\ncorrelations between some flare parameters and $v\\,\\sin{i}$ is given in \nTable~\\ref{tab:vsini_2s} (columns~2~and~3). The weak correlation between\nluminosity, both $L_{\\rm F}$ and $L_{\\rm qui}$, and $v\\,\\sin{i}$ is significant.\nThe decay time $\\tau_{\\rm dec}$ and the relative flare strength \n$L_{\\rm F}/L_{\\rm qui}$, on the other hand, are not related to\n$v\\,\\sin{i}$.\n\nWe have studied the flaring population in terms of differences in\nflare characteristics between\nslow and fast rotators. The boundary was set to 20\\,km/s because this \nchoice gives two samples of about equal size: 16 slow and \n12 fast rotators showed an X-ray flare. Stars from\nTables~\\ref{tab:det_flares_TTS},~\\ref{tab:det_flares_Ple},~and~\\ref{tab:det_flares_Hya}\nfor which no measurement of $v\\,\\sin{i}$ is available are ignored. The result\nof two sample tests for the parameters $L_{\\rm F}$, $L_{\\rm qui}$,\n$\\tau_{\\rm dec}$,\nand $L_{\\rm F}/L_{\\rm qui}$ are presented in the remaining columns of \nTable~\\ref{tab:vsini_2s}. In no case the null \nhypothesis that slow and fast rotators are drawn from the\nsame distribution was rejected at significance level $\\alpha < 0.05$. \n\n\\begin{table}\n\\caption{Relation between flare parameters $L_{\\rm qui}$, $L_{\\rm F}$,\n$\\tau_{\\rm dec}$, and $L_{\\rm F} / L_{\\rm qui}$ and the projected\nrotational velocity $v\\,\\sin{i}$: Columns~2~and~3 are results of\ncorrelation tests between each of the listed parameters and\n$v\\,\\sin{i}$. The remaining columns give results of two-sample tests for\ndifferences between slow and fast rotators with boundary at $20\\,{\\rm\nkm/s}$. The samples consist of 16 slow versus 12 fast rotators.}\n\\label{tab:vsini_2s}\n\\begin{tabular}{lccrr} \\hline\nParameter & Pearson r & Spearman r & Prob. & Prob \\\\ \n & (Signif.) & (Signif.) & GW & logrank \\\\ \\hline\n$\\lg{L_{\\rm F}}$ & 0.479 (0.005) & 0.372 (0.026) & 0.075 & 0.091 \\\\\n$\\lg{L_{\\rm qui}}$ & 0.468 (0.006) & 0.496 (0.004) & 0.269 & 0.528 \\\\\n$\\tau_{\\rm dec}$ & 0.247 (0.103) & 0.221 (0.129) & 0.487 & 0.584 \\\\\n$L_{\\rm F}/L_{\\rm qui}$ & -0.017 (0.466) & -0.287 (0.069) & 0.399 & 0.547\n\\\\ \\hline\n\\end{tabular}\n\\end{table}\n\n\n\n\n\\section{Flare rates}\\label{sect:rate}\n\nIn this section, we will derive flare rates as a means to \ndetermine the activity level for a stellar sample with distinct properties. \nThe characteristic properties which will be\nexamined are (a) stellar age (comparing TTSs, Pleiads, and Hyads),\n(b) stellar rotation (comparing slow and fast rotators), and\n(c) stellar multiplicity (comparing close binaries to other stars).\nFlare rates will be computed separately for each group of stars.\n\nWe assume that the duration of the active state is represented by\nthe decay timescale $\\tau_{\\rm dec}$, i.e. the generally poorly\nrestricted rise times $\\tau_{\\rm ris}$ are neglected. \nThis is certainly wrong for the flare\non hcg\\,144 which seems to have a somehow reversed character (slow rise and\nrapid decay). However, hcg\\,144 is a star of unknown spectral type and\ntherefore not part of the group to be examined here.\nTo compile the flare rates, $F = \\sum{(\\tau_i)} / T_{\\rm obs}$, \nwe have added up the decay timescales $\\tau_{\\rm dec}$ of the flares and \ndivided this sum by the total observing time, $T_{\\rm obs}$, \nof all detections (flaring and non-flaring stars). \nOnly the nearest identification of each X-ray source has been\nconsidered in the compilation of $T_{\\rm obs}$. But for \nmultiple systems we have multiplied the observing time by the number of \ncomponents.\nFor the compilation of $T_{\\rm obs}$ we have eliminated data gaps\nlarger than 1\\,h, the typical flare duration.\nThis provides us the fraction of the total observing \ntime during which the stars\nare observed in the active state.\n\nIn practice $\\sum{(\\tau_i)}$ is computed from the sample mean $\\bar{\\tau}$ \nreturned by ASURV's Kaplan-Meier estimator. This way we ensure that upper\nlimits to $\\tau_{\\rm dec}$ are taken into account. The Kaplan-Meier estimator\nreturns also the uncertainty of $\\bar{\\tau}$. To include the spread\nof the data in the estimation of $F$ we have converted this uncertainty\nof the mean to the sample variance $\\sigma_\\tau$. Consequently:\n\\begin{equation}\nF = \\frac{\\bar{\\tau} \\cdot N}{T_{\\rm obs}} \\pm \\frac{\\sigma_\\tau \\cdot \\sqrt{N}}{T_{\\rm obs}}\n\\end{equation}\n\n\n\n\\subsection{Flare rate and stellar age}\n\nThe evolution of flare rates with stellar age is examined by \ncomparing the flare frequency of TTSs to that of the Pleiades and the Hyades.\n15 flares have occurred on TTSs, 14 on late-type\nPleiads, and 11 on late-type Hyads. \nWe have derived the following values for the flare rate\n$F$: $0.86 \\pm 0.16$\\% (TTSs), \n$0.67 \\pm 0.13$\\% (Pleiads), and $0.86 \\pm 0.32$\\% (Hyads). \nWhen the white-dwarf binaries are excluded the \nflare rate for Hyades declines to \n$F_{\\rm H,no WD} = 0.71 \\pm 0.30$\\%. \n\nThe flare rates are biased for several reasons which will be explained next.\nFirst, \nthe flare detection limit is determined by the S/N, which in turn depends\non the distance to the\nstar. Therefore, flare\nrates of TTSs, Pleiads, and Hyads are only comparable\nabove a limiting minimum strength of the flare, expressed by a \nthreshold $L_{\\rm F} / L_{\\rm qui}$. And, secondly,\nincomplete data sampling might lead to wrong conclusions about the\ndecay timescale of individual events and thus contaminate the \nresulting $F$.\n\nTo solve the first problem we\nhave scaled the quiescent count rate of all flaring stars \nto a distance of 140\\,pc, the distance of most of the TTSs. I.e.\nwe have multiplied all quiescent count rates with a factor \n$(\\frac{d}{140\\,pc})^2$.\nThese theoretical values of $I_{\\rm qui}$ correspond to higher flare\ndetection thresholds $L_{\\rm F} / L_{\\rm qui}$ for all stars except \nthe ones in Perseus. All flares from Perseus stars would be detected at\n140\\,pc, since they are further away than this distance. \nThe observed luminosity ratios of all flaring stars have then been compared\nto the theoretical threshold needed if the star were at 140\\,pc. All\nflares for which the observed value is below this requirement should\nbe neglected when the flare rates are computed. It turns out that\nall flares on Pleiads remain above the 140\\,pc threshold. But only\n7 out of 11 flares on Hyads (one of the 7 is a white-dwarf system) \nhave $L_{\\rm F} / L_{\\rm qui}$ high enough\nto be detected at a distance of 140\\,pc. Now the comparison of our\ndifferent samples is free from the sensitivity bias. And we derive\nflare rates $F$ of \n$0.86 \\pm 0.16$\\% (TTSs), \n$0.67 \\pm 0.13$\\% (Pleiads), and $0.46 \\pm 0.19$\\% (Hyads).\nWithout the white-dwarf binary $F$ decreases for the Hyades\nto $0.32 \\pm 0.17$\\%.\n\nThe uncertainties in the measurement of \nthe flare duration are\nless easy to overcome. The large flare rate of TTSs is partially due to\ntwo extraordinary long events of duration $> 8\\,{\\rm h}$ \n(see Table~\\ref{tab:det_flares_TTS}). The decay times of both of these\nflares are considered to be an upper limit. \nIf these two events are discarded from the sample of flares, \n$F_{\\rm TTS} = 0.74 \\pm 0.14$\\%.\n\nWe have also compiled $F$ for cTTSs and wTTSs separately to see\nwhether the circumstellar environment has any influence on the frequency \nof the flare activity. Among the events on TTSs, \n6 are observed on cTTSs and 8 on wTTSs.\nAn additional flare was seen from the unresolved stars DD\\,Tau\\,/\\,CZ\\,Tau.\nThe classification of this event within the subgroups of TTSs remains\ntherefore unclear, and complicates the comparison of $F$ for the two\nclasses of TTSs. At first, the event on DD\\,Tau\\,/\\,CZ\\,Tau has been\neliminated from the sample, thus that 6 flares on cTTSs are opposed to\n8 flares on wTTSs.\nThe respective flare rates are \n$F_{\\rm c} = 1.09 \\pm 0.39$\\% and\n$F_{\\rm w} = 0.65 \\pm 0.16$\\%. \nWhen the ambiguous event is \ncounted on the side of the cTTSs $F_{\\rm c}$ rises to \n$1.28 \\pm 0.37$\\%.\nWhen it is attributed to the wTTS CZ\\,Tau instead, $F_{\\rm w}$ becomes\n$0.76 \\pm 0.16$\\%. \nNote, that even though the number of flares on wTTSs is higher than the \nnumber of flares on cTTSs,\nthe flare rate for wTTSs is lower than the flare rate for cTTSs.\nThis is possible because of differences in the total observing time.\n\n$F$ as a function of stellar age is displayed in Fig.~\\ref{fig:frates}.\nThe decline of the flare rate with stellar age is obvious. Rates for cTTSs\nand wTTSs are symbolized by diamonds and triangles, respectively. The\nlocation of the lower diamond and triangle describes the flare rates \nwithout the event on DD\\,Tau\\,/\\,CZ\\,Tau. The upper diamond and\ntriangle are values for $F$ if this flare is included \nin the respective group of TTSs.\n\\begin{figure}\n\\begin{center}\n\\resizebox{9cm}{!}{\\includegraphics{./fig57.eps}}\n\\caption{Flare rate $F = \\sum{(\\tau_i)} / T_{\\rm obs}$ as a function of\nstellar age for TTSs, Pleiads, and Hyads. To eliminate biases due to the\nS/N-dependence of the detection sensitivity for flares, only events which\nare bright enough for detection at a uniform distance of 140\\,pc are\nconsidered. Furthermore, flares which can not definitely be assigned to a\nlate-type star are excluded. The flare rates for cTTSs (diamonds) and wTTSs\n(triangles) alone are overplotted. The upper of the two symbols applies if\nthe ambiguous event on DD\\,Tau\\,/\\,CZ\\,Tau is included in the sample (see\ntext). The horizontal bars represent the age spread of TTSs.}\n\\label{fig:frates}\n\\end{center}\n\\end{figure}\n\n\n\n\\subsection{Flare rate and rotational velocity}\n\nHere we examine whether the flare\n{\\em frequency} depends on rotation. This is done by computing $F$ \n(defined as before) for fast rotators on the one hand \n($v\\,\\sin{i} > 20\\,{\\rm km/s}$) and slow\nrotators on the other hand ($v\\,\\sin{i} < 20\\,{\\rm km/s}$).\nAgain, only late-type stars are considered.\nThe resulting rates are \n$F_{\\rm slow} = 0.55 \\pm 0.10$\\% and \n$F_{\\rm fast} = 1.55 \\pm 0.38$\\%.\nThus there is a clear trend towards an increase of\nflare activity with increasing rotational velocity.\n\n\n\n\\subsection{Flare rate and multiplicity}\n\nAnother interesting question is whether the circumstellar\nsurroundings have any influence on the flare frequency.\nThe coronal activity may e.g. change if there are interactions \nbetween the magnetic fields of binaries.\nSuch interactions are expected to take place only in {\\em close}\nbinaries.\nTo search for such a connection we, therefore, discriminate between \nspectroscopic binaries on the one hand and all others,\ni.e. singles or visual multiples.\nThe flare rate $F$ is computed in the same way as before.\nSince the observation time of each\nstellar system has been multiplied by the number of components, the\nflare rates should be about equal for both samples if the \nunderlying physics are the same. \nHowever, we find that the flare rate of spectroscopic binaries\nis enhanced by more than a factor of two:\n$F_{\\rm non-SB} = 0.64 \\pm 0.12$\\%\nand $F_{\\rm SB} = 1.43 \\pm 0.25$\\%.\nNote, that the study of individual flare parameters (similar to \nthe analysis of Sect.~\\ref{sect:statcomp}) has \nshown no difference for these two samples.\n\n\n\n\\section{Hardness Ratios}\\label{sect:hr}\n\nFor most of the flaring sources not enough counts are collected by the PSPC \nto compare the different levels of X-ray emission in a detailed spectral \nanalysis. Therefore, we use hardness ratios to mark spectral changes. \n{\\em ROSAT} PSPC hardness ratios are defined by:\n\\begin{equation}\nHR\\,1 = \\frac{H-S}{H+S} \\quad HR\\,2 = \\frac{H_2-H_1}{H_2-H_1}\n\\end{equation}\nwhere $S$, $H$, $H_1$, and $H_2$ \ndenote the count rates in the {\\em ROSAT} PSPC\nsoft (0.1-0.4\\,keV), hard (0.5-2.0\\,keV), hard1 (0.5-0.9\\,keV) and hard2 \n(0.9-2.0\\,keV) band respectively.\nFor each flare observation $HR\\,1$ and $HR\\,2$ are computed for three activity \nstages representing the quiescent state (pre- and post-flare), the \nrise and the decay, respectively. Sometimes no counts are measured in one\nor more of the energy bands. Whenever this is the case we have derived\nupper limits for the hardness ratio making use of the background counts\nin that energy band at the source location.\n\n\\begin{figure*}\n\\begin{center}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.2cm}{!}{\\includegraphics{./fig58.eps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.2cm}{!}{\\includegraphics{./fig59.eps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.2cm}{!}{\\includegraphics{./fig60.eps}}}\n}\n\\parbox{16cm}{\n\\parbox{4.5cm}{\\resizebox{5.2cm}{!}{\\includegraphics{./fig61.eps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.2cm}{!}{\\includegraphics{./fig62.eps}}}\n\\parbox{1cm}{\\hspace*{1.cm}}\n\\parbox{4.5cm}{\\resizebox{5.2cm}{!}{\\includegraphics{./fig63.eps}}}\n}\n\\caption{Comparison of {\\em ROSAT} PSPC hardness ratios for quiescent state,\nflare rise and flare decay of the late-type stars from\nTables~\\protect\\ref{tab:det_flares_TTS},~\\protect\\ref{tab:det_flares_Ple},\nand~\\protect\\ref{tab:det_flares_Hya}. {\\em top} - $HR\\,1$, {\\em bottom} -\n$HR\\,2$. The meaning of the plotting symbols is the same as in Fig.~\\ref{fig:Lf_Lq}. Stars located on the dashed line show no change in hardness between quiescent and flare state.}\n\\label{fig:hrs}\n\\end{center}\n\\end{figure*}\n\nThe observed hardness ratios, $HR\\,1$ and $HR\\,2$, \nare plotted in Fig.~\\ref{fig:hrs}. \nThe plots comparing quiescent and flare state\nshow marginal evidence that most of the stars lie\nbelow the diagonal in the hardness plot (see lower left panel of \nFig.~\\ref{fig:hrs}) and thus are harder during the\nflare intervals as compared to their quiescence. \nNo significant difference in hardness is observed between flare rise\nand flare decay. \nWhen impulsive heating takes place before the outburst the plasma cools \nquickly by radiation and conduction to the chromosphere. Therefore,\nthe similar hardness observed during rise and decay phase suggests\nthat heating takes place throughout the decay.\n\nTo quantify the differences in hardness between different flare\nstages we have computed mean hardness ratios for each of the stellar\ngroups. In Table~\\ref{tab:hrs} we show the mean hardness \nfor each activity stage (quiescence, rise, and decay) and each\nsample of stars (TTSs, Pleiads, and Hyads).\nThe hardness changes systematically when \nthe three groups are compared to each other:\nTTSs display the hardest spectra, followed by Pleiads, \nwhich in turn are characterized by higher hardness ratios than the\nHyades stars. \nThis is also manifest in the hardness plots of Fig.~\\ref{fig:hrs} \nwhere the three samples occupy different regions.\nIn Sect.~\\ref{subsect:lumfunct} it was shown that the flare luminosity\ndeclines with stellar age. As a consequence, the spectral hardness \nand the flare luminosity are correlated. The relation between hardness\nratios and $L_{\\rm F}$ is displayed in \nFig.~\\ref{fig:hr_Lx} and suggests that the more luminous flares are\nassociated with hotter plasma. \n\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{lrrr} \\hline\n & \\multicolumn{3}{c}{$HR\\,1$} \\\\\n\t& \\multicolumn{1}{c}{Quiescence} & \\multicolumn{1}{c}{Rise} & \\multicolumn{1}{c}{Decay} \\\\ \\hline \nTTS & $0.75 \\pm 0.38$ & $0.54 \\pm 0.47$ & $0.70 \\pm 0.44$ \\\\ \nPleiads & $0.54 \\pm 0.26$ & $0.50 \\pm 0.29$ & $0.58 \\pm 0.30$ \\\\ \nHyads & $-0.09 \\pm 0.24$ & $-0.16 \\pm 0.15$ & $-0.07 \\pm 0.16$ \\\\ \\hline \n & \\multicolumn{3}{c}{$HR\\,2$} \\\\\n\t& \\multicolumn{1}{c}{Quiescence} & \\multicolumn{1}{c}{Rise} & \\multicolumn{1}{c}{Decay} \\\\ \\hline \nTTS & $0.36 \\pm 0.24$ & $0.38 \\pm 0.31$ & $0.39 \\pm 0.21$ \\\\\nPleiads & $0.07 \\pm 0.20$ & $0.08 \\pm 0.22$ & $0.21 \\pm 0.14$ \\\\\nHyads & $-0.01 \\pm 0.12$ & $-0.04 \\pm 0.27$ & $0.14 \\pm 0.27$ \\\\ \\hline\n\\end{tabular}\n\\caption{Evolution of the {\\em ROSAT} PSPC hardness ratios $HR\\,1$ and $HR\\,2$\nduring stellar flares. Given are the weighted means of flares on TTSs,\nPleiads, and Hyads measured during three different phases selected from the\nX-ray lightcurve: Quiescence (pre- and post-flare), Rise, and Decay. \nA slight increase in hardness is observed between quiescence and rise\nphase, but is not significant due to the large spread of the data within\none sample. During the decay the spectrum retains its hardness.\nThis indicates additional heating\ntaking place during the decay phase. For each of the flare stages the spectral hardness decreases from TTSs over Pleiads to Hyads.}\n\\label{tab:hrs}\n\\end{center}\n\\end{table}\n\n\\begin{figure}\n\\begin{center}\n\\resizebox{8cm}{!}{\\includegraphics{./fig64.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{./fig65.eps}}\n\\caption{Correlation between {\\em ROSAT} PSPC hardness ratios and flare\nluminosity $L_{\\rm F}$. The meaning of the plotting symbols is the same as\nin Fig.~\\ref{fig:hrs}. Lower limits for $L_{\\rm F}$ are shown when a \ndata gap proceeds the observed maximum of the lightcurve (see Tables~\\ref{tab:det_flares_TTS},~\\ref{tab:det_flares_Ple}~and~\\ref{tab:det_flares_Hya})}\n\\label{fig:hr_Lx}\n\\end{center}\n\\end{figure}\n\n\n\n\n\\section{Discussion}\\label{sect:discussion}\n\n\n\\subsection{Methods for flare detection}\n\nUsing binned data to detect flares introduces observational \nrestrictions. The sensitivity for detection\nof small flares is lower and \nvery short flares remain unobserved due to the time binning.\nApart from these limitations, our flare detection produces reliable\nresults as verified by comparison to both an alternative approach \nusing Bayesian statistics and, where possible, previous detections of\nflares by visual inspection stated in the literature. \n\nThe importance of Bayesian statistics to astronomical time series analysis \nhas been described by \n\\citey{Scargle98.1} and first applied to {\\em ROSAT} observations \nof flare stars by \\citey{Hambaryan99.1}. This approach, unlike the \n`classical' method used here, \nworks on the raw, unbinned data and therefore has a time resolution\nwhich is only limited by the instrument clock.\n\nWe have performed a detailed comparison of the events recognized by \nthe two methods.\nFor the flare detection with the Bayesian algorithm the prior odds ratio, \n$O_{\\rm pri}$, was set to 1. This means that at\nthe beginning one-rate and two-rate Poisson processes are assumed to \nhave the same probability for being the correct description of the data set.\nThe significance of any detection of variability \nis then given by the value of the\nposterior odds ratio, $O_{\\rm 21}$. \nApplied to our data, 62 events are found at the $5\\,\\sigma$ level,\nand 95 events have $O_{\\rm 21}$ corresponding to at least $3\\,\\sigma$.\nAll but 5 of the flares discussed in this paper were among the $5\\,\\sigma$\ndetections. The remaining ones are detected at $>3\\,\\sigma$. But note \nthat with the Bayesian method we find variability in 182 lightcurves\n(in contrast to our 52 flares).\n\nAlthough the Bayesian approach is sensitive to \nshort events, we have persisted on the criteria explained in \nSect.~\\ref{subsect:method_det} for two reasons:\n(i) While Bayesian statistics are sensitive to all kinds of temporal\nvariability, we are here interested in large flare events only. This makes\nan additional selection process necessary. (ii) Comparison with the\nclassical flare search used in this paper has shown that the Bayesian\nmethod needs further refinement. E.g. the outcome of the \npresent algorithm used to search for flares depends \nsensitively on the value of the prior odds ratio.\n\n\n\n\\subsection{Interpretation of the results}\\label{subsect:results}\n\nBefore flares on different stellar groups are compared, it must be\nchecked whether the composition of these samples is similar. \nThe X-ray luminosity of MS stars depends on their spectral type. \nTherefore it would be desirable to separately \ninvestigate the flare activity from stars of different spectral types.\nHowever this is hindered by the low flare statistics. \nWe have performed statistical tests where the flaring TTSs, Pleiads, \nand Hyads have been compared regarding to their $T_{\\rm eff}$ \nand hence spectral types. These tests have\nshown that it is justified to jointly analyse flares on all late-type stars,\ni.e. stars with spectral type G, K, and M.\n\nWe have shown that the relative number of flares increases \nwhen going from spectral types G to K \n(see Fig.~\\ref{fig:detsens_spt}). Hereby, we have taken into\naccount that the detection sensitivity for\nflares depends on the level of measured quiescent emission and hence on the\nspectral type. \nAn interpretation is that deeper convection zones are\nfavorable to the occurrence of surface flares. \n\n\n\n\\subsubsection{Age}\\label{subsubsect:compare_age}\n\nWe found that\nin terms of absolute flare luminosity and energy output TTSs surpass \nboth Pleiads and Hyads. The mean flare luminosity of TTSs \n($L_{\\rm F,TTS}=1.13~10^{31}\\,{\\rm erg/s}$) is \nalmost an order of magnitude higher than that for Hyads \n($L_{\\rm F,Hya}=1.15~10^{30}\\,{\\rm erg/s}$).\nThe mean \nPleiades flare luminosity is intermediate between that for TTSs \nand Hyades stars \nwith $L_{\\rm F,Ple}=3.26~10^{30}\\,{\\rm erg/s}$\n(see also Fig.~\\ref{fig:Lf_Lq} and Table~\\ref{tab:L_gkm_mean}).\nThis is partly due to the different distances of our stellar samples \nwhich result in different \ndetection sensitivities for flares. Note, however, that\nthis effect can explain only why no events with small $L_{\\rm F}$ are\nobserved on TTSs. But the lack of large events on Hyades stars is real.\nIn Sect.~\\ref{sect:rate} flare rates for TTSs, Pleiads, \nand Hyads have been established \nfrom an evaluation of the observed flare durations and the total\nobserving time. \nBoth, flare rate and\nmean flare luminosity decline with increasing stellar age.\n\nThe quiescent luminosity of Hyades stars which showed a flare is larger than\nthe average $L_{\\rm qui}$ of Hyads (see Sect.~\\ref{subsect:lumfunct}). \nMore than $90$\\% of the detected Hyades stars are bright enough \nfor detection of an average Hyads flare. \nTherefore, this result is not a selection effect, and we can \nconclude that only the most X-ray luminous Hyades stars exhibit X-ray \nflares.\nThe interesting question whether the enhanced\nX-ray luminosity of flaring Hyades stars can be explained by their rotation\nrate can not be pursued with this set of data, because \nonly for half of the flaring Hyades stars measurements of $v\\,\\sin{i}$ are\navailable.\n\n\n\n\\subsubsection{Circumstellar Envelope}\\label{subsubsect:compare_cw}\n\nIf magnetic interactions between star and disk take place, the field lines\nwill constantly become twisted by differential rotation \n(\\cite{Montmerle00.1}). \nThis may provide an environment favorable for magnetic reconnection\nand related flare activity.\n\nSix of the observed flare events \ncan be attributed to cTTSs and 8 events to wTTSs. One of the flares\non TTSs occurred either on DD\\,Tau, a cTTS, or on CZ\\,Tau, a wTTS, both of\nwhich are not resolved in the {\\em ROSAT} PSPC observations. \nTwo-sample tests show clear indications that flares\non cTTSs are more X-ray luminous than those on wTTSs \n(see Table~\\ref{tab:L_gkm_2s}). \nThis holds no matter on which side the ambiguous event is counted.\nThe flare rate is also slightly \nhigher for cTTSs than for wTTSs, however with low significance. \nGiven the fact that quiescent\nX-ray emission of wTTSs is stronger than in cTTSs, this observation is \nsurprising. A possible interpretation is that \nthe stronger flare events on cTTSs may be due to violent\ninteraction with their disks.\n\n\n\n\\subsubsection{Multiple Flares}\\label{subsubsect:multiflares}\n\nDuring four observations a second flare followed the first one\n(see lightcurves of VA\\,334, VB\\,141, RXJ\\,0437.5+1851B, and T\\,Tau in \nFigs.~\\ref{fig:lcs_TTS}~and~\\ref{fig:lcs_Hya}). \nFrom the number of observed flares and the total observing\ntime the average duration between two flare events is estimated to be\n$> 100\\,{\\rm h}$. Therefore, from a statistical point of view it is very\nunlikely to observe so many unrelated `double events'. We note, that double\nflares have been reported in the optical. And \n\\citey{Guenther99.1} have presented two flares that occurred \nwithin a few hours from the wTTS V819\\,Tau.\n\nA possible interpretation of multiple flares is the star-disk scenario\nproposed by \\citey{Montmerle00.1} and mentioned in the previous subsection.\nHowever, this model does not seem to be accurate for our objects, which are\nmore evolved and in part are known not to possess disks.\n\n\n\n\\subsubsection{Projected Rotational Velocity}\\label{subsubsect:compare_sf}\n\nThe statistical tests we have performed to discriminate between slow and\nfast rotators (with boundary drawn at 20\\,km/s) reveal no dependence of\nindividual flare parameters $L_{\\rm F}$, $L_{\\rm qui}$, \n$\\tau_{\\rm dec}$, and $L_{\\rm F}/L_{\\rm qui}$ on the rotation rate. However,\nthe flare frequency is about three times \nhigher for fast rotators as compared to slow rotators: \n$F_{\\rm slow} = 0.55 \\pm 0.10$\\% and $F_{\\rm fast} = 1.55 \\pm 0.38$\\%.\n\n\n\n\\subsubsection {Binary Interactions}\\label{subsubsect:compare_sm}\n \nWe have searched for evidence of binary interaction during X-ray flares\nby dividing our sample of flares into \nspectroscopic binaries and all other systems, i.e. wide (or visual)\nmultiples and single stars, in which such interactions can not take place. \nThe comparison of flare rates $F$ showed that large X-ray flares are\nsignificantly more frequent on spectroscopic binaries:\n$F_{\\rm SB} = 1.43 \\pm 0.25$\\%\nand $F_{\\rm non-SB} = 0.64 \\pm 0.12$\\%.\nWe have taken account of all components in multiple systems when evaluating\nthe flare rate. Therefore, the difference in $F$ between close binaries and\nother stars seems indeed to indicate that magnetic \ninteractions within close binaries leads to increased flare activity.\nBut note, that interbinary events are expected to have longer durations\nbecause of the larger scale of the magnetic configuration. Our statistical\nobservations did not show an increase of the time scales for\n spectroscopic binaries.\n\n\n\n\\subsubsection{Spectral signatures during flares}\n\nFrom the lower panels of Fig.~\\ref{fig:hrs} it can be concluded that\nfor most of the observed events the spectral hardness has increased during the \nflare. Due to the large uncertainties, however, the changes in the\nmean hardness are only marginal. But, note, that the uncertainties\nrepresent the standard deviation (computed by taking into account \nupper/lower limits to the hardness) and thus reproduce the spread in the\ndata.\n\nWe think that\nthe X-ray emission of TTSs is harder than that of Pleiades and Hyades\nstars (see Table~\\ref{tab:hrs}) for two reasons: (i) Because of their\ncircumstellar envelope TTSs suffer from \nmuch stronger absorption than Pleiads and Hyads, and absorption is stronger\nfor Pleiads than for Hyads due to the larger distance of the former, (ii)\nthe younger the stars, the stronger the activity, and therefore the harder\nthe spectrum.\n\n\n\n\n\\section{Conclusions}\\label{sect:conclusions}\n\nWe have determined flare rates for PMS stars, Pleiades and Hyades\non a large data set and found that all stars are observed during flares\nfor less than 1\\% of the observing time. \nBoth frequency and strength of large X-ray flares\ndecline after the PMS phase.\n\nTo probe whether the activity changes in the\npresence of a circumstellar disk, e.g. as a result of magnetic interactions\nbetween the star and the disk, we have compared flares on cTTSs and wTTSs. \nWe find that flares on cTTSs are stronger and more frequent.\n\nA comparison of flares on spectroscopic binaries to \nflares on all other stars of our sample shows that the flare rate is\nby a factor of $\\sim 2$ higher for the close binaries. \n\nThe flare rate of fast rotators is enhanced by a factor of $\\sim$ 3 as\ncompared to slowly rotating stars. \n\nTo summarize, our analysis \nconfirms that age and rotation influence the magnetic activity of\nlate-type stars. All previous studies in this field \nhave focused on the quiescent X-ray emission. Now, \nfor the first time the rotation-activity-age connection has been \nexamined for X-ray flares. \nFurthermore, from the sample of flares investigated here we find evidence \nthat magnetic activity goes beyond solar-type coronal activity: On\nyoung stars interactions between the star and a circumstellar disk\nor the magnetic fields of close binary stars may play a role.\n\n\n\n\\begin{acknowledgements}\nWe made use of the Open Cluster Database, compiled by \nC.F. Prosser and J.R. Stauffer. We thank S. Wolk and W. Brandner\nfor useful discussions and an anonymous referee for valuable comments. RN acknowledges grants from the Deutsche\nForschungsgemeinschaft (Schwerpunktprogramm `Physics of star formation').\nThe {\\em ROSAT} project is supported by the Max-Planck-Gesellschaft and\nGermany's federal government (BMBF/DLR).\n\\end{acknowledgements}\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\astroncite{Anderson et~al.}{1966}]{Anderson66.1}\nAnderson C. M., St\\\"ockly R., Kraft R. P., 1966, ApJ 143, 299\n\n\\bibitem[\\protect\\astroncite{Beckwith et~al.}{1990}]{Beckwith90.1}\nBeckwith S. V. W., Sargent A. I., Chini R. S., G\\\"usten R. 1990, AJ 99, 924\n\n\\bibitem[\\protect\\astroncite{Bertout et~al.}{1988}]{Bertout88.1}\nBertout C., Basri G., Bouvier J. 1988, ApJ 330, 350\n\n\\bibitem[\\protect\\astroncite{Bouvier et~al.}{1993}]{Bouvier93.1}\nBouvier J., Cabrit S., Fern$\\acute{\\rm a}$ndez M., Mart\\'\\i n E. L.,\nMatthews J. M. 1993, A\\&A 272, 176\n\n\\bibitem[\\protect\\astroncite{Bouvier et~al.}{1997a}]{Bouvier97.1}\nBouvier J., Forestini M., Allain S. 1997a, A\\&A 326, 1023\n\n\\bibitem[\\protect\\astroncite{Bouvier et~al.}{1997b}]{Bouvier97.2}\nBouvier J., Rigaut F., Nadeau D. 1997b, A\\&A 323, 139\n\n\\bibitem[\\protect\\astroncite{Brice\\~no et~al.}{1998}]{Briceno98.1}\nBrice\\~no C., Hartmann L., Stauffer J., Mart\\'\\i n E. 1998, AJ 115, 2074\n\n\\bibitem[\\protect\\astroncite{Caillault}{1996}]{Caillault96.1}\nCaillault J.-P., 1996, In: Pallavicini R. and Dupree A. K. (eds.), Cool\nStars, Stellar Systems, and the Sun, 9th Cambridge Workshop, ASP Conf. Ser., Vol.109, 325\n\n\\bibitem[\\protect\\astroncite{Cernicharo et~al.}{1985}]{Cernicharo85.1}\nCernicharo J., Bachiller R., Duvert G., 1985, A\\&A 149, 273\n\n\\bibitem[\\protect\\astroncite{Cohen \\& Kuhi}{1979}]{Cohen79.1}\nCohen M, Kuhi L. V. 1979, ApJS 41, 743\n\n\\bibitem[\\protect\\astroncite{Cruddace et~al.}{1988}]{Cruddace88.1}\nCruddace R. G., Hasinger G. R., Schmitt J. H. M. M., 1988, In: Murtagh F., Heck A. (eds.) Astronomy from large databases, ESO, Garching, p.177\n \n\\bibitem[\\protect\\astroncite{Elias}{1978}]{Elias78.1}\nElias J. H., 1978, ApJ 224, 857\n\n\\bibitem[\\protect\\astroncite{Feigelson \\& DeCampli}{1981}]{Feigelson81.1}\nFeigelson E. D., DeCampli W. M. 1981, ApJ 243, L89\n\n\\bibitem[\\protect\\astroncite{Feigelson \\& Nelson}{1985}]{Feigelson85.1}\nFeigelson E. D., Nelson P. I. 1985, ApJ 293, 192\n\n\\bibitem[\\protect\\astroncite{Gagn$\\acute{\\rm e}$ \\& Caillault}{1994}]{Gagne94.1}\nGagn$\\acute{\\rm e}$ M., Caillault J.-P. 1994, ApJ 437, 361\n\n\\bibitem[\\protect\\astroncite{Gagn$\\acute{\\rm e}$ et~al.}{1995}]{Gagne95.1}\nGagn$\\acute{\\rm e}$ M., Caillault J.-P., Stauffer J. R., 1995, ApJ 450, 217\n\n\\bibitem[\\protect\\astroncite{Ghez et~al.}{1993}]{Ghez93.1}\nGhez A. M., Neugebauer G., Matthews K. 1993, AJ 106, 2005\n\n\\bibitem[\\protect\\astroncite{Gizis \\& Reid}{1999}]{Gizis99.1}\nGizis J. E., Reid I. N. 1999, AJ 117, 508\n\n\\bibitem[\\protect\\astroncite{Grosso et~al.}{1997}]{Grosso97.1}\nGrosso N., Montmerle T., Feigelson E. D., Andr$\\acute{\\rm e}$ P., Casanova S.,\nGregorio-Hetem J. 1997, Nat 387, 56\n\n\\bibitem[\\protect\\astroncite{Griffin et~al.}{1985}]{Griffin85.1}\nGriffin R. F., Gunn J. E., Zimmerman B. A., Griffin R. E. M. 1985, AJ 90, 609\n\n\\bibitem[\\protect\\astroncite{Guenther \\& Ball}{1999}]{Guenther99.1}\nGuenther E. W., Ball M. 1999, A\\&A 347, 508\n\n\\bibitem[\\protect\\astroncite{Guenther et~al.}{1999}]{Guenther99.2}\nGuenther E. W., Lehmann H., Emerson J. P., Staude J. 1999, A\\&A 341, 768\n\n\\bibitem[\\protect\\astroncite{Hambaryan et~al.}{1999}]{Hambaryan99.1}\nHambaryan V., Neuh\\\"auser R., Stelzer B. 1999, A\\&A 345, 121\n\n\\bibitem[\\protect\\astroncite{Haro et~al.}{1982}]{Haro82.2}\nHaro G., Chavira E., Gonzalez G., 1982a, Instituto de Tonantzintla, Boletin\nVol.3, 3\n\n\\bibitem[\\protect\\astroncite{Hartmann \\& Stauffer}{1989}]{Hartmann89.1}\nHartmann L., Stauffer J. R., 1989, AJ 97, 873\n\n\\bibitem[\\protect\\astroncite{Hearty et~al.}{2000}]{Hearty00.1}\nHearty T. J., Neuh\\\"auser R., Stelzer B., Fern$\\acute{\\rm a}$ndez M.,\nAlcal$\\acute{\\rm a}$ J. M., Covino E., et al. 2000, A\\&A, in press\n\n\\bibitem[\\protect\\astroncite{Herbig}{1998}]{Herbig98.1}\nHerbig G. H. 1998, ApJ 497, 736\n\n\\bibitem[\\protect\\astroncite{Herbig \\& Bell}{1988}]{Herbig88.1}\nHerbig G. H., Bell K. R., 1988, Lick Observatory Bulletin, No. 1111 \n\n\\bibitem[\\protect\\astroncite{Hertzsprung}{1947}]{Hertzsprung47.1}\nHertzsprung E. 1947, Ann. Leiden Obs. 19, No. 1A\n\n\\bibitem[\\protect\\astroncite{Hodgkin et~al.}{1995}]{Hodgkin95.1}\nHodgkin S. T., Jameson R. F., Steele I. A., 1995, MNRAS 274, 869 \n\n\\bibitem[\\protect\\astroncite{Johnson \\& Mitchell}{1958}]{Johnson58.1}\nJohnson H. L., Mitchell R. I., 1958, ApJ 128, 31\n\n\\bibitem[\\protect\\astroncite{Jones et~al.}{1996}]{Jones96.1}\nJones B. F., Fischer D. A., Stauffer J. R. 1996, AJ 112, 1562\n\n\\bibitem[\\protect\\astroncite{Kenyon \\& Hartmann}{1995}]{Kenyon95.1}\nKenyon S. J., Hartmann L., 1995, ApJS 101, 117\n\n\\bibitem[\\protect\\astroncite{K\\\"ohler \\& Leinert}{1998}]{Koehler98.1}\nK\\\"ohler R., Leinert Ch. 1998, A\\&A 331, 977\n\n\\bibitem[\\protect\\astroncite{Kraft}{1965}]{Kraft65.1}\nKraft R. P. 1965, ApJ 142, 681\n\n\\bibitem[\\protect\\astroncite{Leinert}{1993}]{Leinert93.1}\nLeinert Ch., Zinnecker H., Weitzel N., et al. 1993, A\\&A 278, 129\n\n\\bibitem[\\protect\\astroncite{Li \\& Hu}{1998}]{Li98.1}\nLi J. Z., Hu J. Y., 1998, A\\&AS 132, 173\n\n\\bibitem[\\protect\\astroncite{Luhman}{1999}]{Luhman99.1}\nLuhman K. L. 1999, ApJ 525, 466\n\n\\bibitem[\\protect\\astroncite{Luyten et~al.}{1981}]{Luyten81.1}\nLuyten W. J., Hill G., Morris S. 1981, Proper Motion Survey, Minneapolis, Uiv. of Minnesota\n\n\\bibitem[\\protect\\astroncite{Magazz\\`u et~al.}{1997}]{Magazzu97.1}\nMagazz\\`u A., Mart\\'\\i n E. L., Sterzik M. F., Neuh\\\"auser R., Covino E.,\nAlcal$\\acute{\\rm a}$ J. M. 1997, A\\&AS 124, 449\n\n\\bibitem[\\protect\\astroncite{Mart\\'\\i n \\& Magazz\\`u}{1999}]{Martin99.1}\nMart\\'\\i n E. L., Magazz\\`u A. 1999, A\\&A 342, 173\n\n\\bibitem[\\protect\\astroncite{McCaughrean \\& O'Dell}{1996}]{McCaughrean96.1}\nMcCaughrean M. J., O'Dell C. R. 1996, AJ 111, 1977\n\n\\bibitem[\\protect\\astroncite{Mendoza \\& Eugenio}{1956}]{Mendoza56.1}\nMendoza V E. E. 1956, ApJ 123, 54\n\n\\bibitem[\\protect\\astroncite{Mermilliod et~al.}{1997}]{Mermilliod97.1}\nMermilliod J. C., Turon C., Robichon N., Arenou F., Lebreton Y. 1997, In:\nBattrick B. (ed.), ESA Symposium `Hipparcos Venice '97', Venice, Italy, ESA SP-402, 643\n\n\\bibitem[\\protect\\astroncite{Mewe et~al.}{1985}]{Mewe85.1}\nMewe R., Gronenschild E. H. B. M., van den Oord G. H. J., 1985, A\\&AS 62, 197\n\n\\bibitem[\\protect\\astroncite{Mewe et~al.}{1986}]{Mewe86.1}\nMewe R., Lemen J. R., van den Oord G. H. J., 1986, A\\&AS 65, 511\n\n\\bibitem[\\protect\\astroncite{Micela et~al.}{1996}]{Micela96.1}\nMicela G., Sciortino S., Kashyap V., Harnden Jr. F. R., Rosner R. 1996, ApJS 102, 75\n\n\\bibitem[\\protect\\astroncite{Micela et~al.}{1999}]{Micela99.1}\nMicela G., Sciortino S., Harnden Jr. F. R., et al. 1999, A\\&A 341, 751\n\n\\bibitem[\\protect\\astroncite{Montmerle et~al.}{1983}]{Montmerle83.1}\nMontmerle T., Koch-Miramond L., Falgarone E., Grindlay J. E. 1983, ApJ 269, 182\n\n\\bibitem[\\protect\\astroncite{Montmerle et~al.}{2000}]{Montmerle00.1}\nMontmerle T., Grosso N., Tsuboi Y., Koyama K., 2000, ApJ in press\n\n\\bibitem[\\protect\\astroncite{Morel \\& Magnenat}{1978}]{Morel78.1}\nMorel M., Magnenat P. 1978, A\\&AS 34, 477\n\n\\bibitem[\\protect\\astroncite{Morgan \\& Hiltner}{1965}]{Morgan65.1}\nMorgan W. W., Hiltner W. A. 1965, ApJ 141, 177\n\n\\bibitem[\\protect\\astroncite{Neuh\\\"auser}{1997}]{Neuhaeuser97.3}\nNeuh\\\"auser R., 1997, Science 276, 1363\n\n\\bibitem[\\protect\\astroncite{Neuh\\\"auser et~al.}{1995}]{Neuhaeuser95.1}\nNeuh\\\"auser R., Sterzik M. F., Schmitt J. H. M. M., Wichmann R., Krautter J. 1995, A\\&A 297, 391\n\n\\bibitem[\\protect\\astroncite{Neuh\\\"auser et~al.}{1997}]{Neuhaeuser97.2}\nNeuh\\\"auser R., Torres G., Sterzik M. F., Randich S. 1997, A\\&A 325, 647\n\n\\bibitem[\\protect\\astroncite{Neuh\\\"auser et~al.}{1999}]{Neuhaeuser99.1}\nNeuh\\\"auser R., Brice\\~no C., Comer$\\acute{\\rm o}$n F., et al. 1999, A\\&A 343, 883\n\n\\bibitem[\\protect\\astroncite{Oppenheimer et~al.}{1997}]{Oppenheimer97.1}\nOppenheimer B. R., Basri G., Nakajima T., Kulkarni S. R. 1997, AJ 113, 296\n\n\\bibitem[\\protect\\astroncite{Pallavicini et~al.}{1981}]{Pallavicini81.1}\nPallavicini R., Golub L., Rosner R., Vaiana G. S., Ayres T., Linsky J. L. 1981, ApJ 248, 279\n\n\\bibitem[\\protect\\astroncite{Panzera et~al.}{1999}]{Panzera99.1}\nPanzera M. R., Tagliaferri G., Pasinetti L., Antonello E. 1999, A\\&A 348, 161\n\n\\bibitem[\\protect\\astroncite{Perryman et~al.}{1998}]{Perryman98.1}\nPerryman M. A. C., Brown A. G. A., Lebreton Y., et al. 1998, A\\&A 331, 81\n\n\\bibitem[\\protect\\astroncite{Pesch}{1968}]{Pesch68.1}\nPesch P. 1968, ApJ 151, 605\n\n\\bibitem[\\protect\\astroncite{Preibisch}{1997}]{Preibisch97.3}\nPreibisch T., 1997, A\\&A 324, 690\n\n\\bibitem[\\protect\\astroncite{Preibisch et~al.}{1993}]{Preibisch93.1}\nPreibisch T., Zinnecker H., Schmitt J. H. M. M., 1993, A\\&A 279, L33\n\n\\bibitem[\\protect\\astroncite{Preibisch et~al.}{1995}]{Preibisch95.1}\nPreibisch T., Neuh\\\"auser R., Alcal$\\acute{\\rm a}$ J. M., 1995, A\\&A 304, L13\n\n\\bibitem[\\protect\\astroncite{Preibisch et~al.}{1996}]{Preibisch96.1}\nPreibisch T., Zinnecker H., Herbig G. H., 1996, A\\&A 310, 456\n\n\\bibitem[\\protect\\astroncite{Prosser et~al.}{1991}]{Prosser91.1}\nProsser C. F., Stauffer J. R., Kraft R. P. 1991, AJ 101, 1361\n\n\\bibitem[\\protect\\astroncite{Pye et~al.}{1994}]{Pye94.1}\nPye J. P., Hodgkin S. T., Stern R. A., Stauffer J. R., 1994, MNRAS 266,798\n\n\\bibitem[\\protect\\astroncite{Queloz et~al.}{1998}]{Queloz98.1}\nQueloz D., Allain S., Mermilliod J.-C., Bouvier J., Mayor M. 1998, A\\&A 335, 183 \n\n\\bibitem[\\protect\\astroncite{Raboud \\& Mermilliod}{1998}]{Raboud98.1}\nRaboud D., Mermilliod J.-C. 1998, A\\&A 329, 101\n\n\\bibitem[\\protect\\astroncite{Reid \\& Hawley}{1999}]{Reid99.1}\nReid I. N., Hawley S. L., 1999, AJ 117, 343\n\n\\bibitem[\\protect\\astroncite{Raymond \\& Smith}{1977}]{Raymond77.1}\nRaymond J. C., Smith B. W., 1977, ApJS 35, 419\n\n\\bibitem[\\protect\\astroncite{Scargle}{1998}]{Scargle98.1}\nScargle J. D., 1998, ApJ 504, 405\n\n\\bibitem[\\protect\\astroncite{Schmitt \\& Favata}{1999}]{Schmitt99.1}\nSchmitt J. H. M. M., Favata F., 1999, Nat 401, 44\n\n\\bibitem[\\protect\\astroncite{Schmidt-Kaler}{1982}]{Schmidt-Kaler82.1}\nSchmidt-Kaler, T. H. 1982, Physical Parameters of Stars, in:\nLandolt-Bornstein New Series, Vol 2b, Astronomy amd Astrophysics Stars\nand Star Clusters (eds. K. Shaifers \\& H. H. Voigt), New York, Springer\n\n\\bibitem[\\protect\\astroncite{Skinner et~al.}{1997}]{Skinner97.1}\nSkinner S. L., G\\\"udel M., Koyama K., Yamauchi S. 1997, ApJ 486, 886\n\n\\bibitem[\\protect\\astroncite{Soderblom et~al.}{1993a}]{Soderblom93.1}\nSoderblom D. R., Jones B. F., Balachandran S., et al. 1993a, AJ 106, 1059\n\n\\bibitem[\\protect\\astroncite{Soderblom et~al.}{1993b}]{Soderblom93.2}\nSoderblom D. R., Stauffer J. R., Hudon J. D., Jones B. F. 1993b, ApJS 85, 315\n\n\\bibitem[\\protect\\astroncite{Stauffer}{1982}]{Stauffer82.1}\nStauffer J. R. 1982, AJ 87, 1507\n\n\\bibitem[\\protect\\astroncite{Stauffer}{1984}]{Stauffer84.1}\nStauffer J. R. 1984, ApJ 280, 189\n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1984}]{Stauffer84.2}\nStauffer J. R., Hartmann L. W., Soderblom D. R., Burnham N. 1984, ApJ 280, 202\n\n\\bibitem[\\protect\\astroncite{Stauffer \\& Hartmann}{1987}]{Stauffer87.1}\nStauffer J. R., Hartmann L. W., 1987, ApJ 318, 337\n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1987}]{Stauffer87.2}\nStauffer J. R., Hartmann L. W., Latham D. W. 1987, ApJ 320, L51\n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1991}]{Stauffer91.1}\nStauffer J. R., Klemola A., Prosser C., Probst R. 1991, AJ 101, 980\n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1994}]{Stauffer94.1}\nStauffer J. R., Caillault, J.-P., Gagn$\\acute{\\rm e}$ M., Prosser C.,\nHartmann L. W. 1994, ApJS 91, 625 \n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1997}]{Stauffer97.1}\nStauffer J. R., Balachandran S. C., Krishnamurthi A., Pinsonneault M.,\nTerndrup D. M., Stern R. A. 1997, ApJ 475, 604\n\n\\bibitem[\\protect\\astroncite{Stefanik et~al.}{1992}]{Stefanik92.1}\nStefanik H. P., Latham D. W. 1992, `Binaries in the Hyades', In:\n`Complementary Approaches to Double and Multiple Star Research', IAU\nColloq. 135, ASP Conf. Ser. 32, (McAlister H. A. \\& Hartkopf W. I., eds.), p. 173\n\n\\bibitem[\\protect\\astroncite{Stern et~al.}{1994}]{Stern94.1}\nStern R. A., Schmitt J. H. M. M., Pye J. P., Hodgkin S. T., Stauffer J. R.,\nSimon T. 1994, ApJ 427, 808\n\n\\bibitem[\\protect\\astroncite{Strom \\& Strom}{1994}]{Strom94.1}\nStrom K. M., Strom S. E., 1994, ApJ 424, 237\n\n\\bibitem[\\protect\\astroncite{Strom et~al.}{1989}]{Strom89.1}\nStrom K. M., Strom S. E., Edwards S., Cabrit S., Skrutskie M. F. 1989, AJ 97, 1451\n\n\\bibitem[\\protect\\astroncite{Tsuboi et~al.}{1998}]{Tsuboi98.1}\nTsuboi Y., Koyama K., Murakami H., Hayashi M., Skinner S., Ueno S. 1998, ApJ 503, 894\n\n\\bibitem[\\protect\\astroncite{Torres et~al.}{1995}]{Torres95.1}\nTorres C. A. O., Quast G., de la Reza R., Gregorio-Hetem J.,\nL$\\acute{\\rm e}$pine J. R. D. 1995, AJ 109, 2146\n\n\\bibitem[\\protect\\astroncite{van Altena}{1969}]{Altena69.1}\nvan Altena W. F. 1969, AJ 74, 2\n\n\\bibitem[\\protect\\astroncite{van Bueren}{1952}]{Bueren52.1}\nvan Bueren H. G. 1952, Bull. Astron. Inst. Netherlands, 11, 385\n\n\\bibitem[\\protect\\astroncite{Walter}{1983}]{Walter83.1}\nWalter F. M. 1983, ApJ 274, 794\n\n\\bibitem[\\protect\\astroncite{Walter et al.}{1987}]{Walter87.1}\nWalter F. M., Brown A., Linsky J. L., et al. 1987, ApJ 314, 297\n\n\\bibitem[\\protect\\astroncite{Wichmann et~al.}{1996}]{Wichmann96.1}\nWichmann R., Krautter J., Schmitt J. H. M. M., Neuh\\\"auser R.,\nAlcal$\\acute{\\rm a}$ J. M., Zinnecker H., et al. 1996, A\\&A 312, 439\n\n\\bibitem[\\protect\\astroncite{Wichmann et~al.}{1998}]{Wichmann98.1}\nWichmann R., Bastian U., Krautter J., Jankovics I., Ruci$\\acute{\\rm n}$ski S. M. 1998, MNRAS 301, L39\n\n\\bibitem[\\protect\\astroncite{Zickgraf et~al.}{1998}]{Zickgraf98.1}\nZickgraf F.-J., Alcala J. M., Krautter J., Sterzik M. F., Appenzeller I.,\nMotch C., et al. 1998, A\\&A 339, 457\n\n\\bibitem[\\protect\\astroncite{Ziskin}{1993}]{Ziskin93.1}\nZiskin V. 1993, Senior Thesis, Harvard University\n\n\\end{thebibliography}\n\n\n\\end{document}\n\n"
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"name": "astro-ph0002354.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\astroncite{Anderson et~al.}{1966}]{Anderson66.1}\nAnderson C. M., St\\\"ockly R., Kraft R. P., 1966, ApJ 143, 299\n\n\\bibitem[\\protect\\astroncite{Beckwith et~al.}{1990}]{Beckwith90.1}\nBeckwith S. V. W., Sargent A. I., Chini R. S., G\\\"usten R. 1990, AJ 99, 924\n\n\\bibitem[\\protect\\astroncite{Bertout et~al.}{1988}]{Bertout88.1}\nBertout C., Basri G., Bouvier J. 1988, ApJ 330, 350\n\n\\bibitem[\\protect\\astroncite{Bouvier et~al.}{1993}]{Bouvier93.1}\nBouvier J., Cabrit S., Fern$\\acute{\\rm a}$ndez M., Mart\\'\\i n E. L.,\nMatthews J. M. 1993, A\\&A 272, 176\n\n\\bibitem[\\protect\\astroncite{Bouvier et~al.}{1997a}]{Bouvier97.1}\nBouvier J., Forestini M., Allain S. 1997a, A\\&A 326, 1023\n\n\\bibitem[\\protect\\astroncite{Bouvier et~al.}{1997b}]{Bouvier97.2}\nBouvier J., Rigaut F., Nadeau D. 1997b, A\\&A 323, 139\n\n\\bibitem[\\protect\\astroncite{Brice\\~no et~al.}{1998}]{Briceno98.1}\nBrice\\~no C., Hartmann L., Stauffer J., Mart\\'\\i n E. 1998, AJ 115, 2074\n\n\\bibitem[\\protect\\astroncite{Caillault}{1996}]{Caillault96.1}\nCaillault J.-P., 1996, In: Pallavicini R. and Dupree A. K. (eds.), Cool\nStars, Stellar Systems, and the Sun, 9th Cambridge Workshop, ASP Conf. Ser., Vol.109, 325\n\n\\bibitem[\\protect\\astroncite{Cernicharo et~al.}{1985}]{Cernicharo85.1}\nCernicharo J., Bachiller R., Duvert G., 1985, A\\&A 149, 273\n\n\\bibitem[\\protect\\astroncite{Cohen \\& Kuhi}{1979}]{Cohen79.1}\nCohen M, Kuhi L. V. 1979, ApJS 41, 743\n\n\\bibitem[\\protect\\astroncite{Cruddace et~al.}{1988}]{Cruddace88.1}\nCruddace R. G., Hasinger G. R., Schmitt J. H. M. M., 1988, In: Murtagh F., Heck A. (eds.) Astronomy from large databases, ESO, Garching, p.177\n \n\\bibitem[\\protect\\astroncite{Elias}{1978}]{Elias78.1}\nElias J. H., 1978, ApJ 224, 857\n\n\\bibitem[\\protect\\astroncite{Feigelson \\& DeCampli}{1981}]{Feigelson81.1}\nFeigelson E. D., DeCampli W. M. 1981, ApJ 243, L89\n\n\\bibitem[\\protect\\astroncite{Feigelson \\& Nelson}{1985}]{Feigelson85.1}\nFeigelson E. D., Nelson P. I. 1985, ApJ 293, 192\n\n\\bibitem[\\protect\\astroncite{Gagn$\\acute{\\rm e}$ \\& Caillault}{1994}]{Gagne94.1}\nGagn$\\acute{\\rm e}$ M., Caillault J.-P. 1994, ApJ 437, 361\n\n\\bibitem[\\protect\\astroncite{Gagn$\\acute{\\rm e}$ et~al.}{1995}]{Gagne95.1}\nGagn$\\acute{\\rm e}$ M., Caillault J.-P., Stauffer J. R., 1995, ApJ 450, 217\n\n\\bibitem[\\protect\\astroncite{Ghez et~al.}{1993}]{Ghez93.1}\nGhez A. M., Neugebauer G., Matthews K. 1993, AJ 106, 2005\n\n\\bibitem[\\protect\\astroncite{Gizis \\& Reid}{1999}]{Gizis99.1}\nGizis J. E., Reid I. N. 1999, AJ 117, 508\n\n\\bibitem[\\protect\\astroncite{Grosso et~al.}{1997}]{Grosso97.1}\nGrosso N., Montmerle T., Feigelson E. D., Andr$\\acute{\\rm e}$ P., Casanova S.,\nGregorio-Hetem J. 1997, Nat 387, 56\n\n\\bibitem[\\protect\\astroncite{Griffin et~al.}{1985}]{Griffin85.1}\nGriffin R. F., Gunn J. E., Zimmerman B. A., Griffin R. E. M. 1985, AJ 90, 609\n\n\\bibitem[\\protect\\astroncite{Guenther \\& Ball}{1999}]{Guenther99.1}\nGuenther E. W., Ball M. 1999, A\\&A 347, 508\n\n\\bibitem[\\protect\\astroncite{Guenther et~al.}{1999}]{Guenther99.2}\nGuenther E. W., Lehmann H., Emerson J. P., Staude J. 1999, A\\&A 341, 768\n\n\\bibitem[\\protect\\astroncite{Hambaryan et~al.}{1999}]{Hambaryan99.1}\nHambaryan V., Neuh\\\"auser R., Stelzer B. 1999, A\\&A 345, 121\n\n\\bibitem[\\protect\\astroncite{Haro et~al.}{1982}]{Haro82.2}\nHaro G., Chavira E., Gonzalez G., 1982a, Instituto de Tonantzintla, Boletin\nVol.3, 3\n\n\\bibitem[\\protect\\astroncite{Hartmann \\& Stauffer}{1989}]{Hartmann89.1}\nHartmann L., Stauffer J. R., 1989, AJ 97, 873\n\n\\bibitem[\\protect\\astroncite{Hearty et~al.}{2000}]{Hearty00.1}\nHearty T. J., Neuh\\\"auser R., Stelzer B., Fern$\\acute{\\rm a}$ndez M.,\nAlcal$\\acute{\\rm a}$ J. M., Covino E., et al. 2000, A\\&A, in press\n\n\\bibitem[\\protect\\astroncite{Herbig}{1998}]{Herbig98.1}\nHerbig G. H. 1998, ApJ 497, 736\n\n\\bibitem[\\protect\\astroncite{Herbig \\& Bell}{1988}]{Herbig88.1}\nHerbig G. H., Bell K. R., 1988, Lick Observatory Bulletin, No. 1111 \n\n\\bibitem[\\protect\\astroncite{Hertzsprung}{1947}]{Hertzsprung47.1}\nHertzsprung E. 1947, Ann. Leiden Obs. 19, No. 1A\n\n\\bibitem[\\protect\\astroncite{Hodgkin et~al.}{1995}]{Hodgkin95.1}\nHodgkin S. T., Jameson R. F., Steele I. A., 1995, MNRAS 274, 869 \n\n\\bibitem[\\protect\\astroncite{Johnson \\& Mitchell}{1958}]{Johnson58.1}\nJohnson H. L., Mitchell R. I., 1958, ApJ 128, 31\n\n\\bibitem[\\protect\\astroncite{Jones et~al.}{1996}]{Jones96.1}\nJones B. F., Fischer D. A., Stauffer J. R. 1996, AJ 112, 1562\n\n\\bibitem[\\protect\\astroncite{Kenyon \\& Hartmann}{1995}]{Kenyon95.1}\nKenyon S. J., Hartmann L., 1995, ApJS 101, 117\n\n\\bibitem[\\protect\\astroncite{K\\\"ohler \\& Leinert}{1998}]{Koehler98.1}\nK\\\"ohler R., Leinert Ch. 1998, A\\&A 331, 977\n\n\\bibitem[\\protect\\astroncite{Kraft}{1965}]{Kraft65.1}\nKraft R. P. 1965, ApJ 142, 681\n\n\\bibitem[\\protect\\astroncite{Leinert}{1993}]{Leinert93.1}\nLeinert Ch., Zinnecker H., Weitzel N., et al. 1993, A\\&A 278, 129\n\n\\bibitem[\\protect\\astroncite{Li \\& Hu}{1998}]{Li98.1}\nLi J. Z., Hu J. Y., 1998, A\\&AS 132, 173\n\n\\bibitem[\\protect\\astroncite{Luhman}{1999}]{Luhman99.1}\nLuhman K. L. 1999, ApJ 525, 466\n\n\\bibitem[\\protect\\astroncite{Luyten et~al.}{1981}]{Luyten81.1}\nLuyten W. J., Hill G., Morris S. 1981, Proper Motion Survey, Minneapolis, Uiv. of Minnesota\n\n\\bibitem[\\protect\\astroncite{Magazz\\`u et~al.}{1997}]{Magazzu97.1}\nMagazz\\`u A., Mart\\'\\i n E. L., Sterzik M. F., Neuh\\\"auser R., Covino E.,\nAlcal$\\acute{\\rm a}$ J. M. 1997, A\\&AS 124, 449\n\n\\bibitem[\\protect\\astroncite{Mart\\'\\i n \\& Magazz\\`u}{1999}]{Martin99.1}\nMart\\'\\i n E. L., Magazz\\`u A. 1999, A\\&A 342, 173\n\n\\bibitem[\\protect\\astroncite{McCaughrean \\& O'Dell}{1996}]{McCaughrean96.1}\nMcCaughrean M. J., O'Dell C. R. 1996, AJ 111, 1977\n\n\\bibitem[\\protect\\astroncite{Mendoza \\& Eugenio}{1956}]{Mendoza56.1}\nMendoza V E. E. 1956, ApJ 123, 54\n\n\\bibitem[\\protect\\astroncite{Mermilliod et~al.}{1997}]{Mermilliod97.1}\nMermilliod J. C., Turon C., Robichon N., Arenou F., Lebreton Y. 1997, In:\nBattrick B. (ed.), ESA Symposium `Hipparcos Venice '97', Venice, Italy, ESA SP-402, 643\n\n\\bibitem[\\protect\\astroncite{Mewe et~al.}{1985}]{Mewe85.1}\nMewe R., Gronenschild E. H. B. M., van den Oord G. H. J., 1985, A\\&AS 62, 197\n\n\\bibitem[\\protect\\astroncite{Mewe et~al.}{1986}]{Mewe86.1}\nMewe R., Lemen J. R., van den Oord G. H. J., 1986, A\\&AS 65, 511\n\n\\bibitem[\\protect\\astroncite{Micela et~al.}{1996}]{Micela96.1}\nMicela G., Sciortino S., Kashyap V., Harnden Jr. F. R., Rosner R. 1996, ApJS 102, 75\n\n\\bibitem[\\protect\\astroncite{Micela et~al.}{1999}]{Micela99.1}\nMicela G., Sciortino S., Harnden Jr. F. R., et al. 1999, A\\&A 341, 751\n\n\\bibitem[\\protect\\astroncite{Montmerle et~al.}{1983}]{Montmerle83.1}\nMontmerle T., Koch-Miramond L., Falgarone E., Grindlay J. E. 1983, ApJ 269, 182\n\n\\bibitem[\\protect\\astroncite{Montmerle et~al.}{2000}]{Montmerle00.1}\nMontmerle T., Grosso N., Tsuboi Y., Koyama K., 2000, ApJ in press\n\n\\bibitem[\\protect\\astroncite{Morel \\& Magnenat}{1978}]{Morel78.1}\nMorel M., Magnenat P. 1978, A\\&AS 34, 477\n\n\\bibitem[\\protect\\astroncite{Morgan \\& Hiltner}{1965}]{Morgan65.1}\nMorgan W. W., Hiltner W. A. 1965, ApJ 141, 177\n\n\\bibitem[\\protect\\astroncite{Neuh\\\"auser}{1997}]{Neuhaeuser97.3}\nNeuh\\\"auser R., 1997, Science 276, 1363\n\n\\bibitem[\\protect\\astroncite{Neuh\\\"auser et~al.}{1995}]{Neuhaeuser95.1}\nNeuh\\\"auser R., Sterzik M. F., Schmitt J. H. M. M., Wichmann R., Krautter J. 1995, A\\&A 297, 391\n\n\\bibitem[\\protect\\astroncite{Neuh\\\"auser et~al.}{1997}]{Neuhaeuser97.2}\nNeuh\\\"auser R., Torres G., Sterzik M. F., Randich S. 1997, A\\&A 325, 647\n\n\\bibitem[\\protect\\astroncite{Neuh\\\"auser et~al.}{1999}]{Neuhaeuser99.1}\nNeuh\\\"auser R., Brice\\~no C., Comer$\\acute{\\rm o}$n F., et al. 1999, A\\&A 343, 883\n\n\\bibitem[\\protect\\astroncite{Oppenheimer et~al.}{1997}]{Oppenheimer97.1}\nOppenheimer B. R., Basri G., Nakajima T., Kulkarni S. R. 1997, AJ 113, 296\n\n\\bibitem[\\protect\\astroncite{Pallavicini et~al.}{1981}]{Pallavicini81.1}\nPallavicini R., Golub L., Rosner R., Vaiana G. S., Ayres T., Linsky J. L. 1981, ApJ 248, 279\n\n\\bibitem[\\protect\\astroncite{Panzera et~al.}{1999}]{Panzera99.1}\nPanzera M. R., Tagliaferri G., Pasinetti L., Antonello E. 1999, A\\&A 348, 161\n\n\\bibitem[\\protect\\astroncite{Perryman et~al.}{1998}]{Perryman98.1}\nPerryman M. A. C., Brown A. G. A., Lebreton Y., et al. 1998, A\\&A 331, 81\n\n\\bibitem[\\protect\\astroncite{Pesch}{1968}]{Pesch68.1}\nPesch P. 1968, ApJ 151, 605\n\n\\bibitem[\\protect\\astroncite{Preibisch}{1997}]{Preibisch97.3}\nPreibisch T., 1997, A\\&A 324, 690\n\n\\bibitem[\\protect\\astroncite{Preibisch et~al.}{1993}]{Preibisch93.1}\nPreibisch T., Zinnecker H., Schmitt J. H. M. M., 1993, A\\&A 279, L33\n\n\\bibitem[\\protect\\astroncite{Preibisch et~al.}{1995}]{Preibisch95.1}\nPreibisch T., Neuh\\\"auser R., Alcal$\\acute{\\rm a}$ J. M., 1995, A\\&A 304, L13\n\n\\bibitem[\\protect\\astroncite{Preibisch et~al.}{1996}]{Preibisch96.1}\nPreibisch T., Zinnecker H., Herbig G. H., 1996, A\\&A 310, 456\n\n\\bibitem[\\protect\\astroncite{Prosser et~al.}{1991}]{Prosser91.1}\nProsser C. F., Stauffer J. R., Kraft R. P. 1991, AJ 101, 1361\n\n\\bibitem[\\protect\\astroncite{Pye et~al.}{1994}]{Pye94.1}\nPye J. P., Hodgkin S. T., Stern R. A., Stauffer J. R., 1994, MNRAS 266,798\n\n\\bibitem[\\protect\\astroncite{Queloz et~al.}{1998}]{Queloz98.1}\nQueloz D., Allain S., Mermilliod J.-C., Bouvier J., Mayor M. 1998, A\\&A 335, 183 \n\n\\bibitem[\\protect\\astroncite{Raboud \\& Mermilliod}{1998}]{Raboud98.1}\nRaboud D., Mermilliod J.-C. 1998, A\\&A 329, 101\n\n\\bibitem[\\protect\\astroncite{Reid \\& Hawley}{1999}]{Reid99.1}\nReid I. N., Hawley S. L., 1999, AJ 117, 343\n\n\\bibitem[\\protect\\astroncite{Raymond \\& Smith}{1977}]{Raymond77.1}\nRaymond J. C., Smith B. W., 1977, ApJS 35, 419\n\n\\bibitem[\\protect\\astroncite{Scargle}{1998}]{Scargle98.1}\nScargle J. D., 1998, ApJ 504, 405\n\n\\bibitem[\\protect\\astroncite{Schmitt \\& Favata}{1999}]{Schmitt99.1}\nSchmitt J. H. M. M., Favata F., 1999, Nat 401, 44\n\n\\bibitem[\\protect\\astroncite{Schmidt-Kaler}{1982}]{Schmidt-Kaler82.1}\nSchmidt-Kaler, T. H. 1982, Physical Parameters of Stars, in:\nLandolt-Bornstein New Series, Vol 2b, Astronomy amd Astrophysics Stars\nand Star Clusters (eds. K. Shaifers \\& H. H. Voigt), New York, Springer\n\n\\bibitem[\\protect\\astroncite{Skinner et~al.}{1997}]{Skinner97.1}\nSkinner S. L., G\\\"udel M., Koyama K., Yamauchi S. 1997, ApJ 486, 886\n\n\\bibitem[\\protect\\astroncite{Soderblom et~al.}{1993a}]{Soderblom93.1}\nSoderblom D. R., Jones B. F., Balachandran S., et al. 1993a, AJ 106, 1059\n\n\\bibitem[\\protect\\astroncite{Soderblom et~al.}{1993b}]{Soderblom93.2}\nSoderblom D. R., Stauffer J. R., Hudon J. D., Jones B. F. 1993b, ApJS 85, 315\n\n\\bibitem[\\protect\\astroncite{Stauffer}{1982}]{Stauffer82.1}\nStauffer J. R. 1982, AJ 87, 1507\n\n\\bibitem[\\protect\\astroncite{Stauffer}{1984}]{Stauffer84.1}\nStauffer J. R. 1984, ApJ 280, 189\n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1984}]{Stauffer84.2}\nStauffer J. R., Hartmann L. W., Soderblom D. R., Burnham N. 1984, ApJ 280, 202\n\n\\bibitem[\\protect\\astroncite{Stauffer \\& Hartmann}{1987}]{Stauffer87.1}\nStauffer J. R., Hartmann L. W., 1987, ApJ 318, 337\n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1987}]{Stauffer87.2}\nStauffer J. R., Hartmann L. W., Latham D. W. 1987, ApJ 320, L51\n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1991}]{Stauffer91.1}\nStauffer J. R., Klemola A., Prosser C., Probst R. 1991, AJ 101, 980\n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1994}]{Stauffer94.1}\nStauffer J. R., Caillault, J.-P., Gagn$\\acute{\\rm e}$ M., Prosser C.,\nHartmann L. W. 1994, ApJS 91, 625 \n\n\\bibitem[\\protect\\astroncite{Stauffer et~al.}{1997}]{Stauffer97.1}\nStauffer J. R., Balachandran S. C., Krishnamurthi A., Pinsonneault M.,\nTerndrup D. M., Stern R. A. 1997, ApJ 475, 604\n\n\\bibitem[\\protect\\astroncite{Stefanik et~al.}{1992}]{Stefanik92.1}\nStefanik H. P., Latham D. W. 1992, `Binaries in the Hyades', In:\n`Complementary Approaches to Double and Multiple Star Research', IAU\nColloq. 135, ASP Conf. Ser. 32, (McAlister H. A. \\& Hartkopf W. I., eds.), p. 173\n\n\\bibitem[\\protect\\astroncite{Stern et~al.}{1994}]{Stern94.1}\nStern R. A., Schmitt J. H. M. M., Pye J. P., Hodgkin S. T., Stauffer J. R.,\nSimon T. 1994, ApJ 427, 808\n\n\\bibitem[\\protect\\astroncite{Strom \\& Strom}{1994}]{Strom94.1}\nStrom K. M., Strom S. E., 1994, ApJ 424, 237\n\n\\bibitem[\\protect\\astroncite{Strom et~al.}{1989}]{Strom89.1}\nStrom K. M., Strom S. E., Edwards S., Cabrit S., Skrutskie M. F. 1989, AJ 97, 1451\n\n\\bibitem[\\protect\\astroncite{Tsuboi et~al.}{1998}]{Tsuboi98.1}\nTsuboi Y., Koyama K., Murakami H., Hayashi M., Skinner S., Ueno S. 1998, ApJ 503, 894\n\n\\bibitem[\\protect\\astroncite{Torres et~al.}{1995}]{Torres95.1}\nTorres C. A. O., Quast G., de la Reza R., Gregorio-Hetem J.,\nL$\\acute{\\rm e}$pine J. R. D. 1995, AJ 109, 2146\n\n\\bibitem[\\protect\\astroncite{van Altena}{1969}]{Altena69.1}\nvan Altena W. F. 1969, AJ 74, 2\n\n\\bibitem[\\protect\\astroncite{van Bueren}{1952}]{Bueren52.1}\nvan Bueren H. G. 1952, Bull. Astron. Inst. Netherlands, 11, 385\n\n\\bibitem[\\protect\\astroncite{Walter}{1983}]{Walter83.1}\nWalter F. M. 1983, ApJ 274, 794\n\n\\bibitem[\\protect\\astroncite{Walter et al.}{1987}]{Walter87.1}\nWalter F. M., Brown A., Linsky J. L., et al. 1987, ApJ 314, 297\n\n\\bibitem[\\protect\\astroncite{Wichmann et~al.}{1996}]{Wichmann96.1}\nWichmann R., Krautter J., Schmitt J. H. M. M., Neuh\\\"auser R.,\nAlcal$\\acute{\\rm a}$ J. M., Zinnecker H., et al. 1996, A\\&A 312, 439\n\n\\bibitem[\\protect\\astroncite{Wichmann et~al.}{1998}]{Wichmann98.1}\nWichmann R., Bastian U., Krautter J., Jankovics I., Ruci$\\acute{\\rm n}$ski S. M. 1998, MNRAS 301, L39\n\n\\bibitem[\\protect\\astroncite{Zickgraf et~al.}{1998}]{Zickgraf98.1}\nZickgraf F.-J., Alcala J. M., Krautter J., Sterzik M. F., Appenzeller I.,\nMotch C., et al. 1998, A\\&A 339, 457\n\n\\bibitem[\\protect\\astroncite{Ziskin}{1993}]{Ziskin93.1}\nZiskin V. 1993, Senior Thesis, Harvard University\n\n\\end{thebibliography}"
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astro-ph0002355
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Relativistic flows in blazars
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"author": "Gabriele Ghisellini"
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The radiation we observe from blazars is most likely the product of the transformation of bulk kinetic energy into random energy. This process must have a relatively small efficiency (e.g. 10\%) if jets are to power the extended radio--structures. Recent results suggest that the average power reaching the extended radio regions and lobes is of the same order of that produced by accretion and illuminating the emission line clouds. Most of the radiative power is produced in a well localized region of the jet, and, at least during flares, is mainly emitted in the $\gamma$--ray band. A possible scenario qualitatively accounting for these facts is the internal shock model, in which the central engine produces a relativistic plasma flow in an intermittent way. \keywords{Jets, AGNs, blazars, radiation processes: synchrotron, inverse Compton, electron--positron pairs}
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"name": "ghisellini.tex",
"string": "%\n% File: bo99_example.tex\n%\n\n% Electronic submission of the paper(s)\n%\n% Paper(s) are due by OCTOBER 31, 1999. Authors must submit a Postscript\n% version of their contributions via ftp following these instructions:\n%\n% ftp tonno.tesre.bo.cnr.it [192.167.166.30]\n% login: xray99\n% password: sent it by e-mail\n% mkdir your surname\n% cd your surname\n% put nameofpaper.ps\n% bye\n%\n% Send an e-mail to bo99@tesre.bo.cnr.it to confirm your submission,\n% containing the directory name where you put the file and the postscript\n% file name.\n% In case of multiple submissions, please append a sequential number to\n% postscript file name (nameofpaper_1.ps, nameofpaper_2.ps, etc).\n%\n\n\\documentstyle[bo99,epsfig]{article}\n\n\\title{Relativistic flows in blazars}\n\n\\author{Gabriele Ghisellini} \n\\affil{Osservatorio Astronomico di Brera, Via Bianchi 46, \nI--23807 Merate, Italy}\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\nThe radiation we observe from blazars is most likely the\nproduct of the transformation of bulk kinetic energy into random energy.\nThis process must have a relatively small efficiency (e.g. 10\\%) if jets\nare to power the extended radio--structures.\nRecent results suggest that the average power reaching the extended\nradio regions and lobes is of the same order of that produced\nby accretion and illuminating the emission line clouds.\nMost of the radiative power is produced in a well localized region of the jet,\nand, at least during flares, is mainly emitted in the $\\gamma$--ray band.\nA possible scenario qualitatively accounting for these facts\nis the internal shock model, in which the central engine produces\na relativistic plasma flow in an intermittent way.\n\\keywords{Jets, AGNs, blazars, radiation processes:\nsynchrotron, inverse Compton, electron--positron pairs} \n\\end{abstract}\n\n\\section{Introduction}\nWe believe that the continuum radiation we see from blazars\ncomes from the transformation of bulk kinetic energy, and possibly\nPoynting flux, into random energy of particles, which quickly produce \nbeamed emission through the synchrotron and the inverse Compton process.\nThis is analogous to what we believe is happening in gamma--ray bursts,\nalthough the bulk Lorentz factor of their flow is initially larger.\n\nEvidences for bulk motion in blazars with Lorentz factors between 5 and 20\nhave been accumulated along the years, especially\nthrough the monitoring of superluminally moving blobs on the VLBI scale\n(Vermeulen \\& Cohen 1994),\nand, more recently, through the detection of very large variable powers\nemitted above 100 MeV (see the third EGRET catalogue,\nHartman et al., 1999), which require beaming for the source to\nbe transparent to photon--photon absorption\n(e.g. Dondi \\& Ghisellini, 1995).\n\nThe explanation of intraday variations of the radio flux, leading\nto brightness temperatures in excess of $T_{\\rm B}=10^{18}$ K \n(much exceeding the Compton limit) are instead still controversial\n(Wagner \\& Witzel 1995).\nInterstellar scintillation is surely involved, but it can work only if the\nangular diameter of the variable sources is so small to nevertheless\nlead to $T_{\\rm B}=10^{15}$ K, which requires either a coherent process\nto be at work (e.g. Benford \\& Lesch 1998)\nor a Doppler factor of the order of a thousand.\n\nAnother controversial issue is the matter content of jets.\nWe still do not know if they are dominated by electron--positron pairs\nor by normal electron--proton plasma\n(see the reviews by Celotti, 1997, 1998).\n\nPart of our ignorance comes from the difficulty of estimating\nintrinsic quantities, such as the magnetic field and the particle \ndensities, using the observed flux, which is strongly modified \nby the effects of relativistic aberration, time contraction and blueshift, \nall dependent on the unknown plasma bulk velocity and viewing angle.\nFurthermore it is now clear (especially thanks to multiwavelength campaigns)\nthat the blazar phenomenon is complex.\n\nOn the optimistic side, we have for the first time a complete information\nof the blazar energy output, after the discovery of their $\\gamma$--ray \nemission, and some hints on the acceleration process, through the behaviour \nof flux variability detected simultaneously in different bands\n(see the review by Ulrich, Maraschi \\& Urry 1996).\nAlso, blazar research can now take advantage of the explosion of \nstudies regarding gamma--ray bursts, which face the same problem of how\nto transform ordered to random energy to produce beamed radiation\n(for reviews: Piran 1999; Meszaros 1999).\n\n\n\\section{Accretion = Rotation?}\n\n% Extragalactic jets, as well as their galactic superluminal counterparts,\n% may well carry more power than what is emitted by their accretion disk.\nDespite the prediction that jets carry plasma in relativistic motion\ndates back to 1966 (Rees, 1966), and intense studies over the last\n20 years (Begelman, Blandford \\& Rees, 1984),\nquantitative estimates of the amount of power transported in jets have \nbeen done only relatively recently, following new observational results.\n\nOne important point is that the extended (or lobe) radio emission of \nradiogalaxies and quasars traces the energy content of the emitting region.\nThrough minimum energy arguments and estimates of the lobe lifetime by\nspectral aging of the observed synchrotron emission and/or by\ndynamical arguments, Rawlings \\& Saunders (1991) found\na nice correlation between the average power that must be supplied to\nthe lobes and the power emitted by the narrow line region.\nAlthough one always expects some correlation between powers (they both scales\nwith the square of the luminosity distance) it is the ratio of the two \nquantities to be interesting, being of order of 100.\nSince we also know that, on average, the total luminosity in narrow lines\nis of the order of one per cent of the ionizing luminosity, we have the\nremarkable indication that the power carried by the jet (supplying the extended\nregions of the radio--source) and the power produced by the accretion\ndisk (illuminating the narrow line clouds) are of the same order.\n\nCelotti, Padovani and Ghisellini (1997) later confirmed this\nby calculating the kinetic power of the jet at the VLBI scale\n(see Celotti \\& Fabian 1993) and the broad line luminosity \n(assumed to reprocess $\\sim 10\\%$ of the ionizing luminosity).\n\nA possible explanation involves the magnetic field being responsible \nfor both the extraction of spin energy of a rotating black \nhole and the extraction of gravitational energy of the accreting matter.\nAssume in fact that the main mechanism to power the jet is the \nBlandford--Znajek (1977) process:\n%\n\\begin{equation}\nL_{\\rm jet} \\, \\simeq \\, \\left( {a\\over m}\\right)^2 U_{\\rm B} (3R_{\\rm s})^2c\n\\end{equation}\n%\nwhere $(a/m)$ is the specific black hole angular momentum ($\\sim 1$ for a\nmaximally rotating Kerr hole), $U_{\\rm B}$ is the magnetic energy density\nand $R_{\\rm s}$ is the Schwarzchild radius.\nNote that Eq. 1 has the form of a Poynting flux.\nAssume now that most of the luminosity of the accretion disk is produced\nat $3 R_{\\rm s}$. \nThe corresponding radiation energy density is then \n$U_{\\rm r} = L_{\\rm disk} / (36 \\pi R_{\\rm s}^2 c)$, leading to\n%\n\\begin{equation}\nL_{\\rm disk} \\, =\\, U_{\\rm r} (3R_{\\rm s})^2c\n\\end{equation}\n%\nTherefore a magnetic field in equipartion with the\nradiation energy density of the disk would lead to\n$L_{\\rm jet} \\sim L_{\\rm disk}$.\n\n\n\\section{Mass outflowing rate}\n\nWe can estimate the ratio of the outflowing (in the jet) to the \ninflowing mass rate, since\n%\n\\begin{equation}\nL_{\\rm disk} \\, =\\, \\eta \\dot M_{\\rm in} c^2; \\,\\,\\,\nL_{\\rm jet} \\, =\\, \\Gamma \\dot M_{\\rm out} c^2;\\qquad \\to \\qquad\n\\dot M_{\\rm out}\\, =\\, { \\eta \\over \\Gamma } \n{L_{\\rm disk} \\over L_{\\rm jet} } \\dot M_{\\rm in}\n\\end{equation}\n%\nIf jets carry as much energy as the one produced by the accretion disk, \nwe then obtain that the mass outflow rate is $\\sim 1\\%$ of the accreting \nmass rate (if $\\eta = 10\\%$ and $\\Gamma=10$).\n\n\n\\section{The blazar diversity}\n\nBL Lac objects and Flat Spectrum Radio Quasars (FSRQ) are characterized \nby very rapid and large amplitude variability, power law spectra in \nrestricted energy bands and strong $\\gamma$--ray emission.\nThese common properties justify their belonging to the same blazar class.\nHowever they differ in many other respects,\nsuch as the presence (in FSRQ) or absence (in BL Lacs) of broad emission lines,\nthe radio to optical flux ratio, the relative importance of the $\\gamma$--ray\nemission, the polarization degree, and the variability behavior.\nWithin the BL Lac class, Giommi \\& Padovani (1994) have subdivided the objects \naccording to where (i.e. at what frequency) the first broad\n(synchrotron) peak is located.\nLow energy peaked BL Lacs (LBL) show a peak in the IR--optical bands,\nwhile in High energy peaked BL Lacs (HBL) this is in the X--ray band\n(see, in this volume, the contributions\nof Costamante et al., Giommi et al., Pian et al.,Tagliaferri et al.,\nTavecchio \\& Maraschi, Wolter et al.).\n\nAs the emission of all blazars is beamed towards us, so there\nmust be a parent population of objects pointing in other directions.\nThe parent populations of BL Lacs and FSRQs are believed to be \nFR I and more powerful FR II radio galaxies, respectively (see\nthe review by Urry \\& Padovani 1995).\nThe absence of broad emission lines in BL Lacs is shared by\nFR I radio galaxies, whose nuclei are well visible\nby Hubble Space Telescope observations\n(Chiaberge, Capetti \\& Celotti 1999).\nThis suggests that in FR I and BL Lac objects broad emission lines\nare intrinsically weaker than in more powerful objects.\n\n\n% \\begin{figure}\n% \\vskip -2. true cm\n% \\centerline{\\psfig{file=../../gro/2005f.ps, width=15cm}}\n% \\vskip -6 true cm\n% \\caption[]{The SED of the HBL PKS 2005--489 observed by {\\it Beppo}SAX\n% in 1997 and again in 1998.\n% The solid circles in the IR are observations simultaneous with the\n% 1998 X--ray data.\n% The solid line is a one--zone homogeneous synchrotron self--Compton model,\n% see Tagliaferri et al. 1999.}\n% \\end{figure}\n\n\n\\section{The re--united blazars}\n\nFossati et al. (1998) found that the SED of all blazars is related \nto their observed luminosity.\nThere is a rather well defined trend:\nlow luminosity objects are HBL--like, and furthermore their high energy\npeak is in the GeV--TeV band.\nAs the bolometric luminosity increases, both peaks shift to lower frequencies,\nand the high energy emission is increasingly more dominating the total output.\n\\footnote{A note of caution: the limited sensitivity of EGRET (onboard CGRO)\nand ground based Cherenkov telescopes allows to detect sources which are\nin high states. Therefore the trend of more high energy dominated spectra \nas the total power increases strictly refers to high states.} \nGhisellini et al. (1998), fitted the SED of all blazars detected \nin the $\\gamma$--ray band for which the distance and some spectral \ninformation of the high energy radiation were available.\nThey found a correlation between the energy $\\gamma_{\\rm peak}m_{\\rm e}c^2$\nof the electrons emitting at the peaks of the spectrum and the amount \nof energy density $U$ (both in radiation and in magnetic field), as measured \nin the comoving frame: $\\gamma_{\\rm peak}\\propto U^{-0.6}$.\nThis indicates that, at $\\gamma_{\\rm peak}$, the radiative cooling rate \n$\\dot\\gamma(\\gamma_{\\rm peak})\\propto \\gamma_{\\rm peak}^2 U \\sim$const.\nIt also suggests that this may be due to a ``universal\" acceleration\nmechanism, which must be nearly independent of $\\gamma$ and $U$:\nin less powerful sources with weak magnetic field and weak lines the\nradiative cooling is less severe and electrons can be accelerated up to\nvery high energies, producing a SED typical of a HBL.\nThe paucity of photons produced externally to the jet leaves synchrotron\nself--Compton as the only channel to produce high energy radiation.\nAt the other extreme, in the most powerful sources with strong emission lines,\nelectrons cannot be accelerated to high energies because of severe cooling.\nTheir spectrum is therefore peaked in the far IR and in the MeV band.\nIn these sources the inverse Compton scattering off externally produced\nphotons is the dominant cooling mechanism, producing a dominant\n$\\gamma$--ray luminosity.\n\n\n\\subsection{Powers}\n\nFor the same sample of blazars fitted in Ghisellini et al. (1998)\nwe can estimate the powers radiated and transported \nby jets in the form of cold protons,\nmagnetic field and hot electrons and/or electron--positron pairs.\nSince the model allows to determine the bulk Lorentz factor,\nthe dimension of the emitting region, the value of the magnetic\nfield and the particle density, we can then determine\n%\n\\begin{equation}\nL_{\\rm p} \\, = \\, \\pi R^2 \\Gamma^2\\beta c\\, n_{\\rm p}^\\prime \nm_{\\rm p} c^2;\\quad\nL_{\\rm e}\\, = \\, \\pi R^2 \\Gamma^2\\beta c\\, n_{\\rm e}^\\prime \n\\langle \\gamma \\rangle m_{\\rm e} c^2 ;\\quad\nL_{\\rm B}\\, = \\, \\pi R^2 \\Gamma^2\\beta c \\, {B^2 \\over 8\\pi} \n\\end{equation}\n%\nwhere $n_{\\rm p}^\\prime$ and $n_{\\rm e}^\\prime$ are the comoving proton and \nlepton densities,\nrespectively, $R$ is the cross section radius of the jet, and\n$\\langle \\gamma \\rangle m_{\\rm e} c^2$ is the average lepton energy.\nThese powers can be compared with the radiated one estimated in the\nsame frame (in which the emitting blob is seen moving). \nThe power radiated {\\it in the entire solid angle} is thus \n$L_{\\rm r}=L^\\prime_{\\rm r} \\Gamma^2$ (the same holds for the power \n$L_{\\rm syn}$ emitted by the synchrotron process).\nAll these quantities are plotted in Fig. 2\n(Celotti \\& Ghisellini 2000, in prep.).\nIn this figure hatched areas correspond to BL Lac objects.\nSeveral facts are to be noted:\n\\begin{itemize}\n%\n\\item If the jet is made by a pure electron--positron plasma,\nthen the associated kinetic power is $L_{\\rm e}$. \nHowever, we note that $L_{\\rm e} \\ll L_{\\rm r}$\nposing a serious energy budget problem.\n%\n\\item If there is a proton for each electron, the bulk kinetic\npower $L_{\\rm p}\\sim 10 L_{\\rm r}$.\nThis corresponds to an efficiency of $\\sim 10\\%$ in converting\nbulk into random energy.\nThe remaining 90\\% is therefore available to power the radio lobes,\nas required.\n%\n\\item The power in the Poynting flux, $L_{\\rm B}$,\nis of the same order of $L_{\\rm e}$, indicating that the magnetic \nfield is close to equipartition with the electron energy density.\nThis suggests that, on these scales, the magnetic field is not a prime \nenergy carrier, but is a sub--product of the process transforming\nbulk into random energy.\n%\n\\end{itemize}\n\n\n\\begin{figure}\n\\vskip -1 true cm\n\\centerline{\\psfig{file=fig1.ps, width=15cm}} % , height=9.0cm}}\n\\caption[]{Histograms of the powers carried by the jet in protons, \ntotal radiation, synchrotron radiation, magnetic field and \nrelativistic electrons, from top to bottom.\nHatched areas correspond to BL Lac objects.\nThe electron distribution was assumed to extend down\nto $\\gamma_{\\rm min}\\sim 1$. From Celotti \\& Ghisellini (2000, in prep.)}\n\\end{figure}\n\n\\begin{figure}\n\\vskip -2. true cm\n\\centerline{\\psfig{file=fig2.ps, width=13cm}}\n\\vskip -7 true cm\n\\caption[]{Cartoon illustrating the internal shock scenario.\nThe intermittent activity of the central engine produces two shells,\ninitially separated by $R_0$. \nThe faster one will catch up the slower one at $R\\sim \\Gamma^2 R_0$.}\n\\end{figure}\n\n\\section{Internal shocks}\n\nThe central engine may well inject energy into the jet in a discontinuous\nway, with individual shells or blobs having different masses, bulk Lorentz\nfactors and energies.\nIf this occurs there will be collisions between shells, with a faster\nshell catching up a slower one.\nThis idea has become the leading model to explain the emission of \ngamma--ray bursts, but it was born in the AGN field, due to Rees (1978)\n(see also Sikora 1994).\n\n\n\\begin{itemize}\n\\item {\\bf Location --- }\nThe $\\gamma$--ray emission of blazars and its rapid variability\nimply that there must be a preferred location where dissipation\nof the bulk motion energy occurs. \nIf it were at the base of the jet, and hence close to the accretion disk,\nthe produced $\\gamma$--rays would be inevitably absorbed by \nphoton--photon collisions, with associated copious pair production,\nreprocessing the original power from the $\\gamma$--ray to the X--ray\npart of the spectrum (contrary to observations).\nIf it were far away, in a large region of the jet, it becomes difficult to \nexplain the observed fast variability,\neven accounting for the time--shortening due to the Doppler effect.\nThe region where the radiation is produced is then most likely located\nat a few hundreds of Schwarzchild radii ($\\sim 10^{17}$ cm) \nfrom the base of the jet, within the broad line region\n(see Ghisellini \\& Madau 1996 for more details).\nThe extra seed photons provided by emission lines enhance the efficiency \nof the Compton process responsible for the $\\gamma$--ray emission. \nThis is indeed the typical distance at which two shells, initially \nseparated by $R_0\\sim 10^{15}$ cm (comparable to a few Schwarzschild radii) \nand moving with $\\Gamma \\sim 10$ and $\\Gamma\\sim 20$ would collide.\n\n\\item {\\bf Variability timescales ---}\nIn fact if the initial separation of the two shells is $R_0$ and\nif they have Lorentz factors $\\Gamma_1$, $\\Gamma_2$, \nthey will collide at\n%\n\\begin{equation}\nR\\, = {2 \\Gamma_1^2 \\over 1-(\\Gamma_1/\\Gamma_2)^2} \\, R_0 \n\\end{equation}\n%\nIf the shell widths are of the same order of their initial separation\nthe time needed to cross each other is of the order of $R/c$.\nThe observer at a viewing angle $\\theta\\sim 1/\\Gamma$ will see this time\nDoppler contracted by the factor $(1-\\beta\\cos\\theta)\\sim \\Gamma^{-2}$.\nThe typical variability timescale is therefore of the same order\nof the initial shell separation.\nIf the mechanism powering GRB and blazar emission is the same,\nwe should expect a similar light curve from both systems, \nbut with times appropriately scaled by the different $R_0$, i.e. \nthe different masses of the involved black holes.\n\n\n\\item {\\bf Efficiencies ---}\nAs most of the power transported by the jet must reach the radio lobes, \nonly a small fraction can be radiatively dissipated.\nThe efficiency $\\eta$ of two blobs/shells for converting ordered into\nrandom energy depends on their masses $m_1$, $m_2$ and \nbulk Lorentz factors $\\Gamma_1$, $\\Gamma_2$, as\n\\begin{equation}\n\\eta \\,=\\, 1-\\Gamma_f\\, { m_1+m_2\\over \\Gamma_1 m_1 +\\Gamma_2m_2}\n\\end{equation}\nwhere $\\Gamma_f=(1-\\beta_f^2)^{-1/2}$ is the bulk Lorentz factor \nafter the interaction and is given by \n(see e.g. Lazzati, Ghisellini \\& Celotti 1999)\n\\begin{equation}\n\\beta_f = {\\beta_1\\Gamma_1m_1+ \\beta_2\\Gamma_2m_2 \\over\n\\Gamma_1m_1+ \\Gamma_2m_2}\n\\end{equation}\nThe above relations imply, for shells of equal masses and \n$\\Gamma_2=2\\Gamma_1=20$, $\\Gamma_f=14.15$ and $\\eta=5.7\\%$.\n\nEfficiencies $\\eta$ around 5--10\\% are just what needed\nfor blazar jets.\n\n\\item {\\bf Peak energies? ---}\nIn the rest frame of the fast shell, the bulk kinetic energy\nof each proton of the slower shell is $\\sim (\\Gamma^\\prime-1)m_pc^2$, \nwhere $\\Gamma^\\prime\\sim 2$. \nThis is what can be transformed into random energy.\nAssume now that the electrons share this available energy\n(through an unspecified acceleration mechanism).\nIn the comoving frame, the acceleration rate can be written as \n$\\dot E_{heat} \\sim (\\Gamma^\\prime-1)m_p c^2 /t^\\prime_{heat}$.\nThe typical heating timescale may correspond to the time needed for the \ntwo shells to cross, i.e. \n$t^\\prime_{heat}\\sim \\Delta R^\\prime/c\\sim R/(c\\Gamma)$,\nwhere $\\Delta R^\\prime$ is the shell width (measured in the same frame).\nThe heating and the radiative cooling rates will balance for some\nvalue of the random electron Lorentz factor $\\gamma_{peak}$:\n%\n\\begin{equation}\n\\dot E_{heat}\\, =\\, \\dot E_{cool}\\, \\to \\,\n{\\Gamma m_p c^3 \\over R} \\, =\\, {4\\over 3} \\sigma_T c U\\gamma^2_{peak}\n\\, \\to \\,\n\\gamma_{peak} \\, =\\, \\left({ 3\\Gamma m_p c^2 \\over 4 \\sigma_T R U}\\right)^{1/2}\n\\end{equation}\n%\nThe agreement of the above simple relation with what\ncan be derived from model fitting the SED of blazars is surprisingly good\n(see Ghisellini 2000).\n\n\\item {\\bf Radio flares ---}\nCollisions between shells may (and should) happen in a hierarchical way.\nAs an illustrative example, assume that one pair of shells\nafter the collision moves with a final Lorentz factor $\\Gamma_1 =14$\n(this number corresponds to $\\Gamma=10$ and 20 for the two shells\nbefore the interaction).\nThe collision produces a flare --say-- in the optical and $\\gamma$--ray bands.\nAfter some observed time $\\Delta t$ two other shells collide and another\nflare is produced.\nAssume that the final Lorentz factor is now $\\Gamma_2=17$ (corresponding to \nan initial $\\Gamma =10$ and 30 before collision).\nSince the second pair is faster, it will catch up the first\none after a distance (from eq. 5) $R \\sim 1200 c \\Delta t$.\nA time separation of $\\Delta t \\sim$ a day between the two flares \nthen corresponds to $R\\sim$ 1 pc, i.e. the region of the radio emission\nof the core.\nDue again to Doppler contraction, this radio flare will be observed\nony a few days after the second optical flare.\nSince the ratio $\\Gamma_2/\\Gamma_1$ is small, the efficiency is also small\n(at least a factor 10 smaller than the firsts shocks).\nThere is then the intriguing possibility of explaining the birth of radio\nblobs after intense activity (i.e. more than one flare) of the\nhigher energy flux.\nRadio light--curves should have {\\it some} memory of what has happened\ndays--weeks earlier at higher frequencies.\n\n\n\\end{itemize}\n\n\n\n\\section{Conclusions}\n\nHere I will dare to assemble different pieces of information\ngathered in recent years in a coherent, albeit still preliminary, picture.\n\nThere is a link between the extraction of gravitational energy\nin an accretion disk and the formation and acceleration of jets,\nsince both have the same power.\nObjects of low luminosity accretion disks also lack strong emission lines,\nsuggesting that it is the paucity of ionizing photons, not of gas, the reason\nfor the lack of strong lines in BL Lacs.\nCorrespondingly, this implies that, if FR I are the parents of BL Lacs,\nthey also have intrinsically weak line emission \n(i.e. no need for an obscuring torus).\nDespite the fact that the jet power in blazars spans at least four orders\nof magnitude, the average bulk Lorentz factor is almost the same,\nsuggesting a link between the power and the mass outflowing rate:\ntheir ratio is constant.\nIn the region where most of the radiation is produced, the jet is heavy,\nin the sense that protons carry most of the bulk kinetic energy.\nThere the jet dissipates $\\sim 10\\%$ of its power and produces\nbeamed radiation.\nThe power dissipated at larger distances is much less, and therefore\nthe jet can transport $\\sim 90\\%$ of its original power to \nthe radio extended regions.\nOne way to achieve this is through internal shocks, which can explain\nwhy the major dissipation occurs at a few hundreds Schwarzchild radii,\nwhy the efficiency is of the order of 10\\%, and give clues\non the observed variability timescales and even on why electrons\nare accelerated at a preferred energy.\nThe spectral energy distribution of blazars depends on where \nshell--shell collisions take place, and on the amount of seed\nphotons present there.\nEven in a single source it is possible that the separation \nof two consecutive shells is sometimes large, resulting in a collision\noccuring outside the broad line region.\nIn this case the corresponding spectrum should be produced\nby the synchrotron self--Compton process only, without the contribution\nof external photons: we then expect a simultaneous \noptical--$\\gamma$--ray flare of roughly equal powers (but with\nthe self--Compton flux varying quadratically, see Ghisellini \\& Maraschi 1966).\nThis is what should always happen in lineless BL Lac objects.\nOn the other hand, if the initial separation of the two shells\nis small (or the $\\Gamma$--factor of the slower one is small),\nthe collision takes place close to the disk.\nX--rays produced by the disk would then absorb all the produced \n$\\gamma$--rays and a pair cascade would develop, reprocessing the power \noriginally in the $\\gamma$--ray band mainly into the X--ray band.\nWe should therefore see an X--ray flare without accompanying \nemission above $\\Gamma m_{\\rm e} c^2$.\n\n\nPairs of shells which have already collided can interact again\nbetween themselves, at distances appropriate for the radio\nemission.\nThis offers the interesting possibility to explain why the radio \nluminosity is related with the $\\gamma$--ray one, and why radio \nflares are associated with flares at higher frequencies.\nWork is in progress in order to quantitatively test\nthis idea against observations.\n\n\n\n\n\n\\begin{acknowledgements}\nI thank Annalisa Celotti for very insightful discussions.\n\\end{acknowledgements}\n\n\\begin{references}\n\n\n\\ref Begelman M.C., Blandford R.D. \\& Rees M.J., 1984,\n Rev. Mod. Phys., 56, 255 \n\\ref Benford G. \\& Lesch H., 1998, MNRAS 301 414\n\\ref Blandford R.D. \\& Znajek R.L., 1977, MNRAS, 176, 465\n\\ref Celotti A., 1997, in Relativistic jets in AGNs,\n eds. M. Ostrowski, M. Sikora, G. Madejski \\& M. Begelman,\n p. 270\n\\ref Celotti A., 1998, in Astrophysical jets: open problems,\n (Gordon \\& Breach Science publ.), eds. S. Massaglia \\& G. Bodo\n (Amsterdam), p. 79\n\\ref Celotti A. \\& Fabian A.C. 1993, MNRAS, 264, 228\n% \\ref Celotti A., Kuncic Z., Rees M.J. \\& Wardle J.F.C. 1998, MNRAS, 293, 288\n\\ref Celotti A., Padovani P. \\& Ghisellini G., 1997, MNRAS, 286, 415\n\\ref Chiaberge, Capetti \\& Celotti, 1999, A\\&A, 349, 77\n\\ref Dondi L. \\& Ghisellini G., 1995, MNRAS, 273, 583\n\\ref Fossati G., Celotti A.,Comastri A., Maraschi L. \\& Ghisellini G.,\n 1998, MNRAS, 299, 433\n\\ref Ghisellini G. \\& Madau P., 1996, MNRAS, 280, 67\n\\ref Ghisellini G. \\& Maraschi L., 1996, in Blazar Continuum Variability,\n ASP Conference series, Vol. 110, 1996, eds. H.R. Miller \\& J.R. Webb, \n p. 436\n\\ref Ghisellini G., Celotti A., Fossati G., Maraschi L. \\&Comastri A., \n 1998, MNRAS, 301, 451\n\\ref Ghisellini G., 2000, in The Asca Symposium, Tokio, March 1999, in press\n% \\ref Ghisellini G., Padovani P., Celotti A. \\& Maraschi L., \n% 1993, ApJ, 407, 65\n\\ref Giommi P. \\& Padovani P., 1994, ApJ, 444, 567\n\\ref Hartman, R.C. et al., 1999, ApJS, 123, 79\n\\ref Lazzati D., Ghisellini G. \\& Celotti A., 1999, MNRAS, 309, L13\n% \\ref Maraschi L., et al., 1994, ApJ, 435, L91\n\\ref M\\'esz\\'aros, P., 1999, Nuclear Phys. B, in press (astro--ph/9904038)\n% \\ref Pian E. et al., 1998, ApJ, 491, L17\n\\ref Piran, P., 1999, Phys. Rep., in press (astro--ph/9810256)\n\\ref Rawlings S.G. \\& Saunders R.D.E., 1991, Nature, 349, 138\n\\ref Rees M.J., 1966, Nature, 211, 468\n\\ref Rees, M.J., 1978, MNRAS, 184, P61\n% \\ref Sikora, M., Begelman, M.C. \\& Rees, M.J.: 1994, ApJ, 421, 153\n\\ref Sikora M., 1994, ApJS, 90, 923\n\\ref Ulrich M.--H., Maraschi L. \\& Urry C.M., 1996, ARA\\&A, 35, 445\n\\ref Urry M.C. \\& Padovani P., 1995, PASP, 107, 803\n% \\ref Yakoob T., George I.M., Turner T.J., Nandra K., Ptak A.\n% \\& Serlemitsos P.J., 1998, ApJ in press (astro-ph/9807349)\n\\ref Vermeulen R.C. \\& Cohen M.H., 1994, ApJ, 430, 467\n\\ref Wagner S.J. \\& Witzel A., 1995, ARA\\&A, 33, 163\n% \\ref Wardle, J.F.C., 1977, Nature, 269, 563\n% \\ref Wehrle A.E. et al., 1998, ApJ, 497, 178\n\n\n\n\\end{references} \n\n\\end{document}\n"
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"name": "ip.tex",
"string": "\\documentstyle[11pt,fleqn,psfig]{article}\n% A4 size definitions\n\\if@twoside \\oddsidemargin 44pt \\evensidemargin 82pt \\marginparwidth 107pt\n\\else \\oddsidemargin -5pt \\evensidemargin -5pt\n\\marginparwidth 90pt\n\\fi\n\\topmargin -25pt \\headheight 12pt \\headsep 25pt \\footheight 12pt\n\\footskip 30pt\n\\textheight 630pt \\textwidth 450pt \\columnsep 10pt \\columnseprule 0pt\n% option for double-spacing\n% \\renewcommand{\\baselinestretch}{1.7}\n\\def\\etal{{\\it et\\thinspace al.}\\ }\n\\begin{document}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\begin{center}\n{\\bf \\Large THE IRON PROJECT}\\\\[5mm]\n{\\large Anil K. Pradhan\\\\Department of Astronomy, The Ohio State \nUniversity,\\\\ Columbus, Ohio, USA 43210}\n\\end{center}\n\\begin{quotation}\n\\noindent {\\bf Abstract}. Recent advances in theoretical atomic physics\nhave enabled large-scale calculation of atomic parameters for a variety\nof atomic processes with high degree of precision. The development and \napplication of these methods is the aim of the Iron Project. At present \nthe primary focus is on collisional processes for all ions of iron, Fe~I~--~FeXXVI, and other iron-peak elements; new work on radiative processes has also \nbeen initiated.\nVaried applications of the Iron Project work to X-ray astronomy are discussed,\nand more general applications to other spectral ranges are pointed out. The\nIP work forms the basis for more specialized projects such as the RMaX Project,\nand the work on photoionization/recombination, and aims to provide a \ncomprehensive and self-consistent set of accurate collsional and radiative \ncross sections, and transition probabilities, within the framework of \nrelativistic close coupling formulation using the Breit-Pauli R-Matrix method.\nAn illustrative example is presented of how the IP data may be utilised\nin the formation of X-ray spectra of the K$\\alpha$ complex at 6.7 keV\nfrom He-like Fe~XXV.\n\n\\end{quotation}\n%\\clearpage\n\n\\section{Introduction}\n\n The main purpose of the Iron Project (IP; Hummer \\etal 1993) is the continuing development\nof relativistic methods for the calculations of atomic data for\nelectron impact excitation and radiative transitions in iron and\niron-peak elements. Its forerunner, the Opacity Project (OP; Seaton\n\\etal 1994; The Opacity Project Team 1995), was concerned with the calculation of radiative parameters for\nastrophysically abundant elements,\noscillator strengths and photoionization cross sections,\nleading to a re-calculation of new stellar opacities (Seaton \\etal\n1994). The OP work, based on the non-relativistic formulation of\nthe close coupling approximation using the R-matrix method (Seaton 1987,\nBerrington \\etal 1987), was carried out in LS coupling, neglecting\nrelativistic fine structure that is not crucial in the calculation\nof mean plasma opacities. Also, collisional processes were not\nconsidered under the OP. The IP collaboration seeks to address both of\nthese factors, and with particular reference to iron and iron-peak elements.\nThe collaboration involves members from six countries: Canada, France,\nGermany, UK, US, and Venezuela.\n\n The relativistic extension of the R-matrix method is\nbased on the Breit-Pauli approximation (Berrington \\etal 1995). Collisional and radiative processes may both be\nconsidered. However, the computational requirements for the Breit-Pauli\nR-matrix (hereafter BPRM) calculations can be orders of magnitude more\nintensive than non-relativistic calculations. Nonetheless, a large body\nof atomic data has been obtained and published in a continuing series\nunder the title {\\bf Atomic Data from the Iron Project} in {\\it Astronomy\nand Astrophysics Supplement Series}, with 43 publications at present.\nA list of the IP publications and related information may be\nobtained from the author's Website: www.astronomy.ohio-state.edu/~pradhan.\n\n The earlier phases of\nthe Iron Project dealt with (A) fine structure transitions among low-lying\nlevels of the ground configuration of interest in Infrared (IR) astronomy,\nparticularly the observations from the Infrared Space Observatory, \n and (B) excitation of the large number of levels in multiply ionized\niron ions (with n = 2,3 open shell electrons, i.e. Fe~VII -- Fe~XXIV)\nof interest in the UV and EUV, particularly for the Solar and Heliospheric\nObservatory (SOHO), the Extreme Ultraviolet Explorer (EUVE), and Far Ultraviolet\nSpectroscopic Explorer (FUSE). In addition, the IP data for the low ionization \nstages of iron (Fe~I -- Fe~VI) is of particular interest in the analysis\nof optical and IR observations from ground based observatories.\n In the present review, we describe the IP work within the context of\napplications to X-ray spectroscopy, where ongoing calculations on \ncollisional and radiative data for H-like Fe~XXVI, He-like Fe~XXV, and \nNe-like Fe~XVII are of special interest. \n\n The sections of this review are organised as follows: 1. Theoretical, 2. collisional,\n3. radiative, 4. collisional-radiative modeling of X-ray spectra, 5.\natomic data, and 6. Discussion and conclusion.\n\n\\section{The Close Coupling approximation and the Breit-Pauli R-matrix Method}\n\nIn the close coupling (CC) approximation\n the total electron {+} ion wave function may be represented as\n\\begin{equation}\n\\Psi = A \\sum_{i=1}^{NF} \\psi_{i}\\theta_{i} + \\sum_{j=1} C_{j} \\Phi_{J},\n\\end{equation}\nwhere $\\psi_{i}$ is a target ion wave function in a specific state\n$S_{i}$\n$L_{i}$ and $\\theta_{i}$ is the wave function for the free electron in a\nchannel labeled as $S_{i}L_{i}k_{i}^{2}\\ell_{i}(SL\\pi)$, $k_{i}^{2}$\nbeing its\nincident kinetic energy relative to $E(S_{i}L_{i})$ and $\\ell_{i}$ its\norbital\nangular momentum. The total number of free channels is $NF$ (``open''\nor\n``closed'' according to whether $k_{i}^{2}$ $<$ or $>$ $E(S_{i}L_{i})$.\n$A$ is\nthe antisymmetrization operator for all $N+1$ electron bound states,\nwith\n$C_{j}$ as variational coefficients. The second sum in Eq. (1)\nrepresents\nshort-range correlation effects and orthogonality constraints between\nthe\ncontinuum electron and the one-electron orbitals in the target. \n\n The target levels included in the first sum on the RHS of Eq.\n(1) are coupled; their number limits the scope of the CC calculations.\nResonances arise naturally when the incident electron energies excite \nsome levels, but not higher ones, resulting in a coupling between ``closed\" and\n``open\" channels, i.e. between free and (quasi)bound wavefunctions.\nThe R-matrix method is the most efficient means of solving the CC\nequations and resolution of resonance profiles (see reviews by K.A.\nBerrington and M.A. Bautista). The relativistic CC approximation may be\nimplemented using the Breit-Pauli Hamiltonian.\n\n Both the continumm wavefunctions at E $>$ 0 for the (e +ion)\nsystem, and bound state wavefunctions may be calculated. Collision\nstrengths are obtained from the continuum (scattering) wavefunctions,\nand radiative transition matrix elements from the continuum and the bound\nwavefunctions that yield transition probabilities\nand photoionization and (e~+~ion) photo-recombination cross sections \n(see the review by S.N. Nahar). \n\n\nRecent IP calculations for the n~=~3 open shell ions include up to\n100 or more coupled fine structure levels. Computational requirements are\nfor such radiative and collisional calculations may be of the order of\n1000 CPU hours even on the most powerful supercomputers.\n\n\n\\section{Electron Impact Excitation} \n\n Collision strengths and maxwellian averaged rate coefficients\nhave been or are being calculated for all ions of iron. While some of\nthe most\ndifficult cases, with up to 100 coupled fine strcture levels from n = 3\nopen shell configurations in Fe~VII -- Fe~XVII, are still in progress,\nmost other ionization stages have been completed. In particular fine\nstructure collision strengths and rates have been computes for thousands\nof transitions in Fe~II -- Fe~VI. For a list of papers see ``Iron Project\" \non www.astronomy.ohio-state.edu/~pradhan. \n\n Work on K-shell and L-shell collisional excitations, begining\nwith the H-like and the He-like ions will be continued under the new RMaX\nproject, which is part of the IP and is focused on X-ray spectroscopy.\nWork is in progress on He-like Fe~XXV (Mendoza \\etal) and Ne-like \nFe~XVII. Fig. 1 presents the collision strength for\na transition in Fe~XVII from the new 89-level BPRM calculation\nincluding the n = 4 complex (Chen and Pradhan 2000). The extensive\nresonance structure is due to the large number of coupled thresholds\nfollowing L-shell excitation.\n\n\\begin{figure}\n\\centering\n\\psfig{figure=fig1.eps,height=10.0cm,width=18.0cm}\n\\caption{The BPRM collision strength $\\Omega (2p^6 \\ ^1S_0\n\\longrightarrow 2p^5 \\ 3s \\ ^3P_2)$ (Chen and Pradhan 2000); \nthe relativistic distorted wave\nvalues are denoted as filled circles (H.L. Zhang, in Pradhan and Zhang\n2000)}\n\\end{figure}\n\n \n\n\\section{Radiative transition probabilities}\n\n There are two sets of IP calculations: (i) with atomic structure \ncodes CIV3 (Hibbert 1973) and SUPERSTRUCTURE (Eissner \\etal 1974), and\n(ii) BPRM calculations. Of particular interest to X-ray work are the\nrecent BPRM calcultions for 2,579 dipole (E1) oscillator strengths for \n Fe~XXV , and 802 transitions in Fe~XXIV (Nahar and Pradhan 1999),\nextending the available datasets for these ions by more than an order of\nmagnitude. Also, these data are shown to be highly accurate, 1 -- 10\\%.\n\n\\section{Collisional-Radiative model for He-like ions: X-ray emission \nfrom Fe~XXV}\n\n Emission from He-like ions provides the most valuable X-ray spectral \ndiagnostics for the temperature, density, ionization state, and other\nconditions in the source (Gabriel 1972, Mewe and Schrijver\n1981, Pradhan 1982).\n The K$\\alpha$ complex of He-like ions consists of the principal \nlines from the allowed (w), intersystem (x,y), and\nthe forbidden (z) transitions $1^1S \\longleftarrow 2(^1P^o, \\ ^3P^o_2,\n\\ ^3P^o_1, \\ ^3S_1$ respectively. (These are also referred as the R,I,F\nlines, where the I is the sum (x+y); we employ the former notation). \nTwo main line ratios are particularly useful, i.e.\n\n\\be \\ R = \\frac{z}{x+y} \\ , \\ee and\n\\be \\ G = \\frac{x+y+z}{w} \\ . \\ee\n\n R is the ratio of forbidden to intersystem lines and is sensitive to \nelectron density N$_e$ since the forbidden\nline z may be collisionally quenched at high densities. G is\nthe ratio of the triplet-multiplicity lines to the `resonance' line, and\nis sensitive to (i) electron temperature, and (ii) ionization balance.\nCondition (ii) results because recombination-cascades from\nH-like ions preferentially populate the triplet levels, enhancing the z\nline intensity in particular (the level $2(^3S_1)$ is like the `ground' \nlevel for the triplet levels). Inner-shell ionization of Li-like \nions may also populate the $2(^3S_1)$ level ($1s^2\n\\ 2s \\longrightarrow 1s2s + e)$ enhancing the z line. \nThe line ratio G is therefore a sensitive indicator of the\nionization state and the temperature of the plasma during ionization,\nrecombination, or in coronal equilibrium.\n\n For Fe~XXV the X-ray lines {w,x,y,z} are at $\\lambda\\lambda$ 1.8505,\n1.8554, 1.8595, 1.8682 $\\AA$, or 6.700, 6.682, 6.668, 6.637 keV, respectively.\nA collisional-radiative model (Oelgoetz and Pradhan, in progress) \nincluding electron impact ionization,\nrecombination, excitation, and radiative cascades is used to compute\nthese line intensties using rates given by Mewe and Schrijver (1978), \nBely-Dubau \\etal (1982), and Pradhan (1985a). New unified electron-ion\nrecombination rates (total and\nlevel-specific) are being calculated by S.N. Nahar and\ncollaborators, and electron excitation rates are being recalculated\nby C. Mendoza and collaborators; these will be employed in a more\naccurate model of X-ray emission from He-like ions.\n\nFig. 2 shows illustrative results for doppler broadened line \nprofiles under different plasma conditions (normalized to I(w) = 1). \nAll are at $N_e = 10^{10} \\ cm^{-3} << N_c$, so that the R dependence is \nonly on T$_e$. Figs. 2(a) and 2(b) are in coronal equilibrium, but\ndiffering widely in T$_e$, $10^7 -- 10^8$K, as reflected in the broader\nprofiles for the latter case. The ratios R and G show a significant\n(though not large) temperature\ndependence in this range. The \nionization fractions Fe~XXIV/FeXXV and Fe~XXVI/FeXXV for the two cases\nare such that the Li-like iron dominates at $10^7$K and the H-like at\n$10^8$K. Figs. 2(a) and (b) illustrate a general property of the He-like\nline ratios: {\\it G $\\approx 1$ in cororal equilibrium} (for other\nHe-like ions it may vary by 10-20\\%).\n\n On the other hand, the situation is quite different when the plasma is\nout of equilibrium. In particular, it is known that \nthe forbidden line z is extremely sensitive to\nthe ionization state since it is predominantly populated via\nrecombination-cascades (Pradhan 1985b). Fig. 2(c) illustrates a case where\nrecombinations are suppressed, and the plasma is at $T_e = 10^8$ K. The\ntotal G value is now only a third of its coronal value, with the z/w\nratio being considerably lower. Although the new recombination and\nexcitation rates may change the number somewhat, it is seen that \n{\\it G $\\approx 0.37$ is a lower limit on an ionization dominated plasma}. \n\nA reverse situation occurs in a recombination dominated plasma. It is\nknown from tomakak studies (Kallne \\etal 1984, Pradhan 1985b) that the z/w ratio, and\nhence G, increases practically without limit, as $T_e$ decreases much below the\ncoronal temperature of maximum abundance. {\\it $G >> 1$ observed values\nimply a recombination dominated source}. However, the z/w ratio may also\nbe enhanced by inner-shell ionization through the Li-like state. More\ndetailed calculations are needed to distinguish precisely between the\ntwo cases, and to constrain the temperature and ionization fractions.\n\n Di-electronic satellite intensities (Gabriel 1972) \n may also be computed using BPRM data for the autoionization and\nradiative rates of the satellite levels from recombination of e~+~FeXXV\n$\\longrightarrow$ Fe~XXIV (Pradhan and Zhang 1997). This work is in\nprogress.\n\n\\begin{figure}\n\\centering\n\\psfig{figure=fig2.eps,height=20.0cm,width=18.0cm}\n\\caption{X-ray spectra of Fe~XXV (Oelgoetz and Pradhan 2000). \nThe principal lines w,x,y,z and the line ratios R and G are computed at plasma \nelectron temperatues shown.\nThe lines are Doppler broadened. I(w) is normalized to unity.}\n\\end{figure}\n\n\n\\section{Atomic Data}\n\n The atomic data from the OP/IP is available from the Astronomy and\nAstrophysics library at CDS, France (Cunto \\etal 1993). The data is also\navailable from a Website at NASA GSFC linked to the author's Website\n(www.astronomy.ohio-state.edu/~pradhan).\n\n A general review of the methods and data, \n(``Electron Collisions with Atomic Ions - Excitation\",\nPradhan and Zhang 2000) is available from the author's website. The\nreview contains an evaluated compilation of theoretical data sources\nfor the period 1992-1999, as a follow-up of a similar review of all data\nsources up to 1992 by Pradhan and Gallagher (1992) -- a total of over\n1,500 data sources with accuracy assessment. Also contained are\ndata tables for many Fe ions, and a recommended data table of effective\ncollision strengths and A-values for radiative-collisional models for\nions of interest in nebular plasmas.\n\n The collisional data from the IP is being archived in a new database\ncalled TIPBASE, complementary to the radiative database from the OP,\nTOPBASE (see the review by C. Mendoza).\n\n\\section{Discussion and Conclusion}\n\n An overview of the work under the Iron Project collaboration was\npresented. Its special relevance to X-ray astronomy was pointed out since the\nIP, and related work, primarily aims to study the dominant atomic processes \nin plasmas, and to compute extensive and accurate set of atomic \ndata for electron impact excitation, photoionization, recombination, and \ntransition probabilities of iron and iron-peak elements.\n The importance of coupled-channel calculations was emphasized, in\nparticular the role of autoionizing resonances in atomic phenomena. \n(A new project RMaX, a part of IP focused on X-ray spectroscopy, is\ndescribed by K.A. Berrington in this review). \n\n During the discussion, a question was raised regarding the resonances\nin Fe~XVII collision strengths (e.g. Fig. 1), and it was mentioned that new \nexperimental measurments appear not to show the expected rapid variations in\ncross sections. A possible explanation may be that there are numerous \nnarrow resonances in the entire near-threshold region, without a clearly\ndiscernible background or energy gap. The measured cross sections are \naverages over the resonances corresponding to the experimental beam-width. \nThese averaged cross sections themselves may not exhibit sharp variations,\nunlike more highly charged He-like ions where the \nthe non-resonant background and the resonance complexes are well\nseparated in energy (e.g. He-like Ti~XXI, Zhang and Pradhan 1993).\n\n%%%%%%%\n%-----------------------%\n\n\\def\\amp{{\\it Adv. At. Molec. Phys.}\\ }\n\\def\\apj{{\\it Astrophys. J.}\\ }\n\\def\\apjs{{\\it Astrophys. J. Suppl. Ser.}\\ }\n\\def\\apjl{{\\it Astrophys. J. (Letters)}\\ }\n\\def\\aj{{\\it Astron. J.}\\ }\n\\def\\aa{{\\it Astron. Astrophys.}\\ }\n\\def\\aasup{{\\it Astron. Astrophys. Suppl.}\\ }\n\\def\\adndt{{\\it At. Data Nucl. Data Tables}\\ }\n\\def\\cpc{{\\it Comput. Phys. Commun.}\\ }\n\\def\\jqsrt{{\\it J. Quant. Spectrosc. Radiat. Transfer}\\ }\n\\def\\jpb{{\\it Journal Of Physics B}\\ }\n\\def\\pasp{{\\it Pub. Astron. Soc. Pacific}\\ }\n\\def\\mn{{\\it Mon. Not. R. astr. Soc.}\\ }\n\\def\\pra{{\\it Physical Review A}\\ }\n\\def\\prl{{\\it Physical Review Letters}\\ }\n\\def\\zpds{{\\it Z. Phys. D Suppl.}\\ }\n\\def\\adndt{Atomic Data And Nuclear Data Tables}\n\n%\\pagebreak\n\\section{References}\n\\parindent=0pt\n\nBely-Dubau, F. Dubau, J., Faucher, P. and Gabriel, A.H. 1982, \\mn,\n198 239\\\\\nBerrington, K.A., Burke, P.G., Butler, K., Seaton, M.J.,\nStorey, P.J., Taylor, K.T., \\& Yan, Yu. 1987, \\jpb 20, 6379\\\\\nBerrington K.A., Eissner W.B., Norrington P.H.,\n1995, \\cpc 92, 290\\\\\nCunto,W.C., Mendoza,C., Ochsenbein,F. and Zeippen, C.J., 1993, \\aa\n 275, L5\\\\\nEissner W, Jones M and Nussbaumer H 1974 \\cpc 8 270\nGabriel, A.H., \\mn 1972, 160, 99\\\\\nHibbert A., 1975, \\cpc 9, 141\\\\\nHummer, D.G., Berrington, K.A., Eissner, W., Pradhan,\nA.K., Saraph, H.E., \\& Tully, J.A. 1993, Astron. Astrophys. 279, 298\\\\\nKallne, E, Kallne, J., Dalgarno, A., Marmar, E.S., Rice, J.E. and\nPradhan, A.K. 1984, \\prl 52, 2245\\\\\nMewe, R. and Schrijver, J. 1978, \\aa, 65, 99\\\\\nNahar, S.N. and Pradhan, A.K. 1999, \\aasup 135, 347\\\\\nPradhan, A.K. 1982 \\apj, 263, 477\\\\\nPradhan, A.K. 1985a \\apjs, 59, 183\\\\\nPradhan, A.K. 1985b \\apj, 288, 824\\\\\nPradhan, A.K. and Gallagher, J.W. 1992, \\adndt, 52, 227\\\\\nPradhan, A.K. and Zhang, H.L. 1997, \\jpb, 30, L571\\\\\nPradhan, A.K. and Zhang, H.L. 2000, {\\it ``Electron Collisions with\nAtomic Ions\"}, In LAND\\\"{O}LT-BORNSTEIN Volume {\\it ``Atomic Collisions\"},\nEd. Y. Itikawa, Springer-Verlag (in press).\\\\\nThe Opacity Project Team, {\\it The Opacity Project}, Vol.1, 1995, \nInstitute of Physics Publishing, U.K.\\\\ \nSeaton, M.J. 1987, \\jpb 20, 6363\\\\\nSeaton, M.J., Yu, Y., Mihalas, D. and Pradhan, A.K. 1994, \\mn, 266, 805\\\\\nZhang H.L. and Pradhan A.K. 1995, \\pra, 52, 3366\n\n\n\\end{document}\n\n\n\n\n\n\n"
}
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astro-ph0002357
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Infrared Spectroscopy of a Massive Obscured Star Cluster in the %Antennae Galaxies (NGC 4038/4039) with NIRSPEC\altaffilmark{1}
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[
{
"author": "Andrea M. Gilbert\\altaffilmark{2,8}"
},
{
"author": "James R. Graham\\altaffilmark{2}"
},
{
"author": "Ian S. McLean\\altaffilmark{3}"
},
{
"author": "E. E. Becklin\\altaffilmark{3}"
},
{
"author": "Donald F. Figer\\altaffilmark{4}"
},
{
"author": "James E. Larkin\\altaffilmark{3}"
},
{
"author": "N. A. Levenson\\altaffilmark{5}"
},
{
"author": "Harry I. Teplitz\\altaffilmark{6,7}"
},
{
"author": "Mavourneen K. Wilcox\\altaffilmark{3}"
}
] |
We present infrared spectroscopy of the Antennae Galaxies (NGC~4038/4039) with NIRSPEC at the W. M. Keck Observatory. We imaged the star clusters in the vicinity of the southern nucleus (NGC~4039) in $0\arcs.39$ seeing in K-band using NIRSPEC's slit-viewing camera. The brightest star cluster revealed in the near-IR (M$_{K}(0) \simeq -17.9$) is insignificant optically, but coincident with the highest surface brightness peak in the mid-IR ($12-18 \mu$m) ISO image presented by \citet{mirabel98}. We obtained high signal-to-noise 2.03$-$2.45 $\mu$m spectra of the nucleus and the obscured star cluster at R $\sim 1900$. The cluster is very young (age $\sim 4$ Myr), massive (M $\sim 16 \times 10^6$ M$_{\odot}$), and compact (density $\sim 115$ M$_{\odot}$ pc$^{-3}$ within a 32 pc half-light radius), assuming a Salpeter IMF (0.1$-$100 M$_{\odot}$). Its hot stars have a radiation field characterized by T$_{eff}\sim 39,000$ K, and they ionize a compact \ion{H}{2} region with n$_{e}\sim 10^4$ cm$^{-3}$. The stars are deeply embedded in gas and dust (A$_{V} \sim 9-10$ mag), and their strong FUV field powers a clumpy photodissociation region with densities n$_{H}\ga 10^5$ cm$^{-3}$ on scales of $\sim 200$ pc, radiating L$_{{H}_2 1-0~{S}(1)}= 9600$ L$_{\odot}$.
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[
{
"name": "preprint.tex",
"string": "\\documentclass{article}\n\\usepackage{natbib,epsfig,emulateapj}\n\n%\\documentstyle[emulateapj,epsf,natbib209]{article}\n%\\documentclass{article} %[preprint]{aastex}\n%\\usepackage{epsfig,emulateapj,natbib}\n\\citestyle{apj} \n\n\\def\\deg{\\ifmmode^\\circ\\else$^\\circ$\\fi}\n\\def\\solar{\\ifmmode_{\\mathord\\odot}\\else$_{\\mathord\\odot}$\\fi}\n\\def\\er{\\relax} \\def\\sr{\\relax}\n\\def\\ls{{_<\\atop^{\\sim}}}\n\\def\\gs{{_>\\atop^{\\sim}}}\n\\def\\mic{~$\\mu$m}\n\\def\\etc{{\\it etc.}}\n\\def\\cf{{\\it cf.}}\n\\def\\ie{{\\it i.e.}}\n\\def\\eg{{\\it e.g.}}\n\\def\\iras{{\\it IRAS}}\n\\def\\iue{{\\it IUE}}\n\\def\\rosat{{\\it Rosat}}\n\\def\\ginga{{\\it Ginga}}\n\\def\\et{{et al.~}}\n\n\\def\\h0{H$_0$}\n\\def\\q0{q$_0$}\n\n\\def\\hf{\\mbox{$H_{1.6}$}}\n\\def\\arcs{\\ifmmode {''}\\else $''$\\fi}\n\\def\\arcm{\\ifmmode {'}\\else $'$\\fi}\n\\def\\parcs{\\sa=.07em \\sb=.03em\n \\ifmmode $\\rlap{.}$^{\\scriptscriptstyle\\prime\\kern -\\sb\\prime}$\\kern -\\sa$\n \\else \\rlap{.}$^{\\scriptscriptstyle\\prime\\kern -\\sb\\prime}$\\kern -\\sa\\fi}\n\\def\\parcm{\\sa=.08em \\sb=.03em\n \\ifmmode $\\rlap{.}\\kern\\sa$^{\\scriptscriptstyle\\prime}$\\kern-\\sb$\n \\else \\rlap{.}\\kern\\sa$^{\\scriptscriptstyle\\prime}$\\kern-\\sb\\fi}\n\n\\def\\Msun{M$_{\\odot}$}\n\\def\\Myr{\\Msun/yr}\n\\def\\kp{{\\rm K}$^{\\prime}$}\n\\def\\lya{{\\rm Ly}$\\alpha$}\n\\def\\Ls{{ L$^{*}$}}\n\\def\\han {\\mbox{{\\rm H}$\\alpha$}}\n\\def\\hb {\\mbox{{\\rm H}$\\beta$}}\n\\def\\hgamma {\\mbox{{\\rm H}$\\gamma$}}\n\\def\\oiii{\\mbox{{\\sc [OIII]}}}\n\\def\\ha{\\han}\n\\def\\xray{\\hbox{X-ray}}\n\\def\\brg {{\\rm Br}$\\gamma$}\n\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar''218$}}\n \\raise 2.0pt\\hbox{$\\mathchar''13C$}}}\n\\def\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar''218$}}\n \\raise 2.0pt\\hbox{$\\mathchar''13E$}}}\n\\def\\lsim{\\rlap{$<$}{\\lower 1.0ex\\hbox{$\\sim$}}}\n\\def\\gsim{\\rlap{$>$}{\\lower 1.0ex\\hbox{$\\sim$}}}\n\n%\\slugcomment{Draft Version 0.0:by \\today}\n%\\pagestyle{myheadings}\n%\\markboth{DRAFT version 0.0: \\today}{DRAFT version 0.0: \\today}\n\n%\\shorttitle{Antennae Star Cluster}\n%\\shortauthors{Gilbert, et al.}\n\n\n%\\slugcomment{Submitted to ApJL October 27, 1999}\n\\slugcomment{To appear in ApJL; submitted Oct. 27, 1999}\n\n\\begin{document}\n\n%\\title{Infrared Spectroscopy of a Massive Obscured Star Cluster in the\n%Antennae Galaxies (NGC 4038/4039) with NIRSPEC\\altaffilmark{1}}\n\n\\title{K-Band Spectroscopy of an Obscured Massive Stellar Cluster in the\nAntennae Galaxies (NGC 4038/4039) with NIRSPEC\\altaffilmark{1}}\n\n\\author{\nAndrea M. Gilbert\\altaffilmark{2,8},\nJames R. Graham\\altaffilmark{2}, \nIan S. McLean\\altaffilmark{3}, \nE. E. Becklin\\altaffilmark{3}, \nDonald F. Figer\\altaffilmark{4},\nJames E. Larkin\\altaffilmark{3}, \nN. A. Levenson\\altaffilmark{5}, \nHarry I. Teplitz\\altaffilmark{6,7}, \nMavourneen K. Wilcox\\altaffilmark{3} \n} \n\\altaffiltext{1}{Data presented herein were obtained\nat the W.M. Keck Observatory, which is operated as a scientific\npartnership among the California Institute of Technology, the\nUniversity of California and the National Aeronautics and Space\nAdministration. The Observatory was made possible by the generous\nfinancial support of the W.M. Keck Foundation.}\n\\altaffiltext{2}{\nDepartment of Astronomy, \nUniversity of California,\n601 Campbell Hall,\n Berkeley, CA, 94720-3411 }\n\\altaffiltext{3}{Department of Physics and Astronomy, \nUniversity of California, \n Los Angeles, CA, 90095-1562 }\n\\altaffiltext{4}{Space Telescope Science Institute, \n 3700 San Martin Dr., Baltimore, MD 21218 }\n\\altaffiltext{5}{\nDepartment of Physics and Astronomy, \nJohns Hopkins University,\n Baltimore, MD 21218}\n\\altaffiltext{6}{Laboratory for Astronomy and Solar Physics, Code 681, Goddard\nSpace Flight Center, Greenbelt MD 20771}\n\\altaffiltext{7}{NOAO Research Associate}\n\\altaffiltext{8}{agilbert@astro.berkeley.edu}\n\n%email{agilbert@astro.berkeley.edu}\n\n\\begin{abstract} \nWe present infrared spectroscopy of the Antennae Galaxies\n(NGC~4038/4039) with NIRSPEC at the W. M. Keck Observatory. We imaged\nthe star clusters in the vicinity of the southern nucleus (NGC~4039)\nin $0\\arcs.39$ seeing in K-band using NIRSPEC's slit-viewing\ncamera. The brightest star cluster revealed in the near-IR (M$_{\\rm\nK}(0) \\simeq -17.9$) is insignificant optically, but coincident with\nthe highest surface brightness peak in the mid-IR ($12-18 \\mu$m) ISO\nimage presented by \\citet{mirabel98}. We obtained high\nsignal-to-noise 2.03$-$2.45 $\\mu$m spectra of the nucleus and the\nobscured star cluster at R $\\sim 1900$.\n\nThe cluster is very young (age $\\sim 4$ Myr), massive (M $\\sim 16\n\\times 10^6$ M$_{\\odot}$), and compact (density $\\sim 115$ M$_{\\odot}$\npc$^{-3}$ within a 32 pc half-light radius), assuming a Salpeter IMF\n(0.1$-$100 M$_{\\odot}$). Its hot stars have a radiation field\ncharacterized by T$_{\\rm eff}\\sim 39,000$ K, and they ionize a compact\n\\ion{H}{2} region with n$_{\\rm e}\\sim 10^4$ cm$^{-3}$. The stars are\ndeeply embedded in gas and dust (A$_{\\rm V} \\sim 9-10$ mag), and their\nstrong FUV field powers a clumpy photodissociation region with\ndensities n$_{\\rm H}\\ga 10^5$ cm$^{-3}$ on scales of $\\sim 200$ pc,\nradiating L$_{{\\rm H}_2 1-0~{\\rm S}(1)}= 9600$ L$_{\\odot}$.\n\n\\end{abstract}\n\n\\keywords{galaxies: individual (NGC4038/39, Antennae Galaxies) ---\ngalaxies: ISM --- galaxies: starburst --- galaxies: star clusters ---\ninfrared: galaxies --- \\ion{H}{2} regions}\n\n\\section{Introduction}\n\nThe Antennae (NGC~4038/4039) are a pair of disk galaxies in an early\nstage of merging which contain numerous massive super star clusters\n(SSCs) along their spiral arms and around their interaction region\n\\citep{whitmore95,whitmore99}. The molecular gas distribution peaks\nat both nuclei and in the overlap region \\citep{stanford90}, but the\ngas is not yet undergoing a global starburst typical of more advanced\nmergers \\citep{nikola98}. Star formation in starbursts appears to\noccur preferentially in SSCs. We chose to observe the Antennae\nbecause their proximity permits an unusually detailed view of the\nfirst generation of merger-induced SSCs and their influence on the \nsurrounding interstellar medium.\n\nThe Infrared Space Observatory (ISO) $12-18~\\mu$m image showed that\nthe hot dust distribution is similar to that of the gas, but peaks at\nan otherwise inconspicuous point on the southern edge of the overlap\nregion \\citep{mirabel98}. This powerful starburst knot is also a\nflat-spectrum radio continuum source \\citep{hummel86} and may be\nassociated with an X-ray source \\citep{fabbiano97}. We imaged the\nregion around this knot, and discovered a bright compact star cluster\ncoincident with the mid-IR peak. We obtained moderate-resolution (R\n$\\sim 1900$) K-band spectra of both the obscured cluster and the\nNGC~4039 nucleus.\n\n\\section{Observations \\& Data Reduction}\n\nNIRSPEC is a new facility infrared ($0.95 - 5.6 \\mu$m) spectrometer\nfor the Keck-II telescope, commissioned during April through July,\n1999 \\citep{mclean98}. It has a cross-dispersed cryogenic echelle\nwith R $\\sim 25,000$, and a low resolution mode with R $\\sim 2000$.\nThe spectrometer detector is a 1024 $\\times$ 1024 InSb ALADDIN focal\nplane array, and the IR slit-viewing camera detector is a 256 $\\times$\n256 HgCdTe PICNIC array.\n\nWe observed the Antennae with NIRSPEC during the June 1999\ncommissioning run. Slit-viewing camera (SCAM) images at 2 $\\mu$m\nreveal that the mid-IR ISO peak is a bright (K $= 14.6$) compact star\ncluster located 20\\arcs.4 east and 4\\arcs.7 north of the K-band\nnucleus. This cluster is associated with a faint (V $= 23.5$) red\n(V$-$I $= 2.9$) source (\\# 80 in \\citealt{whitmore95}) visible with\nSpace Telescope (Whitmore \\& Zhang, private communication). We\nobtained low resolution (R $\\simeq 1900$) $\\lambda \\simeq 2.03 -\n2.45~\\mu$m spectra through a $0\\arcs.57 \\times 42\\arcs$ slit at\nPA=77$^{\\deg}$ located on the obscured star cluster and the nucleus of\nNGC~4039. The total integration time on source was 2100 s.\n\nWe dark-subtracted, mean-sky-subtracted, flat-fielded, and corrected\ntwo-dimensional spectra for bad pixels and cosmic rays before\nrectifying the curved order onto a grid in which wavelength and slit\nposition are perpendicular. We then corrected for residual sky\nemission and divided by a B1.5 standard star spectrum to correct for\natmospheric absorption. The object spectra were extracted using a\nGaussian weighting function matched to their strong continuua\ncollapsed in wavelength (intrinsic FWHM = 0\\arcs.84 for cluster,\n0\\arcs.99 for nucleus)\\footnote{These widths are greater than those\nmeasured from the SCAM images, $\\sim 0.\\arcs69$ and $\\sim 0\\arcs.83$\n(intrinsic), due to the extended line contribution and rectification\nerrors of order $\\la$ 1 pixel at the chip edges.}, and then an\naperture correction was applied to recover the full flux in the\ncontinuua. Thus we neglected more-extended H$_2$ emission, which has\nmaximum FWHM $\\sim 1\\arcs.7$ in the cluster and $\\sim 1\\arcs.2$ in the\nnucleus. We obtained a flux scale by requiring the 2.2 $\\mu$m star\nflux to equal that corresponding to its K magnitude. Reduced spectra\nare shown in Figures 1 and 2.\n%\\ref{clusterspec} and \\ref{nucleusspec}.\n\n%% CLUSTER SPECTRA \n%\\begin{figure}\n%\\begin{center}\n%\\epsfig{file=cluster_cmb.eps}\n{\\plotfiddle{cluster_cmb_col.eps}{3.2in}{0}{100}{100}{0}{10}}\n%\\figcaption[cluster_cmb.eps]\n{\\footnotesize Figure 1. - \nNIRSPEC spectrum of the obscured star\ncluster shows nebular and fluorescent H$_2$ emission with a continuum\nrising toward the red. Scaled sky counts are plotted at 0.1 mJy.\n$\\omega$-shaped curve represents an atmospheric CO$_2$ band at 2.05\n$\\mu$m. \n%label{clusterspec} \n}\n%\\end{center}\n%\\end{figure}\n\\vspace{-0.08in}\n\n\\section{Massive Star Cluster}\n\nThe cluster spectrum is characterized by strong emission\nlines\\footnote{A table of measured line fluxes is available\nelectronically from \n%url\n{http://astro.berkeley.edu/$\\sim$agilbert/antennae}.} and\na continuum (detected with SNR $\\simeq 15$) dominated by the light of\nhot, blue stars and dust. The nebular emission lines are slightly\nmore extended than the continuum, and the H$_2$ emission is even more\nextended. This suggests a picture in which hot stars and dust are\nembedded in a giant compact H~{\\sc ii} region surrounded by clumpy\n(see \\S 3.2) clouds of obscuring gas and dust whose surfaces are\nionized and photodissociated by FUV photons escaping from the star\ncluster.\n\nFor a distance to the Antennae of 19 Mpc (H$_0$=75 km s$^{-1}$\nMpc$^{-1}$, 1\\arcs = 93 pc) \\citep{whitmore99}, we find that the\ncluster has M$_{\\rm K} = -16.8$. We estimate the screen extinction to\nthe cluster by assuming a range of (V$-$K)$_0 \\simeq 0-1$ as expected\nfrom Starburst99 models \\citep{leitherer99}, and that A$_{\\rm K} =\n0.11$ A$_{\\rm V}$ \\citep{rieke85}. We find A$_{\\rm V} = 9-10$ mag,\nwhich implies M$_{\\rm K}(0) = -17.9$, adopting A$_{\\rm K}=1.1$ (which\nis confirmed by our analysis of the \\ion{H}{2} recombination lines in\n\\S 3.1). We can use the intrinsic brightness along with the Lyman\ncontinuum flux inferred from the de-reddened Br$\\gamma$ flux ($3.1\n\\times 10^{-14}$ erg s$^{-1}$ cm$^{-2}$), Q(H$^+)_0 = 1.0 \\times\n10^{53}$ photons s$^{-1}$, to constrain the cluster mass and age.\nUsing instantaneous Starburst99 models we find a total mass of $\\sim 7\n\\times 10^6$ M$_{\\odot}$ (with $\\sim 2600$ O stars) for a Salpeter IMF\nextending from 1 to 100 M$_\\odot$, and an age of $\\sim 4$ Myr. This\nage is consistent with the lack of photospheric CO and metal\nabsorption lines from red supergiants and other cool giants, which\nwould begin to contribute significantly to the 2 $\\mu$m light at an\nage of $\\sim 7$ Myr \\citep{leitherer99}. The cluster's density is\nthen about 115 M$_{\\odot}$ pc$^{-3}$ for stars of 0.1$-$100\nM$_{\\odot}$ within a half-light radius of $32$ pc. This density is 30\ntimes less than that of the LMC SSC, R136 (within a radius of 1.7 pc,\nassuming a Salpeter proportion of low-mass stars) \\citep{hunter95}.\nThus the Antennae cluster may be a complex of clusters rather than one\nmassive cluster.\n\n%% NUCLEUS SPECTRA\n%\\begin{figure}\n%\\begin{center}\n%\\epsfig{file=nucleus_cmb.eps}\n{\\plotfiddle{nucleus_cmb_col.eps}{3.2in}{0}{100}{100}{0}{10}}\n%\\figcaption[nucleus_cmb.eps]\n{\\footnotesize Figure 2. - \nNIRSPEC spectrum of NGC~4039 nucleus shows\nextended collisionally excited H$_2$ emission and a strong stellar\ncontinuum marked by photospheric absorption. No Br$\\gamma$ is present.\nScaled sky counts are shown at 1.5 mJy.\n%label{nucleusspec} \n}\n%\\end{center}\n%\\end{figure}\n\\vspace{-0.1in}\n\n\\subsection{Nebular Emission}\n\nThe cluster spectrum features a variety of nebular lines that reveal\ninformation about the conditions in the ionized gas around the\ncluster, which in turn allows us to constrain the effective\ntemperature of the ionizing stars. \n\nWe detected \\ion{H}{1} Pfund series lines from Pf~19 to Pf~38, and\ndisplay their fluxes relative to that of Br$\\gamma$ in Figure 3.\n%\\ref{pfund}. \nThe filled symbols give fluxes for the blends Pf\n28+H$_2$ 2$-$1 S(0) and Pf 29+[\\ion{Fe}{3}]. They fall well above\nthe other points, which follow closely the theoretical expectation for\nintensities relative to Br$\\gamma$ (solid curve) with no reddening\napplied, for a gas with n$_{\\rm e} = 10^{4}$ cm$^{-3}$ and T$_{\\rm\ne}=10^{4}$ K \\citep{hummer87}. Excluding the two known blends, the\nbest-fit foreground screen extinction is A$_{\\rm K}=1.1 \\pm 0.3 $ mag\n(dashed curve), assuming the extinction law of \\citet{landini84} and\nevaluated at 2.2 $\\mu$m. We consider this an upper limit on A$_{\\rm\nK}$ because a close look at the spectrum shows that the points above the\ndashed line in Figure 3\n%\\ref{pfund}\nfor Pf 22$-$24 at 2.404, 2.393, and\n2.383 $\\mu$m may also be blended or contaminated by sky emission,\nimplying a lower A$_{\\rm K}$ and a much better fit to the theory.\nHence the majority of the extinction to the cluster is bypassed by\nobserving it in K band. \n\n\\vspace{-0.06in}\n% PFUND FIGURE\n%\\begin{figure}[h]\n%\\begin{center}\n%\\epsfig{file=pffluxes_brg.eps}\n{\\plotfiddle{pffluxes_brg.eps}{2.5in}{0}{100}{100}{0}{5}}\n%\\figcaption[pffluxes_brg.eps]\n{\\footnotesize Figure 3. - \nPfund line fluxes relative to Br$\\gamma$\nflux ($1.05 \\times 10^{-14}$ erg s$^{-1}$cm$^{-2}$). Solid curve is\nunextincted theoretical curve for n$_{\\rm e} = 10^{4}$ cm$^{-3}$,\nT$_{\\rm e}=10^{4}$ K (Hummer \\& Storey 1987). Filled symbols\nrepresent lines that are known blends, and the dashed curve shows\ntheoretical fluxes with the best-fit extinction A$_{\\rm K}=1.1$\nmag.\n%label{pfund} \n}\n%\\end{center}\n%\\end{figure}\n\\vspace{0.04in}\n\nThe lack of a strong Pfund discontinuity at 2.28 $\\mu$m indicates that\nnebular free-free and bound-free continuum is diluted by starlight\nand dust emission (signaled by the rising continuum toward longer\n$\\lambda$) in the cluster.\n\nThe ratios of [\\ion{Fe}{3}] lines are nebular density diagnostics;\nTable 1\n%~\\ref{fetable} \npresents observed ratios and theoretical\npredictions of \\citet{keenan92} for emission from a collisionally\nexcited 10$^4$ K gas, as tabulated by \\citet{luhman98}. The ratios of\n[\\ion{Fe}{3}] 2.146 $\\mu$m and [\\ion{Fe}{3}] 2.243 $\\mu$m to\n[\\ion{Fe}{3}] 2.218 $\\mu$m are consistent with n$_{\\rm e}= 10^{3.5} -\n10^4$ cm$^{-3}$. The ratio [\\ion{Fe}{3}] 2.348 $\\mu$m/[\\ion{Fe}{3}]\n2.218 $\\mu$m is 20\\% higher than its theoretical value, which is\nroughly constant over all of parameter space \\citep{keenan92}, but\n[\\ion{Fe}{3}] 2.348 $\\mu$m is blended with Pf 29 and subject to\nmeasurement errors that are larger than the difference in extinctions\nin question (see Figure 3).\n%\\ref{pfund}). \nEven the minimum value we infer for this ratio, with $A_{\\rm K}=0$, is\nsignificantly greater than the model prediction. High values of\n[\\ion{Fe}{3}] 2.348 $\\mu$m/[\\ion{Fe}{3}] 2.218 $\\mu$m were also\nfound by \\citet{luhman98} in Orion. This discrepancy may be due to\nblending with another unknown line, or to theoretical error; ratios\nfrom the latest calculations have an average deviation from data of\n10\\% \\citep{keenan92}.\n\n\\ion{He}{1} line ratios can in principal be used to infer nebular\ntemperature T$_{\\rm e}$, and are fairly insensitive to n$_{\\rm e}$.\nHowever, of the three lines we detected, two are not suitable for such\nan analysis: the \\ion{He}{1} 2.1615+2.1624 $\\mu$m blend falls on the\nwing of strong Br~$\\gamma$ so its flux has a large (50\\%) measurement\nerror, and the strong \\ion{He}{1} 2.0589 $\\mu$m line is subject to\nradiative transfer and density effects.\n\nThe \\ion{He}{1} 2.0589 $\\mu$m/Br~$\\gamma$ ratio is an indicator of the\nT$_{\\rm eff}$ of hot stars in \\ion{H}{2} regions \\citep{doyon92},\nalthough it is sensitive to nebular conditions such as the relative\nvolumes and ionization fractions of He$^+$ and H$^+$, geometry,\ndensity, dustiness, etc. \\citep{shields93}. \\citet{doherty95} studied\nH and He excitation in a sample of starburst galaxies and \\ion{H}{2}\nregions. For starbursts they found evidence for high-T$_{\\rm eff}$,\nlow-n$_{\\rm e}$ ($\\sim 10^2$ cm$^{-2}$) ionized gas from \\ion{He}{1}\n2.0589 $\\mu$m/Br~$\\gamma$ ratios of 0.22 to 0.64. This is consistent\nwith giant extended \\ion{H}{2} regions expected to dominate the\nemission-line spectra of typical starbursts. The ultra-compact\n\\ion{H}{2} regions were characterized by higher ratios (0.8$-$0.9) and\nhigher densities, $\\sim$ 10$^4$ cm$^{-3}$. The cluster has a flux\nratio of 0.70, a value between the two object classes of\n\\citet{doherty95}. Assuming the line emission is purely nebular, this\nratio is consistent with a high-density (10$^4$ cm$^{-3}$) model of\n\\citet{shields93}, and implies T$_{\\rm eff}\\simeq 39,000$ K for the\nassumed model parameters. This temperature is similar to that derived\nby \\citet{kunze96}, $\\simeq 44,000$ K, from mid-IR SWS line\nobservations in a large aperture on the overlap region of the\nAntennae.\n\n\\vspace{-0.05in}\n% Fe III TABLE\n%\\begin{table}\n\\begin{center}\n{\\centering\n%\\footnotesize \n\\begin{tabular}{lccrcc}\n\\multicolumn{6}{c}{TABLE 1} \\\\\n\\multicolumn{6}{c}{\\sc Cluster [\\ion{Fe}{3}] Line Ratios\\tablenotemark{a}} \\\\\n\\tableline\n\\tableline\n\\multicolumn{1}{c}{} & Rest & Observed & \\multicolumn{3}{c}{Model\nRatio\\tablenotemark{c}} \\\\\n\\cline{4-6}\n\\multicolumn{1}{c}{Transition} & $\\lambda$($\\mu$m)\\tablenotemark{b} & Ratio & \n%n$_{\\rm e}=$\n$10^3$ & $10^4$ & $10^5$ \\\\\n\\tableline\n$^3$G$_{3}-^3$H$_4$ & 2.1457 & 0.14$\\pm$0.02 & 0.10 & 0.17 & 0.34 \\\\\n$^3$G$_{5}-^3$H$_6$ & 2.2183 & 1.00 & 1.00 & 1.00 & 1.00 \\\\\n$^3$G$_{4}-^3$H$_4$ & 2.2427 & 0.28$\\pm$0.02 & 0.26 & 0.29 & 0.38 \\\\\n$^3$G$_{5}-^3$H$_5$ & 2.3485 & 0.80$\\pm$0.03\\tablenotemark{d} & 0.66 & 0.66 & 0.66 \\\\ \n\\tableline\n\\end{tabular}}\n\\end{center}\n\\noindent\n%\\tablenotetext{a}\n{\\footnotesize $^{\\rm a}$\nRatios are dereddened fluxes relative to\n[Fe~{\\sc iii}] 2.2183 $\\mu$m, for which the dereddened flux was\n9.11$\\times$10$^{-16}$ ergs s$^{-1}$ cm$^{-2}$.}\\\\\n%\\tablenotetext{b}\n{\\footnotesize $^{\\rm b}$\n\\citet{sugar85}.} \\\\\n%\\tablenotetext{c}\n{\\footnotesize $^{\\rm c}$\nModels for T$_{\\rm e}$=10$^4$K, values of n$_{\\rm e}$ in cm$^{-3}$\n\\citep{keenan92}.}\\\\\n%\\tablenotetext{d}\n{\\footnotesize $^{\\rm d}$\nFlux determined by subtracting Pf 29 contribution\nobtained for the best-fit Landini extinction curve \nwith A$_{\\rm K}=1.1$ mag.}\\\\\n%\\end{table}\n\\vspace{-0.05in}\n\nThe cluster has properties more like those of a compact \\ion{H}{2}\nregion than a diffuse one. It appears to be a young, hot,\nhigh-density \\ion{H}{2} region, one of the first to form in this part\nof the Antennae interaction region (see \\citealt{habing79} for a\nreview of compact \\ion{H}{2} regions).\n\n\\subsection{Molecular Emission}\n\nThe spectrum shows evidence for almost pure UV fluorescence excited by\nFUV radiation from the O \\& B stars; the strong, vibrationally excited\n1$-$0, 2$-$1 \\& 3$-$2 H$_2$ emission has T$_{\\rm vib} \\ga 6000$~K and\nT$_{\\rm rot}\\simeq 970$, 1600, and 1800 K, respectively, and weak\nhigher-v (6$-$4, 8$-$6, 9$-$7) transitions are present as well. The\nH$_2$ lines are extended over $\\simeq 200$~pc, about twice the extent\nof the continuum and nebular line emission, so a significant fraction\nof the FUV (912$-$1108 \\AA) light escapes from the cluster to heat and\nphotodissociate the local molecular ISM.\n\nWe obtained the photodissociation region (PDR) models of\n\\citet{draine96} and compared them with our data by calculating\nreduced $\\chi_\\nu^2$. Models with high densities (n$_{\\rm H} = 10^5$\ncm$^{-3}$), moderately warm temperatures (T $= 500$ to 1500 K at the\ncloud surface), and high FUV fields (G$_0 = 10^3 - 10^5$ times the mean\ninterstellar field) can reasonably fit the data.\nFigure 4\n%\\ref{chisq} \nshows $\\chi_\\nu^2$ contours for all models projected onto the n$_{\\rm\nH} -$G$_0$ plane. The best-fit Draine \\& Bertoldi model is n2023b,\nwhich has n$_{\\rm H}$ = 10$^5$ cm$^{-3}$, T = 900 K, and G$_0=5000$.\nWe fit 22 H$_2$ lines, excluding 3$-$2 S(2) 2.287 $\\mu$m because it\nappears to be blended with a strong unidentified nebular line at 2.286\n$\\mu$m found in higher-resolution spectra of planetary nebulae\n\\citep{smith81}. The weak high-v transitions are all under-predicted\nby this model, and appear to come from lower-density gas (n$_{\\rm H}\n\\la 10^3-10^4$ cm$^{-3}$) exposed to a weaker FUV field (G$_0 \\la\n10^2-10^3$).\n\nThe ortho/para ratio of excited H$_2$ determined from the relative\ncolumn densities in v=1, J=3 and J=2 inferred from 1$-$0 S(1) and S(0)\nlines is 1.62$\\pm$0.07. This is consistent with the ground state v=0,\nJ=1 and J=0 H$_2$ being in LTE with ortho/para ratio of 3 if the FUV\nabsorption lines populating the non-LTE excited states are optically\nthick \\citep{sternberg99}. Indeed, the best-fit PDR models have\ntemperatures that are comparable with T$_{\\rm rot}$ in the lowest\nexcited states, as well as with the warm gas kinetic temperature in\nthe Galactic PDR M16, T = 930$\\pm$50 K, measured by\n\\citet{levenson99}.\n\nIf the extent of the H$_2$ emission indicates that the mean-free path\nof a FUV photon is $\\sim 200$ pc, then $\\langle$n$_{\\rm H}\\rangle$ = 3\ncm$^{-3}$ for a Galactic gas-to-dust ratio, while in the PDR(s)\nn$_{\\rm H}$ = 10$^4-10^6$ cm$^{-3}$. This implies that the molecular\ngas is extremely clumpy, which is consistent with the range of\ndensities inferred from the detection of anomalously strong v = 8$-$6\nH$_2$ emission.\n\n\n\\section{NGC 4039 Nucleus}\n\nThe spectrum of the nucleus of NGC~4039 is marked by strong stellar\ncontinuum and bright, extended H$_2$ emission. Strong photospheric\n\\ion{Mg}{1}, \\ion{Na}{1}, \\ion{Ca}{1} absorption and CO $\\Delta v=2$\nbands indicate that the continuum is dominated by old giants. The CO\nband head is stronger than that of a M2III, suggesting some\ncontribution from red supergiants. The absence of Br$\\gamma$ emission\nimplies that star formation is currently extinct in the nucleus.\nSpatially extended, collisionally excited H$_2$ emission in the\nnucleus may be excited by SNR shocks from the last generation of\nnuclear star formation, or by merger-induced cloud collisions. We\ndefer detailed analysis of the nuclear spectrum to a later paper.\n\n\n\\section{Conclusions}\n\nThe highest surface brightness mid-IR peak in the ISO map of the\nAntennae Galaxies is a massive ($\\sim 16\\times$10$^6$ M$_{\\odot}$),\nobscured (A$_{\\rm V} \\sim 9-10$), young (age $\\sim 4$ Myr) star\ncluster with half-light radius $\\sim$ 32 pc, whose strong FUV flux\nexcites the surrounding molecular ISM on scales of up to 200 pc. The\ncluster spectrum is dominated by extended fluorescently excited\nH$_{2}$ emission from clumpy PDRs and nebular emission from compact\n\\ion{H}{2} regions. In contrast, the nearby nucleus of NGC~4039 has a\nstrong stellar spectrum dominated by cool stars, where the only\nemission lines are due to shock-excited H$_2$. These observations\nconfirm the potential of near-infrared spectroscopy for exploration\nand discovery with the new generation of large ground-based\ntelescopes. Our ongoing program of NIRSPEC observations promises\nto reveal a wealth of information on the nature of star formation in\nstar clusters.\n\n\\vspace{-0.05in}\n% FIGURE chisq contours\n%\\begin{figure}[h]\n%\\begin{center}\n%\\epsfig{file=chi2temp.eps}\n{\\plotfiddle{chi2temp_col.eps}{2.55in}{0}{100}{100}{0}{10}} \n%\\figcaption[chi2temp.eps]\n{\\footnotesize Figure 4. - \nComparison of H$_2$ line strengths with PDR models.\nContours of $\\chi^2_\\nu$ for 22 lines projected onto n$_{\\rm\nH} -$G$_0$ plane peak at n$_{\\rm H} \\sim 10^5$ cm$^{-3}$ and G$_0 \\sim\n5000$. Model points (+) are for T$_0$ = 300 $-$ 2000\nK. White + marks best-fit PDR model of Draine \\& Bertoldi, with T$_0$\n= 900 K and $\\chi_\\nu^2=9.3$. Contours are 50, 25, 20, 15, 12, 10.\n%label{chisq}\n}\n%\\end{center}\n%\\end{figure}\n%\\vspace{0.0005in}\n\n\\acknowledgements \n\nWe acknowledge the hard work of past and present members of the UCLA\nNIRSPEC team: M. Angliongto, O. Bendiksen, G. Brims, L. Buchholz,\nJ. Canfield, K. Chin, J. Hare, F. Lacayanga, S. Larson, T. Liu, N.\nMagnone, G. Skulason, M. Spencer, J. Weiss and W. Wong. We thank\nKeck Director Chaffee and all the CARA staff involved in the\ncommissioning and integration of NIRSPEC, particularly instrument\nspecialist T. Bida. We especially thank Observing Assistants\nJ. Aycock, G. Puniwai, C. Sorenson, R. Quick and W. Wack for their\nsupport. We also thank A. Sternberg for valuable discussions. We are\ngrateful to R. Benjamin for providing us with He~{\\sc i} emissivity\ndata. AMG acknowledges support from a NASA GSRP grant.\n\n\\begin{thebibliography}{27}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n%\\bibitem[{{Benjamin} {et~al.}(1999){Benjamin}, {Skillman}, \\&\n% {Smits}}]{benjamin99}\n%{Benjamin}, R.~A., {Skillman}, E.~D., \\& {Smits}, D.~P. 1999, \\apj, 514, 307\n\n\\bibitem[{{Doherty} {et~al.}(1995){Doherty}, {Puxley}, {Lumsden}, \\&\n {Doyon}}]{doherty95}\n{Doherty}, R.~M., {Puxley}, P.~J., {Lumsden}, S.~L., \\& {Doyon}, R. 1995,\n \\mnras, 277, 577\n\n\\bibitem[{{Doyon} {et~al.}(1992){Doyon}, {Puxley}, \\& {Joseph}}]{doyon92}\n{Doyon}, R., {Puxley}, P.~J., \\& {Joseph}, R.~D. 1992, \\apj, 397, 117\n\n\\bibitem[{{Draine} \\& {Bertoldi}(1996)}]{draine96}\n{Draine}, B.~T. \\& {Bertoldi}, F. 1996, \\apj, 468, 269\n\n\\bibitem[{{Fabbiano} {et~al.}(1997){Fabbiano}, {Schweizer}, \\&\n {Mackie}}]{fabbiano97}\n{Fabbiano}, G., {Schweizer}, F., \\& {Mackie}, G. 1997, \\apj, 478, 542\n\n\\bibitem[{{Habing} \\& {Israel}(1979)}]{habing79}\n{Habing}, H.~J. \\& {Israel}, F.~P. 1979, \\araa, 17, 345\n\n%\\bibitem[{{Hillenbrand}(1997)}]{hillenbrand97}\n%{Hillenbrand}, L.~A. 1997, \\aj, 113, 1733\n\n\\bibitem[{{Hummel} \\& {van der Hulst}(1986)}]{hummel86}\n{Hummel}, E. \\& {van der Hulst}, J.~M. 1986, \\aap, 155, 151\n\n\\bibitem[{{Hummer} \\& {Storey}(1987)}]{hummer87}\n{Hummer}, D.~G. \\& {Storey}, P.~J. 1987, \\mnras, 224, 801\n\n\\bibitem[{{Hunter} {et~al.}(1995){Hunter}, {Shaya}, {Holtzman}, {Light},\n {O'Neil}, \\& {Lynds}}]{hunter95}\n{Hunter}, D.~A., {Shaya}, E.~J., {Holtzman}, J.~A., {Light}, R.~M., {O'Neil},\n E.~J., J., \\& {Lynds}, R. 1995, \\apj, 448, 179\n\n\\bibitem[{{Keenan} {et~al.}(1992){Keenan}, {Berrington}, {Burke}, {Zeippen},\n {Le Dourneuf}, \\& {Clegg}}]{keenan92}\n{Keenan}, F.~P., {Berrington}, K.~A., {Burke}, P.~G., {Zeippen}, C.~J., {Le\n Dourneuf}, M., \\& {Clegg}, R. E.~S. 1992, \\apj, 384, 385\n\n\\bibitem[{{Kunze} {et~al.}(1996)}]{kunze96}\n{Kunze}, D., et~al. 1996, \\aap, 315, L101\n\n\\bibitem[{{Landini} {et~al.}(1984){Landini}, {Natta}, {Salinari}, {Oliva}, \\&\n {Moorwood}}]{landini84}\n{Landini}, M., {Natta}, A., {Salinari}, P., {Oliva}, E., \\& {Moorwood}, A.\n F.~M. 1984, \\aap, 134, 284\n\n\\bibitem[{{Leitherer} {et~al.}(1999)}]{leitherer99}\n{Leitherer}, C., et~al. 1999, \\apjs, 123, 3\n\n\\bibitem[{{Levenson} {et~al.}(1999)}]{levenson99}\n{Levenson}, N.~A., et~al. 2000, to appear in ApJL\n\n\\bibitem[{{Luhman} {et~al.}(1998){Luhman}, {Engelbracht}, \\&\n {Luhman}}]{luhman98}\n{Luhman}, K.~L., {Engelbracht}, C.~W., \\& {Luhman}, M.~L. 1998, \\apj, 499, 799\n\n\\bibitem[{{McLean} {et~al.}(1998)}]{mclean98}\n{McLean}, I.~S., et~al. 1998, \\procspie, 3354, 566\n\n\\bibitem[{{Mirabel} {et~al.}(1998)}]{mirabel98}\n{Mirabel}, I.~F., et~al. 1998, \\aap, 333, L1\n\n\\bibitem[{{Nikola} {et~al.}(1998){Nikola}, {Genzel}, {Herrmann}, {Madden},\n {Poglitsch}, {Geis}, {Townes}, \\& {Stacey}}]{nikola98}\n{Nikola}, T., {Genzel}, R., {Herrmann}, F., {Madden}, S.~C., {Poglitsch}, A.,\n {Geis}, N., {Townes}, C.~H., \\& {Stacey}, G.~J. 1998, \\apj, 504, 749\n\n\\bibitem[{{Rieke} \\& {Lebofsky}(1985)}]{rieke85}\n{Rieke}, G.~H. \\& {Lebofsky}, M.~J. 1985, \\apj, 288, 618\n\n\\bibitem[{{Shields}(1993)}]{shields93}\n{Shields}, J.~C. 1993, \\apj, 419, 181\n\n\\bibitem[{{Smith} {et~al.}(1981){Smith}, {Larson}, \\& {Fink}}]{smith81}\n{Smith}, H.~A., {Larson}, H.~P., \\& {Fink}, U. 1981, \\apj, 244, 835\n\n\\bibitem[{{Stanford} {et~al.}(1990){Stanford}, {Sargent}, {Sanders}, \\&\n {Scoville}}]{stanford90}\n{Stanford}, S.~A., {Sargent}, A.~I., {Sanders}, D.~B., \\& {Scoville}, N.~Z.\n 1990, \\apj, 349, 492\n\n\\bibitem[{{Sternberg} \\& {Neufeld}(1999)}]{sternberg99}\n{Sternberg}, A. \\& {Neufeld}, D.~A. 1999, \\apj, 516, 371\n\n\\bibitem[{{Sugar} \\& {Corliss}(1985)}]{sugar85}\n{Sugar}, J. \\& {Corliss}, C. 1985, Atomic energy levels of the iron-period\n elements: Potassium through Nickel (Washington: American Chemical Society,\n 1985)\n\n\\bibitem[{{Whitmore} \\& {Schweizer}(1995)}]{whitmore95}\n{Whitmore}, B.~C. \\& {Schweizer}, F. 1995, \\aj, 109, 960\n\n\\bibitem[{{Whitmore} {et~al.}(1999){Whitmore}, {Zhang}, {Leitherer}, {Fall},\n {Schweizer}, \\& {Miller}}]{whitmore99}\n{Whitmore}, B.~C., {Zhang}, Q., {Leitherer}, C., {Fall}, S.~M., {Schweizer},\n F., \\& {Miller}, B.~W. 1999, \\aj\n\n%\\bibitem[{{Whitmore} \\& {Zhang}(1999)}]{whitmorecomm}\n%{Whitmore}, B.~C. \\& {Zhang}, Q. 1999, Private Communication\n\n\\end{thebibliography}\n\n\\end{document}\n\n%%% Local Variables: \n%%% mode: latex\n%%% TeX-master: t\n%%% End: \n\n"
}
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[
{
"name": "astro-ph0002357.extracted_bib",
"string": "\\begin{thebibliography}{27}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n%\\bibitem[{{Benjamin} {et~al.}(1999){Benjamin}, {Skillman}, \\&\n% {Smits}}]{benjamin99}\n%{Benjamin}, R.~A., {Skillman}, E.~D., \\& {Smits}, D.~P. 1999, \\apj, 514, 307\n\n\\bibitem[{{Doherty} {et~al.}(1995){Doherty}, {Puxley}, {Lumsden}, \\&\n {Doyon}}]{doherty95}\n{Doherty}, R.~M., {Puxley}, P.~J., {Lumsden}, S.~L., \\& {Doyon}, R. 1995,\n \\mnras, 277, 577\n\n\\bibitem[{{Doyon} {et~al.}(1992){Doyon}, {Puxley}, \\& {Joseph}}]{doyon92}\n{Doyon}, R., {Puxley}, P.~J., \\& {Joseph}, R.~D. 1992, \\apj, 397, 117\n\n\\bibitem[{{Draine} \\& {Bertoldi}(1996)}]{draine96}\n{Draine}, B.~T. \\& {Bertoldi}, F. 1996, \\apj, 468, 269\n\n\\bibitem[{{Fabbiano} {et~al.}(1997){Fabbiano}, {Schweizer}, \\&\n {Mackie}}]{fabbiano97}\n{Fabbiano}, G., {Schweizer}, F., \\& {Mackie}, G. 1997, \\apj, 478, 542\n\n\\bibitem[{{Habing} \\& {Israel}(1979)}]{habing79}\n{Habing}, H.~J. \\& {Israel}, F.~P. 1979, \\araa, 17, 345\n\n%\\bibitem[{{Hillenbrand}(1997)}]{hillenbrand97}\n%{Hillenbrand}, L.~A. 1997, \\aj, 113, 1733\n\n\\bibitem[{{Hummel} \\& {van der Hulst}(1986)}]{hummel86}\n{Hummel}, E. \\& {van der Hulst}, J.~M. 1986, \\aap, 155, 151\n\n\\bibitem[{{Hummer} \\& {Storey}(1987)}]{hummer87}\n{Hummer}, D.~G. \\& {Storey}, P.~J. 1987, \\mnras, 224, 801\n\n\\bibitem[{{Hunter} {et~al.}(1995){Hunter}, {Shaya}, {Holtzman}, {Light},\n {O'Neil}, \\& {Lynds}}]{hunter95}\n{Hunter}, D.~A., {Shaya}, E.~J., {Holtzman}, J.~A., {Light}, R.~M., {O'Neil},\n E.~J., J., \\& {Lynds}, R. 1995, \\apj, 448, 179\n\n\\bibitem[{{Keenan} {et~al.}(1992){Keenan}, {Berrington}, {Burke}, {Zeippen},\n {Le Dourneuf}, \\& {Clegg}}]{keenan92}\n{Keenan}, F.~P., {Berrington}, K.~A., {Burke}, P.~G., {Zeippen}, C.~J., {Le\n Dourneuf}, M., \\& {Clegg}, R. E.~S. 1992, \\apj, 384, 385\n\n\\bibitem[{{Kunze} {et~al.}(1996)}]{kunze96}\n{Kunze}, D., et~al. 1996, \\aap, 315, L101\n\n\\bibitem[{{Landini} {et~al.}(1984){Landini}, {Natta}, {Salinari}, {Oliva}, \\&\n {Moorwood}}]{landini84}\n{Landini}, M., {Natta}, A., {Salinari}, P., {Oliva}, E., \\& {Moorwood}, A.\n F.~M. 1984, \\aap, 134, 284\n\n\\bibitem[{{Leitherer} {et~al.}(1999)}]{leitherer99}\n{Leitherer}, C., et~al. 1999, \\apjs, 123, 3\n\n\\bibitem[{{Levenson} {et~al.}(1999)}]{levenson99}\n{Levenson}, N.~A., et~al. 2000, to appear in ApJL\n\n\\bibitem[{{Luhman} {et~al.}(1998){Luhman}, {Engelbracht}, \\&\n {Luhman}}]{luhman98}\n{Luhman}, K.~L., {Engelbracht}, C.~W., \\& {Luhman}, M.~L. 1998, \\apj, 499, 799\n\n\\bibitem[{{McLean} {et~al.}(1998)}]{mclean98}\n{McLean}, I.~S., et~al. 1998, \\procspie, 3354, 566\n\n\\bibitem[{{Mirabel} {et~al.}(1998)}]{mirabel98}\n{Mirabel}, I.~F., et~al. 1998, \\aap, 333, L1\n\n\\bibitem[{{Nikola} {et~al.}(1998){Nikola}, {Genzel}, {Herrmann}, {Madden},\n {Poglitsch}, {Geis}, {Townes}, \\& {Stacey}}]{nikola98}\n{Nikola}, T., {Genzel}, R., {Herrmann}, F., {Madden}, S.~C., {Poglitsch}, A.,\n {Geis}, N., {Townes}, C.~H., \\& {Stacey}, G.~J. 1998, \\apj, 504, 749\n\n\\bibitem[{{Rieke} \\& {Lebofsky}(1985)}]{rieke85}\n{Rieke}, G.~H. \\& {Lebofsky}, M.~J. 1985, \\apj, 288, 618\n\n\\bibitem[{{Shields}(1993)}]{shields93}\n{Shields}, J.~C. 1993, \\apj, 419, 181\n\n\\bibitem[{{Smith} {et~al.}(1981){Smith}, {Larson}, \\& {Fink}}]{smith81}\n{Smith}, H.~A., {Larson}, H.~P., \\& {Fink}, U. 1981, \\apj, 244, 835\n\n\\bibitem[{{Stanford} {et~al.}(1990){Stanford}, {Sargent}, {Sanders}, \\&\n {Scoville}}]{stanford90}\n{Stanford}, S.~A., {Sargent}, A.~I., {Sanders}, D.~B., \\& {Scoville}, N.~Z.\n 1990, \\apj, 349, 492\n\n\\bibitem[{{Sternberg} \\& {Neufeld}(1999)}]{sternberg99}\n{Sternberg}, A. \\& {Neufeld}, D.~A. 1999, \\apj, 516, 371\n\n\\bibitem[{{Sugar} \\& {Corliss}(1985)}]{sugar85}\n{Sugar}, J. \\& {Corliss}, C. 1985, Atomic energy levels of the iron-period\n elements: Potassium through Nickel (Washington: American Chemical Society,\n 1985)\n\n\\bibitem[{{Whitmore} \\& {Schweizer}(1995)}]{whitmore95}\n{Whitmore}, B.~C. \\& {Schweizer}, F. 1995, \\aj, 109, 960\n\n\\bibitem[{{Whitmore} {et~al.}(1999){Whitmore}, {Zhang}, {Leitherer}, {Fall},\n {Schweizer}, \\& {Miller}}]{whitmore99}\n{Whitmore}, B.~C., {Zhang}, Q., {Leitherer}, C., {Fall}, S.~M., {Schweizer},\n F., \\& {Miller}, B.~W. 1999, \\aj\n\n%\\bibitem[{{Whitmore} \\& {Zhang}(1999)}]{whitmorecomm}\n%{Whitmore}, B.~C. \\& {Zhang}, Q. 1999, Private Communication\n\n\\end{thebibliography}"
}
] |
astro-ph0002358
|
Photometric Properties of Low Redshift Galaxy Clusters
|
[
{
"author": "W.A. Barkhouse and H.K.C. Yee"
}
] |
%
|
[
{
"name": "barkhousew.tex",
"string": "\\documentstyle[11pt,newpasp,twoside]{article}\n\\markboth{Author \\& Co-author}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{Photometric Properties of Low Redshift Galaxy Clusters}\n \\author{W.A. Barkhouse and H.K.C. Yee}\n\\affil{Department of Astronomy, Universiy of Toronto, 60 Saint George St. \nToronto, Ont. M5S 1A7, Canada}\n\\author{O. L{\\'o}pez-Cruz}\n\\affil{INAOE-Tonantzintla, Tonantzintla Pue. M{\\'e}xico}\n\n%\\begin{abstract}\n%\\end{abstract}\n%\\keywords{Galaxies: Clusters: General, Galaxies: Luminosity function: Dwarf,\n%Galaxies} \n%\\section{Introduction and Preliminary Results}\n\\section{Preliminary Results}\n\nA recent comprehensive photometric survey of 45 low-{\\it z} X-ray selected\n Abell \nclusters (L{\\'o}pez-Cruz 1997) has measured significant variations in the \nfaint end slope of the luninosity function (LF). This result has indicated\n that \ndwarf galaxies (dGs) have different mixtures in relation with the cluster\n environment. Clusters having a central ``cD-like'' galaxy have a flatter \nfaint end slope than non-cD clusters. Also, cD clusters were found to have \na dwarf-to-giant ratio (D/G) which was smaller than non-cD clusters. \nL{\\'o}pez-Cruz et al. (1997) has suggested that the light contained in cD envelopes \ncan be accounted for by assuming that it is produced from stars that \noriginally formed dGs. In this simple model, the D/G would be expected to\n increase with radial distance from the cluster centre due to the decrease \nin the disruptive forces. \n\nIn order to test the dG disruption model, {\\it B} and {\\it R} band images\n of a sample of \n27 low-{\\it z} ($0.02 \\leq z \\leq 0.04$) Abell clusters have been obtained \nwith the 8k CCD mosaic camera on the KPNO 0.9m telescope. This\n telescope/detector combination provides a $1^{o}\\times 1^{o}$ field of \nview, giving an areal coverage of $1-2h^{-1}$ Mp$c^{2}$.\nThese observations will allow us to \nprobe several magnitudes deeper than the L{\\'o}pez-Cruz (1997) survey and \nprovide a definitive measure of the dG LF. \nPreliminary LFs \nand D/G ratios have been calculated\n for five clusters (A1185, A1656, A2151, A2152, and A2197). \nA significant increase\n in the faint end slope between the inner (0.0-0.75 Mpc) and outer\n(0.75-1.50 Mpc) LF can be seen for A2151\n ($H_{o}=~50~{\\rm km~s^{-1}~Mpc^{-1}}$).\n This indicates that the number of dGs, defined as the ratio of the number \nof galaxies with $-19\\leq M_{R} \\leq -15$ to those with $M_{R} < -19.5$, \n has increased in the outer radial bin\n as compared to the inner cluster region.\nAll five clusters also show a \nsignificant dip in the LF at $M_{R} \\sim -19$. This dip suggests that the LF\n can be \nmodelled by 2 components: a log-normal bright component, and a Schecheter \nfunction faint component.\n \n\n\n\n\n\\begin{references}\n\n\\reference L{\\'o}pez-Cruz, O., Yee, H.K.C., Brown, J.P., Jones, C.\n \\& Forman, W. 1997, ApJ, 476, L97\n\n\\reference L{\\'o}pez-Cruz, O. 1997, Ph.D thesis, University of Toronto\n\n\\end{references}\n\n\n\n\n\n\n\n\\end{document}\n\n\n\n"
}
] |
[] |
astro-ph0002359
|
[
{
"author": "M. P. Freeman"
},
{
"author": "British Antarctic Survey"
},
{
"author": "Cambridge"
},
{
"author": "CB3 0ET"
},
{
"author": "UK."
},
{
"author": "S.~C. Chapman"
},
{
"author": "Space and Astrophysics Group"
},
{
"author": "Coventry"
},
{
"author": "CV4 7AL"
},
{
"author": "R.~O. Dendy"
},
{
"author": "EURATOM/UKAEA Fusion Association"
},
{
"author": "Culham Science Centre"
},
{
"author": "Abingdon"
},
{
"author": "Oxfordshire"
},
{
"author": "OX14 3DB"
},
{
"author": "UK. %"
}
] |
As noted by Chang, the hypothesis of Self-Organised Criticality provides a theoretical framework in which the low dimensionality seen in magnetospheric indices can be combined with the scaling seen in their power spectra and with observed plasma bursty bulk flows. As such, it has considerable appeal, describing the aspects of the magnetospheric fuelling:storage:release cycle which are generic to slowly-driven, interaction-dominated, thresholded systems rather than unique to the magnetosphere. In consequence, several recent numerical ``sandpile" algorithms have been used with a view to comparison with magnetospheric observables. However, demonstration of SOC in the magnetosphere will require further work in the definition of a set of observable properties which are the unique ``fingerprint" of SOC. This is because, for example, a scale-free power spectrum admits several possible explanations other than SOC. A more subtle problem is important for both simulations and data analysis when dealing with multiscale and hence broadband phenomena such as SOC. This is that finite length systems such as the magnetosphere or magnetotail will by definition give information over a small range of orders of magnitude, and so scaling will tend to be narrowband. Here we develop a simple framework in which previous descriptions of magnetospheric dynamics can be described and contrasted. We then review existing observations which are indicative of SOC, and ask if they are sufficient to demonstrate it unambiguously, and if not, what new observations need to be made?
|
[
{
"name": "astro-ph0002359.tex",
"string": "\\documentstyle[12pt,psfig]{article}\n%\\renewcommand{\\baselinestretch}{2}\n% Uncomment above for double space\n% Incorporates Mark's postsubmission comments 29/11/99. \n \\setcounter{secnumdepth}{0}\n\n% If you want LaTeX to automatically number your \n% sections, type \\setcounter{secnumdepth}{4} in\n% the preamble of your input file, as shown. If \n% you do not want section numbers, type\n% \\setcounter{secnumdepth}{0}.\n \n\\begin{document}\n\n{\\large Testing the\nSOC hypothesis for the magnetosphere}\\\\\n\n%\\author{\n\\noindent N.~W. Watkins\\footnote{Corresponding author: Fax: +44 1223 221226, Email\naddress: NWW@bas.ac.uk}, M. P. Freeman, \\\\\n British Antarctic Survey, Cambridge, CB3 0ET, UK. \\\\ \\\\\n S.~C. Chapman, \\\\ Space and Astrophysics Group,\\\\\nUniversity of Warwick, Coventry, CV4 7AL, UK. \\\\ \\\\\n R.~O. Dendy, \\\\ EURATOM/UKAEA Fusion Association, Culham Science Centre,\\\\\n Abingdon, Oxfordshire, OX14 3DB, UK. \n %}\n\n \n%\\maketitle \n\n \n\\begin{abstract} \n \nAs noted by Chang, the hypothesis of Self-Organised Criticality provides a theoretical framework in\nwhich the low dimensionality seen in magnetospheric indices can be combined with the scaling seen\nin their power spectra and with observed plasma bursty bulk flows. As such, it has considerable\nappeal, describing the aspects of the magnetospheric fuelling:storage:release cycle which are generic\nto slowly-driven, interaction-dominated, thresholded systems rather than unique to the\nmagnetosphere. In consequence, several recent numerical ``sandpile\" algorithms have been used with a\nview to comparison with magnetospheric observables. However, demonstration of SOC in the magnetosphere will\nrequire further work in the definition of a set of observable properties which are the unique ``fingerprint\"\nof SOC. This is because, for example, a scale-free power spectrum admits several possible explanations\nother than SOC. A more subtle problem is important for\nboth simulations and data analysis when dealing with multiscale and \nhence broadband phenomena such\nas SOC. This is that finite length systems such as the magnetosphere \nor magnetotail will by definition give information\nover a small range of orders of magnitude, and so scaling will\ntend to be narrowband. Here we develop a simple framework in which previous descriptions of magnetospheric dynamics\ncan be described and contrasted. We then review existing observations which are indicative of SOC, and\nask if they are sufficient to demonstrate it unambiguously, and if not, what new observations need\nto be made?\n \n\\end{abstract} \n \n\\section{1. Introduction: Few-parameter models for magnetospheric dynamics}\n \n \nThere is growing evidence that the coupled solar wind-magnetosphere\n-ionosphere (SW-M-I) system, viewed as a whole, is non-equilibrium, driven, dissipative\nand nonlinear (V\\\"{o}r\\\"{o}s, 1991). That this should be so is reasonable, given that the magnetosphere\nis a complex system, with multiple self-interacting phenomena, occurring on a vast range of length\nand time scales. A consequence of this view is that part or all of the observed magnetospheric phenomenology may be\na manifestation of physics resulting from the underlying complexity of the whole system.\nBecause of their analytical intractability, such systems in space physics are typically studied using\n a ``large\" (i.e. many-parameter) numerical simulation code.\n More recently, however, some systems of this type in nature have been shown to lend themselves\n to few-parameter descriptions (Hastings and Sugihara, 1993), which arise because, paradoxically, the complexity of the system\n gives rise to simplicity in some of its observable characteristics.\nExamples of such descriptions are shown in the top row of Table 1, \n adapted from figure 7.1 of Hastings and Sugihara, (1993).\n Starting with the simplest, ``linear plus noise\" description, applied\n to the magnetosphere by Bargatze et al., (1985), we go to low dimensional nonlinear ``chaotic\" models such as\n Baker et al. (1990)'s modified ``dripping tap\". We then see fractional Brownian\n motion (fBm), used by Takalo et al., (1994), as a null hypothesis against which chaos\n could be tested and finally we have Self-Organised Criticality (SOC), the magnetospheric application\n of which is due to Chang, (1992).\n Few-parameter models of intrinsically complex systems\n have already demonstrated their value in space physics by their ability \n to describe reproducible aspects of the magnetosphere's behaviour \n and to motivate nonlinear predictive filters for geomagnetic activity\n (see the reviews of Klimas et al., 1996 and Sharma, 1995). The extent to which such models\nare applicable bears directly on the extent to which magnetospheric (and other laboratory\n or astrophysical macroscopic plasma systems) may have predictable phenomenology.\n In consequence the study of few parameter models for energetically open but spatially confined plasma \n systems is a highly topical subject both with respect to the magnetospheric confinement system\n (e.g. Angelopoulos et al., 1999; Baker et al., 1999; Horton et al., 1999) and to magnetically confined \n laboratory plasmas (e.g. Dendy and Helander, 1997; Carreras et al., 1999; Pedrosa\n et al., 1999). One possible new approach of considerable\n current interest is the SOC paradigm introduced\n by Bak et al. (1987).\n \n \n There is a natural hierarchy of few-parameter descriptions, ordered by the extent to which\n the many coupled degrees of freedom of the system manifest themselves.\n Broadly speaking, as we go from left to right along Table 1, we move down the hierarchy\n of description and the large number of degrees of freedom become increasingly\n explicit in the description. In consequence the importance of an underlying theory to define the model fully\n tends to also increase. To make effective use of the theory-model correspondence in such a table, however, \ntheories must be falsifiable, as otherwise the parameters of the simple model may simply be ``tuned\" to bring it into\ncloser and closer agreement with data. This may be a two-way process, as for example, casting \n a given model in falsifiable form by defining which phenomena\n must be tested for helps to clarify the underlying theory.\n \n To make these abstract points more concrete, consider Table 1. The first row shows some notable examples of \n various simple models that have been applied both to the complex magnetospheric system, and\nto other such complex systems. \nThe first column shows various \nproperties that these models have which could be tested for in data, provided that\nsuitable variables are measurable. If a given property can\nbe shown not to be present in data then we can eliminate models which depend on it from consideration.\n In this paper we first describe the construction\n of Table 1 by describing the four levels of description which it encapsulates. As models\n based on the SOC hypothesis are of current\n interest for the SW-M-I coupling problem, we then\n specifically address the tests necessary to cast SOC models in falsifiable form.\n \n % We stress that the approach discussed is more general and applies to any model \n%that are few-parameter in this sense. We do not expect it to\n%be directly applicable to the scenarios usually referred to as ``substorm models\"\n%(see for example those described in the review of (Lui, 199x)) because they evolve incrementally \n%with input from data. It may however be possible to develop falsifiable \n%theories from these scenarios to which the current methods can be applied\n% provided that their predictions can be sufficiently well quantified or differentiated from\n%each other. \n \n\\subsection {2.1 Linear models with optional noise term}\n \n Column 1 of Table 1 is the ``linear + noise\" model, typically a linear\n differential equation with\n optionally a stochastic noise term $\\Delta {\\bf w}(t)$, (adopting \n the notation of Hastings and Sugihara (1993))\n to which we may also add a driving term ${\\bf F(t)}$:\n \\begin{equation}\n \\frac{d {\\bf x}(t)}{dt} ={\\bf g}({\\bf x},t) + \\Delta {\\bf w}(t) + {\\bf F}(t)\n \\end{equation}\n where ${\\bf g}({\\bf x},t)$ can only be linear in the variables ${\\bf x}$.\n Physically an input-output system is linear if the \n form of a system's response closely resembles that of the forcing terms.\n This \n %of course can only apply if the intrinsic nonlinearity of the magnetospheric system's response\n %can be neglected, and \n was the first level of approximation used in the\n input-output analysis of the SW-M-I system (Bargatze et al., 1985). \n %If the evolution of the system described\n %by ${\\bf x}$ is not explicitly time dependent, i.e. if ${\\bf g}({\\bf x},t)\n % = {\\bf g}({\\bf x}(t))$,\n %the noise term $\\Delta {\\bf w}(t)$ is $0$ and the time dependence of ${\\bf F}$ is implicit, we\n %obtain an autonomous linear differential equation. \n %Physically this may result from \n %a driver without ``interesting\" time dependence, so F then becomes incorporated in g i.e. \n %the driver variables become output variables [?].\n The second and third rows of the table, labelled ``Short-\" and ``long-term predictable\" refer to the fact that \nin the absence of noise ($\\Delta {\\bf w}(t) = 0$) the short-and long-term behaviour of equation\n (1) is completely deterministic, while even if an additive stochastic\n noise term is\n present, closely-spaced initial conditions do not show exponential divergence. Such systems\n typically show relatively narrow-band spectral behaviour\n if the ${\\bf g}$ term is dominant i.e. characteristic frequencies,\n and so we have ``no\" in the ``global scaling\" row\n for this model (row 4, column 2) to indicate that they would then\n not be scale free\n across the whole frequency range. They may, however,\n show regions of scale free behaviour in their frequency spectra, indicated in the table by the \n ``sometimes\" in the ``scaling regions\" row (column 2, row 5). The entry ``no\"\n for ``low G-P dimension\" (sixth row, column two), refers to the fact that such a system will usually appear high dimensional to the\n Grassberger-Procaccia (GP) algorithm (Grassberger and Procaccia, 1983), because of many degrees\n of freedom of the noise term.\n \n \n \\subsection{2.2 Nonlinear deterministic models}\n \n Bargatze et al. (1985) confirmed the presence of nonlinearity in the $AE$ family of indices, \n ($AE, AU$, and $AL$) and hence the need for a next level of approximation.\n A prototype for differential equation models which exhibit nonlinear but deterministic dynamics (see the reviews\n of Sharma (1995) and Klimas et al. (1996)) is\n the ``dripping faucet\" of Shaw (1984), which was \n adapted to the magnetospheric problem by Baker at al. (1990).\n These models are of the form\n \\begin{equation}\n \\frac{d {\\bf x}(t)}{dt} ={\\bf g}({\\bf x},t)) + {\\bf F}(t)\n \\end{equation}\n where unlike equation (1) the term ${\\bf g}({\\bf x},t)$ now contains nonlinear terms.\nIn the hierarchy of Table 1, this is a nonlinear model, which can\nexhibit low-dimensional, chaotic dynamics \n(column 3). Familiar examples of such systems in nonlinear physics include the (continuous) driven nonlinear \npendulum and (discrete) logistic map (see e.g. Rowlands, 1990). \nIn the magnetosphere this description was inspired by an analogy between a \ndripping tap and plasmoid ejection during substorms. The analogy was developed into a simplified magnetospheric\n model by estimating the large-scale\nelectrical properties of the M-I system and combining these electrical components into a \ndriven nonlinear oscillator circuit model\n(Klimas et al., 1992). It has been further developed into a plasma physics model by Horton and Doxas (1996).\n\nIn the case of a dissipative, driven, autonomous low dimensional system such\n as the Lorenz model, the dynamics, rather than exploring all of phase space \n ergodically, collapses onto a low dimensional region called an {\\em attractor}. This attractor has \n fractional dimension (i.e. it is a strange attractor, in contrast for example \n with the 2D ellipse described in phase space by a simple linear 1D pendulum). A time series drawn from such\na system will thus also have low fractional dimension when tested with the Grassberger-Procaccia algorithm,\n so we write ``yes\" against ``Low G-P dimension\" in column 3, row 6 of table 1. A\n strange attractor has the property that closely-spaced\n trajectories, with initial conditions identical to within\n measurement error, will diverge strongly if they traverse certain regions of the attractor\n i.e. repulsive fixed points (see figure 1 of Palmer, (1993) for a clear illustration of this). We thus write ``no\" \n against ``long-term predictability\" (column 3, row 3), because\n in this sense, measured by a positive Lyapunov\n exponent (e.g. Rowlands, 1990), it is now not present. The significance of this \n ``new\" low-dimensional, deterministic, chaos is that sensitive dependence on initial conditions\n arises from the ${\\bf g}$ term and so exists without the presence of ``old fashioned\" stochasticity i.e. we need no \n $\\Delta {\\bf w}$ term. \nSuch a model can generate wide-band, scale free ``1/f\" spectral behaviour when \n near a tangent bifurcation leading to intermittency (Lichtenberg and Lieberman, 1992), \nbut this requires choice of certain values of the control parameters i.e. tuning.\n We thus write ``sometimes\" for against ``global scaling\" and ``scaling regions\".\n ``Tuning\" in this sense\n has been considered a weakness in the applicability of low dimensional chaos to any\n complex natural system (Bak, 1997), not only the magnetosphere.\nA second practical question with such methods is that because the model definition usually starts from\n the observables, the map to which one applies nonlinear dynamics must be derived from data rather than given\n {\\em a priori} from theory. One might however see this as a strength, and in practice this is addressed by an iterative\n process whereby the parameters suggested by observation and theory are being brought closer together\n (Klimas et al., 1996).\n \n\\subsection{2.3 Stochastic descriptive models}\n\n Osborne and Provenzale (1989) showed that time series taken from certain random ``coloured \n noise\" processes, when tested with the G-P algorithm, would exhibit low dimensionality,\n and thus behave in this respect as a low dimensional chaotic system would. \nThis led to the application by Takalo et al., (1994 and references therein)\n of a third type of model, fractional Brownian motion \n denoted by fBm in Table 1 (e.g. Malamud\n and Turcotte, 1999), as a hypothesis\n against which to test the low dimensional nonlinear models described by the previous column.\n The suggestion of fBm recognised the possibility that the apparent low dimensionality and fractality of the magnetospheric \n indices was the consequence of their being the output of an otherwise intrinsically many-degree of freedom stochastic system,\n identified by a particular ``coloured noise\" power spectrum \n (hence ``sometimes\" against ``Low G-P dimension\" row 6, column 4). Effectively the model is:\n \n \\begin{equation}\n \\frac{d {\\bf x}(t)}{dt} = \\Delta {\\bf w}(t) \n \\end{equation}\n \nA simple example is Brownian motion where the time evolution is discrete, and each step \n($\\delta {\\bf x} = \\delta t \\ \\Delta {\\bf w}$ )\nis drawn from a white Gaussian distribution (e.g. Malamud and Turcotte, 1999). \nWe then find that neither short term nor long term prediction\nis possible because each step is entirely stochastic, giving us ``no\" \nagainst ``short-\" and ``long-term predictable\" (rows 2\nand 3 of column 3). We note however that closely-spaced initial conditions\ndiverge algebraically rather than exponentially, i.e. the \nimpossibility of long term forecasting here arises from the external \nstochasticity in $\\Delta {\\bf w}(t)$ rather than intrinsic chaos from ${\\bf g}$.\nGlobal scaling (row 4, column 4) must arise, irrespective \nof any free parameters, because there is no time scale in such a model. More complex time evolutions, \nwhere successive steps are taken from a fractional\nGaussian noise, are called fractal Brownian motions. A subset of such motions \nhas been shown to have low G-P dimension (Osborne and Provenzale, 1989). We note that \nthe presence of global scaling or scaling regions in the power spectra drawn from time series, \nor low G-P dimension, cannot distinguish between nonlinear\nlow dimensional models (column 3) and\nfBm (column 4), because they are shared properties. \nThe differences will only be unambiguous when one notes the different physical origins of the low G-P dimension \nbetween chaos and coloured noise, see Takalo et al., (1994), or when one uses \nanother discriminator such as short term predictability.\n \n\\subsection{2.4 Sandpile models of self organised criticality}\n\n The most recently introduced class of models (column 5) in Table 1 are those motivated\n by the hypothesis of Self-Organised Criticality (Chang, 1992; 1999, see also\n V\\\"{o}r\\\"{o}s, (1991); Chen and Holland, (1993); Robinson, (1993)). \n SOC was first identified in (Bak et al., 1987),\n and can be modelled by, numerical cellular automaton\n ``sandpile models\" (Katz, 1986; Bak et al., 1987)\n These discrete-variable models (Consolini, 1997; Uritsky and Pudovkin, 1998)\n and the closely-related continuous-variable discrete-space time models (Chapman et al, 1998;2000,\n Takalo et al., 1999a;1999b; Watkins et al., 1999b) are currently being studied for their possible magnetospheric application.\nConsideration of SOC in our context was motivated \n in particular by the fact that SOC can account for known\n magnetospheric phenomenology such as low dimensionality (Chang, 1992) and scale free power spectra, while \n providing a framework for understanding observed properties of the\n magnetosphere such as bursty transport in the tail (c.f. ``Bursty bulk flows\" (Angelopoulos, 1996)).\n It may be that the long term value of SOC to plasma physics will be as a starting point \n for more realistic ``avalanche\" models of \n turbulent transport (see Dendy and Helander, 1997, for\n more on this question, as applied to laboratory plasmas). However, at this stage of its consideration\n with respect to understanding\n in magnetospheric physics it remains useful to consider Bak et al.'s original, sandpile model-based, definition of SOC\n in the framework of our table of observables, as it is used explicitly\n or implicitly by much of the current work on SOC in this and other fields.\n\nBak et al. (1987, henceforth BTW87) originally proposed SOC to\nexplain the apparent ubiquity of both spatial fractals and\n``1/f\" spectra in nature. \nThey observed it in a class of numerical \ncellular automata, called ``sandpile models\" \nfor which analogous continuous thresholded diffusion \nequations have since been shown to exist (Lu, 1995).\nThe equations are modified from stochastic diffusion equations (Pelletier and\nTurcotte, 1999) which have a form such as\n\\begin{equation}\n\\frac {\\partial {\\bf g}({\\bf x},t)}{\\partial t} = \\nabla^2 {\\bf g}({\\bf x},t) + \\Delta w(x,t)\n\\end{equation}\nby the introduction of a thresholding process (Jensen, 1998), e. g.\n\\begin{equation}\n\\frac {\\partial {\\bf g}({\\bf x},t)}{\\partial t} = \\nabla^2 \n{\\bf g}({\\bf x},t) \\Theta ({\\bf g}({\\bf x},t) - {\\bf g_c}) + \\Delta w(x,t)\n\\end{equation}\nwhere the step function $\\Theta$ initiates diffusive transport when the variable ${\\bf g}$ reaches a critical\ngradient ${\\bf g_c}$.\nThe main debate centres on how to motivate and satisfactorily introduce this {\\it ad hoc} thresholding term \n(see Lu, 1995;Jensen, 1998) but several properties, such as the low frequency \npower spectrum may be\ndependent only on equation (4) and the nature of the boundary terms (Jensen, 1998), \nand so may be common to both SOC and stochastic diffusion.\n\nThe behaviour classified by BTW87 as SOC is the evolution of\nthe medium described by the cellular automaton or \ndifferential equation models from arbitrary initial conditions to a non-equilibrium \nbut steady state, ``self-organisation\". The medium then evolves by dissipating\nenergy on all scales via thresholded reconfiguration/energy \nrelease events called ``avalanches\". \n%This is illustrated in figure 1 where the mean\n%``height\" of a BTW-type sandpile algorithm (appendix ... of Jensen, 1998)is shown versus time.\n\nThe assertion by Bak et al. (1987;1988) that the \nobserved scale free, and hence power law, distribution of the\nsize of these energy release events (the ``avalanche distribution\") measured\n the arbitrary response of a self-organised fractal structure in the medium to perturbations introduced\nby random fuelling was the reason for their use of the term ``critical\". Their\nanalogy was with the scale free critical state \nassociated with phase transitions in critical phenomena (Huang, 1987). The common\n observable features cited by Bak et al. were that both systems \n were globally scale free (hence we may write ``yes\" in column 5, row 4 of table 1),\n and also that a finite size scaling analysis gave a good data collapse, as it would in\n a {\\it bona fide} critical system (Cardy,1996).\n The combination of a scale free response to perturbations with the release of \nthis energy by random unloading events, was expected to give rise to a power law\nfrequency spectrum. This was expected to be ``1/f\" and hence to explain\nthe ubiquity in nature of noise with correlations on all time-scales. Unlike\na ``$1/f^2$\" spectrum above a characteristic frequency which can \nbe explained in many systems simply\nby random switching of levels, the appearance of ``1/f\" ($f^{-\\beta}$)\nspectra where the spectral index is between about 0.8 and 1.4 is a \nlong standing problem in many branches of physics (Jensen, 1998).\n\nIn summary, in this\n picture, the SOC hypothesis would be that: ``extended driven systems will tend to self-organise to \n fractal structures which dissipate energy on all scales in space and time, and hence give rise to\nscale-free ``avalanche\" energy burst distributions and ``1/f\" noise\".\nMore recent sandpile algorithms which allow fuelling to continue while unloading occurs\nhave a broken power law spectrum and so we have added ``yes\" to column 5, row 5\nas well (see also section 3.1.2). \n \nSOC behaviour, as diagnosed by scale-free energy release and/or ``1/f\" \npower spectra, has since been claimed for many systems in nature (see chapter 3 of\n Jensen (1998) for a compact review, and Rodriguez-Itube and Rinaldo (1997) for a longer exposition in the \nparticular context of fractal river networks). \nAt this point, we simply note that a definition of SOC in terms of what an SOC \nsystem does can only be used to identify an SOC system if no other system does\nexactly the same things. Identification of global scaling, shared by SOC, fractal Brownian motion\nand low dimensional chaotic systems when intermittent is, for example, thus\nnot an unambiguous test. It is for this reason that we \nhave used Table 1, as a guide to how the ``footprint\" of SOC may be\nmore unambiguously defined. We have left the other rows as question marks \nbecause BTW87's sandpile model definition of SOC was not unambiguous in these respects,\nand these issues are still under study. \nThe wider definition of SOC used by Chang, (1992), predicts low dimensional behaviour \ni.e. ``yes\" in column 5, row 6, at least close to criticality, while many workers\nhave taken the predictions for column 5, rows 1 and 2 to be ``no\" e.g. the remarks\nof Consolini, (1997): ``In fact, if the magnetospheric dynamics could be the\nresult of a low-dimensional dimensional chaotic dynamics, we could have some \nhope to forecast the evolution. On the contrary, the existence of a critical\nstate removes this possibility, because the fluctuations of the\nsystem at a critical point are completely unpredictable\". This\nis equivalent behaviour to fBm. See also Bak (1994) on this point\nwhere sandpile models are asserted not to show sensitive dependence on initial conditions\ni.e. they are unpredictable on both long and short timescales but not chaotic. \nThe similarity of SOC to fBm with regard to the phenomena in Table 1 might\nsuggest that SOC adds nothing to fBm. However, there are differences. One is\nthe fact that an SOC system releases energy by means of avalanches, \neffectively a new observable property, which we have thus \nindicated by adding a row in Table 1 to those used by \nHastings and Sugihara (1993). We are indebted to a referee for the \nsuggestion that avalanche models may also have different phase\nspectra to the (usually random) phase behaviour of noise.\nA second advantage is that SOC can be explained in terms of an underlying theory and\nencapsulated in terms of sandpile models, which begin to allow explanation in\nterms of the underlying plasma physics of the system. A third advantage is that the release of energy\nby avalanches is suggestive both of bursty transport in plasma confinement \nsystems (e.g Carreras et al., 1999;Pedrosa et al., 1999), and, possibly, the substorm problem (Chang, 1992; Consolini, 1997).\n\n \nThe study of SOC in solar terrestrial-physics has proceeded initially\nthrough comparison of signatures\nin data, particularly the AE/AU/AL indices, \nwith analogous signatures in ``sandpile model\" realisations\n of SOC. However, as we will now show, these signatures are not all unique to SOC, and\n the combinations in which they appear may be model dependent. \n Furthermore, we recall that the original proposal of the relevance of SOC to \n the SW-M-I system (Chang, 1992) was not predicated exclusively on a definition of SOC\n derived from sandpile models. To minimise possible confusion in this\n rapidly developing area, two questions are addressed.\nThese are i) which experimental signatures will be needed to distinguish\n unambiguously between SOC and, for example, deterministic chaos\n and ii) what are the predictions of SOC models which will\n be robust against fluctuations in the input, or limited \n station or satellite coverage etc?\n \n\n\\section{3 Towards unambiguous tests of SOC}\n\nHaving decided what the predictions of SOC are which may be confidently entered in Table 1, we now go on to see what the observations currently available enable us to \nsay. The question immediately arises as to whether, Picture A), the SOC system is seen as being the \ncomplete magnetosphere (``global SOC\"), in which case ${\\bf x}$ in equation (5) are the system state variables, for which the\nAE indices (Davis and Sugiura, 1966) have been taken as proxies; or, Picture B), SOC is more local in scope (``local SOC\"), and \nplays a role in generating, stabilising and destabilising the magnetotail current sheet,\nin which case ${\\bf x}$ might be a locally-measured magnetic field or the field seen\nin an MHD-derived sandpile simulation. Picture A) is closer to that given in Uritsky and Pudovkin (1998) and\n Consolini (1997; 1999), while Picture B) seems to us to be \n %implicit in Chang (1992) and \n the motivation for Takalo et al., (1999a;b;c). Because any approximation will have a natural maximum\nscale of applicability, the idea of ``local SOC\" is not the contradiction it may at first\nappear to be. \n\nIt has been objected that if A) were true, all system-level outputs should\nshow global scaling and that some are observed \nnot to have this property (Borovsky and Nemzek, 1994). However Chapman et al. (1998), used the 1-dimensional\navalanche model of Dendy and Helander (1998), to illustrate a system in which the internal\nenergy release showed scaling while energy flowing out of the system (``systemwide\")\ndid not, a feature seen in some other sandpile models (e.g. Pinho and Andrade, 1998). Until pictures A\nand B can either be distinguished or reconciled, care must be taken not to justify one\nusing measurements consistent with the other and vice versa. We thus first (section 3.1) examine those \nsystem level outputs in which evidence of SOC has been claimed, and then (section 3.2) briefly consider\nevidence for SOC on more internal scales.\n\n\n\\subsection{3.1 Remote Observations of system outputs}\n\nSo far the main global dataset for testing for SOC has been the $AE$ indices. This is because, since Bargatze\net al. (1985), a candidate dynamical variable for all the models discussed above has been the energy \ndissipated by the magnetosphere into the ionosphere, for which most workers have taken \n the Auroral Electrojet Index ($AE$) to be a proxy.\n\n\\subsubsection{3.1.1 Global scaling: Power law power spectra}\n\n The work of Tsurutani et al. (1990) described the power spectrum of $AE$ as ``broken power law\",\n in that the high frequency behaviour is\n approximately $1/f^2$ while the lower frequency behaviour\n is approximately $1/f$, with a break at (1/5) hours$^{-1}$.\nThis ``1/f\" behaviour has been cited as evidence of SOC \nin the magnetosphere (Consolini, 1997; 1999; Uritsky and Pudovkin, 1998). Two\nmain scenarios have been advanced, in one the ``1/f\" spectrum is seen as arising from interactions between\ncorrelated avalanches, which would then be interpreted as substorms (Consolini, 1997); while in the second\nthe ``1/f\" behaviour (Uritsky and Pudovkin, 1998) is related in part to the input,\nwhich is allowed to modulate the threshold values in the sandpile algorithm.\n\nThe first apparent complication in this interpretation \nis that the $AE$ spectrum is ``broken\" i.e. a ``1/f$^2$\" high frequency part has been reported,\n whereas criticality in BTW87's original picture was expected to give \n long-period correlations and hence a ``1/f\" spectrum (Jensen, 1998). The resolution, due to Consolini (1997),\nis discussed in the section 3.1.2. The second, more fundamental,\nproblem is that a ``1/f\" spectrum in the ouput of a system could only be an unambiguous indicator \nof SOC if this spectrum is not being passed through from the input. The fact that the input spectrum\nof the solar wind follows $AE$ closely over the low frequency ``1/f\" range that \nconcerns us here (Tsurutani et al., 1990; Freeman et al., 1998) suggests that the power spectrum \nshould not be used for this purpose. In this context, the high degree of predictability of $AE$ from the\nsolar wind input is suggestive (e.g. Baker et al, 1997), as is the fact that the\npower spectrum of the signal from a neural\nnetwork prediction of $AE$ has ``1/f\" form (Takalo et al., 1996). We return to this question in section 3.1.3 \nwhen we discuss the avalanche statistics. The possible ability of some avalanche\n algorithms to emulate a nonlinear filter, and show sensitivity to the distribution of the input fuelling rate \n(Takalo et al., 1999c); or conversely to eliminate traces of fluctuating input\n (Watkins et al., 1999b), increases the relevance of this question.\n \n\n\\subsection{3.1.2 Scaling Regions: Spectral breaks}\n\nIf the system is known to be SOC {\\it a priori} or from other tests, the presence of a high frequency ``1/f$^2$\" component is\n understandable. This is because recent work (notably Hwa and Kardar, 1992) has shown\nthat a ``running\" sandpile (and hence SOC differential equation models such as the example used by\n(Takalo et al., 1999a)) can show this type of ``broken\" power spectrum. The reason is that allowing the \nfuelling to occur on a similar time scale to the unloading events permits a bursty \n``1/f$^2$\" power spectrum of individual avalanches to co-exist with the ``1/f\" power spectrum \nwhich is ascribed to interactions between events (see Jensen, 1998). If the bursts are identified with substorms then the \nbreak at 5 hours will be related to the maximum duration of a substorm.\nFurthermore, the original Bak et al. (i.e. ``non-running\") sandpile model\n was quickly shown (Jensen et al., 1989) to \n produce a ``1/f$^2$\" spectrum in its energy release events, illustrating \n that the although the pile is in critical state,\n shown in particular by the finite size scaling of the avalanche\n distribution (Bak et al., 1988), the critical state is not revealed by the energy \n release power spectrum. \n \nThe complications in this very appealing simple interpretation \narise for two main reasons. One is that we do not know {\\em a priori} that the\nsystem is SOC, so mapping an output variable of the sandpile model to the observed $AE$ spectrum is not a unique\nprocess. An alternative way to get a broken spectrum of the form shown by \nTsurutani et al. (1990) for $AE$ is in\n a boundary driven 2D sandpile of the BTW87 type (see figure 4.6 of Jensen, 1998).\n In this case the variable whose spectrum is obtained is not the transport\n of sand over the edge of the pile but the sum of the dynamical\n variable ${\\bf g}$ across the pile i.e\n \\begin{equation}\n <g(t)> = \\sum_{i,j} g_{ij} \\equiv \\int d {\\bf x} \\ {\\bf g}({\\bf x},t)\n \\end{equation}\n %The physical interpretation of the ``1/f\" spectrum remains the same, i.e. the interaction between \n %energy release events. \n As with Tsurutani et al, 1990, the spectrum shown by Jensen (1998) is\n $\\sim 1/f$ below a critical frequency and $\\sim 1/f^2$ above, with\n the break set by a time scale $T_{max} (L)$ corresponding to\n the longest avalanche possible in the system. This would imply that\n $T_{max}$ is related to the system size $L$, and furnish a possible test if the system's\n value of $L$ could be varied significantly. In other words, the robust property is the break\n itself rather than the variable whose broken spectrum is being calculated.\n \nThe second problem is that the broken power law spectrum for $AE$ cannot be uniquely interpreted as the\noutput of an SOC system because other types of physical system can produce\npower spectra which show global scaling or scaling\nover a region or regions. The example of global scaling, i.e. \nscaling over a very wide bandwidth, discussed in section 2.3\nwas simple Brownian motion which has an $f^{-2}$ spectrum at all values\nof $f$. A less well known example of scaling over a restricted region is the ``random telegraph\", a random sequence of square pulses (i.e. states +1 or -1) \nswitched at Poisson distributed intervals which gives $f^{-2}$ for frequencies higher than the inverse\ncorrelation time but has a flat spectrum (because uncorrelated) for lower frequencies (Bendat, 1958; Jensen, 1998). \nIt is very important to note that the ``1/f$^2$\" part of the spectrum here is due entirely\nto the exponential autocorrelation of the pulses, and is not the same as the intrinsically\nscale free, and wideband, behaviour of a coloured noise source such as Brownian motion. If the lifetimes of the correlated\npulses extend over two orders of magnitude in time then so will the ``1/f$^2$\" spectrum, and \nso a test such as the second order structure function \n(see Takalo et al., 1994 and references therein), or a variance histogram (i.e. Fourier\npower spectrum) will be unable to distinguish this ``trivial\" apparent\nscaling from the ``interesting\" scaling resulting from coloured noise. \nA similar problem whereby level changes with a $1/f^2$ spectrum might mask an intrinsic Kolmogorov spectrum\nwas treated for solar wind turbulence by Roberts and Goldstein (1987).\n\n The fact that the high frequency scaling region in the spectrum of\n $AE$ might arise from a cause other than SOC is important in our application\nbecause $AE$ is known {\\it a priori} to be a compound index which\n mixes driven and unloading effects (Kamide and Baumjohann, 1991). This mixed origin is reflected by its\npower spectrum (Freeman et al., 1998), structure function (Takalo et al., 1994), and \navalanche distribution (section 3.1.3 and Freeman et al., 2000). In consequence\na suitable ``null hypothesis\" for the power spectrum against which the SOC models so far proposed should be \nevaluated is that $AE$ consists of a solar wind driven ``1/f\" component - arising from the $DP2$ \nconvection electrojet (Kamide and Baumjohann, 1991) - and a\nrandom unloading $DP1$ \nsubstorm electrojet component which looks like ``1/f$^2$\" over two orders of magnitude in frequency\nand appears predominantly in $AL$. By analogy with section 3 we may call this Picture C (``no global \nSOC\").\n\n\nA possible avenue for testing Consolini's (1997) ``interacting burst\" interpretation of the ``1/f\" spectrum would then be to see if the correlation \nproperties of the ``1/f\" part of the power spectrum of $AE$ differ in any way from those of \nAkasofu's $\\epsilon$ parameter, which estimates the componenent of solar wind Poynting flux\nentering the magnetosphere. If they do, this adds\nsupport to the possibility that the bursts may be correlated with each other as a result of\na process which occurs in the magnetosphere itself; rather than\nthe ``1/f\" behaviour being explained by the long-period\ncorrelation already present in the solar wind's power spectrum.\n\n\\subsection{3.1.3 Global scaling: Avalanche distributions}\n\nBecause of the above concerns, we see a better candidate for an unambiguous indicator \nof SOC as being the\nstatistical distribution of energy released by individual ``events\". Since the work of Bak et al.\n an SOC system has been expected to show a ``power law\" probability distribution for \n this quantity. Consolini, (1999) has plotted the distribution $D(s)$ of a burst\n measure $s = \\int_{\\Omega} (AE(t) - L_{AE}) dt$, formed from $AE$\n where $L_{AE}$ was a\n running quiet time background level of $70 \\pm 30$ nT, and each\n integration was taken over a period $\\Omega$ where the integrand was\n positive (a burst). The $AE$ data used covered the period from 1975\n and 1978-1987. The distribution obtained could be described by an\n exponentially cutoff power law (Consolini, personal communication, 1998)\n%$D(s) \n% \\sim (s^{-\\alpha}) e^{-s/\\beta\n% }$ with $\\alpha = 1.23 \\pm 0.01$ and $\\beta = (1.17 \\pm 0.01) \\times\n% 10^{6}$, \n extending the result previously obtained by Consolini, (1997)\nfor data from 1978.\n \n The presence of such a power law suggested a magnetospheric analogue of the Gutenberg-Richter\n law in seismology, and has played a significant role in generating the interest in SOC \n in magnetospheric physics. Both its existence and its apparent robustness with activity level\n require confirmation and explanation whether by an SOC theory or another one. Although\n both a simple power law, or the above exponentially cut off power law are possible fits,\nConsolini (1999) has recently demonstrated that a better description for the burst size\ndistribution of $AE$ is an exponentially modified power law with a small lognormal ``bump\"\ncomponent. If the system is SOC, this requires an explanation of the ``bump\",\nwhich may be found in the different behaviour of internal and systemwide\ndissipation in some sandpile models (Chapman et al., 1998) or in subcritical\ndynamics in the SOC system (Consolini, 1999). \n\n\\subsection{3.1.4 Global scaling: Lifetime distributions}\n\nThe SOC hypothesis had earlier led Takalo (1993) and Consolini (1999) to examine \nthe distribution of lifetimes of the bursts. This is potentially a stronger indicator of SOC than the burst size, \nbecause exponentially modified power-law burst size distributions can also be generated\n by randomly quenched, exponentially growing\ninstabilities in an otherwise non-critical medium (Aschwanden et al., 1998). $AE$ was found (Consolini,1999)\nto show a exponentially modified power law distribution of lifetimes, but with evidence of a ``bump\" \nat around 100 minutes. The ``null hypothesis\" mentioned in 3.1.2 (Picture C)\nled Freeman et al., (2000) to calculate the analogous \nburst lifetime distributions for $AU$, $AL$ and\nthe solar wind quantities $\\epsilon$ and $v B_s$. They found exponentially modified power laws\nwith very similar slopes for all quantities, but\nthe ``bump\" was only found in the AL and AE, magnetospheric component. This suggests that \nthe ``bump\" is of intrinsically magnetospheric origin (due to the DP1\n current (Kamide and Baumjohann, 1991)) while\n the scale-free burst lifetime distribution may actually be of solar wind origin (Freeman et al., 2000),\nif the DP2 current system (Kamide and Baumjohann, 1991) \nis transparent to the driver.\n \n\n\\subsection{3.1.5 Other tests: Predictability, low dimensionality}\n\nIt will be necessary to examine the sandpile models and other realisations of SOC in more detail before\nwe can say with certainty what they predict for the remaining rows of column 5, table 1. Bak (1994)'s arguments about\nlong term prediction are based on the assertion that $\\delta$, the separation of two initially infinitesimally\nclose trajectories in a BTW87-type sandpile model \ngrows with time quadratically, $\\delta = a t^2$, rather than exponentially, $\\delta = e^{\\lambda t}$, as would\nbe the case in a chaotic system such as that of column 3 (where $\\lambda$ is the Lyapunov exponent). This \nassertion needs to be tested in other sandpile models and in data from candidate systems. It is a potential\ndiscriminator between chaos and SOC.\n% It may be that the dominant effect for SOC\n%is the diffusive dynamics in equation (4) or (5) playing a role similar to equivalent to the stochastic force in equation (3) when averaged over an ensemble\n% of realisations, and this is what gives rise to the quadratic rather than exponential divergence.\n\nThe demonstration that an SOC system can show low dimensional behaviour was given by Chang (1992;1999) on\nthe basis of a more general formulation of SOC than the sandpile-inspired one of Bak et al. It thus remains\nto be seen in general what sandpile models predict for dimensionality. \n\n\\subsection{3.1.6 New tests: Intermittency and laminar time}\n\nThe open questions described in the previous section and the ambiguities necessarily present in the data\nreviewed in sections 3.1.1 to 3.1.4 mean that at present it is not possible to completely eliminate any\nof the models discussed in Table 1, except the artificially simple linear model which was included for completeness.\nNew tests are thus required. An example of such a test\nis the degree of intermittency present in the time series. \nConsolini et al. (1996) showed that the $f^{-2}$ spectral regime of $AE$ might be described as an\n$f^{-1.8}$ regime corresponding to the inertial range of a turbulent system, with an exponent modified from the\nKolmogorov value by the presence of intermittency. These authors showed a good fit to the p-model of turbulence, \nalso shown in the solar wind by Horbury and Balogh (1997). We are thus not presently able to distinguish between\nintermittency intrinsic to $AE$ and that due to the solar wind driver. Further work on this topic\nis likely to prove valuable (see also V\\\"{o}r\\\"{o}s et al., 1998).\n\nMore recently, it has been claimed (Boffetta et al., 1999) that the probability density $D(\\tau)$ of \ntime intervals $\\tau$ between bursts (the ``laminar time\") can be used to distinguish an SOC system of\nthe BTW87 type, which has exponential $D(\\tau)$, from a shell model of turbulence,\nwhich has power law $D(\\tau)$. It might seem that the power law $D(\\tau)$ for\nAE shown by Consolini (1999) would rule out SOC in the global magnetosphere.\nHowever, as emphasised by Einaudi and Velli, (1999), the predictions\nfor $D(\\tau)$ are not in general known either for more realistic\nSOC models or for all turbulence models. The relevance of this work to the issue\nof ``sympathetic flaring\" (Boffetta et al., 1999 and references therein)\n in solar physics is likely to give rise to further \nexploration of this topic, and hence magnetospheric application.\n\n\\subsection{3.2 Local observations of current sheet dynamics}\n\nIt is fair to say that, for the above reasons, the evidence of SOC in the largest scale\noutputs of the magnetospheric system, measured by $AE$ and $AL$, is not yet persuasive. \nThe main problem is that the behaviour of the $AE$ indices is similar to that of the solar\nwind in a number of respects. If an intrinsic and a solar wind component are always present,\nthen testing for SOC in these compound indices will always be problematic, as will the \ninterpretation of results based on them (c.f. Consolini, 1999; Freeman et al., 2000).\n\nIt may be more instructive to study regions of the magnetosphere where the effect of\nthe solar wind input is less directly visible, and \nrecent attention has been focused on SOC as a model of the magnetotail\ncurrent sheet. So far this has been achieved by \ntruncating the ideal MHD equations i.e. replacing the convection term in\n\\begin{equation}\n\\frac {\\partial {\\bf B}({\\bf x},t)}{\\partial t} = \\nabla^2 {\\bf B}({\\bf x},t) + \\nabla \\wedge ({\\bf v} \\wedge {\\bf B})\n\\end{equation}\nby a source term, resulting in an equation analogous to (4) \n\\begin{equation}\n\\frac {\\partial {\\bf B}({\\bf x},t)}{\\partial t} = \\nabla^2 {\\bf B}({\\bf x},t) + \\Delta w(x,t)\n\\end{equation}\nand then introducing one of several possible thresholding terms c.f. equation (5)\n(Vassiliadis et al., 1998 ; Takalo et al, 1999a;b;c) to map the problem onto a cellular\nautomaton or a differential equation like that of (Lu, 1995). In view of the limited applicability\nof such non-self consistent models it is encouraging that reduced MHD simulations of turbulence are also\ndemonstrating SOC phenomenology (Einaudi and Velli, 1999). \n \n Consideration of SOC as a model for the magnetotail may also be motivated \nby the suggestion by of Zelenyi et al.,(1998) that the tail exists as a critical percolation cluster.\nCritical percolation, whereby an avalanche can extend exactly to the maximum scale length of a system rather than\njust below or just above it, was the original proposed explanation for the relevance of criticality\nin SOC (Bak et al., 1988). The idea has recently been further developed to explain\nhow self-organisation occurs in sandpiles (Zapperi et al., 1997) in a picture whereby the edge fluctuations\ndrive the system back to a critical percolation state. \n\n \n \n \n\\section{4. What signatures of SOC are robust enough to be detectable in ``real world\" data ?}\n\nSOC is of particular interest to magnetospheric physics because it is\n robust, in the sense that the characteristic observed behaviour does\n not necessarily change greatly over wide ranges of parameter space.\n This robustness is thus distinct from the scale invariant phenomena\n that arise near critical points such as phase transitions and hence\n in restricted regions of parameter space (Huang, 1987). SOC\n systems are in this way also distinct from chaotic systems such as\n the dripping tap which frequently show radically different\n types of behaviour as control parameters change, a point emphasised\n by Bak (1997, pages 29-31). They are not however, as easily distinguishable\n from fBm.\n \n However we still need to ask what\n aspect or aspects of the magnetosphere's behaviour would be both sufficient to\n uniquely identify SOC and yet also robust enough to be seen\n under the wide range of activity levels exhibited by the\n magnetosphere and the solar wind i.e., to pick the specific robust\n discriminator. The slowly driven condition is of particular interest in the\nmagnetospheric context because most SOC simulations have been\nconducted in the limit where the rate of inflow is ``slow\" relative to\ndissipation. Watkins et al., (1999b); and Chapman et al., (1999) have recently studied the\nquestion of how robust \nthe magnetospherically relevant aspects of SOC are to changes in the inflow \nrate. They found that the power law avalanche distribution was preserved for the largest \nvalues of internal energy release, and gave arguments as to why this should be so. This result\nmay give confidence that such a distribution, if shown on other grounds to be unique to SOC, will be\nable to be used as a diagnostic. Similar studies for the power spectrum are being carried out in an MHD-derived\nmodel by Takalo et al., (1999c).\n\n\n\\section{5. Conclusions}\n\n We have attempted to identify the distinguishing observable features of different few-parameter\n models applied to the magnetosphere. The ``linear+noise\" model was abandoned because of observed\n nonlinearity, low dimensionality and lack of long-term predictability in the auroral index time series. Low\n dimensional models have been questioned because the low dimensionality is not unique to them\n and because their scaling properties are not robust against changes in the input parameters.\n An alternative, fractional Brownian motion, which gives low dimensionality and robust scaling\n is unsatifying because it does not lead to an underlying plasma physical description. The newest alternative, \n SOC, chosen for its robust scaling properties, can be seen as providing both a physical explanation \n for fBm and also accounting for the bursty nature of transport in the magnetosphere.\n SOC has yet to have its low dimensionality and predictability properties fully defined, but so far they seem to be similar to those of fBm. Thus attention must be focused\n on other means of distinguishing these last two, such as the observed intermittency and avalanching properties.\n Even so, questions about the application of fBm and SOC as models of the magnetosphere's large \n scale output (picture A) rather than of its solar wind-driven aspects are raised by the similarity of \n input and output power spectra and burst distributions. Resolution of these issues is hampered by the narrow bandwidth \n of even the best available data series, which for example make it difficult to distinguish between wide-band coloured\n noise and random state changes as the origin of the $f^{-2}$ spectrum of AE (Watkins et al., 1999a).\n\n \n This seems to leave four possibilities, not all of which are mutually exclusive:\n \n i) The global ``SOC\"-like properties we have referred to come from outside the magnetosphere, i.e. the magnetosphere\n can be quite well described by a ``weakly nonlinear plus coloured noise\" model; weakly nonlinear to give\n the necessary degree of predictability of the output from the input while\n giving long-term unpredictibility, but with a coloured noise\n input from the fBm or SOC nature of the turbulent solar wind causing the scaling properties. \n This scenario appears to be compatible with picture C, the data in Freeman et\n al. (2000), and alternative iii) below.\n \n ii) Some SOC systems (Watkins et al, 1999b; Consolini, private communication, 1998)\n will destroy the information contained in their input. The scaling observed in their outputs is then\n independent of any present in the input, so any common scaling exponents between\ninput and output are either coincidental or evidence of universality in certain \nconfined plasma systems.\n \n iii) Measuring global properties is the wrong thing to do, i.e. SOC is not an aspect of the global\n magnetosphere but relevant more locally to the magnetotail (compatible with picture B, and\n alternative i) above). This possibility\n is likely to be illuminated by further studies of SOC as a magnetotail model.\n \n or iv) that another type of model is required (e.g. Chapman, 1999). \\\\\n\nIt is also important to emphasise that the extent to which SOC is observable, and \ndistinguishable from other nonlinear physics paradigms (such as those presently used to\nstudy turbulence) is an important generic question in contemporary physics (including\nbut going beyond, plasma physics). The diversity and quality of the existing ground-based\nand space-based magnetospheric databases provide a key testbed with which these\nintrinsically interdisciplinary questions can now be addressed; while ongoing investigations \nin astrophysical and laboratory confinement systems, both in plasma physics and elsewhere will\ncontinue to be applicable to the question of magnetospheric SOC.\n \n The authors wish to acknowledge many enjoyable and valuable discussions\nwith John Barrow, Ben Carreras, Tom Chang, Giuseppe Consolini, Patrick Diamond,\nPer Helander, Henrik Jensen, John King, David Newman, Christophe\nRhodes, David Riley, George Rowlands, Jouni Takalo, Sunny Tam, Dave Tetreault, Vadim Uritsky, Zoltan V\\\"{o}r\\\"{o}s\nand Dave Willis. NWW and SCC would like to acknowledge the hospitality of the MIT Center for Space Research where some of this work\n was carried out. SCC acknowledges a PPARC Lecturer fellowship and ROD the\n support of Euratom and the UK DTI.\n \n \\newpage\n \n \\begin{tabular}{|l|llll|} \\hline\n1.Model: & 2.Linear & 3.Low -dimensional & 4.fBm & 5.SOC \\\\ \n & (plus noise) & nonlinear & nonlinear & sandpile \\\\\n \\hline\n1. Property & & & & \\\\ \n \\hline\n2.Short term predictable & Yes & Yes & No & ? \\\\\n3.Long term predictable & Yes & No & No & ? \\\\ \n4.Global Scaling & No & Sometimes & Yes & Yes \\\\\n5.Scaling Regions & Sometimes & Sometimes & Yes & Yes \\\\\n6.Low G-P Dimension & No & Yes & Sometimes & ? \\\\ \n7. Avalanches & No & ? & ? & Yes \\\\ \\hline\n\n%\\caption{does this work}\n\\end{tabular} \n\n\n\\begin{table}\n\\vspace{0.in}\n\\caption{ Four examples of possible approaches to\nunderstanding magnetospheric time series, adapted from Hastings and Sugihara (1993)}\n\\end{table} \n\n \n\n\\newpage\n\n%Kisabeth, J.L., 1979. On calculating magnetic and vector potential field due\n%to large-scale magnetospheric current systems and induced currents in an\n%infinitely conducting earth. In: Olson, W. P. (Ed.), Quantitative Modelling\n%Magnetospheric Processes. American Geophysical Union.\n\n%Marov, M.Ya., Ioltukhovski, A.A., Kolesnichenko, A.V., Krasitsky, O.P., Shari,\n%V.P., 1994. On earth ozonosphere space monitoring by stars occultation.\n%Keldysh Institute of Applied Mathematics. Reprint No. 33, Moscow (in Russian).\n\n%Vijayakumar, G., Parameswaran, R., Rajan, R., 1998. Aerosols in the atmospheric\n%boundary layer and its association with surface wind speed at a coastal site.\n%Journal of Atmospheric and Solar-Terrestrial Physics 60 (16), 1531-1542.\n \n\n\nAngelopoulos, V., et al., 1996. Multipoint analysis of a bursty bulk flow\nevent on April 11, 1985. Journal of Geophysical Research 101, 4967-4989. \\\\\n\nAngelopoulos, V., Mukai, T., Kokubun, S., 1999. Evidence for intermittency \nin Earth's plasmasheet and implications for self-organised criticality.\nPhysics of Plasmas 6, 4161-4168. \\\\\n\nAschwanden, M. J., Dennis, B. R., Benz, A. O., 1998. Logistic avalanche processes, elementary time\nstructures and frequency distributions in solar flares. Astrophysical Journal 497, 972-993.\\\\\n\nBak, P., 1994. Self-organized criticality: consequences for statistics and predictability of earthquakes.\n In: Newman, W. I., Gabrielov, A., Turcotte, D. L., (Eds.), Nonlinear Dynamics and Predictability of Geophysical\nPhenomena. American Geophysical Union.\\\\\n\nBak, P., 1997. How Nature\nWorks: The Science of Self Organised Criticality. Oxford University\nPress. \\\\\n\nBak, P., Tang, C., Wiesenfeld, K., 1987. Self--organized criticality: an explanation of\n1/f noise. Physical Review Letters 50, 381--384.\\\\\n\nBak, P., Tang, C., Wiesenfeld, K., 1988. Self--organized criticality. Physical Review A 38, 364-374.\\\\\n\nBaker, D. N., Klimas, A. J., McPherron, R. L., Buchner, J., 1990. The evolution from weak to strong\ngeomagnetic activity: an interpretation in terms of deterministic chaos. Geophysical Research Letters\n17, 41-44.\\\\\n\nBaker, D.N., Klimas, A. J., Vassiliadis, D., Pulkkinen, T. I., McPherron, R. L., 1997.\nReexamination of driven and unloading aspects of magnetospheric substorms. Journal of Geophysical Research 102,\n7169-7177.\\\\\n\nBaker, D.N., Kanekai, S. G., Klimas, A. J., Vassiliadis, D., Pulkkinen, T. I., 1999.\nCollective phenomena in the inner magnetosphere.\nPhysics of Plasmas 6, 4195-4199.\\\\\n\n\nBargatze, L. F., Baker, D. N., McPherron, R. L., Hones, E. W., 1985.\nMagnetospheric impulse response for many levels of geomagnetic activity. \nJournal of Geophysical Research 90, 6387-6394.\\\\\n\nBendat, J. S., 1958. Principles and Applications of Random Noise Theory. John Wiley.\\\\\n\nBoffetta, G., Carbone, V., Giuliani, P., Veltri, P., Vulpiani, A., 1999.\nPower laws in solar flares: Self-organised criticality or turbulence?\nPhysical Review Letters 83, 4662-4665.\\\\\n\nBorovsky, J. E., and Nemzek, R. J., 1994. Substorm statistics: occurrences and amplitudes. In: Proceedings of the\nSecond International Conference on Substorms, Fairbanks, Alaska. Geophysical Institute. \\\\\n\nCardy, J. L., 1996. Scaling and Renormalization in Statistical Physics.\n Cambridge University Press. \\\\\n\nCarreras, B. A., van Milligen, B., Hidalgo, C., Balbin, R., Sanchez, E., Garcia-Cortes, I., Pedrosa, M. A.,\nBleuel, J., Endler, M., 1999. Self-similarity properties of the probability\ndistribution function of turbulence-induced particle fluxes at the plasma\nedge. Physical Review Letters 83, 3653-3656.\\\\\n\nChang, T. S., 1992. Low\ndimensional behaviour and symmetry breaking of stochastic systems near\ncriticality - can these effects be observed in space and in the\nlaboratory ?. IEEE Transactions on Plasma Science 20, 691--694.\\\\\n\nChang, T. S., 1999. Self-organized criticality, multi-fractal spectra, sporadic localized\nreconnections and intermittent turbulence in the magnetotail. Physics of Plasmas 6, 4137-4145.\\\\\n\nChapman, S. C., 1999. A deterministic avalanche model with limit cycle exhibiting period\ndoubling, intermittency and self-similarity. Submitted to Physical Review E. \\\\\n \nChapman, S. C., Watkins, N. W., Dendy, R. O., Helander, P., Rowlands, G., 1998.\nA simple avalanche model as an analogue for magnetospheric activity. Geophysical Research Letters 25, 2397-2400. \\\\\n\nChapman, S. C., Dendy, R. O., Rowlands, G., 1999. A sandpile model with dual scaling\nregimes for laboratory, space and astrophysical plasmas. Physics of Plasmas 6, 4169-4177. \\\\\n\nChapman, S. C., Watkins, N. W., Rowlands, G., 2000. Signatures of dual scaling regimes in a simple avalanche\nmodel for magnetospheric activity. In press, Journal of Atmospheric and Solar-Terrestrial Physics.\\\\\n\nChen, J., and Holland, D. L., 1993. Nonlinear dynamics of particles in the magnetosphere: a tutorial review.\n In: Chang, T. S., and Jasperse, J. R. (Eds.), Physics of Space Plasmas (1993). MIT Center for Theoretical\n Geo/Cosmo Plasma Physics.\\\\\n\nConsolini, G., Marcucci, M. F., Candidi, M., 1996. Multifractal structure of auroral electrojet\ndata. Physical Review Letters 76, 4082-4085. \\\\\n\nConsolini G., 1997. Sandpile cellular automata and magnetospheric dynamics. In: Aiello, S., Iucci, N.,\n Sironi, G., Treves A., Villante, U., (Eds.),\n Cosmic Physics in the Year 2000. Proc. vol. 58, Societa Italia di Fisica. \\\\\n\nConsolini, G., 1999. Avalanches, scaling and 1/f noise in magnetospheric dynamics. Submitted to Physical Review Letters.\\\\\n\nDavis, T. N., and Sugiura, M., 1966.\nAuroral electrojet activity index AE and its universal time variations, \nJournal of Geophysical Research 71, 785-801.\\\\\n\nDendy, R. O., and Helander, P., 1997. Sandpiles, silos and tokamak phenomenology: a\nbrief review. Plasma Physics and Controlled Fusion 39,\n1947--1961.\\\\\n\nDendy, R. O., and Helander, P., 1998. On the appearance and non--appearance of\nself--organised criticality in sandpiles. Physical Review E 57, 3641-3644, 1998.\\\\\n\nEinaudi, G., and Velli, M., 1999. The distribution of flares, statistics of magnetohydrodynamic \nturbulence and coronal heating. Physics of Plasmas 6, 4146-4153. \\\\\n\nFreeman, M. P., Watkins, N. W., Rhodes, C., 1998. On the two-component nature of the auroral electrojets. \nAGU Fall Meeting, EOS Transactions, 79 supplement, F793. \\\\\n\nFreeman, M. P., Watkins, N. W, Riley, D. J., 2000. Evidence for a solar wind origin of the power law\nburst lifetime distribution of the AE indices. \nGeophysical Research Letters 27, 1087-1090.\\\\\n\nGrassberger, P., and Procaccia, I., 1983. Characterisation of strange attractors.\nPhysical Review Letters, 50, 346-349.\\\\\n\nHastings, H. M., and Sugihara, G., 1993. Fractals: a Users Guide for the Natural Sciences. Oxford\nUniversity Press. \\\\\n\nHorbury, T. S., and Balogh, A., 1997. Structure function measurements of the intermittent MHD turbulent\ncascade. Nonlinear Processes in Geophysics, 4, 185-199.\\\\\n\nHorton, W., and Doxas, I., 1996. A low dimensional energy conserving state space model for substorm\ndynamics. Journal of Geophysical Research, 101, 27223-27237. \\\\\n\nHorton, W., Smith, J. P., Weigel, R., Crabtree, C., Doxas, I., Goode, B., Cary, J., 1999. \nThe solar-wind driven magnetosphere-ionosphere as a complex dynamical system.\nPhysics of Plasmas 6, 4178-4184. \\\\\n \nHuang K., 1987. Statistical Mechanics, Second Edition. John Wiley.\\\\\n\nHwa, T., and Kardar, M., 1992. Avalanches, hydrodynamics, and discharge events in\nmodels of sandpiles. Physical Review A 45, 7002-7023. \\\\\n\nJensen, H. J., Christensen, K., Fogedby, H. C., 1989. 1/f noise, distribution\nof lifetimes, and a pile of sand. Physical Review B 40, 7425-7427. \\\\\n \nJensen, H. J., 1998. Self-Organised Criticality: Emergent Complex Behaviour in Physical\nand Biological Systems. Cambridge University Press.\\\\\n\nKamide, Y., and Baumjohann, W., 1991. Magnetosphere-Ionosphere Coupling. Springer Verlag. \\\\\n\nKatz, J. I., 1986. A model of propagating brittle failure in\nheterogeneous media. Journal of Geophysical\n Research 91, 10412--10420.\\\\ \n\nKlimas, A. J., Baker, D. N., Roberts, D. A., Fairfield, D. H., Buchner, J., 1992. A nonlinear\ndynamical analogue model of geomagnetic activity. \nJournal of Geophysical Research 97, \n12253-12266.\\\\\n \nKlimas, A. J., Vassiliadis, D., Baker, D. N., Roberts, D. A., 1996.\n The organised nonlinear dynamics of the magnetosphere. Journal of Geophysical\n Research 101, 13089--13113.\\\\\n \nLichtenberg, A. J., and Lieberman, M. A., 1992. Regular and Chaotic Dynamics, Second Edition. Springer Verlag.\\\\\n\nLu, E. T., 1995. Avalanches in continuum dissipative systems. Physical Review Letters 74, 2511-2514.\\\\\n\nMalamud, B. D., and Turcotte, D. L., 1999. Self-Affine Time Series: I. Generation\nand Analyses. In: Dmowska, R., and Saltzman, B. (Eds.), Advances in Geophysics, Volume 40,\n Long-Range Persistence in Geophysical Time Series. Academic Press.\\\\\n\n\n\nOsborne, A. R., and Provenzale, A.,1989. Finite correlation dimension for stochastic\nsystems with power-law spectra. Physica D 35, 357-381. \\\\\n\nPalmer, T. N., 1993. A nonlinear dynamical perspective on climate change.\nWeather 48, 314-326. \\\\\n\nPedrosa, M. A., Hidalgo, C., Carreras, B. A., Balbin, R., Garcia-Cortes, I.,\nNewman, D., van Milligen, B., Sanchez, E., \nBleuel, J., Endler, M., Davies, S., Matthews, G. F., 1999. Empirical similarity of frequency spectra of the edge-plasma fluctuations\nin toroidal magnetic-confinement systems. Physical Review Letters 82, 3621-3624.\\\\\n\nPelletier, J. D., and Turcotte, D. L., 1999. Self-affine time series: II. \n applications and models. In: Dmowska, R., and Saltzman, B. (Eds.), Advances in Geophysics, Volume 40,\n Long-range Persistence in Geophysical Time Series. Academic Press.\\\\\n\nPinho, S. T. R., and Andrade, R. F. S., 1998. An Abelian model for rainfall. Physica A 255, 483-495. \\\\\n\nRobinson, P. A., 1993. Self-organized criticality. In: Chang, T. S., and Jasperse, J. R. (Eds.), \nPhysics of Space Plasmas (1993). MIT Center for Theoretical\n Geo/Cosmo Plasma Physics. \\\\ \n\nRoberts, D. A., and Goldstein, M. L., 1987. Spectral signatures of jumps\nand turbulence in interplanetary speed and magnetic field data. Journal of Geophysical Research 92, \n10105-10110.\\\\\n\nRodr\\'{i}guez-Iturbe and Rinaldo, 1997. Fractal River\nBasins: Chance and Self-Organisation. Cambridge University Press.\\\\\n\nRowlands, G., 1990. Non-Linear Phenomena in Science and Engineering. Ellis Horwood. \\\\\n\nSharma, A. S., 1995. Assessing the magnetosphere's nonlinear behaviour: its dimension is\nlow, its predictability high. Reviews of Geophysics 33, Part 1,\nSuppl. S., 645--650. \\\\\n\nShaw, R., 1984. The Dripping Faucet as a Model Chaotic System. Aerial Press.\\\\\n\nTakalo, J., 1993. Correlation dimension of AE data, Ph. Lic. Thesis, Laboratory Report 3. Department of Physics,\nUniversity of Jyvaskyla.\\\\\n\nTakalo, J., Timonen, J., Koskinen, H., 1994. Properties of AE data and\nbicolored noise. Journal of Geophysical Research 99, 13239-13249.\\\\\n \nTakalo, J., Lohikoski, R., Timonen, J., Lehtokangas, M., and Kaski, K., 1996. Time series\nanalysis and prediction of AE and Dst data. In: Burke, W. and Guyenne, T. D., (Eds.),\nEnvironment Modelling for Space Based Applications, ESA SP-392. European Space Agency.\\\\\n\nTakalo, J., Timonen, J., Klimas, A. J., Valdivia, J. A., Vassiliadis, D., 1999a. Nonlinear energy\ndissipation in a cellular automaton magnetotail field model. Geophysical Research Letters 26, 1813-1816.\\\\\n\nTakalo, J., Timonen, J., Klimas, A. J., Valdivia, J. A., Vassiliadis, D.,1999b.\n A coupled-map model for the magnetotail current sheet. Geophysical Research Letters,\n 26, 2913-2916.\\\\\n\nTakalo, J., Timonen, J., Klimas, A. J., Valdivia, J. A., Vassiliadis, D., 1999c. A coupled-map\nas a model of the dynamics of the magnetotail current sheet. Submitted to\n Journal of Atmospheric and Solar-Terrestrial Physics. \\\\\n\n \nTsurutani, B., Sugiura, M., Iyemori, T., Goldstein, B. E., \nGonzalez, W. D., Akosofu, S.-I., Smith, E. J., 1990. The nonlinear response of\nAE to the IMF $B_s$ driver: a spectral break at 5 hours. Geophysical Research Letters 17, 279-282.\n\\\\\n\n \nUritsky, V. M., and Pudovkin, M. I., 1998. Low frequency 1/f-like\nfluctuations of the AE-index as a possible manifestation of\nself-organised criticality in the magnetosphere. Annales Geophysicae 16, 1580-1588.\\\\\n\nVassiliadis, D., Anastasiadis, A., Georgioulis, M., Vhlahos, L., 1998.\nDerivation of solar flare cellular automaton models from a subset of the magnetohydrodynamic equations.\nAstrophysical Journal 509, L53-56. \\\\\n\nV\\\"{o}r\\\"{o}s, Z., 1991. Synergetic approach to substorm phenomenon. In: Kan, J. R., Potemra, T. A.,\nKokubun, S., Iijima, T., (Eds.), Magnetospheric Substorms. American Geophysical Union.\\\\\n\nV\\\"{o}r\\\"{o}s, Z., Kovacs, P., Juhasz, A., Kormendi, A., Green, A. W., 1998. Scaling\nlaws from geomagnetic time series. Geophysical Research Letters 25, 2621-2624.\\\\\n\nWatkins, N. W., Freeman, M. P., Rhodes, C. S., Rowlands, G. 1999a. Ambiguities\nin determination of self-affinity in ionospheric time\nseries. Submitted to proceedings of the EGS/AGU Richardson\nConference, Roscoff, France, June 1998.\\\\\n\nWatkins, N. W., Chapman, S. C., Dendy, R. O., Rowlands, G., 1999b. Robustness\nof collective behaviour in a strongly driven avalanche model: magnetospheric\nimplications. Geophysical Research Letters 26, 2617-2620.\\\\\n\nZapperi, S., Lauritsen, K. B., Stanley, H. E., 1996. Self-organized branching\nprocesses: a mean field theory for avalanches. Physical Review Letters 75,\n4071-4074.\\\\\n \nZelenyi, L. M., Milovanov, A. V., Zimbardo G., 1998. Multiscale magnetic structure of the distant\ntail: self-consistent fractal approach. In: Nishida, A., Baker, D. N., Cowley, S. W. H. (Eds.),\nNew perspectives on the earth's magnetotail. American Geophysical Union.\\\\\n \n\\newpage\n\n \n\n\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n"
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astro-ph0002360
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Solving the Coincidence Problem: Tracking Oscillating Energy
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[
{
"author": "Scott Dodelson$^{1,2}$"
},
{
"author": "Manoj Kaplinghat$^{2}$"
},
{
"author": "and Ewan Stewart$^{1,3}$"
}
] |
Recent cosmological observations strongly suggest that the universe is dominated by an unknown form of energy with negative pressure. Why is this dark energy density of order the critical density today? We propose that the dark energy has periodically dominated in the past so that its preponderance today is natural. We illustrate this paradigm with a model potential and show that its predictions are consistent with all observations. %An intriguing suggestion is that this energy {\em tracks\/} the other %forms of energy (e.g.\ matter, radiation) in the Universe, thereby explaining %its closeness to the critical density today. %In general tracking models fail, however, because %(i) they give the wrong equation of state and %(ii) they spoil the predictions of Big Bang Nucleosynthesis. %We propose a class of models which track but can avoid these problems. %These models require an oscillatory potential; %the resultant field dynamics not only solves the missing energy %problem but also leads to testable predictions in the Cosmic %Microwave Background (CMB) and Large Scale Structure (LSS).
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"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\documentstyle[aps,twocolumn,prl,tighten,epsfig]{revtex} %eqsecnum,\n\\input epsf\n\\def\\plotone#1{\\centering \\leavevmode\n\\epsfxsize= 0.95\\columnwidth \\epsfbox{#1}}\n\\def\\plottwo#1{\\centering \\leavevmode\n\\epsfxsize= 0.7\\columnwidth \\epsfbox{#1}}\n\\def\\plotfiddle#1#2#3#4#5#6#7{\\centering \\leavevmode\n\\vbox to#2{\\rule{0pt}{#2}}\n\\special{psfile=#1 voffset=#7 hoffset=#6 vscale=#5 hscale=#4 angle=#3}}\n%\\documentstyle[12pt,psfig]{article}\n%,margins\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%% begin local macros %%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\def\\ang{\\,{\\rm\\AA}}\n\\def\\flux{\\,{\\rm erg\\,cm^{-2}\\,arcsec^{-2}\\,\\AA^{-1}\\,s^{-1}}}\n\\def\\GeV{\\,{\\rm GeV}}\n\\def\\TeV{\\,{\\rm TeV}}\n\\def\\gev{\\,{\\rm GeV}}\n\\def\\keV{\\,{\\rm keV}}\n\\def\\MeV{\\,{\\rm MeV}}\n\\def\\sec{\\,{\\rm sec}}\n\\def\\Gyr{\\,{\\rm Gyr}}\n\\def\\yr{\\,{\\rm yr}}\n\\def\\rcm{\\,{\\rm cm}}\n\\def\\pc{\\,{\\rm pc}}\n\\def\\kpc{\\,{\\rm kpc}}\n\\def\\Mpc{\\,{\\rm Mpc}}\n\\def\\mpc{\\,{\\rm Mpc}}\n\\def\\eV{{\\,\\rm eV}}\n\\def\\ev{{\\,\\rm eV}}\n\\def\\erg{{\\,\\rm erg}}\n\\def\\cmm2{{\\,\\rm cm^{-2}}}\n\\def\\cm2{{\\,{\\rm cm}^2}}\n\\def\\cmm3{{\\,{\\rm cm}^{-3}}}\n\\def\\gcmm3{{\\,{\\rm g\\,cm^{-3}}}}\n\\def\\kms{\\,{\\rm km\\,s^{-1}}}\n\\def\\HO{{100h\\,{\\rm km\\,sec^{-1}\\,Mpc^{-1}}}}\n\\def\\mpl{{m_{\\rm Pl}}}\n\\def\\mpp{{m_{\\rm Pl,0}}}\n\\def\\trh{T_{\\rm RH}}\n\\def\\g{\\tilde g}\n\\def\\R{{\\cal R}}\n\\def\\zl{z_{\\rm LSS}}\n\\def\\zeq{z_{\\rm EQ}}\n\\def\\he{$^4$He}\n\\def\\VEV#1{\\left\\langle #1\\right\\rangle}\n\\def\\la{\\mathrel{\\mathpalette\\fun <}}\n\\def\\ga{\\mathrel{\\mathpalette\\fun >}}\n\\def\\fun#1#2{\\lower3.6pt\\vbox{\\baselineskip0pt\\lineskip.9pt\n \\ialign{$\\mathsurround=0pt#1\\hfil##\\hfil$\\crcr#2\\crcr\\sim\\crcr}}}\n\\def\\lcdm{$\\Lambda$CDM~}\n\\def\\eg{{\\it e.g.}}\n\\def\\ie{{\\it i.e.}}\n\\def\\etal{{\\it et al. }}\n\\def\\apriori{{\\it a priori }}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%% end local macros %%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n%\\baselineskip=24pt\n\\twocolumn[\\hsize\\textwidth\\columnwidth\\hsize\\csname @twocolumnfalse\\endcsname\n%\\pagestyle{empty}\n%\\begin{center}\n%\\rightline{{\\large DRAFT} (Ewan; July 28, 1999)}\n%\\bigskip\n%\\rightline{FERMILAB--Pub--}\n%\\rightline{astro-ph/0002360}\n%\\rightline{submitted to {\\it Phys. Rev. Lett.}}\n\n%\\vspace{.2in}\n\\title{Solving the Coincidence Problem: Tracking Oscillating Energy} \n\n%\\vspace{.2in}\n\\author{Scott Dodelson$^{1,2}$,\n Manoj Kaplinghat$^{2}$, and Ewan Stewart$^{1,3}$\n}\n%\\vspace{.2in}\n\n\\address{$^1$NASA/Fermilab Astrophysics Center\nFermi National Accelerator Laboratory, Batavia, IL~~60510-0500}\n\\address{$^2$Department of Astronomy \\& Astrophysics\nEnrico Fermi Institute, The University of Chicago, \nChicago, IL~~60637-1433}\n\\address{$^3$Department of Physics, KAIST, Taejon 305-701,\nSouth Korea}\n\n\\date{\\today}\n\\maketitle\n\n\\begin{abstract}\nRecent cosmological observations strongly suggest that the universe\nis dominated by an unknown form of energy with negative pressure.\nWhy is this dark energy density of order the critical density today? \nWe propose that the dark energy has \nperiodically dominated in the past so that its preponderance \ntoday is natural. We illustrate this paradigm with a model potential \nand show that its predictions are consistent with all observations.\n%An intriguing suggestion is that this energy {\\em tracks\\/} the other\n%forms of energy (e.g.\\ matter, radiation) in the Universe, thereby explaining\n%its closeness to the critical density today.\n%In general tracking models fail, however, because\n%(i) they give the wrong equation of state and\n%(ii) they spoil the predictions of Big Bang Nucleosynthesis.\n%We propose a class of models which track but can avoid these problems.\n%These models require an oscillatory potential;\n%the resultant field dynamics not only solves the missing energy\n%problem but also leads to testable predictions in the Cosmic\n%Microwave Background (CMB) and Large Scale Structure (LSS).\n\\end{abstract}\n]\n\n{\\parindent0pt\\it Introduction.}\nA variety of evidence accumulated over the last several years \npoints to the existence of an unknown, unclumped form of energy in the Universe.\nFirst was an apparent concordance \\cite{Concordance} of different measurements: \nthe age of the Universe; the Hubble constant; the baryon fraction in clusters;\nand the shape of the galactic power spectrum.\nSecond came the stunning observations \\cite{SN} of tens of distant Type Ia Supernovae,\nwhich found a distance-redshift relation in accord with a cosmological constant,\nbut in strong disagreement with a matter dominated Universe.\nFinally, this past year has seen analyses \\cite{cmb} of the experiments \nmeasuring anisotropies in the CMB.\nTaken together, the CMB experiments plot out a rough shape for the power spectrum,\none that is in accord with a flat Universe, but in disagreement with an open Universe.\nIf we believe the estimates of matter density coming from observations of clusters \\cite{cluster},\nthe only way to get a flat Universe, and hence account for the CMB measurements,\nis to have an unclumped form of energy density pervading the Universe.\n\nPerhaps the simplest explanation of these data is that the unclumped form of energy density\ncorresponds to a positive cosmological constant\\cite{coscon}.\nA non-zero but tiny constant vacuum energy density (cosmological constant) could\nconceivably be explained by some unknown string theory symmetry\n(that sets the vacuum energy density to zero) being broken by a small amount.\nHowever, to explain in this way a constant vacuum energy density of\n$2 \\times 10^{-59} \\TeV^4$, which is not only small but is also just the right value\nthat it is just beginning to dominate the energy density of the Universe {\\em now\\/},\nwould require an unbelievable coincidence.\nA different possibility is to \ngive up the dream of finding a mechanism which would set the vacuum\nenergy density to exactly zero and resort to believing that anthropic considerations\nselect amongst $\\gtrsim 10^{100}$ string vacua to find one with a vacuum energy\ndensity sufficiently fine-tuned for life.\nAlthough this anthropic selection mechanism is logically consistent and even predicts\na small but observable cosmological constant, one might think that nature would have\nfound a more efficient mechanism to obtain a sufficiently small cosmological constant\nthan such extreme brute force application of anthropic selection.\n\nAn alternative is to assume that the true vacuum energy density is zero,\nand to work with the idea that the unknown, unclumped energy is due to a scalar field\n$\\phi$ which has not yet reached its ground state.\nThis idea, which is called dynamical lambda or quintessence, has received much\nattention \\cite{quint} over the last several years.\nHowever, two problems still remain.\nFirst, the field's mass has to be extremely small, less than or of order the Hubble\nconstant today $\\sim 10^{-33} \\eV$, to ensure that it is still rolling to its vacuum\nconfiguration.\nThis is in general difficult because scalar fields tend to acquire masses greater than\nor of order the scale of supersymmetry breaking suppressed by at most the Planck scale:\n$ m \\gtrsim F/\\mpl \\gtrsim {\\rm TeV}^2 / \\mpl \\sim 10^{-3} \\eV$.\nAlthough difficult, this could be achieved using pseudo-Nambu-Goldstone bosons\n\\cite{Goldstone}.\nAnother more speculative way to achieve this would be to use the hypothetical symmetry\n(perhaps some sort of hidden supersymmetry) that ensures that the true vacuum energy\ndensity is zero to also protect the flat directions in scalar field space that would\ncorrespond to the very light scalar fields necessary for quintessence.\nThe second, and perhaps even more serious problem is that almost all of these models\nrequire that we live in a special epoch today, when the quintessence is just starting\nto dominate the energy density of the Universe, and furthermore this specialness cannot\neven be justified by use of anthropic arguments.\n\nIn recent years a lot of progress has been made in understanding the\nbehavior of quintessence fields. A broad class of solutions, called tracker \nsolutions \\cite{steinhardt}, has been discovered in which the final value \nof the quintessence energy density is insensitive to the initial conditions.\nFor example, potentials like $V = V_0 \\phi^{-n}$ or $V = V_0 \\exp(1/\\phi)$ \ncan, for suitable choices of $V_0$, catch up with the critical density late \nin the evolution of the Universe for a wide range of initial conditions\nand thus provide a natural setting for explaining the current acceleration \nof the Universe. However, the suitable choice of $V_0$ must be of the order \nof the critical energy density today, \\ie, we are back to the \nproblem of living at a special epoch today and not even being able to use \nanthropic arguments to justify this specialness. \n\nIn a subset of these tracking models, which we call the exact tracker \nsolutions \\cite{tracker,joyce}, the scalar field energy density is always \nrelated to the ambient energy density in the Universe: if the \ndominant component in the Universe is radiation, then the tracking \nfield's energy density also falls off as $a^{-4}$, where $a$ is the \nscale factor of the Universe. If the dominant component is matter, then \nthe field's energy density scales as $a^{-3}$. This behavior arises from \nan exponential potential for $\\phi$ (regardless of the value of $V_0$). \nSince the energy density in this field is always comparable to the \nbackground density, we are not living at a special epoch: any observer \nin the distant past or future would also see the tracking field's energy \ndensity. However, these tracking solutions run into two problems. First, \nif their energy density today truly is dominant, then it should also have \nbeen dominant at the time of Big Bang Nucleosynthesis (BBN). Constraints \nfrom observations of light element abundances preclude such an additional \nform of energy density at early times. Second, tracking models have the \nwrong equation of state at present since the tracking field behaves \nlike matter, with zero pressure, instead of having the necessary negative \npressure to accelerate the Universe.\n\nIn this {\\em letter} we ask the question, what if the Universe has been\naccelerating periodically in the past? Then the fact that the Universe is \naccelerating today would not be surprising. It would merely reflect\nthat the period is such that the Universe is accelerating today.\nOf course, if it turned out that to achieve a presently accelerating\nUniverse the period had to be excessively fine-tuned, then this scenario \nwould not be worth considering. However, note that the assumption that there\nis nothing special about the present time itself argues for the robustness of \nsuch a scenario. If the Universe does accelerate periodically, then there\nis no reason why it should not be accelerating today. If the Universe\ndoes accelerate periodically, then it is, in fact, reasonable to expect it \nto accelerate today. \n\nTo judge the merits of this scenario in a concrete manner, we adopt an\nad-hoc potential. Though worked out for this specific potential, the \npredictions outlined here are the generic predictions of a periodically \naccelerating Universe. The model we adopt for study is a modification of \nthe exponential potential (which leads to the exact tracker solution).\nThe modification to the potential is a sinusoidal modulation, which\ninduces the tracker field to oscillate about the ambient energy density.\nWe show that such a potential can satisfy the the BBN constraints, can produce \nthe right equation of state today and leads to testable features in the \nCMB and matter power spectra.\nWe call this type of energy {\\em Tracking, Oscillating Energy}, or TOE.\n\n{\\parindent0pt\\it The potential and the field evolution.}\nConsider a scalar field $\\phi$ with potential\n$V(\\phi) = V_0 \\exp( - \\lambda \\phi \\sqrt{8\\pi G})$.\nIt is well-known \\cite{tracker} that such a potential leads to an attractor solution with\n$\\Omega_\\phi \\equiv \\rho_\\phi /(\\rho_\\phi + \\rho_o) = n/\\lambda^2$\nwhere $\\rho_o$ is the energy density in the other component of the Universe,\nwhich is assumed to scale as $a^{-n}$. Thus, no matter what the initial\nconditions are for $\\phi$, it always evolves so that it tracks the\nrest of the density in the Universe. \n\nNow consider the potential\n\\begin{equation}\\label{pot}\nV(\\phi) = V_0 \\exp \\left( -\\lambda\\phi \\sqrt{8\\pi G} \\right)\n\\left[ 1 + A \\sin(\\nu\\phi\\sqrt{8\\pi G}) \\right].\n\\end{equation}\nThis potential serves to modulate the tracking behavior.\nFigure \\ref{fig1} shows the resultant evolution of $\\phi$\nand its energy density for a particular set of the parameters\n$A,\\nu$. (The normalization $V_0$ can be set to $G^{-2}$\nby shifting the initial value of $\\phi$.)\nAlso shown is the tracking solution for this\nparticular value of $\\lambda$ without the modulation. \nAs expected, the sinusoidal term in the potential leads to\noscillations about this tracking behavior. \nOne can obtain analytic solutions for the dynamics of the potential\nin Eq.~(1)\nduring radiation ($n=4$) or matter ($n=3$) domination in the\nlimit that $A$ is small by perturbing about the corresponding exact tracker\nmodel which has $\\phi\\sqrt{8\\pi G} = \\frac{n}{\\lambda} \\ln a$. The sine in Eq.~(1) provides\na periodic forcing term with period $\\ln a = \\frac{2 \\pi \\lambda}{n\n\\nu}$,\nwhile the natural period\\cite{tracker} of the damped oscillations about the exact\ntracker solution is $\\ln a = 8 \\pi \\lambda / \\sqrt{(6-n)[3(3n-2)\\lambda^2-8n^2]}$\nwith decay $e$-life $\\ln a = 4/(6-n)$.\nAlthough the above results are strictly valid only for small $A$, they\naccount remarkably well for the behaviour shown in Figure~1. The forced\nperiod corresponds to the longer period of $5.4$ units ($n=4$) and\nsomehwere between $5.4$ units and $7.1$ units ($n=3$), while the natural\nperiod corresponds to the shorter period of $1.6$ units ($n=4,3$) of the\ndamped oscillations which are presumably excited by the non-linear\neffects\nthat appear when $A$ is not small.\n\n\n\\begin{figure}[thbp]\n\\plotone{omphi.eps}\n\\caption[caption]{The fraction of the critical density in $\\phi$\nfor the potential in Eq.~(\\ref{pot}). The dotted line shows the corresponding tracking\nsolution ($A=0$). The upper set of curves shows the evolution in \n$\\phi$ for the TOE and the tracking models.}\n\\label{fig1}\n\\end{figure}\n\nThe energy density due to $\\phi$ is relatively small at the time\nof BBN and relatively large today for the parameter set in Figure~\\ref{fig1}.\nIt is, of course, clear that in order to get the right behavior at BBN and \ntoday, one has to pick the ``correct'' parameter sets. This involves a bit of \nfine-tuning which, as we argue below, is quite reasonable and natural.\nIf one thinks of the parameter set as being randomly selected, then there \nis a finite probability that the Universe will be accelerating today and \nthat the energy density of $\\phi$ will be sub-dominant at BBN. What is this \nprobability? If one selects $A$, $\\nu$ and $\\lambda$ randomly, the chance \nof getting a Universe like ours is of the order of 1 in a 100. The exact \nnumber (for this potential) depends on how stringently we define \n``a Universe like ours''. For example the tight constraints \n$0.4 < \\Omega_\\phi < 0.8$, $w_\\phi < -0.5$, and \n$(\\rho_\\phi/\\rho_0)_{\\rm BBN} < 0.1$ give a probability of 1 in \n450, while the relaxed constraints $0.1 < \\Omega_\\phi < 0.9$ and \n$w_\\phi < -0.25$ and $(\\rho_\\phi/\\rho_0)_{\\rm BBN} < 0.2$\ngive a probability of 1 in 26. It is also very important\nto note that whatever the extent of fine-tuning, all of it is in \n{\\em dimensionless} numbers. There are no energy scales in this scenario \nwhich are to be set by the present expansion rate of the Universe.\n\n{\\parindent0pt\\it Power Spectra.}\nTo compare with CMB and large scale structure observations, we compute \nthe power spectra of the perturbations in a TOE model.\nPerturbations evolve differently in the presence of the scalar field \nenergy density. For example, perturbations typically grow only when \nthe Universe is matter dominated. Therefore, we expect a non-zero\n$\\Omega_\\phi$ to lead directly to power suppression on the scales inside the \nhorizon, with increased suppression for larger $\\Omega_\\phi$. \n\n\\begin{figure}[thbp]\n\\plotone{cl.eps}\n\\caption[caption]{The angular photon power spectrum from the TOE model of \nFigure \\ref{fig1}. Also shown is a cosmological constant model with \nall other parameters equal.}\n\\label{cls}\n\\end{figure}\n\nThe prediction for the CMB angular power spectrum is plotted in Figure \n\\ref{cls}. The primeval power spectrum is scale-invariant with adiabatic \ninitial conditions. Also plotted for comparison is a model ($\\Lambda$CDM) with\ncosmological constant $\\Omega_\\Lambda=\\Omega_\\phi$ today and the rest of the \ncosmological parameters\nalso being the same. In further discussions we will contrast the results from\nthe TOE model against this \\lcdm model. \nA noteworthy feature in Figure \\ref{cls} is the increase in the heights of \nthe first two peaks compared to that of the \\lcdm model. This stems from\nthe fact that the gravitational potential decays \nmore in the presence of the additional quintessence energy density. The decay of the\npotential at and after recombination (the so-called Integrated Sachs-Wolfe\n, or ISW, effect) leads\\cite{HS} to enhanced power on scales $l \\la 600$,\nafter which the potential becomes irrelevant. Note that the increase in the amplitude of both\nthe first and second peak cannot be mimicked by adding more baryons, which raise the odd peaks\nbut lower the even ones.\n\nOn smaller scales $(l\\ga 600)$, the TOE model has smaller anisotropies. Here there are\ntwo competing effects. First, the \ndifference between the TOE and the \\lcdm models (around recombination\nwhen $\\Lambda$ is insignificant) is the presence of the extra quintessence \nenergy density, which leads to the expansion rate in the two models\nbeing related as--\n\\begin{equation}\nH_{\\mathrm{TOE}}(a) = H_{\\mathrm{\\Lambda CDM}} (a)\\; \\times\\; \n\\left(1-\\Omega_\\phi(a)\\right)^{-1/2}\\;.\n\\label{expansion}\n\\end{equation}\nEq. \\ref{expansion} implies that all the relevant scales at recombination \n(which occurs at $a_r\\simeq 10^{-3}$) are smaller in the TOE model by a \nfactor of about $\\sqrt{1-\\Omega_\\phi(a_r)}$. In particular, the damping \nscale is smaller, which increases in the power on small\nscales for the TOE model relative to the \\lcdm model. The second effect is \nthe large scale normalization of the two models \\cite{footnote1}, \nand this second effect more than\ncompensates for the first. COBE normalization is sensitive to scales around \n$\\ell=10$ for which the differences in the two models with regard to the \nlate-ISW effect is important. In particular, since $\\Lambda$ domination \noccurs very late, the ISW contribution around $\\ell=10$ is much larger in\nthe TOE model. This in turn implies that the normalization of the\nprimeval power spectrum is smaller, a fact noticeable in the smaller amplitude\nof the photon power spectrum for the TOE model at small scales (and also the matter\npower spectrum, as we will soon see). \nOne last effect that is worth pointing out concerns the difference in\nthe peak positions in the two models (though unlike the peak amplitudes, it\nis probably not easily discerned). In particular, the TOE model has the acoustic \nfeatures in its angular power spectrum shifted to smaller scales. This \ndirectly traces to the decrease in the angular diameter distance to the \nlast scattering surface, for the TOE model. Of course, there is also \nthe competing effect of the decrease in the size of the sound horizon at \nlast scattering for the TOE model, which minimizes the effect.\n\n\\begin{figure}[thbp]\n\\plotone{power.eps}\n\\caption[caption]{The matter power spectrum from \nthe TOE model of Figure \\ref{fig1}. \nAlso shown is a cosmological constant model with \nall other parameters equal. Power is significantly smaller in the TOE model.}\n\\label{ps}\n\\end{figure}\n\nThe prediction for the matter power spectrum is plotted in Figure \\ref{ps}.\nThe difference in power at the largest scales is due to COBE normalization\nand the difference in the super-horizon growth factor (which is sensitive \nto the equation of state of the cosmic fluid) for the perturbation. \nAs one moves to smaller scales, which entered the horizon well before \nthe present, the differences in the evolution of the matter perturbation\nbecome more pronounced. The presence of the extra quintessence energy \nstunts the growth of perturbation once a mode enters the horizon. So, the \nearlier the mode enters the horizon, the larger the growth suppression \nrelative to the \\lcdm model. In other words, smaller modes are \nmonotonically\nmore suppressed (something that may not be noticeable in the log plot) \ncompared to the same modes in \\lcdm model. It might also be surprising that\nthe $\\phi$ domination around $a=10^{-6}$ does not cause a more appreciable\nfeature (\\ie, suppression) in the power spectrum. The reason is that the\nsmallest scales in Figure \\ref{ps} have just entered the horizon at the\ntime of $\\phi$ domination ($a\\sim 10^{-6}$).\n\nThe normalization on the small scales is generally quoted in terms of \n$\\sigma_8$, the rms mass fluctuation within a $8\\,h^{-1}\\Mpc$ sphere. For the\nparameters in Figure \\ref{fig1}, the TOE model has $\\sigma_8=0.4$. This\nis several sigma smaller than the preferred value (see e.g. \\cite{wang}) of $\\sim 0.8$,\nbut could be rectified by a small blue-shift in the primordial spectrum\n\\cite{stewart}. \n\n\n{\\parindent0pt\\it Conclusions.} We have constructed a model\nwherein the energy density tracks the dominant component\nin the Universe; satisfies the BBN constraints; and has\nthe proper equation of state today. Further, this model\nmakes definite predictions for large scale structure and for the\nCMB.\n\nPerhaps the greatest drawback of this class of models is the\narbitrariness of the potential.\nIn particular we know of no theory which predicts a potential\nof the form given in Eq.~(\\ref{pot}).\nNonetheless, we feel that the testable predictions of the model\nand the aesthetic quality it preserves that we do not live in\na special epoch are of sufficient interest to warrant further\nstudy.\n\n\\bigskip\n\n\n\nWe thank Limin Wang for helpful discussions.\nThe CMB spectra used in this work were generated by an\namended version of CMBFAST \n\\cite{CMBCalculations}.\nThis work was supported by the DOE and the NASA grant NAG\n5-7092 at Fermilab.\nEDS acknowledges support by the KOSEF\nInterdisciplinary Research Program grant 1999-2-111-002-5\nand the Brain Korea 21 Project.\n\n\\newcommand\\sapj[3]{ {\\it Astrophys. J.} {\\bf #1}, #2 (19#3) }\n\\newcommand\\sprd[3]{ {\\it Phys. Rev. D} {\\bf #1}, #2 (19#3) }\n\\newcommand\\sprl[3]{ {\\it Phys. Rev. Letters} {\\bf #1}, #2 (19#3) }\n\\newcommand\\np[3]{ {\\it Nucl.~Phys. B} {\\bf #1}, #2 (19#3) }\n\n\\begin{thebibliography}{99}\n\n\n\\bibitem{Concordance} L. Krauss and M.S. Turner, \n{\\it Gen. Rel. Grav.} {\\bf 27}, 1137 (1995); \nJ.P. Ostriker and P.J. Steinhardt, \n{\\it Nature} {\\bf 377}, 600 (1995); S. Dodelson,\nE.I. Gates, \\& M.S.Turner, Science, {\\bf 274}, 69 (1996);\nA.R. Liddle et al, {\\it Mon. Not. R. astron. Soc.}\n{\\bf 282}, 281 (1996).\n\n\\bibitem{SN} A. Riess et al, Astronom. J.\n116, 1009 (1998);\nS. Perlmutter et al, Astrophys. J., 517, 565 (1999).\n\n\\bibitem{cmb} S. Dodelson \\& L. Knox, astro-ph/9909454 (1999);\nA. Melchiorri et al., astro-ph/9911445 (1999);\nM. Tegmark \\& M. Zaldarriaga, astro-ph/0002091 (2000);\nG.~Efstathiou, astro-ph/0002249 (2000).\nPreviuos work before the most recent data includes\nP.~de Bernardis et al., \\apj {\\bf 480}, 1 (1997);\nC.~H.~Lineweaver, \\apj {\\bf 505}, L69 (1998);\nS.~Hancock et al., MNRAS {\\bf 294}, L1 (1998);\nJ.~Lesgourgues et al., astro-ph/9807019 (1998);\nJ.~Bartlett et al., astro-ph/9804158 (1998); \n P. Garnavich et al., Astrophys. J. {\\bf 509} 74 (1998); \nJ.~R.~Bond \\& A.~H.~Jaffe, astro-ph/98089043 (1998);\nA.~M.~Webster, \\apj {\\bf 509}, L65 (1998);\nM.~White, \\apj {\\bf 506}, 485 (1998);\nB.~Ratra et al., \\apj {\\bf 517}, 549 (1999);\nM.~Tegmark, \\apj {\\bf 514}, L69 (1999);\nN.A. Bahcall, J.P. Ostriker, S. Perlmutter and\nP.J. Steinhardt, Science {\\bf 284}, 1481 (1999).\n\n\n\\bibitem{cluster} E.g. S.D.M. White, J.F. Navarro, A. Evrard and C. Frenk, \nNature {\\bf 366}, 429 (1993).\n\n\\bibitem{coscon} M.S.Turner, G. Steigman, and L. Krauss,\nPhys. Rev. Lett. {\\bf 52}, 2090\n(1984); P.J.E. Peebles, Astrophys. J. {\\bf 284}, 439\n(1984); L. Kofman and A.A. Starobinskii, Sov. Astron. Lett.\n{\\bf 11}, 271 (1985); G. Efstathiou, Nature {\\bf 348}, 705\n(1990); M. S. Turner, Physica Scripta {\\bf T36},\n167 (1991).\n\n\\bibitem{quint} K. Freese {\\it et al.}, Nuc. Phys. {\\bf B287}, 797 (1987);\nN. Weiss, \\prl {\\bf 197}, 42 (1987);\nM. Ozer and M. Taha, Nuc. Phys. {\\bf B287}, 776 (1988); B. Ratra and P.J.E. Peebles, {\\it Phys. Rev. D} {\\bf 37}, \n3406 (1988); W. Chen and\nY. Wu, Phys. Rev. {\\bf D41}, 695 (1990);\nJ. Carvalho, J. Lima, and I. Waga, Phys. Rev. {\\bf D46}, 2404 (1992);\nV. Silveira and I. Waga, Phys. Rev. {\\bf D50}, 4890 (1994);\nJ. Frieman, C. Hill, A. Stebbins, \\& I. Waga, \n{\\it Phys. Rev. Lett.} {\\bf 75}, 2077 (1995); K. Coble, S. Dodelson, \n\\& J.A. Frieman, Phys. Rev. D55, 1851 (1997); \nR. Caldwell, R. Dave, \\& P. S. Steinhardt, Phys. Rev. Lett. {\\bf 80}, 1582 (1998).\n\n\\bibitem{Goldstone} K. Choi, hep-ph/9902292; hep-ph/9912218.\n\n\n\\bibitem{tracker} C. Wetterich, Astron. \\& Astrophys. {\\bf 301}, 321\n(1995).\n\n\\bibitem{joyce} P.G. Ferreira \\& M. Joyce,\nPhys. Rev. D58 023503 (1998).\n\n\n\\bibitem{steinhardt} P.J.E. Peebles \\& B. Ratra, Phys. Rev. {\\bf D37} 3406\n(1988); I. Zlatev, L. Wang, \\& P.J. Steinhardt, \\prl {\\bf 82}, \n896 (1998); P.J. Steinhardt, L. Wang, \\& I. Zlatev, Phys. Rev. {\\bf D59}, \n123504 (1999); A. Albrecht \\& C. Skordis, astro-ph/9908085 (1999).\n\n\\bibitem{wang} L. Wang et al., astro-ph/9901388 (1999).\n\n\\bibitem{HS} W. Hu \\& N. Sugiyama, \\prd {\\bf 50}, 627 (1994). \n\n\\bibitem{footnote1} Note that the normalization affects the first two peaks \nalso: the TOE model would have an even larger relative amplitude there if \nnot for the large scale normalization.\n\n\\bibitem{stewart} Some inflationary models with blue spectra include\nE. Stewart, Phys. Rev. {\\bf D51}, 6847 (1995); ibid. {\\bf D56}, 2019 (1997);\nL. Randall, M. Soljacic, \\& A. H. Guth, Nucl. Phys. B {\\bf 472}, 277 (1996).\n\n\\bibitem{CMBCalculations} \nU.~Seljak and M.~Zaldarriaga, \\sapj{469}{437}{96}.\n\n\n\\end{thebibliography}\n\\end{document}\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002360.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\n\\bibitem{Concordance} L. Krauss and M.S. Turner, \n{\\it Gen. Rel. Grav.} {\\bf 27}, 1137 (1995); \nJ.P. Ostriker and P.J. Steinhardt, \n{\\it Nature} {\\bf 377}, 600 (1995); S. Dodelson,\nE.I. Gates, \\& M.S.Turner, Science, {\\bf 274}, 69 (1996);\nA.R. Liddle et al, {\\it Mon. Not. R. astron. Soc.}\n{\\bf 282}, 281 (1996).\n\n\\bibitem{SN} A. Riess et al, Astronom. J.\n116, 1009 (1998);\nS. Perlmutter et al, Astrophys. J., 517, 565 (1999).\n\n\\bibitem{cmb} S. Dodelson \\& L. Knox, astro-ph/9909454 (1999);\nA. Melchiorri et al., astro-ph/9911445 (1999);\nM. Tegmark \\& M. Zaldarriaga, astro-ph/0002091 (2000);\nG.~Efstathiou, astro-ph/0002249 (2000).\nPreviuos work before the most recent data includes\nP.~de Bernardis et al., \\apj {\\bf 480}, 1 (1997);\nC.~H.~Lineweaver, \\apj {\\bf 505}, L69 (1998);\nS.~Hancock et al., MNRAS {\\bf 294}, L1 (1998);\nJ.~Lesgourgues et al., astro-ph/9807019 (1998);\nJ.~Bartlett et al., astro-ph/9804158 (1998); \n P. Garnavich et al., Astrophys. J. {\\bf 509} 74 (1998); \nJ.~R.~Bond \\& A.~H.~Jaffe, astro-ph/98089043 (1998);\nA.~M.~Webster, \\apj {\\bf 509}, L65 (1998);\nM.~White, \\apj {\\bf 506}, 485 (1998);\nB.~Ratra et al., \\apj {\\bf 517}, 549 (1999);\nM.~Tegmark, \\apj {\\bf 514}, L69 (1999);\nN.A. Bahcall, J.P. Ostriker, S. Perlmutter and\nP.J. Steinhardt, Science {\\bf 284}, 1481 (1999).\n\n\n\\bibitem{cluster} E.g. S.D.M. White, J.F. Navarro, A. Evrard and C. Frenk, \nNature {\\bf 366}, 429 (1993).\n\n\\bibitem{coscon} M.S.Turner, G. Steigman, and L. Krauss,\nPhys. Rev. Lett. {\\bf 52}, 2090\n(1984); P.J.E. Peebles, Astrophys. J. {\\bf 284}, 439\n(1984); L. Kofman and A.A. Starobinskii, Sov. Astron. Lett.\n{\\bf 11}, 271 (1985); G. Efstathiou, Nature {\\bf 348}, 705\n(1990); M. S. Turner, Physica Scripta {\\bf T36},\n167 (1991).\n\n\\bibitem{quint} K. Freese {\\it et al.}, Nuc. Phys. {\\bf B287}, 797 (1987);\nN. Weiss, \\prl {\\bf 197}, 42 (1987);\nM. Ozer and M. Taha, Nuc. Phys. {\\bf B287}, 776 (1988); B. Ratra and P.J.E. Peebles, {\\it Phys. Rev. D} {\\bf 37}, \n3406 (1988); W. Chen and\nY. Wu, Phys. Rev. {\\bf D41}, 695 (1990);\nJ. Carvalho, J. Lima, and I. Waga, Phys. Rev. {\\bf D46}, 2404 (1992);\nV. Silveira and I. Waga, Phys. Rev. {\\bf D50}, 4890 (1994);\nJ. Frieman, C. Hill, A. Stebbins, \\& I. Waga, \n{\\it Phys. Rev. Lett.} {\\bf 75}, 2077 (1995); K. Coble, S. Dodelson, \n\\& J.A. Frieman, Phys. Rev. D55, 1851 (1997); \nR. Caldwell, R. Dave, \\& P. S. Steinhardt, Phys. Rev. Lett. {\\bf 80}, 1582 (1998).\n\n\\bibitem{Goldstone} K. Choi, hep-ph/9902292; hep-ph/9912218.\n\n\n\\bibitem{tracker} C. Wetterich, Astron. \\& Astrophys. {\\bf 301}, 321\n(1995).\n\n\\bibitem{joyce} P.G. Ferreira \\& M. Joyce,\nPhys. Rev. D58 023503 (1998).\n\n\n\\bibitem{steinhardt} P.J.E. Peebles \\& B. Ratra, Phys. Rev. {\\bf D37} 3406\n(1988); I. Zlatev, L. Wang, \\& P.J. Steinhardt, \\prl {\\bf 82}, \n896 (1998); P.J. Steinhardt, L. Wang, \\& I. Zlatev, Phys. Rev. {\\bf D59}, \n123504 (1999); A. Albrecht \\& C. Skordis, astro-ph/9908085 (1999).\n\n\\bibitem{wang} L. Wang et al., astro-ph/9901388 (1999).\n\n\\bibitem{HS} W. Hu \\& N. Sugiyama, \\prd {\\bf 50}, 627 (1994). \n\n\\bibitem{footnote1} Note that the normalization affects the first two peaks \nalso: the TOE model would have an even larger relative amplitude there if \nnot for the large scale normalization.\n\n\\bibitem{stewart} Some inflationary models with blue spectra include\nE. Stewart, Phys. Rev. {\\bf D51}, 6847 (1995); ibid. {\\bf D56}, 2019 (1997);\nL. Randall, M. Soljacic, \\& A. H. Guth, Nucl. Phys. B {\\bf 472}, 277 (1996).\n\n\\bibitem{CMBCalculations} \nU.~Seljak and M.~Zaldarriaga, \\sapj{469}{437}{96}.\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002361
|
Effect of Beam-Plasma Instabilities on Accretion Disk Flares
|
[
{
"author": "Vinod Krishan\\inst{1}"
},
{
"author": "Paul J. Wiita\\inst{2}"
},
{
"author": "S. Ramadurai\\inst{3}"
}
] |
We show that a certain class of flare models for variability from accretion disk coronae are subject to beam-plasma instabilities. These instabilities can prevent significant direct acceleration and greatly reduce the variable X-ray emission argued to arise via inverse Compton scattering involving relativistic electrons in beams and soft photons from the disk. \keywords{accretion disks -- galaxies: active -- plasmas -- Sun(the): flares -- X-rays: general}
|
[
{
"name": "astro-ph0002361.tex",
"string": "% MS A&A/1999/9102\n% Original version submitted 1 July 1999\n% Revised version submitted 25 October 1999\n% Re-revised version submitted 31 January 2000\n%\\documentclass[referee]{aa} % for a referee version\n%\\documentclass[printer]{aa} % not used so the following is fine\n\\documentclass{aa}\n\n%\n\\topmargin=0.23 truecm %MAY NEED AN ADJUSTMENT FOR OUR PRINTER\n\n\\begin{document}\n\n%\\voffset=1.0 true cm\n\\thesaurus{02.01.2; 02.16.1; 06.06.3; 11.01.2; 13.25.3 }\n\\title{Effect of Beam-Plasma Instabilities on \nAccretion Disk Flares}\n\n\\author{Vinod Krishan\\inst{1}\n\\and Paul J. Wiita\\inst{2}\n\\and S. Ramadurai\\inst{3} }\n\n\\offprints{V.\\ Krishan}\n\n\\institute{\nIndian Institute of Astrophysics, Koramangala, Bangalore 560034, \nIndia\\\\\nemail: vinod@iiap.ernet.in\n\\and\nGeorgia State University, Department of Physics and Astronomy,\nAtlanta GA, 30303, USA\\\\\nemail: wiita@chara.gsu.edu\n\\and\nTata Institute of Fundamental Research, Theoretical\nAstrophysics Group, Homi Bhabha Marg, Mumbai 400005, India\\\\\nemail: durai@tifr.res.in}\n\n\\date{Received .../ Accepted ....}\n\n\\authorrunning{Krishan et al.}\n\\titlerunning{Beam-plasma instabilities}\n\\maketitle\n\n\\begin{abstract}\nWe show that a certain class of flare models for variability from accretion\ndisk coronae are subject to beam-plasma instabilities. These instabilities\ncan prevent significant direct acceleration and greatly reduce\nthe variable X-ray emission argued to arise via inverse Compton\nscattering involving relativistic electrons in beams and soft\nphotons from the disk.\n\n\\keywords{accretion disks -- galaxies: active -- plasmas -- Sun(the): flares\n-- X-rays: general}\n\\end{abstract}\n \n\\section{Introduction}\n\nThe origin of fluctuations in the emission from Active Galactic Nuclei\n(AGN) and binary X-ray sources is an important and long-standing problem.\nOne frequently considered possibility employs flares in the coronae around\naccretion disks to produce rapid energy release, particle acceleration\nand radiation (e.g., Galeev, Rosner \\& Vaiana \\cite{galeev}; Kuperus \n\\& Ionson \\cite{kuperus};\nfor a review, see Kuijpers \\cite{kuijpers}).\nThese models usually build upon our understanding of solar flare physics.\n\nA particular model of this type has been proposed by de Vries \\& Kuijpers\n(\\cite{deVries}; hereafter dVK), and was specifically applied by them to \nX-ray variability of\nAGNs. Their model is an elaboration on typical flare scenarios,\nin that, as usual, the source of energy is stored in magnetic fields\n in coronae\nof accretion disks. They estimate the power released\nin flares in a radiation pressure dominated corona, which they stress\nis a different environment from the gas pressure dominated solar corona. \nThey argue this leads to a situation where beams of relativistic\nelectrons are produced in the corona and then lose essentially all\nof their energy through\ninverse Compton scattering on UV disk photons before they can stream\nback to the \ndisk. They further argue that these inverse Compton (IC) photons produce\nthe X-ray variability seen in Seyfert galaxies, and are able to calculate\nspectral power-densities in reasonable agreement with observations.\n\nHowever, the dVK model does not take into account other mechanisms\nthat might vitiate some of their key assumptions. We note that dVK \nbriefly argue that, particularly if radiation pressure dominates the\nenergy density in the corona, as is indeed likely around standard thin\naccretion disks (e.g., Shakura \\& Sunyaev \\cite{shakura})\nwhich they assume, energy losses through scattering on\nplasma waves are unimportant; then\nthe dominant losses will be to IC scattering. However,\nit is well known that an electron beam-plasma system is often susceptible\nto the excitation of beam-plasma instabilities which usually have\nlarge growth rates (Sturrock \\cite{sturrock}). Here we argue that\nwhen these beam-plasma instabilities (BPIs) are\ntaken into account, the rate of loss of energy by the electrons \nfor the accretion disk coronae conditions suggested by dVK is\ntypically much higher than the rate of gain of energy through \ndirect acceleration by the electric fields, which are\npresumed to arise in reconnection events.\nTherefore beams of electrons usually will not reach the high Lorentz factors\nneeded to produce most X-rays by the IC process. In many accretion disk \nmodels X-rays are usually produced through IC scattering of soft photons on\nhot thermal electrons (e.g. Shapiro, Lightman \\& Eardley \\cite{shapiro}; Liang \\&\nPrice \\cite{liang}).\nIn such a situation beam-plasma instabilities are not excited,\nand only thermal spontaneously excited plasma waves should exist. These\nwill have energy\ndensities less than the thermal energy density of the plasma, which in\nturn is much less than the radiation energy density. In this case,\nthe argument of dVK would be valid, but, once they assume a beam is\npresent, then beam-plasma instability effects {\\it must} be included. \n\n\\section{Growth of Beam-Plasma Instabilities}\n\nThe key assumptions of the dVK model are that: 1) relaxation of magnetic\nstructures efficiently produce relativistic electron beams; \n2) the particle beam is a mono-energetic\nstream of electrons with an initial Lorentz factor $\\gamma_0$; 3) the ambient\nradiation is from a quasi-infinite disk and can be considered as uniform and\nisotropic, with a radiation density $u_{\\rm rad}$; 4) the beam is optically\nthin, so multiple scattering of photons can be ignored. Although (3) is an\napproximation, it is a reasonable one, and (4) is certainly plausible under\nmany circumstances. But the core of their argument hinges on the ability of \nthe neutral sheet in the reconnection process to quickly accelerate electrons\nvia a direct electric field. During this acceleration process dVK claim \nthe equation for the acceleration of an single electron suffering\nIC losses is %EQN 1\n\\begin{equation} \n{\\frac {d \\gamma}{dt}} = \\chi_1 {\\frac {(\\gamma^2 - 1)^{1/2}}{\\gamma}}\n - \\chi_2 (\\gamma^2 - 1),\n\\end{equation}\nwhere, $\\chi_1 = eE/m_e c$ and $\\chi_2 = 4\\sigma_T u_{rad} / 3m_e c$,\nwith all symbols having their usual meanings.\nIn that the first (positive) term starts out substantially greater in\nmagnitude than the second (negative) one, acceleration will ensue until \na limiting Lorentz factor is reached when the two terms balance: %EQN 2\n\\begin{equation}\n\\gamma_{\\infty} = 2^{-1/2}[1 + (1 + 4 \\chi_1^2 / \\chi_2^2)^{1/2}]^{1/2}.\n\\end{equation}\n\nThe electric field is reasonably taken by dVK to be the Dreicer value, which\nwe take as: $E_D = 6 \\pi n_p e^3 {\\rm ln} \\Lambda /(k_B T_e)$, where $n_p$ is\nthe electron density of the ambient plasma, ${\\rm ln} \\Lambda \\approx 20$\nis the Coulomb logarithm, and all other symbols have\ntheir usual meanings.\nWith typical AGN values ($n_p \\approx 10^{10}$ cm$^{-3}$, $T_e \\approx 10^6$K,\nand $T_{rad} \\approx 10^5$K) they find $\\gamma_{\\infty} \\approx\n(\\chi_1/ \\chi_2)^{1/2} \\approx 30$. They then conclude that the electrons will\nall reach this terminal Lorentz factor before the acceleration terminates\nand the electrons then lose their energy against\nthe disk photons providing the background radiation field.\n\nWe now show that since a BPI is excited, it will \ndominate the energy losses for the beam and actually\nprevent the electrons from reaching the high Lorentz factors calculated\nby dVK.\nUnder these circumstances there will be very little IC radiation, so that,\nwhile a great deal of energy may be released through magnetic reconnection,\nthe bulk of the energy will probably provide heating to the corona (e.g.,\nLiang \\& Price \\cite{liang}) but is unlikely to yield the bulk of the\nX-rays directly through IC emission.\n\nThe dominant growth rate of the BPI depends on\nthe relative magnitudes of the bulk velocity of the beam, $v_b$, and the \nmean thermal velocity in the beam, $v_{Tb}$; under some conditions,\n$v_{Te}$, the mean thermal velocity of the ambient electrons, also must\nbe taken into account.\nThe standard formula for the BPI growth rate, valid for \n$v_b > (n_p/n_b)^{1/3} v_{Tb}$, is our Case 1 (e.g., Mikhailovskii \n\\cite{mikhailovskii}) %EQN 3\n\\begin{equation}\n\\Gamma_{bp} = 0.7 \\left({\\frac {n_b}{n_p}}\\right)^{1/3} \\omega_{pe},\n\\end{equation}\nwhere $n_b$ is the beam density, $n_p$ is the ambient plasma density\n(here, in the disk corona),\nand $\\omega_{pe}= 5.47 \\times 10^4 n_e^{1/2}$ is the plasma frequency in terms\nof the ambient electron number density in cgs units. The frequency at \nwhich this mode grows is $\\omega_{pe}(1-0.4(n_b/n_p)^{1/3})$. \n\nIf the beam starts out very slowly, with \n$v_b < (n_p/n_b)^{1/3} v_{Tb}$, then\nthe ``weak'' version of the BPI is relevant, and this is\nour Case 2 (e.g., Benz \\cite{benz}) %EQN 4\n\\begin{equation}\n\\Gamma_{bp,w} = \\left({\\frac {n_b}{2n_p}}\\right) \n \\left({\\frac {v_b}{v_{Te}}}\n\t\t\t\\right)^2 \\omega_{pe},\n\\end{equation}\nand the frequency at which this dominant mode is excited is $\\omega_{pe}$.\nUnder the limited circumstances that $v_{Te} > v_b > v_{Tb}$, the\n``hot-electron'' Case 3 yields (e.g., Mikhailovskii \\cite{mikhailovskii}), %EQN 5\n\\begin{equation}\n\\Gamma_{bp,he} = \\left({\\frac {n_b} {n_p}}\\right)^{1/2}\n {\\frac{v_{Te}}{v_b}}\n\t\t\\omega_{pe},\n\\end{equation}\nwhere this dominant mode is at a frequency of $(v_b / v_{Te}) \\omega_{pe}$.\n\n\nThe AGN corona values of dVK for $n_p = 10^{10}$ cm$^{-3}$ and $T = 10^6$ K, \nwhich we also believe are reasonable, will\nbe adopted here. There are, however, additional parameters that \nmust be considered\nnow (basically in lieu of the radiation temperature, or $u_{rad}$,\nneeded by dVK). First, \n$\\zeta \\equiv n_b/n_p$;\nfor solar flares this value is $\\sim 10^{-6}$ -- $10^{-4}$ (Benz \\cite{benz}); \nhowever, we will bear in mind the possibility that this ratio may be \nhigher in this type of radiation dominated plasma. \nWe also need initial values of $v_b$ and $v_{Tb}$, to\ndetermine which of the three Cases defined above should be considered.\nFor us to say that a beam actually exists we must always\ndemand that $v_b > v_{Tb}$. \n\nNote that the BPI directly gives the rate of growth of an electric \nfield in the plasma, and the energy loss goes as the square of the field\nstrength. Then we find that when the relativistic effects that arise if \nthe Lorentz factors really could become large are included, the rate of\nchange of energy of electrons in the beam is, %EQN 6\n\\begin{equation}\n{\\frac {d\\gamma}{dt}} = \\chi_1 {\\frac{(\\gamma^2 - 1)^{1/2}}{\\gamma}} - \n 2 \\alpha \\gamma \\Gamma_{bp}(\\gamma),\n\\end{equation}\nwhere $\\alpha \\equiv W/E = W/\\gamma n_b m c^2$, is the ratio between\nthe wave energy density, $W$, and the electron beam energy density, $E$.\nIn order to determine $W$, knowledge of the saturation mechanisms of the wave\n field are needed. Often, in order to avoid a detailed discussion of the saturation\nmechanisms, which tend to operate in multiplicity in a plasma, the\ncondition of equipartition of energy between the waves and the beam\nparticles is used (Treumann \\& Baumjohann \\cite{treumann}). In that case \n$\\alpha$ is\napproximated to unity, and we consider this situation first. \nCase 4, where $\\alpha \\ll 1$, and the saturation\noccurs earlier by trapping, will then be addressed.\n\n\nIn Eqn.\\ (6) we have ignored the IC term appearing in Eqn.\\ (1), having replaced it with\na generic form of the BPI growth rate; the fact that the BPI term is much\nbigger than the $\\chi_2$ term for all reasonable circumstances \n will soon become evident. \nThe dominant dependence of $\\Gamma_{bp}$ \nupon $\\gamma$ for the first three cases arises through\nthe replacement: $n_b \\longrightarrow n_b/\\gamma^3$ (e.g., Walsh \\cite{walsh};\nKrishan 1999), which effectively\nmodifies $\\zeta$, which is defined as the density ratio at non-relativistic\n relative velocities. In Cases\n(2) and (3) we must also write $v_b/c = (\\gamma^2 - 1)^{1/2}/\\gamma$. \n\nNow, for Cases 1, 2 and 3, respectively, we have:\n\\begin{equation}\n{\\frac {d\\gamma}{dt}} = \\chi_1{\\frac{(\\gamma^2 -1)^{1/2}}{\\gamma}} \n\t\t\t- 2 A_1,\n\\end{equation}\nwith $A_1 = 0.7 \\zeta^{1/3} \\omega_{pe} \\simeq \n8 \\times 10^7 \\zeta_{-5}^{1/3} n_{e,10}^{1/2}$,\nwhere the common notation, $X_{n} = X/10^{n}$, has been employed\nso that the physical parameters will be of order unity; \n\\begin{equation}\n{\\frac {d\\gamma}{dt}} = \\chi_1{\\frac{(\\gamma^2 -1)^{1/2}}{\\gamma}}\n\t\t- 2{\\frac{(\\gamma^2 -1)}{\\gamma^4}}A_2,\n\\end{equation}\nwith $A_2 = 0.5 (c/v_{Tb})^2 \\zeta \\omega_{pe} \\simeq 3 \\times 10^8\n\\eta_{b,-2}^{-2} \\zeta_{-5} n_{e,10}^{1/2}$, where we have now defined\n$\\eta_b \\equiv v_{Tb}/c \\sim 0.01$;\n\\begin{equation}\n{\\frac {d\\gamma}{dt}} = \\chi_1{\\frac{(\\gamma^2 -1)^{1/2}}{\\gamma}} \n\t\t-{\\frac {2 \\gamma A_3}{(\\gamma^3 - \\gamma)^{1/2}}},\n\\end{equation}\nwith $A_3 = \\zeta^{1/2}(v_{Te}/c) \\omega_{pe} \\simeq 2 \\times 10^5\n\\zeta_{-5}^{1/2} \\eta_{e,-2} n_{e,10}^{1/2}$, where now,\n$\\eta_e \\equiv v_{Te}/c \\sim 0.01$.\n \nUnder any of these situations we have $\\chi_1 = 5.2 \\times 10^1 n_{e,10}\n T_{e,6}^{-1}$\nwith our definition of $E_D$ (which is slightly larger than that of\ndVK, thereby only strengthening our argument). For any plausible \ninitial value of $\\gamma \\sim 1$ the different\ndependences of Eqns. (7--9) upon $\\gamma$ are not\nimportant. What is important is that $A_1, A_2, A_3 \\gg \\chi_1 \\gg \\chi_2$;\ni.e., the energy loss term arising from {\\it any} form of the BPI completely\ndominates over the energy gain term from direct electric field\nacceleration. \n\nWe now consider Case 4, where equipartition is not established. \nUnder these circumstances, the growth of the Langmuir waves for\nthe fastest initial beam situation, Case 1, is arrested\nby the trapping of the beam electrons. In this case, the \nratio $\\alpha$ is eventually\ngiven by the saturated value (Melrose \\cite{melrose}; Krishan \\cite{krishan}),\n$\\alpha= 9/2 [n_b/(2 n_p \\gamma^3)]^{2/3}$, and it can be a rather\nsmall number that reduces the loss rate significantly. This gives\na chance for the situation envisioned by dVK to occur.\nIn addition, $\\alpha$ initially can start out below the \nsaturation value as it arises from thermal fluctuations, and thus\nit could allow an\ninitial thermal runaway. The detailed spatial and temporal\nstructure of the reconnection sites will determine if this initial\nacceleration can play a significant role.\n\nIn spite of these uncertainties, we can obtain a reasonable \nestimate of the influence of BPI in the situation \nwhere equipartition is not established. We again consider all \nthree cases discussed above, but we now include electron trapping \nand assume $\\alpha$ to take the saturation value. Here the competition\nbetween the IC losses represented by $\\chi_2$ and \nthe BPI losses\nrepresented by the Melrose $\\alpha$ has to be considered carefully.\n\nThe inverse Compton term\nincreases with $\\gamma$ whereas the $\\alpha$ factor modifying\nthe BPI term decreases \nwith $\\gamma$. Thus\ndemanding that the BPI term is smaller than the IC \nterm fixes the\nminimum value of $\\gamma$ necessary to validate the dVK proposal. \nA detailed\ncalculation yields the results for the three cases as follows: case (1a),\n$\\gamma_{min} = 54$; case (2a), $\\gamma_{min} = 21$; case (3a),\n$\\gamma_{min} = 9.16$. Thus it is clear that only in case (3a), \nis it likely that the IC term dominates and hence the dVK \nproposal is valid. This requires\nrather special conditions for the flare models to work.\n\n\n\nThis type of runaway acceleration has been observed in the laboratory \nunder specific circumstances which lead to a very weak beam plasma \ninstability. \nIn laboratory experiments, the runaway electrons are observed detached\nfrom the main body of the plasma, as for\nexample in a stellarator. If the runaway electrons hit the tungsten\naperture, they generate X-rays which can be detected. Provided the\nconditions are right, the runaway electrons undergo instabilities\nproducing plasma oscillations which then couple to the ions. This\nprinciple is applied in the design of some electron tube\noscillators (Rose \\& Clark \\cite{rose}). \nThus the runaway electrons can stably propagate under certain \ncircumstances, but will be affected by a BPI if they\ndo satisfy the conditions for it. These conditions are essentially on\nthe velocity of the beam and its thermal spread, as we have already\ndiscussed for the first three cases above.\n\n\n Often it is found\nthat a regime of strong Langmuir waves is quickly reached and these\nwaves\nare further subjected to modulational instabilities. Thus, different\nsaturation mechanisms operate at different stages of the development of\nthe instability, depending on beam plasma parameters. However, under the\ncircumstances and parameters proposed by dVK, the damping is severe.\n \n\n\n\n\\section{Discussion and Conclusions}\n\nWe thus conclude that the mechanism proposed by dVK\nshould not generally work unless much greater densities are possible in the\ncoronae at the same time that the temperatures are lower, since $\\chi_1$\nrises faster with $n_p$ than does any form of $\\Gamma_{bp}$,\nand declines faster with temperature. While denser\ncoronae should be available around the accretion disks in X-ray binaries,\nthe ambient temperatures will also be a good deal higher, so we cannot\nsuggest a physically interesting situation where the BPIs do not dominate.\nIf one could somehow begin with very large $\\gamma$ values, then\nthe growth rate of the beam-plasma instabilities are reduced.\nFor Case 1 this does not help, and no solutions for large $\\gamma$\nare possible; however, for Cases 2 and 3, the relativistic decreases in the\nBPI rates are so substantial that high asymptotic $\\gamma$ values\nare allowed. This is also true for Case 4, where the saturation\nreduces the effectiveness of the BPI; however, even then the\nBPI can prevent much acceleration unless the beam already starts\nwith a substantial value of $\\gamma$ or has such a low density\nin comparison to the ambient medium that it could not carry\nsignificant power.\nMoreover, we see no way to achieve these initially\nhigh $\\gamma$ values: that is what the dVK mechanism was supposed\nto accomplish, but now appears to be incapable of achieving. \n\n\nFilamentation, which could produce denser beam fragments, could play a role\nby raising $\\zeta$ locally. If any analogy can be drawn with solar flares,\nthen the presence of rapid irregularities within the Type 3 radio bursts\nstrongly indicates that the flux tubes are filamentary during the acceleration\nphase (e.g., Vlahos \\& Raoult \\cite{vlahos}). However, this possibility\nis still insufficient to salvage this mechanism for AGN coronae, since even\nwith $\\zeta \\sim 1$ the ratios of $A_{1,2,3}/\\chi_1 > 1$. In Case 4,\n where saturation is important in principle, the large value of $\\zeta$\nimplies that\n$\\alpha \\sim 1$ too (for initial $\\gamma \\sim 1$) so the loss term\nstill would dominate.\n\nNonetheless, even with much of the energy going into wave turbulence,\nas we have argued, significant IC emission can be possible. \n This is because (as pointed\nout by the referee) trapping and other nonlinear effects can roughly\nheat the electrons up to $kT_e \\sim e \\phi$, with $\\phi$ the\nelectrostatic amplitude of the waves. Since the energy gain\nterm (the first on the RHS of Eq. [1]) is essentially a constant,\nthese `thermalized/trapped' electrons can attain nearly the\nsame energy as in the dVK picture. However this energy will not\nbe in the form of a beam, as argued by dVK, but rather, will be \npresent in\nan isotropic distribution. Then the IC process still works,\nand one of the points made by dVK, that much of the energy is\nlost by IC hard X-rays instead of `soft' X-rays from material\nevaporated from the disk, can remain valid, as already\nnoted at the end of \\S 1. In order to see\nif the inverse Compton losses actually dominate,\ndetailed computations of these effects should be undertaken\nunder various circumstances.\n\n\nIt is well known that in the case of the solar corona, the directly\naccelerated beams should be thermalized within a very short time through BPI\n(e.g., Sturrock \\cite{sturrock}). In the standard picture, this produces Langmuir waves \nwhich then manifest themselves as various types\nof radio bursts if non-linear effects or transport from faster to\nslower electrons within the beam could dominate (e.g., Vlahos \\& Raoult\n\\cite{vlahos}). \nHowever, energetic electrons have been observed in \nsatellite measurements in near-earth orbit, and the outstanding question\nof the maintenance of these beams through their propagation from the\nsun to the earth has given rise to more complex models involving\ncomplex profiles of the electron beams (Vlahos \\& Raoult \\cite{vlahos}). \nInstead of producing\nX-ray flares via a primary process as proposed by dVK, \nthese secondary processes involving energy input to the plasma could\ncontribute to variability in the radio band. \n\n\\begin{acknowledgements} \nWe thank the anonymous referee for pointing out the incompleteness\nof our analysis in the original version.\nThis work was supported in part by NASA\ngrant NAG 5-3098 and RPI and Strategic International Initiative \nfunds at GSU.\n\\end{acknowledgements} \n\n\n\\begin{thebibliography}{}\n\n\\bibitem[1993]{benz} Benz, A.O., 1993, Plasma Astrophysics. \nKluwer, Dordrecht\n\n\\bibitem[1992]{deVries} de Vries, M., Kuijpers, J., \n1992, A\\&A 266, 77 (dVK)\n\n\\bibitem[1979]{galeev} Galeev, A.A., Rosner, R., Vaiana, G.S., \n1979, ApJ 229, 318\n\n\\bibitem[1999]{krishan} Krishan, V., 1999, Astrophysical Plasmas \nand Fluids. Kluwer, Dordrecht \n\n\\bibitem[1995]{kuijpers} Kuijpers, J., 1995, in: Benz, A.O., Kr\\\"uger, A. (eds.) Coronal\n\tMagnetic Energy Releases. Springer, Berlin, p. 135\n\n\\bibitem[1985]{kuperus} Kuperus, M., Ionson, J.A., 1985, A\\&A 148, 309\n\n\\bibitem[1977]{liang} Liang, E.P., Price, R.H., 1977, ApJ, 218, 247\n\n\\bibitem[1986]{melrose} Melrose, D.B., 1986, Instabilities in Space and Laboratory\nPlasmas. Cambridge University Press, Cambridge, p.\\ 72\n\n\\bibitem[1961]{rose} Rose, D.J., Clark Jr., M., 1961,\nPlasmas and Controlled\nFusion (Massachusetts Institute of Technology Press, Cambridge), p.\\ 448\n\n\\bibitem[1974]{mikhailovskii} Mikhailovskii, A.B., 1974, Theory of Plasma Instabilities, Vol. I.\n\tConsultants Bureau, New York\n\n\\bibitem[1973]{shakura} Shakura, N.I., Sunyaev, R.A., 1973, A\\&A 24, 337\n\n\\bibitem[1976]{shapiro} Shapiro, S.L., Lightman, A.P., Eardley, E.M., 1976, ApJ 204, 187\n\n\\bibitem[1964]{sturrock} Sturrock, P.A., 1964, in: Hess, W.N. (ed.) Proc. AAS--NASA Symp. on the\n\tPhysics of Solar Flares (NASA SP-50), p. 357\n\n\\bibitem[1997]{treumann} Treumann, R.A., Baumjohann, W., 1997, Advanced Space Plasma Physics.\n\tImperial College Press, London, p.\\ 193\n\n\\bibitem[1995]{vlahos} Vlahos, L., Raoult, A., 1995, A\\&A, 296, 844\n\n\\bibitem[1980] {walsh} Walsh, J.E. 1980, in: Jacobs, S.F. et al. (eds.) Free-Electron\n\tGenerators of Coherent Radiation. Addison-Wesley, Reading, p.\\ 255 \n\n\\end{thebibliography}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002361.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1993]{benz} Benz, A.O., 1993, Plasma Astrophysics. \nKluwer, Dordrecht\n\n\\bibitem[1992]{deVries} de Vries, M., Kuijpers, J., \n1992, A\\&A 266, 77 (dVK)\n\n\\bibitem[1979]{galeev} Galeev, A.A., Rosner, R., Vaiana, G.S., \n1979, ApJ 229, 318\n\n\\bibitem[1999]{krishan} Krishan, V., 1999, Astrophysical Plasmas \nand Fluids. Kluwer, Dordrecht \n\n\\bibitem[1995]{kuijpers} Kuijpers, J., 1995, in: Benz, A.O., Kr\\\"uger, A. (eds.) Coronal\n\tMagnetic Energy Releases. Springer, Berlin, p. 135\n\n\\bibitem[1985]{kuperus} Kuperus, M., Ionson, J.A., 1985, A\\&A 148, 309\n\n\\bibitem[1977]{liang} Liang, E.P., Price, R.H., 1977, ApJ, 218, 247\n\n\\bibitem[1986]{melrose} Melrose, D.B., 1986, Instabilities in Space and Laboratory\nPlasmas. Cambridge University Press, Cambridge, p.\\ 72\n\n\\bibitem[1961]{rose} Rose, D.J., Clark Jr., M., 1961,\nPlasmas and Controlled\nFusion (Massachusetts Institute of Technology Press, Cambridge), p.\\ 448\n\n\\bibitem[1974]{mikhailovskii} Mikhailovskii, A.B., 1974, Theory of Plasma Instabilities, Vol. I.\n\tConsultants Bureau, New York\n\n\\bibitem[1973]{shakura} Shakura, N.I., Sunyaev, R.A., 1973, A\\&A 24, 337\n\n\\bibitem[1976]{shapiro} Shapiro, S.L., Lightman, A.P., Eardley, E.M., 1976, ApJ 204, 187\n\n\\bibitem[1964]{sturrock} Sturrock, P.A., 1964, in: Hess, W.N. (ed.) Proc. AAS--NASA Symp. on the\n\tPhysics of Solar Flares (NASA SP-50), p. 357\n\n\\bibitem[1997]{treumann} Treumann, R.A., Baumjohann, W., 1997, Advanced Space Plasma Physics.\n\tImperial College Press, London, p.\\ 193\n\n\\bibitem[1995]{vlahos} Vlahos, L., Raoult, A., 1995, A\\&A, 296, 844\n\n\\bibitem[1980] {walsh} Walsh, J.E. 1980, in: Jacobs, S.F. et al. (eds.) Free-Electron\n\tGenerators of Coherent Radiation. Addison-Wesley, Reading, p.\\ 255 \n\n\\end{thebibliography}"
}
] |
astro-ph0002362
|
COLLISIONAL DARK MATTER AND THE STRUCTURE OF DARK HALOS
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[
{
"author": "Naoki Yoshida\\altaffilmark{1}"
},
{
"author": "Volker Springel\\altaffilmark{1,2}"
},
{
"author": "Simon D.M. White\\altaffilmark{1}"
}
] |
We study how the internal structure of dark halos is affected if Cold Dark Matter particles are assumed to have a large cross-section for elastic collisions. We identify a cluster halo in a large cosmological N-body simulation and resimulate its formation with progressively increasing resolution. We compare the structure found in the two cases where dark matter is treated as collisionless or as a fluid. For the collisionless case the overall ellipticity of the cluster, the central density cusp and the amount of surviving substructure are all similar to those found in earlier high resolution simulations. Collisional dark matter results in a cluster which is more nearly spherical at all radii, has a {steeper} central density cusp, and has less, but still substantial surviving substructure. As in the colisionless case, these results for a ``fluid'' cluster halo are expected to carry over approximately to smaller mass systems. The observed rotation curves of dwarf galaxies then argue that self-interacting dark matter can only be viable if intermediate cross-sections produce structure which does not lie between the extremes we have simulated.
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[
{
"name": "paper.tex",
"string": "\\documentclass{article}\n\\usepackage{emulateapj,epsfig}\n\n\\newcommand{\\vdag}{(v)^\\dagger}\n\\newcommand{\\myemail}{skywalker@galaxy.far.far.away}\n\n\\slugcomment{Revised, accepted for publication in ApJ Letters, May 2, 2000}\n%\\shorttitle{Yoshida et al.}\n%\\shortauthors{COLLISIONAL DARK MATTER AND THE STRUCTURE OF DARK HALOS}\n\n%% This is the end of the preamble. Indicate the beginning of the\n%% paper itself with \\begin{document}.\n\n\\makeatletter\n\\newenvironment{inlinetable}{%\n\\def\\@captype{table}%\n\\noindent\\begin{minipage}{0.999\\linewidth}\\begin{center}\\footnotesize}\n{\\end{center}\\end{minipage}\\smallskip}\n\n\\newenvironment{inlinefigure}{%\n\\def\\@captype{figure}%\n\\noindent\\begin{minipage}{0.999\\linewidth}\\begin{center}}\n{\\end{center}\\end{minipage}\\smallskip}\n\\makeatother\n\n\n\n\n\n\\begin{document}\n\n%% LaTeX will automatically break titles if they run longer than\n%% one line. However, you may use \\\\ to force a line break if\n%% you desire.\n\n\\title{COLLISIONAL DARK MATTER AND THE STRUCTURE OF DARK HALOS}\n\n%% Use \\author, \\affil, and the \\and command to format\n%% author and affiliation information.\n%% Note that \\email has replaced the old \\authoremail command\n%% from AASTeX v4.0. You can use \\email to mark an email address\n%% anywhere in the paper, not just in the front matter.\n%% As in the title, you can use \\\\ to force line breaks.\n\n\\author{Naoki Yoshida\\altaffilmark{1}, Volker\nSpringel\\altaffilmark{1,2}, Simon D.M. White\\altaffilmark{1}}\n\\affil{Max-Planck-Institut f\\\"{u}r Astrophysik Karl-Schwarzschild-Str. 1, 85748 Garching, Germany}\n%\\email{nyoshida@mpa-garching.mpg.de}\n\\and\n\\author{Giuseppe Tormen\\altaffilmark{3}}\n\\affil{Dipartimento di Astronomia, Universita di Padova,\nvicolo dell'Osservatorio 5, 1-35122 Padova, Italy}\n\n\\altaffiltext{2}{present address: Harvard-Smithsonian Center for Astrophysics,\n 60 Garden Street, Cambridge, MA 02138}\n\n\n\\begin{abstract}\nWe study how the internal structure of dark halos is affected if Cold\nDark Matter particles are assumed to have a large cross-section for \nelastic collisions. We identify a cluster halo in a large cosmological \nN-body simulation and resimulate its formation with progressively \nincreasing resolution. We compare the structure found in the two cases\nwhere dark matter is treated as collisionless or as a fluid. For the\ncollisionless case the overall ellipticity of the cluster, the central\ndensity cusp and the amount of surviving substructure are all similar\nto those found in earlier high resolution simulations. Collisional\ndark matter results in a cluster which is more nearly spherical at all\nradii, has a {\\it steeper} central density cusp, and has less, but still\nsubstantial surviving substructure. As in the colisionless case, these\nresults for a ``fluid'' cluster halo are expected to carry over\napproximately to smaller mass systems. The observed rotation curves of\ndwarf galaxies then argue that self-interacting dark matter can only \nbe viable if intermediate cross-sections produce structure which does\nnot lie between the extremes we have simulated.\n\\end{abstract}\n\n%% Keywords should appear after the \\end{abstract} command. The uncommented\n%% example has been keyed in ApJ style. See the instructions to authors\n%% for the journal to which you are submitting your paper to determine\n%% what keyword punctuation is appropriate.\n\n\\keywords{dark matter - galaxy: formation - methods: numerical}\n\n%% From the front matter, we move on to the body of the paper.\n%% In the first two sections, notice the use of the natbib \\citep\n%% and \\citet commands to identify citations. The citations are\n%% tied to the reference list via symbolic KEYs. The KEY corresponds\n%% to the KEY in the \\bibitem in the reference list below. We have\n%% chosen the first three characters of the first author's name plus\n%% the last two numeral of the year of publication as our KEY for\n%% each reference.\n\n\\section{Introduction}\nCold dark matter scenarios within the standard inflationary\nuniverse have proved remarkably successful in fitting a wide range of\nobservations. While structure on large scales is well \nreproduced by the models, the situation is more controversial in the\nhighly nonlinear regime. Navarro, Frenk \\& White (1995, 1996, 1997;\nNFW) claimed that the density profiles of near-equilibrium dark halos \ncan be approximated by a ``universal'' form with singular \nbehaviour at small radii. Higher resolution studies have confirmed \nthis result, finding even more concentrated dark halos than the original\nNFW work and showing, in addition, that CDM halos are predicted to have\na very rich substructure with of order 10\\% of their mass contained\nin a host of small subhalos (Frenk et al 1999, Moore et al 1999a, 1999b,\nGhigna et al 1999, Klypin et al 1999, Gottloeber et al 1999, White \\& \nSpringel 1999). Except for a weak anticorrelation of concentration with \nmass, small and large mass halos are found to have similar structure.\nMany of these studies note that the predicted concentrations appear \ninconsistent with published data on the rotation curves of dwarf\ngalaxies, and that the amount of substructure exceeds that seen in \nthe halo of the Milky Way (see also Moore 1994; Flores and Primack 1994;\nKravtsov et al 1998; Navarro 1998).\n\nIt is unclear whether these discrepancies reflect a fundamental\nproblem with the Cold Dark Matter picture, or are caused\nby overly naive interpretation of the observations of the\ngalaxy formation process (see Eke, Navarro \\&\nFrenk 1998; Navarro \\& Steinmetz 1999; van den Bosch 1999). On the\nassumption that an explanation should be sought in fundamental\nphysics, Spergel \\& Steinhardt (1999) have argued that a large\ncross-section for elastic collisions between CDM particles may\nreconcile data and theory. They suggest a number of modifications\nof standard particle physics models which could give rise to such \nself-interacting dark matter, and claim that cross-sections which\nlead to a transition between collisional and collisionless\nbehaviour at radii of order 10 -- 100 kpc in galaxy halos are\npreferred on astrophysical grounds. Ostriker (1999) argues that\nthe massive black holes observed at the centres of many galactic\nspheroids may arise from the accretion of such collisional dark matter\nonto stellar mass seeds. Miralda-Escude (2000) argues that such dark\nmatter\nwill produce galaxy clusters which are rounder than observed and so can\nbe\nexcluded.\n\nAt early times the CDM distribution is indeed cold, so\nthe evolution of structure is independent of the collision\ncross-section of the CDM particles. At late times, however, a large\ncross-section leads to a small mean free path and so to fluid \nbehaviour in collapsed regions. In this Letter we explore\nhow the structure of nonlinear objects (``dark halos'') is affected\nby this change. We simulate the formation of a massive halo from\nCDM initial conditions in two limits: purely collisionless dark\nmatter and ``fluid'' dark matter. We do not try to simulate the\nthe more complex intermediate case in which the mean free path\nis large in the outer regions of halos but small in their cores.\nIf this intermediate case (which is the one favoured by Spergel \n\\& Steinhardt (1999) and by Ostriker (1999)) produces nonlinear \nstructure intermediate between the two extremes we do treat, then \nour results show that collisional CDM would give poorer fits to \nthe rotation curves of dwarf galaxies than standard collisionless \nCDM. Further work is needed to see if this is indeed the case.\n\n\\section{THE N-BODY/SPH SIMULATION}\nOur simulations use the parallel tree code GADGET developed by\nSpringel (1999, see also Springel, Yoshida \\& White 2000b). \nOur chosen halo is the second most massive cluster\nin the $\\Lambda$CDM simulation of Kauffmann et al (1999). We analyse\nits structure in the original simulation and in two higher resolution\nresimulations. In the collisionless case these are the lowest \nresolution members of a set of four resimulations carried out by\nSpringel et al (2000a) using similar techniques to those of NFW.\nDetails may be found there and in Springel et al(2000b). \nThese collisionless resimulations use GADGET as an N-body solver, \nwhereas our collisional\nresimulations start from identical initial conditions but use the code's\nSmoothed Particle Hydrodynamics (SPH) capability to solve the fluid\nequations. The SPH method regards each simulation particle as a\n``cloud'' of fluid with a certain kernel shape. These clouds interact\nwith each other over a length scale which is determined by the local \ndensity and so varies both in space and time.\nThe basic parameters of our simulations are tabulated in Table 1,\nwhere N$_{\\mbox{\\small{tot}}}$ is the total number of particles in the\nsimulation,\nN$_{\\mbox{\\small{high}}}$ the number of particles in the central\nhigh-resolution\nregion, $m_{p}$ is the mass of each high-resolution particle, and\n$l_{s}$ stands for the gravitational softening length.\nOur cosmological model is flat with matter density $\\Omega_{m}=0.3$,\ncosmological constant $\\Omega_{\\Lambda}=0.7$ and expansion rate\n$H_{0}=70$km$^{-1}$Mpc$^{-1}$. It has a CDM power spectrum normalised\nso that $\\sigma_{8}=0.9$. The virial mass of the final cluster is\n$M_{200}=7.4\\times 10^{14}h^{-1}M_\\odot$, determined as the mass within\nthe radius $R_{200}= 1.46 h^{-1}$Mpc where the enclosed mean\n\n\\begin{inlinetable}\n\\vspace*{0.4cm}\\ \\\\\n\\begin{center}\n\\caption{Simulation parameters}\n\\begin{tabular}{ccccc}\n\\tableline\n\\tableline\nRun & $N_{\\rm tot}$ & $N_{\\rm high}$ & $m_{\\rm p}$ ($h^{-1} M_{\\odot}$)\n& $l_{\\rm s}$($h^{-1}$kpc) \\\\\n\\tableline\nS0 & 3.2$\\times 10^{6}$ & 0.2$\\times 10^{6}$& 1.4 $\\times 10^{10}$ & 30 \\\\\n\\tableline\nS1 & 3.5$\\times 10^{6}$ & 0.5$\\times 10^{6}$& 0.68 $\\times 10^{10}$ & 20\\\\\n\\tableline\nS2 & 5.1$\\times 10^{6}$ & 2.0$\\times 10^{6}$& 0.14 $\\times 10^{10}$ & 3.0\\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\\end{inlinetable}\n\n\n\\section{RESULTS}\nOn scales larger than the final cluster, the matter distribution\nin all our simulations looks similar. This is no surprise. The initial\nconditions in each pair of simulations are identical, so\nparticle motions only begin to differ once pressure forces become\nimportant. Furthermore the initial perturbation fields in simulations \nof differing resolution are identical on all scales resolved in both\nmodels, and even S0 resolves structure down to scales well below that\nof the cluster. As is seen clearly in Figure 1, a major difference \nbetween the collisional and collisionless models is that the final\ncluster\nis nearly spherical in the former case and quite elongated in the\nlatter. The axial ratios determined from the inertia tensors of the \nmatter at densities exceeding 100 times the critical value are \n1.00:0.96:0.84 and 1.00:0.72:0.63 respectively. Again this\nis no surprise. A slowly rotating fluid body in hydrostatic \nequilibrium is required to be nearly spherical, but no such constraint\napplies in the collisionless case (see also Miralda-Escude 2000).\n\n\n\\begin{inlinefigure}\n\\vspace*{0.2cm}\\ \\\\\n\\resizebox{8.5cm}{!}{\\includegraphics{Figure1.eps}}\n\\caption{The projected mass distribution in our two\nhighest resolution simulations. The collisionless case (S2) is on\nthe top and the fluid case (S2F) is on the bottom. The region shown\nis a cube of $15h^{-1}$Mpc on a side. \\label{fig1}}\n\\end{inlinefigure}\n\nIn Figure 2 we show circular velocity profiles for our simulations.\nThese are defined as $V_c(r) = \\sqrt{GM(r)/r}$, where $M(r)$ is the mass \nwithin a sphere radius $r$; they are plotted at radii between 2$l_{s}$\nand $5R_{200}$. \nThey agree reasonably well along each sequence of increasing\nresolution,\nshowing that our results have converged numerically on these scales.\nAlong the fluid sequence the profiles resemble the collisionless\ncase over the bulk of the cluster. In the core, \nhowever, there is a substantial and significant difference; the fluid \ncluster has a substantially steeper central cusp. The difference\nextends out to radii of about $0.5R_{200}$ and has the wrong\nsign to improve the fit of CDM halos to published rotation curves for\ndwarf and low surface brightness galaxies. \n\n\n\\begin{inlinefigure}\n\\vspace*{0.2cm}\\ \\\\\n\\resizebox{8cm}{!}{\\includegraphics{Figure2.eps}}\n\\caption[fig2.ps]{Circular velocity profiles for our cluster\nsimulations, each normalized to its own $R_{200}$ and $V_{200}$. These are\nplotted between twice the gravitational softening and $5R_{200}$. The collisionless sequence is\nplotted using dashed lines and the fluid sequence using solid lines.\n\\label{fig2}}\n\\end{inlinefigure}\n\n(Note that in the fluid\ncase we expect small halos to approximate scaled down but slightly\n{\\it more} concentrated versions of cluster halos, as in the\ncollisionless case studied by Moore et al (1999a); this scaling will\n{\\it fail} for intermediate cross-sections because the ratio of the\ntypical mean free path to the size of the halo will increase with halo\nmass.)\n\nIn Figure 3 we compare the level of substructure within $R_{200}$\nin our various simulations. Subhalos are identified using\nthe algorithm SUBFIND by Springel (1999) which defines them\nas maximal, simply connected, gravitationally self-bound sets \nof particles which are at higher local density than all surrounding \ncluster material. (Our SPH scheme defines a local density in the \nneighbourhood of every particle.) \nUsing this procedure we find\nthat 1.0\\%, 3.4\\% and 6.7\\% of the mass within $R_{200}$ is included\nin subhalos in S0, S1 and S2 respectively. Along the fluid sequence\nthe corresponding numbers are 3.0\\%, 6.4\\% and 3.1\\%. \nThe difference in the total amount results primarily from the \nchance inclusion or exclusion of infalling massive\nhalos near the boundary at $R_{200}$.\nIn Figure 3 we show the mass distributions of\nthese subhalos. We plot each simulation to a mass limit of 40\nparticles, corresponding approximately to the smallest structures we \nexpect to be adequately resolved in our SPH simulations. Along each\nresolution sequence the agreement is quite good, showing this limit to\nbe conservative. For small subhalo masses there is clearly less \nsubstructure in the fluid case, but the difference is\nmore modest than might have been anticipated.\n\n\n\n\\section{Summary and Discussion}\nAn interesting question arising from our results is {\\it why} our\nfluid clusters have more concentrated cores than their collisionless \ncounterparts. The density profile of an equilibrium gas sphere can be\nthought of as being determined by its Lagrangian specific entropy\nprofile, i.e. by the function $m(s)$ defined to be the mass of gas\nwith specific entropy less than $s$. The larger the mass at low\nspecific entropy, the more concentrated the resulting profile. Thus\nour fluid clusters have more low entropy gas than if their profiles\nwere similar to those of the collisionless clusters. The entropy of the\ngas is produced by a variety of accretion and\nmerger shocks during the build-up of the cluster, so the strong central\nconcentration reflects a relatively large amount of weakly\nshocked gas.\n\n\\begin{inlinefigure}\n\\vspace*{0.3cm}\\ \\\\\n\\resizebox{8cm}{!}{\\includegraphics{Figure3.eps}}\n\\caption{The total number of subhalos within $R_{200}$ is\nplotted as a function of their mass in units of $M_{200}$.\nDashed and solid lines correspond to the collisionless \nand fluid cases respectively. Results for each simulation are \nplotted only for halos containing more than 40 particles.\n\\label{fig3}}\n\\end{inlinefigure}\n\nWe study gas shocking in our models by carrying out\none further simulation. We take the initial conditions of S1 and\nreplace each particle by two superposed particles, a collisionless\ndark matter particle containing 95\\% of the original mass and a gas\nparticle\ncontaining 5\\%. These two then move together until SPH pressure forces\nare strong enough to separate them. The situation is similar to the\nstandard 2-component model for galaxy clusters except that our chosen\ngas fraction is significantly smaller than observed values.\n\nIn this mixed simulation the evolution of the collisionless matter\n(and its final density profile) is almost identical to that in the\noriginal S1. This is, of course, a consequence of the small gas\nfraction we have assumed. In agreement with the simulations\nin Frenk et al (1999) we find that the gas density profile parallels\nthat of the dark matter over most of the cluster but is significantly\n{\\it shallower} in the inner $\\sim 200 h^{-1}$kpc. Comparing this new\nsimulation (S1M) with its fluid counterpart (S1F) we find that in both\ncases the gas which ends up near the cluster centre lay\nat the centre of the most massive cluster progenitors at $z= 1\\sim 3$.\nIn addition it is distributed in a similar way among the progenitors \nin the two cases. In Figure 4 we compare the specific entropy profiles\nof the cluster gas. These are scaled so that they would be identical \nif each gas particle had the same shock history in the two simulations. \nOver most of the cluster there is indeed a close correspondence,\nbut near the centre the gas in the mixed simulation has higher\nentropy. (This corresponds roughly to $r < 100h^{-1}$kpc.)\n\n\n\\begin{inlinefigure}\n\\vspace*{0.3cm}\\ \\\\\n\\resizebox{8cm}{!}{\\includegraphics{Figure4.eps}}\n\\caption{We plot Lagrangian specific entropy profiles for\nthe gas fluid simulation (S1F: crosses) and for the mixed simulation\n(S1M: open circles). In each case $m(s)$ is given in units \nof the individual gas particle mass, $m_g$, and the specific entropy\nof a particle is defined as $\\ln (m_g T_g^{1.5}/\\rho_g)$. The \narrows indicate where the\ntimescale $t_{2b}$ for 2-body heating of the gas by encounters with dark matter\nparticles (see equation (5) of Steinmetz \\& White (1997)) is 0.1, 1,\nand 10 times the age \nof the Universe. For each $s$ we calculate $t_{2b}$ \nat the radius where the median specific \nentropy equals $s$. The dashed line with open squares is an\n``entropy'' profile for S1 calculated by using the\nSPH kernel to calculate the density and velocity dispersion in the\nneighborhood of each particle, and then converting from velocity dispersion\nto temperature using the standard relation for a perfect monatomic\ngas.\n\\label{fig4}}\n\\end{inlinefigure}\n\nAs Figure 4 shows, this is partly a numerical artifact; the two \nentropies differ only at radii where two-body heating of the gas by\nthe dark matter particles is predicted to be important in the mixed\ncase. (The effect is absent in the pure fluid simulation.)\nThe weaker shocking in the fluid case is\nevident from the equivalent \"entropy\" profile of S1 in Figure 4. This\nlies between those of the two fluid simulations, and in particular\nsignificantly above that of S1F in the central regions. \n\n\nIn conclusion the effective heating of gas by shocks in the fluid case\nis similar to but slightly weaker than that in the mixed case. This is\npresumably a reflection of the fact that the detailed morphology\nof the evolution also corresponds closely. The difference in \nfinal density profile is a consequence of three effects. In the mixed \ncase the gas is in equilibrium within the external potential \ngenerated by the dark matter, whereas in the pure fluid case it \nmust find a self-consistent equilibrium. In addition the\ncore gas is heated by two-body effects in the mixed case. Finally\nin the pure fluid case the core gas experiences weaker shocks.\n\nOverall our results show that in the large cross-section limit \ncollisional dark matter is not a promising candidate for improving \nthe agreement between the predicted structure of CDM halos and \npublished data on galaxies and galaxy clusters. The increased \nconcentration at halo centre will worsen the apparent conflict \nwith dwarf galaxy rotation curves. Furthermore, clusters are predicted\nto be nearly spherical and galaxy halos to have similar mass in \nsubstructure to the collisionless case, although with fewer low \nmass subhalos. Intermediate\ncross-sections would lead to collisional behaviour in dense regions \nand collisionless behaviour in low density regions with a consequent\nbreaking of the approximate scaling between high and low mass halos.\nThe resulting structure may not lie between the two extremes\nwe have simulated. Self-interacting dark matter might then help\nresolve the problems with halo structure in CDM models, if indeed \nthese problems turn out to be real rather than apparent.\n\n\n\\acknowledgments\nSW thanks Jerry Ostriker and\nMike Turner for stimulating discussions which started him thinking\nabout this project.\n\n\\begin{thebibliography}{11}\n\\bibitem{Eke} Eke, V.R., Navarro, J. \\& Frenk, C.S., 1998, \\apj, {\\bf 503,} 569\n\\bibitem{FP} Flores, R.A. \\& Primack, J.A., 1994, \\apj, {\\bf 427}, L1\n\\bibitem{SB} Frenk, C.S. et al., 1999, \\apj, {\\bf 525}, 554\n\\bibitem{Seb} Ghigna, S., Moore, B., Governato, F., Lake, G., Quinn,\nT. \\& Stadel, J., 1999, astro-ph/9910166\n\\bibitem{Gott} Gottl\\\"{o}ber, S., Klypin, A.A. \\& Kravtsov, A.V.,\n1999, in ASP Conf.Ser.176, Observationl Cosmology, ed G.Giuricin and\nM.Mezzetti (San Francisco), 418\n\\bibitem{GIF} Kauffmann, G., Colberg, J.M., Diaferio, A., \\& White, S.D.M., 1999, \\mnras, {\\bf 303}, 188\n\\bibitem{Klypin} Klypin, A.A., Gottl\\\"{o}ber, S., Kravtsov, A.V. \\& Khokholov, A.M., 1999, \\apj, {\\bf 516,} 530\n\\bibitem{Kra} Kravtsov, A.V., Klypin, A.A., Bullock, J.S. \\& Primack, J.R., 1998, \\apj, {\\bf 502,} 48\n\\bibitem{Mi} Miralda-Escude, J., 2000, astro-ph/0002050\n\\bibitem{BM} Moore, B., 1994, {\\it Nature}, {\\bf 370}, 629\n\\bibitem{M1} Moore, B., Ghigna, S., Governato, F., Lake, G., Quinn,\nT., Stadel, J. \\& Tozzi, P., 1999a, \\apjl, {\\bf 524,} L19\n\\bibitem{M2} Moore, B., Quinn, T., Governato, F., Stadel, J. \\& Lake, G., 1999b, \\mnras, {\\bf 310,} 1147\n\\bibitem{NA} Navarro, J., 1998, astro-ph/9807084\n\\bibitem{NS} Navarro, J. \\& Steinmetz, M., 1999, astro-ph/9908114\n\\bibitem{NFW1} Navarro, J., Frenk, C.S. \\& White, S.D.M., 1995, \\mnras, {\\bf 275}, 720\n\\bibitem{NFW2} ---------, 1996, \\apj, {\\bf 462}, 563\n\\bibitem{NFW3} ---------, 1997, \\apj, {\\bf 490}, 493\n\\bibitem{JO} Ostriker, J.P., 1999, astro-ph/9912548\n\\bibitem{SS} Spergel, D.N. \\& Steinhardt, P.J., 1999, astro-ph/9909386\n\\bibitem{VRS} Springel, V., 1999, PhD thesis, Ludwig-Maximilian University, Munich\n\\bibitem{Bepi} Springel, V., Tormen, G., White, S.D.M. \\& Kauffmann, G., 2000, in preparation\n\\bibitem{VRS2} Springel, V., Yoshida, N. \\& White, S.D.M., 2000, astro-ph/0003162\n\\bibitem{TwoB} Steinmetz, M. \\& White, S.D.M., 1997, \\mnras, {\\bf 288}, 545\n\\bibitem{Bo} van den Bosch, F.C., 1999, astro-ph/9909298\n\\bibitem{First} White, S.D.M. \\& Springel, V., 2000, in The First\nStars, Proc. MPA/ESO workshop, ed. A. Weiss, T.Abel, and V.Hill\n(Springer, Heidelberg), (preprint astro-ph/9911378)\n\n\\end{thebibliography}\n\n\n%% Generally speaking, only the figure captions, and not the figures\n%% themselves, are included in electronic manuscript submissions.\n%% Use \\figcaption to format your figure captions. They should begin on a\n%% new page.\n\n\n%% No more than seven \\figcaption commands are allowed per page,\n%% so if you have more than seven captions, insert a \\clearpage\n%% after every seventh one.\n\n%% There must be a \\figcaption command for each legend. Key the text of the\n%% legend and the optional \\label in curly braces. If you wish, you may\n%% include the name of the corresponding figure file in square brackets.\n%% The label is for identification purposes only. It will not insert the\n%% figures themselves into the document.\n%% If you want to include your art in the paper, use \\plotone.\n%% Refer to the on-line documentation for details.\n\n\n\n\n\n\n\n%\\input{table}\n\t\t\n\n%% The following command ends your manuscript. LaTeX will ignore any text\n%% that appears after it.\n\n\\end{document}\n\n"
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[
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"name": "astro-ph0002362.extracted_bib",
"string": "\\begin{thebibliography}{11}\n\\bibitem{Eke} Eke, V.R., Navarro, J. \\& Frenk, C.S., 1998, \\apj, {\\bf 503,} 569\n\\bibitem{FP} Flores, R.A. \\& Primack, J.A., 1994, \\apj, {\\bf 427}, L1\n\\bibitem{SB} Frenk, C.S. et al., 1999, \\apj, {\\bf 525}, 554\n\\bibitem{Seb} Ghigna, S., Moore, B., Governato, F., Lake, G., Quinn,\nT. \\& Stadel, J., 1999, astro-ph/9910166\n\\bibitem{Gott} Gottl\\\"{o}ber, S., Klypin, A.A. \\& Kravtsov, A.V.,\n1999, in ASP Conf.Ser.176, Observationl Cosmology, ed G.Giuricin and\nM.Mezzetti (San Francisco), 418\n\\bibitem{GIF} Kauffmann, G., Colberg, J.M., Diaferio, A., \\& White, S.D.M., 1999, \\mnras, {\\bf 303}, 188\n\\bibitem{Klypin} Klypin, A.A., Gottl\\\"{o}ber, S., Kravtsov, A.V. \\& Khokholov, A.M., 1999, \\apj, {\\bf 516,} 530\n\\bibitem{Kra} Kravtsov, A.V., Klypin, A.A., Bullock, J.S. \\& Primack, J.R., 1998, \\apj, {\\bf 502,} 48\n\\bibitem{Mi} Miralda-Escude, J., 2000, astro-ph/0002050\n\\bibitem{BM} Moore, B., 1994, {\\it Nature}, {\\bf 370}, 629\n\\bibitem{M1} Moore, B., Ghigna, S., Governato, F., Lake, G., Quinn,\nT., Stadel, J. \\& Tozzi, P., 1999a, \\apjl, {\\bf 524,} L19\n\\bibitem{M2} Moore, B., Quinn, T., Governato, F., Stadel, J. \\& Lake, G., 1999b, \\mnras, {\\bf 310,} 1147\n\\bibitem{NA} Navarro, J., 1998, astro-ph/9807084\n\\bibitem{NS} Navarro, J. \\& Steinmetz, M., 1999, astro-ph/9908114\n\\bibitem{NFW1} Navarro, J., Frenk, C.S. \\& White, S.D.M., 1995, \\mnras, {\\bf 275}, 720\n\\bibitem{NFW2} ---------, 1996, \\apj, {\\bf 462}, 563\n\\bibitem{NFW3} ---------, 1997, \\apj, {\\bf 490}, 493\n\\bibitem{JO} Ostriker, J.P., 1999, astro-ph/9912548\n\\bibitem{SS} Spergel, D.N. \\& Steinhardt, P.J., 1999, astro-ph/9909386\n\\bibitem{VRS} Springel, V., 1999, PhD thesis, Ludwig-Maximilian University, Munich\n\\bibitem{Bepi} Springel, V., Tormen, G., White, S.D.M. \\& Kauffmann, G., 2000, in preparation\n\\bibitem{VRS2} Springel, V., Yoshida, N. \\& White, S.D.M., 2000, astro-ph/0003162\n\\bibitem{TwoB} Steinmetz, M. \\& White, S.D.M., 1997, \\mnras, {\\bf 288}, 545\n\\bibitem{Bo} van den Bosch, F.C., 1999, astro-ph/9909298\n\\bibitem{First} White, S.D.M. \\& Springel, V., 2000, in The First\nStars, Proc. MPA/ESO workshop, ed. A. Weiss, T.Abel, and V.Hill\n(Springer, Heidelberg), (preprint astro-ph/9911378)\n\n\\end{thebibliography}"
}
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astro-ph0002364
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Nonlinear Velocity-Density Coupling: \\Analysis by Second-Order Perturbation Theory
|
[
{
"author": "\\sc Naoki Seto"
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Cosmological linear perturbation theory predicts that the peculiar velocity $\veV(\vex)$ and the matter overdensity $\delta(\vex)$ at a same point $\vex$ are statistically independent quantities, as log as the initial density fluctuations are random Gaussian distributed. However nonlinear gravitational effects might change the situation. Using framework of second-order perturbation theory and the Edgeworth expansion method, we study local density dependence of bulk velocity dispersion that is coarse-grained at a weakly nonlinear scale. For a typical CDM model, the first nonlinear correction of this constrained bulk velocity dispersion amounts to $\sim 0.3\delta$ (Gaussian smoothing) at a weakly nonlinear scale with a very weak dependence on cosmological parameters. We also compare our analytical prediction with published numerical results given at nonlinear regimes. \keywords{cosmology: theory --- large-scale structure of universe}
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"string": "\\documentstyle[12pt,aaspp4]{article}\n%\\documentstyle[aasms4]{article}\n\n\\begin{document}\n%\\baselineskip 8mm\n\n\\newcommand{\\gsim}{\\mbox{\\raisebox{-1.0ex}{$~\\stackrel{\\textstyle >}\n{\\textstyle \\sim}~$ }}}\n\\newcommand{\\lsim}{\\mbox{\\raisebox{-1.0ex}{$~\\stackrel{\\textstyle <}\n{\\textstyle \\sim}~$ }}}\n\\newcommand{\\psim}{\\mbox{\\raisebox{-1.0ex}{$~\\stackrel{\\textstyle \\propto}\n{\\textstyle \\sim}~$ }}}\n\\newcommand{\\vect}[1]{\\mbox{\\boldmath${#1}$}}\n\\newcommand{\\lmk}{\\left(}\n\\newcommand{\\rmk}{\\right)}\n\\newcommand{\\lnk}{\\left\\{ }\n\\newcommand{\\nn}{\\nonumber}\n\\newcommand{\\rnk}{\\right\\} }\n\\newcommand{\\lkk}{\\left[}\n\\newcommand{\\rkk}{\\right]}\n\\newcommand{\\lla}{\\left\\langle}\n\\newcommand{\\p}{\\partial}\n\\newcommand{\\rra}{\\right\\rangle}\n\\newcommand{\\vex}{{\\vect x}}\n\\newcommand{\\vek}{{\\vect k}}\n\\newcommand{\\vel}{{\\vect l}}\n\\newcommand{\\vem}{{\\vect m}}\n\\newcommand{\\ven}{{\\vect n}}\n\\newcommand{\\vep}{{\\vect p}}\n\\newcommand{\\veq}{{\\vect q}}\n\\newcommand{\\veX}{{\\vect X}}\n\\newcommand{\\veV}{{\\vect V}}\n\\newcommand{\\beq}{\\begin{equation}}\n\\newcommand{\\eeq}{\\end{equation}}\n\\newcommand{\\beqa}{\\begin{eqnarray}}\n\\newcommand{\\eeqa}{\\end{eqnarray}}\n\\newcommand{\\mpc}{\\rm Mpc}\n\\newcommand{\\hmpc}{{h^{-1}\\rm Mpc}}\n\\newcommand{\\ch}{{\\cal H}}\n\n%\\if0\n\\title{ Nonlinear Velocity-Density Coupling: \\\\Analysis by Second-Order\n Perturbation Theory }\n\\author{\\sc Naoki Seto }\n\\affil{Department of Physics, Faculty of Science, Kyoto University,\nKyoto 606-8502, Japan\\\\\nseto@tap.scphys.kyoto-u.ac.jp }\n\n\n\\begin{abstract}\nCosmological linear perturbation theory predicts that the peculiar velocity\n$\\veV(\\vex)$ and the matter overdensity $\\delta(\\vex)$ at a same point $\\vex$\nare statistically independent quantities, as log as the initial density\nfluctuations are random Gaussian distributed. However nonlinear\ngravitational effects might change the situation. Using framework of\nsecond-order perturbation theory and the Edgeworth expansion method, we\nstudy local density dependence of bulk velocity dispersion that is\n coarse-grained at a weakly nonlinear scale. For a typical CDM model, the first\nnonlinear correction of this constrained bulk velocity dispersion\namounts to $\\sim 0.3\\delta$ (Gaussian smoothing) at a weakly nonlinear scale\n with a very weak dependence on cosmological\nparameters. We also compare our analytical prediction with published \nnumerical results given at nonlinear regimes.\n\n\\keywords{cosmology: theory --- large-scale structure of universe}\n\\end{abstract}\n%\\fi\n\n\n\\section{Introduction}\nThe peculiar velocity field is one of the most fundamental quantities to\nanalyze the \nlarge-scale structure in the universe ({\\it e.g.} Peebles 1980). It is\nconsidered to reflect \ndynamical nature of density fluctuations of gravitational\nmatter. The peculiar velocity field is usually observed using\n astrophysical objects ({\\it e.g.} galaxies), as determination of\ndistances is crucial for measuring peculiar velocities (Dekel 1994,\nStrauss \\& Willick 1995). There is a\npossibility that statistical aspects of the velocity field traced by these\nobjects and that traced by dark matter particles might be different. This\ndifference is generally called ``velocity bias'' and its elucidation becomes\nhighly important in observational cosmology ({\\it e.g.} Cen \\& Ostriker 1992,\nNarayanan, Berlin \\& Weinberg 1998, Kaufmann et al. 1999).\n\nVelocity bias is often discussed numerically with making ``galaxy \nparticles\" in some effective manners. But here we discussed a more basic\nphenomenon. It is known that \nstatistics of the peculiar velocity field depend largely on local density\ncontrast. For example, both the single particle and\npairwise velocity dispersions of dark matter particles are \nknown to be increasing function of local density (Kepner, Summers, \\&\nStrauss 1997, Strauss, Cen \\& Ostriker 1998, Narayanan et al. 1998). \nAnalysis of pairwise velocity statistics is interesting from theoretical \npoint of views, and also very important in observational cosmology\n(Peebles 1976, Davis \\& Peebles 1983, Zurek et al. 1994, Fisher et\nal. 1994, Sheth 1996,\nDiaferio \\& \nGeller 1996, Suto \\& Jing 1997, Seto \\& Yokoyama 1998a, 1999, Jing \\&\nB$\\ddot{\\rm o}$rner 1998, \nJuszkiewicz, Fisher \\& \nSzapudi 1998, Seto 1999b, Juszkiewicz, Springel \\&\nDurrer 1999). But \nwe do not discuss it here and concentrate on velocity field \ncharacterized by single point which is simpler to analyze\ntheoretically. \n\nLinear perturbation theory predicts that the peculiar velocity\n$\\veV(\\vex)$ and the density contrast $\\delta(\\vex)$ at a given point\n$\\vex$ is statistically independent, as long as the initial density\nfluctuations are random Gaussian distributed. Namely, the joint probability\ndistribution function $P(\\veV, \\delta)$ can be written in a form \nas $P_1(\\veV)P_2(\\delta)$.\n\nIt is not surprising that the peculiar velocity of each particle is largely\naffected by nonlinear gravitational effects and shows local density\ndependence described above. But what can we expect for the smoothed (bulk)\nvelocity that is \nfield coarse grained at some spatial scale $R$? Due to nonlinear mode\ncouplings, the relation $P_1(\\veV)P_2(\\delta)$ valid for linear theory must\nbe modified and bulk velocity dispersion must also depend on local\ndensity contrast defined at the same smoothing scale $R$ (see\nBernardeau 1992,\nChodorowski \\& {\\L}okas 1997, Bernardeau et al. 1999 for the velocity\ndivergence field). \n\nHowever, Kepner, Summers \\& Strauss (1997) showed from cold-dark-matter\n (CDM) and hot-dark-matter (HDM)\n N-body simulations that at nonlinear scales ($0.77\\hmpc\\le R \\le\n 4.88\\hmpc$), such a local density dependence was not observed (see\n Figs.2(a) and 3(a) of their paper). \nThis is an interesting contrast to the behavior of velocity field traced \n by each particle, as described before (Kepner et al. 1997, Narayanan et \n al. 1998).\n\n\nIn this article, we investigate local density dependence of smoothed\n(bulk) velocity dispersion using framework of second-order perturbation\ntheory. We calculate the first-order nonlinear correction of the constrained\n velocity\ndispersion. Our target is weakly nonlinear scale and somewhat larger\nthan scale analyzed by Kepner et al. (1997). Since current survey depth\nof the\ncosmic velocity field is highly limited, our constrained statistics\nmight not be useful in observational cosmology at present ({\\it e.g.}\nSeto \\& Yokoyama 1998b, see also Seto 1999a). Our interest in this\narticle is \ntheoretically motivated one about nonlinear gravitational dynamics. \n\n\nAs the peculiar velocity field is more weighted to large-scale fluctuations\n(smaller wave number $k$) than the density field, perturbative treatment of\nsmoothed velocity field \nwould be reasonable at weakly nonlinear scale. Actually, Bahcall,\nGramann \\& Cen (1994) showed that \nsmoothed unconstrained \nvelocity dispersion in N-body simulations are well predicted by \nlinear theory even at smoothing scale\n$R=3\\hmpc$ (see their Table 1). Second-order\nanalysis by Makino, Sasaki \\&\nSuto (1992) also gives consistent results to their simulations.\n\n\n\n\n\n\\section{Formulation}\nFirst we define the (unsmoothed) density contrast field $\\delta(\\vex)$\nin terms \nof the mean density of the universe $\\bar{\\rho}$ and the local density\nfield $\\rho(\\vex)$ as\n\\beq\n\\delta(\\vex)=\\frac{\\rho(\\vex)-\\bar{\\rho}}{\\bar{\\rho}}.\n\\eeq\nMany theoretical predictions of the large-scale structure are based on\ncontinuous fields, but observations as well as numerical experiments\n(such as, N-body simulations) are usually sampled by points \nwhere point-like\ngalaxies (or mass elements) exist. In comparison of theoretical\npredictions with actual\nobservations or numerical experiments, \nsmoothing operation becomes sometimes \ncrucially important to remove sparseness of particles' system. This\noperation is also important to reduce strong nonlinear effects which are \ndifficult to handle theoretically. Thus it is favorable to make theoretical\npredictions of the large-scale structure including smoothing operation.\nWe can express the smoothed density\ncontrast field $\\delta_R(\\vex)$ and the smoothed velocity field \n$\\veV_R(\\vex)$ with (spatially\nisotropic) filter $W(x,R)$ as \n\\beq\n\\delta_R(\\vex)\\equiv \\int d\\vex'^3 \\delta(\\vex') W(|\\vex-\\vex'|,R),~~~\n\\veV_R(\\vex)\\equiv \\int d\\vex'^3 \\veV(\\vex') W(|\\vex-\\vex'|,R).\n\\eeq\nAs we discuss only the smoothed fields in this article, we hereafter \nomit the suffix $R$ which indicates smoothing radius. \n\nThe velocity dispersion $ \\Sigma_V^2 (\\delta)$ for points $\\vex$ with a\ngiven \noverdensity $\\delta(\\vex)=\\delta$ is formally written as \n\\beq\n \\Sigma_V^2 (\\delta)=\\frac{\\lla \\veV(\\vex)^2\\delta_{Drc}[\\delta(\\vex)-\\delta]\\rra }{\\lla \\delta_{Drc}[\\delta(\\vex)-\\delta]\\rra},\n\\eeq\nwhere $\\delta_{Drc}(\\cdot)$ is Dirac's delta function and brackets\n$\\lla\\cdot\\rra$ \nrepresent to take ensemble average.\n\nWe assume that the initial (linear) density fluctuations are isotropic\nrandom Gaussian. At the linear-order we have $\\veV(\\vex)\\propto \\nabla\n\\Delta^{-1}\\delta(\\vex)$ and $\\lla \\veV(\\vex)\\delta(\\vex)\\rra=0$ due to\nisotropy of matter fluctuations. This means that\n $\\delta$ and $\\veV$ at a same point are statistically \nindependent quantities, as a multivariate probability distribution function\n(hereafter PDF) of Gaussian variables is completely decided by their\n covariance\nmatrix ({\\it e.g.} Bardeen et al. 1986). Thus the\nconstrained velocity dispersion \n$ \\Sigma_V^2 (\\delta)$ does not\ndepend on the density contrast \n$\\delta$ at linear order. However, nonlinear mode couplings would\n change the situation. Let us \nexamine weakly non-Gaussian effects on $ \\Sigma_V^2 (\\delta)$. We can\nexpress the first nonlinear correction of $\\Sigma_V^2 (\\delta)$, using\n framework of the\n Edgeworth expansion method (Cramer 1946, Matsubara 1994, 1995,\n Juszkiewicz et al. 1995, Bernardeau \\& Kofman 1995). This method is an\n excellent tool to explore \n weakly nonlinear effects of the large-scale structure induced by gravity. \n\nWhen a field $F$ is defined by weakly non-Gaussian variables\n$\\{A_\\mu(\\vex)\\}$ with vanishing means, we can expand the expectation\nvalue $\\lla F \\rra$ as (see appendix A) \n\\beq\n\\lla F(A_1,\\cdots,A_m)\\rra=\\lla F \\rra_G+\\frac16 \\sum_{\\mu,\\nu,\\lambda}\n\\lla A_\\mu A_\\nu A_\\lambda \\rra_c \\lla \\frac{\\p^3 F}{\\p A_\\mu\\p A_\\nu\\p\n A_\\lambda } \\rra_G +O(\\sigma^2 F),\n\\eeq\nwhere $\\lla \\cdot \\rra_G$ is the expectation value under the assumption that\nvariables \n$\\{A_\\mu(\\vex)\\}$ are multivariate Gaussian distributed, characterized by\ntheir covariance matrix $\\lla A_\\mu A_\\nu\\rra$. The quantity\n$\\lla A_\\mu A_\\nu A_\\lambda \\rra_c$\nis the third-order connected \nmoment of variables $\\{A_\\mu\\}$, and we have $\\lla A_\\mu A_\\nu A_\\lambda\n\\rra_c=\\lla A_\\mu A_\\nu A_\\lambda\\rra$ at third-order. The variance\n$\\sigma^2=O(A_i^2)$ is the order\nparameter of perturbative expansion around the Gaussian distribution, and \nwe can regard $\\sigma^2=\\lla \n\\delta^2\\rra$ in this article. The denominator of $\\Sigma_V^2 (\\delta)$\nin equation (3) is nothing but the one point PDF of density contrast $\\delta$.\nFrom equation (4) we obtain the famous perturbative \n formula as follows ($\\nu\\equiv \\delta/\\sigma$) \n\\beq\n\\lla\n\\delta_{Drc}[\\delta(\\vex)-\\delta]\\rra=\n\\frac{e^{-\\nu^2/2}}{{\\sqrt{2\\pi\\sigma^2}}} \n \\lmk 1+\\frac{S\\sigma H_3(\\nu )}{6} +O(\\sigma^2)\\rmk,\n\\eeq\n({\\it e.g.} Juszkiewicz et al. 1995, Bernardeau \\& Kofman 1995) and this \nis the most\nsimplified version of the\nEdgeworth expansion.\nHere the function\n$H_n(\\nu)\\equiv (-1)^ne^{\\nu^2/2}(d/d\\nu)^n e^{-\\nu^2/2}$\nis $n$-th order Hermite polynomial, and $S$ is a parameter of order\nunity and called skewness (Peebles 1980, Fry 1984, Goroff et al. 1986,\nsee also Seto 1999c), \n\\beq\nS\\equiv \\frac{\\lla \\delta^3\\rra}{\\sigma^4}.\n\\eeq\nDue to the nonlinear correction term proportional to $S\\sigma$, points with\nhigh-$\\sigma$ overdensity are more abundant than the linear prediction\nby a Gaussian\ndistribution. \n\n\nNext the numerator of $\\Sigma_V^2 (\\delta)$ is given by\n\\beq\n\\lla\\veV(\\vex)^2\n\\delta_{Drc}[ \\delta(\\vex)-\\delta]\\rra=\\sigma_V^2 \n\\frac{e^{-\\nu^2/2}}{{\\sqrt{2\\pi\\sigma^2}}} \n \\lmk 1+\\frac{S\\sigma H_3(\\nu )}{6}+C\\sigma\nH_1(\\nu) +O(\\sigma^2)\\rmk, \n\\eeq\nwhere $\\sigma_V^2\\equiv \\lla\\veV^2\\rra$ is the unconstrained velocity\ndispersion. The parameter $C=O(1)$ is defined by \n\\beq\nC=\\frac{\\lla \\veV(\\vex)^2\\delta(\\vex) \\rra}\n{\\sigma^2 \\sigma_V^2}.\n\\eeq\nIn the studies of the large-scale structure, the Edgeworth expansion or \nthe\nthird-order moments have been mainly discussed for scalar fields, such as \ndensity field $\\delta(\\vex)$ or velocity divergence field $\\nabla\\cdot\n\\veV(\\vex)$ ({\\it e.g.} Chodorowski \\& {\\L}okas 1997). Here we present\nanalytical study for couplings of \n$\\delta(\\vex)$ and $\\veV(\\vex)$, but numerical investigation of our\nmethod is also important as well as interesting. \nFrom equations (5) and (7) we obtain the constrained velocity dispersion \n$\\Sigma_V^2 (\\delta)$ up to the\nfirst-order nonlinear correction as \n\\beqa \\displaystyle\n\\Sigma_V^2(\\delta) &=& \\frac{\\lla \\veV(\\vex)^2\\delta_{Drc}[\\delta(\\vex)-\\delta]\\rra }{\\lla \\delta_{Drc}[\\delta(\\vex)-\\delta]\\rra}\\nn\\\\\n&=& \\frac{ \\displaystyle\\sigma_V^2 \n\\frac{e^{-\\nu^2/2}}{{\\sqrt{2\\pi\\sigma^2}}} \n \\lmk 1+\\frac{S\\sigma H_3(\\nu )}{6}+C\\sigma\nH_1(\\nu) +O(\\sigma^2)\\rmk}{ \\displaystyle\\frac{e^{-\\nu^2/2}}{{\\sqrt{2\\pi\\sigma^2}}} \n \\lmk 1+\\frac{S\\sigma H_3(\\nu )}{6} +O(\\sigma^2)\\rmk}\\nn\\\\\n&=&\\sigma_V^2\\lmk1+\\frac{S\\sigma H_3(\\nu )}6+C\\delta-\\frac{S\\sigma H_3(\\nu\n )}6+O(\\sigma^2)\\rmk \\nn\\\\\n&=&\\sigma_V^2(1+C\\delta+O(\\sigma^2)).\n\\eeqa\nNote that our result $\\Sigma_V^2(\\delta)$ does not depend on the skewness\nparameter $S$. Nonlinear effects appear through the quantity $C$.\n\nNext let us evaluate non-Gausssianity induced by gravity, using\nhigher-order perturbation theory. We perturbatively\n expand the density and velocity fields as\n\\beqa\n\\delta(\\vex)&=&\\delta_1(\\vex)+\\delta_2(\\vex)+\\delta_3(\\vex)+\\cdots,\\\\\n\\veV(\\vex)&=&\\veV_1(\\vex)+\\veV_2(\\vex)+\\veV_3(\\vex)+\\cdots,\n\\eeqa\nwhere $\\delta_1(\\vex)$ and $\\veV_1(\\vex)$ are the linear modes,\n$\\delta_2(\\vex)$ and $\\veV_2(\\vex)$ are the second-order modes, and so\non. We solve the following three basic equations (continuity,\nEuler and Poisson equations) order by order (Peebles 1980)\n\\beqa\n\\frac{\\p}{\\p\n t}\\delta(\\vex)+\\frac{1}{a}\\nabla[\\veV(\\vex)\\{1+\\delta(\\vex)\\}]&=&0,\\\\ \n\\frac{\\p}{\\p\n t}\\veV(\\vex)+\\frac1a[\\veV(\\vex)\\cdot\\nabla]\\veV(\\vex)+\\frac{\\p_t\n a}a\\veV(\\vex)+\\frac1a\\nabla\\phi(\\vex)&=&0,\\\\\n\\nabla^2\\phi(\\vex)-4\\pi a^2\\rho(t)\\delta(\\vex)&=&0,\n\\eeqa\nwhere $a$ represents the scale factor. In these equations we have\nomitted explicit time dependence of fields for notational \nsimplicities. We only discuss quantities at a specific epoch and there\nwould be no confusion.\n\n\nFourier space representation is convenient to analyze the nonlinear\nmode couplings. We denote the unsmoothed\n linear Fourier mode by $\\delta_{lin}(\\vek)$.\nThen $\\delta_1(\\vex)$ and $\\veV_1(\\vex)$ are written in terms of\n$\\delta_{lin}(\\vek)$ and $W(kR)$, the Fourier transform of the filter function\n$W(|\\vex|,R)$, as \n \\beq\n\\delta_1(\\vex)=\\int \\frac{d\\vek}{(2\\pi)^3}\n\\exp(i\\vek\\vex)\\delta_{lin}(\\vek)W(kR),~~~\n\\veV_1(\\vex)={Hf}\\int\\frac{d\\vek}{(2\\pi)^3} \\frac{i\\vek}{k^2} \\exp(i\\vek\\vex)\\delta_{lin}(\\vek)W(kR),\n\\eeq\nwhere $H(\\equiv d\\ln a/dt$) is the Hubble parameter and \n $f(\\equiv d\\ln D/d \\ln a$, $D$: linear growth rate of density\nfluctuation) is a function of cosmological parameters $\\Omega$ and\n$\\lambda$, and well fitted by\n\\beq\nf\\simeq \\Omega^{0.6}+\\lambda/30,\n\\eeq\nin the ranges $0.05\\le \\Omega \\le 1.5 $ and $0 \\le \\lambda \\le 1.5 $\n(Martel 1991).\n\nWe define the linear matter power spectrum $P(k)$ by\n\\beq\n\\lla \\delta_{lin}(\\vek)\n\\delta_{lin}(\\vel)\\rra=(2\\pi)^3\\delta_{Drc}^3(\\vek+\\vel)P(k).\n\\eeq\nThen the dispersions\n $\\sigma^2$ and $\\sigma_V^2$ are given by the following simple integrals \nof $P(k)$ up to required order to evaluate the first nonlinear effects of\n $\\Sigma_V^2(\\delta)$,\n\\beqa\n\\sigma^2&=&\\int\\frac{d\\vek}{(2\\pi)^3} P(k) W(kR)^2+O(\\sigma^4),\\\\\n\\sigma_V^2&=&H^2f^2\\int\\frac{d\\vek}{(2\\pi)^3k^2} P(k) W(kR)^2+O(\\sigma^4),\n\\eeqa\n In this \narticle we only use the Gaussian filter defined by $W(kR)=\\exp[-(kR)^2/2]$.\n\nAs shown in equation (8), the first-order nonlinear correction of the\nconstrained dispersion \n$\\Sigma_V^2(\\delta)$ is \ncharacterized by the factor $C$. We need the second-order modes\n$\\delta_2(\\vex)$ and $\\veV_2(\\vex)$ to calculate the first nonvanishing\ncontributions of \n$\\lla\\veV(\\vex)^2\\delta(\\vex) \\rra$.\nThese second-order modes are given with linear mode\n$\\delta_{lin}(\\vek)$ as (Fry 1984, Goroff 1986)\n\\beqa\n\\delta_2(\\vex)&=&\\int \\frac{d\\vek d\\vel}{(2\\pi)^6}\n\\exp[i(\\vek+\\vel)\\vex]\\delta_{lin}(\\vek)\n\\delta_{lin}(\\vel)\\ch_{2\\delta}(\\vek,\\vel) W(R|\\vek+\\vel|),\\\\ \n%%%%%%%%%%%%%%%%%%%%%5\n\\veV_2(\\vex)&=&{Hf}\\int \\frac{d\\vek d\\vel}{(2\\pi)^6}\n\\frac{i(\\vek+\\vel)}{|\\vek+\\vel|^2} \n\\exp[i(\\vek+\\vel)\\vex]\\delta_{lin}(\\vek)\n\\delta_{lin}(\\vel)\\ch_{2V}(\\vek,\\vel) W(R|\\vek+\\vel|), \n\\eeqa\n\nwhere kernels $\\ch_{2\\delta}$ and $\\ch_{2V}$ are defined as follows\n\\beqa\n\\ch_{2\\delta}(\\vek,\\vel)&=&\\frac12(1+K)\n+\\frac{\\vek\\cdot\\vel}{2kl}\\lmk\\frac{k}{l}+\\frac{l}k\\rmk +\\frac12(1-K) \n\\lmk \\frac{\\vek\\cdot\\vel}{kl}\\rmk^2,\\\\ \n\\ch_{2V}(\\vek,\\vel)&=&L\n+\\frac{\\vek\\cdot\\vel}{2kl}\\lmk\\frac{k}{l}+\\frac{l}k\\rmk +(1-L) \n\\lmk \\frac{\\vek\\cdot\\vel}{kl}\\rmk^2.\n\\eeqa\nThe factors $K$ and $L$ depend very weakly on cosmological parameters\n$\\Omega$ and $\\lambda$, and are fitted as (Matsubara 1995)\n\\beqa\nK(\\Omega,\\lambda)&\\simeq&\\frac37\\Omega^{-1/30}-\\frac{\\lambda}{80}\\lmk1\n-\\frac32\\lambda\\log_{10}\\Omega\\rmk,\\\\ \nL(\\Omega,\\lambda)&\\simeq& \\frac37\\Omega^{-11/200}-\\frac{\\lambda}{70}\\lmk1\n-\\frac73\\lambda\\log_{10}\\Omega\\rmk,\n\\eeqa\nin the ranges $0.1\\le\\Omega\\le 1$ and $0\\le\\lambda\\le 1$. In the\nfollowings we neglect these weak dependence and simply put\n\\beq\nK=L=\\frac37.\n\\eeq\nThus we can write down the third-order moment \n$\\lla \\veV\\cdot\\veV \\delta\\rra$ in the following\nform \n\\beqa\n\\lla \\veV\\cdot\\veV \\delta\\rra&=&\n\\lla \\veV_1\\cdot\\veV_1\\delta_2\\rra+2\\lla\n\\veV_1\\cdot\\veV_2\\delta_1\\rra+O(\\sigma^6)\\\\ \n&=&2H^2f^2\\int\\frac{d\\vek d\\vel}{(2\\pi)^6}P(k)P(l)\\lkk\n-\\frac{\\vek\\cdot\\vel}{k^2l^2}\n\\ch_{2\\delta}(\\vek,\\vel)+2\\frac{\\vek\\cdot(\\vek+\\vel)}{k^2|\\vek+\\vel|^2}\\ch_{2V}\n(\\vek,\\vel)\\rkk \\nn \\\\\n& &\\times W(kR)W(lR)W(|\\vek+\\vel|R)+O(\\sigma^6).\n\\eeqa\nDue to the rotational symmetry around the origin, we can simplify the\nsix dimensional integral $d\\vek d\\vel$ to three dimensional integral\n$dkdldu$. Here, $-1\\le u \\le 1$ is the cosine between two vectors $\\vek$\nand $\\vel$ and \ngiven by $u=\\vek\\cdot\\vel/kl$. Then we obtain the first nonvanishing\norder of $ \\lla \\veV\\cdot\\veV\\delta\\rra$ as\n\\beqa\n\\lla \\veV\\cdot\\veV\n\\delta\\rra&=&2H^2f^2\\int_{-1}^1du\\int\\frac{k^2l^2dkdl}{8\\pi^4}\nP(k)P(l)\\exp[-k^2-l^2-klu] \\nn\\\\\n& &\\times \\Bigg[-\\frac{u}{kl}\\lnk \\frac57+\\frac{u}2\\lmk\\frac{k}{l}+\\frac{l}k\\rmk+\\frac27\nu^2 \\rnk\\nn\\\\\n& &~~~ +2\\frac{k+lu}{k(k^2+l^2+2klu)}\\lnk \\frac37+\\frac{u}2\\lmk\\frac{k}{l}+\\frac{l}k\\rmk+\\frac47\nu^2 \\rnk \\Bigg].\n\\eeqa\nNote that the parameter $C$ does not depend on the normalization of power\nspectrum (see eqs.[18][19] and [29]).\nFurthermore, the factors $Hf$ cancel out between $\\sigma_V^2$ and $\\lla\n\\veV\\cdot\\veV \\delta\\rra$ and cosmological parameters are irrelevant for\nthe factor \n$C$ in our treatment ($K=L=3/7$). Finally, we comment that even though\nthe constrained dispersion \n $\\Sigma_V^2(\\delta)$ changes by $\\sigma_V^2C\\delta$ from the \nunconstrained value $\\sigma_V^2$, the \nshape of the one-point PDF of velocity field with a given $\\delta$\n keeps Gaussian distribution at the same order of nonlinearity. We can\n easily confirm \n this by calculating the ratio\n\\beq\n\\frac{\\lla \\delta_{Drc}^3(\\veV(\\vex)-\\veV)\n \\delta_{Drc}(\\delta(\\vex)-\\delta)\\rra}{\\lla\n \\delta_{Drc}(\\delta(\\vex)-\\delta)\\rra}\n=\\frac1{(2\\cdot3^{-1}\\pi\\Sigma_V^2(\\delta))^{3/2}}\\lkk\n\\exp\\lmk-\\frac{\\veV^2}{2\\cdot3^{-1}\\Sigma_V^2(\\delta) } \\rmk +O(\\sigma^2)\\rkk.\n\\eeq\nThe factor $3^{-1}$ in the right-hand side arises from the dimensionality of \nthe velocity vector.\nFirst-order correction is completely absorbed to the velocity dispersion \n$\\Sigma_V^2(\\delta)$.\n\n\n\n\\section{Results}\nIn this section we numerically evaluate the parameter $C$ for various\npower spectra. \nWe first examine pure power-law spectra $P(k)$ given \nby $(n >-1)$\n\\beq\nP(k)=Ak^n.\n\\eeq\nIn this case $C$ does not depend on the smoothing radius $R$, and we can \nsimply put $R=1$. Then the dispersions $\\sigma^2$ and $\\sigma_V^2$ are given as\n\\beq\n\\sigma^2=\\frac1{(2\\pi)^2}\\Gamma \\lmk \\frac{3+n}2\\rmk,~~~\n\\sigma_V^2=\\frac{(Hf)^2}{(2\\pi)^2}\\Gamma \\lmk \\frac{1+n}2\\rmk,\n\\eeq\nwhere $\\Gamma(n)$ is the Gamma function.\nAs for the nonlinear coupling \n$\\lla\\veV\\cdot\\veV\\delta\\rra=\\lla\\veV_1\\cdot \\veV_1 \\delta_2 \\rra+2\\lla\\veV_1\\cdot \\veV_2 \\delta_1\n\\rra$, we can write down the first \n contribution \n$\\lla \\veV_1\\cdot\\veV_1\\delta_2\\rra$ explicitly in terms of Hypergeometric\nfunctions as in the case of skewness parameter $S$ (Matsubara 1994,\n{\\L}okas et al 1995). However, using {\\it mathematica} (Wolfram 1996), \nwe confirm that the second term $2\\lla \\veV_1\\cdot\\veV_2\\delta_1\\rra$\ncannot be expressed in a closed form and numerical integration is required.\nThese two terms diverge in the limit $n\\to -1$ where velocity dispersion \n$\\sigma_V^2$ also\ndiverges, but the factor $C$ approaches $0$ in this limit.\n\n\nIn Fig.1 we plot $C$ as a function of spectral index $n$ in the range\n$-1<n<2$.\nThe correction $C$ is a positive and increasing function of $n$. \nThis means that the velocity dispersion of high density regions are larger\nthan that of low density regions.\nWe have $C= 0.314$ at the scale-invariant spectrum $n=1$.\n% We can expect that difference of velocity dispersions between\n%points with $\\delta=2$ and points with $\\delta=0$ is smaller than\n%$32\\%$ (for a fixed $R$).\n\n\nNext we examine $C$ for a more realistic power spectrum $P(k)$. We use CDM \n transfer function given in Bardeen, Bond, Kaiser \\& Szalay (1986) \n and assume that the primordial spectral\n index is equal to 1. Then $P(k)$ can be written as\n\\beq\nP(k)=Ak\\lkk\\frac{\\ln(1+2.34q)}{2.34q}\n\\rkk^2[1+3.89q+(16.1q)^2+(5.46q)^3+(6.71q)^4 ]^{-1/2}, \n\\eeq\nwhere $q\\equiv k/[(\\Gamma h){\\rm Mpc^{-1}}]$. $\\Gamma$ is the shape\n parameter of the CDM transfer function \nand recent observational analyses of galaxy clusterings\n support $\\Gamma = 0.2\\sim 0.3$ ({\\it e.g.} Tadros et al. 1999, Dodelson \\& Gazta$\\tilde{\\rm n}$aga 1999).\nIn Fig.2 we plot $C$ as a function of smoothing radius $R$ \nin units of $[(\\Gamma h)^{-1}{\\rm Mpc}]$.\n For this model the factor $C$ depends weakly on the smoothing radius\n$R$ and we have $C\\sim 0.30$ at \na weakly nonlinear regime $R\\sim 10h^{-1}\\mpc$.\nIn the limit $R\\to \\infty$, $C$ converges to $0.314$ which is the same\n value of \n $C$ for the power-law model with $n=1$ presented\nin Fig.1. This is reasonable as we have\n\\beq\n\\lim_{k\\to 0}\\frac{P(k)}{k}=const, \n\\eeq\nfor CDM models analyzed here.\n\n\nOur results obtained so far are the velocity dispersion for points\nconstrained by the \nmatter density contrast $\\delta$. One might have interest in the velocity\ndispersion constrained by the galaxy density contrast $\\delta_g$.\nHere, let us assume deterministic but nonlinear biasing relation for the \nsmoothed galaxy\ndistribution $\\delta_g(\\vex)$ and the matter distribution $\\delta(\\vex)$ as\n\\beq\n\\delta_g(\\vex)=b_1\\delta(\\vex)+b_2(\\delta(\\vex)^2-\\sigma^2)+O(\\sigma^3),\n\\eeq\nwhere $b_1$ and $b_2$ are some constants ({\\it e.g.} Fry \\& Gazta$\\tilde{\\rm n}$aga 1993). In this case we can easily\nshow that the velocity dispersion $\\Sigma_V(\\delta_g)^2$ for points $\\vex$\nwith $\\delta_g(\\vex)=\\delta_g$ is given by\n\\beq\n\\Sigma_V^2(\\delta_g)=\\sigma_V^2(1+C\\delta_g/b_1+O(\\sigma^2)),\n\\eeq\nwhere the factors $C$ and $\\sigma_V$ are same as those appeared in\n$\\Sigma_V^2(\\delta)$ (eq.[9]). Thus $\\Sigma_V^2(\\delta_g)$ does not\ndepend on the nonlinear coefficient $b_2$. This is also apparent when we\nwrite down $\\delta(\\vex)$ using $ \\delta_g(\\vex)$ and then insert this\nsolution to equation (9). The factor proportional to $b_2$ is higher\neffects than analyzed here. Note that in\n equation (36), the linear bias parameter $b_1$\nappears by itself not in the usual form $\\beta\\equiv \\Omega^{0.6}/b_1$,\nand the overdensity $\\delta_g$ dependence becomes smaller for larger $b_1$.\n\nKepner et al. (1997) numerically investigated the mean magnitude\n$\\lla|\\veV(\\vex)|\\rra$ of smoothed \nbulk velocity for points with given overdensity\n$\\delta$.\nFollowing the fact commented in the last paragraph of section 2, we can\neasily calculate this magnitude $ \\mu_V(\\delta)$ and obtain following\nresult (see appendix B)\n\\beq\n \\mu_V(\\delta)=\\sqrt{\\frac8{3\\pi}\\Sigma_V^2(\\delta)(1+O(\\sigma^2))}=\\sqrt{\\frac8{3\\pi}}\\sigma_V \\lmk 1+\\frac{C\\delta}2+O(\\sigma^2)\\rmk.\n\\eeq\nFor a typical CDM model, our analytical result predicts that the magnitude\n$\\mu_V(\\delta)$ is expected to change $\\sim 0.15\\delta$, according to\nthe \nlocal density contrast $\\delta$. If we constrain points using overdensity\nof galaxies instead of that of the gravitating matter, the combination \n$C\\delta$ is replaced by \n$C \\delta_g/b_1$ in the above equation.\n\nNumerical results of Kepner et al. (1997) were given for\n CDM and HDM models \nwith $\\sigma_8=0.67$ normalization. Here $\\sigma_8$ is the linear rms\ndensity fluctuation in a sphere of $8\\hmpc$ radius.\nThey calculated the smoothed density and velocity fields with smoothing\nradius $R$ at $0.77\\hmpc\\le R\\le 4.88\\hmpc$. Thus their results are\n quantities at nonlinear regimes. It is true that simple application of our\nperturbative formula to their results\nwould not be valid. However, surprisingly enough,\nthe quantity $\\mu_V(\\delta)$ shows almost no $\\delta$ dependence in the\nrange $0<\\delta\\lsim 30$. \\footnote{It seems that the function\n $\\mu_V(\\delta)$ in their figures shows extremely weak\n dependence of $\\delta$ around $\\delta\\simeq 0 $.}\n\nIf $\\Sigma_V^2(\\delta)$ (and thus $\\mu_V(\\delta)$) shows no\n$\\delta$-dependence at nonlinear scale and our second-order analysis is\nvalid for \nweakly nonlinear regime, we confront an interesting possibility. \nNamely, with parameterization of overdensity by normalized value $\\nu\\equiv\n\\delta/\\sigma$, velocity dispersion does not depend on $\\nu$ at linear\nand nonlinear regime, but depends on it at (intermediate) weakly\nnonlinear regime. Furthermore, we should notice that the \nvelocity dispersion of dark-matter\nparticles (without coarse graining) depends largely on $\\delta$ (Kepner\net al. 1997, Narayanan et al. 1998).\\footnote{Definitions of velocity\n dispersion in these two papers are not identical. } \n\n\nTo make clear understanding of these transitions, \nwe need to numerically investigate the constrained dispersion\n $\\Sigma_V^2(\\delta)$ in\ndetailed manner with various smoothing length $R$, from linear to\nnonlinear scales. Performance of second-order perturbation theory for\nthe \nvelocity vector is also worth studying.\n\n\n\n\\section{Summary}\nIt is commonly accepted that the large-scale structure observed today \n is formed by\ngravitational instability from small primordial density fluctuations\n(Peebles 1980).\nIn this picture, the peculiar velocity and the density contrast are\nfundamental quantities to characterize inhomogeneities in the universe.\nLinear analysis of cosmological perturbation theory predicts that, as long as\ninitial fluctuations are random Gaussian distributed, the\none-point PDF of the velocity field $\\veV(\\vex)$ is statistically \nindependent of the local density contrast $\\delta(\\vex)$. This is an\n important \naspect of cosmological perturbation.\n\nHowever nonlinear gravitational evolution changes the situation. Due to \nnonlinear mode-couplings, the peculiar velocity field \nis no longer statistically\nindependent of the local density field. \n Here we have investigated bulk velocity dispersion\n ($\\Sigma_V^2(\\delta)$) as a function \nof the local density contrast and calculated its first nonlinear correction\nusing framework of second-order perturbation theory. Our target has\nbeen set at\nweakly nonlinear regimes where perturbative treatment must be\nreasonable. At present, survey depth of velocity field is \nhighly limited and our constrained statistics\n might not be directly useful for\nobservational cosmology. However, we believe that our theoretical study\nis important to understand one interesting aspect of the cosmic velocity field\npeculiar to its nonlinear evolution.\n\nWe have shown that the first nonlinear correction of\n$\\Sigma_V^2(\\delta)$ is proportional to the local \ndensity and strongly depends on the matter power spectra, but weakly on the\ncosmological parameters $\\Omega$ and $\\lambda$. For typical CDM model\nwith primordially scale-invariant fluctuations, this first-order\ncorrection is about \n$0.3\\delta$. If we use overdensity of galaxies $\\delta_g$, this\ncorrection term becomes $0.3 \\delta_g/b_1$ (the factor $b_1$ is defined in\neq.[35]). This dependence might be used to constrain the linear bias\nparameter $b_1$ itself (not in the usual form $\\Omega^{0.6}/b_1$) in future\npeculiar velocity surveys. \nWe have also shown that the constrained one-point PDF of velocity field\nkeeps the Gaussian shape up to second-order of perturbation. First\nnonlinear effects are \ncompletely absorbed to \nthe velocity dispersion $\\Sigma_V^2(\\delta)$. \n\nNumerical results by Kepner et al. (1997) have been compared with our \nanalytical results.\nTheir results show almost no $\\delta$-dependence, \ncontrary to ours. \nHowever spatial scale of their analysis (strongly nonlinear regime) is\nlargely different from ours (weakly nonlinear regime).\nIn the forthcoming paper, detailed numerical analysis \nwill be presented for various smoothing lengths $R$ and power\nspectra (see also Seto 2000). Validity of \nsecond-order analysis as well as the Edgeworth expansion method \n for velocity vector \nwould be also investigated numerically.\n\n \\acknowledgments\nThe author would like to thank J. Yokoyama \nfor useful discussion and the referee R. Juszkiewicz for helpful comments.\nThis work was partially supported by the Japanese Grant\nin Aid for Science Research Fund of the Ministry of Education, Science,\nSports and Culture No.\\ 3161.\n\n\n\\newpage\n\\appendix\n\n\\section{Weakly Non-Gaussian Averages}\nIn this appendix, we derive expression (4) for weakly non-Gaussian\nvariables $\\{A_\\mu\\}~(\\mu=1,\\cdots,n)$ with $\\lla A_\\mu\\rra=0$ ({\\it\n e.g.} Matsubara 1994).\nThe partition function $Z(J_\\mu)$ for a multivariate probability distribution function \n$P(A_\\mu)$ is defined as\n\\beq\nZ(J_\\mu)\\equiv \\int_{-\\infty}^{\\infty} d^n P(A_\\mu)\\exp\\lmk i \\sum J_\\nu A_\\nu \\rmk. \n\\eeq\nAccording to the cumulant expansion theorem (Ma 1985), the function $\\ln\nZ(J_\\mu)$ is a generating function of connected moments $\\lla A_{\\mu_1}\n\\cdots A_{\\mu_N}\\rra_c$. Therefore, taking the inverse Fourier transform of\nequation (A1), the probability distribution function $P(A_\\mu)$ is\nwritten as\n\\beq\nP(A_\\mu)=\\exp \\lmk \\sum_{N=3}^\\infty \\frac{(-1)^N}{N!}\n\\sum_{\\mu_1,\\cdots,\\mu_N}\\lla A_{\\mu_1}\n\\cdots A_{\\mu_N}\\rra_c \\frac{\\p^N}{\\p A_{\\mu_1} A\\cdots\\p A_{\\mu_N} }\n\\rmk P_G(A_\\mu),\n\\eeq \nwhere the function $ P_G(A_\\mu)$ is the multivariate Gaussian\nprobability distribution function determined by a ($n\\times n$)\ncorrelation matrix $M_{\\mu\\nu}\\equiv \\lla \nA_\\mu A_\\nu\\rra$ as\n\\beq\nP_G(A_\\mu)=\\frac1{\\sqrt{(2\\pi)^n {\\rm det}M}} \\exp\\lmk\n-\\frac12 \\sum_{\\mu,\\nu} A_\\mu (M^{-1})_{\\mu\\nu} A_\\nu \\rmk .\n\\eeq\nIf we have relations $\\lla A_{\\mu_1}\n\\cdots A_{\\mu_N}\\rra_c=O(\\sigma^{2N-2}) $ as predicted by higher-order\nperturbation theory, equation (A2) is perturbatively expanded as\n\\beq\nP(A_\\mu)=P_G(A_\\mu)-\\frac16 \\sum_{\\mu,\\nu,\\lambda} \\lla A_\\mu A_\\nu\nA_\\lambda \\rra_c \\frac{\\p^3}{\\p A_\\mu\\p A_\\nu\\p A_\\lambda} P_G(A_\\mu) \n+O(\\delta^2).\n\\eeq\nEvaluating the ensemble average of a field $F(A_\\mu)$ with this\nperturbative expression and taking partial integrals, we\nobtain expansion (4). \n\nOne might consider that formula (3) with Dirac's delta function\nis somewhat indirect. We can obtain same results using formula\nfor probability distribution function $P(\\veV|\\delta)=P(\\veV,\\delta)/P(\\delta)$\nand evaluating $P(\\veV,\\delta)$ and $P(\\delta)$ with expression (A4). \n\\section{Derivation of $\\mu_V(\\delta)$}\nHere we derive expression (37). As in the case of the constrained\nvelocity dispersion $\\Sigma_V^2(\\delta)$ (eq.[3]), the quantity\n$\\mu_V(\\delta)$ is formally defined as\n\\beq\n\\mu_V(\\delta)\\equiv \\frac{\\lla|\\veV(\\vex)|\\delta_{Drc}[\\delta(\\vex)-\\delta]\\rra}{\\lla\\delta_{Drc}[\\delta(\\vex)-\\delta]\\rra}. \n\\eeq\nThe r.h.s. of this equation is written as\n\\beq\n\\mu_V(\\delta)=\\int_{-\\infty}^{\\infty} d\\veV \\frac{\\lla |\\veV| \\delta_{Drc}^3(\\veV(\\vex)-\\veV)\n \\delta_{Drc}(\\delta(\\vex)-\\delta)\\rra}{\\lla\n \\delta_{Drc}(\\delta(\\vex)-\\delta)\\rra}.\n\\eeq\nWith the perturbative expansion given in equation (30) the r.h.s. of this equation is evaluated as\n\\beq\n \\frac1{(2\\cdot3^{-1}\\pi\\Sigma_V^2(\\delta))^{3/2}}\n\\int_{-\\infty}^{\\infty} d\\veV \\lkk\n\\exp\\lmk-\\frac{\\veV^2}{2\\cdot3^{-1}\\Sigma_V^2(\\delta) } \\rmk\n+O(\\sigma^2)\\rkk |\\veV|.\n\\eeq\nIt is straightforward to obtain expression (37) given in the main\ntext as follows\n\\beq\n \\mu_V(\\delta)=\\sqrt{\\frac8{3\\pi}\\Sigma_V^2(\\delta)(1+O(\\sigma^2))}=\\sqrt{\\frac8{3\\pi}}\\sigma_V\n \\lmk 1+\\frac{C\\delta}2+O(\\sigma^2)\\rmk.\n\\eeq\n\n\n\n\n%\\if0%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\newpage\n%\\begin{references}\n\\begin{thebibliography}{}\n\n\\bibitem[]{} Bahcall, N. A., Gramann, M., \\& Cen, R. 1994, ApJ, 436, 23\n\n\\bibitem[]{} Bardeen, J. M., Bond, J. R., Kaiser, N. \\& Szalay, A\n S. 1986, ApJ, 305, 15\n\\bibitem[]{} Bernardeau, F. 1992, ApJ, 390, L61\n\n\\bibitem[]{} Bernardeau, F. \\& Kofman L. 1995, ApJ, 443, 479\n\n\\bibitem[]{} Bernardeau, F., Chodorowski, M., {\\L}okas, E. L., Stompor, \n R. \\& Kudlicki A., 1999, MNRAS, 309, 543\n\n\\bibitem[]{} Cen, R. \\& Ostriker, J. P. 1992, ApJ, 399, L113\n\n\\bibitem{} Chodorowski, M. \\& {\\L}okas, E. L. 1997,\n MNRAS, 287, 591\n\n\\bibitem[]{} Cramer, H. 1946, Mathematical Methods of Statistics\n(Princeton University Press: Princeton) \n\n\\bibitem[]{} Davis, M. \\& Peebles, P. J. E. 1983, ApJ, 267, 465\n\n\\bibitem[]{} Dekel, A., 1994, ARA\\&A, 32, 371\n\n\\bibitem[]{} Diaferio, A. \\& Geller, M. 1996, ApJ 467, 19\n\n\\bibitem[]{} Dodelson, S., \\& Gazta$\\tilde{\\rm n}$aga, E. 1999, preprint\n (astro-ph/9906289)\n\\bibitem[]{} Fisher, K. B. et al. 1994, MNRAS, 267, 927\n\n\\bibitem[]{} Fry, J. N. 1984, ApJ, 279, 499\n\n\\bibitem[]{} Fry, J. N. \\& Gazta$\\tilde{\\rm n}$aga, E. 1993, ApJ, 413, 447\n\n\\bibitem[]{} Goroff, M. H., Grinstein, B., Rey, S. -J., \\& Wise, M. B., 1986, ApJ,\n 311, 6\n\n\\bibitem[]{} Jing, Y. P., \\& B$\\ddot{\\rm o}$rner, G. 1998, ApJ, 503, 502\n\n%\\bibitem[]{} Juszkiewicz, R., 1981, MNRAS, 197, 931 \n\n\\bibitem[]{} Juszkiewicz, R. et al. 1995, ApJ, 442, 39\n\n\\bibitem[]{} Juszkiewicz, R., Fisher, K. B. \\& Szapudi, I. 1998, ApJ,\n504, L1\n\\bibitem[]{} Juszkiewicz, R., Springel, V. \\& Durrer, R. 1999, ApJ,\n518, L25\n\n\\bibitem[]{} Kaufmann, G., et al. 1999, MNRAS, 303, 188\n\n\\bibitem[]{}Kepner, J. V., Summers, F. J. \\& Strauss, M. A. 1997, New\n Astron., 2, 165\n\n\\bibitem[]{} {\\L}okas, E. L., Juszkiewicz, R., Weinberg, D. H. \\& Bouchet, F. R. 1995,\n MNRAS, 274, 730\n\n\\bibitem[]{} Ma, S.-K. 1985, {\\ Statistical Mechanics} (World\n Scientific: Philadelphia)\n\n\\bibitem[]{} Makino, N., Sasaki, M., \\& Suto, Y. 1992, Phys. Rev. D,\n 46, 585 \n\\bibitem[]{} Martel, H. 1991, ApJ, 377, 7\n\n\\bibitem[]{} Matsubara, T. 1994, ApJ, 434, L43\n\n\\bibitem[]{} Matsubara, T. 1995, Ph.D. Thesis, Hiroshima Univ\n\n\\bibitem[]{} Narayanan, V. K., Berlind, A., \\& Weinberg, D. H. 1998,\npreprint (astro-ph/9812002)\n\\bibitem[]{} Peebles, P. J. E. 1976, A\\&A, 53, 131\n\n\\bibitem[]{} Peebles, P. J. E. 1980, {\\ The Large Scale Structure of the Universe}\n (Princeton University Press: Princeton)\n\n\\bibitem[]{}Seto, N. 1999a, ApJ, 516, 527\n\\bibitem[]{}Seto, N. 1999b, ApJ, 520, 409\n\\bibitem[]{}Seto, N. 1999c, ApJ, 523, 24\n\\bibitem[]{}Seto, N. 2000, ApJ, 537 (No.2) in press\n\\bibitem[]{}Seto, N., \\& Yokoyama, J. 1998a, ApJ, 492, 421\n\\bibitem[]{}Seto, N., \\& Yokoyama, J. 1998b, ApJ, 496, L59\n\\bibitem[]{}Seto, N., \\& Yokoyama, J. 1999, PASJ, 51, 233\n\n\\bibitem[]{} Sheth, R. 1996, MNRAS, 2789, 1311\n\n\\bibitem[]{} Strauss, M. A. \\& Willick, J. A. 1995, Phys. Rep., 261, 271\n\n\\bibitem[]{} Strauss, M. A., Cen, R. \\& Ostriker, J. P. 1998, ApJ, 494, 20\n\n\\bibitem[]{} Suto, Y., \\& Jing, Y. P. 1997, ApJS, 110, 167\n\n\\bibitem[]{} Tadros, H. et al. 1999, preprint (astro-ph/9901351)\n\n\\bibitem{} Wolfram, S. 1996, {\\ The Mathematica Book, 3rd ed.}\n (Cambridge University Press: Cambridge)\n\n\\bibitem[]{} Zurek, W. H. Quinn, P. J., Salmon, J. K. \\& Warren,\nM. S. 1994, ApJ, 431, 559\n\n\\end{thebibliography}\n%\\fi%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5\n\n%\\if0%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\newpage\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=7.cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{Fig1.eps} \\end{minipage}\n \\end{center}\n\\caption[]{The second-order correction $C$ for power-law matter\n spectra with Gaussian smoothing. }\n\\end{figure}\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\epsfxsize=7cm\n \\begin{minipage}{\\epsfxsize} \\epsffile{Fig2.eps} \\end{minipage}\n \\end{center}\n\\caption[]{The second-order correction $C$ for the CDM \n spectrum of Bardeen et al. (1986). We plot the factor $C$ as a\n function of the smoothing radius $R$ in\n units of \n $(h\\Gamma)^{-1}$Mpc. }\n\\end{figure}\n\\end{document}\n%\\fi%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\newpage\n\\centerline{\\bf FIGURE CAPTIONS}\n\\begin{description}\n\\item[Figs.\\ 1]The second-order correction $C$ for power-law matter\n spectra with Gaussian smoothing.\n\n\\item[Figs.\\ 2]The second-order correction $C$ for the CDM \n spectrum of Bardeen et al. (1986). We plot the factor $C$ as a\n function of the smoothing radius $R$ in\n units of \n $(h\\Gamma)^{-1}$Mpc.\n\n\\end{description}\n\n\n\n\\end{document}\n\n\n"
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{
"name": "astro-ph0002364.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[]{} Bahcall, N. A., Gramann, M., \\& Cen, R. 1994, ApJ, 436, 23\n\n\\bibitem[]{} Bardeen, J. M., Bond, J. R., Kaiser, N. \\& Szalay, A\n S. 1986, ApJ, 305, 15\n\\bibitem[]{} Bernardeau, F. 1992, ApJ, 390, L61\n\n\\bibitem[]{} Bernardeau, F. \\& Kofman L. 1995, ApJ, 443, 479\n\n\\bibitem[]{} Bernardeau, F., Chodorowski, M., {\\L}okas, E. L., Stompor, \n R. \\& Kudlicki A., 1999, MNRAS, 309, 543\n\n\\bibitem[]{} Cen, R. \\& Ostriker, J. P. 1992, ApJ, 399, L113\n\n\\bibitem{} Chodorowski, M. \\& {\\L}okas, E. L. 1997,\n MNRAS, 287, 591\n\n\\bibitem[]{} Cramer, H. 1946, Mathematical Methods of Statistics\n(Princeton University Press: Princeton) \n\n\\bibitem[]{} Davis, M. \\& Peebles, P. J. E. 1983, ApJ, 267, 465\n\n\\bibitem[]{} Dekel, A., 1994, ARA\\&A, 32, 371\n\n\\bibitem[]{} Diaferio, A. \\& Geller, M. 1996, ApJ 467, 19\n\n\\bibitem[]{} Dodelson, S., \\& Gazta$\\tilde{\\rm n}$aga, E. 1999, preprint\n (astro-ph/9906289)\n\\bibitem[]{} Fisher, K. B. et al. 1994, MNRAS, 267, 927\n\n\\bibitem[]{} Fry, J. N. 1984, ApJ, 279, 499\n\n\\bibitem[]{} Fry, J. N. \\& Gazta$\\tilde{\\rm n}$aga, E. 1993, ApJ, 413, 447\n\n\\bibitem[]{} Goroff, M. H., Grinstein, B., Rey, S. -J., \\& Wise, M. B., 1986, ApJ,\n 311, 6\n\n\\bibitem[]{} Jing, Y. P., \\& B$\\ddot{\\rm o}$rner, G. 1998, ApJ, 503, 502\n\n%\\bibitem[]{} Juszkiewicz, R., 1981, MNRAS, 197, 931 \n\n\\bibitem[]{} Juszkiewicz, R. et al. 1995, ApJ, 442, 39\n\n\\bibitem[]{} Juszkiewicz, R., Fisher, K. B. \\& Szapudi, I. 1998, ApJ,\n504, L1\n\\bibitem[]{} Juszkiewicz, R., Springel, V. \\& Durrer, R. 1999, ApJ,\n518, L25\n\n\\bibitem[]{} Kaufmann, G., et al. 1999, MNRAS, 303, 188\n\n\\bibitem[]{}Kepner, J. V., Summers, F. J. \\& Strauss, M. A. 1997, New\n Astron., 2, 165\n\n\\bibitem[]{} {\\L}okas, E. L., Juszkiewicz, R., Weinberg, D. H. \\& Bouchet, F. R. 1995,\n MNRAS, 274, 730\n\n\\bibitem[]{} Ma, S.-K. 1985, {\\ Statistical Mechanics} (World\n Scientific: Philadelphia)\n\n\\bibitem[]{} Makino, N., Sasaki, M., \\& Suto, Y. 1992, Phys. Rev. D,\n 46, 585 \n\\bibitem[]{} Martel, H. 1991, ApJ, 377, 7\n\n\\bibitem[]{} Matsubara, T. 1994, ApJ, 434, L43\n\n\\bibitem[]{} Matsubara, T. 1995, Ph.D. Thesis, Hiroshima Univ\n\n\\bibitem[]{} Narayanan, V. K., Berlind, A., \\& Weinberg, D. H. 1998,\npreprint (astro-ph/9812002)\n\\bibitem[]{} Peebles, P. J. E. 1976, A\\&A, 53, 131\n\n\\bibitem[]{} Peebles, P. J. E. 1980, {\\ The Large Scale Structure of the Universe}\n (Princeton University Press: Princeton)\n\n\\bibitem[]{}Seto, N. 1999a, ApJ, 516, 527\n\\bibitem[]{}Seto, N. 1999b, ApJ, 520, 409\n\\bibitem[]{}Seto, N. 1999c, ApJ, 523, 24\n\\bibitem[]{}Seto, N. 2000, ApJ, 537 (No.2) in press\n\\bibitem[]{}Seto, N., \\& Yokoyama, J. 1998a, ApJ, 492, 421\n\\bibitem[]{}Seto, N., \\& Yokoyama, J. 1998b, ApJ, 496, L59\n\\bibitem[]{}Seto, N., \\& Yokoyama, J. 1999, PASJ, 51, 233\n\n\\bibitem[]{} Sheth, R. 1996, MNRAS, 2789, 1311\n\n\\bibitem[]{} Strauss, M. A. \\& Willick, J. A. 1995, Phys. Rep., 261, 271\n\n\\bibitem[]{} Strauss, M. A., Cen, R. \\& Ostriker, J. P. 1998, ApJ, 494, 20\n\n\\bibitem[]{} Suto, Y., \\& Jing, Y. P. 1997, ApJS, 110, 167\n\n\\bibitem[]{} Tadros, H. et al. 1999, preprint (astro-ph/9901351)\n\n\\bibitem{} Wolfram, S. 1996, {\\ The Mathematica Book, 3rd ed.}\n (Cambridge University Press: Cambridge)\n\n\\bibitem[]{} Zurek, W. H. Quinn, P. J., Salmon, J. K. \\& Warren,\nM. S. 1994, ApJ, 431, 559\n\n\\end{thebibliography}"
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astro-ph0002366
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The first COMPTEL source catalogue
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"author": "V.~Sch\\\"{o}nfelder et al\\inst{1}"
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The imaging Compton telescope COMPTEL aboard NASA's Compton Gamma-Ray Observatory has opened the MeV gamma-ray band as a new window to astronomy. COMPTEL provided the first complete all-sky survey in the energy range 0.75 to 30 MeV. The catalogue, presented here, is largely restricted to published results. It contains firm as well as marginal detections of continuum and line emitting sources and presents upper limits for various types of objects. The numbers of the most significant detections are 32 for steady sources and 31 for gamma-ray bursters. Among the continuum sources, detected so far, are spin-down pulsars, stellar black-hole candidates, supernova remnants, interstellar clouds, nuclei of active galaxies, gamma-ray bursters, and the Sun during solar flares. Line detections have been made in the light of the 1.809 MeV $^{26}$Al line, the 1.157 MeV $^{44}$Ti line, the 847 and 1238 keV $^{56}$Co lines, and the neutron capture line at 2.223 MeV. For the identification of galactic sources, a modelling of the diffuse galactic emission is essential. Such a modelling at this time does not yet exist at the required degree of accuracy. Therefore, a second COMPTEL source catalogue will be produced after a detailed and accurate modelling of the diffuse interstellar emission has become possible. \keywords{Gamma rays: observations, Catalogs, Surveys}
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"name": "preprint.tex",
"string": "\\documentstyle[lscape,epsfig,supertabular] {l-aa} % diese Zeile fuer endgueltige Version verwenden\n%\\documentclass{l-aa}\n%\\usepackage{lscape}\n%\\usepackage{epsfig}\n%\\usepackage{supertabular}\n%-----------------------------------------------------------------------\n% Special Macros:\n\\def\\phibar{\\bar{\\varphi}}\n\\def\\lsim{\\mbox{$ \\stackrel{\\textstyle _<}{_{\\sim}} $}}\n\\def\\gsim{\\mbox{$ \\stackrel{\\textstyle _>}{_{\\sim}} $}}\n%-----------------------------------------------------------------------\n\\begin{document}\n%------------------------------------------------------------------------\n\\thesaurus{ %Schluesselwoerter! \n (20; 13.09.2; 04.03.1; 04.19.1)} \n% \n\\title{The first COMPTEL source catalogue}\n%\\author{V.~Sch\\\"{o}nfelder et al\\inst{1}}\n\\author{V.~Sch\\\"{o}nfelder\\inst{1} \\and K.~Bennett\\inst{4} \\and J.J.~Blom\\inst{2} \\and H.~Bloemen\\inst{2} \\and W.~Collmar\\inst{1} \\and A.~Connors\\inst{3} \\and R.~Diehl\\inst{1} \\and W.~Hermsen\\inst{2} \n\\and A.~Iyudin\\inst{1} \\and R.M.~Kippen\\inst{3} \\and J.~Kn\\\"odlseder\\inst{5} \\and L.~Kuiper\\inst{2} \\and G.G.~Lichti\\inst{1} \\and M.~McConnell\\inst{3} \\and D.~Morris\\inst{3} \\and R.~Much\\inst{4} \\and U.~Oberlack\\inst{1} \\and J.~Ryan\\inst{3} \\and G.~Stacy\\inst{3} \\and H.~Steinle\\inst{1} \\and A.~Strong\\inst{1} \\and R. Suleiman\\inst{3} \\and R.~van~Dijk\\inst{4} \\and M.~Varendorff\\inst{1} \\and C.~Winkler\\inst{4} \\and O.R.~Williams\\inst{4}} \n\\offprints{\\\\ \\mbox{V.~Sch\\\"onfelder, vos@mpe.mpg.de}}\n\\institute{Max-Planck-Institut f\\\"ur extraterrestrische Physik, \n D--85740 Garching, Germany\n\\and \nSRON--Utrecht, Sorbonnelaan 2, NL--3584 CA Utrecht, The Netherlands\n\\and \nSpace Science Center, University of New Hampshire, Durham NH 03824-3525, USA\n\\and\nAstrophysics Division, ESTEC, NL--2200 AG Noordwijk, The Netherlands \n\\and\nCentre d'Etude Spatiale des Rayonnements (CESR), BP 4346, F-31029 Toulouse Cedex, France\n}\n\n\\date{Received 28 July 1999; Accepted 20 December 1999}\n\n\\maketitle\n \n\\begin{abstract}\nThe imaging Compton telescope COMPTEL aboard NASA's Compton Gamma-Ray Observatory has opened the MeV gamma-ray band as a new window to astronomy. COMPTEL provided the first complete all-sky survey in the energy range 0.75 to 30 MeV. The catalogue, presented here, is largely restricted to published results. It contains firm as well as marginal detections of continuum and line emitting sources and presents upper limits for various types of objects. The numbers of the most significant detections are 32 for steady sources and 31 for gamma-ray bursters. Among the continuum sources, detected so far, are spin-down pulsars, stellar black-hole candidates, supernova remnants, interstellar clouds, nuclei of active galaxies, gamma-ray bursters, and the Sun during solar flares. Line detections have been made in the light of the 1.809 MeV $^{26}$Al line, the 1.157 MeV $^{44}$Ti line, the 847 and 1238 keV $^{56}$Co lines, and the neutron capture line at 2.223 MeV. For the identification of galactic sources, a modelling of the diffuse galactic emission is essential. Such a modelling at this time does not yet exist at the required degree of accuracy. Therefore, a second COMPTEL source catalogue will be produced after a detailed and accurate modelling of the diffuse interstellar emission has become possible. \n\n\\keywords{Gamma rays: observations, Catalogs, Surveys}\n\\end{abstract}\n\n\n\\section{Introduction}\n \nCOMPTEL has demonstrated that the sky is rich in phenomena that can be studied at MeV energies. A variety of gamma-ray emitting objects are visible either in continuum or line emission. Among the continuum sources are spin-down pulsars, stellar black-hole candidates, supernova remnants, interstellar clouds, nuclei of active galaxies, gamma-ray bursters, and the Sun during solar flares. Line detections have been made in the light of the 1.809 MeV $^{26}$Al line, the 1.157 MeV $^{44}$Ti line, the 847 and 1238 keV $^{56}$Co lines, and the neutron capture line at 2.223 MeV. \n\nCOMPTEL has also measured the diffuse interstellar and cosmic gamma radiation, whose properties are described elsewhere (\\cite{strong96,strong99,bloemen99a,kappadath96,weidens99}). For the identification of galactic sources a modelling of the diffuse galactic emission is essential. Such a modelling at this time does not yet exist at the required degree of accuracy. \n\nThis paper is restricted to all those sources that have been definitely or marginally detected so far, and provides upper limits to the MeV flux from different types of objects. A second COMPTEL source catalogue will be produced after a detailed and accurate modelling of the diffuse interstellar emission has become possible. \n\nThe Compton Observatory was launched on April 5, 1991 by the Space Shuttle Atlantis. During Phase-I of the Compton Observatory Program, a full-sky survey - the first ever in gamma-ray astronomy - was performed. Phase-I ended on November 17, 1992. Observations during the subsequent phases of the program resulted in deeper exposures and complemented the survey. This source catalogue is mainly restricted to the results from the first five years of the mission (up to Phase IV/Cycle-5). In a few cases, more recent results have been added.\n\n%\\vspace{1,2cm}\n\n\\section{Instrument description and data analysis}\n\nCOMPTEL was designed to operate in the energy range 0.75 to 30 MeV. It has a large field-of-view of about 1 steradian, and different sources within this field can be resolved, if they are more than about 3 to 5 degrees away from each other (energy dependent). The resulting source location accuracy is of the order of 1$^{\\circ}$. The COMPTEL energy resolution of 5 \\% to 10 \\% FWHM is an important feature for gamma-ray line investigations. A detailed description of COMPTEL is given by \\cite{schoenf93}.\n\nCOMPTEL consists of two detector assemblies, an upper one of liquid scinitillator NE213, and a lower one of NaI (Tl). A gamma-ray is detected by a Compton collision in the upper detector and a subsequent interaction in the lower detector. \n\nThe arrival direction of a detected gamma ray is known to lie on a circle on the sky. The center \nof each circle is the direction of the scattered gamma-ray, and the radius of the \ncircle is determined by the energy losses E1 and E2 in both interactions. The detected \nphotons are binned in a 3-dimensional (3-D) data space, consisting of the scatter direction \n(defined by the two angular coordinates $\\chi$ and $\\psi$) and by the scatter angle \n$\\phibar$ (derived from the measured energy losses in both interactions). Each detected photon is represented by a single point in the 3-D dataspace. \nThe signature of a point source with celestial coordinates ($\\chi_{o}$, $\\psi_{o}$) is a cone of 90$^\\circ$ opening angle with its axis parallel to the $\\phibar$-axis. \nThe apex of the cone is at ($\\chi_{o}$, \n$\\psi_{o}$). Imaging with \nCOMPTEL involves recognizing the cone patterns in the 3-D dataspace. Two main techniques \nare applied: one is a maximum-entropy method that generates model-independent \nimages (\\cite{strong92}) and the other one is a maximum-likelihood method that is \nused to determine the statistical significance, flux and position uncertainty of a source (\\cite{deboer92}).\n \nSignificances are derived in this method from the quantity -2 ln $\\lambda$, where $\\lambda$ is the maximum likelihood ratio L(B) / L(B+S); B represents the background model and S the source model (or sky intensity model). In a point-source search, -2 ln $\\lambda$ formally obeys a $\\chi_{3}^{2}$ distribution; in studies of a given source, $\\chi_{1}^{2}$ applies. [This allows to translate a measured L value into a corresponding probability for it being a noise fluctuation, equivalent to a Gaussian $\\sigma$ description of significances. In studies of a 'known' source, $\\sigma$ = $\\sqrt{-2 ln \\lambda}$ applies.]\n\nWe verified by simulation that the shape of the probability density distribution for our application of the likelihood analysis to the COMPTEL data is indeed Gaussian. Furthermore, we calibrated by the same simulations the number of independent 'trials' we make in a search for source, taking into account the total sky area searched (see \\cite{deboer92}).\n\nOur threshold for detection is a chance probability of 99.7 $\\%$, corresponding to a 3$\\sigma$ Gaussian significance. The applicable statistics, i.e. the relevant trails, are discussed for each source in the original publication.\n\nThe sensitivity of COMPTEL is significantly determined by the instrumental background. A substantial suppression is achieved by the combination of effective charged-particle shield detectors, time-of-flight measurement techniques, pulse-shape discrimination, Earth-horizon angle cuts and proper event selections in energy and $\\phibar$-space. %\n\nThe application of the imaging techniques requires an accurate knowledge of the instrumental and cosmic COMPTEL background. A variety of background models has been investigated and is being used. In one method, the background is derived from averaging high-latitude observations. \nThis assumes that the background has a constant shape in \nthe instrumental system in at least the spatial coordinates (but not in Compton scatter angle) for all observations, and it also assumes that the extragalactic source \ncontribution is small and smeared out by the averaging process (see \\cite{strong99}). A second \nmethod derives the background from the data that are being studied itself. \nThis is accomplished by applying a low-pass filter to the 3-D data, which \nsmooths the photon distribution and eliminates (in the first \napproximation) the source signatures (e.g. \\cite{bloemen94}). By applying iterations of this process the background estimate can be improved, further. All viewing periods have to be handled separately to account for changes of the background during the mission ({\\cite{bloemen99a}). For line studies, we estimate the background below an underlying \ncosmic gamma-ray line by averaging the count rate from neighbouring energy \nintervals (\\cite{diehl94}). \n\nFor sources within the Galactic plane the global diffuse emission from the Galaxy is modelled by fitting a bremsstrahlung, and an inverse Compton component to the data. Also an isotropic component is added to these fits to represent the cosmic gamma-ray background. The amplitude of each of these components is obtained as free parameter from the fits. It has to be admitted, however (see above), that the modelling of the plane, at present, does not yet achieve the required degree of accuracy. \n\nIn addition to the normal double-scatter mode of operation, two of the NaI crystals in the lower detector assembly of COMPTEL are also operated simultaneously as burst detectors. These two modules are used to measure the time history and energy spectra of cosmic gamma-ray bursts and solar flares. \n\nHence, solar flares and cosmic gamma-ray bursts can be measured in the telescope mode (provided the event was within the field-of-view of the instrument), and in the burst mode.\n\nIn its telescope mode COMPTEL has an unprecedented sensitivity. Within a 2-week observation period it can detect sources, which are about 10-times weaker than the Crab. By adding up all data from a certain source that were obtained over the entire duration of the mission, higher sensitivities can be obtained. Table 1 summarizes the achieved point-source sensitivities for a 2-week exposure in Phase-I of the mission (t$_{\\mbox{eff}}$ $\\sim$ 3.5 $\\cdot$ 10$^{5}$ sec), and for the ideal cases, when all data from a certain source in the Galactic center or anticenter (where the exposure is highest) are added from either Phase-I to III (t$_{\\mbox{eff}}$ $\\sim$ 2.5 $\\cdot$ 10$^{6}$ sec) or Phase-I to IV/Cycle-5 (t$_{\\mbox{eff}}$ $\\sim$ 6 $\\cdot$ 10$^{6}$ sec).\n%\n%\n% insert T A B L E 1\n%\n%\n\nFrom this table rough upper limits can be derived for those objects, which are not contained in the later tables 10 to 12 by deriving the effective exposure from Fig.1.\n\n%\\vspace{1,2cm}\n%\n%\n% insert F I G U R E 1\n%\n%\n\n\\section {The first COMPTEL source catalogue}\n\nThis section consists of four different parts. The first part (Sect. 3.1) lists all observations on which the catalogue is based. Sect. 3.2 contains COMPTEL all-sky maps in continuum and line emission. Sect. 3.3 is the catalogue of detected sources, which is subdivided into detections of spin-down pulsars, galactic sources ($\\mid$b$\\mid$ $<$ 10$^{\\circ}$), active galactic nuclei, unidentified high-latitude sources, gamma-ray line sources, gamma-ray burst sources within the COMPTEL field-of-view, and solar flare detections. Sect. 3.4 lists COMPTEL upper limits on source candidates, namely galactic objects, active galactic nuclei, and possible gamma-ray line sources.\n \n\\subsection{Observations and exposure maps}\n\nThis first COMPTEL source catalogue contains mainly results from Phase-I to IV/ Cycle-5 of the Compton mission. The relationship of the viewing periods (VP) to the actual dates of the observations is given in Table 2 (for completeness, the data of Phase-IV/Cycle-6 and 7 have been added in the table). The table also lists the pointing direction of the z-axis (COMPTEL telescope axis) in celestial coordinates, the duration of the pointing and the effective COMPTEL observation time. \n\nThe effective COMPTEL exposure of the entire sky from the sum of all observations from the beginning of the mission to Phase-IV/Cycle-5 and Phase IV/Cycle-7 are illustrated in Fig. 1. The deepest exposures were obtained in the Galactic center and anticenter region, where effective observation times up to 6 $\\cdot$ 10$^{6}$ seconds have been obtained (see also Table 1).\n\n\\subsection{COMPTEL all-sky maps}\n\nCOMPTEL all-sky maps exist for continuum emission in the three standard energy ranges 1--3 MeV, 3--10 MeV, and 10--30 MeV, and for the 1.8 MeV line from radioactive $^{26}$Al. These maps are shown in Fig. 2 and 3.\n\nFig. 2 is a maximum-entropy map using all data from Phase I to Phase IV/Cycle-6 (Strong et al., 1999). The background method used in this map is based on averaging high-latitude observations (see Sect. 2). \n\n%\n%\n% insert F I G U R E 2\n%\n% \n\nWell known sources appear in the map:\n\nCrab (l=184.5$^{\\circ}$, b=5.9$^{\\circ}$), Vela (263.6$^{\\circ}$, -2.5$^{\\circ}$) above 3 MeV, Cyg X-1 (71.1$^{\\circ}$, +3.3$^{\\circ}$), as well as striking excesses at (18$^{\\circ}$,0$^{\\circ}$) and near the Galactic center. At higher latitudes the sky is dominated by extragalactic sources: Cen A (309$^{\\circ}$, +19$^{\\circ}$) below 10 MeV (\\cite{steinle95}), 3C 273 (290$^{\\circ}$, +64$^{\\circ}$) and 3C 279 (305$^{\\circ}$, +57$^{\\circ}$) (\\cite{williams95b}). Various 'MeV blazars': 3C 454 (86$^{\\circ}$, -38$^{\\circ}$), PKS 0208-512 (276$^{\\circ}$, -62$^{\\circ}$), GRO J 0516-609 (270$^{\\circ}$, -35$^{\\circ}$) appear in one or more of the energy ranges. Next to the Crab the quasar PKS 0528+134 is clearly visible (\\cite{collmar94}, \\cite{collmar97a}). Details on these sources can be found in \\cite{blom96} and \nreferences therein. \n\nNote that since these sources are variable, their appearance in these time-averaged maps may not reflect their published fluxes or spectra precisely. Another interesting feature is the apparent presence of significant areas of diffuse emission away from the plane; in particular, the regions around (170$^{\\circ}$, +50$^{\\circ}$) and (85$^{\\circ}$, 35$^{\\circ}$), which have been presented as candidates for assocations with high-velocity cloud complexes (\\cite{blom97b}). Details in the structure of this emission should, however, be viewed with caution and are under further study. \n\nAn alternative approach to derive all-sky continuum maps is described in \\cite{bloemen99a}). This is a new approach combining model fitting, iterative background modelling and maximum entropy imaging, using the first five years of COMPTEL observations. On a coarse scale the maps derived by both methods are similar. However, on a fine scale, there are differences which are not yet fully understood. The uncertainties especially effect the identification of sources in the Galactic plane (see above).\n\n%\n%\n% insert F I G U R E 3 \n%\n%\n\nFig. 3 is a COMPTEL maximum-entropy map at 1.809 MeV from all observations up to VP 522.5 (\\cite{oberlack97}). The brightest regions are in the inner Galaxy (-35$^{\\circ}$ $<$ l $<$ +35$^{\\circ}$), near Carina (l $\\sim$ 285$^{\\circ}$), and Vela (l $\\sim$ 267$^{\\circ}$). Other regions of enhanced emission are Cygnus (l $\\sim$ 80$^{\\circ}$), and Aquila (l $\\sim$ 45$^{\\circ}$). \n\nMore recently, new 1.809 MeV COMPTEL all-sky maps have been produced using different imaging and background modelling methods. In one case (\\cite{knoed99}) the analysis uses a multi-resolution version of the Richardson-Lucy algorithm, based on wavelets. In the other case (\\cite{bloemen99b}), the maximum entropy method is combined with model fitting and iterative background modelling. All three maps are consistent with each other within their statistical and systematic uncertainties, although the multi-resolution map shows substantially less structure along the Galactic plane. \n\nSo far, no all-sky map in the light of the 1.157 MeV $^{44}$Ti gamma-ray line exists. But imaging analysis along the Galactic plane have been performed by \\cite{dupraz97} for data from Phase I to III, and by \\cite{iyudin99} from Phase I to VI/Cycle-6. Two $^{44}$Ti gamma-ray line sources have been discovered so far, these are Cas A (\\cite{iyudin97a}) and GRO J 0852-4642 (\\cite{iyudin98}), a supernova remnant near the Vela region (\\cite{aschenbach98}). \n\n%\n%\n% insert F I G U R E 4\n%\n%\n\nA maximum-entropy map in the light of the 2.2 MeV neutron-capture line based on data from the first five years of the mission (VP 1.0 through VP 523.0) has been produced by \\cite{mcconnell97b}. In general, the sky at 2.2. MeV is relatively featureless, e.g. the galactic plane is not visible. There is, however, evidence for significant ($\\sim$ 3.7$\\sigma$) emission from a point-like feature near (l, b) = (300.5$^{\\circ}$, -29.6$^{\\circ}$), the origin of which remains unknown at this time (\\cite{mcconnell97b}). Flux limits for any candidate source are typically in the range (1 to 2.0) $\\cdot$ 10$^{-5}$ cm$^{-2}$ sec$^{-1}$ (at the 3$\\sigma$ significance level).\n\nFig. 4 is an all-sky map of the statistical location contours of 31 gamma-ray bursters, which happened to be in the COMPTEL field-of-view from the beginning of the mission up to viewing period 419.5 \\cite{kippen98a}. \n%\n%\n% insert F I G U R E 5 \n%\n% insert F I G U R E 6\n%\n%\n\n\\subsection{COMPTEL source detections}\n\nThe COMPTEL source detections are summarized in Table 3 to 9: \n \n\\begin{itemize} \n\\item Table 3: Detected Spin-Down Pulsars \n\\item Table 4: Galactic Sources $\\mid$b$\\mid$ $<$ 10$^{\\circ}$ \n\\item Table 5: Active Galactic Nuclei\n\\item Table 6: Unidentified High-Latitude Sources \n\\item Table 7: Gamma-Ray Line Sources\n\\item Table 8: Gamma-Ray Burst Locations\n\\item Table 9: Solar-Flare Detections. \n\\end{itemize}\n\\medskip\n\\noindent\n\nOut of the 7 spin-down pulsars listed in Table 4 COMPTEL has made firm detections from PSR B0531+21 (Crab), PSR B0833-45 (Vela), and from PSR B1509-58. The analysis of the Vela pulsar, however, is not yet finally settled; the results presented are presently based on Phase 0 and I, only. Because of the good statistics, the Crab pulsar fluxes are listed for smaller energy intervals than the standard ones (0.75--1, 1--3, 3--10 and 10--30 MeV). Only indications for emission in the COMPTEL energy range were found from the four pulsars PSR B1951+32, PSR J0633+1746 (Geminga), PSR 0656+14, and PSR B1055-52. \n\nThe Galactic Sources with $\\mid b \\mid$ $<$ 10$^{\\circ}$ listed in Table 4 are all objects, which were seen by at least one other experiment of the Compton Observatory. These are Cyg X-1, the two EGRET sources 2EG 2227+61 and 2EG J0241+6119 (which both are also COS-B sources), Nova Persei 1992 (GRO J0422+32), the Crab nebula, and an unidentified bright source at l = 18$^{\\circ}$ within the plane (coincident with the EGRET source 2ES J1825-1307). The COMPTEL fluxes for these sources are listed in the standard energy ranges. For some of the sources the fluxes are also given for other energy intervals. The possible contribution of the diffuse galactic emission to the listed source fluxes constitutes a basic uncertainty (see column 11 of the Table). \n\nNine of the Active Galactic nuclei listed in Table 5 are of the $\\gamma$-ray Blazar type, discovered by EGRET (with the exception of 3C 273, earlier discovered by COS-B, \\cite{swanenburg78}). The only non-blazar type object in the table is the radio galaxy Cen A. All $\\gamma$-ray blazars are highly variable in intensity. \n\nThree of the five unidentified high-latitude sources in Table 6 are not point-like, but cover an extended region. Their extent may actually be due to a larger number of - so far - unresolved point sources (GRO J 1823-12 and the two High-Velocity Cloud complexes). \n\nThe gamma-ray line sources listed in Table 7 are ordered with increasing line-energy. Apart from the four point-like sources SN 1991T, Cas A, Carina, and the SNR GRO J0852-4642, also the three extended emission regions of the inner Galaxy and of the Cygnus and Vela regions are included in the table. \n\nThe 31 gamma-ray bursts listed in Table 8 were all recorded in the \\lq telescope mode\\rq\\ . The error radius of the burst location (column 4) is defined as the angular radius, having the same area as the irregularily shaped COMPTEL 1$\\sigma$ confidence region (see also Fig. 5). Columns 5, 6, and 7 provide informations on the COMPTEL accumulation time, the measured 0.75 to 30 MeV fluence and the COMPTEL detection significance of each burst. The parameters for a power-law fit to the spectrum of each burst are listed in columns 8 and 9. Column 10 states, whether variability of the burst spectrum during accumulation was observed in the more sensitive \\lq burst mode\\rq\\ . \n\nSolar Flare gamma-ray measurements taken in the burst mode are summarized in Table 9. Column 1 contains the COMPTEL flare identification, including the year/month/day and UT of the flare start (taken from the GSFC Solar Data Analysis Center (SDAC)). Truncated Julian Day, in column 2 and column 3, contains the GOES X-ray start time (taken from the Solar Geophysical Reports). The X-ray classification is in column 4 and the BATSE flare number, as assigned at the SDAC at Goddard Space Flight Center, is in column 5. The corresponding BATSE trigger number is in column 2. The COMPTEL data measured in this burst mode (see Sect. 6) have been inspected and the flare (integration time) duration as judged by the visible signal in the spectrometer is listed in column 7 with the corresponding integrated counts in the full energy range in column 8. The peak counts (with an integration time of x s) are listed in column 9. The peak count rate as measured by BATSE is in column 10 as obtained from the SDAC at GSFC. Finally, in column 11 is the integrated amount of spacecraft and instrument material between the spectrometer and the Sun. This material attenuates the gamma-ray flux and degrades the spectrum. A small number is better. Large amounts of intervening material can, in principle, be modeled away when producing a photon spectrum, but the results have large errors and are often not unique. \n%\n\n\\subsection{COMPTEL upper limits to source candidates}\n\nThe limits are given at the 2$\\sigma$ confidence level for the following objects:\n\n\\begin{itemize}\n\\item Table 10: Galactic Objects $\\mid$b$\\mid$ $<$ 10$^{\\circ}$ \n\\item Table 11: Active Galactic Nuclei\n\\item Table 12: Possible Sources of Gamma-Ray Line Emission \n\\end{itemize} \n\n\\medskip\n\\noindent\n\nTable 10 contains upper limits to Galactic Sources with $\\mid b \\mid$ $<$ 10$^{\\circ}$. This source list is restricted to black-hole candidates. Due to the above mentioned, still existing, uncertainty in modelling the diffuse Galactic emission, the source limits are at present rather conservative. \n\nPresented in Tables 11a and 11b are the\ncumulative two-sigma upper limits to the MeV-emission measured with\nCOMPTEL from active galactic nuclei (AGN) and other unidentified gamma-ray\nsources detected at high Galactic latitudes. These limits were derived\nusing composite COMPTEL all-sky maximum-likelihood maps for the 4.5 year\nperiod covering Phases I through IV/Cycle-4 of the CGRO mission (1991- 1995). A description of the data-processing procedure used to obtain the\ncomposite all-sky maps can be found in \\cite{stacy97}. \n\nIn the choice of candidate objects, emphasis was placed on known or suspected\ngamma-ray sources, particularly those detected in neighbouring energy bands\nto COMPTEL by the CGRO/EGRET and OSSE instruments (e.g., \\cite{montigny95}, \\cite{mcnaron95}). The flux-extraction routine applied\nto the composite all-sky maps computes average output values within\none-pixel radius of a specified source location. To minimize the number\nof spurious false detections, only those objects for which the summed\nlog-likelihood ratio exceeds the equivalent of a three-sigma source\ndetection (adopting $\\chi^{2}_{1}$ statistics, appropriate for a\npreviously known source at a specified location) are considered to exhibit\npotentially significant MeV emission. \n\nTable 11a lists the COMPTEL cumulative upper limits for MeV-emission from\nAGN through Phase IV/Cycle-4 of the CGRO mission. Column 1 gives the object name in\ncoordinate format; column 11 gives another common name for the source;\ncolumn 10 lists the object \\lq type\\rq\\, which is either the object class (SY\nfor Seyfert galaxy, from the target list of \\cite{maisack95}), or a\nreference to a previously reported gamma-ray detection of this source (1EG\nfor the First EGRET Catalog of \\cite{fichtel94}, 2EG for the Second\nEGRET Catalog of \\cite{thompson95}, 2EGS for the Supplement to the\nSecond EGRET Catalog of \\cite{thompson96}). \n\nTable 11b lists the COMPTEL cumulative upper limits for MeV-emission from\nunidentified high-latitude gamma-ray sources detected by the CGRO/EGRET\ninstrument. In both Tables 11a and 11b the recommended COMPTEL\nteam-standard corrections (for time-of-flight effects, livetime, etc.) are\napplied to obtain final fluxes and upper limits (see \\cite{diehl96}). \n\nInspection of Tables 11a and 11b shows only in a few isolated cases the \ncumulative detection with COMPTEL of significant emission from high-latitude sources. This is no contradiction to the detections listed in Table 5. Note that all these sources are time-variable, and their detection in individual viewing periods does not mean that they are visible in cumulative maps. \n\nIn general, the flux limits presented in Table 11a show that COMPTEL does not\ndetect cumulative MeV-emission from a majority of the extragalactic\nblazar sources detected by EGRET. This result is similar to that obtained\nby \\cite{blom97}, for the case of individual CGRO viewing periods. \nUltimately, these cumulative results will be further compared with other\nsource studies for individual CGRO viewing periods, and used in\nstatistical investigations of source properties by object class (e.g. \n\\cite{blom97}, \\cite{williams97}). \n\nThe upper limits to possible sources of gamma-ray line emission in Table 12 are again ordered with increasing line energies. The line sources considered are SN 1993J ($^{56}$Ni $\\rightarrow$ $^{56}$CO $\\rightarrow$ $^{56}$Fe decay), four supernovae as possible $^{44}$Ti line emitters at 1.157 MeV, eleven recent novae as possible sources of $^{22}$Na line emission at 1.275 MeV, five nebula or cloud complexes as 1.809 MeV $^{26}$Al sources, and six possible 2.223 MeV neutron capture sources. \n\n\\section{Conclusion}\n\nCOMPTEL has opened the MeV gamma-ray band (0.75 to 30 MeV) as a new window to astronomy. The data from five years of COMPTEL observations provided the first COMPTEL source catalogue. It is largely restricted to previously published results, and contains firm as well as marginal detections of continuum and line emitting sources, and presents upper limits for various types of objects. The number of most significant detections ($>$ 3$\\sigma$) are 32 for steady sources and 31 for gamma-ray bursters (see Table 13). Six of the listed sources extend over larger areas. Their extent may actually be due to a larger number of so far unresolved point sources. This may be especially true for the Cygnus region in 1.809 MeV, for GRO J1823-12 and for the two HVC complexes. A second COMPTEL source catalogue will be produced after a more accurate modelling of the diffuse interstellar emission has become possible. \n\n\\begin{acknowledgements} \nThe COMPTEL project is supported by the German government through DLR grant 50 Q 9096 8, by NASA under contract NAS5-26645, and by the Netherlands Organization for Scientific Research NWO. The authors acknowledge the efforts of M. Chupp, H. Haber, J. Englhauser and R. Georgii in implementing the various tables. \n\\end{acknowledgements} \n \n\n\n\\begin{thebibliography}{}\n\n\\bibitem[Aschenbach (1998)]{aschenbach98}\nAschenbach, B., 1998, Nature 396, 141\n\n\\bibitem[Bennett et al. (1993)]{bennett93}\nBennett, K., Sch\\\"onfelder, V., Ryan, J. et al., 1993, IAU Circ. 5749\n \n\\bibitem[Bloemen et al. (1994)]{bloemen94}\nBloemen, H., Hermsen, W., Swanenburg, B.N. et al., 1994, ApJS {\\bf 92}, 419\n\n\\bibitem[Bloemen et al. (1995)]{bloemen95}\nBloemen, H., Bennett, K., Blom, J.J. et al., 1995, A\\&A 293, L1\n\n\\bibitem[Bloemen et al. (1999a)]{bloemen99a}\nBloemen, H., Hermsen, W. Kappadath, S.C. et al., 1999a, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Bloemen et al. (1999b)]{bloemen99b} \nBloemen, H., Diehl, R., Hermsen, W. et al., 1999b, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Bloemen et al., in preparation]{bloemen00}\nBloemen, H. et al., in preparation\n\n\\bibitem[Blom (1997)]{blom97}\nBlom, J. J., 1997, Ph-D Thesis, University of Leiden, The Netherlands \n\n\\bibitem[Blom et al. (1995a)]{blom95a}\nBlom, J.J., Bloemen, H., Bennett, K. et al., 1995a, A\\&A 295, 330\n\n\\bibitem[Blom et al. (1995b)]{blom95b}\nBlom, J.J., Bennett, K., Bloemen, H. et al., 1995b, A\\&A 298, L33 \n\n\\bibitem[Blom et al. (1996)]{blom96}\nBlom, J.J., Bennett, K., Bloemen, H. et al., 1996, A\\&AS 120, 507 \n\n\\bibitem[Blom et al. (1997a)]{blom97a}\nBlom, J.J. Bloemen, H., Bykov, A.M. et al. 1997a, Proc. of 2$^{nd}$ INTEGRAL Workshop, eds.: C. Winkler, T.J.-L. Courvoisier, Ph. Durouchoux, ESA SP-382, p. 119\n\n\\bibitem[Blom et al. (1997b)]{blom97b} \nBlom, J.J., Bloemen, H., Bykov, A.M. et al. 1997b, A\\&A 321, 288\n\n\\bibitem[Collmar et al. (1993)]{collmar93}\nCollmar, W., Bennett, K., Bloemen, H. et al., 1993, A\\&AS 97, 71 \n \n\\bibitem[Collmar et al. (1994)]{collmar94}\nCollmar, W. et al., Bennett, K., Bloemen, H. et al., 1994, Proc. 2$^{nd}$ Compton Symposium, AIP Conf. Proc. 304, eds: C.E. Fichtel, N. Gehrels, J.P. Norris, p. 659\n\n\\bibitem[Collmar et al. (1996)]{collmar96}\nCollmar, W., Bennett, K., Bloemen, H. et al., 1996, A\\&AS 120, 515 \n \n\\bibitem[Collmar et al. (1997a)]{collmar97a}\nCollmar, W., Bennett, K., Bloemen, H. et al., 1997a, A\\&A 328, 33 \n\n\\bibitem[Collmar et al. (1997b)]{collmar97b}\nCollmar, W., Wessolowski, U., Sch\\\"onfelder, V. et al., 1997b, Proc. of 4$^{th}$ Compton Symposium, 1997, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 1587\n\n\\bibitem[Collmar et al. (1997c)]{collmar97c}\nCollmar, W., Blom, J.J., Bennett, K. et al., 1997c, Proc. of 25th ICRC, Durban, eds.: M.S. Potgieter, B.C. Raubenheimer, D.J. v. der Walt, Vol. 3, 101 \n\n\\bibitem[Connors et al. (1993a)]{connors93a}\nConnors, A., Aarts, H.J.M., Bennett, K. et al., 1993a, A\\&AS 97, 75\n\n\\bibitem[Connors et al. (1993b)]{connors93b}\nConnors, A. et al., Collmar, W., Hanlon, L. 1993b, Adv. Space Res. 13(12), 715\n\n\\bibitem[Connors et al. (1997)]{connors97}\nConnors, A., Bennett, K., Collmar, W. et al., 1997, Proc. of 25th ICRC, Durban, eds.: M.S. Potgieter, B.C. Raubenheimer, D.J. v. der Walt, Vol. 3, 13 \n\n\\bibitem[de Boer et al. (1992)]{deboer92} \nde Boer, H. Bennett, K., Bloemen, H. et al., 1992 in: Data Analysis in Astron. IV, ed. V. di Ges\\`u, L. Scarsi, R. Buccheri, P. Crane, M.C. Maccarone, H.U. Zimmermann, Plenum Press, New York, 241 \n \n\\bibitem[del Rio et al (1996)]{delrio96}\ndel Rio, E., v. Ballmoos, P., Bennett, K. et. al., 1996, A\\&A 315, 237 \n\n\\bibitem[Diehl et al. (1994)]{diehl94}\nDiehl, R. , Dupraz, C., Bennett, K. et al., 1994, ApJS 92, 429\n \n\\bibitem[Diehl 1996]{diehl96}\nDiehl, R., 1996, \\lq COMPTEL Data Analysis Standards\\rq\\ , COMPTEL Internal\nReport COM-MO- DRG-MGM-231.9 (3 March 1996) \n\n\\bibitem[Dupraz et al. (1997)]{dupraz97}\nDupraz, C., Bloemen, H., Bennett, K. et al., 1997, A\\&A, 324, 683\n\n\\bibitem[Fichtel et al. (1994)]{fichtel94}\nFichtel, C. E., Bertsch, D.E., Chiang, J. et al., 1994, ApJS 94, 551 (1EG)\n\n\\bibitem[Greiner et al. (1995)]{greiner95}\nGreiner, J. et al., Sommer, M., Bade, N. et al., 1995 A\\&A 302, 121\n\n\\bibitem[Hanlon et al. (1994a)]{hanlon94a}\nHanlon, L.O., Bennett, K., Williams, O.R. et al., 1994a, A\\&A 285, 161\n\n\\bibitem[Hanlon et al. (1994b)]{hanlon94b}\nHanlon, L.O., Bennett, K., Williams, O.R. et al., 1994b, in: AIP Conf. Proc. No 307; Gamma-Ray Bursts, ed. G.J. Fishman, J.J. Brainerd, K. Hurley (New York: AIP Press), p. 275\n\n\\bibitem[Hanlon et al. (1995)]{hanlon95}\nHanlon, L.O., Hermsen, W., Kippen, R.M. et al., 1995, A\\&A 296, L41\n\n\\bibitem[Hermsen et al. (1997)]{hermsen97}\nHermsen, W., Kuiper, L., Sch\\\"onfelder, V. et al., 1997, Proc. of 2$^{nd}$ INTEGRAL Workshop, eds.: C. Winkler, T.J.-L. Courvoisier, Ph. Durouchoux, ESA-SP 382, 287\n\n\\bibitem[Iyudin et al. (1994)]{iyudin94}\nIyudin, A.F., Diehl, R., Bloemen, H. et al., 1994, A\\&A 284, L1 \n\n\\bibitem[Iyudin et al. (1995)]{iyudin95}\nIyudin, A.F., Bennett, K., Bloemen, H. et al., 1995, A\\&A 300, 422\n\n\\bibitem[Iyudin et al. (1996)]{iyudin96}\nIyudin, A.F., Bennett, K., Bloemen, H. et al., 1996, A\\&A 311, L21\n\n\\bibitem[Iyudin et al (1997a)]{iyudin97a}\nIyudin, A., Diehl, R., Lichti, G.G. et al., 1997a, Proc. of 2$^{nd}$ INTEGRAL Workshop, eds.: C. Winkler, T.J.-L. Courvoisier, Ph. Durouchoux, ESA-SP 382, p. 37\n \n\\bibitem[Iyudin et al. (1997b)]{iyudin97b}\nIyudin, A., Reimer, O., Bennett, K. et al., 1997b, Proc. of 25$^{th}$ ICRC, Durban, eds.: M.S. Potgieter, B.C. Raubenheimer, D.J. v. der Walt, Vol. 3, 89 \n\n\\bibitem[Iyudin et al. (1998)]{iyudin98}\nIyudin, A., Sch\\\"onfelder, V., Bennett, K. et al., 1998, Nature, 396, 142 \n\n\\bibitem[Iyudin et al. (1999)]{iyudin99}\nIyudin, A., Sch\\\"onfelder, V., Bennett, K. et al., 1999, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Kappadath et al. (1996)]{kappadath96}\nKappadath, S.C., Ryan, J., Bennett, K., 1996, A\\&AS 120, 619 \n \n\\bibitem[Kippen et al. (1993)]{kippen93}\nKippen, R.M., Connors, A., Collmar, W. et al., 1993, Proc. of 23$^{rd}$ ICRC, The University of Calgary, 1, 85 \n\n\\bibitem[Kippen et al. (1994a)]{kippen94a}\nKippen, R.M., Macri, J. Ryan, J. et al., 1994a, IAU Circ. 5937 \n\n\\bibitem[Kippen et al. (1994b)]{kippen94b}\nKippen, R.M., Macri, J., Ryan, J. et al., 1994b, IAU Circ. 5943\n\n\\bibitem[Kippen et al. (1994c)]{kippen94c}\nKippen, R.M., Connors, A., Macri, J. et al., 1994c, in: AIP Conf. Proc. No 307, Gamma-Ray Bursts, ed. G.J. Fishman, J.J. Brainerd, K. Hurley (New York: AIP Press), p. 420\n\n\\bibitem[Kippen et al. (1995a)]{kippen95a}\nKippen, R.M., Connors, A., McConnell, M. et al., 1995a, Adv. Space Res. 15(5), 139 \n\n\\bibitem[Kippen et al. (1995b)]{kippen95b}\nKippen, R.M., Bennett, K., Connors, A. et al., 1995b, A\\&A 293, L5 \n \n\\bibitem[Kippen et al. (1995c)]{kippen95c}\nKippen, R.M., Ryan, J., Connors, A. et al., 1995c, Ann. N.Y. Acad. Sci. 759, 425\n\n\\bibitem[Kippen (1995d)]{kippen95d}\nKippen, R.M., 1995d, Ph-D Thesis, University of New Hampshire, Durham N.H., USA\n\n\\bibitem[Kippen et al. (1996)]{kippen96}\nKippen, M., Ryan, J., Connors, A. et al., 1996, in AIP Conf. Proc. 384, Gamma-Ray Bursts, ed. C. Kouveliotou, M.S. Briggs, G.J. Fishman (New York AIP), 436\n\n\\bibitem[Kippen et al. (1998a)]{kippen98a}\nKippen, M., Ryan, J., Connors, A. et al., 1998a, Adv. Sp. Research, 22(7), 1097\n\n\\bibitem[Kippen et al. (1998b)]{kippen98b}\nKippen, M., Ryan, J., Connors., A. et al., 1998b, ApJ 492, 246\n\n\\bibitem[Kn\\\"odlseder et al. (1996)]{knoed96}\nKn\\\"odlseder, J., Chen, W., Oberlack, U., Diehl, R., Gehrels, N., 1996, A\\&AS 120, 339\n\n\\bibitem[Kn\\\"odlseder et al. (1999)]{knoed99}\nKn\\\"odlseder, J., Bennett, K., Bloemen, H. et al., 1999, A\\&A, 345, 813\n\n\\bibitem[Kuiper et al. (1996)]{kuiper96}\nKuiper, L., Hermsen, W., Bennett, K. et al., 1996, A\\&AS 120, 73 \n \n\\bibitem[Kuiper et al. (1998a)]{kuiper98a}\nKuiper, L., Hermsen, W., Bennett, K. et al., 1998a, A\\&A 337, 421\n\n\\bibitem[Kuiper et al. (1998b)]{kuiper98b}\nKuiper, L., Hermsen, W., Sch\\\"onfelder, V. et al., 1998b, NATO ASI Series C, Vol. 515, 211\n\n\\bibitem[Kuiper et al. (1999a)]{kuiper99a}\nKuiper, L., Hermsen, W., Krijger, J. et al., 1999a, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Kuiper et al. (1999b)]{kuiper99b}\nKuiper, L., Hermsen, W., Krijger, J. et al., 1999b, A\\&A, submitted \n\n\\bibitem[Lichti et al. (1996)]{lichti96}\nLichti, G.G., Iyudin, A., Bennett, K. et al., 1996, A\\&AS 120, 353 \n\n\\bibitem[Maisack et al. (1995)]{maisack95}\nMaisack, M., Collmar, W., Barr, P. et al., 1995, A\\&A, 298,400\n\n\\bibitem[McConnell et al. (1994)]{mcconnell94}\nMcConnell, M., Forrest, D., Ryan, J. et al., 1994, ApJ 424, 933 \n \n\\bibitem[McConnell et al. (1996)]{mcconnell96}\nMcConnell, M., Bennett, K., Bloemen, H. et al., 1996, A\\&AS 120, 149\n\n\\bibitem[McConnell et al. (1997a)]{mcconnell97a}\nMcConnell, M., Bennett, K., Bloemen, H. et al., 1997a, Proc. of 25$^{th}$ ICRC, Durban, South Africa, eds.: M.S. Potgieter, B.C. Raubenheimer, D.J. v. der Walt, Vol. 3, 93\n\n\\bibitem[McConnell et al. (1997b)]{mcconnell97b}\nMcConnell, M., Bennett, K. Bloemen, H. et al., Proc. of 4$^{th}$ Compton Symposium, 1997b, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 1099 \n\n\\bibitem[McNaron-Brown et al. (1995)]{mcnaron95}\nMcNaron-Brown, K., Johnson, W.N., Jung, G.V. et al., 1995, ApJ, 451, 575\n\n\\bibitem[Morris et al. (1995)]{morris95}\nMorris, D., Bennett, K., Bloemen, H. et al., 1995, Ann. N.Y. Acad. Sci., 759, 397 \n \n\\bibitem[Much et al. (1995a)]{much95a}\nMuch, R., Bennett, K., Buccheri, R. et al., 1995a, A\\&A, 299, 435 \n \n\\bibitem[Much et al. (1995b)]{much95b}\nMuch, R., Bennett, K., Buccheri, R. et al. 1995b, Adv. Sp. Res.15(5), 81\n\n\\bibitem[Much et al. (1997)]{much97}\nMuch, R. et al., Bennett, K., Winkler, C., 1997, Proc. of 4$^{th}$ Compton Symposium, 1997, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 542\n\n\\bibitem[Oberlack et al. (1995)]{oberlack95}\nOberlack, U., Bennett, K., Bloemen, H. et al. 1995, Proc. of 24$^{th}$ ICRC, Istituto Nazionale Fisica Nucleare, Rome, Vol. 2, 207\n\n\\bibitem[Oberlack (1997)]{oberlack97}\nOberlack, U., 1997, Ph-D Thesis, The Technical University Munich, Germany\n\n\\bibitem[Ryan et al. (1993)]{ryan93}\nRyan, J., Kippen, M., Varendorff, M., 1993, IAU Circ. 5702\n\n\\bibitem[Ryan et al. (1994a)]{ryan94a}\nRyan, J.M., et al., McConnell, M., Kippen, R.M. et al., 1994a, IAU Circ. 5950\n\n\\bibitem[Ryan et al. (1994b)]{ryan94b}\nRyan, J.M., Bennett, K., Collmar, W. et al., 1994b, ApJ 422, L67\n\n\\bibitem[Schaefer et al. (1994)]{schaefer94}\nSchaefer,B.E., Teegarden, B.J., Cline, T.L. et al., 1994, in: AIP Conf. Proc. No 307, Gamma-Ray Bursts, ed. G.J. Fishman, J.J. Brainerd, K. Hurley (New York: AIP Press), p. 280\n\n\\bibitem[Sch\\\"onfelder (1991)]{schoenf91}\nSch\\\"onfelder, V., 1991, IAU Circ. 5369\n\n\\bibitem[Sch\\\"onfelder et al. (1993)]{schoenf93}\nSch\\\"onfelder, V., Aarts, H. Bennett, K., 1993, ApJS 86, 657\n\n\\bibitem[Sch\\\"onfelder et al. (1995)]{schoenf95}\nSch\\\"onfelder, V., Bennett, K., Bloemen, H. et al., 1995, Ann. of N.Y. Acad. Sci. 759, 226\n \n\\bibitem[Sch\\\"onfelder et al. (1996)]{schoenf96}\nSch\\\"onfelder, V., Bennett, K., Bloemen, H. et al., 1996, A\\&AS 120, 13\n\n\\bibitem[Share et al. (1994)]{share94}\nShare, G.H., Connors, A., Dingus, B.L. et al., 1994, in: AIP Conf. Proc. No 307, Gamma-Ray Bursts, ed. G.J. Fishman, J.J. Brainerd, K. Hurley (New York: AIP Press), p. 283\n\n\\bibitem[Stacy et al. (1997)]{stacy97}\nStacy, J. G., Ryan, J.M., Collmar, W. et al., 1997, Proc. of 4$^{th}$ Compton Symposium, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 1356\n\n\\bibitem[Steinle et al. (1995)]{steinle95}\nSteinle, H., Collmar, W., Diehl, R. et al., 1995, Adv. Space Res. 15, 37\n\n\\bibitem[Steinle et al. (1998)]{steinle98}\nSteinle, H., Bennett, K., Bloemen, H. et al., 1998, A\\&A 330, 97\n\n\\bibitem[Strong et al. (1992)]{strong92}\nStrong, A.W., Cabeza-Orcel, P., Bennett, K. et al., 1992, in: Data Analysis in Astron. IV, ed. V. di Ges\\`u, L. Scarsi, R. Buccheri, P. Crane, M.C. Maccarone, H.U. Zimmermann, Plenum Press, New York, 251-260\n\n\\bibitem[Strong et al. (1996)]{strong96} \nStrong, A.W., Bennett, K., Bloemen, H., 1996, A\\&AS 120, 381-388 \n% \n%\\bibitem[Strong et al. (1997)]{strong97}\n%Strong, A. et al., 1997, Proc. of 2$^{2nd}$ INTEGRAL Workshop, eds.: C. Winkler, T.J.-L. Courvoisier, Ph. Durouchoux, ESA-SP-382, p. %533-536 \n%\n\n\\bibitem[Strong et al. (1999)]{strong99}\nStrong, A. W., Bloemen, H., Diehl, R. et al., 1999, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Swanenburg et al. (1978)]{swanenburg78}\nSwanenburg, B.N., Bennett, K., Bignami, G.F. et al., 1978, Nature 275, 298 \n\n\\bibitem[Thompson et al. (1995)]{thompson95}\nThompson, D. J., Bertsch, D.L., Dingus, B.L. et al., 1995, ApJS, 101, 259 (2EG)\n\n\\bibitem[Thompson et al. (1996)]{thompson96}\nThompson, D. J., Bertsch, D.L., Dingus, B.L. et al., 1996, ApJS, 107, 227 (2EGS)\n\n\\bibitem[Thompson et al. (1999)]{thompson99}\nThompson, D. J., Bailes, M., Bertsch, D.L. et al., 1999, ApJ, 516, in press\n\n\\bibitem[van der Meulen et al. (1998)]{meulen98}\nvan der Meulen, R.D., Bloemen, H., Bennett, K. et al, 1998, A\\&A 330, 321\n\n\\bibitem[van der Meulen et al. (1999)]{meulen99}\nvan der Meulen, R.D., Bloemen, H., Bykov, A.M. et al, 1999, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[van Dijk et al. (1995)]{vandijk95}\nvan Dijk, R., Bennett, K., Collmar, W. et al., 1995, A\\&A 296, L33 \n\n\\bibitem[van Dijk (1996)]{vandijk96}\nvan Dijk, R., 1996, Ph-D Thesis, The University of Amsterdam, The Netherlands\n\n\\bibitem[Varendorff et al. (1992]{varendorff92}\nVarendorff, M.G., Bennett, K., de Boer, H. et al., 1992, in: AIP Conf. Proc. No 265, Gamma-Ray Bursts, ed. W.S. Paciesas, G.J. Fishman (New York: AIP Press), p. 22\n\n\\bibitem[Varendorff et al. (1993)]{varendorff93}\nVarendorff, M.G., Connors, A., Collmar, W. et al., 1993, Proc. of 23$^{rd}$ ICRC, The University of Calgary, 1, 81\n\n\\bibitem[von Montigny et al. (1995)]{montigny95}\nvon Montigny, C., Bertsch, D.L., Chiang, J. et al., 1995, ApJ, 440, 525\n\n\\bibitem[Weidenspointner et al. (1999)]{weidens99}\nWeidenspointner, G., Varendorff, M., Bennett, K. et al., 1999, Proc. of 3rd INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Williams et al. (1995a)]{williams95a}\nWilliams, O.R., Much, R., Bennett, K. et al., 1995, A\\&A, 297, L21 \n \n\\bibitem[Williams et al. (1995b)]{williams95b}\nWilliams, O.R., Bennett, K., Bloemen, H. et al., 1995b, A\\&A 298, 33 \n\n\\bibitem[Williams et al. (1997)]{williams97}\nWilliams, O. R., Bennett, K., Much, R. et al., 1997, Proc. of 4$^{th}$ Compton Symposium, 1997, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 1582 \n\n\\bibitem[Williams et al. (1999)]{williams99}\nWilliams, O.R., Bennett, K., Much, R. et al., 1999, Proc. of 5th Compton Symposium (Portsmouth N.H., USA), AIP N.Y.: submitted for publication\n\n\\bibitem[Winkler et al. (1992)]{winkler92}\nWinkler, C., Bennett, K., Bloemen, H. et al., 1992, in: AIP Conf. Proc. No 265, Gamma-Ray Bursts, ed. W.S. Paciesas, G.J.Fishman (New York: AIP Press), p. 77 \n\n\\bibitem[Winkler et al. (1993a)]{winkler93a}\nWinkler, C., Bennett, K., Bloemen, H. et al., 1993a, A\\&A 255, L9\n\n\\bibitem[Winkler et al. (1993b]{winkler93b}\nWinkler, C., Bennett, K., Hanlon, L. et al., 1993b, in: AIP Conf. Proc. No 280, Gamma-Ray Observatory, ed. M. Friedlander, N. Gehrels, D.J. Macomb (New York: AIP Press), p. 845\n\n\\bibitem[Winkler et al. (1995)]{winkler95}\nWinkler, C., Kippen, R.M., Bennett, K. et al., 1995, A\\&A 302, 765\n\n\n\n \n\\end{thebibliography}\n\n\n\n\n\n\\clearpage\n\n\n% F I G U R E S \n\n\n% Fig. 1\n\\begin{figure*} [p]\n\\begin{center} \n\\psfig{figure=fig1a.ps,height=15cm,bbllx=0.0cm,bblly=0.0cm,bburx=20.1cm,bbury=28cm,angle=-90,clip=}\n\\vskip .2cm\n\\psfig{figure=fig1b.ps,height=15cm,bbllx=0.0cm,bblly=0.0cm,bburx=20.1cm,bbury=28cm,angle=-90,clip=}\n\\caption{Effective exposure of COMPTEL from the sum of all observations. Top: Sum of all observations up to Phase IV/Cycle-5. Bottom: Sum of all observations up to Phase IV/Cycle-7.\n}\n\\end{center}\n\\end{figure*} \n\n\n\\clearpage\n \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% Fig. 2\n%\n%\\begin{figure*} [p]\n%\\begin{center}\n%\\large {1--3 MeV} %\\psfig{figure=fig2a_strong.ps,width=140mm,bbllx=0,bblly=0,bburx=700,bbury=390,clip=}\n%\\vskip .1cm\n%\\large {3--10 MeV}\n%\\psfig{figure=fig2b_strong.ps,width=140mm,bbllx=0,bblly=0,bburx=700,bbury=390,clip=}\n%\\vskip .1cm\n%\\large {10--30 MeV}\n%\\psfig{figure=fig2c_strong.ps,width=140mm,bbllx=0,bblly=0,bburx=700,bbury=390,clip=}\n%\\caption[]{Full-sky maximum entropy intensity maps from all data between Phase I to IV/Cycle-6. Energy ranges are (from top to bottom): 1-3 MeV, 3-10 MeV, 10-30 MeV (from \\cite{strong99}).\n%}\n%\\end{center}\n%\\end{figure*} \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n% Fig. 2\n\n\\begin{figure*} [p]\n\\begin{center}\n\\large\n\n1--3 MeV\n\n\\psfig{figure=fig2a_strong.ps,width=140mm,bbllx=60,bblly=145,bburx=563,bbury=390,clip=}\n\n\\vskip .1cm\n3--10 MeV\n\n\\psfig{figure=fig2b_strong.ps,width=140mm,bbllx=60,bblly=145,bburx=563,bbury=390,clip=}\n\n\\vskip .1cm\n10--30 MeV\n\n\\psfig{figure=fig2c_strong.ps,width=140mm,bbllx=60,bblly=145,bburx=563,bbury=390,clip=}\n\n\\caption[]{Full-sky maximum entropy intensity maps from all data between Phase I to IV/Cycle-6. Energy ranges are (from top to bottom): 1-3 MeV, 3-10 MeV, 10-30 MeV (from \\cite{strong99}).\n}\n\\end{center}\n\\end{figure*} \n\n\n\\clearpage\n\n\n\n% Fig. 3 (Oberlack)\n\n\\begin{figure*} [p]\n\\psfig{figure=fig3_oberlack_26al.eps,width=\\textwidth}\n\\caption{COMPTEL maximum entropy map from VP 1 to VP 522.5 at 1.809 MeV (from \\cite{oberlack97}).\n}\n\\end{figure*} \n\n\n\n\\clearpage\n\n\n\n% Fig. 4 \n\n\n\\begin{figure*}[p]\n\\begin{center}\n\\psfig{figure=fig4_kippen_newgrbmap.eps,height=61mm,width=85mm}\n% bbllx=99,bblly=183,bburx=463,bbury=381,clip=}\n\\end{center}\n\\caption{Statistical (1-, 2-, and 3-sigma) location contours, in Galactic coordinates of 29 gamma-ray bursts observed through viewing period 419.5. The extent of the contours depends on the strength of the burst (from \\cite{kippen98a}).}\n\\end{figure*} \n\n\n%\\cleardoublepage\n\\clearpage\n\n\n% T A B L E S\n\n\n% TABLE 1\n\\vspace{-5cm}\n\\begin{table*}\n\\begin{center}\n\\bf{ Table 1}: {COMPTEL 3$\\sigma$ Point Source Sensitivity Limits}\n\\smallskip\n\\begin{tabular}{|c|c|c|c|}\\hline\n & \\multicolumn{3}{c|}{3$\\sigma$ Flux Limits [10$^{-5}$ photons cm$^{-2}$ sec$^{-1}$]} \\\\\n E$_{\\gamma}[MeV]$ & 2 weeks in Phase 1 & Phase 1+2+3 & Phase 1+2+3+4 (Cycle-5) \\\\\n\\hline\n0.75 -- 1 & 20.1 & 7.4 & 3.7 \\\\\n 1 -- 3 & 16.8 & 5.5 & 3.8 \\\\\n 3 -- 10 & 7.3 & 2.8 & 1.7 \\\\\n10 -- 30 & 2.8 & 1.0 & 0.8 \\\\\n1.157 & 6.2 & 2.0 & 1.6 \\\\\n1.809 & 6.6 & 2.2 & 1.6 \\\\\n\\hline\n\\end{tabular}\n\\caption[] {From this table rough upper limits can be derived for those objects, which are not contained in the later tables 10 to 12 by deriving the effective exposure from Fig. 1.\n}\n\\end{center}\n\\end{table*}\n\n\n\\clearpage\n\n\n% TABLES 2\n\n\\begin{table*}\n{\\bf Table 2}: {COMPTEL Observations, Pointings and Viewing Periods}\n\n{\\bf Phase I}\n\\begin{flushleft}\n\\begin{tabular}{||r|c|l|r|r|r|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline \n& & & \\multicolumn{2}{c|}{} & & \\\\ & & & \\multicolumn{2}{c|}{} & & eff. COMPTEL \\\\\n Viewing & start & Z-axis & \\multicolumn{2}{c|}{galactic} & duration & observing time \\\\\n Period & (yy-mm-dd) & pointing & LONG & LAT & (days) & (days) \\\\ \n& & & & & & \\\\ \n\\hline\n\\hline \n1.0 & 91-05-16 & Crab pulsar~~~& 190.9 & -4.7 & 14 & 5.3 \\\\\n2.0 & 91-05-30 & Cyg X-1 & 73.3 & 2.6 & 9 & 3.8 \\\\\n2.5 & 91-06-08 & Sun & 194.9 & -7.3 & 7 & 3.5 \\\\\n3.0 & 91-06-15 & SN 1991T & 299.8 & 65.5 & 13 & 5.5 \\\\\n4.0 & 91-06-28 & NGC 4151 & 156.2 & 72.1 & 14 & 4.8 \\\\\n5.0 & 91-07-12 & Gal. Center & 0.0 & -4.0 & 14 & 5.0 \\\\\n6.0 & 91-07-26 & SN 1987A & 278.0 & -29.3 & 13 & 3.9 \\\\ \n7.0 & 91-08-08 & Cyg X-3 & 70.4 & -8.3 & 7 & 3.5 \\\\ \n7.5 & 91-08-15 & gal. 025-14 & 25.0 & -14.0 & 7 & 2.3 \\\\ \n8.0 & 91-08-22 & Vela Pulsar & 262.9 & -5.7 & 14 & 4.6 \\\\ \n9.0 & 91-09-05 & gal. 339-84 & 338.9 & -83.5 & 7 & 2.5 \\\\ \n9.5 & 91-09-12 & Her X-1 & 59.7 & 40.3 & 7 & 2.9 \\\\ \n10.0 & 91-09-19 & Fairall 9 & 287.9 & -54.3 & 14 & 4.4 \\\\ \n11.0 & 91-10-03 & 3C 273 & 294.3 & 63.7 & 14 & 5.3 \\\\ \n12.0 & 91-10-17 & Centaurus A & 310.7 & 22.2 & 14 & 4.5 \\\\ \n13.0 & 91-10-31 & gal. 025-14 & 25.0 & -14.0 & 7 & 2.8 \\\\ \n13.5 & 91-11-07 & gal. 339-84 & 338.9 & -83.5 & 7 & 2.5 \\\\ \n14.0 & 91-11-14 & Eta Carinae & 285.0 & -0.7 & 14 & 3.2 \\\\ \n15.0 & 91-11-28 & NGC 1275 & 152.6 & -13.4 & 14 & 5.9 \\\\ \n16.0 & 91-11-12 & Sco X-1 & 0.0 & 20.3 & 15 & 5.6 \\\\ \n17.0 & 91-12-27 & SN 1987A & 283.2 & -31.6 & 14 & 4.1 \\\\ \n18.0 & 92-01-10 & M 82 & 137.5 & 40.5 & 13 & 5.1 \\\\ \n19.0 & 92-01-23 & gal. 058-43 & 58.2 & -43.0 & 14 & 5.5 \\\\ \n20.0 & 92-02-06 & SS 433 & 39.7 & 0.8 & 14 & 5.8 \\\\ \n21.0 & 92-02-20 & NGC 1068 & 171.5 & -53.9 & 14 & 4.5 \\\\ \n22.0 & 92-03-05 & MRK 279 & 112.5 & 44.5 & 14 & 4.5 \\\\ \n23.0 & 92-03-19 & Cir X-1 & 322.1 & 3.0 & 14 & 2.2 \\\\ \n24.0 & 92-04-02 & gal. 010 57 & 9.5 & 57.2 & 7 & 1.7 \\\\ \n24.5 & 92-04-09 & gal. 010 57 & 9.5 & 57.2 & 7 & 1.8 \\\\ \n25.0 & 92-04-16 & gal. 007 48 & 6.8 & 48.1 & 7 & 1.8 \\\\ \n26.0 & 92-04-23 & MRK 335 & 108.8 & -41.4 & 5 & 1.0 \\\\ \n27.0 & 92-04-28 & 4U 1543-47 & 332.2 & 2.5 & 9 & 1.7 \\\\ \n28.0 & 92-05-07 & MRK 335 & 108.8 & -41.4 & 7 & 1.8 \\\\ \n29.0 & 92-05-14 & gal. 224-40 & 224.0 & -40.0 & 21 & 4.4 \\\\ \n30.0 & 92-06-04 & NGC 2992 & 252.4 & 30.7 & 7 & 1.7 \\\\ \n31.0 & 92-06-11 & MCG 8-11-11~~~~~~~~~ & 163.1 & 11.9 & 14 & 5.2 \\\\ \n32.0 & 92-06-25 & NGC 3783 & 284.2 & 22.9 & 7 & 1.4 \\\\ \n33.0 & 92-07-02 & NGC 2992 & 252.4 & 30.7 & 14 & 2.8 \\\\ \n34.0 & 92-07-16 & Cas A & 108.8 & -2.4 & 21 & 3.6 \\\\ \n35.0 & 92-08-06 & ESO 141-55 & 335.1 & -25.6 & 5 & 0.9 \\\\ \n36.0 & 92-08-11 & GRO J0422 32 & 169.8 & -11.4 & 1 & 0.3 \\\\ \n36.5 & 92-08-12 & GRO J0422 32 & 168.2 & -9.5 & 8 & 2.0 \\\\ \n37.0 & 92-08-20 & MRK 335 & 104.8 & -42.1 & 7 & 1.8 \\\\ \n38.0 & 92-08-27 & ESO 141-55 & 335.1 & -25.6 & 5 & 1.0 \\\\ \n39.0 & 92-09-01 & GRO J0422 32 & 167.2 & -9.2 & 16 & 4.0 \\\\ \n40.0 & 92-09-17 & MCG 5-23-16 & 195.9 & 44.7 & 21 & 5.6 \\\\ \n41.0 & 92-10-08 & gal. 228 03 & 228.0 & 2.8 & 7 & 1.5 \\\\ \n42.0 & 92-10-15 & PKS 2155-304 & 0.0 & -44.6 & 14 & 2.4 \\\\ \n43.0 & 92-10-29 & MRK 509 & 31.1 & -28.3 & 5 & 1.2 \\\\ \n44.0 & 92-11-03 & gal. 228 03 & 228.0 & 2.8 & 14 & 3.2 \\\\ \n & 92-11-17 & end of Phase I & & & & \\\\\n\\hline\\multicolumn{7}{r}{(Table 2 cont.)}\\\\\n%\\hline \n\\end{tabular}\n\\end{flushleft}\n\\end{table*}\n\n\n\\clearpage\n\n\n\\footnotesize\n\n\\begin{table*}\n{\\bf Table 2}: {COMPTEL Observations, Pointings and Viewing Periods}\n\n{\\bf Phase II}\n\\begin{flushleft}\n\\begin{tabular}{||r|c|l|r|r|r|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline \n& & & \\multicolumn{2}{c|}{} & & \\\\ & & & \\multicolumn{2}{c|}{} & & eff. COMPTEL \\\\\n Viewing & start & Z-axis & \\multicolumn{2}{c|}{galactic} & duration & observing time \\\\\n Period & (yy-mm-dd) & pointing & LONG & LAT & (days) & (days) \\\\ \n& & & & & & \\\\ \n\\hline\n\\hline\n201.0 & 92-11-17 & Her X-1 & 66.8 & 39.3 & 7 & 1.1 \\\\ \n202.0 & 92-11-24 & Her X-1 & 70.9 & 40.5 & 7 & 1.2 \\\\ \n203.0 & 92-12-01 & Cygnus & 77.9 & 0.7 & 7 & 2.0 \\\\ \n203.3 & 92-12-08 & Cygnus & 77.9 & 0.7 & 7 & 2.0 \\\\ \n203.6 & 92-12-15 & Cygnus & 77.9 & 0.7 & 7 & 2.0 \\\\ \n204.0 & 92-12-22 & 3C 273 & 294.7 & 61.9 & 7 & 2.0 \\\\ \n205.0 & 92-12-29 & 3C 273 & 294.5 & 61.6 & 7 & 2.0 \\\\ \n206.0 & 93-01-05 & 3C 273 & 294.7 & 61.9 & 7 & 1.9 \\\\ \n207.0 & 93-01-12 & IC 4329A & 314.1 & 31.5 & 21 & 4.8 \\\\ \n208.0 & 93-02-02 & NGC 4507 & 307.4 & 20.8 & 7 & 1.5 \\\\ \n209.0 & 93-02-09 & 2CG 010-31 & 0.2 & -34.0 & 13 & 3.9 \\\\ \n210.0 & 93-02-22 & Gal. Center & 355.6 & 6.3 & 3 & 0.6 \\\\ \n211.0 & 93-02-25 & gal. 123-05 & 125.9 & -4.7 & 12 & 3.2 \\\\ \n212.0 & 93-03-09 & WR 140 & 83.7 & 11.7 & 14 & 3.9 \\\\ \n213.0 & 93-03-23 & Crab Pulsar & 182.6 & -8.2 & 6 & 1.1 \\\\ \n214.0 & 93-03-29 & Gal. Center & 355.6 & 6.3 & 3 & 0.7 \\\\ \n215.0 & 93-04-01 & Centaurus A & 311.7 & 22.9 & 5 & 1.1 \\\\ \n216.0 & 93-04-06 & SN 1993J & 140.8 & 38.1 & 6 & 1.3 \\\\ \n217.0 & 93-04-12 & Centaurus A & 311.7 & 22.9 & 8 & 1.8 \\\\ \n218.0 & 93-04-20 & NGC 4151 & 151.4 & 71.3 & 14 & 2.7 \\\\ \n219.1 & 93-05-04 & reboost testing & & & & \\\\ \n219.4 & 93-05-05 & Gal. Center & 350.1 & 15.9 & 2 & 0.5 \\\\ \n219.7 & 93-05-07 & reboost calibration burn & & & & \\\\ \n220.0 & 93-05-08 & SMC & 298.1 & -44.6 & 5 & 0.9 \\\\ \n221.0 & 93-05-13 & Crab Pulsar & 187.5 & -5.9 & 11 & 2.3 \\\\ \n222.0 & 93-05-24 & NGC 4151 & 157.8 & 70.6 & 7 & 2.0 \\\\ \n223.0 & 93-05-31 & Gal. Center & 359.1 & -0.1 & 3 & 0.7 \\\\ \n224.0 & 93-06-03 & SMC & 298.1 & -44.6 & 12 & 1.8 \\\\ \n225.0 & 93-06-15 & reboost & & & & \\\\ \n226.0 & 93-06-19 & gal. 355 05 & 355.0 & 5.0 & 9 & 2.1 \\\\ \n227.0 & 93-06-28 & SN 1993J & 148.1 & 41.2 & 15 & 3.3 \\\\ \n228.0 & 93-07-13 & SN 1993J & 149.9 & 42.7 & 14 & 3.1 \\\\ \n230.0 & 93-07-27 & Vela region & 276.7 & -2.3 & 3 & 0.7 \\\\ \n230.5 & 93-07-30 & Vela region & 278.8 & 1.4 & 4 & 0.9 \\\\ \n231.0 & 93-08-03 & NGC 6814 & 22.2 & -13.1 & 7 & 1.5 \\\\ \n229.0 & 93-08-10 & gal. 5 05 & 5.0 & 5.0 & 1 & 0.2 \\\\ \n229.3 & 93-08-11 & Perseid meteor shower & & & & \\\\ \n229.5 & 93-08-12 & gal. 5 05 & 5.0 & 5.0 & 5 & 1.1 \\\\ \n301.0 & 93-08-17 & Vela Pulsar & 263.6 & -2.7 & 7 & 1.2 \\\\ \n232.0 & 93-08-24 & gal. 348 00 & 347.5 & 0.0 & 2 & 0.4 \\\\ \n232.5 & 93-08-26 & gal. 348 00 & 347.5 & 0.0 & 12 & 2.6 \\\\ \n & 93-09-07 & end of Phase II & & & & \\\\ \n301.0 & 93-08-17 & Vela Pulsar & 263.6 & -2.7 & 7 & 1.2 \\\\\n232.0 & 93-08-24 & gal. 348+00 & 347.5 & 0.0 & 2 & 0.4 \\\\ 232.5 & 93-08-26 & gal. 348+00 & 347.5 & 0.0 & 12 & 2.6 \\\\ 302.0 & 93-09-07 & N Cyg 1992 & 89.1 & 7.8 & 2 & 0.5 \\\\\n302.3 & 93-09-09 & GX 1+4 & 1.4 & 9.3 & 12 & 2.6 \\\\\n303.0 & 93-09-21 & GRS 1009-45 & 277.2 & 12.8 & 1 & 0.2 \\\\\n303.2 & 93-09-22 & N Cyg 1992 & 89.1 & 7.8 & 9 & 2.3 \\\\\n303.4 & 93-10-01 & pre-reboost & 64.3 & 25.3 & 3 & -.- \\\\\n303.5 & 93-10-04 & reboost & & & & \\\\\n\\hline\\multicolumn{7}{r}{(Table 2 cont.)}\\\\\n%\\hline \n\\end{tabular}\n\\end{flushleft}\n\\end{table*}\n\n\n\\clearpage\n\n\n\\footnotesize\n\n\\begin{table*}\n{\\bf Table 2}: {COMPTEL Observations, Pointings and Viewing Periods}\n\n{\\bf Phase III}\n\\begin{flushleft}\n\\begin{tabular}{||r|c|l|r|r|r|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline \n& & & \\multicolumn{2}{c|}{} & & \\\\ & & & \\multicolumn{2}{c|}{} & & eff. COMPTEL \\\\\n Viewing & start & Z-axis & \\multicolumn{2}{c|}{galactic} & duration & observing time \\\\\n Period & (yy-mm-dd) & pointing & LONG & LAT & (days) & (days) \\\\ \n& & & & & & \\\\ \n\\hline\n\\hline\n& & & & & & \\\\\n 303.7 & 93-10-17 & N Cyg 1992~~~~~~~~~& 89.1 & 7.8 & 2 & 0.5 \\\\\n 304.0 & 93-10-19 & Virgo 278+67 & 278.2 & 66.7 & 6 & 1.7 \\\\\n 305.0 & 93-10-25 & Virgo 278+63 & 277.7 & 62.7 & 8 & 2.2 \\\\\n 306.0 & 93-11-02 & Virgo 278+59 & 277.6 & 58.7 & 7 & 1.8 \\\\\n 307.0 & 93-11-09 & Virgo 269+69 & 268.7 & 69.2 & 7 & 1.8 \\\\\n 308.0 & 93-11-16 & Virgo 283+75 & 283.2 & 74.7 & 3 & 1.1 \\\\\n 308.3 & 93-11-19 & reboost & & & & \\\\\n 308.6 & 93-11-23 & Virgo 283+75 & 283.2 & 74.7 & 8 & 3.0 \\\\\n 310.0 & 93-12-01 & Geminga & 195.1 & 4.3 & 12 & 2.4 \\\\\n 311.0 & 93-12-13 & Virgo 284+75 & 283.7 & 74.5 & 2 & 0.6 \\\\\n 311.3 & 93-12-15 & reboost & & & & \\\\\n 311.6 & 93-12-17 & Virgo 284+75 & 283.7 & 74.5 & 3 & 0.9 \\\\\n 312.0 & 93-12-20 & Virgo 281+71 & 280.5 & 70.7 & 7 & 2.0 \\\\\n 313.0 & 93-12-27 & Virgo 289+79 & 289.3 & 78.7 & 7 & 2.1 \\\\\n 314.0 & 94-01-03 & gal. 304-01 & 304.2 & -1.0 & 13 & 3.6 \\\\\n 315.0 & 94-01-16 & gal. 304-01 & 304.2 & -1.0 & 7 & 1.8 \\\\\n 316.0 & 94-01-23 & Centaurus A & 309.5 & 19.4 & 9 & 2.4 \\\\\n 318.1 & 94-02-01 & Cyg X-1 & 68.4 & -0.4 & 7 & 2.0 \\\\\n 321.1 & 94-02-08 & 1A 0535+262 & 181.4 & -2.6 & 7 & 2.7 \\\\\n 321.5 & 94-02-15 & 1A 0535+262 & 181.4 & -2.6 & 2 & 0.8 \\\\\n 317.0 & 94-02-17 & NGC 1068 & 158.5 & -45.4 & 12 & 4.6 \\\\\n 319.0 & 94-03-01 & QSO 0716+714 & 144.0 & 28.0 & 7 & 1.7 \\\\\n 320.0 & 94-03-08 & gal. 083-45 & 83.1 & -45.5 & 7 & 2.5 \\\\\n 319.5 & 94-03-15 & QSO 0716+714 & 146.4 & 26.0 & 7 & 1.9 \\\\\n 323.0 & 94-03-22 & gal. 357-11 & 356.8 & -11.3 & 14 & 4.3 \\\\\n 322.0 & 94-04-05 & MRK 421 & 197.0 & 58.6 & 14 & 2.5 \\\\\n 324.0 & 94-04-19 & gal. 015+05 & 15.0 & 5.6 & 7 & 2.5 \\\\\n 325.0 & 94-04-26 & gal. 147-09 & 147.0 & -9.0 & 14 & 3.6 \\\\\n 326.0 & 94-05-10 & NGC 3227 & 195.9 & 58.3 & 7 & 2.7 \\\\\n 327.0 & 94-05-17 & gal. 083-50 & 82.9 & -49.6 & 7 & 2.0 \\\\\n 328.0 & 94-05-24 & PSR 1951+32 & 64.9 & -0.0 & 7 & 1.8 \\\\\n 329.0 & 94-05-31 & gal. 253-42 & 253.4 & -42.0 & 7 & 1.7 \\\\\n 331.0 & 94-06-07 & PSR 1951+32 & 64.9 & -0.0 & 3 & 1.1 \\\\\n 330.0 & 94-06-10 & gal. 018+00 & 18.0 & 0.0 & 4 & 1.4 \\\\\n 331.5 & 94-06-14 & PSR 1951+32 & 64.9 & -0.0 & 4 & 1.6 \\\\\n 332.0 & 94-06-18 & gal. 018+00 & 18.0 & 0.0 & 17 & 6.1 \\\\\n 333.0 & 94-07-05 & PSR 1951+32 & 64.9 & -0.0 & 7 & 2.2 \\\\\n 335.0 & 94-07-12 & gal. 253-42 & 253.4 & -42.0 & 6 & 1.5 \\\\\n 334.0 & 94-07-18 & gal. 009-08 & 9.0 & -8.4 & 7 & 2.1 \\\\\n 335.5 & 94-07-25 & gal. 253-42 & 253.4 & -42.0 & 7 & 1.8 \\\\\n 336.0 & 94-08-01 & gal. 088-47 & 88.4 & -46.8 & 3 & 1.2 \\\\\n 336.5 & 94-08-04 & GRO J1655-40 & 340.4 & 2.9 & 5 & 1.5 \\\\\n 337.0 & 94-08-09 & PKS 0528+134 & 205.0 & 13.0 & 20 & 6.2 \\\\\n 338.0 & 94-08-29 & GRO J1655-40 & 345.0 & 2.5 & 2 & 0.6 \\\\\n 338.5 & 94-08-31 & Vela Pulsar & 263.6 & -2.7 & 20 & 5.6 \\\\\n 339.0 & 94-09-20 & 3C 317 & 4.1 & 40.4 & 14 & 4.8 \\\\\n & 93-10-04 & end of Phase III~~~~~~~~~ & & & & \\\\ \n 401.0 & 94-10-04 & Cas A & 113.9 & 6.2 & 14 & 3.8 \\\\\n 402.0 & 94-10-18 & GPlane 310 & 310.3 & -5.0 & 7 & 1.6 \\\\\n 402.5 & 94-10-25 & GPlane 310 & 306.7 & -3.8 & 7 & 1.6 \\\\\n & & & & & & \\\\\n\\hline\\multicolumn{7}{r}{(Table 2 cont.)}\\\\\n%\\hline \n\\end{tabular}\n\\end{flushleft}\n\\end{table*}\n\n\\clearpage\n\n\\footnotesize\n\n\\begin{table*}\n{\\bf Table 2}: {COMPTEL Observations, Pointings and Viewing Periods}\n\n{\\bf Phase IV/Cycle-4}\n\\begin{flushleft}\n\\begin{tabular}{||r|c|l|r|r|r|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline \n& & & \\multicolumn{2}{c|}{} & & \\\\ & & & \\multicolumn{2}{c|}{} & & eff. COMPTEL \\\\\n Viewing & start & Z-axis & \\multicolumn{2}{c|}{galactic} & duration & observing time \\\\\n Period & (yy-mm-dd) & pointing & LONG & LAT & (days) & (days) \\\\ \n& & & & & & \\\\ \n\\hline\n\\hline\n& & & & & & \\\\\n 403.0 & 94-11-01 & Her X-1 & 58.2 & 37.5 & 8 & 2.1 \\\\\n 403.5 & 94-11-09 & OJ 287 & 206.8 & 35.8 & 6 & 1.6 \\\\\n 404.0 & 94-11-15 & S Gal. Pole & 7.2 & -73.4 & 14 & 4.2 \\\\\n 405.0 & 94-11-29 & 3C 279 & 306.7 & 56.5 & 9 & 3.2 \\\\\n 405.5 & 94-12-07 & GRO J1655-40 & 306.7 & 56.5 & 6 & 2.1 \\\\\n 406.0 & 94-12-13 & Virgo & 336.3 & 67.2 & 7 & 2.4 \\\\\n 407.0 & 94-12-20 & Virgo & 334.3 & 63.0 & 14 & 4.1 \\\\\n 408.0 & 95-01-03 & 3C 279 & 305.1 & 57.1 & 7 & 2.0 \\\\\n 409.0 & 95-01-10 & LMC & 274.7 & -39.2 & 14 & 3.9 \\\\\n 410.0 & 95-01-24 & gal. 082-33 & 82.2 & -32.6 & 21 & 5.7 \\\\\n 411.1 & 95-02-14 & QSO 0716+714 & 145.1 & 23.9 & 7 & 2.1 \\\\\n 411.5 & 95-02-21 & QSO 0716+714 & 143.3 & 22.7 & 7 & 2.1 \\\\\n 412.0 & 95-02-28 & Anticenter & 185.3 & 0.7 & 7 & 2.1 \\\\\n 413.0 & 95-03-07 & Anticenter & 191.8 & -3.4 & 14 & 4.2 \\\\\n 414.0 & 95-03-21 & Vela & 281.4 & -13.5 & 8 & 1.5 \\\\\n 414.3 & 95-03-29 & GRO J1655-40 & 347.3 & 0.6 & 7 & 2.0 \\\\\n 419.1 & 95-04-04 & Orion & 207.4 & -19.1 & 7 & 2.5 \\\\\n 415.0 & 95-04-11 & LMC & 275.7 & -24.0 & 14 & 3.5 \\\\\n 418.0 & 95-04-25 & MRK 421 & 158.1 & 65.8 & 14 & 4.2 \\\\\n 419.5 & 95-05-09 & Orion & 211.9 & -17.6 & 14 & 4.5 \\\\\n 420.0 & 95-05-23 & Orion & 198.2 & -18.3 & 14 & 5.0 \\\\\n 421.0 & 95-06-06 & Gal. Center & 355.3 & 0.4 & 7 & 2.2 \\\\\n 422.0 & 95-06-13 & Gal. Center & 355.4 & -0.4 & 7 & 2.1 \\\\\n 423.0 & 95-06-20 & Gal. Center & 2.6 & -0.2 & 10 & 3.2 \\\\\n 423.5 & 95-06-30 & PKS 1622-297 & 345.7 & 13.5 & 10 & 2.8 \\\\\n 424.0 & 95-07-10 & Cen A & 312.7 & 19.0 & 15 & 4.2 \\\\\n 425.0 & 95-07-25 & gal. 137-47 & 137.4 & -47.3 & 14 & 5.0 \\\\\n 426.0 & 95-08-08 & Anticenter & 184.5 & -5.9 & 14 & 3.8 \\\\\n 427.0 & 95-08-22 & gal. 154-10 & 153.8 & -10.0 & 16 & 5.1 \\\\\n 428.0 & 95-09-07 & S Gal. Pole & 270.6 & -82.5 & 13 & 3.9 \\\\\n 429.0 & 95-09-20 & gal. 018+04 & 18.3 & 4.0 & 7 & 2.4 \\\\\n 429.5 & 95-09-27 & GRO J2058+42 & 86.3 & -12.5 & 6 & 2.1 \\\\\n & 95-10-03 & end of Phase IV / Cycle-4 & & & & \\\\\n 501.0 & 95-10-03 & gal. 028+04 & 28.0 & 3.6 & 14 & 4.8 \\\\\n 502.0 & 95-10-17 & PKS 0528+134 & 190.7 & -11.5 & 14 & 4.9 \\\\\n 505.0 & 95-10-31 & Cas A - 4 & 118.0 & -2.0 & 7 & 2.4 \\\\\n 506.0 & 95-11-07 & Cas A - 1 & 111.0 & 5.0 & 7 & 2.5 \\\\\n 503.0 & 95-11-14 & Cas A - 3 & 104.0 & -2.0 & 7 & 2.2 \\\\\n 504.0 & 95-11-21 & Cas A - 2 & 111.0 & -10.0 & 7 & 2.2 \\\\\n 507.0 & 95-11-28 & CTA 102 & 77.4 & -38.6 & 9 & 2.5 \\\\\n 507.5 & 95-12-07 & CTA 102 & 77.4 & -38.6 & 7 & 2.0 \\\\\n 508.0 & 95-12-14 & gal. 005+00 & 6.5 & -0.2 & 6 & 1.7 \\\\\n 509.0 & 95-12-20 & gal. 021+14 & 21.6 & 13.1 & 13 & 3.8 \\\\\n 510.0 & 96-01-02 & Monoceros & 231.0 & 3.7 & 3 & 0.8 \\\\\n 510.5 & 96-01-05 & Monoceros & 229.0 & 3.5 & 9 & 2.5 \\\\\n 511.0 & 96-01-16 & 3C 273 & 298.3 & 62.9 & 14 & 4.9 \\\\\n 511.5 & 96-01-30 & 3C 273 & 310.6 & 53.2 & 7 & 2.5 \\\\\n 513.0 & 96-02-06 & PKS 2155-304 & 17.6 & -52.1 & 7 & 2.0 \\\\\n 514.0 & 96-02-13 & gal. 060-60 & 62.3 & -60.6 & 7 & 2.4 \\\\\n 515.0 & 96-02-20 & QSO 1219+285 & 159.4 & 82.9 & 14 & 3.8 \\\\\n& & & & & & \\\\\n\\hline\\multicolumn{7}{r}{(Table 2 cont.)}\\\\\n%\\hline \n\\end{tabular}\n\\end{flushleft}\n\\end{table*}\n\n\n\\clearpage\n\n\n\\footnotesize\n\n\\begin{table*}\n{\\bf Table 2}: {COMPTEL Observations, Pointings and Viewing Periods}\n\n{\\bf Phase IV/Cycle-5}\n\\begin{flushleft}\n\\begin{tabular}{||r|c|l|r|r|r|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline \n& & & \\multicolumn{2}{c|}{} & & \\\\ & & & \\multicolumn{2}{c|}{} & & eff. COMPTEL \\\\\n Viewing & start & Z-axis & \\multicolumn{2}{c|}{galactic} & duration & observing time \\\\\n Period & (yy-mm-dd) & pointing & LONG & LAT & (days) & (days) \\\\ \n& & & & & & \\\\ \n\\hline\n\\hline\n& & & & & & \\\\\n 517.0 & 96-03-05 & PKS 0208-512 & 276.8 & -59.6 & 13 & 3.5 \\\\\n 516.1 & 96-03-18 & GRO J1655-40 & 341.1 & 5.6 & 3 & 0.8 \\\\\n 516.5 & 96-03-21 & MRK 501 & 61.0 & 41.2 & 13 & 4.7 \\\\\n 518.5 & 96-04-03 & 0716+714 & 144.0 & 28.0 & 20 & 5.4 \\\\\n 519.0 & 96-04-23 & 3C 345 & 63.0 & 40.0 & 14 & 5.0 \\\\\n 520.0 & 96-05-07 & Orion - 1 & 208.8 & -4.6 & 14 & 4.9 \\\\\n 520.4 & 96-05-21 & PKS 2155-304 & 17.7 & -52.3 & 7 & 2.0 \\\\\n 521.0 & 96-05-28 & GRO J0516-609 & 275.6 & -36.3 & 14 & 3.2 \\\\\n 522.0 & 96-06-11 & Cen X-3 & 285.7 & -1.5 & 3 & 0.8 \\\\\n 522.5 & 96-06-14 & Cyg X-1 & 65.8 & 2.7 & 11 & 3.1 \\\\\n 523.0 & 96-06-25 & Orion - 2 & 207.1 & -21.0 & 14 & 4.5 \\\\\n 524.0 & 96-07-09 & GX 339-4 & 343.1 & -3.6 & 14 & 3.8G\\\\\n 525.0 & 96-07-23 & gal. 340-49 & 338.8 & -54.5 & 7 & 1.4 \\\\\n 526.0 & 96-07-30 & Geminga & 187.7 & -3.6 & 14 & 3.8 \\\\\n 527.0 & 96-08-13 & Crab - 1 & 190.1 & -1.8 & 7 & 2.1 \\\\\n 528.0 & 96-08-20 & Crab - 2 & 185.9 & -0.2 & 7 & 2.4 \\\\\n 529.5 & 96-08-27 & GRO J1655-40 & 345.0 & 2.5 & 10 & 2.7 \\\\\n 530.0 & 96-09-06 & GRO J0004+73 & 124.7 & 6.4 & 27 & 8.4 \\\\\n 531.0 & 96-10-03 & PSR B1055-52 & 283.8 & -0.2 & 11 & 2.4 \\\\\n & 96-10-15 & end of Phase IV / Cycle-5 & & & & \\\\\n 601.1 & 96-10-15 & PSRJ2043+274 & 70.1 & -10.5 & 14 & 4.9 \\\\\n 520.9 & 96-10-29 & Orion-1 & 214.4 & 3.2 & 14 & 4.5 \\\\\n 602.0 & 96-11-12 & GAL 60+65 & 60.0 & 65.0 & 7 & 2.4 \\\\\n 603.0 & 96-11-19 & GAL 60+65 & 60.0 & 65.0 & 7 & 2.5 \\\\\n 605.1 & 96-11-26 & GAL 43+57 & 43.2 & 56.8 & 7 & 2.5 \\\\\n 604.1 & 96-12-03 & GAL 48+61 & 48.4 & 60.7 & 7 & 2.4 \\\\\n 606.0 & 96-12-10 & 3C 279 & 306.4 & 56.4 & 7 & 2.2 \\\\\n 607.0 & 96-12-17 & 3C 279 & 306.5 & 56.4 & 6 & 1.7 \\\\\n 608.0 & 96-12-23 & 3C 279 & 306.8 & 56.7 & 7 & 1.9 \\\\\n 609.0 & 96-12-30 & 3C 279 & 306.9 & 56.8 & 8 & 2.4 \\\\\n 610.0 & 97-01-07 & 3C 279 & 306.9 & 56.8 & 7 & 2.3 \\\\\n 610.5 & 97-01-14 & 3C 279 & 306.6 & 58.9 & 7 & 2.5 \\\\\n 611.1 & 97-01-21 & 3C 279 & 306.9 & 56.8 & 7 & 2.5 \\\\\n 612.1 & 97-01-28 & Cyg X-1 & 71.3 & 3.1 & 7 & 2.0 \\\\\n 624.1 & 97-02-04 & GAL 16+00 & 15.9 & 3.4 & 7 & 2.0 \\\\\n 614.5 & 97-02-11 & GAL 40-60 & 39.8 & -60.3 & 7 & 2.0 \\\\\n 616.1 & 97-02-18 & PKS 0528+134 & 191.4 & -11.0 & 28 & 8.1 \\\\\n 617.1 & 97-03-18 & Orion-3 & 220.0 & - 5.0 & 6 & 2.0 \\\\\n 617.2 & 97-03-24 & Reboost Test & ~~~ & ~~~ & 1 & ~~~ \\\\\n 617.3 & 97-03-25 & Orion-3 & 220.0 & - 5.0 & 1 & 0.3 \\\\\n 617.4 & 97-03-26 & Reboost Test & ~~~ & ~~~ & 1 & ~~~ \\\\\n 617.5 & 97-03-27 & Orion-3 & 220.0 & - 5.0 & 5 & 1.7 \\\\\n 617.6 & 97-04-01 & Reboost (1) & ~~~ & ~~~ & 6 & ~~~ \\\\\n 617.7 & 97-04-07 & Orion-3 & 220.0 & - 5.0 & 2 & 0.7 \\\\\n 617.8 & 97-04-09 & MRK 501 & 66.8 & 37.3 & 6 & 1.8 \\\\\n 618.0 & 97-04-15 & Carina-2 & 274.3 & - 3.0 & 21 & 5.5 \\\\\n 619.0 & 97-05-06 & Cir X-1 & 319.6 & - 1.6 & 8 & 2.1 \\\\\n 619.2 & 97-05-14 & GRS 1915 & 47.3 & - 0.9 & 6 & 1.8 \\\\\n 619.4 & 97-05-20 & Cir X-1 & 319.6 & - 1.6 & 28 & 7.3 \\\\\n 619.5 & 97-05-28 & Reboost (2) & ~~~ & ~~~ & 7 & ~~~ \\\\\n 619.7 & 97-06-04 & Cir X-1 & 319.6 & - 1.6 & 6 & 1.6 \\\\\n& & & & & & \\\\\n\\hline\\multicolumn{7}{r}{(Table 2 cont.)}\\\\\n%\\hline \n\\end{tabular}\n\\end{flushleft}\n\\end{table*}\n\n\n\\clearpage\n\n\n\\footnotesize\n\n\\begin{table*}\n{\\bf Table 2}: {COMPTEL Observations, Pointings and Viewing Periods}\n\n{\\bf Phase IV/Cycle-6}\n\\begin{flushleft}\n\\begin{tabular}{||r|c|l|r|r|r|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline \n& & & \\multicolumn{2}{c|}{} & & \\\\ & & & \\multicolumn{2}{c|}{} & & eff. COMPTEL \\\\\n Viewing & start & Z-axis & \\multicolumn{2}{c|}{galactic} & duration & observing time \\\\\n Period & (yy-mm-dd) & pointing & LONG & LAT & (days) & (days) \\\\ \n& & & & & & \\\\ \n\\hline\n\\hline\n& & & & & & \\\\\n 620.0 & 97-06-10 & GAL 16+4~~~~~~~~~& 15.8 & 3.6 & 7 & 2.4 \\\\\n 621.5 & 97-06-17 & 3C 279 & 301.7 & 57.8 & 7 & 2.5 \\\\\n 622.0 & 97-06-24 & Orion-1 & 226.6 & -21.3 & 21 & 6.7 \\\\\n 623.5 & 97-07-15 & BL Lac & 92.6 & -10.4 & 7 & 2.5 \\\\\n 623.0 & 97-07-22 & Orion-2 & 207.5 & -28.4 & 14 & 4.3 \\\\\n 625.0 & 97-08-05 & GRS 1758-258 & 1.4 & 0.8 & 14 & 4.3 \\\\\n 615.1 & 97-08-19 & PKS 1622-297 & 348.8 & 13.3 & 7 & 2.1 \\\\\n 626.0 & 97-08-26 & GAL 270-75 & 270.0 & -75.0 & 7 & 2.0 \\\\\n 627.0 & 97-09-02 & PSR 1055-52 & 288.1 & 2.0 & 7 & 1.9 \\\\\n 628.0 & 97-09-09 & GAL 300-74 & 300.2 & -74.3 & 7 & 1.8 \\\\\n 629.0 & 97-09-16 & GAL 300-74 & 300.2 & -74.3 & 7 & 2.0 \\\\\n 630.0 & 97-09-23 & PSR 1055-52 & 288.1 & 2.0 & 14 & 3.2 \\\\\n 632.1 & 97-10-07 & Carina-1 & 307.9 & - 7.5 & 27 & 5.9 \\\\\n 631.0 & 97-11-03 & PKS 0235+164 & 156.8 & -39.1 & 8 & 2.4 \\\\\n & 97-11-11 & End of & ~~~ & ~~~ & ~~~ & ~~~ \\\\\n & & Phase IV/Cycle-6~~~~~~~~ & ~~~ & ~~~ & ~~~ & ~~~ \\\\\n 701.0 & 97-11-11 & PKS 2155-304 & 10.1 & -54.1 & 7 & 2.1 \\\\\n 702.0 & 97-11-18 & PKS 2155-304 & 10.1 & -54.1 & 7 & 2.2 \\\\\n 703.0 & 97-11-25 & GAL 035+20 & 34.9 & 19.3 & 7 & 2.5 \\\\\n 704.0 & 97-12-02 & GAL 035+20 & 34.6 & 13.9 & 7 & 2.4 \\\\\n 705.0 & 97-12-09 & PSR B1509-58 & 319.6 & 7.8 & 7 & 2.0 \\\\\n 706.0 & 97-12-16 & PSR B1509-58 & 320.4 & 3.5 & 7 & 2.0 \\\\\n 707.0 & 97-12-23 & PSR B1509-58 & 316.9 & - 0.2 & 7 & 1.9 \\\\\n 708.0 & 97-12-30 & PKS 2155-304 & 10.1 & -54.1 & 7 & 2.1 \\\\\n 709.1 & 98-01-06 & PKS 2155-304 & 10.1 & -54.1 & 7 & 2.1 \\\\\n 710.0 & 98-01-13 & J1835+5919 & 85.9 & 29.4 & 8 & 3.0 \\\\\n 711.0 & 98-01-21 & J1835+5919 & 85.9 & 29.4 & 6 & 2.1 \\\\\n 712.0 & 98-01-27 & GAL 035+20 & 32.8 & 20.3 & 28 & 8.4 \\\\\n 713.0 & 98-02-24 & GAL 110-20 & 108.8 & -24.6 & 14 & 5.0 \\\\\n 714.0 & 98-03-10 & GAL 350-70 & 39.7 & -72.3 & 7 & 2.2 \\\\\n 715.0 & 98-03-17 & GAL 350-70 & 57.3 & -73.6 & 3 & 0.9 \\\\\n 715.5 & 98-03-20 & 1156+295 & 189.6 & 78.2 & 7 & 2.8 \\\\\n 716.5 & 98-03-27 & MRK 421 & 176.6 & 61.8 & 6 & 2.1 \\\\\n 716.7 & 98-04-02 & MRK 421 & 177.9 & 63.8 & 12 & 4.2 \\\\\n 717.0 & 98-04-14 & Cen X-3 & 289.1 & - 3.7 & 9 & 2.4 \\\\\n 718.0 & 98-04-22 & Cen X-3 & 287.8 & 2.5 & 7 & 1.9 \\\\\n 719.0 & 98-04-29 & Cen X-3 & 292.1 & 0.3 & 6 & 1.7 \\\\\n 720.5 & 98-05-05 & GRS 1915+105 & 44.6 & 0.4 & 10 & 3.5 \\\\\n 721.0 & 98-05-15 & MRK 501 & 63.6 & 38.9 & 4 & 1.4 \\\\\n 721.5 & 98-05-19 & SN 1998bu & 234.4 & 57.0 & 3 & 1.1 \\\\\n 722.5 & 98-05-22 & MRK 501 & 63.6 & 38.9 & 5 & 1.5 \\\\\n 723.5 & 98-05-27 & SN 1998bu & 230.1 & 55.2 & 6 & 2.1 \\\\\n 725.5 & 98-06-02 & SN 1998bu & 230.2 & 55.2 & 14 & 4.9 \\\\\n 726.5 & 98-06-16 & SN 1998bu & 230.2 & 55.1 & 7 & 2.5 \\\\\n 727.5 & 98-06-23 & Vela pulsar & 269.0 & - 3.0 & 7 & 2.0 \\\\\n 727.7 & 98-06-30 & SN 1998bu & 239.0 & 58.8 & 7 & 2.0 \\\\\n 724.5 & 98-07-07 & Geminga & 191.5 & 0.8 & 14 & 5.0 \\\\\n 728.5 & 98-07-21 & SN 1998bu & 231.6 & 55.8 & 35 & 11.2 \\\\\n 728.1 & 98-08-21 & aspect lost & ~~~ & ~~~ & 4 & ~~~ \\\\\n 728.2 & 98-08-25 & aspect tests & ~~~ & ~~~ & 1 & ~~~ \\\\\n & & & & & & \\\\\n\\hline\\multicolumn{7}{r}{(Table 2 cont.)}\\\\\n%\\hline \n\\end{tabular}\n\\end{flushleft}\n\\end{table*}\n\n\n\\clearpage\n\n\\footnotesize\n\\begin{table*} [t]\n\\vspace{-8cm}\n{\\bf Table 2}: {COMPTEL Observations, Pointings and Viewing Periods}\n{\\bf Phase IV/Cycle-7}\n\\begin{flushleft}\n\\begin{tabular}{||r|c|l|r|r|r|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline \n& & & \\multicolumn{2}{c|}{} & & \\\\ & & & \\multicolumn{2}{c|}{} & & eff. COMPTEL \\\\\n Viewing & start & Z-axis & \\multicolumn{2}{c|}{galactic} & duration & observing time \\\\\n Period & (yy-mm-dd) & pointing & LONG & LAT & (days) & (days) \\\\ \n& & & & & & \\\\ \n\\hline\n\\hline\n& & & & & & \\\\\n 730.6 & 98-08-26 & SN 1998bu & 254.9 & 45.5 & 14 & 4.6 \\\\\n 731.5 & 98-09-08 & SN 1998bu & 235.7 & 55.4 & 7 & 2.2 \\\\\n 732.5 & 98-09-15 & GAL 058-12 & 232.3 & 58.7 & 7 & 2.5 \\\\\n 728.7 & 98-09-22 & J0218+4232 & 139.4 & -18.7 & 3 & 1.1 \\\\\n 729.5 & 98-09-25 & J1550-564 & 324.9 & - 0.2 & 11 & 3.0 \\\\\n 734.0 & 98-10-06 & GAL 190-70 & 204.1 & -72.0 & 14 & 4.5 \\\\\n 728.9 & 98-10-13 & J0218+4232 & 139.4 & -18.7 & 21 & 6.1 \\\\\n 734.5 & 98-11-03 & GAL 190-70 & 204.1 & -72.0 & 14 & 4.6 \\\\\n 736.0 & 98-11-10 & Orion B1 & 227.9 & - 4.3 & 6 & 1.9 \\\\\n 736.5 & 98-11-16 & Leonid Save & 17.3 & -37.5 & 2 & ~~~ \\\\\n 736.7 & 98-11-18 & Orion B1 & 227.9 & - 4.3 & 6 & 1.9 \\\\\n 737.0 & 98-11-24 & GAL 044-09 & 44.3 & - 9.1 & 7 & 2.6 \\\\\n & 98-12-01 & End of & & & & \\\\\n & & Phase IV/Cycle-7~~~~~~~~~& & & & \\\\\n& & & & & & \\\\\n\\hline\n\\hline \n\\end{tabular}\n\\end{flushleft}\n\\end{table*}\n\n\n\n\\clearpage\n\n\n%TABLE 3\n\n\n\\landscape\n\\footnotesize\n\n%\\begin{table*}\n{\\bf Table 3}: {Spin-Down Pulsars}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|l|l|c|c|c|c|c|c|c|l|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n & & & & & &\\multicolumn{5}{c|}{ }& & \\\\\nPulsar & l & b &\\ \\ P & \\ \\ \\.{P} & d \n & \\multicolumn{5}{c|}{Phase Averaged Flux (10$^{-5}$ cm$^{-2}$ \n s$^{-1}$)} & \n VP or Phase & Ref. \\\\\n\n & & & & & & (0.75--1) & (1--3) & (3--10) & (10--30) & Other energy & & \\\\\n& [deg.] & [deg.] & \\ [ms] & [$10^{-15}$] & \\ \\ [kpc] & [MeV] & [MeV] \n& [MeV] & [MeV] & ranges [MeV] & & \\\\\n\n& & & & & & & & & & & & \\\\\n\\hline \n\\hline\n& & & & & &\\multicolumn{4}{c|} {}& & & \\\\\nPSR B1951+32 & 68.77 & 2.82 & 39.53 & 5.849 & 2.5 \n & \\multicolumn{4}{c|}{(2.3 $\\pm$ 1.4)} & & Phase & 6 \\\\\n & & & & & & & & & & & I--IV/Cycle-6 & \\\\\n\nPSR B0531+21 & 184.56 & -5.78 & 33.34 & 421.2 & 2.0 \n & 16.6$\\pm$ 3.0 & & & 1.5$\\pm$0.5 & 18.4$\\pm$2.2(1.0-1.6MeV)\n & Phase & 1,2\\\\\n (Crab) & & & & & & & & & & 6.5$\\pm$1.2(1.6-2.1MeV) \n & I--IV/Cycle-5 & \\\\\n & & & & & & & & & & 5.6$\\pm$1.1(2.36-4.0MeV) & & \\\\\n & & & & & & & & & & 1.6$\\pm$0.6(4.0-5.6MeV) & & \\\\\n & & & & & & & & & & 1.9$\\pm$0.5(5.6-10 MeV) & & \\\\\n\nPSR J0633+1746 & 195.13 & 4.65 & 237.1 & 10.98 & 0.16 \n & -2.7$\\pm$1.5 & +3.2$\\pm$2.2 & +2.4$\\pm$1.1 \n & -0.1$\\pm$0.4 & & Phase & 3 \\\\\n (Geminga) & & & & & & & & & & & I--III & \\\\\n\nPSR B0656+14 & 201.11 & 8.26 & 384.87 & 55.03 & 0.77 & 0.0$\\pm$1.9 \n & -0.9$\\pm$2.3 & -0.7$\\pm$1.2 \n & 0.8$\\pm$0.6 & & Phase I--IV & 4 \\\\ \n\nPSR B833-45 & 263.55 & -2.79 & 89.29 & 124.3 & 0.5 & 3.6$\\pm$1.9&\n2.8$\\pm$2.2 & 2.9$\\pm$1.0 & 2.3$\\pm$0.4 & & Phase & 5,7 \\\\\n(Vela) & & & & & & & & & & & 0 + I & \\\\\n\nPSR B1055-52 & 286.0 & 6.6 & 197.1 & 5.8 & 1.5 & \\multicolumn{4}{c|}{1.8 $\\pm$ 0.5$^{d}$} & & Phase & 8 \\\\\n & & & & & & \\multicolumn{4}{c|}{}& & I--IV/Cycle-6 & \\\\\n\nPSR B1509-58 & 320.32 & -1.16 & 150.65 & 1537 & 4.4. & \\multicolumn{2}{c|}{8.3 $\\pm$ 1.7} & 3.2$\\pm$0.6 & 0.2$\\pm$0.2$^a$ & & Phase & 9,10 \\\\ \n (Circinus) & & & & & & & & & 0.7$\\pm$0.2$^b$ & & I--IV/Cycle-6 & \\\\\n & & & & & & & & & 1.1$\\pm$0.2$^c$ & & & \\\\ \n& & & & & & & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n\\end{flushleft}\n%\\end{table*}\n\n\\vskip6pt\n\\noindent\n{\\bf Notes}\n \\vskip6pt\n\\noindent\n(a) Flux main pulse from timing analysis.\n\\noindent\n(b) Flux main pulse above background from spatial analysis.\n\\noindent\n(c) Total flux from spatial analysis.\n\\noindent\n(d) Note that the flux given in ref. (8) should be in units ph cm$^{-2}$ sec$^{-1}$ MeV$^{-1}$.\n\n\\vskip6pt\n\\noindent\n{\\bf References}\n\\vskip6pt\n\\noindent\n(1) \\cite{much95a}.\n\n\\noindent\n(2) \\cite{much97}.\n\n\\noindent \n(3) \\cite{kuiper96}.\n\n\\noindent \n(4) \\cite{hermsen97}. \n\n\\noindent\n(5) \\cite{schoenf95}.\n\n\\noindent\n(6) \\cite{kuiper98a}.\n\n\\noindent\n(7) \\cite{kuiper98b}. \n\n\\noindent \n(8) \\cite{thompson99}.\n\n\\noindent\n(9) \\cite{kuiper99a}.\n\n\\noindent\n(10) \\cite{kuiper99b}. \n \n\\endlandscape\n\n\n\n\\clearpage\n\n\n\n\n% begin TABLE 4\n\n\n\\landscape\n%\\vspace*{-2cm}\n\\def \\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\\footnotesize\n%\\tiny\n%\\begin{table*}\n{\\bf Table 4}: {Galactic Sources $|b|< 10^\\circ$}\n\\begin{flushleft}\n\\begin{tabular}{||l|r|r|c|c|c|c|c|c|c|c|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n & \\multicolumn{2}{r|}{} & \\multicolumn{5}{c|}{} & & & & \\\\\nSource & \\multicolumn{2}{r|}{Position} & \\multicolumn{5}{c|}{Fluxes$^{\\rm a}$\n (10$^{-5}$ photon cm$^{-2}$ \n s$^{-1}$)} & Spect. & VP or & Notes & Ref. \\\\ \n& l & b & (0.75--1) & (1--3) & (3--10) & (10--30)\n & Other Energy & Fits & Phase & & \\\\\n& & & & & & & Ranges & & & & \\\\\n& [deg] & [deg] & [MeV] & [MeV] & [MeV] & [MeV] & [MeV] & & & & \\\\\n& & & & & & & & & & & \\\\\n\\hline\n\\hline\n& & & & & & & & & & & \\\\\nGRO J 1823-12&18.5&-0.5& 4.1\\p 1.7 & 9.9\\p 1.5 & 3.5\\p 0.6 & 1.0\\p 0.2 & ~~~~~~~& f & VP 1 to 522.5 & c & (9) \\\\\n(2 EG J 1825-1307) & & & & & & & & & & & \\\\\n& & & & & & & & & & & \\\\\n\\hline\n& & & & & & & & & & & \\\\\nCygnus X--1 & 71.3 & 3.1 & & & & $<$1.39 & \n 11.9\\p 3.0 (0.75--0.85) & \n & Phase I to III & b & (3) \\\\\n& & & & & & & 9.5\\p 2.2 ((0.85--1) & a & (up to VP 318.1) & & (3a)\\\\\n& & & & & & & 16.7\\p 2.7 (1--2) & & & & \\\\\n& & & & & & & 6.9\\p 1.6 (3--5) & & & &\\\\\n& & & & & & & $<$1.15 (5--10) & & & & \\\\\n& & & & & & & & & & & \\\\\n\\hline\n& & & & & & & & & & & \\\\\nGRO J 2227+61 & 106.6 & 3.1 & 12.6\\p 4.5 & 30.8\\p 5.5 & $\\leq$6.3 \n& $\\leq$1.48 & & e & VP 2+7+34 & & (6) \\\\\n (2 EG 2227+61) & & & & & & & & & & & \\\\\n (2CG 106+1.5) & & & & & & & & & & & \\\\\n& & & & & & & & & & & \\\\\n\\hline\n& & & & & & & & & & & \\\\\nGT 0236+610 & 135.7 & 1.1 & $<$ 4.8 & 11.2\\p 3.2 & 5.0\\p 1.2 \n & 1.24\\p 0.38 &\n & b & VP 15+31+34+211 & b & (5) \\\\\n(2EG J0241+6119) & & & $<$ 4.8 & 5.6 \\p 3.0 & 3.2\\p 1.3 & $<$ 1.3 \n& & & +319+325 & c & \\\\ \n(2CG 135+01) & & & & & & & & & & & \\\\\n & & & & & & & & & & & \\\\\n\\hline\n & & & & & & & & & & & \\\\\nNova Per 1992 & 165.9 & -11.9 & $<$ 35.0 & & $<$11.9 & $<$2.8 \n & 28.0\\p 10.0 (1--2) & c & VP 36.5 & b & (4) \\\\\n(GRO J0422+32) & & & & & & & $<$8.1 (2--3) & & & & \\\\\n & & & 27.5\\p 10.00 & & $<$6.0 & $<$2.2 & $<$15.0 (1--2)& & VP 39 & & \\\\\n & & & & & & & $<$6.6 (2--3) & & & & \\\\\n & & & & & & & & & & & \\\\\n\\hline\n& & & & & & & & & & & \\\\\nCrab Unpulsed~~~~~~~ & 184.6 & -5.8 & \n & & & & 34.07\\p 1.57(0.78-0.96) & & Phase I to IV/Cycle-5 & & \\\\\n& & & & & & & 31.11\\p 1.30(0.96-1.16) & & & a,b & ~~ \\\\\n& & & & & & & 21.54\\p 1.09(1.16-1.38) & & & & \\\\\n& & & & & & & 18.68\\p 1.04(1.38-1.62) & & & & \\\\\n& & & & & & & 13.03\\p 0.82(1.62-1.88) & & & & \\\\\n& & & & & & & 8.90\\p 0.71(1.88-2.16) & & & & \\\\\n& & & & & & & 7.84\\p 0.70(2.16-2.48) & & & & \\\\\n& & & & & & & & & & & \\\\\n\\hline\\multicolumn{12}{r}{(Table 4 cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{table*}\n%\\end{document}\n%\\null\n%\\vskip-2cm\n\n\n\\clearpage\n\n\n%\\vspace*{-2cm}\n%\\textwidth=30cm\n%\\textheight=6.6truein\n%\\begin{table*}\n\\hoffset=-3cm\n{\\bf Table 4}: {Galactic Sources $|b|< 10^\\circ$ (cont.)}\n\\begin{flushleft}\n\\begin{tabular}{||l|r|r|c|c|c|c|c|c|c|c|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n & \\multicolumn{2}{r|}{} & \\multicolumn{5}{c|}{} & & & & \\\\\nSource & \\multicolumn{2}{r|}{Position} & \\multicolumn{5}{c|}{Fluxes$^{\\rm a}$\n (10$^{-5}$ photon cm$^{-2}$ \n s$^{-1}$)} & Spect. & VP or & Notes & Ref. \\\\ \n& l & b & (0.75--1) & (1--3) & (3--10) & (10--30)\n & Other Energy & Fits & Phase & & \\\\\n& & & & & & & Ranges & & & & \\\\\n & [deg] & [deg] & [MeV] & [MeV] & [MeV] & [MeV] & [MeV] \n & & & & \\\\\n& & & & & & & & & & & \\\\\n\\hline\n\\hline\n& & & & & & & & & & & \\\\\nCrab Unpulsed cont. \n& ~~&~~ & ~~~~~~~~~~~~~& ~~~~~~~~& ~~~~~~~~~& & 8.66\\p 0.57(2.48-2.84) & &~~~~~~~~~~~~~~~~~~~~~~~ & & \\\\\n& & & & & & & 6.14\\p 0.52(2.84-3.22) & & & & (1),(2) \\\\\n& & & & & & & 4.41\\p 0.46(3.22-3.62) & & & & (7) \\\\\n& & & & & & & 4.28\\p 0.41(3.62-4.08) & & & & \\\\\n& & & & & & & 4.44\\p 0.36(4.08-4.56) & & & & \\\\\n& & & & & & & 2.94\\p 0.33(4.56-5.08) & & & & \\\\\n& & & & & & & 3.42\\p 0.32(5.08-5.66) & & & & \\\\\n& & & & & & & 2.30\\p 0.28(5.66-6.26) & & & & \\\\\n& & & & & & & 2.15\\p 0.28(6.26-6.94) & & & & \\\\\n& & & & & & & 1.60\\p 0.25(6.94-7.64) & & & & \\\\\n& & & & & & & 1.17\\p 0.20(7.64-8.42) & & & & \\\\\n& & & & & & & 1.36\\p 0.17(8.42-9.26) & & & & \\\\\n& & & & & & & 1.24\\p 0.15( 9.26-10.16)& & & & \\\\\n& & & & & & & 1.05\\p 0.15(10.00-11.20)& & & & \\\\\n& & & & & & & 1.12\\p 0.14(11.20-12.48)& & & & \\\\\n& & & & & & & 1.12\\p 0.14(12.48-13.92)& & & & \\\\\n& & & & & & & 0.62\\p 0.13(13.92-15.52)& & & & \\\\\n& & & & & & & 0.83\\p 0.14(15.52-17.28)& & & & \\\\\n& & & & & & & 0.50\\p 0.14(17.28-19.28)& & & & \\\\\n& & & & & & & 0.31\\p 0.14(19.28-21.60)& & & & \\\\\n& & & & & & & 0.23\\p 0.15(21.60-24.08)& & & & \\\\\n& & & & & & & 0.16\\p 0.18(24.08-26.88)& & & & \\\\\n& & & & & & & 0.13\\p 0.27(26.88-30.00)& & & & \\\\\n& & & & & & & & & & & \\\\\n\\hline\n& & & & & & & & & & & \\\\\nVela/Carina & 273$^{\\circ}$~ & -6$^{\\circ}$ & $<$ 6.0~~~~~~ & $<$ 5.4~~~ & 7.5\\p 1.1 &\n$<$ 1.1 & & & VP 1 to 522.5~~~~~~~~~ & a,c,d & (8) \\\\\n& & & & & & & & & & & \\\\\n\\hline\\multicolumn{12}{r}{(Table 4 cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n\n\n\\clearpage\n\n\n{\\bf Spectral Fits}\n\\vskip6pt\n%\\noindent\n\na. Wien spectrum with kT $\\sim$ 190 keV; for fits to 1991 data only\n see McConnell et al. 1994.\n\nb. 1.75 $\\cdot$ 10$^{-4}$(E/1 MeV$^{-1.95}$ photon cm$^{-2}$ s$^{-1}$ \n MeV$^{-1}$ (ref. 5).\n\nc. See ref. 4.\n\nd. (1.12\\p 0.03) $\\cdot$ 10$^{-4}$(E/3.5 MeV)$^{-(2.02\\mbox{\\small \\p}0.03)}$ photon cm$^{-2}$ s$^{-1}$ MeV$^{-1}$ $<$ 10 MeV (ref. 7).\n\ne. Power-law spectrum $\\sim$ E$^{-\\alpha}$, with $\\alpha$ = 2.20 $\\pm$ 0.14.\n\nf. Power-law spectrum $\\sim$ E$^{-\\alpha}$, with $\\alpha$ = 2.0.\n\n\\vskip6pt\n%\\noindent\n{\\bf Notes}\n%\\noindent\n\\vskip6pt\n\na. Flux values with statistical 1 \\s \\ uncertainties and 2 \\s \\ upper limits\n are given.\n\nb. No model for Galactic diffuse emission is included in this analysis.\n\nc. Model for Galactic diffuse emission is included.\n\nd. The excess is extended and can be explained by a 2-source model with sources at (273.8, -3.5) and (271.9, -9.0).\n\n\\vskip6pt\n%\\noindent\n{\\bf References}\n%\\noindent\n\\vskip6pt\n(1) \\cite{much95a}.\n\n(2) \\cite{much95b}.\n\n(3) \\cite{mcconnell97b}.\n\n(3a) \\cite{mcconnell94}.\n\n(4) \\cite{vandijk95}.\n\n(5) \\cite{vandijk96}.\n\n(6) \\cite{iyudin97b}.\n\n(7) \\cite{meulen98}.\n\n(8) \\cite{meulen99}.\n\n(9) \\cite{bloemen00}.\n \n%\\end{table*}\n%\\noindent\n\n\\endlandscape\n\n\n\\clearpage\n\n\n% TABLE 5 begin\n\n%\\landscape\n\\footnotesize\n%\\begin{flushleft}\n{\\bf Table 5}: {Active Galactic Nuclei}\n \\vskip12pt\n%\n%\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c||}\n%& & & & & & & & & \\\\\n\\hline\\hline \\noalign{\\smallskip}\n & & \\multicolumn{2}{c|}{} & \\multicolumn{4}{c|}{} & & \\\\\nSource & Z-Value & \\multicolumn{2}{c|}{Position} & \\multicolumn{4}{c|}{Flux (10$^{-5}$ photon cm$^{-2}$ s$^{-1}$)} & VP & Ref. \\\\\n & & & & & & & & or & \\\\\n& & l & b & (0.75--1) & (1--3) & ~~(3--10)~~ & (10--30) & Phase & \\\\\n& & [deg] & [deg] & [MeV] & [MeV] & [MeV] & [MeV] & & \\\\\n& & & & & & & & & \\\\\n\\hline\n\\hline\n& & & & & & & & & \\\\\nCTA 102 & 1.037 & 77.4 & -38.6 & $<$10.4 & $<$12.1\n & $<$7.4 & 1.4$\\pm$1.1 & VP 19 & (1) \\\\\n(PKS 2230+114)& & & & $<$15.1 & $<$24.7 & $<$10.7 & $<$6.9 & VP 26+28 & \\\\ \n & & & & $<$17.9 & $<$30.0 & $<$13.5 & $<$6.5 & VP 37 & \\\\\n & & & & $<$7.8 & $<$12.2 & $<$6.4 & 1.9$\\pm$0.9 & Phase 1 & \\\\\n& & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\n3C 454.3 & 0.859 & 86.1 & -38.2 & $<$10.5 & $<$12.9 & 6.9$\\pm$3.3 \n & $<$3.8 & VP 19 & (1) \\\\\n(PKS 2251+15) & & & & $<$17.5 & $<$23.0 & $<$8.1 & 6.1$\\pm$1.80 & VP 26+28 & \\\\\n & & & & $<$20.2 & 12.4 $\\pm$10.4 & $<$13.0 & 2.2$\\pm$1.8 & VP 37 & \\\\\n & & & & $<$10.4 & $<$9.2 & 2.8$\\pm$2.3 & 2.9$\\pm$1.0 & Phase 1 & \\\\\n& & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\nPKS 0528+134 & 2.06 & 191.4 & -11 & 9.4$\\pm$8.2 & 9.7$\\pm$6.3 & 4.4$\\pm$2.5 \n & 3.2$\\pm$1.0 & VP 0 & \\\\\n(OG 147) & & & & 16.6$\\pm$8.7 & $<$13.8 & $<$7.7 & 3.0$\\pm$1.0& VP 1 & \\\\\n & & & & $<$16.2 & $<$21.8 & $<$9.4 & $<$3.2 & VP 2.5 & \\\\\n & & & & $<$15.6 & $<$18.7 & $<$8.4 & $<$2.8 & VP 36/39 & \\\\\n & & & & $<$32.1 & 15.3 $\\pm$12.3 & $<$15.2$\\pm$4.7 & 3.3$\\pm$1.7 \n & VP 213 & \\\\\n & & & & $<$24.4 & $<$14.0$\\pm$9.5 & $<$4.4$\\pm$3.6 & $<$2.7 & VP 221 & \\\\\n& & & & $<$20.9 & $<$17.4 & 5.0$\\pm$3.6 & $<$4.3 & VP 310 & \\\\\n & & & & 11.3$\\pm$10.0 & 18.1 $\\pm$8.3 & $<$6.3 & $<$3.1 & VP 321 \n & (2) \\\\ \n & & & & 23.8$\\pm$7.9 & 20.6 $\\pm$6.6 & $<$5.0 & $<$1.8 & VP 337 \n & \\\\ \n& & & & $<$32.1 & 15.3$\\pm$12.3 & 15.2 $\\pm$4.7 & 3.3$\\pm$1.7 & VP213 \n & \\\\\n & & & & $<$8.7 & 5.8$\\pm$3.4 & 4.3$\\pm$1.4 & 2.0$\\pm$0.5 & Phase I+II\n & \\\\\n & & & & 4.2$\\pm$3.4 & 8.5$\\pm$2.7 & 2.3$\\pm$1.0 & 1.3$\\pm$0.4 \n & Phase I--III & \\\\\n & & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\nGRO J0516--609 & & 270 & -35 & $<$12.8 & $<$18.1 & $<$8.3 & $<$2.1 & VP 6 \n & (3) \\\\\n(PKS 0506-612/& & & & $<$18.6 & 20.0$\\pm$7.2 & $<$12.4 & $<$4.2 & VP 10\n & \\\\\nPKS 0522-611) & & & & $<$11.0 & 9.2 $\\pm$6.2 & 8.9$\\pm$3.2 & $<$1.7 & VP 17 \n & \\\\\n& & & & $<$9.4 & 15.1$\\pm$4.6 & 5.7$\\pm$2.5 & $<$1.5 & VP 10+17 & \\\\\n& & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\nPKS 0208-512 & 1.003 & 276.1 & -61.8 & & 21$\\pm$9 & & & VP 6 & \\\\\n(RX J02107--5100)& & & & & $<$26 & & & VP 9 & \\\\\n& & & & & $<$15 & & & VP 10 & \\\\\n& & & & & $<$18 & & & VP 13.5 & \\\\\n& & & & & $<$23 & & & VP 17 & (4) \\\\\n& & & & & 35$\\pm$12 & & & VP 220 & \\\\\n& & & & & 44$\\pm$9 & & & VP 224 & \\\\\n& & & & $<$12 & 41$\\pm$7 & $<$7 & $<$3 & Phase II & \\\\\n& & & & & & & & & \\\\\n\\hline\\multicolumn{10}{r}{(Table 5 cont.)}\\\\\n\\end{tabular}\n%\\endlandscape\n\n\n\\clearpage\n\n\n%\\landscape\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c||}\n%& & & & & & & & & \\\\\n\\hline\\hline \\noalign{\\smallskip}\n & & \\multicolumn{2}{c|}{} & \\multicolumn{4}{c|}{} & & \\\\\nSource & Z-Value & \\multicolumn{2}{c|}{Position} & \\multicolumn{4}{c|}{Flux (10$^{-5}$ photon cm$^{-2}$ s$^{-1}$)} & VP & Ref. \\\\\n & & & & & & & & or & \\\\\n& & l & b & (0.75--1) & (1--3) & ~~(3--10)~~ & (10--30) & Phase & \\\\\n& & [deg] & [deg] & [MeV] & [MeV] & [MeV] & [MeV] & & \\\\\n& & & & & & & & & \\\\\n\\hline\n\\hline\n & & \\multicolumn{2}{c|}{} & \\multicolumn{4}{c|}{} & & \\\\\n3C273 & 0.158 & 290.0 & 64.4 & \\multicolumn{2}{c|} {25.9$\\pm$6.2} \n & \\multicolumn{2}{c|}{ $<$1.7} & VP 3 & (5) \\\\\n(1226+023)& & & & \\multicolumn{2}{c|}{(0.75--8 MeV)}\n & \\multicolumn{2}{c|}{(8--30 MeV)}& & \\\\\n & & & & 13.8$\\pm$4.8 & 10.7$\\pm$3.7 & 5.6$\\pm$1.9 & $<$1.7 & VP 3 & \\\\\n & & & & (0.75--1.25) & (1.25--3) & (3--8) & (8--30) & & \\\\\n& & & & \\multicolumn{2}{c|}{$<$19.2}\n & \\multicolumn{2}{c|}{$<$2.5}& VP 11 & \\\\\n & & & & \\multicolumn{2}{c|}{(0.75--8 MeV)}\n & \\multicolumn{2}{c|}{(8--30 MeV)} & & \\\\\n& & & & $<$8.5 & 14.5$\\pm$2.2 & 3.9$\\pm$0.9 & 0.6$\\pm$0.3 & Phase I to III \n & (6) \\\\\n& & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\nGROJ1224+2155 & & 255.1 & +81.7 & & & & & & \\\\\n(PKS 1222+216) & & & & $<$4.8 & $<$5.4 & 2.6$\\pm$0.9 \n & $<$0.9 & Phase I--III & (6) \\\\\n& & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\n3C279 & & & &\\multicolumn{2}{c|}{} & \\multicolumn{2}{c|}{} & & \\\\\n(1253--055) & 0.538 & 305.1 & 57.1 & \\multicolumn{2}{c|}{$<$13.8}\n & \\multicolumn{2}{c|}{2.9$\\pm$0.9}\n & 3 & (5) \\\\\n & & & & \\multicolumn{2}{c|}{(0.75--8 MeV)}\n & \\multicolumn{2}{c|}{(8--30 MeV)} & & \\\\\n & & & & \\multicolumn{2}{c|}{$<$12.1}& \\multicolumn{2}{c|}{$<$3.2} \n & 1 & \\\\\n & & & & \\multicolumn{2}{c|}{(.75--8 MeV)}\n & \\multicolumn{2}{c|}{(8--30 MeV)} & & \\\\\n& & & & & & & & & \\\\\n& & & & $<$8.8 & 6.3$\\pm$2.0 & $<$3.2 & 0.8$\\pm$0.3 & Phase I to III & (6) \\\\ \n& & & & 5.9$\\pm$3.0 & 6.9$\\pm$2.4 & 1.5$\\pm$1.0 & 1.0$\\pm$0.3 & Phase I to IV & (9) \\\\ \n& & & & & & & & & \\\\\n\\hline\nCentaurus A & $\\sim$3 Mpc & 309.5 & 19.4 & 16.4$\\pm$8.1 & $<$17.6 & 4.0$\\pm$2.4 & 1.6$\\pm$0.8 & VP 12 & (7) \\\\\nNGC 5128 & & & & 31.0$\\pm$ 12. & 16.4$\\pm$ 11 & $<$9.2 & $<$5.8\n & VP 14$^{\\rm a}$ & \\\\\n& & & & 16.8$\\pm$ 16. & $<$28.6 & $<$15.8 & $<$ 2.9\n & VP 23$^{\\rm b}$ & \\\\\n & & & & $<$20.1 & 30.3$\\pm$13. & 7.1$\\pm$6.2 & $<$3.9 & VP 27 & \\\\\n & & & & $<$20.5 & $<$35.0 & $<$14.9 & $<$5.7 & VP 32 & \\\\\n& & & & 14.1$\\pm$5.2 &10.8$\\pm$4.5 & 2.2$\\pm$1.9 & $<$ 1.4\n & Phase I & \\\\\n& & & & & & & & & \\\\\n& & & & $<$12.2 & $<$14.3 & 8.8$\\pm$2.6 & 1.3$\\pm$0.9 & VP 207 & \\\\\n& & & & 18.8$\\pm$15. & 14.5$\\pm$12. & 5.1$\\pm$4.4 & $<$3.8 \n & VP 208 & \\\\\n& & & & $<$23.3 & 21.3$\\pm$8.3 & 10.8$\\pm$3.1 & $<$1.7 & VP 215 +217 & \\\\\n& & & & $<$11.9 & 5.8 $\\pm$4.6 & 8.6$\\pm$1.8 & $<$1.7 & Phase II & \\\\\n& & & & & & & & & \\\\\n\\hline\\multicolumn{10}{r}{(Table 5 cont.)}\\\\\n\\end{tabular}\n%\\endlandscape\n\n\n\\clearpage\n\n\n%\\landscape\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c||}\n%& & & & & & & & & \\\\\n\\hline\\hline \\noalign{\\smallskip}\n & & \\multicolumn{2}{c|}{} & \\multicolumn{4}{c|}{} & & \\\\\nSource & Z-Value & \\multicolumn{2}{c|}{Position} & \\multicolumn{4}{c|}{Flux (10$^{-5}$ photon cm$^{-2}$ s$^{-1}$)} & VP & Ref. \\\\\n & & & & & & & & or & \\\\\n& & l & b & (0.75--1) & (1--3) & ~~(3--10)~~ & (10--30) & Phase & \\\\\n& & [deg] & [deg] & [MeV] & [MeV] & [MeV] & [MeV] & & \\\\\n& & & & & & & & & \\\\\n\\hline\n\\hline\n& & \\multicolumn{2}{c|}{} & \\multicolumn{4}{c|}{} & & \\\\\nCentaurus A ~~~~ & & & & 28.1$\\pm$9.9 & $<$26.6 & $<$6.7 & 2.3$\\pm$1.4~ \n & VP 314 & \\\\ \n(NGC 5128) & & & & $<$6.9 & 4.5$\\pm$2.9 & $<$2.2 & $<$2.4 & VP 315 & \\\\\n & & & & $<$30.6 & $<$17.1 & $<$9.0 & $<$1.6 & VP 316 & \\\\\n& & & & 24.1 $\\pm$6.2 & $<$14.9 & $<$3.9 & $<$1.2\n & Phase III & \\\\\n& & & & & & & & & \\\\\n& & & & 18.7$\\pm$14. & $<$36.1 & $<$9.1 & $<$3.0 \n & VP 402.0 & \\\\\n& & & & $<$28.7 & 26.6$\\pm$12. & $<$8.9 & $<$4.2 & VP 402.5 & \\\\ \n& & & & $<$13.5 & 18.6$\\pm$7.7 & 3.6$\\pm$2.7 & $<$1.3 & VP 424.0 & \\\\\n& & & & $<$15.2 & ~~21.9$\\pm$5.8~~ & ~$<$4.5~ & $<$1.1 & Phase IV & \\\\ \n& & & & & & & & & \\\\\n& & & & 9.1$\\pm$3.0 & 6.4$\\pm$2.5 & ~2.1$\\pm$1.0 & $<$0.6 & Phase I to IV & \\\\ & & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\nPKS 1622--297 & 0.815 & 348.5 & 13.5 & $<$22.0\n & $<$13.5 & $<$6.1 & 3.3$\\pm$0.7 & VP 421--423.5 & (8) \\\\\n& & & & & & & & & \\\\\n\\noalign{\\smallskip}\\hline\\hline\n\\end{tabular} \n\\vskip6pt\n{\\bf Notes}\n\\vskip6pt\n$^{\\rm a}$Heavily influenced by Earth in field-of-view.\n\n$^{\\rm b}$Large data loss due to malfunctioning tape recorder.\n\\vskip6pt\n{\\bf References}\n\\vskip6pt\n(1) \\cite{blom95a}.\n \n(2) \\cite{collmar97a}.\n \n(3) \\cite{bloemen95}.\n\n(4) \\cite{blom95b}.\n\n(5) \\cite{williams95b}.\n\n(6) \\cite{collmar96}.\n\n(7) \\cite{steinle98}.\n\n(8) \\cite{collmar97b}.\n\n(9) \\cite{collmar97c}.\n%\\end{flushleft} \n%\\include{notes}\n%\\endlandscape\n\n\n\n\\clearpage\n\n\n\n\n% TABLE 6\n\n\\landscape\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 6}: {Unidentified High-LatitudeSource}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|l|l|l|l|l|l|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n& \\multicolumn{2}{c|}{} & \\multicolumn{5}{c|}{} & & \\\\\n & \\multicolumn{2}{c|}{COMPTEL Position}\n & \\multicolumn{5}{c|}{Flux (10$^{-5}$ cm$^{-2}$ s$^{-1}$)} & & \\\\\nSource & l & b & (0.75--1) & (1--3) & (3--10) & \n (10--30) & Other Energy & VP/Phase\n & Ref. \\\\\n&[deg] &[deg] & [MeV] & [MeV] & [MeV] & [MeV] & Ranges [MeV] & & \\\\\n\\hline\n\\hline\n& & & & & & & & & \\\\\nGRO J 1753+57$^{\\rm a}$ & 85.5 & 30.5 & $<$13.9 & $<$14.0 &\n $<$13.5 & $<$2.4 & & VP 2 & (1) \\\\\n& & & $<$17.9 & $<$13.8 & $<$7.2 &\n $<$2.8 & & VP 9.5 & (6) \\\\\n& & & $<$24.7 & 48.9$\\pm$9.1 & $<$12.2 & $<$2.2 \n & & VP 201 & \\\\ \n& & & 18.6$\\pm$9.9 & 28.8$\\pm$9.4 & $<$12.1 &\n $<$4.9 & & VP 202 & \\\\ \n& & & $<$7.0 & $<$8.8 & 5.6$\\pm$2.7 & $<$2.8 \n & & VP 203 & \\\\ \n& & & $<$9.4 & 11.0$\\pm$5.1 & $<$8 & $<$2.0 \n & & VP 212 & \\\\ \n%& & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\nGRO J 1040+48 & 165 & 57 & & & & $<$0.56 & 19.8$\\pm$3.2 (0.75--1.36) \n & Phase I - II& (2) \\\\\n& & & & & & & 6.48$\\pm$1.08(1.56--2.1 & & \\\\\n& & & & & & & 1.97$\\pm$1.6(2.3--4.0 & & \\\\\n& & & & & & & $<$2.58 (4--10)& & \\\\\n& & & & & & & 24$\\pm$3 (0.75--3 & Phase I - II & \\\\\n& & & & & & & 7$\\pm$4 (0.75--3) & Phase III - IV & \\\\\n%& & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\nGRO J 1214+06 & 278.9 & +66.6 & $<$5.1 & $<$6.8 & 4.0$\\pm$0.9 & $<$0.7 \n & & Phase I - III & (3) \\\\\n%& & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\nExtended emission & 145$<$l$<$195 \n& 35$<$b$<$65 & & & & & 150$\\pm$10 (0.75--3) & Phase I to IV &\n (4) \\\\\nfrom the HVC & & & & & & & & &\\\\\ncomplexes & & & & & & & & & \\\\\nM and A area$^{\\rm b}$ & & & & & & & & & \\\\\n%& & & & & & & & & \\\\\n\\hline\n& & & & & & & & & \\\\\nExtended emission & 75$<$l$<$95 & 25$<$b$<$45 & & & & & \n 110$\\pm$10(0.75-3) & Phase I to IV & (5) \\\\\nfrom the HVC & & & & & & & & & \\\\\ncomplex C area$^{\\rm c}$ & & & & & & & & & \\\\\n%& & & & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\vskip6pt\n\\noindent\n$^{\\rm a}$The emission cannot arise from a single source, but it can be modelled as a combination of emission from both GRO J1837+59 (a bright \\\\\n\\phantom{$^{\\rm a }$}unidentified EGRET source), and the steep spectrum EGRET blazar QSO 1739+522. \\\\\n\\noindent\n$^{\\rm b}$Cloud region contains: 2EG J0917+4420, 2EG J0957+5515, GRO J1040+48.\\\\\n\\noindent\n$^{\\rm c}$Cloud region contains: GRO J1753+57, 2EG J1739+5152,\n 2EG 1731+6007, 2EG J 1835+5913\n\\vskip6pt\n{\\bf References} \n\\vskip6pt\n(1) \\cite{williams95a}.\n\n(2) \\cite{iyudin96}.\n\n(3) \\cite{collmar96}.\n\n(4) \\cite{blom97b}.\n\n(5) \\cite{blom97a}.\n\n(6) \\cite{williams99}.\n%\\end{table}\n\n\\clearpage\n\\endlandscape\n\n\n\n% TABLE 7\n\\landscape\n\n\\footnotesize\n%\\begin{flushleft}\n{\\bf Table 7}: {Gamma-Ray Line Sources}\n\\vskip12pt\n%\\tablecaption{{\\bf Table 7}: {Gamma-Ray Line Sources}\n\\begin{tabular}{||l|c|c|c|c|l|l|c||} \n%\\tablehead{\\hline \\hline \\noalign{\\smallskip} \n\\hline \\hline \\noalign{\\smallskip} \n& \\multicolumn{2}{c|}{} & & & & & \\\\\nName & \\multicolumn{2}{c|}{Position} & Line Energy & Flux \n & VP or Phase & Note & Ref. \\\\\n & l & b & & & & & \\\\\n & [deg] & [deg] & [MeV] \n & [10$^{-5}$ photons & & & \\\\\n& & & & cm$^{-2}$ s$^{-1}$] & & & \\\\\n & & & & & & & \\\\\n\\hline \n\\hline %\\tabletail{\\hline\\multicolumn{7}{r}{(Table 7 cont.)}\\\\} \n%\\tablelasttail{\\noalign{\\smallskip}\\hline\\hline} \n%\\begin{supertabular}{||l|c|c|c|c|l|l|c||} \n& & & & & & & \\\\ \nSN 1991T~~~~~~~~~~~~~~~ & ~~~~292.61~~~~ & ~~~~65.19~~~~ & 0.847 \n & $5.3 \\pm 2.0 $ & VP 3.0, 11.0, 204.0, & & \\\\\n & & & & &205.0, 206.0 & &\\\\\n & & & 1.238\n & 3.6 $\\pm$ 1.4 & & & (1) \\\\\n & & & & & & & \\\\\n & & & both & 8.9 $\\pm$ 3.4 & & & \\\\\n & & & combined & & & & \\\\\n & & & & & & & \\\\\n\\hline\n & & & & & & & \\\\ \nCas A & 111.7 & -2.1 & 1.157 \n & 4.2 $\\pm$ 0.9 & VP 34.0, 211.0, & possibly broadened & (2) \\\\\n & & & & & 302.0, 303.2, & line & (3)\\\\\n & & & & & 303.7, 401.0 & result from all obs. & \\\\\n & & & & & & up to 401 & \\\\\n & & & & & & & \\\\\n & & & & 3.4 $\\pm$ 0.9 & Phase I to III & & (7) \\\\\n& & & & & & & \\\\\n\\hline\n & & & & & & & \\\\ \nSNR G266.5-1.5 & 266.5 & -1.5 & 1.157 & 3.8 $\\pm$ 0.7 & Phase I to IV/ & &(8)\\\\\n & & & & & Cycle-6 (VP 617.1)& & \\\\\n & & & & & & & \\\\\n\\hline\n & & & & & & & \\\\\nInner Galaxy & -32$<$l$<$35 & -5$<$b$<$5 & 1.809 \n & 28.0$\\pm$ 1.5 & Phase I to IV/ \n & emission extended & \\\\\n & & & & & Cycle-5 & beyond this region & (4)\\\\\n & & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nVela Region & 257$<$l$<$273 & -5$<$b$<$5 \n & 1.809 & 2.9$\\pm$ 0.6& Phase I to IV / & possibly extended & \\\\\n& & & & & Cycle-5 & emission (few deg.) & (4)\\\\\n& & & & & & & \\\\\n\\hline\\multicolumn{8}{r}{(Table 7 cont.)}\\\\\n\\end{tabular}\n\\endlandscape\n\n\n\n\n\\landscape\n%\\footnotesize\n\\begin{tabular}{||l|c|c|c|c|l|l|c||} \n\\hline \\hline \\noalign{\\smallskip} \n& \\multicolumn{2}{c|}{} & & & & & \\\\\nName & \\multicolumn{2}{c|}{Position} & Line Energy & Flux \n & VP or Phase & Note & Ref. \\\\\n & l & b & & & & & \\\\\n & [deg] & [deg] & [MeV] \n & [10$^{-5}$ photons & & & \\\\\n& & & & cm$^{-2}$ s$^{-1}$] & & & \\\\\n & & & & & & & \\\\\n\\hline \n\\hline\n & & & & & & & \\\\ \n Cygnus Region ~~& 73$<l<$93 & -7$<b<7$\n & 1.809 & 7.0 $\\pm$ 1.4 & VP 2.0, 7.0, 34.0 & extended source & \\\\\n & & & & & 203.x, 212.0, 302.0, & & \\\\\n & & & & & 303.x, 318.1, 328.0, & & (5)\\\\\n & & & & & 331.x, 333.0 & & \\\\\n & & & & & & & \\\\\n\\hline\n & & & & & & & \\\\\nCygnus Superbubble & ~~73$<l<$87~~ & -7$<b<$+7\n & 1.809 & 4.6 $\\pm$ 1.1 & see Cygnus region & extended source & (5) \\\\\n & & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nCarina Region & 286.5 & 0.5\n & 1.809 & 2.7 $\\pm$ 0.6 & Phase I to IV/& point-like source & (4) \\\\\n & & & & & Cycle-5 & & \\\\\n & & & & & & & \\\\ \n\\hline\n& & & & & & & \\\\\nPerseus/Cas-Tau~~~& 125$<$l$<$168 & -17$<$b$<$28 & 1.809 & 8.4$\\pm$ 1 & \nPhase I to IV/ & low level extended & (4) \\\\\nRegion & & & & & Cycle-5 & emission & \\\\ \n& & & & & & & \\\\ \n\\hline\n& & & & & & & \\\\\nNeutron capture~~~ & ~~300~~~~~ &~~~~~ -30~~~~~ & 2.223 & 3.3$\\pm$ 0.9 & \nVP 1.0 to & & (6) \\\\\nsource & & & & & VP 523.0 & white dwarf & \\\\\n& & & & & ~~~~~~~~ & RE J0317-853 & \\\\\n& & & & & ~~~~~~~~ & as possible source & \\\\ \n& & & & & ~~~~~~~~ & candidate & \\\\\n\\noalign{\\smallskip}\\hline\\hline\n\\end{tabular} \n\\vskip12pt\n{\\bf References}\n\\vskip3pt\n(1) \\cite{morris95}.\n\n(2) \\cite{iyudin94}.\n\n(3) \\cite{schoenf96}.\n\n(4) \\cite{oberlack97}.\n\n(5) \\cite{delrio96}.\n\n(6) \\cite{mcconnell97a}.\n\n(7) \\cite{dupraz97}.\n \n(8) \\cite{iyudin98}. \n%\\end{flushleft}\n\\endlandscape \n\n\n\\clearpage\n\n\n% TABLE 8\n\n\\landscape\n\\def\\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 8}: {Gamma-Ray Burst Source Locations}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c|l||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n & \\multicolumn{3}{c|}{} & & & & \\multicolumn{2}{c|}{} & & \\\\\nBurst & \\multicolumn{3}{c|}{COMPTEL Location} & Accum.\n& (0.75--30) & Detect.\n&\\multicolumn{2}{c|}{Spectral Fit in Telescope Mode$^{\\rm a}$}\n & Variability & References \\\\ \n & & & & Time & [MeV] \n & Signif. & \n & & of Spect. in & \\\\ \n & l & b & Error & & Fluence & & A & $\\alpha$ \n & Single Det. & \\\\\n & & & Radius$^{b}$& & [10$^{-5}$ & &[ph cm$^{-2}$ s$^{-1}$ & & Mode & \\\\\n & [deg] & [deg] & [deg] & [s] & erg cm$^{-2}$] & $\\sigma$\n & MeV$^{-1}$] & & & \\\\\n & & & & & & & & & & \\\\\n\\hline\n\\hline\n & & & & & & & & & & \\\\\nGRB 910425 & 228.1 & -20.6 & 0.92 & 39.27 & 9.07 & 5.7 \n& 0.29\\p 0.04 & 1.8\\p 0.18 & yes ($>$0.6 MeV) & 1, 2, 7, 17, \\\\\n& & & & & & & & & & 20, 22, 23, 24 \\\\\nGRB 910503 & 172.0 & +5.4 & 0.44 & 57.34 & 13.90 & 12.8 & 0.54\\p 0.05 \n& 2.19\\p 0.10 & yes ($>$0.6 MeV) & 1, 2, 7, 17,\\\\\n& & & & & & & & & & 18, 21, 22, 23, \\\\\n& & & & & & & & & & 25, 26 \\\\\nGRB 910601 & 74.1 & -5.4 & 0.46 & 19.83 & 3.72 & 14.4 & 1.11\\p 0.10 \n& 3.41\\p 0.18 & yes ($>$0.6 MeV) & 1, 2, 7, 17,\\\\\n& & & & & & & & & & 20, 22, 23, 24,\\\\\n& & & & & & & & & & 26, 27 \\\\ \nGRB 910627 & 315.1 & +57.3 & 1.63 & 9.13 & 0.56 & 4.0 & 0.16\\p 0.04 \n& 2.31\\p 0.26 & yes ($>$0.6 MeV) & 1, 2, 7, 17,\\\\\n& & & & & & & & & & 20, 22, 23, 26 \\\\\nGRB 910709 & 136.3 & +36.0 & 1.80 & 0.60 & 0.53 & 5.4 & 4.19\\p 0.99 \n& 2.99\\p 0.48 & yes ($>$0.6 MeV) & 1, 2, 7, 26 \\\\\nGRB 910814 & 94.7 & -26.9 & 0.39 & 33.24 & 8.53 & 13.4 & 0.79\\p 0.06 \n& 2.46\\p 0.13 & yes ($>$0.6 MeV) & 1, 2, 7, 17,\\\\\n& & & & & & & & & & 20, 22, 23, 24, 26\\\\\nGRB 911118 & 273.0 & +34.2 & 1.11 & 9.12 & 0.68 & 5.9 & 0.50\\p 0.09 \n& 3.82\\p 0.58 & yes ($>$0.6 MeV) & 1, 2, 7, 17,\\\\\n& & & & & & & & & & 19, 26\\\\\nGRB 920622 & 161.3 & +57.9 & 0.81 & 24.17 & 5.74 & 13.5 & 0.91\\p 0.09 \n& 2.69\\p 0.17 & yes & 1, 2, 3, 6, 19 \\\\\nGRB 920627 & 263.9 & +46.4 & 1.18 & 59.37 & 0.96 & 5.0 & 0.04\\p 0.01 & 2.27\\p 0.40 & & 29, 30 \\\\\nGRB 920830 & 318.0 & -20.1 & 1.35 & 4.05 & 0.40 & 5.4 & 0.32\\p 0.08 \n& 2.51\\p 0.35 & no & 1, 2, 6, 16 \\\\\nGRB 930118 & 328.4 & +22.3 & 1.47 & 4.00 & 0.27 & 3.9 & 0.21\\p 0.07 \n& 2.46\\p 0.55 & no & 1, 2, 6, 16 \\\\\nGRB 930131 & 291.6 & +54.4 & 1.77 & 1.02 & 6.83 & 5.1 & 9.32\\p 2.22 \n& 1.88\\p 0.25 & yes (1--30) MeV & 1, 2, 6, 8, \\\\\n& & & & & & & & & & 9, 14, 15, 16\\\\ \nGRB 930309 & 96.9 & +2.8 & 0.74 & 39.98 & 0.82 & 6.0 & 0.09\\p 0.02 \n& 2.87\\p 0.35 & no & 1, 2, 6, 9,\\\\\n& & & & & & & & & & 13, 16 \\\\\nGRB 930612 & 282.0 & -24.4 & 1.60 & 12.83 & 0.77 & 4.1 & 0.11\\p 0.03 \n& 2.05\\p 0.26 & no & 1, 2\\\\ \nGRB 930704 & 152.5 & +22.4 & 1.08 & 18.15 & 0.44 & 4.0 & 0.08\\p 0.02\n& 2.54\\p 0.40 & yes& 1, 2, 5, 12, 28\\\\\nGRB 931229 & 36.2 & +45.1 & 2.35 & 0.60 & 0.39 & 5.0 & 3.65\\p 1.23\n& 3.32\\p 0.75 & no & 1, 2 \\\\\n& & & & & & & & & & \\\\\n\\hline\n\\hline\\multicolumn{11}{r}{(Table 8 cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\endlandscape\n%\\pagebreak\n\n%\\clearpage\n\n\\landscape\n\n%\\textwidth=30cm\n%\\textheight=6.6truein\n\n%\\def \\p{{$\\pm$}}\n%\\def\\s{{$\\sigma$}}\n\n%\\voffset=-4cm\n\n%\\topmargin=-4cm\n\\footnotesize\n%\\begin{table}\n{\\bf Table 8}: {Gamma-Ray Burst Source Locations (cont.)}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c|l||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n & \\multicolumn{3}{c|}{} & & & & \\multicolumn{2}{c|}{} & & \\\\\nBurst & \\multicolumn{3}{c|}{COMPTEL Location} & Accum.\n& (0.75--30) & Detect.\n&\\multicolumn{2}{c|}{Spectral Fit in Telescope Mode$^{\\rm a}$}\n & Variability & References~~~~~ \\\\ \n & & & & Time & [MeV] \n & Signif. & \n & & of Spect. in & \\\\ \n & l & b & Error & & Fluence & & A & $\\alpha$ \n & Single Det. & \\\\\n & & & Radius & & [10$^{-5}$ & &[ph cm$^{-2}$ s$^{-1}$ & & Mode & \\\\\n & [deg] & [deg] & [deg] & [s] & erg cm$^{-2}$] & $\\sigma$\n & MeV$^{-1}]$ & & & \\\\\n% & & & & & & & & & & \\\\\n\\hline\n\\hline\n& & & & & & & & & & \\\\\nGRB 940217 ~~~~ & 154.5 & -55.5 & 0.69 & 162.79 & 17.40& 18.8 & 0.38 $\\pm$ 0.02\n& 2.60 $\\pm$ 0.07 & yes ($>$ 0.3 MeV) & 1, 2, 4, 10 \\\\\nGRB 940301 & 151.6 & +24.1 & 0.40 & 42.20 & 4.55 & 11.8 & 0.25 $\\pm$ 0.02\n& 2.22 $\\pm$ 0.11 & yes& 1, 2, 5 11,\\\\\n& & & & & & & & & & 12 28 \\\\\nGRB 940314 & 88.0 & -59.6 & 1.43 & 51.00 & 1.43 & 5.2 & 0.11 $\\pm$ 0.02\n& 2.72 $\\pm$ 0.24 & no & 1, 2 \\\\\nGRB 940520 & 62.5 & -31.8 & 0.70 & 30.00 & 2.09 & 6.9 & 0.23 $\\pm$ 0.03 & 2.53 $\\pm$ 0.18 & & 29, 30, 31 \\\\\nGRB 940619 & 9.3 & -26.3 & 1.15 & 102.00 & 2.92 & 4.6 & 0.07 $\\pm$ 0.01& 2.26 $\\pm$ 0.22 & & 29, 30, 31 \\\\\nGRB 940708 & 61.1 & -4.2 & 1.03 & 12.00 & 0.76 & 7.8 & 0.35 $\\pm$ 0.08 & 3.25 $\\pm$0.60 & & 29, 30, 31 \\\\\nGRB 940728 & 243.2 & -29.6 & 1.10 & 11.87 & 0.66 & 3.9 & 0.10 $\\pm$ 0.03 & 2.04 $\\pm$ 0.29 & & 29, 30, 31 \\\\\nGRB 940921 & 322.3 & +44.4 & 0.68 & 24.00 & 4.62 & 11.3 & 0.58 $\\pm$ 0.06& 2.44 $\\pm$ 0.14 & & 29, 30, 31 \\\\\nGRB 941017 & 53.7 & -10.0 & 2.10 & 78.45 & 10.32 & 7.7 & 0.45 $\\pm$ 0.09& 2.57 $\\pm$ 0.27& & 29, 30, 31 \\\\\nGRB 950208 & 107.6 & -3.5 & 1.95 & 62.00 & 3.82 & 5.7 & 0.23 $\\pm$ 0.02 & 2.66 $\\pm$ 0.21 & & 29, 30, 31 \\\\\nGRB 950421 & 272.1 & -39.0 & 1.43 & 3.00 & 0.75 & 5.4 & 0.49 $\\pm$ 0.11 & 2.10 $\\pm$ 0.24 & & 29, 30, 31 \\\\\nGRB 950425 & 277.8 & +23.6 & 0.34 & 70.00 & 21.51 & 18.0 & 0.72 $\\pm$ 0.05 & 2.23 $\\pm$ 0.10& & 29, 30, 31 \\\\\nGRB 950522 & 197.9 & +15.9 & 1.14 & 26.00 & 2.69 & 9.5 & 0.24 $\\pm$ 0.03 & 2.22$\\pm$ 0.18 & & 29, 30, 31 \\\\\nGRB 960808 & 173.5 & +3.95 & 0.91 & 14 & 0.90 & 6.5 & 0.27 $\\pm$ 0.05 & \n2.71$\\pm$ 0.39 & & 32 \\\\\nGRB 961001 & 137.1 & -5.30 & 1.74 & 12 & 1.01 & 3.8 & 0.26 $\\pm$ 0.06 & \n2.36$\\pm$ 0.40 & & 32 \\\\\n& & & & & & & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\noindent\n$^{a}$ Power-law fit: dn/dE=\nA (ph cm$^{-2}$ s$^{-1}$ MeV$^{-1}$) $\\cdot$ (E/1 MeV) $^{-\\alpha}$\\\\\n$^{b}$ The error radius is defined as the angular radius of a circle having the same area as the irregularly shaped COMPTEL 1$\\sigma$ confidence region.\\\\\n%\\end{table}\n\\vskip8pt\n\\noindent\n%\\vskip-3cm\n%\\begin{table}\n{\\bf References}\n\\vskip12pt\n\\begin{flushleft}\n\\begin{tabular}{llllll}\n1. \\cite{kippen95d}. & 7. \\cite{hanlon94a}. & 13. \\cite{bennett93}. & 19. \\cite{connors93b}. & 25. \\cite{schaefer94}. & 31. \\cite{kippen98b}. \\\\ \n%\n2. \\cite{kippen95c}. & 8. \\cite{ryan94b}. & 14. \\cite{ryan93}. & 20. \\cite{connors93a}. & 26. \\cite{hanlon94b}. & 32. \\cite{connors97}. \\\\\n%\n3. \\cite{greiner95}. & 9. \\cite{kippen94c}. & 15. \\cite{kippen93}. & 21. \\cite{winkler92}. & 27. \\cite{share94}. & \\\\\n%\n4. \\cite{winkler95}. & 10. \\cite{kippen94a}. & 16. \\cite{varendorff93}. & 22. \\cite{varendorff92}. & 28. \\cite{hanlon95}. & \\\\\n%\n5. \\cite{kippen95b}. & 11. \\cite{kippen94b}. & 17. \\cite{winkler93b}. & 23. \\cite{schoenf91}. & 29. \\cite{kippen96}. & \\\\ \n%\n6. \\cite{kippen95a}. & 12. \\cite{ryan94a}. & 18. \\cite{winkler93a}. & 24. \\cite{collmar93}. & 30. \\cite{kippen98a}. & \\\\\n%\n%\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\n\\endlandscape\n\n\n\\clearpage\n\n\n \n\n% begin TABLE 9\n\n%\\clearpage\n\n\n\\landscape\n\\def\\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 9}: {Solar Flare Detections}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n& & & & & & & & & & \\\\\n% &\\multicolumn{4}{c|}{}&\\multicolumn{4}{c|}{}&\\multicolumn{2}{c||}{}\\\\\nCOMPTEL & TJD & GOES Start & GOES & BATSE & BATSE & COMPTEL & COMPTEL & \nCOMPTEL & Peak BATSE & GRO mass \\\\ \nFlare No. & & time & Class & Flare No. & Trigger No. & Int. time (s) & \ntotal cts & Peak cts & cts/area & g/cm$^{2}$ \\\\ \n& & & & & & & & & & \\\\\n\\hline\n\\hline\n & & & & & & & & & & \\\\\nsf 910604-033651 & 8411 & 03:37 & X 12.0 & 387 & 262 & 900 & ${\\ast}$\n& ${\\ast}$ & N / A & 39.5 \\\\\nsf 910606-005900 & 8413 & 00:54 & X 12.0 & 388 & 281 & 6845 & 31198 \n& 589 & N / A & 44.4 \\\\\nsf910609-013433 & 8416 & 01:37 & X 10.0 & 419 & 299 & 5075 & 5880 \n& 550 & N / A & 22.8 \\\\ \nsf 910611-015335 & 8418 & 02:09 & X 12.0 & 485 & 319 & 1440 & 13056 \n& 565 & N / A & 25.8 \\\\\nsf 910630-025434 & 8437 & 02:43 & M 5.0 & 665 & 468 & 600 & 2761 \n& 440 & 3.71 E+05 & 6.8 \\\\\nsf 910702-193346 & 8439 & 19:35 & M 4.6 & 684 & 479 & 830 & 2158 \n& 319 & 4.67 E+05 & 6.5 \\\\\nsf 910717-062456 & 8454 & 06:18 & X 1.1 & 786 & 544 & 1350 & 490 \n& 28 & 3.79 E+05 & 6.7 \\\\\nsf 910825-004153 & 8493 & 00:31 & X 2.1 & 1140 & 721 & 837 & 3332 \n& 89 & 2.22 E+05 & 6.1 \\\\\nsf 911005-065039& 8534& 08:00 & C 6.1 & 1410 & N / A&812 & $\\dagger$ \n& $\\dagger$ & 2.2 E+03 & 5.1 \\\\ \nsf 911014-173340 & 8543 & 17:34 & M 6.6 & 1491 & 901 & 500 & $\\dagger$ \n& $\\dagger$ & 2.35 E+05 & 25.5 \\\\ \nsf 911015-091400 & 8544 & 09:12 & C 7.7 & 1498 & 904 & 352 & 343 \n& 50 & 2.14 E+04 & 24.7 \\\\\nsf 911024-041512 & 8553 & 05:30 & X 2.1 & 1552 & 922 & 360 & 2800 \n& 681 & 3.5 ~E+03 & 22 \\\\\nsf 911027-020404 & 8556 & 02:06 & X 1.9 & 1643 & 943 & 807 & 1782 \n& 142 & 3.35 E+05 & 25 \\\\\nsf 911027-053621 & 8556 & 05:38 & X 6.1 & 1648 & 945 & 2000 & 24206 \n& 817 & N / A & 25 \\\\\nsf 911030-061616 & 8559 & 06:11 & X 2.5 & 1723 & 965 & 2500 & 2463 \n& 39 & 2.00 E+05 & 24 \\\\\nsf 911030-191140 & 8559 & 19:13 & M 4.3 & 1743 & 968 & 500 & 413 \n& 38 & 1.60 E+05 & 24 \\\\\nsf 911030-222354 & 8559 & 22:23 & C 5.3 & 1749 & 970 & 236 & 778 \n& 46 & 1.95 E+04 & 24 \\\\\nsf 911115-223311 & 8575 & 22:34 & X 1.5 & 1901 & 1066 & 876 & 3214 \n& 329 & 1.30 E+06 & 6.4 \\\\\nsf 911130-034430 & 8590 & 03:44 & M 5.7 & 1928 & 1131 & 447 & 362 \n& 73 & 7.18 E+05 & 8.6 \\\\\nsf 911215-020341 & 8605 & 02:01 & C 3.5 & 2087 & 1175 & 533 & $\\dagger$ \n& $\\dagger$ & 1.53 E+04 & 25.1 \\\\\nsf 911215-113305 & 8605 & 11:38 & C 8.6 & 2096 & 1178 & 658 & $\\dagger$ \n& $\\dagger$ & 1.98 E+05 & 24.6 \\\\\nsf 911215-183201 & 8605 & 18:29 & M 1.4 & 2102 & 1181 & 483 & $\\dagger$ \n& $\\dagger$ & 4.89 E+05 & 23.9 \\\\\nsf 911220-135723 & 8610 & 14:00 & X 3.5 & 2174 & 1199 & 800 & 2706 \n& 169 & 1.20 E+06 & 11.7 \\\\\nsf 920126-145023 & 8647 & 14:32 & C 5.3 & 2511 & 1316 & 300 & 438 \n& 36 & 1.75 E+03 & 6.8 \\\\\nsf 920202-090451 & 8654 & 08:59 & M 2.3 & 2551 & 1336 & 500 & 214 \n& 68 & 1.13 E+05 & 14.0 \\\\\nsf 920202-224407 & 8654& 22.46 & M 1.3 & 3088 & 1340 & 500 & 853 \n& 68 & 1.82 E+04 & 17.5 \\\\\nsf 920204-075349 & 8656 & 07:41 & C 3.7 & 2596 & 1351 & 250 & $\\dagger$ \n& $\\dagger$ & 4.40 E+03 & 22.7 \\\\\n& & & & & & & & & & \\\\\n\\hline\n\\hline\n%\\multicolumn{11}{r}{(Table 9 cont.)}\\\\\n\\end{tabular}\n%\\end{flushleft}\n%\\end{table}\n%\\endlandscape\n%\\pagebreak\n\n\\vskip6pt\n{\\bf Notes:}\n%\\vskip6pt\n\\noindent\n$\\dagger$ ~~Marginal detection. \\\\\n\\hspace{1,1cm}$\\ast$ ~~Detector saturation.\n\\end{flushleft} \n%\\include{notes} \n \\endlandscape\n\n\n\n\\clearpage\n\n% TABLE 10 begin\n\n\n%\\landscape\n\\footnotesize\n{\\bf Table 10}:\n{Upper Limits to Galactic Black Hole Candidates} \\\\\n\\hspace{2cm}{$|b|<10^\\circ$} \\\\\n\\begin{flushleft}\n% \\vskip12pt\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c||}\n%\\tablehead{\\hline\\hline \\noalign{\\smallskip}\n\\hline\\hline \\noalign{\\smallskip}\n & \\multicolumn{2}{c|}{} & \\multicolumn{4}{c|}{} & & \\\\\nSource & \\multicolumn{2}{c|}{Position} \n & \\multicolumn{4}{c|}{2$ \\sigma$ Flux (10$^{-5}$ \ncm$^{-2}$ s$^{-1}$)} & Note & Ref. \\\\\n & & & & & & & & \\\\\n & l & b & (0.75--1) & (1--3) & (3--10) & (10--30)\n & & \\\\\n & [deg] & [deg] & [MeV] & [MeV] & [MeV] & [MeV] & & \\\\\n& & & & & & & & \\\\\n\\hline\n\\hline \n%\\tabletail{\\hline\\multicolumn{9}{r}{(Table 11 cont.)}\\\\} \n%\\tablelasttail{\\noalign{\\smallskip}\\hline\\hline} \n%\\begin{supertabular}{||l|c|c|c|c|c|c|c|c||}\n& & & & & & & & \\\\\nGRO J1719-24 & 2.4 & 7.0 & $<$3.5 & 7.8$\\pm$2.6 & $<$2.2 & $<$0.78 \n & a,b,c & (1) \\\\ \n& & & $<$3.68 & $<$ 3.64 & $<$1.54 & $<$0.76 & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nGRS 1758--258 & 4.5 & -1.4 & $<$3.5 & $<$3.8 & $<$1.7 & $<$0.64 \n & a,c & (1) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nGRS 1826--238 & 9.3 & -6.0 & $<$6.8 & $<$8.8 & $<$3.4 & $<$1.10 \n & a,c & (1) \\\\ \n& & & $<$7.2 & $<$3.6 & $<$2.97 & $<$1.22 & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nEXO 1846--031 & 29.9 & -0.9 & $<$5.0 & $<$3.2 & $<$2.8 & $<$0.88 \n & a,c & (1) \\\\ \n& & & $<$4.5 & $<$4.63 & $<$1.99 & $<$1.09 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nSS433 & 39.7& -2.2 & $<$4.3 & $<$3.0 & $<$2.8 & $<$0.78 \n & a,c & (1) \\\\\n & & & $<$9.13 & $<$4.37 & $<$2.41 & $<$0.76 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nGRS 1915+105 & 45.3& -0.9 & $<$5.3 & $<$3.4 & $<$3.2 & $<$0.76 \n & a,c & (1) \\\\\n & & & 5.70$\\pm$2.69 & $<$4.29 & $<$2.56 & $<$0.76 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\n4U 1957+115 & 51.3 & -9.30 & $<$2.8 & $<$9.8 & 3.6$\\pm$1.0 & $<$0.86 \n & a,b,c & (1) \\\\\n & & & $<$4.05 & $<$8.17 & $<$3.66 & $<$0.96 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nGS 2000+251 & 63.4 & -3.1 & $<$2.8 & $<$3.4 & $<$3.5 & $<$0.66 \n & a,c & (1) \\\\\n(QZ Vul) & & & $<$4.55 & $<$4.38 & $<$2.14 & $<$0.63 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nGS 2023+338 & 73.2 & -2.2 & $<$6.3 & $<$6.8 & $<$2.6 & $<$0.54 \n & a,c & (1) \\\\\n(V 404) & & & 10.25$\\pm$3.03 & 8.95$\\pm$2.50 & $<$2.33 & $<$0.58 \n & a,b,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\ \nWR 148 & 90.08 & 6.47 & $<$4.60 & $<$9.87 & $<$2.71 & $<$0.65 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nA 0620--00 & 210.0 & -6.5 & $<$3.5 & $<$3.8 & $<$2.4 & $<$0.98 \n & a,c & (1) \\\\\n(Nova Mon 1975) & & & $<$5.46 & $<$5.38 & $<$3.17 & $<$1.51 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n%\\hline\n%& & & & & & & & \\\\\n\\hline\\multicolumn{8}{r}{(Table 10 cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\endlandscape\n\n\\clearpage\n\n\n%\\landscape\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c||}\n\\hline \\hline \\noalign{\\smallskip} \n & \\multicolumn{2}{c|}{} & \\multicolumn{4}{c|}{} & & \\\\\nSource & \\multicolumn{2}{c|}{Position} \n & \\multicolumn{4}{c|}{2$ \\sigma$ Flux (10$^{-5}$ \ncm$^{-2}$ s$^{-1}$)} & Note & Ref. \\\\\n & & & & & & & & \\\\\n & l & b & (0.75--1) & (1--3) & (3--10) & (10--30)\n & & \\\\\n & [deg] & [deg] & [MeV] & [MeV] & [MeV] & [MeV] & & \\\\\n& & & & & & & & \\\\\n\\hline\n\\hline\n& & & & & & & & \\\\\nGRS 1009--45 & 275.9 & 9.4 & $<$7.0 & $<$5.6~~ & $<$3.6~~ & $<$1.06 \n & a,c & (1) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\n(Nova Vel 1993)& & & $<$11.69 & $<$5.52 & $<$1.94 & $<$0.93 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\nGRS 1124--684 & 295.0 & -7.1 & $<$6.8 & $<$3.4 & $<$4.7 & $<$1.28 \n & a,c & (1) \\\\\n (Nova Mus 1991)& & & $<$4.4 & $<$4.55 & $<$2.05 & $<$1.32 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nGS 1354--645 & 310.0 & -2.8 & $<$9.8 & $<$6.8 & $<$2.7 & $<$2.00 \n & a,c & (1) \\\\\n & & & $<$10.2 & $<$7.89 & $<$4.61 & $<$1.17 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nTrA X--1 & 320.32 & -4.43 & 8.58$\\pm$3.80 & $<$12.97 & $<$3.17 & $<$2.60 \n & a,b,c & (2) \\\\\n (A1524-617)& & & $<$7.3 & $<$8.2 & $<$2.8 & $<$2.80 \n & a,c & (1) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\n4U 1543--475 & 330.9 & 5.4 & $<$6.0 & $<$4.2 & $<$1.7 & $<$0.74 \n & a,c & (1) \\\\\n & & & $<$7.45 & $<$8.97 & $<$2.23 & $<$0.96 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\n4U 1630--472 & 336.9 & 0.3 & $<$3.3 & $<$3.4 & $<$1.8 & $<$1.20 \n & a,c & (1) \\\\\n & & & $<$3.93 & $<$4.22 & $<$1.96 & $<$1.03 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nGX 339--4 & 338.9 & -4.3 & $<$0.35 & $<$3.6 & $<$1.8 & $<$0.74 \n & a,c & (1) \\\\\n & & & $<$5.48& $<$7.75 & $<$2.60 & $<$0.78 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nGRO J 1655--40 & 344.9 & 2.5 & $<$3.8 & $<$3.8 & $<$1.7 & $<$1.16 \n & a,c & (1) \\\\\n (Nova Sco 1994)& & & $<$7.07 & $<$5.42 & $<$1.73 & $<$0.99 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nH 1741--322 & 357.1 & -1.6 & $<$4.0 & $<$4.2 & $<$2.0 & $<$0.72 \n & a,c & (1) \\\\\n & & & $<$3.68 & $<$6.68 & $<$2.26 & $<$0.60 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\n4U 1755--338 & 357.2 & -4.9 & $<$4.0 & & $<$2.0 & $<$0.72 \n & a,c & (1) \\\\\n(Nova Oph 1977) & & & $<$3.67 & $<$4.97 & $<$2.17 & $<$0.60 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\nH 1705--250 & 358.6 & 9.1 & $<$4.0 & $<$4.2 & $<$2.0 & $<$0.86 \n & a,c & (1) \\\\\n & & & $<$4.93 & $<$6.09 & $<$1.58 & $<$0.60 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n%\\hline\n%& & & & & & & & \\\\\n\\hline\\multicolumn{8}{r}{(Table 10 cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{landscape}\n\n\\clearpage\n\n\n%\\landscape\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c||}\n\\hline \\hline \\noalign{\\smallskip} \n & \\multicolumn{2}{c|}{} & \\multicolumn{4}{c|}{} & & \\\\\nSource & \\multicolumn{2}{c|}{Position} \n & \\multicolumn{4}{c|}{2$ \\sigma$ Flux (10$^{-5}$ \ncm$^{-2}$ s$^{-1}$)} & Note & Ref. \\\\\n & & & & & & & & \\\\\n & l & b & (0.75--1) & (1--3) & (3--10) & (10--30)\n & & \\\\\n & [deg] & [deg] & [MeV] & [MeV] & [MeV] & [MeV] & & \\\\\n& & & & & & & & \\\\\n\\hline \\hline\n& & & & & & & & \\\\\nGRS 1734--292 & 358.84~~~~~ & 1.40 & $<$3.68~~ & $<$5.69~~ & $<$1.53 & $<$1.25 \n & a,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n& & & & & & & & \\\\\n 1E 1740.7--2942 & 359.1 & -0.1 & $<$4.0 & $<$ 4.2 & $<$2.0 & $<$1.66 \n & a,c & (1) \\\\\n & & & $<$3.67 & $<$5.53 & $<$2.17 & 0.93$\\pm$0.36\n & a,b,c & (2) \\\\\n& & & & & & & & \\\\\n\\hline\n\\hline \n\\end{tabular} \n\\vskip6pt\n{\\bf Notes}\n\\vskip6pt\n\\noindent\n(a) Model for diffuse galactic emission included in analysis. \\\\\n\n(b) A positive flux measurement does not \n necessarily indicate \n \\phantom{(b)} a source detection (see ref. 1). \n\n(c) All upper limit fluxes are applied to data from Phase \n \\phantom{(c) }I~to~III. \n\n\\vskip6pt\n{\\bf References}\n\\vskip6pt\n(1) \\cite{mcconnell96}.\n \n(2) \\cite{vandijk96}.\n\n\\end{flushleft} \n%\\include{notes} \n \n%\\endlandscape\n\n\n\n\\clearpage\n\n\n% TABLE 11a begin\n\n\\landscape\n\\def\\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 11a}: {COMPTEL 2$\\sigma$ upper limits to AGN (EGRET sources and Seyferts)}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c|l||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n&\\multicolumn{4}{c|}{}&\\multicolumn{4}{c|}{}&\\multicolumn{2}{c||}{}\\\\\nName & \\multicolumn{4}{c|}{Location} & \\multicolumn {4}{c|}{Upper limit (10$^{-5}$ cm$^\n{-2}$ sec$^{-1}$)} & Type& Other name\\\\ \n&RA &DEC &l&b& (0.75--1.0) & (1 - 3) & (3 - 10) & (10 - 30) & & \\\\ \n& [deg] & [deg] &[deg] &[deg] & [MeV] & [MeV] & [MeV] & [MeV] & & \\\\\n\\hline\n\\hline\n & & & & & & & & & & \\\\\n0003 + 199 & 1.59 & 20.21 & 108.77 & - 41.42 & $<$ 4.24 & $<$ 4.92 \n& $<$ 5.03 & $<$ 0.90 & SY & MRK 335 \\\\\n0007 + 107 & 2.63 & 10.97 & 106.98 & - 50.63 & $<$ 3.70 & $<$ 5.12 \n& $<$ 2.46 & $<$ 0.89 & SY & IIIZW2 \\\\\n0121 - 590 & 20.94 & - 58.81 & 295.08 & - 57.82 & $<$ 4.67 \n& $<$ 7.72 & $<$ 2.14 & $<$ 0.84 & SY & FAIRALL 9 \\\\ \n0130-171 & 23.18 & -16.91 & 168.12 & -76.02 & $<$ 6.60\n& $<$ 7.70 & $<$ 7.84 & $<$ 1.52 & 2 EG & \\\\\n0202 + 149 & 31.21 & 15.24 & 147.93 & -44.04 & $<$ 8.57 \n& $<$ 10.56 & $<$ 2.51 & $<$ 0.90 & 2 EG & \\\\\n0208 - 512 & 32.69 & -51.02 & 276.10 & -61.78 & $<$ 8.98 \n& $<$ 12.94 & $<$ 2.97 & $<$ 1.76 & 2 EG & \\\\\n0219 + 428 & 35.66 & 43.03 & 140.14 & -16.77 & $<$ 2.95 \n& $<$ 3.74 & $<$ 2.17 & $<$ 0.80 & 2 EG & \\\\\n0234 + 285 & 39.47 & 28.80 & 149.47 & -28.53 & $<$ 2.94 \n& $<$ 3.78 & $<$ 1.90 & $<$ 0.76 & 2 EG & \\\\\n0235 + 164 & 39.66 & 16.62 & 156.77 & -39.11 & $<$ 3.03 \n& $<$ 6.24 & $<$ 3.70 & $<$ 1.20 & 2 EG & \\\\ \n0240 - 002 & 40.67 & -0.01 & 172.11 & -51.93 & $<$ 7.15\n& $<$ 8.64 & $<$ 2.84 & $<$ 1.19 & SY & NGC 1068 \\\\ \n0420 - 014 & 65.82 & -1.34 & 195.29 & -33.14 & $<$ 3.33 \n& $<$ 4.38 & $<$ 2.59 & $<$ 1.11 & 2 EG & \\\\\n0430 + 052 & 68.29 & 5.35 & 190.37 & -27.40 & $<$ 3.74 \n& $<$ 6.42 & $<$ 2.62 & $<$ 0.98 & SY & 3C 120 \\\\\n0440 - 003 & 70.66 & -0.30 & 197.20 & -28.46 & $<$ 2.59\n& $<$ 4.00 & $<$ 1.83 & $<$ 0.94 & 2 EGS & \\\\ \n0446 + 112 & 72.28 & 11.35 & 187.43 & -20.74 & $<$ 2.67 \n& $<$3.42 & $<$1.68 & $<$ 0.65 & 2 EG & \\\\ \n0454 - 463 & 73.97 & -46.27 & 251.97 & - 38.81 & $<$ 2.98\n& $<$ 4.08 & $<$ 5.97 & $<$ 0.88 & 1 EG & \\\\\n0454 - 234 & 74.26 & -23.42 & 223.71 & -34.90 & $<$ 2.95\n& $<$ 9.08 & $<$ 2.39 & $<$ 1.19 & 1 EG & \\\\\n0458 - 020 & 75.30 & -1.99 & 201.45 & -25.30 & $<$ 2.57 \n& $<$ 3.60 & $<$ 1.97 & $<$ 0.68 & 2 EG & \\\\\n0513 - 002 & 79.05 & -0.15 & 201.69 & -21.13 & $<$ 2.50 \n& $<$ 3.42 & $<$ 2.27 & $<$ 0.61 & SY & ARK 120 \\\\\n0521-365 & 80.74 & -36.46 & 240.61 & -32.72 & $<$ 4.03 \n& $<$ 5.40 & $<$ 2.66 & $<$ 1.03 & 2 EG & \\\\\n0528 + 134 & 82.74 & 13.53 & 191.37 & -11.01 & $<$ 6.79 \n& 13.44 & 5.02 & $<$ 1.46 & 2 EG & \\\\\n0537 - 441 & 84.71 & -44.08 & 250.08 & -31.09 & $<$ 5.32 \n& $<$ 6.05 & $<$ 2.07 & $<$ 1.02 & 2 EG & \\\\\n0551 + 464 & 88.73 & 46.44 & 165.73 & 10.41 & $<$ 2.34 \n& $<$ 3.16 & $<$ 1.67 & $<$ 0.65 & SY & MCG+8-11-11 \\\\\n0716 + 714 & 110.48 & 71.34 & 143.98 & 28.02 & $<$ 2.87 \n& $<$ 3.60 & $<$ 3.72 & $<$ 0.68 & 2 EG & \\\\\n0735 + 178 & 114.53 & 17.70 & 201.85 & 18.07 & $<$ 1.56 \n& $<$ 3.21 & $<$ 1.20 & $<$ 1.05 & 2 EG & \\\\\n0805 - 077 & 122.06 & -7.85 & 229.04 & 13.16 & $<$ 11.57 \n& $<$ 16.50 & $<$ 3.85 & $<$ 1.59 & 2 EG & \\\\\n0804 + 499 & 122.16 & 49.85 & 169.16 & 32.56 & $<$ 2.16 \n& $<$ 2.63 & $<$ 1.04 & $<$ 1.95 & 2 EG & \\\\\n& & & & & & & & & & \\\\\n\\hline\n%\\hline\n\\multicolumn{11}{r}{(Table 11a cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\endlandscape\n%\\pagebreak\n\n%\\clearpage\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\landscape\n\\def\\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 11a}: {COMPTEL 2$\\sigma$ upper limits to AGN (EGRET sources and Seyferts (cont.))}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c|l||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n&\\multicolumn{4}{c|}{}&\\multicolumn{4}{c|}{}&\\multicolumn{2}{c||}{}\\\\\nName & \\multicolumn{4}{c|}{Location} & \\multicolumn {4}{c|}{Upper limit (10$^{-5}$ cm$^{-2}$ sec$^{-1}$)} & Type& Other name \\\\ \n&RA &DEC &l&b& (0.75--1.0) & (1 - 3) & (3 - 10) & (10 - 30) & & \\\\ \n& [deg] & [deg] &[deg] &[deg] & [MeV] & [MeV] & [MeV] & [MeV] & & \\\\\n\\hline\n\\hline\n & & & & & & & & & & \\\\\n0827 + 243 & 127.71 & 24.18 & 200.02 & 31.87 & $<$ 1.92 \n& $<$ 1.97 & $<$ 1.05 & $<$ 1.10 & 2 EG & \\\\\n0829 + 046 & 127.95 & 4.50 & 220.69 & 24.33 & $<$ 2.13 \n& $<$ 2.98 & $<$ 3.52 & $<$ 1.56 & 2 EG & \\\\\n0836 + 710 & 130.36 & 70.89 & 143.54 & 34.43 & $<$ 2.89 \n& $<$ 3.55 & $<$ 2.39 & $<$ 0.66 & 2 EG & \\\\\n0917 + 449 & 140.25 & 44.70 & 175.70 & 44.82 & $<$ 3.04 \n& $ $ 2.30 & $<$ 0.87 & $<$ 1.16 & 2 EG & \\\\\n0931 + 275 & 143.57 & 27.33 & 200.83 & 46.47 & $<$ 1.68 \n& $<$ 1.89 & $<$ 0.94 & $<$ 0.85 & SY & MCG+5-23-16 \\\\\n0954 + 556 & 149.41 & 55.38 & 158.60 & 47.93 & $<$ 1.39 \n& $<$ 4.84 & $<$ 0.99 & $<$ 0.62 & 2 EG & \\\\\n0954 + 658 & 149.69 & 65.56 & 145.75 & 43.13 & $<$ 2.70 \n& $<$ 3.35 & $<$ 1.94 & $<$ 0.62 & 2 EG & \\\\\n1020 + 201 & 155.88 & 19.84 & 217.03 & 55.44 & $<$ 1.70 \n& $<$ 2.89 & $<$ 1.18 & $<$ 0.90 & SY & NGC 3227 \\\\\n1101 + 384 & 166.11 & 38.21 & 179.83 & 65.03 & $<$ 2.50 \n& $<$ 4.58 & $<$ 0.98 & $<$ 0.69 & 2 EG & MRK 421 \\\\\n1127 - 145 & 172.53 & -14.82 & 275.28 & 43.64 & $<$ 2.61 \n& $<$ 3.66 & $<$ 7.73 & 0.82 & 2 EG & \\\\\n1136 - 374 & 174.76 & -37.74 & 287.46 & 22.95 & $<$ 3.41 \n& $<$ 7.22 & $<$ 2.49 & $<$ 1.44 & SY & NGC 3783 \\\\\n1156 + 295 & 179.89 & 29.24 & 199.42 & 78.38 & $<$ 2.42 \n& $<$ 3.17 & $<$ 4.80 & 0.80 & 2 EG & \\\\\n1200 + 448 & 180.79 & 44.54 & 148.88 & 70.08 & $<$ 2.56 \n& $<$ 3.49 & $<$ 1.95 & $<$ 1.04 & SY & NGC 4051 \\\\\n1208 + 396 & 182.63 & 39.41 & 155.08 & 75.06 & $<$ 2.88 \n& $<$ 3.85 & $<$ 2.13 & 1.11 & SY & NGC 4151 \\\\\n1219 + 285 & 185.38 & 28.23 & 201.74 & 83.29 & $<$ 2.30 \n& $<$ 3.09 & $<$ 2.34 & $<$ 0.84 & 1 EG & \\\\\n1219 + 285 & 185.38 & 28.23 & 201.74 & 83.29 & $<$ 2.30 \n& $<$ 3.09 & $<$ 2.34 & $<$ 0.84 & 2 EGS & \\\\\n1226 + 023 & 187.28 & 2.05 & 289.95 & 64.36 & $<$ 2.41 \n& 9.66 & 5.19 & $<$ 0.89 & 2 EG & 3C 273 \\\\ \n1229 - 021 & 188.00 & -2.40 & 293.16 & 60.10 & $<$ 2.38 \n& $<$ 5.56 & $<$ 3.84 & $<$ 0.74 & 2 EG & \\\\\n1237 - 050 & 189.92 & -5.35 & 297.49 & 57.40 & $<$ 2.50 \n& $<$ 3.07 & $<$ 1.98 & $<$ 0.95 & SY & NGC 4593 \\\\\n1253 - 055 & 194.04 & -5.79 & 305.10 & 57.06 & $<$ 3.23 \n& $<$ 6.64 & $<$ 2.91 & $<$ 0.97 & 2 EG & 3C 279 \\\\\n1313 - 333 & 199.03 & -33.65 & 308.80 & 28.94 & $<$ 2.80 \n& $<$ 3.48 & $<$ 2.38 & $<$ 0.70 & 2 EG & \\\\\n1317 + 520 & 199.94 & 51.80 & 112.63 & 64.76 & $<$ 2.92 \n& $<$ 4.04 & $<$ 2.18 & $<$ 1.27 & 2 EG & \\\\\n1322 - 428 & 201.37 & -43.02 & 309.52 & 19.42 & $<$ 5.60 \n& $<$ 12.04 & $<$ 3.87 & $<$ 0.84 & 2 EG & CEN A \\\\\n1331 + 170 & 203.40 & 16.82 & 348.51 & 75.81 & $<$ 4.57 \n& $<$ 3.91 & $<$ 2.26 & $<$ 0.68 & 2 EG & \\\\\n1333 - 340 & 203.96 & -34.29 & 313.28 & 27.69 & $<$ 2.54 \n& $<$ 3.45 & $<$ 1.79 & $<$ 0.71 & SY & MCG-6-30-15 \\\\\n1346 - 300 & 207.32 & -30.31 & 317.49 & 30.92 & $<$ 2.71 \n& $<$ 3.65 & $<$ 1.76 & $<$ 0.70 & SY & IC4329A \\\\\n& & & & & & & & & & \\\\\n\\hline\n%\\hline\n\\multicolumn{11}{r}{(Table 11a cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\endlandscape\n%\\pagebreak\n\n%\\clearpage\n\n\n\n\\landscape\n\\def\\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 11a}: {COMPTEL 2$\\sigma$ upper limits to AGN (EGRET sources and Seyferts (cont.))}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c|l||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n&\\multicolumn{4}{c|}{}&\\multicolumn{4}{c|}{}&\\multicolumn{2}{c||}{}\\\\\nName & \\multicolumn{4}{c|}{Location} & \\multicolumn {4}{c|}{Upper limit (10$^{-5}$ cm$^{-2}$ sec$^{-1}$)} & Type& Other name \\\\ \n&RA &DEC &l&b& (0.75--1.0) & (1 - 3) & (3 - 10) & (10 - 30) & & \\\\ \n& [deg] & [deg] &[deg] &[deg] & [MeV] & [MeV] & [MeV] & [MeV] & &\\\\\n\\hline\n\\hline\n & & & & & & & & & & \\\\\n1460 - 076 & 212.24 & -7.88 & 333.88 & 50.28 & $<$ 4.48 \n& $<$ 7.51 & $<$ 1.74 & $<$ 0.68 & 2 EG & \\\\\n1410 - 029 & 213.31 & -3.21 & 339.15 & 53.81 & $<$ 3.80 \n& $<$ 10.68& $<$ 1.69 & $<$ 0.69 & SY & NGC 5506 \\\\\n1415 - 253 & 214.49 & 25.14 & 31.96 & 70.50 & $<$ 6.36 \n& $<$ 14.14& $<$ 4.49 & $<$ 1.20 & SY & NGC 5548 \\\\\n1424 - 418 & 216.99 & -42.10 & 321.45 & 17.27 & $<$ 3.22 \n& $<$ 3.44 & $<$ 3.39 & $<$ 0.98 & 2 EGS & \\\\\n1510 - 089 & 228.21 & -9.10 & 351.29 & 40.14 & $<$ 6.63 \n& $<$ 10.74& $<$ 4.41 & $<$ 1.29 & 2 EG & \\\\\n1517 + 656 & 229.46 & 65.43 & 102.26 & 45.38 & $<$ 4.68 \n& $<$ 7.21 & $<$ 10.07 & $<$ 4.13 & O & \\\\\n1604 + 159 & 241.78 & 15.86 & 29.38 & 43.41 & $<$ 4.02 \n& $<$ 16.26& $<$ 8.21 & $<$ 1.81 & 2 EG & \\\\\n1606 + 106 & 242.19 & 10.49 & 23.03 & 40.79 & $<$ 3.99 \n& $<$ 6.53 & $<$ 6.43 & 1.55 & 2 EG & \\\\\n1611 + 343 & 243.42 & 34.21 & 55.15 & 46.38 & $<$ 5.70 \n& $<$ 6.28 & 3.21 & $<$ 1.46 & 2 EG & \\\\\n1622 - 253 & 246.44 & -25.46 & 352.14 & 16.32 & $<$ 2.23 \n& $<$ 3.02 & $<$ 1.58 & $<$ 0.70 & 2 EG & \\\\\n1622 - 297 & 246.52 & -29.85 & 348.82 & 13.32 & $<$ 2.44 \n& $<$ 3.12 & $<$ 1.62 & $<$ 0.83 & 2 EG & \\\\\n1633 + 382 & 248.81 & 38.14 & 61.09 & 42.34 & $<$ 5.45 \n& $<$ 6.56 & $<$ 6.78 & $<$ 2.16 & 2 EG & \\\\ 1730 - 130 & 263.26 & -13.08 & 12.30 & 10.81 & $<$ 2.07 \n& $<$ 6.00 & $<$ 2.35 & $<$ 0.66 & 2 EG & \\\\\n1739 + 522 & 265.15 & 52.19 & 79.56 & 31.75 & $<$ 3.27 \n& $<$ 8.74 & $<$ 4.65 & 0.99 & 2 EG & \\\\\n1741 - 038 & 265.99 & -3.83 & 21.59 & 13.13 & $<$ 4.01 \n& $<$ 4.19 & $<$ 5.43 & $<$ 0.76 & 1 EG & \\\\\n1908 - 201 & 287.79 & -20.12 & 16.87 & -13.22 & $<$ 2.13 \n& $<$ 2.90 & $<$ 2.63 & $<$ 1.08 & 2 EG & \\\\\n1916 - 587 & 290.31 & -58.67 & 338.18 & -26.71 & $<$ 3.42 \n& $<$ 5.00 & $<$ 3.00 & $<$ 1.04 & SY & ESO 141-55 \\\\\n1933 - 400 & 294.32 & -39.97 & 359.16 & -25.37 & $<$ 2.83 \n& $<$ 3.34 & $<$ 1.74 & $<$ 0.84 & 2 EG & \t\t\\\\\n1939 - 104 & 295.67 & -10.32 & 29.35 & -16.01 & $<$ 5.43 \n& $<$ 3.62 & $<$ 2.27 & $<$ 0.79 & SY & NGC 6814 \t\\\\\n2005 - 489 & 302.35 & -48.83 & 350.37 & -32.60 & $<$ 3.74 \n& $<$ 4.96 & $<$ 2.49 & $<$ 0.97 & 1 EG & \t\t\t\\\\\n2022 - 077 & 306.41 & -7.59 & 36.90 & -24.38 & $<$ 3.28 \n& $<$ 4.44 & $<$ 2.38 & $<$ 1.04 & 2 EG & \t\t\t\\\\\n2041 - 109 & 311.04 & -10.73 & 35.97 & -29.86 & $<$ 5.07 \n& $<$ 6.56 & $<$ 2.52 & $<$ 1.08 & SY & MRK 509\t\t\\\\\n2052 - 474 & 314.07 & -47.25 & 352.59 & -40.38 & $<$ 4.42 \n& $<$ 5.84 & $<$ 2.93 & $<$ 1.03 & 2 EG & \t\t\t\\\\\n2155 - 304 & 329.72 & -30.23 & 17.73 & -52.25 & $<$ 5.37 \n& $<$ 5.36 & $<$ 2.93 & $<$ 1.35 & O & \t\t\t\\\\\n2209 + 236 & 333.02 & 23.92 & 82.24 & -26.09 & $<$ 2.43 \n& $<$ 3.50 & $<$ 3.53 & $<$ 0.72 & 2 EG & \t\t\t\\\\\n2221 - 023 & 335.95 & -2.10 & 61.86 & -46.71 & $<$ 4.47 \n& $<$ 5.04 & $<$ 2.34 & $<$ 0.90 & SY & 3C 445\t\t\\\\\n& & & & & & & & & & \\\\\n\\hline\n%\\hline\n\\multicolumn{11}{r}{(Table 11a cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\endlandscape\n%\\pagebreak\n\n%\\clearpage\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\landscape\n\\def\\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 11a}: {COMPTEL 2$\\sigma$ upper limits to AGN (EGRET sources and Seyferts (cont.))}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c|l||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n&\\multicolumn{4}{c|}{}&\\multicolumn{4}{c|}{}&\\multicolumn{2}{c||}{}\\\\\nName & \\multicolumn{4}{c|}{Location} & \\multicolumn {4}{c|}{Upper limit (10$^{-5}$ cm$^{-2}$ sec$^{-1}$)} & Type& Other name \\\\ \n&RA &DEC &l&b& (0.75--1.0) & (1 - 3) & (3 - 10) & (10 - 30) & & \\\\ \n& [deg] & [deg] &[deg] &[deg] & [MeV] & [MeV] & [MeV] & [MeV] & &\\\\\n\\hline\n\\hline\n & & & & & & & & & & \\\\\n2230 + 114 & 338.15 & 11.73 & 77.44 & -38.58 & $<$ 3.36 \n& $<$ 8.06 & $<$ 2.96 & $<$ 0.98 & 2 EG & CTA 102 \\\\\n2233 - 263 & 338.94 & -26.05 & 27.14 & -59.74 & $<$ 3.89 \n& $<$ 5.48 & $<$ 5.74 & $<$ 1.34 & SY & NGC 7314\t\t\\\\\n2251 + 158 & 343.49 & 16.15 & 86.11 & -38.18 & $<$ 4.37 \n& $<$ 9.28 & $<$ 6.63 & $<$ 1.53 & 2 EG & 3C 454.3\t\t\\\\\n2300 + 086 & 345.82 & 8.87 & 83.10 & -45.47 & $<$ 3.52 \n& $<$ 6.98 & $<$ 4.25 & $<$ 1.17 & SY & NGC 7469\t\t\\\\\n2302 - 090 & 346.23 & -8.73 & 64.08 & -58.82 & $<$ 3.46 \n& $<$ 4.68 & $<$ 5.78 & $<$ 1.30 & SY & MCG-2-58-22 \t\t\\\\\n2315 - 426 & 349.60 & -42.37 & 348.08 & -65.70 & $<$ 5.81 \n& $<$ 8.86 & $<$ 5.27 & $<$ 1.30 & SY & NGC 7582\t\t\\\\\n2356 + 196 & 359.69 & 19.92 & 106.38 & -41.25 & $<$ 3.47 \n& $<$ 4.84 & $<$ 4.12 & $<$ 0.91 & 2 EG &\t\t\t\t\\\\\n& & & & & & & & & & \\\\\n\\hline\n\\hline\n%\\multicolumn{11}{r}{(Table 11a cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\endlandscape\n%\\pagebreak\n\n\n\n\\clearpage\n\n\n\n% TABLE 11b begin\n\n\\landscape\n\\def\\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 11b}: {COMPTEL 2$\\sigma$ upper limits to unidentified high-latitude EGRET sources}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n&\\multicolumn{4}{c|}{} &\\multicolumn{4}{c|}{} & \\\\\nName & \\multicolumn{4}{c|}{Location} & \\multicolumn {4}{c|}{Upper limit (10$^{-5}$ cm$^{-2}$ sec$^{-1}$)} & Type \\\\ \n&RA &DEC &l&b& (0.75--1.0) & (1 - 3) & (3 - 10) & (10 - 30) & \\\\ \n& [deg] & [deg] &[deg] &[deg] & [MeV] & [MeV] & [MeV] & [MeV] & \\\\\n\\hline\n\\hline\n & & & & & & & & & \\\\\n2EGJ0008 + 7307 & 2.09 & 73.13 & 119.77 & 10.52 & $<$ 5.29 & $<$ 4.48 \n& $<$ 2.18 & $<$ 1.01 & 2 EG\t\\\\\n2EGJ0119 + 0312 & 19.97 & 3.21 & 136.77 & -58.90 & $<$ 4.63 & $<$ 5.36 \n& $<$ 8.43 & $<$ 1.03 & 2 EG\t\\\\\n2EGJ0159 - 3557 & 29.85 & -35.95 & 248.55 & -73.08 & $<$ 9.06 & $<$ 11.08 \n& $<$ 3.95 & $<$ 2.46 & 2 EG \t\\\\\n2EGJ0216 + 1107 & 34.00 & 11.12 & 153.93 & -46.60 & $<$ 6.12 & $<$ 6.12 \n& $<$4.51 & $<$ 0.94 & 2 EG\t\\\\\n2EGJ0403 + 3357 & 60.95 & 33.96 & 162.40 & -13.79 & $<$ 3.23 & $<$ 3.25 \n& $<$ 1.61 & $<$ 0.72 & 2 EG\t\\\\\n2EGJ0406 + 1704 & 61.67 & 17.08 & 175.61 & -25.23 & $<$ 2.38 & $<$ 3.26 \n& $<$ 2.01 & $<$ 0.69 &\t2 EG\t\\\\\n2EGJ0422 + 1414 & 65.53 & 14.24 & 180.65 & -24.26 & $<$ 2.24 & $<$ 3.10 \n& $<$ 2.04 & $<$ 0.66 & 2 EG\t\\\\\n2EGJ0426 + 6618 & 66.52 & 66.31 & 142.24 & 11.87 & $<$ 2.42 & $<$ 5.58 \n& $<$ 2.16 & $<$ 0.74 & 2 EG\t\\\\\n2EGSJ0426 + 1636 & 66.66 & 16.61 & 179.40 & -21.92 & $<$ 2.31 & $<$ 3.10 \n& $<$ 1.93 & $<$ 0.66 & 2EGS\t\\\\\n2EGJ0432 + 2910 & 68.21 & 29.18 & 170.34 & -12.68 & $<$ 2.34 & $<$ 2.98 \n& $<$ 1.48 & $<$ 0.60 & 2 EG\t\\\\\n2EGJ0437 + 1524 & 69.30 & 15.41 & 182.10 & -20.68 & $<$ 2.36 & $<$ 3.06 \n& $<$ 1.57 & $<$ 0.64 & 2 EG\t\\\\\n2EGSJ0500 + 5902 & 75.15 & 59.04 & 150.50 & 10.26 & $<$ 3.38 & $<$ 5.59 \n& $<$ 1.97 & $<$ 0.69 & 2 EGS\t\\\\\n2EGJ0532 - 6914 & 83.24 & -69.24& 279.70 & -32.16 & $<$ 2.78 & $<$ 4.51 \n& $<$ 2.98 & $<$ 0.66 & 2 EG\t\\\\\n2EGSJ0552 - 1026 & 88.12 & -10.45& 215.78 & -17.78 & $<$ 2.54 & $<$ 3.76 \n& $<$ 2.38 & $<$ 0.67 & 2 EGS\t\\\\\n2EGSJ0555 + 0408 & 88.95 & 4.14 & 202.77 & -10.40 & $<$ 2.49 & $<$ 3.29 \n& $<$ 1.84 & $<$ 0.59 & 2 EGS\t\\\\\n2EGJ0617 - 0652 & 94.42 & -6.88 & 215.27 & -10.62 & $<$ 2.42 & $<$ 3.52 \n& $<$ 4.91 & $<$ 0.84 & 2 EG\t\\\\\n2EGJ0720 - 4746 & 110.12& -47.78& 259.24 & -15.19 & $<$ 2.84 & $<$ 8.64 \n& $<$ 4.75 & $<$ 0.68 & 2 EG\t\\\\\n2EGSJ0724 - 5157 & 111.02& -51.97& 263.47 & -16.34 & $<$ 2.59 & $<$ 4.61 \n& $<$ 2.42 & $<$ 0.64 & 2 EGS\t\\\\\n2EGJ0744 + 5438 & 116.12& 54.64 & 163.18 & 29.34 & $<$ 2.33 & $<$ 2.12 & $<$ 1.55 & $<$ 0.95 & 2 EG \t\\\\\n2EGJ0809 + 5117 & 122.27 & 51.29 & 167.46 & 32.74 & $<$ 1.96 & $<$ 2.14 \n& $<$ 1.05 & $<$ 1.97 & 2 EG\t\\\\\n2EGJ0852 - 1237 & 133.12 & -12.63& 239.35 & 19.75 & $<$ 9.25 & $<$ 21.56 \n& $<$ 3.93 & $<$ 1.39 & 2 EG\t\\\\\n2EGSJ0909 + 6558 & 137.43 & 65.97 & 148.29 & 38.47 & $<$ 2.74 & $<$ 3.42 \n& $<$ 1.61 & $<$ 0.64 & 2 EGS\t\\\\\n2EGSJ1050 - 7650 & 162.53 & -76.85& 296.08 & -15.62 & $<$ 2.88 & $<$ 3.86 \n& $<$ 4.35 & $<$ 0.78 & 2 EGS\t\\\\\n2EGJ1054 + 5736 & 163.70 & 57.61 & 148.80 & 53.26 & $<$ 3.06 & $<$ 3.58 \n& $<$ 1.38 & 0.60& 2 EG\t\\\\\n2EGSJ1133 + 0037 & 173.33 & 0.63 & 264.41 & 57.54 & $<$ 2.48 & $<$ 3.32 \n& $<$ 2.35 & $<$ 1.01 & 2 EGS\t\\\\\n2EGJ1136 - 0414 & 174.23 & -4.24& 270.26 & 53.84 & $<$ 2.52 & $<$ 3.32 \n& $<$ 1.68 & $<$ 0.66 & 2 EG\t\\\\\n& & & & & & & & & \\\\\n\\hline\n%\\hline\n\\multicolumn{10}{r}{(Table 11b cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\endlandscape\n%\\pagebreak\n\n\n\n\\clearpage\n\n\n\n\\landscape\n\\def\\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 11b}: {COMPTEL 2$\\sigma$ upper limits to unidentified high-latitude EGRET sources (cont.)}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n&\\multicolumn{4}{c|}{} &\\multicolumn{4}{c|}{} & \\\\\nName & \\multicolumn{4}{c|}{Location} & \\multicolumn {4}{c|}{Upper limit (10$^{-5}$ cm$^{-2}$ sec$^{-1}$)} & Type \\\\ \n&RA &DEC &l&b& (0.75--1.0) & (1 - 3) & (3 - 10) & (10 - 30) & \\\\ \n& [deg] & [deg] &[deg] &[deg] & [MeV] & [MeV] & [MeV] & [MeV] & \\\\\n\\hline\n\\hline\n & & & & & & & & & \\\\\n2EGJ1220 - 1510 & 185.00 & -15.17& 291.77 & 47.02 & $<$ 3.76 & $<$ 2.90 \n& $<$ 5.12 & $<$ 1.53 & 2 EGS\t\\\\\n2EGJ1233 - 1407 & 188.27 & -14.13& 296.20 & 48.50 & $<$ 4.94 & $<$ 2.80 \n& $<$ 4.19 & $<$ 0.72 & 2 EG\t\\\\\n2EGSJ1236 - 0416 & 189.00 & -4.27 & 295.58 & 58.38 & $<$ 2.28 & $<$ 3.73 \n& $<$ 2.41 & $<$ 0.90 & 2 EGS\t\\\\\n2EGJ1239 + 0441 & 189.82 & 4.69 & 295.04 & 67.38 & $<$ 2.59 & $ $ 9.24 \n& $<$ 4.38 & $<$ 1.14 & 2 EG\t\\\\\n2EGJ1248 - 8308 & 192.06 & -83.14 & 302.83 & -20.27 & $<$ 2.89 & $<$ 4.04 \n& $<$ 2.65 & $<$ 0.88 & 2 EG\t\\\\\n2EGSJ1324 + 2210 & 201.20 & 22.18 & 1.59 & 80.95 & $<$ 2.26 & $<$ 3.07 \n& $<$ 3.63 & $<$ 0.68 & 2 EGS\t\\\\\n2EGJ1332 + 8821 & 203.03 & 88.35 & 122.60 & 28.75 & $<$ 4.98 & $<$ 3.99 \n& $<$ 2.03 & $<$ 0.83 & 2 EG\t\\\\\n2EGJ1346 + 2942 & 206.70 & 29.70 & 48.11 & 77.57 & $<$ 2.79 & $<$ 8.00 \n& $<$ 2.40 & $<$ 1.06 & 2 EG\t\\\\\n2EGJ1430 + 5356 & 217.66 & 53.95 & 95.52 & 57.58 & $<$ 3.91 & $<$ 8.72 \n& $<$ 6.21 & $<$ 1.42 & 2 EG \t\\\\\n2EGJ1457 - 1916 & 224.36 & -19.27 & 339.68 & 34.46 & $<$ 2.92 & $<$ 8.78 \n& $<$ 2.10 & $<$ 0.88 & 2 EG\t\\\\\n2EGSJ1504 - 1537 & 226.22 & -15.63 & 344.06 & 36.37 & $<$ 5.01 & $<$ 9.66 \n& $<$ 2.23 & $<$ 0.92 & 2 EGS\t\\\\\n2EGJ1528 - 2352 & 232.15 & -23.87 & 343.23 & 26.45 & $<$ 2.33 & $<$ 3.45 \n& $<$ 3.00 & $<$ 0.84 & 2 EG\t\\\\\n2EGJ1631 - 2845 & 247.76 & -28.75 & 350.40 & 13.26 & $<$ 2.37 & $<$ 3.00 \n& $<$ 1.57 & $<$ 0.78 & 2 EG\t\\\\\n2EGJ1635 - 1427 & 248.76 & -14.46 & 2.57 & 21.67 & $<$ 2.28 & $<$ 3.23 \n& $<$ 1.67 & $<$ 0.72 & 2 EG\t\\\\\n2EGSJ1642 - 2659 & 250.62 & -26.99 & 353.46 & 12.48 & $<$ 2.96 & $<$ 2.97 \n& $<$ 1.51 & $<$ 0.92 & 2 EGS\t\\\\\n2EGSJ1703 - 6302 & 255.79 & -63.05 & 327.39 & -12.88 & $<$ 3.22 & $<$ 4.52 \n& $<$ 2.38 & $<$ 1.20 & 2 EGS\t\\\\\n2EGSJ1708 - 0927 & 257.16 & -9.47 & 11.92 & 17.80 & $<$ 2.25 & $<$ 3.11\n& $<$ 3.88 & $<$ 0.68 & 2 EGS\t\\\\\n2EGJ1709 - 0350 & 257.32 & -3.84 & 17.07 & 20.63 & $<$ 2.43 & $<$ 3.29 \n& $<$ 4.76 & $<$ 0.80 & 2 EG\t\\\\ \n2EGJ1731 + 6007 & 262.90 & 60.12 & 88.93 & 33.14 & $<$ 5.09 & $<$ 9.06\n& $<$ 3.17 & $<$ 1.16 & 2 EG\t\\\\\n2EGJ1815 + 2950 & 273.83 & 29.84 & 56.89 & 20.37 & $<$ 2.74 & $<$ 3.70 \n& $<$ 2.83 & $<$ 2.09 & 2 EG\t\\\\\n2EGJ1821 - 7915 & 275.43 & -79.26 & 314.72 & -25.25 & $<$ 3.78 & $<$ 5.12 \n& $<$ 5.59 & $<$ 1.06 & 2 EG\t\\\\\n2EGJ1835 + 5919 & 278.78 & 59.33 & 88.74 & 25.12 & $<$ 3.12 & $<$ 8.64 \n& $<$ 2.13 & $<$ 1.28 & 2 EG\t\\\\\n2EGJ1847 - 3220 & 281.84 & -32.35 & 3.17 & -13.33 & $<$ 2.14 & $<$ 2.86 \n& $<$ 1.43 & $<$ 0.62 & 2 EG\t\\\\\n2EGJ1850 - 2638 & 282.74 & -26.65 & 8.82 & -11.70 & $<$ 3.90 & $<$ 2.91 \n& $<$ 2.68 & $<$ 0.62 & 2 EG\t\\\\\n2EGJ1950 - 3503 & 297.51 & -35.06 & 5.17 & -26.50 & $<$ 5.16 & $<$ 3.38 \n& $<$ 1.72 & $<$ 0.74 & 2 EG\t\\\\\n2EGSJ1954 - 1419 & 298.75 & -14.33 & 26.85 & -20.42 & $<$ 2.62 & $<$ 3.50 \n& $<$ 2.97 & $<$ 1.57 & 2 EGS\t\\\\\n& & & & & & & & & \\\\\n\\hline\n%\\hline\n\\multicolumn{10}{r}{(Table 11b cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\endlandscape\n%\\pagebreak\n\n\n\n\\clearpage\n\n\n\n\\landscape\n\\def\\p{{$\\pm$}}\n\\def\\s{{$\\sigma$}}\n\n\\footnotesize\n\n%\\begin{table}\n{\\bf Table 11b}: {COMPTEL 2$\\sigma$ upper limits to unidentified high-latitude EGRET sources (cont.)}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c|c|c|c|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n&\\multicolumn{4}{c|}{} &\\multicolumn{4}{c|}{} & \\\\\nName & \\multicolumn{4}{c|}{Location} & \\multicolumn {4}{c|}{Upper limit (10$^{-5}$ cm$^{-2}$ sec$^{-1}$)} & Type \\\\ \n&RA &DEC &l&b& (0.75--1.0) & (1 - 3) & (3 - 10) & (10 - 30) & \\\\ \n& [deg] & [deg] &[deg] &[deg] & [MeV] & [MeV] & [MeV] & [MeV] & \\\\\n\\hline\n\\hline\n & & & & & & & & & \\\\\n2EGJ2006 - 2253 & 301.62 & -22.90 & 19.32 & -26.17 & $<$ 2.95 & $<$ 3.68 \n& $<$ 3.88 & $<$ 0.77 & 2 EG\t\\\\\n2EGJ2027 + 1054 & 306.79 & 10.91 & 54.24 & -15.55 & $<$ 2.39 & $<$ 8.02 \n& $<$ 4.73 & $<$ 1.01 & 2 EG\t\\\\\n2EGJ2243 + 1545 & 340.82 & 15.75 & 83.17 & -37.04 & $<$ 3.89 & $<$ 7.42 \n& $<$ 4.96 & $<$ 1.64 & 2 EG\t\\\\\n2EGSJ2322 - 0321 & 350.60 & -3.36 & 77.24 & -58.10 & $<$ 3.68 & $<$ 4.76 \n& $<$ 3.27 & $<$ 1.27 & 2 EGS\t\\\\\n2EGJ2354 + 3811 & 358.56 & 38.19 & 110.73& -23.32 & $<$ 4.41 & $<$ 5.41 \n& $<$ 3.42 & $<$ 0.93 & 2 EG\t\\\\\n& & & & & & & & & \\\\\n\\hline\n\\hline\n%\\multicolumn{10}{r}{(Table 11b cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\endlandscape\n%\\pagebreak\n\n\n\n\\clearpage\n\n\n\n\n% TABLE 12 begin\n\n\n\\landscape\n\\footnotesize\n%\\begin{flushleft}\n{\\bf Table 12}: {Upper Limits to Possible Sources of\nGamma-Ray Line Emission}\n\\vskip12pt\n\\begin{tabular}{||l|c|c|c|c|l|c|c||}\n\\hline \\hline \\noalign{\\smallskip}\n& \\multicolumn{2}{c|}{} & & & & & \\\\\nName & \\multicolumn{2}{c|}{Position} & Line Energy & Flux (2 $\\sigma$)\n & ~~~~~Observation & Note & Ref. \\\\\n & l & b & & & ~~~~~Period & & \\\\\n & [deg] & [deg] & [MeV] \n & [10$^{-5}$ photons & & & \\\\\n& & & & cm$^{-2}$ s$^{-1}$] & & & \\\\\n& & & & & & & \\\\\n\\hline \n\\hline\n& & & & & & & \\\\\nSN 1993J & 142.15$^\\circ$ & 40.92$^\\circ$ & 0.847 \n & $<$6.2 & VP 227.0, 228.0, 319.0, & & \\\\\n & & & 1.238 & $<$2.9 & 319,0, 319.5 & (a) & (2) \\\\\n & & & & & & & \\\\\n\\hline\n & & & & & & & \\\\ \nKepler SN (1604) & 4.52 & +6.84 & 1.157 & $<$1.43 & Phase I to III & & (1) \\\\\n & & & & & & & \\\\ \n\\hline\n & & & & & & & \\\\ \nTycho SN (1572) & 120.09 & +1.42 & 1.157 & $<$1.78 & Phase I to III & & (1) \\\\\n & & & & & & & \\\\ \n\\hline\n & & & & & & & \\\\ \n3C 58 & 130.72 & +3.08 & 1.157 & $<$1.78 & Phase I to III & & (1) \\\\\n & & & & & & & \\\\ \n\\hline\n & & & & & & & \\\\ \nLupus SN (1006) & 327.51 & +14.69 & 1.157 & $<$1.50 & Phase I to III & &(1) \\\\\n & & & & & & & \\\\ \n\\hline\n & & & & & & & \\\\ \nNovae (general) & & & 1.275 MeV & $<$3 \n & April 1991--Aug 1993 & & (4) \\\\\n & & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\n%\\tabletail{\\hline\\multicolumn{7}{r}{(continued)}\\\\\nNova Cen 1991 & 309$^\\circ$ & -1.04$^\\circ$ & 1.275 \n& $<$4.0 & VP 12.0, 14.0, 23.0, 27.0, & & \\\\ \n& & & & & 208.0, 215,0, 217.0, & (b) & (4) \\\\\n& & & & & 314.0, 315.0, 316.0 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nNova Her 1991 ~~~~~ & 43.3$^\\circ$ & 6.6 $^\\circ$ & 1.275 MeV \n& $<$3.3 & VP 20.0, 328.0, 331.x, & & \\\\\n\t & & & & & 333.0 & (b) & (4) \\\\\n& & & & & & & \\\\\n\\hline\\multicolumn{8}{r}{(Table 12 cont.)}\\\\\n\\end{tabular}\n%\\end{flushleft}\n\\endlandscape\n\n\\clearpage\n\n\\landscape\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|l|c|c||}\n%\\tablehead{\\hline \\hline \\noalign{\\smallskip} \n\\hline \\hline \\noalign{\\smallskip} \n& \\multicolumn{2}{c|}{} & & & & & \\\\\nName & \\multicolumn{2}{c|}{Position} & Line Energy & Flux (2 $\\sigma$)\n & ~~~~~Observation & Note & Ref. \\\\\n & l & b & & & ~~~~~Period & & \\\\\n & [deg] & [deg] & [MeV] \n & [10$^{-5}$ photons & & & \\\\\n& & & & cm$^{-2}$ s$^{-1}$] & & & \\\\\n& & & & & & & \\\\\n\\hline \n\\hline\n& & & & & & & \\\\\nNova SGR 1991~~~~~& ~ 0.18$^{\\circ}$ ~ & -6.94$^\\circ$ & ~ 1.275 ~ & $<$6.2 & 5.0, 210.0, 214.0, & & \\\\\n& & & & & 219.4, 223.0, 226.0, & & \\\\\n& & & & & 231.0, 229.x, 232.x, & & \\\\\n& & & & & 302.3, 223.0, 324.0, & (b) & (4) \\\\\n& & & & & 330.0, 332.0, 334.0, & & \\\\\n& & & & & 336.5, 338.0 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nNova Sct 1991 & \\ \\ 25.1$^\\circ$ & \\ -2.80$^\\circ$ & 1.275 \n & $<$3.6 & 7.5, 13.0, 20.0, & & \\\\\n & & & & & 231.0, 229.x, 324.0, & (b) & (4) \\\\\n\t & & & & & 330.0, 332.0, 334.0 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nNova Pup 1991 ~~~~ & ~ 252.7$^\\circ$ ~ & ~ -0.72$^\\circ$ ~ & 1.275 \n & $<$ 5.5 & 41.0, 44.0, 230.0, & & \\\\\n & & & & & 301.0, 338.5 & (b) & (4) \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nNova Cyg 1992 & 89.14$^\\circ$ & 7.82$^\\circ$ & 1.275 \n & $<$2.3 & 34.0, 203.x, 212.0, & (b) & (4) \\\\\n & & & & & 302.x, 318.1 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nNova Sco 1992 & 343.8$^\\circ$ & -1.61$^\\circ$ & 1.275 \n & $<$5.9 & 27.0, 210.0, 214.0, & & \\\\\n & & & & & 219.4, 223.0, 226.0 & & \\\\\n\t & & & & & 229.x, 232.x, 302.3 & (b) & (4) \\\\\n\t & & & & & 323.0, 336.5, 338.0 & & \\\\\n& & & & & & & \\\\\n\\hline\\multicolumn{8}{r}{(Table 12 cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n\\endlandscape\n\n\n\\clearpage\n\n\n\\landscape\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|l|c|c||}\n%\\tablehead{\\hline \\hline \\noalign{\\smallskip} \n\\hline \\hline \\noalign{\\smallskip} \n& \\multicolumn{2}{c|}{} & & & & & \\\\\nName & \\multicolumn{2}{c|}{Position} & Line Energy & Flux (2 $\\sigma$)\n & ~~~~~Observation & Note & Ref. \\\\\n & l & b & & & ~~~~~Period & & \\\\\n & [deg] & [deg] & [MeV] \n & [10$^{-5}$ photons & & & \\\\\n& & & & cm$^{-2}$ s$^{-1}$] & & & \\\\\n & & & & & & & \\\\\n\\hline \n\\hline\n& & & & & & & \\\\\nNova Sgr 1992--1 ~~~~~ & ~ 4.75$^\\circ$ ~ & ~ -2.0 $^\\circ$ ~ & 1.275 \n & $<$6.0 & 210.0, 214.0, 219.4, & & \\\\\n\t & & & & & 223.0, 226.0, 231.0, & & \\\\\n\t & & & & & 229.x, 232.0, 302.3, & (b) & (4) \\\\\n & & & & & 323.0, 324.0, 330.0, & & \\\\\n\t & & & & & 332.0, 334.0, 336.5, & & \\\\\n\t & & & & & 338.0 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nNova Sgr 1992--2 & 4.56$^\\circ$ & -6.96$^\\circ$ & 1.275 \n & $<$3.0 & 214.0, 223.0, 226.0, & & \\\\\n\t & & & & & 231.0, 229.x, 232.x, & & \\\\\n\t & & & & & 302.3, 323.0, 324.0, & (b) & (4) \\\\\n\t & & & & & 330.0, 332.0, 334.0, & & \\\\\n\t & & & & & 334.0, 338.0 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nNova Sgr 1992--3 ~~~ & ~ 9.38$^\\circ$ ~ & ~ -4.54$^\\circ$ ~ & 1.275 \n & $<$4.4 & 210.0, 214.0, 219.4, & & \\\\\n\t & & & & & 223.0, 226.0, 231.0, & & \\\\\n\t & & & & & 229.x, 232.x, 302.3, & (b) & (4) \\\\\n\t & & & & & 323.0, 324.0, 330.0, & & \\\\\n\t & & & & & 332.0, 334.0 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nNova Aql 1993 & 36.81$^\\circ$ & -4.10$^\\circ$ & 1.275 \n & $<$6.2 & 231.0, 324.0, 330.0, & (b) & (4) \\\\\n\t & & & & & 332.0 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nCygnus Loop & 74.01 & -8.56 & 1.809 & $<$1.50 & Phase I to III \n & (c) & (6) \\\\\n& & & & & & & \\\\\n\\hline\\multicolumn{8}{r}{(Table 12 cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n\\endlandscape\n\n\\clearpage\n\n\\landscape\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|l|c|c||}\n%\\tablehead{\\hline \\hline \\noalign{\\smallskip} \n\\hline \\hline \\noalign{\\smallskip} \n& \\multicolumn{2}{c|}{} & & & & & \\\\\nName & \\multicolumn{2}{c|}{Position} & Line Energy & Flux (2 $\\sigma$)\n & ~~~~~Observation & Note & Ref. \\\\\n & l & b & & & ~~~~~Period & & \\\\\n & [deg] & [deg] & [MeV] \n & [10$^{-5}$ photons & & & \\\\\n& & & & cm$^{-2}$ s$^{-1}$] & & & \\\\\n & & & & & & & \\\\\n\\hline \n\\hline\n& & & & & & & \\\\\nHB 21 ~~~~~~~~~~~~ & ~ 88.86 ~ & ~ 4.80 ~ & 1.809 & $<$2.30 & Phase I to III ~~~~~~ & (d) & (6) \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nMon Nebula ~~~~~~~ & ~ 204.96 ~ & ~ 0.45 ~ & 1.809 & $<$1.60 & Phase I to III ~~~~~~\n & (c) & (6) \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nLupus Loop & 329.67 & 15.97 & 1.809 & $<$1.40 & Phase I to III\n& (e) & (6) \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nOrion & 209.0$^\\circ$ & -19.4$^\\circ$ & 1.809\n& $<$1.7 & VP 1.0 & & \\\\\n& & & & & VP 2.5 (solar mode) & & \\\\\n& & & & & VP 221.0 & & (3) \\\\\n& & & & & VP 337.0 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nCyg X-1 & 71.3 & +3.1 & 2.223 & $<$1.53 & VP 1--523 & & (5) \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nSco X-1 & 359.09 & 23.78 & 2.223 & $<$ 1.7 & Phase I to IV / & & (5) \\\\\n & & & & & Cycle-5 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\nCyg X-3 & 79.85 & 0.70 & 2.223 & $<$ 1.2 & Phase I to IV / & & (5) \\\\\n & & & & & Cycle-5 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\n4U 1916-05 & 31.38 & -8.22 & 2.223 & $<$ 1.2 & Phase I to IV / & & (5) \\\\\n & & & & & Cycle-5 & & \\\\\n& & & & & & & \\\\\n\\hline\\multicolumn{8}{r}{(Table 12 cont.)}\\\\\n\\end{tabular}\n\\end{flushleft}\n\\endlandscape\n\n\n\\clearpage\n\n\n\\landscape\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|l|c|c||}\n%\\tablehead{\\hline \\hline \\noalign{\\smallskip} \n\\hline \\hline \\noalign{\\smallskip} \n& \\multicolumn{2}{c|}{} & & & & & \\\\\nName & \\multicolumn{2}{c|}{Position} & Line Energy & Flux (2 $\\sigma$)\n & ~~~~~Observation & Note & Ref. \\\\\n & l & b & & & ~~~~~Period & & \\\\\n & [deg] & [deg] & [MeV] \n & [10$^{-5}$ photons & & & \\\\\n& & & & cm$^{-2}$ s$^{-1}$] & & & \\\\\n & & & & & & & \\\\\n\\hline \n\\hline\n& & & & & & & \\\\\n4U 1626-67 ~~~~~~~~~~~& 321.79~& -13.09~& 2.223 & $<$ 1.7 & Phase I to IV / ~~~~~& & (5)\\\\\n & & & & & Cycle-5 & & \\\\\n& & & & & & & \\\\\n\\hline\n& & & & & & & \\\\\n4U 1820-30 ~~~~~~~~~~ & 2.79& -7.91 & 2.223 & $<$ 1.1 & Phase I to IV / ~~~~~& & (5)\\\\\n & & & & & Cycle-5 & & \\\\\n& & & & & & & \\\\\n\\hline\\hline \n\\end{tabular} \n\\vskip6pt\n{\\bf References}\n\\vskip6pt\n(1) \\cite{dupraz97}.\n \n(2) \\cite{lichti96}.\n \n(3) \\cite{oberlack95}.\n\n(4) \\cite{iyudin95}.\n\n(5) \\cite{mcconnell97b}.\n\n(6) \\cite{knoed96}.\n\n\\vskip6pt \n\\vskip12pt\n (a) Only VP 227/228 used for upper flux limit.\n\n (b) Only observations up to VP 232 used for upper flux limit.\n\n (c) radius 2$^\\circ$\n\n (d) radius 1$^\\circ$\n\n (e) radius 1.5$^\\circ$\n\\end{flushleft} \n%\\include{notes}\n\\endlandscape \n\n\\clearpage\n\n\n\n% TABLE 13 begin\n\n\n\\landscape\n\\footnotesize\n\n%\\begin{table*}\n{\\bf Table 13}: {Summary of Most Significant COMPTEL Source Detections.}\n\\begin{flushleft}\n%\\noalign{\\smallskip}\n\\begin{tabular}{||l|c|l||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n & & \\\\\n \\ {\\bf Type of Source} & {\\bf Number of} & \\ {\\bf Comments} \\\\\n & {\\bf Sources} & \\\\\n & & \\\\\n\\hline\n\\hline\n & & \\\\\n{\\bf Spin-Down Pulsars:} & 3 & Crab, Vela, PSR B1509-58. \\\\\n & & \\\\\n\\hline\n & & \\\\\n{\\bf Stellar Black Hole} & 2 & Cyg X-1, Nova Persei 1992 (GRO J0422+32). \\\\\n{\\bf Candidates:} & & \\\\\n & & \\\\\n\\hline\n & & \\\\\n{\\bf Supernova Remnants:} & 1 & Crab nebula. \\\\\n(Continuum Emission) & & \\\\\n & & \\\\\n\\hline\n\\ & & \\\\\n {\\bf Active Galactic Nuclei:} & 10 & CTA 102, 3C 454.3, PKS 0528+134, GRO J 0516-609, PKS 0208-512, 3C 273, \\\\\n & & PKS 1222+216, 3C 279, Cen A, PKS 1622-297. \\\\\n\\ & & \\\\ \n\\hline\n & & \\\\\n{\\bf Unidentified Sources:} & & \\\\\n$\\bullet$ $\\mid$b$\\mid$ $<$ 10$^{\\circ}$ & 4 & GRO J1823-12, GRO J2228+61 (2CG 106+1.5), GRO J0241+6119 (2CG 135+01), \\\\\n & & Carina/Vela region (extended). \\\\\n% & & \\\\\n$\\bullet$ $\\mid$b$\\mid$ $>$ 10$^{\\circ}$ & 5 & GRO J1753+57 (extended), GRO J1040+48, GRO J1214+06, \\\\\n & & HVC complexes M and A area (extended), HVC complex C (extended). \\\\ \n & & \\\\\n\\hline\n & & \\\\\n{\\bf Gamma-Ray Line Sources:} & & \\\\\n$\\bullet$ 1.809 MeV ($^{26}$Al)& 3 & Cygnus region (extended), Vela region (extended, may include RX J0852-4621), \\\\ \n & & Carina region. \\\\\n% & & \\\\\n$\\bullet$ 1.157 MeV ($^{44}$Ti)& 2 & Cas A, RX J0852-4621 (GRO J0852-4642). \\\\\n% & & \\\\\n$\\bullet$ 0847 and 1.238 MeV ($^{56}$Co) & 1 & SN 1991T. \\\\\n%& & \\\\\n$\\bullet$ 2.223 MeV (n-capture) & 1 & GRO J0317-853. \\\\\n & & \\\\\n\\hline\n & & \\\\\n{\\bf Gamma-Ray Burst Sources:} & 31 & Location error radii vary from 0.34$^{\\circ}$ to 2.79$^{\\circ}$ (mean error radius: view 1.13$^{\\circ}$). \\\\ \n(within COMPTEL field-of- & & \\\\\nup to Phase IV/Cycle-5) & & \\\\\n & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n%\\caption[] {}\n\\end{flushleft}\n%\\end{table*}\n\n\\endlandscape\n\n\n\\end{document}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\nReserve !!! (wurde gestrichen, 19.4.99)\n\n\n\n%\\cleapage\n\n\n\n\n% TABLE 10\n\n\\landscape\n\n\\footnotesize\n%\\begin{table}\n{\\bf Table 10}: {Upper Flux Limits to Spin-Down Pulsars}\n\\begin{flushleft}\n\\begin{tabular}{||l|c|c|c|c|c||}\n\\noalign{\\smallskip}\n\\hline\n\\hline\n & & \\multicolumn{4}{c||}{} \\\\\nPulsar & Observing & \\multicolumn{4}{c||}\n {2 $\\sigma$ DC Upper Limit ($10^{-4} \\ photons \\ cm^{-2} \n \\ s^{-1})^{\\rm a}$} \\\\ \nPSR B & Period & (0.75--1.0) MeV & (1.0--3.0) MeV & (3.0--10.0) MeV \n& (10.0--30.0) MeV \\\\ \n & & & & & \\\\\n\\hline\n\\hline\n & & & & & \\\\\n0740--28 & 8 & $\\leq$ 1.10 & $\\leq$ 1.39 & $\\leq$ 0.46 & $\\leq$ 0.19 \\\\\n1046--58 & 14 & $\\leq$ 0.59 & $\\leq$ 2.74 & $\\leq$ 0.99 & $\\leq$ 0.33 \\\\\n1055--52 & 14 & $\\leq$ 0.91 & $\\leq$ 0.16 & $\\leq$ 0.65 & $\\leq$ 0.13 \\\\\n1259--63 & 23& $\\leq$ 1.91 & $\\leq$ 1.58 & $\\leq$ 0.81 & $\\leq$ 0.30 \\\\\n1338--62 & 23& $\\leq$ 1.92 & $\\leq$ 1.50 & $\\leq$ 1.34 & $\\leq$ 0.24 \\\\\n1509--58 & 23& $\\leq$ 3.43 & $\\leq$ 3.53 & $\\leq$ 2.14 & $\\leq$ 0.73 \\\\\n1706--44 & 5 & $\\leq$ 2.25 & $\\leq$ 2.35 & $\\leq$ 0.57 & $\\leq$ 0.42 \\\\\n1758--24 & 5 & $\\leq$ 1.08 & $\\leq$ 0.95 & $\\leq$ 0.85 & $\\leq$ 0.15 \\\\\n1800--21 & 5 & $\\leq$ 1.01 & $\\leq$ 1.03 & $\\leq$ 1.05 & $\\leq$ 0.16 \\\\\n1821--24 & 5 & $\\leq$ 0.81 & $\\leq$ 0.74 & $\\leq$ 0.99 & $\\leq$ 0.35 \\\\\n1823--13 & 7.5+13.0 & $\\leq$ 1.60 & $\\leq$ 5.32 & $\\leq$ 1.53 & $\\leq$ 0.38 \\\\\n1929+10 & 20 & $\\leq$ 1.33 & $\\leq$ 1.97 & $\\leq$ 0.60 & $\\leq$ 0.19 \\\\\n1937+21 & 20 & $\\leq$ 1.60 & $\\leq$ 2.11 & $\\leq$ 0.54 & $\\leq$ 0.23 \\\\\n1951+32 & 2.0 & $\\leq$ 1.90 & $\\leq$ 2.11 & $\\leq$ 0.76 & $\\leq$ 0.20 \\\\\n& & & & & \\\\\n\\hline\n\\hline\n\\end{tabular}\n\\end{flushleft}\n%\\end{table}\n\\vskip 0,5 cm\n%\\noindent\n\n%\\vskip3cm \n\\noindent\n\\flushleft\n$^{\\rm a}$2$\\sigma$ DC upper limits of the pre-selected pulsars. The values\n are derived from direct imaging \\\\\nanalysis at the position of the object. From Carami\\~nana et al. 1995, \n\n\\endlandscape\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002366.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Aschenbach (1998)]{aschenbach98}\nAschenbach, B., 1998, Nature 396, 141\n\n\\bibitem[Bennett et al. (1993)]{bennett93}\nBennett, K., Sch\\\"onfelder, V., Ryan, J. et al., 1993, IAU Circ. 5749\n \n\\bibitem[Bloemen et al. (1994)]{bloemen94}\nBloemen, H., Hermsen, W., Swanenburg, B.N. et al., 1994, ApJS {\\bf 92}, 419\n\n\\bibitem[Bloemen et al. (1995)]{bloemen95}\nBloemen, H., Bennett, K., Blom, J.J. et al., 1995, A\\&A 293, L1\n\n\\bibitem[Bloemen et al. (1999a)]{bloemen99a}\nBloemen, H., Hermsen, W. Kappadath, S.C. et al., 1999a, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Bloemen et al. (1999b)]{bloemen99b} \nBloemen, H., Diehl, R., Hermsen, W. et al., 1999b, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Bloemen et al., in preparation]{bloemen00}\nBloemen, H. et al., in preparation\n\n\\bibitem[Blom (1997)]{blom97}\nBlom, J. J., 1997, Ph-D Thesis, University of Leiden, The Netherlands \n\n\\bibitem[Blom et al. (1995a)]{blom95a}\nBlom, J.J., Bloemen, H., Bennett, K. et al., 1995a, A\\&A 295, 330\n\n\\bibitem[Blom et al. (1995b)]{blom95b}\nBlom, J.J., Bennett, K., Bloemen, H. et al., 1995b, A\\&A 298, L33 \n\n\\bibitem[Blom et al. (1996)]{blom96}\nBlom, J.J., Bennett, K., Bloemen, H. et al., 1996, A\\&AS 120, 507 \n\n\\bibitem[Blom et al. (1997a)]{blom97a}\nBlom, J.J. Bloemen, H., Bykov, A.M. et al. 1997a, Proc. of 2$^{nd}$ INTEGRAL Workshop, eds.: C. Winkler, T.J.-L. Courvoisier, Ph. Durouchoux, ESA SP-382, p. 119\n\n\\bibitem[Blom et al. (1997b)]{blom97b} \nBlom, J.J., Bloemen, H., Bykov, A.M. et al. 1997b, A\\&A 321, 288\n\n\\bibitem[Collmar et al. (1993)]{collmar93}\nCollmar, W., Bennett, K., Bloemen, H. et al., 1993, A\\&AS 97, 71 \n \n\\bibitem[Collmar et al. (1994)]{collmar94}\nCollmar, W. et al., Bennett, K., Bloemen, H. et al., 1994, Proc. 2$^{nd}$ Compton Symposium, AIP Conf. Proc. 304, eds: C.E. Fichtel, N. Gehrels, J.P. Norris, p. 659\n\n\\bibitem[Collmar et al. (1996)]{collmar96}\nCollmar, W., Bennett, K., Bloemen, H. et al., 1996, A\\&AS 120, 515 \n \n\\bibitem[Collmar et al. (1997a)]{collmar97a}\nCollmar, W., Bennett, K., Bloemen, H. et al., 1997a, A\\&A 328, 33 \n\n\\bibitem[Collmar et al. (1997b)]{collmar97b}\nCollmar, W., Wessolowski, U., Sch\\\"onfelder, V. et al., 1997b, Proc. of 4$^{th}$ Compton Symposium, 1997, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 1587\n\n\\bibitem[Collmar et al. (1997c)]{collmar97c}\nCollmar, W., Blom, J.J., Bennett, K. et al., 1997c, Proc. of 25th ICRC, Durban, eds.: M.S. Potgieter, B.C. Raubenheimer, D.J. v. der Walt, Vol. 3, 101 \n\n\\bibitem[Connors et al. (1993a)]{connors93a}\nConnors, A., Aarts, H.J.M., Bennett, K. et al., 1993a, A\\&AS 97, 75\n\n\\bibitem[Connors et al. (1993b)]{connors93b}\nConnors, A. et al., Collmar, W., Hanlon, L. 1993b, Adv. Space Res. 13(12), 715\n\n\\bibitem[Connors et al. (1997)]{connors97}\nConnors, A., Bennett, K., Collmar, W. et al., 1997, Proc. of 25th ICRC, Durban, eds.: M.S. Potgieter, B.C. Raubenheimer, D.J. v. der Walt, Vol. 3, 13 \n\n\\bibitem[de Boer et al. (1992)]{deboer92} \nde Boer, H. Bennett, K., Bloemen, H. et al., 1992 in: Data Analysis in Astron. IV, ed. V. di Ges\\`u, L. Scarsi, R. Buccheri, P. Crane, M.C. Maccarone, H.U. Zimmermann, Plenum Press, New York, 241 \n \n\\bibitem[del Rio et al (1996)]{delrio96}\ndel Rio, E., v. Ballmoos, P., Bennett, K. et. al., 1996, A\\&A 315, 237 \n\n\\bibitem[Diehl et al. (1994)]{diehl94}\nDiehl, R. , Dupraz, C., Bennett, K. et al., 1994, ApJS 92, 429\n \n\\bibitem[Diehl 1996]{diehl96}\nDiehl, R., 1996, \\lq COMPTEL Data Analysis Standards\\rq\\ , COMPTEL Internal\nReport COM-MO- DRG-MGM-231.9 (3 March 1996) \n\n\\bibitem[Dupraz et al. (1997)]{dupraz97}\nDupraz, C., Bloemen, H., Bennett, K. et al., 1997, A\\&A, 324, 683\n\n\\bibitem[Fichtel et al. (1994)]{fichtel94}\nFichtel, C. E., Bertsch, D.E., Chiang, J. et al., 1994, ApJS 94, 551 (1EG)\n\n\\bibitem[Greiner et al. (1995)]{greiner95}\nGreiner, J. et al., Sommer, M., Bade, N. et al., 1995 A\\&A 302, 121\n\n\\bibitem[Hanlon et al. (1994a)]{hanlon94a}\nHanlon, L.O., Bennett, K., Williams, O.R. et al., 1994a, A\\&A 285, 161\n\n\\bibitem[Hanlon et al. (1994b)]{hanlon94b}\nHanlon, L.O., Bennett, K., Williams, O.R. et al., 1994b, in: AIP Conf. Proc. No 307; Gamma-Ray Bursts, ed. G.J. Fishman, J.J. Brainerd, K. Hurley (New York: AIP Press), p. 275\n\n\\bibitem[Hanlon et al. (1995)]{hanlon95}\nHanlon, L.O., Hermsen, W., Kippen, R.M. et al., 1995, A\\&A 296, L41\n\n\\bibitem[Hermsen et al. (1997)]{hermsen97}\nHermsen, W., Kuiper, L., Sch\\\"onfelder, V. et al., 1997, Proc. of 2$^{nd}$ INTEGRAL Workshop, eds.: C. Winkler, T.J.-L. Courvoisier, Ph. Durouchoux, ESA-SP 382, 287\n\n\\bibitem[Iyudin et al. (1994)]{iyudin94}\nIyudin, A.F., Diehl, R., Bloemen, H. et al., 1994, A\\&A 284, L1 \n\n\\bibitem[Iyudin et al. (1995)]{iyudin95}\nIyudin, A.F., Bennett, K., Bloemen, H. et al., 1995, A\\&A 300, 422\n\n\\bibitem[Iyudin et al. (1996)]{iyudin96}\nIyudin, A.F., Bennett, K., Bloemen, H. et al., 1996, A\\&A 311, L21\n\n\\bibitem[Iyudin et al (1997a)]{iyudin97a}\nIyudin, A., Diehl, R., Lichti, G.G. et al., 1997a, Proc. of 2$^{nd}$ INTEGRAL Workshop, eds.: C. Winkler, T.J.-L. Courvoisier, Ph. Durouchoux, ESA-SP 382, p. 37\n \n\\bibitem[Iyudin et al. (1997b)]{iyudin97b}\nIyudin, A., Reimer, O., Bennett, K. et al., 1997b, Proc. of 25$^{th}$ ICRC, Durban, eds.: M.S. Potgieter, B.C. Raubenheimer, D.J. v. der Walt, Vol. 3, 89 \n\n\\bibitem[Iyudin et al. (1998)]{iyudin98}\nIyudin, A., Sch\\\"onfelder, V., Bennett, K. et al., 1998, Nature, 396, 142 \n\n\\bibitem[Iyudin et al. (1999)]{iyudin99}\nIyudin, A., Sch\\\"onfelder, V., Bennett, K. et al., 1999, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Kappadath et al. (1996)]{kappadath96}\nKappadath, S.C., Ryan, J., Bennett, K., 1996, A\\&AS 120, 619 \n \n\\bibitem[Kippen et al. (1993)]{kippen93}\nKippen, R.M., Connors, A., Collmar, W. et al., 1993, Proc. of 23$^{rd}$ ICRC, The University of Calgary, 1, 85 \n\n\\bibitem[Kippen et al. (1994a)]{kippen94a}\nKippen, R.M., Macri, J. Ryan, J. et al., 1994a, IAU Circ. 5937 \n\n\\bibitem[Kippen et al. (1994b)]{kippen94b}\nKippen, R.M., Macri, J., Ryan, J. et al., 1994b, IAU Circ. 5943\n\n\\bibitem[Kippen et al. (1994c)]{kippen94c}\nKippen, R.M., Connors, A., Macri, J. et al., 1994c, in: AIP Conf. Proc. No 307, Gamma-Ray Bursts, ed. G.J. Fishman, J.J. Brainerd, K. Hurley (New York: AIP Press), p. 420\n\n\\bibitem[Kippen et al. (1995a)]{kippen95a}\nKippen, R.M., Connors, A., McConnell, M. et al., 1995a, Adv. Space Res. 15(5), 139 \n\n\\bibitem[Kippen et al. (1995b)]{kippen95b}\nKippen, R.M., Bennett, K., Connors, A. et al., 1995b, A\\&A 293, L5 \n \n\\bibitem[Kippen et al. (1995c)]{kippen95c}\nKippen, R.M., Ryan, J., Connors, A. et al., 1995c, Ann. N.Y. Acad. Sci. 759, 425\n\n\\bibitem[Kippen (1995d)]{kippen95d}\nKippen, R.M., 1995d, Ph-D Thesis, University of New Hampshire, Durham N.H., USA\n\n\\bibitem[Kippen et al. (1996)]{kippen96}\nKippen, M., Ryan, J., Connors, A. et al., 1996, in AIP Conf. Proc. 384, Gamma-Ray Bursts, ed. C. Kouveliotou, M.S. Briggs, G.J. Fishman (New York AIP), 436\n\n\\bibitem[Kippen et al. (1998a)]{kippen98a}\nKippen, M., Ryan, J., Connors, A. et al., 1998a, Adv. Sp. Research, 22(7), 1097\n\n\\bibitem[Kippen et al. (1998b)]{kippen98b}\nKippen, M., Ryan, J., Connors., A. et al., 1998b, ApJ 492, 246\n\n\\bibitem[Kn\\\"odlseder et al. (1996)]{knoed96}\nKn\\\"odlseder, J., Chen, W., Oberlack, U., Diehl, R., Gehrels, N., 1996, A\\&AS 120, 339\n\n\\bibitem[Kn\\\"odlseder et al. (1999)]{knoed99}\nKn\\\"odlseder, J., Bennett, K., Bloemen, H. et al., 1999, A\\&A, 345, 813\n\n\\bibitem[Kuiper et al. (1996)]{kuiper96}\nKuiper, L., Hermsen, W., Bennett, K. et al., 1996, A\\&AS 120, 73 \n \n\\bibitem[Kuiper et al. (1998a)]{kuiper98a}\nKuiper, L., Hermsen, W., Bennett, K. et al., 1998a, A\\&A 337, 421\n\n\\bibitem[Kuiper et al. (1998b)]{kuiper98b}\nKuiper, L., Hermsen, W., Sch\\\"onfelder, V. et al., 1998b, NATO ASI Series C, Vol. 515, 211\n\n\\bibitem[Kuiper et al. (1999a)]{kuiper99a}\nKuiper, L., Hermsen, W., Krijger, J. et al., 1999a, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Kuiper et al. (1999b)]{kuiper99b}\nKuiper, L., Hermsen, W., Krijger, J. et al., 1999b, A\\&A, submitted \n\n\\bibitem[Lichti et al. (1996)]{lichti96}\nLichti, G.G., Iyudin, A., Bennett, K. et al., 1996, A\\&AS 120, 353 \n\n\\bibitem[Maisack et al. (1995)]{maisack95}\nMaisack, M., Collmar, W., Barr, P. et al., 1995, A\\&A, 298,400\n\n\\bibitem[McConnell et al. (1994)]{mcconnell94}\nMcConnell, M., Forrest, D., Ryan, J. et al., 1994, ApJ 424, 933 \n \n\\bibitem[McConnell et al. (1996)]{mcconnell96}\nMcConnell, M., Bennett, K., Bloemen, H. et al., 1996, A\\&AS 120, 149\n\n\\bibitem[McConnell et al. (1997a)]{mcconnell97a}\nMcConnell, M., Bennett, K., Bloemen, H. et al., 1997a, Proc. of 25$^{th}$ ICRC, Durban, South Africa, eds.: M.S. Potgieter, B.C. Raubenheimer, D.J. v. der Walt, Vol. 3, 93\n\n\\bibitem[McConnell et al. (1997b)]{mcconnell97b}\nMcConnell, M., Bennett, K. Bloemen, H. et al., Proc. of 4$^{th}$ Compton Symposium, 1997b, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 1099 \n\n\\bibitem[McNaron-Brown et al. (1995)]{mcnaron95}\nMcNaron-Brown, K., Johnson, W.N., Jung, G.V. et al., 1995, ApJ, 451, 575\n\n\\bibitem[Morris et al. (1995)]{morris95}\nMorris, D., Bennett, K., Bloemen, H. et al., 1995, Ann. N.Y. Acad. Sci., 759, 397 \n \n\\bibitem[Much et al. (1995a)]{much95a}\nMuch, R., Bennett, K., Buccheri, R. et al., 1995a, A\\&A, 299, 435 \n \n\\bibitem[Much et al. (1995b)]{much95b}\nMuch, R., Bennett, K., Buccheri, R. et al. 1995b, Adv. Sp. Res.15(5), 81\n\n\\bibitem[Much et al. (1997)]{much97}\nMuch, R. et al., Bennett, K., Winkler, C., 1997, Proc. of 4$^{th}$ Compton Symposium, 1997, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 542\n\n\\bibitem[Oberlack et al. (1995)]{oberlack95}\nOberlack, U., Bennett, K., Bloemen, H. et al. 1995, Proc. of 24$^{th}$ ICRC, Istituto Nazionale Fisica Nucleare, Rome, Vol. 2, 207\n\n\\bibitem[Oberlack (1997)]{oberlack97}\nOberlack, U., 1997, Ph-D Thesis, The Technical University Munich, Germany\n\n\\bibitem[Ryan et al. (1993)]{ryan93}\nRyan, J., Kippen, M., Varendorff, M., 1993, IAU Circ. 5702\n\n\\bibitem[Ryan et al. (1994a)]{ryan94a}\nRyan, J.M., et al., McConnell, M., Kippen, R.M. et al., 1994a, IAU Circ. 5950\n\n\\bibitem[Ryan et al. (1994b)]{ryan94b}\nRyan, J.M., Bennett, K., Collmar, W. et al., 1994b, ApJ 422, L67\n\n\\bibitem[Schaefer et al. (1994)]{schaefer94}\nSchaefer,B.E., Teegarden, B.J., Cline, T.L. et al., 1994, in: AIP Conf. Proc. No 307, Gamma-Ray Bursts, ed. G.J. Fishman, J.J. Brainerd, K. Hurley (New York: AIP Press), p. 280\n\n\\bibitem[Sch\\\"onfelder (1991)]{schoenf91}\nSch\\\"onfelder, V., 1991, IAU Circ. 5369\n\n\\bibitem[Sch\\\"onfelder et al. (1993)]{schoenf93}\nSch\\\"onfelder, V., Aarts, H. Bennett, K., 1993, ApJS 86, 657\n\n\\bibitem[Sch\\\"onfelder et al. (1995)]{schoenf95}\nSch\\\"onfelder, V., Bennett, K., Bloemen, H. et al., 1995, Ann. of N.Y. Acad. Sci. 759, 226\n \n\\bibitem[Sch\\\"onfelder et al. (1996)]{schoenf96}\nSch\\\"onfelder, V., Bennett, K., Bloemen, H. et al., 1996, A\\&AS 120, 13\n\n\\bibitem[Share et al. (1994)]{share94}\nShare, G.H., Connors, A., Dingus, B.L. et al., 1994, in: AIP Conf. Proc. No 307, Gamma-Ray Bursts, ed. G.J. Fishman, J.J. Brainerd, K. Hurley (New York: AIP Press), p. 283\n\n\\bibitem[Stacy et al. (1997)]{stacy97}\nStacy, J. G., Ryan, J.M., Collmar, W. et al., 1997, Proc. of 4$^{th}$ Compton Symposium, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 1356\n\n\\bibitem[Steinle et al. (1995)]{steinle95}\nSteinle, H., Collmar, W., Diehl, R. et al., 1995, Adv. Space Res. 15, 37\n\n\\bibitem[Steinle et al. (1998)]{steinle98}\nSteinle, H., Bennett, K., Bloemen, H. et al., 1998, A\\&A 330, 97\n\n\\bibitem[Strong et al. (1992)]{strong92}\nStrong, A.W., Cabeza-Orcel, P., Bennett, K. et al., 1992, in: Data Analysis in Astron. IV, ed. V. di Ges\\`u, L. Scarsi, R. Buccheri, P. Crane, M.C. Maccarone, H.U. Zimmermann, Plenum Press, New York, 251-260\n\n\\bibitem[Strong et al. (1996)]{strong96} \nStrong, A.W., Bennett, K., Bloemen, H., 1996, A\\&AS 120, 381-388 \n% \n%\\bibitem[Strong et al. (1997)]{strong97}\n%Strong, A. et al., 1997, Proc. of 2$^{2nd}$ INTEGRAL Workshop, eds.: C. Winkler, T.J.-L. Courvoisier, Ph. Durouchoux, ESA-SP-382, p. %533-536 \n%\n\n\\bibitem[Strong et al. (1999)]{strong99}\nStrong, A. W., Bloemen, H., Diehl, R. et al., 1999, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Swanenburg et al. (1978)]{swanenburg78}\nSwanenburg, B.N., Bennett, K., Bignami, G.F. et al., 1978, Nature 275, 298 \n\n\\bibitem[Thompson et al. (1995)]{thompson95}\nThompson, D. J., Bertsch, D.L., Dingus, B.L. et al., 1995, ApJS, 101, 259 (2EG)\n\n\\bibitem[Thompson et al. (1996)]{thompson96}\nThompson, D. J., Bertsch, D.L., Dingus, B.L. et al., 1996, ApJS, 107, 227 (2EGS)\n\n\\bibitem[Thompson et al. (1999)]{thompson99}\nThompson, D. J., Bailes, M., Bertsch, D.L. et al., 1999, ApJ, 516, in press\n\n\\bibitem[van der Meulen et al. (1998)]{meulen98}\nvan der Meulen, R.D., Bloemen, H., Bennett, K. et al, 1998, A\\&A 330, 321\n\n\\bibitem[van der Meulen et al. (1999)]{meulen99}\nvan der Meulen, R.D., Bloemen, H., Bykov, A.M. et al, 1999, Proc. of 3$^{rd}$ INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[van Dijk et al. (1995)]{vandijk95}\nvan Dijk, R., Bennett, K., Collmar, W. et al., 1995, A\\&A 296, L33 \n\n\\bibitem[van Dijk (1996)]{vandijk96}\nvan Dijk, R., 1996, Ph-D Thesis, The University of Amsterdam, The Netherlands\n\n\\bibitem[Varendorff et al. (1992]{varendorff92}\nVarendorff, M.G., Bennett, K., de Boer, H. et al., 1992, in: AIP Conf. Proc. No 265, Gamma-Ray Bursts, ed. W.S. Paciesas, G.J. Fishman (New York: AIP Press), p. 22\n\n\\bibitem[Varendorff et al. (1993)]{varendorff93}\nVarendorff, M.G., Connors, A., Collmar, W. et al., 1993, Proc. of 23$^{rd}$ ICRC, The University of Calgary, 1, 81\n\n\\bibitem[von Montigny et al. (1995)]{montigny95}\nvon Montigny, C., Bertsch, D.L., Chiang, J. et al., 1995, ApJ, 440, 525\n\n\\bibitem[Weidenspointner et al. (1999)]{weidens99}\nWeidenspointner, G., Varendorff, M., Bennett, K. et al., 1999, Proc. of 3rd INTEGRAL Workshop, Taormina, Italy, September 14-18, 1998, Eds: G. Palumbo, A. Bazzano, C. Winkler, Astrophys. Letters and Communications, in press\n\n\\bibitem[Williams et al. (1995a)]{williams95a}\nWilliams, O.R., Much, R., Bennett, K. et al., 1995, A\\&A, 297, L21 \n \n\\bibitem[Williams et al. (1995b)]{williams95b}\nWilliams, O.R., Bennett, K., Bloemen, H. et al., 1995b, A\\&A 298, 33 \n\n\\bibitem[Williams et al. (1997)]{williams97}\nWilliams, O. R., Bennett, K., Much, R. et al., 1997, Proc. of 4$^{th}$ Compton Symposium, 1997, eds. C.D. Dermer, M.S. Strickman, J.D. Kurfess, AIP New York 410, p. 1582 \n\n\\bibitem[Williams et al. (1999)]{williams99}\nWilliams, O.R., Bennett, K., Much, R. et al., 1999, Proc. of 5th Compton Symposium (Portsmouth N.H., USA), AIP N.Y.: submitted for publication\n\n\\bibitem[Winkler et al. (1992)]{winkler92}\nWinkler, C., Bennett, K., Bloemen, H. et al., 1992, in: AIP Conf. Proc. No 265, Gamma-Ray Bursts, ed. W.S. Paciesas, G.J.Fishman (New York: AIP Press), p. 77 \n\n\\bibitem[Winkler et al. (1993a)]{winkler93a}\nWinkler, C., Bennett, K., Bloemen, H. et al., 1993a, A\\&A 255, L9\n\n\\bibitem[Winkler et al. (1993b]{winkler93b}\nWinkler, C., Bennett, K., Hanlon, L. et al., 1993b, in: AIP Conf. Proc. No 280, Gamma-Ray Observatory, ed. M. Friedlander, N. Gehrels, D.J. Macomb (New York: AIP Press), p. 845\n\n\\bibitem[Winkler et al. (1995)]{winkler95}\nWinkler, C., Kippen, R.M., Bennett, K. et al., 1995, A\\&A 302, 765\n\n\n\n \n\\end{thebibliography}"
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\\textfont2=\\sevensy \\scriptfont2=\\sixsy \n\\scriptscriptfont2=\\fivesy\n\\def\\doublespace{\\baselineskip=18pt\\lineskip=0pt\n\\lineskiplimit=-5pt}\n\\def\\singlespace{\\baselineskip=9pt\\lineskip=0pt\n\\lineskiplimit=-5pt}\n\\def\\oneandahalf{\\baselineskip=15pt\\lineskip=0pt\n\\lineskiplimit=-5pt}\n}\n\n%IAU format macro\n\\def\\iaufmt{\\vsize=20.45cm\\hsize=16.45cm\n\\voffset=-1.6cm\\hoffset=-0.2cm}\n\n\n\\def\\nH2{$n_{\\rm H_2}~$}\n\\def\\nh2{$n_{\\rm H_2}~$}\n\\def\\H2{${\\rm H_2}~$}\n\\def\\h2{${\\rm H_2}~$}\n\\def\\cm{{\\rm cm}}\n\\def\\cm3{cm$^{-3}$}\n \n\\def\\Tbr{$T_{br}~$}\n\\def\\T{$T_{\\rm H_2}~$}\n\\def\\pil{$^2\\Pi_{3/2}$}\n\\def\\pir{$^2\\Pi_{1/2}$}\n\\def\\fo{$f_{\\rm ortho-H_2}$}\n\\def\\fp{$f_{\\rm para-H_2}$}\n\\def\\fOH{$f_{\\rm OH}$}\n\n\\begintex\n\\centerline{\\bf 5 cm OH MASERS AS DIAGNOSTICS OF PHYSICAL CONDITIONS}\n\\centerline{\\bf IN STAR-FORMING REGIONS. }\n\\bigskip\n\\centerline{KONSTANTINOS G. PAVLAKIS$^{1,2,3}$ \\& NIKOLAOS D. KYLAFIS$^{2,3}$}\n\\bigskip\n\\leftline {$^1$University of Leeds, Department of Physics and Astronomy,\n Woodhouse Lane, Leeds LS2 9JT}\n\\leftline {$^2$University of Crete, Physics Department, 714 09 Heraklion, \nCrete, Greece}\n\\leftline{$^3$Foundation for Research and Technology-Hellas, P.O. Box 1527, \n711 10 Heraklion, Crete, Greece}\n\n\\centerline{pavlakis@ast.leeds.ac.uk, kylafis@physics.uch.gr}\n\\bigskip\n\n\\centerline{{\\it Received:}~~\\underbar{~~ \\ \\ \\ \\ \\ \\ \\ ~~}{\\it~;}\n{\\it accepted:}~~\\underbar{~~ \\ \\ \\ \\ \\ \\ \\ ~~}}\n\\bigskip\n\n\\centerline{ABSTRACT}\n\\bigskip\n\nWe demonstrate that the observed characteristics of the\n5 cm OH masers in star-forming regions can be \nexplained with the same model and the same parameters as the 18 cm and the \n6 cm OH masers. In our already published study of the 18 cm and the 6 cm\nOH masers in star-forming regions we had examined the pumping of the 5 cm\nmasers, but did not report the results we had found because of some missing\ncollision rate coefficients, which in principle could be important. The\nrecently published observations on the 5 cm masers of OH encourage us to\nreport our old calculations along with some new ones that we have performed.\nThese calculations, in agreement with the observations, reveal the\nmain lines at 5 cm as strong masers, the 6049 MHz satellite line as a weak\nmaser, and the 6017 MHz satellite line as never inverted for reasonable\nvalues of the parameters.\n\n\\bigskip \\noindent\n{\\it Subject headings:} ISM: molecules --- masers --- molecular processes \n--- radiative transfer --- stars: formation\n\\vfill \\eject\n\\centerline{1. INTRODUCTION}\n\\bigskip\n\nThe OH molecules in star-forming regions are rich in maser emission. \nThey exhibit: \na) Four maser lines (at 18 cm) in the ground state \\pil, $J=3/2$ \n(e.g., Gaume \\& Mutel 1987; Cohen, Baart, \\&\nJonas 1988; for reviews see Reid \\& Moran 1981; Cohen 1989; Elitzur 1992).\nb) Three maser lines (at 5 cm) in the first excited state \\pil, $J=5/2$ \n(Knowles, Caswell, \\& Goss 1976; Guilloteau et al. 1984; \nSmits 1994; Caswell \\& Vaile 1995;\nBaudry et al. 1997; Desmurs et al. 1998; Desmurs \\& Baudry 1998).\nc) Three maser lines (at 6 cm) in the next level \\pir, $J=1/2$ \n(Gardner \\& Martin Pintado 1983; \nGardner \\& Whiteoak 1983; Palmer, Gardner, \\& Whiteoak 1984;\nGardner, Whiteoak, \\& Palmer 1987; Baudry et al. 1988; Baudry \\& Diamond 1991;\nCohen, Masheder, \\& Walker 1991).\nd) One maser line (at 2 cm) in the level \\pil, $J=7/2$ \n(Turner, Palmer, \\& Zuckerman 1970; Baudry et al. 1981; \nBaudry \\& Diamond 1998).\n\nIn our recently reported calculations (Pavlakis \\& Kylafis 1996a, hereafter\nPaper I; Pavlakis \\& Kylafis 1996b, hereafter Paper II) we explained\ntheoretically the observed characteristics of the 18 cm and the 6 cm maser\nlines of OH. Naturally, we had computed also the maser emission of the 5 cm \nlines of OH, but we decided to ``not show or discuss the maser lines in the\nexcited state \\pil, $J=5/2$ because this state is directly connected with the\nstate \\pir, $J=7/2$, which is not included in our calculations.\nWe urge quantum chemists to compute collision rate coefficients for as \nmany transitions as possible'' (Paper I). \n\nSoon after our calculations were published, Baudry et al. (1997) reported \nan extensive study of the 5 cm maser lines of OH in star-forming regions.\nTo our surprise, {\\it our already performed calculations explain the\nobserved characteristics.} This probably means that, for temperatures\nbetween 100 and 200 K that are thought appropriate for OH maser regions,\nthe missing collision rate coefficients are not important for the 5 cm masers.\nThus, we are encouraged to publish \nour results. Of course, when the missing collision rate coefficients are \ncomputed, it will be reassuring to show that they are indeed not important \nfor the 5 cm masers.\n\nIn \\S 2 we discuss briefly the model that we used,\nin \\S 3 we present the results of the calculations, \nin \\S 4 we compare our calculations with the observations and\nin \\S 5 we present our conclusions.\n \n\n\\bigskip\n\\centerline{2. MODEL}\n\\bigskip\n\nOur model is the same as that in Papers I and II. Not only this,\nbut {\\it the values of the parameters are exactly the same.} \nThus, no parameters are adjusted for any qualitative or quantitative \nexplanation of the observations.\n\nThe maser regions are modeled as cylinders of length $l=5 \\times 10^{15}$ cm\nand diameter $d=10^{15}$ cm. The characteristic bulk velocity\nin the maser region is denoted by $V$ and the assumed velocity field there\nis given \nby $ \\vec {\\bf v} =V/(d/2) \\rho {\\bf\\hat \\rho} +(V/l) \nz {\\bf\\hat z}$, where ($\\rho, z$) are the cylindrical coordinates,\nand ${\\bf\\hat\\rho}$ and ${\\bf\\hat z}$ are the corresponding unit vectors.\n\nThe fractional abundances of OH and ortho-H$_2$ with\nrespect to density of H$_2$ molecules in the maser region\nare denoted by \\fOH \\ and \\fo, respectively, while the density \nof H$_2$ molecules and the \nkinetic temperature there are denoted by \\nH2 and $T_{\\rm H_2}$, respectively.\nFinally, the brightness temperature of the maser lines is denoted by\n$T_{br}$, the dilution factor of the far infrared radiation field by $W$\n(see eq. [5] of Paper II), \nthe dust optical depth parameter by $p$\n(see eq. [4] of Paper II), \nand the dust temperature by $T_d$.\n\nIn addition to the exploration of the parameters used in Papers I and II,\nwe also explore here the effects of the fractional abundance of OH.\n\nIn the figures of this paper the key is as follows:\nThe brightness temperature of the 6049 MHz transition is shown as a solid \nline, that of the 6035 MHz transition by a dotted line, that of the 6017 MHz\nby a dashed line and that of the 6031 MHz by a dot-dashed line.\n\n\\bigskip\n\\centerline{3. CALCULATIONS AND PRESENTATION OF RESULTS}\n\\bigskip\n\\centerline{3.1. Collisions Only}\n\\bigskip\n\nFor kinetic temperatures $100 \\ltorder T_{\\rm H_2} \\ltorder 200$ K, which are \nthought to be prevailing in H II/OH maser regions, there are several locally \n(i.e., thermally) overlapping lines of OH. Nevertheless, it is interesting \nto look at calculations, which take into account collisions only, in order to \nsee what their effects are on the pumping of OH molecules (see also Paper I).\nInterestingly, we have found that for temperatures $T_{\\rm H_2} \\ltorder 150$ \nK, which are highly likely for H II/OH regions, the effects of locally \noverlapping lines are insignificant on the pumping of the 5 cm maser lines\nand their inclusion changes the results \nof our calculations by less than a factor of two. Thus, if there are no \nlarge velocity gradients in the maser regions and the external FIR\nfield is weak, collisions alone determine the 5 cm maser emission\nof OH at $T_{\\rm H_2} \\ltorder 150$ K.\n\nWe have found that collisions alone are unable to invert the main lines\nat 5 cm. For \\fo$=1$ and \\fOH$=10^{-5}$ \nonly the 6049 MHz satellite line is masing for hydrogen\ndensities $2 \\times 10^5 \\ltorder n_{\\rm H_2} \\ltorder 7 \\times 10^6$ \ncm$^{-3}$. \nThe peak of the brightness temperature occurs at $n_{\\rm H_2} \\sim 10^6$ \ncm$^{-3}$ and it is $T_{br} \\sim 10^9$ K above $T_{\\rm H_2} = 100$ K\n(see Figure 1 below and the discussion in the next subsection).\n\nAs \\fo decreases, the brightness temperature of the 6049 MHz line decreases\nfaster than exponential. For \\fo$=0.5$ the peak of the \nbrightness temperature is\n$T_{br} = 6 \\times 10^6$ K and it is at the limits of dedectability.\nFor values of \\fo below 0.2 the inversion disappears and no 5 cm line\nshows inversion.\n\n\\bigskip\n\\centerline{3.2. Collisions and Local Line Overlap}\n\\bigskip\n\nThe effects of collisions and local line overlap \n{\\it cannot} be separated. It is simply a good fortune that for temperatures \nup to about 150 K \nthe effects of\ncollisions dominate \nthose of\nlocal line overlap.\n\nAssuming that large velocity gradients and a significant FIR radiation \nfield are absent in the maser regions (see below for their effects), \nwe have computed the 5 cm OH\nmaser emission as a function of \\nH2 taking into account both collisions and\nlocal line overlap.\nFor \\T$= 150$ K, \\fo$=1$, $f_{\\rm OH} = 10^{-5}$ and $V=0.6$ km s$^{-1}$\n(for which we do not have any non-locally overlapping lines),\nwe show in Figure 1 the brightness temperature \\Tbr of the 6049 MHz line\n(the only inverted OH line at 5 cm) as a function of \\nH2. \nThis is a \nquite strong maser line with a peak brightness temperature $T_{br} = 6 \n\\times 10^8$ K.\nAs the temperature \\T\nincreases further, more and more pairs of lines overlap locally and their\ndegree of overlap also increases. For temperatures up to 170 K, local\noverlap causes only quantitative (not qualitative) changes in the results.\nThe peak brightness temperature decreases with increasing kinetic temperature \nand the range of densities over which inversion occurs also\ndecreases. For \\T$=170$ K, the peak $T_{br}$ of the 6049 MHz maser line\nfalls to $10^7$ K \nand inversion occurs for $10^5 \\ltorder n_{\\rm H_2} \\ltorder 10^6$ cm$^{-3}$.\n\nAbove \\T$=170$ K, the effects of local line overlap introduce qualitative\nchanges. \nThe 6049 MHz line continues to weaken, while the 6035 MHz line now\nappears.\nAs the temperature approaches 200 K, there are fifteen pairs and one\ntriple of locally overlapping lines. Figure 2 shows \\Tbr as a function of\n\\nH2 for \\T$=200$ K, \\fo$=1$, $f_{\\rm OH} = 10^{-5}$ and $V=0.6$ km s$^{-1}$.\nAt this relatively high temperature, the peak \\Tbr of the 6049 MHz maser\nline is only $10^6$ K, \nwhile for the 6035 MHz main line, \n\\Tbr $\\sim 10^9$ K at $n_{\\rm H_2} \\sim 10^7$ cm$^{-3}$.\n\nWhen \\fo$=0$, no OH 5 cm maser line appears\nfor kinetic temperatures lower than 170 K.\nFor \\T$=200$ K, \\fo$=0$, \\fOH$=10^{-5}$ and $V=0.6$ km s$^{-1}$\nthe results are shown in Figure 3. The peak \\Tbr of the 6035 MHz\nline is one order of magnitude stronger than that for \\fo$=1$, but the \n6049 MHz line is absent. Thus, as with the 1720 MHz maser line (see Paper I),\nthe 6049 MHz maser line could be a diagnostic (but see below) of the\nabundance of ortho-H$_2$ in maser regions. \n\nThe fractional \nabundance of OH in star-forming regions is probably not constant\nindependent of density. To explore this possibility we have computed models\nwith \\fOH$=10^{-6}$ \n(the results are not shown in a Figure).\nNo qualitative changes occur in comparison with\nthe results for \\fOH$=10^{-5}$ (see Figures 2 and 3). The 6035 MHz line\nis of the same intensity as in Figures 2 and 3, but it is inverted at \ndensities a factor of three higher. The 6049 MHz line is reduced in \nintensity to the point of being unobservable ($T_{br} \\ltorder 10^3$ K). \nFor this line also the inversion occurs at densities a factor of three\nhigher than those in Figure 2.\n\n\\bigskip\n\\centerline{3.3. Collisions, Local and Non-local Line Overlap}\n\\bigskip\n\nIn addition to collisions and local line overlap, we now take into account\nthe effects of non-local line overlap (for details see Paper II).\nIn order to avoid showing a multitude of models, we take the representative \nvalue of 150 K for $T_{\\rm H_2}$. For \\fo $ = 1$ and \\fOH$= 10^{-5}$,\nwe start with a characteristic velocity $V=1$ km s$^{-1}$, for \nwhich the effects of non-local line overlap are already important. Figure 4 \nshows the brightness temperature of the masing lines as a function of \\nH2.\nComparing Figure 4 with Figure 1 we see the dramatic effects that non-local\nline overlap has on the maser transitions. \nFor relatively high hydrogen densities, two 5 cm lines\nare inverted. The 6035 MHz main line with high brightness temperature \nand the 6017 MHz satellite line.\n\nIncreasing the characteristic velocity to $V=2$ km s$^{-1}$, but keeping the\nrest of the parameters the same, results in a significant reduction of the \n6049 MHz line (Figure 5). For \\nH2$\\sim 10^8$ \\cm3, the 6031 MHz main\nline and the 6017 MHz satellite one are inverted with high \nbrightness temperatures. At even higher densities the 6035 MHz main line\nis inverted, the 6017 MHz line remains strongly inverted, while the 6031 MHz\none is suppressed. A further increase of the velocity to\n$V=3$ km s$^{-1}$ results in the complete disappearance of the 6049 MHz\nline (Figure 6). \n\nAs in the previous subsection, a significant \nreduction of the abundance of ortho-H$_2$ \nresults in the disappearance of the 6049 MHz line as a maser line. This is\ntrue for $V=1$, 2 or 3 km s$^{-1}$. As a characteristic example we show\nthe case of \\fo$=0$, \\fOH$= 10^{-5}$ and $V=2$ km s$^{-1}$ (Figure 7). \nBelow \\nH2$\\sim 3 \\times 10^7$ \\cm3 no maser line appears.\n\nFinally, a reduction of \\fOH~ by an order of magnitude has the general result \nof significantly reducing the brightness temperature of the 6049 MHz line\n($T_{br} \\ltorder 10^4$ K),\nas it was also seen in the previous subsection. Furthermore, our calculations\nhave shown that \\fOH$= 10^{-6}$ results in destroying the inversion of all\n5 cm maser lines at relatively high densities \n(\\nH2$\\gtorder 4 \\times 10^7$ \\cm3).\n \n\\bigskip\n\\centerline{3.4. Effects of a FIR Radiation Field}\n\\bigskip\n\nFrom the calculations presented so far, it is evident that the 5 cm {\\it main \nlines} of OH {\\it are never inverted together} for densities thought \nprevailing in star-forming regions (i.e., \\nH2$\\ltorder {\\rm few} \\times \n10^7$ \\cm3),\nwhen a far infrared (FIR) radiation field is absent. In this subsection we \nwill demonstrate that a FIR radiation field is necessary to reproduce the \nobserved features of the 5 cm lines and their correlations with the ground\nstate $^2\\Pi_{3/2}$, $J=3/2$ and the excited state $^2\\Pi_{1/2}$, $J=1/2$ \nOH masers.\n\nFor \\T $ =150$ K, $f_{\\rm OH}= 10^{-5}$, $f_{\\rm ortho-H_2}$=1, $V$=1 \nkm s$^{-1}$ and dilution factor $W=0.01$ (see Paper II), \nthe main lines at 5 cm are inverted at low densities \n(\\nH2$\\ltorder {\\rm \nfew} \\times 10^7$ \\cm3)\nwhen\n$T_d > T_{\\rm H_2}$. When $T_d < T_{\\rm H_2}$ (see Figures 8a and 8b) the \nresults are similar i.e., differences less than a factor of 2 in the\n$T_{br}$ to those of Figure 4, where there was no external \nFIR radiation field. However, when $T_d > T_{\\rm H_2}$ \n(see Figures 8c and 8d), \nthe main line at 6035 and 6031 MHz make their appearance as masers.\n\nIncreasing the strength of the FIR radiation field by taking $W=0.1$ has\ndramatic effects on the 5 cm lines of OH.\nFigures 9a - 9d show $T_{br}$ of the maser lines as a function of \n$n_{\\rm H_2}$ for \\T $ =150$ K, $f_{\\rm OH}= 10^{-5}$,\n$f_{\\rm ortho-H_2}$=1, $V$=1 km s$^{-1}$ and dilution factor\nW=0.1. Both 5 cm main lines are masing with the 6035 MHz line stronger than\nthe 6031 MHz one in the range of densities where both lines are inverted.\nThe satellite line at 6049 MHz is also masing but the other satellite line\nat 6017 MHz is never inverted for \\nH2$\\ltorder {\\rm few} \\times 10^7$ \n\\cm3.\n\nRemarkably, the abundance of ortho-H$_2$ causes no \nchanges as to which 5 cm lines of OH are masers. \nFigures 10a - 10d are made with \\fo$=0$ and the rest\nof the parameters the same as in Figures 9a - 9d, respectively.\n\nWhat has dramatic effects on the pumping of the 5 cm lines is the \ncharacteristic velocity. For $V=2$ km s$^{-1}$ and $V=3$ km s$^{-1}$\nwith the rest of the parameters the same as in Figures 9a - 9d, the results\nare shown in Figures 11a - 11d and 12a - 12d, respectively.\nAs it is clear from these Figures, an increase of $V$ (i.e., \nincrease of nonlocal overlap) causes suppression of the 5 cm main lines.\nThe 6035 MHz line is not inverted at all. The 6031 MHz either is not\ninverted (compare Figs. 9a and 12a) or it is much weaker (compare \nFigs. 9d and 12d) depending on the strength of the FIR field. The reader\nshould notice the competition between the FIR field, which inverts the main \nlines (as we go from a to d in Figs. 9, 11, and 12 the FIR field increases)\nand the nonlocal overlap, which suppresses the inversion (as we go from \nFig. 9 to Fig. 11 and then to Fig. 12 the nonlocal overlap increases).\n\nFor completeness, we take one of our \ncases that agrees qualitatively well with the observational data, \nnamely\nthe case presented in Figure 9c, and explore the effects of the abundance\nof OH. For \\fOH$=10^{-4}$ and \\fOH$=10^{-6}$ the results are shown in\nFigures 13 and 14, respectively. The abundance of OH introduces only \nquantitative changes. An enhanced abundance of OH increases the brightness\ntemperature of the 6049 MHz maser line, while a reduced abundance has the \nopposite effect. The main lines at 6035 and 6031 MHz remain essentially\nunaffected.\n\nSince the effects of the abundance of OH on the ground state \n$^2\\Pi_{3/2}$, $J=3/2$ and the excited state $^2\\Pi_{1/2}$, $J=1/2$ were not\ninvestigated in Paper II, we show in Figure 15 the case of \\fOH$=10^{-6}$ and \nall the other parameters the same as in Figure 6c of Paper II.\n \n\\bigskip\n\\centerline{4. COMPARISON WITH OBSERVATIONS} \n\nSince the original discovery of emission from the \\pil, $J=5/2$\n(Yen et al. 1969), many surveys were made for detection of 5 cm maser\nemission toward a variety of sources (Knowles et al. 1976; Guilloteau et al. \n1984; Smits 1994). Caswell and Vaile (1995) surveyed for 6035 MHz masers in\n208 OH sources with peak 1665MHz flux density greater than 0.8 Jy. \nOnly 35 masers at 6035 MHz were detected, `` a result that agrees well \nwith our calculations ''. Since these observations were made with\na single dish, and the authors have not proven that any of the 1665-6035\nMHz ``pairs'' come from the same region, these observations must be \ninterpreted solely as a tendency of the 1665 MHz line to be inverted\nmore easily than the 6035 MHz one. Our results qualitatively agree with\nthis. \nThe 1665 MHz line (see Paper II) is inverted in a much\nbroader range of densities, velocity fields and strengths of a FIR field\nthan the 6035MHz line. \n\nLet's for the rest of this section \nrestrict to our results in the\npresence of a FIR field, $V < 1.5$ km s$^{-1}$ and $n_{\\rm H_2} < 10^7$ \ncm$^{-3}$. The 6035 MHz line is weaker than the 1665 MHz one and is inverted\nin a range of densities which is a subset \nof the range of densities over which the 1665 MHz line is \ninverted. As the FIR field gets stronger, this subregion becomes broader \nand the 6035 MHz line tends to be inverted in the same range of densities\nas the 1665 MHz line. By taking also into account our result that the \nstronger the FIR radiation field is the stronger the 1665 and 6035 MHz masers \nare, and assuming that both lines come from the same region, \nour models are in qualitative agreement with the observational result of\nCaswell and Vaile (1995) that the greater the peak of 1665 MHz maser intensity,\nthe greater the detection rate of 6035 MHz masers.\n\nAn extensive search for all four maser lines in 5 cm has been made \nby Baudry et al. (1997)\ntoward 265 strong FIR sources and the general observed characteristics\nof these 5 cm masers can be explained by our calculations. Their observations\nshow (see also Desmurs et al. 1998) that \nthe main-line masers at 6035 MHz, in the $^2\\Pi_{3/2}$, \n$J=5/2$ state of OH, are generally stronger and more common than \nthose at 6031 MHz in H II/OH regions. \nNevertheless the 6031 MHz line is frequently observed to be masing.\nStrong 5 cm satellite line masers are not observed in the $J=5/2$ state \nof OH. The 6017 MHz line is often found in absorption while the other\nsatellite line at 6049 MHz is observed in weak emission which could \ncorrespond to low gain masers. Our theoretical calculations are in \ngood qualitative agreement with these observations. \nThe 6017 MHz line is never \ninverted in our calculations and the 6049 MHz line is weak in a wide range\nof parameters thought to be prevailing in star-forming regions.\n\nOur calculations show that a combination of a FIR radiation field, collisions \nand line overlap is necessary to reproduce the general features of 6 GHz \nH II/OH masers. Nevertheless, simultaneous or nearly simultaneous\nVLBI observations at 1.6 GHz,\n4.7 GHz and 6 GHz are necessary to restrict the range of parameters for\nthe inversion of these masers and a search of the correlation between \n5 cm maser and FIR radiation field strength would be important to prove \nor not the importance of FIR radiation for the inversion of these masers. \n\n\\bigskip\n\\centerline{5. SUMMARY AND CONCLUSIONS}\n\\bigskip\nWe have performed a detailed, systematic study of OH maser pumping in order\nto attempt to invert the problem and from the OH maser observations to infer\nthe physical conditions in H II/OH regions. This was partially accomplished\nin Papers I and II. With the present study of the 5 cm masers of OH \nthe predictions of our model are:\n\n1) When strong 5 cm maser main lines are seen, a FIR radiation field must\nbe strong there, \ni.e., high value of $W$ or $p$ or $T_d$ or a combination of them.\n\n2) Inversion of both main lines at 5 cm requires relatively small \nvelocity gradients. For $V \\ltorder 1$ km s$^{-1}$\nand a FIR radiation field present, these lines are always seen. If these lines \nare seen together in the same spatial region, the 1665 MHz OH ground state\nmain line maser will also be observed in the same region, while there is a\nhigh probability the other ground state main line maser at 1667 MHz to be \nobserved too (see Paper II).\n\n3) When the 6031 MHz maser line is observed in a region where there is no \ndetection of 6035 MHz maser, the 1665 MHz ground state line is\ninverted in the same spatial region. This situation has a great probability\nto be indicative of relatively large velocity gradients ($V > 1$ km s$^{-1}$). \n\n4) When the 6049 MHz maser line is seen as a strong line (say, as strong as the\n5 cm main lines are typically seen), then \\fOH$\\gtorder 10^{-5}$.\n\n5) We predict that maser spots showing very strong 18 cm main lines should\nexhibit 5 cm maser main lines also. This may have already been seen \n(Caswell \\& Vaile 1995), but VLBI observations are needed to confirm or\nreject our prediction. \n\n6) We also predict that 18 cm maser main lines with $V \\gtorder 2$ km s$^{-1}$\nwill not be accompanied by 5 cm maser main lines. \n\nThis research has been supported in part by a grant from the General \nSecretariat of Research and Technology of Greece and a Training and Mobility\nof Researchers Fellowship of the \nEuropean Union under contract No ERBFMBICT972277.\n\n\n\\vfill \\eject\n\\centerline{REFERENCES}\n\n\\beginrefs\n\nBaudry, A., \\& Diamond, P. J. 1991, A\\&A, 247, 551\n\n------------ 1998, A\\&A, 331, 697\n\nBaudry, A., Desmurs, J. F., Wilson, T. L., \\& Cohen, R. J. 1997, A\\&A, \n325, 255\n\nBaudry, A., Diamond, P. J., Booth, R. S., Graham, D., \\& Walmsley, C. M.\n1988, A\\&A, 201, 105\n\nBaudry, A., Walmsley, C. M., Winnberg, A., \\& Wilson, T. L. 1981, A\\&A, \n102, 287\n\nCaswell, J. L., \\& Vaile, R. A. 1995, MNRAS, 273, 328\n\nCohen, R. J. 1989, Rep. Prog. Phys., 52, 881\n\nCohen, R. J., Baart, E. E., \\& Jonas, J. L. 1988, MNRAS, 231, 205\n\nCohen, R. J., Masheder, M., \\& Walker, R. N. F. 1991, MNRAS, 250, 611\n\nDesmurs, J. F., Baudry, A., Wilson, T. L., Cohen, R. J., \\& Tofani, G.\n1998, A\\&A, 334, 1085\n\nDesmurs, J. F., \\& Baudry, A. 1998, A\\&A, in press\n\nElitzur, M. 1992, ARA\\&A, 30, 75\n\nGardner, F. F. \\& Martin-Pintado, J. 1983, A\\&A, 121, 265\n\nGardner, F. F., \\& Whiteoak, J. B. 1983, MNRAS, 205, 297\n\nGardner, F. F., Whiteoak, J. B., \\& Palmer, P. 1987, MNRAS, 225, 469\n\nGaume, R. A., \\& Mutel, R. L. 1987, ApJ Suppl., 65, 193\n\nGuilloteau, S., Baudry, A., Walmsley, C. M., Wilson, T. L., \\& Winnberg, A.\n1984, A\\&A, 131, 45\n\nKnowles, S. H., Caswell, J. L., \\& Goss, W. M. 1976, MNRAS, 175, 537\n \nPalmer, P., Gardner, F. F., \\& Whiteoak, J. B. 1984, MNRAS, 211, 41p\n\nPavlakis, K. G., \\& Kylafis, N. D. 1996a, ApJ, 467, 300 (Paper I)\n\n------------ 1996b, ApJ, 467, 309 (Paper II)\n\nReid, M. J., \\& Moran, J. M. 1981, ARA\\&A, 19, 231\n\nSmits, D. P. 1994, MNRAS, 269, L11\n\nTurner, B. E., Palmer, P., \\& Zuckerman, B. 1970, ApJ, 160, L125\n\nYen, J. L., Zuckerman, B., Palmer, P., \\& Penfield, H. 1969, \nApJ 156, L27\n\n\\endrefs\n\n\n\\vfill \\eject\n\\centerline{FIGURE CAPTIONS}\n\\noindent\nFIG. 1.--- Brightness temperature \\Tbr as a function of density \\nH2 for\n\\T$=150$ K, \\fo $ =1$, \\fOH$=10^{-5}$ and $V = 0.6$ km s$^{-1}$.\nThe values of the other parameters are given in \\S 2.\n\\bigskip \\noindent\nFIG. 2.--- Same as in Figure 1, but \\T$=200$ K.\n\\bigskip \\noindent\nFIG. 3.--- Same as in Figure 2, but \\fo$=0$.\n\\bigskip \\noindent\nFIG. 4.--- Brightness temperature \\Tbr as a function of density \\nH2 for\n\\T$=150$ K, \\fo $ =1$, \\fOH$=10^{-5}$ and $V = 1$ km s$^{-1}$.\nThe values of the other parameters are given in \\S 2.\n\\bigskip \\noindent\nFIG. 5.--- Same as in Figure 4, but for $V = 2$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 6.--- Same as in Figure 4, but for $V = 3$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 7.--- Same as in Figure 5, but for \\fo$=0$.\n\\bigskip \\noindent\nFIG. 8a.--- Brightness temperature \\Tbr as a function of density \\nH2 for\n\\T$=150$ K, \\fo$=1$, \\fOH$=10^{-5}$, $V=1$ km s$^{-1}$, $T_d=100$ K, $p=1$\nand $W=0.01$. The values of the other parameters are given in \\S 2.\n\\bigskip \\noindent\nFIG. 8b.--- Same as in Figure 8a, but for $p=2$.\n\\bigskip \\noindent\nFIG. 8c.--- Same as in Figure 8a, but for $T_d = 200$ K.\n\\bigskip \\noindent\nFIG. 8d.--- Same as in Figure 8b, but for $T_d = 200$ K.\n\\bigskip \\noindent\nFIG. 9a.--- Same as in Figure 8a, but for $W=0.1$.\n\\bigskip \\noindent\nFIG. 9b.--- Same as in Figure 8b, but for $W=0.1$.\n\\bigskip \\noindent\nFIG. 9c.--- Same as in Figure 8c, but for $W=0.1$.\n\\bigskip \\noindent\nFIG. 9d.--- Same as in Figure 8d, but for $W=0.1$.\n\\bigskip \\noindent\nFIG. 10a.--- Same as in Figure 9a, but for \\fo$=0$.\n\\bigskip \\noindent\nFIG. 10b.--- Same as in Figure 9b, but for \\fo$=0$.\n\\bigskip \\noindent\nFIG. 10c.--- Same as in Figure 9c, but for \\fo$=0$.\n\\bigskip \\noindent\nFIG. 10d.--- Same as in Figure 9d, but for \\fo$=0$.\n\\bigskip \\noindent\nFIG. 11a.--- Same as in Figure 9a, but for $V=2$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 11b.--- Same as in Figure 9b, but for $V=2$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 11c.--- Same as in Figure 9c, but for $V=2$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 11d.--- Same as in Figure 9d, but for $V=2$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 12a.--- Same as in Figure 9a, but for $V=3$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 12b.--- Same as in Figure 9b, but for $V=3$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 12c.--- Same as in Figure 9c, but for $V=3$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 12d.--- Same as in Figure 9d, but for $V=3$ km s$^{-1}$.\n\\bigskip \\noindent\nFIG. 13.--- Same as Figure 9c, but for \\fOH$=10^{-4}$.\n\\bigskip \\noindent\nFIG. 14.--- Same as Figure 9c, but for \\fOH$=10^{-6}$.\n\\bigskip \\noindent\nFIG. 15.--- Same as Figure 6c of Paper II, but for \\fOH$=10^{-6}$.\n\n\\bye\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
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astro-ph0002368
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Quasar variability: correlations with amplitude
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[
{
"author": "M.R.S. Hawkins"
}
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The relation between quasar variability and parameters such as luminosity and redshift has been a matter of hot debate over the last few years with many papers on the subject. Any correlations which can be established will have a profound effect on models of quasar structure and evolution. The sample of quasars with redshifts in ESO/SERC field 287 contains over 600 quasars in the range $0 < z < 3.5$ and is now large enough to bin in luminosity and redshift, and give definitive measures of the correlations. We find no significant correlation between amplitude and redshift, except perhaps at very low redshift, but an inverse correlation between amplitude and luminosity. This is examined in the context of various models for quasar variability. \keywords{ quasars: general }
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[
{
"name": "qamp.tex",
"string": "% aa.dem\n% AA vers. 4.01, LaTeX class for Astronomy & Astrophysics\n% demonstration file\n% (c) Springer-Verlag HD\n%-----------------------------------------------------------------------\n%\n%\\documentclass[referee]{aa} % for a referee version\n%\n\\documentclass{aa}\n\n\\usepackage{graphics}\n%\n\\begin{document}\n\n \\thesaurus{11 % A&A Section 11: Galaxies\n (11.17.3)} % (Galaxies:) quasars: general\n%\n \\title{Quasar variability: correlations with amplitude}\n\n\n \\author{M.R.S. Hawkins}\n\n \\offprints{M.R.S. Hawkins}\n\n \\institute{Institute for Astronomy (IfA), University of Edinburgh,\n Royal Observatory, Blackford Hill Edinburgh EH9 3HJ,\n Scotland\\\\\n email: mrsh@roe.ac.uk}\n\n \\date{Received <date> / accepted <date>}\n\n \\maketitle\n\n \\begin{abstract}\n\nThe relation between quasar variability and parameters such as\nluminosity and redshift has been a matter of hot debate over the last\nfew years with many papers on the subject. Any correlations which can\nbe established will have a profound effect on models of quasar\nstructure and evolution. The sample of quasars with redshifts in\nESO/SERC field 287 contains over 600 quasars in the range\n$0 < z < 3.5$ and is now large enough to bin in luminosity and\nredshift, and give definitive measures of the correlations. We find\nno significant correlation between amplitude and redshift, except\nperhaps at very low redshift, but an inverse correlation between\namplitude and luminosity. This is examined in the context of various\nmodels for quasar variability.\n\n \\keywords{ quasars: general }\n\n \\end{abstract}\n\n%\n%________________________________________________________________\n\n\\section{Introduction}\n\nOne of the most important constraints on the structure of quasars is\nvariability. Short term variations set limits on the size of the\nemitting region, and differences in the nature of the variation in the\nXray, optical and radio domains give clues to the underlying structure.\nVariations on longer timescales of a few years are not so easily\naccounted for by the current black hole paradigm, and microlensing has\nbeen put forward as an alternative explanation for the observations.\nAlthough the most extensive monitoring of quasar variability has been\ndone in optical wavebands, there is still little consensus even over\nthe broad picture. One of the first problems is to parametrise the\nvariation in such a way that it can be compared with models, or even\nmore general expectations. The timescale of variation and the\namplitude are the two parameters which have been mostly studied,\nalthough some authors have succeeded in confusing the two. This\ntypically involves claiming that in a short run of data, objects\nvarying on a short timescale will achieve a larger amplitude than\nthose varying on a longer timescale, and so amplitude can be taken\nas an (inverse) measure of timescale (Hook et al. \\cite{hoo94}).\\\\\n\nIn this paper we shall confine our attention to the correlation of\namplitude with other parameters. Amplitude is an easy parameter to\nmeasure, and involves none of the difficulties inherent in estimating\ntimescale of variation. There are modes of variability in which\nsome uncertainty will be introduced by the length of the run of\nobservations, but this is a problem which can arise in any time\nseries analysis. Most attention has so far been given to possible\ncorrelations of amplitude with redshift or luminosity (eg Trevese\net al. \\cite{tre89}, Giallongo et al. \\cite{gia91},\nHook et al. \\cite{hoo94}, Cristiani et al. \\cite{cri96}), but even\nin such straightforward situations there has been little agreement.\\\\\n\nThe reasons for the lack of consensus are not easy to understand,\nbut it is clear that any effect which is present is not large compared\nwith the cosmic scatter in the data, which in the case of amplitude\nappears to be about one magnitude, much larger than any photometric\nerrors. Perhaps the most likely cause of disagreement is in the\nselection of samples for analysis. In order to obtain a meaningful\nmeasure of correlation it is essential that unbiassed samples are used,\nand that they cover a large range of redshift and luminosity. In this\npaper particular attention is paid to the sample selection process, and\nby extending the analysis to high redshifts the baseline for the\nmeasurement of correlations is greatly extended over earlier samples.\\\\\n\n\\section{Quasar samples}\n\n\\subsection{Observational material}\n\nThe parent sample of quasars for the analysis of variability amplitude\ncomes from a large scale survey and monitoring programme being\nundertaken in the ESO/SERC field 287, at 21h 28m, -45$^{\\circ}$.\nQuasars have been selected according to a number of criteria,\nincluding colour, variability, radio emission and objective prism\nspectra, or a combination of these techniques. Redshifts for over 600\nquasars have so far been obtained, and several complete samples\ndefined within specific limits of magnitude, redshift and position\non the sky (Hawkins \\& V\\'{e}ron \\cite{haw95}). A detailed description\nof the survey is given by Hawkins \\& V\\'{e}ron (\\cite{haw95}) and\nHawkins (\\cite{haw96}). Briefly, a large set of UK 1.2 Schmidt plates\nspanning 20 years was scanned with the COSMOS and SuperCOSMOS measuring\nmachines to provide a catologue of some 200,000 objects in the central\n19 square degrees of the plate. These were calibrated with CCD frames\nto provide light curves in $B_{J}$ and $R$, and colours in $UBVRI$.\nPhotometric errors have been discussed in detail in earlier papers\n(Hawkins 1996 and references therein) and are $\\sim 0.08$ magnitudes\nfor any individual machine measurement, and only weakly dependent on\nmagnitude. There are approximately four plates in each year\nwhich reduces the error to $\\sim 0.04$ magnitudes per epoch. This is\nsmall compared with the amplitudes of interest in this paper, and\nno attempt has been made to deconvolve it.\n\n\\subsection{Sample selection}\n\nFor the analysis in this paper three samples will be defined.\nThe first (UVX) is based only on position on the sky and ultraviolet\nexcess. The area on the sky containing the sample is defined by a\nnumber of AAT AUTOFIB fields and a 2dF field (Folkes et al. \\cite{fol99}\nand references therein), covering a total area of 7.0 square degrees.\nWithin this area all objects with $U-B < -0.2$ and $B_{J} < 21.0$ were\nobserved. This was extended to $B_{J} < 21.5$ in the 2dF field.\nThe ultra-violet excess (UVX) cut although necessary to give a\nrelatively clean sample of quasar candidates, has the well known\nlimitation of only being effective for redshifts $z < 2.2$. Beyond\nthis redshift quasars become red in $U-B$ as the Lyman forest enters\nthe $U$ band. For samples at higher redshift, variability has\nbeen found to provide a very useful criterion for quasar selection\n(Hawkins \\cite{haw96}). The second sample for consideration herei\n(VAR), was selected on this basis, with the requirement that the object\nshould lie in the same area of sky as for the first sample with a\nmagnitude limit $B_{J} < 21$, or anywhere in the measured area of the\nplate with a magnitude limit $B_{J} < 19.5$, and should have an\namplitude $\\delta m > 0.35$. The defining epoch for the magnitudes\nwas the year 1977. This sample was selected without any reference to\ncolour and so can be used to measure trends over a large range of\nredshift ($z < 3.5$). The third sample (AMP) was selected in a similar\nmanner, but over the whole measured area of the plate (19 square\ndegrees), and with an amplitude cut $\\delta m > 1.1$. There is some\nevidence that these large amplitude objects form a distinct group,\nwhich is discussed below.\\\\\n \nThe development of fibre fed spectrographs has meant that every\nobject included within a given set of search criteria can be\nobserved to give a high completeness level. In the case of\nfields observed with AUTOFIB, the existence of forbidden regions\nin the 40 arcminute field, and the very variable throughput for\ndifferent fibres aligned at different positions on the spectrograph\nslit meant that up to 20\\% of spectra did not have sufficient signal\nto provide an unambiguous redshift. These objects where re-observed\nlater with the faint object spectrograph EFOSC on the ESO 3.6m\ntelescope at La Silla. The 2dF observations where of very uniform\nquality, and the redshift measures or other classification were almost\n100\\% successful from the fibre-feed spectra.\\\\\n\nDetails of all three samples, containing a total of 384 quasars,\nare given in the Appendix. $B$ magnitudes\nare in the $B_{J}$ system defined by the IIIa-J emulsion and the GG395\nfilter, and refer to the year 1977. The amplitude $\\delta m$ is the\ndifference between maximum and minmum magnitude achieved over the 20\nyear run of data. The samples which each quasar belongs to are\nindicated by 1, 2 and 3 corresponding to VAR, UVX and AMP respectively,\nas defined above. Data for many of the quasars have already been\npublished by Hawkins \\& V\\'{e}ron (\\cite{haw95}), but are given again\nhere for completeness. Any small differences in the parameters are the\nresult of further refinement of the calibration, and more extended\nmonitoring of the light curves.\\\\\n\nUVX selected samples have been used many times in the past for quasar\nsurveys, and the constraints are quite well known. Variability\nselection has been less often used, and some additional comments are\nappropriate. In particular, there is the important question of\ncompleteness. Hawkins \\& V\\'{e}ron (\\cite{haw95}) use a small sample of\nquasars in field 287 from Morris et al. (\\cite{mor91}) selected by\nobjective prism to test completeness. In 1993, 79\\% of the objective\nprism quasars would have also been detected according to the variability\ncriterion $\\delta m > 0.35$; by 1997 this figure had risen to 93\\%,\nwith two quasars remaining below the variability threshold. In fact\nboth of these quasars are clearly variable, with amplitudes 0.32 and\n0.29 magnitudes. Strangely, they lie at either extreme of the\nredshift and luminosity range of the sample, with redshifts 3.23,\n0.29 and luminosities -27.55, -22.33 respectively. \nFig.~\\ref{1}(a) shows the distribution of epoch at which quasars first\nsatisfy the detection criterion given by Hawkins (\\cite{haw96}). This\nis generally speaking equivalent to attaining an amplitude of 0.35\nmagnitudes. The distribution peaks between 2 and 4 years, and most\nquasars have satisfied the criterion after 7 years. Fig.~\\ref{1}(b)\nshows the cumulative distribution of detection epochs, illustrating\nthe point that after 15 years nearly all quasars have varied\nsufficiently to put them in the variability selected sample.\\\\\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig1.eps}}\n \\caption{The top panel shows a histogram of the epochs at which\nquasars could first have been detected on the basis of the variability\ncriterion. The bottom panel shows the same plot in cumulative form.}\n \\label{1}\n\\end{figure}\n\nThe distribution of amplitudes is best shown with the UVX sample,\nwhich was selected without any reference to variability.\nFig. ~\\ref{2}(a)\nis a histogram of amplitudes over a 20 year baseline, and shows a\nmedian amplitude of around 0.7 magnitudes. As would be expected\nfrom Fig.~\\ref{1}, nearly all of the sample lies above the threshold\namplitude of the variability selected sample of 0.35 mags. With\nthis in mind it is worth investigating the possibility of using\nthe variability selected sample to look for correlations at higher\nredshift. Fig. ~\\ref{2}(b) shows a histogram of amplitudes for the VAR\nsample, which from the way it was selected has a cut-off at an\namplitude of 0.35 mags. More interestingly, the distribution as\na whole peaks at an amplitude of about 0.7, similar to the UVX\nsample. This peak is well clear of the cut-off, and implies\nthat only a small fraction of quasars are missed from the VAR sample.\nThere may however be a problem detecting the most luminous quasars,\n($M_{B} < -27$) for which there is evidence for relatively small\nvariations (Cristiani et al. \\cite{cri96}). Nonetheless, the sample\ncan be used with caution to extend quasar correlations to high\nredshift.\\\\\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig2.eps}}\n \\caption{The top panel shows a histogram of amplitudes for the complete\nUVX detected sample. The bottom panel shows a similar histogram for\nthe variability detected sample (VAR). Quasars are constrained to\nhave an amplitude greater than 0.35 mags.}\n \\label{2}\n\\end{figure}\n\n\\section{Amplitude correlations}\n\nThe top two panels in Fig. ~\\ref{3} show the distribution of amplitudes\nas a function of redshift and luminosity for the UVX sample. The\nmost striking thing about these figures is the marked drop in amplitude\ntowards low redshift and luminosity. This is illustrated more clearly\nin the top two panels of Fig. ~\\ref{4}, where the data is binned in\nintervals\nof 0.5 in redshift and unit absolute magnitude, and the mean plotted\nwith $\\sqrt{N}$ error bars. The fall towards low redshift and\nluminosity is highly significanti (a 3-$\\sigma$ effect), although it is\nnot clear from these data alone whether it is primarily a luminosity or\nredshift effect. The correlation coeffecient for the top left panel of\nFig. ~\\ref{3} with $z < 0.5$ is 0.46, and for the top right panel with\n$M_{B} > -22$ is -0.67, confirming the reality of the correlation.\nThere is also some evidence for a decrease in amplitude for the most\nluminous quasars ($M_{B} < -25$), and an even weaker decline for high\nredshift objects. Correlation coefficients for all the data in the\ntop two panels are 0.12 and -0.10 for left and right panels\nrespectively, emphasising the weakness of the effect. This is another\nmanifestation of the well known degeneracy between redshift and\nluminosity. This point will be investigated further below by dividing\nthe data into sub-samples.\\\\\n\n\\begin{figure*}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig3.eps}}\n \\caption{The top two panels show plots of amplitude versus redshft\nand absolute magnitude for quasars selected solely on the basis\nof ultra-violet excess. The bottom two panels are similar plots\nfor quasars selected on the basis of variability.}\n \\label{3}\n\\end{figure*}\n\n\\begin{figure*}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig4.eps}}\n \\caption{Plots based on the same data as for Fig. 3, but binned in\nredshift intervals of 0.5 and unit absolute magnitude intervals.\nThe error bars show the uncertainty in the position of the mean.}\n \\label{4}\n\\end{figure*}\n\nThe bottom two panels in Figs ~\\ref{3} and ~\\ref{4} show similar plots\nfor the VAR sample. The greater redshift range allowed by variability\nselection still shows little trend of amplitude with\nredshift, but the decrease in amplitude for luminous quasars is\nshown to continue to greater luminosities, although the effect is\ninevitably lessened by the absence of quasars with\n$\\delta m < 0.35$.\\\\\n\nIt has been mentioned above that there is a degeneracy between\nredshift and luminosity. This results from the fact that in a\nmagnitude limited sample high redshift quasars tend to be high\nluminosity objects, and vice versa. Thus a trend with one parameter\nwill be mimicked by a trend with the other, and the true relation will\nbe hard to disentangle. This degeneracy can in principle be broken byi\nbinning the data in redshift and luminosity, and the result of doing\nthis is shown in Figs. ~\\ref{5} and ~\\ref{6}. The VAR sample was used\nas it covers a wider range of luminosity and redshift, making binning\nfeasible. The left hand panel shows amplitude as a function of\nluminosity in two redshift bins, $z < 1.5$ and $z > 1.5$. Data for\nthe two redshift ranges overlap nicely, and clearly show a decrease\nin the relation between amplitude and luminosity. The right hand\npanel shows amplitude as a function of redshift in two luminosity\nbins. In this case there is some evidence for an increase in the\nrelation at low redshift, but it is essentially flat beyond $z = 0.5$\nfor both luminosity ranges. It is however worth noting that the less\nluminous quasars have larger amplitudes, as expected from the data in\nthe left hand panel. It would thus appear that while for $M_{B} > -25$\namplitude does indeed decrease with luminosity, it does not change\nwith redshift for $z > 0.5$.\\\\\n\n\\begin{figure*}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig5.eps}}\n \\caption{Plots of amplitude versus redshift and absolute magnitude\nfor the variability detected sample (VAR). The top two panels\nshow amplitude versus absolute magnitude for two redshift ranges,\nand the bottom two panels show amplitude versus redshift for\ntwo absolute magnitude ranges.}\n \\label{5}\n\\end{figure*}\n\n\\begin{figure*}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig6.eps}}\n \\caption{Plots based on the same data as for Fig. 5, but binned in\nunit absolute magnitude intervals and redshift intervals of 0.5.\nThe left hand panel shows the relation between amplitude and\nabsolute magnitude for quasars with $z < 1.5$ (small dots)\nand $z > 1.5$ (large dots). The right hand panel shows the\nrelation between amplitude and redshift for quasars with\n$M_{B} > -25$ (small dots) and $M_{B} < -25$ (large dots).\nThe error bars show the uncertainty in the position of the mean.}\n \\label{6}\n\\end{figure*}\n\nExamination of Fig. ~\\ref{3}, especially the bottom panels, suggests\nthat there may be population of low luminosity and/or low redshift\nquasars distinct from the parent population. This is particularly\nevident in the bottom left hand panel of Fig. ~\\ref{3}, which is\nuniformly populated between amplitudes of 1.1 and 1.8 up to a redshift\nof 2 at which point\nthere is a sharp cut-off with no amplitudes greater than 1.1 at higher\nredshift. To investigate this population with better statistics all\nvariables with $\\delta m > 1.1$ in the measured area of field 287 were\nobserved on the 3.6m at La Silla to confirm their identification as\nquasars and measure redshifts. This became the AMP sample.\nFig. ~\\ref{7}\nshows amplitude as a function of both redshift and luminosity, and it\nwill be seen that there is indeed a cut-off in redshift at $z \\sim 2$\nand $M_{B} \\sim -25$. It is clear that this cut-off must in fact\nbe related to luminosity. If it were a redshift cut-off there is\nno reason why such objects should not be seen with greater luminosity.\nOn the other hand if it were a luminosity cut-off, then this\ncombined with a magnitude limit will indeed produce an effective\ncut-off in redshift.\\\\\n\n\\begin{figure*}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig7.eps}}\n \\caption{Plots of amplitude versus redshift and absolute magnitude\nfor the most variable quasars in the sample.}\n \\label{7}\n\\end{figure*}\n\n\\section{Discussion}\n\nAttempts to measure correlations of amplitude (or some related \nvariability parameter) with redshift and luminosity have a long history,\nwhich is summarised by Hawkins (\\cite{haw96}). Among recent work, a\nuseful place to start is with the paper by Hook et al. (\\cite{hoo94}).\nThey analyse a sample of $\\sim 300$ quasars in the SGP area from 12 UK\n1.2m Schmidt plates taken in 5 separate yearly epochs spanning 16 years.\nThey find a convincing anti-correlation between their variability\nparameter $\\sigma_{v}$ (a measure of variation about the mean) and\nluminosity, but a much weaker anti-correlation with redshift. They\nattribute this to the degeneracy between redshift and luminosity\nin their sample. The same sample is re-analysed by Cid Fernandes\net al. (\\cite{cid96}) who use a variability index related to variance,\nand also one related to the structure function. They concur with\nHook et al. (\\cite{hoo94}) that there is an anti-correlation between\ntheir variability indices and luminosity, but claim a positive\ncorrelation with redshift. This effect is not apparent to the\neye, but is interpreted as a variability-wavelength dependence\nrather than an intrinsic variability-redshift dependence. The\nnet result in an un-binned sample cancels out with the luminosity\nvariability relationship. Cid Fernandes et al.'s claim for a\npositive correlation between amplitude and redshift appears to be\nmotivated at least in part by expectations arising from a paper by\nDi Clemente et al. (\\cite{dic96}). This interesting paper examines\nthe relation between their variability parameter $S_{1}$ (an amplitude\nbased on the structure function) and wavelength. Their sample is\ncomposed of PG quasars (Schmidt and Green \\cite{sch83}), which are\nmostly low redshift and relatively low luminosity objects. With the\nhelp of archival IUE observations they find that $S_{1}$ decreases\nwith wavelength. This effect can clearly be seen in the light curve\nfrom the intensive monitoring programme of the Seyfert galaxy NGC 5548\n(Clavel et al. \\cite{cla91}), which has a larger amplitude at shorter\nwavelength. Fig. ~\\ref{8} shows the relation between amplitude and\nwavelength taken from the light curves, with a best-fit quadratic\ncurve.\\\\\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig8.eps}}\n \\caption{Relation between amplitude and wavelength for the Seyfert\ngalaxy NGC 5548 from IUE data published by Clavel et al. 1991.}\n \\label{8}\n\\end{figure}\n\nThe relation between rest wavelength and amplitude is essentially\nequivalent to the relation between redshift and amplitude, where one\nis seeing progressively shorter wavelengths at higher redshift. This\nis illustrated in the top panel of Fig. ~\\ref{9} which shows the UVX\nsample with two curves superimposed. The solid line is converted from\nFig. ~\\ref{8} and does not appear to follow the trend of the data,\nbut the large scatter makes it hard to construct a convincing test.\nNonetheless it suggests that any relation which holds for Seyfert\ngalaxies might have to be modified for quasars. The dotted line is\nfrom Di Clemente et al. (\\cite{dic96}), and shows a very small effect,\nwhich does nonetheless follow the flat distribution of the data.\\\\\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig9.eps}}\n \\caption{Plots of amplitude versus redshift and luminosity for UVX\nselected quasars. In the top panel the solid line represents\nthe relation from Fig. 8, with wavelength converted to redshift;\nthe dotted line is the model from Di Clemente et al. (1996).}\n \\label{9}\n\\end{figure}\n\nThe decrease of amplitude for the smallest redshift and luminosity\nseen in the top two panels of Fig. ~\\ref{4} has a number of possible\nexplanations. It could be the effect of the underlying galaxy\ndominating any change in nuclear brightness for low luminosity\nobjects, it could be a consequence of the small optical depth to\nmicrolensing at low redshift, or it could be a consequence of the\nwavelength dependence of variability (Cristiani et al. \\cite{cri97}).\nThe present dataset is not adequate to settle the question, which\nis best done by looking at luminous quasars at very low redshift\nand Seyfert galaxies at high redshift.\\\\\n\nAll the plots in Figs ~\\ref{3} and ~\\ref{4} show a trend of decreasing\namplitude\ntowards higher redshift or more luminous objects. Although\nthe trend as a function of luminosity is more marked, the old\nproblem of degeneracy makes it hard to say for certain that it is\na luminosity effect which is being observed. However, if we look\nat Fig. ~\\ref{6} where the data are binned in luminosity and redshift\nwe see that while there is no significant trend of amplitude with\nredshift in either luminosity bin, there is a marked inverse\ncorrelation between amplitude and luminosity.\\\\\n\nThe relation between amplitude and luminosity is in agreement with that\nfound in earlier work (Hook et al. \\cite{hoo94}, Hawkins \\cite{haw96},\nCristiani et al. \\cite{cri96}) and may well turn out to be a useful way\nof distinguishing between various schemes for quasar variability.\nThe evidence for a constant amplitude with redshift is more\ndebatable. It would appear to be consistent with the early\nclaim of Hook et al. (\\cite{hoo94}) for a weak anti-correlation with\nredshift which they ascribed to degeneracy with luminosity. It\nis also in agreement with the results of Cristiani et al. in\nthe observer's frame. When they correct their structure function\nto the quasar rest frame they inevitably imprint a positive\ncorrelation between their variability parameter and redshift.\\\\\n\nTo investigate this dependence of amplitude on redshift for the\npresent sample, Fig. ~\\ref{10} shows the epoch at which quasars achieve\ntheir maximum amplitude as a function of redshift. Apart from\nvery low redshifts ($z < 0.3$) this relation is flat, implying\nthat at least over the 21 years of the present dataset, time\ndilation effects will not bias the measurement of amplitude. Since\nthe conclusions of Cid Fernandes et al. (\\cite{cid96}) are largely\nbased on a sample for which a time dilation correction has been\napplied, it is not feasible to make a direct comparison with the \npresent work. However, it appears that the main difference\nbetween their results and those of Hook et al. is in the definition\nof a variability parameter and the method of analysis (both papers\nare based on the SGP sample).\\\\\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{fig10.eps}}\n \\caption{Plot of the epoch at which the largest magnitude difference\nis achieved in quasar light curves at different redshifts. Poisson\nerror bars are shown based on the number of objects in each bin.}\n \\label{10}\n\\end{figure}\n\nThere are perhaps three currently discussed schemes for quasar\nvariability. The least well constrained is the accretion disk model,\nwhere instabilities are propagated across the disk leading to\nvariation in light. The details of this approach have proved hard to\nwork out, especially in the context of the constraints imposed by\nexisting observations, but it does not seem to lead to an inverse\ncorrelation between amplitude and luminosity. An interesting recent\nattempt to model variation on the basis of accretion disk\ninstabilities by Kawaguchi et al. (\\cite{kaw98}) may provide a means for\nproducing the observed variations. It does however appear to predict\nvariations which are either too asymmetric or of too small an\namplitude to be consistent with the current observations. The\ntimescales which they predict are also rather short, around 200\ndays for reasonable input parameters, and much shorter than the\nobserved timescale of a few years.\\\\\n\nAn alternative approach, developed by Terlevich and his collaborators,\naccounts for the variation by postulating that the quasar is powered\nby a series of supernova explosions. Qualitatively, this model can\naccount for the observed relation between luminosity and amplitude,\nand works quite well for Seyfert galaxies (Aretxaga \\& Terlevich\n\\cite{are94}). However, for quasars (Aretxaga et al. \\cite{are97})\nlarge numbers of supernovae are required to achieve the luminosity,\nwhich results in smaller variations. For example, even a relatively\nmodest quasar with absolute magnitude $M_{B} \\sim -26$ would need\nsome 300 type II supernovae per year to power it, which given typical\ndecay times would lead to very little variation at all. This clearly\nconflicts with observations in this paper which show that most quasars\nvary by around 0.5 to 1 magnitude on a timescale of a few years.\\\\\n\nThe third way of explaining quasar variability is to invoke\nmicrolensing. This approach has been explored in several recent papers\n(Hawkins \\cite{haw93}, \\cite{haw96}, Hawkins \\& Taylor \\cite{haw97}),\nand seems to account well for a number of statistical properties of\nquasar light curves. It can also explain the inverse correlationi\nbetween luminosity and amplitude in a natural way. It is well known\nthat when a point source is microlensed by a population of compact\nbodies of significant optical depth, the lenses combine non-linearly\nto form a caustic pattern which produces sharp spikes in the resulting\nlight curves (Schneider \\& Weiss \\cite{sch87}). As the source becomes\ncomparable in size with, or larger than, the Einstein radius of the\nlenses the amplitude decreases (Refsdal \\& Stabell \\cite{ref91}).\nThus if one assumes a uniform temperature for quasar disks, and that\nthe luminosity is determined by the disk area, the larger more luminous\ndisks will be amplified less. Using a relation between source size\n(in terms of Einstein radius) and amplitude given by Refsdal \\& Stabell\n(\\cite{ref91}) (eqn 1), one can thus derive a relation between\namplitude $\\delta m$ and absolute magnitude $M$ of the form:\n\n\\[ \\delta m = 10^{0.2(M+c)} \\]\n\n\\noindent\nwhere $c$ is a constant. The bottom panel of Fig. ~\\ref{9} shows a\nplot of amplitude versus absolute magnitude for the UVX sample with this\nrelation superimposed. The constant $c$ was adjusted to allow the\ncurve to track the upper envelope of the points, which has the effect\nof defining the quasar disk size. This ranges from 1.1 Einstein radii\nfor $M_{B} = -23$ to 11 for $M_{B} = -28$. The points scatter\ndownwards from the upper envelope because the quasars do not\nnecessarily attain their maximum possible amplitude. Although one\ncannot say that the curve provides a fit to the data, the trend is\ncertainly well represented.\\\\\n\nThe possibility of a distinct population of large amplitude, low\nluminosity quasars suggested by Fig. ~\\ref{7} may also be used to test\nthe models of quasar variability. Again, an accretion disk provides\nno obvious mechanism for such an effect. The Christmas Tree model\ncertainly does imply large amplitude variations for low luminosity\nobjects, where each event is of comparable brightness to the nucleus\nitself. Perhaps the most natural explanation comes from microlensing,\nwhere the nucleus of low luminosity quasars would plausibly become\nvery small compared with the Einstein radii of the lenses, resulting\nin large amplifications from caustic crossing events.\\\\\n\n\\section{Conclusions}\n\nIn this paper we have examined the dependance of amplitude on redshift\nand luminosity for large samples of quasars selected on the basis\nof ultra-violet excess and variability. The quasars span a redshift\nrange $0 < z < 3.5$ and a luminosity range $-20 > M_{B} > -28$.\nThere is evidence for a correlation of amplitude with luminosity and/or\nredshift for the sample as a whole, but when it is binned in redshift\nthe correlation with luminosity becomes significant. This result could\nbe strengthened by the possible existence of a population of large\namplitude low luminosity objects in the sample. No convincing evidence\nis found for a correlation between amplitude and redshift, either for\nthe sample as a whole or when it is binned in luminosity.\\\\\n\nVarious models of quasar variability are examined with respect\nto the observed correlations. It is concluded that any straightforward\ninterpretation of an accretion disk model is incompatible with the\ndata. The Christmas Tree model has some merits, especially in the\nregime of low luminosity quasars and Seyfert galaxies, but for\nluminous quasars the rate of supernovae required is too large to\nbe compatible with the observed variability. The microlensing model\ncan be used to explain all the data, although it does require that\nthe Einstein radius of the microlensing bodies is comparable in size\nto the quasar nucleus.\\\\\n\n\\begin{acknowledgements}\n\nI thank Andy Lawrence and Omar Almaini for making some excellent\nsuggestions for improvements to the paper.\n\n\\end{acknowledgements}\n\n\\section*{References}\n\\begin{thebibliography}{}\n\n\\bibitem[1994]{are94} Aretxaga I., Terlevich R., 1994, MNRAS 269, 462\n\\bibitem[1997]{are97} Aretxaga I., Cid Fernandes R., Terlevich R.,\n 1997, MNRAS 286, 271\n\\bibitem[1996]{cid96} Cid Fernandes R., Aretxaga I., Terlevich R.,\n 1996, MNRAS 282, 1191\n\\bibitem[1991]{cla91} Clavel J. et al., 1991, ApJ 366, 64\n\\bibitem[1996]{cri96} Cristiani S., Trentini S., La Franca F.,\n Andreani P., 1996, A\\&A 321, 123\n\\bibitem[1996]{cri96} Cristiani S., Trentini S., La Franca F.,\n Aretxaga I., Andreani P., Vio R., Gemmo A., 1996, A\\&A 306, 395\n\\bibitem[1996]{dic96} Di Clemente A., Giallongo E., Natali G.,\n Tr\\`{e}vese D., Vagnetti F., 1996, ApJ 463, 466\n\\bibitem[1999]{fol99} Folkes S. et al., 1999, MNRAS 308, 459\n\\bibitem[1991]{gia91} Giallongo E., Trevese D., Vagnetti F., 1991,\n ApJ 377, 345\n\\bibitem[1993]{haw93} Hawkins M.R.S., 1993, Nat 366, 242\n\\bibitem[1996]{haw96} Hawkins M.R.S., 1996, MNRAS 278, 787\n\\bibitem[1997]{haw97} Hawkins M.R.S., Taylor A.N., 1997, ApJ 482, L5\n\\bibitem[1995]{haw95} Hawkins M.R.S. \\& V\\'{e}ron P., 1995, MNRAS\n 275, 1102\n\\bibitem[1994]{hoo94} Hook I.M., McMahon R.G., Boyle B.J., Irwin M.J.,\n 1994, MNRAS 268, 305\n\\bibitem[1998]{kaw98} Kawaguchi T., Mineshige S., Umemura M.,\n Turner E.L., 1998, ApJ 504, 671\n\\bibitem[1991]{mor91} Morris S.L., Weymann R.J., Anderson S.F.,\n Hewett P.C., Foltz C.B., Chaffee F.H., Francis P.J., MacAlpine G.M.,\n 1991, AJ 102, 1627\n\\bibitem[1991]{ref91} Refsdal S., Stabell R., 1991, A\\&A 250, 62\n\\bibitem[1983]{sch83} Schmidt M., Green R.F., 1983, ApJ 269, 352\n\\bibitem[1987]{sch87} Schneider P., Weiss A., 1987, A\\&A 171, 49\n\\bibitem[1989]{tre89} Trevese D., Pitella G., Kron R.G., Bershady M.,\n 1989, AJ 98, 108\n\n\\end{thebibliography}\n\n\\pagestyle{empty}\n\n\\section*{Appendix}\n\n\\begin{table}[h]\n\n\\begin{tabular}[b]{rrrrrrrrrrrrrr}\n\\multicolumn{3}{c}{R.A. (1950)}&\\multicolumn{3}{c}{Dec (1950)}&\n\\multicolumn{1}{c}{$B$}&\\multicolumn{1}{c}{$U\\!-\\!B$}&\n\\multicolumn{1}{c}{$\\delta m$}& \\multicolumn{1}{c}{$z$}&\n\\multicolumn{1}{c}{$M_{B}$}&\\multicolumn{3}{c}{Samples}\\\\\n &&&&&&&&&&&&&\\\\\n 21& 16& 28.38& -44& 0& 57.3& 19.34& -0.42& 0.64& 2.062& -26.04& 1& 0& 0\\\\\n 21& 16& 22.50& -44& 29& 13.9& 19.33& -0.77& 1.19& 1.270& -25.03& 1& 0& 3\\\\\n 21& 16& 44.32& -44& 9& 28.0& 20.29& -0.59& 1.72& 1.375& -24.24& 0& 0& 3\\\\\n 21& 16& 13.41& -46& 42& 47.3& 18.71& -0.40& 0.87& 1.498& -26.00& 1& 0& 0\\\\\n 21& 16& 25.78& -46& 10& 42.1& 18.92& -0.37& 0.54& 0.748& -24.32& 1& 0& 0\\\\\n 21& 16& 55.05& -44& 39& 37.1& 17.89& -0.09& 0.80& 1.480& -26.80& 1& 0& 0\\\\\n 21& 17& 24.47& -42& 41& 4.1& 19.51& -0.35& 1.12& 0.363& -22.17& 0& 0& 3\\\\\n 21& 16& 46.14& -46& 14& 21.7& 19.08& -0.23& 0.59& 0.297& -22.17& 1& 0& 0\\\\\n 21& 17& 30.01& -44& 2& 40.4& 18.30& -0.45& 0.44& 1.710& -26.69& 1& 0& 0\\\\\n 21& 17& 25.61& -45& 4& 58.1& 20.40& 0.25& 0.72& 2.313& -25.22& 1& 0& 0\\\\\n 21& 17& 26.97& -45& 30& 20.9& 20.28& 1.15& 1.06& 2.993& -25.86& 1& 0& 0\\\\\n 21& 17& 21.81& -47& 3& 49.0& 18.80& 0.01& 0.45& 2.260& -26.77& 1& 0& 0\\\\\n 21& 17& 53.12& -46& 0& 44.8& 19.71& 0.31& 0.82& 2.955& -26.41& 1& 0& 0\\\\\n 21& 17& 55.61& -46& 9& 17.1& 20.38& 0.10& 0.82& 2.120& -25.06& 1& 0& 0\\\\\n 21& 17& 48.23& -46& 47& 36.2& 19.35& -0.50& 0.48& 1.038& -24.59& 1& 0& 0\\\\\n 21& 17& 57.12& -46& 20& 47.4& 20.50& 0.46& 0.84& 2.884& -25.57& 1& 0& 0\\\\\n 21& 18& 21.07& -44& 59& 51.9& 19.19& -0.12& 0.59& 2.194& -26.32& 1& 0& 0\\\\\n 21& 18& 34.84& -43& 49& 45.2& 19.29& -0.43& 0.90& 1.121& -24.81& 1& 0& 0\\\\\n 21& 18& 34.30& -44& 0& 44.9& 20.44& 1.01& 0.70& 3.140& -25.80& 1& 0& 0\\\\\n 21& 18& 41.77& -43& 24& 38.6& 20.78& -0.47& 1.57& 1.076& -23.23& 0& 0& 3\\\\\n\\end{tabular}\n\n\\end{table}\n\n\\begin{table*}[t]\n\n\\begin{tabular}[b]{rrrrrrrrrrrrrr}\n\\multicolumn{3}{c}{R.A. (1950)}&\\multicolumn{3}{c}{Dec (1950)}&\n\\multicolumn{1}{c}{$B$}&\\multicolumn{1}{c}{$U\\!-\\!B$}&\n\\multicolumn{1}{c}{$\\delta m$}& \\multicolumn{1}{c}{$z$}&\n\\multicolumn{1}{c}{$M_{B}$}&\\multicolumn{3}{c}{Samples}\\\\\n &&&&&&&&&&&&&\\\\\n 21& 18& 47.48& -43& 1& 9.5& 18.81& -0.62& 0.75& 2.123& -26.63& 1& 0& 0\\\\\n 21& 18& 11.92& -46& 56& 3.6& 18.35& -0.37& 0.41& 1.720& -26.65& 1& 0& 0\\\\\n 21& 18& 55.69& -43& 3& 36.1& 18.66& -0.01& 0.70& 2.201& -26.85& 1& 0& 0\\\\\n 21& 19& 0.54& -43& 48& 0.5& 20.72& 0.63& 0.82& 3.064& -25.47& 1& 0& 0\\\\\n 21& 18& 29.22& -47& 2& 34.9& 18.36& -0.42& 1.05& 1.332& -26.10& 1& 0& 0\\\\\n 21& 19& 14.89& -43& 7& 27.0& 19.81& 0.43& 0.84& 2.929& -26.29& 1& 0& 0\\\\\n 21& 19& 37.27& -43& 23& 9.2& 20.31& 0.07& 1.04& 2.730& -25.65& 1& 0& 0\\\\\n 21& 19& 20.05& -45& 30& 52.3& 20.38& 0.00& 0.51& 2.410& -25.32& 1& 0& 0\\\\\n 21& 19& 45.46& -43& 32& 19.3& 20.65& -0.65& 1.40& 0.652& -22.29& 0& 0& 3\\\\\n 21& 19& 47.61& -43& 46& 23.9& 19.16& -0.40& 1.02& 1.000& -24.70& 1& 0& 0\\\\\n 21& 19& 37.16& -45& 48& 22.3& 19.98& 0.03& 0.81& 2.210& -25.54& 1& 0& 0\\\\\n 21& 19& 55.45& -44& 17& 54.7& 20.73& 0.59& 0.79& 3.080& -25.47& 1& 0& 0\\\\\n 21& 20& 14.92& -42& 55& 30.5& 20.89& 0.15& 0.53& 0.619& -21.94& 1& 0& 0\\\\\n 21& 19& 49.62& -45& 49& 8.4& 20.65& -0.26& 0.67& 1.715& -24.35& 1& 2& 0\\\\\n 21& 20& 18.19& -44& 10& 40.6& 20.69& -0.10& 1.10& 0.580& -22.00& 0& 0& 3\\\\\n 21& 20& 28.49& -43& 38& 36.6& 19.23& -0.35& 0.51& 0.840& -24.26& 1& 0& 0\\\\\n 21& 20& 4.87& -46& 34& 17.3& 19.56& 0.02& 0.59& 2.375& -26.11& 1& 0& 0\\\\\n 21& 20& 21.60& -45& 52& 12.2& 20.22& 0.85& 0.60& 2.989& -25.92& 1& 0& 0\\\\\n 21& 20& 50.81& -43& 27& 55.6& 17.92& -0.49& 0.63& 1.240& -26.39& 1& 0& 0\\\\\n 21& 20& 58.76& -44& 13& 48.6& 20.94& 0.02& 0.81& 1.741& -24.09& 1& 0& 0\\\\\n 21& 20& 47.86& -45& 32& 44.2& 20.03& 1.10& 0.61& 2.941& -26.08& 1& 0& 0\\\\\n 21& 20& 57.48& -46& 20& 36.2& 20.09& -0.35& 0.64& 0.739& -23.12& 1& 2& 0\\\\\n 21& 21& 26.81& -43& 51& 34.2& 19.20& -0.49& 0.79& 1.946& -26.06& 1& 0& 0\\\\\n 21& 21& 20.68& -44& 45& 7.7& 20.29& 0.98& 0.46& 2.963& -25.83& 1& 0& 0\\\\\n 21& 21& 19.34& -45& 5& 0.8& 21.18& -0.07& 1.24& 0.748& -22.06& 0& 0& 3\\\\\n 21& 21& 12.02& -46& 4& 1.4& 20.34& 0.09& 0.95& 2.260& -25.23& 1& 0& 0\\\\\n 21& 21& 22.69& -45& 58& 25.6& 20.74& -0.32& 0.60& 1.650& -24.17& 0& 2& 0\\\\\n 21& 21& 41.90& -44& 6& 57.6& 17.80& -0.46& 0.52& 1.735& -27.22& 1& 0& 0\\\\\n 21& 21& 33.83& -45& 15& 9.2& 20.39& -0.11& 1.83& 0.758& -22.88& 0& 0& 3\\\\\n 21& 21& 23.86& -46& 38& 7.0& 19.92& -0.21& 1.64& 0.912& -23.74& 0& 0& 3\\\\\n 21& 21& 31.37& -46& 13& 36.3& 20.51& -0.48& 0.59& 1.047& -23.45& 0& 2& 0\\\\\n 21& 21& 43.13& -44& 56& 36.3& 20.40& 0.38& 0.63& 2.950& -25.71& 1& 0& 0\\\\\n 21& 21& 40.68& -45& 51& 23.9& 18.89& -0.43& 0.46& 0.947& -24.85& 1& 2& 0\\\\\n 21& 21& 42.39& -45& 49& 26.6& 20.10& -0.28& 1.10& 0.520& -22.36& 1& 2& 3\\\\\n 21& 21& 35.46& -46& 42& 27.4& 19.11& -0.41& 0.76& 1.347& -25.38& 1& 0& 0\\\\\n 21& 21& 41.39& -45& 59& 53.9& 19.73& -0.58& 0.90& 0.887& -23.87& 1& 2& 0\\\\\n 21& 21& 39.65& -46& 41& 17.2& 20.35& -0.52& 1.12& 1.352& -24.15& 0& 0& 3\\\\\n 21& 21& 56.68& -45& 8& 33.6& 18.83& -0.31& 0.65& 1.353& -25.67& 1& 0& 0\\\\\n 21& 22& 12.50& -43& 9& 36.5& 20.83& 0.46& 0.65& 3.060& -25.36& 1& 0& 0\\\\\n 21& 22& 0.52& -45& 57& 24.8& 17.75& -0.42& 0.46& 0.953& -26.01& 0& 2& 0\\\\\n 21& 22& 25.85& -42& 43& 24.2& 20.16& 0.17& 0.68& 2.457& -25.58& 1& 0& 0\\\\\n 21& 22& 30.46& -43& 28& 38.6& 20.01& -0.10& 1.14& 0.401& -21.89& 0& 0& 3\\\\\n 21& 22& 25.60& -44& 22& 18.5& 18.87& 0.22& 0.49& 2.465& -26.88& 1& 0& 0\\\\\n 21& 22& 16.68& -46& 31& 54.8& 20.27& -0.10& 1.60& 0.820& -23.17& 0& 0& 3\\\\\n 21& 22& 39.06& -44& 33& 4.8& 20.32& 0.05& 0.80& 2.600& -25.54& 1& 0& 0\\\\\n 21& 22& 41.46& -44& 47& 46.1& 19.92& 0.06& 1.05& 1.137& -24.21& 1& 0& 0\\\\\n 21& 22& 52.08& -43& 33& 58.6& 18.71& -0.07& 0.45& 0.552& -23.88& 1& 0& 0\\\\\n 21& 22& 35.59& -46& 22& 5.7& 19.06& -0.37& 0.81& 2.093& -26.35& 1& 0& 0\\\\\n 21& 22& 48.18& -45& 55& 30.6& 19.96& -0.53& 0.51& 1.425& -24.65& 1& 2& 0\\\\\n 21& 22& 49.75& -45& 58& 24.4& 19.41& -0.31& 0.86& 0.986& -24.42& 1& 2& 0\\\\\n 21& 22& 56.31& -45& 57& 17.2& 20.13& -0.28& 0.78& 0.858& -23.40& 1& 2& 0\\\\\n 21& 23& 1.03& -46& 3& 38.1& 19.42& -0.61& 0.96& 1.384& -25.13& 1& 2& 0\\\\\n 21& 23& 3.18& -46& 5& 48.0& 20.53& 0.70& 0.42& 3.220& -25.76& 1& 0& 0\\\\\n 21& 23& 21.19& -43& 38& 29.5& 18.37& -0.18& 0.66& 0.480& -23.92& 1& 0& 0\\\\\n 21& 23& 3.71& -46& 54& 52.7& 18.63& -0.24& 0.79& 1.429& -25.98& 1& 0& 0\\\\\n\\end{tabular}\n\n\\end{table*}\n\n\\begin{table*}[t]\n\n\\begin{tabular}[b]{rrrrrrrrrrrrrr}\n\\multicolumn{3}{c}{R.A. (1950)}&\\multicolumn{3}{c}{Dec (1950)}&\n\\multicolumn{1}{c}{$B$}&\\multicolumn{1}{c}{$U\\!-\\!B$}&\n\\multicolumn{1}{c}{$\\delta m$}& \\multicolumn{1}{c}{$z$}&\n\\multicolumn{1}{c}{$M_{B}$}&\\multicolumn{3}{c}{Samples}\\\\\n &&&&&&&&&&&&&\\\\\n 21& 23& 14.08& -45& 48& 53.9& 19.12& -0.22& 0.80& 1.549& -25.66& 1& 0& 0\\\\\n 21& 23& 31.47& -42& 56& 35.7& 19.49& 0.23& 1.26& 0.141& -20.15& 1& 0& 3\\\\\n 21& 23& 13.92& -46& 54& 33.0& 20.34& -0.10& 2.31& 0.422& -21.67& 0& 0& 3\\\\\n 21& 23& 37.93& -43& 46& 58.0& 18.91& -0.44& 0.58& 1.000& -24.95& 1& 0& 0\\\\\n 21& 23& 43.22& -44& 29& 5.9& 19.66& -0.66& 0.84& 1.353& -24.84& 1& 2& 0\\\\\n 21& 23& 45.16& -44& 29& 9.8& 20.06& -0.08& 1.17& 1.586& -24.77& 0& 0& 3\\\\\n 21& 23& 48.33& -45& 38& 4.0& 19.50& -0.28& 0.39& 1.642& -25.40& 1& 0& 0\\\\\n 21& 24& 7.74& -44& 12& 53.9& 19.39& -0.16& 1.50& 0.542& -23.16& 1& 0& 3\\\\\n 21& 24& 5.49& -44& 43& 57.5& 19.83& -0.32& 0.26& 1.589& -25.01& 0& 2& 0\\\\\n 21& 24& 9.52& -44& 12& 58.3& 20.26& -0.43& 1.20& 1.239& -24.05& 0& 0& 3\\\\\n 21& 24& 3.30& -46& 27& 37.3& 20.78& 0.00& 0.52& 1.140& -23.36& 1& 0& 0\\\\\n 21& 24& 7.41& -46& 5& 44.6& 20.45& 0.06& 1.51& 0.705& -22.66& 1& 0& 3\\\\\n 21& 24& 11.89& -45& 40& 17.0& 18.78& -0.52& 0.52& 1.395& -25.78& 1& 0& 0\\\\\n 21& 24& 19.46& -45& 15& 1.7& 20.03& -0.51& 0.61& 1.935& -25.22& 1& 2& 0\\\\\n 21& 24& 30.39& -43& 3& 34.7& 19.46& -0.39& 0.54& 1.286& -24.93& 1& 0& 0\\\\\n 21& 24& 33.74& -44& 12& 3.5& 20.01& -0.34& 1.88& 1.625& -24.87& 0& 0& 3\\\\\n 21& 24& 21.85& -46& 52& 0.4& 19.90& 0.58& 0.58& 2.495& -25.87& 1& 0& 0\\\\\n 21& 24& 49.75& -43& 20& 36.0& 19.01& 0.07& 0.64& 0.820& -24.43& 1& 0& 0\\\\\n 21& 24& 46.25& -44& 32& 24.7& 20.66& 0.16& 0.47& 0.677& -22.37& 1& 0& 0\\\\\n 21& 24& 46.53& -45& 53& 46.9& 20.48& -0.62& 1.10& 1.961& -24.79& 0& 2& 3\\\\\n 21& 24& 54.69& -45& 4& 54.4& 20.48& -0.32& 0.30& 0.388& -21.35& 0& 2& 0\\\\\n 21& 24& 56.51& -45& 53& 2.6& 19.76& 0.03& 0.61& 2.322& -25.86& 1& 0& 0\\\\\n 21& 25& 5.28& -44& 48& 42.3& 19.91& -0.40& 0.82& 1.733& -25.11& 0& 2& 0\\\\\n 21& 25& 25.85& -43& 35& 13.5& 20.32& 0.01& 0.59& 2.260& -25.25& 1& 0& 0\\\\\n 21& 25& 23.50& -44& 24& 24.2& 20.01& -0.16& 0.69& 2.500& -25.77& 1& 0& 0\\\\\n 21& 25& 23.30& -45& 16& 17.9& 20.62& -0.28& 0.66& 0.242& -20.19& 1& 2& 0\\\\\n 21& 25& 28.96& -45& 9& 50.0& 19.41& -0.38& 0.93& 1.590& -25.43& 1& 2& 0\\\\\n 21& 25& 28.12& -45& 36& 53.9& 20.44& 0.24& 0.63& 2.766& -25.54& 1& 0& 0\\\\\n 21& 25& 28.84& -46& 39& 17.1& 19.11& -0.41& 0.45& 1.601& -25.74& 1& 0& 0\\\\\n 21& 25& 46.60& -44& 32& 58.3& 20.39& -0.04& 0.56& 2.503& -25.39& 1& 0& 0\\\\\n 21& 25& 53.43& -43& 43& 39.9& 20.44& -0.29& 0.65& 0.451& -21.71& 1& 2& 0\\\\\n 21& 25& 56.64& -44& 8& 32.1& 18.48& -0.33& 0.63& 0.366& -23.22& 1& 0& 0\\\\\n 21& 25& 49.78& -46& 11& 32.1& 20.32& -0.78& 1.12& 1.305& -24.10& 1& 2& 3\\\\\n 21& 25& 49.84& -46& 47& 52.4& 19.07& -0.45& 0.50& 1.888& -26.13& 1& 0& 0\\\\\n 21& 26& 10.02& -42& 56& 30.8& 17.79& -0.28& 0.67& 0.405& -24.13& 1& 0& 0\\\\\n 21& 26& 1.19& -47& 8& 26.6& 19.28& -0.10& 0.52& 0.698& -23.81& 1& 0& 0\\\\\n 21& 26& 7.35& -45& 34& 52.2& 21.27& -0.22& 0.51& 0.719& -21.88& 0& 2& 0\\\\\n 21& 26& 12.68& -47& 8& 30.4& 20.04& 0.02& 0.68& 2.200& -25.47& 1& 0& 0\\\\\n 21& 26& 33.72& -45& 58& 45.3& 18.17& -0.23& 0.80& 1.579& -26.65& 1& 2& 0\\\\\n 21& 26& 40.88& -43& 34& 19.4& 18.48& -0.27& 0.86& 0.584& -24.23& 1& 2& 0\\\\\n 21& 26& 43.20& -43& 36& 13.8& 20.71& -0.49& 0.68& 1.280& -23.67& 1& 2& 0\\\\\n 21& 26& 39.70& -45& 2& 43.9& 20.54& -0.49& 0.77& 2.156& -24.93& 0& 2& 0\\\\\n 21& 26& 41.19& -45& 31& 12.6& 19.93& -0.56& 0.71& 0.980& -23.89& 1& 2& 0\\\\\n 21& 26& 45.68& -43& 50& 6.3& 20.08& -0.37& 1.14& 1.120& -24.02& 1& 2& 3\\\\\n 21& 26& 50.42& -43& 46& 50.6& 20.29& -0.47& 1.05& 1.110& -23.79& 1& 2& 0\\\\\n 21& 26& 49.67& -45& 26& 56.3& 18.59& -0.47& 0.44& 1.382& -25.95& 1& 2& 0\\\\\n 21& 26& 52.97& -46& 19& 0.7& 18.90& -0.66& 0.67& 1.880& -26.29& 1& 0& 0\\\\\n 21& 27& 0.30& -44& 56& 34.0& 20.33& -0.16& 1.94& 0.522& -22.14& 0& 0& 3\\\\\n 21& 26& 58.26& -47& 2& 58.9& 20.69& 0.08& 0.90& 2.592& -25.16& 1& 0& 0\\\\\n 21& 27& 8.64& -44& 29& 24.6& 20.83& -0.20& 0.90& 2.122& -24.61& 0& 2& 0\\\\\n 21& 27& 13.56& -44& 35& 17.7& 18.82& -0.57& 0.69& 2.015& -26.51& 1& 2& 0\\\\\n 21& 27& 19.33& -42& 42& 44.3& 17.71& -0.41& 0.66& 0.799& -25.67& 1& 0& 0\\\\\n 21& 27& 14.13& -45& 55& 19.9& 20.12& 0.15& 0.66& 2.440& -25.61& 1& 0& 0\\\\\n 21& 27& 19.62& -43& 45& 11.4& 20.08& -0.46& 0.72& 1.722& -24.92& 1& 2& 0\\\\\n 21& 27& 17.65& -46& 1& 39.1& 19.98& -0.94& 1.37& 1.285& -24.41& 1& 2& 3\\\\\n\\end{tabular}\n\n\\end{table*}\n\n\\begin{table*}[t]\n\n\\begin{tabular}[b]{rrrrrrrrrrrrrr}\n\\multicolumn{3}{c}{R.A. (1950)}&\\multicolumn{3}{c}{Dec (1950)}&\n\\multicolumn{1}{c}{$B$}&\\multicolumn{1}{c}{$U\\!-\\!B$}&\n\\multicolumn{1}{c}{$\\delta m$}& \\multicolumn{1}{c}{$z$}&\n\\multicolumn{1}{c}{$M_{B}$}&\\multicolumn{3}{c}{Samples}\\\\\n &&&&&&&&&&&&&\\\\\n 21& 27& 21.35& -44& 56& 24.6& 19.83& 0.43& 0.63& 2.880& -26.24& 1& 0& 0\\\\\n 21& 27& 31.32& -44& 45& 6.4& 18.72& -0.35& 0.78& 1.536& -26.04& 1& 0& 0\\\\\n 21& 27& 39.34& -43& 8& 36.7& 20.46& 0.00& 0.84& 2.674& -25.45& 1& 0& 0\\\\\n 21& 27& 37.22& -45& 28& 57.0& 18.60& 0.84& 0.44& 2.730& -27.36& 1& 0& 0\\\\\n 21& 27& 52.99& -43& 50& 37.0& 19.40& -0.15& 0.64& 0.493& -22.94& 1& 0& 0\\\\\n 21& 27& 54.41& -45& 52& 55.5& 19.94& -0.48& 1.17& 1.101& -24.12& 0& 0& 3\\\\\n 21& 27& 55.93& -45& 49& 0.5& 19.04& -0.15& 1.07& 0.871& -24.52& 1& 0& 0\\\\\n 21& 27& 55.24& -47& 6& 50.1& 18.42& -0.24& 0.57& 0.578& -24.27& 1& 0& 0\\\\\n 21& 27& 59.09& -45& 11& 9.3& 19.83& -0.89& 0.83& 2.001& -25.49& 1& 2& 0\\\\\n 21& 28& 2.17& -45& 25& 10.3& 19.01& -0.37& 0.59& 0.961& -24.76& 0& 2& 0\\\\\n 21& 28& 4.28& -46& 39& 7.9& 20.73& 0.05& 0.71& 2.610& -25.13& 1& 0& 0\\\\\n 21& 28& 5.82& -46& 33& 24.7& 17.44& 0.19& 0.65& 0.153& -22.37& 1& 0& 0\\\\\n 21& 28& 14.96& -42& 45& 41.9& 19.44& -0.38& 0.64& 1.420& -25.16& 1& 0& 0\\\\\n 21& 28& 13.84& -44& 43& 32.1& 20.49& -0.23& 0.62& 1.229& -23.81& 1& 2& 0\\\\\n 21& 28& 17.05& -44& 34& 56.0& 19.52& -0.53& 0.68& 1.434& -25.10& 1& 2& 0\\\\\n 21& 28& 21.96& -46& 10& 53.2& 17.65& -0.50& 0.40& 0.833& -25.82& 1& 2& 0\\\\\n 21& 28& 24.69& -45& 37& 3.4& 19.77& 0.00& 0.70& 0.204& -20.67& 1& 0& 0\\\\\n 21& 28& 40.98& -45& 20& 20.8& 20.56& -0.25& 1.75& 0.544& -22.00& 0& 0& 3\\\\\n 21& 28& 42.00& -43& 30& 59.2& 18.91& -0.60& 0.42& 1.905& -26.30& 1& 0& 0\\\\\n 21& 28& 44.77& -46& 4& 16.3& 20.51& -0.20& 1.12& 0.831& -22.95& 1& 2& 0\\\\\n 21& 28& 56.74& -45& 48& 1.9& 20.45& -0.42& 0.98& 1.087& -23.59& 0& 2& 0\\\\\n 21& 29& 1.26& -46& 6& 30.4& 20.07& -0.40& 0.81& 1.025& -23.84& 1& 2& 0\\\\\n 21& 29& 4.08& -42& 55& 55.0& 20.65& -0.46& 1.10& 2.070& -24.74& 0& 0& 3\\\\\n 21& 29& 4.72& -44& 42& 39.7& 19.22& -0.38& 0.99& 1.025& -24.69& 1& 2& 0\\\\\n 21& 29& 8.42& -45& 15& 39.0& 19.80& -0.67& 0.61& 1.260& -24.55& 1& 2& 0\\\\\n 21& 29& 10.18& -46& 17& 2.3& 20.74& -0.30& 1.31& 0.998& -23.11& 1& 2& 0\\\\\n 21& 29& 10.53& -44& 50& 18.5& 19.07& -0.68& 1.03& 1.942& -26.18& 1& 2& 0\\\\\n 21& 29& 24.73& -45& 27& 7.0& 20.21& -0.66& 0.84& 1.375& -24.32& 1& 2& 0\\\\\n 21& 29& 27.63& -45& 1& 15.8& 20.89& -0.08& 0.56& 2.170& -24.59& 1& 0& 0\\\\\n 21& 29& 32.92& -45& 51& 30.9& 20.58& -0.35& 0.82& 1.286& -23.81& 1& 2& 0\\\\\n 21& 29& 38.02& -45& 12& 11.6& 19.31& 0.11& 0.90& 2.180& -26.18& 1& 0& 0\\\\\n 21& 29& 38.26& -44& 13& 47.1& 19.85& -0.45& 0.83& 1.452& -24.80& 1& 2& 0\\\\\n 21& 29& 39.50& -46& 24& 19.2& 17.80& -0.30& 0.67& 0.435& -24.27& 1& 0& 0\\\\\n 21& 29& 39.63& -46& 29& 40.3& 19.71& 0.02& 0.65& 2.465& -26.04& 1& 0& 0\\\\\n 21& 29& 41.25& -45& 22& 49.0& 20.21& 9.99& 0.48& 3.580& -26.30& 1& 0& 0\\\\\n 21& 29& 42.67& -45& 16& 27.2& 20.62& -0.54& 0.73& 1.030& -23.30& 1& 2& 0\\\\\n 21& 29& 45.45& -46& 53& 47.6& 18.85& -0.02& 0.61& 2.230& -26.69& 1& 0& 0\\\\\n 21& 29& 47.37& -46& 2& 7.8& 18.97& -0.27& 0.51& 0.299& -22.29& 1& 2& 0\\\\\n 21& 29& 50.05& -45& 46& 56.6& 20.29& -0.25& 0.62& 2.034& -25.06& 0& 2& 0\\\\\n 21& 29& 51.34& -44& 25& 9.8& 20.71& -0.19& 0.86& 0.744& -22.52& 1& 0& 0\\\\\n 21& 29& 57.55& -46& 53& 51.1& 19.85& 0.02& 0.62& 2.208& -25.67& 1& 0& 0\\\\\n 21& 29& 56.13& -44& 23& 10.5& 20.76& -0.67& 0.78& 2.011& -24.57& 0& 2& 0\\\\\n 21& 30& 1.27& -46& 3& 4.9& 19.61& -0.14& 0.52& 2.244& -25.94& 1& 0& 0\\\\\n 21& 30& 1.99& -44& 3& 36.7& 20.88& 0.68& 0.74& 2.970& -25.25& 1& 0& 0\\\\\n 21& 30& 2.98& -45& 8& 45.2& 19.07& 0.05& 1.38& 0.740& -24.15& 1& 0& 3\\\\\n 21& 30& 8.22& -43& 52& 59.0& 19.93& 0.11& 0.84& 2.634& -25.95& 1& 0& 0\\\\\n 21& 30& 16.27& -43& 10& 28.9& 21.37& -0.16& 1.41& 0.914& -22.30& 0& 0& 3\\\\\n 21& 30& 20.02& -44& 40& 42.8& 20.25& -0.07& 0.47& 0.610& -22.55& 1& 0& 0\\\\\n 21& 30& 20.78& -44& 45& 36.3& 20.00& -0.48& 0.59& 1.460& -24.66& 0& 2& 0\\\\\n 21& 30& 22.37& -44& 50& 58.9& 19.65& -0.12& 0.61& 0.725& -23.52& 1& 0& 0\\\\\n 21& 30& 24.58& -44& 42& 19.8& 20.29& 0.96& 0.40& 3.040& -25.89& 1& 0& 0\\\\\n 21& 30& 27.93& -45& 55& 32.9& 18.91& -0.31& 0.40& 1.556& -25.88& 1& 2& 0\\\\\n 21& 30& 30.00& -45& 45& 38.2& 20.65& 0.23& 0.59& 2.645& -25.24& 1& 0& 0\\\\\n 21& 30& 30.16& -44& 45& 24.4& 19.71& -0.63& 0.64& 1.324& -24.74& 0& 2& 0\\\\\n 21& 30& 30.63& -43& 6& 51.6& 19.51& -0.23& 0.69& 1.645& -25.40& 1& 2& 0\\\\\n\\end{tabular}\n\n\\end{table*}\n\n\\begin{table*}[t]\n\n\\begin{tabular}[b]{rrrrrrrrrrrrrr}\n\\multicolumn{3}{c}{R.A. (1950)}&\\multicolumn{3}{c}{Dec (1950)}&\n\\multicolumn{1}{c}{$B$}&\\multicolumn{1}{c}{$U\\!-\\!B$}&\n\\multicolumn{1}{c}{$\\delta m$}& \\multicolumn{1}{c}{$z$}&\n\\multicolumn{1}{c}{$M_{B}$}&\\multicolumn{3}{c}{Samples}\\\\\n &&&&&&&&&&&&&\\\\\n 21& 30& 38.92& -43& 50& 22.4& 20.22& -0.69& 1.31& 1.229& -24.08& 1& 2& 3\\\\\n 21& 30& 41.40& -43& 48& 1.0& 19.56& -0.40& 0.61& 1.597& -25.29& 1& 2& 0\\\\\n 21& 30& 45.86& -45& 56& 38.6& 20.58& -0.26& 0.61& 1.498& -24.13& 1& 2& 0\\\\\n 21& 30& 50.85& -44& 32& 7.2& 18.85& -0.27& 0.54& 0.793& -24.51& 1& 2& 0\\\\\n 21& 31& 1.26& -46& 7& 4.0& 20.73& -0.39& 0.41& 2.010& -24.60& 0& 2& 0\\\\\n 21& 31& 0.28& -44& 36& 23.0& 19.99& -0.36& 0.47& 1.234& -24.31& 1& 2& 0\\\\\n 21& 31& 7.60& -46& 12& 42.8& 20.71& -0.40& 0.83& 1.978& -24.58& 0& 2& 0\\\\\n 21& 31& 4.84& -44& 14& 6.4& 20.23& -0.44& 0.62& 0.999& -23.63& 0& 2& 0\\\\\n 21& 31& 12.57& -46& 0& 12.2& 19.90& 0.10& 0.65& 2.719& -26.05& 1& 0& 0\\\\\n 21& 31& 14.89& -46& 56& 9.1& 19.26& -0.30& 0.37& 0.980& -24.56& 1& 0& 0\\\\\n 21& 31& 9.87& -43& 39& 29.7& 20.76& -0.33& 0.65& 1.390& -23.79& 1& 2& 0\\\\\n 21& 31& 15.15& -45& 7& 35.1& 19.19& -0.73& 0.52& 1.966& -26.09& 1& 2& 0\\\\\n 21& 31& 15.80& -45& 1& 19.0& 19.67& -0.22& 1.15& 0.418& -22.32& 0& 0& 3\\\\\n 21& 31& 21.94& -46& 38& 23.6& 18.71& -0.45& 0.54& 1.720& -26.29& 1& 0& 0\\\\\n 21& 31& 15.90& -42& 43& 18.9& 20.20& 0.08& 0.99& 0.365& -21.50& 1& 0& 0\\\\\n 21& 31& 22.52& -43& 43& 53.5& 20.55& -0.41& 0.70& 0.844& -22.95& 1& 2& 0\\\\\n 21& 31& 26.19& -45& 15& 3.1& 20.69& -0.72& 1.12& 1.920& -24.54& 1& 2& 3\\\\\n 21& 31& 27.03& -45& 4& 49.3& 19.85& 0.00& 1.12& 0.715& -23.29& 1& 0& 0\\\\\n 21& 31& 23.41& -42& 59& 60.0& 20.13& -0.39& 0.80& 1.648& -24.78& 1& 2& 0\\\\\n 21& 31& 37.75& -45& 48& 53.2& 20.65& -0.20& 1.37& 0.781& -22.68& 0& 0& 3\\\\\n 21& 31& 35.99& -44& 10& 45.4& 21.12& -0.62& 1.25& 0.529& -21.38& 0& 2& 3\\\\\n 21& 31& 33.39& -42& 57& 51.0& 18.22& -0.67& 0.74& 2.096& -27.19& 1& 2& 0\\\\\n 21& 31& 43.86& -46& 57& 13.0& 17.97& 0.03& 0.54& 0.684& -25.08& 1& 0& 0\\\\\n 21& 31& 36.21& -44& 3& 24.2& 20.35& -0.36& 0.63& 1.660& -24.58& 0& 2& 0\\\\\n 21& 31& 36.77& -43& 39& 43.3& 19.90& -0.35& 0.74& 0.843& -23.59& 0& 2& 0\\\\\n 21& 31& 38.88& -43& 54& 22.2& 20.40& -0.34& 0.42& 1.216& -23.87& 0& 2& 0\\\\\n 21& 31& 38.93& -42& 47& 29.3& 20.39& -0.36& 1.23& 0.982& -23.43& 1& 2& 3\\\\\n 21& 31& 43.86& -43& 39& 11.8& 20.52& -0.53& 0.55& 0.715& -22.62& 0& 2& 0\\\\\n 21& 31& 50.98& -43& 19& 14.5& 20.05& -0.38& 0.51& 1.656& -24.87& 0& 2& 0\\\\\n 21& 31& 54.25& -44& 29& 23.0& 19.14& -0.49& 0.50& 1.414& -25.45& 1& 0& 0\\\\\n 21& 32& 2.95& -45& 16& 9.7& 18.91& -0.55& 0.79& 1.890& -26.29& 1& 0& 0\\\\\n 21& 31& 56.70& -42& 55& 39.3& 21.08& -0.36& 1.70& 1.730& -23.93& 0& 2& 3\\\\\n 21& 32& 10.46& -46& 14& 20.6& 19.60& 0.34& 0.72& 2.769& -26.39& 1& 0& 0\\\\\n 21& 32& 4.70& -42& 45& 41.3& 19.02& -0.61& 0.70& 1.992& -26.29& 1& 0& 0\\\\\n 21& 32& 13.49& -45& 16& 50.0& 17.68& -0.59& 0.55& 0.507& -24.72& 1& 2& 0\\\\\n 21& 32& 13.00& -44& 14& 14.0& 19.65& -0.22& 0.63& 1.645& -25.26& 1& 2& 0\\\\\n 21& 32& 11.55& -43& 24& 45.8& 19.87& -0.35& 1.71& 0.860& -23.67& 1& 2& 3\\\\\n 21& 32& 18.25& -45& 6& 59.8& 19.20& -0.45& 0.61& 0.520& -23.26& 1& 0& 0\\\\\n 21& 32& 18.33& -44& 18& 48.4& 19.87& -0.35& 0.97& 1.451& -24.77& 1& 2& 0\\\\\n 21& 32& 21.72& -43& 24& 47.5& 20.43& -0.11& 0.52& 2.240& -25.12& 1& 0& 0\\\\\n 21& 32& 23.85& -43& 48& 10.8& 20.19& 0.23& 0.86& 2.790& -25.81& 1& 0& 0\\\\\n 21& 32& 23.30& -43& 9& 42.2& 20.82& -0.56& 0.45& 0.959& -22.95& 0& 2& 0\\\\\n 21& 32& 27.48& -44& 5& 24.8& 20.41& -0.28& 0.98& 0.478& -21.87& 1& 2& 0\\\\\n 21& 32& 36.44& -46& 34& 0.5& 19.46& -0.53& 1.33& 1.320& -24.99& 1& 0& 3\\\\\n 21& 32& 35.27& -46& 11& 31.5& 19.01& -0.46& 0.66& 1.600& -25.84& 1& 2& 0\\\\\n 21& 32& 26.58& -43& 18& 4.3& 19.66& -0.31& 0.82& 1.710& -25.33& 1& 2& 0\\\\\n 21& 32& 31.07& -44& 18& 57.9& 19.08& -0.77& 1.25& 1.258& -25.26& 1& 2& 3\\\\\n 21& 32& 37.49& -45& 8& 31.6& 20.12& -0.56& 0.59& 1.377& -24.41& 1& 2& 0\\\\\n 21& 32& 37.63& -44& 51& 1.2& 18.55& -0.41& 0.91& 0.920& -25.13& 1& 0& 0\\\\\n 21& 32& 38.00& -44& 20& 41.8& 20.61& -0.53& 1.12& 0.655& -22.34& 1& 2& 0\\\\\n 21& 32& 54.14& -47& 5& 8.9& 19.38& -0.44& 1.59& 0.244& -21.44& 1& 0& 3\\\\\n 21& 32& 53.63& -45& 58& 49.2& 20.29& -0.41& 0.76& 1.003& -23.57& 1& 2& 0\\\\\n 21& 32& 51.16& -44& 31& 17.9& 21.33& -0.09& 1.76& 0.430& -20.72& 0& 0& 3\\\\\n 21& 33& 3.03& -46& 20& 24.7& 20.87& 0.27& 0.78& 2.760& -25.11& 1& 0& 0\\\\\n 21& 32& 55.05& -43& 21& 44.1& 17.93& 0.27& 0.48& 2.420& -27.78& 1& 0& 0\\\\\n\\end{tabular}\n\n\\end{table*}\n\n\\begin{table*}[t]\n\n\\begin{tabular}[b]{rrrrrrrrrrrrrr}\n\\multicolumn{3}{c}{R.A. (1950)}&\\multicolumn{3}{c}{Dec (1950)}&\n\\multicolumn{1}{c}{$B$}&\\multicolumn{1}{c}{$U\\!-\\!B$}&\n\\multicolumn{1}{c}{$\\delta m$}& \\multicolumn{1}{c}{$z$}&\n\\multicolumn{1}{c}{$M_{B}$}&\\multicolumn{3}{c}{Samples}\\\\\n &&&&&&&&&&&&&\\\\\n 21& 33& 2.60& -44& 16& 33.7& 20.06& -0.29& 0.28& 0.327& -21.40& 0& 2& 0\\\\\n 21& 33& 6.66& -44& 28& 26.5& 20.80& -0.68& 0.99& 0.544& -21.76& 1& 2& 0\\\\\n 21& 33& 7.60& -44& 16& 50.7& 20.76& 9.99& 0.75& 3.340& -25.61& 1& 0& 0\\\\\n 21& 33& 13.11& -45& 20& 2.1& 20.65& 0.34& 0.49& 2.898& -25.43& 1& 0& 0\\\\\n 21& 33& 7.84& -43& 4& 13.9& 20.25& 0.19& 1.00& 2.470& -25.50& 1& 0& 0\\\\\n 21& 33& 12.34& -42& 58& 51.0& 19.40& -0.22& 0.43& 1.190& -24.83& 1& 2& 0\\\\\n 21& 33& 22.63& -44& 20& 23.7& 19.96& -0.37& 0.45& 0.999& -23.90& 1& 2& 0\\\\\n 21& 33& 31.09& -46& 11& 38.3& 19.72& -0.37& 0.65& 0.888& -23.89& 1& 2& 0\\\\\n 21& 33& 31.37& -46& 13& 34.8& 19.58& -0.44& 1.36& 1.448& -25.06& 1& 2& 3\\\\\n 21& 33& 21.32& -43& 30& 55.6& 21.29& -0.55& 0.92& 1.720& -23.71& 0& 2& 0\\\\\n 21& 33& 23.97& -43& 36& 17.3& 20.42& -0.20& 0.46& 0.669& -22.58& 1& 2& 0\\\\\n 21& 33& 29.69& -44& 4& 8.7& 20.37& -0.22& 0.90& 1.756& -24.67& 1& 2& 0\\\\\n 21& 33& 39.37& -46& 3& 3.6& 20.75& 0.03& 1.45& 0.423& -21.26& 1& 0& 3\\\\\n 21& 33& 26.75& -42& 55& 1.3& 20.45& -0.14& 1.57& 0.580& -22.24& 0& 0& 3\\\\\n 21& 33& 38.98& -45& 34& 51.6& 19.44& -0.24& 1.54& 0.868& -24.12& 1& 2& 3\\\\\n 21& 33& 41.36& -45& 53& 0.8& 18.34& -0.54& 0.36& 1.000& -25.52& 1& 2& 0\\\\\n 21& 33& 51.84& -46& 17& 51.0& 20.75& -0.49& 1.21& 1.571& -24.06& 0& 2& 0\\\\\n 21& 33& 53.98& -46& 17& 24.2& 19.65& -0.40& 0.85& 0.844& -23.85& 1& 2& 0\\\\\n 21& 33& 58.56& -47& 8& 7.8& 19.35& -0.62& 1.10& 1.097& -24.70& 1& 0& 3\\\\\n 21& 33& 45.77& -43& 58& 44.9& 18.27& -0.33& 0.83& 1.560& -26.53& 1& 2& 0\\\\\n 21& 33& 45.15& -43& 49& 23.8& 20.09& -0.59& 0.77& 1.850& -25.06& 1& 2& 0\\\\\n 21& 33& 47.57& -44& 17& 35.9& 20.35& 0.44& 0.45& 2.838& -25.69& 1& 0& 0\\\\\n 21& 33& 48.75& -44& 28& 48.7& 20.21& -0.51& 0.51& 2.059& -25.17& 0& 2& 0\\\\\n 21& 34& 1.71& -46& 46& 47.6& 19.90& 0.63& 0.74& 3.065& -26.29& 1& 0& 0\\\\\n 21& 33& 53.80& -44& 56& 27.5& 20.08& 0.03& 0.62& 2.745& -25.89& 1& 0& 0\\\\\n 21& 33& 46.40& -43& 21& 34.2& 20.24& -0.69& 0.83& 2.022& -25.10& 1& 2& 0\\\\\n 21& 33& 51.02& -43& 6& 10.0& 20.81& -0.55& 0.85& 1.400& -23.76& 1& 2& 0\\\\\n 21& 34& 8.30& -45& 6& 3.0& 20.59& -0.31& 0.53& 0.880& -23.00& 1& 2& 0\\\\\n 21& 34& 2.22& -43& 10& 38.6& 21.12& -0.50& 0.56& 0.524& -21.36& 0& 2& 0\\\\\n 21& 34& 8.13& -43& 51& 26.6& 19.56& -0.24& 1.03& 1.663& -25.37& 1& 2& 0\\\\\n 21& 34& 19.95& -46& 2& 17.9& 20.41& -0.65& 1.52& 1.292& -23.99& 1& 2& 3\\\\\n 21& 34& 8.81& -43& 11& 33.7& 19.92& -0.24& 0.74& 1.650& -24.99& 1& 2& 0\\\\\n 21& 34& 19.94& -45& 16& 58.6& 20.44& -0.48& 0.84& 1.106& -23.63& 1& 2& 0\\\\\n 21& 34& 17.90& -43& 50& 8.8& 19.88& -0.35& 0.82& 1.558& -24.91& 1& 2& 0\\\\\n 21& 34& 13.93& -42& 57& 43.8& 19.30& 0.11& 0.60& 2.608& -26.56& 1& 0& 0\\\\\n 21& 34& 18.64& -43& 52& 39.7& 20.71& -0.61& 0.64& 1.370& -23.81& 1& 2& 0\\\\\n 21& 34& 37.07& -46& 45& 4.8& 19.37& -0.23& 0.82& 0.704& -23.74& 1& 0& 0\\\\\n 21& 34& 30.32& -44& 35& 55.7& 20.27& -0.72& 1.48& 1.319& -24.17& 0& 0& 3\\\\\n 21& 34& 29.90& -44& 3& 5.5& 20.47& -0.12& 1.11& 1.576& -24.35& 1& 0& 0\\\\\n 21& 34& 47.85& -46& 2& 39.1& 20.15& -0.52& 0.56& 1.340& -24.33& 0& 2& 0\\\\\n 21& 34& 50.90& -46& 1& 49.4& 17.81& 0.12& 0.46& 0.528& -24.68& 1& 0& 0\\\\\n 21& 34& 37.41& -43& 40& 37.4& 19.39& -0.25& 0.48& 0.837& -24.09& 0& 2& 0\\\\\n 21& 34& 49.15& -44& 43& 0.2& 19.53& 0.15& 0.64& 2.526& -26.27& 1& 0& 0\\\\\n 21& 35& 0.95& -46& 11& 36.5& 18.87& -0.41& 0.27& 1.903& -26.34& 0& 2& 0\\\\\n 21& 34& 43.15& -43& 6& 56.5& 19.67& -0.36& 0.81& 1.423& -24.93& 1& 2& 0\\\\\n 21& 35& 6.63& -46& 32& 27.6& 18.66& -0.08& 1.02& 2.222& -26.87& 1& 0& 0\\\\\n 21& 35& 2.90& -45& 49& 32.5& 20.06& -0.59& 0.72& 1.832& -25.07& 1& 2& 0\\\\\n 21& 35& 4.13& -45& 47& 3.5& 20.36& -0.46& 1.15& 1.845& -24.79& 0& 2& 0\\\\\n 21& 35& 0.77& -44& 16& 28.6& 20.67& -0.27& 0.26& 0.285& -20.49& 0& 2& 0\\\\\n 21& 34& 56.25& -43& 13& 47.4& 20.08& -0.30& 0.85& 2.141& -25.38& 1& 2& 0\\\\\n 21& 35& 19.47& -46& 20& 47.4& 18.41& -0.21& 0.53& 0.505& -23.99& 1& 0& 0\\\\\n 21& 35& 0.16& -43& 4& 14.3& 19.60& -0.26& 1.96& 0.511& -22.82& 1& 2& 3\\\\\n 21& 35& 4.58& -43& 46& 13.0& 20.87& 0.50& 0.59& 3.100& -25.35& 1& 0& 0\\\\\n 21& 35& 14.93& -45& 16& 31.0& 20.94& -0.20& 1.21& 0.655& -22.01& 1& 2& 3\\\\\n 21& 35& 5.14& -43& 3& 48.9& 19.62& -0.45& 0.47& 2.029& -25.72& 1& 2& 0\\\\\n\\end{tabular}\n\n\\end{table*}\n\n\\begin{table*}[t]\n\n\\begin{tabular}[b]{rrrrrrrrrrrrrr}\n\\multicolumn{3}{c}{R.A. (1950)}&\\multicolumn{3}{c}{Dec (1950)}&\n\\multicolumn{1}{c}{$B$}&\\multicolumn{1}{c}{$U\\!-\\!B$}&\n\\multicolumn{1}{c}{$\\delta m$}& \\multicolumn{1}{c}{$z$}&\n\\multicolumn{1}{c}{$M_{B}$}&\\multicolumn{3}{c}{Samples}\\\\\n &&&&&&&&&&&&&\\\\\n 21& 35& 12.41& -44& 2& 15.0& 19.30& -0.33& 0.34& 0.929& -24.40& 0& 2& 0\\\\\n 21& 35& 28.41& -45& 59& 2.1& 19.95& -0.56& 0.72& 0.568& -22.70& 1& 2& 0\\\\\n 21& 35& 13.86& -43& 24& 17.3& 19.18& -0.42& 0.77& 1.935& -26.07& 1& 2& 0\\\\\n 21& 35& 28.59& -45& 29& 56.1& 20.77& -0.27& 0.64& 2.148& -24.69& 1& 2& 0\\\\\n 21& 35& 28.35& -45& 23& 57.7& 18.69& -0.47& 0.66& 1.097& -25.36& 1& 2& 0\\\\\n 21& 35& 22.69& -44& 7& 50.2& 20.89& -0.36& 0.75& 1.168& -23.30& 1& 2& 0\\\\\n 21& 35& 20.13& -42& 53& 29.7& 17.89& -0.45& 0.64& 1.469& -26.78& 1& 2& 0\\\\\n 21& 35& 23.26& -43& 20& 7.1& 20.33& -0.33& 1.00& 1.535& -24.43& 1& 2& 0\\\\\n 21& 35& 34.64& -43& 49& 30.6& 21.12& -0.54& 0.86& 1.395& -23.44& 0& 2& 0\\\\\n 21& 35& 41.40& -44& 0& 49.2& 18.45& -0.32& 0.87& 0.461& -23.75& 0& 2& 0\\\\\n 21& 35& 38.64& -43& 26& 25.7& 20.65& 0.06& 0.46& 2.483& -25.11& 1& 0& 0\\\\\n 21& 35& 43.33& -44& 8& 11.1& 20.59& -0.48& 1.23& 1.785& -24.49& 0& 2& 0\\\\\n 21& 35& 47.12& -44& 1& 23.2& 20.41& -0.18& 0.60& 1.708& -24.58& 1& 0& 0\\\\\n 21& 35& 43.26& -43& 20& 54.9& 20.38& -0.11& 0.55& 2.186& -25.12& 1& 0& 0\\\\\n 21& 36& 6.35& -46& 26& 0.5& 19.48& -0.37& 1.31& 0.920& -24.20& 0& 0& 3\\\\\n 21& 35& 53.01& -44& 21& 44.3& 18.69& -0.15& 0.70& 0.408& -23.25& 1& 0& 0\\\\\n 21& 35& 54.17& -44& 14& 32.4& 21.14& -0.51& 0.27& 0.412& -20.82& 0& 2& 0\\\\\n 21& 35& 54.42& -43& 45& 24.2& 20.47& -0.43& 0.98& 1.633& -24.42& 1& 2& 0\\\\\n 21& 36& 19.27& -46& 48& 48.0& 18.88& -0.11& 0.54& 1.124& -25.23& 1& 0& 0\\\\\n 21& 36& 17.27& -44& 30& 11.6& 19.80& -0.46& 0.41& 0.931& -23.91& 0& 2& 0\\\\\n 21& 36& 28.18& -45& 38& 4.6& 19.14& -0.22& 0.59& 1.695& -25.83& 1& 0& 0\\\\\n 21& 36& 21.01& -43& 17& 51.2& 20.29& -0.39& 0.98& 1.048& -23.67& 0& 2& 0\\\\\n 21& 36& 31.16& -44& 20& 53.9& 21.14& -0.35& 0.29& 0.433& -20.92& 0& 2& 0\\\\\n 21& 36& 28.71& -43& 47& 29.6& 18.96& -0.34& 0.61& 1.520& -25.78& 1& 2& 0\\\\\n 21& 36& 30.45& -43& 1& 22.7& 18.12& -0.57& 0.62& 1.343& -26.36& 1& 0& 0\\\\\n 21& 36& 39.18& -44& 11& 35.1& 19.63& -0.41& 0.69& 1.925& -25.61& 1& 2& 0\\\\\n 21& 36& 52.42& -45& 29& 1.7& 19.43& -0.09& 0.75& 1.174& -24.77& 1& 0& 0\\\\\n 21& 36& 34.83& -42& 48& 0.0& 20.10& 0.08& 0.40& 0.168& -19.92& 1& 0& 0\\\\\n 21& 37& 4.86& -46& 20& 11.6& 19.22& -0.02& 0.52& 2.495& -26.55& 1& 0& 0\\\\\n 21& 36& 42.71& -43& 30& 28.1& 20.86& -0.33& 1.41& 1.028& -23.06& 1& 2& 3\\\\\n 21& 36& 49.17& -44& 20& 47.4& 20.23& -0.30& 0.35& 0.275& -20.85& 0& 2& 0\\\\\n 21& 36& 42.52& -43& 28& 46.6& 18.38& -0.43& 0.54& 0.250& -22.50& 1& 2& 0\\\\\n 21& 36& 59.31& -45& 17& 26.5& 20.67& -0.38& 0.86& 1.105& -23.40& 1& 2& 0\\\\\n 21& 36& 44.29& -42& 51& 36.2& 19.67& -0.41& 0.78& 1.510& -25.06& 1& 2& 0\\\\\n 21& 37& 8.20& -45& 23& 36.4& 20.45& -0.38& 0.94& 1.645& -24.46& 1& 2& 0\\\\\n 21& 37& 2.10& -44& 22& 56.2& 20.64& -0.52& 0.75& 2.050& -24.73& 0& 2& 0\\\\\n 21& 37& 12.13& -45& 20& 33.6& 20.70& -0.34& 0.58& 2.113& -24.73& 0& 2& 0\\\\\n 21& 37& 6.81& -43& 54& 27.7& 19.70& -0.77& 0.75& 1.915& -25.52& 1& 2& 0\\\\\n 21& 37& 25.87& -45& 29& 27.9& 20.33& -0.39& 0.60& 1.438& -24.30& 1& 2& 0\\\\\n 21& 37& 14.45& -44& 6& 39.4& 20.30& -0.05& 0.62& 2.250& -25.26& 1& 0& 0\\\\\n 21& 37& 17.79& -44& 21& 10.6& 19.72& -0.35& 1.42& 0.346& -21.86& 1& 2& 3\\\\\n 21& 37& 17.76& -44& 10& 44.8& 20.87& -0.42& 0.65& 0.798& -22.51& 0& 2& 0\\\\\n 21& 37& 10.59& -43& 5& 26.6& 20.92& -0.42& 1.32& 1.393& -23.64& 1& 2& 3\\\\\n 21& 37& 29.30& -44& 49& 49.2& 19.54& 0.49& 0.72& 0.136& -20.02& 1& 0& 0\\\\\n 21& 37& 15.41& -43& 1& 47.3& 19.83& -0.22& 1.11& 1.520& -24.91& 1& 2& 3\\\\\n 21& 37& 31.36& -44& 22& 18.3& 19.42& 0.32& 0.54& 1.320& -25.03& 1& 0& 0\\\\\n 21& 37& 53.50& -46& 45& 21.6& 20.42& 0.24& 1.11& 2.800& -25.59& 1& 0& 0\\\\\n 21& 37& 32.47& -43& 36& 56.0& 19.53& -0.10& 0.48& 2.310& -26.08& 1& 0& 0\\\\\n 21& 37& 38.02& -43& 43& 5.3& 19.16& -0.74& 0.50& 1.964& -26.12& 1& 2& 0\\\\\n 21& 38& 0.90& -46& 11& 10.3& 19.48& 0.04& 0.66& 2.287& -26.11& 1& 0& 0\\\\\n 21& 37& 51.68& -44& 35& 48.8& 18.34& -0.34& 0.35& 0.632& -24.54& 1& 0& 0\\\\\n 21& 37& 45.95& -43& 56& 50.9& 20.02& -0.63& 1.67& 2.039& -25.34& 0& 2& 3\\\\\n 21& 38& 17.41& -46& 35& 7.3& 21.02& -0.37& 1.40& 0.780& -22.31& 0& 0& 3\\\\\n 21& 38& 15.98& -46& 21& 31.8& 19.45& -0.16& 0.61& 0.618& -23.38& 1& 0& 0\\\\\n 21& 38& 16.48& -45& 12& 28.1& 19.34& -0.24& 0.25& 2.164& -26.14& 0& 2& 0\\\\\n\\end{tabular}\n\n\\end{table*}\n\n\\begin{table*}[t]\n\n\\begin{tabular}[b]{rrrrrrrrrrrrrr}\n\\multicolumn{3}{c}{R.A. (1950)}&\\multicolumn{3}{c}{Dec (1950)}&\n\\multicolumn{1}{c}{$B$}&\\multicolumn{1}{c}{$U\\!-\\!B$}&\n\\multicolumn{1}{c}{$\\delta m$}& \\multicolumn{1}{c}{$z$}&\n\\multicolumn{1}{c}{$M_{B}$}&\\multicolumn{3}{c}{Samples}\\\\\n &&&&&&&&&&&&&\\\\\n 21& 38& 11.93& -44& 20& 28.7& 19.66& -0.59& 0.51& 2.102& -25.76& 1& 2& 0\\\\\n 21& 38& 5.54& -43& 20& 26.1& 19.91& -0.17& 0.54& 0.574& -22.76& 1& 0& 0\\\\\n 21& 38& 41.58& -46& 50& 33.2& 18.26& -0.20& 1.02& 0.762& -25.02& 1& 0& 0\\\\\n 21& 38& 14.85& -43& 45& 49.7& 19.26& -0.48& 0.93& 1.320& -25.19& 1& 2& 0\\\\\n 21& 38& 12.87& -43& 9& 10.4& 20.22& -0.17& 2.08& 0.687& -22.84& 1& 0& 3\\\\\n 21& 38& 25.45& -44& 5& 15.3& 19.85& -0.31& 0.73& 0.862& -23.69& 1& 2& 0\\\\\n 21& 38& 15.73& -42& 55& 44.8& 20.13& -0.23& 0.83& 1.597& -24.72& 1& 2& 0\\\\\n 21& 38& 33.14& -44& 16& 15.2& 20.53& -0.33& 1.73& 0.623& -22.32& 0& 0& 3\\\\\n 21& 38& 28.59& -43& 7& 4.9& 20.50& -0.30& 0.26& 0.255& -20.42& 0& 2& 0\\\\\n 21& 38& 43.40& -44& 32& 17.9& 0.00& -0.51& 1.44& 1.660& -44.93& 0& 0& 3\\\\\n 21& 38& 31.80& -43& 13& 51.2& 20.06& -0.75& 0.79& 1.287& -24.33& 1& 2& 0\\\\\n 21& 38& 56.08& -45& 26& 4.1& 20.08& -0.51& 0.36& 1.197& -24.16& 1& 2& 0\\\\\n 21& 38& 56.93& -45& 16& 15.5& 20.50& -0.50& 1.50& 2.013& -24.83& 0& 2& 3\\\\\n 21& 39& 0.08& -45& 20& 38.8& 20.01& -0.20& 0.64& 2.210& -25.51& 1& 2& 0\\\\\n 21& 38& 53.72& -44& 38& 39.4& 19.50& -0.53& 0.61& 1.078& -24.52& 1& 0& 0\\\\\n 21& 39& 12.24& -46& 14& 18.8& 20.15& 1.14& 0.59& 3.340& -26.22& 1& 0& 0\\\\\n 21& 38& 57.01& -44& 16& 52.4& 19.31& -0.37& 0.62& 1.735& -25.71& 1& 2& 0\\\\\n 21& 38& 54.54& -43& 41& 29.9& 20.74& -0.33& 1.02& 2.210& -24.78& 1& 2& 0\\\\\n 21& 38& 59.14& -43& 50& 57.6& 18.71& 0.21& 0.40& 0.142& -20.94& 1& 0& 0\\\\\n 21& 38& 52.05& -42& 58& 42.7& 20.26& -0.46& 0.56& 0.937& -23.46& 1& 2& 0\\\\\n 21& 38& 54.79& -42& 55& 28.0& 19.87& -0.20& 1.18& 0.542& -22.68& 1& 2& 3\\\\\n 21& 39& 25.50& -45& 20& 14.0& 19.97& -0.69& 0.79& 1.394& -24.59& 1& 2& 0\\\\\n 21& 39& 20.18& -44& 43& 60.0& 20.96& 0.09& 0.77& 2.380& -24.71& 1& 0& 0\\\\\n 21& 39& 27.52& -45& 21& 30.5& 20.73& -0.24& 0.79& 1.671& -24.21& 1& 2& 0\\\\\n 21& 39& 9.07& -42& 54& 48.2& 20.62& -0.32& 0.73& 1.905& -24.59& 0& 2& 0\\\\\n 21& 39& 22.45& -43& 32& 4.6& 18.40& 0.11& 0.61& 2.190& -27.10& 1& 0& 0\\\\\n 21& 39& 32.94& -43& 55& 45.4& 19.47& -0.51& 0.64& 0.679& -23.56& 1& 2& 0\\\\\n 21& 39& 44.37& -44& 49& 37.2& 20.10& -0.14& 1.46& 1.640& -24.80& 0& 0& 3\\\\\n 21& 39& 27.24& -43& 8& 28.0& 20.86& -0.20& 1.04& 0.752& -22.39& 1& 2& 0\\\\\n 21& 40& 3.43& -46& 20& 2.2& 18.78& -0.22& 0.65& 0.548& -23.79& 1& 0& 0\\\\\n 21& 39& 30.84& -42& 59& 26.0& 19.81& -0.35& 0.59& 1.890& -25.39& 1& 2& 0\\\\\n 21& 39& 42.04& -43& 28& 17.4& 20.55& -0.29& 0.85& 0.708& -22.57& 0& 2& 0\\\\\n 21& 39& 48.87& -43& 36& 18.4& 20.86& -0.56& 1.21& 1.379& -23.68& 0& 0& 3\\\\\n 21& 40& 16.52& -45& 52& 37.0& 18.11& -0.34& 0.71& 1.688& -26.85& 1& 0& 0\\\\\n 21& 39& 51.98& -43& 14& 14.2& 21.21& -0.15& 1.48& 1.645& -23.70& 0& 0& 3\\\\\n\\end{tabular}\n\n\\end{table*}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002368.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1994]{are94} Aretxaga I., Terlevich R., 1994, MNRAS 269, 462\n\\bibitem[1997]{are97} Aretxaga I., Cid Fernandes R., Terlevich R.,\n 1997, MNRAS 286, 271\n\\bibitem[1996]{cid96} Cid Fernandes R., Aretxaga I., Terlevich R.,\n 1996, MNRAS 282, 1191\n\\bibitem[1991]{cla91} Clavel J. et al., 1991, ApJ 366, 64\n\\bibitem[1996]{cri96} Cristiani S., Trentini S., La Franca F.,\n Andreani P., 1996, A\\&A 321, 123\n\\bibitem[1996]{cri96} Cristiani S., Trentini S., La Franca F.,\n Aretxaga I., Andreani P., Vio R., Gemmo A., 1996, A\\&A 306, 395\n\\bibitem[1996]{dic96} Di Clemente A., Giallongo E., Natali G.,\n Tr\\`{e}vese D., Vagnetti F., 1996, ApJ 463, 466\n\\bibitem[1999]{fol99} Folkes S. et al., 1999, MNRAS 308, 459\n\\bibitem[1991]{gia91} Giallongo E., Trevese D., Vagnetti F., 1991,\n ApJ 377, 345\n\\bibitem[1993]{haw93} Hawkins M.R.S., 1993, Nat 366, 242\n\\bibitem[1996]{haw96} Hawkins M.R.S., 1996, MNRAS 278, 787\n\\bibitem[1997]{haw97} Hawkins M.R.S., Taylor A.N., 1997, ApJ 482, L5\n\\bibitem[1995]{haw95} Hawkins M.R.S. \\& V\\'{e}ron P., 1995, MNRAS\n 275, 1102\n\\bibitem[1994]{hoo94} Hook I.M., McMahon R.G., Boyle B.J., Irwin M.J.,\n 1994, MNRAS 268, 305\n\\bibitem[1998]{kaw98} Kawaguchi T., Mineshige S., Umemura M.,\n Turner E.L., 1998, ApJ 504, 671\n\\bibitem[1991]{mor91} Morris S.L., Weymann R.J., Anderson S.F.,\n Hewett P.C., Foltz C.B., Chaffee F.H., Francis P.J., MacAlpine G.M.,\n 1991, AJ 102, 1627\n\\bibitem[1991]{ref91} Refsdal S., Stabell R., 1991, A\\&A 250, 62\n\\bibitem[1983]{sch83} Schmidt M., Green R.F., 1983, ApJ 269, 352\n\\bibitem[1987]{sch87} Schneider P., Weiss A., 1987, A\\&A 171, 49\n\\bibitem[1989]{tre89} Trevese D., Pitella G., Kron R.G., Bershady M.,\n 1989, AJ 98, 108\n\n\\end{thebibliography}"
}
] |
astro-ph0002369
|
Breaking the degeneracy of cosmological parameters in galaxy redshift surveys
|
[
{
"author": "Mikel Susperregi"
},
{
"author": "Fisika Teorikoaren Saila"
},
{
"author": "Zientzi Fakultatea"
},
{
"author": "Euskal Herriko Unibertsitatea"
},
{
"author": "PO Box 644"
},
{
"author": "48080 Bilbao"
},
{
"author": "Spain"
}
] |
The measurement of cosmological parameters is investigated in a representation of the least-action method that uses a redshift-space dataset to simultaneously constrain the real-space fields $\delta$,$\b v$. This method is robust in recovering the entire evolution of the matter density contrast and peculiar velocities of galaxies in real space from current galaxy redshift surveys. The main strength of the method is that it permits us to break the degeneracy of the parameters $b$ and $\Omegam$ (customarily measured in the ratio $\beta\equiv \Omegam^{0.6}/b$ from redshift-space distortions), and these are evaluated in the current context separately. The procedure provides a simple numerical means to extract as much information as possible from a given sample, in the simplest linear bias model, before resorting to cosmic complementarity to resolve the degeneracy in the measurement of $\Omegam$. The same premise applies to more sophisticated choices of bias models. We construct a likelihood parameter $\lambda(b,\Omegam)$ to evaluate the relative likelihood of different values of $b$ and $\Omegam$. The method is applied to the \iras~redshift survey with a low-resolution Gaussian smoothing length of 1200 \km within a spherical region $x_{max} \sim 15,000$ \km and the reconstructed velocity field is then compared with POTENT-reconstructed velocities from the Mark III radial-velocity dataset within a radius $\sim 5000$ \km, which have been suitably prepared to account for Malmquist bias and other systematic errors. The analysis yields a likelihood for the parameters that is overall consistent with $\Omegam\approx 0.3$ and $b\approx 1.1$, thus lending support to a non-vanishing cosmological constant $\Omega_{\Lambda}\approx 0.7$ in a flat universe.
|
[
{
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Susperregi]\n {Mikel Susperregi\\\\\nFisika Teorikoaren Saila, Zientzi Fakultatea, \nEuskal Herriko Unibertsitatea, PO Box 644, 48080 Bilbao, Spain\\\\\nEmail: wtpsuxxm@ehu.es}\n\\date{\\today}\n\n\\pagerange{0--0}\n\\pubyear{0000}\n\n\\begin{document}\n\n\\maketitle\n\n\\label{firstpage}\n\n\\begin{abstract}\nThe measurement of cosmological parameters is investigated \nin a representation of the least-action method that uses a \nredshift-space dataset to simultaneously constrain \nthe real-space fields $\\delta$,$\\b v$. This method is robust \nin recovering the entire evolution of the matter density \ncontrast and peculiar velocities of galaxies in real space \nfrom current galaxy redshift surveys. The main strength \nof the method is that it permits us to break the degeneracy \nof the parameters $b$ and $\\Omegam$ (customarily measured \nin the ratio $\\beta\\equiv \\Omegam^{0.6}/b$ from redshift-space \ndistortions), and these are evaluated in the current \ncontext separately. The procedure provides a simple numerical \nmeans to extract as much information as possible from a given \nsample, in the simplest linear bias model, before resorting to cosmic \ncomplementarity to resolve the degeneracy in the measurement of \n$\\Omegam$. The same premise applies to more sophisticated choices \nof bias models. We construct a likelihood parameter \n$\\lambda(b,\\Omegam)$ to evaluate the relative likelihood of different \nvalues of $b$ and $\\Omegam$. The method is applied to the \n\\iras~redshift survey with a low-resolution Gaussian \nsmoothing length of 1200 \\km within a spherical region \n$x_{\\rm max} \\sim 15,000$ \\km and the reconstructed \nvelocity field is then compared with POTENT-reconstructed \nvelocities from the Mark III radial-velocity dataset within \na radius $\\sim 5000$ \\km, which have been suitably prepared to \naccount for Malmquist bias and other systematic errors. The \nanalysis yields a likelihood for the parameters that is \noverall consistent with $\\Omegam\\approx 0.3$ and $b\\approx 1.1$, thus \nlending support to a non-vanishing cosmological constant \n$\\Omega_{\\Lambda}\\approx 0.7$ in a flat universe. \n\\end{abstract}\n\n\\begin{keywords}\nlarge-scale structure of universe -- cosmology \n-- galaxies: distances and redshifts \n\\end{keywords}\n\n\\section{Introduction}\n\n\\begin{figure*}\n\\centering\n\\begin{picture}(210,210)\n\\special{psfile='fig0.ps' angle=-90\nvoffset=290 hoffset=-160 vscale=60 hscale=67}\n\\end{picture}\n\\caption[]{Qualitative distribution of errors in the reconstruction \nof the matter fields from redshift surveys. The error $\\epsilon_0$ in \nthe current redshift sample increases monotonically in (a) as the \nperturbative solutions propagate $\\epsilon_0$ to increasing amplitudes \nwhen integrated back in time; in the boundary condition problem of the \nLAP method, shown in (b), errors fluctuate between the fixed end-points.}\n\\end{figure*}\n\nGalaxy redshift surveys are undoubtedly extremely valuable tools \nto investigate the evolution of the universe at large scales. \nThe cosmologist's prerogative is to determine the evolution \nof the matter density contrast $\\delta$ and peculiar \nvelocity $\\b v$ that yields such cosmic structure, customarily \nassuming that it formed solely by gravity, and the cosmological \nparameters that determine their dynamics. In the standard paradigm \nof a FRW expanding universe, the interplay of both fields is \ngoverned by the density parameter $\\Omega_0$ and the Hubble \nparameter $H_0$. On the other hand, a relationship between \nthe fields $\\delta$,$\\b v$ and the survey data is established \nby adopting a bias model that purports the correlation \nbetween the $z$-space galaxy number-count and the underlying matter field. \nDevoid of such a relationship, the edifice of measuring cosmological \nparameters from galaxy redshift surveys has no foundation \nwhatsoever. A standard working hypothesis, that I shall \naccept throughout this paper, is that of linear bias, \ni.e. $b^2 \\equiv P(k)_{\\rm gals}/P(k)_{\\rm matter}$ \n(more elaborate bias models are propounded in e.g. \nDekel \\& Lahav 1999). For simplicity we shall also \nleave out the scale-dependence of $b$. \nTherefore, three relevant parameters that are interesting \nto pin down from redshift-space samples are in this context \n$\\Omegam$,$H_0$ and $b$. In this paper I shall be chiefly \nconcerned with $\\Omegam$ and $b$ ($H_0$ will be scaled out \nwith distance). \n\nTracing back in time the matter fields takes us \nto an initial epoch of fluctuations of very small amplitude \n$\\delta\\lsim 10^{-4}$, seeded by a period of inflationary expansion. \nAt that point the information derived from the galaxy \nsurveys connects with early-universe data such as \nthe spectrum of fluctuations on the CMB. \nIf the matter fields could realistically be \ntraced back to such a primordial stage by integrating \nthe equations of gravitational instability, then \nthe statistics of the $\\delta$ field would be a potentially key \ndiscriminant to rule out cosmological models. For instance,\nnon-gaussianity in the initial $\\delta$ field rules out most \ninflationary models, and only those leading to a non-Gaussian \nprimordial spectrum remain acceptable (such models are \nsuggested in e.g. Linde, Sasaki \\& Tanaka 1999). \n\nKaiser (1987) proposed measuring cosmological parameters from \nredshift-space distortions by virtue of the fact that overdense \nregions appear to be flatter along the line-of-sight in redshift \nspace. This distortion, quantified by the parameter \n$\\beta=\\Omegam^{0.6}/b$, permits us to solve the equations \nfor $\\delta$,$\\b v$, at least perturbatively (see e.g. Dekel 1994; \nColes \\& Sahni 1995), and measurements of $\\beta$ have been\ninvestigated in much detail in the literature (Strauss \\& Willick\n1995; Dekel 1994,1999a; Dekel, Burstein \\& White 1997). \nAlso, in view of the fact that the bias parameter is almost \ncertainly dependent on the selected sample, estimates have been \ncomputed for $\\beta_{IRAS}$ given $b_I$ for {\\it IRAS} galaxies \n(Dekel \\etal 1993; Fisher \\etal 1995a; Willick \\etal 1997a,b; \nSigad \\etal 1998; more recently from the PSC$z$ sample, Canavezes \n\\etal 1998; Tadros \\etal 1999; Saunders \\etal 2000) \nand from the Optical Redshift Survey (ORS) (Hudson \\etal 1995; \nSantiago \\etal 1995; Baker \\etal 1998). The Mark III peculiar \nvelocity survey similarly yields estimates of $\\beta$ from redshift \ndistortions (Willick \\etal 1995,1996,1997a,b; \nDekel, Burstein \\& White 1997; Sigad \\etal 1998). It is only beyond \nthe linear approximation (i.e. $\\delta \\propto \\nabla\\cdot\\b v$) \nand, indeed, beyond the assumption of linear bias, \nthat one can break down the degeneracy between $\\Omegam$ and $b$ and \nestimate these parameters separately, rather than via $\\beta$ \n(Fry 1994; Bernardeau \\etal 1995). Verde \\etal (1998) achieved \nthis by proposing the bispectrum as a measure of cosmological\nparameters, in a model of non-linear bias. In this paper we also \npursue breaking the degeneracy of $\\Omegam$ and $b$ from the\nredshift-space data and show that by using the least-action \nframework it is indeed possible to do so within the linear \nbias model. \n\nThe least-action principle (LAP) was first used in \nthe Local Group by Peebles (1989,1990). The trajectories \nof nearby galaxies were computed subject to two boundary \nconditions: vanishing initial velocities and fixed \npresent positions. This simple scenario of self-gravitating \npoint-like masses with two boundary conditions produced an estimate\nof $\\Omegam$ by fitting to the observations the predicted \npeculiar velocities of nearby galaxies. The LAP method has also been \nused as a test of $\\Omegam=1$ CDM models (Branchini \\& Carlberg 1994), \nas well as to integrate the orbits of a significant number of galaxies \nfrom partial coverage redshift samples (e.g. Shaya, Peebles \n\\& Tully 1995). An equivalent representation of the LAP method \nin terms of continuous fields, i.e. the density contrast and \nvelocity fields was proposed by Giavalisco \\etal (1993), \nand employed in Susperregi \\& Binney (1994)(hereafter SB94) and \nSusperregi (1995) in the reconstruction of $\\Omegam=1$ simple models, \nsuch as exact solutions and Gaussian random fields. More recently, \nSchmoldt \\& Saha (1998) proposed a variant of the customary LAP \nformulation by rewriting the equations motion in redshift space. \n\nThe key difference between the variational and perturbative \napproaches lies on how the errors are spread over the time-reversed \nevolution. This is qualitatively sketched in Fig.~1. A $n$th-order \nsolution differs, in the time-reversed direction, from the true solution \nby a monotonically growing parameter $\\epsilon$ which sets out from a \nsmall value $\\epsilon(t_0)$ (at any rate $\\epsilon_0$ is at \nleast the sum of the systematic and random errors of the dataset) \nand the conservation of kinematical quantities is preserved up to \n$O(\\epsilon^{n})$. This is adequate within a time span \n$t_c \\ll t \\lsim t_0$ where $\\epsilon(t_c)\\sim 1$, and $t_c$ marks \na transition into the loss of convergence. The distribution \nof errors in the LAP method on the other hand, is by construction \nevenly distributed along the trajectory; the initial and final \nboundary conditions are fixed, though not without systematic \nand numerical errors, and the parameter $\\epsilon$ fluctuates \nalong the trajectory between both end-points (Fig.~1b). \nHence the solution is well-behaved whether the errors remain \nwithin the bound $\\epsilon \\lsim 1$ or not. In that respect there \nis an advantage with respect to perturbative solutions; the downside \nof it is of course that within the span of time where perturbative \nsolutions are valid, LAP errors may fluctuate with larger amplitude \nthan the perturbative equivalent. The LAP method, in a nutshell, \nthus consists in finding Ansatze for the matter fields that optimize \nthe distribution of $\\epsilon$ along the phase-space trajectory, \nand hence minimize the overall departure with respect to the \nexact solution. The following two difficulties may arise: \n\\begin{itemize}\n\\item {\\bf A} {\\it Finding ``dynamically plausible'' solutions}. \nIf the matter field is sparsely sampled or the errors in the dataset \nare substantial, then the boundary condition given by the survey, \ntaken at face value, may not correspond to the outcome of \ngravitational evolution from \nthe initial fluctuations (typically $\\delta\\sim 0$ or vanishing peculiar \nvelocities). The LAP method will in this case find a {\\it dynamically \nplausible} fit between the end-points, which will be as faithful a \nrepresentation of the true evolution as is the quality of the dataset. \n\\item {\\bf B} {\\it Formation of multistreams in over-dense regions}. \nMultistreams are characterised by galaxies at the same redshift which \nare located at different positions along the line of \nsight and have different infalling velocities. The \ndegeneracy in redshift among streams makes them indistinguishable \nand hence compatible but inequivalent solutions result, as many as \nthere are streams. The LAP method cannot discriminate among \nthese solutions; multistreams indeed erase the memory of their \npast evolution. \n\\end{itemize}\nThe second problem can only be overcome by casting aside part of \nthe information contained in the sample and smoothing \nover the existing non-linearities to transform the multivalued \nfield into a single-valued one, typically with a smoothing length \n$\\sim 500 - 1000$ \\km. The resulting smoothed field is \nclearly a less resolved representation of the underlying \ngalaxy orbits, albeit the only tractable one. \n\nThe advent of large galaxy redshift surveys strengthens the motivation \nto use the LAP method. Near all-sky redshift surveys, e.g. PSC$z$, \n\\iras~and ORS provide an excellent sky coverage (within a galactic \nlatitude $|b|\\gsim 8^{\\circ}$ for {\\it IRAS} galaxies and \n$|b|\\gsim 20^{\\circ}$ for ORS), that may be extended further to \ncover the Zone of Avoidance via a Wiener reconstruction \n(Fisher \\etal 1995b; Zaroubi \\etal 1999). They are therefore \na fairly thorough representation of the underlying matter \ndensity field. Obviously the greater number of galaxies \nin the sample the more accurate is the representation \nof the field, and this is best achieved with a redshift survey. \nReal-space datasets require Tully-Fisher distance \ncalibrations of individual galaxies, and consequently the end \nresult is a sparser sampling than is achieved with the same \ncomputational effort by measuring redshifts and \nangular coordinates. The goal of this paper is to exploit \ngalaxy redshift surveys to the best effect and extract as much \ninformation from them as is possible; the main thesis put forward is \nthe LAP method demonstrably breaks down the degeneracy in the \ndetermination of $\\Omegam$ and $b$. This entails very tangible \nadvantages. On the one hand, the freedom to investigate those two \nparameters separately permits us not to take the idea of bias \nseriously. A form of bias will certainly always be present \nin one form or another so that we can make sense of the galaxy \nnumber-count with respect to the underlying matter field. However, \nwhether that is a linear or non-linear bias, the more one \ndissociates this phenomenological relationship from our \nmeasurements of $\\Omegam$, the more credible those measurements \nwill be. This is indeed what LAP does. On the other hand, the \nLAP method produces a reconstruction on the basis of the \nredshift-space sample alone, free of any proviso regarding the \nshape of the power spectrum. Assuming a given shape for $P(k)$ \nunduly overconstrains the system, as will the addition of other \ndatasets. \n\nIn this article, I shall mainly apply the LAP method to the \n\\iras~survey and study the predicted values of $b$ and $\\Omegam$. \nThe reconstructed \\iras~velocity field is then compared with the \nMark III velocity sample to seek a fine-tuning of the parameters. \nA more thorough undertaking, in terms of the quality of the sample, \nis to apply the LAP method to PSC$z$, which is by a factor \nof 3 a more densely sampled survey than \\iras, and it will \nbe interesting to tackle this in future work. The article \nis structured as follows: Section 2 describes the LAP method in \nsome detail and how to find solutions that are consistent\nwith a redshift-space dataset; in Section 3 we test the method \nwith several {\\it IRAS} mock catalogues obtained via $n$-body \nsimulations; in Section 4 we apply the method to the \\iras~galaxy \nredshift survey, optimizing the predicted velocities with \nthe Mark III dataset; finally, in Section 5 we summarize the main \nconclusions. \n\n\n\\section{The LAP method}\n\\subsection{Redshift-space coordinates}\n\nThe redshift coordinates of galaxies are defined \n\\be\\label{sdef1}\n\\b z= H_0\\b r+\\hat r(\\hat r\\cdot\\b v),\n\\ee\n where $\\b r\\equiv (r,\\theta,\\varphi)$ is the physical position, \n$H_0$ is the present value of the Hubble parameter, $\\b v$ the \npeculiar velocity, and $\\hat r$ a unit vector in the radial \n(line-of-sight) direction. $\\b z$ has units of velocity; its \nradial component is the redshift $z_r=cz$, and the angular \ncomponents are the same in both {\\it x}-space and {\\it z}-space, up to \nthe distance scale. Henceforth we shall measure distances in \\km, \nhence $H_0$ is scaled out of the equations. In comoving coordinates, \n(\\ref{sdef1}) reads\n \\be \\label{sdef2}\n\\b s= \\b x+ \\hat{x}(\\hat x\\cdot\\nabla_{x}\\alpha),\n\\ee\n where the scale factor of the universe is normalized \nto $a(t_0)=1$; $\\alpha(t,\\b x)$ is the velocity potential, \n$\\b v \\equiv a^{-1}\\nabla\\alpha$. Hereafter we adopt $t_0=1$. \n\n\\subsection{Dynamics}\n\nThe cosmological perturbations are derived from the action \n\\be \\label{action}\n{\\cal S}=\\int_0^{1}\\!\\d t\\!\\int_{\\rm sample}\\!\\d\\b x {\\cal L},\n\\ee\nwhere ${\\cal L}$ is given by \n\\be \\label{lagrangian}\n{\\cal L}={1\\over 2}(1+\\delta){\\b v}^{2} +\\alpha\\xi\n-\\phi\\delta-{|\\nabla\\phi|^2\\over 3\\Omegam a^2};\n\\ee\n$\\delta$ is the density contrast and $\\phi$ the gravitational \npotential caused by the perturbations and \n\\be\n\\xi\\equiv \\dot\\delta+{1\\over a}\\nabla\\cdot[(1+\\delta){\\b v}] \n\\ee\nis the {\\it excess flux}. The variations \n$\\delta{\\cal S}/\\delta {v_i}=\\delta{\\cal S}/{\\delta\\phi}=0$ yield \n\\be \\label{zveloc-alpha}\n{\\b v}={1\\over a}\\nabla\\alpha,\n\\ee\n\\be \\label{zpoisson}\n\\nabla^2\\phi={3\\over 2}a^2\\Omegam\\delta.\n\\ee\nSimilarly, \n$\\delta{\\cal S}/\\delta\\delta=\\delta{\\cal S}/\\delta\\alpha=0$ yield \nrespectively \n \\be \\label{zbern}\n\\xi=0,\n\\ee\n\\be \\label{zbern2}\n\\dot\\alpha+{|\\nabla\\alpha|^2\\over2a^2}+\\phi=0, \n\\ee\nwhere we have eliminated $\\b v$ via (\\ref{zveloc-alpha}) and we \ndo not consider $\\Omega_{\\Lambda}$. The field equations \n(\\ref{zbern}),(\\ref{zbern2}) are subject to the following \nboundary conditions:\n\n\\newcounter{bean}\n\\begin{list}{\\Roman{bean}}{\\usecounter{bean}}\n\\item {\\it Homogeneity of the density field at} $t\\to0$. Density \nperturbations grow from initial fluctuations of negligible amplitude:\n\\be \\label{bcd}\n\\delta(t\\to0,{\\b x})\\approx 0.\n\\ee\n\\item {\\it Galaxy redshift survey at the present time}. The \ngalaxy number-count density $\\rho_s$ in $z$-space constrains \nthe real fields $\\delta(\\b x)$ and $\\alpha(\\b x)$ via \n\\be \\label{constraint}\n\\rho_s(\\b s)=x^2 \\gal \\biggl({1+b\\delta\\over 1+\\alpha''}\\biggr),\n\\ee\n\\end{list} \n\n\\noindent where the tilde denotes derivation along the radial \ndirection, $x$ is the radial comoving distance and $b$ is the bias \nparameter. Condition $(I)$ is motivated by the CMB Sachs-Wolfe \nconstraint $\\delta\\lsim 10^{-4}$ over $r\\sim 100,000$ \\km, \nso we accept that perturbations \nare negligible in the limit $t\\to 0$. A proof for $(II)$ is given \nin Appendix A. In order to solve (\\ref{zbern}),(\\ref{zbern2}), \nwe construct the trial fields: \n\\be \\label{zd1}\n\\delta=\\sum_{n=0}^N f_n(t)\\delta_n(\\b x),\n\\ee\n\\be \\label{zd2}\n\\alpha=\\sum_{n=0}^N g_n(t)\\alpha_n(\\b x),\n\\ee\nwhere the basis functions $f_n$,$g_n$ are adjusted to numerical convenience. SB94 \nconsidered $f_n\\equiv D(D-1)^n$, and $g_n=(\\dot{D}/D)f_n$, where $D$ is the \nlinear growth factor, normalized to unity at $t=1$, so that the lowest-order \nseries (\\ref{zd1}),(\\ref{zd2}) \nare identical to the perturbative solutions. \nThis is however strictly speaking not a compelling choice, and a sensible \nchoice of orthogonal polynomials leads to an Ansatz of better \nconvergence. As we have discussed in the Introduction \n(point {\\bf A}), the sparseness of the dataset obscures the \ndynamical evolution and the LAP method is reduced to a numerical fit \nof the fields to the truncated equations, that we derive \nbelow, subject to (\\ref{bcd}),(\\ref{constraint}). In trying to \napproximate a function $f(t)$ by orthogonal polynomials $P_m(t)$ \nin $0\\lsim t\\lsim 1$, a weight function $w(t)\\geq 0$ tells us \nthe relative importance of the errors spread over the domain. \nFor a uniform $w$, $f_n$ are the [spherical] Legendre polynomials \n$L_m(t)$, whereas for a weight function that is larger at the \nendpoints (\\ref{bcd}),(\\ref{constraint}) than throughout the \ntrajectory, e.g. $w(t)=(1-t^2)^{-1/2}$ (by shifting the domain \nfrom $[0,1]$ to $[-1,1]$), the optimal choice are in this case \nChebyshev polynomials $T_n(t)$. This choice minimizes the errors \naround the endpoints and it gives a greater weight to the \nsolutions (matching the boundary conditions) in this region. \nIn the analysis that follows, we shall adopt $f_n=T_n$ and \n$g_n= a^2 f_n$. The fields $\\delta_n$,$\\alpha_n$ \nare expanded in terms of spherical harmonics,\n\\be\n\\delta_n =\\sum_{rlm}\\delta^{(n)}_{rlm}\\,j_l(k_rx)\\,Y_{lm},\n\\ee\n\\be \\label{zalphan}\n\\alpha_n =\\sum_{rlm}\\alpha^{(n)}_{rlm}\\,j_l(k_rx)\\,Y_{lm},\n\\ee\nwhere $j_l$ are spherical Bessel functions. Substituting \n(\\ref{zd1}),(\\ref{zd2}) into (\\ref{zveloc-alpha}),(\\ref{zpoisson}) \nwe get\n\\be \\label{v_spher}\n\\b v = a\\!\\! \\sum_{rlmn} \\Big[\n\\hat{x} \\alphap_{rlm}^{(n)}j_l(k_rx) \n+{1\\over x}(\\hat{x}\\wedge\\b J_{lm}^{(n)})\\Big] T_n Y_{lm},\n\\ee\n\\be \\label{phi_spher}\n\\phi=-{3\\over 2}a^2\\Omegam\\!\\!\\sum_{rlmn}\n{\\delta_{rlm}^{(n)}\\over k_r^2}\\,T_n j_l(k_rx)Y_{lm};\n\\ee \nthe coefficients $\\alphap_{rlm}^{(n)}$ and $\\b J_{lm}^{(n)}$ \nare given in Appendix B. The \nboundary conditions (\\ref{bcd}),(\\ref{constraint}) then read \n\\be \\label{constraint1}\n0= \\sum_{n=0}^N (-1)^n\\delta_n,\n\\ee\n\\be \\label{constraint2}\n\\rho_s =x^2 \\biggl({N_{\\rm gals}\\over V}\\biggr)\n\\Big[1+b\\,\\delta(1,\\b x)\\Big]\n\\Big[1+\\alphapp(1,\\b x)\\Big]^{-1},\n\\ee\nwhere $t$ is rescaled to the interval $[-1,1]$ for convenience \nin using $T_n$, and in (\\ref{constraint1}) we have used \n$T_n(-1)=(-1)^n$. The choice of basis functions of SB94 satisfy \n(\\ref{constraint1}) by construction, and in our choice of basis \nfunctions the constraint \nis less trivial, but still it is easily tackled numerically. If we \nrestrict ourselves to the interval $0\\leq t\\leq 1$, then \n(\\ref{constraint1}) evaluated at $t=0$ eliminates all the Chebyshev \npolynomials of odd order. This is an \nequivalent approach but we shall adopt the convention above, \n$-1\\leq t\\leq 1$. The constraint (\\ref{constraint2}) is the \ncore of the problem as it is where all the information of the dataset \nis contained. The remainder of the paper will focus on the \ndifferent ways one can use that constraint. \n\n\\subsection{Finding LAP solutions}\n\nSubstituting (\\ref{zd1})--(\\ref{zalphan}) into equations \n(\\ref{zbern}),(\\ref{zbern2}), we get \n\\[\n\\sum_{n=0}^{N}\\sum_{rlm}\n\\Big[\\dot{T}_n\\delta_{rlm}^{(n)}-k_r^2 T_n \\alpha_{rlm}^{(n)}\\Big]\n\\,j_l(k_rx)\\,Y_{lm}\n\\]\n\\be \\label{zceqI}\n= -\\sum_{p,q=0}^{N}\\!\\!\\!\\sum_{\\scriptstyle{rlm}\\atop\\scriptstyle{r'l'm'}}\n\\!\\!T_p T_q\\biggl\\{{\\alphap_{rlm}^{(q)}} \n{{\\delta^\\prime}_{r'l'm'}^{(p)}}j_l(k_rx) j_{l'}(k_{r'}x)\n\\ee \n\\[\n+{1\\over x^2}\\Big[\\hat{x}\\wedge\\b J_{lm}^{(p)}(\\delta)\\Big]\n\\cdot\\Big[\\hat{x}\\wedge\\b J_{l'm'}^{(q)}(\\alpha)\\Big]\\biggr\\}\nY_{lm}Y_{l'm'},\n\\]\nand\n\\[\n\\sum_{n=0}^{N}\\sum_{rlm}\n\\Big[-{3\\over 2}\\Omegam k_r^{-2}\\delta_{rlm}^{(n)}\n+\\biggl({\\dot{T}_n\\over T_n}+2{\\dot a\\over a}\\biggr)\\alpha_{rlm}^{(n)}\\Big]\nT_n j_l(k_rx)Y_{lm}\n\\]\n\\be \\label{zceqII}\n= -{1\\over 2}\\!\\!\\sum_{p,q=0}^{N}\\!\\!\n\\sum_{\\scriptstyle{rlm}\\atop\\scriptstyle{r'l'm'}}\\!\\!\nT_p T_q\\biggl\\{\\alphap_{rlm}^{(q)}\\alphap_{r'l'm'}^{(p)}\nj_l(k_rx)j_{l'}(k_{r'}x)\n\\ee\n\\[\n+{1\\over x^2}\\Big[\\hat{x}\\wedge\\b J_{lm}^{(p)}(\\alpha)\\Big]\n\\cdot\\Big[\\hat{x}\\wedge\\b J_{l'm'}^{(q)}(\\alpha)\\Big]\\biggr\\}\nY_{lm}Y_{l'm'},\n\\]\nwhere the coefficients \n$\\b J_{lm}^{(p)}(\\delta)$,$\\b J_{lm}^{(q)}(\\alpha)$ are defined as in \n(\\ref{jlmn}) in Appendix B and ${\\delta^\\prime}_{rlm}^{(n)}$ \nas in (\\ref{alphap}) via the trivial substitution $\\alpha\\to\\delta$. \nBy multiplying (\\ref{zceqI}),(\\ref{zceqII}) by $T_rj_lY_{lm}$\nand integrating over all coordinates, we get\n\\[\n\\sum_{n=0}^{N} \\langle T_r\\dot T_n\\rangle \nC^{\\delta}_y\\delta_{y}^{(n)}+ \\sum_{n=0}^{N}\n\\langle T_r T_n\\rangle C^{\\alpha}_{y}\\alpha_{y}^{(n)}\n\\]\n\\be\\label{zshortI}\n= -\\sum_{p,q=0}^{N}\\langle T_r T_p T_q\\rangle\\!\\! \n\\sum_{y'y''}D^{y}_{y'y''}\n\\delta_{y'}^{(p)}\\,\\alpha_{y''}^{(q)},\n\\ee\n\\[\n\\sum_{n=0}^{N} \\Omegam \\langle T_r T_n\\rangle \nS^{\\delta}_{y}\\delta_{y}^{(n)}\n+ \\sum_{n=0}^{N}\n\\langle T_r (\\dot{T}_n+2{\\dot a\\over a}T_n)\\rangle \nS^{\\alpha}_{y}\\alpha_{y}^{(n)}\n\\]\n\\be\\label{zshortII}\n= -\\sum_{p,q=0}^{N}\\langle T_r T_p T_q\\rangle \\!\\!\n\\sum_{y'y''} E^{y}_{y'y''}\n\\alpha_{y'}^{(p)}\\,\\alpha_{y''}^{(q)},\n\\ee\nwhere $y\\equiv (rlm)$ and the angle brackets $\\langle\\rangle$ \nfor the Chebyshev polynomials are defined in Appendix C. In deriving \n(\\ref{zshortI}),(\\ref{zshortII}), the coefficients $C^{\\delta}_{y}$, \n$C^{\\alpha}_{y}$, $S^{\\delta}_{y}$, $S^{\\alpha}_{y}$, \n$D^{y}_{y'y''}$ and $E^{y}_{y'y''}$ are calculated via Clebsch-Gordan \ncoefficients for cross-products of $Y_{lm}$ and via the standard \northogonality relations for $Y_{lm}$ and $j_l$, given in Appendix D. \nCross-products of $j_l$ terms are estimated numerically. \nWe proceed to solve (\\ref{zshortI}),(\\ref{zshortII}) numerically \nwith the following iterative procedure. We first construct an \nAnsatz of the coefficients ${\\delta}_{y}^{(n)}$,${\\alpha}_{y}^{(n)}$ \nthat satisfies, to linear order, (\\ref{zshortI}),(\\ref{zshortII}) \nas well as (\\ref{constraint1}),(\\ref{constraint2}). We start out with \nthe galaxy number-count density $\\rho_s$. Following its definition in \nAppendix A, this quantity has units of inverse velocity, and we \ndefine its associated $z$-space density contrast via\n\\be \\label{delta_s}\n\\rho_s \\equiv {4\\pi N_{\\rm gals}\\over s_{\\rm max}} \n( 1+\\delta_s),\n\\ee\nwhere $s_{\\rm max}\\equiv cz_{\\rm max}$ is the maximum redshift \nin the sample. Our first Ansatz entails $b=1$ and linear evolution, \nso that $\\delta_s \\propto -\\nabla^2\\alpha$, and on inverting this \nrelation to obtain the coefficients $\\alpha_y^{(n)}$, we estimate \n$\\delta(\\b x)\\propto \\delta_s (\\b x+ \\hat{x}\\alpha^{\\prime})$ by using \nthe expression for the radial derivatives (\\ref{alphap}). This \nyields a first Ansatz for $\\delta_y^{(n)}$, $\\alpha_y^{(n)}$, \nderived from the dataset, that satisfies the linearized equations, \ngiven by the LHS of (\\ref{zshortI}),(\\ref{zshortII}):\n\\be \\label{homog}\n\\left[\\ba{cc}\n {\\rm C}^{\\alpha} & {\\rm C}^{\\delta} \\\\\n {\\rm S}^{\\alpha} & {\\rm S}^{\\delta}\n \\ea\n\\right]\\left[\\ba{c}\n{\\b\\alpha_y}\\\\\n{\\b\\delta_y}\n\\ea\n\\right]\\approx 0,\n\\ee\nwhere the column vectors are $(\\b \\alpha_y)_r= \\alpha_y^{(r)}$ and \n$(\\b \\delta_y)_r= \\delta_y^{(r)}$, with $r=0,\\dots, N$. \nThe solutions of the homogeneous system are then re-adjusted to \nsatisfy (\\ref{constraint1}),(\\ref{constraint2}) and we use these \nto construct the quadratic terms on the RHS of \n(\\ref{zshortI}),(\\ref{zshortII}). This leads to an inhomogeneous \nsystem that again we solve for $\\b \\delta_y$,$\\b \\alpha_y$. On \neach iteration we improve the solutions by least-squaring them to satisfy \n(\\ref{constraint1}),(\\ref{constraint2}) to the best accuracy and \nwe are also free to vary the parameters ($b$,$\\Omegam$) for improved \nconvergence. This procedure is very accurate, as we will show in \nthe next sections, and it permits us to improve the estimate of \nthe mapping $\\b x\\to \\b s$ at each iteration using the full \nnon-linear relationship (\\ref{constraint2}). At each iteration, \nthe fields $\\b \\delta_y$,$\\b \\alpha_y$ are used to obtain an \nestimate $\\tilde\\rho_s(\\b s)$ of the RHS of (\\ref{constraint2}). \nWe then vary these fields to obtain a minimum of the quantity \n$\\sum_{\\b s}(\\rho_s-\\tilde\\rho_s)^2$. Therefore we do not \nperform a $j_lY_{lm}$ expansion of the dataset, and it \nis very convenient not to do so, as a relationship of this \nkind between the redshift and real-space coordinates entails \nthat we compare them via a Taylor expansion $j_l(k_rs)\\approx \nj_l(k_rx)+k_r\\alphap j_l^{\\prime}$; an approximation of this kind \n$\\sim {\\cal O}(\\partial^2 j_l)$ introduces an error of up to 15\\% \nfor $l\\gsim 10$ as can be shown from (\\ref{jprime}) in Appendix B. \n\n\\subsection{Normal modes}\n\nWe have noted that the linearized equations (\\ref{homog}) \nare a homogeneous matrix system. If the determinant of the matrix \nis non-zero, then the only possible solution is $\\b \\delta_y=0$ \nand $\\b \\alpha_y=0$. We know however that (\\ref{homog}) is also valid \nfor linear fields, and these have non-vanishing coefficients. \nTherefore we conclude that the determinant of the system vanishes. \nSuch a system of equations is tackled through the Singular Value \nDecomposition (SVD) procedure. It factorises the singular matrix \nin (\\ref{homog}) in a product of three matrices: two orthogonal \nmatrices U and V, and a diagonal one W, which has one \nor more vanishing {\\it weights} along the diagonal. After SVD, \n(\\ref{homog}) reads\n\\be \\label{SVD}\n\\mathrm{U}\n \\left[\\ba{cccc}\n 0&&& \\\\\n &w_1&& \\\\\n &&w_2& \\\\\n &&&\\ddots \n \\ea\n\\right]\n\\mathrm{V}\\left[\\ba{c}\n{\\b\\alpha_y} \\\\\n{\\b\\delta_y}\n\\ea\\right]\n=0,\n\\ee\nwhere the weights $w_1,w_2,\\ldots w_N$ are non-zero real numbers. Therefore, \nthe vector \n\\be\n\\b N_y=\\mathrm{V}\\left[\\ba{c}\n{\\b\\alpha_y} \\\\\n{\\b\\delta_y}\n\\ea\\right]\n\\ee\ngives a coordinate basis on which the first component, the \n{\\it normal mode}, is unconstrained by the system (\\ref{homog}). \n$N_y^{(0)}$ is solely determined by \n(\\ref{constraint1}),(\\ref{constraint2}). The rest of the components \nof $\\b N_y$ (which are identically zero for linear fields) are \nfunctions of the normal mode. Therefore, one can rewrite the full \nnon-linear system (\\ref{zshortI}),(\\ref{zshortII}) in terms of the \nfields $\\b N_y$ and this would be strictly speaking the natural \nbasis to investigate the underlying mode coupling induced by \ngravity. In the Fourier formulation with a set of basis \nfunctions like those used in SB94, $f_n=D(D-1)^n$, it is easy \nto show numerically that the $\\b k$-th normal mode is \ngiven by \n\\be \\label{k-normal}\nN_{\\b k}^{(0)}= \\delta^{(0)}_{\\b k}+k^2\\alpha^{(0)}_{\\b k}. \n\\ee \nThis has a simple physical interpretation: (\\ref{k-normal}) is a\nvanishing scalar for linear fields and thus its departure from zero \ngives us a measure of non-linearity. This quantity is determined \nby the boundary conditions. In the spherical harmonic formulation, \nthe normal modes (equivalent to (\\ref{k-normal})) are \n\\be \\label{normal}\nN_y^{(0)}= \\sum_{n=0}^N h_n (\\delta_y^{(n)}-k_r^{-2}\\alpha_y^{(n)}),\n\\ee\nwhere \n\\be \nh_n= {\\eta\\over \\pi}\\int_0^1 \\!\\!\\d t w(t)D(t) T_n \n\\ee \nwhere $\\eta=1$ for $n=0$ and $\\eta=2$ otherwise. The quantity \n(\\ref{normal}) vanishes in the linear regime and, like\n(\\ref{k-normal}), its departure from zero is a measure of \nnon-linearity. \n\n\\subsection{Using the method in practice}\n\nThe apparent mathematical complexity of the LAP method \nhas precluded its wider use in practice. The fraction of papers \nin the literature that employ LAP techniques to investigate \nlarge-scale structure is minute in contrast to analyses \nbased on perturbation theory techniques, such as POTENT, VELMOD \nand others. The latter unquestionably have the virtue of simplicity, \nand are as efficient as they are easy to implement. \nHowever, in practice the method described in this \nsection entails no more complexity than programming an $n$-body \ncode; an undertaking that merits the effort, so as to estimate \n$b$ and $\\Omegam$, rather than merely $\\beta$. The chief difficulty \nresides in writing an algorithm for an effective numerical resolution of \n(\\ref{zshortI}),(\\ref{zshortII}). This may be a somewhat arduous \ntask, but at any rate a very straightforward one with a very basic \ngrasp of numerical methods. \n\nThe LAP method is very flexible in its implementation. The basic \ninput in the problem are the boundary conditions (\\ref{bcd}),\n(\\ref{constraint}) and the procedure that is to be followed \nto find a stationary action linking both end-points is largely \na matter of numerical convenience. The algorithm used in this section \nemploys Chebyshev polynomials to fit the trial fields $\\delta$ and \n$\\alpha$ to the dynamics. A myriad of other choices (e.g. binomial \nexpansions, Legendre and Hermite polynomials, etc) is also feasible \nand thus the LAP implementation set out above is by no means \na straightjacket recipe (for a more condensed presentation of \nthe algorithm, see Susperregi 2000). \n\nIn short, the algorithm can be summarized as follows. \n\n\\begin{itemize}\n\\item A galaxy redshift survey is a dataset ${\\cal D}$ of points \n($z$,$\\varphi$,$\\theta$). Those raw data are transformed to \na smoothed redshift-space field $\\rho_s(\\b s)$, given a smoothing \nlength and a window function $W(k)$. In this article we shall \nexclusively implement Gaussian smoothing. \n\\item The name of the game is to compute a fit for $\\delta$,$\\alpha$. \nThe starting point is to make a linear Ansatz that is consistent \nwith $\\delta_s$, which is derived from (\\ref{delta_s}). This is \nachieved by inverting the relation $\\delta_s\\propto -\\nabla^2\\alpha$ \nand next estimating $\\delta\\propto \\delta_s(\\b x\n+\\hat{x}\\alpha^{\\prime})$. \n\\item The linear Ansatz is the first input to be used in equations \n(\\ref{zshortI}),(\\ref{zshortII}). These yield the homogeneous system \n(\\ref{homog}), which is our second port of call. The solutions \n$\\delta_y$,$\\alpha_y$ obtained are least-square fitted to \n(\\ref{constraint1}),(\\ref{constraint2}). This requires adopting \na value of $b$. \n\\item The adjusted values of $\\delta_y$,$\\alpha_y$ are brought back \nto construct the RHS of (\\ref{zshortI}),(\\ref{zshortII}), and from \nthere one computes the new $\\delta_y$,$\\alpha_y$ in the LHS of \n(\\ref{zshortI}),(\\ref{zshortII}). This part of the operation entails \nan assumed value for $\\Omegam$. In the normal mode coordinates \ndiscussed in 2.4, the modes $\\delta_y$,$\\alpha_y$ of the cosmic \nfields are merely excitation modes of a harmonic oscillator and \nthe terms in the RHS of (\\ref{zshortI}),(\\ref{zshortII}) represent \nnonlinear perturbations of those excitation modes. \n\\item Successive iterations of the procedure eventually yield the \ncorrect values of $\\delta_y$,$\\alpha_y$. The values of $b$ and \n$\\Omegam$ are readjusted in the process and their estimated \nvalues are those that result in the most rapid \nconvergence of the solutions. \n\\end{itemize}\n\nThe algorithm thus produces the cosmic fields and an estimate \nof the cosmological parameters. In the remainder of the article \nwe shall investigate how to make the best use of the procedure \nand how to quantify the relative likelihood of different values \nof the cosmological parameters. \n\n\\section{Test of the method} \n\n\\begin{figure*}\n\\centering\n\\begin{picture}(360,360)\n\\special{psfile='fig1.ps' angle=0\nvoffset=-370 hoffset=-140 vscale=100 hscale=100}\n\\end{picture}\n\\caption[]{Likelihood contours for the reconstruction of the nine \ndatasets $d(b,\\Omegam)$. The cross on each panel indicates the real\nvalues of $(b,\\Omegam)$ in each reconstruction, and the likelihood \ncontours are computed following (\\ref{likelihood}) with a suitable \nnormalization. The concentric contours represent a likelihood of \n95\\%, 75\\%, 50\\%, 25\\% and 10\\% from the inner curves to the outer, \non the two upper rows, and 95\\%, 75\\% and 50\\% on the lower row.}\n\\end{figure*}\n\nWe test the LAP method on mock catalogues derived from $n$-body \nsimulations, using a Gaussian smoothing length of 600 \\km. The \n\\iras~power spectrum (Fisher \\etal 1993) is adopted as a prior, \nand the simulations are performed over a periodic box \n$L= 25,600$ \\km~with $128^3$ grid-points and $128^3$ particles. \nThe simulations are performed from Gaussian initial conditions, \nfor the following values of the parameters: $b=0.8, 1.0, 1.2$ and \n$\\Omegam=0.3, 0.6, 1.0$. The fields are evolved forward in time \nuntil $\\sigma_8\\approx 0.7$ over $\\sim 800$ \\km, using a Gaussian \ncutoff. We choose a two-powerlaw functional form of selection \nfunction (Yahil \\etal 1991): \n\\be\n\\phi(r\\geq r_s)=\\Big({r_s\\over r}\\Big)^{2\\alpha}\\Big(\n{r_*^2 + r_s^2\\over r_*^2 + r^2}\\Big)^{\\beta},\n\\ee\nand $\\phi(r\\leq r_s)=1$, where $r_s= 500$ \\km, \n$r_* = 5034$ \\km, $\\alpha= 0.483$ and \n$\\beta=1.79$ (Fisher \\etal (1995a); we adopt the estimated \ncentral values of these parameters and will not test the fine \ndetail of the variations of $\\phi(r)$ due to their errors), \nand thus we compute the redshift-space dataset over a sphere of radius \n$x_{\\rm max}\\sim 17,000$ \\km. The resulting mock catalogue has \nan effective radius of $\\sim 13,000$ \\km~beyond which the galaxy \nnumber-count is sparse and is cut off for the purpose of the\nreconstruction. The number of realizations are nine in total, \nand we denote $d(b,\\Omegam)$ the $z$-space mock samples \nderived in this way. Each dataset $d(b,\\Omegam)$ results \nfrom a unique pair of real-space fields $\\delta$,$\\alpha$ \nwhich are the density contrast and velocity potential that \nwe obtain via the $n$-body simulations. \n\nThe tests are carried out by using $d(b,\\Omegam)$ as an input dataset in \n(\\ref{constraint2}) without any prior assumption on the real values of \nthe parameters of the mock sample. We use (\\ref{constraint2}) to solve\n(\\ref{zshortI}),(\\ref{zshortII}) following the iterative procedure\ngiven in \\S 2.3 and derive the estimated fields \n$\\tilde\\delta$,$\\tilde\\alpha$ for different values of the parameters \n$\\tilde b$,$\\tilde \\Omegam$. The likelihood of these parameters is \nestimated on the basis of the performance of the solutions \n$\\tilde\\delta$,$\\tilde\\alpha$ in terms of their convergence and \nability to satisfy the constraints. We use a likelihood \nfunction given by the inverse of the $\\chi$-squared sum of the \ndifferences of the fields between successive iterations in solving \n(\\ref{zshortI}),(\\ref{zshortII}), i.e. \n\\be \\label{likelihood} \n\\lambda(b,\\Omegam) \\propto \\Big[\\sum_x \n\\Big({\\delta_n-\\delta_{n-1}\\over\\sigma_{\\delta}}\\Big)^2\n+\\Big({\\alpha_n-\\alpha_{n-1}\\over\\sigma_{\\alpha}}\\Big)^2\n\\Big]^{-1},\n\\ee\nwhere $n\\geq 25$, $\\sigma_{\\delta}\\approx 0.20$, \n$\\sigma_{\\alpha}$ is a normalization factor that \nrescales the coefficients $\\sigma_n$ so that $\\alpha$ becomes \na dimensionless field within the range $-1\\lsim \\alpha \\lsim 1$ \nand we have used $N=10$ and $l\\leq 15$ and an initial linear Ansatz. \nThe results are shown in Fig.~2. The likelihood contours are the \nLAP reconstructions and the crosses on all nine panels of Fig.~2 \nindicate the values of the real parameters in each mock\ndataset on the $(b,\\Omegam)$ plane. As can be observed, \nthe likelihood contours are certainly well correlated \nwith the location of the crosses, where the innermost contours \nmark the level of 95\\% likelihood, that in all cases lie in the \nneighbourhood of the real values of the parameters. The likelihood \ncontours show an approximately elliptical shape, with the major \nsemiaxes tilted at approximately 45 degrees, suggesting a correlation \nbetween both parameters that merely arises in the numerical \ncomputation. The estimates in the reconstruction are fairly good, \nwith a trend in underestimating slightly the values of both\nparameters. The best reconstructions are for the intermediate \nvalue of the density parameter $\\Omegam=0.6$, shown in the second \nrow. In this case the crosses actually lie within the highest\nlikelihood contours, with very little scatter. Overall, in the \nnine reconstructions the rms scatter in $b$ and $\\Omegam$ lie within \nthe region $0.26\\lsim \\sigma^2_{\\Omega}\\lsim 0.44$, \n$0.15\\lsim \\sigma^2_{b} \\lsim 0.32$. The largest scatter in \n$\\Omegam$ is for $\\Omegam=0.6$, and a similar situation \narises with $b$, whereby the intermediate value $b=1.0$ has the \nlarger error. \n\nThe effect of underestimating the true values of the parameters \nis systematic and can be calibrated. This effect can be largely \nascribed to the unconventional choice of likelihood estimator \n(\\ref{likelihood}). One could argue that, for slowly varying \nvariances, $\\lambda\\propto b^{-2}$ (chiefly from the $\\delta$ \npart of the RHS of (\\ref{likelihood})) and therefore smaller values \nof the bias factor (and consequently, by correlation, also of \n$\\Omegam$) are favoured. \nHowever, it is not straightforward to disentangle the \ndependence of the solutions on the parameters after successive \niterations. The likelihood estimator used is thus to some extent \nbiased. However, we find that the criterion of convergence \ngiven by the RHS of (\\ref{likelihood}), suitably normalised, \nis the sharpest discriminator to pin down the best estimates of \nthe cosmological parameters. We have carried out numerous tests \nwith more conventional likelihood estimators (e.g. Fisher likelihood \nmatrix, etc) obtaining much poorer results than with (\\ref{likelihood}). \n\nFig.~3 shows the density constrast reconstructions for the same \ndatasets $d(b,\\Omegam)$. The reconstructed density contrast \n$\\delta_{\\rm LAP}$ is shown on the horizontal axis plotted \npoint-by-point within the selected spherical volume ($r\\sim \n13,000$ \\km) against the real density contrast of the mock datasets. \nA solid line of slope 1.0 is plotted across each panel that \ndoes not correspond to the regression line on each panel \nthough the differences are tiny. The slopes of the regression \nlines lie within the range $0.99\\pm 0.08$. The rms value \ncorresponding to the random and numerical errors lies in the \nrange $0.19\\lsim \\sigma_{\\delta} \\lsim 0.28$. The reconstructions \nin Fig.~3 have been carried out with a prior knowledge of \nthe values of $b,\\Omegam$ for each dataset. Alternatively, \nthe test can be carried out by putting together the procedure \nfollowed to obtain the likelihood in Fig.~2 and investigate \nthe scatter resulting in the plots $\\delta_{\\rm mock}$ vs. \n$\\delta_{\\rm LAP}$ for different values of $b$,$\\Omegam$. \nSupposedly estimating the values of $b,\\Omegam$ and finding the \noptimal correlation between $\\delta_{\\rm mock}$,$\\delta_{\\rm LAP}$ \nought to be two not unrelated operations. However these two \nappear to be fairly independent: it turns out that whereas \n(\\ref{likelihood}) gives us the correct likelihood estimates \nfollowing the criterion of convergence of the solutions at each \niteration, the variations in $\\sigma_\\delta$ for a large range \nof $b$,$\\Omegam$ are fairly small, and $\\sigma_{\\delta}$ (as computed \nfrom tests such as the nine reconstructions in Fig.~3) is too \ninsensitive to be helpful in the estimate of the parameters. \nTherefore the tests show that the estimate of the parameters \nand the reconstruction of the fields are two operations that \nare to a large extent independent. For an arbitrary sample, one \nwould thus first compute (\\ref{likelihood}), pick the values of \n$b,\\Omegam$ at the maximum of the likelihood surface and use \nthese to solve the equations to compute $\\delta$,$\\alpha$. \nSimilarly, Fig.~4 shows the comparison of the LAP results with \nthe mock data in the reconstruction of the velocity potential. \nThe values of the fields have been scaled to $\\alpha_{\\rm max}$ \nand are dimensionless. It is apparent that the regression line \nis in all cases slightly greater than unity, with a more accentuated \ntilt for larger values of ($b$,$\\Omegam$). The smaller values of\n$\\alpha$ adjust better to a slope of unity, but with larger \nscatter than larger $\\alpha$. \n\nFig.~5 shows a cross-section on the $Z=0$ plane of a particular \nvelocity field reconstruction, that of the dataset $d(b=1.0,\\Omegam=0.3)$. \nThe figure shows several prominent features of the underlying \ndensity field in this case: three overdense regions to which \nthe field vectors converge, on the lower left, middle right \nand upper left parts of the panel, and two prominent underdense \nregions, from which the velocities diverge, one at the central \nregion and another one at the middle-left boundary of the \ncircle. It is apparent that the LAP velocities are not vanishing \nin the normal direction of the boundary surface of the selected \nsubvolume, and therefore the customary Neumann spatial boundary \nconditions employed on spherical Bessel functions (i.e. vanishing \nnormal velocities at the boundary) do not apply. We note that \nspatial boundary conditions are unnecessary in the LAP\nreconstruction, thus we have not brought up the issue in \\S 2. \nThe velocity field agrees within 10\\% accuracy with the $n$-body \nexact field within 78\\% of the selected volume, and the remaining \n22\\% differs from the mock sample velocities by an error of \n$\\gsim 10\\%$ (shown in Fig.~4 by the regions enclosed by the \nsolid curves) and withing this volume 6\\% differs by an error \n$\\gsim 20\\%$ (regions enclosed by broken curves). These regions \nare mostly located in the neighbourhood of peaks, right at the very \nslopes, where the largest velocities are found. The central regions \nof peaks and troughs are very accurately reconstructed, and it \nis indeed the intermediate regions that yield $\\delta$ points \nwith greater scatter in Fig.~3 and worse velocity reconstructions \nin Fig.~5. \n\n\\begin{figure*}\n\\centering\n\\begin{picture}(360,360)\n\\special{psfile='fig2.ps' angle=0\nvoffset=-360 hoffset=-135 vscale=100 hscale=100}\n\\end{picture}\n \\caption[]{Density field reconstructions of the nine datasets \n$d(b,\\Omegam)$. The smoothed density contrast of the mock samples \n(vertical axis) is compared at each point within a selected \nspherical volume of the $128^3$ grid with the LAP-reconstructed \ndensities (horizontal axis) over a sphere of radius $\\sim 13,000$ \\km.\nThe systematic errors are caused by the sparseness of the \nsampling.} \n\\end{figure*}\n\n\\begin{figure*}\n\\centering\n\\begin{picture}(360,360)\n\\special{psfile='fig3.ps' angle=0\nvoffset=-360 hoffset=-135 vscale=100 hscale=100}\n\\end{picture}\n \\caption[]{Velocity potential field reconstructions of nine datasets \n$d(b,\\Omegam)$. The velocity potential values are scaled to\n$\\alpha_{\\rm max}$, so that they are dimensionless and consigned to \nthe range $-1.0\\lsim \\alpha\\lsim 1.0$. The smoothed \nvelocity potential of the \nmock samples (vertical axis) is compared at each point within the \nsame selected volume as in Fig.~3.} \n\\end{figure*}\n\n\n\\begin{figure}\n\\centering\n\\begin{picture}(300,260)\n\\special{psfile='fig4.ps' angle=0\nvoffset=-65 hoffset=-35 vscale=50 hscale=50}\n\\end{picture}\n \\caption[]{$Z=0$ plane reconstruction of the velocity field within \na selected subvolume $x_{\\rm max}\\lsim 12,000$ \\km~for the mock\n sample $d(b=1.0,\\Omegam=0.3)$. The solid lines enclose regions where \nthe reconstruction entails an error \n$|{\\b v}_{\\rm mock}-{\\b v}_{\\rm LAP}|/v_{\\rm mock}\\gsim 0.10$ \nand within the broken lines this error is $\\gsim 0.20$.}\n\\end{figure}\n\n\\section{Bias and $\\Omegam$ from \\iras}\n\nWe apply the LAP method to the \\iras~ sample \n(Strauss \\etal 1990,1992; Fisher \\etal 1995a) in the same \nway as we have used it in the reconstruction of the mock catalogs \nin \\S 3. \\iras~ is not the largest existing near all-sky galaxy \nredshift catalogue, and it is now superseded by PSC$z$ \n(Canavezes \\etal 1998) which contains $\\sim 15,000$ \ngalaxies, so this application is simply an illustration on \nhow the LAP method can be used to break the degeneracy \nin the estimates of $b$ and $\\Omegam$. Other large redshift \nsamples of partial coverage can also be looked at with the LAP method, \ne.g., Las Campanas and the forthcoming Anglo-Australian 2dF \n($\\sim 250,000$ galaxies) and US Sloan Digital Sky Survey (SDSS) \n($\\sim 10^6$ galaxies and 25\\% coverage), \nwith the caveat that boundary regions will be a source of \npropagating errors in the dynamical evolution. Even so, a large \nnumber of galaxies in a redshift survey of limited \ncoverage can provide a good representation of the underlying \ndensity field, almost definitely outweighing the disadvantages \nof sampling a partial region of the sky, and it will be thus\npredictably worthwhile to apply the LAP method to those surveys. \nThe \\iras~sample contains 5320 galaxies distributed over 87.6\\% \nof the projected celestial sphere. The remaining unsampled \n2.4\\% is an approximately disk-shaped region at a \ngalactic latitude $|b|\\lsim 5^{\\circ}$. \n\nWe adopt a Gaussian smoothing length of 1200 \\km, and make no \nassumption regarding the power spectrum. The data $d_{\\rm IRAS}$ \nare distributed within a spherical region of radius \n$x_{\\rm max}\\sim 15,000$ \\km. We use the dataset in a similar \nfashion as the mock samples $d(b,\\Omegam)$ in the previous section \nto derive the $x$-space fields $\\delta,\\alpha$. In \\S 3 \nwe have established that $\\sigma_{\\delta},\\sigma_{\\alpha}$ \nare fairly insensitive to the values of $b,\\Omegam$. One can thus \nset out to investigate the likelihood function $\\lambda(b,\\Omegam)$ \nas defined in (\\ref{likelihood}) prior to determining the \nreconstructed fields. Evidently this is the simplest \nway to proceed for, unlike in \\S 3, we do not have any clue about the \nreal-space underlying fields (such as $\\delta_{\\rm mock}$,\n$\\alpha_{\\rm mock}$ in \\S 3) to compare them with the reconstructed \nfields. \n\n\n\\begin{figure}\n\\centering\n\\begin{picture}(300,200)\n\\special{psfile='fig5.ps' angle=0\nvoffset=-200 hoffset=-35 vscale=55 hscale=50}\n\\end{picture}\n \\caption[]{Likelihood contours for \\iras. \nThe concentric contours represent a likelihood of 95\\%, 75 \\%, \n50\\%, 25 \\%, 10\\% from the inner curve to the outer. The shaded \nregion $A$ corresponds to the estimate of $\\beta$ by Willick \\etal \n(1997a) and the shaded region $B$ corresponds to an estimate of $\\beta$ \nby Sigad. \\etal (1998).}\n\\end{figure}\n\n\nThe likelihood contour plot is shown in Fig.~6. Clearly the largest \nvalues of the likelihood function are centered around $b\\sim 1$ and \nsmall $\\Omegam$. From the test of the LAP method in \\S 3 with $n$-body \nsimulations we already know that the likelihood function \n(\\ref{likelihood}) underestimates both $b$ and $\\Omegam$, as \nis apparent in all nine panels of Fig.~2. We accept this\ntrend is fairly inherent to the numerical application of the \nmethod and thus infer that the result presented in Fig.~6 is \nno different in this respect, \nand therefore the {\\it real} values of the parameters are \nsituated somewhat above their maxima in the likelihood function. \nFrom Fig.~2 one can quantify these errors to be of the order \nof $\\Delta\\Omegam \\approx 0.12$, $\\Delta b\\approx 0.15$. Therefore, \nwe infer that in Fig.~6 the likelihood maxima and the real values \nof the parameters are likely to be offset by a similar margin of \nerror. At face value, Fig.~6 estimates that the most likely values \nof the parameters are $\\Omegam\\approx0.18$ and $b\\approx 0.94$. \nIf we offset these estimates by the errors derived from Fig.~2, \nthen the likely ``real'' values of the parameters that we obtain \nfor Fig.~6 are $\\Omegam\\approx 0.31$ and $b\\approx 1.1$. As a matter \nof fact, these offset values are still within the region enclosed \nby the 95\\% confidence contour. \n\nTo put our results in perspective with previous analyses of \\iras, we \nhave overlaid on the contour plot of Fig.~6 two previous estimates of \n$\\beta\\equiv \\Omegam^{0.6}/b$. An estimate by Willick \\etal (1997a) \nyields $\\beta_I=0.49\\pm 0.07$ (shaded region $A$) and an estimate \nby Sigad \\etal (1998) yields $\\beta_I=0.89\\pm 0.12$ (shaded region \n$B$). The estimate of Willick \\etal (1997a) is clearly in better \nagreement with our results as the location of the offset maximum of \nthe likelihood is contained within the shaded region $A$ that corresponds \nto the error margin of their estimate. The estimate given by shaded \nregion $B$ is consistent with a scenario $b\\approx 1$, $\\Omegam\\approx\n1$, which in our analysis falls well outside the 10\\% likelihood\ncontour. \n\nFig.~7 shows a $z$-space comparison between the reconstructed \nfields and the dataset. The data on the horizontal axis, \n$\\delta_{\\rm LAP}^{s}$, is obtained from the reconstructed $x$-space \nfields $\\delta,\\alpha$ via (\\ref{constraint}). The combination \nof both fields via the relationship $\\delta_{\\rm LAP}(\\b x) \n\\propto \\delta_s (\\b x+ \\hat{x}\\alpha_{\\rm LAP}^{\\prime})$ permits us to \nreconstruct $\\delta_s$ which is our only possible point of comparison \nwith $\\delta_{IRAS}$, and this is shown in Fig.~7. The vertical \naxis shows the $z$-space data \npoints of the smoothed \\iras~sample. The data are plotted in a \npoint-by-point comparison for all the grid points within the selected\nsubvolume. A solid line of slope 1.0 is plotted across the diagonal \nof the plot. The slope of the regression line is slightly over the \ndiagonal line, at approximately 1.03. The corresponding rms due to \nrandom and numerical errors in the LAP reconstruction is \n$\\sigma\\approx 0.27$. The values of the parameters that have been \nused in the reconstruction are $b=1.0,\\Omegam=0.3$. \n\n\n\\begin{figure}\n\\centering\n\\begin{picture}(300,200)\n\\special{psfile='fig6.ps' angle=0\nvoffset=-200 hoffset=-35 vscale=55 hscale=50}\n\\end{picture}\n \\caption[]{Redshift-space density contrast in the LAP reconstruction \nversus the corresponding \\iras~data for a Gaussian smoothing of \n1200 \\km within a spherical region of radius \n$x_{\\rm max}\\sim$ 12,000 \\km. The field $\\delta_{\\rm LAP}$ is \nevaluated at $b=1.0$, $\\Omegam=0.3$.}\n\\end{figure}\n\n\\subsection{Velocity fields}\n\n\\begin{figure*}\n\\centering\n\\begin{picture}(550,550)\n\\begin{tabular}{cc}\n\\special{psfile='iras1.ps' voffset=250 hoffset=-50 vscale=50 hscale=50}&\n\\special{psfile='vel1.ps' voffset=250 hoffset=180 vscale=50 hscale=50} \\\\ \n\\special{psfile='iras2.ps' voffset=80 hoffset=-50 vscale=50 hscale=50} &\n\\special{psfile='vel2.ps' voffset=80 hoffset=180 vscale=50 hscale=50} \\\\\n\\special{psfile='iras3.ps' voffset=-90 hoffset=-50 vscale=50 hscale=50} & \n\\special{psfile='vel3.ps' voffset=-90 hoffset=180 vscale=50 hscale=50} \\\\ \n\\end{tabular}\n\\end{picture}\n \\caption[]{$\\delta_{\\rm LAP}$ and $\\b v_{\\rm LAP}$ fields for \\iras. \n$SGX$ and $SGY$ units are in 100 \\km, spanning over a sphere \nof radius $\\sim 8000$ \\km. {\\it Left:} from top to bottom panels, \ndensity contrast for a Gaussian smoothing of 1200 \\km, \nfor $Z= 2000,0,-2000$ \\km. Thick solid line corresponds to \n$\\delta=0$, continuous contours are $\\delta>0$ and slashed \ncontours are $\\delta<0$; contour spacing is 0.2. {\\it Right:} \nfrom top to bottom, reconstructed velocities at same values of $Z$.}\n\\end{figure*}\n\nThe resulting velocity field for the parameters \nof Fig.~7 is shown in Fig.~8. The six panels show the reconstructed \n\\iras~fields $\\delta_{\\rm LAP}$ and $\\b v_{\\rm LAP}$ \nin supergalactic coordinates, for three different \nslices $Z=0,\\pm 2000$ \\km. The velocity panels on the right column \ncorrespond to the densities on the left, at the same value of $Z$. \nThe velocity field follows the main features observed on the \n$\\delta_{\\rm LAP}$ field, with a general flow towards the overdense\nregions and outflow from voids. The largest velocities are located in \nthe intervening regions between overdense and underdense regions, e.g. in \n$Z=0$ (middle panels), large infall velocities are visible in the vicinity \nof the Comma supercluster (0,80,0), the Hydra-Centaurus \n(H-C) supercluster (-30,15,0), and Perseus-Pisces (P-P) (50,-5,0). \nIn $Z=0$ the largest velocities are located at the lower right region \nof the H-C overdensity maximum, and also to the left of the P-P \nmaximum. There is a velocity flow from the main void on the lower left \nof the figure, in the direction of Virgo, and it splits up to left \nand right, in manner of a ridge, to create an outflow in opposite \ndirections, towards H-C and P-P. In the case of $Z=-2000$ \\km \n(lower row), large velocities are also present around the steeper \nregions of the prominent overdensities, following a similar pattern \nas in $Z=0$, whereas the field shows more erratic features in \n$Z=2000$ \\km (upper row), where the outflow from the main void \n(centre left) shows a general trend towards the main overdense \nfeatures but is at the same time prone to local variations. \n\nThe results presented in Figs.~6-8, can be optimized by using the \nMark III velocity redshift survey to pin down $b$,$\\Omegam$ \nmore accurately. We shall pursue this and look for the optimal \nvalues of $b$,$\\Omega_m$ by computing the LAP solutions that satisfy \n\\be \\label{vchi}\n\\delta \\sum (\\b v_{\\rm LAP}-\\b v_{\\rm Mark III})^2=0, \n\\ee \nwhere $\\delta$ denotes a variation, not the density contrast. In \npractice, this is achieved as follows. One adds (\\ref{vchi}) to \nthe two already existing constraints of the LAP method \n(\\ref{constraint1}),(\\ref{constraint2}). Those are tackled in \nthe manner summarized in \\S 2.5. In actual terms, it's far \nmore practical to deal with (\\ref{vchi}) in terms of the \nvelocity potential, so what we have done in the present analysis \nis in reality to compute $\\alpha_{\\rm Mark III}$ from the smoothed \nobserved velocity field, and thus used (\\ref{vchi}) in the manner \nof a second constraint on $\\alpha$. \n\nThe comparison with the $\\b v_{\\rm Mark III}$ data sets \nfurther constraints on the likelihood contours of Fig.~6 as \nis shown below. Mark III contains approximately 3,400 galaxies, \nwhich are compiled from several sets of elliptical and SO galaxies \n(Willick \\etal 1995,1996,1997a). The sample spans out to $\\sim 6000$ \n\\km, though in some directions it is irregularly sampled \nto $x_{\\rm max} \\sim 8000$ \\km and $x_{\\rm min}\\sim 4000$ \\km. \nThe distances are inferred via forward Tully-Fisher and \n$D_n-\\sigma$ distance indicators which may entail an error \nin the region 17-21\\%. Mark III predicts a bulk flow \n$v_B \\sim 194\\pm 32$ \\km towards the Shapley concentration \n(Zaroubi, Hoffman \\& Dekel 1999)(for a low-resolution Gaussian \nsmoothing $\\sim 1200$ \\km, within a sphere $r\\sim 6000$ \\km), \nin contrast to $v_B \\sim 250-400$ \\km~that is estimated in most \nother samples, including PSC$z$ (a compilation of $v_B$ \nestimates is summarized in Dekel 1999b). $\\delta_{IRAS}$ \nand $\\delta_{\\rm Mark III}$ are consistent with mildly non-linear \ngravitational instability and linear bias (Sigad \\etal 1998), \nthough there are some differences, e.g. the Mark III sample \nappears to show a strong shear across the Hydra-Centaurus \ncomplex that is absent in \\iras~(as indeed also in ORS). Recent \npapers have studied in detail the differences between the \n\\iras~and Mark III velocity and density fields (Sigad \\etal 1998; \nalso Dekel \\etal 1999 following an improved version of POTENT). \n\n\\begin{figure}\n\\centering\n\\begin{picture}(300,200)\n\\special{psfile='fig7.ps' angle=0\nvoffset=-200 hoffset=-35 vscale=55 hscale=50}\n\\end{picture}\n \\caption[]{Solid contours represent the likelihood \nfor \\iras~as in Fig.~6, and dotted contours represent \nthe likelihood in the \\iras/Mark III comparison \nfollowing (\\ref{vchi}). The relative likelihood of the \nconcentric contours is as in Fig.~6 in both solid and dotted.}\n\\end{figure}\n\nWe consider the Mark III sample with a Gaussian smoothing \nlength of 1200 \\km. The data are carefully corrected for \nMalmquist biases (following the recipe set out in Sigad \\etal \n(1998) for the preparation of the data), and the distances \nof 1,241 objects are modified as a result. The LAP method \nis solved for \\iras~within spherical volume of radius \n$x_{\\rm max}\\sim 15,000$ \\km, and the minimization fit \nwith Mark III (\\ref{vchi}) is done within a spherical \nsubvolume of radius $\\langle x\\rangle \\sim 6000$ \\km. \nTherefore most of the volume of the LAP solutions remains free of \nthe constraint (\\ref{vchi}) and the fraction of the volume where \n$\\b v_{\\rm LAP}$ is least-squared to $\\b v_{\\rm Mark III}$ is only 0.064. \nNaturally such a small fraction forecasts an almost negligible impact \nin the fine-tuning of the parameters, unless the fields differred \ndrastically to start with, which they do not. The $\\b v_{\\rm LAP}$ \nsolution in the remainder of the volume is indirectly affected \nby this fit, and the variations in modulus $\\Delta v_{\\rm LAP}$ \noutside the comparison subvolume are $\\lsim 12$\\%. \n\nFig.~9 shows the likelihood contours for ($b$,$\\Omegam$) computed \nvia the adjustment entailed in (\\ref{vchi}). The solid contours \nare the purely \\iras~prediction, as in Fig.~6, and the dotted \ncontours are the result of the comparison with Mark III. The contours \nare ever so slightly shifted towards greater values of the \nparameters and, as expected, the effect is small. The shift \ntowards larger $b$,$\\Omegam$ is not in fact an altogether undesirable \nmodification, as we have already discussed that the LAP solutions \nare found to be per se offset to smaller values than their ``real'' \nvalues. The important conclusion to be drawn from Fig.~9 is \nthat the comparison with Mark III is entirely consistent with \nthe predictions for $b$ and $\\Omegam$ extracted from the \\iras~sample \nalone.\n\n\n\\section{Conclusions}\n\nThe LAP method provides a practical means to break the \ndegeneracy between $\\Omegam$ and $b$ in galaxy redshift surveys. \nThe method is employed in the manner of a nonlinear constraint \non the redshift-space dataset and, although in formulation it \ncomes across as algebraically cumbersome, it is of considerable \nsimplicity and efficiency from the numerical point of view. The method is \nsound in that it does not require an a priori approximation of \nthe map $\\b x\\to\\b s$ to pin down the solution and it provides \nconsiderable freedom to ascribe relative importance to the data \navailable, i.e. the initial and final endpoints, to which we wish \nto invariably assign greater weight than intermedate stages \nof which little or no data are available. \n\nThe method can prove significant to measure $\\Omegam$ in the latest \nlargest samples, and extract the most accurate information prior \nto comparison with other datasets, such as the CMB radiation power \nspectrum and SN data. One important challenge for the future \nis to attain a better grasp of the concept of bias and this will \nbe probably achieved via microlensing data and $n$-body simulations \nof the formation of galaxies and clusters from primordial\nfluctuations, rather than from galaxy redshift surveys. Once a \nmodel of bias is adopted on a sound footing, then clearly the \nLAP model is impeccable in producing an estimate of $\\Omegam$. \nIn the simple linear bias model we have employed we have totally \nrelegated any consideration of scale-dependence in $b$. This \nis a point I have deliberately omitted for simplicity. Thus, \nthe estimates computed in this paper ought to be regarded \nqualitatively as weighted averages of the ``real'' $b$ over \ndifferent scales, if indeed scale-dependent bias models are \nto be believed. \n\nIn this paper, we have employed the likelihood function \n(\\ref{likelihood}) to investigate the values of $b$,$\\Omegam$. \nClearly this is not a unique choice. However, our choice is \nguided by the argument of relative convergence of the solutions, \nwhich is justifiably a reasonable criterion to get close to \nthe ``real'' solutions. In view of the performance of the $\\lambda$ \nfunction in the reconstruction of the mock samples, this \nchoice does not appear to be totally off the mark. A potential \nreason for concern could be the offset observed between the maxima \nof the likelihood functions and the real values of the parameters \nin the $n$-body simulations. However the recurrence of this offset \nin a predictable manner lends strength to the argument that \nit arises as a numerical fault that is easy to account for\nsystematically in the analysis of the datasets. The reconstructions \nof the fields are, on the other hand, of considerable accuracy \nand no numerical defficiency or hindrance is observed. \nThe application of the method to \\iras~predicts the\nparameters to be fairly accurately located in the immediate \nneighbourhood of the maxima $\\Omegam\\approx 0.3$ and \n$b\\approx 1.1$, which is found to be most compatible with \nthe estimate of $\\beta$ given by Willick \\etal (1997a). \nIn a flat universe such predicted values are perfectly consistent \nwith a non-vanishing cosmological constant or a quintessence \nscalar field component. The likelihood examined in this way is only very \nslightly modified when the velocities predicted via the LAP method \nare finely-tuned with data from the Mark III sample. The shift of \nthe predicted values is towards slightly greater values of the\nparameters but it remains comfortably consistent with the results \nobtained from \\iras. \n\n\n\\section*{Acknowledgments}\n\nThe numerical analysis has been performed in the {\\it Starlink} \nfacilities at Queen Mary \\& Westfield College (London), and \nthanks are due to a number of people for supplying \nand lending a helping hand with technicalities regarding the data. \nThe author thanks an anonymous referee for insightful comments \nthat have greatly improved the readability of the manuscript. \nThis research has been funded in part at EHU by research grant \nUPV172.310-G02/99. \n\n\n\\begin{thebibliography}{99}\n\\bibitem{}\n Abramowitz M., Stegun I.A., 1972, {\\it Handbook of Mathematical \nFunctions}, Dover, New York\n\n\\bibitem{}\n Baker, J.E., Davis M., Strauss M.A., Lahav O., Santiago B.X., \n1998, ApJ 508, 6 \n\n\\bibitem{}\n Bernardeau F., Juszkiewicz R., Dekel A., Bouchet F., 1995, MNRAS \n274, 20\n\n\\bibitem{}\n Branchini E., Carlberg R.G., 1994, ApJ 434, 37\n\n\\bibitem{}\n Canavezes A. et al., 1998, MNRAS 297, 777\n\n\\bibitem{}\n Coles P., Sahni V., 1995, Phys. Rep. 262, 1\n\n\\bibitem{}\n Courant R. and Hilbert D., 1989, {\\it Methods of Mathematical\n Physics}, John Wiley \\& Sons, New York, vol. I \n\n\\bibitem{}\n Dekel A., 1994, Annu. Rev. Astron. Astrophys., 32, 371--418\n\n\\bibitem{}\n Dekel A., 1999a, in {\\it Formation of Structure in the Universe}, \ned. A. Dekel and J.P. Ostriker, Cambridge University Press, 250 \n\n\\bibitem{}\n Dekel A., 1999b, in {\\it Cosmic Flows: Towards an Understanding of Large-Scale \nStructure}, eds. S. Courteau, M.A. Strauss and J.A. Willick, ASP Conf. Series\n\n\\bibitem{}\nDekel A., Lahav O., 1999, ApJ 520, 24 \n\n\\bibitem{}\nDekel A., Bertschinger E., Yahil A., Strauss M.A., Davis M., Huchra \nJ.P., 1993, ApJ 412, 1 \n\n\\bibitem{}\n Dekel A., Burstein D., White S.D.M., 1997, in \n{\\it Critical Dialogues in Cosmology},\n ed. N.G. Turok, World Scientific, Singapore\n\n\\bibitem{}\n Dekel A., Eldar A., Kolatt T., Yahil A., Willick J.A., Faber S.M., \nCourteau S., Burstein D., 1999, ApJ 522, 1\n\n\\bibitem{}\n Fisher K.B., Davis M., Strauss M.A., Yahil A., Huchra J.P., 1993, \nAp. J. 402, 42\n\n\\bibitem{}\n Fisher K.B., Huchra J.P., Strauss M.A., Davis M., \n Yahil A., Schlegel D., 1995a, ApJS 100, 69\n\n\\bibitem{}\n Fisher K.B., Lahav O., Hoffman Y., Lynden--Bell D., Zaroubi S., \n 1995b, MNRAS 272, 885\n\n\\bibitem{}\n Fry J.N., 1994, Phys. Rev. Lett. 73, 2\n\n\\bibitem{}\n Giavalisco M., Mancinelli B., Mancinelli P.J., Yahil A., \n 1993, ApJ 411, 9\n\n\\bibitem{}\n Hudson M.J., Dekel A., Courteau S., Faber S.M., Willick J.A., 1995, \n MNRAS 274, 305\n\n\\bibitem{}\n Kaiser N., 1987, MNRAS 227, 1\n\n\\bibitem{}\n Linde A., Sasaki M., Tanaka T., 1999, Phys. Rev. D59, 123522\n\n\\bibitem{} \n Peebles P.J.E., 1989, ApJ 344, L53\n\n\\bibitem{} \n Peebles P.J.E., 1990, ApJ 362, 1\n\n\\bibitem{}\nSantiago B.X., Strauss M.A., Lahav O., Davis M., Dressler A., \nHuchra J.P., 1995, ApJ 446, 457 \n\n\\bibitem{}\n Saunders W., Sutherland W., Maddox S., Keeble O., Oliver S.J., \nRowan-Robinson M., Mahon R.G., Efstathiou G.P., Tadros H., \nWhite S.D.M., Frenk C.S., Carrami\\~{n}ana A., Hawkins M.R.S., \n2000, MNRAS submitted, astro-ph/0001117\n\n\\bibitem{}\n Schmoldt I.M., Saha P., 1999, AJ 115, 2231 \n\n\\bibitem{}\n Shaya E.J., Peebles P.J.E., Tully R.B., 1995, ApJ 454, 15\n\n\\bibitem{}\n Sigad Y., Eldar A., Dekel A., Strauss M.A., Yahil A., 1998, \nApJ 495, 516\n\n\\bibitem{}\n Strauss M.A., Davis M., Yahil A. and Huchra J.P., 1990, ApJ 361, 49; \ngeneral descriptive information on \\iras~can be found in \nhttp://www.gsfc.nasa.gov/astro/iras/irs.html \n\n\\bibitem{}\n Strauss M.A., Huchra J.P., Davis M., Yahil A., Fisher K.B., \n Tonry J., 1992, ApJS 83, 29\n\n\\bibitem{}\n Strauss M.A., Willick J., 1995, Phys. Rep. 261, 271 \n\n\\bibitem{}\n Susperregi M., 1995, D.Phil. thesis (Oxford), unpublished\n\n\\bibitem{}\n Susperregi M., 2000, in proc. 4th RESCEU symposium on {\\it The Birth \nand Evolution of The Universe}, Tokyo, World Scientific, in press \n\n\\bibitem{}\n Susperregi M., Binney J., 1994, MNRAS 271, 719 (SB94) \n\n\\bibitem{}\n Tadros H., Ballinger W.E, Taylor A.N., Heavens A.F., Efstathiou G., \nSaunders W., Frenk C.S., Keeble O., McMahon R., Maddox S.J., Oliver\nS., Rowan-Robinson M., Sutherland W.J., White S.D.M., 1999, MNRAS \n305, 527\n\n\\bibitem{}\nVerde L., Heavens A.F., Matarrese S., Moscardini L., 1998, MNRAS \n300, 747\n\n\\bibitem{}\n Willick J.A., Courteau S., Faber S.M., Burstein D., Dekel A., \nKollat T., 1995, Ap. J. 446, 12 (paper I)\n\n\\bibitem{}\n Willick J.A., Courteau S., Faber S.M., Burstein D., Dekel A., \nStrauss M.A., Kollat T., 1996, Ap. J. 457, 460 (paper II)\n\n\\bibitem{}\n Willick J.A., Courteau S., Faber S.M., Burstein D., Dekel A., \nStrauss M.A., 1997a, ApJS 109, 333 (paper III)\n\n\\bibitem{}\n Willick J.A., Strauss M.A., Dekel A., Kolatt T., 1997b, \nApJ 486, 629\n\n\\bibitem{}\nYahil A., Strauss M.A., Davis M., Huchra J.P., 1991, ApJ 372, 380 \n\n\\bibitem{}\nZaroubi S., Hoffman Y., Dekel A., 1999, ApJ 520, 413 \n\n\\end{thebibliography}\n\n\\appendix\n\n\\section[]{Orbit-crossing in redshift space}\nWe shall prove the boundary condition (\\ref{constraint}). \nThe number-counts of galaxies $n$ in $x$-space and $z$-space satisfy, \nby conservation of the number of galaxies:\n\\be \\label{nsnx} \n\\d n(\\b s)=\\sum_{\\rm streams}\\d n(\\b x_i), \n\\ee\nfor all streams at the same redshift, \n$\\b s=\\b x_i+\\hat{x}(\\hat{x}\\cdot\\nabla_{x}\\alpha_i)$. \nIn our analysis we shall only consider single-valued solutions, \nand therefore there is just one stream only in (\\ref{nsnx}), \ni.e. $\\d n(\\b s)=\\d n(\\b x)$. Hence \n\\be \\label{masscons}\n\\rho_s(\\b s)\\,\\d{\\sl \\Omega}\\equiv {\\d n(\\b s)\\over\\d s}=\nx^2(1+b\\delta)\\gal {\\d x\\over\\d s}\\d{\\sl \\Omega},\n\\ee\nwhere $n(\\b s)$ is the galaxy number-count, $\\d{\\sl \\Omega}$ a solid angle \nelement and the $x$-space selected volume of the sample is \n$V\\sim {4\\over 3}\\pi x_{\\rm max}^3$, and \n\\be\ns\\equiv \\hat{x}\\cdot\\b s=x+\\alpha'.\n\\ee\nTherefore\n\\be\n{\\d x\\over\\d s}={1\\over 1+\\alpha''},\n\\ee\nand substituting this in (\\ref{masscons}), we get \n\\be \\label{qed}\n\\rho_s =x^2 \\gal \\biggl({1+b\\delta\\over 1+\\alpha''}\\biggr).\n\\ee\nIn the case of multistreams, the RHS of (\\ref{qed}) is integrated \nover all streams, bearing in mind that {\\it turn-around} regions, \nwhich occur at $\\delta\\gg 1$ and for which $\\d s/\\d x=0$, are \nexcluded from the sum. An example of such a region in shown in Fig.~A1. \nAn initial saddle-point $\\d s/\\d x=0$ on the $s(x)$ curve starts the \ncreation of a turn-around region. At the stage shown in Fig.~A1, \nboth points $A$ and $B$ satisfy this condition and obviously \nthey departed from an initial saddle-point $A=B$. The region \nspanning between $A$ and $B$ is three-valued (each redshift \nin the interval $z_B < z < z_A$ corresponds to three $x$ positions), \nwhereas $z_A$ and $z_B$ are bivalued. To make such \nan scenario tractable, we need to replace $s(x)$ over the interval \n$z_B<z<z_A$ by a monotonic curve that matches the existing curve at \n$z_B$ and $z_A$ and its first derivative. This is obviously tantamount to \napplying a larger smoothing length than the existing one to erase the \noverdense region that is the cause of the turn-around. \n\n\\begin{figure}\n\\centering\n\\begin{picture}(240,240)\n\\special{psfile='stream1.ps' angle=-90\nvoffset=330 hoffset=-150 vscale=70 hscale=70}\n\\end{picture}\n \\caption[]{Illustration of a turn-around region.}\n\\end{figure}\n\n\\section[]{Evaluation of radial derivatives}\nThe radial derivative of the velocity potential coefficients \n(\\ref{zalphan}) can be written as \n\\be\n{\\d\\over\\d x}\\alpha_n =\n\\sum_{rlm}\\alphap_{rlm}^{(n)}j_l(k_rx) Y_{lm},\n\\ee\nwhere, using the equality \n\\be \\label{jprime}\n{\\d\\over\\d u}j_l(u)=(2l+1)^{-1}\n\\Big[ lj_{l-1}(u)-(l+1)j_{l+1}(u)\\Big],\n\\ee\nwe have \n\\be \\label{alphap}\n\\alphap_{rlm}^{(n)}=k_r\\biggl[{(l+1)\\over\n(2l+3)}\\alpha_{r(l+1)m}^{(n)} \n-{l\\over(2l-1)}\\alpha_{r(l-1)m}^{(n)}\\biggr].\n\\ee\nSimilarly\n\\[\n\\alphapp_{rlm}^{(n)}= k_r^2\\biggl\\{{(l+1)\n\\over(2l+3)}{(l+2)\\over (2l+5)} \\alpha_{r(l+2)m}^{(n)}\n\\]\n\\be\n-\\biggl[{(l+1)^2\\over(2l+3)(2l+1)}+{l^2\\over(2l-1)(2l+1)}\\biggr]\n\\alpha_{rlm}^{(n)}\n\\ee\n\\[\n+{l\\over (2l-1)}{(l-1)\\over(2l-3)}\\alpha_{r(l-2)m}^{(n)}\\biggr\\}.\n\\]\nOn the other hand, the coefficients $\\b J_{lm}^{(n)}$ given in \n(\\ref{v_spher}) are \n\\[\n\\b J_{lm}^{(n)}=\\sum_r\\biggl[{\\alpha(l,m+1)\\over 2}\\alpha_{rl(m+1)}^{(n)}\n\\,(i\\hat{x}_1-\\hat{x}_2)\n\\]\n\\be \\label{jlmn}\n+{\\beta(l,m-1)\\over 2}\\alpha_{rl(m-1)}^{(n)}\n\\,(i\\hat{x}_1+\\hat{x}_2)+im\\,\\alpha_{rlm}^{(n)}\\,\\hat{x}_3\\biggr],\n\\ee\nwhere \n\\be\n\\alpha(l,m)=\\Big[l(l+1)-m(m-1)\\Big]^{1/2},\n\\ee\n\\be\n\\beta(l,m)=\\Big[l(l+1)-m(m+1)\\Big]^{1/2}. \n\\ee\n\n\\section[]{Chebyshev polynomials}\n\nThe Chebyshev polynomials are defined \n$T_n(\\cos\\theta)\\equiv \\cos (n\\theta)$ (following the normalization \nof Abramowitz \\& Stegun 1972). We define the angle brackets \n$\\langle,\\rangle$ according to the orthogonality \nproperties of $T_n$ (e.g. Courant \\& Hilbert 1989): \n\\be\n\\langle u\\rangle \\equiv \\int_{-1}^{1}\\d t w(t) u(t),\n\\ee\nwhere $w(t)=(1-t^2)^{-1/2}$ is a weight function and therefore \n\\be \\label{TT}\n\\langle T_n T_m\\rangle =\\delta_{nm}{\\pi\\over 2},\n\\ee\nfor $n\\neq 0$ and $\\langle T_0^2\\rangle =\\pi$. In \n(\\ref{zshortI})(\\ref{zshortII}) we encounter two types of angle \nbrackets to evaluate (other than (\\ref{TT}): \n$\\langle T_n\\dot{T}_m\\rangle$ and $\\langle T_n T_m T_r\\rangle$ \n(we have deliberately omitted $\\langle \\Omegam T_n T_m\\rangle$, by \napproximating $\\Omegam$ by a constant, and \nditto for $H$. The second type \nof product is trivially transformed into (\\ref{TT}) via \n\\be \n2 T_n T_m = T_{n+m}+T_{n-m}\n\\ee \nfor $n\\geq m$, and the first requires a little numerical \nmanipulation using the relation\n\\be \n(1-t^2)\\dot{T}_n = -nt\\, T_n + T_{n-1}. \n\\ee \n\n\\section[]{Orthogonality relations}\n\nThe orthogonality relations for the spherical harmonics and \nthe Bessel functions are respectively \n\\be \\label{orthoI}\n\\int_0^{2\\pi}\\!\\!\\d\\varphi\\int_0^{\\pi}\\!\\!\\d(\\cos\\theta)\nY_{lm}Y_{l'm'}=\\delta_{ll'}\\delta_{mm'},\n\\ee\n\\be \\label{orthoII}\n\\int_0^1\\!\\!\\d x x^2 j_l(k_rx)j_l(k_sx)\n={1\\over2k_rk_s} \\Big[j_l(k_rx)+xj_l'(k_rx)\\Big]^2\\delta_{rs}.\n\\ee\n\n\n\\bsp\n\n\\label{lastpage}\n\n\n\n\n\\end{document}\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002369.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{}\n Abramowitz M., Stegun I.A., 1972, {\\it Handbook of Mathematical \nFunctions}, Dover, New York\n\n\\bibitem{}\n Baker, J.E., Davis M., Strauss M.A., Lahav O., Santiago B.X., \n1998, ApJ 508, 6 \n\n\\bibitem{}\n Bernardeau F., Juszkiewicz R., Dekel A., Bouchet F., 1995, MNRAS \n274, 20\n\n\\bibitem{}\n Branchini E., Carlberg R.G., 1994, ApJ 434, 37\n\n\\bibitem{}\n Canavezes A. et al., 1998, MNRAS 297, 777\n\n\\bibitem{}\n Coles P., Sahni V., 1995, Phys. Rep. 262, 1\n\n\\bibitem{}\n Courant R. and Hilbert D., 1989, {\\it Methods of Mathematical\n Physics}, John Wiley \\& Sons, New York, vol. I \n\n\\bibitem{}\n Dekel A., 1994, Annu. Rev. Astron. Astrophys., 32, 371--418\n\n\\bibitem{}\n Dekel A., 1999a, in {\\it Formation of Structure in the Universe}, \ned. A. Dekel and J.P. Ostriker, Cambridge University Press, 250 \n\n\\bibitem{}\n Dekel A., 1999b, in {\\it Cosmic Flows: Towards an Understanding of Large-Scale \nStructure}, eds. S. Courteau, M.A. Strauss and J.A. Willick, ASP Conf. Series\n\n\\bibitem{}\nDekel A., Lahav O., 1999, ApJ 520, 24 \n\n\\bibitem{}\nDekel A., Bertschinger E., Yahil A., Strauss M.A., Davis M., Huchra \nJ.P., 1993, ApJ 412, 1 \n\n\\bibitem{}\n Dekel A., Burstein D., White S.D.M., 1997, in \n{\\it Critical Dialogues in Cosmology},\n ed. N.G. Turok, World Scientific, Singapore\n\n\\bibitem{}\n Dekel A., Eldar A., Kolatt T., Yahil A., Willick J.A., Faber S.M., \nCourteau S., Burstein D., 1999, ApJ 522, 1\n\n\\bibitem{}\n Fisher K.B., Davis M., Strauss M.A., Yahil A., Huchra J.P., 1993, \nAp. J. 402, 42\n\n\\bibitem{}\n Fisher K.B., Huchra J.P., Strauss M.A., Davis M., \n Yahil A., Schlegel D., 1995a, ApJS 100, 69\n\n\\bibitem{}\n Fisher K.B., Lahav O., Hoffman Y., Lynden--Bell D., Zaroubi S., \n 1995b, MNRAS 272, 885\n\n\\bibitem{}\n Fry J.N., 1994, Phys. Rev. Lett. 73, 2\n\n\\bibitem{}\n Giavalisco M., Mancinelli B., Mancinelli P.J., Yahil A., \n 1993, ApJ 411, 9\n\n\\bibitem{}\n Hudson M.J., Dekel A., Courteau S., Faber S.M., Willick J.A., 1995, \n MNRAS 274, 305\n\n\\bibitem{}\n Kaiser N., 1987, MNRAS 227, 1\n\n\\bibitem{}\n Linde A., Sasaki M., Tanaka T., 1999, Phys. Rev. D59, 123522\n\n\\bibitem{} \n Peebles P.J.E., 1989, ApJ 344, L53\n\n\\bibitem{} \n Peebles P.J.E., 1990, ApJ 362, 1\n\n\\bibitem{}\nSantiago B.X., Strauss M.A., Lahav O., Davis M., Dressler A., \nHuchra J.P., 1995, ApJ 446, 457 \n\n\\bibitem{}\n Saunders W., Sutherland W., Maddox S., Keeble O., Oliver S.J., \nRowan-Robinson M., Mahon R.G., Efstathiou G.P., Tadros H., \nWhite S.D.M., Frenk C.S., Carrami\\~{n}ana A., Hawkins M.R.S., \n2000, MNRAS submitted, astro-ph/0001117\n\n\\bibitem{}\n Schmoldt I.M., Saha P., 1999, AJ 115, 2231 \n\n\\bibitem{}\n Shaya E.J., Peebles P.J.E., Tully R.B., 1995, ApJ 454, 15\n\n\\bibitem{}\n Sigad Y., Eldar A., Dekel A., Strauss M.A., Yahil A., 1998, \nApJ 495, 516\n\n\\bibitem{}\n Strauss M.A., Davis M., Yahil A. and Huchra J.P., 1990, ApJ 361, 49; \ngeneral descriptive information on \\iras~can be found in \nhttp://www.gsfc.nasa.gov/astro/iras/irs.html \n\n\\bibitem{}\n Strauss M.A., Huchra J.P., Davis M., Yahil A., Fisher K.B., \n Tonry J., 1992, ApJS 83, 29\n\n\\bibitem{}\n Strauss M.A., Willick J., 1995, Phys. Rep. 261, 271 \n\n\\bibitem{}\n Susperregi M., 1995, D.Phil. thesis (Oxford), unpublished\n\n\\bibitem{}\n Susperregi M., 2000, in proc. 4th RESCEU symposium on {\\it The Birth \nand Evolution of The Universe}, Tokyo, World Scientific, in press \n\n\\bibitem{}\n Susperregi M., Binney J., 1994, MNRAS 271, 719 (SB94) \n\n\\bibitem{}\n Tadros H., Ballinger W.E, Taylor A.N., Heavens A.F., Efstathiou G., \nSaunders W., Frenk C.S., Keeble O., McMahon R., Maddox S.J., Oliver\nS., Rowan-Robinson M., Sutherland W.J., White S.D.M., 1999, MNRAS \n305, 527\n\n\\bibitem{}\nVerde L., Heavens A.F., Matarrese S., Moscardini L., 1998, MNRAS \n300, 747\n\n\\bibitem{}\n Willick J.A., Courteau S., Faber S.M., Burstein D., Dekel A., \nKollat T., 1995, Ap. J. 446, 12 (paper I)\n\n\\bibitem{}\n Willick J.A., Courteau S., Faber S.M., Burstein D., Dekel A., \nStrauss M.A., Kollat T., 1996, Ap. J. 457, 460 (paper II)\n\n\\bibitem{}\n Willick J.A., Courteau S., Faber S.M., Burstein D., Dekel A., \nStrauss M.A., 1997a, ApJS 109, 333 (paper III)\n\n\\bibitem{}\n Willick J.A., Strauss M.A., Dekel A., Kolatt T., 1997b, \nApJ 486, 629\n\n\\bibitem{}\nYahil A., Strauss M.A., Davis M., Huchra J.P., 1991, ApJ 372, 380 \n\n\\bibitem{}\nZaroubi S., Hoffman Y., Dekel A., 1999, ApJ 520, 413 \n\n\\end{thebibliography}"
}
] |
astro-ph0002370
|
Dynamical and chemical evolution of gas-rich dwarf galaxies
|
[
{
"author": "Francesca Matteucci$^{1,2}$ and Annibale D'Ercole$^{3}$"
},
{
"author": "$^1$Dipartimento di Astronomia"
},
{
"author": "Universit\\`a di Trieste"
},
{
"author": "Via G.B. Tiepolo"
},
{
"author": "11"
},
{
"author": "34131 Trieste"
},
{
"author": "Italy"
},
{
"author": "$^2$SISSA/ISAS"
},
{
"author": "Via Beirut 2-4"
},
{
"author": "34014 Trieste"
},
{
"author": "$^3$Osservatorio Astronomico di Bologna"
},
{
"author": "via Ranzani 1"
},
{
"author": "44127 Bologna"
}
] |
We study the effect of a single, instantaneous starburst on the dynamical and chemical evolution of a gas-rich dwarf galaxy, whose potential well is dominated by a dark matter halo. We follow the dynamical and chemical evolution of the ISM by means of an improved 2-D hydrodynamical code coupled with detailed chemical yields originating from type II SNe, type Ia SNe and single low and intermediate mass stars (IMS). In particular we follow the evolution of the abundances of H, He, C, N, O, Mg, Si and Fe. We find that for a galaxy resembling IZw18, a galactic wind develops as a consequence of the starburst and it carries out of the galaxy mostly the metal-enriched gas. In addition, we find that different metals are lost differentially in the sense that the elements produced by type Ia SNe are more efficiently lost than others. As a consequence of that we predict larger [$\alpha$/Fe] ratios for the gas inside the galaxy than for the gas leaving the galaxy. A comparison of our predicted abundances of C, N, O and Si in the case of a burst occurring in a primordial gas shows a very good agreement with the observed abundances in IZw18 as long as the burst has an age of $\sim 31$ Myr and IMS produce some primary nitrogen. However, we cannot exclude that a previous burst of star formation had occurred in IZw18 especially if the preenrichment produced by the older burst was lower than $Z=0.01$ Z$_{\odot}$. Finally, at variance with previous studies, we find that most of the metals reside in the cold gas phase already after few Myr. This result is mainly due to the assumed low SNII heating efficiency, and justifies the generally adopted homogeneous and instantaneous mixing of gas in chemical evolution models.
|
[
{
"name": "recchi.tex",
"string": "\\documentstyle[twocolumn,epsfig]{mn}\n\\oddsidemargin=0pt\n\\evensidemargin=0pt\n\\textwidth=6.5truein\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\\def\\refer{\\bibitem {}}\n\\def\\pc{{\\rm pc}}\n\\def\\kpc{{\\rm kpc}}\n\\def\\lw{L_{\\rm w}}\n\\def\\lb{L_{\\rm b}}\n\\def\\ln{L_{\\rm n}}\n\\def\\hef{H_{\\rm eff}}\n\\def\\nn{{\\cal\\char'116}}\n%\\renewcommand{\\baselinestretch}{1.2}\n%\\setlength{\\textwidth}{150mm}\n%\\setlength{\\textheight}{235mm}\n%\\setlength{\\topmargin}{-5mm}\n%\\setlength{\\oddsidemargin}{0mm}\n%\\setlength{\\evensidemargin}{0mm}\n%\\setlength{\\parindent}{10mm}\n%\\setlength{\\parskip}{\\medskipamount}\n%\\setlength{\\unitlength}{1mm}\n\n\\title{Dynamical and chemical evolution of gas-rich dwarf galaxies}\n\\author[Recchi et al.]\n{Simone Recchi$^{1,2}$\\thanks{E-mail: recchi@sissa.it (SR); \nfrancesc@sissa.it (FM); annibale@astbo3.bo.astro.it (AD)}, \nFrancesca Matteucci$^{1,2}$ and \nAnnibale D'Ercole$^{3}$ \\\\\n$^1$Dipartimento di Astronomia, Universit\\`a di Trieste, Via G.B. Tiepolo, 11,\n34131 Trieste, Italy \\\\\n$^2$SISSA/ISAS, Via Beirut 2-4, 34014 Trieste, Italy \\\\\n$^3$Osservatorio Astronomico di Bologna, via Ranzani 1, 44127 Bologna, Italy}\n\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\nWe study the effect of a single, instantaneous starburst on the\ndynamical and chemical evolution of a gas-rich dwarf galaxy, whose\npotential well is dominated by a dark matter halo. We follow the\ndynamical and chemical evolution of the ISM by means of an improved\n2-D hydrodynamical code coupled with detailed chemical yields\noriginating from type II SNe, type Ia SNe and single low and\nintermediate mass stars (IMS). In particular we follow the evolution\nof the abundances of H, He, C, N, O, Mg, Si and Fe. We find that for\na galaxy resembling IZw18, a galactic wind develops as a consequence\nof the starburst and it carries out of the galaxy mostly the\nmetal-enriched gas. In addition, we find that different metals are\nlost differentially in the sense that the elements produced by type Ia\nSNe are more efficiently lost than others. As a consequence of that we\npredict larger [$\\alpha$/Fe] ratios for the gas inside the galaxy than\nfor the gas leaving the galaxy. A comparison of our predicted\nabundances of C, N, O and Si in the case of a burst occurring in a\nprimordial gas shows a very good agreement with the observed\nabundances in IZw18 as long as the burst has an age of $\\sim 31$ Myr\nand IMS produce some primary nitrogen. However, we cannot exclude\nthat a previous burst of star formation had occurred in IZw18\nespecially if the preenrichment produced by the older burst was lower\nthan $Z=0.01$ Z$_{\\odot}$. Finally, at variance with previous studies,\nwe find that most of the metals reside in the cold gas phase already\nafter few Myr. This result is mainly due to the assumed low SNII\nheating efficiency, and justifies the generally adopted homogeneous\nand instantaneous mixing of gas in chemical evolution models.\n\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: individual: IZw18 -- hydrodynamics -- ISM: abundances --\nISM: bubbles.\n\n\\end{keywords}\n\n\\section{Introduction}\n\nDwarf irregular galaxies (DIG) are playing an increasingly central\nrole in understanding galaxy evolution. This kind of galaxies\ngenerally has a low metallicity (from 0.5 Z$_{\\odot}$ to\n0.02 Z$_{\\odot}$), a high gas content (up to $\\sim$ 10 times the\nstellar content) and their stellar populations appear to be mostly\nyoung. All these features indicate that these galaxies are\npoorly evolved objects.\n\nMany gas-rich dwarf galaxies are known to be in a starburst phase, or\nare believed to have experienced periods of intense star formation in\nthe recent past. These galaxies are generally called blue compact\ndwarf (BCD) galaxies (Sandage \\& Binggeli 1984). In general, dwarf\ngas-rich galaxies, given their simple structures and small sizes, are\nexcellent laboratories to investigate the feedback of starbursts\non the interstellar medium (ISM), and to study their chemical\nevolution. The aim is to reproduce the observed abundance ratios, to\ntrace their recent star formation history and to discover if these\ngalaxies could be the source of the intracluster gas (Gibson \\&\nMatteucci 1997).\n\nMany authors have tried to connect late-type gas-rich (DIG and BCD)\nand early-type gas-poor dwarf galaxies (dwarf ellipticals and dwarf\nspheroidals) in an unified evolutionary scenario. The favourite theory\nabout ISM depletion in gas-rich dwarf galaxies is based on the\nstarburst-driven mass loss. The basis of this model, proposed by\nLarson (1974) and then applied specifically to dwarfs by Vader (1986)\nand Dekel \\& Silk (1986), is that the ISM is blown out of the galaxy\nby the energetic events associated with the star formation (stellar\nwinds and supernovae). The well-known correlation between mass and\nmetallicity found for both late-type and early-type dwarf galaxies\n(Skillman, Kennicut \\& Hodge 1989) is a natural result of the\nincreasing inability of massive galaxies to retain the heavy\nelements produced in each stellar generation. At the present time is\nnot yet clear if galactic winds are really the key point for\nunderstanding the formation and evolution of dwarf galaxies (see\nSkillman \\& Bender 1995 and Skillman 1997 for critical reviews about\nthis point), but they certainly play an important role, regulating the\nmass, metal enrichment and energy balance of the ISM.\n\nObservational evidences in support of the presence of outflows have\nbeen found recently in a lot of gas-rich dwarf galaxies, like NGC1705\n(Meurer et al. 1992), NGC1569 (Israel 1988), IZw18 (Martin 1996)\nand many others. In their search for outflows in dwarf galaxies,\nMarlowe et al. (1995) pointed out that this kind of phenomena is\nrelatively frequent in centrally star-forming galaxies. Again, they\nnote a preferencial direction of propagation along the galaxy minor\naxis. In spite of these observational evidences, it is often difficult\nto estabilish if the gas will leave definitively the parent galaxy. In\norder to understand the final fate of both the swept-up gas and the\nmetals ejected during the starburst and to study possible links\nbetween early and late-type dwarfs, numerical simulations are needed.\n \nThere are a lot of recent hydrodynamical simulations concerning the\nbehaviour of the ISM and the metals ejected by massive stars after\na starburst. These simulations generally agree on the fact that\ngalactic winds are not so effective in removing the ISM from dwarf\ngalaxies, but disagree on the final fate of the metal-enriched gas\nejected by massive stars. Many authors (D'Ercole \\& Brighenti 1999,\nhereafter DB; MacLow \\& Ferrara 1999, hereafter MF; De Young \\&\nHeckman 1994; De Young \\& Gallagher 1990) have found that galactic\nwinds are able to eject most of the metal-enriched gas, preserving a\nsignificant fraction of the original ISM. Other authors (Silich \\&\nTenorio-Tagle 1998; Tenorio-Tagle 1996) have suggested that the\nmetal-rich material is hardly lost from the galaxies, since it is at\nfirst trapped in the extended haloes and then accreted back on to the\ngalaxy.\n\nHowever, all these models consider only the effects of stellar winds and\nSNII explosions on the dynamics of the ISM. In this paper we present\nmodels which take into account also the energetic contribution and the\nfeedback from intermediate-mass stars and SNeIa, using the most\nup-to-date supernova rates. The effect of SNIa explosions is certainly\nfundamental for the late dynamical evolution of the ISM (up to $\\sim$ 500\nMyr after the burst), even if their number is small.\n\nThere is an extensive literature about the chemical evolution of starburst\nand blue compact dwarf galaxies (see e.g. Matteucci \\& Chiosi 1983;\nMatteucci \\& Tosi 1985; Olofsson 1995). Pilyugin (1992, 1993) and\nMarconi et al. (1994) suggested the idea that the spread in the\nchemical properties of these galaxies, in particular the observed\nspread in He/H vs. O/H and N/O vs. O/H, could be due to self-pollution\nof H\\,{\\sc ii} regions coupled with `enriched' or `differential' galactic\nwinds.\n\nTherefore it is interesting to test the differential wind hypothesis\nwith an hydrodynamical approach. In our models we are able to follow\nthe evolution in space and time of the abundances of several\nchemical elements (H, He, C, N, O, Mg, Si, Fe); in particular we\nfollow, with suitable tracers, the gas released by stars of different\ninitial mass. The chemical composition of each of these tracers is\nobtained by adopting the nucleosynthesis prescriptions from various\nauthors (Woosley \\& Weaver 1995, hereafter WW; Renzini \\& Voli 1981,\nhereafter RV; Nomoto, Thielemann \\& Yokoi 1984, hereafter NTY).\n\nIn section 2 we describe the model and the assumptions adopted in our\nsimulations. The results are presented in section 3 and compared with\nthe observational constraints available for the BCG IZw18. A\ndiscussion is presented in section 4 while some conclusions and future\nimprovements of the model are discussed in section 5.\n\n\\section{Assumptions and equations}\n\n\\subsection{The gravitational potential and the gas distribution}\n\nIt is convenient, for computational reasons, to model BCD galaxies.\nIn these galaxies, in fact, the starburst occurs near the optical\ncentre and the ISM structure is highly axisymmetric. In particular, we\nwill focus on the galaxy IZw18 which is a well-studied, very\nmetal-poor BCD galaxy. IZw18 shows very blue colors ($U-B\\,=-0.88$, Van\nZee et al. 1998), which are indicative of a dominating very young\nstellar population, although one cannot exclude an underlying older\none (Aloisi et al. 1999). Therefore, IZw18 is an excellent\ncandidate to compare with a single-burst model, although our model\ncannot reproduce the real galaxy in detail.\n \nMany ingredients play an important role in the dynamical evolution of\nthe ISM: the galactic structure (stellar component, gaseous component,\ndark halo), the energy and mass injection rate of newly formed stars\nand the size of the starburst region.\n\nWe model the ISM of IZw18 assuming a rotating gaseous component in\nhydrostatic isothermal ($T_{\\rm g}=10^3$ K) equilibrium with the\ngalactic potential and the centrifugal force. The potential well is\nthe sum of two components. The first is given by a spherical,\nquasi-isothermal dark halo truncated at a distance $r_{\\rm {t h}}$, in\norder to obtain a finite mass:\n\\begin{equation}\n\\rho_{\\rm h}(r)=\\rho_{\\rm h 0}\\biggl\\lbrack{1+\\biggl({r \\over \nr_{\\rm {c h}}}\\biggr)^2}\n\\biggr\\rbrack^{-1},\n\\end{equation}\n\\noindent\nwhere $r=\\sqrt{R^2+z^2}$ and $r_{\\rm {c h}}$ is the core radius of the\ndark component (we are using cylindrical coordinates). According to\nvalues found in literature for the total mass of IZw18 (Lequeux \\&\nViallefond 1980; Van Zee et al. 1998), the halo mass is assumed to\nbe $6.5 \\times 10^8$ M$_{\\odot}$. Since we do not take into account\nthe self gravity of the gas, in order to reproduce the oblate\ndistribution of gas inside IZw18 (Van Zee et al. 1998), we\nintroduce a fictitious `stellar' component described by an oblate\nKing stellar profile:\n\\begin{equation}\n\\rho_{\\star}(R,z)=\\rho_{\\star 0}\\biggl\\lbrack{1+\\biggl({R \\over R_{\\rm\nc \\star}} \\biggr)^2+\\biggl({z \\over z_{\\rm c\n\\star}}\\biggr)^2}\\biggr\\rbrack^{-{3 \\over 2}},\n\\end{equation} \n\\noindent\nwhere $R_{\\rm c \\star}$ and $z_{\\rm c \\star}$ are the core radius\nalong the $R$-axis and the $z$-axis respectively. This profile is\ntruncated at the tidal radii $R_{\\rm t \\star}$ and $z_{\\rm t \\star}$,\nin order to obtain a finite mass $M_{\\star}=6\\times 10^5$ M$_{\\odot}$.\nThis structure is flattened along the $z$-axis and we assume $R_{\\rm c\n\\star}/z_{\\rm c \\star}= R_{\\rm t \\star}/z_{\\rm t \\star}=5$ and $R_{\\rm\nt \\star}/R_{\\rm c \\star}= z_{\\rm t \\star}/z_{\\rm c \\star}=4.29$. All\nthe structural parameters of our galactic model are summarized in\nTable 1. The atomic number density of the neutral ISM is defined as\n$n_{\\rm g}={\\rho\\over 2 \\mu m_{\\rm H}}$, where $\\rho$ is the ISM mass\ndensity and $\\mu=7/11$ is the mean mass per particle of the fully\nionized gas, assuming a primordial abundance.\n\nAlthough this structure is rather flat, its potential is rounder. The\ngas settled in such a potential assumes an oblate structure resembling\nthat of the ISM of IZw18 in a region $R\\leq 1$ Kpc and $z\\leq 730$\npc, which we call `galactic region'. We note however that the\nelongation is also due to the assumed rotation of the gas which is\nresponsible for the flaring at large radii (see Fig. 1, upper panel).\nDetails of how to build such an equilibrium configuration can be found\nin DB. The lower panel in Fig. 1 shows the resulting column density of\nthe ISM.\n\nWe ran several models varying the gas mass and the burst\nluminosity. We discuss in detail three of them, M1, M2 and M3\n(see Table 2). We also describe model MC, similar to M1, in\nwhich heat conduction is allowed.\n\n\\par\n\\hbox{}\n\\begin{table*}\n\\caption[]{Galactic parameters}\n\\begin{flushleft}\n\\begin{tabular}{llllll}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n$M_{\\star}$(M$_{\\odot}$) & $M_{\\rm {halo}}$(M$_{\\odot}$) & \n$R_{\\rm c \\star}(\\pc)$ & $R_{\\rm t \\star}(\\pc)$ & $r_{\\rm {ch}}(\\pc)$ & \n$r_{\\rm {t h}}(\\kpc)$\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n$6\\times 10^5$ & $6.5\\times 10^8$ & 233 & 1000 & \n700 & 10\\\\ \n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\end{table*} \n\n\\par \n\\hbox{}\n\\begin{table*}\n\\caption[]{ISM parameters}\n\\begin{flushleft}\n\\begin{tabular}{lllll}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nModel &\n$M_{\\rm burst}$(M$_{\\odot}$) & \n$M_{\\rm g}$(M$_{\\odot}$) & \n$n_{\\rm g0}(\\rm cm^{-3})$ & $E_{\\rm b}({\\rm erg})$\\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nM1 & $6\\times 10^5$ & $1.7\\times 10^7 $& $ 1.81$ & $1.5\\times 10^{53}$\\\\\nM2 & $3.6\\times 10^5$ & $1.7\\times 10^7$ & $1.81$ & $1.5\\times 10^{53}$\\\\\nM3 & $6\\times 10^5$ & $4.6\\times 10^6$ & $0.49$ & $4\\times 10^{52}$\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\n$M_{\\rm g}$ is the ISM mass inside the galactic region defined in the\ntext, $M_{\\rm {burst}}$ is the mass of the stars formed during the\nburst and $n_{\\rm g0}$ is the central atomic number density. \n$E_{\\rm b}$ is the binding energy of the gas inside the galaxy.\n\\end{flushleft}\n\\end{table*} \n\n\\begin{figure}\n\\centering\n\\vspace{-0.2cm}\n\\epsfig{file=recchi1.eps, height=8cm,width=8cm}\n\\caption[]{\\label{fig:fig 1} Upper panel: initial gas density\nprofiles. The density scale is logharitmic varies linearly between \n-33 and -24. Lower panel: column density of the initial ISM seen\nedge-on (dashed line) and face-on (solid line).}\n\\end{figure}\n\n\n\\subsection{The equations}\nTo describe the evolution of the gas we solve the time-dependent, \nEulerian equations of gasdynamics with source terms, that we write \nin the form:\n\\begin{equation}\n{\\partial\\rho\\over\\partial t}+\\nabla\\cdot(\\rho {\\bmath{v}})=\n\\alpha\\rho_*,\n\\end{equation}\n\\begin{equation}\n{\\partial\\varrho^i\\over\\partial t}+\\nabla\\cdot(\\varrho^i {\\bmath{v}})=\n\\alpha^i\\rho_*,\n\\end{equation}\n\\begin{equation}\n{\\partial {\\bmath{m}}\\over\\partial t}+\\nabla\\cdot({\\bmath{m}}\\otimes \n{\\bmath{v}})=\\rho{\\bmath{g}}-(\\gamma-1)\n\\nabla\\varepsilon + \\alpha {\\rho_*} {\\bmath{v}}_*,\n\\end{equation}\n\\begin{equation}\n{\\partial\\varepsilon\\over\\partial t}+\\nabla\\cdot(\\varepsilon {\\bmath{v}})=\n-(\\gamma-1)\\varepsilon\\nabla\\cdot{\\bmath{v}}-L+\\alpha\\rho_*\n\\biggl(\\epsilon_0+{1\\over 2}v^2\\biggr),\n\\end{equation}\n\\noindent\nwhere $\\rho$, ${\\bmath{m}}$ and $\\varepsilon$ are the density of mass,\nmomentum and internal energy of the gas, respectively. The parameter\n$\\gamma=5/3$ is the ratio of the specific heats, ${\\bmath{g}}$ and\n${\\bmath{v}}$ are the gravitational acceleration and the fluid\nvelocity, respectively. The source terms on the r.h.s. of equations\n(3)--(6) describe the injection of total mass and energy in the gas due\nto the mass return and energy input from the stars. In our\nsimulations the burst is located in the centre of the galaxy,\ntherefore both energy sources (SNeII and SNeIa) and mass return are\nconcentrated inside a small central sphere of $\\sim$ 40 pc of\nradius. We treat both sources as continuous, although the SNIa rate is\nrather low ($\\sim 1.6$ Myr$^{-1}$, see section 2.3.1). However, an a\nposteriori analysis of our results, following Mac Low \\& McCray\n(1988), reveals that the continuous energy input assumption is still\nvalid during the SNIa stage. ${\\cal V}$ being the volume of the burst,\n$\\rho_*=M_{\\rm burst}/ {\\cal V}$, where $M_{\\rm burst}$ is the total\nmass of stars formed during the burst (see next\nsection). ${\\bmath{v}}_*$ is the circular velocity of these stars, and\n$\\alpha(t)=\\alpha_*(t)+\\alpha_{\\rm SNII}(t)+\\alpha_{\\rm SNIa}(t)$ is\nthe sum of specific mass return rates from stars and SNe, respectively\n(see next section). $\\epsilon_0$ is the injection energy per unit mass\ndue to the stellar random motions and to SN explosions (see next\nsection). Finally, $L=n_{\\rm e}n_{\\rm p}\\Lambda(T)$ is the cooling\nrate per unit volume, where for the cooling law $\\Lambda(T)$ we follow\nthe approximation to the equilibrium cooling curve given by Mathews \\&\nBregman (1978).\n\n$\\varrho^i$ represents the mass density of the $i$ element, and\n$\\alpha^i$ the specific mass return rate for the same element, with \n$\\sum^\\nn_{i=1} \\alpha^i=\\alpha$.\nEq. (4) represents a subsystem of $\\nn$ equations which follow the\nhydrodynamical evolution of $\\nn$ different ejected elements (namely\nH, He, C, N, O, Mg, Si and Fe). This enables us to calculate the\nabundance of the ejecta relative to the pristine ISM.\n\nTo integrate numerically the eqs. (3)--(6) we used a 2-D hydrocode,\nbased on the original work of Bedogni \\& D'Ercole (1986). We adopted a\nnon-uniform cylindrical axisymmetric grid whose meshes expand\ngeometrically. The first zone is $\\Delta R=\\Delta z=5$ pc and the\nsize ratio between adiacent zones is 1.03.\n\n\\subsection{The starburst}\nFor the sake of simplicity we focus on a single, instantaneous,\nstarburst event located at the centre of the galaxy. The stars are\nall born at the same time but they die and restore material into the\nISM according to their lifetimes.\n\nHere we will describe the main assumptions about the initial mass function \n(IMF), stellar lifetimes and nucleosynthesis prescriptions adopted to\ncalculate $\\alpha_*$ and $\\alpha_{\\rm SN}$.\n\\subsubsection{Mass return}\nIn order to obtain the number d$N$ of stars with initial masses in the\ninterval d$M$, we adopt the Salpeter (1955) initial mass function\n(IMF) $\\phi(M)={{\\rm d}N\\over {\\rm d}M}$ assumed to be constant in\nspace and time:\n\n\\begin{equation}\n\\phi(M){\\rm d}M=B M^{-(1+x)}{\\rm d}M,\n\\end{equation}\n\\noindent\nwhere $x=1.35$, and $B$ is the normalization constant obtained from:\n\n\\begin{equation}\n\\int^{40}_{0.1}{M \\phi(M) {\\rm d}M}=M_{\\rm burst},\n\\end{equation}\n\\noindent\nWith $M_{\\rm burst}=6\\times 10^5$ M$_{\\odot}$ we get a mass of $\\sim 1.5\n\\times 10^{5}$ M$_{\\odot}$ for the stars with masses larger than 2\nM$_{\\odot}$, in agreement with the estimate of the stellar content in\nIZw18 by Mas-Hesse \\& Kunth (1996). Since the stellar yields are\ncalculated only for stellar masses not larger than 40 M$_{\\odot}$\n(WW), we adopt this value as an upper limit in eq. (8). Given the very\nlow number of stars more massive than this limit, the chemical and\ndynamical evolution of the gas is not affected by this choice.\n\nWe assume that all the stars of initial mass between 8 and 40 solar\nmasses end their lifecycle as type II supernovae. The SNII rate is\ndefined as:\n\n\\begin{equation}\nR_{\\rm {SNII}}(t)=\\phi(M)|\\dot M|,\n\\end{equation}\n\\noindent\nwhere $M$ represents the mass of the dying stars at the time $t$. \nThe mass return rate from SNII is then given by:\n\n\\begin{equation}\n\\alpha_{\\rm {SNII}}(t)=R_{\\rm {SNII}}(t) \\Delta M/M_{\\rm burst}.\n\\end{equation}\n\\noindent\nHere $\\Delta M$ is the mass restored into the ISM by a star of initial\nmass $M$, and is defined as $M-M_{\\rm\nrem}$, where $M_{\\rm rem}$ is the mass of the stellar remnant.\n\nIn terms of single elements we have:\n\n\\begin{equation}\n\\alpha^{i}_{\\rm {SNII}}(t)=R_{\\rm {SNII}}(t) \\Delta M_i/M_{\\rm burst},\n\\end{equation}\n\\noindent\nwhere $\\Delta M_i$ is the mass restored by a star of mass \n$M$ in the form of the specific element $i$.\n\nThe specific mass return from stars with $M<8$ M$_{\\odot}$ is given by:\n\n\\begin{equation}\n\\alpha_*(t)=\\phi(M)|\\dot M|\\Delta M/M_{\\rm burst},\n\\end{equation}\n\\noindent\nand:\n\n\\begin{equation}\n\\alpha^{i}_*(t)=\\phi(M)|\\dot M|\\Delta M_i/M_{\\rm burst},\n\\end{equation}\n\\noindent\nwhere, again, $M$ is the mass of the dying stars at the time $t$.\n\nTo calculate the time derivative of the mass in eqs. (9), (12) and (13) we\nadopt the stellar lifetimes given by Padovani \\& Matteucci (1993):\n\n\\begin{equation}\nt(M)=\\cases{1.2 M^{-1.85}+0.003\\;{\\rm Gyr} &if $M\\geq 8$ M$_{\\odot}$\\cr\n 10^{f(M)}\n\\;{\\rm Gyr} &if $M<8$ M$_{\\odot}$,\\cr}\n\\end{equation}\n\\noindent\nwhere $f(M)={{\\bigl\\lbrack 0.334-\\sqrt{1.79-0.2232\\times(7.764-\\log(M))}\n\\bigr\\rbrack\\over 0.1116}}$.\n\nTo obtain the quantity $\\Delta M$ appearing in eq. (10) and eq. (12)\nwe took into account the results of WW for massive stars ($M \\ge10$\nM$_{\\odot}$) and RV for low and intermediate mass stars ($0.8 \\le\nM/{\\rm M}_{\\odot} \\le 8$), which give the mass restored into the ISM\nby the stars at the end of their lifetime. For the range 8\nM$_{\\odot}\\leq M\\leq 10$ M$_{\\odot}$ we have adopted suitable\ninterpolations between the previous two sets of data.\n\nIn WW the total ejected masses (processed and unprocessed) are given\nfor each chemical element. In general, however, in nucleosynthesis\npapers only the `yield' is given, namely the fraction in mass of a\ngiven element $i$ which is newly formed and ejected by a star of\ninitial mass $M$, the quantity $P_{i \\rm M}$. In this case, the\nejected total masses are computed in the following way:\n\n\\begin{equation}\n\\Delta M_i=\\Delta M X_i +MP_{i \\rm M},\n\\end{equation}\n\\noindent\nwhere $X_i$ is the original abundance of the element $i$ in the star.\nThis is the case of the yields of RV.\n\nFrom the tables of WW (which contain also the products of explosive\nnucleosynthesis) and RV we have derived several relations between the\ninitial stellar mass and the mass restored into the ISM in the form of\nchemical elements for single stars of masses between 0.8 and\n40 M$_{\\odot}$, obtained by fitting the tabulated values with an\neighth degree polynomial. The results are shown in Figg. 2--4 for\ndifferent initial chemical compositions and different mixing lenght\nparameters. This enables us to obtain the temporal behaviour of\n$\\alpha_{*}^i(t)$ and $\\alpha_{\\rm SNII}^i(t)$ for each element $i$.\nThe total mass ejection rates obtained by summing over all the\nchemical elements are: $\\alpha_{\\rm SNII}(t)\\propto t^{-0.27}$ and\n$\\alpha_*(t)\\propto t^{-1.36}$ (see also Ciotti et al. 1991).\n\nFinally, in analogy with eq. (10) we define the specific mass return\nfrom the SNeIa as:\n\\begin{equation}\n\\alpha_{\\rm {SNIa}}(t)=1.4R_{\\rm {SNIa}}(t)/M_{\\rm burst},\n\\end{equation}\n\\noindent\nand:\n\\begin{equation}\n\\alpha^{i}_{\\rm {SNIa}}(t)=R_{\\rm {SNIa}}(t) \\Delta M_i/M_{\\rm burst},\n\\end{equation}\n\\noindent\nwhere the mass ejected by each SNIa is assumed to be 1.4 M$_{\\odot}$\n(the Chandrasekhar mass). According to the single degenerate model\n(SD), SNe Ia are assumed to originate from C-O white dwarfs in binary\nsystems which explode after reaching the Chandrasekhar mass as a\nconsequence of mass transfer from a red giant companion. This kind of\nsupernova explosion occurs only after the death of stars of initial\nmass less or equal than 8 M$_{\\odot}$, which is $\\sim$ 29 Myr after\nthe burst. $R_{\\rm SNIa}(t)$ is given by the following formula,\nobtained by the best-fitting of the SNIa rate computed in detail\nnumerically by the model of Bradamante et al. (1998), when applied to\nthe case of a single starburst:\n\n\\begin{equation}\nR_{\\rm {SNIa}}(t)=4.2\n\\times 10^{-9}\\biggl({{t_9+1}\\over 15}\\biggr)^{-1.9}\\;{\\rm yr}^{-1},\n\\end{equation}\n\\noindent \nwhere $t_9$ is the time expressed in Gyr. \n\nIt is worth noting that the SNIa rate in BCG is practically unknown\nand therefore it is very difficult to choose the right fraction of\nbinary systems, in the IMF of such galaxies, of the type required to\noriginate a SNIa. The rate of eq. (18) corresponds to the rate of\nGreggio \\& Renzini (1983) for a starburst with a fraction of binary\nsystems $A=0.006$. This rate switches on somewhat more gradually than\nin our approximation, reaching a maximum after $\\sim$ 40 Myr (see Greggio \\&\nRenzini, fig. 1), but this difference has no consequences in the\ndynamical evolution of our models. To show this, we ran a model (not\nshown in this paper), up to $\\sim$ 80 Myr, using the rate computed by\nGreggio \\& Renzini and the differences with the results shown in\nsection 3 were negligible. With our assumed rate, SNeIa\ncontribute by $\\sim 60$ per cent of the total iron production after 15 Gyr,\nin agreement with predictions for the solar neighbourhood (Matteucci\n\\& Greggio 1986).\n\n\\begin{figure*}\n\\centering\n\\vspace{0.1cm}\n\\epsfig{file=recchi2.eps,height=12.8cm,width=13.8cm}\n\\caption[]{\\label{fig:fig 2} Yields from massive and intermediate stars \n(data taken from WW and RV yields) together with our fits (eighth degree \npolynomial best-fittings) for the case A. \n$M_{\\rm {ej}}$ is the total \nmass of gas ejected by the star and corresponds to $\\Delta M$ \nas defined in the text.}\n\\end{figure*}\n\n\\begin{figure*}\n\\centering\n\\vspace{0.1cm}\n\\epsfig{file=recchi3.eps,height=12.8cm,width=13.8cm}\n\\caption[]{\\label{fig:fig 3} Yields from massive and intermediate stars \nfor the case B.}\n\\end{figure*}\n\n\\begin{figure*}\n\\centering\n\\vspace{0.1cm}\n\\epsfig{file=recchi4.eps,height=12.8cm,width=13.8cm}\n\\caption[]{\\label{fig:fig 4} Yields from massive and intermediate stars \nfor the case C.}\n\\end{figure*}\n\nIn summary, stars in different mass ranges contribute to galactic \nenrichment in a different way:\n\n\\begin{enumerate}\n\\item For low and intermediate stars (0.8 M$_{\\odot}\\leq M\\leq 8$ \nM$_{\\odot}$) we have used the RV nucleosynthesis calculations for a\nvalue of the mass loss parameter $\\eta=0.33$ (Reimers 1975) and the\nmixing lenght $\\alpha_{\\rm {RV}}=0$ and $\\alpha_{\\rm {RV}}=1.5$. The\ninitial chemical composition is either $Z=0$ or $Z=1/100$ Z$_{\\odot}$.\nThese stars mainly produce He, C, N and s-process elements (not\nconsidered here). In particular, N is a `secondary' element, namely\nproduced from the original C and O present in the star at\nbirth. Therefore, for zero metallicity initial chemical composition no\nN would be produced. However, there is the possibility of producing N\nin a `primary' way, namely starting from the C and O newly formed in\nthe star. This is the case of the IMS which can produce primary N during\nthe third dredge-up episode in conjunction with the hot-bottom\nburning, during the thermal-pulsing phase occurring when these stars\nare on the asymptotic giant branch (AGB) (case $\\alpha_{RV}=1.5$ of\nRV). Moreover, massive stars can also produce primary N, as suggested\nby Matteucci (1986). In the nucleosynthesis prescriptions of WW there\nis some primary N from massive stars but is negligible.\n\n\\item \nFor massive stars ($M>10$ M$_{\\odot}$) we have adopted the case B in\nthe WW nucleosynthesis results, focusing our attention on the models\nwith $Z=0$ and $Z=1/100$ Z$_{\\odot}$. These stars are responsible for the\nproduction of the $\\alpha$-elements (O, Mg and Si) and for part of the\niron. The stars in the mass range 8 M$_{\\odot}\\leq M\\leq\n10$ M$_{\\odot}$ produce mainly He and some C, N and O.\n\n\\item \nFor type Ia SNe we have followed the results of NTY adopting their model\nW7. In this model, every type Ia SN restores into the ISM $\\sim$ 1.4\nM$_{\\odot}$ of gas. Most of this gas is ejected in the\nform of Fe ($\\sim$ 0.6 M$_{\\odot}$) and the rest is in the form of\nelements from C to Si.\n\\end{enumerate}\n\nIn Table 3 we present a brief summary of the nucleosynthesis\nprescriptions adopted in our models. Note that each of these cases can\nbe adopted for the three different hydrodynamical models. Thus, for\ninstance, hereafter with model M1B we intend the hydrodinamical model\nM1 with the chemical option B.\n\n\\par\n\\hbox{}\n\\begin{table}\n\\caption[]{Nucleosynthesis prescriptions}\n\\begin{flushleft}\n\\begin{tabular}{lll}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nCase & $Z$ & $\\alpha_{\\rm {RV}}$ \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\nA & 0 & 0 \\\\\nB & 0 & 1.5 \\\\\nC & 0.01 Z$_{\\odot}$ & 0 \\\\\nD & 0.01 Z$_{\\odot}$ & 1.5\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n$Z$ is the abundance of the unprocessed gas. If $Z=0$, we assume\n$X=0.77$, $Y=0.23$. The solar abundances adopted are taken from \nAnders \\& Grevesse (1989).\n\\end{table} \n\\noindent\n\n\\subsubsection{Energy input}\nThe energy input into the ISM due to the stellar activity is taken\ninto account in eq. (6) through the term $\\epsilon_0=3kT_0/2\\mu$,\nwhere $k$ is the Boltzmann constant. The injection temperature can be\nwritten as:\n\\begin{equation}\nT_0=(\\alpha_*T_*+\\eta_{\\rm II}\\alpha_{\\rm SNII}T_{\\rm II}+\\eta_{\\rm\nIa}\\alpha_{\\rm SNIa}T_{\\rm Ia})/\\alpha,\n\\end{equation}\n\\noindent\nwhere $kT_*$, $kT_{\\rm II}$ and $kT_{\\rm Ia}$ are the energy per unit\nmass in the ejecta of stars, SNeIa and SNeII, respectively (see\ne.g. Loewenstein \\& Mathews 1987 for more details). $\\eta_{\\rm II}$\nand $\\eta_{\\rm Ia}$ represent the efficiency with which the energy of\nthe stellar explosions is transferred into the ISM for SNeII and\nSNeIa, respectively. We assume that 10$^{51}$ erg of mechanical energy\nare produced during the explosion of both types of supernova. However,\nwe assume $\\eta_{\\rm II}=0.03$; only 3 per cent of the energy explosion is\navailable to thermalize the ISM, while the rest is radiated away.\nThis prescription is taken from the work of Bradamante et al. (1998),\nwho studied in detail the chemical evolution of blue compact\ngalaxies. Actually, some debate is present in literature about the\nefficiency of the SNII in heating the ISM in starbursts. We thus run\nalso a model with $\\eta_{\\rm II}=1$ which however is not succesful in\ndescribing IZw18, as discussed at the end of section 3.1.5.\n\nFor the SNIa explosions, instead, we assume\n$\\eta_{\\rm Ia}=1$ because the SNRs expansion occur in a medium already\nheated and diluted by the previous activity of SNII.\n\nIt is worthwhile to note that we neglected the energetic contribution\nof stellar winds from massive stars, according to the results of\nBradamante et al. (1998) who showed that the injected stellar wind\nenergy is negligible relative to the SN energy in this\nkind of galaxies and to the results of Leitherer et al. (1999). This\nis mostly a consequence of the low initial metallicity adopted ($Z=0$ or\n$Z=0.01$ Z$_{\\odot}$), because the mass loss from stars strongly depends\non their metallicity (see e.g. Portinari et al. 1998 and references\ntherein).\n\n\\section{Simulations}\n\n\\subsection{Dynamical results}\n\nOur reference model is M1. In addition, we run two other models, M2\nand M3, which have the same potential well (see Table 2). In model M2\nthe mass $M_{\\rm burst}$ of gas turned into stars is halved in\ncomparison with M1. In this case two competing effects are\nexpected. On one hand, half of the metals are produced and the\nresulting increase in the metallicity of the ISM is expected to be\nlower; on the other hand, the galactic wind luminosity powered by SNe\nis also halved, stellar ejecta are expelled less effectively from the\ngalaxy and the enrichment of the galactic ISM tends to be higher. Two\ncompeting tendencies are also present in model M3 which has nearly one\nfourth of the ISM mass in comparison with M1. In this case the stellar\nejecta mixes with less gas and the metallicity of this gas is thus\nexpected to become higher than in M1, but in this case the wind is\nfavoured and less metals are retained by the galaxy, resulting in a\nlower chemical enrichment. We also show model MC, similar to M1, to\nstudy the action of heat conduction.\n\nIn order to discuss the hydrodynamical behaviour of the gas we recall\nbriefly a few results about bubble expansion in stratified media (Koo\n\\& McKee 1992, and references therein). The freely expanding wind\nproduced by the starburst interacts supersonically with the\nunperturbed ISM thus creating a classical bubble (Weaver et al. 1977)\nstructure in which two shocks are present. The external one propagates\nthrough the ISM giving rise to an expanding cold and dense shell,\nwhile the inner one thermalizes the impinging wind producing the hot,\nrarefied gas of the bubble interior. The shocked starburst wind and\nthe shocked ISM are separated by a contact discontinuity. The density\ngradient of the unperturbed ISM being much steeper along the $z$ axis,\nthe expansion of the outer shell occurs faster along this direction. A\nbubble powered by a constant wind with velocity $V_{\\rm w}$, mass loss\nrate $\\dot M$ and mechanical luminosity $L_{\\rm w}=0.5\\dot MV^2_{\\rm\nw}$ is able to break out from a gaseous disc if $L_{\\rm w}>3L_{\\rm\nb}$, where the critical luminosity is $\\lb=17.9\\rho_0 H_{\\rm\neff}^2C_0^3$. $C_0$ is the sound speed of the unperturbed medium and\n$\\rho_0$ is its central density. $H_{\\rm eff}$ is the effective scale\nlength of the ISM distribution in the vertical ($z$) direction and is\ndefined as:\n\\begin{equation}\nH_{\\rm eff}={1 \\over\\rho_0} \\int_0^{\\infty} \\rho dz.\n\\end{equation}\n\\noindent\nIn our models $H_{\\rm eff}\\sim 300$ pc. If the wind luminosity is\nlarger than $L_{\\rm n}\\sim 0.35 m L_{\\rm b}$, where $m=V_{\\rm w}/C_0$,\nthe wind blows directly out of the planar medium, at least in\ndirections close to the axis. If, instead, $L_{\\rm w} \\simlt L_{\\rm\nn}$ the formation of a jet is possible, in which the wind is shocked\nand then accelerated again to supersonic speeds through a sort of de\nLaval nozzle created by the shocked ambient medium. Kelvin-Helmholtz\ninstabilities tend to distort the nozzle, and stable jets can exist\nonly for $\\beta=C_{\\rm h}/C_{0}\\simlt 30$, where $C_{\\rm h}$ is the\ncavity sound speed (Smith et al. 1983).\n\n\n\\subsubsection {Model M1}\n\nFor model M1 $L_{\\rm b}=2.8\\times 10^{36}$ erg s$^{-1}$. Actually,\n$\\lw$ is not constant in our simulations. However, as a representative\nvalue, for the wind powered by SNeII we have $L_{\\rm w}\\sim 2\\times\n10^{38}$ erg s$^{-1}$ (cf. Fig. 9) and $m\\sim 300$, thus the bubble\ncarved by this wind is able to break out. Note that $\\lw < L_{\\rm\nn}$, so that a jet-like structure is expected. As shown in Fig. 5, a\njet actually propagates with a shock velocity $V_{\\rm s}\\sim 3\\times\n10^6$ cm s$^{-1}$ after 30 Myr. This figure also shows that the\nbubble shell on the simmetry plane has reached the maximum allowed\nvalue (Koo \\& McKee 1992) $R_{\\max}=0.72 H_{\\rm eff}(\\lw /\\lb)^{1/6}\n\\sim 440$ pc.\n\nThe SNII wind lasts a relatively short time (29 Myr), and is then\nreplaced by a weaker SNIa wind with $L_{\\rm w}\\sim 2\\times 10^{37}$\nerg s$^{-1}$ (cf. Fig. 9) and $m\\sim 200$. The existing jet cannot be\nsustained by this wind and is inhibited before breaking out. The\nbubble as a whole stops to grow, and the incoming shocked wind pushes\na large fraction of the hot SNII ejecta against the dense and cold\ncavity walls. Thus most of these ejecta would be located close to the\ncavity edge. The thermal evolution of these ejecta is difficult to\nasses. Given the spread of contact discontinuities due to the\nnumerical diffusion, the ejecta partially mixes with the cold wall of\nthe cavity, so that a large fraction of these metals cools off\n(cf. Fig. 14). Actually, as discussed by DB, several physical\nprocesses, such as thermal conduction and turbulent mixing, produce a\nsimilar effect. In section 3.2 we consider explicitly heat conduction,\nbut neglect the turbulent mixing (Breitschwerdt \\& Kahn 1988, Kahn \\&\nBreitschwerdt 1989, Begelman \\& Fabian 1990, Slavin, Shull \\& Begelman\n1993) which is very complex and nearly impossible (and probably even\nmeaningless out of a fully 3D simulation) to implement into the code.\n\nThe bubble inflated by the SNIa wind is likely to break out through a\nnozzle. We note, however, that the gas distribution in front of the\nbubble along the $z$ direction is modified by the expansion of the\nouter shock generated by the previous SNII activity; although the\npowerful SNII wind is ceased, this shock continues to expand with\nincreasing velocities ($V_{\\rm s}\\sim 10^7$ cm s$^{-1}$ at $t=342$\nMyr) because of the steep gradient of the unperturbed ISM density\nprofile. At these shock velocities, the post-shock gas cools quickly\nand its temperature is $T=10^3$ K (the minimum allowed in our\ncomputations) everywhere with the exception of a `rim' behind the\nshock, where $T\\sim 3\\times 10^5$ K. The density gradient of the\nupwind gas experienced by the SNIa bubble is shallower, and the break\nout is contrasted. This can be seen in Fig. 5, where the hot bubble\nis shown to grow very little up to $t\\sim 300$ Myr.\n\nThe gas in the bubble radiates inefficently because of its low density\n($n\\sim 3\\times 10^{-4}$ cm$^{-3}$) and its temperature is $\\sim\n2\\times 10^6$ K. Shears are present at the contact surface between\nhot and cold gas, which is thus Kelvin-Helmholtz unstable. For this\nreason the cavity is irregularly shaped at this stage.\n\nSubsequently, since the surrounding cold gas is in expansion, the hot\ngas is finally able to break out carving a long tunnel. This tunnel\nhas the de Laval nozzle structure, with the transverse section\nincreasing with $z$. We note the presence of Kelvin-Helmholtz\ninstabilities at the wall of the nozzle. This is due to the fact that\n$\\beta\\sim 30$, so the nozzle is only marginally stable.\n\nThe shocked wind is accelerated again to supersonic speeds through\nthis nozzle (velocities $V\\sim 4\\times 10^7$ cm s$^{-1}$ and mach\nnumbers ${\\cal M}\\sim 8$). When the jet is well developed ($t=342$ Myr\nin Fig. 5b), the minimum radius of the nozzle is $R_{\\rm n}\\sim 100$ pc.\n\nThe acceleration of the cold shell in front of the jet causes it to be\ndisrupted by the Rayleigh-Taylor instabilities, and the hot gas leaks\nout. Contrary to the previous works where the SNIa activity was not\nconsidered, at these late times the central galactic region is not yet\nreplenished by the cold surrounding gas. Taking into account equation\n(18), we stress that this will happen after $\\sim 2$ Gyr, when $\\lw\n=2\\,\\lb$.\n\nIn Fig. 9 we have plotted mass, energy and luminosity budget inside\nthe galaxy. From the central panel of this figure we note that the\nenergy of SNe never becomes larger than the binding energy, although\nsome gas is definitively lost from the galaxy, as it is apparent from\nthe numerical simulation. This indicates that ballistic arguments\ncannot be adopted properly to calculate ejection efficiencies. In fact,\nan element of fluid can acquire energy at the expense of the rest of the gas\nthrough opportune pressure gradients, thus increasing its velocity\nbeyond the escape velocity.\n\nThe thermal energy shows in particular two drops at $t\\sim$ 30 Myr and\nat $t\\sim$ 160 Myr. The second drop reflects a decrease in the hot gas\ncontent, while the first one cannot be associated at any particular\nhot gas loss. In fact this drop coincides with the discontinuity\nSNII/SNIa, when the specific energy injection falls by a factor $\\sim$\n10. Thus the thermal content of the bubble decreases via radiative\ncooling, although its temperature remains larger than $2\\times\\,10^4$\nK, which is the threshold adopted to define hot regions in the upper\npanel of Fig. 9. The fall-off at $t\\sim$ 160 Myr is instead due to the\npresence of large eddies which move part of the hot gas outside the\ngalaxy. We finally point out that at the beginning of the SNII\nactivity the X-ray emission is absent (see lower panel of Fig. 9)\nbecause the energy injection is not able to rise the cavity\ntemperature over $T=7\\times 10^5$ K, which is the threshold adopted to\ndefine the X-ray emitting gas.\n\n\\begin{figure*}\n\\centering\n\\vspace{-6.5cm}\n%\\epsfig{file=recchi5a.eps,height=15cm,width=15cm}\n%\\epsfig{file=recchi5b.eps,height=15cm,width=15cm}\n\\vskip 30cm\n\\vspace{-0.5cm}\n\\caption{Density contours and velocity fields for the model M1 at\ndifferent epochs. The density scale (logarithmic) is given in the\nstrip on top of the figure. In order to avoid confusion, we draw only\nvelocities with values greater than 1/10 of the maximum value. This is\ntrue also for Figg. 6, 7 and 8.}\n\\end{figure*}\n\n\\begin{figure*}\n\\centering\n\\vspace{-7cm}\n%\\epsfig{file=recchi6a.eps,height=15cm,width=15cm}\n%\\epsfig{file=recchi6b.eps,height=15cm,width=15cm}\n\\vskip 30cm\n\\vspace{-1.5cm}\n\\caption{As Fig. 5, but for model M2.}\n\\end{figure*}\n\n\\begin{figure*}\n\\vspace{-5cm}\n\\centering\n%\\epsfig{file=recchi7a.eps,height=15cm,width=15cm}\n%\\epsfig{file=recchi7b.eps,height=15cm,width=15cm}\n\\vskip 30cm\n\\vspace{-3.5cm}\n\\caption{As Fig. 5, but for the model M3.}\n\\end{figure*}\n\n\\begin{figure*}\n\\vspace{-5cm}\n\\centering\n%\\epsfig{file=recchi8a.eps,height=15cm,width=15cm}\n%\\epsfig{file=recchi8b.eps,height=15cm,width=15cm}\n\\vskip 30cm\n\\vspace{-3.5cm}\n\\caption{As Fig. 5, but for the model MC.}\n\\end{figure*}\n\n\\subsubsection {Model M2}\n\nIn this model, $\\lb$ is the same as in M1, but $\\lw$ is a factor of\n0.6 lower. The dynamical evolution is rather similar to that of the\nprevious model. Obviously the bubble is smaller at the end of the SNII\nactivity. Quite surprisingly, however, the nozzle carved by the SNeIa\nbreaks out earlier than in M1. Note that in this case $\\lw / \\lb <\n10$, and the nozzle is stable and well shaped. Actually, this\ncondition is equivalent to the condition $\\beta\\simlt 30$ expressed\nabove (Koo \\& McKee 1992) and, for this model, we find $\\beta\\sim 25$.\nKelvin-Helmholtz instabilities are present, but they are carried away\nby the flow before they can grow significantly. Less energy is\ndissipated by the turbulence and is more easily channelled through the\nnozzle.\n\n\\subsubsection {Model M3}\n\nBecause of the lower ISM density, we have $\\lb = 7.5\\times 10^{35}$ erg\ns$^{-1}$ for this model, so that $\\lw > \\ln$ during the SNII stage. In\nthis case the galactic wind breaks out rather vigorously, and the\nevolution of the gas is similar to that found in other theoretical\nworks (Suchkov et al. 1994, De Young \\& Heckman 1994, MF, DB). A\nprominent lobe is formed, which is similar to that described by Mac\nLow, McCray \\& Norman (1989) in their fig. 2. The shell accelerates\nand becomes Rayleigh-Taylor unstable, expelling the hot interior. The\nbreakup occurs at the polar cap, where the ISM has the lower density\nand pressure. The hot gas which blows out of the bubble produces the\njet-like structure visible in Fig. 7a. Note that the outer shock\ninitially is rather slow ($V_{\\rm s}\\sim 5\\times 10^6$ cm s$^{-1}$),\nand then accelerates somewhat up to $V_{\\rm s}=1.6\\times 10^7$ cm\ns$^{-1}$. Thus, also in this model the shocked gas never reaches high\ntemperatures and most of the lobe volume is cold.\n\nFig. 7b shows the late dynamical evolution of the gas. The gas flow\nexpands along a conical configuration, inside a solid angle which\nremains constant during all the simulation. The ISM outside this\nfunnel remains substantially unperturbed. Actually, the aperture of\nthe cone in our model is evidently dictated by the assumed structure\nof the ISM and could be not realistic. However, given that no falling\nback or fountain is expected by the expelled material which is kept in\nexpansion by the SNeIa, the final chemical characteristics of the gas\ninside the galaxy are not affected by the exact structure of the\n`chimney'.\n\nConcerning the distribution along the $z$ direction, the lobe of\noutflowing gas can be grossly divided in three regions. The most\nexternal, far from the galaxy, is bounded by the outer shock and hosts\nmainly shocked, low-density external medium. The inner region is filled\nwith gas ejected by SNeIa and low-mass stars. Between these two\nregions there is the gas of the `first' bubble (where the ejecta of\nSNII are present), which is quickly cooled to low temperatures. At\n$t\\sim 150$ Myr, the shell of the small bubble breaks, like the first\none, and the hot gas flows forward into the lobe rising its\ntemperature up to 10$^6$ K.\n\nJust before breaking out, the superbubble reaches the edge of the\ngalaxy even along the $R$-axis, pushing out all the unprocessed gas\npresent, and almost all the galaxy is covered by the hot cavity. As\nthe breakout occurs, the bubble shell shrinks slightly and part of it\ncomes back into the galactic region producing the rise of the mass of\nhydrogen and the other elements (cf. Fig. 11). This happens in\ncoincidence with the pressure decrease in the SNIa bubble following\nthe rupture of the unstable shell, as discussed above.\n\n\n\\subsubsection{Model MC}\n\nIn Fig. 8 we show model MC, identical to model M1 but with the heat\nconduction activated. In order to take into account the thermal\nconduction, we solve the heat transport term through the\nCrank-Nicholson method which is unconditionally stable and second\norder accurate (see DB for more details). In this model the cavity is\nless extended than in M1 because of the increased radiative losses due\nto the evaporation front. During the SNII stage the bubble never\nextends beyond $H_{\\rm eff}$. Thus the ``nose'' present in M1 does not\ndevelop, and the bubble has a more round aspect (Fig. 8a). Thermal\nconduction smooths temperature inhomogeneities and the cavity is more\nregularly shaped also at later times (see Fig. 8b). Less energy is\ndissipated through eddies, and the final break out is\nslightly anticipated compared to model M1. The resulting outflow is\nstable and well-shaped. The fraction of cold ejecta does not change\nsubstantially compared to model M1 (see section 3.2 for a discussion\nabout this point).\n\n\n\n\n\\begin{figure}\n\\centering\n\\vspace{-0.2cm}\n\\epsfig{file=recchi9.eps,height=12.4cm,width=8.5cm}\n\\caption[]{\\label{fig:fig 9} Energy, luminosity and mass budget inside\nthe galaxy for model M1. Hot regions are defined as the regions where\n$T>2\\times 10^4 K$. $L_X$ indicates the emission from gas with\n$T>7\\times 10^5 K$ (emission in the X-ray band), while $L_{\\rm tot}$\nis the total emission.}\n\\end{figure}\n\n\n\\subsubsection{ISM ejection efficiencies}\n\nIt is useful to define the efficiency of gas removal from the galaxy.\nThis efficiency cannot be unambigously defined as in the case of\nballistic motions because of dissipative effects which may play a very\nimportant role (DB). For this reason we simply define the efficiency\n$f_{\\rm ISM}$ by dividing the mass of the gas which has left the\ngalaxy by the total mass of the ISM. In a similar way we calculate the\nefficiency in the ejection of material from SNII ($f_{\\rm {SNII}}$),\nintermediate-mass stars ($f_{\\rm {IMS}}$) and SNIa ($f_{\\rm {SNIa}}$).\n\nThe upper panels of Fig. 11 shows the masses of the different elements\nremoved from the galaxy as functions of time. The relative proportions\nbetween masses of different elements is essentially that expected by a\nSalpeter IMF and is not substantially affected by selective dynamical\nlosses. For the model M1B, we point out that the mass of metals lost\nfrom the galaxy declines after reaching a maximum at $t\\sim$ 200\nMyr. This maximum is mirrored by a minimum in the masses of metals\ninside the galaxy. This behaviour is due to the fact that, at this\ntime, the large hot blob visible in Fig. 5b (second panel) extends\nover the galactic edge ($R$ direction) thus inducing a large loss of\nISM (mostly H and He). We calculate the efficiency at $t\\sim$ 200 Myr\nand at the end of the simulation ($t\\sim$ 375 Myr), obtaining $(f_{\\rm\nISM},f_{\\rm SNII},f_{\\rm SNIa},f_{\\rm IMS})$=(0.43,0.38,0.25,0.38) and\n$(f_{\\rm ISM},f_{\\rm SNII},f_{\\rm SNIa},f_{\\rm\nIMS})$=(0.07,0.17,0.20,0.26), respectively. Thus, at $t\\sim$ 200 Myr\nthe products of the SNII and IMS have been ejected more easily than\nthe products of SNeIa. This is of course due to the fact that SNIa\nmaterial is located in a region closer to the galactic centre. After\nthe break up all the efficiencies decrease, and in particular $f_{\\rm\nSNII}$ shows the greatest reduction. In fact, the SNII ejecta inside\nthe galaxy are `incorporated' into the cold, dense shell of the cavity\nand do not experience any substantial further dynamical evolution (see\ndiscussion in section 3.1.1 and Fig. 5b); at the break out the bubble\nshrinks and its walls recede entirely in the galaxy, increasing its\ncontent of SNII ejecta. Contrary to the expectations, the higher\nefficiency is given by $f_{\\rm IMS}$ instead of $f_{\\rm SNIa}$. This\nis due to strongly unsteady behaviours of the nozzle wall.\n\nIn model M2, where a nearly steady flow is obtained, we actually have\n$f_{\\rm SNII}<f_{\\rm IMS}<f_{\\rm SNIa}$. At $t\\sim$ 300 Myr it is\n$(f_{\\rm ISM},f_{\\rm SNII},f_{\\rm SNIa},f_{\\rm IMS})$\n=(0,0.06,0.32,0.12) in this model. For this model the difference in\nefficiencies between the total gas and metals is particulary striking\nand indicates that the differential galactic wind assumption, adopted\nin several one-zone chemical models, is a natural outcome in this\nscenario. In particular we note that at late times the galaxy is\nalmost completely replenished by gas. In fact, as apparent in Fig. 6b,\nthe nozzle has a rather small section ($R_{\\rm n}\\sim 85$ pc) and the\nvolume of the cavity is negligible in comparison with the galactic\nvolume. The more regular hydrodynamical behaviour reflects also in the\nmore regular temporal trend of the ejected masses. Note that, as\nexpected, in M2 the galactic wind starts later in comparison with M1.\n\nModel M3 predicts of course the maximum amount of metals lost and is\nalso the first in which the break out occurs. The striking minimum in\nthe metal contents of the galaxy occurring at $t\\sim$ 130 Myr is due\nto the dynamical behaviour of the buble shell, as discussed above. \nThe efficiencies for the model M3 at the end of the simulation ($t\\sim$ \n470 Myr) are $(f_{\\rm ISM},f_{\\rm SNII},f_{\\rm SNIa},f_{\\rm IMS})$\n=(0.77,0.85,0.97,0.87).\n\nFinally, we mention that, as outlined in section\n2.3.2, we run a model (not shown here) similar to M1, but with\n$\\eta_{\\rm II}=1$. At the end of the SNII stage, the galaxy is almost\ndevoided of gas (a part for the tenuous galactic wind). The time-scale\nfor the galactic replenishment (the SNIa wind cannot preserve an empty\nregion so large) is at least $R_{\\rm t*}/C_0 \\sim$ 200 Myr. Actually,\ndue to the retarding effect of the centrifugal force, in our\nsimulation most of the galaxy is replenished after $\\sim$ 450 Myr. The\nage of the (last) burst occurred in IZw18 is estimated to be $\\simlt$\n27 Myr (see below), thus its actual content of gas rules out the\npossibility of an high $\\eta_{\\rm II}$. Note that our assumption that\nall energy injection occurs in the central region leads to the most\neffective gas removal for a given luminosity (Strickland \\& Stevens\n1999). Models with a more realistic burst diffuse across the galaxy\nwill be presented in a next paper.\n\n\\subsection{Instantaneous versus delayed mixing}\n\nIn the previous models a large fraction of the stellar ejecta cools\nquite soon and a rapid mixing is expected given the relatively short\ndiffusion time at these temperatures (for a comparison of the\ndiffusion times in the different ISM phases, see for example\nTenorio-Tagle 1996). This is an important point in view of the confrontation of\nthe results of our models with the $observable$ abundances of IZw18\n(cf. section 4.2), and deserves some discussion.\n\nRieschick\n\\& Hensler (2000), for instance, presented a chemodynamical model of\nthe ISM of a dwarf galaxy in which the metal enrichment undergoes a\ncycle lasting almost 1 Gyr. This model is based on the scenario\ndescribed in Tenorio-Tagle (1996). In this scenario the break out is\ninhibited and the SNII ejecta (SNeIa are not considered), mixed with\nhot evaporated ISM, are located inside a large cavity which extends\nabove (and below) the galactic disc. Typical parameters of this cavity\nare the linear size $d>1$ kpc, the density $n_{\\rm c}=10^{-2}$\ncm$^{-3}$ and the temperature $T_{\\rm c}=10^6$ K. After the last SN\nexplosion, strong radiative losses occur. However, given the density\nand temperature fluctuations in the hot medium, cooling acts in a\ndifferential way. This leads to condensation of the metal-rich gas\ninto small molecular droplets ($R_{\\rm c}\\sim 0.1$ pc, $M_{\\rm c}\\sim\n1$ $M_{\\odot}$) able to fall back and settle on to the\ndisc of the galaxy. With the next exploding stellar generation, the\ndroplets are dissociated and disrupted, and their gas is eventually\nmixed in the HII regions.\n\n\n\n\nHere we point out some $caveat$ concerning this scenario which\nshould be taken into account.\n\\par\\noindent\n\\smallskip\n\n{\\it Thermal conduction} - Thermal conduction, if not impeded by\nmagnetic fields and/or plasma instabilities, introduce, together with\nradiative losses, the characteristic Field length\n(Begelman \\& McKee 1990, Lin \\& Murray 2000)\n\n$$\n\\lambda_{\\rm F}=\\left ({3\\kappa(T)T \\over n^2\\beta \n\\zeta \\Lambda(T)}\\right )^{1/2}\n$$ \n\\noindent \nwhere $\\kappa(T)=6\\times 10^{-7}T^{2.5}$ erg cm$^{-1}$ K$^{-1}$ is the\nclassical thermal conductivity (Spitzer 1956) and $n$ the gas\ndensity. The cooling rate scales linearly with the metal content\n$\\zeta$ of the gas ($\\zeta=1$ for solar abundance). The parameter\n$\\beta$ takes into account the possibility that the cooling gas may be\nout of ionization equilibrium; Borkowski, Balbus \\& Fristrom (1990)\nhave shown that $\\beta$ may be as high as 10 through conductive\nfronts.\n \nClouds undergo evaporation unmodified by radiative losses if they are\nsufficiently small, $R_{\\rm c}<\\lambda_{\\rm F}$. Assuming $T_{\\rm\nc}=10^6$ K and $n_{\\rm c} =10^{-2}$ cm$^{-3}$, Tenorio-Tagle obtains\n$R_{\\rm c}< 10$ pc for the radius of the overdense zones at the\nbeginning of their implosion. Adopting $\\beta=\\zeta=1$ and\n$\\Lambda=1.6\\times 10^{-18}T^{-0.7}$ ergs cm$^3$ s$^{-1}$ for $10^5$ K\n$\\leq T \\leq$ 10$^{7.5}$ K (Mac Low \\& McCray 1988), we obtain\n$\\lambda_{\\rm F}\\sim$ 138 pc. Even assuming $\\beta=10$, $\\lambda_{\\rm\nF}\\sim 44$ pc remains larger than $R_{\\rm c}$. Thus the rate of\nconductive heat input exceeds that of the radiative losses and the cloud\ncollapse is inhibited. This result derives from the general property\nof the evaporation to stabilize thermal instabilities (Begelman \\&\nMcKee 1990). Actually, Tenorio-Tagle obtained $R_{\\rm c}\\sim 10$ pc as\na $lower$ limit for the radius value of clouds able to implode. As a\nconsequence, perturbations with a size larger than $\\lambda_{\\rm F}$\ncan actually grow. A non negligible fraction of gas mass would\ncondense only for a rather flat size spectrum of the fluctuations.\n\nWe point out that, even if droplets actually form, they evaporate in a\ntime $\\tau_{\\rm e}=M_{\\rm c}/\\dot M$. Droplets have rather small final\nradii of order 0.1 pc (Tenorio-Tagle 1996). In this case they undergo\nthe satured evaporation $\\dot M=1.22\\times 10^{-14}T^{2.5}R_{\\rm\nc}\\sigma^{-5/8}$ g s$^{-1}$, where $\\sigma=3\\times\n10^{18}(T/1.54\\times 10^7)^2/(nR_{\\rm c})$ is the saturation parameter\n(Cowie, McKee \\& Ostriker 1981). For $M_{\\rm c}\\sim 1$ $M_{\\odot}$ we\nhave $\\tau_{\\rm e}\\sim 40$ Myr, comparable to the dynamical time\n$\\tau_{\\rm d}$ (see below). Thus all the droplet material, or at\nleast a large fraction of it, returns into the hot phase before\nreaching the galactic plane. \\par\\noindent\n\\smallskip\n\n{\\it Drag disruption} - Suppose that thermal conduction is impeded and\nthat droplets with final $R_{\\rm c}\\sim 0.1$ pc actually form and fall\ntoward the galactic plane. During their descent the droplets\nexperience a drag reaching a terminal speed $V_{\\rm t} \\sim (\\chi\nR_{\\rm c} /d)^{0.5}V_{\\rm c}$, where $\\chi=10^5$ is the ratio of the\ndroplet density to the hot gas density, $d\\sim 1$ kpc is the droplet\ndistance to the galactic plane, and $V_{\\rm c}$ is the circular\nvelocity of the halo potential. The motion of the droplet relative to\nthe hot gas leads to mass loss through Kelvin-Helmholtz\ninstability. For wavelengths $\\lambda \\sim R_{\\rm c}$ the stripping\ntime-scale is $\\tau_{\\rm s}\\sim R_{\\rm c} \\chi^{0.5}/V_{\\rm\nt}=\\tau_{\\rm d}(R_{\\rm c}/d)^{0.5}$ (cf. Lin \\& Murray 2000), where\n$\\tau_{\\rm d}=d/V_{\\rm c}$ is the dynamical time. The droplets are\nthus disintegrated before they settle to the galactic plane, returning\nto the hot diluted phase. Larger droplets may not be able to attain\ntheir terminal velocity, but even in this case we have $\\tau_{\\rm\ns}/\\tau_{\\rm d}\\sim \\chi ^{0.5}R_{\\rm c}/d<1$.\n\nAs an aside, we note that, if\na large fraction of the hot gas becomes locked into droplets, the\npressure of the remaining diluted phase reduces and the cavity\nshrinks. Whether the bubble deflates slowly or suddenly and producing\nturbulence depends on the droplet formation efficiency. Thus,\nthe scenario depicted by Tenorio-Tagle of a nearly steady hot cavity\nwith size of $> 1$ kpc waiting for the onset of radiative cooling\ncould be incorrect. Part of the droplets could be overrun by the edge of\nthe imploding bubble, undergoing an even faster stripping.\n\n\\par\\noindent \n\\smallskip\n%{\\it Ram pressure effect} - Recently Murakami \\& Babul (1999) carried\n%out 2D hydrodynamical simulations in order to study the interaction\n%between SN powered galactic wind and the local intergalactic medium\n%(IGM) in the case of low-mass galaxies. The IGM pressure can bring the\n%bubble shell blown by the wind to a halt before it escapes the galaxy\n%(as assumed by Tenorio-Tagle). However the galaxy moves relatively to\n%the IGM, and its ISM is also subject to ram pressure. Murakami \\&\n%Babul find that the bubble is eventually dragged out of the halo and\n%carried downstream even in the case of relatively low velocities\n%characteristic of poor clusters and galaxy groups.\n%\n%In contrast, the relatively unhindered outflows in low-density,\n%low-temperature environments can drive the shell of swept-up gas\n%out to distances of 40 kpc. These results are obtained assuming\n%a spherical symmetry for the galaxy and its initial gas content.\n%Differences must of course be expected in the case of a two-lobes\n%morphology of the cavity deriving from the assumption of an\n%initially plane stratified ISM.\n\nLet us consider now the results shown in the present paper. Contrary\nto the scenario sketched above, the ejecta cool rapidly without\nleaving the galaxy (until the break-out, which occurs at late times)\nand without undertaking a long journey before mixing with the ISM. How\nmuch these results are reliable? Mac Low \\& McCray (1988) showed that\na conductive bubble expanding in an uniform medium becomes radiative\n(i.e. radiates an energy comparable to the thermal energy content of\nthe shocked wind) after a time:\n$$t_{\\rm R}\\sim 16(\\beta \\zeta)^{-35/22}L_{38}^{3/11}n^{-8/11}\\; {\\rm Myr,}$$\n\\noindent\nwhen the cavity radius is:\n$$R_{\\rm R}\\sim 350(\\beta \\zeta)^{-27/22}L_{38}^{4/11}n^{-7/11}\\; {\\rm\npc.}$$ \n\\noindent\nFor $t>t_{\\rm R}$ the bubble goes out of the energy conserving\nregime, although a fully momentum conserving regime is never\nattained. Considering model M1, we assume $\\beta=\\zeta=1$, $L_{38}=2$\nand $n=1.8$ cm$^{-3}$, and we obtain $t_{\\rm R}=12.6$ Myr and $R_{\\rm\nR}=310$ pc. Thus, in the case of an uniform unperturbed medium the\nbubble interior would cool quite early, when it is still well inside\nthe galaxy.\n\nMac Low \\& McCray also considered the expansion in a stratified medium.\nEquating the radius of a spherical bubble to approximatively one scale height\n$H$ they define the dynamical time\n$$t_{\\rm D}\\sim H^{5/3}(\\rho/L_{\\rm w})^{1/3}.$$\n\\noindent\nThen the ratio of cooling to dynamical time-scales is:\n\\begin{equation}\n{t_{\\rm R}\\over t_{\\rm D}}=8.22n^{-35/33}L_{38}^{20/33}\n\\left ({H\\over 100 {\\rm pc}}\\right )^{-5/3}(\\beta \\zeta)^{-35/22},\n\\end{equation}\n\\noindent\n(note that the numerical coefficient in this expression slightly\ndiffers from that obtained by Mac Low \\& McCray). For model M1 we\nobtain $t_{\\rm R}/ t_{\\rm D}\\sim 1.08$ during the SNII stage. Thus a\nnon negligible fraction of the wind luminosity is radiated away (see\nalso Fig. 9), and the break out does not occur. For M3, where $n\\sim\n0.5$, we have $t_{\\rm R}/ t_{\\rm D}\\sim 4.2$, and the situation, in\nprinciple, is less clear-cut (see, however, below in this section).\n\nAlthough models M1, M2, M3 do not take explicitly into account heat\nconduction, yet they obtain results according to the above\nscenario. In fact, as pointed out in section 3.1.1, numerical\ndiffusion simulates thermal conduction originating spurious radiative\nlosses which otherwise would be absent. Of course, this spurious\ncooling does not reproduce $quantitatively$ the same amount of\nradiation lost through a real heat conduction front, and the fraction\nof cold ejecta obtained in our models could be larger than the correct\none. Some algorithms may be conveniently adopted to reduce this\neffect. Consistent advection (Stone \\& Norman 1992) is implemented in\nour code and helps in reducing somewhat the diffusion, making it\nconsistent for the all advecteded quantities (mass, momentum,\nenergy). We also made tests modifing the cooling algorithm in presence\nof unresolved contacts, following Stone \\& Norman (1993). Although the\nfraction of cold ejecta reduces of 15 per cent, most of the metals ($\\sim$\n80 per cent) remains cold. We point out, however, that in presence of an\nunresolved conduction front, the above algorithm may lead to an\nexcessive reduction of the radiative losses (see below).\n\nIn any case the intrinsic diffusion of the code may be alleviated but\nnot eliminated by algorithms as those described. In principle, more\nrealistic models can be done explicitly adding the physical terms\nwhich produce diffusion. For this reason we also ran model MC, where\nthe heat transfer is included. In this model the amount of cold metals\ndoes not change appreciably. However, although model MC is useful to\nunderstand the stabilizing effect of heat conduction on a turbulent\nflow, it turns out to be inadequate to obtain the correct cooling rate\nat the conduction front. Consider the temperature profile of a\n``standard\" bubble $T_{\\rm b}(1-r/r_{\\rm b})^{2/5}$ (Weaver et al. \n1977), where $T_{\\rm b}=10^6$ K is the central temperature, and\n$r_{\\rm b}=300$ pc is the bubble radius (cf Fig. 7). The cooling curve\nmaximum occurs at $T\\sim 2\\times 10^5$ K. This temperature is found at\n$r/r_{\\rm b}=0.98$, i.e. at a distance of 6 pc to the cold shell. At a\ndistance of 300 pc the mesh size is $\\sim 15$ pc, and the conduction\nfront is not resolved properly. Thus, we also ran models MCH and MCHH\n(not shown here) with heat conduction and with an uniform grid with\nmesh size of 2 and 1 pc respectively. These models were computed only\nup to the end of the SNII activity because of the large number of grid\npoints involved.\n\nThe four panels in Fig. 10 show the profiles along the galactic plane\n($z=0$) of several quantities for models M1, MC, MCH and MCHH at\nnearly 30 Myr. As expected, the resolution of the temperature profile\nis not improved in MC and the temperature jump remains unresolved. In\nMCH, instead, this jump extends over 2-3 meshes and in MCHH over 4-5,\nas expected. The fraction of cold ejecta is 0.95, 0.95, 0.93, 0.92 for\nM1, MC, MCH, MCHH respectively. Although the greater accuracy, the\nfraction of cold ejecta in MCH and MCHH is only few percent lower than\nin M1. This occurs because the bubble is ``genuinely'' radiative, and\nan high spatial resolution may retard a little the cooling, but cannot\navoid it.\n\nWe stress once more (cf. section 3.1.1) that it is very difficult to\ngive the correct description of the contact discontinuity at the outer\nedge of the hot cavity, for the presence of complex hydrodynamical\nphenomena occurring there. These phenomena tend to produce a finite\nthickness of the contact, giving rise to a substantial cooling\notherwise absent. The correct evaluation of such a cooling is however\nvery difficult to assess. Even restricting ourselves on the simple\ncase of heat conduction, the possible lack of ionizing equilibrium and\nthe numerical diffusion both increase radiative losses. The first\neffect is physical and could be described solving step by step the\ntime dependent set of ionization equation. The second is a spurious\nresult due to numerical diffusion of the code which must be reduced as\nmuch as possible. We believe that our convergence test (cf. fig. 10),\nas well other 1D tests not shown here, indicates that our results are\nsignificative. We are aware of the fact that more refined simulations\nmay produce somewhat different values of the cooled mass of the\nejecta, but we think that the large fraction of resulting cooled\nejecta is a genuine result.\n\n\\begin{figure*}\n\\centering\n\\vspace{-0.2cm}\n\\epsfig{file=recchi10.eps,height=18.5cm,width=18.5cm}\n\\caption[]{\\label{fig:fig 10} Density (heavy solid lines), ejecta\n(dashed lines) and temperature (light solid lines) profiles for models\nM1 (first panel starting from top), MC (second panel), MCH (third\npanel) and MCHH (bottom panel) near the conduction front, along the\n$R$ direction, after $\\sim$ 30 Myr. The diamonds superimposed to the\ntemperature profiles, indicate the mesh points of the grid for each\nnumerical simulation. }\n\\end{figure*}\n\n\n\nAs pointed out above, equation (21) gives an ambiguous prevision about\nthe behaviour of M3. We therefore ran also this model on a uniform\ngrid with 2 pc resolution (up to $t=30$ Myr) adding heat\nconduction. The overall dynamics of the superbubble remains the same,\nand the fraction of cold ejecta turns out to be 6 per cent lower than\nin the low resolution model. We thus conclude that the results\nobtained by our models are reliable.\n\nAt the end of this section we mention the effects expected in the case\nof a non-uniform initial ISM. Actually, gas clouds are embedded in the\npervasive diffuse gas of the galaxy. However, a correct numerical\ntreatment of the interaction between these clouds and the ambient gas\nintroduces enormous complications in the description of the involved\nphysics and needs full 3D computations with an huge number of\nmeshes. We here just make some simple considerations following McKee,\nVan Buren \\& Lazareff (1984). These authors describe the behaviour of\na bubble generated by an O star and expanding in a cloudy\nmedium. Because of the flux of ionizing photons emitted by the star,\nthe nearby clouds undergo photoevaporation and accelerate away through\nthe rocket effect. Essentially no cloud survives up to a radius\n$R_{\\rm h}$, and the gas density inside this radius increases to a\nvalue 0.5$n_{\\rm m}$, i.e. half of the mean density the cloud gas\nwould have if it were homogenized. The wind bubble evolution depends\non the value of $L_*=L_{\\rm w}/L_{\\rm St}$, where $L_{\\rm\nSt}=1.26\\times 10^{36}(S_{49}^2/n_{\\rm m})^{1/3}$ and $S_{49}$ is the\nrate at which the star emits ionizing photons in units of 10$^{49}$\ns$^{-1}$. For weak winds ($L_*\\ll 1$) the bubble radius is smaller\nthan $R_{\\rm h}$ and it evolves ``normally'' (Weaver et al.\n1977). For moderate winds ($L_*\\sim 1$) the bubble expands to the edge\nof the cloud distribution because photo-evaporated gas induces\nradiative losses reducing the pressure. Finally, for $L_*\\gg 1$ the\nbubble rapidly engulfs a number of clouds and radiates away most of\nits internal energy. This scenario cannot be directly applied to a\nstar burst as a whole. In fact clouds are also present inside the star\nformation region, partially screening the flux of ionizing photons\nescaping from this region. However, even assuming that this effect is\nnegligible, in our model $L_*\\sim 3$. We in fact computed $S_{\\rm 49}$\nrunning remotly at the site www.stsci.edu/science/starburst99\n(Leitherer et al. 1999) a burst model tailored on that assumed here. \nThe number of UV photons produced by massive stars remains nearly constant\n($S_{49}=584$ s$^{-1}$) up to 5 Myr, and then drops as $t^{-4}$. For\n$n_{\\rm m}=1.8$ cm$^{-3}$ close to the galactic disc, we have $L_{\\rm\nSt}=7\\times 10^{37}$ erg s$^{-1}$, lower than $L_{\\rm w}$. Of\ncourse, along the $z$ direction $R_{\\rm h}$ could move much further,\nbut the ionizing flux starts to decline rather soon, and the cloud\ndistribution remains nearly unaffected. Thus the bubble is expected to\nbecome radiative sooner than in the case of a smoothly distributed ISM.\n\nIn conclusion, in the scenario of our models, most of the metals\nactually cools off in a few Myr. It is worth noting that this result\ndepends essentially on the assumption of a low heating efficiency of\nSNIIs. In the model similar to M1, but with $\\eta_{\\rm II}=1$\n(sect. 2.3.2), the break out quickly occurs and the metals have no\ntime to cool. In fact, following Eq. (21), in this case the bubble results to\nbe adiabatic and not radiative. Thus the SN efficiency value is\ncrucial, and a future paper will be devoted to it (D'Ercole \\&\nMelioli, in preparation).\n\n\n\\subsection{Chemical results}\n\nIn Fig. 10 is shown the evolution of the element abundances for the\nmodels M1B, M2B and M3B. In this figure, the evolution of the masses\nand the abundances in the form of the various elements is shown. It\nis interesting to note that the mass of the lost metals for the model\nM3B is larger than that retained from the galaxy, whereas it is the\ncontrary for models M1B and M2B. This means that the initial\nconditions, namely the assumed burst luminosity and gas mass in the\ngalaxy, are playing a very crucial role in the development and\nevolution of the galactic wind. The abundances are calculated as [Z/H]\n, where $Z$ indicates the abundance of the following elements, O, C, N,\nMg, Si and Fe, relative to the solar abundances of Anders \\& Grevesse\n(1989), and as 12+log(Z/H), which is the notation normally used for\nthe abundances in extragalactic H\\,{\\sc ii} regions. These abundances are\nderived in the following way: for the galactic abundances we have\naveraged in the previously defined galactic region (approximatively an\nellipsoid with major semi-axis of 1 Kpc and minor semi-axis of 730\npc), whereas for the abundances leaving the galaxy the integral is\nmade over the rest of the grid.\n\nThe $\\alpha$-elements show a very similar evolution and this is due\nmostly to their common origin. The $\\alpha$-elements are, in fact,\nmainly produced by massive stars (see Figg. 2--4), and thus their\nabundances inside the galaxy grow in the first 6-7 Myr -- the time\ninterval where most of massive stars die -- then show a slowly\ndecreasing trend, with however a little maximum around 100 Myr. This\nbehaviour is related to the dynamics of gas flows described before.\n\nThe evolution of iron is not too different with respect to the\nevolution of the $\\alpha$-elements although this element is\nsubstantially produced by SNeIa. This is due to the fact that at the\nend of our simulations the iron produced by SNIa is only $\\sim$\n30 per cent of the total, because the bulk of SNeIa appears at later\ntimes. The evolution of N shows a sharp increase at around 29 Myr\nwhich corresponds to the lifetime of a 8 M$_{ \\odot}$ star, which is\nthe first star producing a substantial amount of N (of primary\norigin). For times less than 29 Myr the N production is negligible.\n\n\\begin{figure*}\n\\centering\n\\epsfig{file=recchi11.eps,height=18cm, width=18cm}\n\\caption[]{ Time evolution of several quantities for the models M1B,\nM2B and M3B (first, second and third column, respectively). \nThe upper pannels show the evolution of the mass of\nvarious elements outside the galaxy, while the masses inside the galaxy are \nshown by the second raw of pannels. The third and the last raws of panels \nillustrate the behaviour of the ISM abundances (relative to the sun and \nby number, respectively).} \n\\end{figure*} \n\n\\section{Discussion}\n\nWe want to compare now our models with observational data \nfound in literature for the galaxy IZw18.\n\\subsection{Morphology and dynamics}\n\n\\par\n\\hbox{}\n\\begin{table*}\n\\begin{flushleft}\n\\caption[]{Predicted abundances in the galactic region after 31 Myr\nfor models M1, M2, M3. We also show the results for model MC (with \nnucleosynthetic prescriptions B), in order to emphasize the\nsimilarities with model M1B. Only models M1 and MC should be compared with\nIZw18. These values are compared with some abundances found in\nliterature for IZw18.}\n\\begin{tabular}{cccc|c}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n12+log(O/H) \\hspace{0.6cm}& \nlog C/O & \nlog N/O & \n\\hspace{0.5cm} log Si/O \\hspace{0.5cm} & \nFonts \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n$7.12$ & $-0.47$ & $-5.24$ & $-1.40$ & M1A\\\\\n\\underline{$7.12$} & \\underline{$-0.58$} & \\underline{$-1.52$} & \n\\underline{$-1.40$} & \\underline{M1B}\\\\\n$7.51$ & $-0.57$ & $-1.46$ & $-1.29$ & M1C\\\\\n$7.51$ & $-0.63$ & $-1.33$ & $-1.29$ & M1D\\\\\n$6.90$ & $-0.49$ & $-5.02$ & $-1.40$ & M2A\\\\\n$6.90$ & $-0.58$ & $-1.61$ & $-1.40$ & M2B\\\\ \n$7.36$ & $-0.54$ & $-1.31$ & $-1.30$ & M2C\\\\\n$7.36$ & $-0.58$ & $-1.24$ & $-1.30$ & M2D\\\\\n$7.67$ & $-0.49$ & $-5.22$ & $-1.38$ & M3A\\\\\n$7.67$ & $-0.59$ & $-1.60$ & $-1.38$ & M3B\\\\\n$7.97$ & $-0.64$ & $-1.90$ & $-1.26$ & M3C\\\\\n$7.97$ & $-0.71$ & $-1.61$ & $-1.26$ & M3D\\\\\n$7.12$ & $-0.58$ & $-1.49$ & $-1.39$ & MC\\\\\n\\noalign{\\bigskip}\n$7.24$ & $-0.54$ & $-1.54$ & - & DH\\\\\n$7.17/7.26$ & - & $-1.54/-1.60$ & - & SK\\\\\n$7.17/7.26$ & $-0.63/-0.56$ & $-1.56/-1.60$ & - & G97\\\\\n- & - & - & $-1.52$ & G95\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\nReferences: DH: Dufour \\& Hester (1990); SK: Skillman \\& Kennicut (1993); \nG97: Garnett et al. (1997); G95: Garnett et al. (1995).\n\\end{flushleft}\n\\end{table*} \n\nTo compare our dynamical results we should first summarize the\nstructural and dynamical properties of IZw18. IZw18 has a\n`peanut-shaped' main body, consisting of two starbursting regions\n(Dufour et al. 1996). There are also two H\\,{\\sc ii} regions (also\ncalled NW and SE), associated with the main body, but shifted $\\sim$ 1\narcsec east of the brightest continuum emission (Martin 1996). The\nH$\\alpha$ emission is bipolar-shaped along a direction orthogonal to\nthe main body, and show clear evidences of shell structures. In fact a\nprominent shell stretches 15 arcsec (720 pc) north-northeast from the\nnorthwest H\\,{\\sc ii} region and bright H$\\alpha$ emission extends\nsymmetrically south-southwest from the NW region (Martin\n1996). Moreover a partial shell of 3.6 arcsec of diameter (173 pc)\nprotrudes from the north-west side. The H\\,{\\sc i} velocity field (Van\nZee et al. 1998; Viallefond et al. 1987) shows a significant velocity\ngradient along minor axis, suggesting a flow in this direction (Meurer\n1991).\n\nWe first note that the distance of 720 pc between the shells and the\nNW H\\,{\\sc ii} region is quite compatible with models M1, M2, M3 (in\nthese models, after 31 Myr, the bubble has covered a distance of\n$\\sim$ 600--800 pc along the $z$-axis). Martin, starting from\ngeometrical considerations, found a shell speed of 35--60 Km s$^{-1}$,\nand in our model M1, after 31 Myr, the velocity of the outer shock\nalong the $z$-axis is approximatively 30 Km s$^{-1}$, in agreement\nwith the observations. We note instead that the model MC does not\ndevelop an outflow along the $z$ direction (see Fig. 8a), and this is\ndue to the fact that the bubble never extends beyond $H_{\\rm eff}$, as\nexplained in section 3.1.4. Actually, the uncertainties on the real\nvalue of $H_{\\rm eff}$ in IZw18 are significant and a small reduction\nof $H_{\\rm eff}$ could lead to the formation of an outflow also for\nmodel MC.\n\nThese comparisons between observation and theory depend strongly on\nthe adopted distance of IZw18. In a recent work, Izotov et al. (1999)\nfound that the distance of IZw18 should be at least 20 Mpc, twice the\ndistance generally adopted for this galaxy. With this new distance,\nColor-Magnitude Diagram (CMD) studies give an age, derived from the\nmain sequence turn-off, of 5 Myr for the main body. They suppose that\nthe star formation in the main body has started $\\sim$ 20 Myr ago in\nthe NW edge, propagating then toward the SE direction and then\ntriggering the main starburst $\\sim$ 5 Myr ago. This estimate is also\nconsistent with the stellar population analysis of Hunter \\& Thronson\n(1995).\n\nHere we have assumed a coeval stellar population, so we cannot\ncorrectly verify the hypothesis of Izotov et al., but in our models a\nslightly pre-enriched burst with an age of 5 Myr cannot account for\nthe observed abundances and the nearly flat metallicity gradient\nobserved in IZw18 (see next section). Moreover, with the new\nestimated distance the above-mentioned shell structures double their\ndimensions and it is hard to reproduce these morphological features\nwith a burst 5 Myr old.\n\n\\subsection{Chemical abundances}\n\nIn Table 4 the abundance ratios log(C/O), log(N/O), log(Si/O) as well\nas 12+log(O/H) predicted by our models are reported. At the beginning\nof section 3 we described several factors which affect the metal\ncontent of the ISM. From an inspection of Fig. 11 and Table 4 we\nconclude that a reduction in the burst luminosity produces a reduction\nin the total abundances, while a decrease in the ISM mass leads to an\nincrease of the metallicity.\n\nIn Table 4 the observed abundances of IZw18 are also\nreported. However, only the model M1 (cases A,B,C,D) should be\ncompared with IZw18, since the total mass and the gas mass of this\nmodel have been chosen to match this galaxy. Before to continue the\ndiscussion on our results, we point out that the abundances shown in\nTable 4 refer to the whole gas into the galaxy, while the comparison\nwith the data should be valid only for the cold ($T<2\\times 10^4$ K)\nphase. In fact, chemical composition of stellar winds and supernovae\nejecta are mainly measured through the relative intensities of visual\n[O\\,{\\sc ii}], [O\\,{\\sc iii}], [S\\,{\\sc ii}] and [N\\,{\\sc ii}]\nforbidden lines compared to H and He recombination lines, but this\napproach is sensitive only to emission from warm, photo- or\nshock-ionized gas at $\\sim$ 10000 K (Kobulnicky \\& Skillman 1997).\n\nHowever, although the metal abundances in the hot regions are quite\nlarge, reaching also extrasolar values (cf. Fig. 14), in our models\nthe majority of the metals is in the cold gas phase. Thus the\nabundances in Table 4 are essentially the same as those in the cold\ngas, and their comparison with the observed metallicities is\nmeaningfull. Note that, in making such a comparison, we suggest that\nthe present time burst in IZw18 can be responsible of the observed\nchemical enrichment in the H\\,{\\sc ii} regions. This is in agreement\nwith the arguments illustrated in section 3.2, and at variance with\nprevious suggestions of different authors (see e.g. Larsen et\nal. 2000). Recent observations (Pettini \\& Lipman 1995; Van Zee et\nal. 1998), although uncertain, indicate an oxygen abundance in the\nH\\,{\\sc i} regions of IZw18 comparable with that in the H\\,{\\sc ii}\nregions, in agreement with our predictions.\n\n\nTable 4 reports the abundances of our models after 31 Myr. The\nlifetime of a 8 M$_{\\odot}$ star is approximatively 29 Myr, according\nto eq. (14). Therefore, since at $Z=0$ secondary N is not produced and\nprimary N from massive stars is negligible, only for ages larger than\n29 Myr we can expect some N which is the one produced in a primary\nfashion by IMS during the third dredge-up episode. As one can see\nfrom Table 4, the abundances and abundance ratios predicted by the\nyields for $Z=0$ and $\\alpha_{RV}=1.5$ (model M1B) are in good\nagreement with those measured in IZw18, thus we could conclude that\nthe abundances in this galaxy are compatible with only one burst, the\nfirst, but only if the burst age is of the order of 31 Myr. In fact,\nfor times shorter than that the N abundance is too low and for times\nlarger the agreement worsens.\n\nThe abundance of C and particularly the predicted C/O ratio in model\nM1B is in very good agreement with observations at variance with\nprevious works (Kunth et al. 1995). The difference between the low\nabundance of $^{12}$C predicted by Kunth et al. (1995) and here is, in\nour opinion, due to the fact that the total amount of stars produced\nthere was smaller ($M_{\\rm burst} = 2 \\times 10^{5}$ M$_{\\odot}$) and\nless in agreement with the observations than that produced here\n($M_{\\rm burst} = 6\\times 10^{5}$ M$_{\\odot}$), therefore we predict\nhigher abundances for all the elements. In addition, the yields for\nmassive stars used here are different from those used in Kunth et\nal. (1994) (those of Woosley 1987). It is also worth mentioning that\nthe estimated ages for the present burst in IZw18 are between 15 and\n27 Myr (Martin 1996) in good agreement with our suggestion, although\nother authors suggest ages as short as 5 Myr (Izotov et al. 1999;\nStasi\\`nska \\& Schaerer 1999).\n\nIn order to see if we can exclude a previous burst besides the present\none in IZw18, as suggested by previous papers (Aloisi et al. 1999;\nKunth et al. 1995), or a recent burst coupled with a low but\ncontinuous star formation (Legrand 1999), we computed the expected ISM\nabundances for a preenriched gas with $Z=0.01$ Z$_{\\odot}$ and we show\nin Table 4 the abundances for this case at an age of 31 Myr (cases C\nand D). The results for the C case show that at an age of 31 Myr the\nabundance of oxygen is too high; the results at the end of the\nsimulation (375 Myr for model M1) give better values for oxygen and\nN/O but they predict a too high C/O. If one assumes then $Z=0.01$\nZ$_{\\odot}$ and $\\alpha_{RV}=1.5$ (case D), the agreement worsens at\nany age since one predicts a too high N/O ratio while the rest is\npractically unchanged. Therefore, we have two considerations: first,\nthe single first burst hypothesis seems to give the best agreement\nwith observations as long as primary N production in IMS is\nconsidered; second, we cannot really exclude a previous burst before\nthe present one, or at least we cannot exclude a burst which enriched\nonly sligthly the ISM. In other words, the preenrichment should be\nless than $Z=0.01$ Z$_{\\odot}$. From the previous discussion, it\narises that the best age for the burst in IZw18 should be around 31\nMyr.\n\n\n\\begin{figure}\n\\centering\n\\epsfig{file=recchi12.eps,height=5.5cm,width=7.5cm}\n\\caption[]{\\label{fig:fig 12} Abundance gradients for oxygen \n(solid line) and iron (dotted line) after 31 Myr, for the model M1B.}\n\\end{figure} \n\nAt this age the abundance gradient in a region of 600 pc is almost\nflat, at least if the galaxy is seen edge-on (see Fig. 12), in\nagreement with what is observed in IZw18 (Legrand 1999). Actually, if\na bipolar-shaped expanding bubble is present in IZw18, the inclination\nof the symmetry axis with respect to the normal to the observer would\nbe very small (Martin 1996, suggested an inclination of\n10$^{\\circ}$). \n\n\\begin{figure*}\n\\centering\n\\epsfig{file=recchi13.eps,height=17.7cm,width=18cm}\n\\caption[]{\\label{fig:fig 13} Predicted [$\\alpha$/Fe] vs. time and vs. [Fe/H] \nfor models M1B, M2B, M3B (first, second and third raw respectively) for both \nexpelled gas and ISM}\n\\end{figure*}\n\nFinally, in Fig. 13 we show the predicted [$\\alpha$/Fe] vs. time and\nvs. [Fe/H] for the gas inside and outside the galaxy, corresponding to\nthe results of Models M1B, M2B and M3B. The interesting feature of\nthis figure is that the [$\\alpha$/Fe] ratios in the gas outside the\ngalaxy are lower than those in the gas inside the galaxy. This is due\nto the fact that Fe, in particular that produced by type Ia SNe, is\nlost more efficiently than $\\alpha$ elements.\n\n\\begin{figure*}\n\\centering\n\\epsfig{file=recchi14.eps,height=15.5cm,width=15.5cm}\n\\caption[]{\\label{fig:fig 14} Abundance evolution in hot and cold \nregions for the model M1B. The threshold temperature is $2\\times \n10^4$ K.}\n\\end{figure*}\n\nWe shall also note in these two figures the peculiar behaviour of\nsilicon relative to the other $\\alpha$-elements. Silicon is, in fact,\nsynthetized by SNeIa at variance with what happens for O and Mg, which\nare mainly produced by SNeII (see Gibson et al. 1997). This is the\nreason for the relatively low and flat [Si/Fe] ratio as a function of\n[Fe/H].\n\n\n\\section{Conclusions}\n\nWe have studied the dynamical and chemical evolution of a dwarf galaxy\nas due to the effect of a single, instantaneous, point-like starburst\noccurring in its centre. We adopted galactic structural parameters\nwhich resemble those of IZw18, the most unevolved dwarf blue compact\ngalaxy known locally. We ran different models, which differ\nfor the burst luminosity and the ISM mass. We considered the mass and\nenergy inputs from the single low and IMS, the SNeII and the SNeIa\n(white dwarfs in binary systems) and we followed the evolution of the\ngas and its chemical abundances (H, He, C, N, O, Mg, Si and Fe) in\nspace and time for several hundreds Myr from the burst.\n\nOur results can be summarized as follows:\n\n\\begin{enumerate}\n\n\\item The starburst can inject enough energy into the ISM to trigger\na metal enriched galactic wind: the metals synthetized and ejected\nthrough supernova explosions leave the galaxy more easily than the\nunprocessed gas. This result is not new since it has already been\nsuggested by previous works (e. g. MF and DB). However, our new\nresult is that the SNIa products have the largest ejection efficiency\n(more than the products of type II SNe), with the consequence that the\n[$\\alpha$/Fe] ratios in the gas outside the galaxy are predicted to be\nlower than those inside. This is due to the fact that SNeIa produce a\nsubstantial fraction of iron. \n\n\\item The energy injection in the ISM by SNII has a rather low efficiency.\nInstead, the energetic contribution of SNeIa, in spite of their\nrelatively small number (a total of 240 SNeIa against 4800 SNeII), has\nimportant consequences in the dynamical behaviour of the galaxy. Since\nthe SNIa explosions occur in a medium heated and diluted by the\nprevious activity of SNeII, the thermal energy of the explosions is\neasily converted into kinetic energy and so the gas reaches quickly\nthe outer regions of the bubble along the galactic chimney. DB showed\nthat after the end of SNII activity, a fraction of the gas tends to\nrecollapse toward the central region of the galaxy, achieving the\nthreshold density for a new star formation event ($N({\\rm H}\\,{\\sc i})\\simgt\n10^{21}\\;{\\rm cm}^{-2}$, Skillman et al. 1988; Sait\\=o et al. 1992)\nin $\\sim$ 0.5--1 Gyr. With the energetic contribution of SNeIa, it is\nnot possible to reach, at least for the time considered in our\nsimulation, such a threshold in column density (it can be obtained\nonly after many Gyr).\n\n\\item One single burst, occurring in a primordial gas, with an age of\n$\\sim$ 31 Myr reproduces quite well both the dynamical structures and\nthe abundances in IZw18. This value is consistent with other\nindependent age estimates for the burst (Martin 1996). From the\nnucleosynthetic point of view the age of 31 Myr ensures that there is\nenough time for the primary N from IMS to be produced and ejected.\nThe adopted yields for massive stars (Woosley \\& Weaver 1995) include\nsome primary N, but its amount is negligible. This result suggests that\nIZw18 is probably experiencing its first major burst of star\nformation, although we cannot exclude a previous burst (see Aloisi et\nal. 1999) of moderate intensity, which enriched the gas to a\nmetallicity $Z < 0.01$ Z$_{\\odot}$.\n\n\\item At variance with previous studies we find that the majority of\nmetals (in mass) are found in the cold gas. In fact, mainly because of the\nlow SNII efficiency, the wind superbubble remains several hundreds of\nMyr inside the galaxy before the break out occurs. Moreover, the\nsuperbubble becomes radiative after a few Myr, and most of the SNII\nejecta cool without leaving the galaxy (SNIa ejecta, instead, are\nshown to be vented more easily). Given the relatively short mixing time, the\nabundances predicted by our models for the cold gas are those that\nshould be compared with the abundances observed in IZw18. Actually,\nthey are in very good agreement with the observed ones. This result\nsupports the common assumption made in chemical evolution models of an\ninstantaneous mixing.\n \n\n\\end{enumerate}\n\nFuture improvements of this work will include models with continuous\nbursts, sequential bursts, as well as a more detailed study\nof the formation of the H\\,{\\sc ii} regions (Recchi et al. in\npreparation). \n\n\\section*{Acknowledgements}\nWe are grateful to Guillermo Tenorio-Tagle and Andrea Ferrara for\nuseful suggestions and discussions. We also thank the referee whose\nsuggestions improved the paper. We acknowledge financial support from\nthe Italian Ministry for University and for Scientific and\nTechnological Research (MURST).\n\n\\begin{thebibliography}{}\n\\bibitem[]{}\nAloisi A., Tosi M., Greggio L., 1999, AJ, 118, 302\n\\bibitem[]{}\nAnders E., Grevesse N., 1989, Geochim. Cosmochim. Acta, 53, 197\n\\bibitem[]{}\nBedogni R., D'Ercole A., 1986, A\\&A, 157, 101\n\\bibitem[]{}\nBegelman M.C., Fabian A., 1990, MNRAS, 244, 26p\n\\bibitem[]{}\nBegelman M.C., McKee C.F., 1990, ApJ, 358, 375\n\\bibitem[]{} \nBorkowski K.J., Balbus S.A., Fristrom C.C., 1990, ApJ, 355, 501\n\\bibitem[]{}\nBradamante F., Matteucci F., D'Ercole A., 1998, A\\&A, 337, 338\n\\bibitem[]{}\nBreitschwerdt P., Kahn F.D., 1988, MNRAS, 235, 1011\n\\bibitem[]{}\nCiotti L., D'Ercole A., Pellegrini S., Renzini A. 1991, ApJ, 376, \n380\n\\bibitem[]{}\nCowie L.L., McKee C.F., 1977, ApJ, 215, 213\n\\bibitem[]{}\nCowie L.L., McKee C.F., Ostriker J.P., 1981, ApJ, 247, 908\n\\bibitem[]{}\nDekel A., Silk J., 1986, ApJ, 303, 39\n\\bibitem[]{}\nD'Ercole A., Brighenti F., 1999, MNRAS, 309, 941 (DB)\n\\bibitem[]{}\nDevost D., Roy J.R., Drissen R., 1997, ApJ, 482, 765\n\\bibitem[]{}\nDe Young D.S., Gallagher J.S., 1990, ApJ, 356, L15\n\\bibitem[]{}\nDe Young D.S., Heckman T.M., 1994, ApJ, 431, 598\n\\bibitem[]{} \nDufour R.J., Esteban C., Casta\\~neda H.O., 1996, ApJ, 471, L87\n\\bibitem[]{}\nDufour R.J., Hester J.J., 1990, ApJ, 350, 149\n\\bibitem[]{}\nGarnett D.R., Dufour R.J., Peimbert M., Torres-Peimbert S., Shields\nG.A., Skillman E.D., Terlevich E., Terlevich R.J., 1995, ApJ, 449, L77\n\\bibitem[]{}\nGarnett D.R., Skillman E.D., Dufour R.J., Shields G.A., 1997, ApJ, 481, 174\n\\bibitem[]{}\nGibson B.K., Loewenstein M., Mushotzky R.F., 1997, MNRAS, 290, 623\n\\bibitem[]{}\nGibson B.K., Matteucci F., 1997, ApJ, 475, 47\n\\bibitem[]{}\nGreggio L., Renzini A., 1983, A\\&A, 217, 222\n\\bibitem[]{}\nHunter D.A., Thronson H.A., 1995, ApJ, 452, 238\n\\bibitem[]{}\nIsrael F. P., 1988, A\\&A, 194, 24\n\\bibitem[]{}\nIzotov Y.I., Paparedos P., Thuan T.X., Fricke K.J., Foltz G.B., Guseva N.G., \n1999, {\\tt Astro-ph/9907082}\n\\bibitem[]{}\nKahn F.D., Breitschwerdt P., 1989, MNRAS, 242, 209\n\\bibitem[]{}\nKobulnicky H.A., Skillman E.D., 1997, ApJ, 489, 636\n\\bibitem[]{}\nKoo B.C., McKee C.F., 1992, ApJ, 388, 9\n\\bibitem[]{}\nKunth D., Lequeux J., Sargent W.L.W., Viallefond F., 1994, A\\&A, \n282, 709\n\\bibitem[]{}\nKunth D., Matteucci F., Marconi G., 1995, A\\&A, 297, 634\n\\bibitem[]{} \nLarsen T.I., Sommer-Larsen J., Pagel B.E.J., 2000, {\\tt Astro-ph/0005249}\n\\bibitem[]{}\nLarson R.B., 1974, MNRAS, 169, 229 \n\\bibitem[]{}\nLegrand F., 1999, Ph. D. Thesis, Univ. Paris 6\n\\bibitem[]{}\nLeitherer C., Schaerer D., Goldader J.D., Gonzales Delgado R.M., \nRobert C., Kune R.F., de Mello D.F., Devost D., Heckman T.M., 1999, \nApJS, 123, 3\n\\bibitem[]{}\nLequeux J., Viallefond F., 1980, A\\&A, 91, 269\n\\bibitem[]{}\nLin D.N.C., Murray S.D., 2000, {\\tt Astro-ph/0004055}\n\\bibitem[]{}\nLoewenstein M., Mathews W.G., 1987, ApJ, 319, 471\n\\bibitem[]{}\nMac Low M.-M., Ferrara A., 1999, ApJ, 513, 142 (MF)\n\\bibitem[]{}\nMac Low M.-M., McCray R., 1988, ApJ, 324, 776\n\\bibitem[]{}\nMac Low M.-M., McCray R., Norman M.L., 1989, ApJ, 337, 141\n\\bibitem[]{}\nMarconi G., Matteucci F., Tosi M., 1994, MNRAS, 217, 391\n\\bibitem[]{}\nMarlowe A.T., Heckman T.M., Wyse R.F.G., Schommer R., 1995 \nApJ, 438, 563\n\\bibitem[]{}\nMartin C.L., 1996, ApJ, 465, 680\n\\bibitem[]{} \nMas-Hesse J.M., Kunth D., 1996, in The Interplay between\nMassive Star Formation, the ISM and Galaxy Evolution, ed. D. Kunth,\nB. Guideroni, M. Heydari-Malayeri \\& T.X. Thuan (Gif-Sur-Yvette:\nEd. Fronti\\`eres), 401\n\\bibitem[]{}\nMathews W.G., Bregman J.N., 1978, ApJ, 224, 308\n\\bibitem[]{}\nMatteucci F., 1986, MNRAS, 221, 911\n\\bibitem[]{}\nMatteucci, F., 1996, Fond. Cosm. Phys., 17, 283\n\\bibitem[]{}\nMatteucci F., Chiosi C., 1983, A\\&A, 123, 121\n\\bibitem[]{}\nMatteucci F., Tosi M., 1985, MNRAS, 217, 391\n\\bibitem[]{}\nMcKee C.F., Begelman M.C., 1990, ApJ, 358, 392\n\\bibitem[]{}\nMcKee C.F., Van Buren D., Lazareff B., 1984, ApJ, 278, L115\n\\bibitem[]{}\nMeurer G.R., 1991, Proc. Astron. Soc. Australia, 9, 98\n\\bibitem[]{}\nMeurer G.R., Freeman K.C., Dopita M.A., Cacciari C., 1992, AJ, 103, 60\n\\bibitem[]{}\nNomoto K., Thielemann F.K., Yokoi K., 1984, ApJ, 286, 644 (NTY)\n\\bibitem[]{}\nOlofsson K., 1995, A\\&A, 293, 652\n\\bibitem[]{}\nPadovani P., Matteucci F., 1993, ApJ, 416, 26\n\\bibitem[]{}\nPettini M., Lipman K., 1995, A\\&A, 297, L63\n\\bibitem[]{}\nPilyugin L.S., 1992, A\\&A, 260, 58\n\\bibitem[]{}\nPilyugin L.S., 1993, A\\&A, 277, 42\n\\bibitem[]{}\nPortinari L., Chiosi C., Bressan A., 1998, A\\&A, 334, 505\n\\bibitem[]{}\nReimers D.: 1975, Mem. R. Sci. Liege 6 eme Ser., 8, 369\n\\bibitem[]{}\nRenzini A., Voli M., 1981, A\\&A, 94, 175 (RV)\n\\bibitem[]{}\nRieschick A., Hensler G., 2000, in Cosmic Evolution and Galaxy Formation: \nStructure, Interactions and Feedback, ASP Conferences Series, eds. J. Franco, \nE. Terlevich, O. L\\`opez Cruz and I. Aretxaga\n\\bibitem[]{}\nRoy J.-R., Kunth D., 1995, A\\&A, 294, 432\n\\bibitem[]{}\nSait\\=o M., Sasaki M., Ohta K., Yamada T., 1992, PASJ, 44, 593\n\\bibitem[]{}\nSalpeter E.E., 1955, ApJ, 121, 161\n\\bibitem[]{}\nSandage A., Binggeli B., 1984, AJ, 89, 919\n\\bibitem[]{}\nSilich S.A., Tenorio-Tagle G., 1998, MNRAS, 299, 249\n\\bibitem[]{}\nSkillman E.D., 1997, Rev. Mex. SC, 6, 36\n\\bibitem[]{}\nSkillman E.D., Bender R., 1995, Rev. Mex. SC, 3, 25\n\\bibitem[]{} \nSkillman E.D., Kennicut R.C.J., 1993, ApJ, 411, 655\n\\bibitem[]{}\nSkillman E.D., Kennicut R.C.J., Hodge P.W., 1989, ApJ, 347, 875\n\\bibitem[]{}\nSkillman E.D., Terlevich R., Teuben P.J., van Woerden H., 1988, A\\&A, 198, 33\n\\bibitem[]{}\nSlavin J.D., Shull J.M., Begelman M.C., 1993, ApJ, 407, 83\n\\bibitem[]{}\nSmith M.D., Smarr L., Norman M.L., Wilson J.R., 1983, ApJ, 264, 432\n\\bibitem[]{}\nSpitzer L., 1956, Physics of Fully Ionized Gases (New York: Interscience)\n\\bibitem[]{}\nStasi\\`nka G., Schaerer D., 1999, A\\&A, 351, 72\n\\bibitem[]{}\nStone J.M., Norman M.L., 1992, ApJS, 80, 573\n\\bibitem[]{}\nStone J.M., Norman M.L., 1993, ApJ, 413, 198\n\\bibitem[]{}\nStrickland D.K., Stevens L.R., 1999, MNRAS, 306, 43 \n\\bibitem[]{}\nSuchkov A.A., Balsara T.S., Heckman T.M., Leiterher C., 1994, ApJ, 430, 511\n\\bibitem[]{} \nTenorio-Tagle G., 1996, AJ, 111, 1641\n\\bibitem[]{}\nVader J.P., 1986, ApJ, 379, L1\n\\bibitem[]{}\nVan Zee L., Westpfahl D., Haynes M.P., Salzer J.J., 1998, AJ, \n115, 1000\n\\bibitem[]{}\nViallefond F., Lequeux J., Comte G., 1987, in Starburst\nand Galaxy Evolution, ed. T.X. Thuan, T. Montmerle \\& J. Tran Thanh\nVan (Gif-sur-Yvette: Ed. Fronti\\`eres), 139\n\\bibitem[]{}\nWeaver R., McCray R., Castor J., Shapiro P., Moore R., 1977, ApJ, 218, 377\n\\bibitem[]{}\nWoosley S.E., 1987, in Nucleosynthesis and Chemical evolution, 16th Saas-Fee \nAdvanced Course, Geneva Observatory, 1\n\\bibitem[]{}\nWoosley S.E., Weaver, T.A., 1995, ApJS, 101, 181 (WW)\n\\end{thebibliography}{}\n\\end{document}\n\n"
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[
{
"name": "astro-ph0002370.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[]{}\nAloisi A., Tosi M., Greggio L., 1999, AJ, 118, 302\n\\bibitem[]{}\nAnders E., Grevesse N., 1989, Geochim. Cosmochim. Acta, 53, 197\n\\bibitem[]{}\nBedogni R., D'Ercole A., 1986, A\\&A, 157, 101\n\\bibitem[]{}\nBegelman M.C., Fabian A., 1990, MNRAS, 244, 26p\n\\bibitem[]{}\nBegelman M.C., McKee C.F., 1990, ApJ, 358, 375\n\\bibitem[]{} \nBorkowski K.J., Balbus S.A., Fristrom C.C., 1990, ApJ, 355, 501\n\\bibitem[]{}\nBradamante F., Matteucci F., D'Ercole A., 1998, A\\&A, 337, 338\n\\bibitem[]{}\nBreitschwerdt P., Kahn F.D., 1988, MNRAS, 235, 1011\n\\bibitem[]{}\nCiotti L., D'Ercole A., Pellegrini S., Renzini A. 1991, ApJ, 376, \n380\n\\bibitem[]{}\nCowie L.L., McKee C.F., 1977, ApJ, 215, 213\n\\bibitem[]{}\nCowie L.L., McKee C.F., Ostriker J.P., 1981, ApJ, 247, 908\n\\bibitem[]{}\nDekel A., Silk J., 1986, ApJ, 303, 39\n\\bibitem[]{}\nD'Ercole A., Brighenti F., 1999, MNRAS, 309, 941 (DB)\n\\bibitem[]{}\nDevost D., Roy J.R., Drissen R., 1997, ApJ, 482, 765\n\\bibitem[]{}\nDe Young D.S., Gallagher J.S., 1990, ApJ, 356, L15\n\\bibitem[]{}\nDe Young D.S., Heckman T.M., 1994, ApJ, 431, 598\n\\bibitem[]{} \nDufour R.J., Esteban C., Casta\\~neda H.O., 1996, ApJ, 471, L87\n\\bibitem[]{}\nDufour R.J., Hester J.J., 1990, ApJ, 350, 149\n\\bibitem[]{}\nGarnett D.R., Dufour R.J., Peimbert M., Torres-Peimbert S., Shields\nG.A., Skillman E.D., Terlevich E., Terlevich R.J., 1995, ApJ, 449, L77\n\\bibitem[]{}\nGarnett D.R., Skillman E.D., Dufour R.J., Shields G.A., 1997, ApJ, 481, 174\n\\bibitem[]{}\nGibson B.K., Loewenstein M., Mushotzky R.F., 1997, MNRAS, 290, 623\n\\bibitem[]{}\nGibson B.K., Matteucci F., 1997, ApJ, 475, 47\n\\bibitem[]{}\nGreggio L., Renzini A., 1983, A\\&A, 217, 222\n\\bibitem[]{}\nHunter D.A., Thronson H.A., 1995, ApJ, 452, 238\n\\bibitem[]{}\nIsrael F. P., 1988, A\\&A, 194, 24\n\\bibitem[]{}\nIzotov Y.I., Paparedos P., Thuan T.X., Fricke K.J., Foltz G.B., Guseva N.G., \n1999, {\\tt Astro-ph/9907082}\n\\bibitem[]{}\nKahn F.D., Breitschwerdt P., 1989, MNRAS, 242, 209\n\\bibitem[]{}\nKobulnicky H.A., Skillman E.D., 1997, ApJ, 489, 636\n\\bibitem[]{}\nKoo B.C., McKee C.F., 1992, ApJ, 388, 9\n\\bibitem[]{}\nKunth D., Lequeux J., Sargent W.L.W., Viallefond F., 1994, A\\&A, \n282, 709\n\\bibitem[]{}\nKunth D., Matteucci F., Marconi G., 1995, A\\&A, 297, 634\n\\bibitem[]{} \nLarsen T.I., Sommer-Larsen J., Pagel B.E.J., 2000, {\\tt Astro-ph/0005249}\n\\bibitem[]{}\nLarson R.B., 1974, MNRAS, 169, 229 \n\\bibitem[]{}\nLegrand F., 1999, Ph. D. Thesis, Univ. Paris 6\n\\bibitem[]{}\nLeitherer C., Schaerer D., Goldader J.D., Gonzales Delgado R.M., \nRobert C., Kune R.F., de Mello D.F., Devost D., Heckman T.M., 1999, \nApJS, 123, 3\n\\bibitem[]{}\nLequeux J., Viallefond F., 1980, A\\&A, 91, 269\n\\bibitem[]{}\nLin D.N.C., Murray S.D., 2000, {\\tt Astro-ph/0004055}\n\\bibitem[]{}\nLoewenstein M., Mathews W.G., 1987, ApJ, 319, 471\n\\bibitem[]{}\nMac Low M.-M., Ferrara A., 1999, ApJ, 513, 142 (MF)\n\\bibitem[]{}\nMac Low M.-M., McCray R., 1988, ApJ, 324, 776\n\\bibitem[]{}\nMac Low M.-M., McCray R., Norman M.L., 1989, ApJ, 337, 141\n\\bibitem[]{}\nMarconi G., Matteucci F., Tosi M., 1994, MNRAS, 217, 391\n\\bibitem[]{}\nMarlowe A.T., Heckman T.M., Wyse R.F.G., Schommer R., 1995 \nApJ, 438, 563\n\\bibitem[]{}\nMartin C.L., 1996, ApJ, 465, 680\n\\bibitem[]{} \nMas-Hesse J.M., Kunth D., 1996, in The Interplay between\nMassive Star Formation, the ISM and Galaxy Evolution, ed. D. Kunth,\nB. Guideroni, M. Heydari-Malayeri \\& T.X. Thuan (Gif-Sur-Yvette:\nEd. Fronti\\`eres), 401\n\\bibitem[]{}\nMathews W.G., Bregman J.N., 1978, ApJ, 224, 308\n\\bibitem[]{}\nMatteucci F., 1986, MNRAS, 221, 911\n\\bibitem[]{}\nMatteucci, F., 1996, Fond. Cosm. Phys., 17, 283\n\\bibitem[]{}\nMatteucci F., Chiosi C., 1983, A\\&A, 123, 121\n\\bibitem[]{}\nMatteucci F., Tosi M., 1985, MNRAS, 217, 391\n\\bibitem[]{}\nMcKee C.F., Begelman M.C., 1990, ApJ, 358, 392\n\\bibitem[]{}\nMcKee C.F., Van Buren D., Lazareff B., 1984, ApJ, 278, L115\n\\bibitem[]{}\nMeurer G.R., 1991, Proc. Astron. Soc. Australia, 9, 98\n\\bibitem[]{}\nMeurer G.R., Freeman K.C., Dopita M.A., Cacciari C., 1992, AJ, 103, 60\n\\bibitem[]{}\nNomoto K., Thielemann F.K., Yokoi K., 1984, ApJ, 286, 644 (NTY)\n\\bibitem[]{}\nOlofsson K., 1995, A\\&A, 293, 652\n\\bibitem[]{}\nPadovani P., Matteucci F., 1993, ApJ, 416, 26\n\\bibitem[]{}\nPettini M., Lipman K., 1995, A\\&A, 297, L63\n\\bibitem[]{}\nPilyugin L.S., 1992, A\\&A, 260, 58\n\\bibitem[]{}\nPilyugin L.S., 1993, A\\&A, 277, 42\n\\bibitem[]{}\nPortinari L., Chiosi C., Bressan A., 1998, A\\&A, 334, 505\n\\bibitem[]{}\nReimers D.: 1975, Mem. R. Sci. Liege 6 eme Ser., 8, 369\n\\bibitem[]{}\nRenzini A., Voli M., 1981, A\\&A, 94, 175 (RV)\n\\bibitem[]{}\nRieschick A., Hensler G., 2000, in Cosmic Evolution and Galaxy Formation: \nStructure, Interactions and Feedback, ASP Conferences Series, eds. J. Franco, \nE. Terlevich, O. L\\`opez Cruz and I. Aretxaga\n\\bibitem[]{}\nRoy J.-R., Kunth D., 1995, A\\&A, 294, 432\n\\bibitem[]{}\nSait\\=o M., Sasaki M., Ohta K., Yamada T., 1992, PASJ, 44, 593\n\\bibitem[]{}\nSalpeter E.E., 1955, ApJ, 121, 161\n\\bibitem[]{}\nSandage A., Binggeli B., 1984, AJ, 89, 919\n\\bibitem[]{}\nSilich S.A., Tenorio-Tagle G., 1998, MNRAS, 299, 249\n\\bibitem[]{}\nSkillman E.D., 1997, Rev. Mex. SC, 6, 36\n\\bibitem[]{}\nSkillman E.D., Bender R., 1995, Rev. Mex. SC, 3, 25\n\\bibitem[]{} \nSkillman E.D., Kennicut R.C.J., 1993, ApJ, 411, 655\n\\bibitem[]{}\nSkillman E.D., Kennicut R.C.J., Hodge P.W., 1989, ApJ, 347, 875\n\\bibitem[]{}\nSkillman E.D., Terlevich R., Teuben P.J., van Woerden H., 1988, A\\&A, 198, 33\n\\bibitem[]{}\nSlavin J.D., Shull J.M., Begelman M.C., 1993, ApJ, 407, 83\n\\bibitem[]{}\nSmith M.D., Smarr L., Norman M.L., Wilson J.R., 1983, ApJ, 264, 432\n\\bibitem[]{}\nSpitzer L., 1956, Physics of Fully Ionized Gases (New York: Interscience)\n\\bibitem[]{}\nStasi\\`nka G., Schaerer D., 1999, A\\&A, 351, 72\n\\bibitem[]{}\nStone J.M., Norman M.L., 1992, ApJS, 80, 573\n\\bibitem[]{}\nStone J.M., Norman M.L., 1993, ApJ, 413, 198\n\\bibitem[]{}\nStrickland D.K., Stevens L.R., 1999, MNRAS, 306, 43 \n\\bibitem[]{}\nSuchkov A.A., Balsara T.S., Heckman T.M., Leiterher C., 1994, ApJ, 430, 511\n\\bibitem[]{} \nTenorio-Tagle G., 1996, AJ, 111, 1641\n\\bibitem[]{}\nVader J.P., 1986, ApJ, 379, L1\n\\bibitem[]{}\nVan Zee L., Westpfahl D., Haynes M.P., Salzer J.J., 1998, AJ, \n115, 1000\n\\bibitem[]{}\nViallefond F., Lequeux J., Comte G., 1987, in Starburst\nand Galaxy Evolution, ed. T.X. Thuan, T. Montmerle \\& J. Tran Thanh\nVan (Gif-sur-Yvette: Ed. Fronti\\`eres), 139\n\\bibitem[]{}\nWeaver R., McCray R., Castor J., Shapiro P., Moore R., 1977, ApJ, 218, 377\n\\bibitem[]{}\nWoosley S.E., 1987, in Nucleosynthesis and Chemical evolution, 16th Saas-Fee \nAdvanced Course, Geneva Observatory, 1\n\\bibitem[]{}\nWoosley S.E., Weaver, T.A., 1995, ApJS, 101, 181 (WW)\n\\end{thebibliography}"
}
] |
astro-ph0002371
|
Chemical and dynamical evolution in gas-rich dwarf galaxies
|
[
{
"author": "Simone Recchi"
},
{
"author": "Francesca Matteucci"
}
] |
We study the effect of a single, instantaneous starburst in a gas-rich dwarf galaxy on the dynamical and chemical evolution of its interstellar medium. We consider the energetic input and the chemical yields originating from SNeII, SNeIa and intermediate-mass stars. We find that a galaxy resembling IZw18 develops a galactic wind carrying out mostly the metal-rich gas. The various metals are lost differentially and the metals produced by the SNeIa are lost more efficiently than the others. As a consequence, we find larger [$\alpha$/Fe] ratios for the gas inside the galaxy than for the gas leaving the galaxy. Finally we find that a single burst occurring in primordial gas (without pre-enrichment), gives chemical abundances and dynamical structures in good agreement with what observed in IZw18 after $\sim$ 29 Myr from the beginning of star formation.
|
[
{
"name": "recchibis.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsfig]{article}\n\\markboth{Recchi, Matteucci \\& D'Ercole}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{Chemical and dynamical evolution in gas-rich dwarf galaxies}\n\\author{Simone Recchi, Francesca Matteucci}\n\\affil{Dipartimento di Astronomia, Universit\\`a di Trieste, Via G.B. \nTiepolo 11, 34131 Trieste, Italy}\n\\author{Annibale D'Ercole}\n\\affil{Osservatorio Astronomico di Bologna, Via Ranzani 1, 44127 Bologna, \nItaly}\n\n\\begin{abstract}\nWe study the effect of a single, instantaneous starburst in a gas-rich\ndwarf galaxy on the dynamical and chemical evolution of its\ninterstellar medium. We consider the energetic input and the chemical\nyields originating from SNeII, SNeIa and intermediate-mass stars. We\nfind that a galaxy resembling IZw18 develops a galactic wind carrying\nout mostly the metal-rich gas. The various metals are lost\ndifferentially and the metals produced by the SNeIa are lost more\nefficiently than the others. As a consequence, we find larger\n[$\\alpha$/Fe] ratios for the gas inside the galaxy than for the gas\nleaving the galaxy. Finally we find that a single burst occurring in\nprimordial gas (without pre-enrichment), gives chemical abundances and\ndynamical structures in good agreement with what observed in IZw18\nafter $\\sim$ 29 Myr from the beginning of star formation.\n\n\\end{abstract}\n\n\\section{Introduction}\nBlue compact dwarf galaxies (BCD) are gas-rich systems experiencing an\nintense star formation. These galaxies have very simple structures,\nsmall sizes and are very metal poor. For these reasons, BCD are\nexcellent laboratories to investigate the effect of a starburst on the\nchemical and dynamical evolution of the interstellar medium (ISM).\n\nPrevious dynamical and chemical studies of these galaxies have\nsuggested the existence of a `differential galactic wind', in the\nsense that after a starburst event these objects would loose mostly\nmetals (ref. Mac Low \\& Ferrara 1999; D'Ercole \\& Brighenti 1999;\nPilyugin 1992, 1993; Marconi et al. 1994). However, in none of these\nstudies, detailed chemical and dynamical evolution was taken into\naccount at the same time. The aim of this paper is to include the\neffects (both energetic and chemical) of type II and type Ia SNe in a\ndetailed dynamical model.\n\n\\section{Model description}\n\nWe consider a rotating gaseous component in hydrostatic isothermal\nequilibrium with the gravitational and the centrifugal forces. The\npotential well is given by the sum of a spherical, quasi-isothermal\ndark halo and an oblate King profile. The resulting gas distribution\nresembles that observed in IZw18 in a region $R\\le$ 1 Kpc and $z\\le$\n730 pc, which we call `galactic region'. \n\nTo describe the evolution of the ISM we solve a set of time-dependent,\nhydrodynamical equations, with source terms describing the rate of\nenergy and mass return from the starburst. Mass is returned mostly by\nSNeII and intermediate-mass stars (IMS), while the energy is injected\nessentially by SNe. For the first time, here we take into account also\nthe contribution by SNeIa. These supernovae start to explode after 29\nMyr, at the end of the SNII activity, occurring with the explosion of\nstars with 8 M$_{\\odot}$ (see Nomoto, Thielemann \\& Yokoi 1984).\n\nFollowing Bradamante et al. (1998), we suppose that SNeII convert only\n3\\% of their explosion energy into thermal energy of the ISM. SNeIa,\ninstead, do not suffer radiative losses because they explode in a\nmedium heated and diluted by the previous SNeII activity and\nrelease all their energy into the ISM.\n\nWe solve an ancillary set of equations which keep track of the\nevolution in space and time of some specific elements lost by stars,\nnamely H, He, C, N, O, Mg, Si, Fe. The production of these elements\nare obtained following the nucleosynthetic prescriptions from various\nauthors: Woosley \\& Weaver (1995) for the SNeII, Renzini \\& Voli\n(1981) for IMS and Nomoto et al. (1984) for SNeIa. For more details,\nsee Recchi et al. (2000).\n\nThe standard model, called M1, has a gaseous mass inside the galactic\nregion of $\\sim 1.7\\times 10^7\\,{\\rm M}_{\\sun}$ and a mass of gas\nturned into stars of $\\sim 6\\times 10^5\\,{\\rm M}_{\\sun}$, in\nreasonable agreement with the observations of IZw18. We run other two\nmodels obtained by reducing the burst luminosity of a factor 0.6\n(model M2) and by reducing the mass of gas of a factor 0.25 (model M3).\nMoreover, we consider four nucleosynthetic options: we consider an\ninitial abundance of the ISM of $Z=0$ and $Z=0 .01\\,{\\rm Z}_{\\odot}$\nand two possible values for the mixing lenght parameter $\\alpha_{\\rm\nRV}=0$ and $\\alpha_{\\rm RV}=1.5$. In the models with $\\alpha_{\\rm\nRV}=1.5$ we can produce N in a primary way in IMS.\n\n\\section{Results}\n\nIn model M1 a classical bubble develops as a consequence of SNII\nexplosions (see Fig. 1). It expands faster along the $z$ direction,\nwhere the ISM density gradient is steeper. The SNII wind stops before\nthe possible breakout, and the subsequent SNIa wind is not strong\nenough to expand the cavity further. The size of the bubble thus does\nnot change for nearly 300 Myr, although the shape varies irregularly\nbecause of the Kelvin-Helmholtz instabilities along the interface\nbetween the hot cavity and the surrounding gas. After $\\sim$ 340 Myr\nthe expanding ISM is diluted enough and the hot bubble finally breaks\nout through a funnel. Most of the SNII ejecta remain locked into the\nbubble wall inside the galaxy, while the SNIa elements, ejected later,\nare easily channelled along the funnel. Iron is mostly produced by\nSNeIa and, when the breakup occurs, most of it is lost. Thus the gas\n[$\\alpha$/Fe] ratio results lower outside the galaxy than inside (see\nFig. 2).\n\n\\begin{figure}\n\\plotone{recchibis1.ps}\n\\caption{Isodensity curves (in logarithmic scale) and velocity field for \nthe model M1 at various burst ages.}\n\\end{figure}\n\n\n\\begin{figure}\n\\vspace{-6cm}\n\\plotone{recchibis2.ps}\n\\caption{Predicted [$\\alpha$/Fe] vs. time and vs. [Fe/H] for both\nexpelled gas and ISM for the model M1}\n\\end{figure}\n\nAfter $\\sim$ 29 Myr [the burst in IZw18 is evaluated to be 15 - 27 Myr\nold by Martin (1996)] the galactic abundances found in this model are\nin good agreement with those observed in IZw18 once the\nnucleosynthetic prescriptions with $Z=0$ and $\\alpha_{\\rm RV}=1.5$ are\nassumed. At this time a substantial fraction of N is produced by IMS\nin a primary way. An initial metallicity of $Z=0.01\\,{\\rm Z}_{\\sun}$\n(simulating a pre-enriched burst), worsens the agreement between data\nand model results. Also the observed dimensions of the dynamical\nstructures are in reasonable agreement with our result after $\\sim$ 29\nMyr.\n\nModels M2 and M3 have similar dynamical behaviours. However, due to\nthe different quantity of metals produced and gas mass lost, their\nabundances are overestimated (M3) or underestimated (M2) compared to\nIZw18. We also run a model similar to M1 but with a 100\\% efficiency\nof SNeII in heating the gas. In this case the galaxy results devoided\nof gas 450 Myr after the burst, at variance with the substantial\namount of ISM in IZw18.\n\n\n\\begin{references}\n\n\\reference Bradamante, F., Matteucci, F. \\& D'Ercole, A. 1998, \\aap, 337, 338\n\n\\reference D'Ercole, A. \\& Brighenti, F. 1999, \\mnras, 309, 941\n\n\\reference Mac Low, M.-M. \\& Ferrara, A. 1999, \\apj, 513, 142\n\n\\reference Marconi, G., Matteucci, F. \\& Tosi, M. 1994, \\mnras, 217, 391\n\n\\reference Martin, C.L., 1996, \\apj, 465, 680\n\n\\reference Nomoto, K., Thielemann, F.K. \\& Yokoi K. 1984, \\apj, 286, 644\n\n\\reference Pilyugin, L.S., 1992, \\aap, 260, 58\n\n\\reference Pilyugin, L.S., 1993, \\aap, 277, 42\n\n\\reference Recchi, S., Matteucci, F. \\& D'Ercole, A. 2000, submitted to \\mnras\n\n\\reference Renzini, A. \\& Voli, M. 1981, \\aap, 94, 175\n\n\\reference Woosley, S.E. \\& Weaver, T.A. 1995, \\apjs, 101, 181\n\n\\end{references}\n\n\\end{document}\n\n\n\n\n\n \n \n"
}
] |
[] |
astro-ph0002372
|
The Luminosity Function of MS2255.7+2039 at $z=0.288$\thanks{Based on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.}
|
[
{
"author": "Magnus N\\\"aslund"
},
{
"author": "Claes Fransson"
},
{
"author": "Monica Huldtgren"
}
] |
The luminosity function of MS2255.7+2039 at $z=0.288$ is determined down to a total magnitude of $R \sim 24$, corresponding to $M_{\mbox{\tiny{R}}} \sim -17 \, ({H}_{\mbox{\tiny{0}}} = 50 \ {km \ s}^{-1} \ {Mpc}^{-1})$. The data are corrected for incompleteness and crowding using detailed simulations. We find that the luminosity function is steeper than a standard Schechter function at faint magnitudes, and shows an excess of galaxies below $ M_{\mbox{\tiny{R}}} \sim -19$. After corrections for light loss and crowding, the data can be described by a sum of two Schechter functions, one with $M_{\mbox{\tiny{R}}}^{*} = -22.8$ and $\alpha = -1.0$, and one steeper with $M_{\mbox{\tiny{R}}}^{*} = -18.9$ and $\alpha = -1.5$, representing the dwarf population. A straight-line fit to the faint part yields a slope similar to the Schechter $\alpha = -1.5$ of the dwarf population. The luminosity function of MS2255.7+2039 is compared to other clusters at lower redshifts, and does not show any significant difference. The redshift range for clusters in which increased number of dwarf galaxies have been found is therefore extended to higher redshifts. \keywords{ Galaxies: clusters: general -- Galaxies: clusters: individual: MS2255.7+2039 -- Galaxies: evolution -- Galaxies: formation -- Galaxies: luminosity function, mass function -- Cosmology: observations}
|
[
{
"name": "defs.tex",
"string": "\\def\\KK{\\rm ~K}\n\n\\def\\abs#1{\\left| #1 \\right|}\n\n\\def\\EE#1{\\times 10^{#1}}\n\n\\def\\gcm{\\rm ~g~cm^{-3}}\n\n\\def\\ccm{\\rm ~cm^{-3}}\n\n\\def\\kms{\\rm ~km~s^{-1}}\n\n\\def\\ergs{\\rm ~erg~s^{-1}}\n\n\\def\\etal{\\rm et. al.~}\n\n\\def\\isotope#1#2{\\hbox{${}^{#1}\\rm#2$}}\n\\def\\wl{~\\lambda~}\n\\def\\wll{~\\lambda~\\lambda~}\n\\def\\HI{{\\rm H\\,I}}\n\\def\\HII{{\\rm H\\,II}}\n\\def\\HeI{{\\rm He\\,I}}\n\\def\\HeII{{\\rm He\\,II}}\n\\def\\HeIII{{\\rm He\\,III}}\n\\def\\CI{{\\rm C\\,I}}\n\\def\\CII{{\\rm C\\,II}}\n\\def\\CIII{{\\rm C\\,III}}\n\\def\\CIV{{\\rm C\\,IV}}\n\\def\\NI{{\\rm N\\,I}}\n\\def\\NII{{\\rm N\\,II}}\n\\def\\NIII{{\\rm N\\,III}}\n\\def\\NIV{{\\rm N\\,IV}}\n\\def\\NV{{\\rm N\\,V}}\n\\def\\NVI{{\\rm N\\,VI}}\n\\def\\NVII{{\\rm N\\,VII}}\n\\def\\OI{{\\rm O\\,I}}\n\\def\\OII{{\\rm O\\,II}}\n\\def\\OIII{{\\rm O\\,III}}\n\\def\\OIV{{\\rm O\\,IV}}\n\\def\\OV{{\\rm O\\,V}}\n\\def\\OVI{{\\rm O\\,VI}}\n\\def\\CaI{{\\rm Ca\\,I}}\n\\def\\CaII{{\\rm Ca\\,II}}\n\\def\\NeI{{\\rm Ne\\,I}}\n\\def\\NaI{{\\rm Na\\,I}}\n\\def\\NaII{{\\rm Na\\,II}}\n\\def\\NiI{{\\rm Ni\\,I}}\n\\def\\NiII{{\\rm Ni\\,II}}\n\\def\\FeI{{\\rm Fe\\,I}}\n\\def\\FeII{{\\rm Fe\\,II}}\n\\def\\FeIII{{\\rm Fe\\,III}}\n\\def\\FeV{{\\rm Fe\\,V}}\n\\def\\FeVII{{\\rm Fe\\,VII}}\n\\def\\CoII{{\\rm Co\\,II}}\n\\def\\CoIII{{\\rm Co\\,III}}\n\\def\\ArI{{\\rm Ar\\,I}}\n\\def\\MgI{{\\rm Mg\\,I}}\n\\def\\MgII{{\\rm Mg\\,II}}\n\\def\\SiI{{\\rm Si\\,I}}\n\\def\\SiII{{\\rm Si\\,II}}\n\\def\\SiIII{{\\rm Si\\,III}}\n\\def\\SiIV{{\\rm Si\\,IV}}\n\\def\\SI{{\\rm S\\,I}}\n\\def\\SII{{\\rm S\\,II}}\n\\def\\SIII{{\\rm S\\,III}}\n\\def\\FeI{{\\rm Fe\\,I}}\n\\def\\FeII{{\\rm Fe\\,II}}\n\\def\\kI{{\\rm k\\,I}}\n\\def\\kII{{\\rm k\\,II}}\n\n\\def\\La{{\\rm Ly}\\alpha}\n\\def\\Ha{{\\rm H}\\alpha}\n\\def\\Hb{{\\rm H}\\beta}\n\\def\\Hg{{\\rm H}\\gamma}\n\\def\\Hd{{\\rm H}\\delta}\n\n\\def\\etscale#1{e^{-t/#1^{\\rm d}}}\n\\def\\etscaleyr#1{e^{-t/#1\\,{\\rm yr}}}\n\n\\def\\sigmaKN{\\sigma_{\\rm KN}}\n\n\\def\\ncrit{n_{\\rm crit}}\n\n\\def\\Emax{E_{\\rm max}}\n\n\\def\\chieff{\\chi_{\\rm eff}^{\\phantom{0}}}\n\\def\\chieffi{\\chi_{{\\rm eff},i}^{\\phantom{0}}}\n\\def\\chiion{\\chi_{\\rm ion}^{\\phantom{0}}}\n\\def\\chiioni{\\chi_{{\\rm ion},i}^{\\phantom{0}}}\n\\def\\Gammaion{\\Gamma_{\\!\\rm ion}}\n\n\\def\\Mcore{M_{\\rm core}}\n\\def\\Rcore{R_{\\rm core}}\n\\def\\Vcore{V_{\\rm core}}\n\n\\def\\Menv{M_{\\rm env}}\n\\def\\Venv{V_{\\rm env}}\n\\def\\Vej{V_{\\rm ej}}\n\n\\def\\Vcthou{\\left( {\\Vcore \\over 2000 \\rm \\,km\\,s^{-1}} \\right)}\n\n\n\\def\\Msun{~{\\rm M}_\\odot}\n\\def\\Msunyr{~{\\rm M}_\\odot~yr^{-1}}\n\\def\\Mdot{\\dot M}\n\n\\def\\tyr{t_{\\rm yr}}\n\\def\\gff{g_{\\rm ff}}\n\n\\def\\Tex{T_{\\rm ex}}\n\n\n\\def\\lsim{\\!\\!\\!\\phantom{\\le}\\smash{\\buildrel{}\\over\n {\\lower2.5dd\\hbox{$\\buildrel{\\lower2dd\\hbox{$\\displaystyle<$}}\\over\n \\sim$}}}\\,\\,}\n\n\\def\\gsim{\\!\\!\\!\\phantom{\\ge}\\smash{\\buildrel{}\\over\n {\\lower2.5dd\\hbox{$\\buildrel{\\lower2dd\\hbox{$\\displaystyle>$}}\\over\n \\sim$}}}\\,\\,}\n\n"
},
{
"name": "fgpaper1.tex",
"string": "\\documentclass{aa}\n\\usepackage{graphics}\n\\usepackage{latexsym}\n\\input defs.tex\n\\def\\HI{H\\,{\\sc i}}\n\\def\\HII{H\\,{\\sc ii}}\n\\def\\degr{\\hbox{$^\\circ$}}\n\\def\\arcmin{\\hbox{$^\\prime$}}\n\\def\\arcsec{\\hbox{$^{\\prime\\prime}$}}\n\\def\\fd{\\hbox{$.\\!\\!^{\\rm d}$}}\n\\def\\fh{\\hbox{$.\\!\\!^{\\rm h}$}}\n\\def\\fm{\\hbox{$.\\!\\!^{\\rm m}$}}\n\\def\\fs{\\hbox{$.\\!\\!^{\\rm s}$}}\n\\def\\fdg{\\hbox{$.\\!\\!^\\circ$}}\n\\def\\farcm{\\hbox{$.\\mkern-4mu^\\prime$}}\n\\def\\farcs{\\hbox{$.\\!\\!^{\\prime\\prime}$}}\n\\def\\fp{\\hbox{$.\\!\\!^{\\scriptscriptstyle\\rm p}$}}\n\\def\\sun{\\hbox{$\\odot$}}\n\\def\\la{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n<\\cr\\sim\\cr}}}}}\n\\def\\ga{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr>\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n>\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n>\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n>\\cr\\sim\\cr}}}}}\n\\def\\Msunyr{\\Msun ~\\rm yr^{-1}}\n\\begin{document}\n\n\\thesaurus{11\n (11.03.1; % Galaxies: clusters: general,\n 11.03.4 MS2255.7+2039; % Galaxies: clusters: individual,\n 11.05.2; % Galaxies: evolution,\n 11.06.1; % Galaxies: formation,\n 11.12.2; % Galaxies: luminosity function, mass function,\n 12.03.3)} % Cosmology: observations\n\n \\title{The Luminosity Function of MS2255.7+2039 at \n$z=0.288$\\thanks{Based on observations made with the Nordic Optical Telescope,\n operated on the island of La Palma jointly by Denmark, Finland,\n Iceland, Norway, and Sweden, in the Spanish Observatorio del \n Roque de los Muchachos of the Instituto de Astrofisica de \n Canarias.}}\n\n \\author{Magnus N\\\"aslund \\and Claes\n Fransson \\and Monica Huldtgren}\n% \\offprints{M. N\\\"aslund}\n\n \\institute{Stockholm Observatory,\\\\ SE-133 36 Saltsj\\\"obaden,\\\\ \n\tSweden}\n\n \\mail{magnus@astro.su.se}\n \\date{Received; accepted }\n\n \\titlerunning{Luminosity Function of MS2255.7+2039}\n \\authorrunning{M. N\\\"aslund et al.}\n \\maketitle\n%\t\\markboth{N\\\"aslund et al.: Luminosity Function of \n%MS2255.7+2039}{}\n%\n%\n%1234567890123456789012345678901234567890123456789012345678901\n\n\\begin{abstract}\nThe luminosity function of MS2255.7+2039 at $z=0.288$ is determined down to a \ntotal magnitude of $R \\sim 24$, corresponding to $M_{\\mbox{\\tiny{\\rm R}}} \n\\sim -17 \\, ({\\rm H}_{\\mbox{\\tiny{0}}} = 50 \\ {\\rm km \\ s}^{-1} \\ {\\rm Mpc}^{-1})$. \nThe data are corrected for incompleteness and crowding using detailed \nsimulations. We find that the luminosity function is steeper than a standard \nSchechter function at faint magnitudes, and shows an excess of galaxies \nbelow $ M_{\\mbox{\\tiny{\\rm R}}} \\sim -19$. After corrections for light loss and crowding, the \ndata can be described by a sum of two Schechter functions, one with \n$M_{\\mbox{\\tiny{\\rm R}}}^{*} = -22.8$ and $\\alpha = -1.0$, and one steeper \nwith $M_{\\mbox{\\tiny{\\rm R}}}^{*} = -18.9$ and $\\alpha = -1.5$, representing \nthe dwarf population. A straight-line fit to the faint part yields a slope similar to the Schechter $\\alpha = -1.5$ of the dwarf population. The luminosity function of MS2255.7+2039 is compared \nto other clusters at lower redshifts, and does not show any significant \ndifference. The redshift range for clusters in which increased number of dwarf \ngalaxies have been found is therefore extended to higher redshifts. \n\\keywords{ Galaxies: clusters: general -- Galaxies: clusters: individual: MS2255.7+2039 -- Galaxies: evolution -- Galaxies: formation -- Galaxies: luminosity function, mass function -- Cosmology: observations}\n\\end{abstract}\n\n\n\n\n\n\n\\section{Introduction} \\label{sectintrod}\n\nThe faint end of the \nluminosity function (LF) is of great interest both in connection to the excess \nfound in number counts of faint galaxies and for theories of cluster formation.\nThe latter is demonstrated especially in a series of papers by Kaufmann et \nal. (1993), Kaufmann (1995a, b), Heyl et al. (1995) and Baugh et al. (1996), \nwhich show how the LF is related to the hierarchical clustering in e.g. the \nCold Dark Matter (CDM) model. A steep faint end of the LF is unique not only to \nthe CDM scenario, \nbut is a generic prediction of hierarchical models of cluster formation\n(White \\& Frenk 1991). The difference of the LF in the field and in clusters of \ngalaxies also gives important information about environmental effects related \nto the galaxy formation process. In particular, ram pressure stripping and \neffects of interaction are likely to be more important for clusters than in \nthe field (e.g., Moore et al. 1996). There is in this respect a clear \nconnection to the Butcher-Oemler effect (Butcher \\& Oemler 1984), seen for \nclusters, but not apparent in the field. The fraction of blue galaxies in \nclusters is larger at higher redshifts, which is often interpreted as an \nevolutionary effect. The evolution of the cluster LF is therefore of obvious \ninterest.\n\nThe field LF has been investigated locally by several groups. Some of \nthese report local LFs with flat faint-end slopes of $-1.1 \\la \\alpha \\la \n-1.0$ (Loveday et al. 1992; Ellis et al. 1996), while others have found a\nsignificantly steeper LF with $\\alpha \\la -1.5$ (Marzke et al. 1994; Lilly \net al. 1995). \nAt higher redshifts especially the CFRS survey (Lilly et al. 1995) and the \nAutofib survey (Ellis et al. 1996) give information about the \nLF in the field up to $z \\sim 1$. Lilly et al. find that, \nwhile strong evolution is seen for the blue sample at $z \\gsim 0.5$, \nthe red LF is changing little. At $z \\sim 0.5$ the \nLF has brightened by $\\sim 1$ magnitude in B. At higher \nredshifts the bright end stays constant, while the faint continues to \nincrease, leading to a steepening of the faint end of the LF, from $\\alpha = -1.1$ locally \nto $\\alpha = -1.5$ at $z \\simeq 0.5$, in broad agreement with the Autofib survey. A \nsteepening of the LF can explain the excess counts found in deep surveys, as discussed \nby Gronwall \\& Koo (1995).\n\nWhile the field LF has been studied in fair detail, there have been only a \nfew CCD investigations of the LF of clusters of galaxies until recently. \nRelatively nearby clusters, like Virgo, Fornax and Coma, have been studied \nby a number of authors (e.g., Bernstein et al. 1995, hereafter BNTUW; Lobo \net al. 1997; Biviano et al. 1995; De Propris et al. 1995; Trentham 1998a). \nWhile some earlier investigations yield faint-end slopes of $\\alpha \\simeq \n-1.3$ (e.g., Ferguson \\& Sandage 1988), more recent investigations, taking low \nsurface brightness galaxies into account, point to steeper slopes, $\\alpha \n\\la -1.5$ (e.g., Bothun et al. 1991).\n\n\nAt higher redshifts the information about the cluster LF is scarce. The first \ndetailed study was that by Driver et al. (1994b, henceforth DPDMD), who \nstudied the R-band LF to $R = 24$ for the cluster Abell 963 at $z = 0.206$. \nWhile the high luminosity end can be well fitted with a Schechter function, \nthey found an increase of faint galaxies between $-19 \\lsim M_{\\mbox{\\tiny{\\rm R}}} \n\\lsim -16.5$, with a slope of $\\alpha \\simeq -1.8$. Further investigations at \n$0.1 \\la z \\la 0.2$ have strengthened the case for \nsteep slopes, $\\alpha \\la -1.7$, at $-19 \\la M_{\\mbox{\\tiny{\\rm R}}}$ (Smith \net al. 1997; Wilson et al. 1997, hereafter WSEC), although examples of flatter LFs also exist \n(Trentham 1998b). \n\nIt is obvious that these results need confirmation for more clusters, \nespecially at higher redshifts. Because of the strong evolution of the \nButcher-Oemler effect, as well as from numerical simulations of cluster \nevolution (e.g., Kauffmann 1995a,b), one expects substantial evolution even\nfrom $z = 0.2$ to $z = 0.4$. The detection of the faint end of the LF then becomes more difficult, both because the galaxies are fainter, and \nbecause of increasing contamination from the background. As a first step we \nhere report observations of the cluster MS2255.7+2039 at $z = 0.288$. We will \nin this paper use ${\\rm H}_{\\mbox{\\tiny{0}}} = 50 \\kms~Mpc^{-1}$ and $\\Omega_{\\mbox{\\tiny{\\rm M}}} = 1$.\n\n\n\\section{The data}\n\nThe coordinates of the center of MS2255.7+2039 = Zw 8795, hereafter MS2255, \nare $\\alpha~=~22^{\\rm h}~55^{\\rm m}~40\\fs6$, \n$\\delta~=~20\\degr~30\\arcmin~04\\farcs2$ (1950.0), and \nthe redshift is $z = 0.288$ (Stocke et al. 1991). MS2255 was \ndetected as an X-ray cluster in the Einstein Observatory Extended Medium \nSensitive Survey (EMSS), with an X-ray luminosity of $2.0\\EE{44} \\ergs$ \nin the $0.3 - 3.5$ keV band (Gioia \\& Luppino 1994), fairly \ntypical for the EMSS selected sample. \n\nThe galactic extinction can be estimated in several ways. Based on the \\HI\\ \ncolumn density, the absorption in the direction of MS2255 ($l~=~90\\fdg32, \nb~=~-34\\fdg67$) is $A_{\\mbox{\\tiny{\\rm B}}} = 0.18$ (Burstein \\& Heiles 1982). With $A_{\\mbox{\\tiny{\\rm R}}} = \n0.61~A_{\\mbox{\\tiny{\\rm B}}}$ we get $A_{\\mbox{\\tiny{\\rm R}}} = 0.11$. On the other hand, the estimated X-ray column \ndensity is $5.0\\EE{20} \\rm~ cm^{-2}$ (Gioia et al. 1990). With $N_{\\mbox{\\tiny{\\rm H}}} = \n4.8\\EE{21}~E_{\\mbox{\\tiny{\\rm B-V}}}$ (Bohlin et al. 1978) and $A_{\\mbox{\\tiny{\\rm R}}} = 2.4E_{\\mbox{\\tiny{\\rm B-V}}}$ this \ngives $A_{\\mbox{\\tiny{\\rm R}}} = 0.25$, considerably higher than the value deduced from the \\HI\\ \ncolumn density. Finally, the recently presented COBE/DIRBE - IRAS/ISSA dust \nmaps (Schlegel et al. 1998) yield $E_{\\mbox{\\tiny{\\rm B-V}}} = 0.06$, which leads to $A_{\\mbox{\\tiny{\\rm R}}} = \n0.14$. We will in this paper use $A_{\\mbox{\\tiny{\\rm R}}} = 0.14$, but note that this may be in \nerror by $\\sim 0.1$ magnitude.\n\n\n\\subsection{Observations}\n\nThe data were obtained with the 2.56 m Nordic Optical Telescope and the \nAndalucia Faint Object Spectrograph (ALFOSC) in June 1997. The ALFOSC \ncontained a thinned, back-side illuminated Ford-Loral 2K$^{2}$ chip \nthat yielded a field of $6\\farcm5 \\times 6\\farcm5$ and an image scale of \n0\\farcs189/pixel. Every data set consists of the usual \nbias, dark, twilight-flatfield, and standard-star images, beside the science \nframes.\n\n\nTo determine the LF of the cluster it is crucial to correct for the \ncontribution from the field. A nearby field at $\\alpha = 22^{\\rm h} 54^{\\rm m} \n55\\fs04, \\delta = 21\\degr 32\\arcmin 19\\farcs00 \\ (1950.0)$ was chosen in order\nto have similar galactic latitude and extinction properties as the cluster. \nFurthermore, the \nseeing conditions during the observations turned out to be similar. All these factors are crucial\n to ensure that the foreground and background will be as similar to the \ncluster field as possible. Systematic errors may otherwise easily enter into \nthe subtraction of the background. \n\nThe total exposure time was 5400 seconds for both the cluster and the \nbackground field, respectively, divided into exposures of 900 seconds. During the \nobservations we rotated the instrument by 90\\degr \\ and/or made offsets \nby 10\\arcsec \\ between different frames. This was done in order to suppress \nthe influence of bad regions on the chip and to make it possible to create a \nnight-sky flatfield from the object frames (e.g., Tyson 1988). A pointing \nerror of the telescope at the time of the observations may have \ncaused the centre of the cluster and the image field centre to differ \nslightly. \n\n\n\n\\subsection{Reductions}\n\nThe bias level was determined from the overscan of each frame. These \nvalues \nwere used to scale a master bias that was subtracted from the frames. We \nthen used the shifted, bias-subtracted science frames to create a night-sky \nflatfield by removing objects with a 'smooth-and-clip' (N\\\"aslund 1995), \nfollowed by an averaging of the frames. We corrected the \nlarge-scale gradients of the twilight flatfield by the night-sky master flat, \nand used the corrected twilight flatfield to flat the science frames.\n\nA narrow strip along the edges had to be excluded in the frames due to the \nstructure of the thinned CCD. The flat-fielded frames were sky-subtracted, \ncorrected for atmospheric extinction, aligned and finally combined (see \nN\\\"aslund 1995). \nThe rotation and shifting of the frames decreased the effective area of \nthe combined image, so that the area of the background and cluster images \nbecame $5\\farcm6 \\times 5\\farcm5 = 31.0 \\Box$\\,\\arcmin \\ and $5\\farcm4 \n\\times 5\\farcm6 = 30.2 \\Box$\\,\\arcmin, respectively \n(the final detection areas were reduced somewhat in order to avoid edge \neffects; see below). The images \nwere calibrated using standard stars observed at intervals during the night. \nThe seeing in the combined images was in both cases $0\\farcs85$ (FWHM). \nThe background \nfield is shown in Fig.~{\\ref{FigBkg}}, while Fig.~{\\ref{FigCl}} displays the \ncluster.\n\n\\begin{figure}\n%\\resizebox{\\hsize}{!}{\\includegraphics{MSSbkg900cf.eps}}\n\\vspace{88 mm}\n\\caption{The $5\\farcm6 \\times 5\\farcm5$ background field image in the\nR band. The total exposure time is 5400 seconds.}\n \\label{FigBkg}\n\\end{figure}\n\n\nThe individual frames of the cluster and background fields were checked \nfor 'internal consistency'. We selected a few common objects in the magnitude \nrange 17-21 and determined their brightness both in FOCAS (Jarvis \\& Tyson \n1981; Valdes 1982, 1993) and DAOPHOT (Stetson 1987). All objects were \nconsistent within a few hundredths of a magnitude or better. The weighted \naverage of the standard stars observations \nyielded an statistical uncertainty of $\\pm 0.01$ magnitude.\n\n\n\\section{Analysis of the fields}\n\n\\subsection{Object catalogue}\n\nThe reduced fields were analyzed using the FOCAS package. As a limit to our detections we used a value of $2.5 \n\\sigma$ of the sky noise and a detection area $A$ of 20 pixels, which \ncorresponds to the seeing. We then utilized the ordinary FOCAS procedure, \nincluding sky \ncorrection and splitting of multiple objects. The splitting procedure was \nchecked by simulations and worked satisfactory in most cases. A region of 50 \npixels along the edges was excluded when counting galaxies, which decreased \nthe effective area of the background field to $27.65 \\Box$\\,\\arcmin \\ and of \nthe cluster field to $27.02 \\Box$\\,\\arcmin. This procedure resulted in a \ncatalogue of objects with a number of parameters such as isophotal R \nmagnitudes $(m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}})$ and intensity \nweighted first-moment radii $(r)$. A plot of the detected galaxies is shown \nin (Fig.~{\\ref{Figmiphir1}}).\n\n\\subsection{Simulations}\n\nA substantial part of the analysis consists of simulations in order to \ndetermine completeness levels, fraction of noise detections, and magnitude \ncorrections. When we approach the level of \nthe sky noise we will obviously lose some galaxies in the noise, as well as \npick up false detections. This problem is for a given total magnitude most \nsevere \nfor galaxies with large scale lengths and therefore low surface brightness. \nAs discussed by, e.g., DPDMD and WSEC, the determination of this \nfactor is far from trivial, and unfortunately, model-dependent assumptions \nabout the galaxies are necessary. In one approach, discussed by DPDMD, one \ngenerates artificial galaxies with fixed parameters shifted to \ndifferent redshifts, to describe the surface brightness distribution. An \nalternative method, used by WSEC, is to use real galaxies at brighter \nmagnitudes, typical for the population in the field, as templates, and then \nrescale these to fainter magnitudes. This approach has the advantage of using \nrealistic brightness profiles. It, however, implicitly assumes that the \nrelative fractions of the different morphological types are the same for faint \nmagnitudes as for bright, and also that the brightness profiles of a given \ntype is independent of luminosity, except for a normalization factor. \nNeither of these assumptions are obvious. \n\nWe used a generalized version of the DPDMD method in this investigation; the \nobjects were not only characterized by their brightness, but also by their \nscale size. \nSimulated exponential disks were added to the background-field image, and \nthese artificial galaxies were then detected with the same criteria as were \nused for the real data. After detection we could determine the magnitude \ncorrection depending on the objects position in the magnitude-scale length \ndiagram (see Section~{\\ref{sec:magcorr}}). \n\n\\begin{figure*}\n%\\center{\\resizebox{13cm}{!}{\\includegraphics{MSS6_900f.eps}}}\n\\center{\\vspace{13cm}}\n\\caption{R-band image of MS2255.7+2039. The field covers $5\\farcm4 \\times \n5\\farcm6$ and the total exposure time is 5400 seconds. North is up and East\nis to the left.}\n \\label{FigCl}\n\\end{figure*}\n\n\\subsubsection{Noise simulations}\n\nFirst, a number of Poisson-noise frames were created, with a noise level \ncorresponding to that of the data. We then used FOCAS to detect spurious \nfeatures with different combinations of the upper sigma limit and \ndetection area. The parameters we settled for, $\\sigma = 2.5$ and $A = \n20$ pixels ($\\approx$ seeing), yielded six noise detections in an area of \n$27 \\Box$\\arcmin. This amounts to about 0.2\\% of the actual detections in \nthe \nbackground field.\n\n\\subsubsection{Completeness}\n\nTo estimate the completeness we simulated exponential disks of different \nmagnitudes, scale lengths and inclinations. For each set of parameters, 51 \nexponential disks were generated in empty regions of the background-field \nimage. The reason for positioning the simulated galaxies in empty regions \nwas to isolate the detection completeness due to surface brightness, and treat \nother effects, like overlapping (cf. Section~{\\ref{sec:crowding}}), \nseparately. We used FOCAS with the same detection criteria as for the real \ndata. The parameters of the detected artificial objects could then be \nextracted from the resulting catalogue. As mentioned below, and discussed by \nother authors (DPDMD, Trentham 1997), the possibility of detection, as well \nas the fraction of the total light recovered, varies with surface brightness, \nwhich in turn depends on scale length and inclination for a given magnitude. \nAt fainter magnitudes, galaxies with short scale length are, as expected, more \neasily detected than those with long scale lengths. The simulations indicate \nthat we detect all dwarf galaxies, modelled as exponential disks ($0.5 \\la \nr_{\\mbox{\\tiny{\\rm d}}} \\la 2$ kpc, where $r_{\\mbox{\\tiny{\\rm d}}}$ is the \ndisk scale length), down to $R \\sim 25$. \n\nAn important complication is the possible presence of low surface \nbrightness galaxies (LSBGs). These come in different flavours, such as the \nsample of blue Low-Surface-Brightness Galaxies of McGaugh \\& Bothun\n(1994) and the Giant Low-Surface-Brightness Galaxies of Sprayberry et\nal. (1995). The central surface brightness distribution of galaxies is\nnot well known, although research during the last decade has shed\nmore light on this particular type of object (Impey \\& Bothun\n1997). If LSBGs are peaked around \n$\\mu_{\\mbox{\\tiny{\\rm B}}}^{\\mbox{\\tiny{0}}} \\simeq 23.2 \\ \n\\rm{mag}/\\Box$\\,\\arcsec (corresponding to $\\mu_{\\mbox{\\tiny{\\rm\nR}}}^{\\mbox{\\tiny{0}}} \\simeq 22.0 \\ \\rm{mag}/\\Box$\\,\\arcsec), as those\nobserved by Sprayberry et al. and McGaugh \\& Bothun, we would detect\nLSBGs with small and intermediate scale lengths \n($r_{\\mbox{\\tiny{\\rm d}}} \\sim 3$ kpc), given the colours of the Sprayberry \net al. sample. Even objects with lower surface brightness, like UGC 9024 \n($\\mu_{\\mbox{\\tiny{\\rm B}}}^{\\mbox{\\tiny{0}}} = 24.5, \nr_{\\mbox{\\tiny{\\rm d}}} = 5.6/h$ kpc), should be possible to detect at \n$z = 0.288$, although such galaxies are close to our detection limit. \nGalaxies with lower surface brightness will accordingly escape \ndetection. The most extreme cases known (e.g. Malin 1) are far beyond \ndetection, but galaxies of this type are likely to be an order of \nmagnitude fewer than objects of higher surface brightness (Davies et al. 1994).\nFurthermore, a study of Hubble Deep Field data by Driver (1999) shows that \nluminous low surface brightness galaxies are rare compared to their high \nsurface brightness counterparts. One should, in any case, bear in mind that \nLSBGs below the surface-brightness detection limits may influence the \nfaint-end slope by an unknown amount.\n\n\\subsubsection{Magnitude correction}\n\\label{sec:magcorr}\n\nFrom the simulations above, used to determine the completeness, \nwe also estimated the total magnitude for each parameter set. During the \nanalysis we developed \na technique for magnitude corrections (N\\\"aslund 1998), which turned out to be \nsimilar to that of Trentham (1997). A large number of simulated galaxies, \nwith different values of scale length ($r_{\\mbox{\\tiny{\\rm d}}}$), axial \nratio ($b/a$) and total magnitude ($m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm \ntot}}}$), were generated in the background-field image. These objects were \ndetected with the same setup as for the real data. We could at this \nstage calculate the magnitude correction as a function of isophotal magnitude \n($m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}}$) and intensity weighted \nfirst-moment radius ($r$). We, finally, corrected the magnitudes of the detected \ngalaxies from their position in the \n$(m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}},r)$ plane (Fig.~{\\ref{Figmiphir1}}). \n\nThis method will obviously not be fully correct for elliptical galaxies that \nare better described by de Vaucouleur profiles than by exponential disks. \nMost of these are, however, of comparatively bright magnitudes, where the \ncorrection is small. If we assume that the faintest cluster members, for \nwhich the corrections are largest, have exponential profiles the application \nof the method is justified. This is plausible if the faintest galaxies are \nlate-type spirals or dwarf spheroidals and/or dwarf irregulars. However, some \nof the galaxies close to our magnitude limit ($R \\sim 24$) may be {\\em \nluminous} dwarf ellipticals ($-16 < M_{\\mbox{\\tiny{B}}}$) that are better \nfitted by de Vaucouleurs profiles (Ferguson \\& Binggeli 1994). We performed a \nfew simulations of de Vaucouleurs profiles with short scale lengths to mimic \nluminous dwarf ellipticals, and compared them to exponential disks of the same \nbrightness. We find that the total magnitudes for the $r^{1/4}$ profile \ngalaxies are underestimated by 0.15 magnitudes, similar to the findings of \nTrentham (1997). \n\nThe magnitude correction can be applied in two ways. One can either correct \nfor 'light loss' without any assumptions about the cluster population, or one \nmay use {\\em a priori} information to constrain the distribution of points in \nthe ($m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}},r)$ plane. If the faintest \ncluster members that we detect are exclusively dwarfs, this has two \nimplications. Firstly, for objects with $r_{\\mbox{\\tiny{\\rm d}}} \\la 2$ kpc \nthe catalogue should be more than 50\\% complete for \n$m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}} < 26$. Secondly, the magnitude \ncorrection would in this case be fairly small, and the ambiguity at the \nfaintest magnitudes is reduced, compared to a more complex population. This is \nbecause faint galaxies are found in a comparatively small region of the \n$(m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}},r)$ plane, and the reason is \nsimply that faint, intrinsically large galaxies (i.e. LSBGs), will have \ntheir apparent scale lengths substantially reduced, and thereby be closer to \nthe true dwarf region of the $(m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}},r)$ \nplane. As a result, the uncertainties in the magnitude correction \nincrease at the faint end. If one for good reasons could justify the \nexclusion of non-dwarfs from this region of the \n$(m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}},r)$ plane, the corresponding \nmagnitude correction would be more accurate. In addition, if all faint \ngalaxies are dwarfs and have $r^{1/4}$ profiles, the luminosity after \ncorrection would be systematically underestimated (see above). On the other \nhand, if they {\\em all} are luminous dwarf ellipticals the \nmagnitude correction would not be increasing with magnitude as steeply as the \none applied here, and the LF would therefore be less steep at faint \nmagnitudes. However, there is no strong motivation for such an exclusion of \nintrinsically larger objects, and for the data presented here we used the \nfirst, more general, approach. The possible presence of larger, faint objects \nalso calls for the use of exponential profiles.\n\nThe magnitude-correction procedure was tested by generating a number of \nexponential disks distributed in magnitude according to a power law of \nslope 0.4. The \ngalaxies were positioned along a grid in order to avoid crowding effects in \nthis particular test. The simulations showed that the procedure managed to \ncorrect for the light loss well down to $R \\simeq 24$, \nclose \nto the actual completeness limit (for $r_{\\mbox{\\tiny{\\rm d}}} \\la 6$ kpc) \nof the data (N\\\"aslund 1998).\n\n\n\\begin{figure}\n%\\rotatebox{0}{\\resizebox{\\hsize}{!}{\\includegraphics{miphir1.eps}}}\n\\vspace{88mm}\n\t\\caption[]{The detected galaxies in the $(m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}},r)$ plane of the cluster image. $m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}}$ is the isophotal R-band magnitude and $r$ the intensity weighted first-moment radius.}\n \\label{Figmiphir1}\n\\end{figure}\n\n\n\n\\subsubsection{Crowding}\n\\label{sec:crowding}\n\nOverlapping objects is another important factor, especially for faint\nobjects. \nOne way \nto see this is by noting that fainter objects have smaller effective \nfield areas at their disposal. Stars and galaxies that are brighter in general \noccupy a larger apparent area in the image and fainter objects are shielded \nby them. \n\nWe have tested different methods for this correction. In the first \napproach we added simulated compact objects of different magnitudes to the \ncluster and background images. To a first approximation, the fraction\nof recovered objects gives the detection probability as a function\nof magnitude. However, non-linear effects, connected with obscuration\nbetween especially the faint galaxies themselves, are likely to be\nimportant, and full simulations of the cluster and background would be\nneeded to address these aspects. \n\nInstead of this method we adopted a more conservative correction procedure \nfor the obscuration of faint objects. The cumulative area covered by objects \nup to a certain magnitude was calculated in half-magnitude intervals for the \nbackground and cluster field, respectively. It was then found that there is \na clear difference between the area covered in the cluster image and the \nbackground~-~field image when it comes to {\\em bright} objects. However, for \nfainter objects there is no substantial difference; the covered area increases \nsimilarly in both fields. In practice, this means that for objects brighter \nthan $R \\sim 22$ the obscured area is 8\\% in the cluster image, while the \ncorresponding number for the background image is only 3.4\\%. We accordingly \nused these numbers to correct for the obscuration for objects fainter than \n$R = 22$. We do therefore not include any magnitude dependence of the \ncorrection \nfactor below $R = 22$, as Smith et al. (1997) do, which implies that apparently small \nobjects are not an important source of obscuration in our fields. Furthermore, these effects \ndo not add linearly with brightness for faint objects.\nIn the case that faint objects contribute somewhat themselves to the \nobscuration, we would have underestimated the faint~-~end slope of the \nLF slightly. We hope to perform a more thorough study of crowding effects \nelsewhere.\n\n\n\n\\subsection{Foreground and background corrections}\n\n\\subsubsection{Stars}\n\nMS2255 is at comparatively low galactic latitude ($b = -34\\fdg67$), \nand a substantial contamination by stars is expected. Because our comparison\nfield is close to the cluster, this contamination is to a large extent \nreduced when we subtract the background counts from the cluster counts. \nWith FOCAS, we can nevertheless separate stars from galaxies, based on the \nbrightness profile, for $R \\la 20$. This eliminates the statistical errors \nin the cluster counts from this source. The saturated stars were removed \ninteractively from the galaxy list, while remaining stars brighter than \n$R = 20$ were detected and classified by FOCAS. We found in this way 25 \nstars in the cluster field, and 17 in the background field. This can be \ncompared to the number expected from the galactic model by Bahcall \\& \nSoneira (1980) and Bahcall (1995), which for a field of $27 \\ \\Box\\arcmin$ \ngives 30 stars brighter than $R = 20$. Within the statistical errors we \nconsider the number of stars \nin the cluster field to be consistent with that expected from the model. The \nlower number for the background field is simply explained by the fact that \nthe field was selected in a region void of bright objects. \n\nBesides bright stars, we also excluded small spurious objects\naround bright stars or galaxies, which can be a result of false\ndetections by FOCAS in the cluster and background field (see Trentham\n1997 for a discussion). This effect does not affect the faint-end slope\nsignificantly. \n\n\n\\subsubsection{Background counts}\n\nGuided by the completeness simulations, we decided to set the isophote \nlimit for inclusion in the catalogue at $m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}} \n= 26$, approximately corresponding to the magnitude limit after correction given above. \nAccording to the simulations we detect all pointlike sources at this isophotal \nmagnitude. \n\nInspection of the ($m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}},r$) plane shows that some of \nthe detected objects fall below the simulated point sources, i.e. they have \nscale lengths smaller than the seeing. The apparent small scale length may \nbe a result of the small number of counts (ADUs) for the faint objects. There \nis then a substantial probability that even for a point-like object the scale \nlength will be smaller than the width of the PSF. \nMoreover, the simulations showed that disks with large scale lengths that are \nbelow the completeness limit could be detected as such compact objects, but \nalmost all of them have $m_{\\mbox{\\tiny{R}}}^{\\mbox{\\tiny{\\rm iph}}}$ beyond our catalogue limit \nanyway, and hence cause no problem. The ambiguity in the interpretation of the \nnature of these objects made us test whether they influenced the shape of the \ncluster LF. We generated one list that included these objects, and one in which \nthey were removed for both the cluster image and the background-field image. \nThe resulting faint-end slope is in the latter case somewhat flatter compared \nto the slope including these objects, which is the one presented in this paper.\n\nIn Fig.~{\\ref{FigCount_Bkgcorr}} we show the corrected R\\,-\\,band background\ncounts, together with those obtained by the Hitchhiker team at WHT (Driver et al. 1994a) and the counts from BNTUW. As seen in the figure, the corrected \nbackground counts agree well with each other down to $R \\sim 24$, within the \nlimited statistics. While we have a total background area of $27.65 \n\\Box\\arcmin$, Driver et al. had a total area of $15.9 \\Box\\arcmin$. Their \nexposures with the WHT were, however, deeper in these fields. We also note \nthat our counts are within the variations of other recent investigations \nsuch as those by Arnouts el al. (1999) and Fontana et al. (1999).\n\n\\begin{figure}\n\\resizebox{!}{88mm}{\\includegraphics{bkg_comp_land.eps}}\n\t\\caption[]{Differential number of galaxies as a function of \n isophotal R-magnitude for the background field (filled circles). The background counts of DPDMD (open squares) and BNTUW (open triangles) are also shown.}\n \\label{FigCount_Bkgcorr}\n\\end{figure}\n\n\n\\section{The cluster luminosity function}\n\n\n\\subsection{Error estimation of cluster counts}\n\nBecause of both statistical and systematic errors a careful error analysis\nhas to be made. The standard method has been to assume \nPoisson statistics for the galaxies in the background field and cluster field, \nrespectively, in some cases supplemented by an error for the\nfield\\,-\\,to\\,-\\,field variation caused by large scale structures. Because we have only one background\nfield, we cannot \ndetermine the field-to-field variation from our material. We therefore use the \nfield\\,-\\,to\\,-\\,field statistics of BNTUW, with the characteristics of our data, \nto estimate the \nvariation in the background counts as a function of magnitude (see also Trentham 1997). This value \nwas added in quadrature to the Poisson variation in the cluster counts and \nthe error due to the magnitude correction. The latter was estimated as \nthe $1\\sigma$ dispersion in a number of simulations (see \nSection~{\\ref{sec:magcorr}}). The two error sources are generally of \ncomparable magnitude, but the field-to-field variation is systematically \nlarger for fainter magnitudes ($R > 22.5$).\n\n\n\\begin{figure}\n\\resizebox{!}{88mm}{\\includegraphics{ms_2255_uncorr.eps}}\n\t\\caption[]{Background-subtracted differential\n number of galaxies per 0.5 mag and square degree \n as a function of isophotal R-magnitude for MS2255.7+2039. No \ncorrections have been applied.\n }\n \\label{FigCount_Cl_bkg}\n\\end{figure}\n\n\n\\begin{figure}\n\\resizebox{!}{88mm}{\\includegraphics{ms_2255_corr.eps}}\n\t\\caption[]{Background-subtracted and corrected differential number \n of galaxies per 0.5 mag and square degree as function of isophotal R-magnitude for MS2255.7+2039. \n }\n \\label{fig:FigCount_Cl_bkgcorr}\n\\end{figure}\n\n\n\n\\subsection{The raw LF}\n\\label{sec:rawLF}\n\nBy subtracting the background counts from the cluster counts, we obtain\nthe LF in terms of the apparent, isophotal magnitude. This 'raw' LF is \nshown in Fig.~{\\ref{FigCount_Cl_bkg}}. Then we applied the\nsame distance modulus, including $K$-correction, as for the corrected\ndistribution (see below). \nThe resulting distribution can be fitted by a single Schechter function with $\\alpha \n= -1.4$ and $M_{\\mbox{\\tiny{\\rm R}}}^{*} = -24$.\nIt is important to note that these numbers are arrived at partly because of \nthe two 'low' bins at $M_{\\mbox{\\tiny{\\rm R}}}=-20.75$ and \n$M_{\\mbox{\\tiny{\\rm R}}}=-20.25$. If we exclude \nthese points, we obtain $\\alpha = -1.3$ and $M_{\\mbox{\\tiny{\\rm R}}}^{*} \n= -22.8$. Although the shape of the LF suggests that \nthe bright end would be better fitted by a Gaussian, these low values can \nbe explained as a statistical effect. Both points are fitted within \nthe $2\\sigma$ level by a Schechter function with parameters \n$M_{\\mbox{\\tiny{\\rm R,giants}}}^{*} = -22.5$, $\\alpha = -1.0$ (see \nFig.~{\\ref{fig:ThreeLFs}}). Monte Carlo simulations of this Schechter function \nwith the same total number of galaxies as observed, show that a dip similar to \nthat in Fig.~{\\ref{FigCount_Cl_bkg}} appears in $(10-20)\\%$ of the simulations. \nWe therefore conclude that this dip is of marginal significance.\n\nThe Schechter parameters can be compared to those of Valotto \net al. (1997), who found $\\alpha = -1.4$ for rich clusters and $\\alpha = \n-1.2$ for poor. A linear fit for the range $-19 < M_{\\mbox{\\tiny{\\rm R}}} < \n-17$ also yielded $\\alpha = -1.3$, which is the least model dependent \nestimate of the uncorrected faint-end slope. A comparison of 'raw' LFs at \ndifferent redshifts is, however, misleading.\n\n\n\\subsection{The corrected LF} \\label{seccorrLF}\n\nFor an unbiased comparison with samples at other redshifts, the isophotal \nmagnitudes have to be related to the total magnitude, and then translated \ninto absolute magnitudes. \nFor the latter we included an R-band $K$-correction given by \nMetcalfe et al. (1991), who found a $K$-correction of 0.41 magnitudes for \nE/S0 galaxies at $z = 0.288$, while the average for spirals was 0.09. \nWe used a straight mean value $K = 0.15$, but realize that the true range \nmay be $-0.1 \\la K \\la 0.41$. Because of the type dependence of the \n$K$-correction the intrinsic cluster LF is expected to be slightly \nredistributed, compared to the one observed. This redistribution should, \nhowever, be within the limits just mentioned. Thus, the distance modulus \nbecame $(m-M) = 41.47 - K$.\n\nIn order to estimate the influence of the $K$-correction on the measured slope \nwe made two tests. In both cases we kept the correction of the bright \npopulation fixed at $K = 0.15$, but applied values of $K = 0.1$ and $K = 0.4$, \nrespectively, to the dwarfs. This was done by simply assuming that all bins in \nthe LF at $R > 23$ represent the dwarf population, since \nthis is the region where the dwarfs dominate in the corrected LF (see \nFig.~{\\ref{fig:ThreeLFs}}). In neither case is the faint-end slope for the \nthe fitting method described below affected. \n\n\nThe uncorrected LF presented in Section~{\\ref{sec:rawLF}} represents a strict lower \nlimit to the true LF. By applying the magnitude and crowding corrections, \ndescribed in previous sections, to the cluster field and background field, \nrespectively, we arrive at the LF shown in \nFig.~{\\ref{fig:FigCount_Cl_bkgcorr}}. \n\nWhile providing a useful description of the data, a Schechter fit is not \nunique, and we have tested different parametrizations of the corrected \ndata. A single Schechter function with $M_{\\mbox{\\tiny{\\rm R}}}^{*}=-23.9$ \nand $\\alpha \\simeq -1.43$ gives a decent fit, although there is an \nindication of a break at $M_{\\mbox{\\tiny{\\rm R}}} \\simeq -20$.\n\nBinggeli et al. (1988) discussed the separation of the total LF \ninto components for each Hubble type for the Virgo cluster. This is not \npossible for our data, because of the distance to the cluster, the lack of \ncolour information, etc. We can, however, use the {\\em a priori} information \nthat the transition region between giants and dwarfs is at $-18 \\la \nM_{\\mbox{\\tiny{\\rm B}}} \\la -16$. For comparison reasons, we add two separate \nSchechter functions, one representing giant galaxies and the other representing dwarfs. \nIf the slope of the giants is fixed at $\\alpha = -1.0$, \nthe procedure yields $M_{\\mbox{\\tiny{\\rm R,giant}}}^{*}=-22.8$ and \n$M_{\\mbox{\\tiny{\\rm R,dwarf}}}^{*}=-18.9$ for the two populations. \nThis is close to the corresponding values found by DPDMD ($-22.5, -19.0$). \nThe main discrepancy is in the slope of the dwarf population. For MS2255\nwe find $\\alpha \\simeq -1.5$. This can be compared to A963 for which DPDMD\nfind $\\alpha \\simeq -1.8$. It is, however, \nimportant to note the coupling between $M^{*}$ and $\\alpha$. For \n$M_{\\mbox{\\tiny{\\rm R,dwarf}}}^{*} = -19.5$ our faint-end slope yields \n$\\alpha \\simeq -1.8$, while $M_{\\mbox{\\tiny{\\rm R,dwarf}}}^{*} = -18.5$ \nresults in $\\alpha \\simeq -1.2$ (the dwarf/giant ratio was, however, not \nconstrained in these tests, as in the case of DPDMD's fit). The strong \ncoupling between $\\alpha$ and $M_{\\mbox{\\tiny{\\rm R}}}^{*}$ makes it \ndangerous to draw any firm conclusions based on Schechter-function fits only. \nInstead, {\\em one should directly compare any two LFs, magnitude by magnitude}, as \nshown below. In order to avoid the coupling of the Schechter-function \nparameters for the faint end of the LF, we also used a simple straight-line \nfit to the last five data bins, $-19.5 \\le M_{\\mbox{\\tiny{\\rm R}}} \\le -17$ \n(as proposed by Trentham 1998b), which yielded $-1.6 \\la \\alpha \\la -1.5$. \nThis is somewhat steeper than the 'raw' LF, and is caused by the magnitude \nand obscuration corrections. This steepening of the LF is consistent with \nthe bright end of the dwarf population detected in more nearby clusters \n(see discussion below). Although the procedures discussed above yield a \nformal value of the faint-end slope of $\\alpha \\simeq -1.5$, the uncertainties\ninvolved in these kind of studies make us emphasize that one should not focus\non the exact value of the slope, but rather on the qualitative appearance of\nthe LF.\n\n\\subsection{Comparison with other clusters}\n\\label{comparison}\n\nA major reason for the interest in the cluster LF is to study the \nevolutionary effects with redshift. As we have just discussed, this is \ndone best by a direct comparison of the different LFs, i.e. by plotting \nthem together, including all corrections. \nA problem is that the observations are in different filters and/or that the \n$K$-corrections are uncertain. A possibility to avoid some of these \nuncertainties is to compare the LFs in filters with central wavelengths \nadjusted to the redshift. In our case we note that at $z=0.288$, the R \nband corresponds to a wavelength between B and V at $z=0$. The other, more \nmodel dependent, method is to use a $K$-correction for a given $z$ and a \ngiven filter. This depends, however, on the population (section~\\ref{seccorrLF}), as well as on \nevolution. Unfortunately, we are in most cases forced to use this alternative. \n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{cl_comp_newer.eps}}\n\t\\caption[]{Luminosity functions of three galaxy clusters. Filled \ncircles represent MS2255.7+2039, open squares A963 (DPDMD), and open \ntriangles Coma (Trentham 1998a). A963 and Coma have been normalized to \nMS2255.7+2039 for $M_{\\mbox{\\tiny{\\rm R}}} \\le -21$. The curve represents \na combination of two Schechter functions ($M_{\\mbox{\\tiny{\\rm R,giants}}}^{*} \n= -22.5$, $\\alpha = -1.0$, dotted line; $M_{\\mbox{\\tiny{\\rm R,dwarf}}}^{*} = -19.0$, \n$\\alpha \\simeq -1.5$, dashed line) and is shown here in order to guide the eye.\n }\n \\label{fig:ThreeLFs}\n\\end{figure}\n\n\n\nIn Fig.~{\\ref{fig:ThreeLFs}} we display the LF for MS2255 together with \nTrentham's (1998a) LF of Coma ($z = 0.023$) and the LF of A963 ($z = 0.206$) \n by DPDMD, all adjusted to ${\\rm H}_{\\mbox{\\tiny{0}}} = 50 \\ {\\rm km \\ s}^{-1} \n{\\rm Mpc}^{-1}$. Both LFs were normalized to the same level as MS2255 for \ngalaxies brighter than $M_{\\mbox{\\tiny{{\\rm R}}}} = -21$. Although a fainter \nlimit for this normalization would have been preferable, this value was \nchosen to avoid influence from the low points in the LF of MS2255 at \n$M_{\\mbox{\\tiny{{\\rm R}}}} \\simeq -21$. \n\nIt is evident that all three clusters exhibit steep slopes at the faint end, \nand there is accordingly no qualitative difference between nearby and distant \nclusters in that respect. The slope of Coma is actually as steep as that of \nA963, while MS2255 displays a somewhat flatter faint end of the LF. The steep \nslope of the Coma LF was also noted by Smith et al. (1997), who used Coma \ndata from Thompson \\& Gregory (1993). The steepening occurs at slightly \ndifferent magnitudes. A963 has its break point around \n$M_{\\mbox{\\tiny{{\\rm R}}}} = -19.5$. The steepening in MS2255 starts at \napproximately the same magnitude, while that in Coma occurs at a somewhat \nfainter magnitude ($M_{\\mbox{\\tiny{{\\rm R}}}} \\simeq -18.5$). \n\nThe shape of the faint end of the cluster LF is a matter of controversy. \nWhile both nearby and more distant clusters show a steepening of the \nLF, the magnitude where this occurs differs substantially. To some extent \nthis may be caused by a simple zero-point shift between filters. Most studies \nat intermediate redshifts ($0.1 \\le z \\le 0.2$) yield steep slopes ($-2 \\la \n\\alpha \\la -1.7$) for $-19 \\la M_{\\mbox{\\tiny{{\\rm R}}}}$ (DPDMD; Smith et \nal. 1997; WSEC). However, the studies by Trentham (1998b, c), \nwhich in some cases are based on local clusters, give a more shallow slope \n($\\alpha \\simeq -1.4$). In some local clusters, the steep slope starts at \n$M_{\\mbox{\\tiny{{\\rm R}}}} \\simeq -14$, which is a region beyond the \nlimits of present studies for clusters around $0.2 \\la z \\la 0.3$. One reason \nfor the discrepancies can be the different correction methods applied.\nIt should be noted that earlier photographic investigations of \nnearby clusters also suffered from severe selections effects that work against \nlow surface brightness objects. When such effects have been corrected for, the \nresulting slope is in the range $-1.5 \\la \\alpha \\la -1.8$ (Impey et al. \n1988; Bothun et al. 1991). \n\nAnother subject of interest is the possible existence of a universal \ncluster LF. In view of the discussion above, this is highly controversial \nand depends e.g. on the correction procedures applied. Composite LFs of \nclusters at $0.02 \\simeq z \\simeq 0.2$ have been presented both in B and \nin R, based on more than 15 (in B) and six clusters and groups (in R), \nrespectively (Trentham 1998c, d). The composite R-band LF has a slope of \n$\\alpha \\simeq -1.5$ at $M_{\\mbox{\\tiny{{\\rm R}}}} \\simeq -17$, which is \nsimilar to what has been found here for MS2255. The steep slope of Coma \n(Trentham 1998a) seems to have been averaged out by the weighting procedure \nin the composite LF. Trentham noted, \nhowever, that his composite function may be valid only for the centres of \nrich clusters, i.e. regions dominated by ellipticals. \n\nWSEC studied two clusters, A665 and A1689, both at $z = 0.18$, \nin V and I. This study is especially interesting because it gives some \ninformation about the colour dependence of the LF. WSEC found rising \nLFs with breaks around $M_{\\mbox{\\tiny{\\rm V}}} =\n-19$ and $M_{\\mbox{\\tiny{\\rm I}}} = -21$. Their V-band slope, \nafter correction for incompleteness and obscuration, is very steep \n($\\alpha \\sim -2$), while that in the I band is significantly flatter \n($\\alpha \\sim -1.1$). This difference is interesting, since it indicates \nthat the faintest detected galaxies indeed are blue. If this effect is real, \none would expect an even steeper slope in B. Somewhat surprisingly, Trentham \n(1998b) did not find a comparatively steep B-band LF in his study of A665. \nFurthermore, while displaying \nvery steep slopes ($\\alpha < -2$), the four Abell clusters investigated by\nDe Propris et al. (1995) did not show any differences between B and I in \nthis respect. The question of colour dependent slopes is therefore still \nunanswered. \n\nFew numerical simulations of cluster LFs exist. White \\& Springel (1999) \ndiscuss in a recent paper a combination of $N$-body and semianalytical \nmodelling of the cluster population. Unfortunately, they only present the \nB-band LF, for which they find a faint end slope of $\\alpha = -1.2$. Although \na direct comparison is difficult (R at $z = 0.3$ corresponds approximately to \nV at $z = 0$), this is considerably flatter than the observed slope presented \nhere.\n\n\n\\section{Summary and conclusions}\n\nWe have observed the galaxy cluster MS2255.7+2039 ($z = 0.288$) and a\nbackground field at similar galactic latitude with the aim of\ndetermining the cluster LF. The isophotal magnitudes have been\ncorrected for light loss according to results obtained from\nsimulations. We have also compensated for obscuration due to bright,\napparently large, objects in the images. The resulting cluster LF \nhas a fairly steep faint-end slope ($\\alpha \\simeq -1.5$) faintward of the \nbreak in the profile around $M_{\\mbox{\\tiny{\\rm R}}} = -19$. This slope is\nmore shallow than some LFs found in clusters both locally and at $z \\simeq \n0.2$, but similar to the slope of the composite LF derived by Trentham \n(1998c). Without focusing too strongly on the precise value of the slope, we conclude that MS2255.7+2039 exhibits a steepening LF at faint magnitudes.\n\nThe evidence for steep faint-end slopes of cluster LFs is accumulating. There \nare now a number of fairly deep CCD investigations of nearby, as well as a few \nmedium distant ($z \\la 0.3$) clusters, that all point to rising LFs at faint \nmagnitudes. It therefore seems clear that a flat LF (i.e., $\\alpha = -1$) can \nbe ruled out even at intermediate magnitudes ($ -20 \\la M_{\\mbox{\\tiny{\\rm \nR}}} \\la -17$). However, several questions remain unanswered. The \nuncertainties in the measured slopes are probably considerable, since \ndifferent correction methods seem to yield deviating results, which probably \nexplains the discrepancies between the LFs found for the same clusters as \ndetermined by different investigators (see section~\\ref{comparison}). \n\nBecause of these uncertainties, it is too early to discuss any variation of \nthe faint-end slope with $z$. The accuracy of the present study only allows \nus to claim that the cluster LF is non-flat at faint magnitudes ($-19 \\la \nM_{\\mbox{\\tiny{\\rm R}}}$). The exact values of the slope and the magnitude \nwhere the steepening sets in are uncertain, and any trend with $z$ that may \nbe present is dominated by these uncertainties. In addition, environmental differences, \nlike richness or density, between clusters at the same $z$ could affect \nindividual LFs, making distinctions in $z$ even more difficult to isolate. The \nuncertainties in the background subtraction is also a source of error, \nalthough the simulations by Driver et al. (1998) show that the faint-end \nslope of the LF can be reliably determined out to $z \\simeq 0.3$ with seeing \nand depth similar to those of the present data. Nevertheless, the errors \ndue to the statistical background subtraction can probably be substantially \nreduced by using photometric redshifts. Work based on this approach is in \nprogress.\n\nThere are in the context of cluster LFs several important questions to \nanswer in the future: Is there a universal LF for galaxy clusters at low \nredshifts, or is the steepness of the dwarf population different between \nclusters? Is there a colour dependence of the steepness of the dwarf \npopulation, as may be indicated in the study by WSEC? \nThe K-band observations of five clusters by Trentham \\& Mobasher (1998) are \nespecially interesting in this context. These data were, however, not deep \nenough to\ndraw any conclusions about the faint end of the luminosity function. From \nthe clear signs of evolution between $z = 0.5$ and the present epoch for the \nfield (e.g., Lilly et al. 1995), one would expect a corresponding \nevolution in clusters. From the galaxy harassment scenario for the \nButcher-Oemler effect (Moore et al. 1996) one may expect a larger fraction \nof low luminosity galaxies in the past, and therefore a steeper LF. \nWe hope to address some of these issues in the future. \n\n\n\\begin{acknowledgements}\n\nWe are grateful to Helmuth Kristen for obtaining a few images of the \ncluster in September 1995 and to Steven J\\\"ors\\\"ater for some initial \nobservations in 1994. We also thank Leif Festin for supplying some \nALFOSC images that we could use to test the image quality prior to our \nobservations. We are grateful to Margrethe Wold for discussions about \ncompleteness \nand to Tomas Dahl\\'en for discussions and assistance with an additional \nconsistency check. We also thank the referee, C. Gronwall, who provided \nseveral important suggestions that improved the presentation of this\nwork. Last but not least, M.~N. is very grateful to Stefan Larsson for \ndiscussions about statistics and related topics. The data presented here \nhave been taken using ALFOSC, which is owned by the Instituto de \nAstrofisica \nde Andalucia (IAA) and operated at the Nordic Optical Telescope under \nagreement\n between IAA and the NBIfA of the Astronomical Observatory of \nCopenhagen. This \nresearch was supported by the Swedish Natural Sciences Research Council, \nand the G\\\"oran Gustafsson Foundation\n for Research in Natural Sciences and Medicine.\n\\end{acknowledgements}\n\n\n\\begin{thebibliography}{}\n\n\\bibitem{}\tArnouts S., D'Odorico S., Cristiani S., Zaggia S., Fontana A., Giallongo E., 1999, A\\&A 341, 641\n\\bibitem{}\tBahcall J. N., 1995, \nhttp://www.sns.ias.edu/\\~\\,jnb/Html/galaxy.html\n\\bibitem{} \tBahcall, J. N., Soneira, R. M. , 1980, ApJS, 44, 73\n\\bibitem{} \tBernstein, G. M., Nichol, R. C., Tyson, J. A., Ulmer,\n \tM. P., Wittman, D. 1995, AJ, 110, 1507 (BNTUW)\n\\bibitem{}\tBinggeli B., Sandage A., Tammann G. A., 1988, ARA\\&A 26, 509\n\\bibitem{} \tBiviano, A., Durret, F., Gerbal, D., Le Fevre, O., Lobo, C.,\n\t\tMazure, A. \\& Slezak, E., 1995, ApJ, 455, 108\n\\bibitem{} \tBaugh, C.M., Cole, S. \\& Frenk, C. S. 1996, MNRAS, 283, 1361\n\\bibitem{}\tBohlin, R. C., Savage, B. D., Drake, J. F. 1978, ApJ,\n\t\t224, 132B \n\\bibitem{}\tBothun G. D., Impey C. D., Malin D. F., 1991, ApJ 376, 404\n\\bibitem{}\tBurstein, D., Heiles, C. 1982, AJ, 87, 1165\n\\bibitem{}\tButcher H., Oemler A.. 1984, ApJ, 285, 426\n\\bibitem{}\tDavies J. I., Disney M. J., Phillipps S., Boyle B. J., Couch \n\t\tW. J., 1994, MNRAS 269, 349\n\\bibitem{}\tDriver, S.~P., 1999, ApJ 526, L69\n\\bibitem{}\tDriver, S.~P., Phillipps, S., Davies, J.~I., Morgan,\n\t\tI., and Disney, M.~J. 1994a, MNRAS 266, 155 % counts \n\\bibitem{}\tDriver, S.~P., Phillipps, S., Davies, J.~I., Morgan, I., \n\t\tDisney, M.~J. 1994b, MNRAS 268, 393 (DPDMD) % Abell 963 \n\\bibitem{}\tDriver, S.~P., Couch W.~J., Phillipps, S., Smith R., \n\t\t1998, MNRAS 301, 357\n\\bibitem{}\tEllis, R. S., Colless, M., Broadhurst, T., Heyl, J.,\n\t\tGlazebrook, K. 1996, MNRAS, 280, 235\n\\bibitem{}\tFerguson H. C., Binggeli B., 1994, A\\&AR 6, 67\n\\bibitem{}\tFerguson H. C., Sandage A., 1988, AJ 96, 1520\n\\bibitem{}\tFontana A., D'Odorico S., Fosbury R., Giallongo E., Hook R., Poli F., Renzini A., Rosati P., Viezzer R., 1999, A\\&A 343, L19\n\\bibitem{} \tGioia, I.M. \\& Luppino, G.A. 1994, ApJ Suppl, 94, 583\n\\bibitem{} \tGioia, I. M., Maccacaro, T., Schild, R. E., Wolter,\n\t\tA., Stocke, J. T., Morris, S. L., Henry, J. P. 1990,\n\t\tApJS, 72, 567 \n\\bibitem{}\tGronwall, C. \\& Koo, D. C. 1995 ApJ, 440, L1\n\\bibitem{} \tHeyl, J. S., Cole, S., Frenk, C. S., Navarro,\n\t\tJ. F. 1995, MNRAS, 274, 755\n\\bibitem{}\tImpey C., Bothun G., Malin D., 1988, ApJ 330, 634\n\\bibitem{}\tImpey C., Bothun G., 1997, ARA\\&A 35, 267\n\\bibitem{}\tJarvis J. F., Tyson J. A., 1981, AJ 86, 476\n\\bibitem{}\tKaufmann, G. 1995a, MNRAS, 274, 153\n\\bibitem{}\tKaufmann, G. 1995b, MNRAS, 274, 161\n\\bibitem{}\tKaufmann, G., White, S. D. M., Guiderdoni, B. 1993,\n\t\tMNRAS, 264, 201 \n\\bibitem{} \tLilly, S. J., Tresse, L., Hammer, F., Crampton, D. Le\n\t\tFevre, O. 1995, ApJ, 455, 108 \n\\bibitem{}\tLobo, C., Biviano, A., Durret, F., Gerbal, D.,\n\t\tLeFevre, O., Mazure, A., Slezak, E. 1997, A\\&A 317, 385\n\\bibitem{}\tLoveday, J., Peterson, B. A., Efstathiou, G., Maddox,\n\t\tS. J. 1992, ApJ, 390, 338\n\\bibitem{}\tMarzke, R. O., Geller, M. J., Huchra, J. P., Corwin,\n\t\tH. G., Jr. 1994b, AJ 108, 437\n\\bibitem{}\tMcGaugh S. S., Bothun G. D., 1994, AJ 107, 530\n\\bibitem{} \tMetcalfe, N., Fong, R., Shanks, T., \\& Jones, L.R.\n \t\t1991, MNRAS, 249, 498\n\\bibitem{}\tMoore B., Katz N., Lake G., Dressler A., Oemler A., 1996,\n\t\tNat 379, 613\n\\bibitem{}\tN\\\"aslund M., 1995, Licentiate thesis, Stockholm Observatory, \n\t\tStockholm University\n\\bibitem{}\tN\\\"aslund M., 1998, Ph. D. thesis, Stockholm Observatory, \n\t\tStockholm University \n(the part dealing with the simulations can be found at http://www.astro.su.se/\\~\\,magnus/research/publications.html)\n\\bibitem{}\tPropris, R. de, Pritchet, C.\n\t\tJ., Harris, W. E., McClure, R. D., 1995, ApJ, 450, 534\n\\bibitem{}\tSchlegel D.J., Finkbeiner D.P., Davis M., 1998, ApJ, 500, 525\n\\bibitem{}\tSmith R. M., Driver S. P., Phillipps S., 1997,\n\t\tMNRAS 287, 415\n\\bibitem{}\tSprayberry D., Impey C. D., Bothun G. D., Irwin M. J., 1995,\n\t\tAJ 109, 558\n\\bibitem{}\tStetson, P. B., 1987, PASP 99, 191\n\\bibitem{}\tStocke, J. T., Morris, S. L., Gioia, I. M., Maccacaro,\n\t\tT., Schild, R., Wolter, A., Fleming, T. A., Henry,\n\t\tJ. P. 1991, ApJS, 76, 813\n\\bibitem{}\tThompson L. A., Gregory S. A., 1993, AJ 106, 2197\n\\bibitem{}\tTrentham N., 1997, MNRAS 286, 133\n\\bibitem{}\tTrentham N., 1998a, MNRAS 293, 71\n\\bibitem{}\tTrentham N., 1998b, MNRAS 294, 193\n\\bibitem{}\tTrentham N., 1998c, MNRAS 294, 193\n\\bibitem{}\tTrentham N., 1998d, preprint (astro-ph/9804013)\n\\bibitem{}\tTrentham N., Mobasher B.,1998, MNRAS 299, 488\n\\bibitem{}\tTyson, J.A. 1988, AJ, 96, 1\n\\bibitem{}\tValdes F., 1982, {\\em Faint Object Classification and\n\t\tAnalysis System}, NOAO, Tucson, AZ\n\\bibitem{}\tValdes F., 1993, {\\em FOCAS User's Guide}, NOAO, Tucson, AZ\n\\bibitem{}\tValotto C. A., Nicotra M. A., Muriel H., Lambas D. G., 1997,\n\t\tApJ 479, 90\n\\bibitem{}\tWhite S. D. M., Frenk, C. S. 1991, ApJ 379, 52\n\\bibitem{}\tWhite S. D. M., Springel V., 1999, preprint (astro-ph/9911378)\n\\bibitem{}\tWilson G., Smail I., Ellis R. S., Couch \n\t\tW. J. 1997, MNRAS, 284, 915 (WSEC)\n\\end{thebibliography}{}\n \\vfill\n\\eject\n\\end{document}\n\n\n"
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[
{
"name": "astro-ph0002372.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem{}\tArnouts S., D'Odorico S., Cristiani S., Zaggia S., Fontana A., Giallongo E., 1999, A\\&A 341, 641\n\\bibitem{}\tBahcall J. N., 1995, \nhttp://www.sns.ias.edu/\\~\\,jnb/Html/galaxy.html\n\\bibitem{} \tBahcall, J. N., Soneira, R. M. , 1980, ApJS, 44, 73\n\\bibitem{} \tBernstein, G. M., Nichol, R. C., Tyson, J. A., Ulmer,\n \tM. P., Wittman, D. 1995, AJ, 110, 1507 (BNTUW)\n\\bibitem{}\tBinggeli B., Sandage A., Tammann G. A., 1988, ARA\\&A 26, 509\n\\bibitem{} \tBiviano, A., Durret, F., Gerbal, D., Le Fevre, O., Lobo, C.,\n\t\tMazure, A. \\& Slezak, E., 1995, ApJ, 455, 108\n\\bibitem{} \tBaugh, C.M., Cole, S. \\& Frenk, C. S. 1996, MNRAS, 283, 1361\n\\bibitem{}\tBohlin, R. C., Savage, B. D., Drake, J. F. 1978, ApJ,\n\t\t224, 132B \n\\bibitem{}\tBothun G. D., Impey C. D., Malin D. F., 1991, ApJ 376, 404\n\\bibitem{}\tBurstein, D., Heiles, C. 1982, AJ, 87, 1165\n\\bibitem{}\tButcher H., Oemler A.. 1984, ApJ, 285, 426\n\\bibitem{}\tDavies J. I., Disney M. J., Phillipps S., Boyle B. J., Couch \n\t\tW. J., 1994, MNRAS 269, 349\n\\bibitem{}\tDriver, S.~P., 1999, ApJ 526, L69\n\\bibitem{}\tDriver, S.~P., Phillipps, S., Davies, J.~I., Morgan,\n\t\tI., and Disney, M.~J. 1994a, MNRAS 266, 155 % counts \n\\bibitem{}\tDriver, S.~P., Phillipps, S., Davies, J.~I., Morgan, I., \n\t\tDisney, M.~J. 1994b, MNRAS 268, 393 (DPDMD) % Abell 963 \n\\bibitem{}\tDriver, S.~P., Couch W.~J., Phillipps, S., Smith R., \n\t\t1998, MNRAS 301, 357\n\\bibitem{}\tEllis, R. S., Colless, M., Broadhurst, T., Heyl, J.,\n\t\tGlazebrook, K. 1996, MNRAS, 280, 235\n\\bibitem{}\tFerguson H. C., Binggeli B., 1994, A\\&AR 6, 67\n\\bibitem{}\tFerguson H. C., Sandage A., 1988, AJ 96, 1520\n\\bibitem{}\tFontana A., D'Odorico S., Fosbury R., Giallongo E., Hook R., Poli F., Renzini A., Rosati P., Viezzer R., 1999, A\\&A 343, L19\n\\bibitem{} \tGioia, I.M. \\& Luppino, G.A. 1994, ApJ Suppl, 94, 583\n\\bibitem{} \tGioia, I. M., Maccacaro, T., Schild, R. E., Wolter,\n\t\tA., Stocke, J. T., Morris, S. L., Henry, J. P. 1990,\n\t\tApJS, 72, 567 \n\\bibitem{}\tGronwall, C. \\& Koo, D. C. 1995 ApJ, 440, L1\n\\bibitem{} \tHeyl, J. S., Cole, S., Frenk, C. S., Navarro,\n\t\tJ. F. 1995, MNRAS, 274, 755\n\\bibitem{}\tImpey C., Bothun G., Malin D., 1988, ApJ 330, 634\n\\bibitem{}\tImpey C., Bothun G., 1997, ARA\\&A 35, 267\n\\bibitem{}\tJarvis J. F., Tyson J. A., 1981, AJ 86, 476\n\\bibitem{}\tKaufmann, G. 1995a, MNRAS, 274, 153\n\\bibitem{}\tKaufmann, G. 1995b, MNRAS, 274, 161\n\\bibitem{}\tKaufmann, G., White, S. D. M., Guiderdoni, B. 1993,\n\t\tMNRAS, 264, 201 \n\\bibitem{} \tLilly, S. J., Tresse, L., Hammer, F., Crampton, D. Le\n\t\tFevre, O. 1995, ApJ, 455, 108 \n\\bibitem{}\tLobo, C., Biviano, A., Durret, F., Gerbal, D.,\n\t\tLeFevre, O., Mazure, A., Slezak, E. 1997, A\\&A 317, 385\n\\bibitem{}\tLoveday, J., Peterson, B. A., Efstathiou, G., Maddox,\n\t\tS. J. 1992, ApJ, 390, 338\n\\bibitem{}\tMarzke, R. O., Geller, M. J., Huchra, J. P., Corwin,\n\t\tH. G., Jr. 1994b, AJ 108, 437\n\\bibitem{}\tMcGaugh S. S., Bothun G. D., 1994, AJ 107, 530\n\\bibitem{} \tMetcalfe, N., Fong, R., Shanks, T., \\& Jones, L.R.\n \t\t1991, MNRAS, 249, 498\n\\bibitem{}\tMoore B., Katz N., Lake G., Dressler A., Oemler A., 1996,\n\t\tNat 379, 613\n\\bibitem{}\tN\\\"aslund M., 1995, Licentiate thesis, Stockholm Observatory, \n\t\tStockholm University\n\\bibitem{}\tN\\\"aslund M., 1998, Ph. D. thesis, Stockholm Observatory, \n\t\tStockholm University \n(the part dealing with the simulations can be found at http://www.astro.su.se/\\~\\,magnus/research/publications.html)\n\\bibitem{}\tPropris, R. de, Pritchet, C.\n\t\tJ., Harris, W. E., McClure, R. D., 1995, ApJ, 450, 534\n\\bibitem{}\tSchlegel D.J., Finkbeiner D.P., Davis M., 1998, ApJ, 500, 525\n\\bibitem{}\tSmith R. M., Driver S. P., Phillipps S., 1997,\n\t\tMNRAS 287, 415\n\\bibitem{}\tSprayberry D., Impey C. D., Bothun G. D., Irwin M. J., 1995,\n\t\tAJ 109, 558\n\\bibitem{}\tStetson, P. B., 1987, PASP 99, 191\n\\bibitem{}\tStocke, J. T., Morris, S. L., Gioia, I. M., Maccacaro,\n\t\tT., Schild, R., Wolter, A., Fleming, T. A., Henry,\n\t\tJ. P. 1991, ApJS, 76, 813\n\\bibitem{}\tThompson L. A., Gregory S. A., 1993, AJ 106, 2197\n\\bibitem{}\tTrentham N., 1997, MNRAS 286, 133\n\\bibitem{}\tTrentham N., 1998a, MNRAS 293, 71\n\\bibitem{}\tTrentham N., 1998b, MNRAS 294, 193\n\\bibitem{}\tTrentham N., 1998c, MNRAS 294, 193\n\\bibitem{}\tTrentham N., 1998d, preprint (astro-ph/9804013)\n\\bibitem{}\tTrentham N., Mobasher B.,1998, MNRAS 299, 488\n\\bibitem{}\tTyson, J.A. 1988, AJ, 96, 1\n\\bibitem{}\tValdes F., 1982, {\\em Faint Object Classification and\n\t\tAnalysis System}, NOAO, Tucson, AZ\n\\bibitem{}\tValdes F., 1993, {\\em FOCAS User's Guide}, NOAO, Tucson, AZ\n\\bibitem{}\tValotto C. A., Nicotra M. A., Muriel H., Lambas D. G., 1997,\n\t\tApJ 479, 90\n\\bibitem{}\tWhite S. D. M., Frenk, C. S. 1991, ApJ 379, 52\n\\bibitem{}\tWhite S. D. M., Springel V., 1999, preprint (astro-ph/9911378)\n\\bibitem{}\tWilson G., Smail I., Ellis R. S., Couch \n\t\tW. J. 1997, MNRAS, 284, 915 (WSEC)\n\\end{thebibliography}"
}
] |
astro-ph0002373
|
Properties of Proto--Planetary Nebulae
|
[
{
"author": "Margaret Meixner"
}
] |
This review describes some general properites of proto-planetary nebulae with particular emphasis on the recent work of morpholgical studies. The weight of observational evidence shows that proto-planetary nebulae (PPNe) are most certainly axisymmetric like planetary nebulae. Recent work suggests two subclasses of PPNe optical morphology, DUst-Prominent Longitudinally-EXtended (DUPLEX) and Star-Obvious Low-level Elongated (SOLE). Radiative transfer models of an example DUPLEX PPN and SOLE PPN, presented here, support the interpretation that DUPLEX and SOLE are two physically distinct types of PPNe. The DUPLEX PPNe and SOLE PPNe may well be the precursors to bipolar and elliptical PNe, respectively.
|
[
{
"name": "proceed.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Author \\& Co-author}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{Properties of Proto--Planetary Nebulae}\n \\author{Margaret Meixner}\n\\affil{University of Illinois, Dept. of Astronomy, MC-221, \n1002 W. Green St., Urbana, IL 61801}\n%\\author{Ima Co-Author}\n%\\affil{The Name of My Institution, The Full Address of My Institution}\n\n\\begin{abstract}\nThis review describes some general properites of proto-planetary\nnebulae with particular emphasis on the recent work of\nmorpholgical studies. The weight of observational evidence\nshows that proto-planetary nebulae (PPNe) are most certainly axisymmetric\nlike planetary nebulae. Recent work \nsuggests two subclasses of PPNe optical morphology,\nDUst-Prominent Longitudinally-EXtended\n(DUPLEX) and Star-Obvious Low-level Elongated (SOLE).\nRadiative transfer models of an example DUPLEX PPN and SOLE PPN, \npresented here, support the interpretation that DUPLEX and SOLE are\ntwo physically distinct types of PPNe. The DUPLEX PPNe and SOLE PPNe may\nwell be the precursors to bipolar and elliptical PNe, respectively.\n\n\\end{abstract}\n\n\\section{What is a Proto-Planetary Nebula?}\n\nThe proto-planetary nebula (PPN;a.k.a. post-AGB or pre-PN) stage of \nevolution immediately precedes\nthe planetary nebula (PN) stage. The lifetime for this phase is \n$\\; \\buildrel < \\over \\sim \\;$1000 years and marks the time from when the \nstar was forced\noff the asymptotic giant branch (AGB) by intensive mass loss to when\nthe central star becomes hot enough (T$_{\\rm eff} \\sim 3\\times 10^4$ K)\nto photoionize the neutral circumstellar shell (Kwok 1993). \n%The term post-AGB\n%is also used for this stage and has the conotation that some objects\n%in this group may not become planetary nebulae because their central\n%stars are evolving too slowly compared to the expansion timescales of\n%their circumstellar shells and, thus, they will fail to appear as PN when\n%photoionized. For example, R Cor Bor stars, discussed by\n%Clayton in this volume fall into this category. \n%The term, Pre-PN has been introduced at this conference\n%presumably to avoid the confusion with pre-main sequence stars which\n%include proto-stars and have proto-planetary disks. \nWe refer the reader to Kwok (1993) for a comprehensive review of PPN.\nFor short recent reviews, see Hrivnak (1997) and van Winckel (1999).\nIn this short review, I summarize the basic properties of PPN\nbut focus primarily on the morphological studies because there\nhave been numerous morphological studies in the past few years and because\nthis particular conference is focused on morphology.\n\n\\section{General Characteristics of PPN}\n\nPPN are like PN in that the central star illuminates a\ndetached circumstellar shell, however, we observe PPN using quite\ndifferent techniques. Because PPN do not have ionized gas,\nwe can not use the optically bright emission lines or radio\nfree-free continuum commonly used for studies of PN.\nInstead tracers of dust and neutral gas are employed.\nIn fact, PPN are identified as stars of spectral type\nB-K, luminosity class I with infrared excesses. These infrared excesses\narise from the circumstellar dust which was originally created\nin the AGB wind. They \nemit broad ($\\sim$20 km s$^{-1}$), parabolic or double--horned \nlines of CO rotational lines \nand OH maser lines indicative of a remnant AGB circumstellar shell.\nThese broad lines distinguish these PPN from pre-main sequence\nand Vega-excess stars which also have infrared excesses but typically\nnarrower or non-existent molecular lines.\n\nCandidates for PPN are discovered using infrared sky surveys.\nOne of the most famous PPN, AFGL 2688 (a.k.a the Egg Nebula),\nwas discovered by Ney et al. (1975) in an infrared sky survey\ndone by the airforce. Studies using the IRAS all sky survey\nhave used two approaches to identify candidates. \nOne way is to use IRAS colors ([25]-[60] vs. [12]-[25]),\nmark the locations of known AGB stars and PN and choose PPN candidates\nfrom the regions in between (van der Veen, Habing \\& Geballe 1989;\nHrivnak, Kwok \\& Volk 1989; Hu et al. 1993).\nThe second way is to cross correlate the IRAS catalog with optical\nstar catalogs and choose objects in common (Oudmaijer et al. 1992).\n\nSeveral initial followup studies focused on ground based photometry \nobservations and models of the spectral\nenergy distributions (SEDs) of these PPN candidates. Van der Veen et al.\n(1989) identified four types of SEDs which they attributed to\noptical depth differences in the dust shells. Type I has a flat spectrum\nfrom 4 to 25 $\\mu$m with a steep fall off at short wavelengths.\nType II have a maximum near 25 $\\mu$m and a gradual fall-off to shorter\nwavelengths. Type III have a maximum near 25 $\\mu$m, a steep fall off\nat shorter wavelengths to a plateau between 1 and 4 $\\mu$m.\nType IV have two distinct maxima, one near 25 $\\mu$m and the second\nat $\\lambda < 2$ $\\mu$m. Hrivnak \\& Kwok (1991) suggested\nthat the 21$\\mu$m PPN were quite similar to objects like AFGL 2688\nexcept for viewing angle based on the differences in their SEDs.\nThe 21$\\mu$m PPN have a Type IV SED while AFGL 2688 has a Type III SED\nand we could be viewing the 21$\\mu$m PPN down the poles while we\nview AFGL 2688 edge-on.\n\n\n\\section{ Morphologies}\n\nThe study of PPN morphologies offers us insight on the axisymmetric\nPN issue because they are the missing link between two well studied\ngroups: PN and AGB stars. Moreover, their morphologies are relatively\npristine fossil records of the AGB mass loss process because \nshaping by the hot, fast stellar wind of a PN nucleus has \nprobably not occured (see Schonberner in this volume). Hence we\ncan determine ``initial conditions'' for the interacting winds models. \nFigure 1 shows our working model for a PPN circumtellar shell based\non the observed evidence that most PN are axially symmetric (e.g. Balick 1987)\nwhile the outer shells of AGB circumstellar shells are spherically\nsymmetric (e.g. Neri et al. 1998). In the PPN fossil record, radial\ndistance directly corresponds to time. The maximum\nradius, $\\rm R_{max}$ marks when the mass loss began. As we move\ninwards, we see the spherically symmetric shell created by the\nAGB wind. The superwind radius, $\\rm R_S$, corresponds to when\nthe mass loss began\nto increase in rate and to assume an axial as opposed to spherical\nsymmetry. We note that our use of the term superwind is slightly modified\nfrom the intention of Iben \\& Renzini (1983) in that we include the\nsymmetry change in addition to an increase in mass loss rate.\nThe inner radius, $\\rm R_{in}$\nmarks when the mass loss stopped and the size of the inner radius reflects\nthe dynamical age that has passed since the star left the AGB (Meixner\net al. 1997).\n\nStudies of PPN morphologies have used tracers of dust (thermal\ninfrared radition or optical/near-infared scattered starlight) or\nmolecular gas (CO maps or maser maps). Since the molecular gas\nobservations are covered by others in this volume (see Huggins; Alcolea;\nFong et al.), I will focus on the tracers of dust. In PPN,\nthe central star heats the dust and the dust both scatters the starlight\nand radiates in the thermal infrared ($\\lambda > 5 \\mu$m). \nIn our working model, we expect that the scattered starlight will\npreferentially leak out of the lower density bipolar openings of the\ndustshell and will be the most intense in the inner regions where both\nthe starlight and dust density are highest. In the thermal infrared,\nwhat we see depends on the wavelength we observe because dust radiates\nas a modified black body and hence depends sensitively on temperature.\nIn these dust shells, the temperature decreases from \nat $\\sim$200 K at the inner radius to $\\sim$30 K at the outer radius.\nMid-infrared (Mid-IR; 8-25$\\mu$m) \nemission arises exclusively from the inner regions\nwhere the dust is warm. Far-IR and submillimeter\nradiation ($>$50 $\\mu$m) arises from the outer regions as well as the\ninner regions, however, the angular resolution at these wavelengths is \npresently quite poor (10-40\\arcsec) which prevents investigation of the inner,\naxisymmetric regions. \n\n\\begin{figure}\n\\plotfiddle{meixner_fig1.eps}{2.0in}{0}{35}{35}{-70}{0}\n\\caption{Schematic representation of our working model of a \nProto-Planetary Nebula Dustshell.}\n\\end{figure}\n\n\n\\subsection{ Mid-IR Imaging Studies}\n\nGround based mid-IR imaging studies of PPN have had typical angular\nresolutions of about 1\\arcsec~ and enough spectral resolution to\nseparate dust features and dust continuum. The larger telescopes\ncoming on line, e.g. Keck, VLT, Gemini and MMT, promise diffraction limited\nperformance as good as 0.\\arcsec 2 (e.g. see Morris in this volume,\nand Jura \\& Werner 2000).\nA number of published mid-IR imaging studies of PPN have\nfocused on one to five well resolved PPN and \nusually include radiative transfer\nmodeling (Skinner et al. 1994; Hawkins et al. 1995; Hora et al. 1996;\nDayal et al. 1998; Meixner et al. 1997; Skinner et al. 1997). \nA recent survey paper of 66 PPNe (Meixner et al. 1999) \nprovides the largest data base of PPNe candidate mid-IR images to date. \nIt also incorprates the results of previously published works. \nConsidering all the published mid-IR images to date, there are three\nmain points that can be made (Meixner et al. 1999). \nFirst, of the 73 PPNe candidates, 33\\% have\nbeen resolved with $\\sim$1\\arcsec~ resolution. The cooler and\nbrighter objects are easier to resolve probably because cooler shells\nare more distant from the central star and hence larger and brighter\nshells are either closer or more luminous which create larger mid-IR \nemission regions. Second, all of the well resolved PPNe are axisymmetric.\nThirdly, there appear to be two morphological types in the well-resolved\nmid-IR PPNe candidates which we have called toroidal and core/elliptical.\nToroidals, as exemplified by IRAS 07134+1005 (Fig. 2), \nhave elliptical/round outer\nperimeters and two peaks which can be interpreted as limb brightened\npeaks of an equatorial density enhancement. The central star usually appears\nbetween the two peaks.\n%If the central star \n%emits enough radiation at mid-IR wavelengths, \n%it appears near the center of the dust shell. \nCore/ellipticals, as exemplified by the Red Rectangle (Fig. 2), \nhave tremendously\nbright, unresolved cores at their centers and low surface brightness\nelliptical shaped nebulae surrounding these cores. The extension of\nthe low surface brightness emission is in the same direction as the\noptical reflection nebulosity found in these objects. \n\n\\begin{figure}\n\\plotfiddle{meixner_fig2.eps}{1.5in}{0}{80}{80}{-150}{-20}\n\\caption{Mid-IR images of two types of PPNe with the wavelengths in the\nupper right corner. Left: IRAS 07134+1005, an\nexample of a Toroidal PPN (Meixner et al. 1997). Right: Red Rectangle,\nan example of a core/elliptical (Meixner et al. 1999).}\n\\end{figure}\n\n\\subsection{Optical Polarimetry and Imaging Studies}\n\nThe optical and near-IR polarimetry and imaging observations of \nthe scattered starlight in PPN predate (1970's)\nand far out number these mid-IR studies. Here I only have room to summarize\nsome recent work. Two large survey polarimetry studies \nof PPN have revealed a large amount of polarization at the PPN stage \nwhich indicates that the PPN stage is axisymmetric. Using broad band\npolarimetry, Johnson \\& Jones (1991)\ninvestigated 38 objects ranging from the AGB to PPN to PN stages \nand found that the polarization increased from the AGB to PPN stage\nand then decreased in the PN stage. Using spectropolarimetry, Trammell,\nDinerstein \\& Goodrich (1994), studied 31 PPN and found 80\\% had\nsome intrinsic polarization. They also classified polarized PPN into\nType 1 and Type 2. Both have large polarizations, but Type 1's also have\na large position angle rotation with wavelength which suggests that\nType 1's may be more bipolar in shape. See Gledhill et al. and\nSu et al. in this volume for recent near-IR polarimetry work on PPN.\n\nHigh angular resolution \noptical and imaging studies of PPN are numerous and have exploded\nwith use of HST because the compact nature of PPNe is well suited for\nHST. \n%Interestingly, they only \n%cover all about 44 PPN candidates\n%which suggests that much more work can be done in this area.\nA number of the studies focus on one or a few objects and range\nfrom phenomenological discussions to quantitative modelling in their\ninterpretations (e.g. Sahai, Bujarrabal \\& Zijlstra 1999; Sahai et al. 1999; \nKwok, Su \\& Hrivnak 1998; Su et al. 1998; Sahai et al. 1998; Kwok et al. 1996;\nSkinner et al. 1997; Trammell \\& Goodrich 1996;\nBobrowsky et al. 1995; Latter et al. 1993; \nin this volume see Trammell et al., Hrivnak et al., Bobrowsky et al.\nand Bieging et al.). Two recent papers cover\na significant number of PPN and strive for a more global picture of PPN.\nHrivnak et al. (1999) pursued a ground based imaging study of 10 PPN\nwith angular resolutions of $\\sim$0.\\arcsec 75.\nUeta, Meixner \\& Bobrowsky (2000) imaged 27 PPN using the HST WFPC2 with\nangular resolutions of 0.\\arcsec 046 (see also Ueta et al. in this volume).\nIf we combine the imaging results from all these papers, we find that\n80\\% of the 44 PPN have resolvable optical reflection nebulosities\nand all of the well resolved reflection nebulosities are axisymmetric.\nWhile many of these studies have focused on PPN with obscured central\nstars, the Ueta et al. (2000) survey included many PPN with optically\nvisible, prominent stars and they discovered two types of optical\nmorphology in the PPN. \n\n \n\\section{Two Types of PPN}\n\n\\begin{figure}\n\\plotfiddle{meixner_fig3.eps}{1.0in}{0}{80}{80}{-150}{-30}\n\\caption{The spectral energy distributions for DUPLEX PPN,\nIRAS 17150-3224 (left) and for SOLE PPN IRAS 17436+5003 (right).\nPhotometry data are the squares, spectroscopy the solid lines\nand the model in dashed lines. From Meixner et al. (2000).}\n\\end{figure}\n\nThe two types of PPN have been called DUst-Prominent Longitudinally-EXtended\n(DUPLEX) and Star-Obvious Low-level Elongated (SOLE) PPN (see Ueta et al.\nin this volume).\nThese names describe their optical morphological appearance and \ntheir acronyms describe the two lobed structures seen \nin DUPLEX PPNe and the continuous structures seen in SOLE PPNe.\nBesides their optical appearances, DUPLEX and SOLE PPNe differ in\ntheir mid-IR morphologies: DUPLEX are core-ellipticals, while SOLE\nare toroidals. They also have distinctly different\nSEDs: DUPLEX have type II or III SEDs, while\nSOLE have type IV SEDs in the van der Veen et al. 1989 classification.\nUeta et al. (2000) claim that the cause of these differences is the\noptical depth of the dust shell. SOLE nebulae have less dust optical\ndepth than DUPLEX nebulae and, hence, the central star is visible no\nmatter the inclination angle. They further suggest that DUPLEX PPNe\nmay well be the precursors of bipolar PNe while SOLE PPNe may be\nthe precursors to the elliptical PNe based on their differences\nin morphologies and galactic height distributions.\n\nThis interpretation is controversial, judging by the avid discussion after \nmy talk. The other point of view, presented by Hrivnak (in this volume)\nis that these optical morphological differences are due primarily to\ninclination angle differences. That is, all these PPNe are the same physical\ntype of beast, just viewed from different angles on the sky.\nThe best way to resolve such controversy is to make radiative transfer\nmodels using axially symmetric dust codes to derive optical depths,\nand structures for all of the PPNe and compare their derived properties.\nHere, we present model results of one DUPLEX PPN, IRAS 17150-3224, and one\nSOLE PPN, IRAS 17436+5003, to demonstrate that these two sources, which\nare among the best examples of their classes, are physically quite different.\nWe use a radiative transfer code that we used in Meixner et al. (1997)\nand Skinner et al. (1997). Su et al. (1998 and in this volume) are using \na different code with similar aims but have concentrated on primarily on \nDUPLEX PPN so far. \n\n\\begin{figure}\n\\plotfiddle{meixner_fig4.eps}{1.7in}{0}{80}{80}{-160}{-30}\n\\caption{The model images and data for DUPLEX PPN,\nIRAS 17150-3224.\nGrayscale is the HST B band images and the contours are\nthe 9.8$\\mu$m mid-IR images. From Meixner et al. (2000). }\n\\end{figure}\n\n\\begin{figure}\n\\plotfiddle{meixner_fig5.eps}{1.7in}{0}{80}{80}{-160}{-30}\n\\caption{The model images and data for for SOLE PPN IRAS 17436+5003.\nGrayscale is the HST V band images and the contours are\nthe 12.5$\\mu$m mid-IR images. From Meixner et al. (2000). }\n\\end{figure}\n\n\nWe have constrained the model using our HST and mid-IR images\nand photometry from the literature. A full discussion of these models\nwill appear in Meixner, Ueta \\& Bobrowsky (2000). Comparison of\nthe model images and SED data demonstrates\na reasonable match of the model with the data (Figs. 4 and 5). The derived\nparameters from the models appear in the Table and reveal the \nphysical reasons for the apparent morphological differences.\nFirst, both objects are best fit by a 90$^\\circ$ inclination\nangle; i.e. we are viewing both edge-on. Thus, we are not viewing\nthe SOLE PPN, IRAS 17436+5003, near the pole which would be\nexpected if our viewing angle were the main cause of the morphological\ndifferences. We note that other PPN in the Ueta et al. (2000) sample\nshow qualitative evidence for inclination angles different than 90$^\\circ$;\ne.g. unbalanced lobes for DUPLEX and less elliptical nebulae for SOLE.\nSecond, the optical depth for the DUPLEX PPN, IRAS 17150-3224, is\nsignificantly higher than for the SOLE PPN, IRAS 17436+5003\nand explains why we do not see the central star in the former but do\nin the latter. The cause for the difference in optical depth is\nthe history of mass loss. IRAS 17150-3224 experienced a more\nintensive mass loss rate than IRAS 17436+5003 that resulted in\na denser dust cocoon of significantly higher mass. Both this\nhigher mass and the higher luminosity for this source suggest\nthat IRAS 17150-3224 originated from a higher mass star. \nThese results are, of course, distance dependent and the distance\nmaybe uncertain by a factor of two. However, the optical\ndepth is distance independent and even with the distance uncertainty\nit seems reasonable to conclude that IRAS 17150-3224 is more luminous\nand had a higher mass progenitor.\n\n\\begin{table}\n\\begin{tabular}{lccccccc}\n\\hline\nObject & $\\tau_{eq,9.7\\mu m}$& incl. & \\.M$_{sw}$ ($\\rm M_\\odot yr^{-1}$) & \nL$_*$ (L$_\\odot$) & D (kpc) \\\\ \\hline\nDUPLEX: \\\\\nIRAS 17150-3224 & 1.8 & 90$^\\circ \\pm$5 & $50\\times 10^{-5}$ & 27000 & 3.6 \\\\\n SOLE: \\\\\nIRAS 17436+5003 & 0.9 & 90$^\\circ \\pm$20& $6\\times 10^{-5}$ & 3900 & 1.2 \\\\\n\\end{tabular}\n\\end{table}\n\n\\section{Summary points}\n\nThe observational evidence from a number of independent studies\nclearly shows that PPNe are intrinsically axisymmetric.\nThus the axisymmetry that we observe in PNe must predate the PPNe\nstage. Most likely the axisymmetry originates at the end of the\nAGB phase, because observations of the outer regions of AGB envelopes\nshow a spherical symmetry. With the variety of PNe morphologies discussed\nat this conference (e.g. round, elliptical, bipolar and point symmetric),\nwe must now begin to ask: Do we see examples of PPNe with\nthese corresponding subtle differences in morphologies?\nI think we are beginning to see these differences. The DUPLEX and\nSOLE PPNe may well be the precursors for bipolar and elliptical PNe.\n\n\\begin{references}\n\n\\reference Balick, B. 1987, AJ, 94, 671\n\n\\reference Bobrowsky, M. et al. 1995; \\apj, 446, L89\n\n\\reference Dayal, A., Hoffmann, W.F., Bieging, J.H., Hora, J.L, Deutsch, L.K.,\n\\& Fazio, G.G. 1998, \\apj, 492, 603\n\n\\reference Hawkins, G.W., Skinner, C.J., Meixner, M.M., Jernigan, J.G., Arens, J.F.\nKeto, E., and Graham, J. 1995, ApJ, 452, 314. \n\n\\reference Hora, J.L, Deutsch, L.K., Hoffmann, W.F., Fazio, \\& Giovanni, G.\n1996, AJ, 112, 2064\n\n\\reference Hrivnak, B.J. \\& Kwok, S. 1991, \\apj, 371, 631\n\n\\reference Hrivnak, B.J., Kwok, S. \\& Volk, K. 1989, \\apj, 346, 265\n\n\\reference Hrivnak, B.J. 1997, Proceedings of IAU Symposium No. 180, \ned. Habing, H.J. \\& Lamers H.J.G.L.M. \n(Dordrecht: Kluwer Academic Publishers), p. 303\n\n\n\\reference Hrivnak, B.J., Langhill, P.P., Su, K.Y.L. \\& Kwok, S. 1999,\n\\apj, 513, 421\n\n\\reference Hu, J.Y., Slijkhuis, S., De Jong, T. \\& Jiang, B.W. 1993,\n\\aaps, 100, 413\n\n\\reference Iben, I. \\& Renzini, A. 1983, \\araa, 21, 271\n\n\\reference Jura, M. \\& Werner, M.W. 2000, \\apj, in press\n\n\\reference Kwok, S. 1993, \\araa, 31, 63\n\n\\reference Kwok, S., Hrivnak, B.J., Zhang, C.Y., \\& Langhill, P.L. 1996, \\apj, 472, 287\n\n\\reference Kwok, S., Su, K.Y.L, Hrivnak, B.J. 1998, \\apj, 501, L117\n\n\n\\reference Latter, W. B., Hora, J.L., Kelly, D. M., Deutsch, L.K., \\&\nMaloney, P.R. 1993, \\aj, 106, 260\n\n\\reference Meixner, M., Skinner, C.J., Graham, J.R., Keto, E., Jernigan,\nJ.G., \\& Arens, J.F. 1997, \\apj, 482, 897\n\n\\reference Meixner et al. 1999, \\apjs, 122, 221\n\n\n\\reference Meixner, M., Ueta, T., \\& Bobrowsky, M. 2000, \\apj Let., submitted\n\n\\reference Neri, R., Kahane, C., Lucas, R., Bujarrabal, V. \\& Loup, C.\n1998, \\aaps, 122, 221\n\n\\reference Ney, E. P., Merrill, K. M., Becklin, E. E.,\n Neugebauer, G., Wynn-Williams, C. G. 1975, \\apj, 198, L129\n\n\\reference Oudmaijer, R.D., van der Veen, W.E.C.J., Waters, L.B.F.M.,\nTrams, N.R., Waelkens, C. \\& Engelsman, E. 1992, \\aaps, 96, 625\n\n\\reference Sahai et al. 1998, \\apj, 493, 301\n\n\\reference Sahai, R., Bujarrabal, V. \\& Zijlstra, A. 1999, \\apj, 518, L115\n\n\\reference Sahai, R., Zijlstra, A., Bujarrabal, V., Te Lintel Hekkert, P. 1999,\n\\aj, 117, 1408\n\n\n\\reference Skinner, C.J., Meixner, M.M., Hawkins, G., Keto, E., Jernigan, J.G.,\nand Arens, J.F. 1994, ApJ, 423, L135\n\n\\reference Skinner et al. 1997, \\aap, 328, 290\n\n\\reference Su, K.Y.L., Volk, K., Kwok, S., \\& Hirvnak, B.J. 1998, \\apj, 508, \n744\n\n\\reference Trammell, S.R. \\& Goodrich, R. W. 1996, \\apj, 468, L107\n\n\\reference Ueta, T., Meixner, M. \\& Bobrowsky, M. 2000, \\apj, 528, in press\n\n\\reference van der Veen, W.E.C.J., Habing, H.J. \\& Geballe, T.R. 1989,\n\\aap, 226, 108\n\n\\reference Van Winckel, H. 1999, Proceedings of IAU Symposium No. 191, \ned. Le Betre, T., Lebre, A. \\& Waelkens, C. (San Francisco: ASP), p. 465\n\n\\end{references}\n\n\\end{document}\n\n"
}
] |
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astro-ph0002374
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OBSERVATIONS OF THE CRAB NEBULA AND ITS PULSAR IN THE FAR-ULTRAVIOLET AND IN THE OPTICAL \altaffilmark{1,2}
|
[
{
"author": "Jesper Sollerman\\altaffilmark{3,4,5}"
},
{
"author": "Peter Lundqvist\\altaffilmark{3}"
},
{
"author": "Don Lindler\\altaffilmark{6}"
},
{
"author": "Roger A. Chevalier\\altaffilmark{7}"
},
{
"author": "Claes Fransson\\altaffilmark{3} Theodore R. Gull\\altaffilmark{6}"
},
{
"author": "Chun S.J. Pun\\altaffilmark{6}"
},
{
"author": "George Sonneborn\\altaffilmark{6}"
}
] |
We present far-UV observations of the Crab nebula and its pulsar made with the Space Telescope Imaging Spectrograph onboard the {Hubble Space Telescope}. Broad, blueshifted absorption arising in the nebula is seen in C~IV~$\lambda$1550, reaching a blueward velocity of $\sim 2500 \kms$. This can be interpreted as evidence for a fast outer shell surrounding the Crab nebula, and we adopt a spherically symmetric model to constrain the properties of such a shell. From the line profile we find that the density appears to decrease outward in the shell. A likely lower limit to the shell mass is $\sim 0.3\Msun$ with an accompanying kinetic energy of $\sim 1.5\EE{49}$~ergs. %This occurs for the density structure $\rho(R) \propto R^{-3}$. A fast massive shell with $10^{51}$~ergs cannot be excluded, but is less likely if the density profile is much steeper than $\rho(R) \propto R^{-4}$ and the maximum velocity is $\lesssim 6000 \kms$. The observations cover the region $1140-1720$ \AA, which is further into the ultraviolet than has previously been obtained for the pulsar. With the time-tag mode of the spectrograph we obtain the pulse profile in this spectral regime. The profile is similar to that previously obtained by us in the near-UV, although the primary peak is marginally narrower. Together with the near-UV data, and new optical data from the {Nordic Optical Telescope}, our spectrum of the Crab pulsar covers the entire region from $1140 - 9250$~\AA. Dereddening the spectrum with a standard extinction curve we achieve a flat spectrum for the reddening parameters $E(B-V)=0.52$, $R=3.1$. This dereddened spectrum of the Crab pulsar can be fitted by a power law with spectral index $\alpha_{\nu} = 0.11\pm0.04$. The main uncertainty in determining the spectral index is the amount and characteristics of the interstellar reddening, and we have investigated the dependence of $\alpha_{\nu}$ on $E(B-V)$ and $R$. %In the optical we do not see the absorption %feature reported by Nasuti et al. In the extended emission covered by our $25 \arcsec \times 0\farcs5$ slit in the far-UV, we detect C~IV~$\lambda$1550 and He~II~$\lambda$1640 emission lines from the Crab nebula. Several interstellar absorption lines are detected along the line of sight to the pulsar. The Ly$\alpha$ absorption indicates a column density of $(3.0\pm0.5)\EE{21}$ cm$^{-2}$ of neutral hydrogen, which agrees well with our estimate of $E(B-V)$=0.52 mag. Other lines show no evidence of severe depletion of metals in atomic gas.
|
[
{
"name": "ms_prep.tex",
"string": "%\\documentstyle[11pt,aasms4]{article}\n\\documentstyle[emulateapj]{article}\n\n\\begin{document}\n\n\\oddsidemargin -0.5pc\n\\evensidemargin -0.5pc\n\n\\slugcomment{Submitted to ApJ October 14, 1999; Accepted February 02, 2000}\n\n\n%---------------start of defs.-----------------------------------------\n%defs.tex\n\\def\\abs#1{\\left| #1 \\right|}\n\\def\\EE#1{\\times 10^{#1}}\n\\def\\gcm{\\rm ~g~cm^{-3}}\n\\def\\cm3{\\rm ~cm^{-3}}\n%\\def\\cm2{\\rm ~cm^{-2}}\n\\def\\kms{\\rm ~km~s^{-1}}\n\\def\\cms{\\rm ~cm~s^{-1}}\n\\def\\isotope#1#2{\\hbox{${}^{#1}\\rm#2$}}\n\\def\\wl{~\\lambda}\n\\def\\wll{~\\lambda\\lambda}\n\\def\\Ha{{\\rm H}\\alpha}\n\\def\\Hb{{\\rm H}\\beta}\n\\def\\Lya{{\\rm Ly}\\alpha}\n\\def\\Vej{V_{\\rm ej}}\n\\def\\Msun{~M_\\odot}\n\\def\\no{\\hang\\noindent}\n\\def\\dots{$\\ldots$}\n\\def\\etal{{\\it et al.}}\n\\def\\ie{{\\it i.~e.\\ }}\n\\def\\Pdot{\\dot P}\n\n%---------------end of defs.-----------------------------------------\n \n\\title{OBSERVATIONS OF THE CRAB NEBULA AND ITS PULSAR IN THE FAR-ULTRAVIOLET \nAND IN THE OPTICAL\n\\altaffilmark{1,2}\n}\n\n\\author{Jesper Sollerman\\altaffilmark{3,4,5}, \nPeter Lundqvist\\altaffilmark{3},\nDon Lindler\\altaffilmark{6},\nRoger A. Chevalier\\altaffilmark{7},\nClaes Fransson\\altaffilmark{3}\nTheodore R. Gull\\altaffilmark{6},\nChun S.J. Pun\\altaffilmark{6},\nGeorge Sonneborn\\altaffilmark{6}\n}\n\n\\altaffiltext{1}{\nBased on observations with the NASA/ESA {\\it Hubble Space Telescope},\nobtained at the Space Telescope Science Institute, which is operated by the\nAssociation of Universities for Research in Astronomy, Inc. under NASA\ncontract No. NAS5-26555.}\n\\altaffiltext{2}{Based on observations obtained at the {\\it Nordic Optical \nTelescope} on La Palma, using the Andalucia Focal Reducer and Spectrograph.}\n\n\n\\altaffiltext{3}{Stockholm Observatory, SE-133 36 Saltsj\\\"obaden, Sweden.} \n\\altaffiltext{4}{European Southern Observatory, \nKarl-Schwarzschild-Strasse 2, D-857 48 Garching bei M\\\"unchen, Germany.}\n\\altaffiltext{5}{Send offprint requests to Jesper Sollerman; \nE-mail: jesper@astro.su.se}\n\\altaffiltext{6}{Goddard Space Flight Center, Code 681, Greenbelt, MD 20771} \n\\altaffiltext{7}{Department of Astronomy, University of Virginia, P.O. \nBox 3818, Charlottesville, VA 22903} \n\n\n\\begin{abstract}\nWe present far-UV observations of the Crab nebula and its \npulsar made with the Space Telescope Imaging Spectrograph onboard \nthe {\\it Hubble Space Telescope}. Broad, blueshifted absorption arising in the\nnebula is seen in C~IV~$\\lambda$1550, reaching a blueward velocity of \n $\\sim 2500 \\kms$. This can be interpreted as evidence for a fast outer shell \nsurrounding the Crab nebula, and we adopt a spherically symmetric model to\nconstrain the properties of such a shell. From the line profile we find that\nthe density appears to decrease outward in the shell. A likely lower limit \nto the shell mass is $\\sim 0.3\\Msun$ with an accompanying kinetic energy\nof $\\sim 1.5\\EE{49}$~ergs. \n%This occurs for the density structure $\\rho(R) \\propto R^{-3}$. \nA fast massive shell with $10^{51}$~ergs \ncannot be excluded, but is less likely if the density profile is \nmuch steeper than $\\rho(R) \\propto R^{-4}$ and the maximum velocity \nis $\\lesssim 6000 \\kms$. The observations cover the \nregion $1140-1720$ \\AA, which is further into the ultraviolet \nthan has previously been obtained for the pulsar. With the \ntime-tag mode of the spectrograph we obtain the pulse profile in this \nspectral regime. The profile is similar to that previously obtained by\nus in the near-UV, although the primary peak is marginally narrower.\nTogether with the near-UV data, and new optical data\nfrom the {\\it Nordic Optical Telescope}, our spectrum of the Crab pulsar \ncovers the entire region from $1140 - 9250$~\\AA. \nDereddening the spectrum with a standard extinction curve we achieve \na flat spectrum for the reddening parameters $E(B-V)=0.52$, $R=3.1$. This \ndereddened spectrum of the Crab pulsar can be fitted by a power law with \nspectral index $\\alpha_{\\nu} = 0.11\\pm0.04$. The main uncertainty in \ndetermining the spectral index is the amount and characteristics of the \ninterstellar reddening, and we have investigated the dependence of \n$\\alpha_{\\nu}$ on $E(B-V)$ and $R$.\n%In the optical we do not see the absorption \n%feature reported by Nasuti et al. \nIn the extended emission covered \nby our $25 \\arcsec \\times 0\\farcs5$ slit in the far-UV, we detect \nC~IV~$\\lambda$1550 and He~II~$\\lambda$1640 emission lines from the Crab nebula.\nSeveral interstellar absorption lines are detected along the line of sight \nto the pulsar. The Ly$\\alpha$ absorption indicates a column density of\n$(3.0\\pm0.5)\\EE{21}$ cm$^{-2}$ of neutral hydrogen, which agrees well\nwith our estimate of\n$E(B-V)$=0.52 mag. Other lines show no evidence of severe depletion \nof metals in atomic gas. \n\\end{abstract}\n\n\\keywords{pulsars: individual (Crab pulsar) --- ultraviolet: stars --- \n ultraviolet: ISM --- dust: extinction --- supernova remnants ---\n instrumentation: spectrographs}\n\n\\section{Introduction}\n%--------------------%\nThe Crab nebula and its pulsar (PSR 0531+21) are among the most studied\nobjects in the sky. The discovery of the Crab pulsar \nas a fast rotating radio pulsar\n(\\cite{SR68};~\\cite{C69}) paved the way for the interpretation of pulsars as \nneutron stars (\\cite{G68}). \nAlso, the position of the Crab pulsar in the center of the Crab\nnebula, \nwhich is the remnant of supernova 1054, clearly supports the supernova -\nneutron star connection. Soon after the radio detection the pulsar was\nalso shown to emit optical pulsations (Cocke, Disney, \\& Taylor\n1969). This established\nthat the pulsating star was the well known south preceding star in\nthe center of the nebula, which early optical spectroscopy showed to\nemit a featureless continuum (\\cite{M42}). To date, more than 1000 \n%press release http://www.jb.man.ac.uk/news/pr9803.html nov 98 was#1000\nradio pulsars are known, but only the following few \nhave optical counterparts known \nto pulsate also in visible light: \nthe Crab pulsar (\\cite{Co69}), the LMC pulsar 0540-69 (\\cite{MP85}),\nthe Vela pulsar (\\cite{Wa77}), PSR 0656+14 (\\cite{Sh97}) and \n(possibly) the Geminga pulsar (\\cite{Sh98}). In the near-UV (NUV), \npulsations have only been established for the Crab pulsar \n(\\cite{P93};~\\cite{G98}, henceforth G98).\nDue to the faintness of these objects in the optical and in the ultraviolet,\nthe spectroscopic information is very limited. PSR 0540-69 was observed with\nthe Faint Object Spectrograph (FOS) onboard {\\it Hubble Space Telescope (HST)}\nin the $2500-5000$~\\AA\\ range (\\cite{H97}) and showed a rather steep \npower law spectrum. These observations were, however, contaminated by nebular \nemission. The Geminga pulsar was observed with the {\\it Keck} telescope \n(Martin, Halpern, \\& Schiminovich 1998), but\nthe spectrum has very \nlow signal-to-noise because this pulsar is exceedingly faint in the optical.\nThe only pulsar for which good signal-to-noise spectroscopy in the \noptical and ultraviolet\ncan be obtained is the Crab pulsar. Surprisingly enough,\nvery little has been done in this respect\nsince the optical observations of\nOke (1969).\nIn particular, until\nthe study by G98, no UV spectroscopy of the Crab pulsar had been published\nsince the first attempts by the {\\it International Ultraviolet Explorer\n(IUE)} (\\cite{Ben80}). The {\\it IUE} data cover only the NUV region \n($2000-3150$~\\AA) \nand have poor signal-to-noise. The {\\it HST}/STIS (Space Telescope Imaging \nSpectrograph) data from G98, and the new data presented here, clearly \nsupersede these early attempts.\n\nThe Crab pulsar has been extensively studied over a very broad wavelength \nrange, from the radio up to $\\gamma$-rays (e.g., \\cite{LGS98}). \nThe high energy emission, from infrared (IR) to $\\gamma$-rays, is believed \nto be the result of the same emission mechanism (e.g., \\cite{LGS98}).\nIt is therefore of interest to fill in the gaps in the observed spectrum of \nthe pulsar in this range. Although the pulsar is relatively\nbright in the optical, UV observations are difficult due to the large \nextinction toward the Crab, $E(B-V)\\sim0.5$ mag \n(e.g., \\cite{DF85}, and references\ntherein). Here, we present UV observations of the Crab pulsar further into the \nfar-UV (FUV) ($1140-1720$ \\AA) than has previously been obtained. \nThese are presented together with our previous NUV-data ($1600-3200$ \\AA)(G98)\nand new optical data from the {\\it Nordic Optical Telescope (NOT)}.\nDue to the large extinction correction, \ngreat care must be taken to draw conclusions \nabout the intrinsic spectrum, and thus the emission mechanism of \nthe pulsar. However, this procedure might also give a hint on the absorption\nproperties of the dust in the direction toward the pulsar.\n\n\nIn addition to\nthe pulsar emission, we detect emission lines from the Crab nebula \nitself in the FUV. In particular, the strength of the C~IV~$\\lambda$1550 \nemission can be of interest for abundance determinations.\nEven more interesting is the broad C~IV~$\\lambda$1550 \nabsorption line from the nebula detected against the pulsar continuum.\nThis line provides information on the nature of the SN 1054 event.\n\nAlthough the Crab nebula has \nbeen studied extensively, the nature of the progenitor remains unknown. \nAccording to models based on the existence of the central neutron\nstar, as well \nas on nucleosynthesis arguments, the zero-age main\nsequence (ZAMS) mass of the progenitor was probably \nin the range $8-13 \\Msun$ (Nomoto 1985). The amount of material observed \nin the nebula ($4.6\\pm1.8 \\Msun$) seems too low to account for this \n(Fesen, Shull, \\& Hurford\n1997). Furthermore, the velocities of the filaments ($\\sim 1400 \\kms$,\nDavidson \\& Fesen 1985) give an uncomfortably low kinetic energy \n($\\lesssim 1\\EE{50}$ ergs) \ncompared to other supernova remnants, i.e., at least an order of\nmagnitude less \nthan the canonical energy of supernovae, $10^{51}$ ergs. \n\nThe ``missing mass'' could either be in a slow progenitor wind, or in a fast,\nhitherto undetected, shell ejected at the explosion (Chevalier 1977). \nIf the latter is true, as is\nhinted by the observations of the outer [O~III] skin of the nebula \n(Hester et al. 1996; Sankrit \\& Hester 1997),\nthis shell might account for the missing mass and kinetic energy of\nthe nebula.\nThe question remains, however, why such a \nshell has escaped detection despite many efforts to observe it \n(see, e.g., \\cite{Fe97}). One possibility is that the low density of\nthe surrounding gas is not high enough to give rise to detectable \ncircumstellar emission when interacting with the ejecta; \nneither X-ray nor radio searches have \nindicated any evidence of circumstellar interaction \nbetween fast ejecta and ambient gas\n(Mauche \\& Gorenstein 1989; Frail et al. 1995).\nIf a fast shell is absent, the birth of the Crab was definitely a low energy\nevent. This would call for a revision of our understanding of \nsupernova explosions, especially since SN 1054 apparently was not unusually \ndim according to historical records (Chevalier 1977; Wheeler 1978). \n\nIt is thus of great interest to further investigate whether there is a stellar \nwind or supernova ejecta outside the observed nebula, and what velocity this \ngas may have. Lundqvist, Fransson, \\& Chevalier \n(1986, henceforth LFC86) proposed to search for a \nfast shell by looking in the UV toward the Crab pulsar. Their time\ndependent photoionization calculations showed that \nC~IV~$\\lambda$1550 could show up in blueshifted absorption if \nthe ionization history of the shell was as predicted in some models of \nReynolds \\& Chevalier (1984). Here, we present the detection of this\nbroad absorption line, and discuss its implications for the fast shell\naround the Crab nebula.\n\nFirst we discuss the observations and reductions (\\S 2). We then \n(\\S 3) discuss the pulse profile, the amount of reddening toward\nthe pulsar and the intrinsic pulsar spectrum in the optical/UV. In \\S 3 we\nalso discuss the lines originating from the interstellar gas toward\nthe pulsar and from the Crab nebula itself. \nSome of these observations constrain the properties of a possible outer shell.\nIn \\S 4 we summarize our conclusions.\n\n\n%--------------------------------%\n\\section{Observations, Reductions and Results}\n\\subsection{{\\it HST} Far-UV Observations}\n\nThe Crab pulsar was observed on January 22, 1999 using {\\it HST}/STIS \n(\\cite{K98}) with the FUV Multi Anode Micro-channel Array (MAMA) detector. \nThe low resolution grating G140L was used,\nwhich covers the wavelength interval $1140 - 1720$ \\AA. These observations\nwere made in the time-tag mode and used a slit of $52\\arcsec \\times 0\\farcs5$. \nThe spectral resolution is 0.58 \\AA\\ pixel$^{-1}$, and the plate scale\nis $0\\farcs0244$ pixel$^{-1}$. This means that only 25\\arcsec\\ of \nthe long-slit is actually projected onto the detector.\nIn total, six orbits of observations, including target acquisition, were used. \nThese were divided into two visits. A log of\nthe observations is shown in Table 1. The total on-target exposure\ntime amounted to 14,040 seconds.\nThe orientation of the slit is shown in Figure 1.\n\n\n\\subsubsection{Time-resolved emission}\n\nThe time-tag mode on the STIS allows us to resolve the emission from\nthe Crab pulsar both in wavelength and time. The time resolution\nobtained in this mode is 125 $\\mu$s.\nAs these observations were the first to utilize the time-tag\ncapabilities of {\\it HST}/STIS in the FUV for a known periodic variable,\nspecial software, developed at Goddard Space Flight Center (GSFC) was used \nto obtain the pulse profile for the pulsar.\nThe analysis followed the procedures outlined in G98. \nFor each of the six datasets, a time averaged image was produced to trace \nthe position of the pulsar spectrum. A 13 pixel wide window was \nused to extract events in \nthe pulsar spectrum as well as in the background emission at\nboth sides of the pulsar emission. \nThe arrival time of each 125 $\\mu$s sample was converted to a solar system\nbarycenter arrival time. \n%The difference in the {\\it HST} and solar system barycenter arrival time \n%is the dot product of the combined {\\it HST} position w.r.t. the solar\n%system barycenter and the unit vector in the direction of the crab pulsar\n%divided by the velocity of light. \nThe position of the {\\it HST} with respect to earth\ncenter was computed by the Flight Dynamics Facility at GSFC with errors less\nthan 200 meters. The position of the earth with respect to the solar system\nbarycenter was computed using a routine, SOLSYS, supplied by the U. S. Naval\nObservatory (Kaplan et al. 1989). \nAll events in the pulsar spectrum (and in the \nbackground regions) were assigned a (barycentric) arrival time with respect \nto the start of the first exposure. As we found a small drift in the times\nrecorded in the FITS headers, we used the internal clock from the engineering\nmode header to do this.\n%\n%({\\bf JS! Why do we say the engineer clock is better?)}\n% because doing the pulse profile analysis with the FITS-header times\n% basically smeared the peak of the profile\n%\nTo determine the period we folded the arrival times modulo a grid of\ntest frequencies, \n$f_{i}$, and corrected for the slowdown rate of the pulsar. \nPulse profiles were calculated as histograms\nof the function $f(t)=f_{i} t + \\dot{f} t^{2}/2$, where the data were\ncoadded into 512 phase bins.\nThe appropriate value of $f_{i}$ was then determined by \nmaximizing the sum of squares of the values in the pulse profile.\n\nIn this procedure we used a value \nfor $\\dot{f}$ from radio observations at Jodrell bank (Lyne, Pritchard, \\&\nRoberts 1999), while the \nsecond time derivative is unimportant for this purpose.\nThis resulted in a measured period of P=33.492675 ms at Modified Julian Date \n(MJD) 51200.549, the time of the beginning of our first observation \n(number O4ZP01010). \nAs the data were obtained during a time period of eight hours, \nwe could also determine the pulsar slowdown rate from our observations. \nWe obtained $\\dot P = (4.0\\pm0.4) \\times 10^{-13}$ s s$^{-1}$,\nwhich is consistent with the value used above from \nthe radio observations, $4.2\\times 10^{-13}$ s s$^{-1}$.\n% NB need 6 decimal accuracy to get this accuracy on Pdot\n\nIn Figure 2 we show the Crab pulsar pulse profile in the FUV regime. It was \nobtained by subtracting the background from the pulse profile obtained for \nthe period given above. For comparison, the figure also shows the NUV pulse\nprofile from G98.\n\n\n\\subsubsection{Phase-averaged spectrum}\n\nAveraging over the pulse we obtain a phase-averaged spectrum of the\npulsar which covers the region $1140 - 1720$~\\AA. \nThis spectrum probes the emission of the Crab pulsar further \ninto the UV than has previously been done and is\nshown in Figure~3, together with the NUV spectrum of G98.\nThese spectra \noverlap nicely and cover together the whole range from $1140-3200$~\\AA. \nThe combined spectrum offers the possibility to deduce the\namount and characteristics of the interstellar reddening, as well as\nto determine the dereddened pulsar spectrum itself. \n\nThe FUV-spectrum\nwas extracted with a 13 pixel wide window. The reductions were made using the\nCALSTIS software developed at the GSFC. \nThese IDL-routines flatfield the images and then \nthe point source spectrum is localized and traced on the detector. \nThe extracted pulsar spectrum is background subtracted and converted to \nabsolute flux units using the G140L sensitivity table.\nThe accuracy of the absolute flux calibration is $\\sim 15\\%$ \nover the full wavelength scale. \n% got the 15% from Don (priv.comm), it is the absolute uncertainty in the \n%white dwarf model, this is the possible offset/difference to optical. the \n%repeatability of G140L is better, a few %, also my countstatictics is\n%better (can do a lot of binning for the fluxlevel) at least everywhere \n%except farfarfarUV\nWavelengths are assigned from a library dispersion solution, while \nthe zero point adjustments are determined from arc frames taken \nthrough the $0\\farcs05$ slit for each science \nobservation. The wavelengths are then converted to heliocentric \nwavelengths. The accuracy of the wavelength solution is about 0.4 \\AA.\n% wavelength 0.3 + o.3 as we did no peak up +0.12 from differences to #6\n% ->0.44AA\n% note for accuracy\n% flux, the 6 different exposures gave slightly different fluxes. rms can give \n% a measure of this in the extracted spectrum I have added errors from \n% extraction procedure as well as from RMS of 6 observations\n% wavelengths, I have simply used wavelenghtsscale for observation #6 !\n% this is similar to crude binning, must be accounted for in errorestimate \n% above\n\n\n\\subsection{Optical observations}\nIn addition to the UV spectrum, we have also collected data in the\noptical regime. During several nights in December 1998 we did spectroscopy\nof the Crab pulsar using the Andalucia Focal Reducer and Spectrograph (ALFOSC)\nat the 2.56m {\\it NOT} on La Palma. \nIn total we obtained 11.25 hours of data in five \ndifferent grisms.\nThe 1\\farcs2 slit was used for all observations (see Table 2 for more details).\nNot all nights were photometric and the seeing was generally\njust above 1\\arcsec. The data were bias subtracted and flatfielded. \nWavelength calibrations were done using arc frames obtained\nwith a helium lamp. Flux calibration\nof the spectra was accomplished by comparison to\nthe spectrophotometric standard stars Feige~34 and G191-B2B. To avoid\nsystematic errors due to background subtraction the slit was put at two\ndifferent position angles.\n%PA 75 and -70?\nAll observations were made at low\nair masses and close to the parallactic angle to reduce the effects of\natmospheric\ndispersion; the Crab pulsar passes just $7\\arcdeg$ from zenith as\nviewed from La Palma in December.\nThe slit positions for the {\\it NOT} observations are shown in Figure~1. \n\n\\subsection{Combined UV/optical spectrum}\n\nThe combined optical and UV observations (both NUV and FUV) are shown in \nFigure~4. It covers the region $1140 - 9250$~\\AA. \nAlthough great care was given to the background subtraction of the \nnebula, the optical spectrum of the Crab pulsar was contaminated by over- \nand under-subtractions of strong nebular emission lines.\n% as well as telluric features. \nThese had to be taken out by hand, and\nwe used the IRAF task SPLOT to interactively clean the spectrum. Points that \ndeviated more than 4$\\sigma$ from a smooth continuum fit were rejected. \nThis procedure was robust enough \nto exclude only clear cases of nebular contamination.\nThe optical spectrum used is a combination of all the different\nspectra in Table~2.\nNote that an absolute flux calibration\nwas not applied to the optical spectrum, as \nthe observing conditions were often non-photometric. Instead we have applied \na grey shift to the spectrum to match the $V$-band observations of Percival\net al. (1993) and Nasuti et al. (1996).\nAs seen in Figure 4, this is well matched with the\nUV spectrum from the {\\it HST}.\n\n%--------------------%\n\n\\section{Discussion}\n\n\\subsection{Pulse profile}\nThe work of Percival et al. (1993) showed small differences in the \noptical versus NUV pulse profile shapes.\nThey observed the Crab pulsar with the High Speed Photometer (HSP)\nonboard {\\it HST} and found that the main pulse is slightly narrower in \nthe UV than in the optical. \nEikenberry et al. (1997) extended the analysis into the \nnear-IR and found that the trend for a decreasing Full Width Half Maximum \n(FWHM) with decreasing wavelength seems to hold over the full UV-IR range. \n\nThe time-tag mode of STIS/FUV-MAMA allows us to examine if the pulse profile\nof the emission is different in this wavelength region from that in the NUV. \nThe most striking feature of the FUV pulse profile shown in Figure 2 is\ncertainly that it is very similar to the profile previously obtained in \nthe NUV (G98). It appears, however, that the primary peak is slightly narrower\nin the FUV than in the NUV, as indicated\nby the blow-up of that region in Figure 2.\nWe measured the FWHM of the \nFUV and NUV primary peak to be 0.0405 and 0.0426 periods, respectively.\nThe position of the peak was determined by a polynomial fit to the central \n10 phase bins. The phase at half-maximum was then simply determined by linear \ninterpolation between the two closest phase bins. \n%We note that our 125 $\\mu$s\n%resolution does not resolve the peaks, which might introduce some smearing\n%of the peaks. As the NUV and FUV data were obtained \n%and reduced in exactly the same way, \n%we do, however, believe that the difference is significant.\nTo estimate a statistical\nerror on the procedure used to measure the FWHM, we computed\nthe FWHM for each of our six FUV observations. \nThe standard deviation obtained in\nthis procedure was 0.001 phase bins. The measured difference in the FWHM of\nthe primary peak can therefore be considered marginally significant.\n% sqrt[(mean-fwhm(i))^2/5]/sqrt(5)\nThe secondary peak in Figure~2 might actually appear broader in the FUV.\nIt is, however, much noisier than the primary peak and\nthe same \nprocedure as above could not determine any significant difference to the\n13$\\%$ (3$\\sigma$) level.\nThe above findings are in agreement with the trend seen in Percival et al. \n(1993) and Eikenberry et al. (1997).\nThe pulse period obtained from the FUV observations is P=33.492675 ms.\nRadio data from Jodrell Bank (\\cite{LPR99}) determined the pulse period \nto be P=33.492402 ms on January 15 1999. Using their values for the pulse \nperiod and its first time derivative on this date we can calculate the \nperiod at the time of our {\\it HST} observations. \nThe result is P=33.492676 ms.\n%http://www.jb.man.ac.uk/~pulsar/crab.html\nThis agrees with our estimate to 7 significant digits. \nThe limiting errors in our computation of the\nperiod are the accuracy of the SOLSYS routine which has a barycentric velocity\nerror of less than $8.0\\EE{-7}$ AU/day and the unknown accuracy of the rate\nof the STIS onboard clock.\n\n\n\\subsection{The UV extinction curve}\n\nThe phase averaged UV spectrum of the Crab pulsar must be corrected\nfor a substantial amount of interstellar reddening.\nThe value for $E(B-V)$ has been estimated by a number of authors; \nWu (1981) obtained $E(B-V)=0.50\\pm0.03$ mag by using the 2200 \\AA\\ dust\nabsorption feature, the nebular synchrotron continuum and an extinction\ncurve derived from eight stars. Blair et al. (1992) also used the best\nfit to the UV nebular continuum and obtained\n$E(B-V)=0.51^{+0.04}_{-0.03}$ mag.\nA different method was used by Miller (1973), who determined the\nreddening of the Crab nebula from observations of [S II] lines. \nUsing modern values for the atomic parameters (Keenan et al. 1993; \nRamsbottom, Bell, \\& Stafford 1996), and the extinction curve of \nFitzpatrick (1999), his measurements gives\n$E(B-V)=0.50^{+0.04}_{-0.06}$ mag.\n\nOur data of the pulsar itself allows us to estimate the value for $E(B-V)$\nby ``ironing out'' the 2200 \\AA\\ bump.\nTo do this we assumed a standard value $R=3.1$ and\ndereddened the UV spectrum for different values of $E(B-V)$. \nThe dereddened spectra were then fitted by a power law and we chose \nthe value for $E(B-V)$ that minimized $\\sigma_{\\alpha_{\\nu}}$,\nthe standard deviation of the power law fit in the region \nlog $\\nu$=[14.98, 15.41],\nwhere the region including the Ly$\\alpha$ absorption was excluded.\nThis procedure used the\ngalactic mean extinction curve from Fitzpatrick (1999) and gave\n$E(B-V)=0.52$ mag.\nThis is in excellent agreement with the previous results stated\nabove. As our data have better signal-to-noise and sampling than\nprevious continuum fits, we \nwill use this value as the best estimate of the extinction toward\nthe Crab nebula throughout this paper. \n\n% wu gets EBV=0.50 +- 0.03\n% miller 73 says Av=1.6+-0.2 which gets EBV=0.516+-0.07 for R=3.1\n% blair says ebv=0.51 +0.04 -0.03 from UV continuum fit\n%; davidson fesen says: (based on miller and Wu)\n%; av=1.46+-0.12 and ebv=0.47+-0.04 \n%;this would mean Rv=3.106\n%; 1.46+0.12 / 0.47-0.04 = 3.6744 ; 1.46-0.12 / 0.47+0.04 = 2.6275\n%; thats a bit pessimistic 3.11+-0.13 is rootmeansquareerror\n\nFrom the NUV spectrum\ntaken of the Crab pulsar by {\\it IUE}, claims were made for a peculiar\nextinction curve (\\cite{Ben80}). In particular, the 2200 \\AA\\ bump\nwas reported to be substantially narrower than for the galactic mean \nextinction curve,\na finding that could indicate that the\nsupernova event itself had altered the grain composition in the\nCrab nebula.\nIn principle both the extinction curve and the\nintrinsic pulsar spectrum are unknown, which of course makes it\ntroublesome to disentangle these quantities. We take the following\napproach to this problem: theoretical models favor a power \nlaw spectrum (e.g., \\cite{LGS98}) and dereddening with \n$E(B-V)=0.52$, $R=3.1$ indeed gives a power law pulsar spectrum (Fig. 4), \nso we will simply assume the intrinsic spectrum of the Crab pulsar to\nfollow a power law $F_{\\nu}$ = $K(\\nu/\\nu_{0}$)$^{\\alpha_{\\nu}}$\nergs~s$^{-1}$~cm$^{-2}$~Hz$^{-1}$. Here $\\nu$ is the frequency of the\nradiation and $K$ is a constant that is nearly independent of\n$\\alpha_{\\nu}$ when $\\nu_{0}$ \nis the logarithmic mean frequency of the fitted bandpass (\\cite{P93}). \nUsing the extinction parameters above, $E(B-V)=0.52$ and\n$R=3.1$, the spectral index is $\\alpha_{\\nu}=-0.035$ in the UV range.\n%To find the extinction\n%parameters E(B-V) and R we dereddened the UV spectrum for a fine grid\n%of values in the range E(B-V)=[0.4,0.7], R=[2.5,5.0], and chose the\n%parameters that minimized $\\sigma_{\\alpha_{\\nu}}$, the standard\n%deviation of the power law fit in the region log $\\nu$=[14.98,15.41],\n%where the region including the Ly$\\alpha$ absorption was excluded.\n%At this stage, we have used only the UV data, as these are more\n%sensitive to the extinction and less affected by atmospheric\n%dispersion and nebular contribution. This procedure, that used the\n%galactic mean extinction curve from Fitzpatrick (1999), gave E(B-V)=0.514\n%and R=3.70 for a power law with spectral index\n%$\\alpha_{\\nu}$=$-0.66$. Although E(B-V) seems to be well constrained by\n%this procedure, the value of R is not. This hampers the determination\n%of $\\alpha_{\\nu}$, see the discussion in section 3.3. \n\nBy assuming that the intrinsic pulsar spectrum is indeed well represented by \nthe obtained power law we derived\nan extinction curve toward the pulsar. This is shown in\nFigure 7 together with the mean galactic extinction curve for $R=3.1$ from\nFitzpatrick (1999). The derived extinction curve has a moderately narrower dip\n(15$\\%$) \nand a somewhat shallower rise in the extreme FUV. Apart from this, it\noverlaps nicely with the galactic mean extinction curve.\n% for the same value of $R$. \nConsidering the large variety of measured UV\nextinction curves (see Fig. 2 in Fitzpatrick 1999), \nthe derived extinction curve\ntoward the Crab can hardly be claimed to be peculiar. \nAssuming that the pulsar spectrum follows a power law, we conclude that\nwe find no evidence for a non-standard extinction curve toward the\nCrab pulsar.\n\n\\subsection{The spectral index of the pulsar continuum}\n\nAccording to models, the high energy pulsar emission, from IR to\n$\\gamma$-rays, is produced by (curvature) synchrotron radiation \n(e.g., \\cite{LGS98}, and references therein). \nA number distribution of \nelectrons following a power law\n$N(E) dE = C E^{-\\gamma} dE$, where $E$ is the energy, $C$ is a constant and \n$\\gamma$ is the electron spectral index, will produce synchrotron \nradiation that has a power-law distribution in flux density\n$F_{\\nu} = K(\\nu/\\nu_{0})^{\\alpha_{\\nu}}$ \nergs~s$^{-1}$~cm$^{-2}$~Hz$^{-1}$.\n%(Shklovsky 1960).\nThe photon spectral index, $\\alpha_{\\nu}$, is related to the electron\nspectral index, $\\gamma$, via $\\alpha_{\\nu} = -(\\gamma-1)/2$ for\nsynchrotron radiation. \n% took this from hill et al., the def. of alpha is standard and we\n% must stick to it for comparison with oke, percival etc.\n% def of -gamma also pretty standard, I guess,\n% NB I think hill et al. makes a mistake in their formula relating\n% alpha and gamma, I think the above is correct (JS)\n\nThe early low resolution spectroscopy of Oke (1969) appears to peak in the\nmiddle of the observed region ($\\sim 3400-8000$ \\AA). He reports a slope of \n$\\alpha_{\\nu} = -0.2$ with no stated errors, although he cautions that the \nuncertainty in the reddening correction could allow also for a positive slope. \nMuch of the theoretical work on the optical emission mechanism of pulsars \nhas been based on this finding \n(cf. Ginzburg \\& Zheleznyakov 1975; \\cite{LGS98}).\nMore recently, Percival et al. (1993) used \nground-based optical broadband photometry together with a \nNUV photometric point \nfrom {\\it HST}/HSP to determine a slope of $\\alpha_{\\nu}=0.11\\pm0.13$, while\nNasuti et al. (1996) obtained a spectrum in the limited wavelength \nrange $4900-7000$ \\AA\\ (see below) and \ndetermined $\\alpha_{\\nu} = -0.10\\pm0.01$.\n%While the minimization procedure above gave a reasonable value \n%for E(B-V) the obtained value for R appears rather high. As mentioned, this \n%parameter is in fact not very well constrained in this procedure. Allowing\n%the RMS of the power law fit to increase by 1$\\%$ above the minimum gives the\n%allowed parameter surface E(B-V)=[0.50,0.53], R=[3.3,4.2]. \n%If we would force R to the standard value R=3.1, we obtain E(B-V)=0.519\n%and a power law fit to the UV region for these parameters gives \n%$\\alpha_{\\nu}$=-0.038.\n\nApplying $R=3.1$ and $E(B-V)=0.52$ from \\S 3.2 to\nour UV spectrum gives a spectral index of\n$\\alpha_{\\nu}=-0.035\\pm0.040$, \nwhere the error is simply the RMS around the fit. \nObviously, the main uncertainty in this procedure is the extinction \nparameters. For $E(B-V)$ in the range [0.48, 0.55], \nthe uncertainty due to reddening becomes \n$\\alpha_{\\nu}=-0.035^{+0.094}_{-0.13}$.\nAn accurate estimate of the spectral index obtained in the UV,\nfor the given extinction range, can be obtained by \n$\\alpha_{\\nu}=-0.035+3.12[E(B-V)-0.52]$.\n%correcting the spectral index obtained above for\n%$-1.24 \\delta R + 3.12 \\delta E(B-V)$, where $\\delta R=R-3.1$ and \n%$\\delta E(B-V)=E(B-V)-0.53$. \n%This linear estimate\n%, where $\\alpha_{\\nu}$ becomes more positive for larger \n%$E(B-V)$ and smaller R, \n%is accurate to within 0.001 units of $\\alpha_{\\nu}$ in\n%the above mentioned extinction range.\nNote that the spectral \nindex for $E(B-V)=0.55$ was erroneously reported in G98.\nThe analysis in this paper supersedes this previous report.\n\nIncluding the optical spectrum from the {\\it NOT} \ngives a wider wavelength \nrange for the fit. \nThe dereddened spectrum shown in Figure 4 was obtained with $R=3.1$ and\n$E(B-V)=0.52$. The best power law fit to the complete spectrum \n(excluding Ly$\\alpha$)\n% and the bluest optical part (see Fig. 6)) \ngives $\\alpha_{\\nu}=0.11$.\n\n \nUsing the full wavelength range we have also tried to constrain \nboth $E(B-V)$ and $R$. This can be done using the extinction curves\nfrom Fitzpatrick (1999), which are a one-parameter family in $R$.\nBy assuming an intrinsic power law we thus allowed both $R$ and $E(B-V)$ to \nvary, and chose the values that minimized $\\sigma_{\\alpha_{\\nu}}$, \nthe standard deviation of the power law fit.\nThis procedure gives $R=3.0$ and $E(B-V)=0.51$,\nwhich is consistent with the values used above. \nIn Figure 6 we show the dereddened spectrum of the Crab pulsar for several \ndifferent values of $R$ and $E(B-V)$. In this figure we have also included IR \ndata from Eikenberry et al. (1997). These plots clearly show the ambiguity\nof the reddening correction. \n\nWe can express the spectral index of the power law fit for the \nvalues $E(B-V)=0.52$ and $R=3.1$ as $\\alpha_{\\nu}=0.11\\pm0.04^{+0.21}_{-0.22}$.\nThe first error represents the RMS around the power law fit, \nand the last errors include all power law fits in the extinction \nintervals $R=[2.9, 3.3]$, $E(B-V)=[0.48, 0.55]$.\nA linear fit, \n%$\\alpha_{\\nu}$=0.11-0.38$(R-3.1)$+3.88[$E(B-V)-0.52$]\n$\\alpha_{\\nu}=0.11-0.38(R-3.1)+3.88[E(B-V)-0.52]$\nreproduces the obtained $\\alpha_{\\nu}$ in this interval to better \nthan 0.02 units.\n% largest error is 0.0122\n\nWe can only echo Oke (1969) in his conclusion that the \nuncertainties in reddening corrections are large enough to allow both for\nnegative and positive slopes.\nThe inferred energy distribution for the electrons is \ngiven by $\\gamma = 0.8 \\pm 0.5$.\nIt is worth noting that the only other young pulsar for which a spectrum has\nbeen obtained in the optical, PSR B0540-69, had $\\alpha_{\\nu}=-1.6\\pm{0.4}$ \n(\\cite{H97}). This is clearly steeper than the Crab pulsar spectrum.\n\nFinally, the time tag mode of our FUV observations also allows us to extract \nphase-resolved spectra, and we have looked for spectral differences during \nthe pulse phase. We found no significant differences above the $5 \\%$ level, \nneither in the spectrum of the primary versus the secondary peak, \nnor in the leading versus trailing part of the primary peak.\n\n\n\\subsection{The $5900$~\\AA\\ feature}\nIn the first report on the optical spectrum of the Crab pulsar,\nMinkowski (1942) reported a featureless continuum with no\nabsorption or emission lines. The observations of Oke (1969) indicated a\nsimilar conclusion, although the spectral resolution was not very good. Since\nthen, few attempts have been made to obtain a better optical spectrum of \nthe Crab\npulsar, despite that technical development certainly admits\nimprovements. The only modern optical spectrum of the Crab pulsar was \nobtained with the {\\it New Technology Telescope (NTT)} by \nNasuti et al. (1996). \nThis phase-averaged spectrum covered a rather small wavelength \nregion ($4900-7000$~\\AA) and was flat with $\\alpha_{\\nu} = -0.10\\pm0.01$ \nif dereddened with $E(B-V)=0.51$. \nThe spectrum was also reported to show a\nlarge dip at $\\sim5900$~\\AA, the width being $\\sim100$ \\AA. \nAccording to the authors this feature probably originates close to the pulsar\nitself, but no detailed physical mechanism was proposed.\n\nWe have searched for this feature in our optical spectra, but found no\nsign for a dip. This is true for all the different gratings covering\nthis region during all of the nights of data obtained in December 1998 \n(see Fig.~4). \nNeither do we see the feature in unpublished\ndata taken by us at {\\it NOT} one year earlier (December 1997). Nasuti et\nal. (1996) noted that the feature became enhanced after\nflux calibration. This suggests that the dip may be an artefact of the \nreduction procedure. While their investigation used a single \nspectrophotometric \nstandard star\nwith flux sampled only every 100 \\AA, we have\nused two standard stars with 2 \\AA\\ sampling in the relevant\nwavelength region.\nAlthough the feature could be time dependent, we propose\nto regard it as an artefact until confirmed by other observations.\n\n\n\\subsection{Absorption lines}\n\nAs in the NUV spectrum of the pulsar (G98), the FUV spectrum contains several \nabsorption lines. The identified lines are shown in Figures 7 and 8, and \ntheir equivalent widths (EWs) and\ncorresponding column densities, $N$, are listed in Table 3. \nFor completeness, we have also included the lines \nin the NUV spectrum identified and measured by G98.\n\nThe strongest line is Ly$\\alpha$, and its damping wings can be used to \nestimate $N$(H~I). To do this we\nassume that the optical depth in the damping wings is defined \nby $\\sigma(\\lambda)N$(H~I) (Shull \\& Van Steenberg, 1985). \nHere the absorption cross \nsection $\\sigma(\\lambda) = (4.26\\EE{-20}~{\\rm cm}^2)/(\\lambda - \\lambda_0)^2$,\nwhere the wavelengths are in \\AA\\, and $\\lambda_0 = 1215.67$~\\AA. We have\nnot considered the instrumental profile, which is much narrower ($\\sim 1$~\\AA)\nthan the line width (see Fig. 7). From this analysis we\nobtain $N$(H~I)$ = (3.0\\pm0.5)\\EE{21}$ cm$^{-2}$.\nThe spectrum corrected for Ly$\\alpha$ absorption is shown in Figure 7. Our \nestimated uncertainty in $N$(H~I) reflects the uncertainty in the \ncontinuum fit of the corrected spectrum. The column density of\nfree electrons toward the Crab is measured from pulsar dispersion to\nbe \n$N_{\\rm e}$~$=~(0.1755\\pm0.0007)\\EE{21}$~cm$^{-2}$~(\\cite{C69}). \nThe amount of atomic\nhydrogen is thus $N$(H)$ = (3.2\\pm0.5)\\EE{21}$ cm$^{-2}$.\nThis value agrees well with \nboth the result of Schattenburg \\& Canizares (1986) \nwho obtained $N$(H) $= (3.45\\pm0.42)\\EE{21}$ cm$^{-2}$ from an estimate\nof the X-ray absorption toward the Crab, and the value we estimate \nfrom $E(B-V)$ using the relation in de Boer, Jura, \\& Shull (1987), \nwhich gives $N$(H~I)$\\simeq 3.0\\EE{21}$ cm$^{-2}$ for $E(B-V) = 0.52$. \n\nThe other absorption lines we identify around zero velocity in the FUV \nspectrum are: C~I~$\\lambda\\lambda$ 1277,1329,1561,1658, C~II~$\\lambda$1335,\nO~I~$\\lambda$1303, Al~II~$\\lambda$1671, Si~II~$\\lambda\\lambda$ 1260,1527 and \nSi~IV~$\\lambda$1394. The Si~IV line is close to noise level, which explains \nwhy the Si~IV~$\\lambda$1403 component is not seen. \nThe C~I~$\\lambda\\lambda$ 1277,1329 lines are also marginal detections, but \ntheir strengths correspond to those expected when compared with the \nstrengths of C~I~$\\lambda\\lambda$ 1561,1658. \nThe C~IV~$\\lambda\\lambda$ 1548,1551 \ndoublet is absent at zero velocity, but shows a blueshifted absorption with a \nmaximum shift of $\\sim 2500 \\kms$. We return to this line in \\S 3.7.\n\nAll lines except Ly$\\alpha$, and \nthe C~IV doublet which is not \ninterstellar or from a slow wind (\\S 3.7), are unresolved by the \nmoderate spectral resolution in \nthe STIS spectra ($\\approx 1.2$ \\AA\\ in FUV and $\\approx 3.2$ \\AA\\ in NUV, \ncorresponding to $250 \\kms$ and $400 \\kms$ for the central wavelengths of the \ntwo gratings, respectively). \nThe measured EWs of the absorption lines are rather large, which\nmeans that we\ncannot assume that the lines are resolved and optically thin\n(i.e., we cannot use \n``weak-line'' theory [e.g., Morton 1991]) to derive abundances of \nthe various species, as this would severely underestimate the abundances. \n\nIn the absence of a proper model for the distribution of intervening matter, \nwe assume that the absorption is dominated by a single cloud component. We \nset the intrinsic ``Doppler'' width in this component to $1 \\kms$, and assume \nthat this is the same for all lines.\n% (which, e.g., would be the case for turbulence). \nFurthermore, we consider only one spectral component of the lines listed in \nTable~3. All these assumptions cause us to systematically overestimate the \ncolumn densities and abundances so that our estimates will be upper\nlimits to these. With this in mind, we calculate \nVoigt line profiles and EWs as functions of column density, using the atomic \ndata in Morton (1991). From the measured EWs we then obtain column densities \nand abundances for the interstellar gas toward the Crab. The abundances in \nTable~3 are presented in the standard logarithmic form where the value for \nhydrogen is set to 12.0. \n\nIn Table~4, where we have simply coadded the abundances of the different \nionization stages of each element, we give the abundances of C, O, Mg, Al, Si \nand Fe from our analysis. We also list the solar values for these elements\naccording to Anders \\& Grevesse (1989). \nThere appears to be no extreme \ndepletion of any element, contrary to what was stated in G98, \nwhere ``weak-line'' theory was used. \nThis is in agreement with the X-ray observations \nby Schattenburg \\& Canizares (1986) which were consistent with a solar\nabundance of oxygen.\nOur oxygen abundance from the single O~I~$\\lambda$1303 line is, however,\nrather uncertain due to geocoronal airglow corrections, \nand a possible blending with \nSi~II~$\\lambda$1304.\nAs pointed out above, our method is likely to systematically \noverestimate abundances. Broader lines, or more cloud components,\n%than assumed above \nwould lower the abundances derived in accordance with \ndepletion seen in the normal interstellar medium (e.g., 0.65 dex for carbon\nat 2 kpc, Welty et al. 1999).\nSpectra with higher resolution are required to refine this analysis. \n\n\n\\subsection{Emission lines}\n%Although our study concentrates on the pulsar itself, t\nThe FUV-spectrum contains\nalso information about the Crab nebula. The long slit \ncovers \n$\\sim$ 25\\arcsec $\\times$ 0\\farcs5 of the nebula, along position \nangle (PA) $40\\arcdeg.5$.\n% Pa aper is the correct one to use\n%PA-APER = 0.405058677856E+02 position ang of aperture used with target(deg)\n%ORIENTAT= 40.8892 position angle of image y axis (deg. e of n) \nThe orientation of the slit is shown in Figure 1.\nTo extract the pulsar spectrum \nwe used only 13 of the 1024 pixels of the MAMA detector. \nTo obtain a spectrum of the nebular emission outside this extraction window \nwe again used CALSTIS to produce rectified, wavelength- and flux-calibrated \nimages. As the count rates were very low, we summed the\nemission from two 8\\farcs2 long regions positioned 0\\farcs66\nabove and below the pulsar position. This safely excludes any contribution \nfrom the point spread function (PSF) wings of the pulsar. \nAll emission from all 6 observations was combined and \naveraged to increase the \nsignal-to-noise. We present this nebular spectrum in \nFigure 9, which shows only the wavelength region $1400 - 1700$ \\AA. \nThis is to exclude the %strong \ngeocoronal lines of Ly$\\alpha$ and \nO~I~$\\lambda\\lambda$ 1303,1356. %{\\bf PL: do we see the 1356 component?} \nThe spectrum is the average of the regions above and below the pulsar.\nFor the spectrum extracted above (North-East of) the pulsar, the\ncontinuum level was flattened artificially. This is because\nwe observed a rising continuum in the red part of this spectrum, \nwhich is probably due to contamination\nof the nearby star seen in Figure 1.\nMoreover, \nthe count rates in the continuum are only $\\sim 7.5 \\times 10^{-5}$ \ncounts pixel$^{-1}$ s$^{-1}$.\nAt such low count rates, trends in the dark currents might influence the \ncontinuum. No dark images are subtracted \nfrom the FUV-MAMA observations, because the \ndark images are known to be variable\nand to have low count statistics.\nTherefore, we will not discuss further the slope of the continuum emission\nfrom the nebula. \n\nOnly two emission lines intrinsic to the Crab nebula can be\nseen, C~IV~$\\lambda$1550 and He~II~$\\lambda$1640.\nThe measured intensities\nare $\\sim (2.1\\pm0.8)\\times10^{-15}$ and $\\sim (1.4\\pm0.8)\\times10^{-15}$ \nergs~s$^{-1}$~cm$^{-2}$, respectively. This is an average for the two\n8\\farcs2 $\\times$ 0\\farcs5 regions, just above and below the pulsar. \nOur detection of these two lines\nis in accordance with the two previous spectroscopic \nobservations of the Crab nebula in the FUV. \nDavidson et al. (1982) used the {\\it IUE} to detect \nthese two lines, as well as C~III]~$\\lambda1909$. \nBlair et al. (1992) recalibrated the {\\it IUE} data and complemented\nthese with \nobservations from the {\\it Hopkins Ultraviolet Telescope (HUT)}. \n\nThe widths of the lines are approximately 13~\\AA~and 10~\\AA,\nfor C~IV~$\\lambda$1550 and He~II~$\\lambda$1640, respectively.\nThe width is due to the velocity distribution of the material, the\ndoublet nature of C~IV~$\\lambda$1550 as well as to the spectral\nresolution for extended sources for the spectrograph.\nThe bulk of the emission is redshifted by $\\sim 1000~\\kms$,\nalthough a narrower zero-velocity component is seen from the region\nabove the pulsar.\n\nThe flux ratio of C~IV~$\\lambda$1550 to He~II~$\\lambda$1640\nis thus $\\sim1.5$, which is in accordance with the \nfindings of Davidson et al. (1982), who sampled the fluxes over \na larger field, $20\\arcsec \\times 10\\arcsec$. They used this\nto argue that the Crab nebula has no overabundance of carbon. However, \nthe subsequent investigation by Blair et al. (1992) showed that variations in \nthe He II/C IV line ratio exist in the nebula. They cautioned on conclusions\nregarding the carbon abundance, as differences in physical parameters (e.g.,\nionization, density, temperature, clumping) are difficult to disentangle from \nabundance variations. \n%In fact, variations on these line ratios can almost \n%be seen directly on our 2-dimensional frames. \nTo determine the carbon abundance is important because it holds the potential\nto provide information about the \nZAMS mass of the progenitor. \nComparisons to detailed photoionization \nmodels for the large apertures used by {\\it IUE} and {\\it HUT} are hampered by \nthe fact that ionization conditions are known to change over very small spatial\nscales (\\cite{Sa98}). The observations we present have finer spatial resolution\nand are not biased toward bright filaments. {\\it HST} \nobservations {\\it of the same regions} in the optical, to establish the \nionization conditions, could make more quantitative estimates of the \ncarbon abundance possible.\n\n\\subsection{The outer shell}\n\nAs was mentioned in \\S 3.5, and shown in Figure 8, C~IV~$\\lambda$1550 is the \nonly line in the UV spectrum which shows clear evidence of blueshifted \nabsorption. No evidence for absorption can be seen at zero velocity. The \ngreatest absorption appears to arise in material moving at $\\sim 1200 \\kms$, \nand can thus \nbe due to ``normal'' Crab nebula material. However, the absorption\nseems to continue to higher velocities, and can be traced out to \n$\\sim 2500 \\kms$ (see Fig.~10). \nTo estimate the significance of the detection we have calculated an average\nand RMS from two 50~\\AA~regions redward and blueward of the C~IV\nline. Although the line is too noisy for individual pixels to be\nsignificant, it consists of many pixels that are consistently below\nthe average. The eleven pixels between $1650 - 2780~\\kms$\ngive a detected absorption with a significance of $5.8\\sigma$.\nFor the five points in the region $2330 - 2780~\\kms$\nthe significance is $3.0\\sigma$.\n\n\nTogether with Clark et al. (1983), who also reported velocities\nin excess of $2000 \\kms$, this is the highest velocity ever measured \nin the Crab, and can be interpreted as evidence for the existence of the long \nsought fast outer shell (cf. \\S 1). The column density of C~IV in \nTable 4, $N($C~IV$) = (3.0\\pm1.1)\\EE{14}$ cm$^{-2}$, \nassumes the line to be resolved and optically thin. \nThis should be the case for velocity broadening caused by the tentative fast \nshell, though we caution that the material moving at $\\sim 1200 \\kms$ may \nnot be spectrally resolved. The total column density of C~IV is therefore \nlikely to be higher, while that of the proposed fast shell is lower\nthan the value given in Table 4. We will now investigate whether the detection \nis consistent with a fast outer shell model and what information can be \nprovided about the supernova ejecta.\n\n\\subsubsection{Constraints from C~IV~$\\lambda$1550}\n\nWe adopt a model similar to that of LFC86, i.e., outside the \nobserved filaments we attach a massive, \nfreely coasting, spherically symmetric shell. \nThe inner radius, $R_{\\rm in}$, is set to $5.0\\EE{18}$ cm, which agrees\nwith the ``mean'' inner radius of the presumed shell used by Sankrit \\& \nHester (1997, see their Fig.~7). For free expansion this corresponds to a \nvelocity of $\\approx 1680 \\kms$. Furthermore, we \nassume that the mass of the shell, $M_{\\rm sh}$, is $4 \\Msun$, and that the \nouter radius of the shell, $R_{\\rm out}$, is $1.9\\EE{19}$ cm. The maximum \nvelocity, $V_{\\rm out}$, is then $\\approx 6370 \\kms$, and the \ntotal kinetic energy of the shell, $E_{\\rm sh}$, is $1.0\\EE{51}$ ergs, if the \ndensity is constant in the shell. For a density which decreases with \nradius, $E_{\\rm sh}$ is lower, if $M_{\\rm sh}$ is held constant. This is\nshown in Table 5 for density slopes up to $\\eta = 9$, where $\\eta$ is defined\nas $\\rho(R) = \\rho(R_{\\rm in})~(R/R_{\\rm in})^{-\\eta}$.\n\nIn our model we have used the relative \nabundances $X($H$)$: $X($He$)$: $X($C$)$ = 1.0: 0.1: $3.5\\EE{-4}$, where \nthe $X($C$)$/$X($H$)$ ratio corresponds to the solar value.\nWith these abundances we have calculated the absorption in \nC~IV~$\\lambda\\lambda$ 1548,1551 as a function of $\\eta$\nand the relative fraction of carbon in C~IV, $X($C~IV$)$.\nThe parameter $X($C~IV$)$ is unity when carbon is all in C~IV. \n\nIn Figure 10 we show results for two models where $X($C~IV$)$ has been kept\nconstant throughout the shell. The dotted line shows the C~IV line in the \ncase of $\\eta = 0$ and $X($C~IV$) = 1$, while the dashed line is \nfor $\\eta = 3$ and $X($C~IV$) = 0.14$. Both models are described in Table 5. \nThe photoionization models of \nLFC86 show a case similar to our $\\eta = 0$ case (their model 1). There,\ncarbon is ionized beyond C~IV, and only a very small fraction, concentrated \nto the outer edge of the shell, remains in C~IV. This gives maximum absorption \nin the $\\eta = 0$ case around $-6000 \\kms$ (see Fig. 1 of LFC86 for such a \ncase). This is clearly not what is seen in the FUV data. On the contrary, the \nobserved absorption peaks at lower velocities, meaning that the C~IV number \ndensity %, $n({\\rm C~IV})$,\nmust be the highest closer to $R_{\\rm in}$. \nThe photoionization models of LFC86 make the $\\eta = 0$ case rather \nunlikely from this point of view. Instead we turn our attention to \nsteeper density profiles.\n\nSuch a situation is highlighted by the $\\eta = 3$ case in Figure 10. \nOur assumption of constant $X($C~IV$)$ in the shell is probably more realistic \nfor $\\eta = 3$ than for $\\eta = 0$. This is because the ionization \nparameter, $\\xi = {\\rm n}_{\\gamma} / {\\rm n}_{\\rm e}$, \nwhere ${\\rm n}_{\\gamma}$ and ${\\rm n}_{\\rm e}$ are number densities of\nionizing photons and electrons, respectively, has the radial\ndependence $\\xi \\propto R^{\\eta-2}$, if absorption can be neglected. With \nabsorption included, $\\eta$ must be $>2$ to obtain a near-constant $\\xi (R)$. \nOur choice of $X($C~IV$) = 0.14$ has only been made to fit\nthe data. Any combination of $X($C~IV$)$ and $M_{\\rm sh}$, so \nthat $X($C~IV$) M_{\\rm sh} \\approx 0.56 \\Msun$, would fit the data equally \nwell. In our model, for $\\eta = 3$, this gives a minimum mass \n(for $X($C~IV$)=1$)\nof the shell of $M_{\\rm sh} \\sim 0.6 \\Msun$, and a minimum kinetic energy \nof $E_{\\rm sh} \\sim 8\\EE{49}$ ergs. \n\nWhile a constant $X($C~IV$)$ in the shell gives a good fit to the line\nprofile for $\\eta = 3$, cases with a steeper density dependence must have an \nionization structure where $X($C~IV$)$ increases outward through the shell.\nFrom the radial dependence on the ionization parameter this could be possible,\nbut may require a fine-tuning between the $R^{\\eta-2}$ and exp$(-\\tau)$ parts\nof $\\xi$. Time dependent effects are also likely to be important, and the\nlikelihood of an increasing $X($C~IV$)$ with radius can only be explored by\nnumerical models. We postpone this to a future study. To give the same \nabsorption at $2500 \\kms$ as the $\\eta = 3$ model in Figure 10, models \nwith other $\\eta$ must have $X($C~IV$) \\sim 1.49^{\\eta-3}~X($C~IV$)_{\\rm in}$. \nThe parameter $X($C~IV$)_{\\rm in}$ is the value of $X($C~IV$)$ at $R_{\\rm in}$,\nand is the value given in Table 5.\nFor example, for $\\eta = 9$, $X($C~IV$)$ must be $\\sim 11$ times higher at \nthe radius of $2500 \\kms$ compared to $X($C~IV$)_{\\rm in}$.\n\nIt thus appears as if the observed line profile of the C~IV~$\\lambda1550$ \nabsorption is consistent with the outer shell being fast and massive. \nThat is, the C~IV line cannot exclude that the shell could carry an energy\nof $10^{51}$ ergs, because the absorption in the gas with the highest \nvelocities ($\\sim 6000 \\kms $) in the outer shell model would simply disappear \nin the noise of our rather poor signal-to-noise spectrum.\n\nTo limit ourselves to the observed velocities, \nwe adopt a maximum velocity of $3000 \\kms$ to obtain\nlower limits on the mass and energy of the shell.\nTable 5 shows that $M_{\\rm sh}$\ncould be very low (i.e., $M_{\\rm sh} = M_{\\rm trunc}~X($C~IV$)$, \nwith $M_{\\rm trunc}$ defined in Table 5) if $\\eta$ is large and if we only \nuse the absorption at $R_{\\rm in}$ as a criterion. However, if we also \nrequire that the absorption at $2500 \\kms$ should be the same for \nany $\\eta$ as in the $\\eta = 3$ model shown in Figure 10, \nthe minimum mass for models with $\\eta \\geq 3$ is given \nby $M_{\\rm sh} \\gtrsim 1.49^{\\eta-3}~ X($C~IV$)_{\\rm in}~M_{\\rm trunc} \\Msun$,\nwhich for $\\eta = 3$ (4, 5, 7, 9) \nbecomes $M_{\\rm sh} \\gtrsim 0.27~(0.31,~0.37,~0.55,~0.90) \\Msun$.\nThe kinetic energy corresponding to \nthis $M_{\\rm sh}$ (i.e., for $V_{\\rm out} = 3000 \\kms$)\nis $E_{\\rm sh} \\gtrsim 1.5~(1.7,~1.8,~2.4,~3.4) \\EE{49}$~ergs.\nThe limits on $M_{\\rm sh}$ and $E_{\\rm sh}$ for shallower density profiles\nare fixed by the product $X($C~IV$) M_{\\rm trunc}$ (cf. Table 5), and \nare $M_{\\rm sh} \\gtrsim 0.48~(0.36) \\Msun$ \nand $E_{\\rm sh} \\gtrsim 3.1~(2.2) \\EE{49}$~ergs, respectively,\nfor $\\eta = 1~(2)$. All these limits scale inversely with the overall \nabundance of carbon.\n\nTo summarize the constraints from C~IV~$\\lambda$1550, we first emphasize\nthat the line shows that an outer shell with maximum velocity \nof $V_{\\rm out} \\sim 2500 \\kms$ appears to be present. \nWe have a $\\gtrsim5\\sigma$ detection of velocities between $1650 - 2780 \\kms$.\nThe kinetic energy of the shell depends on its\nmass, density structure and extent. \nFor a relatively shallow density \nprofile ($\\rho \\propto R^{-3}$, or shallower) \nthe kinetic energy of the shell could be as high as $10^{51}$ ergs, \nif the shell is spherically symmetric and extends to velocities higher \nthan those we can detect with the obtained signal-to-noise. \nFor a maximum velocity of $\\sim 6000 \\kms$, the mass of the shell required to\nobtain this kinetic energy would be $4-8 \\Msun$.\nA completely flat density profile, however, seems unlikely from the results\nof LFC86, both in the fast case (LFC86, model 1), and for a model\nsimilar to our $V_{\\rm out} \\approx 3000 \\kms$ case (LFC86, model~4).\n\nFor a density profile steeper than $\\rho \\propto R^{-3}$ the kinetic \nenergy is most likely $< 10^{51}$ ergs since the shell mass should be lower \nthan $\\sim 8 \\Msun$ to be compatible with progenitor models. The lowest \nmass and energy we estimate for a shell with $V_{\\rm out} = 3000 \\kms$ \nis for $\\eta \\sim 3$, and are $\\sim 0.3 \\Msun$\nand $\\sim 1.5\\EE{49}$~ergs, respectively. These values are approximate\nas they depend on spherical symmetry, the value of $R_{\\rm in}$, and a model \nfit to the line profile of C~IV~$\\lambda1548$ at $-2500 \\kms$ where the line \nprofile is rather uncertain. To distinguish between models with different \ndensity slopes (see Table 5), photoionization calculations are needed.\n\n\n\\subsubsection{Other constraints on the shell}\n\nThere are, unfortunately, no other lines detected in the UV data that can \nconstrain our current analysis further. \nTwo potentially useful doublets are \nSi~IV~$\\lambda\\lambda$ 1394,1403 and N~V~$\\lambda\\lambda$ 1239,1243,\nbut we cannot identify absorption at high velocities in any of these two \ndoublets. The absence of the two doublets is, however, not surprising. \nSilicon should be more highly ionized than carbon, \nand LFC86 found that C~IV~$\\lambda1550$ \nshould produce significantly stronger absorption than N~V~$\\lambda1240$. The \nspectral region around N~V~$\\lambda1240$ is also rather noisy and the line \nsits in the damping wing of Ly$\\alpha$. Although the absence of the lines \ncannot constrain models in this simple analysis, it can be used\nin conjunction with photoionization calculations to test different models.\n\nThe tentative outer shell has been \npreviously searched for also in the optical. Searches\nin [O~III] have been negative for the region outside the observed [O~III]\nskin (cf. Fesen et al. 1997, and references therein). This is not surprising\nfrom the point of view of the models of LFC86, where oxygen is more\nhighly ionized than O~III.\n\nA highly ionized massive shell is bound to give rise to H$\\alpha$ emission.\nThe deepest search for such emission was done by Fesen et al. (1997) who \nfound a surface brightness limit in H$\\alpha$ \nof $1.5\\EE{-7}$~ergs~cm$^{-2}$~s$^{-1}$~sr$^{-1}$. With the dereddening\nsuggested by Fesen et al. (1997), i.e., $A_{{\\rm H}\\alpha} = 2.536E(B-V)$, \nand $E(B-V) = 0.52$ (cf. above), the dereddened surface brightness limit \nbecomes $5.1\\EE{-7}$~ergs~cm$^{-2}$~s$^{-1}$~sr$^{-1}$. We have calculated the\nsurface brightness in our models to see how it compares with the observed \nlimit. We use a temperature of the tentative shell of $2\\EE4$~K, \nwhich is nearly three times higher than that used by Fesen et al. (1997) and \nMurdin (1994), but in accordance with the models of LFC86. \n\nThe maximum (dereddened) surface brightness in\nH$\\alpha$, $\\Sigma_{{\\rm H}\\alpha}$, occurs at the impact \nparameter, $p = R_{\\rm in}$, i.e., just at the edge of the observed nebula. \nThe value of $\\Sigma_{{\\rm H}\\alpha}$ for this impact parameter is given as\na function of $\\eta$ in Table 5 for the model with $M_{\\rm sh} = 4 \\Msun$.\nIt is seen that the modeled surface brightness exceeds the observed\nlimit for $\\eta \\gtrsim 4$. However, $\\Sigma_{{\\rm H}\\alpha}$ decreases\nrapidly with $p$ for large $\\eta$. Table 5 shows that \nat $p = 1.1 \\times R_{\\rm in}$ (corresponding to $\\sim 17\\arcsec$ \noutside the observed nebula for a distance of 2 kpc, and roughly\nwhere the search by Fesen et al. (1997) was conducted), \nthe surface brightness exceeds the observed limit only \nfor $\\eta \\gtrsim 5$. For a shell mass as low as $0.3-0.9 \\Msun$, which we \nfound to be likely lower limits to the shell mass \nfor the density slopes investigated, the shell \nwould easily have escaped detection in H$\\alpha$.\n% with the current observational limit. \n\nA method to derive parameters for the outer shell was devised by\nSankrit \\& Hester (1997). They estimated the density needed to form a\nradiative shock at the interface between the nebula and the presumed outer\nshell, as such a shock is needed in their model to explain the observed\n[O~III] skin. They estimate that a minimum density \nof $\\rho/{\\rm m}_{\\rm H} \\sim 12$~cm$^{-3}$ is needed, at least in the \npresumed equatorial plane of the nebula. If this is true also in the \ndirection toward the pulsar, the models of Sankrit \\& Hester \nyield $N($C~IV$) \\sim 10^{14}$~cm$^{-2}$\nfor the radiative tail of the shock. \nThis would escape detection in our data since the intrinsic line width in \ntheir model should be small (much less than our spectral resolution). We can \ntherefore not distinguish between a radiative or adiabatic shock (or no\nshock at all) in the direction to the pulsar. This also means that it is \nunlikely that any of the absorption we detect occurs in a region similar to \nthe radiative region in the model of Sankrit \\& Hester.\n\nSankrit \\& Hester (1997) estimate that a mean density at the inner edge\nof the shell, averaged over all polar angles, should be $\\sim 8$~cm$^{-3}$. \nThis would correspond to $n_{\\rm H}(R_{\\rm in}) \\approx 5.7 \\cm3$ for \nthe He/H ratio used in Table 5. \nTo see if we can make a consistent model including the C~IV line,\nthe H$\\alpha$ surface brightness limit by Fesen et al. (1997) and the model \nby Sankrit \\& Hester (1997), we have assumed an upper limit to the shell \nmass of $8 \\Msun$ (inside $V = 3000 \\kms$), \nand used the information in Table 5. We then find \nthat $n_{\\rm H}(R_{\\rm in}) \\gtrsim 5.7~(M_{\\rm trunc}/8 \\Msun) \\cm3$\nis required \nto get a high enough density at $R_{\\rm in}$ to agree with the model of\nSankrit \\& Hester (1997). According to the values in Table 5 this is \nfulfilled for $\\eta \\gtrsim 3$. The mass and kinetic energy for a shell with \nsuch a high $n_{\\rm H}(R_{\\rm in})$ and with $V_{\\rm out} = 3000 \\kms$ would \nbe $6.8~(5.0, 3.8, 2.4, 1.7) \\Msun$ \nand $3.9~(2.7, 1.8, 1.0, 0.7)\\EE{50}$~ergs, respectively,\nfor $\\eta = 3$ (4, 5, 7, 9). A caveat for this model is \nthat $\\Sigma_{{\\rm H}\\alpha}$ at $p = 1.1 \\times R_{\\rm in}$ then\nbecomes $2.0~(1.4, 1.0, 0.60, 0.35)\\EE{-6}$~ergs~cm$^{-2}$~s$^{-1}$~sr$^{-1}$\nfor $\\eta = 3$ (4, 5, 7, 9), which is close to, or higher than, the observed\nlimit. In this scenario, a limit on the H$\\alpha$ surface brightness improved\nby a factor of a few, close to the observed nebula, \nshould be able to distinguish between models with \ndifferent density slopes even if the He/H ratio is higher than we have\nassumed. \n%In particular, if the search for H$\\alpha$ emission is made very \n%close to the observed nebula, and close to what may be the equatorial \n%plane. \nPhotoionization models to accurately calculate the temperature \nand to check the radial dependence on $X($C~IV$)$, are also needed.\n\n\n\\section{Conclusions}\n\nUsing STIS onboard the {\\it HST} we have observed the \nCrab nebula and its pulsar \nin the far-UV ($1140-1720$ \\AA). We have obtained the pulse profile of \nthe pulsar, which is very similar to our previous near-UV profile, although\nthe primary peak appears to be marginally narrower than in\nthe near-UV data ($5\\%,2\\sigma$). \nCombining the far- and near-UV data, and assuming \nan intrinsic power law for the pulsar continuum, we have derived an \nextinction of $E(B-V)=0.52$ mag toward the Crab. No evidence for a non-standard\nextinction curve was found. We have also added optical spectra taken with \nthe {\\it NOT} to obtain a spectrum of the pulsar from 1140 \\AA~to 9250 \\AA. \nWe have shown that the pulsar spectrum can be well fitted over the full \nUV/optical range by a power law with spectral index $\\alpha_{\\nu}=0.11$. \nThe exact value of the spectral index is, however, sensitive to the \namount and characteristics of the interstellar reddening, and \nwe have investigated this dependence for a likely range of $E(B-V)$ and $R$.\nIn the optical,\nwe find no evidence for the dip in the pulsar spectrum around 5900 \\AA\\\nreported by Nasuti et al. (1996).\n\nThe interstellar absorption lines detected in the UV have been\nanalyzed, and are consistent with normal interstellar abundances. The\ncolumn density of neutral hydrogen is $(3.0\\pm0.5)\\EE{21}$~cm$^{-2}$, which\ncorresponds well to the value derived for $E(B-V)$. \nFrom the Crab nebula itself we detect the emission lines \nC~IV~$\\lambda$1550 and He~II~$\\lambda$1640. The ratio of the fluxes of these\nlines is similar to what has been derived previously, although obtained \nwith much improved spatial resolution.\n%our field of view was considerable smaller than in the earlier studies.\n\nC~IV~$\\lambda$1550 is also seen in absorption toward the pulsar. The line is\nbroad and blueshifted with a maximum velocity of $\\sim 2500 \\kms$, and there\nis no absorption at zero velocity. \nThese are the highest velocities measured in the Crab and shows that there\nexists material outside the visible nebula. This can be interpreted as \nevidence for the fast shell that has been predicted to surround the Crab\nnebula (Chevalier 1977).\n%For an optically thin line, the total column density of C~IV \n%is $(3.0\\pm1.1)\\EE{14}$ cm$^{-2}$. \nWe have used a simple, spherically \nsymmetric model in which the density in the shell falls off with radius\nas $R^{-\\eta}$ from $5\\EE{18}$~cm (corresponding \nto $\\approx 1680 \\kms$) to derive the mass and energy of such a shell.\nThe conclusions from our model depend on how we tie our model into other \nobservations and models. From the C~IV line alone, we find \n%for a solar abundance of carbon \nthat the minimum mass and kinetic energy \nof the fast gas are $\\sim 0.3 \\Msun$ and $\\sim 1.5\\EE{49}$~ergs,\nrespectively. This occurs for a density slope $\\eta \\sim 3$. A model with \na flat ($\\eta = 0$) density profile appears unlikely as the required \nionization structure disagrees with the modeling of Lundqvist et al. (1986). \nThe maximum mass of the shell is set by progenitor models, and is unlikely \nto be much larger than $8 \\Msun$. With a high shell mass, and the velocity\nextending to velocities much higher than we can detect, \nthe shell could carry an\nenergy of $10^{51}$~ergs. The signal-to-noise of C~IV~$\\lambda$1550 is too \nlow at high velocities to reject or confirm such a conclusion.\n\nAdding constraints from the model of Sankrit \\& Hester (1997) to those\nfrom the C~IV line narrows down the parameter space for the shell. \nIn particular, a density slope of $\\eta \\gtrsim 3$ is required to agree with\nthe interpretation of the observed [O III]-skin being a radiative shock.\n%(for which the shell mass is close \n%to the upper limit of $8 \\Msun$). \nFor $\\eta \\leq 9$, the shell mass is then $\\gtrsim 1.7 \\Msun$ and the kinetic \nenergy $\\gtrsim 7\\EE{49}$~ergs. Although the limit on the H$\\alpha$ surface \nbrightness from the search of Fesen et al. (1997) tend to favor models with \nsteep density profiles, a model with $\\eta = 3$ might still be possible, \nif the He/H ratio is higher than solar also in the fast shell, and the \nasymmetry of the outer shell different from that in the model of Sankrit \\&\nHester (1997). \n%Given also that we are only probing the C~IV line profile along\n%one line of sight, we cannot completely reject that the Crab was\n%a $10^{51}$~erg event, although the combined model favors a lower energy.\n%To distinguish between various models, \n%photoionization calculations and deeper H$\\alpha$ searches are needed.\n\n\\acknowledgments\n\nWe thank Rob Fesen for help during preparations of the {\\it HST}\nobservations, and \nfor discussions and comments on the manuscript. We also thank Phil Plait \nfor help with barycentric corrections, and Stefan Larsson for advice \non period determination.\nWe thank the Swedish National Space Board, and GSFC/NASA for support which \nenabled JS and PL to visit GSFC. We are also grateful to The Swedish\nNatural Science Research Council for support. JS was also supported by grants \nfrom the Holmberg, Hierta and Magn. Bergvall foundations. The research of \nRAC is supported through grant NAG5-8130.\n\n\n\\clearpage\n\n\\begin{thebibliography}{}\n\n\\bibitem[Anders \\& Grevesse\\ 1989]{AG89} Anders, E., \\& Grevesse, N. 1989,\nGeochim. Cosmochim. Acta, 53, 197\n\n\\bibitem [Benvenuti et al.\\ 1980]{Ben80} Benvenuti, P., Bianchi, L.,\nCassatella, A., Macchetto, F., Selvelli, P.~L., Zamorano, J., Clavel, J.,\nDarius, J., Heck, A., \\& Henston, M. 1980, in Proc. Second European {\\it IUE}\nConference (ESA SP-157), 339\n\n\\bibitem[Blair et al.\\ 1992]{Bl92} Blair, W.~P., Long, K.~S., Vancura, O.,\nBowers, C.~W., Conger, S., Davidsen, A.~F., Kriss, G.~A., \\& Henry, R.~B.~C.\n1992, \\apj, 399, 611\n\n%\\bibitem[Bohlin et al.\\ 1998]{Boh98} Bohlin, R., Collins, N., \\& Gonella, A.\n%1998, Instrument Science report STIS 97-14 (Baltimore:STScI)\n\n\\bibitem[Chevalier\\ 1977]{C77} Chevalier, R.~A. 1977, in Supernovae, ed. D.~N.\nSchramm, 53\n\n%\\bibitem[Clark \\& Stephenson\\ 1977]{CS77} Clark, D.~H., \\& Stephenson,\n%F.~R. 1977, The Historical Supernovae, Pergamon Press\n\n\\bibitem[Clark et al.\\ 1983]{C83} Clark, D.~H., Murdin, P., Wood, \nR., Gilmozzi, R., Danziger, J., \\& Furr, A.~W. 1983, \\mnras, 204, 415\n\n\\bibitem[Cocke et al.\\ 1969]{Co69} Cocke, W.~J., Disney M.~J., \\& Taylor,\nD.~J. 1969, \\nat, 221, 525\n\n\\bibitem [Comella et al.\\ 1969]{C69}\nComella, J.~M., Craft, H.~D. Jr., Lovelace, R.~V.~E., Sutton, J.~M., \\&\nTyler, G.~I. 1969, \\nat, 221, 453\n\n\\bibitem[Davidson \\& Fesen\\ 1985]{DF85} Davidson, K., \\& Fesen, R.~A. 1985,\n\\araa, 23, 199\n\n\\bibitem[Davidson et al.\\ 1982]{D82} Davidson, K., Gull, T.~R., Maran, \nS.~P., Stecher, T.~P., Fesen, R.~A., Parise, R.~A., Harvel, C.~A., Kafatos, M.,\n\\& Trimble, V.~L. 1982, \\apj, 253, 696 \n\n\\bibitem[de Boer et al.\\ 1987]{dB87} de Boer, K.~S., Jura, M.~A., \\& Shull,\nJ.~M. 1987, in Exploring the Universe with the {\\it IUE} satellite, ed. Y.\nKondo, W. Wamsteker, A. Boggess, M. Grewing, C. de Jager, A.~L. Lane, \nJ.~L. Linsky, \\& R. Wilson (Dordrecht: Reidel), 485\n\n\\bibitem[Eikenberry et al.\\ 1997]{EIK97} Eikenberry, S. S., Fazio, G. G.,\nRansom, S. M., Middleditch, J., Kristian, J., \\& Pennypacker, C. R. 1997, \\apj,\n477, 465\n\n\\bibitem[Fesen et al.\\ 1997]{Fe97} Fesen, R.~A., Shull, M.~J., \\& Hurford,\nA.~P. 1997, \\aj, 113, 354\n\n\\bibitem[Fitzpatrick\\ 1999]{Fi99} Fitzpatrick, E.~L. 1999, \\pasp, 111, 63\n\n\\bibitem[Frail et al.\\ 1995]{Fr95} Frail, D.~A., Kassim, N.~E.,\nCornwell, T.~J., \\& Goss, W.~M. 1995, \\apj, 454, L129\n\n\n\\bibitem[Ginzburg \\& Zheleznyakov\\ 1975]{GZ75} Ginzburg, V.~L., \\& Zheleznyakov\nV.~V. 1975, \\araa, 13, 511\n\n\\bibitem[Gold\\ 1968]{G68} Gold, T. 1968, \\nat, 218, 731\n\n\\bibitem [Gull et al.\\ 1998]{G98} Gull, T.~R., Lindler, D., Crenshaw, M.,\nDolan, J.~F., Hulbert, S.~J., Kraemer, S.~B., Lundqvist, P., Sahu, K.~C.,\nSollerman, J., Sonneborn, G., \\& Woodgate, B.~E. 1998, \\apj, 495, L51 (G98)\n\n\\bibitem [Hester et al.\\ 1996]{H96} Hester, J.~J., et al.\n1996, \\apj, 456, 225 \n%21 authors\n\n\\bibitem[Hill et al.\\ 1997]{H97} Hill, R.~J., Dolan, J.~F., Bless,\nR.~C., Boyd, P.~T., Percival, J.~W., Taylor, M.~J., \\& Van Citters, G.~W.\n1997, \\apj, 486, L99\n\n%\\bibitem[Jun 1998]{Jun98} Jun, B.-I. 1998, \\apj, 499, 282\n\n\\bibitem[Kaplan et al.\\ 1989]{Ka89} Kaplan, G.~H., Hughes, J.~A., Seidelmann, \nP.~K., Smith, C.~A., \\& Yallop, B.~D. 1989, \\aj, 97, 1197\n\n\\bibitem[Keenan et al.\\ 1993]{keen93} Keenan, F.~P., Hibbert, A., Ojha,\nP.~C., \\& Conlon, E. S. 1993, Phys. Scripta, 48, 129\n\n\\bibitem[Kimble et al.\\ 1998]{K98} Kimble, R.~A., et al. 1998, \\apj, 492, L83\n%\\bibitem[Kimble et al.\\ 1998]{K98} Kimble, R.~A., Woodgate, B.~E.,\n%Bowers, C.~W., Kraemer, S.~B., Kaiser, M.~E., Gull, T.~R., Heap, S.~R., \n%Danks, A.~C., Boggess, A., Green, R.~F., et al. 1998, \\apj, 492, L83\n%79 more authors!\n\n%\\bibitem[Lindler at al.\\ 1997]{L97} Lindler, D. J., Gull, T. R., Kraemer, \n%S.~B., et al. 1998, in {\\it Hubble Space Telescope} \n%calibration workshop Proc. \n%(Baltimore: STSci), 138\n\n\\bibitem [Lundqvist, Fransson \\& Chevalier\\ 1986]{P86} Lundqvist, P., Fransson,\nC., \\& Chevalier, R.~A. 1986, \\aap, 162, L6 (LFC86)\n\n\\bibitem[Lyne et al.\\ 1999]{LPR99}\nLyne, A.~G., Pritchard, R.~S., \\& Roberts, M.~E. 1999,\nJodrell Bank Crab Pulsar Timing Results Monthly Ephemeris\n(Manchester: Univ. Manchester; http://www.jb.man.ac.uk/$\\sim$pulsar/crab.html)\n\n\\bibitem[Lyne \\& Graham-Smith\\ 1998]{LGS98}\nLyne, A.~G., \\& Graham-Smith, F. 1998,\nPulsar Astronomy (Cambridge Astrophysics series)\n\n\\bibitem[Martin et al.\\ 1998]{MHS98} Martin, C., Halpern, J.~P., \\& \nSchiminovich, D. 1998, \\apj, 494, L211 \n\n\\bibitem[Mauche \\& Gorenstein\\ 1989]{MG89} Mauche, C.~W., \\& Gorenstein,\nP. 1989, \\apj, 336, 843 \n\n%\\bibitem[Meyer et al.\\ 1998]{MJC98} Meyer, D. M., Jura, M., \\& Cardelli, J. A.\n%1998, \\apj, 493, 222\n\n\\bibitem[Middleditch \\& Pennypacker\\ 1985]{MP85}Middleditch, J., \\& \nPennypacker, C. 1985, \\nat, 313, 659\n\n\\bibitem[Miller\\ 1973]{M73} Miller, J.~S. 1973, \\apj, 180, L83\n\n\\bibitem[Minkowski\\ 1942]{M42} Minkowski, R. 1942, \\apj, 96, 199\n\n\\bibitem[Morton\\ 1991]{Mort91} Morton, D.~C. 1991, \\apjs, 77, 119\n\n\\bibitem[Murdin\\ 1994]{Murd94} Murdin, P. 1994, \\mnras, 269, 89\n\n\\bibitem[Nasuti et al.\\ 1996]{Na96} Nasuti, F.~P., Mignani, R., Caraveo.\nP.~A., \\& Bignami, G.~F. 1996, \\aap, 314, 849\n\n\\bibitem[Nomoto\\ 1985]{No85} Nomoto, K. 1985, in The Crab Nebula and Related\nSupernova Remnants, ed. M. C. Kafatos \\& R. B. C. Henry (Cambridge: CUP), 97\n\n\\bibitem[Oke\\ 1969]{069} Oke, J.~B. 1969, \\apj, 156, L49\n\n\\bibitem[Percival et al.\\ 1993]{P93} Percival, J.~W., Biggs, J.~D.,\nDolan, J.~F., Robinson, E.~L., Taylor, M.~J., Bless, R.~C., Elliot, J.~L.,\nNelson, M.~J., Ramseyer, T.~F., Van Citters, G.~W., \\& Zhang, E.\n1993, \\apj, 407, 276\n\n%\\bibitem[Perryman et al.\\ 1999]{Perr95} Perryman, M.~A.~C., Favata, F.,\n%Peacock, A., Rando, N., \\& Taylor, B.~G. 1999, \\aap, 346, L30\n\n%\\bibitem[Pskovskii 1999]{Psk78} Pskovskii, Y.~P. 1978, Sov. Astron. AJ, 22, 420\n\n\\bibitem[Ramsbottom et al.\\ 1996]{ram96} Ramsbottom, C.~A., Bell, K.~L.,\n \\& Stafford, R.~P. 1996, Atomic Data Nucl. Data Tables, 63, 58\n\n\\bibitem[Reynolds \\& Chevalier\\ 1984]{RC84} Reynolds, S.~P., \\& Chevalier, \nR.~A. 1984, \\apj, 281, 33\n\n\\bibitem[Sankrit \\& Hester\\ 1997]{Sa97} Sankrit, R., \\& Hester, J.~J.\n1997, \\apj, 491, 796\n\n\\bibitem[Sankrit et al.\\ 1998]{Sa98} Sankrit, R., et al.\n%\\bibitem[Sankrit et al.\\ 1998]{Sa98} Sankrit, R., Hester, J.~F., Scowen, P.~A.,\n%Ballester, G.~E., Burrows, C.~J., Clarke, J.~T, Crisp, D., Evans, R.~W.,\n%Gallagher, J.~S., Griffiths, R.~E, et al.\n%18 authors\n1998, \\apj, 504, 344\n\n%\\bibitem[Savage \\& Mathis\\ 1979]{SM79} Savage, B.~D., \\& Mathis, J.~S. 1979, \n%\\araa, 17 73\n\n\\bibitem[Schattenburg \\& Canizares\\ 1986]{SC86} Schattenburg, M.~L., \\& \nCanizares, C.~R. 1986, \\apj, 301, 759\n\n\\bibitem[Shearer et al.\\ 1998]{Sh98} Shearer, A., et al. 1998, \\aap, 335, L21\n%\\bibitem[Shearer et al.\\ 1998]{Sh98} Shearer, A., Golden, A., Harfst, S.,\n%Butler, R., Redfern, R.~M., O'Sullivan, C.~M.~M., Beskin, G.~M.,\n%Neizvestny, S.~I., Neustroev, V.~V., Plokhotnichenko, V.~L., Cullum, M.,\n%\\& Danks, A. 1998, \\aap, 335, L21\n\n\\bibitem[Shearer et al.\\ 1997]{Sh97} Shearer, A., Redfern, R.~M., Gorman, G.,\nButler, R., Golden, A., O'Kane, P., Beskin, G.~M., \nNeizvestny, S.~I., Neustroev, V.~V., Plokhotnichenko, V.~L., \\& Cullum, M.\n1997, \\apj, 487, L181\n% 11 authors, we cut at this -> 12 authors=et al\n\n%\\bibitem[Shklovsky\\ 1960]{S60} Shklovsky, I.~S. 1960, Cosmic radio waves \n%(Cambridge:Harvard Univ. Press)\n\n\\bibitem[Shull \\& Van Steenberg\\ 1985]{SV85} Shull, J.~M., \\& Van Steenberg,\nM.~E. 1985, \\apj, 294, 599\n\n\\bibitem [Staelin \\& Reifenstein\\ 1968]{SR68}\nStaelin, D.~H., \\& Reifenstein, E.~C., III. 1968, Science, 162, 1481\n\n%\\bibitem [Trimble\\ 1973]{Tr73} Trimble, V. 1973, \\pasp, 85, 579\n\n%\\bibitem [Van Tassell et al.\\ 1999]{VT99} Van Tassell, H.~A., Hester, J.~J.,\n%Szentgyorgyi, A., \\& Sankrit, R. 1999, \\baas, 31, 973\n\n%\\bibitem[Wallace et al.\\ 1999]{Wa99}Wallace, B.~J., Landecker, T.~L.,\n%Kalberla, P.~M.~W., \\& Taylor, A.~R. 1999, \\apjs, in press, (astro-ph/9903416)\n\n\\bibitem[Wallace et al.\\ 1977]{Wa77}Wallace, P.~T., et al. 1977, \\nat, 266, 692\n%\\bibitem[Wallace et al.\\ 1977]{Wa77}Wallace, P.~T., Peterson, B.~A., Murdin, \n%P.~G., Danziger, I.~J., Manchester, R.~N., Lyne, A.~G., Goss, W.~M., Smith,\n%F.~G., Disney, M.~J., Hartley, K.~F., Jones, D.~H.~P., \\& Wellgate, G.~W.\n%1977, \\nat, 266, 692\n% Steiner, J.~E., A\\&A 61, L35 recived september 29,77 claims to be first\n% but wallace published first Apr. 21, 1977\n\n\\bibitem[Welty et al.\\ 1999]{Wel99}Welty, D.~E., Frisch, P.~C., Sonneborn,\nG., \\& York, D.~G. 1999, \\apj, 512, 636\n\n\\bibitem[Wheeler\\ 1978]{Whe78} Wheeler, J.~C. 1978, \\apj, 225, 212\n\n\\bibitem[Wu\\ 1981]{Wu81} Wu, C.~C. 1981, \\apj, 245, 581\n\n\\end{thebibliography}\n\n\n\\newpage\n\n%\n\\begin{deluxetable}{lcc}\n\\footnotesize\n\\tablewidth{0pc}\n\\tablecaption{LOG OF STIS FUV OBSERVATIONS}\n\\tablehead{\n\\colhead{Observation} & \\colhead{Start time (MJD)} \n& \\colhead{Exposure time} \\nl\n\\multicolumn{1}{c}{{\\scriptsize }}\n&\\multicolumn{1}{c}{{\\scriptsize (51200.0+)}}\n&\\multicolumn{1}{c}{{\\scriptsize (seconds)}}\n}\n\n\\startdata\n\nO4ZP01010 & .54924 & 2100 \\\\\n \nO4ZP01020 & .60619 & 2460 \\\\\n \nO4ZP01030 & .67384 & 2460 \\\\\n \nO4ZP01040 & .74103 & 2460 \\\\\n \nO4ZP02010 & .81802 & 2100 \\\\\n\nO4ZP02020 & .87488 & 2460 \\\\\n\n\\enddata\n\\end{deluxetable}\n\n%------table 2\n\n\\begin{deluxetable}{cccc}\n\\footnotesize\n\\tablewidth{0pc}\n\\tablecaption{LOG OF {\\it NOT} OBSERVATIONS}\n\\tablehead{\n\\colhead{Grism} & \\colhead{Date} & \\colhead{Wavelength range} &\n\\colhead{Resolution} \n%& \\colhead{Exposure time} & \\colhead{Date} & \\colhead{Standard\n%star} & \\colhead{Position angle} \n\\nl\n\\multicolumn{1}{c}{{\\scriptsize }}\n&\\multicolumn{1}{c}{{\\scriptsize (Dec 1998)}}\n&\\multicolumn{1}{c}{{\\scriptsize (\\AA)}}\n&\\multicolumn{1}{c}{{\\scriptsize (\\AA)}}\n%&\\multicolumn{1}{c}{{\\scriptsize (minutes)}}\n%&\\multicolumn{1}{c}{{\\scriptsize }}\n%&\\multicolumn{1}{c}{{\\scriptsize (degrees)}}\n}\n\\startdata\n%CRAB-PULSAR & 05 34 32 +22 00 53 & STIS/TIME-TA & 1425 & 2100 \\\\\n3 & 24+25 & 3300-6400 & 6.6 \\\\\n5 & 24+25 & 5200-9250 & 9.0 \\\\\n6 & 27 & 3200-5500 & 4.7 \\\\\n7 & 25 & 3820-6100 & 5.0 \\\\\n8 & 25 & 5830-8340 & 3.6 \\\\\n\n%\\tablecomments{no comments} \n%\\tablenotetext{1}{Days since July 14.0, 1994.} \n\\enddata\n\\end{deluxetable}\n\n\n%----------Table 3----------\n\n\\begin{deluxetable}{lccccc}\n\\footnotesize\n\\tablewidth{40pc}\n\\tablecaption{ABSORPTION LINES}\n\\tablehead{\n\\colhead{Species} & \\colhead{$\\lambda$\\tablenotemark{a}} & \\colhead{$f_{\\rm osc}\\tablenotemark{a}$}\n& \\colhead{Equivalent width} & \\colhead{Log (Column density)} & Log (Abundance)\\nl\n%\\cline{2-3} \\\\\n\\multicolumn{1}{c}{{\\scriptsize }}\n&\\multicolumn{1}{c}{{\\scriptsize (\\AA)}}\n&\\multicolumn{1}{c}{{\\scriptsize }}\n&\\multicolumn{1}{c}{{\\scriptsize (\\AA)}}\n&\\multicolumn{1}{c}{{\\scriptsize (cm$^{-2}$)}}\n%&\\multicolumn{1}{c}{{\\scriptsize (relative to H~I)}}\n}\n\\startdata\nH~I & 1215.67 & 0.416 & $37\\pm5$ & $21.48\\pm0.08$ & 12.0\\\\\nC~I & 1277.46 & 0.0966 & $0.18\\pm0.12$ & $17.49\\pm0.71$ & $7.96\\pm0.76$\\\\\nC~I & 1329.34 & 0.0580 & $0.11\\pm0.11$ & $\\lesssim 18.11$ & $\\lesssim 8.71$\\\\\nC~I & 1561.05 & 0.0804 & $0.35\\pm0.17$ & $18.20\\pm0.46$ & $8.70\\pm0.48$\\\\\nC~I & 1657.59 & 0.140 & $0.54\\pm0.17$ & $17.89\\pm0.29$ & $8.40\\pm0.30$\\\\\nC~II & 1335.31 & 0.128 & $0.46\\pm0.24$ & $18.15\\pm0.50$ & $8.65\\pm0.53$\\\\\nC~IV & 1549.05 & 0.286 & $1.84\\pm0.65$ & $14.45\\pm0.16$\\tablenotemark{b} & N/A\\tablenotemark{b}\\\\\nO~I\\tablenotemark{c} & 1303.49 & 0.0488 & $0.54\\pm0.21$ & $18.51\\pm0.36$ & $9.02\\pm0.38$ \\\\\nMg~I & 2852.96 & 1.830 & $0.93\\pm0.33$ & $16.11\\pm0.34$ & $6.62\\pm0.35$\\\\\nMg~II & 2796.35 & 0.612 & $0.79\\pm0.25$ & $16.79\\pm0.28$ & $7.30\\pm0.30$\\\\\nMg~II & 2803.53 & 0.305 & $0.55\\pm0.27$ & $16.70\\pm0.47$ & $7.20\\pm0.49$\\\\\nAl~II & 1670.79 & 1.833 & $0.56\\pm0.34$ & $16.04\\pm0.57$ & $6.54\\pm0.60$\\\\\nSi~II & 1260.42 & 1.007 & $0.60\\pm0.18$ & $16.82\\pm0.28$ & $7.33\\pm0.29$\\\\\nSi~II & 1526.71 & 0.230 & $0.32\\pm0.14$ & $16.57\\pm0.39$ & $7.08\\pm0.41$\\\\\nSi~IV & 1393.75 & 0.514 & $0.33\\pm0.20$ & $16.63\\pm0.63$ & $7.12\\pm0.66$\\\\\nFe~II & 2586.65 & 0.0646 & $0.27\\pm0.20$ & $17.15\\pm0.86$ & $7.58\\pm0.96$\\\\\nFe~II & 2600.17 & 0.224 & $0.40\\pm0.21$ & $16.71\\pm0.53$ & $7.21\\pm0.56$\\\\\n\n%\\tablecomments{no comments}\n\\tablenotetext{a}{Morton (1991)}\n\\tablenotetext{b}{Not interstellar. The column density is calculated from ``weak-line'' theory (Morton 1991).}\n\\tablenotetext{c}{Could be affected by subtraction of geocoronal emission, and is probably also blended \nwith Si~II~$\\lambda$1304.37}\n\n\\enddata\n\n\\end{deluxetable}\n\n\n%----------Table 4----------\n\n\\begin{deluxetable}{lcc}\n\\footnotesize\n\\tablewidth{0pc}\n\\tablecaption{ABUNDANCES}\n\\tablehead{\n\\colhead{Element} & \\colhead{Solar value\\tablenotemark{a}} & \\colhead{This \npaper\\tablenotemark{b}} \\nl\n%\\cline{2-3} \\\\\n%\\multicolumn{1}{c}{{\\scriptsize }}\n%&\\multicolumn{1}{c}{{\\scriptsize (\\AA)}}\n%&\\multicolumn{1}{c}{{\\scriptsize }}\n%&\\multicolumn{1}{c}{{\\scriptsize (relative to H~I)}}\n}\n\\startdata\n%C & 8.55 & $8.89\\pm0.42$ \\\\\n%O & 8.87 & $9.02\\pm0.38$ \\\\\n%Mg & 7.58 & $7.38\\pm0.31$ \\\\\n%Al & 6.47 & $6.54\\pm0.60$ \\\\\n%Si & 7.55 & $7.55\\pm0.41$ \\\\\n%Fe & 7.51 & $7.21\\pm0.56$ \\\\\nC & 8.55 & $8.9\\pm0.4$ \\\\\nO & 8.87 & $9.0\\pm0.4$ \\\\\nMg & 7.58 & $7.4\\pm0.3$ \\\\\nAl & 6.47 & $6.5\\pm0.6$ \\\\\nSi & 7.55 & $7.6\\pm0.4$ \\\\\nFe & 7.51 & $7.2\\pm0.6$ \\\\\n\n%\\tablecomments{no comments}\n\\tablenotetext{a}{Anders \\& Grevesse (1989)}\n\\tablenotetext{b}{Our method is likely to systematically overestimate the\nabundances.\nSee \\S 3.5.}\n\n\\enddata\n\\end{deluxetable}\n\n%----------Table 5----------\n\n\\begin{deluxetable}{ccccccc}\n\\footnotesize\n\\tablewidth{40pc}\n\\tablecaption{PROPERTIES OF A $4 \\Msun$ FAST SHELL.\\tablenotemark{a}}\n\\tablehead{\n\\colhead{$\\eta$\\tablenotemark{b}} \n&\\colhead{$n_{\\rm H}(R_{\\rm in})$\\tablenotemark{b}} \n&\\colhead{$E_{\\rm sh}$}\n&\\colhead{$\\Sigma_{{\\rm H}\\alpha}$\\tablenotemark{c}}\n&\\colhead{$\\Sigma_{{\\rm H}\\alpha}$\\tablenotemark{d}}\n&\\colhead{$X($C~IV$)$\\tablenotemark{e}} \n&\\colhead{$M_{\\rm trunc}$\\tablenotemark{f}} \\nl\n%\\cline{2-3} \\\\\n\\multicolumn{1}{c}{{\\scriptsize }}\n&\\multicolumn{1}{c}{{\\scriptsize ($0.714 \\times \\rho/{\\rm m}_{\\rm H}$, cm$^{-3}$)}}\n&\\multicolumn{1}{c}{{\\scriptsize ($10^{51}$ ergs)}}\n&\\multicolumn{1}{c}{{\\scriptsize (ergs~cm$^{-2}$~s$^{-1}$~sr$^{-1}$)}}\n&\\multicolumn{1}{c}{{\\scriptsize (ergs~cm$^{-2}$~s$^{-1}$~sr$^{-1}$)}}\n&\\multicolumn{1}{c}{{\\scriptsize }}\n&\\multicolumn{1}{c}{{\\scriptsize ($\\Msun$)}}\n}\n\\startdata\n0 & 0.12 & 0.99 (0.03)\\tablenotemark{g} & $9.3(4.1)\\tablenotemark{g}~\\EE{-9}$ & $9.2(3.9)\\tablenotemark{g}~\\EE{-9}$ & 1\\tablenotemark{h} & 0.43 \\\\\n1 & 0.32 & 0.86 (0.05) & $2.4(1.8)\\EE{-8}$ & $2.1(1.6)\\EE{-8}$ & 0.62 & 0.78 \\\\\n2 & 0.77 & 0.72 (0.08) & $8.1(7.6)\\EE{-8}$ & $6.1(5.6)\\EE{-8}$ & 0.28 & 1.29 \\\\\n3 & 1.62 & 0.56 (0.11) & $2.7(2.7)\\EE{-7}$ & $1.7(1.6)\\EE{-7}$ & 0.14 & 1.92 \\\\\n4 & 2.94 & 0.42 (0.14) & $7.4(7.4)\\EE{-7}$ & $3.8(3.8)\\EE{-7}$ & 0.081 & 2.57 \\\\\n5 & 4.66 & 0.32 (0.15) & $1.6(1.6)\\EE{-6}$ & $6.9(6.9)\\EE{-7}$ & 0.053 & 3.11 \\\\\n7 & 8.71 & 0.21 (0.16) & $4.7(4.7)\\EE{-6}$ & $1.4(1.4)\\EE{-6}$ & 0.030 & 3.71 \\\\\n9 & 13.0 & 0.17 (0.15) & $9.1(9.1)\\EE{-6}$ & $1.8(1.8)\\EE{-6}$ & 0.021 & 3.92 \\\\\n\n%\\tablecomments{no comments}\n\\tablenotetext{a}{Minimum and maximum radii are $5\\EE{18}$~cm and $1.9\\EE{19}$~cm, respectively, corresponding to the velocities $\\approx 1680 \\kms$ and $\\approx 6370 \\kms$.}\n\\tablenotetext{b}{$n_{\\rm H}(R) = n_{\\rm H}(R_{\\rm in})~(R/R_{\\rm in})^{- \\eta}$}\n\\tablenotetext{c}{H$\\alpha$ surface brightness at impact parameter $p = R_{\\rm in}$, i.e., just at the edge of the observed nebula. ($T = 2\\EE4$ K).}\n\\tablenotetext{d}{H$\\alpha$ surface brightness at impact parameter $p = 1.1 R_{\\rm in}$, i.e., $\\sim 17\\arcsec$ outside the observed nebula. ($T = 2\\EE4$ K).}\n\\tablenotetext{e}{Fraction of carbon in C IV to obtain the observed optical depth in C~IV~$\\lambda1550$ at $\\sim 1680 \\kms$. ($X($C$)/X($H$) = 3.5\\EE{-4}$).}\n\\tablenotetext{f}{How much of the $4\\Msun$ shell that resides inside $3000 \\kms$. Density and $X($C~IV$)$ at $R_{\\rm in}$ are assumed to be the same as for the $4 \\Msun$ shell with maximum velocity $6370 \\kms$.}\n%\\tablenotetext{f}{Mass of the shell if gas with velocity $> 3000 \\kms$ is absent. Density and $X($C~IV$)$ at $R_{\\rm in}$ are the same as for the $4 \\Msun$ shell with maximum velocity $6370 \\kms$.}\n\\tablenotetext{g}{Values in parentheses are for the case with the shell only reaching $3000 \\kms$, i.e., for the masses in the last column in the table.}\n\\tablenotetext{h}{For $\\eta = 0$ the maximum optical depth in C~IV~$\\lambda1550$ is too small even with $X($C~IV$) = 1$. (See Fig. 10).}\n\n\\enddata\n\\end{deluxetable}\n\n\n\\newpage\n\\clearpage\n\n\\begin{figure*} \\centering \\vspace{10.0 cm}\n\\special{psfile=Fig1.ps \nhoffset=50 voffset=400 hscale=60 vscale=60 angle=270}\n\\caption{\nAn $R$-band image of the Crab nebula obtained at \nthe {\\it NOT} in December, 1998. \nShown are the extents and position angles of the slits \nused in the optical and in the FUV. The STIS-FUV slit is 25\\arcsec~long.\nThe NUV observation (G98) used \na 2\\arcsec$\\times$2\\arcsec aperture centered on the pulsar.\n}\n\\label{ima}\n\\end{figure*} \n\n\n\\clearpage\n\n\\begin{figure*} \\centering \\vspace{8.0 cm}\n\\special{psfile=Fig2.ps hoffset=0 voffset=-230 hscale=65 vscale=65 angle=0}\n\\caption{\nPulse profile of the Crab pulsar in the FUV (full line). \nAlso shown is the NUV pulse profile from G98 (dashed line). \nThe FUV and NUV data were processed in the same way. \nThe blow-up of the primary peak shows the FUV to be slightly narrower.\nThe statistical errors range from 0.003 in the valleys to 0.014 at the peak \nfor both the FUV and NUV profiles, as illustrated by the \n($\\pm1\\sigma$) error bars in the insert. \nNote that the count rate of the pulsar signal is close to zero in the \ninterpulse region.\n}\n\\label{pulse}\n\\end{figure*} \n\n\n\n\\begin{figure*} \\centering \\vspace{8.0 cm}\n\\special{psfile=Fig3.ps hoffset=0 voffset=-230 hscale=65 vscale=65 angle=0}\n\\caption{ \nSpectrum of the Crab pulsar in the UV. This is a combination of our\nFUV ($1140-1730$~\\AA) observations obtained in January 1999, and the NUV \n($1600-3200$~\\AA) data from G98. The spectra overlap nicely. \nThe ${\\rm Ly}\\alpha$ absorption dip shows some residuals from the\nsubtraction of strong geocoronal emission.\n}\n\\label{uv}\n\\end{figure*} \n\n\n\\clearpage\n\n\n\\begin{figure*} \\centering \\vspace{10.0 cm}\n\\special{psfile=Fig4.ps hoffset=0 voffset=-220 hscale=65 vscale=65 angle=0}\n\\caption{ \nSpectrum of the Crab pulsar in the UV and in the optical. The optical\ndata are from\n{\\it NOT}. The lower spectrum shows the flux-calibrated spectrum without \ndereddening. The optical spectrum connects rather well to the NUV data. \n%although the bluest part is rather uncertain. \nThe uppermost spectrum has \nbeen dereddened with $E(B-V)=0.52$ and $R=3.1$. \nThe full line shows the best power law fit, which has\nthe spectral index $\\alpha_{\\nu}=0.11$.\nThe insert shows a blowup of the optical\nregion where Nasuti et al. (1996) reported a broad absorption dip in the \nspectrum.\n}\n\\label{pulse}\n\\end{figure*} \n\n\n\\begin{figure*} \\centering \\vspace{8.0 cm}\n\\special{psfile=Fig5.ps hoffset=0 voffset=-230 hscale=65 vscale=65 angle=0}\n\\caption{\nThe UV extinction curve in the direction toward the Crab. This curve\nwas obtained by assuming the pulsar intrinsic spectrum to follow a power law.\nFor comparison, the mean galactic extinction curve from Fitzpatrick (1999) is\nalso shown.\n}\n\\label{redcurve}\n\\end{figure*} \n\n\\clearpage\n\n\\begin{figure*} \\centering \\vspace{10.0 cm}\n\\special{psfile=Fig6.ps hoffset=0 voffset=-215 hscale=65 vscale=65 angle=0}\n\\caption{\nThe Crab pulsar spectrum dereddened with different values of $E(B-V)$ and $R$.\nThe upper panel shows the dereddened spectrum for $E(B-V)=0.52$ and three\ndifferent values of $R$: 2.9 (upper), 3.1 and 3.3 (lower). The IR data points\nare from Eikenberry et al. (1997) and are not included in the power law fits.\nThe fitted power laws have $\\alpha_{\\nu}=$\n0.19, 0.11 and 0.041, respectively.\nThe lower panel shows dereddening for $R=3.1$ and $E(B-V)=$0.49 (upper), 0.52\nand 0.55 (lower). The fitted power laws have spectral \nindices $\\alpha_{\\nu}= -0.005, 0.11$ and $0.23$, respectively. \nThe individual spectra in both panels have been shifted by $-0.3$, 0.0, \nand +0.3 dex in the vertical direction for clarity.\n}\n\\label{reddall}\n\\end{figure*} \n\n\n\\begin{figure*} \\centering \\vspace{8.0 cm}\n\\special{psfile=Fig7.ps hoffset=0 voffset=-230 hscale=65 vscale=65 angle=0}\n\\caption{\nFUV spectrum around Ly$\\alpha$. The dashed line shows the original\ndata, and the solid line shows the spectrum after compensation for\nabsorption in the damping wings of Ly$\\alpha$. The column density of neutral\nhydrogen toward the Crab determined in this way \nis $N$(H~I) = $(3.0\\pm0.5)\\EE{21}$ cm$^{-2}$. The straight dashed line shows \na continuum fit to the spectrum after correction for Ly$\\alpha$ absorption.\n}\n\\label{lyalpha}\n\\end{figure*} \n\n\\clearpage\n\n\\begin{figure*} \\centering \\vspace{15.0 cm}\n\\special{psfile=Fig8.ps hoffset=450 voffset=0 hscale=65 vscale=65 angle=90}\n\\caption{\nAbsorption lines seen in the spectrum toward the Crab pulsar. Only\nC~IV~$\\lambda$1550 shows absorption which cannot be interstellar (see Fig.\n10). The difference in velocity between the two components of the C~IV\ndoublet is shown by the two vertical lines marked by ``$\\Delta\\lambda$''.\nThe equivalent widths of all lines are given in Table 3. Note that the\nzero velocity of the C~II and C~IV multiplets in the figure corresponds to\nthe most blueward component of the multiplets, while Table 3 lists \nweighted wavelengths.\n}\n\\label{abslines}\n\\end{figure*} \n\n\\clearpage\n\n\\begin{figure*} \\centering \\vspace{8.0 cm}\n\\special{psfile=Fig9.ps hoffset=0 voffset=-230 hscale=65 vscale=65 angle=0}\n\\caption{\nFUV emission from the Crab nebula in the region around the pulsar. The \nspectrum was obtained by averaging the emission from two 8\\farcs2 long\nregion above and below \nthe pulsar position along the 0\\farcs5 slit. The continuum has been flattened \nout and the spectrum smoothed with a 3 pixel boxcar average.\n}\n\\label{pulse}\n\\end{figure*} \n\n\n\\begin{figure*} \\centering \\vspace{8.0 cm}\n\\special{psfile=Fig10.ps hoffset=0 voffset=-230 hscale=65 vscale=65 angle=0}\n\\caption{\nPulsar spectrum around C~IV~$\\lambda1550$. No absorption at zero velocity\nof C~IV~$\\lambda1550$ is seen. Instead the line is blueshifted, reaching a\nmaximum velocity $\\sim 2500 \\kms$. The spectrum also shows the interstellar\nlines Si~II~$\\lambda$1527 and C~I~$\\lambda$1561, neither of which blends with\nthe C~IV line. Si~II~$\\lambda$1533, which sometimes accompanies \nSi~II~$\\lambda$1527 in interstellar spectra, appears to be absent, and cannot\nexplain the observed absorption at velocities $\\lesssim 2700 \\kms$. Overlaid \non the observed spectrum are two of the models for the fast shell in Table \n5: $\\eta = 0$ (dotted) and $\\eta = 3$ (dashed), where $\\eta$ is defined \nfrom $\\rho(R) = \\rho(R_{\\rm in})~(R/R_{\\rm in})^{-\\eta}$, and $R_{\\rm in}$\nis the inner radius of the shell. We have assumed \nthat $R_{\\rm in}=5\\EE{18}$~cm, which corresponds to a minimum shell velocity\nof $\\approx 1680 \\kms$. See Table 5 for details of these and other models of\nthe shell.\n}\n\\label{CIVline}\n\\end{figure*} \n\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002374.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Anders \\& Grevesse\\ 1989]{AG89} Anders, E., \\& Grevesse, N. 1989,\nGeochim. Cosmochim. Acta, 53, 197\n\n\\bibitem [Benvenuti et al.\\ 1980]{Ben80} Benvenuti, P., Bianchi, L.,\nCassatella, A., Macchetto, F., Selvelli, P.~L., Zamorano, J., Clavel, J.,\nDarius, J., Heck, A., \\& Henston, M. 1980, in Proc. Second European {\\it IUE}\nConference (ESA SP-157), 339\n\n\\bibitem[Blair et al.\\ 1992]{Bl92} Blair, W.~P., Long, K.~S., Vancura, O.,\nBowers, C.~W., Conger, S., Davidsen, A.~F., Kriss, G.~A., \\& Henry, R.~B.~C.\n1992, \\apj, 399, 611\n\n%\\bibitem[Bohlin et al.\\ 1998]{Boh98} Bohlin, R., Collins, N., \\& Gonella, A.\n%1998, Instrument Science report STIS 97-14 (Baltimore:STScI)\n\n\\bibitem[Chevalier\\ 1977]{C77} Chevalier, R.~A. 1977, in Supernovae, ed. D.~N.\nSchramm, 53\n\n%\\bibitem[Clark \\& Stephenson\\ 1977]{CS77} Clark, D.~H., \\& Stephenson,\n%F.~R. 1977, The Historical Supernovae, Pergamon Press\n\n\\bibitem[Clark et al.\\ 1983]{C83} Clark, D.~H., Murdin, P., Wood, \nR., Gilmozzi, R., Danziger, J., \\& Furr, A.~W. 1983, \\mnras, 204, 415\n\n\\bibitem[Cocke et al.\\ 1969]{Co69} Cocke, W.~J., Disney M.~J., \\& Taylor,\nD.~J. 1969, \\nat, 221, 525\n\n\\bibitem [Comella et al.\\ 1969]{C69}\nComella, J.~M., Craft, H.~D. Jr., Lovelace, R.~V.~E., Sutton, J.~M., \\&\nTyler, G.~I. 1969, \\nat, 221, 453\n\n\\bibitem[Davidson \\& Fesen\\ 1985]{DF85} Davidson, K., \\& Fesen, R.~A. 1985,\n\\araa, 23, 199\n\n\\bibitem[Davidson et al.\\ 1982]{D82} Davidson, K., Gull, T.~R., Maran, \nS.~P., Stecher, T.~P., Fesen, R.~A., Parise, R.~A., Harvel, C.~A., Kafatos, M.,\n\\& Trimble, V.~L. 1982, \\apj, 253, 696 \n\n\\bibitem[de Boer et al.\\ 1987]{dB87} de Boer, K.~S., Jura, M.~A., \\& Shull,\nJ.~M. 1987, in Exploring the Universe with the {\\it IUE} satellite, ed. Y.\nKondo, W. Wamsteker, A. Boggess, M. Grewing, C. de Jager, A.~L. Lane, \nJ.~L. Linsky, \\& R. Wilson (Dordrecht: Reidel), 485\n\n\\bibitem[Eikenberry et al.\\ 1997]{EIK97} Eikenberry, S. S., Fazio, G. G.,\nRansom, S. M., Middleditch, J., Kristian, J., \\& Pennypacker, C. R. 1997, \\apj,\n477, 465\n\n\\bibitem[Fesen et al.\\ 1997]{Fe97} Fesen, R.~A., Shull, M.~J., \\& Hurford,\nA.~P. 1997, \\aj, 113, 354\n\n\\bibitem[Fitzpatrick\\ 1999]{Fi99} Fitzpatrick, E.~L. 1999, \\pasp, 111, 63\n\n\\bibitem[Frail et al.\\ 1995]{Fr95} Frail, D.~A., Kassim, N.~E.,\nCornwell, T.~J., \\& Goss, W.~M. 1995, \\apj, 454, L129\n\n\n\\bibitem[Ginzburg \\& Zheleznyakov\\ 1975]{GZ75} Ginzburg, V.~L., \\& Zheleznyakov\nV.~V. 1975, \\araa, 13, 511\n\n\\bibitem[Gold\\ 1968]{G68} Gold, T. 1968, \\nat, 218, 731\n\n\\bibitem [Gull et al.\\ 1998]{G98} Gull, T.~R., Lindler, D., Crenshaw, M.,\nDolan, J.~F., Hulbert, S.~J., Kraemer, S.~B., Lundqvist, P., Sahu, K.~C.,\nSollerman, J., Sonneborn, G., \\& Woodgate, B.~E. 1998, \\apj, 495, L51 (G98)\n\n\\bibitem [Hester et al.\\ 1996]{H96} Hester, J.~J., et al.\n1996, \\apj, 456, 225 \n%21 authors\n\n\\bibitem[Hill et al.\\ 1997]{H97} Hill, R.~J., Dolan, J.~F., Bless,\nR.~C., Boyd, P.~T., Percival, J.~W., Taylor, M.~J., \\& Van Citters, G.~W.\n1997, \\apj, 486, L99\n\n%\\bibitem[Jun 1998]{Jun98} Jun, B.-I. 1998, \\apj, 499, 282\n\n\\bibitem[Kaplan et al.\\ 1989]{Ka89} Kaplan, G.~H., Hughes, J.~A., Seidelmann, \nP.~K., Smith, C.~A., \\& Yallop, B.~D. 1989, \\aj, 97, 1197\n\n\\bibitem[Keenan et al.\\ 1993]{keen93} Keenan, F.~P., Hibbert, A., Ojha,\nP.~C., \\& Conlon, E. S. 1993, Phys. Scripta, 48, 129\n\n\\bibitem[Kimble et al.\\ 1998]{K98} Kimble, R.~A., et al. 1998, \\apj, 492, L83\n%\\bibitem[Kimble et al.\\ 1998]{K98} Kimble, R.~A., Woodgate, B.~E.,\n%Bowers, C.~W., Kraemer, S.~B., Kaiser, M.~E., Gull, T.~R., Heap, S.~R., \n%Danks, A.~C., Boggess, A., Green, R.~F., et al. 1998, \\apj, 492, L83\n%79 more authors!\n\n%\\bibitem[Lindler at al.\\ 1997]{L97} Lindler, D. J., Gull, T. R., Kraemer, \n%S.~B., et al. 1998, in {\\it Hubble Space Telescope} \n%calibration workshop Proc. \n%(Baltimore: STSci), 138\n\n\\bibitem [Lundqvist, Fransson \\& Chevalier\\ 1986]{P86} Lundqvist, P., Fransson,\nC., \\& Chevalier, R.~A. 1986, \\aap, 162, L6 (LFC86)\n\n\\bibitem[Lyne et al.\\ 1999]{LPR99}\nLyne, A.~G., Pritchard, R.~S., \\& Roberts, M.~E. 1999,\nJodrell Bank Crab Pulsar Timing Results Monthly Ephemeris\n(Manchester: Univ. Manchester; http://www.jb.man.ac.uk/$\\sim$pulsar/crab.html)\n\n\\bibitem[Lyne \\& Graham-Smith\\ 1998]{LGS98}\nLyne, A.~G., \\& Graham-Smith, F. 1998,\nPulsar Astronomy (Cambridge Astrophysics series)\n\n\\bibitem[Martin et al.\\ 1998]{MHS98} Martin, C., Halpern, J.~P., \\& \nSchiminovich, D. 1998, \\apj, 494, L211 \n\n\\bibitem[Mauche \\& Gorenstein\\ 1989]{MG89} Mauche, C.~W., \\& Gorenstein,\nP. 1989, \\apj, 336, 843 \n\n%\\bibitem[Meyer et al.\\ 1998]{MJC98} Meyer, D. M., Jura, M., \\& Cardelli, J. A.\n%1998, \\apj, 493, 222\n\n\\bibitem[Middleditch \\& Pennypacker\\ 1985]{MP85}Middleditch, J., \\& \nPennypacker, C. 1985, \\nat, 313, 659\n\n\\bibitem[Miller\\ 1973]{M73} Miller, J.~S. 1973, \\apj, 180, L83\n\n\\bibitem[Minkowski\\ 1942]{M42} Minkowski, R. 1942, \\apj, 96, 199\n\n\\bibitem[Morton\\ 1991]{Mort91} Morton, D.~C. 1991, \\apjs, 77, 119\n\n\\bibitem[Murdin\\ 1994]{Murd94} Murdin, P. 1994, \\mnras, 269, 89\n\n\\bibitem[Nasuti et al.\\ 1996]{Na96} Nasuti, F.~P., Mignani, R., Caraveo.\nP.~A., \\& Bignami, G.~F. 1996, \\aap, 314, 849\n\n\\bibitem[Nomoto\\ 1985]{No85} Nomoto, K. 1985, in The Crab Nebula and Related\nSupernova Remnants, ed. M. C. Kafatos \\& R. B. C. Henry (Cambridge: CUP), 97\n\n\\bibitem[Oke\\ 1969]{069} Oke, J.~B. 1969, \\apj, 156, L49\n\n\\bibitem[Percival et al.\\ 1993]{P93} Percival, J.~W., Biggs, J.~D.,\nDolan, J.~F., Robinson, E.~L., Taylor, M.~J., Bless, R.~C., Elliot, J.~L.,\nNelson, M.~J., Ramseyer, T.~F., Van Citters, G.~W., \\& Zhang, E.\n1993, \\apj, 407, 276\n\n%\\bibitem[Perryman et al.\\ 1999]{Perr95} Perryman, M.~A.~C., Favata, F.,\n%Peacock, A., Rando, N., \\& Taylor, B.~G. 1999, \\aap, 346, L30\n\n%\\bibitem[Pskovskii 1999]{Psk78} Pskovskii, Y.~P. 1978, Sov. Astron. AJ, 22, 420\n\n\\bibitem[Ramsbottom et al.\\ 1996]{ram96} Ramsbottom, C.~A., Bell, K.~L.,\n \\& Stafford, R.~P. 1996, Atomic Data Nucl. Data Tables, 63, 58\n\n\\bibitem[Reynolds \\& Chevalier\\ 1984]{RC84} Reynolds, S.~P., \\& Chevalier, \nR.~A. 1984, \\apj, 281, 33\n\n\\bibitem[Sankrit \\& Hester\\ 1997]{Sa97} Sankrit, R., \\& Hester, J.~J.\n1997, \\apj, 491, 796\n\n\\bibitem[Sankrit et al.\\ 1998]{Sa98} Sankrit, R., et al.\n%\\bibitem[Sankrit et al.\\ 1998]{Sa98} Sankrit, R., Hester, J.~F., Scowen, P.~A.,\n%Ballester, G.~E., Burrows, C.~J., Clarke, J.~T, Crisp, D., Evans, R.~W.,\n%Gallagher, J.~S., Griffiths, R.~E, et al.\n%18 authors\n1998, \\apj, 504, 344\n\n%\\bibitem[Savage \\& Mathis\\ 1979]{SM79} Savage, B.~D., \\& Mathis, J.~S. 1979, \n%\\araa, 17 73\n\n\\bibitem[Schattenburg \\& Canizares\\ 1986]{SC86} Schattenburg, M.~L., \\& \nCanizares, C.~R. 1986, \\apj, 301, 759\n\n\\bibitem[Shearer et al.\\ 1998]{Sh98} Shearer, A., et al. 1998, \\aap, 335, L21\n%\\bibitem[Shearer et al.\\ 1998]{Sh98} Shearer, A., Golden, A., Harfst, S.,\n%Butler, R., Redfern, R.~M., O'Sullivan, C.~M.~M., Beskin, G.~M.,\n%Neizvestny, S.~I., Neustroev, V.~V., Plokhotnichenko, V.~L., Cullum, M.,\n%\\& Danks, A. 1998, \\aap, 335, L21\n\n\\bibitem[Shearer et al.\\ 1997]{Sh97} Shearer, A., Redfern, R.~M., Gorman, G.,\nButler, R., Golden, A., O'Kane, P., Beskin, G.~M., \nNeizvestny, S.~I., Neustroev, V.~V., Plokhotnichenko, V.~L., \\& Cullum, M.\n1997, \\apj, 487, L181\n% 11 authors, we cut at this -> 12 authors=et al\n\n%\\bibitem[Shklovsky\\ 1960]{S60} Shklovsky, I.~S. 1960, Cosmic radio waves \n%(Cambridge:Harvard Univ. Press)\n\n\\bibitem[Shull \\& Van Steenberg\\ 1985]{SV85} Shull, J.~M., \\& Van Steenberg,\nM.~E. 1985, \\apj, 294, 599\n\n\\bibitem [Staelin \\& Reifenstein\\ 1968]{SR68}\nStaelin, D.~H., \\& Reifenstein, E.~C., III. 1968, Science, 162, 1481\n\n%\\bibitem [Trimble\\ 1973]{Tr73} Trimble, V. 1973, \\pasp, 85, 579\n\n%\\bibitem [Van Tassell et al.\\ 1999]{VT99} Van Tassell, H.~A., Hester, J.~J.,\n%Szentgyorgyi, A., \\& Sankrit, R. 1999, \\baas, 31, 973\n\n%\\bibitem[Wallace et al.\\ 1999]{Wa99}Wallace, B.~J., Landecker, T.~L.,\n%Kalberla, P.~M.~W., \\& Taylor, A.~R. 1999, \\apjs, in press, (astro-ph/9903416)\n\n\\bibitem[Wallace et al.\\ 1977]{Wa77}Wallace, P.~T., et al. 1977, \\nat, 266, 692\n%\\bibitem[Wallace et al.\\ 1977]{Wa77}Wallace, P.~T., Peterson, B.~A., Murdin, \n%P.~G., Danziger, I.~J., Manchester, R.~N., Lyne, A.~G., Goss, W.~M., Smith,\n%F.~G., Disney, M.~J., Hartley, K.~F., Jones, D.~H.~P., \\& Wellgate, G.~W.\n%1977, \\nat, 266, 692\n% Steiner, J.~E., A\\&A 61, L35 recived september 29,77 claims to be first\n% but wallace published first Apr. 21, 1977\n\n\\bibitem[Welty et al.\\ 1999]{Wel99}Welty, D.~E., Frisch, P.~C., Sonneborn,\nG., \\& York, D.~G. 1999, \\apj, 512, 636\n\n\\bibitem[Wheeler\\ 1978]{Whe78} Wheeler, J.~C. 1978, \\apj, 225, 212\n\n\\bibitem[Wu\\ 1981]{Wu81} Wu, C.~C. 1981, \\apj, 245, 581\n\n\\end{thebibliography}"
}
] |
astro-ph0002375
|
Asymmetric, arc minute scale structures around NGC 1275
|
[
{
"author": "E.Churazov \\inst{1,2}"
},
{
"author": "W.Forman \\inst{3}"
},
{
"author": "C.Jones \\inst{3}"
},
{
"author": "H.B\\\"{o}hringer \\inst{4}"
}
] |
ROSAT HRI observations show complicated substructure in the X--ray surface brightness within $\sim$5 arcminutes around NGC 1275 -- the dominant galaxy of the Perseus cluster. The typical amplitude of the variations is of the order of 30\% of the azimuthally averaged surface brightness at a given distance from NGC 1275. We argue that this substructure could be related to the activity of NGC 1275 in the past. Bubbles of relativistic plasma, inflated by jets, be forced to rise by buoyancy forces, mix with the ambient intracluster medium (ICM), and then spread. Overall evolution of the bubble may resemble the evolution of a hot bubble during a powerful atmospheric explosion. From a comparison of the time scale of the bubble inflation to the rise time of the bubbles and from the observed size of the radio lobes which displace the thermal gas, the energy release in the relativistic plasma by the active nucleus of NGC 1275 can be inferred. Approximate modeling implies a nuclear power output of the order of $10^{45}$ erg s$^{-1}$ averaged over the last $\sim 3~10^7$ years. This is comparable with the energy radiated in X-rays during the same epoch. Detailed measurements of the morphology of the X--ray structure, the temperature and abundance distributions with Chandra and XMM may test this hypothesis.
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[
{
"name": "aa_per_55.tex",
"string": "\\documentstyle{aa}\n\\input epsf.sty\n\\def\\kms{~km~s$^{-1}${}}\n\\def\\gax {{_>\\atop^{\\sim}}}\n\\def\\deg{$^{\\circ}$}\n\\def\\plotone#1{\\centering \\leavevmode \\epsfxsize=\\columnwidth \\epsfbox{#1}}\n\n\n\\def\\apj{ApJ}\n\\def\\aj{AJ}\n\\def\\aap{A\\&A}\n\\def\\aj{{\\it AJ}}\n\\def\\mnras{MNRAS}\n\\def\\nature{Nature}\n\n\n\n\\begin{document}\n\\thesaurus{11 (11.03.4 A426; 11.03.3; 11.09.1 NGC 1275; 11.09.4;\n 13.25.2)}\n\\title{Asymmetric, arc minute scale structures around NGC 1275}\n\n\\author{E.Churazov \\inst{1,2}\n\\and W.Forman \\inst{3}\n\\and C.Jones \\inst{3}\n\\and H.B\\\"{o}hringer \\inst{4}}\n\n\\institute{MPI f\\\"{u}r Astrophysik, Karl-Schwarzschild-Str.1, 85740\nGarching, Germany\n\\and Space Research Institute, Profsouznaya 84/32, Moscow 117810, \nRussia\n\\and Harvard-Smithsonian Center for Astrophysics, 60 Garden St.,\nCambridge, MA 02138\n\\and MPI f\\\"{u}r Extraterrestrische Physik, P.O.Box 1603, 85740\nGarching, Germany\n}\n\n\\maketitle\n\n\\sloppypar\n\n\\begin{abstract}\nROSAT HRI observations show complicated substructure in the X--ray\nsurface brightness within $\\sim$5 arcminutes around NGC 1275 -- the\ndominant galaxy of the Perseus cluster. The typical amplitude of the\nvariations is of the order of 30\\% of the azimuthally averaged surface\nbrightness at a given distance from NGC 1275. We argue that this\nsubstructure could be related to the activity of NGC 1275 in the\npast. Bubbles of relativistic plasma, inflated by jets, be forced to\nrise by buoyancy forces, mix with the ambient intracluster medium\n(ICM), and then spread. Overall evolution of the bubble may resemble\nthe evolution of a hot bubble during a powerful atmospheric\nexplosion. From a comparison of the time scale of the bubble inflation\nto the rise time of the bubbles and from the observed size of the\nradio lobes which displace the thermal gas, the energy release in\nthe relativistic plasma by the active nucleus of NGC 1275 can be\ninferred. Approximate modeling implies a nuclear power output of the\norder of $10^{45}$ erg s$^{-1}$ averaged over the last $\\sim 3~10^7$\nyears. This is comparable with the energy radiated in X-rays during\nthe same epoch. Detailed measurements of the morphology of the X--ray\nstructure, the temperature and abundance distributions with Chandra\nand XMM may test this hypothesis.\n\\end{abstract}\n\n\\keywords{galaxies: active - galaxies: clusters: individual: Perseus -\ncooling flows - galaxies: individual: NGC 1275 - X-rays: galaxies} \n\n\\section{INTRODUCTION}\nThe Perseus cluster of galaxies (Abell 426) is one of the best studied\nclusters, due to its proximity ($z=0.018$, $1'$ corresponds to $\\sim$\n30 kpc for $H_0=50~km~s^{-1}~Mpc^{-1}$) and brightness. Detailed X--ray\nimages were obtained with the Einstein IPC (Branduardi--Raymont et\nal. 1981) and HRI (Fabian et al. 1981) and the ROSAT PSPC (Schwarz et\nal. 1992, Ettori, Fabian, White 1999) and HRI (B\\\"{o}hringer et al. 1993;\nsee also Heinz et al. 1998). The cluster has a prominent X--ray surface\nbrightness peak at its center along with cool gas, which is usually\ninterpreted as due to the pressure induced flow of gas releasing its thermal\nenergy via radiation. The cooling flow is centered on the active galaxy\nNGC1275, containing a strong core-dominated radio source (Per A, 3C 84)\nsurrounded by a lower surface brightness halo (e.g. Pedlar et\nal. 1990, Sijbring 1993). Analysis of the ROSAT HRI observations of\nthe central arcminute has shown that the X-ray emitting gas is\ndisplaced by the bright radio emitting regions (B\\\"{o}hringer et\nal. 1993), suggesting that the cosmic ray pressure is at least\ncomparable to that of the hot intracluster gas. Many other studies\nexplored correlations of X-ray, radio, optical, and ultraviolet\nemission (see e.g. McNamara, O'Connell \\& Sarazin, 1996 and references\ntherein). In this contribution, we discuss asymmetric structure in the\nX--ray surface brightness within $\\sim$ 5 arcminutes of NGC 1275\nand suggest that buoyant bubbles of relativistic plasma may be\nimportant in defining the properties of this structure.\n\n\\section{IMAGES}\nThe longest ROSAT HRI pointing towards NGC~1275 was made in August 1994\nwith a total exposure time of about 52 ksec. The $8' \\times 8'$ subsection of\nthe HRI image, smoothed with a $3''$ Gaussian, is shown in\nFig.~\\ref{raw}. The image is centered at NGC 1275. Two X--ray minima\nimmediately to the north and south of NGC 1275 coincide (B\\\"{o}hringer et\nal. 1993) with bright lobes of radio emission at 332 MHz, mapped with the\nVLA by Pedlar et al. (1990). Another region of reduced brightness ($\\sim\n1.5'$ to the north--west from NGC 1275) was detected earlier in Einstein IPC\nand HRI images (Branduardi--Raymont et al. 1981, Fabian et al. 1981). It was\nsuggested that reduced brightness in this region could be due to a\nforeground patch of a photoabsorbing material or pressure driven asymmetry\nin the thermally unstable cooling flow (Fabian et al. 1981). The\ncomplex shape of the X-ray surface brightness is much more clearly seen in\nFig.~\\ref{wv} which shows the same image, adaptively smoothed using the\nprocedure of Vikhlinin, Forman, Jones (1996). The ``compressed'' isophotes in the\nfigure delineate a complex spiral--like structure. Comparison of Fig.~\\ref{wv}\nand Fig.~\\ref{raw} shows that the same structure is present in both images,\ni.e. it is not an artifact of the adaptive smoothing procedure. \n\nIn order to estimate the amplitude of the substructure relative to\nthe undisturbed ICM, we divided the original image (Fig.\\ref{raw}) by the\nazimuthally averaged radial surface brightness profile. The resulting\nimage, convolved with \nthe $6''$ Gaussian is \nshown in Fig.\\ref{radio}. The regions having surface brightness higher than \nthe azimuthally averaged value appear grey in this image and form a long\nspiral--like structure starting near the cluster center and ending $\\sim 5'$ from\nthe center to the south--east. Of course the appearance of the excess\nemission as a ``spiral'' strongly depends on the choice of the ``undisturbed''\nICM model (which in the case of Fig.\\ref{radio} is a symmetric distribution\naround NGC 1275). Other models would imply different shapes for the regions\nhaving excess emission. In particular a substantial part of the subtructure\nseen in Fig.\\ref{raw} and \\ref{wv} can be accounted for by a model\nconsisting of a sequence of ellipses with varying centers and position\nangles (e.g. using the IRAF procedure {\\bf ellipse} due to Jedrzejewski,\n1987). Nevertheless the image shown in Fig.\\ref{radio} provides a convenient\ncharacterization of the deviations of the X--ray surface brightness relative\nto the \nazimuthally averaged value. Comparison of Fig.\\ref{radio} and Fig.\\ref{raw},\n\\ref{wv} allows one to trace all features visible in Fig.\\ref{radio} back\nto the original image. \n\nSuperposed onto the image shown in Fig.\\ref{radio} are the contours of\nthe radio image of 3C 84 at 1380 MHz (Pedlar et al. 1990). The radio\nimage was obtained through DRAGN atlas ({\\bf\nhttp://www.jb.man.ac.uk/atlas} edited by J. P. Leahy, A . H. Bridle,\nand R. G. Strom). In this image, having a resolution of $22 \\times 22$\narcsec$^2$, the central region is not resolved (unlike the higher\nresolution image of the central area used in B\\\"{o}hringer et\nal. 1993) and it does not show features, corresponding to the\ngas--voids north and south of the nucleus. The compact feature to the\nwest of NGC 1275, visible both in X--rays and radio, is the radio\ngalaxy NGC 1272. Fig.\\ref{radio} hints at possible relations between\nsome prominent features in the radio and X--rays. In particular, the\nX--ray underluminous region to the North--West of NGC 1275\n(Branduardi--Raymont et al. 1981, Fabian et al. 1981) seems to\ncoincide with a ``blob'' in radio. A somewhat better correlation is\nseen if we compare our image with the radio map of Sijbring (1993),\nwith its better angular resolution), but again the correlation is not\none to one\\footnote{Note, that some random correlation is expected\nsince both the X--ray and radio emission are asymmetric and centrally\nconcentrated around NGC 1275}. A similar partial correlation of\nX--rays and radio images also was found for another well studied\nobject -- M87 (B\\\"{o}hringer et al. 1995). For M87, the relatively\ncompact radio halo surrounds the source and some morphological\nsimilarities of the X--ray and radio images are observed. Gull and\nNorthover (1973) suggested that buoyancy plays an important role in\nthe evolution of the radio lobes. B\\\"{o}hringer et al. (1993, 1995)\npointed out that buoyant bubbles of cosmic rays may affect the X--ray\nsurface brightness distribution in NGC 1275 and M87. Below we\nspeculate on the hypothesis that this mechanism is operating in both\nsources and the disturbance of X--ray surface brightness is related,\nat least partly, with the activity of an AGN in the past.\n\n\\begin{figure}\n\\plotone{raw2.ps}\n\\caption[]{The $8' \\times 8'$ subsection of the ROSAT HRI image \nconvolved with a $3''$ Gaussian. The image is centered at NGC 1275. Two\nX--ray minima immediately to the north and south of NGC 1275 coincide\n(B\\\"{o}hringer et al. 1993) with bright lobes of radio emission at 332 MHz.\nAnother region of reduced brightness ($\\sim\n1.5'$ to the north--west from NGC 1275) was detected earlier in Einstein IPC\nand HRI images (Branduardi--Raymont et al. 1981, Fabian et al. 1981).}\n\\label{raw}\n\\end{figure}\n\n\n\\begin{figure}\n\\plotone{c3.ps}\n\\caption[]{The same image as in Fig.1 adaptively smoothed using the\nwavelet--based procedure of Vikhlinin, Forman, Jones (1996). Contours are\nplotted with multiplicative increments of 1.05.} \n\\label{wv}\n\\end{figure}\n\n\\begin{figure}\n\\plotone{r4.ps}\n\\caption[]{The $12' \\times 12'$ subsection of the HRI image divided by the\nazimuthally averaged surface brightness profile at a given distance from\nNGC 1275 and convolved with a $6''$ Gaussian. It characterizes the value of\nthe surface brightness relative to the azimuthally averaged value. The\ndarker the color, the larger is the value \n(white color corresponds to regions with surface brightness lower than\nazimuthally averaged value; dark grey corresponds to region which are $\\sim$\n30\\% brighter than the azimuthally averaged value). Superposed onto the image\nare the contours of the radio flux at 1380 MHz (Pedlar et al. 1990). The\nradio data have a resolution of $22 \\times 22$ arcsec$^2$ and the central\nregion is not resolved. The compact feature to the west of NGC 1275, visible\nboth in X--rays and radio is the radio galaxy NGC 1272. \n} \n\\label{radio}\n\\end{figure}\n\n\\section{EVOLUTION OF THE OLD RADIO LOBES}\nThe complex substructure of the X--ray emission in the Perseus cluster is\nseen at various spatial scales. At large\nscales (larger than $\\sim 10'$ -- $20'$), excess emission to the east of NGC\n1275 was observed in the HEAO--2 IPC and ROSAT images (Branduardi--Raymont\net al. 1981, Fabian et al. 1981, Schwarz et al. 1992, Ettori, Fabian, White\n1999). Schwarz et al. (1992), using ROSAT PSPC data, found that the\ntemperature is lower in this region and suggested that there is a\nsubcluster projected on the A426 cluster and merging with the main cluster.\nAt much smaller scales ($\\le 1'$), there are two X--ray minima\n(symmetrically located to the north and south of NGC 1275) which\nB\\\"{o}hringer et al. (1993) explained as due to the displacement of the\nX--ray emitting gas by the high pressure of the radio emitting plasma\nassociated with the radio lobes around NGC 1275. As is clear from\nFig.\\ref{raw},\\ref{wv} at intermediate scales (arcminutes), \nsubstructure is also present. We concentrate below on the possibility that\nat these spatial scales, the disturbed X--ray surface brightness\ndistribution is affected by the bubbles of radio emitting plasma, created by\nthe jets in the past and moving away from the center due to buoyancy. \n\nRecently Heinz, Reynolds \\& Begelman (1998) argued that the\ntime-averaged power of the jets in NGC 1275 exceeds $\\sim\n10^{45}~ergs~s^{-1}$. This conclusion is based on the observed\nproperties (in particular -- sharp boundaries) of the X--ray cavities\nin the central $1'$, presumably inflated by the relativistic particles\nof the jet. Such a high power input is comparable to the total X--ray\nluminosity of the central $6'$ region (i.e. $\\sim$ 200 kpc) around NGC\n1275. If the same power is sustained for a long time (e.g. cooling\ntime of the gas $\\sim 10^{10}$ years at a radius of 200 kpc) then the\nentire cooling flow region could be affected. Following Gull and\nNorthover (1973) we assume that buoyancy (i.e. Rayleigh--Taylor\ninstability) limits the growth of the cavities inflated by the\njets. After the velocity of rise due to buoyancy exceeds the expansion\nvelocity, the bubble detaches from the jet and begins rising. As we\nestimate below, for the jet power of $\\sim 10^{45}~ergs~s^{-1}$ the\nbubble at the time of separation from the jet should have a size\n$\\sim$10--20 kpc ($\\le 1'$). The subsequent evolution of the bubble\nmay resemble the evolution of a powerful atmospheric explosion or a\nlarge gas bubble rising in a liquid (e.g. Walters and Davison 1963,\nOnufriev 1967, Zhidov et al. 1977). If the magnetic field does not\nprovide effective surface tension to preserve the quasi--spherical\nshape of the bubble, then it quickly transforms into a torus and\nmixes with the ambient cooling flow gas. The torus keeps rising until\nit reaches the distance from the center where its density (accounting\nfor adiabatic expansion) is equal to the density of the ambient\ngas. Since the entropy of the ICM rises with distance from the center\nin the cooling flow region, the torus is unlikely to travel a very\nlarge distance from the center. Then the torus extends in the lateral\ndirection in order to occupy the layer having a similar mass density.\nBelow we give order of magnitude estimates characterizing the\nformation and evolution of the bubble.\n\nFor simplicity we assume a uniform ICM in the cluster center, characterised by\nthe density $\\rho_0$ and pressure $P_0$. The bubble is assumed to be\nspherical. During the initial phase (Scheuer 1974,\nHeinz et al., 1998) jets with a power $L$ inflate the cocoon \nwith\nrelativistic plasma and surrounded by a shell of the compressed ICM.\nThe expansion is supersonic and from dimensional arguments\nit follows that the radius of the bubble $r$ as a function of time $t$ is\ngiven by the expression \n\\begin{eqnarray} \\label{r1}\nr=C_1 \\left (\\frac{L}{\\rho_0}t^3 \\right )^{1/5} \n\\end{eqnarray} \nwhere $C_1$ is a numerical constant (see e.g. Heinz et al., 1998 for a more\ndetailed treatment). At a later stage, expansion slows and becomes\nsubsonic. The evolution of the bubble radius is then given by the expression\n\\begin{eqnarray} \\label{r2}\nr=C_2 \\left (\\frac{L}{P_0}t \\right )^{1/3}=\\left (\\frac{3}{4\\pi}\\frac{\\gamma-1}{\\gamma} \\right )^{1/3}\\left (\\frac{L}{P_0}t \\right )^{1/3}\n\\end{eqnarray} \nwhere $\\gamma$ is the adiabatic index of the relativistic gas in the bubble\n(i.e. $\\gamma=4/3$). The above equation follows from\nthe energy conservation law, if we equate the power of the jet with\nthe change of internal energy plus the work done by the expanding gas at constant pressure:\n$\\frac{\\gamma}{\\gamma-1}P_04\\pi r^2 \\dot{r}=L$. The expansion velocity is\nthen simply the time derivative of equation (\\ref{r1}) or (\\ref{r2}). \n\nThe velocity at which the bubble rises due to buoyancy can be estimated as \n\\begin{eqnarray} \\label{v1}\nv_b=C_3 \\sqrt{\\frac{\\rho_{0}-\\rho_{r}}{\\rho_{0}+\\rho_{r}}rg}=C_3\\sqrt{\\frac{r}{R}}\\sqrt{\\frac{GM}{R}}=C_3\\sqrt{\\frac{r}{R}}v_K\n\\end{eqnarray} \nwhere $C_3$ is a numerical constant of order unity, $\\rho_{r}$ is\nthe mass density of the relativistic gas in the bubble, $g$ is the\ngravitational acceleration, $R$ is the distance of the bubble from the\ncluster center, $M$ is the gravitating mass within this radius and,\n$v_K$ is the Keplerian velocity at this radius. In equation (\\ref{v1})\nwe assumed that $\\rho_{r}\\ll\\rho_{0} $ and therefore replaced the\nfactor $\\frac{\\rho_{0}-\\rho_{r}}{\\rho_{0}+\\rho_{r}}$ (Atwood number)\nwith unity. The presently observed configuration of the bubbles on\neither side of NGC 1275 suggests that $r\\sim R$. Assuming that such a\nsimilar relation is approximately satisfied during the subsequent\nexpansion phase of the bubble we can further drop the factor\n$\\sqrt{\\frac{r}{R}}$ in equation (\\ref{v1}). Thus as a crude estimate\nwe can assume that $v_b\\sim C_3~v_K$ ($C_3\\sim 0.5$ is a commonly\naccepted value for incompressible fluids). Following Ettori, Fabian,\nand White (1999) we estimate the Keplerian velocity taking the gravitating\nmass profile as a sum of the Navarro, Frenk and White (1995) profile\nfor the cluster and a de Vaucouleurs (1948) profile for the\ngalaxy. For the range of parameters considered in Ettori, Fabian,\nWhite (1999), the Keplerian velocity between a few kpc and $\\sim$ 100 kpc\nfalls in the range 600-900 km/s. We can now equate the expansion\nvelocity (using equation (\\ref{r2}) for subsonic expansion) and the\nvelocity due to buoyancy in order to estimate the parameters of the\nbubble when it starts rising:\n\\begin{eqnarray} \\label{tb}\n\\nonumber t_b= \\left (\\frac{1}{36\\pi}\\frac{\\gamma-1}{\\gamma}\\right\n)^\\frac{1}{2} \\left (\\frac{L}{P_0}\\right\n)^\\frac{1}{2}\\left (\\frac{1}{C_3 v_K}\\right )^\\frac{3}{2} \\approx \n\\\\ 1.6~10^7~ \\left (\\frac{L}{10^{45}}\\right )^\\frac{1}{2} \n\\left (\\frac{P_0}{2~10^{-10}}\\right )^{-\\frac{1}{2}} \n\\left (\\frac{v_K}{700}\\right )^{-\\frac{3}{2}} ~ years\n\\end{eqnarray} \n\\begin{eqnarray} \\label{rb}\n\\nonumber r_b=\\left ( \\frac{L}{P_0C_3v_k} \\frac{\\gamma -1}{\\gamma}\n\\frac{1}{4\\pi}\\right )^\\frac{1}{2}\\approx \\\\ \n17~ \n\\left (\\frac{L}{10^{45}}\\right )^\\frac{1}{2} \n\\left (\\frac{P_0}{2~10^{-10}}\\right )^{-\\frac{1}{2}} \n\\left (\\frac{v_K}{700}\\right )^{-\\frac{1}{2}} ~ kpc\n\\end{eqnarray} \nHere $t_b$ and $r_b$ are the duration of the expansion phase and the radius of\nthe bubble respectively. \nIn the above equation we neglected the contribution to the radius (and time)\nof the initial supersonic expansion phase. Thus for $L\\sim 10^{45}~erg/s$\nand for $P_0=2~10^{-10}~erg~cm^{-3}$ (B\\\"{o}hringer et al. 1993) we expect\n$r_b\\sim17~kpc$, which approximately corresponds to the size of the X--ray\ncavities reported by B\\\"{o}hringer et al. (1993). If, as suggested by Heinz et\nal. (1998), the jet power is larger than $10^{46}~erg~s^{-1}$ then the bubble\nsize will exceed 50 kpc ($> 1'$) before the buoyancy velocity exceeds \nthe expansion velocity. Of course these estimates of the expanding\nbubble are based on many simplifying assumptions (e.g. constant\npressure assumption in equation (2)). In a subsequent publication we\nconsider the expansion of the bubble in more realistic density and\ntemperature profiles expected in cluster cooling flows.\n\nAccording to e.g. Walters and Davison (1963), Onufriev (1967), Zhidov\net al. (1977), a large bubble of light gas rising through much heavier\ngas under a buoyancy force will quickly transform into a rotating\ntorus, which consists of a mixture of smaller bubbles of heavier and\nlighter gases. This transformation occurs on times scales of the\nRayleigh--Taylor instability (i.e. $t\\sim r_b/v_b\\sim t_b$) and during\nthis transformation the whole bubble changes its distance from the\ncenter by an amount $\\sim r_b$. The torus then rises until its\naverage mass density is equal to the mass density of the ambient\ngas. The rise is accompanied by adiabatic expansion and further mixing\nwith the ambient gas. Accounting for adiabatic expansion the mass\ndensity of the torus $\\rho_t(R)$ will change during the rise according\nto\n\\begin{eqnarray} \\label{dens}\n\\rho_t(R)=\\rho_0 \\frac{\\phi}{(1-\\phi) \\left ( \\frac{P_0}{P(R)} \\right )^{1/\\gamma_{cr}} +\n\\phi \\left ( \\frac{P_0}{P(R)} \\right ) ^{1/\\gamma_{th}}} \n\\end{eqnarray}\nwhere $P(R)$ is the ICM pressure at a given distance from the center, $\\phi$\nis volume fraction of the ambient ICM gas mixed with the relativistic plasma\nat the stage of torus formation, $\\gamma_{cr}$ and $\\gamma_{th}$ are the\nadiabatic indices of the relativistic plasma and the ICM. Note that in\nequation (\\ref{dens}) we (i) neglected further mixing with the ICM during\nthe rise of the torus and (ii) mixing was assumed to be macroscopic (i.e.\nseparate bubbles of the relativistic plasma and ICM occupy the volume of the\ntorus). The equilibrium position of the torus can be found if we\nequate the torus\ndensity $\\rho_t(R)$ and the ICM density $\\rho(R)$ and solve this equation for\n$R$. We consider two possibilities here. One possibility is to assume that in\nthe inhomogeneous cooling flow, the hot phase is almost isothermal and gives\nthe dominant contribution to the density of the gas. Adopting the\ntemperature of \n$kT=6$ keV for the hot phase and using the same gravitational potential as\nabove, one can conclude that if a roughly equal amount (by volume) of the\nrelativistic plasma and the ambient gas are mixed (i.e. $\\phi\\sim0.5$),\nduring the formation of the torus, then it could rise 100-200 kpc\n before reaching an equilibrium position. Accounting for additional\nmixing will lower this estimate. Alternatively we can adopt the model of a\nuniform ICM with the temperature declining towards the center (e.g.\ntemperature is decreasing from 6 keV at 200 kpc to 2 keV at 10 kpc). Then\nfor the same value of mixing ($\\phi\\sim0.5$) the equilibrium position will\nbe at the distance of $\\sim$60 kpc from NGC 1275. Once at this distance the\ntorus as a whole will be in equilibrium and it will further expand laterally\nin order to occupy the equipotential surface at which the density\nof the ambient gas is equal to the torus density. If the cosmic rays and\nthermal gas within the torus are uniformly mixed (or a magnetic field binds\nthe blobs of thermal plasma and cosmic rays), the torus will not move \nradially. If, on the contrary, separate (and unbound) blobs of \nrelativistic plasma exist then they will still be buoyant, but since their\nsize is now much smaller than the distance from the cluster center the\nvelocity of their rise will be much smaller than the Keplerian velocity.\nAnalogously overdense blobs (with uplifted gas) may then (slowly) fall back\nto the center. \n\nWe now consider how radio and X--ray emission from the torus evolve with\ntime. Duration of the rise phase of the torus will be at least several times\nlonger than the time of the bubble formation (see eq. (\\ref{tb})), since the\nvelocity of rise is a fraction of the Keplerian velocity (see e.g. Zhidov et\nal., 1977), i.e., $t_{rise} \\ge 10^8$ years. Adiabatic expansion and change of\nthe transverse size of the torus in the spherical potential tend to further\nincrease this estimate. Even if we neglect energy losses\nof the relativistic electrons due to adiabatic expansion we can\nestimate an upper\nlimit on the electron lifetime due to synchrotron and inverse Compton (IC) \nlosses. \n\\begin{eqnarray} \\label{lifet}\nt=5~10^8~ \\left ( \\frac{\\lambda}{20~cm} \\right )^{1/2} \\left ( \\frac{B}{\\mu\nG} \\right )^{1/2}\n\\left ( \\frac{B_t}{\\mu G} \\right )^{-2}~~years\n\\end{eqnarray}\nwhere $\\lambda$ is the wavelength of the observed radio emission, $B$\nis the strength of the magnetic field, $\\frac{B_t^2}{8\\pi}$ is the\nvalue characterizing the total energy density of the magnetic field\nand cosmic microwave background. This life time (of the electrons\nemitting at a given frequency) will be longest if the energy density\nof the magnetic field approximately matches the energy density of the\nmicrowave background, i.e., $B\\sim3.5\\mu G$. Then the maximum life\ntime of the electrons producing synchrotron radiation at 20 cm is\n$\\sim 5~10^7$ years. This time is comparable to the time needed for\nthe torus to reach its final position. Therefore, the torus could be\neither radio bright or radio dim during its evolution. If no\nreacceleration takes place, then the torus will end up as a radio dim\nregion. We note here that, although the electrons may lose their energy\nvia synchrotron and IC emission, the magnetic field and especially\nrelativistic ions have a much longer lifetime (e.g. Soker \\& Sarazin\n1990, Tribble 1993) and will provide pressure support at all stages of\nthe torus evolution.\n\nAs we assumed above, the bubble detaches from the jet when the expansion\nvelocity of the bubble is already subsonic. This means that there will be no\nstrongly compressed shell surrounding the bubble and the emission measure along the\nline of sight going through the center of the bubble will be smaller than\nthat for the undisturbed ICM, i.e., at the moment of detachment the bubble\nappears as an X--ray dim region. The X--ray brightness of the torus\nduring final stages of evolution (when the torus has the same mass density\nas the ambient ICM) depends on how the relativistic plasma is mixed with the\nambient gas (B\\\"{o}hringer et al. 1995). If mixing \nis microscopic (i.e. relativistic and thermal particles are uniformly\nmixed over the torus volume on spatial scales comparable with\nthe mean free\npath) then the emission measure of the torus is the same as that for a similar\nregion of the undisturbed ICM. Since part of the pressure support in the\ntorus is provided by magnetic field and cosmic rays then the temperature of the\ntorus gas must be lower than the temperature of the ambient gas\n(B\\\"{o}hringer et al. 1995). Thus emission from the torus will be softer\nthan the emission from the ambient gas.\n\nIf, on the contrary, mixing is macroscopic (i.e. separate bubbles \nof relativistic and thermal plasma occupy the volume of the torus), then the\ntorus will appear as an X--ray bright region (the average density is the\nsame as of ICM, but only a fraction of the torus volume is occupied by the thermal\nplasma). For example, if half of the torus volume is occupied by the bubbles\nof the relativistic plasma then the emissivity of the torus will be a factor\nof 2 larger than that of the ambient gas. The X--ray emission \nof the torus is again expected to be softer than the emission of the ambient gas\nfor two reasons (i) gas uplifted from the central region has lower entropy\nthan the ambient gas and therefore will have lower temperature when maintaining\npressure equilibrium with the ambient gas (ii) gas, uplifted from the central\nregion, can be multiphase with stronger density contrasts between\nphases than the ambient gas and as a result a dense, cooler phase would\ngive a strong contribution to the soft emission. Cosmic rays may heat the gas,\nbut at least for the relativistic ions, the time scale for energy transfer is\nvery long (comparable to the Hubble time). Trailing the torus could be the\nfilaments of cooling flow gas dragged by the rising torus in a similar\nfashion as the rising (and rotating) torus after an atmospheric\nexplosion drags the air in the form of a skirt. \n\nWe note here that the morphology predicted by such a picture is very similar\nto the morphology of the ``ear--like'' feature in the radio map of M87,\nreported by B\\\"{o}hringer et al. (1995). The ``ear'' could be a torus viewed\nfrom the side. The excess X--ray emission trailing the radio feature\ncould then be due to the cooling flow gas uplifted by the torus from the\ncentral region. For Perseus the X--ray underluminous \nregion to the North--West of NGC 1275 could have the same origin (i.e.\nrising torus). In fact, the whole ``spiral'' structure seen in\nFig.\\ref{wv} could \nbe the remains of one very large bubble (e.g. with the initial size of the\norder of arminutes -- corresponding to a total jet power of $\\sim\n10^{46}~erg~s^{-1}$) inflated by the nucleus over a period of $10^8$\nyears. Alternatively \nmultiple smaller bubbles, produced at different periods may contribute to\nthe formation of the X--ray feature. If the jets maintain their direction over\na long time then a quasi--continuous flow of bubbles will tend to mix the\nICM in these directions uplifting the gas from the central region to larger\ndistances. If the jet direction varies (e.g. precession of the jet on a\ntimescale of $10^8$ years) then a complex pattern of disturbed X--ray and\nradio features may develop. \n\n\n\\section{ALTERNATIVE SCENARIOS}\nOf course there are other possible explanations for disturbed X--ray surface\nbrightness. We briefly discuss a few alternative scenarios below.\n\nAssuming that the undisturbed ICM is symmetric around NGC 1275 (as was assumed\nin Fig.\\ref{radio}) one may try to attribute the observed spiral-shaped\nemission to the gas stripped from an infalling galaxy or group of\ngalaxies. Stripped gas (if denser and cooler than the ICM) will be\ndecelerated by ram pressure and will fall toward the center of the\npotential, producing spiral--like structure. Rather narrow and long\nfeatures tentatively associated with stripped gas were observed e.g.,\nfor the NGC 4921 group in Coma (Vikhlinin et al. 1996) and NGC\n4696B in the Centaurus cluster (Churazov et al. 1999). We note here\nthat to prevent stripping at much larger radii, the gas \nmust be very dense (e.g., comparable to the molecular content of a\nspiral galaxy). A crude estimate of the gas mass needed to produce the\nobserved excess emission (assuming a uniform cylindrical feature with\na length of 200 kpc and radius of 15 kpc, located 60 kpc away from \nNGC1275) gives values of the order of a few$\\times~10^{10}$ --\n$10^{11}~M_\\odot$. Here we adopted a density for the undisturbed ICM of\n$\\sim 10^{-2}~cm^{-3}$ at this distance from NGC 1275 following the\ndeprojection analysis of Fabian et al. (1981) and Ettori, Fabian, and White\n(1999). The factor of two higher density within the feature will\ncause a $\\sim$ 20--40\\%\nexcess in the surface brightness. In the above estimate for the mass of hot\ngas in the filament, it is assumed that this medium is approximately\nhomogeneous and in ionization equilibrium. If the medium is very clumpy, the\nradiative emission of the plasma would be enhanced and this would result in an\noverestimate of the relevant gas mass. Such clumps should be easily\nseen with the high angular resolution of Chandra. Also if the medium consists of\nturbulently mixed hot and cold plasma, the very efficient excitation\nof lines in cold ions by hot electrons could lead to enhanced\nradiation (see e.g. B\\\"ohringer and Fabian 1989, Table 4) which may\nlead to an overestimate of the gas mass by up to an order of magnitude.\nThe signature of this effect is a strongly line dominated spectrum,\n(see e.g. B\\\"ohringer and Hartquist, 1987) which could be tested by\nChandra or XMM, in particular for the important iron L-shell lines.\nThus it is possible that the inferred gas mass could be lower by up to\nan order of magnitude which makes the stripping scenario more likely\nand future observations with the new X-ray observatories\ncan help to differentiate between these interpretations. \n\nAs was suggested by Fabian et al. (1981) a large scale pressure--driven\nasymmetry may be expected in a thermally unstable cooling flow. This is\nperhaps the most natural explanation which does not invoke any additional\nphysics. The same authors gave an estimate of the amount of neutral\ngas needed to explain the NW dip due to photoabsorption: excess\nhydrogen column density around $10^{22}~cm^{-2}$ is required to\nsuppress the soft count rate in this region. \n\nYet another possibility is that the motion of NGC 1275 with respect to\nthe ICM causes the observed substructure. As pointed out in\nB\\\"{o}hringer et al. (1993), NGC 1275 is perhaps oscillating at the\nbottom of the cluster potential well causing the excess emission $1'$ to the\neast of the nucleus. Since the X-ray surface brightness peak is well\ncentered on NGC 1275, it is clear that the galaxy drags the central part of the\ncooling flow as it moves in the cluster core. At a distance larger\nthan 2-3 arcminutes from NGC 1275, the cluster potential dominates\nover the potential of the galaxy. The gas at this distance should be very\nsensitive to the ram pressure of the ambient cluster gas and might give rise\nto the asymmetric (and time dependent) features. \n\nThe motion of NGC~1275 could also contribute to the X-ray structure\nthrough the formation of a ``cooling wake'' (David et al. 1994). If\nNGC~1275 is moving significantly, then inhomogeneities in the cooling\ngas would be gravitationally focussed and compressed into a wake. The\nwake would mark the, possibly complex, motion of NGC~1275, as it is\nperturbed by galaxies passing through the cluster core. Such a feature\nwould be cool, since it arises from overdense concentrations of gas.\n\nFinally, one can assume that cooling gas may have some angular\nmomentum (e.g., produced by mergers) and the observed spiral structure\nsimply reflects slow rotation of the gas combined with non-uniform\ncooling. Following Sarazin et al. (1995), one can assume that this gas\nwill preserve the direction of its angular momentum and\nthat this infalling material would eventually feed an AGN --\nNGC~1275. One then might expect the radio jets to be aligned\nperpendicular to the rotation plane of the gas. At first glance, the\n``spiral'' feature appears approximately face-on, suggesting that jets\nshould be directed along the line of sight as indeed is derived from\nthe radio observations (see Pedlar et al. 1990).\n\n\\section{CONCLUSIONS}\nThe X--ray surface brightness around NGC 1275 (dominant galaxy of the\nPerseus cluster) is perturbed at various spatial scales. We suggest that\non arcminute scales, the disturbance is caused by bubbles\nof relativistic plasma, inflated by jets during the past $\\sim 10^8$ years. \nOverall evolution of the buoyant bubble will resemble the evolution of a hot\nbubble during a powerful atmospheric explosion. Colder gas from the central\nregion of the cooling flow may be uplifted by the rising bubbles and (in the\ncase of continuous jet activity) may make several cycles (from the center to\nthe outer regions and back) on time scales comparable to the cooling\ntime of the gas in the cooling flow.\n\nA very important result that can be inferred from this model\nis the total power output of the nuclear energy source in \nNGC 1275 in the form of relativistic plasma. This energy\nrelease averaged over a time scale of about $3~10^7$ to $10^8$\nyears is estimated as a function of the inflation time of the\ncentral radio lobes, the rise time of the inflated bubbles\ndue to buoyancy forces, and the actual size of the central \nbubbles. A geometrically simplified model yields a power \noutput on the order of $10^{45}$ erg s$^{-1}$. This is comparable with\nthe energy lost at the same time by thermal X-ray radiation from the\nentire central cooling flow region. This raises the question, where\ndoes all this energy go, especially if the energy release is persistent over a\nlonger epoch during which the relativistic electrons can lose their\nenergy by radiation, but the energy in protons and in the\nmagnetic field is mostly conserved. The complicated X-ray\nmorphology discussed in this paper may indicate long\nlasting nuclear activity, if we interpret the peculiar structure\nin the X-ray surface brightness as remnants of decaying radio\nlobe bubbles.\n\nDetailed measurements of the morphology of the X--ray structure and\nthe temperature and abundance distribution with Chandra and XMM may\ntest this hypothesis. The gas uplifted from the central region is\nexpected to be cooler than the ambient gas and to have an abundance of\nheavy elements typical of the innermost region. If cosmic rays are\nmixed with the thermal gas, then the pressure, as derived from X--ray\nobservations, may be lower than the pressure of the ambient gas.\n\n\\acknowledgements\n\nWe thank the referees for several helpful comments and\nsuggestions. We are grateful to Nail Inogamov and Nail Sibgatullin\nfor useful discussions.\nThis research has made use of data obtained through the High Energy\nAstrophysics Science Archive Research Center Online Service, provided\nby the NASA/Goddard Space Flight Center. W. Forman and C. Jones\nacknowledge support from NASA contract NAS8-39073.\n\n\n\n\\begin{thebibliography}{}\n\\bibitem[B\\\"ohringer \\& Hartquist 1987]{bh87} B\\\"ohringer H. \\&\n Hartquist, T.W., 1987, \\mnras, 228, 915 \n\\bibitem[B\\\"ohringer \\& Fabian 1989]{bf89} B\\\"ohringer H. \\&\n Fabian A.C., 1989, \\mnras, 237, 1147 \n\\bibitem[B\\\"{o}hringer et al.\\ (1993)]{boh93} B\\\"{o}hringer, H., Voges,\n W., Fabian, A.C., Edge, A.C., Neumann, D.M., 1993\n \\mnras, 264, L25\n\\bibitem[B\\\"{o}hringer \\& Morfill 1993]{bm93} B\\\"{o}hringer, H.,\n Morfill, G.E., 1993 \n \\apj, 330, 609\n\\bibitem[B\\\"{o}hringer et al.\\ (1995)]{boh95} B\\\"{o}hringer, H.,\n Nulsen, P. E.J., Braun, R., Fabian, A. C., 1995\n \\mnras, 274, L67\n\\bibitem[Branduardi-Raymont et al.\\ (1981)]{br81} Branduardi-Raymont,\n G., Fabricant, D., Feigelson, E., Gorenstein, P.,\n Grindlay, J., Soltan, A., Zamorani, G., 1981 \n \\apj, 248, 55\n\\bibitem[Churazov et al.\\ (1999)]{cgfj99} Churazov E., Gilfanov M.,\n Jones C., Forman W., 1999 \n \\apj, 520, 105\n\\bibitem[David et al.\\ (1994)]{da94} David, L., Jones, C., Forman, W.,\n Daines, S. 1994, \\apj, 428, 544\n\\bibitem[de Vaucouleurs 1948]{dva48} de Vaucouleurs 1948 \n Ann. Astrophys, 11, 247\n\\bibitem[Ettori, Fabian and White 1999]{efw99} Ettori, S. Fabian, A.C.\n White, D.A. 1999, \\mnras, 300, 837\n\\bibitem[Fabian et al.\\ (1981)]{fa81} Fabian, A. C., Hu, E. M., Cowie,\n L. L., Grindlay, J., 1981\n \\apj, 248, 47\n\\bibitem[Gull and Northover 1973]{g73} Gull, S.F., Northover, K. J. E.\n 1973 \\nature, 244, 80\n\\bibitem[Jedrzejewski 1987]{jed87} Jedrzejewski, R.I.\n 1987, \\mnras, 226, 747\n\\bibitem[Heinz, Reynolds, Begelman 1998]{hrb98} Heinz, S., Reynolds,\n C.S., Begelman, M.C., 1998\n \\apj, 501, 126\n\\bibitem[McNamara,O'Connell, Sarazin 1996]{mcn96} McNamara, B.R.,\n O'Connell, R.W., Sarazin, C.L., 1996\n \\aj, 112, 91\n\\bibitem[Navarro, Frenk, White 1995]{nfw95} Navarro, J.F. Frenk, C.S. White,\n S.D.M. 1995 \n \\mnras, 275, 720\n\\bibitem[Onufriev 1967]{on67} Onufriev, A.T. \n 1967, Zhurnal Prikladnoi Mekhaniki i Tehnicheskoi Fisiki, 2, 101\n\\bibitem[Pedlar et al.\\ (1990)]{ped90} Pedlar, A., Ghataure, H.S.,\n Davies, R.D., Harrison, B.A., Perley, R.,\n Crane, P.C., Unger, S.W., 1990\n \\mnras, 246, 477\n\\bibitem[Sarazin et al.\\ (1995)]{sar95} Sarazin, C.L., Burns, J.O.,\n Roettiger, K., McNamara, B.R., 1995\n \\apj, 447, 559\n\\bibitem[Scheuer 1974]{sch74} Scheuer, P.A.G. 1974 \n \\mnras, 166, 513\n\\bibitem[Schwarz et al.\\ (1992)]{sch92} Schwarz, R. A., Edge, A. C.,\n Voges, W., Boehringer, H., Ebeling, H., Briel,\n U. G., 1992, \n \\aap, 256, L11\n\\bibitem[Sijbring 1993]{sij93} Sijbring D., 1993, Ph.D., Groningen Univ.\n\\bibitem[Soker \\& Sarazin 1990]{ss90} Soker, N., Sarazin, C., 1990\n \\apj, 348, 73\n\\bibitem[Tribble 1993]{tri93} Tribble, P.C., 1993 \n \\mnras, 263, 31\n\\bibitem[Vikhlinin, Forman, \\& Jones (1996)]{vfj96} Vikhlinin A., Forman\n W., Jones C, 1996 \n \\apj, 474, L7\n\\bibitem[Walters and Davidson 1963)]{wd63} Walters, J.K. Davidson, J.F.\n 1963, J.Fluid.Mech., 17, 321\n\\bibitem[Zhidov et al.\\ 1977]{zhi77} Zhidov, I.G. Meshkov, E.E. Popov,\n V.V.Rogachev, V.G. Tolshmyakov A.I.\n 1977, Zhurnal Prikladnoi Mekhaniki i Tehnicheskoi Fisiki , 3, 75\n\\end{thebibliography}\n\n\\end{document}\n\n"
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[
{
"name": "astro-ph0002375.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[B\\\"ohringer \\& Hartquist 1987]{bh87} B\\\"ohringer H. \\&\n Hartquist, T.W., 1987, \\mnras, 228, 915 \n\\bibitem[B\\\"ohringer \\& Fabian 1989]{bf89} B\\\"ohringer H. \\&\n Fabian A.C., 1989, \\mnras, 237, 1147 \n\\bibitem[B\\\"{o}hringer et al.\\ (1993)]{boh93} B\\\"{o}hringer, H., Voges,\n W., Fabian, A.C., Edge, A.C., Neumann, D.M., 1993\n \\mnras, 264, L25\n\\bibitem[B\\\"{o}hringer \\& Morfill 1993]{bm93} B\\\"{o}hringer, H.,\n Morfill, G.E., 1993 \n \\apj, 330, 609\n\\bibitem[B\\\"{o}hringer et al.\\ (1995)]{boh95} B\\\"{o}hringer, H.,\n Nulsen, P. E.J., Braun, R., Fabian, A. C., 1995\n \\mnras, 274, L67\n\\bibitem[Branduardi-Raymont et al.\\ (1981)]{br81} Branduardi-Raymont,\n G., Fabricant, D., Feigelson, E., Gorenstein, P.,\n Grindlay, J., Soltan, A., Zamorani, G., 1981 \n \\apj, 248, 55\n\\bibitem[Churazov et al.\\ (1999)]{cgfj99} Churazov E., Gilfanov M.,\n Jones C., Forman W., 1999 \n \\apj, 520, 105\n\\bibitem[David et al.\\ (1994)]{da94} David, L., Jones, C., Forman, W.,\n Daines, S. 1994, \\apj, 428, 544\n\\bibitem[de Vaucouleurs 1948]{dva48} de Vaucouleurs 1948 \n Ann. Astrophys, 11, 247\n\\bibitem[Ettori, Fabian and White 1999]{efw99} Ettori, S. Fabian, A.C.\n White, D.A. 1999, \\mnras, 300, 837\n\\bibitem[Fabian et al.\\ (1981)]{fa81} Fabian, A. C., Hu, E. M., Cowie,\n L. L., Grindlay, J., 1981\n \\apj, 248, 47\n\\bibitem[Gull and Northover 1973]{g73} Gull, S.F., Northover, K. J. E.\n 1973 \\nature, 244, 80\n\\bibitem[Jedrzejewski 1987]{jed87} Jedrzejewski, R.I.\n 1987, \\mnras, 226, 747\n\\bibitem[Heinz, Reynolds, Begelman 1998]{hrb98} Heinz, S., Reynolds,\n C.S., Begelman, M.C., 1998\n \\apj, 501, 126\n\\bibitem[McNamara,O'Connell, Sarazin 1996]{mcn96} McNamara, B.R.,\n O'Connell, R.W., Sarazin, C.L., 1996\n \\aj, 112, 91\n\\bibitem[Navarro, Frenk, White 1995]{nfw95} Navarro, J.F. Frenk, C.S. White,\n S.D.M. 1995 \n \\mnras, 275, 720\n\\bibitem[Onufriev 1967]{on67} Onufriev, A.T. \n 1967, Zhurnal Prikladnoi Mekhaniki i Tehnicheskoi Fisiki, 2, 101\n\\bibitem[Pedlar et al.\\ (1990)]{ped90} Pedlar, A., Ghataure, H.S.,\n Davies, R.D., Harrison, B.A., Perley, R.,\n Crane, P.C., Unger, S.W., 1990\n \\mnras, 246, 477\n\\bibitem[Sarazin et al.\\ (1995)]{sar95} Sarazin, C.L., Burns, J.O.,\n Roettiger, K., McNamara, B.R., 1995\n \\apj, 447, 559\n\\bibitem[Scheuer 1974]{sch74} Scheuer, P.A.G. 1974 \n \\mnras, 166, 513\n\\bibitem[Schwarz et al.\\ (1992)]{sch92} Schwarz, R. A., Edge, A. C.,\n Voges, W., Boehringer, H., Ebeling, H., Briel,\n U. G., 1992, \n \\aap, 256, L11\n\\bibitem[Sijbring 1993]{sij93} Sijbring D., 1993, Ph.D., Groningen Univ.\n\\bibitem[Soker \\& Sarazin 1990]{ss90} Soker, N., Sarazin, C., 1990\n \\apj, 348, 73\n\\bibitem[Tribble 1993]{tri93} Tribble, P.C., 1993 \n \\mnras, 263, 31\n\\bibitem[Vikhlinin, Forman, \\& Jones (1996)]{vfj96} Vikhlinin A., Forman\n W., Jones C, 1996 \n \\apj, 474, L7\n\\bibitem[Walters and Davidson 1963)]{wd63} Walters, J.K. Davidson, J.F.\n 1963, J.Fluid.Mech., 17, 321\n\\bibitem[Zhidov et al.\\ 1977]{zhi77} Zhidov, I.G. Meshkov, E.E. Popov,\n V.V.Rogachev, V.G. Tolshmyakov A.I.\n 1977, Zhurnal Prikladnoi Mekhaniki i Tehnicheskoi Fisiki , 3, 75\n\\end{thebibliography}"
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astro-ph0002376
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Evidence of self-interacting cold dark matter from galactic to galaxy cluster scales
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"author": "a"
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Within the framework of the cold dark matter (CDM) cosmogony, a central cusp in the density profiles of virialized dark haloes is predicted. This prediction disagrees with the soft inner halo mass distribution inferred from observations of dwarf and low surface brightness galaxies, and some clusters of galaxies. By analysing data for some of these objects, we find that the halo central density is nearly independent of the mass from galactic to galaxy cluster scales with an average value of around $0.02 \ M_{\odot}/pc^3$. We show that soft cores can be produced in the CDM haloes by introducing a lower cut-off in the power spectra of fluctuations and assuming high orbital thermal energies during halo formation. However, the scale invariance of the halo central density is not reproduced in these cases. The introduction of self-interaction in the CDM particles offers the most attractive alternative to the core problem. We propose gravothermal expansion as a possible mechanism to produce soft cores in the CDM haloes with self-interacting particles. A global thermodynamical equilibrium can explain the central density scale invariance. We find a minimum cross section capable of establishing isothermal cores in agreement with the observed shallow cores. If $\sigma$ is the cross section, $m_x$ is the mass of the dark matter particle and $v$ is the halo velocity dispersion, then $\sigma /m_x \approx 4 \ 10^{-25} (100 \ km s^{-1}/v)$ $cm^2/GeV$.
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[
{
"name": "msfin.tex",
"string": "%\\documentstyle[referee,epsfig]{mn}\n\\documentstyle[twocolumn,psfig]{mn}\n%\\documentstyle[psfig]{mn}\n\\def\\plotfiddle#1#2#3#4#5#6#7{\\centering \\leavevmode\n\\vbox to#2{\\rule{0pt}{#2}}\n\\special{psfile=#1 voffset=#7 hoffset=#6 vscale=#5 hscale=#4 angle=#3}}\n\n\n%\\psfull\n\\def\\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\n\\def\\lsim{\\lower.5ex\\hbox{\\ltsima}}\n\\def\\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def\\gsim{\\lower.5ex\\hbox{\\gtsima}}\n\n\\begin{document}\n\\title[Evidence of self-interacting cold dark matter]\n{Evidence of self-interacting cold dark matter from\ngalactic to galaxy cluster scales}\n\n\n\\author[Firmani, D'Onghia, Avila-Reese, Chincarini, Hern\\'{a}ndez] \n{Firmani C.$^{1,3}$, D'Onghia E.$^{2}$, \n Avila-Reese V.$^{3}$, Chincarini G.$^{1,4}$ $\\&$ \n Hern\\'{a}ndez X.$^{5}$\\\\\n $^{1}$ Osservatorio Astronomico di Brera, \n via E. Bianchi 46, 23807 Merate (LC), Italy\\\\\n$^{2}$ Universit\\'{a} degli Studi di Milano, via Celoria 16, \n 20100 Milano, Italy\\\\\n$^{3}$ Instituto de Astronom{\\'\\i}a, UNAM, A.P. 70-264, 04510 \nM\\'{e}xico D.F.,\n M\\'{e}xico \\\\\n$^{4}$ Universit\\'{a} degli Studi di Milano-Bicocca, Italy\\\\\n$^{5}$ Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5,\n 50125 Firenze, Italy \\\\\nE--mail: {\\tt firmani@merate.mi.astro.it}, {\\tt elena@merate.mi.astro.it}, \n{\\tt avila@astroscu.unam.mx},\\\\ {\\tt guido@merate.mi.astro.it}, \n{\\tt xavier@arcetri.astro.it}\n}\n\n\\date{\\underline{Submitted to MNRAS, January 20, 2000}}\n\\maketitle\n\n\\begin{abstract}\n\nWithin the framework of the cold dark matter (CDM) \ncosmogony, a central cusp in the density \nprofiles of virialized dark haloes is predicted. \nThis prediction disagrees with the soft inner halo mass \ndistribution inferred from observations of dwarf and low \nsurface brightness galaxies, and some clusters of galaxies. \nBy analysing data for some \nof these objects, we find that the halo central\ndensity is nearly independent of the mass from galactic to galaxy\ncluster scales with an average value of around\n$0.02 \\ M_{\\odot}/pc^3$. We show that soft cores can be produced in the CDM\nhaloes by introducing a lower cut-off in the power\nspectra of fluctuations and assuming high orbital thermal \nenergies during halo formation. However, the scale invariance\nof the halo central density is not reproduced in these cases. The \nintroduction of self-interaction in the CDM particles offers the \nmost attractive alternative to the core problem. We propose\n gravothermal expansion as a possible mechanism to \nproduce soft cores in the CDM haloes with self-interacting\nparticles. A global thermodynamical equilibrium can explain the\ncentral density scale invariance. We find a minimum\n cross section capable of establishing isothermal cores in agreement with\nthe observed shallow cores. If $\\sigma$ is the cross section, $m_x$\nis the mass of the dark matter particle and $v$ is the halo velocity \ndispersion, then \n$\\sigma /m_x \\approx 4 \\ 10^{-25} (100 \\ km s^{-1}/v)$ $cm^2/GeV$.\n\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: formation - galaxies: haloes - clusters: haloes - \n cosmology: theory - dark matter \n\\end{keywords}\n\n\\section{Introduction}\n\nConstraining the nature of dark matter is presently one of the most \nrelevant problems in cosmology and particle physics. The \ncurrent most popular scenarios for structure formation in \nthe universe are based on the inflationary \n CDM theory, according to which cosmic structures arise \nfrom small Gaussian density fluctuations composed\nmostly of non-relativistic collisionless particles. Luminous \ngalaxies are thought to form by \ngas cooling and condensing into the dark matter haloes \nwhich grow by gravitational accretion and merging in a hierarchical fashion.\n\nThe question on the inner density profiles of \nthe virialized dark matter haloes is at present controversial.\nIn the last few years much observational and theoretical \neffort has been employed into investigating the inner structure \nof dark haloes. On galactic\nscales, the rotation curves of dwarf galaxies offer a \nway to study the inner mass distribution of their dark haloes\n directly since these galaxies are dominated by dark matter. By\nanalysing the rotation curves of some near dwarf galaxies, \nMoore (1994), Flores $\\&$ Primack (1994) and Burkert (1995) have \nshown that the central mass distribution of their dark haloes is \nsoft, i.e. the haloes have a constant density core. A similar result \nconcerns low surface brightness galaxies (LSB, hereafter) (de Blok \n$\\&$ McGaugh 1997) even though the uncertainty in \nthe observational data is larger than in the case of dwarf spirals.\nHern\\'{a}ndez $\\&$ Gilmore (1998) showed that the observed\nrotation curves of both LSB and normal large galaxies are\nconsistent with a fixed initial halo shape, characterized by a significant\nsoft core inner region.\nOn scales of clusters of galaxies, unfortunately there is not \nmuch information available. Recently, from strong gravitational \nlensing observations, Tyson, Kochanski, \\& Dell'Antonio (1998) have\nobtained an unprecedent high-resolution mass map for the cluster \nCL0024+1654, which has not a central cD galaxy, and found the \nexistence of a soft core. Taken together these studies suggest \nthe univesality of constant density cores across both large mass\nscales and galactic types.\n\nOn the theoretical side, the structure of the CDM\nhaloes was studied over a wide range of masses by \nmeans of high-resolution N-body cosmological simulations \n(e.g., Navarro, Frenk, \\& White 1997; NFW hereafter) \nand semi-analytical \napproaches (e.g., Avila-Reese, Firmani, \\& Hern\\'{a}ndez 1998).\n It was found that\nthe universal density profile firstly introduced by NFW describes very well \nthe mass distribution of most of the CDM haloes. This profile is \nunivocally determined by the mass, and in the centre diverges as \n$\\rho \\propto r^{-1}$ producing a cusp in the core. Recent high-resolution \nN-body simulations have shown that, as the numerical \nresolution is increased, the inner profiles result even steeper than\n$r^{-1}$ (e.g., Moore et al. 1999b), making the CDM haloes\nmore cuspy than in the case of the NFW profile.\n\nSo far, the predicted inner density profile of the CDM haloes seems \nto be in conflict with the observations. Another potential \ndifficulty for the CDM models was recently reported: the N-body \nsimulations predict an overly large number of haloes within group-like \nsystems compared to observations (Klypin et al. 1999; Moore et al. 1999a). \nIn light of these difficulties, the current stance of the \n hierarchical CDM-based \nscenario of structure formation remains somewhat confusing\nbecause, in fact, this scenario successfully accounts for: the distribution \nof matter at large scales (Bahcall et al. 1999), the \nuniformity of the cosmic microwave radiation and its small temperature \nanisotropies, and the observationally inferred cosmological \nparameters. \n\nThe aim of this letter is to analyse the halo core properties inferred\nfrom observations which might suggest explanations of the origin as to the\nsoft halo cores and clarify the discrepancies that appear on small scales\nwith the hierarchical scenario of structure formation.\nWe investigate whether some modifications on the initial\nconditions of this scenario\nare able to improve the results with respect to the observations. \nWe demonstrate that the introduction of self-interaction in the\nCDM particles as was suggested by Spergel \\& Steinhardt (1999) \noffers the most viable solution to the core problem in a context\nthat preserves the hierarchical CDM-based scenario. \n\n\n\\section{Halo central density from observations}\n\nWe select from the literature dwarf and LSB galaxies with \naccurately measured rotation curves and clearly dominated\nby dark matter. These restrictions considerably reduce \nambiguities in the estimates of the dark matter mass distribution \ndue to uncertain stellar mass-to-light ($M/L$) ratios and \nmodifications of the original halo profile produced by the \ngravitational drag of baryons during disc formation. Hence \nthe dark haloes of these galaxies can be rightly assumed almost ``virgin''. \nThese constraints reduce the sample to six dwarf galaxies: \nDDO154 (Carignan et al. 1998), DDO170 (Lake et al. 1990), \nDDO105 (Schramm 1992, quoted by Moore 1994), \nNGC3109 (Jobin et al. 1990), IC2574 (Martimbeau et al. 1994),\nNGC5585 (C\\'{o}te et al. 1991).\nSix LSB galaxies are selected with\nthe same criterion from a published sample: \nF568-v1, F571-8, F574-1; F583-1, F583-4, UGC5999\n(de Blok $\\&$ McGaugh 1997).\nThe rotation curves measured for all these galaxies were used\nby the different authors to estimate the halo parameters,\nparticularly the central density.\n\nOur analysis also includes the density profile obtained for the \ncluster CL0024+1654 from a high resolution mass map derived using\nstrong lensing techniques (Tyson et al. 1998). \nBecause of the lack of a massive cD galaxy in the core, this \ncluster can be assumed to be dark matter dominated at the centre. \nTwo clusters of galaxies, CL1455+22 and CL0016+16, \nwith evident shallow mass profiles in the inner regions obtained by\nweak gravitational lensing studies (Smail et al. 1995)\nhave also been considered, even though the uncertainty of \nthe observational data is larger in these cases.\n\nIn Figure 1 we plot a very suggestive result: for a broad range of\nmasses, the central density of the dark haloes is independent of\n mass (or circular velocity). Most dwarf galaxies \n(filled squares), LSB galaxies (open squares) and clusters \n(circles) indicate an average halo core density \nclose to $\\rho_c=0.02 \\ M_{\\odot}/pc^3$. \nThe arrow shows a fiducial value derived from a published sample\nof LSB galaxies (de Blok $\\&$ McGaugh 1997).\nThe galaxy error bars\nare based on the observational uncertainty, and when possible from\nthe range given by the maximum and minimum disc models. \n The cluster error bars take into account the uncertainty\nin observations and in a normalization factor of three in \ngoing from strong to weak lensing techniques (Wu et al. 1998).\n\nThis observational evidence makes the cosmological puzzle quite complex:\nhow can one explain the origin of soft halo cores with roughly the same \ncentral density over the entire mass range sampled? \n\n\n\\section{Shallow cores from collisionless cold dark matter}\n\n\nAs was discussed above, observations seem to show that the\ninner density profile of the dark matter haloes is (i) shallow, and\n(ii) with a central value independent\nfrom the total halo mass (or maximum circular velocity $V_m$). \nThese facts disagree with the \npredictions of the hierarchical CDM models. Now, we investigate\nsome alternatives which might alleviate these difficulties within the \ncosmological context. For this we have performed a quantitative\nstudy of the CDM halo profiles using a semi-numerical method \n(Avila-Reese, Firmani, \\& Hern\\'{a}ndez 1998) aimed at calculating\nthe collapse and virialization of spherically symmetric density \nfluctuations starting from an arbitrary mass aggregation history. \nResults obtained with this method are in excellent agreement\nwith those of the N-body simulations (see Avila-Reese et al. 1999;\nFirmani \\& Avila-Reese 2000). The\nmethod is based on a generalization of the secondary infall model\nwhere non-radial motions and adiabatic invariance are \ntaken into account. The only free parameter is the orbital \nparameter of particles (the perihelion \nto aphelion ratio) which regulates the thermal orbital energy of the\nsystem. This parameter is fixed independently of the halo mass\nand is constant during halo formation. Cosmological\nN-body simulations suggest $r_{\\rm peri}/r_{\\rm apo}\\approx 0.2-0.3$ \n(see Ghigna et al. 1998).\n\nRecently, Moore et al. (1999b) have simulated CDM haloes formed by\nmonolithic collapse with N-body simulations introducing for this\na lower cut-off at some wavelength in the power spectrum \nof fluctuations which suppresses substructures.\nThe result was that the steep inner density profile of the haloes persisted. \nWe suggest that this result might be partially a consequence of the \nlack of thermal orbital energy. \nIn a monolithic collapse scenario the \nthermal orbital energy plays a significant role in producing soft cores:\nas $r_{\\rm peri}/r_{\\rm apo}$ increases a larger soft core is obtained.\nThe density profiles of our haloes obtained for a CDM model with \na lower cut-off in the variance of the power spectrum and a non zero initial\nthermal content, present soft cores. However, these\nmodels are unable to predict the observed central density trend \nshown in Figure 1 (Avila-Reese et al. 1998). In fact, the \ncentral density $\\rho _c$ increases with $V_m$ in such a way\nthat if $\\rho_c$ is reproduced at galactic scales, for the cluster \nscales, $\\rho_c$ overshoots the observed value by more than an order of\nmagnitude. A hypothetical injection of\nthermal energy to the dark matter at a specific time in the life of the\nuniverse leads to a similar negative result.\n\nAn interesting way to \nproduce soft halo cores in agreement with observations is to \n simply truncate the hierarchical\nhalo mass aggregation histories at a given redshift towards the \npast. This may be done assuming that the halo mass fraction \ninstantaneously collapses with some thermal energy (monolithic \n thermal collapse),\nwhile the rest of the mass is aggregated at the normal hierarchical rate.\n We have calculated the \ndensity profiles for haloes whose mass aggregation histories \ncorrespond to a hierarchical flat $\\Lambda $CDM model \n($\\Omega _m=0.3$, h=0.7, $\\sigma _8=1$) from $z=5$ and \n$r_{peri}/r_{apo}=0.3$; before this \nepoch the hierarchical aggregation\nwas truncated. The results for this toy model are in good \nagreement with the observations: the haloes have a soft core,\nthe core densities are independent from the mass and have\na value similar to that what observational inferences indicate.\nIt is interesting to note that the most distant QSOs and galaxies \nare at redshifts $z\\approx 5$.\nAlthough the toy model presented here might look attractive, it is\ndifficult to imagine a physical process capable of delaying the\ncollapse of the central parts of the CDM haloes until $z\\approx 5$. \n\n\\section{Shallow cores from self-interacting cold dark matter}\n\n Self-interacting dark \nmatter has been proposed as a possible\nsolution for two potential conflicts of the hierarchical CDM\nmodels (Spergel \\& Steinhardt 1999; Hannestad 1999): \nthe shallow core of the haloes and the dearth of dwarf galaxies \nin the Local Group. Astrophysical consequences of collisional dark\nmatter have been pointed out by Ostriker (1999).\nIt is easy to show that a configuration \nwith the NFW density distribution is very far from thermal \nequilibrium: the inner velocity dispersion (temperature) has \na positive gradient. Consequently, the presence of some \nself-interaction in the CDM particles introduces in the dark \nhaloes a process of thermalization with heat transfer inwards, \navoiding the formation of a cuspy profile. Heat capacity in the core \nis negative. This is a typical property of \nself-gravitating systems, like the interiors of the stars. \nFor this reason, the heat transfer inwards cools the core exacerbating\neven more the temperature gradient. The heat transfer inwards increases \ncausing the core to expand and cool due to gravothermal instability,\nleading to runaway core expansion. This physical\nmechanism is the key point for core expansion if \nself-interaction is effective. This process is similar to \nthe post-collapse gravothermal instability well-known in dynamical \nstudies of globular clusters (Bettwieser \\& Sugimoto 1983) \nwhere the minimum central density is reached roughly \nafter a thermalization time. \n\nThe expansion of the core does not last forever. Since as the core \nexpands the central density decreases, this would make the \nself-interaction less efficient and the core formation\nmechanism a self-limiting process. Although\nattractive, this mechanism is difficult to investigate because of our lack\nof knowledge regarding the cross section of the self-interacting \ndark matter particles.\nFor this reason we start our analysis with a thermodynamical approach: \nwe shall \nestimate the central density of CDM haloes assuming a \nthermodynamical equilibrium is reached due to strong self-interaction\nof the CDM particles. The final result will be the formation in the\nCDM halo of a central isothermal non-singular density profile \nestablished by competition\nbetween 1) mass and energy hierarchical aggregation, and 2) \nthe thermalization due to\nself-interaction. The hierarchical mass and energy aggregation \ntends to stablish a NFW density profile (with the corresponding heat \ntransfer inwards) while the self-interaction process tends to lead the \nsystem to a thermal equilibrium with the corresponding formation\nof a shallow core. For a given mass, the halo formed by a hierarchical\nmass aggregation identifies a gravitational binding energy (or $V_m$).\nUsing this mass and binding energy to rescale a thermodynamical equilibrium\nconfiguration it is easy to find:\\\\\n\\begin{equation}\n\\rho_c = \\alpha \\ \\frac{V_m^6}{M^2} \\ M_{\\odot}/pc^3\n\\end{equation}\nwhere $V_m$ is in km/s, $M$ is the halo mass in M$_{\\odot}$ \nand $\\alpha$ is a constant given by the detailed shape of the final\nequilibrium configuration. Since for the CDM haloes a tight relationship \nbetween their mass and circular velocity of the kind $M \\propto V_m^n$ with\n$n\\approx 3.2$ is predicted (Avila-Reese et al. 1998,1999), eq. (1)\nimplies that $\\rho _c$ is roughly invariant with respect to the mass\nor $V_m$ as observations point out (Fig. 1). This strongly suggests \n that indeed a thermalization process due to dark matter \nself-interaction is acting in the CDM haloes.\n\nUnfortunately, there is not a single final thermal \nequilibrium configuration, and as Lynden-Bell \\& Wood (1968)\npointed out, some of configurations\nare even unstable. The King and Wooley configurations\nare examples of systems that have reached thermal equilibrium. They are \ncharacterized by a form parameter that may be related to the \nentropy of the system. A fiducial value for the central density \nof the CDM haloes with self-interaction may be estimated using a \nKing or a Wooley profile at the state of maximum entropy \n(Lynden-Bell $\\&$ Wood 1968). For these cases we derive respectively \n$\\alpha = 1.3 \\ 10^{9}$ (short-dashed line in Fig. 1) and $\\alpha = \n2.6 \\ 10^{9}$ (long-dashed line in Fig. 1) in the appropriate units.\nThe case of maximum entropy for a King profile corresponds to \na value of the form parameter of $8.5$. A lower limit for \nthe density may be roughly estimated from \nthe dynamical evolution of globular clusters based on the \nFokker-Planck approximation (Spitzer $\\&$ Thuan 1972),\nstarting from a uniform spherical distribution (this initial condition\nwill lead to a central density lower than the density reached by the\nthermalization of a steep initial profile).\nThe rescaling for this model taken at the first thermal equilibrium\nstate gives us $\\alpha = 1.7 \\ 10^{8} $ (dotted curve in\nFig.1).\n\nGlobal thermal equilibrium is reached when the self-interaction\ncross section is sufficiently large in order for the characteristic time\nscale of interactions across the overall halo to be shorter than the halo \nlifetime.\nAn opposite situation of minimum cross section is given when\nself-interaction induces thermal equilibrium only in the region \nof the shallow core. In this case the central isothermal core \nappears surronded by a matter distribution characterised \nby a NFW profile. From the observational data it is possible now to\ninfer an estimate of the self-interaction cross section. If $n$ is\nthe dark particle number density, $\\sigma$ the cross section and $v$\nthe dispersion velocity, assuming the collision time in the core \n $\\tau = 1/(n \\ \\sigma \\ v)$ close to the Hubble time we obtain:\\\\\n\\begin{equation}\n\\frac{\\sigma}{m_x} \\approx 4 \\ 10^{-25} \n \\Big( \\frac{0.02 \\ M_{\\odot} \\ pc^{-3}}{\\rho_c} \\Big)\n \\Big( \\frac{100 \\ km \\ s^{-1}}{v} \\Big) \\ cm^2/GeV\n\\end{equation} \nwith $m_x$ the mass of the dark matter particle and $\\rho_c$ the\ncentral density.\nIt is interesting to point out that for velocity dispersions \ncorresponding to galaxy clusters this value is close to the upper limit \nestimated by Miralda-Escud\\'{e} (2000) from the \nobservationally inferred ellipticity \nof the cluster MS21137-23. \n\n\\section{Summary}\n\nThe discovery of a soft core in the cluster of galaxies CL0024+1254 \nby strong gravitational lensing measurements and the rotation \ncurves of dark-matter dominated dwarf and LSB galaxies indicate \nthat dark matter haloes have shallow inner density profiles\nfrom galactic to cluster scales. Studying in detail the observational\ndata available for these cosmic objects, we found that\nthe halo central density is nearly invariant with respect\nto the mass from galactic to cluster sizes.\n\nWe investigated different mechanisms\nand models for halo core formation within the hierarchical CDM \nscenario. We have shown that a lower cut-off at some wavelength\nin the CDM power spectrum and the assumption of high particle \norbital thermal energies \nproduce soft cores in the haloes, but the invariance of $\\rho_c$\nwith respect to the mass is not reproduced. A more viable\nsolution to the core problem is the introduction of self-interaction \nin the CDM particles. Being this the case, we proposed the \ngravothermal expansion as the mechanism responsible for the \nformation of soft cores in a hierarchical CDM scenario. \n\nUsing a thermodynamical approach we have estimated the central \ndensity of haloes in the case of maximum efficiency for self-\ninteraction and found good agreement with the values inferred\nfrom observations. The central density in this case scales with the halo \nmass and its maximum circular velocity as $\\rho _c\\propto V_m^6/M^2$. \nThis result implies that $\\rho _c$ is roughly constant because for the \nCDM haloes $M\\propto V_m^n$ with $n\\approx 3.2$. If thermal equilibrium\nis restricted to the core, then the cross section given by eq.(2) may\nbe derived consistently with observations. The cases analysed here,\ncorresponding to a global and a local thermal equilibrium respectively,\nrepresent two limiting cases between which dark matter\nself-interaction may generate isothermal cores compatible with \nobservations.\nWe exclude from our analysis the extreme case of a {\\it very} strong\nself-interaction which may lead the core to a gravothermal catastrophe\nwith a central density profile steeper than NFW. Such extreme \nassumption of large cross section may be immediately ruled out because\na singular isothermal core will be produced in contradiction with \nobservations.\n\nWe stress the relevance confirming the existence of soft\ncores with scale invariant densities would have. In particular, the \nconstruction of high-resolution mass maps with gravitational lensing\ntechniques for the inner regions of clusters is of great interest. \n\n\n\\section*{Acknowledgments}\nED thanks Fondazione CARIPLO for financial support. \n\n\\begin{thebibliography}{}\n\n\\bibitem []{}{Avila-Reese V., Firmani C., Hern\\'{a}ndez X., 1998, ApJ, 505, 37}\n\n\\bibitem []{}{Avila-Reese V., Firmani C., Klypin A., Kravtsov A., 1999, \n MNRAS, 309, 507}\n\n\\bibitem []{} {Bahcall N., Ostriker J.P., Perlmutter S., Steinhardt P.J.,\n 1999, Science, 284, 1481}\n\n\\bibitem []{} {Bettwieser E., Sugimoto D., 1984, MNRAS, 208, 493}\n\n\\bibitem []{} {Burkert A., 1995, ApJ, 477, L25}\n\n\\bibitem []{} {Carignan C., Burton C., 1998, ApJ, 506, 125}\n\n\\bibitem []{} {C\\'{o}te S., Carignan C., Sancisi R., 1991, \n AJ, 102, 904}\n\n\\bibitem []{} {de Blok W.J.G., McGaugh S. S., 1997, \n MNRAS, 290, 533}\n\n\\bibitem []{} {Jobin M., Carignan C., 1990, AJ, 100, 648}\n\n\\bibitem []{} {Firmani C., Avila-Reese V., 2000, MNRAS, in press}\n\n\\bibitem []{} {Flores R., Primack J.R., 1994, ApJ, 427, L1}\n\n\\bibitem []{} {Ghigna S., Moore B., Governato F., Lake G., \nQuinn T., Stadel J., 1998, MNRAS, 300, 146}\n\n\\bibitem []{} {Hannestad S., 1999, preprint (astro-ph/9912558)}\n\n\\bibitem []{} {Hern\\'{a}ndez X., Gilmore G., 1998, MNRAS, 294, 595}\n\n\\bibitem []{} {Klypin A., Kravtsov A.V., Valenzuela O., Prada\nF., 1999, ApJ, 522, 82}\n\n\\bibitem []{} {Lake G., Schommer R.A., van Gorkom J.H., 1990, \n AJ, 99, 547}\n\n\\bibitem []{} {Lynden-Bell D., Wood R., 1968, \n MNRAS, 138, 495}\n\n\\bibitem []{} {Martimbeau N., Carignan C., Roy, J.R., 1994, \n AJ, 107, 543}\n\n\\bibitem []{} {Miralda-Escud\\'{e} J., 2000, ApJ, submitted (astro-ph/0002050)}\n\n\\bibitem []{} {Moore B., 1994, Nature, 370, 629 }\n\n\\bibitem []{} {Moore B., Ghigna S., Governato F., Lake G., \nQuinn T., Stadel J., 1999a, ApJ, 524, L19}\n\n\\bibitem []{} {Moore B., Quinn T., Governato F., Stadel J., Lake G., \n 1999b, MNRAS, submitted (astro-ph/9903164)}\n\n\\bibitem []{} {Navarro J., Frenk C.S., White S.D.M., 1997, ApJ, 490, 493}\n\n\\bibitem []{} {Ostriker J.P, 1999, preprint (astro-ph/9912548)}\n\n\\bibitem []{} {Smail I., Ellis R., Fitchett M.J., Edge A.C., 1995,\n MNRAS, 273, 277}\n\n\\bibitem []{} {Schramm D.N., 1992, Nucl. Phys. B. proc suppl. 28A, 243}\n\n\\bibitem []{} {Spergel D.N., Steinhardt P.J., 1999, preprint \n(astro-ph/9909386)}\n\n\\bibitem []{} {Spitzer L., Thuan T. 1972, AJ, 175, 31}\n\n\\bibitem []{} {Tyson J.A., Kochanski G.P., Dell'Antonio I.P., \n 1998, ApJ, 498, L107}\n\n\\bibitem []{} {Wu X.P., Chiueh T., Fang L.Z., Xue Y.J., 1998, \n MNRAS, 301, 861} \n\n\\end{thebibliography}\n\n%\\clearpage\n\n\\begin{figure*}\n%\\psfig{figure=rho_v.ps,bbllx=62pt, bblly=216pt, bburx=510pt, bbury=670pt,\n% clip=}\n%\\plotfiddle{rho_v.ps}{9.cm}{0}{55}{70}{-160}{-210}\n\\vspace{15cm}\n\\special{psfile=rho_v.ps hoffset=-30 voffset=-220 hscale=95 vscale=95}\n%\\resizebox{\\hsize}{!}{\\includegraphics{rho_v.ps}}\n\\caption{ Halo central density vs. maximum rotation velocity\nfor dwarf galaxies (filled squares), LSB galaxies (open squares) \nand galaxy clusters (filled circles).\n The plot shows a region predicted by gravothermal models \n where a thermodynamical equilibrium is reached. The upper limit\n of the region (state of maximum entropy) is \n estimated for a Wooley (long-dashed line)\n and a King (short-dashed line) density profile. A dynamical model \n starting from a homogeneous sphere provides an estimate of the \n lower limit for the halo \n central density (dotted curve).}\n\\end{figure*}\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
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{
"name": "astro-ph0002376.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem []{}{Avila-Reese V., Firmani C., Hern\\'{a}ndez X., 1998, ApJ, 505, 37}\n\n\\bibitem []{}{Avila-Reese V., Firmani C., Klypin A., Kravtsov A., 1999, \n MNRAS, 309, 507}\n\n\\bibitem []{} {Bahcall N., Ostriker J.P., Perlmutter S., Steinhardt P.J.,\n 1999, Science, 284, 1481}\n\n\\bibitem []{} {Bettwieser E., Sugimoto D., 1984, MNRAS, 208, 493}\n\n\\bibitem []{} {Burkert A., 1995, ApJ, 477, L25}\n\n\\bibitem []{} {Carignan C., Burton C., 1998, ApJ, 506, 125}\n\n\\bibitem []{} {C\\'{o}te S., Carignan C., Sancisi R., 1991, \n AJ, 102, 904}\n\n\\bibitem []{} {de Blok W.J.G., McGaugh S. S., 1997, \n MNRAS, 290, 533}\n\n\\bibitem []{} {Jobin M., Carignan C., 1990, AJ, 100, 648}\n\n\\bibitem []{} {Firmani C., Avila-Reese V., 2000, MNRAS, in press}\n\n\\bibitem []{} {Flores R., Primack J.R., 1994, ApJ, 427, L1}\n\n\\bibitem []{} {Ghigna S., Moore B., Governato F., Lake G., \nQuinn T., Stadel J., 1998, MNRAS, 300, 146}\n\n\\bibitem []{} {Hannestad S., 1999, preprint (astro-ph/9912558)}\n\n\\bibitem []{} {Hern\\'{a}ndez X., Gilmore G., 1998, MNRAS, 294, 595}\n\n\\bibitem []{} {Klypin A., Kravtsov A.V., Valenzuela O., Prada\nF., 1999, ApJ, 522, 82}\n\n\\bibitem []{} {Lake G., Schommer R.A., van Gorkom J.H., 1990, \n AJ, 99, 547}\n\n\\bibitem []{} {Lynden-Bell D., Wood R., 1968, \n MNRAS, 138, 495}\n\n\\bibitem []{} {Martimbeau N., Carignan C., Roy, J.R., 1994, \n AJ, 107, 543}\n\n\\bibitem []{} {Miralda-Escud\\'{e} J., 2000, ApJ, submitted (astro-ph/0002050)}\n\n\\bibitem []{} {Moore B., 1994, Nature, 370, 629 }\n\n\\bibitem []{} {Moore B., Ghigna S., Governato F., Lake G., \nQuinn T., Stadel J., 1999a, ApJ, 524, L19}\n\n\\bibitem []{} {Moore B., Quinn T., Governato F., Stadel J., Lake G., \n 1999b, MNRAS, submitted (astro-ph/9903164)}\n\n\\bibitem []{} {Navarro J., Frenk C.S., White S.D.M., 1997, ApJ, 490, 493}\n\n\\bibitem []{} {Ostriker J.P, 1999, preprint (astro-ph/9912548)}\n\n\\bibitem []{} {Smail I., Ellis R., Fitchett M.J., Edge A.C., 1995,\n MNRAS, 273, 277}\n\n\\bibitem []{} {Schramm D.N., 1992, Nucl. Phys. B. proc suppl. 28A, 243}\n\n\\bibitem []{} {Spergel D.N., Steinhardt P.J., 1999, preprint \n(astro-ph/9909386)}\n\n\\bibitem []{} {Spitzer L., Thuan T. 1972, AJ, 175, 31}\n\n\\bibitem []{} {Tyson J.A., Kochanski G.P., Dell'Antonio I.P., \n 1998, ApJ, 498, L107}\n\n\\bibitem []{} {Wu X.P., Chiueh T., Fang L.Z., Xue Y.J., 1998, \n MNRAS, 301, 861} \n\n\\end{thebibliography}"
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astro-ph0002377
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Quantum corrections to the ground state energy of inhomogeneous neutron matter
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[
{
"author": "Aurel BULGAC $^{1,2}$ and Piotr MAGIERSKI $^{1,3}$"
}
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We estimate the quantum corrections to the ground state energy in neutron matter (which could be termed as well either shell correction energy or Casimir energy) at subnuclear densities, where various types of inhomogeneities (bubbles, rods, plates) are energetically favorable. We show that the magnitude of these energy corrections are comparable to the energy differences between various types of inhomogeneous phases. We discuss the dependence of these corrections on a number of physical parameters (density, filling factor, temperature, lattice distortions).
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[
{
"name": "nm.tex",
"string": "\\documentstyle[aps,prl,twocolumn,epsf]{revtex}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\newcommand{\\beq}{\\begin{equation}}\n\\newcommand{\\eeq}{\\end{equation}}\n\\newcommand{\\bea}{\\begin{eqnarray}}\n\\newcommand{\\eea}{\\end{eqnarray}}\n\\voffset=1.0cm\n\n\\begin{document}\n\n\\title{ Quantum corrections to the ground state energy of\ninhomogeneous neutron matter }\n\n\\author{ Aurel BULGAC $^{1,2}$ and Piotr MAGIERSKI $^{1,3}$}\n\n\\address{ $^1$Department of Physics, University of Washington,\nSeattle, WA 98195--1560, USA }\n\\address{$^2$ Max--Planck--Institut f\\\"ur Kernphysik, Postfach 10 39\n 80, 69029 Heidelberg, GERMANY}\n\\address{$^3$ Institute of Physics, Warsaw University of Technology,\n ul. Koszykowa 75, PL--00662, Warsaw, POLAND }\n\n\n\\date{\\today }\n\n\\maketitle\n\\begin{abstract}\n\nWe estimate the quantum corrections to the ground state\nenergy in neutron matter (which could be termed as well either\nshell correction energy or Casimir energy) at\nsubnuclear densities, where various types of inhomogeneities (bubbles,\nrods, plates) are energetically favorable. We show that the magnitude\nof these energy corrections are comparable to the energy differences\nbetween various types of inhomogeneous phases. We discuss the\ndependence of these corrections on a number of physical parameters\n(density, filling factor, temperature, lattice distortions).\n\n\n\n\\end{abstract}\n\n\n\n{PACS numbers: 21.10.Dr, 21.65.+f, 97.60.Jd}\n% 21.10.Dr -- Binding energies and masses,\n% 21.65.+f -- Nuclear matter\n% 97.60.Jd -- Neutron stars\n\n%----------------------------------------------------------------------\n\\vspace{0.5cm}\n\\narrowtext\n\nThe investigation of the nuclear matter in the neutron star crust\nbelow the saturation density leads to the consideration of exotic\nshapes of the nuclei immersed in a neutron gas. It was realized long\nago \\cite{baym} that when the nuclei in dense matter occupy more than\nhalf of the space it is energetically favorable to ``turn the nuclei\ninside out'' and form a bubble phase \\cite{rav,hash,oya}. To date a\nlarge number of calculations have been performed pertaining to the\nstructure of the neutron star crust. The liquid drop model or the\nThomas--Fermi approximation calculations\n\\cite{lat,wil,las,oya1,lor,pet,wat} predict rather small energy\ndifferences between different phases, of the order of a few\n$keV/fm^{3}.$ (N.B. even though we often refer to energy, we actually\nmean energy density.). Apparently an agreement has been reached\nconcerning the existence of the following chain of phase changes as\nthe density is increasing: nuclei $\\rightarrow$ rods $\\rightarrow$\nplates $\\rightarrow$ tubes $\\rightarrow$ bubbles $\\rightarrow$ uniform\nmatter. The density range for these phase transitions is $0.04 - 0.1\nfm^{-3}$ \\cite{lor,pet}. Moreover, it was established that these\nphases exist up to temperatures of about $10 MeV$ \\cite{lat}. At\ndensities of the order of several nuclear densities the quark degrees\nof freedom get unlocked and the formation of various quark matter\ndroplets embedded in nuclear matter becomes then energetically\nfavorable \\cite{heiselberg}.\n\nThe appearance of different phases is attributed to the interplay\nbetween the Coulomb and surface energies. Since most of the published\nworks were based on the minimization of some density functional in a\nsingle Wigner--Seitz cell, the calculation of the shell correction or\nCasimir energy has been omitted. In Hartree--Fock calculations\n\\cite{negele} these quantum corrections to the ground state energy of\nneutron matter are obviously automatically incorporated. The\nHartree--Fock calculations performed so far were limited to\n``spherical Wigner--Seitz cells'', which is arguably a reasonable\napproximation for the ``nuclei in neutron gas'' phase only. To our\nknowledge there exist only one study on this subject where the shell\neffects due to the bound nucleons only however (mainly protons) have\nbeen taken into account \\cite{oya2}. It was determined that the shell\ncorrection energy is smaller than the energy difference between\ndifferent phases and it was thus concluded that quantum corrections to\nthe ground state energy will not lead to any qualitative changes in\nthe sequence of the nuclear shape transitions in the neutron star\ncrust.\n\n\nOur goal is to reach a comprehensive understanding of the so called\nshell correction or Casimir energy in neutron stars. There is no well\nestablished terminology for the energy corrections we are considering\nhere, even though the problem has been addressed before to some extent\nby other authors. In the case of finite systems, the energy difference\nbetween the true binding energy and the liquid drop energy of a given\nsystem is typically refered to as shell correction energy. In field\ntheory a somewhat similar energy appears, due to various fluctuation\ninduced effects and it is generically referred to as the Casimir\nenergy \\cite{casimir}:\n%----------------------------------------------------------------------\n\\beq\nE_{Casimir} = \\int _{-\\infty }^\\infty d\\varepsilon\n\\varepsilon [g(\\varepsilon ,{\\bf l} )-g_0(\\varepsilon )],\n\\eeq\n%----------------------------------------------------------------------\nwhere $g_0 (\\varepsilon )$ is the density of states per unit volume\nfor the fields in the absence of any objects, $g (\\varepsilon ,{\\bf\nl})$ is the density of states per unit volume in the presence of some\n``foreign''objects, such as plates, spheres, etc., and ${\\bf l}$ is an\nensemble of geometrical parameters describing these objects and their\nrelative geometrical arrangement. A similar formula can be written for\nneutron matter energy\n%----------------------------------------------------------------------\n\\beq\nE_{nm}=\n \\int_{-\\infty}^ \\mu d\\varepsilon\\varepsilon g (\\varepsilon ,{\\bf l})\n-\\int_{-\\infty}^{\\mu _0}d\\varepsilon\\varepsilon g_0(\\varepsilon ,{\\bf l}),\n\\eeq\n%----------------------------------------------------------------------\nwith the notable difference in the upper integration limit. In the\nabove equation $g _0(\\varepsilon , {\\bf l})$ stands for the\nThomas--Fermi or liquid drop density of states of the inhomogeneous\nphase and $g (\\varepsilon ,{\\bf l} )$ for the true quantum density of\nstates in the presence of inhomogeneities. The parameters: $\\mu$ and\n$\\mu _0$ are determined from the requirement that the system has a\ngiven average density\n%----------------------------------------------------------------------\n\\beq\n\\rho =\\int _{-\\infty }^\\mu d\\varepsilon g (\\varepsilon ,{\\bf l} )\n= \\int _{-\\infty }^{\\mu _0} d\\varepsilon g _0(\\varepsilon ,{\\bf l} ).\n\\eeq\n%----------------------------------------------------------------------\nSince in infinite matter the presence of various inhomogeneities does\nnot lead to the formation of discrete levels, one might expect to\nrefer to corresponding energy correction for neutron matter as the\nCasimir energy. In Ref. \\cite{oya2} the authors computed a somewhat\ndifferent quantity however, than the one we are interested in this\nwork, the correction to the ground state energy arising from existence\nof almost discrete levels inside a nucleus in an infinite\nmedium. Strictly speaking these levels are not discrete, but form\nnarrow energy bands due to the tunneling between neighboring\nnuclei. The effects we shall consider here arise from the ``outside''\nstates, which is in complete analogy with the procedure for computing\nthe Casimir energy. As we shall show, these energy corrections,\narising from the existence of these truly delocalized states, are\nlarger than those considered in Ref. \\cite{oya2}. We have considered\nsimilar issues earlier in finite systems and to some extent in\ninfinite 2--dimensional systems as well in Refs. \\cite{bub1,bub2}.\n\nIn order to better appreciate the nature of the problem we are\naddressing in this work, let us consider the following situation. Let\nus imagine that two spherical identical bubbles have been formed in an\notherwise homogeneous neutron matter. For the sake of simplicity, we\nshall assume that the bubbles are completely hollow. We shall\nsidestep the question of stability of each bubble for the moment and\nassume that they are stable and rigid as well. We shall ignore the\nrole of long range forces, namely the Coulomb interaction in the case\nof neutron stars, as their main contribution is to the smooth, liquid\ndrop or Thomas--Fermi part of the total energy. Under such\ncircumstances one can ask the following apparently innocuous question:\n``What determines the most energetically favorable arrangement of the\ntwo bubbles?'' According to a liquid drop model approach (completely\nneglecting for the moment the possible stabilizing role of the Coulomb\nforces) the energy of the system should be insensitive to the relative\npositioning of the two bubbles. A similar question was raised in\ncondensed matter studies, concerning the interaction between two\nimpurities in an electron gas. In the case of two ``weak'' and\npoint--like impurities the dependence of the energy of the system as a\nfunction of the relative distance between the two impurities ${\\bf a}$\nis given by (spin coordinates are not displayed)\n%--------------------------------------------------------------------\n\\begin{equation}\nE({\\bf a})=\\frac{1}{2}\\int d{\\bf r}_{1} \\int d{\\bf r}_{2}\nV_{1}({\\bf r}_{1})\\chi ({\\bf r}_{1}-{\\bf r}_{2}-{\\bf a})V_{2}({\\bf r}_{2}),\n\\end{equation}\n%--------------------------------------------------------------------\nwhere $\\chi ({\\bf r}_{1}-{\\bf r}_{2}-{\\bf a}) $ is the Lindhard\nresponse function of a homogeneous Fermi gas and $V_{1}({\\bf r}_{1})$\nand $V_{2}({\\bf r}_{2})$ are the potentials describing the interaction\nbetween impurities and the surrounding electron gas. At large\ndistances $k_{F}a \\gg 1$ this expression leads to the interaction\nfirst derived by Ruderman and Kittel \\cite{rk,fw}:\n%--------------------------------------------------------------------\n\\begin{equation} \\label{r-k}\nE ({\\bf a}) \\propto \\frac{\\hbar ^2}{2 m k_{F}a^{3}} \\cos (2\nk_{F} a),\n\\end{equation}\n%--------------------------------------------------------------------\nwhere $k_{F}$ is the Fermi wave vector and $m$ is the fermion mass\n%--------------------------------------------------------------------\n\\begin{equation}\n\\mu=\\frac{\\hbar ^2k_F^2}{2 m}.\n\\end{equation}\n%--------------------------------------------------------------------\nThis asymptotic behavior is valid only for point--like impurities,\nwhen $k_{F}R \\ll 1$, and where $R$ stands for the radius of the two\nimpurities. This condition is typically violated for either nuclei\nembedded in a neutron gas or bubbles, when typically $k_FR\\gg 1$. As\nwe shall show, in the case of large ``impurities'' (when $k_FR\\gg 1$)\nthe interaction energy changes in a rather dramatic manner. If one\nreplaces the ``weak'' impurities with ``strong'' point--like\nimpurities, only the magnitude of the interaction changes at large\ndistances, but not the form \\cite{bub2}. The interaction (\\ref{r-k})\nhas a pure quantum character, and any ``noise'' (e.g. temperature)\nleads to a quick disappearance of the oscillatory behavior and with it\nof the power law character, and the regular Debye screening (which is\nexponential in character) sets in instead.\n\nThe lesson one can learn from this analysis however, is that quantum\ncorrections are most likely responsible for the interaction of two\nbubbles/nuclei embedded in a Fermi gas and the form of the interaction\n(\\ref{r-k}) suggests the most natural way to proceed. The argument of\nthe cosine is nothing else but the classical action in units of\n$\\hbar$ of the bouncing periodic orbit between the two impurities.\nThe exact form and magnitude of the coefficient in front of the cosine\ncan be obtained in a semiclassical approximation only after a careful\nestimation of the leading order correction to the leading\nsemiclassical result. Using the 3--dimensional extension of the\nsemiclassical approximation to the so called small disks problem\n\\cite{small}, we were able to obtain a significantly simpler and more\ntransparent derivation of this interaction than the original\nderivation \\cite{fw} as follows. The correction to the\nsingle--particle propagator, which depends on the presence of the two\nweak widely separated point--like impurities ($R/a\\ll 1$ and $k_FR\\ll\n1$) is\n%--------------------------------------------------------------------\n\\begin{eqnarray}\n \\delta G ({\\bf r} , {\\bf r}^\\prime, k) &\\propto &\n G_0({\\bf r} , {\\bf r}_1, k)\n G_0({\\bf r}_1, {\\bf r}_2, k)\n G_0({\\bf r}_2, {\\bf r}^\\prime, k) \\nonumber \\\\\n & + & G_0({\\bf r} , {\\bf r}_2, k)\n G_0({\\bf r}_2, {\\bf r}_1, k)\n G_0({\\bf r}_1, {\\bf r}^\\prime, k),\n\\end{eqnarray}\n%--------------------------------------------------------------------\nwhere\n%--------------------------------------------------------------------\n\\begin{equation}\nG_0({\\bf r}_1, {\\bf r}_2, k)=-\n\\frac{m\\exp ( ik|{\\bf r}_1-{\\bf r}_2|)}{2\\pi\\hbar ^2|{\\bf r}_1-{\\bf r}_2|}\n\\end{equation}\n%--------------------------------------------------------------------\nis the free single--particle propagator. Since only ``periodic\norbits'' contribute to the density of states, the correction to the\ndensity of states, due to the presence of the two impurities and which\ndepends on their relative separation only is given by\n%--------------------------------------------------------------------\n\\begin{equation}\n\\delta g (k,|{\\bf r}_1-{\\bf r}_2| ) \\propto\n{\\mathrm{Im}}\\left [\n\\frac{i\\exp ( 2i|{\\bf r}_1-{\\bf r}_2|)}{k|{\\bf r}_1-{\\bf r}_2|}\n\\right ]\n\\end{equation}\n%--------------------------------------------------------------------\nand the corresponding correction to the ground state energy is given\nby the obvious formula\n%--------------------------------------------------------------------\n\\begin{eqnarray}\n\\delta {\\cal{E}} (|{\\bf r}_1-{\\bf r}_2|)& \\propto &\n\\int _{k\\le k_F} kdk\n \\left ( \\frac{\\hbar ^2 k^2}{2m}-\\mu \\right )\n\\delta g (k,|{\\bf r}_1-{\\bf r}_2| ) \\nonumber \\\\\n& \\propto &\n\\frac{\\cos ( 2k_F|{\\bf r}_1-{\\bf r}_2|)}{|{\\bf r}_1-{\\bf r}_2|^3} .\n\\end{eqnarray}\n%--------------------------------------------------------------------\nOnly the leading term in the limit $|{\\bf r}_1-{\\bf r}_2|\\rightarrow\n\\infty$ is explicitly shown here. The proportionality coefficient is\nnaturally determined by the impurity strength.\n\nThe formation of various inhomogeneities in an otherwise uniform Fermi\ngas can be characterized by several natural dimensionless parameters,\n$k_Fa\\gg 1$, where as above $a$ is a characteristic separation\ndistance between two such inhomogeneities, $k_FR\\gg 1$, where $R$ is a\ncharacteristic size of such an inhomogeneity, and $k_Fs \\approx 1$,\nwhere $s$ is a typical ``skin'' thickness of such objects. The fact\nthat the first two parameters, $k_Fa$ and $k_FR$, are both very large\nmakes a semiclassical approach natural. Since the third parameter,\n$k_Fs$, is never too large or too small, one might be tempted to\ndiscard a semiclassical treatment of the entire problem\naltogether. However, there is a large body of evidence pointing\ntowards the fact that even though this parameter in real systems is of\norder unity, the approximation $k_Fs\\ll 1$, which we shall adopt in\nthis work, is surprisingly accurate \\cite{brack}. Moreover the\ncorrections arising from considering $k_Fs = {\\cal O}(1)$ should lead\nto an overall energy shift mainly, which is largely independent of the\nseparation among various objects embedded in a Fermi gas. On one\nhand, this type of shift can be accounted for in principle in a\ncorrectly implemented liquid drop model or Thomas--Fermi\napproximation. On the other hand, the semiclassical corrections to the\nground state energy arising from the relative arrangement of various\ninhomogeneities have to be computed separately, as they have a\ndifferent physical nature. We are thus lead to the natural assumption\nthat a simple hard--wall potential model for various types of\ninhomogeneities appearing in a neutron Fermi gas is a reasonable\nstarting point to estimate quantum corrections to the ground state\nenergy, see Refs. \\cite{bub1,bub2,brack,caio} and earlier references\ntherein. We shall refer to these quantum corrections to the energy as\nshell effects in the rest of the paper. One might expect that such\nsimplifications will result in an overestimation of the magnitude of\nshell effects, but the qualitative pattern should remain the same.\n\nWe shall consider spherical bubble--like, rod--like and plate--like\nphases only here and we shall estimate the shell correction or Casimir\nenergy arising due to a regular arrangement of such inhomogeneities in\nan otherwise homogeneous neutron gas. One can distinguish two types of\n``bubbles'': {\\it i)} nuclei--like structures embedded in a neutron\ngas and {\\it ii)} void--like structures. By voids we mean the regions\nin which the nuclear density is significantly lower than in the\nsurrounding space. In the first case {\\it i)}, the single particle\nwave functions can be separated into roughly two classes, those\nlocalized mostly inside the nuclei--like structures and those which\nare completely delocalized. A fermion in a delocalized state will\nspend some time inside the ``nuclei'' too, but since the potential\nexperienced by a nucleon is deeper there, the local momentum is larger\nand thus the relative time and relative probability to find a nucleon\nin this region is smaller. One can approximately replace then the\n``nuclei'' with an effective repulsive potential of roughly the same\nshape. In the case of a ``bubble'', when the probability to find a\nnucleon inside a ``bubble'' is reduced, again such an approximation\nappears as reasonable. The ``nuclei'' and ``bubbles'' we are refering\nto here, are not necessarily spherical, but could have the shape of a\nrod or plate as well. There are of course a number of ``resonant''\ndelocalized states, whose amplitude behaves in a manner just opposite\nto the one we have described here. However, the number of such\n``resonant'' states is typically small and we thus do not expect large\neffects due to them. Moreover, since such states are concentrated\nmostly inside a ``nucleus'' or a ``bubble'' one does not expect them\nto affect in a major way the relative positioning of two ``nuclei'' or\ntwo ``bubbles''. Nevertheless, these are some issues, which certainly\ndeserve more scrutiny in the future, even though we hardly expect that\na more comprehensive analysis will lead to qualitative changes of our\nconclusions. In all these phases the shell effects depend on the\nstructure and stability of periodic orbits in the system\n\\cite{brack}. Except for the plate--like nuclei phase, where the shell\nenergy can be computed exactly, for other geometries one should\ncalculate the contribution from all periodic orbits. This is rather\ntedious task, since they proliferate exponentially as a function of\ntheir length \\cite{pri}, and moreover this is not really necessary to\nperform. If one is interested in the gross structure only of the shell\neffects, the contribution of the shortest periodic orbits should\nsuffice for defining the gross shell structure. (We remind the reader,\nin an infinite medium there are really no shells as in a finite\nsystem, but we refer to the corresponding effects in this manner only,\ndue to their similar origin because of the appearance of periodic\norbits.) Since the contribution of any given periodic orbit leads to\nan oscillatory contribution to the density of states any suitably chosen\nenergy averaging over the spectrum, and in particular\na finite temperature as well, will leave only the contributions due to\nthe shortest periodic orbits. Since a periodic orbit of length\n${\\cal{L}}$ will lead to detail on an energy scale of the order\n$\\Delta E = \\hbar^2 \\pi^2/2m{\\cal{L}}^2$, performing an averaging over\nan energy interval $\\Delta E $ will effectively mask the contribution\nof orbits of length ${\\cal{L}}$ or larger. Moreover, since the\ngeometry of the rod--like and spherical phases admit only unstable\n(hyperbolic) orbits, the longer the orbits, the lesser their\ncontribution is, due their decreased stability.\n\nThe simplest system consist of plate--like nuclei with the neutron gas\nfilling the space between slabs. The shell energy for this system per\nunit volume can be easily evaluated:\n%--------------------------------------------------------------------\n\\begin{eqnarray}\n\\frac{E_{shell}}{L^3}&=&\\frac{E - E_{Weyl} + \\Delta E}{L^{3}}, \\\\\n\\Delta E &=& -\\mu ( \\rho_{0} -\n \\rho_{Weyl} )L^3\n\\nonumber \\end{eqnarray}\n%--------------------------------------------------------------------\nwhere\nthe exact and the Weyl (smooth) energy \\cite{brack,hilf} per unit\nvolume are given by\n%--------------------------------------------------------------------\n\\begin{eqnarray}\n \\frac{E}{L^3}&=&\\frac{2}{L^3}\\frac{\\hbar^{2}}{2 m a^{2}}\n\\frac{\\pi^{3} }{2}\\left ( \\frac{L}{a}\\right ) ^{2}\n\\Bigg{[}\\frac{1}{4} \\left ( \\frac{k_{F} a}{\\pi} \\right\n )^{4} N \\\\ \\nonumber\n&- &\\frac{N(N+1)(2N+1)(3N^{2}+3N-1)}{120} \\Bigg{]}, \\\\\n\\frac{E_{Weyl}}{L^{3}}&= &\\frac{2}{L^3}\n\\frac{\\hbar^{2}}{2 m a^{2}}\n\\frac{\\pi^{3} }{2}\\left ( \\frac{L}{a}\\right ) ^{2}\n\\Bigg{[}\\frac{1}{5} \\left ( \\frac{k_{F} a}{\\pi} \\right ) ^{5}\n\\nonumber \\\\\n&-&\\frac{1}{8} \\left ( \\frac{k_{F} a}{\\pi} \\right ) ^{4} \\Bigg{]}\n\\end{eqnarray}\n%--------------------------------------------------------------------\nIn the above formula\n%--------------------------------------------------------------------\n\\begin{equation}\nN={\\mathrm {Int}}\\left [ \\frac{ k_{F} a}{\\pi} \\right ]\n\\end{equation}\n%--------------------------------------------------------------------\nstands for the integer part of the argument in the square brackets,\nand $a=L - 2 R$ is the distance between slabs and $R$ is the half of\nthe width of the slab. Here $L^3$ is the volume of an elementary\n(cubic) cell and the factor $'2'$ in front stands for the two spin\nstates. The average matter density (the number of neutrons per unit\nvolume) $\\rho _0$ and the smoothed density $\\rho_{Weyl}$ are\ndetermined by relations\n%--------------------------------------------------------------------\n\\begin{eqnarray}\n& &\\rho_0= 2\\sum _{n=1}^\\infty \\int \\frac{d^2k}{(2\\pi )^2}\\Theta\n\\left ( \\mu -\\frac{\\hbar^2k^2}{2m}-\n\\frac{\\hbar ^2n^2\\pi^2}{2ma^2}\\right ) \\\\\n& &= \\frac{2}{L^3}\\frac{\\pi}{4}\n\\left ( \\frac{L}{a} \\right )^{2}\n\\left [ \\left ( \\frac{k_{F} a}{\\pi} \\right )^{2} N\n-\\frac{N(N+1)(2N+1)}{6} \\right ] . \\nonumber \\\\\n& &\\rho_{Weyl} = \\frac{2}{L^{3}}\\frac{\\pi}{2}\\left ( \\frac{L}{a} \\right )^2\n\\Bigg{[} \\frac{1}{3}\\left ( \\frac{k_{F}a}{\\pi} \\right )^3 -\n\\frac{1}{4}\\left ( \\frac{k_{F}a}{\\pi} \\right )^2 \\Bigg{]} \\nonumber .\n\\end{eqnarray}\n%--------------------------------------------------------------------\nUsing these formulas one can show that the shell correction\nenergy has the behavior\n%----------------------------------------------------------------------\n\\beq\n\\frac{E_{shell}}{L^3}= \\frac{\\hbar^2k_{F}^{2}}{40 a^2L m}\nG\\left ( \\frac{k_Fa}{\\pi} \\right ),\n\\eeq\n%----------------------------------------------------------------------\nwhere $G(x)$ is an approximate periodic function of its argument, for\n$x\\ge 1$), $G(x+1)\\approx G(x)$, with properties $G(x=n/2)\\approx 0$\nand approximately $-1\\le G(x)\\le 1$. Furthermore\n%----------------------------------------------------------------------\n\\begin{equation}\n\\rho _{out} = \\frac{\\rho_0}{v}\n\\end{equation}\n%----------------------------------------------------------------------\nis the actual density of the neutron gas between the two slabs and\n%----------------------------------------------------------------------\n\\begin{equation}\nv=1-u=\\frac{L-2R}{L}\n\\end{equation}\n%----------------------------------------------------------------------\n\n\n\\noindent is the filling factor, which is the ratio of the occupied\nvolume to the volume of the cell. One can show also that\n%----------------------------------------------------------------------\n\\begin{equation}\n\\rho _0 = \\rho _{Weyl} + \\frac{k_F}{12La}F\\left\n (\\frac{k_fa}{\\pi}\\right) ,\n\\end{equation}\n%----------------------------------------------------------------------\nwhere $\\rho _{Weyl}$ is the Weyl approximation to the\ndensity and $F(x+1)\\approx F(x)$ is an approximate periodic function\nof its argument too, for $x\\ge 1$, with properties $-1\\le F(x)\\le 0.5$\nand $F(x=n)=-1$. This periodicity leads to the clear pattern of\n``valleys'' ($k_Fa =(n+3/4)\\pi$) and ``ridges'' ($k_Fa \\approx\n(n+1/4)\\pi$) in the profile of the shell energy shown in\nFig. 1a. These features of the energy and density are naturally\nrelated to fact that these quantities are almost periodic functions in\nthe classical action along the only periodic orbit in the system,\ni.e. in the variable $S=2k_Fa$.\n\n\nIn the case of rod--like and spherical voids we shall use the\nsemiclassical theory in order to compute the shell energy. Since we\nare interested only in the ``gross shell structure'' we have to take\ninto account a few of the shortest periodic orbits among the nearest\nneighbors only. The lengths of the shortest periodic orbits depend on\nthe lattice type. In the following we will assume the simple cubic\nand simple square lattices for spherical and rod--like phases\nrespectively. The expression for the shell energy density and the\nneutron density reads:\n%--------------------------------------------------------------------\n\\begin{eqnarray}\n\\frac{E_{shell}}{L^{3}} &=&\n\\frac{1}{L^{3}}\n\\int_{0}^{\\mu} (\\varepsilon - \\mu) \\sum_{i}\ng_{shell}(\\varepsilon, L_{i})d\\varepsilon \\\\\n\\rho_0 &=&\n\\frac{1}{L^{3}}\n\\int_{0}^{\\mu}\\left [ g_{Weyl}(\\varepsilon ) +\n\\sum_{i} g_{shell}(\\varepsilon, L_{i})\\right ] d\\varepsilon ,\n\\end{eqnarray}\n%--------------------------------------------------------------------\nwhere $g_{shell}(\\varepsilon , L_i )$ denotes the contribution to the\nlevel density due to the orbit $L_i $ and $g_{Weyl}$ is the smooth\nlevel density determined using the Weyl prescription \\cite{hilf}.\n\nFor the rod--like phase we took into account four orbits of the length\n$2L_{1}=2(L-2R)$ and four orbits of the length\n$2L_{2}=2(L\\sqrt{2}-2R)$. Introducing longer orbits did not lead to\nnoticeable changes in the patterns presented here. Hence the shell\nenergy per volume is equal to:\n%--------------------------------------------------------------------\n\\begin{equation}\n\\frac{E_{shell}}{L^3}=\\frac{1}{L^{3}}\\int_{0}^{\\mu} (\\varepsilon- \\mu)\n\\sum _{i=1}^2 A_ig_{shell}(\\varepsilon ,L_i) d\\varepsilon ,\n\\end{equation}\n%--------------------------------------------------------------------\nwhere $A_1=A_2=4$ and the chemical potential $\\mu$ is determined by\nthe condition:\n%--------------------------------------------------------------------\n\\begin{equation}\n\\rho_0=\\rho _{Weyl}+ \\frac{1}{L^3}\\int_{0}^{\\mu}\n\\sum _{i=1}^2A_i g_{shell}(\\varepsilon ,L_i)\nd\\varepsilon.\n\\end{equation}\n%--------------------------------------------------------------------\nA periodic orbit of the type considered by us gives actually a\ncontribution with a factor 1/2, since only half of it belongs to a\nparticular elementary cell. Because there are two spin states, and\nthus eight orbits in total, each type of orbit eventually is weighted\nby four. The density of states was evaluated using the convolution of\nthe exact 1--dimensional density of states and the density of states\ngiven by Gutzwiller trace formula for the 2--dimensional system of\ndisks, which is the cross section of the rod--like system we are\ninterested in. In some cases such a procedure can lead to spurious\ncontributions, which are however rather easy to single out, see\nRefs. \\cite{niall}. For a given periodic orbit of length $2L_i$, the\nshell correction to the density of states is given by the following\nexpression:\n%--------------------------------------------------------------------\n\\begin{eqnarray} \\label{corg}\n& & g_{shell}(\\varepsilon ,L_i)=\\frac{m L L_{i}}{2\\pi \\hbar^{2} }\n\\sum_{n=1}^\\infty\n\\frac{\\mbox{J}_0(2nkL_i)}{\\sinh{n\\kappa_i}}, \n\\end{eqnarray}\n%--------------------------------------------------------------------\nwhere the summation is over repetitions of this orbit and\n%--------------------------------------------------------------------\n\\begin{equation}\n\\varepsilon = \\frac{\\hbar ^2 k^2}{2 m}.\n\\end{equation}\n%--------------------------------------------------------------------\nWhen one is interested in the gross shell structure then the\ncontribution of long orbits as well as the contributions due to\nrepetitions of short primitive orbits vanish under energy averaging.\n\n\n\nThe explicit form of the shell energy and of the fluctuating part\nof the density reads:\n%--------------------------------------------------------------------\n\\begin{eqnarray} \\label{core}\n& &\\frac{E_{shell}}{L^3}=\n-\\frac{1}{L^3}\\frac{\\hbar^2k_F^2}{2m\\pi}\\frac{1}{4}\n\\sum_{i=1}^2A_i \\frac{L}{L_i} \\sum_{n=1}^\\infty\n\\frac{{\\mbox{J}}_2(2nk_FL_i)}{n^2\\sinh(n\\kappa_i)}, \\\\\n& &\\rho_0=\\rho_{Weyl}\n +\\frac{k_F}{4\\pi L^2} \\sum_{i=1}^2 A_i\n\\sum_{n=1}^{\\infty}\n\\frac{{\\mbox{J}}_1(2nk_FL_i)}{n\\sinh(n\\kappa_i)}.\n\\end{eqnarray}\n%--------------------------------------------------------------------\nThe parameter $\\kappa_{i}$ determines the stability of the orbit\n$L_{i}$:\n%--------------------------------------------------------------------\n\\begin{equation}\n\\kappa_i =\n\\ln \\left [ 1 +\\frac{L_i }{R} +\n\\sqrt{ \\frac{L_i }{R}\\left ( \\frac{L_i }{R}+2 \\right ) } \\right ] .\n\\end{equation}\n%--------------------------------------------------------------------\n\n\n\\noindent The shell energy as a function of the anti--filling factor\n(relative void volume) $u=\\displaystyle{\\frac{\\pi R^2}{L^2}}$ and\n$\\rho_0$ is shown in Fig 1b. The shell energy has a smaller\namplitude then in the case of the plate--like phase. This comes about\nbecause the periodic orbits are now hyperbolic in the plane\nperpendicular to the rods. Note however that the pattern of\n``valleys'' and ``ridges'' looks very similar to the one for the\nslabs. This is because the main contribution due to the classical\norbit of length $2L_{1}$ is the same. There are small interference\neffects caused by the orbit of length $2L_{2}$ however. Since it is\nlonger, this second trajectory contributes with a smaller weight.\n\nFor the case of spherical voids there are $26$ periodic orbits between\nnearest neighbors of three different lengths $2L_{1}=2(L-2R)$,\n$2L_{2}=2(L\\sqrt{2}-R)$ and $2L_{3}=2(L\\sqrt{3}-R)$. Thus the shell\nenergy and density are equal to:\n%--------------------------------------------------------------------\n\\begin{eqnarray}\n\\frac{E_{shell}}{L^3}&=&\\frac{1}{L^{3}}\\int_{0}^{\\mu}(\\varepsilon- \\mu )\n\\sum _{i=1}^3 A_i g_{shell}(\\varepsilon ,L_i)\nd\\varepsilon , \\\\\n\\rho_0&=&\\rho_{Weyl} + \\frac{1}{L^3}\\int_{0}^{\\mu}\n\\sum _{i=1}^3 A_i g_{shell}(\\varepsilon ,L_i)\nd\\varepsilon .\n\\end{eqnarray}\n%--------------------------------------------------------------------\n\n\\noindent The contribution due to one periodic orbit to the\nfluctuating part of the level density reads:\n%--------------------------------------------------------------------\n\\begin{equation}\ng_{shell}(\\varepsilon ,L_i )=\\frac{m L_{i}}{2\\pi\\hbar^2 k}\\sum_{n=1}^{\\infty}\n\\frac{\\cos(2 n k L_{i})}{\\sinh^{2}(n\\kappa_{i})}.\n\\end{equation}\n%--------------------------------------------------------------------\nHence we get:\n%--------------------------------------------------------------------\n\\begin{eqnarray}\n& &\\frac{E_{shell}}{L^{3}}=\\frac{1}{L^{3}}\n\\frac{\\hbar^{2}k_F^2}{2m}\\sum_{i=1}^{3}\n\\frac{A_i}{8\\pi (k_F L_{i})^2} \\times \\\\\n& &\\sum_{n=1}^{\\infty}\n\\frac{ [ 2 n k_{F} L_{i}\n \\cos (2 n k_{F} L_{i}) -\n \\sin (2 n k_{F} L_{i}) ]}\n{n^{3} \\sinh ^{2}(n\\kappa_{i} )}, \\nonumber \\\\\n& &\\rho_0=\\rho_{Weyl}+\n\\frac{1}{L^3}\\frac{1}{4\\pi}\n\\sum_{i=1}^{3} A_{i}\n\\sum_{n=1}^{\\infty}\\frac{\\sin(2 n k_{F} L_{i} )}\n{n \\sinh ^{2}(n\\kappa_{i} )},\n\\end{eqnarray}\n%--------------------------------------------------------------------\nwhere $A_{1}=6, A_{2}=12, A_{3}=8$ respectively. The shell energy for\nthe spherical phase is shown in Fig 1c. In this case the\nanti--filling factor is given by $u=\n\\displaystyle{\\frac{4}{3}\\frac{\\pi R^3}{L^{3}}}$. A stronger\ninterference pattern due to the orbits $L_2$ and $L_3$ can be\nseen. The amplitude of the shell effects is also lower due to the\ngreater instability of the orbit on one hand, and due to the smaller\nrelative volume of the scatterers on the other hand.\n\n\n\nIn a similar manner one can obtain the interaction energy between two\nisolated bubbles at large separations ($a=L-2R\\gg R$)\n%----------------------------------------------------------------------\n\\beq\nE_{\\circ \\circ} \\approx \\frac{\\hbar ^2 k_{F} R^2}{8 \\pi m}\n\\frac{\\cos (2k_F a)}{a ^3} .\n\\eeq\n%----------------------------------------------------------------------\nWhen compared with the interaction (\\ref{r-k}) one observes a similar\nbehaviour, even though now the two ``impurities'' are large $k_FR\\gg\n1$. It can be shown however that if one computes instead the same\nenergy for fixed chemical potential, instead of particle number as was\ndone here, the bubble--bubble interaction will decay inversely\nproportional to the square of the separation \\cite{andreas}. \nIn a recent paper\n\\cite{spruch} the Casimir energy for similar arrangements has been\ncalculated using the semiclassical approximation. In the case of\nCasimir energy the situation is somewhat simple, since instead of two\nindependent dimensionless parameters, $k_FR$ and $k_FL$, only one\ndimensionless parameter exists, $R/L$. Thus the Casimir energy for two\nspheres has naturally the form\n%----------------------------------------------------------------------\n\\beq\nE^{Cas}_{\\circ \\circ}= \\frac{\\hbar c}{L} F\\left ( \\frac{R}{L}\\right ),\n\\eeq\n%----------------------------------------------------------------------\nwith an unknown function $F(x)$. A similar, but much stronger result\ncan be obtained for the critical Casimir energy \\cite{cas}, where one\ncan show that the theory is conformal invariant. The authors of\nRefs. \\cite{spruch} provide also a very compelling argument why the\nsemiclassical approximation should be particularly accurate for the\ncalculation of the Casimir energy in case of ideal metallic boundaries\nand they show that using only the single periodic orbit the Casimir\nenergy for two spheres is given by\n%----------------------------------------------------------------------\n\\beq\nE^{Cas}_{\\circ \\circ}= -\\frac{\\pi ^3 \\hbar cR}{720L^2} ,\n\\eeq\n%----------------------------------------------------------------------\nand dismiss this result as being valid for large separations, since it\ncontradicts their expectations that it should agree with the\nCasimir--Polder interaction \\cite{CP}\n%----------------------------------------------------------------------\n\\beq\nE^{CP}_{\\circ \\circ}\\propto -\\frac{\\hbar c R^6}{L^7} .\n\\eeq\n%----------------------------------------------------------------------\nThe authors of Ref. \\cite{spruch} argue that the contributions arising\nfrom the diffractive paths discussed in Refs. \\cite{wirzba}, should\neventually lead to additional contributions, which will cancel exactly\nthis longer range interaction and in the end, the authors hope that\nthe Casimir--Polder result will be retrieved. The difference between\nthese two results for the Casimir energy is very similar to the\ndifference between the interaction (\\ref{r-k}) between two point--like\nimpurities ($k_FR\\ll 1$) and the interaction between two ``fat''\nbubbles ($k_FR\\gg 1$) \\cite{andreas}. In the case of\n``fat'' bubbles, the contribution of diffractive orbits are\nexponentially small ($\\propto \\exp (-\\alpha k_FR )$, where $\\alpha$ is\nof order unity) \\cite{wirzba}, as one would naturally expect in the\ncase when rays are a very good approximation to the wave\nphenomena. The resolution of this apparent conundrum lies in resolving\nthe clear clash of limits. When the size of the scatterer $R$\ndecreases the contribution of the diffractive paths (creeping orbits)\nincreases and an increasingly larger number of them contribute\nsignificantly to the scattering and thus to the propagator. In the\nlimit $k_F R\\rightarrow 0$ the standard geometric orbit approach has\nto be modified, see Ref. \\cite{small} and our discussion around\nEqs. (7--10). It is notable that in the case of the critical Casimir\neffect, even longer range interactions ($\\propto 1/a^{1+\\epsilon}$,\nwith very small $\\epsilon$) between two spheres are possible\n\\cite{cas}.\n\nThe structure of the shell energies shown in the Fig. 1 indicates the\nexistence of the optimal void sizes (with respect to the shell\neffects) for a given outside nucleon density. Note that for all\nphases and for $\\rho_0>0.05 fm^{-3}$ the shell energy exhibits a\nremarkable softness toward adding additional neutrons to the system\n(the ``valleys'' and ``ridges'' are almost horizontal in the Fig. 1).\nHence one can conclude that once the size of the voids have been\ndetermined by minimization of the total energy of the system, an\nincrease in the number of neutrons outside the voids will not affect\nmuch the shell energy of the system. However, the surface energy will\nbe affected.\n\nIn the Fig. 2 we show the shell energies as a function of $\\rho_0$\nfor the optimal filling factors and nuclear radii determined in\nRef. \\cite{oya1}. One can see that the amplitudes of the shell\nenergies in the region $\\rho_0 \\approx 0.04-0.07 $ are of the order of\n$10 keV/fm^{3}$, $3 keV/fm^{3}$ and $0.05 keV/fm^{3}$ for\nplate--like, rod--like and bubble--like phases, respectively. There\nare usually one or two shallow shell energy minima for the density\nrange $\\rho_0>0.03 fm^{-3}$. The minima are more pronounced in the\ncase of spherical bubble--like phase mainly due to the stronger\ninterference effects caused by longer orbits.\n\n\nOnce a phase is formed there is a positional order maintained by the\nCoulomb repulsion between spherical nuclei, rods or slabs\n\\cite{rav,hash,oya,wil,las,lor}. Although the Coulomb energy is a\nsmooth function of the void displacement \\cite{pet1}, the shell energy\nis not. Since several different orbits contribute to the shell\neffects (except for slab--like phase) the displacement of a single\nbubble--like or rod--like void from its equilibrium position in the\nlattice will give rise to the interference effects. The interference\npattern will depend on the type lattice. For the simple cubic and\nsimple square lattices for spherical nuclei and rods, respectively, we\nshow in the Fig. 3 the changes in the energy due to such ``defects''.\nFor the plate--like system there is only one direction of displacement\n(we do not consider the shear mode) denoted by $x$ perpendicular to\nthe slab (Fig. 3a). Since the rod--like phase is a two-dimensional\nsystem, in the Fig 3b we have shown the shell energy as a function of\ntwo perpendicular displacements $x$ and $y$. They are perpendicular\nto the rods and point in the direction of the nearest neighbor. The\nsame axes have been chosen for the spherical system although it will\nnot exhaust all possible directions in the system. The behavior of\nthe shell energy in this case is shown in Fig 3c.\n\nThe structure of the shell energy surface as a function of a\ndisplacement depends on the lengths of the shortest periodic orbits.\nExcept for the trivial plate--like phase, in the rod--like and\nspherical phase there exist directions into which is easier to locally\ndeform the lattice.\n\n\n\nIn Fig. 4 we show the pattern of the energy changes induced by\ndeforming the rod--like lattice. We considered only volume conserving\ndeformations. The square lattice was stretched by a factor $\\alpha $\nin the $x$--direction, by a factor $\\beta $ in the $y$--direction and\nalso the angle between the two axes has been changed to $\\gamma$. In\norder to preserve the volume all these three parameters should satisfy\nthe condition\n%--------------------------------------------------------------------\n\\beq\n\\alpha \\beta \\sin \\gamma =1.\n\\eeq\n%--------------------------------------------------------------------\nThe case $\\alpha =\\beta$ and \n$\\gamma = \\pi /3$ correspond to a perfect triangular lattice.\n\n\n\nIncreasing the temperature will weaken the shell effects. At\nsufficiently high temperatures the nuclear lattice will disappear. At\nsmaller temperatures however, when the lattice can be regarded as\nfrozen, the rise of the temperature will affect mainly shell effects\nin the neutron gas. In order to wash out completely the shell effects\nthe temperature $T$ should be of the order of half of the\ndistance between shells The spacing between two consecutive shells is\ndetermined by the length of the shortest orbit, $a = L-2R$. Thus the\nenergy distance between shells can be determined from the requirement:\n$2 k a = 2\\pi$ and is given by the expression:\n%--------------------------------------------------------------------\n\\begin{equation}\n\\Delta E = \\frac{\\hbar^{2}\\pi^2}{2m (L-2R)^2}.\n\\end{equation}\n%--------------------------------------------------------------------\nFor the optimal filling factors and lattice constants\nof various phases obtained in Ref. \\cite{oya1}\none obtains the following estimates for the critical temperature:\n%--------------------------------------------------------------------\n\\begin{eqnarray}\nT_{c} &\\approx& 32 MeV \\mbox{ for plate--like system}, \\nonumber \\\\\nT_{c} &\\approx& 19 MeV \\mbox{ for rod--like system}, \\\\\nT_{c} &\\approx& 12 MeV \\mbox{ for spherical system}. \\nonumber\n\\end{eqnarray}\n%--------------------------------------------------------------------\n\n\nAn accurate description of the shell effects as a function of the\ntemperature can be obtained using the temperature averaged level\ndensity \\cite{brack,kol}:\n%--------------------------------------------------------------------\n\\begin{equation}\ng_{shell}(\\varepsilon , T)=\n\\sum_{p.o.}\\frac{A_i\\tau_{i,n}(T)}{\\sinh\\tau_{i,n}(T)}\ng_{shell}(\\varepsilon ,L_i),\n\\end{equation}\n%--------------------------------------------------------------------\nwhere the sum is taken over all periodic orbits including the number\nof repetitions $n$ of the orbit and\n%--------------------------------------------------------------------\n\\begin{equation}\n\\tau_{i,n}=\\displaystyle{\\frac{2 \\pi T m n L_{i}}{\\hbar^2 k}}.\n\\end{equation}\n%--------------------------------------------------------------------\n\nConsequently the oscillating part of the free energy density is given by the\nformula:\n%--------------------------------------------------------------------\n\\begin{equation}\n\\frac{F_{shell}}{L^3} = \\frac{1}{L^{3}}\\int_{0}^{\\mu}(\\varepsilon - \\mu\n)g_{shell}(\\varepsilon ,T)\n d\\varepsilon .\n\\end{equation}\n%--------------------------------------------------------------------\nThe estimates for different phases are shown in Fig. 5. For simplicity\nwe have retained in these calculations the value of the Fermi momentum\n$k_F$ equal to its zero temperature limit, and therefore the neutron\nmatter density is not temperature independent in these figures. One\ncan see that thermal effects will wash out the shell correction energy\nat temperatures of the order of 10 MeV and higher.\n\nNow at the end of this analysis we suspect that there are a lot of\nother effects, which might be relevant. We did not consider periodic\norbits bouncing between three or more objects. An orbit bouncing\nbetween two bodies leads to a pairwise interaction. Orbits bouncing\nbetween three or more bodies would lead to genuine many body\ninteractions. We have also considered only perfectly smooth\nobjects. If one allows for some degree of corrugation of these\nsurfaces, many more periodic orbits are likely to appear and that\nwould lead to even more complicated interactions and more complicated\ninterference patterns. The fact that corrugation can influence in a\nsignificant, perhaps major way, the Casimir energy, has already been\npredicted and measured experimentally \\cite{corrugation}. The long\nrange character of the interaction together with its oscillatory\nnature could very easily be at the origin of disorder, even at zero\ntemperature. At finite temperature disorder is more likely to occur,\ndue to entropic effects \\cite{bub1,bub2}. We did not consider here\nthe role of pairing, which we expect however to lead to a certain\nflattening of the shell effects \\cite{bub1,bub2}, which, however,\nshould not be interpreted as disappearance of shell effects.\nEspecially at subnuclear densities neutron pairing should be rather\nstrong \\cite{pairing}. A completely different type of softness of\nthese structures has been argued in Ref. \\cite{pet1}, according to\nwhich the mantles of neutron stars resembles more liquid crystals than\nsolids.\n\n\nIn the paper we have studied the shell effects in the neutron medium\nfilled by different nuclear phases. To our knowledge this is the\nfirst approach which considers specifically the shell effects in the\noutside neutron gas and we aimed at discussing its basic features.\nEven though in principle Hartree--Fock calculations include in\nprinciple such effects already, the calculations performed so far\n\\cite{negele} were too narrow in scope and did not address this issue\nspecifically. Using semiclassical methods, we have analyzed the\nstructure of the shell energy as a function of the density, filling\nfactor, lattice distortions and temperature. We expect that our\nresult overestimate somewhat the amplitude of the shell\neffects. However, the emerging qualitative overall picture should\nremain valid and further microscopic studies are highly desirable. The\nmain lesson one should remember from this work is that the amplitude\nof the shell energy effects is comparable with the energy differences\nbetween various phases determined in simpler liquid drop type models.\nThe magnitude of the quantum corrections to the ground state energy of\nthe inhomogeneous neutron matter we have found is significantly larger\nthan that determined in Ref.\\cite{oya2}. The analysis of\nRef.\\cite{oya2} was limited however to the motion of nucleons inside\nnuclei embedded in a lower density neutron gas.\n\nOur results suggest that the inhomogeneous phase has perhaps an\nextremely complicated structure, maybe even completely disordered,\nwith several types of shapes present at the same time.\n\nThe DOE financial support is gratefully acknowledged. This research\nwas supported in part by the Polish Committee\n for Scientific Research (KBN) under Contract No. 2 P03B 040 14. AB\nthanks N.D. Whelan, O. Agam, T. Guhr and S.C. Creagh for discussions\nand correspondence concerning various aspects of the semiclassical\napproximation. PM thanks the Nuclear Theory Group for hosting his\nvisit in Seattle. AB thanks the members of the Nuclear Theory Group at\nthe Institute of Theoretical Physics in Warsaw for their\nhospitality. And last but not least, AB thanks W.A. Weidenm\\\"uller for\nbeing such a gracious host.\n\n\n\\begin{thebibliography}{99}\n\n\\bibitem{baym} G. Baym {\\it et al.}, Nucl. Phys.\n{\\bf A175}, 225 (1971).\n\n\\bibitem{rav} D.G. Ravenhall {\\it et al.},\nPhys. Rev. Lett. {\\bf 50}, 2066 (1983).\n\n\\bibitem{hash} M. Hashimoto {\\it et al.}, Prog. Theor. Phys.\n{\\bf 71}, 320 (1984).\n\n\\bibitem{oya} K. Oyamatsu {\\it et al.}, Prog. Theor. Phys.\n{\\bf 72}, 373 (1984).\n\n\\bibitem{lat} J.M. Lattimer {\\it et al.},\nNucl. Phys. {\\bf A432}, 646 (1985).\n\n\\bibitem{wil} R.D. Wilson and S.E. Koonin, Nucl. Phys. {\\bf A435}, 844\n(1985).\n\n\\bibitem{las} M. Lassaut {\\it et al.},\nAstron. Astrophys. {\\bf 183}, L3 (1987).\n\n\\bibitem{oya1} K. Oyamatsu, Nucl. Phys. {\\bf A561}, 431 (1993).\n\n\\bibitem{lor} C.P. Lorenz {\\it et al.},\nPhys. Rev. Lett. {\\bf 70}, 379 (1993).\n\n\\bibitem{pet} C.J. Pethick and D.G. Ravenhall, Annu. Rev. Nucl. Part. Sci.\n{\\bf 45}, 429 (1995).\n\n\\bibitem{wat} G. Watanabe {\\it et al.}, see Los Alamos e--print\narchive astro--ph/0001273.\n\n\\bibitem{heiselberg} H. Heiselberg {\\it et al.}, Phys. Rev. Lett.\n{\\bf 70}, 1355 (1992).\n\n\\bibitem{negele} J.W. Negele and D. Vautherin, Nucl. Phys. {\\bf A207},\n 298 (1973); P. Bonche and D. Vautherin, Nucl. Phys. {\\bf A372}, 496\n (1981); Astron. Astrophys. {\\bf 112}, 268 (1982).\n\n\\bibitem{oya2} K. Oyamatsu, M. Yamada, Nucl. Phys. {\\bf A578}, 181 (1994).\n\n\\bibitem{casimir} M. Kardar and R. Golestanian, Rev. Mod. Phys. {\\bf\n 71}, 1233 (1999) and references therein.\n\n\\bibitem{bub1} Y. Yu {\\it et al.}, Phys. Rev. Lett. {\\bf 84}, 412 (2000).\n\n\\bibitem{bub2} A. Bulgac {\\it et al.}, in {\\it Proc. Intern. Work. on\nCollective excitations in Fermi and Bose systems}, eds. C.A. Bertulani\nand M.S. Hussein (World Scientific, Singapore 1999), pp 44--61 and\nLos Alamos e--preprint archive, nucl--th/9811028.\n\n\\bibitem{rk} M.A. Ruderman, C. Kittel, Phys. Rev. {\\bf 96}, 99 (1954).\n\n\\bibitem{fw} A.L. Fetter and J.D. Walecka, {\\it Quantum Theory of Many\n Particle Systems}, (McGraw--Hill, New York, 1971).\n\n\\bibitem{small} P.E. Rosenqvist {\\it et al.}, J. Phys. {\\bf A 29},\n 5441 (1996).\n\n\\bibitem{brack} M. Brack, R.K. Bhaduri, {\\em Semiclassical Physics},\nAddison Wesley Publishing Company, Inc. (1997).\n\n\\bibitem{caio}\nA. Bulgac and C. Lewenkopf, Phys. Rev. Lett. {\\bf 71}, 4130 (1993).\n\n\\bibitem{pri} H. Primack and Uzy Smilansky, Phys. Rev. Lett. {\\bf 74},\n 4831 (1995); Phys. Rep. {\\bf 327}, 1 (2000).\n\n\\bibitem{hilf} R.T. Waechter, Proc. Camb. Phil. Soc. {\\bf 72}, 439\n(1972); H.P. Baltes and E.R. Hilf, {\\it Spectra of Finite Systems},\nWissenschaftsverlag, Mannheim, Wien, Z\\\"urich: Bibliographisches\nInstitut, (1976).\n\n\\bibitem{niall} J. Sakhr and N.D. Whelan, see Los Alamos e--preprint\narchive nlin.CD/0001051; R.K. Bhaduri {\\it et al.}, Phys. Rev. A {\\bf\n 59}, R911 (1999).\n\n\\bibitem{andreas} A. Bulgac, P. Magierski and A. Wirzba, unpublished;\nA. Bulgac and P. Magierski, astro-ph/0007423.\n\n\\bibitem{spruch} M. Schaden and L. Spruch, Phys. Rev. A {\\bf 58}, 935\n (1998); Phys. Rev. Lett. {\\bf 84}, 459 (2000).\n\n\\bibitem{cas} A. Hanke {\\it et al.}, Phys. Rev. Lett. {\\bf\n{81}}, 1885 (1998) and references therein.\n\n\\bibitem{CP} H.B.G. Casimir and D. Polder, Phys. Rev. {\\bf 73}, 360 (1948).\n\n\\bibitem{wirzba} G. Vattay {\\it et al.}, Phys. Rev. Lett. {\\bf 73},\n2304 (1994); M. Henseler {\\it et al.}, Ann. Phys. {\\bf 258}, 286 (1997).\n\n\\bibitem{kol} V.M. Kolomietz {\\it el.}, Sov. J. Nucl. Phys.\n{\\bf 29}, 758 (1979).\n\n\\bibitem{corrugation} G.L. Klimchitskaya {\\it et al.}. Phys. Rev. A {\\bf\n 60}, 3487 (1999); A. Roy {\\it et al.}, Phys. Rev. D {\\bf 60},\n 111101(R) (1999).\n\n\\bibitem{pairing} V.A. Khodel {\\it et al.}, Nucl. Phys. {\\bf A598},\n 390 (1996).\n\n\\bibitem{pet1} C.J. Pethick and A.Y. Potekhin, Phys. Lett. {\\bf B427},\n 7 (1998).\n\n\\end{thebibliography}\n\n\n\n\n\n\\end{document}\n\n"
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{
"name": "astro-ph0002377.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{baym} G. Baym {\\it et al.}, Nucl. Phys.\n{\\bf A175}, 225 (1971).\n\n\\bibitem{rav} D.G. Ravenhall {\\it et al.},\nPhys. Rev. Lett. {\\bf 50}, 2066 (1983).\n\n\\bibitem{hash} M. Hashimoto {\\it et al.}, Prog. Theor. Phys.\n{\\bf 71}, 320 (1984).\n\n\\bibitem{oya} K. Oyamatsu {\\it et al.}, Prog. Theor. Phys.\n{\\bf 72}, 373 (1984).\n\n\\bibitem{lat} J.M. Lattimer {\\it et al.},\nNucl. Phys. {\\bf A432}, 646 (1985).\n\n\\bibitem{wil} R.D. Wilson and S.E. Koonin, Nucl. Phys. {\\bf A435}, 844\n(1985).\n\n\\bibitem{las} M. Lassaut {\\it et al.},\nAstron. Astrophys. {\\bf 183}, L3 (1987).\n\n\\bibitem{oya1} K. Oyamatsu, Nucl. Phys. {\\bf A561}, 431 (1993).\n\n\\bibitem{lor} C.P. Lorenz {\\it et al.},\nPhys. Rev. Lett. {\\bf 70}, 379 (1993).\n\n\\bibitem{pet} C.J. Pethick and D.G. Ravenhall, Annu. Rev. Nucl. Part. Sci.\n{\\bf 45}, 429 (1995).\n\n\\bibitem{wat} G. Watanabe {\\it et al.}, see Los Alamos e--print\narchive astro--ph/0001273.\n\n\\bibitem{heiselberg} H. Heiselberg {\\it et al.}, Phys. Rev. Lett.\n{\\bf 70}, 1355 (1992).\n\n\\bibitem{negele} J.W. Negele and D. Vautherin, Nucl. Phys. {\\bf A207},\n 298 (1973); P. Bonche and D. Vautherin, Nucl. Phys. {\\bf A372}, 496\n (1981); Astron. Astrophys. {\\bf 112}, 268 (1982).\n\n\\bibitem{oya2} K. Oyamatsu, M. Yamada, Nucl. Phys. {\\bf A578}, 181 (1994).\n\n\\bibitem{casimir} M. Kardar and R. Golestanian, Rev. Mod. Phys. {\\bf\n 71}, 1233 (1999) and references therein.\n\n\\bibitem{bub1} Y. Yu {\\it et al.}, Phys. Rev. Lett. {\\bf 84}, 412 (2000).\n\n\\bibitem{bub2} A. Bulgac {\\it et al.}, in {\\it Proc. Intern. Work. on\nCollective excitations in Fermi and Bose systems}, eds. C.A. Bertulani\nand M.S. Hussein (World Scientific, Singapore 1999), pp 44--61 and\nLos Alamos e--preprint archive, nucl--th/9811028.\n\n\\bibitem{rk} M.A. Ruderman, C. Kittel, Phys. Rev. {\\bf 96}, 99 (1954).\n\n\\bibitem{fw} A.L. Fetter and J.D. Walecka, {\\it Quantum Theory of Many\n Particle Systems}, (McGraw--Hill, New York, 1971).\n\n\\bibitem{small} P.E. Rosenqvist {\\it et al.}, J. Phys. {\\bf A 29},\n 5441 (1996).\n\n\\bibitem{brack} M. Brack, R.K. Bhaduri, {\\em Semiclassical Physics},\nAddison Wesley Publishing Company, Inc. (1997).\n\n\\bibitem{caio}\nA. Bulgac and C. Lewenkopf, Phys. Rev. Lett. {\\bf 71}, 4130 (1993).\n\n\\bibitem{pri} H. Primack and Uzy Smilansky, Phys. Rev. Lett. {\\bf 74},\n 4831 (1995); Phys. Rep. {\\bf 327}, 1 (2000).\n\n\\bibitem{hilf} R.T. Waechter, Proc. Camb. Phil. Soc. {\\bf 72}, 439\n(1972); H.P. Baltes and E.R. Hilf, {\\it Spectra of Finite Systems},\nWissenschaftsverlag, Mannheim, Wien, Z\\\"urich: Bibliographisches\nInstitut, (1976).\n\n\\bibitem{niall} J. Sakhr and N.D. Whelan, see Los Alamos e--preprint\narchive nlin.CD/0001051; R.K. Bhaduri {\\it et al.}, Phys. Rev. A {\\bf\n 59}, R911 (1999).\n\n\\bibitem{andreas} A. Bulgac, P. Magierski and A. Wirzba, unpublished;\nA. Bulgac and P. Magierski, astro-ph/0007423.\n\n\\bibitem{spruch} M. Schaden and L. Spruch, Phys. Rev. A {\\bf 58}, 935\n (1998); Phys. Rev. Lett. {\\bf 84}, 459 (2000).\n\n\\bibitem{cas} A. Hanke {\\it et al.}, Phys. Rev. Lett. {\\bf\n{81}}, 1885 (1998) and references therein.\n\n\\bibitem{CP} H.B.G. Casimir and D. Polder, Phys. Rev. {\\bf 73}, 360 (1948).\n\n\\bibitem{wirzba} G. Vattay {\\it et al.}, Phys. Rev. Lett. {\\bf 73},\n2304 (1994); M. Henseler {\\it et al.}, Ann. Phys. {\\bf 258}, 286 (1997).\n\n\\bibitem{kol} V.M. Kolomietz {\\it el.}, Sov. J. Nucl. Phys.\n{\\bf 29}, 758 (1979).\n\n\\bibitem{corrugation} G.L. Klimchitskaya {\\it et al.}. Phys. Rev. A {\\bf\n 60}, 3487 (1999); A. Roy {\\it et al.}, Phys. Rev. D {\\bf 60},\n 111101(R) (1999).\n\n\\bibitem{pairing} V.A. Khodel {\\it et al.}, Nucl. Phys. {\\bf A598},\n 390 (1996).\n\n\\bibitem{pet1} C.J. Pethick and A.Y. Potekhin, Phys. Lett. {\\bf B427},\n 7 (1998).\n\n\\end{thebibliography}"
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astro-ph0002378
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The Least-Action Principle: Theory of Cosmological Solutions and the Radial-Velocity Action
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"author": "Alan B. Whiting"
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Formulating the equations of motion for cosmological bodies (such as galaxies) in an integral, rather than differential, form has several advantages. Using an integral the mathematical instability at early times is avoided and the boundary conditions of the integral correspond closely with available data. Here it is shown that such a least-action calculation for a number of bodies interacting by gravity has a finite number of solutions, possibly only one. Characteristics of the different possible solutions are explored. The results are extended to cover the motion of a continuous fluid. A method to generalize an action to use velocities, instead of positions, in boundary conditions, is given, which reduces in particular cases to those given by Giavalisco et al. (1993) \markcite{G93} and Schmoldt \& Saha (1998) \markcite{SS98}. The velocity boundary condition is shown to have no effect on the number of solutions.
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"string": "\\documentstyle[12pt,aasms4]{article}\n\\oddsidemargin 0pt\n\\evensidemargin 0pt\n\\textwidth 460pt\n\\topmargin -50pt\n\\textheight 700pt\n\\setlength{\\parskip}{\\baselineskip} % Blank line between paragraphs\n\\renewcommand{\\baselinestretch}{1.1}\n\\newcommand{\\rf}{\\par\\noindent\\hangindent 15pt {}}\n\\lefthead{Whiting}\n\\righthead{Least-Action Theory}\n\\begin{document}\n\n\\noindent \\today\n\n\\title{The Least-Action Principle: Theory of Cosmological Solutions\nand the Radial-Velocity Action}\n\\author{Alan B. Whiting}\n\\affil{ Physics Department, U. S. Naval Academy}\n\\authoraddr{Annapolis, MD 21403}\n\n\\begin{abstract}\nFormulating the equations of motion for cosmological bodies (such as\ngalaxies) in an integral, rather than differential, form has several\nadvantages. Using an integral the mathematical instability at early\ntimes is avoided and the boundary conditions of the integral correspond\nclosely with available data.\nHere it is shown that such a least-action calculation\nfor a number of bodies interacting by gravity has a finite\nnumber of solutions, possibly only one. \nCharacteristics of the different\npossible solutions are explored. \nThe results are extended to cover the motion of a continuous fluid.\nA method to generalize an action to use velocities, instead of\npositions, in boundary conditions, is given, which reduces in\nparticular cases to those given by Giavalisco et al. (1993)\n\\markcite{G93} and Schmoldt \\& Saha (1998) \\markcite{SS98}.\nThe velocity boundary condition is shown to have no effect on\nthe number of solutions.\n\\end{abstract}\n\\keywords{cosmology:theory---galaxies: kinematics and dynamics---galaxies:\nformation---methods: numerical}\n\n\\section{Introduction}\n\nThe present motions of cosmological objects, in particular galaxies,\nare functions of their past history. In principle one might\ndiscover the shape of the past by calculating presently observed\npositions and motions backward. However, in doing this \n we are faced immediately with two problems. First,\ntheir velocities in the plane of the sky are not known, and their distances\nnot known accurately; so perhaps half the information needed to start \nthe calculation by Newton's equations is there. Second, if the trajectories\nof the galaxies are to be traced back to very early times distances become\nvery small and corresponding gravitational forces very large. Small errors\nin present velocities or positions become heavily magnified, resulting in\ngalaxies being formed at infinite speeds. The problem is mathematically\nunstable, rather like trying to roll a marble to the top of a glass\nmountain, and requiring that it stop exactly on the summit\\footnote{Valtonen \net al. \\markcite{V93} (1993) have found some possible solutions for\nthe motion of the major galaxies in the Local Group and the \nMaffei 1/IC 342 Group by integrating equations of motion forward from\nan early time. However, it is not clear that this method is generally\napplicable, and in any case requires a great deal of hunting about in\nparameter space; for their result, the Valtonen group integrated ten\nthousand situations.}.\n\nTo avoid these difficulties Peebles (\\markcite{P89}1989, \\markcite{P90} \n1990, \\markcite{P94} 1994) \nformulated the problem in integral\nrather than differential form. This traded the relative simplicity and\ndefiniteness of differential equations for the stability of the integral.\nThe most important consideration in moving from the differential to \nintegral form of the problem (apart from the mechanics of implementation)\nis the fact that, with the same boundary conditions, an integral calculation\nmay produce several (or many) solutions. An obvious question to answer\nis just how many there are. This is something more than a purely mathematical\nconcern. Of course, if the numerical calculation of solutions can be\nguided in some way there is the potential for a large savings in computer\ntime, and if the number of solutions is limited the search may be stopped\nwhen all are found. Conversely, if the number of solutions is very large\nor infinite, the usefulness of the calculation is thrown into doubt\n(unless some method of selecting more probable solutions is found). But\nthe question is more fundamental than that, for the variational formulation of\nthe cosmological problem corresponds closely to the limits of our knowledge.\nWhen the present radial velocities and positions on the sky\nof a number of bodies are specified and the\nBig Bang postulated, \nwe find the end conditions are fixed; the action is determined by\nrelevant physics. The mathematical question is thus transformed\ninto a cosmological one.\n\nThe subject of this study is the mathematical theory of variational\ncalculations as applied to the cosmological problem. That problem is\ndefined as the determination of \nthe motion of a number of bodies moving under gravitational interaction,\nwith the requirement\nthat all bodies must be at the same point (in proper coordinates)\nat $t=0$. Newtonian, rather than relativistic, calculations\nare employed throughout\\footnote{See Peebles \\markcite{P80} (1980) and\nBondi \\markcite{B60} (1960) for the validity of this approach.}.\n\nThe cosmological problem may be interpreted as a rough approximation of the\nmotion of galaxies, each galaxy simulated by a point mass interacting\nonly through gravity. This is the way most least-action calculations have\nproceeded, and is not a bad approximation considering the uncertainties\nin such data as distances and masses. It would be more accurate, however,\nto consider the objects to represent the dark matter halos of galaxies (which\nas far as is known interact {\\em only} through gravity). The point-mass\napproximation provides a reasonable simulation of gravitational effects,\nsince multipole moments decay rapidly with distance (Dunn \\& Laflamme 1995\nfound them to be quite unimportant), and in any case the conclusions of\nthis study are not affected by the detailed form of the gravitational\npotential used.\n\nOf course, identifying whole galaxies with single bodies ignores internal\nstructure (which may be significant in some cases) and the effects of\nmergers (which certainly are significant); Dunn \\& Laflamme (1995)\nfound some additional problems. To address these matters one\nmust turn to a continuous fluid formulation of the problem. Section 6\ngeneralizes the discrete-body results to this more complicated situation.\n \n\\section{The First Variation}\n\nConsider first the problem of minimizing the integral \n\\begin{equation}\nI = \\int_{t_0}^{t_1} \\left( T - V \\right) dt\n= \\int_{t_0}^{t_1} L \\left( q_i,\\dot{q_i},t \\right) dt\n\\label{eq:integral}\n\\end{equation}\nwhere the kinetic energy $T$ is quadratic in the generalized velocities\n$\\dot{q_i}$ (or, alternatively, in the generalized momenta $\\partial L /\n\\partial \\dot{q_i} = p_i$) and the potential $V$ does not depend on velocity.\nThe end points $q_i(t_0)$ and $q_i(t_1)$ are given. \n(This is interpreted dynamically\nby constructing a path ${\\bf r}(t)$\nin 3n-dimensional space\nusing the vectors ${\\bf r}_j(q_i(t))$, $j =1$ to $n$, $i=1$ to $3n$,\nwhere the ${\\bf r}_j$ are\nthe paths of the $n$ bodies in 3-dimensional space.)\nFor small variations\nthe change in the action is given by a truncated expansion in a Taylor's\nseries (treating $q_i,\\dot{q}_i$ as independent variables):\n\\begin{equation}\n\\delta \\int_{t_0}^{t_1} L \\left( q_i,\\dot{q_i},t \\right) dt =\n\\int_{t_0}^{t_1} \\sum_i \\left[ \\frac{\\partial L}{\\partial q_i}\n\\delta q_i +\n\\frac{\\partial L}{\\partial \\dot{q}_i} \\delta \\dot{q}_i\n\\right] dt = 0. \n\\label{eq:variation}\n\\end{equation}\nEquation\n(\\ref{eq:variation}) can be integrated by parts to give\n\\begin{equation}\n\\int_{t_0}^{t_1} \\sum_i \\left[ \\frac{\\partial L}{\\partial q_i} -\n\\frac{d}{dt} \\left( \\frac {\\partial L}{\\partial \\dot{q}_i} \\right)\n\\right] \\delta q_i dt + \\sum_i\n\\left[ \\frac {\\partial L}{\\partial \\dot{q}_i} \\delta q_i\n\\right]_{t_0}^{t_1} = 0\n\\end{equation}\nand if the variation in ${\\bf r}$ vanishes at the end points (that is, if\nthe end points are fixed) the boundary term is zero. The requirement\nthat the integral\nvanish for arbitrary variations $ \\delta {\\bf r}$ results in \nthe Euler-Lagrange equations:\n\\begin{equation}\n\\frac{\\partial L}{\\partial q_i}\n-\\frac{d}{dt} \\left( \\frac {\\partial L}{\\partial \\dot{q}_i} \\right)\n=0.\n\\end{equation}\nThese are the dynamic equations, identical with those derived from (for\nexample) forces and accelerations. The correspondence between the\ndynamic equations and the vanishing of the first variation of equation \n(\\ref{eq:integral}) is {\\em Hamilton's Principle}.\n\nA path which minimizes the integral will thus always satisfy the\ndynamic equations. However, the converse is not necessarily true:\na path satisfying the Euler-Lagrange equations is not guaranteed\nto provide a minimum of the corresponding integral. For sufficiently\nsmall path lengths a minimum does result (see, for example, Whittaker \n\\markcite{W59} 1959,\npp. 250-2); beyond a certain point the path \nwill make the integral stationary, but not necessarily a minimum.\nFinding the point that determines the limit of application\nof the least-action technique (strictly interpreted)\nto the dynamical problem will be discussed\nbelow\\footnote{Whittaker calls Euler's Principle, which appears later,\nthe {\\em Least Action} Principle; however, Hamilton's Principle has\nalso been called this. To distinguish between the two I will use\nthe names of the mathematicians and call them collectively Least Action\nPrinciples.}.\n\nAdding a total derivative (in multiple dimensions, a divergence expression)\nwill not change the Euler-Lagrange equations\n(see Courant and Hilbert \\markcite{CH53} 1953,\np. 296) but can change the boundary terms. For instance, varying\n\\begin{equation}\n\\int_{t_0}^{t_1} \\left[ L - \\sum_j \\frac{d}{dt} \\left( q_j\n\\frac {\\partial L}{\\partial \\dot{q}_j} \\right) \\right] dt\n\\label{eq:velaction}\n\\end{equation}\nleads to\n\\begin{equation}\n\\int_{t_0}^{t_1} \\sum_j \\left[ \\frac{\\partial L}{\\partial q_j} -\n\\frac{d}{dt} \\left( \\frac {\\partial L}{\\partial \\dot{q}_j} \\right)\n\\right] \\delta q_j dt - \\sum_j \\left[\nq_j \\delta \\left( \\frac{\\partial L}{\\partial \\dot{q}_j} \\right)\n\\right]_{t_0}^{t_1} = 0.\n\\label{eq:velbdry}\n\\end{equation}\nIf the original Lagrangian is quadratic in $\\dot{q}_j$,\nrecovery of the Euler-Lagrange equations requires \nthat either $q_j =0$ or $\\delta \\dot{q}_j =0$ in each boundary term.\nIn the second case, it is the velocity at the end point which is\nthe fixed boundary condition, rather than the position.\nThis raises the possibility\nof using a radial velocity, rather than a distance, as the end point\nin a cosmological calculation.\nIn fact Giavalisco et al. \\markcite{G93} (1993) have considered such a\nmixed boundary condition, in one place using it to modify a set of \napproximating functions and in another expressing it as a canonical\ntranformation of variables. Their approaches are in practice equivalent\nto this one. Schmoldt \\& Saha \\markcite{SS98} \n(1998) have succeeded in using a velocity endpoint in their numerical\ncalculation.\n\nIt is straightforward to show\nthat the boundary term added here does not\nchange Whittaker's conclusion above. \nNote that the coordinates $q_j$\nwhich provide velocity boundary conditions may be all or only some of\nthe total number of coordinates $q_i$, as long as the total derivative\nis adjusted accordingly. \n \n\\subsection{Variable Endpoints}\n\nIf the radial velocity is to be used as a form of endpoint, rather\nthan the (less accurately known) radial distance, the theory of\n``free'' endpoints (constrained to move on a manifold of some description)\ncomes into play. In addition to the Euler-Lagrange equations, the\nsolution must now satisfy the\n{\\em transversality condition} \nwhich results from the minimization of\nthe variation at a free end point\\footnote{\nSee Appendix A for detailed formulae.}.\nAs expressed in Morse's \\markcite{Mo34} (1934) notation, this condition is\n\\begin{equation}\n\\left( L - \\sum_i \\dot{q}_i \\frac{\\partial L}{\\partial \\dot{q}_i}\n\\right) dt^s\n+ \\sum_i \\frac{\\partial L}{\\partial \\dot{q}_i}dq_i^s = 0\n\\label{eq:transverse}\n\\end{equation}\nwhere the superscript $s$ denotes a differential taken along\nthe end manifold ($s$ takes on values designating the initial or\nfinal end points) and $L$ is the integrand. \n\nApplied to the Lagrangian for a number of bodies moving under their\nmutual gravity\n\\begin{equation}\nL = \\sum_i m_i \\left( \\frac{1}{2} \\left( \\dot{r}^2_i + r_i^2 \\dot{\\theta}^2_i\n+r^2_i \\sin^2 \\theta_i \\dot{\\phi}^2_i \\right) + G \\sum_{j < i}\n\\frac{m_j}{|{\\bf r}_{ij}|} \\right)\n\\label{eq:lagrange}\n\\end{equation}\nand fixing the time, the transversality condition is\n\\begin{equation}\n\\sum_i m_i \\left( \\dot{r}_i dr^s_i + r_i^2 \\dot{\\theta}_i d \\theta^s_i\n+r^2_i \\sin^2 \\theta_i \\dot{\\phi}_i d \\phi^s_i \\right) = 0\n\\label{eq:xverse1} \n\\end{equation}\nor more compactly\n\\begin{equation}\n{\\bf P} \\cdot d{\\bf r}^s = 0\n\\label{eq:xverse2}\n\\end{equation}\nwhere ${\\bf P}$ is the total momentum and $d{\\bf r}^s$ any vector\nin the end manifold,\na general result constraining the end manifold. If the velocity action,\nexpression (\\ref{eq:velaction}), is used a modified form of the\ntransversality condition applies:\n\\begin{equation}\n\\sum_i m_i \\left( \\dot{r}_i dr^s_i + r_i^2 \\dot{\\theta}_i d \\theta^s_i\n+r^2_i \\sin^2 \\theta_i \\dot{\\phi}_i d \\phi^s_i \\right)\n- \\sum_i m_i \\dot{r}_i d r_i^s - \\sum_i m_i r_i d \\dot{r}_i^s = 0.\n\\label{eq:velocipede}\n\\end{equation}\nIf the end point under consideration has fixed angles and radial velocities,\nthe left hand side of equation (\\ref{eq:velocipede})\nvanishes identically. The velocity-action\ntransversality condition thus tells us nothing about the manifolds on which\nthe end-points lie.\nAt the same time, the velocity action imposes\nno additional restrictions on the end manifolds over the position action.\n\n\\section{The Second Variation}\n\nWe now come to the question of how far the minimization of the action\nintegral can be used to reproduce the dynamic equations, that is, the\nlimit of the least-action method strictly defined. \nThe limit may be pictured geometrically\nby using {\\em kinetic foci} as defined by Thompson and Tait \\markcite{TT96}\n(1896, section\n357, p. 428)\\footnote{Page and section numbers are identical\nin the 1962 Dover reprint.}: ``If, from any one\nconfiguration, two courses differing infinitely little from one\nanother have again a configuration in common, this second\nconfiguration will be called a kinetic focus relatively to the first:\nor (because of the reversibility of the motion) these two\nconfigurations will be called conjugate kinetic foci.'' It can be\nshown (for instance, by Whittaker \\markcite{W59}\n1959, pp. 251-3) that the action is\nneither a maximum nor a minimum over a path which includes a pair of\nkinetic foci.\n\nMore intuitively, if two paths infinitesimally \nclose to each other between the same\npair of end points both satisfy the Euler-Lagrange equations, \nthe action (along either path) can no longer be a minimum\n(and the variation of the variation between them must vanish).\n\nIt is easiest to picture kinetic foci using a\ntoy dynamical problem, that of finding the motion of a ball rolling\non a large sphere, without friction or other complicating effects. \nGeodesics on the spherical surface are paths of least\naction in this case. Clearly there is a unique minimum path for\npoints close together; that is, if two end points are chosen near each\nother, a portion of the great circle joining them gives the least\naction. As the points are taken farther and farther apart\nthe action \nincreases while staying a minimum. When the points are taken to be opposite\neach other, however, there is an infinite number\nof solutions all of the same length. Dynamically, the ball leaves the\nstarting point and follows a geodesic to the antipode; but if it had left\nthe starting point at a slightly different angle, it would still pass\nthrough the same antipode. On a sphere, then, \nkinetic foci are exactly opposite each other.\n\nStill considering the motion of the ball dynamically,\nif the trajectory is extended, worse happens. The path taken, which\npasses more than halfway around the sphere, is actually longer than paths\nwhich follow the complement of the great circle. In fact it is longer\nthan some small circles. \n\nGeodesics on a torus provide greater complexity.\nGiven any two points on the torus there will be a global minimum; a local\nminimum path, going the other way around the major radius; and an\ninfinite series of other local minima, wrapping around one leg or the other\nof the torus. None of these can be continuously varied into another\nbecause of the different number of wrappings. The action (the length of\nthe geodesic) tends to infinity as the wrappings increase.\n\nA more mathematically rigorous and useful, but also more complicated,\ntreatment of the second variation takes us into Morse Theory. \n\n\\subsection{Morse Theory}\n\nMarston Morse \\markcite{Mo34}\n(1934) conducted an extensive study of the general\ntopological properties of variational problems and their solutions.\nA summary of some of his results is presented below\\footnote{A shorter\nand somewhat more accessible presentation of most of Morse's results\nis found in Milnor \\markcite{M63} (1963).}.\n\nAn {\\em extremal} is a path which satisfies the Euler-Lagrange\nequations. A {\\em critical} extremal is one which makes the action\na minimum.\n\nA function which will play a part in what follows is defined by\n\\begin{equation}\n2 \\Omega (s_i, \\dot{s}_i) =\n\\frac{\\partial^2 L}{\\partial r_i^2}\ns_i^2 + 2\n\\frac{\\partial^2 L}{\\partial r_i \\partial \\dot{r}_i}\ns_i \\dot{s}_i +\n\\frac{\\partial^2 L}{\\partial \\dot{r}_i^2}\n\\dot{s}_i^2\n\\end{equation}\nfor some integrand $L$ and functions $s_i(t)$.\nThe {\\em characteristic form} is\\footnote{Here $z$ is used as\na shorthand symbol for the collection of functions $s_i$, and below\nit includes also $u_h$ and $u_k$.}\n\\begin{equation}\nQ(z, \\lambda) = \\int_{t_0}^{t_1}2 \\left( \\Omega (s_i, \\dot{s}_i)\n- \\lambda s_i s_j \\right) dt.\n\\end{equation}\nFor a given extremal with fixed end points, the\n{\\em accessory boundary problem} is defined as\n\\begin{equation}\n\\frac{d}{dt} \\left( \\frac{\\partial \\Omega}{\\partial \\dot{s}_i}\n\\right) - \\frac{\\partial \\Omega}{\\partial s_i} + \\lambda s_i = 0.\n\\label{eq:accessory}\n\\end{equation}\nA solution $s_i$ to this equation not identically zero is an\n{\\em eigensolution} (sometimes {\\em eigenvector}) and $\\lambda$ an\n{\\em eigenvalue}.\n The {\\em index} of an eigenvalue is the number of linearly independent\neigensolutions corresponding to the eigenvalue.\n\nFor free end points the characteristic\nform is\n\\begin{equation}\nQ(z, \\lambda) = \\sum_{h,k} b_{hk} u_h u_k +\n\\int_{t_0}^{t_1}2 \\left( \\Omega (s_i, \\dot{s}_i)\n- \\lambda s_i s_j \\right) dt\n\\end{equation}\nwhere $b_{hk}$, $u_h$ and $u_k$ are derived from the second variation\nat the end points and are given in Appendix A. The accessory\nboundary problem, equation (\\ref{eq:accessory}), stays the same in\nform but the solution $s_i$ must now satisfy the transversality condition. \n\nIf the problem is to find the geodesic in a space of a given metric\nbetween two manifolds of some description, the coefficients $b_{hk}$\nare a measure of the curvature of the manifolds.\nIn particular, when the coefficients\nvanish the manifolds are flat.\n\nIf $\\lambda = 0$ the accessory boundary problem becomes\nthe {\\em Jacobi equation} (not to be\nconfused with the Hamilton-Jacobi equation), which is identical to\nthe perturbed Euler-Lagrange equation. If there exist two points\non an extremal at which an eigensolution with eigenvalue\nzero vanishes, these points are {\\em conjugate points}.\nA {\\em non-degenerate} extremal is one which has no zero eigenvalues\nin the accessory boundary problem. It is easily shown that conjugate\npoints (mathematically defined) and kinetic foci (dynamically defined)\nare identical.\n\nDetermining the least-action limit for a given variational problem\nis thus the same as determining the first zero of the Jacobi\nfunction (after the initial point). This determination is\nnot generally an easy thing to do. To take a specific example, \nfor a group of bodies moving under\neach other's gravity\nthe Jacobi function ${\\bf s}$ satisfies\n\\begin{equation}\n{\\bf \\ddot{s}}_i = G \\sum_{j \\not= i} m_j \\left(\n\\frac{3 {\\bf r}_{ij}{\\bf r}_{ij}}{|{\\bf r}_{ij}|^5}\n- \\frac{1}{|{\\bf r}_{ij}|^3} \\right) \\cdot {\\bf s}_i.\n\\end{equation}\nClearly, solving this is not a convenient way of\nfinding kinetic foci. Not only\nis this less amenable to integration than the original\ndynamic equation, but the original equation must be solved first (which\nmakes the locating of kinetic foci as a step in solving the dynamical\nproblem rather pointless). A more practical method for use in calculation is\ncalled for. \n\n\\subsection{Choquard's Criterion}\n\nChoquard \\markcite{C55} \n(1955) studied the motion of bodies in strongly anharmonic potentials\nin the context of a semi-classical treatment of Feynman integrals.\nHe found that multiple solutions to a dynamical problem were possible\nthrough the action of ``forces of reflection'', which allowed indirect\npaths from one end point to the other. In an indirect path, which\ncorresponds to a stationary rather than a minimum action, at some\ntime between the end points\n\\begin{eqnarray}\n\\frac{d}{dt} \\left( T \\right)& =& 0\\nonumber \\\\\n& =& \\frac{d}{dt} \\left(\\frac{1}{2m} {\\bf p}^2 \\right)\n\\nonumber \\\\\n& = & \\frac{1}{m} {\\bf p} \\cdot \\left( - \\nabla V \\right).\n\\end{eqnarray}\nThat is, the momentum must be normal to the force.\n\nTo make this reasoning directly applicable to\n the problem at hand, consider a \nsolution to the dynamical equations with a given set of end points,\n${\\bf r}(t)$; it must\nconserve total energy $E$, made up of a kinetic part\n$T$ and a potential part $V$. A varied path ${\\bf r}(t) + {\\bf s}(t)$ \n(where ${\\bf s}(t)$ is a Jacobi function) also conserves an energy\n$E + \\delta E = T + \\delta T + V + \\delta V$,\nand thus the Jacobi function itself conserves $\\delta T +\\delta V$. Since\n$V$ is a function only of ${\\bf r}$, not $\\dot{\\bf r}$, $\\delta V$ is\na function only of ${\\bf s}$, and for $|{\\bf s}|$ small (which it is by\ndefinition) a linear function. This means that $\\delta V$ reaches\nits extreme value when ${\\bf s}$ does, and at the same point $\\delta T$\nhas an extremum. Since $|{\\bf s}|$ can vanish only after its maximum,\nthis point of extremum must occur before a conjugate point.\nThe extremum of $\\delta T$ is given by\n\\begin{equation}\n\\frac{d}{dt} \\left(\\delta T\\right) = 0.\n\\nonumber\n\\end{equation}\nWriting kinetic energy in terms of momentum,\n\\begin{eqnarray}\nT + \\delta T & = & \\frac{1}{2m} \\left( {\\bf p} + \n\t\\delta {\\bf p} \\right)^2 \\nonumber\\\\\n\\delta T & \\simeq & \\frac{1}{m} {\\bf p} \\cdot \\delta {\\bf p} \\nonumber \\\\\n& = & \\frac{1}{m} {\\bf p} \\cdot \\left( - \\nabla V \\right) \\delta t \n\\end{eqnarray}\nso the condition for an extremum of the variation in kinetic energy is\n\\begin{eqnarray}\n\\frac{d}{dt} \\left(\\delta T\\right) & = & 0 \\nonumber\\\\\n\\frac{1}{m} {\\bf p} \\cdot \\left( - \\nabla V \\right) & = & 0\n\\end{eqnarray}\nand Choquard's criterion is recovered. For a situation with\nmultiple particles, the varied path ${\\bf s}$ may be taken to be\ndifferent from zero for only one of the particles. This leads to\nthe conclusion that\n{\\em a conjugate point may occur\nonly after the point where the momentum is normal to the \nforce on some body in the system.} \nKeeping in mind the identity of conjugate points and\nkinetic foci as well as Whittaker's result (above),\nChoquard's criterion gives a lower bound to the applicability of\nthe least-action calculation. Following the trajectory of a dynamic\nsystem from the initial point, it is a minimum of the action at least\nuntil the momentum of some body is normal to the force on that body.\nThis provides some insight into the shape of\nstationary-solution trajectories, as well as (with a further result of\nMorse, below) allowing a conclusion to be drawn \nas to the total number of solutions\nof all kinds\\footnote{Choquard \\markcite{C55} \n(1955) notes that his criterion does\nnot apply to situations in which the trajectory is {\\em always} normal\nto the acceleration, as in (for example) circular motion. However,\nthese situations are generally symmetrical enough to allow the useful\napplication of Jacobi functions.}.\n\n\\subsection{More Morse}\n\nThere are several more results from Morse \\markcite{Mo34}\n(1934) which are of use in the\npresent problem. First we require a few more definitions:\n\nA {\\em Riemannian} space possesses a positive-definite metric which\ncan be expressed as a quadratic form:\n\\begin{equation}\nds^2 = \\sum_{i,j} g_{ij} dx^i dx^j.\n\\label{eq:Riemann}\n\\end{equation}\n\nThe {\\em connectivity} $P_k$ of a space\\footnote{\nThis is not to be confused with the {\\em connection} of a space,\nor whether a space is {\\em simply connected} (themselves\ndistinct topological concepts).} is the\nnumber of distinct homologous families of figures of dimension\n$k+1$; that is, within each family one figure can be transformed\ninto another by a continuous transformation, but a figure in one\nfamily cannot be so transformed into a figure in another. On a\nsphere, for instance, the connectivity $P_0$ is one, since any\nline may be transformed into another by a continuous transformation.\nOn a torus $P_0$ is infinite, since there is an infinite number of\nfamilies of curves distinguished from each other by the number of times\nthey wrap about the large or small radii.\n\nMorse is concerned with the connectivities of the {\\em functional\ndomain} $\\Omega$ of\nadmissible curves for a given variational problem\\footnote{This is\n{\\em not} the function $\\Omega (s, \\dot{s})$ found above and in\nAppendix A. The ambiguity in notation is regretted, but it should\nnot lead to confusion.}, that is those\ncurves which have the required end points and are continuous along\nwith their first derivatives. For the case of a set of trajectories\nin three dimensional space it is easiest to consider them\ntransformed into a\nsingle trajectory in $3n$-dimensional space, between two end points\nrepresenting the starting and ending configurations. Each point in\n$\\Omega$ represents a trajectory in the $3n$-dimensional space. \nSince no points in $3n$-space are\nexcluded,\nany trajectory can be continuously transformed into any other; so\nany point in $\\Omega$ can be continuously\ntransformed into any other. Any line\nin $\\Omega$ can then be transformed point by point into any other\nline, any plane figure likewise, and so on for all dimensions.\nConsequently each connectivity of the space of trajectories\nis one.\n\nMorse's important results are:\n\n{\\em An extremal which affords a minimum has no negative\n eigenvalues in the associated boundary problem.}\nThis is equivalent to saying it contains no conjugate points.\nFurther, {\\em the number\nof conjugate points of an end point of an extremal $g$ on $g$\nis equal to the number of negative eigenvalues in the\nassociated boundary problem.}\n\n{\\em The index of an extremal is the sum of the indices of the\nconjugate points of an end point on the extremal.}\n\n{\\em The conjugate points of an end point of an extremal $g$\non $g$ form a set of measure zero.} \nThis means they are isolated (and thus much easier to\ndeal with). More importantly, it means that the probability of\nchoosing a pair of conjugate points by chance\nwhen setting up the variational problem is essentially zero.\n\n{\\em If for a given Riemannian space R and terminal manifold Z\nthere exists an integral I defined on R such that all\ncritical extremals are non-degenerate, then the number of\ndistinct extremals of index $k$ is greater than or equal to\nthe connectivity $P_k$ of the functional domain $\\Omega$. If the\nextremals are of increasing type, the number of extremals\n of index $k$ is equal to the connectivity\n$P_k$.}\n \nThe last is a most useful result. However, to apply it we must\nshow that the variational problem meets the requirements.\n\nAs demonstrated for example by Whittaker \\markcite{W59}\n(1959, pp. 247-8, 254)\\footnote{See also Arnold (1989), pp. 245ff.} \nthe dynamic equations\nof a system which has an integral of energy $E$ can be derived\nby requiring that the variation of the integral\n\\begin{equation}\n\\int 2T dt\n\\label{eq:euler1}\n\\end{equation}\n(where $T$ is the kinetic energy) vanish, for a fixed value\nof $E$. This formulation is known as Euler's Principle. \nFor a system in which the total energy $E$ is the sum of the\nkinetic energy $T$ (quadratic in velocities) and potential energy $V$, the\nintegral (\\ref{eq:euler1}) can also be written as\n\\begin{eqnarray}\nI & = & \\int 2 \\left( E - V \\right)^{1/2} \\left( T \\right)^{1/2} dt\n\\nonumber \\\\\n & = & \\int 2 \\left( E - V \\right)^{1/2} \\left( a_{ij} \\dot{x}^i \n\\dot{x}^j \\right)^{1/2} dt.\n\\label{eq:euler2}\n\\end{eqnarray}\nThis is\nthe integral giving arc length on a surface of metric\n\\begin{equation}\ng_{ij} = 4 \\left( E - V \\right) a_{ij}\n\\end{equation}\nand the space of the possible solutions to our variational problem \nwhen formulated this way is\nindeed Riemannian, with geodesics corresponding to variational solutions.\nThe cosmological variational problem in proper coordinates \ncan be put into this form, so Morse's results apply.\nFurther, the integral is of increasing type (since kinetic energy\nis always positive), so the\nnumber of solutions is given definitely.\n\nUnfortunately, Morse's result cannot be applied directly \nto Hamilton's principle, as\nthe functional domain is not Riemannian. The Lagrangian cannot be put\nin the necessary form of expression (\\ref{eq:euler2}), since the potential\nenergy forms a separate term which is not quadratic in the velocity\ndifferentials. This means that, if\nthe preceding theory is to be used, either the problem must be\nput in Euler's form or some\nconnection of a topological nature must be made between the two\nLeast Action principles. The latter is addressed in the next section.\n\nBefore leaving Morse Theory, however, it is worthwhile\nto note the effect of the end manifolds of the\nvelocity action on the number\nof solutions. Comparing the characteristic forms and accessory\nboundary problems between fixed-point and manifold situations, we find\nthat the difference lies in the transversality condition and the\nquantities $b_{hk} u_h u_k$. It has already been shown that, using \nEuler's Principle, the transversality condition\nholds identically. \n\nFor an initial configuration manifold and Hamilton's Principle, combining two\nformulae from Appendix A,\n\\begin{eqnarray}\nb_{hk} u_h u_k& = & \\left[ \\left( L - \\sum_i \\dot{q_i}\n\\frac{\\partial L}{\\partial \\dot{q_i}} \\right) \\frac{d^2 t^s}\n{de^2} + \\left( \\frac{\\partial L}{\\partial t} - \\sum_i\n\\frac{\\partial \\dot{q_i}}{\\partial t} \\frac{\\partial L}{\\partial q_i}\n\\right) \\left( \\frac{dt^s}{de} \\right)^2 \\right. \\nonumber \\\\\n&+& \\left.\n2 \\sum_i \\left( \\frac{\\partial L}{\\partial q_i} \\frac{dt^s}{de}\n\\frac{dq_i^s}{de} + \\frac{\\partial L}{\\partial \\dot{q_i}}\n\\frac{d^2 q_i^s}{de^2} \\right) \\right]_1^2 \\nonumber \\\\\n& = & \\sum_i m_i \\left(\\dot{r}_i \\frac{d^2r^s_i}{d e^2}\n + r_i^2 \\dot{\\theta}_i \\frac{d^2 \\theta^s_i}{d e^2}\n+r^2_i \\sin^2 \\theta_i \\dot{\\phi}_i \\frac{d^2 \\phi^s_i}{d e^2} \\right). \n\\end{eqnarray}\nComparing this with equations (\\ref{eq:xverse1}) and (\\ref{eq:xverse2})\nthe manifold curvature expression $b_{hk} u_h u_k$ is seen to be \nthe dot product of the total momentum vector\nwith a vector in the end-manifold surface:\n\\begin{equation}\nb_{hk} u_h u_k = {\\bf P} \\cdot \\frac{d^2}{de^2} {\\bf x}^s\n\\end{equation}\nwhich is, near an extremal,\n\\begin{equation}\nb_{hk} u_h u_k = {\\bf P} \\cdot \\Delta {\\bf x}^s/e^2.\n\\end{equation}\nFor an extremal, the tansversality condition requires that ${\\bf P} \\cdot\n\\Delta {\\bf x}^s = 0$ (see equation \\ref{eq:xverse2}). More generally,\nsince ${\\bf P}$ is a constant of motion belonging to the solution\n(not related to any particular variation around it) and $e$ and\n$\\Delta {\\bf x}^s$ are independently arbitrary, \n${\\bf P} \\cdot \\Delta {\\bf x}^s$ cannot vary with $e$, and\nthus must vanish (unless $b_{hk} u_h u_k$ is allowed to be\ninfinite, a pathological case I propose to ignore).\nThe dot product vanishing causes $b_{hk} u_h u_k$ to vanish\nas well. The same result holds if Euler's Principle is used.\n\nFor the velocity action and the final end manifold, with angles and radial\nvelocities fixed, $b_{hk} u_h u_k$ vanishes identically using either Least\nAction Principle. Thus for each\ncase {\\em the fact that the ends of the action integral lie on manifolds and\nnot on fixed points is irrelevant to the number of solutions.} Interpreted\ngeometrically, the manifolds are flat surfaces.\n\n\\section{The Number of Solutions}\n\n\\subsection{Catastrophe Theory}\n\nApplying Morse's result on the number of solutions to the problem formulated\nusing Euler's Principle (which is the only way it is directly\napplicable), we find that\nthere is one minimal extremal, plus one non-minimal\nextremal for each integral number of conjugate points.\nThere are values\nof total energy for which there are no solutions. Most obvious are\n those below the potential\nenergy of the final end point; those are excluded from the functional\ndomain at the outset. For values of the total energy in a gravitational\nsystem which are positive, especially strongly so, there can be only\none solution since the\nJacobi function for a nearly straight-line trajectory never returns to zero; the\nsaddle-point solutions for these situations can be thought of as occurring\nat infinite values of total time.\n\nBut the calculation\ncontemplated (and as performed by Peebles and those following his technique) \nuses Hamilton's Principle. To\napply Morse to Hamilton a connection must be made between them. This can\nbe done by way of the dynamical equations and Catastophe Theory.\n\nConsider a two-dimensional slice of the functional domain $\\Omega$, \nthe dimensions\nbeing the Eulerian action (time integral of the kinetic energy $T$)\nand the Hamiltonian action (time integral of the Lagrangian function $T-V$). \nChoose the slice\nso that it contains all the extremals of the problem (see Figure \n\\ref{poincare}). A given value of\ntotal energy will plot as a curve in this slice, with a minimum of \n$\\int T dt$ at the\nlocation of the least-action trajectory and other extremals spaced along it\n(the latter may show as maxima, minima or points of \ninflection in this plot). Since the integrand of Euler's Principle is\npositive-definite, the least-action solution takes the mimimum time of\nall the solutions for a given energy; the saddle-point solutions take increasing\namounts of time for increasing index. \nAll solutions will be equilibrium points for the\npotential represented by the action. The slice is thus a\nPoincar\\'{e} diagram to which Catastrophe\nTheory applies, with total energy as the control parameter. The minimum\nsolutions correspond to stable equilibria, the saddle-points to unstable\nequilibria.\n\nIn the same slice plot curves of constant total time. The index\nof a given extremal depends only on the number of \nkinetic foci of the trajectory,\nnot on the action principle (if any) used to calculate it; in addition, all\nextremals are solutions to the dynamic equations. Thus the minimum of \n$\\int L dt$ for each time corresponds to a minimum of $\\int T dt$ for\nfixed total energy, and the non-minimum extremals will similarly correspond\nto non-minimum extremals of the Eulerian action\nfor other values of total energy. Again, we have constructed\na Poincar\\'{e} diagram (rotated $90^{\\rm{o}}$ with respect to the first), \nwith total time as the control parameter.\n\nThere is at least one least-action solution for a given value of time. If\nthere were two (or more), the chain of Eulerian least-action solutions would\nhave a maximum or a minimum in total time, as shown in Figure \\ref{poincare}. \nThere are several reasons why this cannot happen; two are outlined below. \n\nFirst, viewed as\na Poincar\\'{e} diagram in Hamiltonian extremals, Figure \\ref{poincare}\nrequires two chains of\n{\\em similar} (stable or unstable)\nequilibria to meet. \nThis sort of topology, a bifurcation without an exchange of stability,\n is forbidden by Catastrophe\nTheory; therefore there is only one least-action Hamiltonian extremal. \nSimilarly,\nthere can only be one saddle-point Hamiltonian extremal for each saddle-point\nEulerian extremal\\footnote{Expositions of Catastrophe Theory are found in\nLamb \\markcite{L32} (1932, sect. 377, pp. 710-12) and Jeans \\markcite{J19}\n(1919, sect. 18-23, pp. 20-6);\nthe detailed demonstration of the \nnecessity of an exchange of stability is found in in Poincar\\'{e} \n\\markcite{P85} (1885).}.\n\nSecond, note that at a bifurcation point (point C in figure\n\\ref{poincare})\n\\begin{equation}\n\\left| \\frac{\\partial^2 I}{\\partial q_i \\partial q_j} \\right| = 0\n\\end{equation}\nfor the action $I$ and variables $q$ in the two-dimensional slice; \nbut this is just the requirement for a degenerate\nextremal, to which Morse's results specifically do not apply. Since, as\nnoted above, these require some special symmetry in the problem and are\nalmost impossible to generate by chance, it is reasonable to assume that\nour problem does not have them\\footnote{It might be possible to exclude\nthem explicitly from the functional domain $\\Omega$, avoiding any\nproblems at the start. However, it is conceivable that such an exclusion\nwould change the topology of $\\Omega$ and thus complicate the\nquestion of the connectivities of the space. For present purposes\nit is easier to deny them any place in the problem at the end.}.\n\nWe are finally in a position to determine how many solutions there\nare to the cosmological variational problem.\n\nIf the question is posed in a strictly proper-coordinate,\nNewtonian manner it comes out\nsomething like this: given a number of bodies moving under the influence\nof each other's gravity, all constrained to occupy the same position at\ntime zero, and having given positions (or positions in two dimensions,\nradial velocities in the third) now; how many possible trajectories are\nthere?\n\nIf the problem is formulated using the Eulerian action (minimum kinetic\nenergy for fixed total energy), the\nspace of solutions is Riemannian and the extremals are of increasing type.\nThere is thus one minimum (and one stationary solution for each number\nof kinetic foci). By way of Catastrophe Theory this is connected to\nthe Hamiltonian action (the form in which the question is asked above),\nwhich excludes some solutions which require a different value of total time.\n{\\em There is one minimum solution and a finite number of stationary\nsolutions.}\n\nFor small values of total time the energy will be forced to be \npositive (in order\nfor the system to get from one configuration to the other, the speeds must be\nlarge, hence the kinetic energy large and positive) and only the least action\nsolution will appear. This idea will be expanded below.\n\nNote that if there is no integral of energy these results do not \napply. Thus if a calculation attempts to compute the trajectories of a \nnumber of galaxies in a time-dependent,\nexternal tidal field, or any other case in which\nonly part of an interacting system is modelled, the number of solutions\ncannot be determined from this development\\footnote{This does not mean that\nLayzer's (1963) cosmic energy equation exempts all interesting distributions\nof astronomical objects from the results obtained here. An integral of\nenergy still exists for any collection of masses interacting through \ngravity; Layzer's equation only states that a quantity based on comoving\nmotions and coordinates, which resembles Newtonian energy in some\nrespects, is not conserved. Since the number of solutions a problem has\nshould not depend on which particular variables are used to write it down,\nresults obtained herein using proper, inertial coordinates apply also to\ncalculations performed in other ways.}.\n\n\\section{A Dynamical Example}\n\nThe simplest useful example of a dynamical system in astronomy is the\ntwo-body problem, dealing with a pair of\nbodies of reduced mass $M$ \nin an orbit of total energy $E$ and angular momentum $J$.\nImposing a spherical coordinate system ($r, \\theta, \\phi$)\nwith the orbit in the plane\nof the equator ($\\theta = \\pi /2$), the trajectory is given\nby\n\\begin{equation}\nr = \\frac {R_0}{1+e \\cos \\phi}\n\\label{eq:basic}\n\\end{equation}\nwith $e$ the eccentricity of the orbit and $R_0 = J^2/GM$.\nDefining the Jacobi functions in each of the coordinates\nas $\\delta r = s$, $\\delta \\theta = \\xi$, $\\delta \\phi = \\eta$\nand the perturbations in energy and angular momentum as $h$ and $l$\nrespectively, one eventually finds\n\\begin{eqnarray}\n\\xi &=& \\xi_0 \\sin (\\phi - \\phi_0) \\\\\n\\frac{d \\eta}{d \\phi} &=& \\frac{l}{J} - 2 \\frac{s}{r} \\\\\n{\\rm for}\\; e < 1, \\;s &=& \\frac{h G M}{2 E^2} \\left[ F \\sin\\phi + e + \\left(\n\t\\frac{E l}{J h} \\frac{e^2-1}{e} - \\frac{e^2+1}{2} \\right)\n\t\\cos\\phi \\right. \\nonumber\\\\\n\t& & \\left. -\\frac{1}{2} \\frac{e \\sin^2 \\phi}{1+e \\cos \\phi} -\n\t\\frac{3 e^2}{\\sqrt{1-e^2}} \\sin \\phi \\arctan \\left(\n\t\\frac{\\sqrt{1-e^2}}{1+e} \\tan \\frac{\\phi}{2} \\right) \\right] \\\\\n & & \\nonumber \\\\\n{\\rm for}\\; e>1, \\; s &=& \\frac{h G M}{2 E^2} \\left[ F \\sin\\phi + e + \\left(\n \\frac{E l}{J h} \\frac{e^2-1}{e} - \\frac{e^2+1}{2} \\right)\n \\cos\\phi \\right. \\nonumber\\\\\n & & \\left. -\\frac{1}{2} \\frac{e \\sin^2 \\phi}{1+e \\cos \\phi} -\n\t\\frac{3 e^2}{2 \\sqrt{e^2-1}} \\sin \\phi \\ln \\left|\n\t\\frac{\\sqrt{e^2-1} \\tan (\\phi /2) + 1 + e}\n\t{\\sqrt{e^2-1} \\tan (\\phi /2) - 1 - e} \\right| \\right] \\\\\n & & \\nonumber\n\\end{eqnarray}\nwhere $F$ is a constant used to adjust the zero point of $s$.\nThe first expression for $s$ is used for bound (elliptical) orbits,\nthe second for unbound (hyperbolic).\nThe practical difficulty of calculations using Jacobi functions\nis evident.\n\nThe out-of-plane Jacobi function $\\xi$ is, however, simple and gratifyingly\ngeneral. For any eccentricity (indeed, even for unbound trajectories)\nconjugate points are found on diametrically \nopposite sides of the orbit. This\nis easy to picture: rotation of the orbit through an infinitesimal\n(or even larger) angle\naround a line from the orbiting body through the primary, certainly\nan allowed variation, leaves the\nopposite point unchanged.\n\nFor very small $e$, that is for orbits close to circular, $s$ becomes\na simple sine function also, returning to zero after half an\norbit. For $e \\sim 1$, that is for orbits close to a parabola, analysis is\na bit more complicated, though $s$ is approximately sinusoidal and\nin no case does $s$ reach zero\nagain until after half an orbit. For $e>1$, but not by much, $s$\nremains approximately sinusoidal. For very large $e$ the approximation\nis better, that is the points where $s$ vanishes \nare closer to being $180^{\\rm o}$ in longitude\naway from each other; but the (unbound)\ntrajectory might not include enough movement\nin longitude to provide a conjugate point for some initial points.\n\n\nThe Jacobi function in longitude, $\\eta$, has a behavior which is in \nfull even more complicated. However, note that its derivative is\ndirectly related to $s$. It can therefore not return to zero until\nwell after $s$ changes sign. Among the three Jacobi functions, then,\n$\\xi$ has its first zero after exactly half an orbit, while the other\ntwo take longer; so\n{\\em The earliest zero for any perturbation in a two-body system\noccurs after half an\norbit, so kinetic foci are $180^{\\rm o}$ apart.}\n\nChoquard's criterion is much easier to apply. There are two points\nwhere the momentum is normal to the gradient of the potential, at\npericenter and apocenter; any pair of conjugate points must lie on\nopposite sides of one of these. Together with Morse's count of\nsolutions to the Eulerian\nvariational problem this means that there is an\ninfinite number of solutions for a given set of end points, one for \neach half-integral number of\nrevolutions of the orbit. As noted above, trajectories with energy\nlower than the lower of the potential energies of the end points are\nexcluded from consideration. Those with positive energy have one\nleast-action solution and possibly one saddle-point solution at finite\ntimes (depending on whether the first end point is taken far enough\naway from perihelion to allow the kinetic focus, $180\\arcdeg$ away in\nlongitude, to appear on the trajectory); the rest at infinite times.\n\nApplied to systems with many bodies, saddle-point\nsolutions correspond to some sort of multiple-pass trajectory.\nIf there are two bodies in an orbit that\napproximates isolated two-body motion, they can generate kinetic\nfoci for the whole system. \n\nGiven a bound two-body system with a set of endpoints and a fixed \ntime taken to go between them, the minimum-action solution will \ngive a trajectory made up of less than half an orbit. The first \nstationary-action solution will contain more than half an orbit, \na longer distance, which means a higher speed and thus higher kinetic \nenergy. The second stationary solution will require at least three\ntimes the speed of the minimum solution, thus nine times the kinetic \nenergy; few such orbits are bound. The situation for a many-body\nsystem is rather more complicated, but for most astronomical systems\na significant increase\nin the kinetic energy will make total energy positive and\nthus the system will become unbound. In this way the relatively small binding\nenergy of astronomical systems severely limits the number of saddle-point\nsolutions (unless there is, say, one or more tightly orbiting pairs of\nobjects).\n\n\\section{Continuum Solutions}\n\nThe discrete body approach to galaxy dynamics is of course an\napproximation. It may be justified by the fact that present distances\nbetween galaxies are significantly larger than galaxy dimensions, \nor (more practically) on the basis of our ignorance\nof their detailed mass distributions (including such things as dark\nmatter halos). But if we are to consider the motions of galaxies\nall the way back to their formation it becomes an increasingly bad\napproximation, and it would be better to consider a continuous fluid\nof gravitating matter.\n\nIndeed, the present picture of galaxy formation has them condensing\nout of a smooth fluid. It would be highly desirable to be able to\nfollow this process in detail while requiring a certain configuration\nas a final end point. One could investigate, for example, the \nimportance of mergers in galaxy dynamics, as well as the problems\nencountered by Dunn and Laflamme \\markcite{DL95}\n(1995) in matching a least-action\ncalculation to an n-body simulation.\n\nHowever, in attempting this\nwe are faced with a massive theoretical complication as\nthe number of degrees of freedom goes from $3n$ to infinite\\footnote{This is\nof less practical importance, as a continuum calculation always has\nsome sort of short-wavelength cutoff (which is addressed in more detail\nbelow).}. Additional practical difficulty is involved\nwith the increased complexity of the calculation, using three equations\n(continuity, Euler's and Poisson's) instead of one. However, it can\nbe done, as Susperreggi and Binney \\markcite{SB94}\n(1994) have shown (though it tends to be computationally intensive).\n\nConsider, as a first approximation to a continuous-fluid situation, a\nlarge N-body calculation. Since the results of Morse Theory do not\ndepend on the number of bodies, there still remains one minimum action\nsolution and a finite number of stationary action solutions. (The bodies\nare now of all the same mass, and are labelled with, say, their ending\ncoordinates instead of ``M31''; but the Morse-based results are unchanged.)\nAdding more bodies increases the resolution of the simulation and the\ncomputational burden, but does nothing to the theory of solutions. Therefore,\nso far as a continuous fluid may be considered as made up of discrete masses,\nhowever tiny, there remains one least-action solution and one stationary\nsolution for each possible value of the index.\n\n\n\\subsection{Orbit-Crossing and Kinetic Foci}\n\nGiavalisco et al. \\markcite{G93}\n(1993) identified orbit-crossing as a major cause of\nmultiple solutions, that is, when trajectories from different parts of\nthe fluid occupy the same point at the same time. This makes\nthe mapping of velocity to distance (a major concern of observational\ncosmology) multiple-valued. However, our question---the number of ways\nthe present velocity and density distribution can arise from the Big\nBang---is different, and orbit-crossing is not necessarily relevant.\n\nTo see this, consider a spherically symmetric part of a nearly uniform\nuniverse, of critical density for definiteness. Suppose that a small\nperturbation makes one shell slightly more dense than average and the\nshell contained immediately within it less dense. Over time the dense\nshell will expand at a slower rate than the universe as a whole, and\nthe less dense shell faster; eventually their trajectories will meet, and\nthere will be orbit-crossing (even with all shells expanding).\n\nTo locate the kinetic foci, first write the dynamical equation of a\nshell which contains a mass $m(r)$ within a radius $r$:\n\\begin{equation}\n\\ddot{r} = - \\frac{Gm(r)}{r^2}\n\\end{equation}\nwhich has the Jacobi equation\n\\begin{equation}\n\\ddot{s} = \\frac{2 G m(r)}{r^3}s\n\\end{equation}\nwhich, for shells near critical density, becomes\n\\begin{equation}\n\\ddot{s} = \\frac{1}{9t^2}s.\n\\end{equation}\nIn any spherically symmetric case $s$ can start from zero and go back\nto zero only after $r$ changes sign. In a critical universe (and, indeed,\nin any universe before a Big Crunch) this never happens; thus there\nare no kinetic foci. {\\em \nOrbit-crossing does not necessarily generate kinetic foci}.\n\nNow consider another nearly uniform universe, but this time allow \nseveral mass condensations to form. Place them in such a way as to\ngenerate two binary systems, and allow the tidal torque of each on the\nother to send them into bound orbits. In all this allow none of the\ntrajectories of mass elements to cross. After half an orbit kinetic\nfoci will be generated. {\\em Kinetic foci do not necessarily generate\norbit-crossing}.\n\nCertainly an orbit-crossing situation in the context of the cosmological\nproblem demands that two mass elements start in the same place (where\nall mass elements start, the origin) and end in the same place (where\ntheir trajectories cross). At first glance this appears to involve two\ntrajectories with identical (proper space) endpoints, and thus two solutions\nto the equations of motion. But a solution is made up of all the\ntrajectories of the bodies included, and whether it is a saddle-point\nor a minimum is an attribute of the solution as a whole, not of any\nof these bodies. In fact the two bodies that share end points in an\norbit-crossing situation are two solutions to slightly different\nequations of motion, not two different solutions to the same equation.\n\n\\subsection{Potential Flow and Kinetic Foci}\n\nA useful simplification, then, for a continuum least-action calculation\nwould be one that eliminates closed\norbits; that is, one in which there is no\nrotation. Susperreggi and Binney \\markcite{SB94}\n(1994) used a velocity field derived\nfrom a potential suggested by Herivel \\markcite{H55} (1955):\n\\begin{equation}\n{\\bf v}(x,y,z,t) = \\nabla \\alpha (x, y, z, t).\n\\end{equation}\nThe field thus derived is both laminar and irrotational; the first term\nrefers to the fact that it can have no orbit-crossing, and the second to\nthe fact that it can have no vorticity:\n\\begin{equation}\n\\nabla \\times {\\bf v} = 0\n\\label{eq:vorticity}\n\\end{equation}\nso they appear to have satisfied all parties.\n\nUnfortunately, it is possible to have rotation in a flow that has no\nvorticity. Equation (\\ref{eq:vorticity}) is satisfied by a velocity\nfield whose longitudinal ($\\phi$) component varies inversely with radius, $v_{\\phi}\n\\propto R^{-1}$; Lynden-Bell has pointed this out and, moreover,\nshows that it is just the sort of field one expects from tidal \ninteractions (Lynden-Bell\\markcite{LB96} 1996). \n{\\em A velocity field derived from a scalar potential\ncan generate kinetic foci.}\n\n\\subsection{Resolution and Kinetic Foci}\n\nThe number of solutions in a continuum calculation thus formally remains\nthe same, even if the restriction to potential flow is imposed: one\nminimum and one or several stationary solutions. Considering the latter\nthe situation can appear rather depressing, since any two-body orbit by\nany pair of mass-elements, no matter how small, will generate kinetic\nfoci and thus multiple solutions. It seems somehow unfair that a\ncosmological simulation should lose its minimum status through half the orbit\nof its smallest binary star. In practical terms, this means that a continuum\nleast-action algorithm which is strictly minimizing will find only one\nsolution, the one without so much as a half-orbit, which is not necessarily\nthe right one; while an algorithm which finds all stationary solutions\nwill find many possible answers, with no clue as to which is more probable.\n\nBut cosmological simulations rarely depict single stars. In practice\nthere is always a scale below which no detail can be seen; kinetic foci\non this scale cannot affect the minimum status of the calculation. In\na very simple example, consider a triple star made up of one tight binary\nand one wide component. If all bodies are included, a solution will only\nbe a minimum through half the orbital period of the close double. However\nif the binary is modeled by a single mass, a solution will be a minimum through\nhalf the period of the wide component. It is a matter of choice which\nis the more important trajectory to calculate--or, alternatively, \nwhether the\ncomputational burden of calculating several, perhaps many, stationary\nsolutions is worth maintaining the higher resolution.\n\nIn a more complicated situation setting the desirable resolution is \nalso more\ncomplicated. In a rich galaxy cluster, for instance, the dynamical\ntimescale of the center regions is much shorter than the outskirts, and\nvaries continuously with radius.\nWhat particular scale is best for the calculation? The answer is not\nobvious. However, the question is not restricted to least action \ncalculations, so it is at least a familiar one.\n\n\\section{Summary}\n\nThe important results of this study are as follows:\n\n{\\em If the action for the cosmological\nvariational problem can be written in proper\ncoordinates and an integral of energy exists, there is one minimum\nsolution.}\nAssuming Hamilton's Principle is used,\nthere may be additional, stationary solutions, one for each number\nof kinetic foci, if multiple-pass trajectories exist. There is a\nfinite number in total, limited by possible values of energy.\n{\\em Solutions containing at least one approximately two-body\norbit which passes through more than $180\\arcdeg$ in longitude\nare not minima.}\n\n{\\em Kinetic foci are reached only after the momentum is normal\nto the force for some body in the system.}\n\nIn so far as a continuous mass distribution may be approximated by an\narbitrarily large number of individual masses,\n{\\em a continuum least-action calculation also has a single minimum \nsolution, but generally a very large number of stationary solutions.} \nThese can be limited by setting a lower limit to the resolution of the \ncalculation. The specific size of this resolution may be difficult \nto determine.\n\n{\\em A radial velocity, rather than a distance, can be used as an\nend point in a numerical variational calculation.} Forms of the\nmodified action required have been discovered by Giavalisco et al.\n(1993) and used by Schmoldt \\& Saha (1998). {\\em Using such an\nendpoint has no effect on the number or character of solutions.}\n\n{\\em Orbit-crossing is not necessarily related to the number of\nsolutions of a continuum calculation.} \n\n\\acknowledgements\n\nIt is a pleasure to thank Donald Lynden-Bell for drawing my\nattention to the least-action problem and suggesting the radial velocity\naction. I received valuable assistance in interpreting topological\nideas from Wendelin Werner and Anthony Quas. Sverre Aarseth kindly\nprovided a copy of his n-body code to check \na sample least-action calculation. Peter McCoy made many useful\ncomments on an early version of this paper.\nThis work has been supported in part by\ngrants from Herschel Whiting, Marion and Jack Dowell, the British\nSchools and Universities Foundation May and Ward Fund, and the University of\nCambridge Institute of Astronomy.\n\n\n\\appendix\n\\section{Variable End Points}\n\nThe following derivations follow Morse \\markcite{Mo34}\n(1934) with some\nchanges in notation and terminology. \nCourant and Hilbert \\markcite{CH53} (1953) have a derivation\nfor the transversality condition which in fact results in the same\nformula; however, they require some assumptions about\nthe end manifold which do not hold in the present situation.\n\n\\subsection{The Transversality Condition}\n\nSuppose the problem to be that of minimizing the integral\n\\begin{equation}\nI = \\int_{t_1}^{t_2} L \\left( q_i,\\dot{q_i},t \\right) dt\n\\label{eq:integral1}\n\\end{equation} \nsubject to the condition that one or both of \nthe end points are not fixed but must\nlie on end manifolds of some description. \nThe solution to the problem\nis given by some extremal $g = g(t)$.\nAdmissible curves for the problem will be those with end points\nnear those of $g$ and which are continuous along with their first and\nsecond derivatives. These curves\nare described by the $r$ functions $\\alpha_h (e)$\nsuch that $\\alpha_h (0)$ gives $g$. The end points in particular\nare given by\n\\begin{eqnarray}\nt^s & = & t^s(\\alpha_1, \\ldots, \\alpha_r) \\nonumber \\\\\nq_i^s & =& q_i^s(\\alpha_1, \\ldots, \\alpha_r) \\nonumber \\\\\ns & \\in & \\left( 1,2 \\right) \\nonumber\n\\end{eqnarray}\n(the superscript 1 or 2 refers to the initial or final end point).\n Observe\n\\begin{equation}\nq_i^s(\\alpha_h (e)) = q_i^s(t^s (\\alpha_h (e)), e)\n\\label{eq:end}\n\\end{equation}\nwhere $h$ takes on the values 1 to $r$.\n \nIntegral (\\ref{eq:integral1}) is now a function of $e$; considered\nthis way, the first variation (by Liebnitz' Rule) is\n\\begin{equation}\nI'(e) = \\left[ L(t^s) \\frac{dt^s}{de} \\right]_1^2\n+ \\int_{t_1(e)}^{t_2(e)} \\sum_i \\left( \\frac{\\partial L}{\\partial q_i}\n\\frac{\\partial q_i}{\\partial e} + \\frac{\\partial L}{\\partial \\dot{q_i}}\n\\frac{\\partial \\dot{q_i}}{\\partial e} \\right) dt.\n\\label{eq:liebnitz}\n\\end{equation}\nAfter integration by parts and a bit of algebra, one obtains the\nEuler-Lagrange equations and\n\\begin{equation}\n\\left[ \\left( L - \\sum_i \\dot{q_i}\\frac{\\partial L}{\\partial \\dot{q_i}}\n\\right) \\frac{dt^s}{de} + \\sum_i \\frac{\\partial L}{\\partial \\dot{q_i}}\n\\frac{d q_i^s}{d e} \\right]_1^2 = 0.\n\\label{eq:transverse1}\n\\end{equation}\nAgain, the parametrization by $e$ is arbitrary. \nIf $de$ is multiplied out of the above equation,\nthe normal form\nof the {\\em transversality condition} is obtained.\nIf the manifold\non which the end point is allowed to vary is specified\nby means of the differentials $dq^s_i$ and $dt^s$, (\\ref{eq:transverse1})\ncontains a condition\nfulfilled by the true minimizing end point. Conversely, \nthe transversality condition can sometimes be used\nto gain some insight into the end manifold when only the Lagrangian and\nthe fact of minimization are given.\n\nIf the integral to be varied is changed from (\\ref{eq:integral1}) to the\nvelocity action,\n\\begin{eqnarray}\nI^* &=& \\int_{t_1}^{t_2} \\left( L \\left( q_i,\\dot{q_i},t \\right) \n- \\sum_j \\frac{d}{dt} \\left( q_j \\frac{\\partial L}{\\partial \\dot{q_j}} \n\\right) \\right) dt\n\\nonumber \\\\\n&=& I - \\left[\\sum_j q_j \\frac{\\partial L}{\\partial \\dot{q_j}} \\right]_1^2\n\\label{eq:velocity}\n\\end{eqnarray}\nwhere $j$ denotes those coordinates in which velocity rather than coordinate\nis fixed at the end point, the variation of the boundary term must be included\nin the transversality condition. A similar derivation to the above\nresults in the\n{\\em velocity-action transversality condition}:\n\\begin{eqnarray}\n\\left[ \\left( L - \\sum_i \\dot{q_i}\\frac{\\partial L}{\\partial \\dot{q_i}}\n- \\sum_j q_j \\frac{\\partial^2 L}{\\partial t \\partial \\dot{q}_j}\n\\right) \\frac{dt^s}{de} \\right. & + & \\sum_i \n\\frac{\\partial L}{\\partial \\dot{q_i}}\n\\frac{d q_i^s}{de} \n \\nonumber \\\\\n - \\sum_j \\left( \\frac{\\partial L}{\\partial \\dot{q_j}} + q_j\n\\frac{\\partial^2 L}{\\partial q_j \\partial \\dot{q}_j} \\right)\n\\frac{d q_j^s}{de} & -& \\left. \n\\sum_j q_j \\frac{\\partial^2 L}{\\partial \\dot{q}_j^2}\n\\frac{d \\dot{q}_j}{de} \\right]_1^2 = 0.\n\\label{eq:velocitytransverse}\n\\end{eqnarray}\n\n\\subsection{The Second Variation}\n\nApplying Liebnitz' Rule again gives\n\\begin{eqnarray}\nI''(e)&=& \\int_{t_1(e)}^{t_2(e)} \\frac{\\partial}{\\partial e}\n\\sum_i \\left(\\frac{\\partial L}{\\partial q_i} \\frac{\\partial q_i}\n{\\partial e} + \\frac{\\partial L}{\\partial \\dot{q_i}} \\frac{\\partial \\dot{q_i}}\n{\\partial e} \\right) dt \\nonumber \\\\ &+& \n\\left[ \\sum_i \\left( \\frac{\\partial L}{\\partial q_i} \\frac{\\partial q_i}\n{\\partial e} + \\frac{\\partial L}{\\partial \\dot{q_i}} \\frac{\\partial \\dot{q_i}}\n{\\partial e} \\right) \\frac{dt^s}{de} \\right]_1^2 \\nonumber \\\\ &+&\n\\left[ \\frac{\\partial}{\\partial e} \\left( L(t^s) \\right) \\frac{dt^s}{de}\n\\right]_1^2 +\n\\left[ L \\frac{d^2 t^s}{d e^2} \\right]_1^2.\n\\label{eq:bigsecond}\n\\end{eqnarray}\nAfter some algebra this becomes\n\\begin{eqnarray}\nI''(e) & = & \\int_{t_1(e)}^{t_2(e)} \\sum_i\n2 \\Omega \\left( \\frac{\\partial q_i}{\\partial e},\n\\frac{\\partial \\dot{q}_i}{\\partial e} \\right) dt +\n\\int_{t_1(e)}^{t_2(e)} \\sum_i \\frac{\\partial^2 q_i}{\\partial e^2}\n\\left( \\frac{\\partial L}{\\partial q_i}- \\frac{d}{dt} \\left(\n\\frac{\\partial L}{\\partial \\dot{q_i}} \\right) \\right) dt \\nonumber \\\\\n&+& \\left[ \\left( L - \\sum_i \\dot{q_i}\n\\frac{\\partial L}{\\partial \\dot{q_i}} \\right) \\frac{d^2 t^s}\n{de^2} + \\left( \\frac{\\partial L}{\\partial t} - \\sum_i\n\\frac{\\partial \\dot{q_i}}{\\partial t} \\frac{\\partial L}{\\partial q_i}\n\\right) \\left( \\frac{dt^s}{de} \\right)^2 \\right. \\nonumber \\\\\n&+& \\left. \n2 \\sum_i \\left( \\frac{\\partial L}{\\partial q_i} \\frac{dt^s}{de} \n\\frac{dq_i^s}{de} + \\frac{\\partial L}{\\partial \\dot{q_i}}\n\\frac{d^2 q_i^s}{de^2} \\right) \\right]_1^2. \n\\label{eq:firstsecond}\n\\end{eqnarray}\nThe second integral vanishes for extremals. \n\nWhile this version\nof the second variation is useful,\nit may be made a manifestly symmetric quadratic form\nin the variations\n\\begin{equation}\nu_h = \\frac{d \\alpha_h}{de}. \n\\end{equation}\nUsing these in equation (\\ref{eq:firstsecond}) there results \n\\begin{eqnarray}\nI''(e) & = & \\sum_{h,k} \\left[ \\left( L - \\sum_i \\frac{\\partial q_i}\n{\\partial t}\n\\frac{\\partial L}{\\partial \\dot{q_i}} \\right) \\frac{\\partial^2 t^s}\n{\\partial \\alpha_h \\partial \\alpha_k} + \\left( \\frac{\\partial L}{\\partial t} -\n\\sum_i \\dot{q_i} \\frac{\\partial L}{\\partial q_i}\n\\right) \\frac{\\partial t^s}{\\partial \\alpha_h}\n\\frac{\\partial t^s}{\\partial \\alpha_k} \\right. \\nonumber \\\\\n& +& \\left. \\sum_i \\frac{\\partial L}{\\partial q_i}\n\\left( \\frac{\\partial t^s}{\\partial \\alpha_h}\n\\frac{\\partial q_i^s}{\\partial \\alpha_k} + \n\\frac{\\partial t^s}{\\partial \\alpha_k}\n\\frac{\\partial q_i^s}{\\partial \\alpha_h} \\right) + \\sum_i\n\\frac{\\partial L}{\\partial \\dot{q}_i} \\frac{\\partial^2 q_i^s}\n{\\partial \\alpha_h \\partial \\alpha_k} \\right]_1^2 u_h u_k \\nonumber \\\\\n& + & \\sum_h \\left[ \\left( L - \\sum_i \\dot{q_i} \\frac{\\partial L}\n{\\partial \\dot{q_i}}\n\\right) \\frac{\\partial t^s}{\\partial \\alpha_h} + \\sum_i \n\\frac{\\partial L}{\\partial \\dot{q_i}}\n\\frac{\\partial q_i^s}{\\partial \\alpha_h} \\right]_1^2 \n \\frac{\\partial^2 \\alpha_h}{\\partial e^2} \\nonumber \\\\\n&+& \\int_{t_1(e)}^{t_2(e)} \\sum_i \n2 \\Omega \\left( \\frac{\\partial q_i}{\\partial e},\n\\frac{\\partial \\dot{q}_i}{\\partial e} \\right) dt \\nonumber \\\\\n&+& \\int_{t_1(e)}^{t_2(e)} \\sum_i \\frac{\\partial^2 q_i}{\\partial e^2}\n\\left( \\frac{\\partial L}{\\partial q_i}- \\frac{d}{dt} \\left(\n\\frac{\\partial L}{\\partial \\dot{q_i}} \\right) \\right) dt. \n\\label{eq:secondsecond}\n\\end{eqnarray}\n\nFor an extremal satisfying the transversality condition, the\ncoefficients of $\\partial^2 \\alpha_h / \\partial e^2$ as well as the\nlast integral vanish; and\nwe are left with the second variation integral, as in the case of\nfixed end points, and a symmetrical quadratic form in the variations\nat the end points. The variations at the end points and within\nthe integral are related by\n\\begin{eqnarray}\n\\frac{\\partial q_i}{\\partial e}& = & \\sum_h \\left[ \n \\frac{\\partial q_i}{\\partial \\alpha_h} -\n\\dot{q}_i \\frac{\\partial t}{\\partial \\alpha_h}\n \\right] u_h \\nonumber \\\\\n\\frac{\\partial \\dot{q_i}}{\\partial e}& = & \\sum_h \\left[\n\\frac{\\partial \\dot{q_i}}{\\partial \\alpha_h} -\n\\ddot{q}_i \\frac{\\partial t}{\\partial \\alpha_h}\n\\right] u_h\n\\end{eqnarray}\nwhere evaluation is carried out at the end points. Morse defines the\nquantities $b_{hk}$ for an extremal satisfying the transversality\ncondition via\n\\begin{equation}\nI''(0) = \\int_{t_1(e)}^{t_2(e)} \\sum_i\n2 \\Omega \\left( \\frac{\\partial q_i}{\\partial e},\n\\frac{\\partial \\dot{q}_i}{\\partial e} \\right) dt\n+\\sum_{h,k} b_{hk} u_h u_k\n\\end{equation}\nand uses this notation for his definitions of the index form.\n\nIf the velocity action is used, the second variation of the boundary\nterm must be calculated and added to the expression above. \nFollowing the lines of the above derivation\none finds\n\\begin{eqnarray}\nI^*{}''(e) & = & \\int_{t_1(e)}^{t_2(e)} \\sum_i\n2 \\Omega \\left( \\frac{\\partial q_i}{\\partial e},\n\\frac{\\partial \\dot{q}_i}{\\partial e} \\right) dt +\n\\int_{t_1(e)}^{t_2(e)} \\sum_i \\frac{\\partial^2 q_i}{\\partial e^2}\n\\left( \\frac{\\partial L}{\\partial q_i}- \\frac{d}{dt} \\left(\n\\frac{\\partial L}{\\partial \\dot{q_i}} \\right) \\right) dt \\nonumber \\\\\n&+& \\left[ \\left( L - \\sum_i \\dot{q_i}\n\\frac{\\partial L}{\\partial \\dot{q_i}} \n- \\sum_j q_j \\frac{\\partial^2 L}{\\partial t \\partial \\dot{q}_j}\n\\right) \\frac{d^2 t^s}\n{de^2} + \\left( \\frac{\\partial L}{\\partial t} - \\sum_i\n\\frac{\\partial \\dot{q_i}}{\\partial t} \\frac{\\partial L}{\\partial q_i}\n- \\sum_j q_j \\frac{\\partial^3 L}{\\partial t^2 \\partial \\dot{q_j}}\n\\right) \\left( \\frac{dt^s}{de} \\right)^2 \\right. \\nonumber \\\\\n&+& \n2 \\sum_i \\left( \\frac{\\partial L}{\\partial q_i} \\frac{dt^s}{de}\n\\frac{dq_i^s}{de} + \\frac{\\partial L}{\\partial \\dot{q_i}}\n\\frac{d^2 q_i^s}{de^2} \\right) -\\sum_j 2 \\left( \n\\frac{\\partial^2 L}{\\partial t \\partial \\dot{q_j}} + q_j\n\\frac{\\partial^3 L}{\\partial t \\partial q_j \\partial \\dot{q_j}}\n\\right) \\frac{d q_j}{d e} \\frac{d t^s}{d e} - \\nonumber \\\\\n&-& \\sum_j \\left( \\frac{\\partial L}{\\partial \\dot{q_j}}\n+ q_j \\frac{\\partial^2 L}{\\partial q_j \\partial \\dot{q_j}}\n\\right) \\frac{d^2 q_j^s}{d e^2} - \\sum_j q_j \\frac{\\partial^2 L}\n{\\partial \\dot{q_j}^2} \\frac{d^2 \\dot{q}_j^s}{d e^2}\n- \\sum_j q_j \\frac{\\partial^3 L}{\\partial \\dot{q_j}^3}\n\\left( \\frac{ d \\dot{q}_j^s}{d e} \\right)^2 \\nonumber \\\\\n&-& \\sum_j \\left( 2 \\frac{\\partial^2 L}{\\partial q_j \\partial \\dot{q_j}}\n+ q_j \\frac{\\partial^3 L}{\\partial q_j^2 \\partial \\dot{q_j}} \\right)\n\\left( \\frac{d q_j^s}{d e} \\right)^2 - \\sum_j \\left( 2 \n\\frac{\\partial^2 L}{\\partial \\dot{q_j}^2}\n+ q_j \\frac{\\partial^3 L}{\\partial q_j \\partial \\dot{q_j}^2} \\right)\n\\frac{d q_j^s}{d e} \\frac{d \\dot{q}_j^s}{d e} \\nonumber \\\\\n&-& \\left. \\sum_j 2 \\frac{\\partial^3 L}{\\partial t \\partial \\dot{q_j}^2}\n\\frac{d \\dot{q}_j^s}{d e} \\frac{dt^s}{de}\n\\right]_1^2.\n\\end{eqnarray}\n\nAgain, a symmetric form may be found for extremals which satisfy the\ntransversality condition. Following the above derivation, one obtains\n\\begin{eqnarray}\nI^*{}''(0) & = & \\sum_{h,k} \\left[ \\left( L - \\sum_i \\frac{\\partial q_i}\n{\\partial t}\n\\frac{\\partial L}{\\partial \\dot{q_i}} \n- \\sum_j q_j \\frac{\\partial^2 L}{\\partial t \\partial \\dot{q_j}}\n\\right) \\frac{\\partial^2 t^s}\n{\\partial \\alpha_h \\partial \\alpha_k} \\right. \\nonumber \\\\\n&+& \\left( \\frac{\\partial L}{\\partial t} -\n\\sum_i \\dot{q_i} \\frac{\\partial L}{\\partial q_i}\n- \\sum_j q_j \\frac{\\partial^3 L}{\\partial t^2 \\partial \\dot{q_j}}\n\\right) \\frac{\\partial t^s}{\\partial \\alpha_h}\n\\frac{\\partial t^s}{\\partial \\alpha_k} \\nonumber \\\\\n& +& \\sum_i \\frac{\\partial L}{\\partial q_i}\n\\left( \\frac{\\partial t^s}{\\partial \\alpha_h}\n\\frac{\\partial q_i^s}{\\partial \\alpha_k} +\n\\frac{\\partial t^s}{\\partial \\alpha_k}\n\\frac{\\partial q_i^s}{\\partial \\alpha_h} \\right) + \\sum_i\n\\frac{\\partial L}{\\partial \\dot{q}_i} \\frac{\\partial^2 q_i^s}\n{\\partial \\alpha_h \\partial \\alpha_k} \\nonumber \\\\\n&-& \\sum_j \\left( \\frac{\\partial L}{\\partial \\dot{q}_j}\n+ q_j \\frac{\\partial^2 L}{\\partial q_j \\partial \\dot{q_j}} \\right)\n\\frac{\\partial^2 q_j^s}\n{\\partial \\alpha_h \\partial \\alpha_k}\n-\\sum_j q_j \\frac{\\partial^2 L}{\\partial \\dot{q_j}^2}\n\\frac{\\partial^2 \\dot{q}_j^s}\n{\\partial \\alpha_h \\partial \\alpha_k} \\nonumber \\\\\n&-& \\sum_j 2 \\left( \\frac{\\partial^2 L}{\\partial t \\partial \\dot{q_j}}\n+ q_j \\frac{\\partial^3 L}{\\partial t \\partial q_j \\partial \\dot{q_j}}\n\\right) \\frac{\\partial q_j^s}{\\partial \\alpha_h}\n\\frac{\\partial t^s}{\\partial \\alpha_k} - \\sum_j q_j\n\\frac{\\partial^3 L}{\\partial \\dot{q}_j^3} \\frac{\\partial q_j^s}{\\partial \\alpha_h}\n\\frac{\\partial \\dot{q}_j^s}{\\partial \\alpha_k} \\nonumber \\\\\n&-& \\sum_j \\left( \\frac{\\partial^2 L}{\\partial q_j \\partial \\dot{q_j}}\n+ q_j \\frac{\\partial^3 L}{\\partial q_j^2 \\partial \\dot{q_j}}\n\\right) \\frac{\\partial q_j^s}{\\partial \\alpha_h}\n\\frac{\\partial q_j^s}{\\partial \\alpha_k}\n- \\sum_j \\left( \\frac{\\partial^2 L}{\\partial \\dot{q_j}^2}\n+ q_j \\frac{\\partial^3 L}{\\partial q_j \\partial \\dot{q_j}^2}\n\\right) \\frac{\\partial q_j^s}{\\partial \\alpha_h}\n\\frac{\\partial \\dot{q}_j^s}{\\partial \\alpha_k} \\nonumber \\\\\n&-& \\left. \\sum_j 2 q_j \\frac{\\partial^3 L}{\\partial t \\partial \\dot{q_j}^2}\n\\frac{\\partial \\dot{q}_j^s}{\\partial \\alpha_h}\n\\frac{\\partial t^s}{\\partial \\alpha_k}\n\\right]_1^2 u_h u_k \\nonumber \\\\\n&+&\\int_{t_1}^{t_2} \\sum_i\n2 \\Omega \\left( \\frac{\\partial q_i}{\\partial e},\n\\frac{\\partial \\dot{q}_i}{\\partial e} \\right) dt \\\\\n&=& \\sum_{h,k} b_{hk}u_h u_k + \\int_{t_1}^{t_2} \\sum_i\n2 \\Omega \\left( \\frac{\\partial q_i}{\\partial e},\n\\frac{\\partial \\dot{q}_i}{\\partial e} \\right) dt.\n\\end{eqnarray}\n\n\n\\begin{references}\n\n\\reference{A89} Arnold, V. I. 1989, Mathematical Methods of Classical Mechanics, 2nd. ed. (New York: Springer-Verlag, Inc.) \\\\\n\\reference{B60} Bondi, H. 1960, Cosmology, 2nd. ed. (Cambridge: Cambridge University Press); see especially chapter IX \\\\\n\\reference{C55} Choquard, P. 1955, Helvetica Physca Acta, 28, 89 \\\\\n\\reference{CH53} Courant, R., \\& Hilbert, D. 1953, Methods of Mathematical Physics, Volume I (London: Wiley-Interscience) \\\\\n\\reference{DL95} Dunn, A. M., \\& Laflamme, R. 1995, \\apjl, 443, L1 \\\\\n\\reference{H55} Herivel, J. W. 1955, Proceedings of the Cambridge Philosophical Society, 51, 344 \\\\\n\\reference{G93} Giavalisco, M., Mancinelli, B., Mancinelli, B. J. \\& Yahil, A. 1993, \\apj, 411, 9 \\\\\n\\reference{J19} Jeans, J. H. 1919, Problems of Cosmogony and Stellar Dynamics (Cambridge: Cambridge University Press) \\\\\n\\reference{L32} Lamb, H. 1932, Hydrodynamics, sixth edition (Cambridge: Cambridge University Press) \\\\\n\\reference{L63} Layzer, D. 1963, \\apj, 138, 174 \\\\\n\\reference{LB96} Lynden-Bell, D. 1996, Current Science, 70, 789 \\\\\n\\reference{M63} Milnor, J. 1963, Morse Theory (Princeton: Princeton University Press) \\\\\n\\reference{Mo34} Morse, Marston 1934, The Calculus of Variations in the Large (New York: American Mathematical Society) \\\\\n\\reference{P80} Peebles, P. J. E. 1980, The Large-Scale Structure of the Universe (Princeton: Princeton University Press) \\\\\n\\reference{P89} Peebles, P. J. E. 1989, \\apjl, 344, L53 \\\\\n\\reference{P90} Peebles, P. J. E. 1990, \\apj, 362, 1 \\\\\n\\reference{P94} Peebles, P. J. E. 1994, \\apj, 429, 43 \\\\\n\\reference{P85} Poincar\\'{e}, H. 1885, Acta Mathematica, VII, 259 \\\\\n\\reference{SS98} Schmoldt, I. \\& Saha, P. 1998, \\aj, 115, 2231 \\\\\n\\reference{SB94} Susperregi, M., \\& Binney, J. 1994, \\mnras, 271, 719 \\\\\n\\reference{TT96} Thompson, Sir William (Lord Kelvin), \\& Tait, P. G. 1896, A Treatise on Natural Philosophy, Volume 1 (Cambridge: Cambridge University Press); revised and published in 1912 as Principles of Mechanics and Dynamics, also by Cambridge University Press; the latter reprinted 1962 (New York: Dover). \\\\\n\\reference{V93} Valtonen, M. J., Byrd, G. G., McCall, M. L., \\& Innanen, K. A. 1993, \\aj, 105, 886 \\\\\n\\reference{W59} Whittaker, E. T. 1959, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 4th edition (Cambridge: Cambridge University Press) \\\\\n\\end{references}\n\n\\clearpage\n\n\\figcaption[poincare.eps]{Poincar\\'{e} diagram connecting the two\nLeast Action Principles. For a given set of end points (or manifolds)\na slice of the functional domain, which by construction contains all\nthe solutions to the problem, is plotted. The Hamiltonian action\nis the vertical\ncoordinate, the Eulerian action the horizontal coordinate.\nFor a given value of total\nenergy (the Eulerian control parameter; say, $E_1$, $E_2$ or $E_3$)\nthere will be a single minimum\nsolution and a series of stationary solutions. For a given value of\ntotal time (the Hamiltonian control parameter, say $t_1$, $t_2$ or $t_3$)\nthere will be at least\none minimum solution. In terms of Catastrophe Theory, the minimum\nsolutions form a chain of stable equilibria (shown as a solid line in\nthe figure), the stationary solutions\na chain of unstable equilibria (not shown in this figure for clarity).\nIf there were two Hamiltonian solutions\non any Eulerian branch of solutions, as shown here, it would require\nthe meeting of two chains of Hamiltonian similar equilibria (at point\nC) without\nan exchange of stability. Such a situation is forbidden by Catastrophe\nTheory, as described in the text. \\label{poincare}}\n\n\n\\end{document}\n\n"
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astro-ph0002379
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HV~Ursae Majoris, a new contact binary with early-type components \thanks{Based on the data obtained at the David Dunlap Observatory, University of Toronto}
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[
{
"author": "B. Cs\\'ak\\inst{1}\\thanks{Guest Observer, Sierra Nevada Observatory}"
},
{
"author": "L.L. Kiss\\inst{2}"
},
{
"author": "J. Vink\\'o\\inst{1,}\\inst{3}"
},
{
"author": "E.J. Alfaro\\inst{4}"
}
] |
We present the first $UBV$ and $uvby$ photometric observations for the short period variable star HV~Ursae~Majoris classified as a field RRc variable. The observed differences between the consecutive minima and the lack of colour variations disagree with the RRc-classification and suggest the possible binary nature of HV~UMa. In order to reveal the real physical status of this star, we took medium resolution ($\lambda/\Delta \lambda \approx 11000$) spectra in the red spectral region centered at 6600 \AA. Spectra obtained around the assumed quadratures clearly showed the presence of the secondary component. An improved ephemeris calculated using our and Hipparcos epoch photometry is Hel. JD$_{min}=2451346.743\pm0.001$, P$=0\fd7107523(3)$. A radial velocity curve was determined by modelling the cores of H$\alpha$ profiles with two Gaussian components. This approximative approach gave a spectroscopic mass ratio of q$_{sp}$=0.19$\pm$0.03. A modified Lucy model containing a temperature excess of the secondary was fitted to the V light curve. The obtained set of physical parameters together with the parallax measurement indicate that this binary lies far from the galactic plane, and the primary component is an evolved object, probably a subgiant or giant star. The large temperature excess of the secondary may suggest a poor thermal contact between the components due to a relatively recent formation of this contact system. \keywords{stars: binaries: eclipsing -- stars: fundamental parameters -- stars: individual: HV~UMa}
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[
{
"name": "h1918.tex",
"string": "\\documentclass[]{aa}\n\\usepackage{psfig}\n\\begin{document}\n\n\\thesaurus{06(08(08.02.2, 08.06.3, 08.09.2 HV UMa))}\n\n\\title{HV~Ursae Majoris, a new contact binary with early-type components\n\\thanks{Based on the data obtained at the David Dunlap Observatory,\nUniversity of Toronto}}\n\n\\author{B. Cs\\'ak\\inst{1}\\thanks{Guest Observer, Sierra Nevada \nObservatory} \\and L.L. Kiss\\inst{2} \\and J. Vink\\'o\\inst{1,}\\inst{3}\n\\and E.J. Alfaro\\inst{4}}\n\n\\institute{Department of Optics \\& Quantum Electronics, University of Szeged,\nPOB 406, H-6701 Szeged, Hungary\n\\and Department of Experimental Physics and Astronomical Observatory,\nUniversity of Szeged,\nSzeged, D\\'om t\\'er 9., H-6720 Hungary\n\\and\nResearch Group on Laser Physics of the Hungarian Academy of Sciences,\nSzeged \\and\nInstituto de Astrof\\'\\i sica de Andaluc\\'\\i a, CSIC, P.O. Box 3004,\nE-18080, Spain}\n\n\\titlerunning{HV Ursae Majoris, a new contact binary}\n\\authorrunning{Cs\\'ak et al.}\n\\offprints{l.kiss@physx.u-szeged.hu}\n\\date{received 15 December 1999, accepted 28 January 2000}\n\n\\maketitle\n \n\\begin{abstract}\nWe present the first $UBV$ and $uvby$ photometric observations for\nthe short period variable star HV~Ursae~Majoris classified as a\nfield RRc variable. The observed differences between the consecutive minima\nand the lack of colour variations disagree with the RRc-classification\nand suggest the possible binary nature of HV~UMa. In order to\nreveal the real physical status of this star,\nwe took medium resolution ($\\lambda/\\Delta \\lambda \\approx\n11000$) spectra in the red spectral region centered at 6600 \\AA.\nSpectra obtained around the assumed quadratures clearly\nshowed the presence of the secondary component.\n\nAn improved ephemeris calculated using our and Hipparcos\nepoch photometry is Hel. JD$_{\\rm min}=2451346.743\\pm0.001$,\nP$=0\\fd7107523(3)$.\nA radial velocity curve was determined by modelling the cores of H$\\alpha$\nprofiles with two Gaussian components.\nThis approximative approach gave a spectroscopic\nmass ratio of q$_{\\rm sp}$=0.19$\\pm$0.03. A modified Lucy model\ncontaining a temperature excess of the secondary was fitted to\nthe V light curve. The obtained set of physical parameters together\nwith the parallax measurement indicate that this binary lies\nfar from the galactic plane, and the primary component is\nan evolved object, probably a subgiant or giant star.\nThe large temperature excess of the secondary may suggest\na poor thermal contact between the components due to a relatively\nrecent formation of this contact system.\n\n\\keywords{stars: binaries: eclipsing -- stars: fundamental parameters --\nstars: individual: HV~UMa}\n \n\\end{abstract}\n\n\\section{Introduction}\nThe first note on the possible light variability\nof HV~Ursae~Majoris (= HD~103576 = HIP~58157,\n$\\langle V \\rangle=8.69$, $\\Delta V=0.28$, $P=0\\fd355385$,\n$\\pi_{\\rm Hipp}=3.12\\pm1.23$ mas, $d_{\\rm Hipp}=320^{+210}_{-90}$ pc) was\npublished by Penston (1973) who gave an 'uncertain'\nmark to the range of V-magnitude (``var? V=8.60--8.83'').\nThe periodic nature of the light variation was discovered by \nthe Hipparcos satellite (ESA 1997)\nand the star was classified as an RRc variable. There is\na note in ESA (1997) about the possibility of a double period but no\nfirm conclusion was drawn. ESA (1997) gives a spectral type\nA3, while Slettebak \\& Stock (1959) published A7.\n\nWe started a long-term observational project of Str\\\"omgren photometry and\nspectroscopy of the newly discovered bright Hipparcos variables. The\nfirst results have already appeared in Kiss et al. (1999a, b). Since the\nperiod, spectral type and light curve do not exclude the possibility of\nwrong classification, accurate determination of the fundamental physical\nparameters is highly desirable.\n\nThe main aim of this paper is to present the first $UBV$ and $uvby$\nphotometry for HV~UMa. Also, our radial velocity measurements are\nthe first time-resolved spectroscopic observations of this\nstar to date. The paper is organised as follows: the observations\nare described in Sect.\\ 2, Sect.\\ 3 deals with data analysis\nand the obtained physical parameters, while a discussion\nof the results is given in Sect.\\ 4. A final list of conclusions\nis presented in Sect.\\ 5.\n\n\\section{Observations}\n\n\\subsection{Photometry}\n\nThe Str\\\"omgren $uvby$ photometric observations\nwere carried out on 9 nights\nin June, 1999, using the\n0.9 m telescope at Sierra Nevada Observatory (Spain) equipped with a\nsix-channel (uvby+$\\beta$)\nspectrograph photometer (Nielsen 1983).\nEarlier, $UBV$ measurements were obtained on one single night\nin March, 1999, using the 0.4 m Cassegrain-type telescope of\nSzeged Observatory equipped with a single-channel Optec SSP-5A\nphotometer. These observations covered only 5 hours and\nrevealed a 0.2 mag variation between two consecutive minima.\nWe carried out differential photometry with respect to HD~103150\n($V$=8.45, $B-V$=0.54, $b-y$=0.335, $m_{\\rm 1}$=0.149, $c_{\\rm 1}$=0.381 mag).\nThe overall accuracy of the standard transformation\nis about $\\pm0.01$ mag for $V$, $b-y$\nand $m_1$ and $\\pm0.02$ mag for $c_1$.\nThe light and colour curves were phased using the\ncorrected ephemeris (see below) and are plotted in Fig.\\ 1.\n\n%Table 1.\n\\begin{table}\n\\caption{The journal of observations}\n\\begin{center}\n\\begin{tabular} {ll}\n\\hline\nJulian Date & type\\\\\n\\hline\n2451263 & $UBV$\\\\\n2451309 & spectr.\\\\\n2451310 & spectr.\\\\\n2451340 & $uvby$\\\\\n2451341 & $uvby$\\\\\n2451342 & $uvby$\\\\\n2451343 & $uvby$\\\\\n2451345 & $uvby$\\\\\n2451346 & $uvby$\\\\\n2451347 & $uvby$\\\\\n2451349 & $uvby$\\\\\n2451350 & $uvby$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n%Fig. 1.\n\\begin{figure}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=fig1.eps,width=\\linewidth}\n\\caption{The light and colour curves of HV~UMa phased with the\nadopted ephemeris (see text)}\n\\end{center}\n\\label{fig1}\n\\end{figure}\n\n\\subsection{Spectroscopy}\n\n%Fig. 2.\n\\begin{figure}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=fig2.eps,width=\\linewidth}\n\\caption{Sample spectra around the quadratures and minima.\nThe presence of the secondary component is obvious.}\n\\end{center}\n\\label{fig2}\n\\end{figure}\n\nThe spectroscopic observations were carried out at David Dunlap Observatory\nwith the Cassegrain spectrograph attached to the 74\" telescope on two\nnights in May, 1999. The detector and the spectrograph setup were the same\nas used by Vink\\'o et al. (1998). The resolving power\n ($\\lambda / \\Delta \\lambda$) was 11,000 and the signal-to-noise\nratio reached 30--50, depending on the weather conditions.\nThe spectra were centered on 6600 \\AA\\ and\nreduced with standard IRAF tasks, including bias removal,\nflat-fielding, cosmic ray elimination, aperture extraction (with the task\n$doslit$) and wavelength calibration. For the latter, two FeAr spectral\nlamp exposures were used, which were obtained before and\nafter every three stellar exposures. The sequence of observations\nFeAr-var-var-var-FeAr was chosen because of the short period of\nHV~UMa. Careful linear interpolation between the two comparison\nspectra was applied in order to take into account the sub-pixel\nshifts of the three stellar spectra caused by the movement of\nthe telescope. We chose an exposure time of 10 minutes, which corresponds\nto 0.01 in binary orbital phase, avoiding phase smearing of the radial\nvelocity curve. The spectra were normalized to the continuum by fitting\na cubic spline, omitting the region of H$\\alpha$.\n\nBesides a few telluric features, only the H$\\alpha$ line\ncould be detected with acceptable S/N ratio in our\n200 \\AA-wide spectra. At the phases of maximum light\nthe $H\\alpha$ line exhibited significant broadening and\nan excess bump appeared on the wings alternating between\nthe blue and the red side (see Fig.\\ 2). It can be interpreted\nmost easily as the effect of a close companion star,\ntherefore HV UMa is most probably a spectroscopic binary.\nFig.\\ 2 shows a few sample spectra with the calculated\norbital phase indicated on the right side of every spectrum.\n\n\\section{Physical parameters}\n\n\\subsection{Epoch and period}\n\nThe Hipparcos data suggested that the light variation\nof HV~UMa can be described with a single period of\n$0\\fd355385$ (ESA 1997). We observed only\none moment of minimum (Hel. JD = 2451346.388), but the consecutive\nminimum appeared to be slightly fainter, therefore, we adopted a\ndoubled Hipparcos period as a first approach ($0\\fd71077$) and shifted\nthe observed time of minimum with $0\\fd355385$ to obtain the final\nepoch Hel. JD$_{\\rm min}=2451346.743\\pm0.001$.\n\nThe next step was to refine the period. This was done by\nphasing Hipparcos epoch photometry with the newly determined\nepoch and the doubled Hipparcos-period. The resulting phase diagram\nshowed a shift of $\\Delta \\phi \\approx 0.1$ (=$0\\fd071$).\nThat shift was eliminated by recalculating the period until\ncorrect phase diagrams for both our and Hipparcos data (Fig.\\ 3) were\nreached.\nThe resultant period is $P=0\\fd7107523(3)$. The fact that\nearlier Hipparcos data agree very well with our data suggests a\nquite stable period of HV~UMa.\n\n%Fig. 3.\n\\begin{figure}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=fig3.eps,width=\\linewidth}\n\\caption{Hipparcos epoch photometry data phased with\nthe finally adopted ephemeris (see text)}\n\\end{center}\n\\label{fig3}\n\\end{figure}\n\n\\subsection{Classification}\n\nThe shape of the light curve, i.e. the continuous light\nvariation and the very deep secondary minimum (almost\nas deep as the primary one), the absence of significant\ncolour variation, the appearance of the secondary line in the spectra\nat the quadrature phases all suggest that HV~UMa is probably\nan eclipsing contact binary. This is confirmed\nby its low mass ratio and a consistent model of the\nlight curve (see below).\n\nComparing the light curve phased with the final epoch\nand period (Fig.\\ 1) with the line profiles\nobserved at phases of maximum light (Fig.\\ 2) it is visible\nthat the secondary line appears on the {\\it blue} side\nat the $\\phi = 0.27$ quadrature phase that follows the\ndeeper minimum, while this bump is redshifted at\n$\\phi = 0.77$. This indicates that the smaller companion star\napproaches us after the primary minimum, therefore that\nminimum is due to an occultation eclipse. The weak\npoint of this analysis is that the light curve is\nnot very well covered around the minima either by\nthe Hipparcos data or our observations. The\ndata obtained at Sierra Nevada have better inner precision\n(less scatter) than those provided by Hipparcos,\nand these data indicate that the\nminimum at $\\phi = 0.0$ is slightly deeper. Therefore,\nwe adopted this eclipse as primary minimum, but this needs\nfurther confirmation. If the deeper minimmum is really\ndue to an occultation eclipse then HV~UMa is a so-called\nW-type contact binary.\n\nContact binaries can contain early (O--B) or\nlate (G--K) spectral type stars. The latter group is\nreferred to as the W~UMa stars, while the former is known\nas early-type contact systems. The colours of HV~UMa\nindicate early F spectral type, therefore HV~UMa is\nan ``intermediate'' type contact binary between the\nW~UMa stars and the OB-type contact systems. The\nsurface temperature and the line profile of the HV~UMa\nsystem makes it similar to the known contact systems\nUZ~Leo and CV~Cyg (Vink\\'o et al., 1996).\n\n\\subsection{Radial velocities and spectroscopic mass ratio}\n\nSince the secondary component is only partly resolved, the\nradial velocities must be determined by modelling the individual\nline profiles in order to avoid blending effects (e.g. systematic\ndecrease of the velocity amplitude). For this purpose\nwe chose those spectra that were obtained around the quadratures.\nThese show the presence of the secondary most clearly. One spectrum\naround light minimum was also modelled to test the applied method.\n\nBecause the H$\\alpha$ profile is strongly affected by the\nStark broadening and shows wide non-gaussian wings, we\nnormalized the profiles to the surrounding continuum,\nand selected\nthe lower part of the profiles below the 0.9 intensity value.\nWe fitted two individual Gaussian profiles to the line cores adjusting\nthe amplitudes, FWHM values and line core positions. The initial\nvalues of these parameters were estimated from two spectra very close to\nthe quadratures ($\\phi$=0.25 and 0.77). \nThe FWHM converged very quickly to the final values, being 7.6 \\AA\\ and\n4.0 \\AA\\ for the primary and secondary components, respectively.\nLine depths changed slightly from spectrum to spectrum, as the\ncontributions are phase-dependent, resulting in 0.29--0.30 for the primary\nand 0.07--0.10 for the secondary (note, that these values mean\nline depths below 0.9 normalized intensity). The fitted\nline core positions resulted in the radial velocity variations for\nboth components. Sample spectra with the fitted profile are shown\nin Fig.\\ 4, while the radial velocities are presented in Table\\ 2.\nThe estimated accuracy of the individual velocities is about 5 km~s$^{-1}$ for the\nprimary, and 10 km~s$^{-1}$ for the secondary, which is mainly\ndetermined by the resolution of the line core in wavelength.\nThe velocity amplitudes resulting from this method\nare 47$\\pm$1.5 km~s$^{-1}$ and 254$\\pm$10\nkm~s$^{-1}$, where the uncertainties\nare due to the random errors caused\nby the observational scatter. The corresponding mass-ratio is\n$q_{\\rm sp}=m_{\\rm sec}/m_{\\rm pri}=0.185\\pm0.01$.\n\nHowever, as was also pointed out by the referee, this kind of\nvelocity determination may contain a large amount of systematic\nerror, mainly due to the assumed Gaussian shape of the individual\nline profiles. The intrinsic H$\\alpha$ profiles of the components\nof HV~UMa are probably quite different from Gaussian, therefore\nthis approach can be considered as only the first approximation\nfor extracting the radial velocities from the H$\\alpha$ profiles.\nThe major part of the systematic error is governed by the shape of the \nwing of the primary component's model profile on the side where the\nsecondary star appears (blueward at $\\phi = 0.25$ and redward\nat $\\phi = 0.75$ phases). It is well visible in Fig.\\ 4 that the\nposition of the secondary line is shifted toward larger velocities with\nrespect to the position of the ``hump'' on the observed profile,\ndue to the increasing contribution of the primary line toward\nthe main minimum of the combined line. If the primary line was steeper on \nthe side where the secondary line exists, overlapping the secondary\nby a smaller amount, then the\nsecondary line would be less shifted, thus, its position would be\ncloser to the local hump on the observed profile, resulting in \na smaller radial velocity of the secondary. On the other hand,\na shallower secondary profile would give us systematically\nhigher velocities due to the same reason.\n\nIn order to estimate\nthe amount of this kind of systematic error, we simply determined\nthe positions of the two local minima (the main minimum and the \nsecondary's hump) on the profiles observed around quadratures \n(four spectra around $\\phi = 0.25$ and two around $\\phi = 0.75$)\nwhen the presence of the hump appeared to be most prominent.\nThis was done interactively, by eye, plotting the line profiles\non the computer screen, which again introduced some subjectivity\ninto the procedure, but it is stressed that this is done only\nfor estimating the {\\it errors} of the velocities and not \nfor obtaining their actual values. Of course, the velocities\nof the secondary measured in this way were systematically smaller\nthan those obtained by the Gaussian fitting. The velocities\nof the primary were almost the same, as could be expected.\nThe total amplitude turned out to be $K' = 280$ km~s$^{-1}$, while \nthe mass ratio changed to $q' = 0.22$. Comparing these values\nwith the results of the Gaussian fitting, we conclude that\nthe errors of the radial velocity amplitude and the spectroscopic\nmass ratio (both random and systematic) are approximately $\\pm 23$ \nkm~s$^{-1}$ and $\\pm 0.03$, respectively. The finally adopted\nparameters determined spectroscopically, together with their\nerrors are collected in Table\\ 3. It is important to note\nthat the mass ratio can be refined by modelling the light curve\n(Sect. 3.4), but the total velocity amplitude is tied only \nto the spectroscopic data, thus, its uncertainty will directly\nappear in the absolute parameters of the system.\n\n%Table 2.\n\\begin{table}\n\\caption{The observed heliocentric radial velocities obtained\nby the Gaussian fit.\nThe velocity resolution is about 5 km~s$^{-1}$.}\n\\begin{center}\n\\begin{tabular} {llrr}\n\\hline\nHel. JD & $\\phi$ & $V_{\\rm rad}(prim.)$ & $V_{\\rm rad}(sec.)$ \\\\\n2400000+ & & [km/s] & [km/s] \\\\\n\\hline\n51309.6206 & 0.77 & $-$47 & 251\\\\\n51309.6396 & 0.80 & $-$51 & 242\\\\\n51309.6471 & 0.81 & $-$42 & 246\\\\\n51310.6411 & 0.21 & 41 & $-$252\\\\\n51310.6485 & 0.22 & 45 & $-$243\\\\\n51310.6562 & 0.23 & 50 & $-$243\\\\\n51310.6643 & 0.24 & 54 & $-$238\\\\\n51310.6719 & 0.25 & 50 & $-$243\\\\\n51310.6794 & 0.26 & 50 & $-$243\\\\\n51310.6893 & 0.27 & 45 & $-$238\\\\\n51310.6964 & 0.28 & 41 & $-$252\\\\\n51310.7037 & 0.29 & 45 & $-$247\\\\\n51310.7436 & 0.35 & 41 & $-$233\\\\\n51310.8423 & 0.49 & 9 & 9\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n%Fig. 4.\n\\begin{figure}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=fig4.eps,width=\\linewidth}\n\\caption{The observed (crosses) and fitted (solid lines) Gaussian\nline profiles at two quadrature phases.}\n\\end{center}\n\\label{fig4}\n\\end{figure}\n\n\\subsection{Light curve modelling}\n\nThe V-light curve was synthesized with the computer\ncode {\\it BINSYN} described briefly in Vink\\'o et al. (1996).\nThis code is based\non the usual Roche-model characterized by the\ngeometric parameters $q_{\\rm ph}$ (photometric mass-ratio),\n$F$ (fill-out) and $i$ (orbital inclination).\nThe relative depth\nof the eclipses were modelled introducing the relative\ntemperature excess of the secondary\n$X = (T_{\\rm sec} - T_{\\rm pri})/ T_{\\rm pri}$ (hot-secondary model).\nBecause the primary minimum turned out to be due to occultation,\nthe phases were shifted by 0.5 assigning $\\phi = 0.0$\nto the transit eclipse (built-in default in {\\it BINSYN}).\n\n%Fig. 5.\n\\begin{figure}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=fig5.eps,width=\\linewidth}\n\\caption{The observed (crosses) and calculated H$\\alpha$ profiles at\n$\\phi$=0.25. The spectrum was calculated by an ATLAS9 code adopting\n$T_{\\rm eff}=7000$ K, log~$g$=4.0 and full radial velocity amplitude\nof 300 km~s$^{-1}$. The bottom panel shows the residual intensities\nfor the adopted fit compared with two other models (6750 K and 7250 K).\nThe overall agreement is the best for $T_{\\rm eff}=7000$ K. The sharp\nabsorption features are atmospheric telluric lines.}\n\\end{center}\n\\label{fig5}\n\\end{figure}\n\nFirst, the effective temperature of the primary component\nwas estimated based on synthetic colour\ngrids by Kurucz (1993) and the observed mean Str\\\"omgren colour\nindices ($\\langle b-y \\rangle = 0.19$ mag, $ \\langle m_1 \\rangle\n= 0.15$ mag,\n$\\langle c_1 \\rangle = 0.77$ mag), resulting in $T_{\\rm eff} = 7300 \\pm 200$\nK and $\\log g = 4.0 \\pm 0.3$ dex (assuming $E(B-V) = 0$\nand solar chemical abundance). The interstellar reddening\nin the direction and distance of HV UMa is expected to be small,\nbecause this variable lies far from the galactic plane.\nTU UMa, an RR Lyr variable lying 17$^\\circ$ SE from HV UMa also has a\nnegligible colour excess (Liu \\& Janes, 1989).\n\nOther parameters necessary for modelling the binary star\nwere as follows.\nA linear limb-darkening law with coefficient\n$u = 0.61$ was adopted from tables of Al-Naimiy (1977).\nThe gravity darkening exponent and the bolometric\nalbedo were chosen at their usual values for\nradiative atmospheres: $\\beta = 0.25$ and $A = 1.0$.\nAll these parameters were kept fixed during the\nsolution for the best light-curve model.\n\nThe light-curve fitting was computed using a controlled\nrandom search method, the so-called Price algorithm\n(Barone et al., 1990, Vink\\'o et al., 1996).\nThe optimized parameters were $q_{\\rm ph}$, $F$, $i$ and\n$X$. The best solution was searched for in the following\nparameter domains: $0.05 < q < 0.5$, $1.01 < F < 1.99$,\n$50 < i < 90$ and $<-0.2 < X < +0.2$. The fit quickly\nconverged to low inclination and low mass ratio values\nthat were expected from the shallow eclipses\n($\\Delta V \\approx 0.3$ mag) and\nthe small spectroscopic mass ratio ($q_{\\rm sp} = 0.19$).\nAlso, it turned out that there are strong correlations\nbetween the optimized parameters.\nDue to this correlation, the physical parameters\ndetermined from the light curve fitting cannot\nbe considered as a unique solution: certain\nparameter combinations describe the light curve\nalmost equally well. In these cases the combination\nof photometric and spectroscopic information is\nvery important: one can use the spectroscopic\ndata to determine a consistent set of physical\nparameters that gives the best model fitting all\nthe available data.\n\nIn order to combine the photometric and spectroscopic\ninformation and find a consistent description of the system,\nwe modelled the observed H$\\alpha$ line profiles using\nthe parameters from the light curve fitting.\nThe model line profiles were computed by\nconvolving an intrinsic H$\\alpha$ profile of a\nnon-rotating star with the Doppler-broadening profile\nof the contact binary. The broadening profiles were\ncalculated with the WUMA4 code (Rucinski, 1973).\nFor the determination of the intrinsic H$\\alpha$ profile\nwe used Kurucz's ATLAS9 code modified by John Lester.\nThis approach, however, has some limitations, because\nthe H$\\alpha$ line is strongly affected by NLTE-mechanisms,\ntherefore the ATLAS9-model profile will be somewhat\ndifferent from the real intrinsic profile, especially\nnear the line core. Thus, only a crude comparison\nbetween the modelled and observed line profiles was\npossible, neglecting the differences in the line core.\n\n%Fig. 6.\n\\begin{figure}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=fig6.eps,width=\\linewidth}\n\\caption{Fitted light curve of HV~UMa. Note a 0.5 shift in phase\nto get a transit eclipse at $\\phi$=0.}\n\\end{center}\n\\label{fig6}\n\\end{figure}\n\nHowever, it turned out that the originally adopted\neffective temperature $T_{\\rm eff} = 7300$ K was too high.\nWith this temperature, the Stark-wings of the H$\\alpha$\nline are so strong that they overwhelm the rotational\nbroadening, producing much wider line profiles than\nobserved. Thus, we reduced the value of the effective\ntemperature until satisfactory agreement was found\nbetween the observations and the broadened model profiles.\nThe resulting fit is plotted in Fig.\\ 5 together with the\nobserved line at $\\phi = 0.25$.\nThe residuals of three model profiles are also shown.\nIt can be seen that\nat $T_{\\rm eff} = 6750$ K the wings can be fitted quite\nwell, but the computed line core is too shallow.\nOn the other hand, if $T_{\\rm eff} = 7250$ K is used,\nthe computed line core agrees better, but the wings\nare wider. Thus, $T_{\\rm eff} = 7000$ K was accepted\nas a compromise. The Str\\\"omgren-colours of the\nKurucz-grid for this temperature are almost the\nsame as for the originally adopted 7300 K, therefore\nthis temperature is still consistent with the\nphotometric colours.\n\nThe light curve modelling was recomputed with\n$T_{\\rm eff} = 7000$ K. The optimized parameters changed\nonly slightly, resulted in a slightly smaller mass ratio\nand a slightly higher temperature excess. Table\\ 3 shows\nthe final set of physical parameters, while the fitted\nlight curve is visible in Fig.\\ 6. The distribution\nof the random points around the $\\chi^2$-minimum in\nthe parameter space is plotted in Fig.\\ 7. The structure\nof the sub-spaces in this diagram indicates the\ncorrelation between the different parameters.\n\n%Fig. 7.\n\\begin{figure}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=fig7.eps,width=\\linewidth}\n\\caption{Distribution of random points around the minimum of $\\chi^2$.}\n\\end{center}\n\\label{fig7}\n\\end{figure}\n\nAnother light curve model was computed in order to test\nthe effect of the gravity darkening and reflection\nparameters that were originally fixed as if the\natmosphere was radiative. The model with their\n``convective'' values $\\beta = 0.08$ and $A = 0.5$\nresulted in an even larger temperature excess than\nin the radiative case. Because the temperature excess\nof the secondary is only a ``correction'' parameter\nin the light curve solution and it may not mean\nreal temperature difference, it would be difficult\nto explain physically a very large value of the temperature\nexcess that still does not cause significant colour\nvariation. Thus, we adopted the model\nwith radiative atmospheric parameters as our final\nsolution, and this model is listed in Table\\ 3.\nNote that the errors\nof the fitted parameters (3rd column) are difficult to estimate,\nbecause of the parameter correlation. We monitored the behaviour\nof the $\\chi^2$ function during the optimization and assigned\nuncertainties to each parameter according to the spread of\nthe random points for which $\\chi^2~<~0.5$. This criterion\ndefines those solutions when the fitted curve runs well within\nthe error bar at each measured normal point, giving a feasible\nfit to all observations. The parameter correlation means that\nthe uncertainties are also not independent of each other:\ne.g. slightly decreasing $q$ forces increasing $F$ or $X$ \n(see Fig.7). The uncertainties of the calculated parameters\n(3rd panel in Table 3) were estimated assuming a $\\pm23$ km~s$^{-1}$\nerror in the radial velocity amplitude $K$.\n\nBecause of the correlation between the optimized\nparameters, it is very important to check whether\nthe radial velocities calculated from the model\nmatch the observed velocities. This comparison\nis plotted in Fig.\\ 8 where an almost perfect\nagreement can be seen. The low mass ratio results\nin the distortion of the sinusoidal velocity curves,\nwhich is a well-known effect in close binaries.\n\n%Table 3\n\\begin{table}\n\\caption{Physical parameters of HV~UMa.}\n\\begin{center}\n\\begin{tabular} {lll}\n\\hline\nFitted parameters & Value & $\\sigma$ \\\\\n\\hline\n{\\it spectroscopy} & &\\\\\n\\hline\n$K$~(km~s$^{-1})$ & 300 & 23\\\\\n$q_{sp}$ & 0.19 & 0.03\\\\\n$T_{eff}$~(K) & 7000 & 200\\\\\n\\hline\n{\\it photometry} & &\\\\\n\\hline\n$q_{ph}$ & 0.184 & 0.05\\\\\n$F$ & 1.77 & 0.15\\\\\n $i$ & 57.3 & 0.4\\\\\n$X$ & 0.13 & 0.03\\\\\n\\hline\nCalculated parameters & Value & $\\sigma$ \\\\\n\\hline\n$a$ (10$^6$ km) & 3.48 & 0.25 \\\\\n$M_1 (M_\\odot)$ & 2.8 & 0.6 \\\\\n$M_2 (M_\\odot)$ & 0.5 & 0.17 \\\\\n$R_1 (R_\\odot)$ & 2.62 & 0.25 \\\\\n$R_2 (R_\\odot)$ & 1.18 & 0.16 \\\\\n$\\rho_{pri}$~(g~cm$^{-3}$) & 0.2 & 0.05 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n%Fig. 8.\n\\begin{figure}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=fig8.eps,width=\\linewidth}\n\\caption{The radial velocity curves of the primary and secondary components.\nSymbols correspond to the directly measured values, while solid lines\ndenote the calculated ones from the photometric model.}\n\\end{center}\n\\label{fig8}\n\\end{figure}\n\n\\section{Discussion}\n\nThe spectroscopic detection of the secondary component\nand the success of modelling the light- and velocity\ncurves as well as the H$\\alpha$ line profile supports\nour conclusion that HV~UMa is not a short-period\nRR Lyr variable, but an eclipsing binary system.\nThe physical parameters listed in Table\\ 3 give\na deep contact configuration of this binary, explaining\nnaturally the lack of significant colour change\nduring the light variation cycle, which would be\npeculiar in a pulsating variable. Since the primary\nminimum is due to occultation, HV~UMa is a so-called\nW-type contact binary (systems exhibiting transit\neclipses as primary minima are called A-type).\n\nIt is well known that contact binaries can be\nformed either from hot, early-type stars or\ncool, late-type stars, the latter representing the\nclass of W~UMa-type variables (see e.g. Rucinski, 1993;\nFigueiredo et al., 1994 for reviews).\nThe surface temperatures of W~UMa-systems are\nusually below 7000 K, while the temperatures\nof early-type contact binaries show a much wider\nrange, between 10,000 and 40,000 K. Thus, HV~UMa\nfalls into the temperature regime between 7000 and\n10,000 K that is relatively rarely occupied by\ncontact binaries. Systems like HV~UMa may\nrepresent a transition population between early-type\nand late-type contact binaries (although even the\nexistence of such transition is questionable).\nThese systems\nlie on the boundary between radiative and convective\natmospheres, at about late A - early F spectral\ntypes. Detailed studies of such\nsystems would be important, because the formation\nand the structure of early-type systems having radiative\nenvelopes and late-type contact binaries having\nconvective envelopes is probably quite different.\n\nThe period value $P \\approx 0.711$ day\nalso indicates that HV~UMa is not a typical contact\nsystem. Recent statistical studies based on\nthe data from the $OGLE$ microlensing survey\n(Rucinski, 1998 and references therein) have shown\nthat the number of contact systems strongly decreases\nabove $P = 0.7$ day, and there is a well-defined limit\nat $P \\approx 1.5$ days. Therefore, HV~UMa is a member\nof the relatively rare ``longer-period'' contact\nbinaries, although a few contact systems with\n$P > 2$ days definitely exist, at least close to the\ngalactic bulge. On the other hand, there exists a\nperiod-colour relation of ``normal'' W~UMa-stars\nwith period $P < 1$ day, which indicates that longer\nperiod systems have bluer colour. On the plot of\nthe empirical $\\log P - (b-y)_0$ relation (Rucinski,\n1983) the position of HV UMa, using the mean colour\n$\\langle b-y \\rangle = (b-y)_0 = 0.19$ (Fig.1, assuming zero reddening)\nand our revised period $\\log P = -0.1483$ (Sect. 3.1),\nis close to the upper boundary of the relation,\nsuggesting an atypical, but not peculiar contact system.\n\nA more recent\n$\\log P - (B-V)_0$ diagram based on Hipparcos-parallaxes\nhas been published by Rucinski (1997, see his Fig.2).\nThe position of HV~UMa on this diagram was calculated \nassuming $E(B-V) = 0$ and $(b-y) / (B-V) = 0.7$, \nresulting in $(B-V)_0 \\approx 0.27$. These data show that\nthe position of HV~UMa is entirely consistent with that of\ninvolving the older $\\log P - (b-y)$ relation, being close to\nthe blue short-period envelope (BSPE, Rucinski, 1997),\nbut the system is definitely redder than the upper limit\ndefined by the BSPE, consistently with other contact binaries.\nAlso, a rough comparison of HV~UMa with other contact binaries\non the $\\log P - (V-I)_0$ diagram based on $OGLE$-photometry \n(Rucinski, 1998) strengthens the status of HV~UMa outlined above,\nagain, being closer to the BSPE than other systems with similar\nperiod,\nalthough the lack of observed $(V-I)$ colour of HV~UMa limits\nthe reliability of this comparison at present. \nIt can be concluded that all available measurements and pieces\nof information consistently support the contact binary nature of\nHV~UMa.\n\nThe new physical parameters collected in Table\\ 3, together with\nthe Hipparcos-parallax ($\\pi = 3.12 \\pm 1.23$ mas) enable\nus to estimate the evolutionary status of HV~UMa, provided it\nis indeed a contact binary with those parameters. The coordinates\nand the distance based on the Hipparcos-parallax indicate\nthat HV UMa is a halo object: its distance from the galactic\nplane is $z \\approx 300$ pc, which means that $[$Fe/H$] = 0$ \n(assumed during the analysis of the line profiles and the colour \nindices) may not be true. Because the spectroscopic observations\npresented in this paper have limited spectral range \n($\\Delta \\lambda = 200$ \\AA\\ around 6600 \\AA), and this region\ndoes not contain significant metallic lines in early-type stars,\nthe spectroscopic derivation of $[$Fe/H$]$ was not possible.\nThus, because of the lack of further information we assumed\n$[$Fe/H$] = 0$, which is not impossible for halo objects, but\n$[$Fe/H$] < 0$ is also likely.\n\n\\begin{figure*}\n\\begin{center}\n\\leavevmode\n\\psfig{file=fig9a.eps,height=5cm,width=7cm}\n\\psfig{file=fig9b.eps,height=5cm,width=7cm}\n\\end{center}\n\\caption{Effect of metallicity on the H$\\alpha$ line profile. Left panel:\nthe dependence of the H$\\alpha$ equivalent width on the metallicity\nfor three temperatures (labeled) and two $\\log g$ values (4 and 3.5)\nfor each temperature. Right panel: comparison of the H$\\alpha$ of low\nmetallicity models (for $T_{\\rm eff} = 7000$ and $7500$ K)\nwith the observed profile.}\n\\end{figure*}\n\nThe referee suggested the possibility that\nthe low metal content of HV~UMa critically affects the\nStark broadening of the hydrogen lines, thus, significantly\ninfluencing the temperature derived from the H$\\alpha$ profile\nin Sect.\\ 3.4. We investigated this effect in detail using\nthe pre-computed H$\\alpha$ profiles by Kurucz (1979) including\nStark broadening. In the left panel of Fig.\\ 9 the dependence\nof the H$\\alpha$ equivalent width on metallicity is plotted.\nFor each temperature, two model sequences for $\\log g = 4.0$\nand 3.5 are shown.\nIt can be seen that the decrease of the metallicity indeed\naffects the strength of H$\\alpha$, but in this temperature\nrange the variation of the equivalent width is governed mainly\nby the change of the effective temperature. The gravity (pressure)\ndependence is very weak. Because the equivalent\nwidth of the broad H$\\alpha$ line strongly depends on the\nstrength of the Stark wings, it is expected that the wings\nof the H$\\alpha$ profile presented in Fig.\\ 5 (corresponding\nto $[$A/H$] = 0$) are not affected very largely by the possible\nlower metallicity of HV~UMa, thus, the derived temperature\n$T_{\\rm eff} = 7000$ K is only slightly dependent on metal content.\nThis is illustrated in the right panel of Fig.\\ 9, where two model\nprofiles corresponding to two different temperatures \n($T_{\\rm eff} = 7000$ and $7500$ K) and $[$A/H$] = -1.0$ i.e.\nsignificantly lower metallicity than assumed in the previous section\nare presented together with the observed line profile at quadrature.\nIt can be seen that the $T_{\\rm eff} = 7500$ K model still gives\na broader line profile than observed, while the $T_{\\rm eff} = 7000$ K\nmodel results in a much better agreement in the wings, very similar\nto the case of solar metallicity presented in Fig.\\ 5. Note, however,\nthat the lower metal content causes a less deep line core of H$\\alpha$,\nthus, the problem of fitting the whole H$\\alpha$ line is \nexaggerated when the effect of metallicity is taken\ninto account. Nevertheless, it is concluded that the \n$T_{\\rm eff} = 7000 \\pm 200$ km~s$^{-1}$ temperature derived from\nthe wings of H$\\alpha$ probably does not contain a significant\nsystematic error due to the unknown metallicity of HV~UMa.\n\nAs was mentioned in Sect.\\ 3.4, the colour excess of HV~UMa\nis $E(B-V) \\approx 0$. This is supported by the effective temperature\nderived spectroscopically (discussed above) and \nphotometrically (from observed and tabulated Str\\\"omgren indices), \nbecause both methods resulted in a consistent value. The \nnegligible reddening is also in agreement with the statement that\nHV~UMa belongs to the halo population.\n\nAt first glance, the absolute geometric parameters collected in Table\\ 3\nwould indicate that the HV~UMa system consists of main-sequence\ncomponents: both stars have $\\log g = 4.0$ and the mass and radius values\nof the primary are also similar to those of a main sequence star (the\nsecondary is oversized in relation to its mass, typical of contact systems).\nHowever, the surface temperatures and luminosities indicate that HV~UMa is\nprobably an evolved object. First, the combined absolute magnitude of the\nsystem based on parallax measurement and $E(B-V) = 0$ results in \n$M_{\\rm V} = 1.0 \\pm 0.8$ mag, where the large error is due to the uncertainty\nof the Hipparcos-parallax. Using tabulated bolometric corrections, the\ntotal luminosity of the system is $L_{\\rm T} = 30 \\pm 20 L_\\odot$.\nSecond, the luminosities of the components\nare $L_{\\rm i} = 4 \\pi R_{\\rm i}^2 \\sigma T_{\\rm eff}^4 = 15.4 L_\\odot$\nand $2.9\nL_\\odot$ for the primary and secondary, respectively, giving\n$L_{\\rm T} = 18.3 L_\\odot$ for the combined luminosity, which is\nwithin the error of the distance-based total luminosity estimated above.\nHowever, both of these luminosities are much less than the expected\nluminosity $L \\approx 60 \\pm 10 L_\\odot$ of a main sequence star with\n$M \\approx 3 M_\\odot$ (Lang, 1991). Moreover, this kind of main sequence\nstar would have $T_{\\rm eff} = 9500$ K, much higher than the surface\ntemperature of HV~UMa. Therefore, the primary component of HV~UMa\nis too cool and too faint for its mass if it is assumed to be\na main sequence object.\n\nThe agreement with a class III giant star having \n$L \\approx 30 \\pm 10 L_\\odot$ for $M \\approx 3 M_\\odot$ is much better.\nThe temperature of \nsuch giant star is $T_{\\rm eff} \\approx 7400 \\pm 300$ K which is not\nvery far from the surface temperature of HV~UMa. Taking into\naccount the energy transfer between the components in the\ncontact binary (assuming that the total luminosity of the system is due to\nthe energy production of only the more massive primary component), \nthe corrected effective temperature of\nthe primary component is $T_{\\rm 1,corr} = 7300 \\pm 100$ K. The\nradius and the surface gravity of this giant star, \n$R = 2.9 R_\\odot$ and $\\log g \\approx 3.8$, also agrees well\nwith the derived parameters of HV~UMa. Therefore, the\ncomparison of empirical and theoretical values of the physical \nparameters suggests that the primary component of HV~UMa is\nan evolved object, probably a IV-III class subgiant, or giant star.\nBecause W~UMa stars are generally accepted to belong to the\nold disk population (e.g. Rucinski, 1993, 1998), it is reasonable\nthat a long-period contact system, containing a more massive\nprimary than most of other W~UMa systems, is significantly evolved\nfrom the main sequence. Therefore, the evolved status of HV~UMa\nqualitatively agrees with the age of other contact binaries.\n\nIt is interesting to compare the direct empirical absolute magnitude \nof HV~UMa derived above ($M_V = 1.0$ mag) with the prediction of\nthe period-colour-luminosity relation of W~UMa stars calibrated\nby Rucinski \\& Duerbeck (1997) as $M_{\\rm V} = 0.10 + 3.08 (B-V)_0 - 4.42 \\log P$.\nUsing the same estimated $(B-V)_0$ index as above, the\npredicted absolute magnitude for HV~UMa becomes \n$M_{\\rm V} = 1.59 \\pm 0.35$ mag, which agrees with\nthe empirical value within the errors. Note, that the deviation\nof some of the calibrating W~UMa stars in the sample of Rucinski\n\\& Duerbeck (1997) from the value predicted by this relation is as\nlarge as $0.5 - 0.7$ mag (see Fig.\\ 4 in Rucinski \\& Duerbeck 1997),\ntherefore the difference between\nthe observed and the predicted absolute magnitude of HV~UMa \ndoes not make this system discrepant with respect to other contact\nbinaries. On the other hand, it is a bit surprising that the \nrelation that is mainly based on main sequence objects \ngave such a good prediction for the more evolved HV~UMa system. \nThis agreement is probably limited to the particular range on\nthe HR-diagram close to the position of HV~UMa, and may not\nhold on for more evolved systems with $P > 1$ day. \nVery few known contact systems exist above the $P = 1$ day period\nvalue, as recently discussed by Rucinski (1998), this lack of\nsystems also gives a natural limit for the applicability of this\nrelation for longer periods.\n\nThe separation of the components in the HV~UMa system and\nthe evolved physical state of the primary may suggest that\nthis contact system formed during a case B mass transfer.\nThis may also give a reasonable explanation for the poor\nthermal contact $\\Delta T = 900$ K between the\ncomponents. Model computations of the formation of\ncontact binaries via evolution induced mass transfer\nfrom the more massive component (Sarna \\& Fedorova, 1989) \npredict large amount of temperature excess\n($\\Delta T \\approx 2000 - 3000$ K) at the moment of reaching\nthe contact configuration. The result that the eclipse\ndepths of HV~UMa can be modelled with only such high\ntemperature excess may indicate that this contact\nsystem formed only recently and did not have enough time\nto reach better thermal contact. Note, that the temperature\nexcess in W~UMa-type contact binaries is usually considered\nunphysical, because the lack of the colour index variation\nsuggests very good thermal contact for late-type stars.\nThe physically consistent model of the eclipse depths of \nW~UMa-stars contains large starspots on the surface of one\nor both components (e.g. Hendry et al., 1992). However,\nin the case of HV~UMa with $T_{\\rm eff} >= 7000$ K,\nthe presence of such starspots is less likely, thus, the\neclipse depths of this system may indeed mean a 900 K\ntemperature difference between the secondary and the primary.\n\n\\section{Conclusions}\n\nThe new results presented in this paper can be summarized\nas follows.\n\n\\noindent 1. We reported the first $uvby$ photometric and medium\nresolution spectroscopic observations of the short-period\nvariable star HV~Ursae~Majoris. Contrary to the RRc classification\ngiven by ESA (1997), the star turned out to be a new\ncontact binary with early-type components.\n\n\\noindent 2. An improved ephemeris was determined using our\nand Hipparcos epoch photometric data:\nHel.JD$_{min}$=2451346.743+0.7107523(3)$\\cdot$E. There is\nno indication of changing period over almost 10 years.\n\n\\noindent 3. A radial velocity curve was measured directly from\nthe H$\\alpha$ profiles by two-component Gaussian fitting of the line core\nregions in spectra recorded around the quadratures. We\ncalculated a spectroscopic mass ratio of 0.19$\\pm$0.03.\n\n\\noindent 4. The effective temperature and the surface gravity were\ndetermined using the mean Str\\\"omgren indices, synthetic\ncolours of Kurucz (1993) and theoretical (ATLAS9)\nline profiles giving\n$T_{eff}=7000\\pm200$ K and log~$g=4.0\\pm0.3$.\nThe light curve modelling resulted in a complete set of physical parameters.\n\n\\noindent 5. The physical parameters of HV UMa together with the\nparallax measurement indicate that this binary is situated\nfar from the galactic plane, and the primary component\nis an evolved object, probably a subgiant or giant star.\nThe large temperature excess of the secondary may be\nindicative of a poor thermal contact between the\ncomponents due to a relatively recent formation of this\ncontact system via case B mass transfer.\n\n\n\\begin{acknowledgements}\nThis research was supported by MTA-CSIC Joint Project No.15/1998,\nHungarian OTKA Grants \\#F022249, \\#T022259, \\#T032258,\nPro Renovanda Cultura\nHungariae Foundation Grant DT 1999 \\'apr./36. and\nSzeged Observatory Foundation.\nLLK wishes to express his thanks to the staff of the DDO for\ngranting the necessary observing time. Also, LLK and\nBCS acknowledge the helpful assistance by \\'E. Bar\\'at and B. Gere\nduring the observations. Fruitful discussions with\nK. Szatm\\'ary are also gratefully acknowledged.\nThanks are due to the referee, Prof. S. Rucinski,\nwhose criticism and many suggestions led to significant\nimprovement of the paper.\nThe NASA ADS Abstract\nService was used to access data and references.\n\\end{acknowledgements}\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[1977]{alnaim77}\n Al-Naimiy H.M. 1977, Ap\\&SS 66, 281\n\n\\bibitem[1990]{barone}\n Barone F., Milano L., Russo G. 1990, in: Active Close\n Binaries (ed. C.Ibanoglu), Kluwer Acad. Publ., p. 161.\n\n\\bibitem[1997]{esa97}\n ESA 1997, The Hipparcos and Tycho Catalogues, ESA SP-1200\n\n\\bibitem[1994]{figu94}\n Figueiredo J., De Greve J.P., Hilditch R.W. 1994, A\\&A 283, 144\n\n\\bibitem[1992]{hendry92}\n Hendry P.D., Mochnacki S.W., Collier Cameron A. 1992, ApJ 399, 246\n\n\\bibitem[1999]{kiss99a}\n Kiss L.L., Cs\\'ak B., Thomson J.R., Szatm\\'ary K. 1999a,\n IBVS No. 4660\n\n\\bibitem[1999]{kiss99b}\n Kiss L.L., Cs\\'ak B., Thomson J.R., Vink\\'o J. 1999b,\n A\\&A 345, 149\n\n\\bibitem[1979]{kur79}\n Kurucz R.L. 1979, ApJ S. 40, 1\n\n\\bibitem[1993]{kurucz}\n Kurucz R.L. 1993, ATLAS9 Stellar Atmosphere Programs and 2 km/s\n Model Grids, CR-ROM No.13\n\n\\bibitem[1991]{lang91}\n Lang K.L. 1991, Astrophysical Data: Planets and Stars, Springer-Verlag\n\n\\bibitem[1989]{liu89}\n Liu T., Janes K.A. 1989, ApJS 69, 593\n\n\\bibitem[1983]{niels83}\n Nielsen R. F. 1983, Institute Theoric. Astrophysics Oslo Report No. 59,\n ed. O. Hauge, p 141\n\n\\bibitem[1973]{penston}\n Penston M.J. 1973, MNRAS 164, 133\n\n\\bibitem[1973]{ruc73}\n Rucinski S.M. 1973, Acta Astron 23, 79\n\n\\bibitem[1983]{ruc83}\n Rucinski S.M. 1983, A\\&A 127, 84\n\n\\bibitem[1993]{ruc93}\n Rucinski S.M. 1993, in: The Realm of Interacting Binary Stars\n eds. J Sahade et al., Kluwer, p.111.\n\n\\bibitem[1997]{ruc97a}\n Rucinski S.M. 1997, AJ 113, 1112\n\n\\bibitem[1997]{ruc97b}\n Rucinski S.M., Duerbeck H.W. 1997, PASP 109, 1340\n\n\\bibitem[1998]{ruc98}\n Rucinski S.M. 1998, AJ 115, 1135\n\n\\bibitem[1989]{sarna89}\n Sarna M.J., Fedorova A.V. 1989, A\\&A 208, 111\n\n\\bibitem[1959]{slett}\n Slettebak A., Stock J. 1959, Astron. Abh. Hamburg Sternwarte 5, 105\n\n\\bibitem[1996]{vinko96}\n Vink\\'o J., Heged\\\"us T., Hendry P.D. 1996, MNRAS 280, 489\n\n\\bibitem[1998]{vinko98}\n Vink\\'o J., Evans N.R., Kiss L.L., Szabados L. 1998, MNRAS, 296, 824\n\n\\end{thebibliography}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002379.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1977]{alnaim77}\n Al-Naimiy H.M. 1977, Ap\\&SS 66, 281\n\n\\bibitem[1990]{barone}\n Barone F., Milano L., Russo G. 1990, in: Active Close\n Binaries (ed. C.Ibanoglu), Kluwer Acad. Publ., p. 161.\n\n\\bibitem[1997]{esa97}\n ESA 1997, The Hipparcos and Tycho Catalogues, ESA SP-1200\n\n\\bibitem[1994]{figu94}\n Figueiredo J., De Greve J.P., Hilditch R.W. 1994, A\\&A 283, 144\n\n\\bibitem[1992]{hendry92}\n Hendry P.D., Mochnacki S.W., Collier Cameron A. 1992, ApJ 399, 246\n\n\\bibitem[1999]{kiss99a}\n Kiss L.L., Cs\\'ak B., Thomson J.R., Szatm\\'ary K. 1999a,\n IBVS No. 4660\n\n\\bibitem[1999]{kiss99b}\n Kiss L.L., Cs\\'ak B., Thomson J.R., Vink\\'o J. 1999b,\n A\\&A 345, 149\n\n\\bibitem[1979]{kur79}\n Kurucz R.L. 1979, ApJ S. 40, 1\n\n\\bibitem[1993]{kurucz}\n Kurucz R.L. 1993, ATLAS9 Stellar Atmosphere Programs and 2 km/s\n Model Grids, CR-ROM No.13\n\n\\bibitem[1991]{lang91}\n Lang K.L. 1991, Astrophysical Data: Planets and Stars, Springer-Verlag\n\n\\bibitem[1989]{liu89}\n Liu T., Janes K.A. 1989, ApJS 69, 593\n\n\\bibitem[1983]{niels83}\n Nielsen R. F. 1983, Institute Theoric. Astrophysics Oslo Report No. 59,\n ed. O. Hauge, p 141\n\n\\bibitem[1973]{penston}\n Penston M.J. 1973, MNRAS 164, 133\n\n\\bibitem[1973]{ruc73}\n Rucinski S.M. 1973, Acta Astron 23, 79\n\n\\bibitem[1983]{ruc83}\n Rucinski S.M. 1983, A\\&A 127, 84\n\n\\bibitem[1993]{ruc93}\n Rucinski S.M. 1993, in: The Realm of Interacting Binary Stars\n eds. J Sahade et al., Kluwer, p.111.\n\n\\bibitem[1997]{ruc97a}\n Rucinski S.M. 1997, AJ 113, 1112\n\n\\bibitem[1997]{ruc97b}\n Rucinski S.M., Duerbeck H.W. 1997, PASP 109, 1340\n\n\\bibitem[1998]{ruc98}\n Rucinski S.M. 1998, AJ 115, 1135\n\n\\bibitem[1989]{sarna89}\n Sarna M.J., Fedorova A.V. 1989, A\\&A 208, 111\n\n\\bibitem[1959]{slett}\n Slettebak A., Stock J. 1959, Astron. Abh. Hamburg Sternwarte 5, 105\n\n\\bibitem[1996]{vinko96}\n Vink\\'o J., Heged\\\"us T., Hendry P.D. 1996, MNRAS 280, 489\n\n\\bibitem[1998]{vinko98}\n Vink\\'o J., Evans N.R., Kiss L.L., Szabados L. 1998, MNRAS, 296, 824\n\n\\end{thebibliography}"
}
] |
astro-ph0002380
|
The Dependence of Tidally-Induced Star Formation on Cluster Density
|
[
{
"author": "C. Moss"
}
] |
A survey of H$\alpha$ emission in 320 spiral galaxies in 8 nearby clusters shows an enhancement of circumnuclear starburst emission with increasingly rich clusters. These observations provide convincing evidence that spirals have been transformed into S0s in clusters predominantly by tidal forces, a picture fully in accord with the most recent numerical simulations of clusters. For the richest clusters, the enhancement of starburst emission is greater than would be expected on the basis of increasing galaxy surface density alone, which may explain the anomalous result for the type--galaxy surface density (T--$\Sigma$) relation found for low richness clusters at intermediate redshift.
|
[
{
"name": "mwasp.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Moss \\& Whittle}{The Dependence of Tidally-Induced Star Formation\non Cluster Density}\n\\pagestyle{myheadings}\n\n\\begin{document}\n\n\\title{The Dependence of Tidally-Induced Star Formation on Cluster Density}\n\\author{C. Moss}\n\\affil{Vatican Observatory Research Group, Steward Observatory,\nUniversity of Arizona, Tucson, AZ 85721, USA}\n\\author{M. Whittle}\n\\affil{Department of Astronomy, University of Virginia,\nCharlottesville, VA 22903, USA}\n\n\\begin{abstract}\nA survey of H$\\alpha$ emission in 320 spiral galaxies in 8 nearby\nclusters shows an enhancement of circumnuclear starburst emission with\nincreasingly rich clusters. These observations provide convincing\nevidence that spirals have been transformed into S0s in clusters\npredominantly by tidal forces, a picture fully in accord with the most\nrecent numerical simulations of clusters. For the richest clusters,\nthe enhancement of starburst emission is greater than would be\nexpected on the basis of increasing galaxy surface density alone,\nwhich may explain the anomalous result for the type--galaxy surface\ndensity (T--$\\Sigma$) relation found for low richness clusters at\nintermediate redshift.\n\n\\end{abstract}\n\n%Keywords stars:formation -- galaxies:clusters -- galaxies:evolution\n%-- galaxies:interactions -- galaxies:spiral -- galaxies:starburst\n \n\\section{Introduction}\n\\label{intro}\n\nThe remarkable changes in cluster disk galaxy populations between\nintermediate redshifts (z $\\sim$ 0.5) and the present are well known.\nUp to 50\\% of the population of intermediate redshift clusters are\ncomprised of blue, star-forming galaxies, which have been shown to be\npredominantly normal spiral and irregular galaxies, a fraction of\nwhich are interacting or obviously disturbed. By the present epoch,\nthis population has been depleted by a factor of 2 and replaced by a\npopulation of S0 galaxies. However the processes by which this has\noccurred are still not fully understood (cf. Dressler 1980; Dressler\net al. 1997)\n\nThe processes which cause the transformation of the cluster spiral\ngalaxy population to S0s are expected to have very significant effects\non cluster galaxy star formation rates (SFRs). We have undertaken\na comparison of SFRs between field and cluster spirals in 8 low\nredshift clusters in order to investigate whether these SFRs show\nevidence of continuing morphological transformation of disk galaxies\nat the present epoch. The comparison survey, details of which are\npublished elsewhere (Moss, Whittle \\& Irwin 1988; Moss \\& Whittle\n1993; Moss, Whittle \\& Pesce 1998; Moss \\& Whittle 1999) uses\nH$\\alpha$ emission, resolved into disk and circumnuclear emission, as\nan estimator of the SFRs.\n\n\\section{Comparison of Star Formation Rates in Cluster and Field Spirals}\n\nOur cluster sample (viz. galaxies in 8 clusters Abell 262, 347, 400,\n426, 569, 779, 1367 and 1656), and our field sample (viz. galaxies in\nadjacent supercluster fields) were observed in an identical manner,\nthus eliminating systematic effects in detection efficiency.\nFurthermore, both (supercluster) field and cluster samples\napproximated volume limited samples, largely eliminating the\nsystematic bias between cluster and field detection rates which may\nhave been present in many earlier comparison studies (cf. Biviano et\nal. 1997).\n\nA difficult question is which criterion to choose to normalise field\nand cluster disk galaxy samples. Some authors (e.g. Hashimoto et\nal. 1998; Balogh et al. 1998) have chosen to use bulge to disk (B/D)\nratio on the grounds that it is a less subjective and star formation\ncontaminated normalisation parameter. However the relation between\nB/D ratio and Hubble T-type has considerable scatter (Baugh, Cole \\&\nFrenk 1996; Simien \\& de Vaucouleurs 1986; de Jong 1995) such that an\nincrease in the S0/S ratio in clusters is likely to mask systematic\nchanges of SFR between field and cluster spirals. Since the latter\nchanges are of interest for the present study, the B/D ratio is not a\nsuitable normalisation parameter.\n\nAccordingly we have chosen Hubble type as the normalisation parameter,\nand further restricted field and cluster samples to a total of 320\nspirals (Sa and later) and peculiars. Some 39\\% of spirals and 75\\% of\npeculiars were detected in H$\\alpha$ emission. It is estimated that\nemission detection is 90\\% complete to an equivalent width limit of 20\n\\AA, and $\\sim$ 29\\% efficient below this limit (cf. Moss et al. 1998).\nThe detected emission divides approximately equally between {\\it\ndiffuse} and {\\it compact} emission which is identified with disk\nemission and circumnuclear starburst emission respectively. Examples\nof both types of emission are given in Figure 1.\n\nA particular difficulty which arises in adopting the Hubble type as\nthe normalisation parameter is the relation between the star formation\nproperties of the galaxy and its Hubble type. In\nparticular, a decrease in disk star formation rate may shift a galaxy\nto an earlier type. This shift in type may not be detected in any\ncomparison of field and cluster spirals (Hashimoto et al. 1998). This\nmakes any comparison of {\\it disk} emission between field and cluster\nspirals uncertain. By contrast, circumnuclear emission is relatively\nindependent of type (Kennicutt 1998), and in this case a reliable\ncomparison of field and cluster spirals is possible.\n\nAs is characteristic of circumnuclear starburst emission\n(cf. Kennicutt 1998), the detected compact emission correlates with\nboth a disturbed morphology of the galaxy (significance level,\n8.7$\\sigma$) indicative of tidally-induced star formation, and with\nthe presence of a bar (significance level, 3.1$\\sigma$). Furthermore\nthis emission correlates with both local galaxy surface density\n(significance level, 3.9$\\sigma$) and cluster central galaxy space\ndensity (significance level, 5.3$\\sigma$). Since there is no\nsignificant difference in the incidence of galaxy bars between the\nfield and cluster samples, whereas disturbed galaxies are more common\nin the cluster environment, it is considered that the observed\nenhancement of circumnuclear emission is due to tidally-induced star\nformation, whether from galaxy--galaxy, galaxy--group or\ngalaxy--cluster interactions.\n\nFinally, the enhancement of circumnuclear starburst emission with\nincreasing cluster density is not wholly accounted for by the\ncorrelation of this emission with local galaxy surface density. A\nKendall partial rank correlation test shows an additional 'cluster\neffect' (significance level, 3.3$\\sigma$) such that there is a\nhigher incidence of circumnuclear emission for galaxies in a region\nof a given local galaxy surface density in richer clusters, as compared\nto that for galaxies in regions of the same surface density in poorer\nclusters. \n\n\\begin{figure}[t]\n\\plottwo{figure1.epsi}{figure2.epsi}\n\\caption{R band and H$\\alpha$ images for 4 detected galaxies in \nthe cluster survey. The cumulative H$\\alpha$ equivalent width with\nradial distance from the galaxy center is shown below each pair of\ngalaxy images. This decreases with radial distance for compact\n(circumnuclear starburst) emission (CGCG nos. 127-046, 521-074), whereas it\nincreases for diffuse (disk) emission (CGCG nos. 540-049, 522-100).}\n\\end{figure}\n\n\\section{Discussion}\n\nAlthough Lavery \\& Henry (1988) first proposed that the Butcher-Oemler\neffect could be explained as star formation triggered by\ngalaxy--galaxy interactions in intermediate redshift clusters, it was\nlong considered that the typical cluster velocity dispersion ($\\sim$\n1000 ${\\rm km}$ ${\\rm s}^{-1}$) was too high for strong tidal interactions\nto occur. However recent work (e.g. Gnedin 1999) has shown that a\nnon-static cluster potential can enhance tidal interactions for\ncluster galaxies. Such a non-static potential can arise in\nsub-cluster merging, and indeed there is evidence that the two richest\nclusters in our sample (Abell 1367 and 1656) are recent\npost-merger systems (Donnelly et al. 1998; Honda et al. 1996). It\nappears that the merger events in these clusters leading to a rapidly\nvarying cluster potential, may have caused an increase in galaxy tidal\ninteractions and the associated observed enhancement of circumnuclear\nstarburst emission.\n\nTidal interactions of galaxies in clusters are likely to be an\neffective mechanism for the transformation of spirals to S0 galaxies\n(e.g. Gnedin 1999). It was noted above that the observed enhancement\nof circumnuclear emission in spirals with increasing cluster density\nis not wholly accounted for by that due to increasing local galaxy surface\ndensity. This implies that tidal interactions, and associated\nmorphological transformation of spirals to S0s, proceeds faster in\nricher as compared to poorer clusters, perhaps because sub-cluster\nmerging is more common for the former. This in turn may explain the\nhitherto anomalous absence of a type--local galaxy surface density\n($T-\\Sigma$) relation in irregular clusters at intermediate redshift\n(Dressler 1980; Dressler et al. 1997). Whereas significant morphological\ntransformation of the cluster disk galaxy population may be expected\nfor regular (rich) clusters at $z \\sim 0.5$ (for which the timescale\nfor transformation is shorter) and for irregular (poor) clusters at $z\n\\sim 0$ (for which a longer time duration for transformation is\navailable), for irregular clusters at $z \\sim 0.5$, there\nhas been insufficient time for this\nto take place, leading to the observed absence of a\n$T-\\Sigma$ relation.\n\n\\acknowledgements {We thank S.M. Bennett for preparation of the Figure.}\n \n\\begin{references}\n\n\\reference Balogh, M.L., Schade, D., Morris, S.L., Yee, H.K.C., \nCarlberg, R.G., Ellingson, E. 1998, \\apj, 504, L75\n\n\\reference Baugh, C.M., Cole, S., Frenk, C.S. 1996, \\mnras, 283, 1361\n\n\\reference Biviano, A., Katgert, P., Mazure, A., Moles, M., \nden Hartog, R., Perea, J., Focardi, P. 1997, \\aap, 321, 84\n\n\\reference de Jong, R.S. 1995, PhD thesis, Univ. Groningen\n\n\\reference Donnelly, R.H., Markevitch, M., Forman, W., Jones, C., \nDavid, L.P., Churazov, E., Gilfanov, M. 1998, \\apj, 500, 138\n\n\\reference Dressler, A. 1980, \\apj, 236, 351\n\n\\reference Dressler, A., Oemler, A., Couch, W. J., Smail, I.,\nEllis, R. S., Barger, A., Butcher, H., Poggianti, B. M.,\nSharples, R. M. 1997, \\apj, 490, 577\n\n\\reference Gnedin, O.Y. 1999, PhD thesis, Princeton Univ.\n\n\\reference Hashimoto, Y., Oemler, A., Lin, H., Tucker, D.L. \n1998, \\apj, 499, 589\n\n\\reference Honda, H., Hirayama, M., Watanabe, M., Kunieda, H.,\nTawara, Y., Yamashita, K., Ohashi, T., Hughes, J. P., Henry, J. P\n1996, \\apj, 473, L71\n\n\\reference Kennicutt, R.C. 1998, \\araa, 36, 189\n\n\\reference Lavery, R.J., Henry, J.P. 1988, \\apj, 330, 596\n\n\\reference Moss, C., Whittle, M. 1993, \\apj, 407, L17\n\n\\reference Moss, C., \\& Whittle, M. 1999, \\mnras, submitted for publication\n\n\\reference Moss, C., Whittle, M., Irwin, M.J. 1988, \\mnras, 232, 381\n\n\\reference Moss, C., Whittle, M., Pesce, J.E. 1998, \\mnras, 300, 205\n\n\\reference Simien, F., de Vaucouleurs, G. 1986, \\apj, 302, 564\n\n\\end{references}\n\n\\end{document}\n\n"
}
] |
[] |
astro-ph0002381
|
series Fossils of turbulence and non-turbulence in the primordial universe: the fluid mechanics of dark matter
|
[
{
"author": "Carl H. Gibson"
}
] |
[
{
"name": "gibson.tex",
"string": "\\documentclass[10pt, twoside]{article}\n\\usepackage{epsf,graphicx,color,amsbsy}\n%\\pagestyle{myheadings}\n%\\special{papersize=15.5 cm, 23 cm} \n%\\renewcommand{\\columnsep}{10mm} \n%\\evensidemargin=0mm %use as necessary for your printer \n%\\oddsidemargin=3mm %use as necessary for your printer \n%\\topmargin=-1mm %use as necessary for your printer \n%\\textheight=1.8cm \n%\\textwidth=122cm \n%\\renewcommand{\\baselinestretch}{2} %use for draft printing -doublespaced \n%\\renewcommand{\\thesection}{{\\normalsize \\arabic{section}}} \n%\\font=cmssbx10 \n%\\font=cmssbx10 \n%\\font=cmss10 \n%\\font=cmssbx10 scaled 900 \n%\\font=cmss10 scaled 900 \n%\\font=cmr9 \n%\\font=cmr8 \n%\\setlength{\\unitlength}{1in} \n\\begin{document} \n \n\\title{\\bfseries \nFossils of turbulence and non-turbulence in the primordial universe:\n the fluid mechanics of dark matter} \n\\vspace{10mm} \n% \n\\author{ Carl H. Gibson} \n\\date{} \n\\maketitle \n\\vspace*{-9 mm} \n{\\small \n\\begin{center} \nDepartments of Mechanical and Aerospace Engineering\\\\\n and Scripps Institution of Oceanography\\\\ \nUniversity of California at San Diego, La Jolla, CA 92093-0411, USA \nContact e-mail:{\\texttt cgibson@ucsd.edu, http://www-acs.ucsd.edu/$\\sim$\nir118} \n\\end{center} \n} \n\\thispagestyle{empty}\n%\\normalsize \n\\section{Introduction} \nWas the primordial universe turbulent or non-turbulent soon after the Big Bang? \nHow did the hydrodynamic state of the early universe affect the formation of\nstructure from gravitational forces, and how did the formation of structure by\ngravity affect the hydrodynamic state of the flow? What can be said about the\ndark matter that comprises $99.9 \\%$ of the mass of the universe according to\nmost cosmological models? Space telescope measurements show answers to these\nquestions persist literally frozen as fossils of the primordial turbulence\nand nonturbulence that controlled structure formation, contrary to standard\ncosmology which relies on the erroneous Jeans 1902 linear-inviscid-acoustic\ntheory and a variety of associated misconceptions (e. g., cold dark matter). When\neffects of viscosity, turbulence, and diffusion are included, vastly different\nstructure scenarios and a clear explanation for the dark matter\nemerge~\\cite{gib96}. From Gibson's 1996 theory the baryonic (ordinary) dark\nmatter is comprised of proto-globular-star-cluster (PGC) clumps of hydrogenous\nplanetoids termed ``primordial fog particles''(PFPs), observed by Schild 1996 as\n``rogue planets ... likely to be the missing mass'' of a quasar lensing\ngalaxy~\\cite{sch96}. The weakly collisional non-baryonic dark matter diffuses\nto form outer halos of galaxies and galaxy clusters~\\cite{tys95}.\n\\\\\n\n\\section{Fluid mechanics of structure formation} \nBefore the $1989$ Cosmic Microwave Background Experiment (COBE) satellite, it\nwas generally assumed that the fluid universe produced by the hot Big Bang\nsingularity must be enormously turbulent, and that galaxies were nucleated by\ndensity perturbations produced by this primordial turbulence. George Gamov\n$1954$ suggested galaxies were a form of ``fossil turbulence'', thus coining a\nvery useful terminology for the description of turbulence remnants in the\nstratified ocean and atmosphere, Gibson $1980-1999$. Other galaxy models based\non turbulence were proposed by von Weizsacker $1951$, Chandrasekhar $1952$, \nOzernoi and colleagues in $1968-1971$, Oort $1970$, and Silk and Ames $1972$. \nAll such theories were rendered moot by COBE measurements showing temperature\nfluctuation values $\\delta{T}/T$ of only $10^{-5}$ at $300,000$ years compared\nto at least $10^{-2}$ for the plasma if it were turbulent. At this time, the\nopaque plasma of hydrogen and helium had cooled to $3,000$ K and become a\ntransparent neutral gas, revealing a remarkable photograph of the universe as it\nexisted at $10^{13}$ s, with spectral redshift z of $1100$ due to straining of\nspace at rate $\\gamma \\approx 1/t$. \n\\\\\n\\\\\nWhy was the primordial plasma before $300,000$ years not turbulent? \nSteady inviscid flows are absolutely \nunstable. Turbulence always forms in flows with Reynolds number $Re =\n\\delta{v} L/\\nu$ exceeding $Re_{cr} \\approx 100$, where $\\nu$ is the kinematic\nviscosity of a fluid with velocity differences $\\delta v$ on scale $L$,\nLandau-Lifshitz 1959. Thus either $\\nu$ at $10^{13}$ s had an\nunimaginably large value of $9\\times10^{27}$ m$^2$ s$^{-1}$ at horizon scales\n$L_H = ct$ with light speed velocity differences $c$, or else gravitational\nstructures formed in the plasma at earlier times and viscosity plus buoyancy\nforces of the structures prevented strong turbulence.\\\\\n\n\\section{Fossils of first structure (proto-supervoids)}\nThe power spectrum of temperature fluctuations $\\delta T$ measured by \nCOBE peaks at a length $3 \\times 10^{20}$ m which is only $1/10$ the horizon\nscale ct, suggesting the first structure formed earlier at $10^{12}$ s\n($30,000$ years). The photon viscosity of the plasma $\\nu=c/n\\sigma_{\\tau}$ was\n$4\\times{10^{26}} $ m$^{2}$ s$^{-1}$ then, with free electron number\ndensity\n$n=10^{10}$ m$^{-3}$ and $\\sigma_{\\tau}$ the Thomson cross section for Compton\nscattering. The baryon density $\\rho$ was\n$3\\times10^{-17}$ kg m$^{-3}$, which matches the density of present \nglobular-star-clusters as a fossil of the weak turbulence at this time of first\nstructure. The fragmentation mass\n$\\rho(ct)^{3}$ of $10^{46}$ kg matches the observed mass of superclusters of\ngalaxies, the largest structures of the universe. Because $Re \\approx\nRe_{crit}$, the horizon scale\n$ct=3\\times{10^{20}}$ m matches the Schwarz viscous scale $L_{SV} =\n(\\gamma\\nu/\\rho{G})^{1/2}$ at which viscous forces\n$F_{V}=\\rho\\gamma{L}^{2}$ equal gravitational forces $F_{G}=\\rho^{2}GL^{4}$, and\nalso the Schwarz turbulence scale $L_{ST} = \\varepsilon^{1/2}/(\\rho\nG)^{3/4}$ at which inertial-vortex forces\n$F_I = \\rho \\varepsilon^{2/3} L^{8/3}$ equal $F_{G}$, where $\\varepsilon$ is the\nviscous dissipation rate~\\cite{gib96}. Further fragmentation to proto-galaxy\nscales is predicted in this scenario, with the nonbaryonic dark matter\ndiffusing to fill the voids between constant density proto-supercluster to\nproto-galaxy structures for scales smaller than the diffusive Schwarz scale\n$L_{SD}=(D^{2}/\\rho{G})^{1/4}$, where $D$ is the diffusivity of the nonbaryonic\ndark matter~\\cite{gib96}. Fragmentation of the nonbaryonic material to form\nsuperhalos implies\n$D=10^{28}$ m$^{2}$ s$^{-1}$, from observation of present superhalo sizes\n$L_{SD}$ and densities\n$\\rho$~\\cite{tys95}, trillions of times larger than $D$ for H-He gas with the\nsame $\\rho$. \n\\\\\n\n\\section{Fossils of the first condensation (as ``fog'')}\nPhoton decoupling dramatically reduced viscosity values to $\\nu =\n3\\times{10^{12}}$ m$^{2}$ s$^{-1}$ in the primordial gas of the nonturbulent\n$10^{20}$ m size proto-galaxies, with $\\gamma = 10^{-13}$ s$^{-1}$ and $\\rho =\n10^{-17}$ kg m$^{-3}$, giving a PFP fragmentation mass range $M_{SV} \\approx\nM_{ST}\n\\approx 10^{23}-10^{25}$ kg, the mass of a small planet. Pressure decreases in\nvoids during fragmentation as the density decreases, to maintain constant\ntemperature from the perfect gas law\n$T=p/\\rho{R}$, where $R$ is the gas constant, for scales smaller than the\nacoustic scale $L_{J} = V_{S}/(\\rho{G})^{1/2}$ of Jeans $1902$, where $V_{S}$ is\nthe sound speed. However, the pressure cannot propagate fast enough in\nvoids larger than $L_J$ so they cool. Hence radiation from the warmer\nsurroundings can heat such large voids, increasing their pressure and\naccelerating the void formation, causing a fragmentation within\nproto-galaxies at the Jeans mass of $10^{35}$ kg, the mass of\nglobular-star-clusters. These proto-globular-cluster (PGC) clumps of PFPs\nprovide the materials of construction for everything else to follow, from stars\nto people. Leftover PGCs and PFPs thus comprise present galactic dark matter\ninner halos which typically have expanded to about\n$10^{21}$ m (30 kpc) of the core and exceed the luminous (star) mass by factors\nof\n$10-30$.\n\\\\\n\n\\section{Observations}\nObservations of quasar image twinkling frequencies reveal that the point mass\nobjects which dominate the mass of the lens galaxy are not stars, but ``rogue\nplanets... likely to be the missing mass'', Schild $1996$, independently\nconfirming this prediction of Gibson $1996$. Other evidence of the predicted\nprimordial fog particles (PFPs) is shown in Hubble Space Telescope photographs,\nsuch as thousands of \n$10^{25}$ kg ``cometary globules'' in the halo of the Helix planetary nebula and\npossibly like numbers in the Eskimo planetary nebula halo. These dying stars are\nvery hot ($100,000$ K versus $6,000$ K normal) so that many \nPFPs nearby can be brought out of cold storage by evaporation to produce the\n$10^{13}$ m protective cocoons that make them visible to the HST at $10^{19}$ m\ndistances.\n\\\\ \n \n\\section{Summary and conclusions}\nThe Figure summarizes the evolution of structure and turbulence in the early\nuniverse, as inferred from the present nonlinear fluid mechanical theory. It is\nvery different, very early, and very gentle compared to the standard model, where\nstructure formation in baryonic matter is forbidden in the plasma epoch because\n$L_J$ is larger than $L_H = ct$ and \ngalaxies collapse at 140 million years (redshift\nz=20) producing $10^{36}$ kg Population III superstars\nthat explode and re-ionize the universe to explain the missing gas (sequestered\nin PFPs). No such stars, no galaxy collapse, and no re-ionization occurs in the\npresent theory. To produce the structure observed today, the concept ``cold\ndark matter'' (CDM) was invented; that is, a hypothetical non-baryonic fluid of\n``cold'' (low speed) collisionless particles with adjustable $L_J$ small enough\nto produce gravitational potential wells to drive galaxy collapse. Cold dark\nmatter is unnecessary in the present theory. Even if it exists it would not\nbehave as required by the standard model. Its necessarily small collision cross\nsection requires\n$L_{SD} \\gg L_J$ so it would diffuse out of its own well, without fragmentation\nif $L_{SD} \\gg L_H$. The immediate formation of ``primordial fog\nparticles'' from all the neutral gas of the universe emerging from the plasma\nepoch permits their gradual accretion to form the observed small ancient stars in\ndense globular-star-clusters known to be only slightly younger than the\nuniverse. These could never form in the intense turbulence of galaxy collapse in\nthe standard model because\n$L_{ST}$ scales would be too large. \n\\\\\n\n\\begin{figure}[!h] \n \\vspace{1mm} \n \\begin{center} \n \\includegraphics[width= 0.8 \\linewidth]{etc8_fig.eps} \n \\end{center} \n\n\\vskip-2.8in\n \n \\caption{Evolution of structure and turbulence in the early universe} \n \\end{figure} \n \n\n\n\\begin{thebibliography}{1} \n \n\\bibitem{gib96} \nC.~H. Gibson. \n\\newblock Turbulence in the ocean, atmosphere, galaxy, and universe. \n\\newblock {\\em Applied Mechanics Reviews}, 49:299--315, 1996. \n \n\\bibitem{sch96} \nR.~E. Schild. \n\\newblock Microlensing variability of the gravitationally lensed quasar\nQ0957+561 A,B. \n\\newblock {\\em Astrophysical Journal}, 464:125--130,\n1996. \n \n\\bibitem{tys95} \nJ.~A. Tyson and P.~Fischer.\n\\newblock Measurement of the mass profile of Abell 1689.\n\\newblock {\\em Astrophysical Journal}, 446:L55--L58, \n1995. \n \n%\\bibitem{yodhesins94} \n%.~Yoda, L.~Hesselink, and M.~G. Mungal. \n%\\newblock Instantaneous three-dimensional concentration measurements in the \n% self-similar region of a round high-schmidt-number jet. \n%\\newblock {\\em J. Fluid Mech.}, 279:313--350, 1994. \n \n\\end{thebibliography} \n \n\\end{document} \n"
}
] |
[
{
"name": "astro-ph0002381.extracted_bib",
"string": "\\begin{thebibliography}{1} \n \n\\bibitem{gib96} \nC.~H. Gibson. \n\\newblock Turbulence in the ocean, atmosphere, galaxy, and universe. \n\\newblock {\\em Applied Mechanics Reviews}, 49:299--315, 1996. \n \n\\bibitem{sch96} \nR.~E. Schild. \n\\newblock Microlensing variability of the gravitationally lensed quasar\nQ0957+561 A,B. \n\\newblock {\\em Astrophysical Journal}, 464:125--130,\n1996. \n \n\\bibitem{tys95} \nJ.~A. Tyson and P.~Fischer.\n\\newblock Measurement of the mass profile of Abell 1689.\n\\newblock {\\em Astrophysical Journal}, 446:L55--L58, \n1995. \n \n%\\bibitem{yodhesins94} \n%.~Yoda, L.~Hesselink, and M.~G. Mungal. \n%\\newblock Instantaneous three-dimensional concentration measurements in the \n% self-similar region of a round high-schmidt-number jet. \n%\\newblock {\\em J. Fluid Mech.}, 279:313--350, 1994. \n \n\\end{thebibliography}"
}
] |
|
astro-ph0002382
|
Eclipse studies of the dwarf-nova Ex Draconis
|
[
{
"author": "R. Baptista $^1$"
},
{
"author": "M.\\"
},
{
"author": "S. Catal\\'an $^2$ and L. Costa $^1$"
},
{
"author": "$^1$ Departamento de F\\'\\i sica"
},
{
"author": "Universidade Federal de Santa Catarina"
},
{
"author": "Campus Trindade"
},
{
"author": "88040-900"
},
{
"author": "Florian\\'opolis - SC"
},
{
"author": "Brazil"
},
{
"author": "$^2$ Department of Physics"
},
{
"author": "Keele"
},
{
"author": "Staffordshire"
},
{
"author": "ST5 5BG"
},
{
"author": "UK"
}
] |
We report on $V$ and $R$ high speed photometry of the dwarf nova EX~Dra in quiescence and in outburst. The analysis of the outburst lightcurves indicates that the outbursts do not start in the outer disc regions. The disc expands during the rise to maximum and shrinks during decline and along the following quiescent period. The decrease in brightness at the later stages of the outburst is due to the fading of the light from the inner disc regions. At the end of two outbursts the system was seen to go through a phase of lower brightness, characterized by an out-of-eclipse level $\simeq 15$ per cent lower than the typical quiescent level and by the fairly symmetric eclipse of a compact source at disc centre with little evidence of a bright spot at disc rim. New eclipse timings were measured from the lightcurves taken in quiescence and a revised ephemeris was derived. The residuals with respect to the linear ephemeris are well described by a sinusoid of amplitude 1.2 minutes and period $\simeq 4$ years and are possibly related to a solar-like magnetic activity cycle in the secondary star. Eclipse phases of the compact central source and of the bright spot were used to derive the geometry of the binary. By constraining the gas stream trajectory to pass through the observed position of the bright spot we find $q=0.72\pm 0.06$ and $i= 85^{+3}_{-2}$ degrees. The binary parameters were estimated by combining the measured mass ratio with the assumption that the secondary star obeys an empirical main sequence mass-radius relation. We find $M_1 = 0.75\pm 0.15 \; M_\odot$ and $M_2 = 0.54\pm 0.10 \; M_\odot$. The results indicate that the white dwarf at disc centre is surrounded by an extended and variable atmosphere or boundary layer of at least 3 times its radius and a temperature of $T\simeq 28000 \;K$. The fluxes at mid-eclipse yield an upper limit to the contribution of the secondary star and lead to a lower limit photometric parallax distance of $D= 290 \pm 80\; pc$. The fluxes of the secondary star are well matched by those of a M$0\pm2$ main sequence star.
|
[
{
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Baptista et~al.]\n {R. Baptista $^1$, M.\\,S. Catal\\'an $^2$ and L. Costa $^1$ \\\\\n $^1$ Departamento de F\\'\\i sica, Universidade Federal de Santa Catarina,\n Campus Trindade, 88040-900, Florian\\'opolis - SC, Brazil, \\\\\n email: bap@fsc.ufsc.br \\\\\n $^2$ Department of Physics, Keele University, Keele, Staffordshire,\n ST5 5BG, UK, email: msc@astro.keele.ac.uk \\\\ }\n\n\\date{Submitted to MNRAS (1999 December 14)}\n\n\\pubyear{2000}\n\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\n\nWe report on $V$ and $R$ high speed photometry of the dwarf nova EX~Dra\nin quiescence and in outburst. The analysis of the outburst lightcurves\nindicates that the outbursts do not start in the outer disc regions.\nThe disc expands during the rise to maximum and shrinks during decline\nand along the following quiescent period. The decrease in brightness at\nthe later stages of the outburst is due to the fading of the light from the\ninner disc regions. At the end of two outbursts the system was seen to go\nthrough a phase of lower brightness, characterized by an out-of-eclipse\nlevel $\\simeq 15$ per cent lower than the typical quiescent level and by\nthe fairly symmetric eclipse of a compact source at disc centre with\nlittle evidence of a bright spot at disc rim.\n\nNew eclipse timings were measured from the lightcurves taken in quiescence\nand a revised ephemeris was derived. The residuals with respect to the\nlinear ephemeris are well described by a sinusoid of amplitude 1.2 minutes\nand period $\\simeq 4$ years and are possibly related to a solar-like \nmagnetic activity cycle in the secondary star. Eclipse phases of the\ncompact central source and of the bright spot were used to derive the\ngeometry of the binary. By constraining the gas stream trajectory to pass\nthrough the observed position of the bright spot we find $q=0.72\\pm 0.06$\nand $i= 85^{+3}_{-2}$ degrees. The binary parameters were estimated by\ncombining the measured mass ratio with the assumption that the secondary\nstar obeys an empirical main sequence mass-radius relation. We find\n$M_1 = 0.75\\pm 0.15 \\; M_\\odot$ and $M_2 = 0.54\\pm 0.10 \\; M_\\odot$.\nThe results indicate that the white dwarf at disc centre is surrounded\nby an extended and variable atmosphere or boundary layer of at least 3\ntimes its radius and a temperature of $T\\simeq 28000 \\;K$. The fluxes\nat mid-eclipse yield an upper limit to the contribution of the secondary\nstar and lead to a lower limit photometric parallax distance of $D= 290\n\\pm 80\\; pc$. The fluxes of the secondary star are well matched by those\nof a M$0\\pm2$ main sequence star.\n\n\\end{abstract}\n\n\\begin{keywords}\nbinaries: close -- novae, cataclysmic variables -- eclipses -- accretion,\naccretion discs -- stars: individual: (EX Draconis).\n\\end{keywords}\n\n\\section{Introduction}\n\nDwarf novae are mass-exchanging binaries in which a late type star (the\nsecondary) overfills its Roche lobe and transfers matter to a companion\nwhite dwarf (the primary) via an accretion disc. \nThese systems show recurrent outbursts\nof 2--5 magnitudes on timescales of a few weeks to months caused either\nby an instability in the mass transfer from the secondary star or by a\nthermal instability in the accretion disc which switches the disc from\na low to a high-viscosity regime (Warner 1995 and references therein).\nDuring outburst most of the light arises from the bright, optically thick\naccretion disc, while in quiescence the dominant sources of light are the\nwhite dwarf and the bright spot formed by the impact of the infalling\ngas stream with the edge of the disc.\n\nEclipsing dwarf novae are probably the best sites for the study of \naccretion physics as the occultation of the accretion disc and white\ndwarf by the secondary can be used to constrain the geometry and \nparameters of the binary, and tomographic techniques such as eclipse\nmapping (Horne 1985) and Doppler tomography (Marsh \\& Horne 1988) can\nbe applied to probe the structure and dynamics of the accretion flow.\n\nEX Draconis (= HS1804+67) was detected in the Hamburger Quasar Survey\n(Bade et~al. 1989) and shown to be an eclipsing dwarf nova with an\norbital period of 5.04 hr by Barwig et~al. (1993). From spectroscopic\nobservations made in quiescence, Billington, Marsh \\& Dhillon (1996)\nfound that the secondary star is of spectral type M1 to M2 and that\nit contributes almost all of the light at mid-eclipse. Their analysis\nshowed that the inner face of the secondary is significantly irradiated\nby the white dwarf. They found a rotational broadening of $v\\sin i =\n140\\; km\\,s^{-1}$ and a radial velocity semi-amplitude of $K_2 = 210\\;\nkm\\,s^{-1}$ for the secondary star which leads to a spectroscopic mass\nratio of $q=0.8$ when combined with the $K_1= 167\\; km\\,s^{-1}$ of Barwig\net~al. (1993). A relatively small value for the radius of the accretion\ndisc ($0.4\\;R_{L1}$) is derived but no explanation is given of how this\nestimate was made.\n\nIn a follow up study using spectroscopy and photometry of EX~Dra in\nquiescence and in outburst, Fiedler, Barwig \\& Mantel (1997) measured\nradial velocity semi-amplitudes of $K_1= 167\\; km\\,s^{-1}$ and $K_2=\n223\\; km\\,s^{-1}$ and derived a spectroscopic model for the binary with\n$q=0.75$, $i= 84.2\\degr$, $M_1= 0.75\\;M_\\odot$ and $M_2= 0.56\\;M_\\odot$.\nHowever, the radial velocity curve of the H$\\alpha$ line shows a large\nphase shift ($\\simeq 0.2$ cycle) with respect to photometric conjunction\nwhich casts doubt on the derived value of $K_1$. They use the eclipse \nphases of the bright spot and white dwarf to derive a photometric mass\nratio between 0.7 and 0.8, supporting the spectroscopic model. From the\nratios of Ca\\,I and TiO absorption features they infer a spectral type\nof M0 for the secondary star. Smith \\& Dhillon (1998) use the values of\n$v\\sin i$ and $K_2$ of Billington et~al. (1996) and the eclipse phase\nwidth $\\Delta\\phi$ of Fiedler et~al. (1997) to infer a $K_1= 176 \n\\;km\\,s^{-1}$.\n\nIn this paper we present and discuss high-speed photometry of EX~Dra in\nquiescence and in outburst. Section~\\ref{obs} describes the observations.\nIn section~\\ref{results} we present and discuss the eclipse lightcurves,\nprovide an updated ephemeris, derive the binary parameters from the\neclipse phases of the white dwarf and bright spot, and obtain estimates\nof the distance to the binary. The results are summarized in\nsection~\\ref{final}.\n\n\n\\section{Observations and data reduction} \\label{obs}\n\nTime-series of differential photometry of EX~Dra in the $V$ and $R$ bands\nwas obtained with a Wright Instruments CCD camera (1.76 arcsec/pixel, \n$385 \\times 578$ pixels) attached to the 0.9-m James Gregory Telescope\nof the University Observatory, St.\\,Andrews, in 1995 and 1996. This pixel\nsize is matched to the seeing at this sea-level site, where typical stellar\nimages have FWHM values of 3.0 pixels, and are therefore well sampled.\nExposure times ranged from 15 to 40\\,s with a dead-time between exposures\nof about 5\\,s to read the CCD chip. Details of the observations are listed\nin Table~\\ref{tab1}. The observations include five outbursts of EX~Dra \nand sample various phases along the outburst cycle.\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TABLE 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table*}\n \\centering\n \\begin{minipage}{140mm}\n \\caption{Journal of the observations.} \\label{tab1}\n \\begin{tabular}{@{}lrcrccccl@{}}\n~~~ Date & Start & $\\Delta t$ & No. of ~~ & Band & Cycle & Phase range &\nQuality \\footnote{ A= photometric (main comparison stable), B= good (some\nsky variations), C= poor (large variations and/or clouds).} & State \\\\ [-0.5ex]\n& (UT) & (s) & exposures & & & (cycles) \\\\ [1ex]\n1995 Sep 20 & 21:23 & 30 & 96~~~ & R & 7540 & $+0.06,+0.32$ & C & maximum \\\\\n1995 Sep 24 & 20:36 & 30 & 113~~~ & R & 7559 & $-0.04,+0.19$ & A & decline \\\\\n1995 Sep 25 & 21:28 & 30 & 103~~~ & R & 7564 & $-0.10,+0.18$ & A & decline \\\\\n1995 Sep 26 & 22:45 & 30 & 97~~~ & R & 7569 & $-0.08,+0.12$ & B & quiescence\\\\\n[0.5ex]\n1995 Oct 15 & 20:32 & 30 & 101~~~ & R & 7659 & $-0.02,+0.19$ & B & maximum \\\\\n1995 Oct 16 & 0:48 & 30 & 54~~~ & R & 7660 & $-0.17,-0.01$ & C & maximum \\\\\n1995 Oct 17 & 22:07 & 30 & 178~~~ & R & 7669 & $-0.18,+0.19$ & B & decline \\\\\n1995 Oct 18 & 3:34 & 30 & 71~~~ & R & 7670 & $-0.10,+0.09$ & C & decline \\\\\n1995 Oct 18 & 18:41 & 30 & 74~~~ & R & 7673 & $-0.10,+0.04$ & B & decline \\\\\n\t\t\t& 0:17 & 30 & 78~~~ & R & 7674 & $+0.01,+0.16$ & C & decline \\\\\n[0.5ex]\n1995 Nov 14 & 1:20 & 30 & 156~~~ & R & 7798 & $+0.07,+0.52$ & B & quiescence\\\\\n1995 Nov 16 & 22:24 & 30 & 149~~~ & R & 7812 & $-0.22,+0.19$ & C & rise \\\\\n1995 Nov 17 & 3:39 & 30 & 113~~~ & R & 7813 & $-0.18,+0.12$ & B & rise \\\\\n1995 Nov 18 & 0:21 & 30 & 82~~~ & R & 7817 & $-0.07,+0.09$ & B & rise \\\\\n1995 Nov 19 & 21:37 & 30 & 53~~~ & R & 7826 & $-0.09,+0.12$ & C & maximum \\\\\n1995 Nov 20 & 2:34 & 30 & 88~~~ & R & 7827 & $-0.11,+0.09$ & B & maximum \\\\\n1995 Nov 24 & 22:59 & 30 & 49~~~ & R & 7850 & $-0.00,+0.10$ & C & decline \\\\\n[0.5ex]\n1995 Dec 11 & 2:04 & 15/18 & 252~~~ & R & 7927 & $-0.18,+0.13$ & A & rise \\\\\n1995 Dec 20 & 3:01 & 15 & 220~~~ & R & 7970 & $-0.12,+0.13$ & A & decline \\\\\n1995 Dec 20\t& 22:59 & 30 & 160~~~ & R & 7974 & $-0.16,+0.18$ & A & quiescence\\\\ \n1995 Dec 26 & 20:14 & 30 & 172~~~ & R & 8002 & $-0.12,+0.23$ & A & low state \\\\\n1995 Dec 27 & 1:12 & 30 & 182~~~ & R & 8003 & $-0.13,+0.24$ & A & low state \\\\\n\t\t\t& 6:19 & 30/40 & 91~~~ & V & 8004 & $-0.12,+0.07$ & A & low state\\\\\n1995 Dec 27 & 21:31 & 30 & 148~~~ & R & 8007 & $-0.10,+0.19$ & A & quiescence\\\\\n1995 Dec 28 & 2:10 & 30 & 188~~~ & R & 8008 & $-0.18,+0.21$ & A & quiescence\\\\\n1995 Dec 28 & 17:46 & 30 & 177~~~ & R & 8011 & $-0.09,+0.26$ & A & quiescence\\\\\n\t\t\t& 22:25 & 30 & 188~~~ & V & 8012 & $-0.16,+0.25$ & A & quiescence\\\\\n1995 Dec 29 & 3:20 & 30 & 202~~~ & R & 8013 & $-0.19,+0.22$ & A & quiescence\\\\\n1995 Dec 29 & 18:13 & 30 & 214~~~ & R & 8016 & $-0.23,+0.20$ & B & quiescence\\\\\n\t\t\t& 23:43 & 30/40 & 132~~~ & R & 8017 & $-0.14,+0.14$ & C &\nquiescence \\\\ [0.5ex]\n1996 Jan 10 & 21:40 & 15-40 & 224~~~ & R & 8074 & $-0.39,+0.28$ & B &\nquiescence \\\\ [0.5ex]\n1996 Nov 22\t& 18:00 & 30 & 152~~~ & R & 9583 & $-0.14,+0.18$ & B & decline \\\\\n[-3ex]\n\\end{tabular}\n\\end{minipage}\n\\end{table*}\n\nThe data was reduced using standard {\\sc IRAF}\\footnote{ \nIRAF is distributed by National Optical Astronomy Observatories,\nwhich is operated by the Association of Universities for Research in\nAstronomy, Inc., under contract with the National Science Foundation.}\nprocedures and included bias and flat-field corrections and cosmic rays\nremoval. Photometry was obtained with the automated aperture photometry\nroutine JGTPHOT (Bell, Hilditch \\& Edwin 1993). Fluxes were extracted for\nthe variable and for five selected comparison stars in the field. The\nrelative brightness of the comparison stars in all data sets is constant\nto better than 0.01 mag. We adopted a mean comparison star magnitude for\neach frame from the intensity-added values of these five stars. Time-series\nwere constructed by computing the magnitude difference between the variable\nand the mean comparison star. From the dispersion in the magnitude \ndifference of the comparison stars with similar brightness we estimate\nan uncertainty in the photometry of EX~Dra of 0.025 mag in quiescence \nand better than 0.01~mag in outburst.\n\nObservations of spectrophotometric standard stars of Massey et~al. (1998)\nand Massey \\& Gronwall (1990) were used to calibrate the photometry in\nthe EX~Dra field. These observations demonstrate that the transformation\ncoefficients from the natural to the standard $VR$ system (Bessell 1983)\nare unity to a precision of one per cent. Hence differential instrumental\nmagnitudes obtained from individual frames are differential $V$ and $R$\nmagnitudes. We found the mean of the combined $V$ and $R$ magnitudes of\nthe five comparison stars to be $V= 13.21 \\pm 0.09$ mag and $R= 12.84\n\\pm 0.05$ mag. We used the relations $V= 16.40 - 2.5\\; \\log_{10}f_\\nu\n[{\\rm mJy}]$ and $R= 16.22 - 2.5\\; \\log_{10}f_\\nu [{\\rm mJy}]$ (Lamla 1982)\nto transform the calibrated magnitudes to absolute flux units.\n\n\n\\section{Results} \\label{results}\n\n\\subsection {Eclipse lightcurves} \\label{cluz}\n\nWe adopted the following convention regarding the phases: conjunction\noccurs at phase zero, the phases are negative before conjunction and\npositive afterwards. The lightcurves were phased according to the\nephemeris of eq.\\,\\ref{efem} (section~\\ref{rev_efem}).\n\nFigure~\\ref{fig1} shows the visual lightcurve of EX~Dra for the period\nSeptember 1995 to January 1996 from AAVSO and VSNET observations.\n%\n%%%%%%%%%%%%%%%%%%%%% FIGURE 1 %%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n%\\vspace{8cm}\n\\centerline{\\psfig{figure=xfig01.ps,angle=-90,width=12cm,rheight=8cm}}\n \\caption{ Visual lightcurve of EX~Dra during the period September 1995\n to January 1996, constructed from observations made by the AAVSO (crosses)\n and VSNET (open squares). Arrows indicate upper limits on the visual\n magnitude. Vertical dotted lines mark the epochs of our observations.\n $R$-band out-of-eclipse magnitudes from our dataset are shown as filled\n circles for illustration purposes.} \n\\label{fig1}\n\\end{figure*}\n%\nVertical dotted lines mark the epochs of our observations while filled\ncircles show the corresponding $R$-band out-of-eclipse magnitudes.\nThere were six recorded outbursts during this period (labeled from\nA to F in Fig.\\,\\ref{fig1}), with typical amplitudes of $\\simeq 2.0$ mag,\nduration of $\\simeq 10$ days, and average time between outbursts of\n$20\\pm 3$ days. Outburst C was shorter ($\\simeq 5$ days) and weaker\n($\\Delta m\\simeq 1.5$ mag) than the others and, unfortunately, was not\ncovered by our observations. The visual magnitude is typically $m_v\n\\simeq 12.7$ at maximum and $m_v\\simeq 15$ in quiescence. At the end\nof outbursts A and E the star went through a faint state (hereafter \nnamed low state) before recovering its usual quiescent level.\n\nOur dataset frames eclipse lightcurves during most relevant phases\nthrough the outburst cycle: early rise to maximum (cycles 7812, 7813,\n7817), late rise to maximum (7927), maximum light (7540, 7659, 7660,\n7826 and 7827), end of maximum (7669, 7670, 7673, 7674 and 9583),\nearly decline (7559, 7850), late decline (7564, 7970), low state\n(8002 to 8004), and quiescence (7569, 7798, 8007 to 8017, and 8074).\n\nIndividual lightcurves of EX~Dra in quiescence are shown in \nFig.~\\ref{fig2}. \n%\n%%%%%%%%%%%%%%%%%%%%% FIGURE 2 %%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig02.ps,width=10.3cm,rheight=13cm}}\n \\caption{ Lightcurves of EX~Dra in quiescence. The curves are \n progressively displaced upwards by 4~mJy. Horizontal lines at \n mid-eclipse show the true zero level in each case. Vertical dotted\n lines mark the phases of ingress/egress of the bright spot and the\n egress of the white dwarf as measured in section~\\ref{param}. \n Labels indicate the cycle number. } \n\\label{fig2}\n\\end{figure}\n%\nSharp changes in the slope reflect the occultation of\na compact source at disc centre and of the bright spot at disc rim. The\ningress of the central source and of the bright spot overlap in phase\nto form a unique sharp break in the slope. The egress of the central\nsource is variable both in duration and in flux and sometimes is hardly\nvisible (e.g., cycle 8074). The eclipses have a flat-bottomed, `U'\nshape indicating that the eclipse is close from being total. There is\nno pronounced flickering (amplitude $\\simlt 2.5$ per cent). In some of\nthe lightcurves the flux level is the same before and after eclipse\nwhile others show a perceptible orbital hump prior to eclipse (usually\ninterpreted as being the result of anisotropic emission from the bright\nspot) and a slow recovery from eclipse where the bright spot egress\nis hardly discernible.\n\nFigure~\\ref{fig3} shows lightcurves of EX~Dra along the outburst cycle.\nThe left panel shows the behaviour during rise and maximum light while\nthe right panel shows the behaviour during decline and in the low state.\nThe lightcurves were grouped by outburst phase. Only a subset of the\noutburst lightcurves are shown for clarity. The fact that, for a given\noutburst stage, the lightcurves of different outbursts have similar \neclipse shapes and out-of-eclipse levels gives confidence that the\nobserved sequence is representative of the general behaviour of EX~Dra\nduring outburst (at least for the epoch of our observations).\n%\n%%%%%%%%%%%%%%%%%%%%% FIGURE 3 %%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n\\centerline{\\psfig{figure=xfig03.ps,angle=-90,width=18.5cm,rheight=13cm}}\n \\caption{ Lightcurves of EX~Dra through the outburst cycle. Vertical \n dotted lines mark the phases of ingress/egress of the bright spot and\n the egress of the white dwarf as measured in section~\\ref{param}. \n Labels indicate the cycle number. The left panel shows lightcurves on\n the rise to maximum and at maximum while the right panel shows lightcurves\n during decline and in the low state. The quiescent lightcurve of cycle\n 7974 is shown in the left panel for reference. } \n\\label{fig3}\n\\end{figure*}\n%\n\nLightcurve 7812+7813 frames the early rise to maximum. The eclipse shape\nis asymmetric and mid-eclipse occurs after phase zero, indicating that\nthe receding side of the disc is brighter. The mid-eclipse level and the\ntotal eclipse width are the same as in quiescence, showing that the\nbrightening does not start in the outer disc regions. This is in agreement\nwith the symmetric shape of the outbursts, with comparable rise and \ndecline timescales (cf. Fig.\\,\\ref{fig1}), which is typical of inside-out\noutbursts (e.g., Cannizzo, Wheeler \\& Polidan 1986).\n\nThe eclipse profile changes during the rise to maximum, from the \nasymmetric `U' shape eclipse of a compact central source plus the bright\nspot at disc rim to a more symmetric `V' shape indicating the partial\noccultation of a bright extended disc. The total width of the eclipse\nincreases during the rise (from 0.196 cycle in quiescence to about 0.22\ncycle at lightcurve 7927 and larger at maximum) indicating that the\ndisc radius also increases as the system approaches maximum light. A\nprecise measurement of the total width of the eclipse at maximum light\nis precluded due to the limited phase coverage of the corresponding\nlightcurve.\n\nThe disc shrinks during decline (as indicated by the eclipse egress\nphase) until it reaches the quiescent radius close to the end of the\noutburst (lightcurve 7564+7970). The low state is characterized by an\nout-of-eclipse level $\\simeq 15$ per cent lower than the typical\nquiescent level and by a fairly symmetric eclipse shape, corresponding\nto the eclipse of a compact source at the disc centre with little \nevidence of a bright spot at the disc rim. The mid-eclipse level of\nlightcurves 7564+7970 and 8002+8003 is the same, showing that the\ndecrease in brightness at this stage is due to the fading of the light\nfrom the inner disc regions.\n\nFlickering is much more pronounced in outburst than in quiescence.\nFlickers of an amplitude of $\\simeq 10-15$ per cent can be seen in\nmany lightcurves in outburst.\n\nNone of our outburst lightcurves resembles the flat-bottomed outburst\nlightcurve of Fiedler et~al. (1997, see their fig.~6). Their outburst\nlightcurve is a factor of only $\\simeq 2$ brighter than their typical\nquiescent lightcurve indicating that it corresponds to outbursts of\nlower amplitude than the ones sampled by our observations.\n\n\n\\subsection {Revised ephemeris} \\label{rev_efem}\n\nThe ingress feature of the white dwarf and of the bright spot overlap\nin quiescent lightcurves of EX~Dra (Fig.~\\ref{fig2}). Since the bright\nspot ingress depends on the variable disc radius, the mid-ingress time\nis not a stable feature of the eclipse. We therefore adopted the same\nprocedure of Fiedler et~al. (1997) and used the mid-egress times of the\nwhite dwarf plus the inferred duration of its eclipse (see \nsection~\\ref{param}) to obtain a revised ephemeris for the mid-eclipse\ntimes.\n\nMid-egress times were measured by computing the time of maximum derivative\nin a median-filtered version of the lightcurve (section~\\ref{param}). \nThe uncertainty in determining mid-egress times depends on the time\nresolution and signal-to-noise of the lightcurve and is in the range\n$(1-2) \\times 10^{-4}$~d. The barycentric correction and the difference\nbetween universal times (UT) and dynamical ephemeris time scales are \nsmaller than the uncertainties in the measured timings and were neglected.\nThe new heliocentric (HJD) times of the egress of the white dwarf are\nlisted in Table~\\ref{tab2} with corresponding cycle number and \nuncertainties (quoted in parenthesis).\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TABLE 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table}\n \\centering\n \\begin{minipage}{50mm}\n \\caption{New eclipse timings.} \\label{tab2}\n \\begin{tabular}{@{}ccl@{}}\ncycle & white dwarf egress & (O$-$C) \\footnote{Observed minus Calculated\ntimes with respect to the linear part of the ephemeris of eq.~\\ref{efem}.} \n\\\\ [-0.5ex]\n & HJD (2\\,400\\,000 +) & ~(cycle) \\\\ [1ex]\n7569 & 49987.4778 (2) & $+0.0009$ \\\\\n7974 & 50072.5023 (2) & $+0.0014$ \\\\\n8002 & 50078.3799 (2) & $-0.0017$ \\\\\n8003 & 50078.5900 (1) & $-0.0010$ \\\\\n8004 & 50078.8000 (1) & $-0.0006$ \\\\\n8007 & 50079.4296 (2) & $-0.0017$ \\\\\n8008 & 50079.6404 (1) & $+0.0025$ \\\\\n8011 & 50080.2700 (2) & $+0.0015$ \\\\\n8012 & 50080.4793 (1) & $-0.0016$ \\\\\n8013 & 50080.6893 (1) & $-0.0015$ \\\\\n8016 & 50081.3191 (1) & $-0.0015$ \\\\\n8017 & 50081.5290 (1) & $-0.0015$ \\\\\n8074 & 50093.4955 (1) & $-0.0010$ \\\\ [-3ex]\n\\end{tabular}\n\\end{minipage}\n\\end{table}\n\nWe assumed equal errors of $10^{-4}$~d for the timings of Fiedler et~al.\n(1997) and combined them with the timings of Table~\\ref{tab2} to obtain\na least-squares linear fit with a reduced $\\chi^2= 13.8$ for 54 d.o.f.\nand a standard deviation of $\\sigma= 0.0019$ cycle. The residuals with\nrespect to the linear ephemeris show a clear cyclical behaviour and can\nbe well described by a sinusoidal function. Assuming a duration of the\neclipse of the white dwarf of $\\Delta t=0.0228$~d (section~\\ref{param}),\nthe best-fit linear plus sinusoidal ephemeris for the mid-eclipse times\nis,\n\\[\nT_{mid} = {\\rm HJD}\\; 2\\,448\\,398.4530(\\pm 1) + 0.209\\,936\\,98(\\pm 4)\\,E +\n\\]\n\\begin{equation}\n+ (8.2 \\pm 1.5) \\times 10^{-4} \\; \\sin \\left[ 2\\pi \\frac{(E-968)}{7045}\n\\right] \\; d \\;\\;\\; ,\n\\label{efem}\n\\end{equation}\n%\nwith $\\chi^2= 2.7$ for 51 d.o.f. and $\\sigma= 0.0010$ cycle.\nResiduals with respect to the linear part of eq.(\\ref{efem}) are listed\nin Table~\\ref{tab2} and shown in Fig.~\\ref{fig4}. The sinusoidal term\nof eq.(\\ref{efem}) is indicated in Fig.~\\ref{fig4} as a dotted line.\n%\n%%%%%%%%%%%%%%%%%%%%% FIGURE 4 %%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig04.ps,angle=-90,width=9.5cm,rheight=6.8cm}}\n \\caption{ The $(O-C)$ diagram for the eclipse mid-egress times calculated\n from the linear part of eq.(\\ref{efem}). The timings of Fiedler et~al.\n (1997) are plotted as open squares while those in Table~\\ref{tab2} are\n shown as filled circles. } \n\\label{fig4}\n\\end{figure}\n%\n\nThe amplitude (1.18 minutes) and timescale ($\\simeq 4$ years) of the\nperiod variation are similar to the quasi-periodic orbital period changes\nfound in many other eclipsing CVs (Warner 1995 and references therein)\nand are possibly related to a solar-like magnetic activity cycle in\nthe secondary star (Applegate 1992; Richman, Applegate \\& Patterson \n1994). It may also be possible that the period changes are due to a\nthird body in the system, as suggested by Fiedler et~al. (1997), if the\nvariation proves to be strictly periodic. Regular observations of eclipse\ntimings during the next decade are required in order to check the \nstability of the period of the variation and test the above hypotheses.\n\n\n\\subsection {Binary parameters} \\label{param}\n\n\\subsubsection {Measuring eclipse phases} \\label{phases}\n\nThe ingress/egress phases of the occultation of the compact central\nsource (hereafter CS) and of the bright spot (BS) by the secondary star\nprovide information about the geometry of the binary system and the\nrelative sizes of these components (e.g., Wood et~al. 1986).\n\nWe used the lightcurves of the low state -- where the effect of the BS\nis minimal on the eclipse shape -- to measure the ingress and egress\nphases of the CS and to derive the width of its eclipse as well as the\nduration of its ingress/egress feature. The contact phases can be \nidentified as rapid changes in slope visible in the lightcurves of\nthe low state (Fig.~\\ref{fig3}) and were measured with the aid of a\ncursor on a graphic display of a median filtered version of the\nlightcurve. We defined $\\phi_{c1},\\phi_{c2}$ as those phases during\nwhich the CS disappears behind the secondary star and $\\phi_{c3},\n\\phi_{c4}$ as the phases corresponding to its reappearance from eclipse.\nThe mid-ingress (egress) phases ($\\phi_{ci},\\phi_{ce}$) were computed\nas the phases at which half of the central source light is eclipsed\nand also as the phases of minimum (maximum) derivative in the lightcurve\n(e.g., Wood, Irwin \\& Pringle 1985).\n\nFigure~\\ref{fig5} illustrates the measurement procedure with the \nderivative for the combined lightcurve 8002+8003. The ingress/egress\nof the CS can be seen as those intervals for which the derivative curve\nis significantly different from zero. \n%\n%%%%%%%%%%%%%%%%%%%%% FIGURE 5 %%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig05.ps,angle=-90,width=9.5cm,rheight=7cm}}\n \\caption{ Measuring the eclipse phases of the compact central source.\n (a) Lightcurve 8002+8003. (b) The median-filtered derivative of (a), \n multiplied by a factor 2. The dashed line is a spline fit to the\n extended and slowly varying eclipse of the disc. (c) The reconstructed\n central source lightcurve, shifted downwards by 1.5 mJy. (d) Lightcurve\n (a) after subtraction of the central source component, shifted \n downwards by 5 mJy. Dashed lines mark mid-ingress and mid-egress\n phases of the central source and dotted lines mark its four contact\n phases. Arrows indicate the beginning and end of the eclipse of the\n disc. } \n\\label{fig5}\n\\end{figure}\n%\nThe width at half-peak intensity of these features yields a preliminary\nestimate of their duration. A spline function is fitted to the remaining\nregions in the derivative curve to remove the contribution from the\nextended and slowly varying eclipse of the disc. Estimates of the CS\nflux at ingress (egress) are obtained by integrating the flux in the\nspline-subtracted derivative curve between the first and second (third\nand fourth) contact phases. The lightcurve of CS is then reconstructed\nby assuming that the flux is zero between ingress and egress and that it\nis constant outside eclipse. The reconstructed CS lightcurve can be seen\nin Fig.~\\ref{fig5}(c) and the lightcurve after removal of the CS component\nis shown in Fig.~\\ref{fig5}(d).\n\nThe measured contact phases, mid-ingress and mid-egress phases of the CS\nfrom the lightcurves of the low state are collected in Table~\\ref{tab3}.\nThe quoted mid-ingress/egress values are the average of both procedures\ndescribed above and have an estimated error of 0.0005 cycle.\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TABLE 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table*}\n \\centering\n \\begin{minipage}{163mm}\n \\caption{Eclipse parameters from lightcurves of the low state.} \\label{tab3}\n \\begin{tabular}{@{}lcccccccrcc@{}}\ncycle & $\\phi_{c1}$ & $\\phi_{c2}$ & $\\phi_{c3}$ & $\\phi_{c4}$ &\n$\\phi_{ci}$ & $\\phi_{ce}$ & $\\Delta\\phi$ & $\\phi_0\\;\\;\\;$ &\n$\\Delta_{ci}$ & $\\Delta_{ce}$ \\\\ [1ex]\n8002 \t\t& $-0.0595$ & $-0.0515$ & +0.0515 & +0.0595 &\n$-0.0545$ & +0.0545 & 0.1090 & 0.0000 & 0.0080 & 0.0080 \\\\\n8003 \t\t& $-0.0575$ & $-0.0490$ & +0.0515 & +0.0600 &\n$-0.0540$ & +0.0540 & 0.1080 & 0.0000 & 0.0085 & 0.0085 \\\\\n8004V \t\t& $-0.0580$ & $-0.0500$ & +0.0515 & +0.0600 &\n$-0.0540$ & +0.0550 & 0.1090 & +0.0005 & 0.0080 & 0.0085 \\\\\n8002+8003\t& $-0.0595$ & $-0.0515$ & +0.0515 & +0.0595 &\n$-0.0540$ & +0.0540 & 0.1080 & 0.0000 & 0.0080 & 0.0080 \\\\ [0.5ex]\nmean \t\t& $-0.0586$ & $-0.0505$ & +0.0515 & +0.0598 &\n$-0.0541$ & +0.0544 & 0.1085 & +0.0001 & 0.0081 & 0.0082 \\\\\nerror \t\t& $\\pm 0.0010$ & $\\pm 0.0010$ & $\\pm 0.0005$ & $\\pm 0.0003$ &\n$\\pm 0.0003$ & $\\pm 0.0005$ & $\\pm 0.0006$ & $\\pm 0.0003$ & $\\pm 0.0003$ &\n$\\pm 0.0003$ \\\\\n\\end{tabular}\n\\end{minipage}\n\\end{table*}\n\nThe duration of the CS eclipse (the eclipse of the disc centre) is \ndefined as\n\\begin{equation}\n\\Delta\\phi= \\phi_{ce} - \\phi_{ci} \\; ,\n\\end{equation}\nand the mid-eclipse phase (the inferior conjunction of the binary) \nis written as\n\\begin{equation}\n\\phi_0 = 1/2\\:(\\phi_{ce} + \\phi_{ci}) \\; .\n\\end{equation}\n%\nThese quantities are collected in Table~\\ref{tab3}.\nThe mean of the measurements from all lightcurves yields $\\Delta\\phi =\n0.1085 \\pm 0.0006$ cycle (=0.0228 d), where the quoted error is the\nstandard deviation of the mean. Similarly, we have $\\phi_0 = +0.0001\n\\pm 0.0003$ cycle, which indicates that the centre of the CS eclipse\ncorresponds to phase zero.\nThe difference between the first and second (third and fourth) CS\ncontact phases yield the phase width of the CS ingress (egress),\n$\\Delta_{\\rm ci}$ ($\\Delta_{\\rm ce}$). These quantities are also listed\nin Table~\\ref{tab3}. A mean from all values of $\\Delta_{\\rm ci}$\nand $\\Delta_{\\rm ce}$ yields $\\Delta_{\\rm cs}= 0.0082 \\pm 0.0003$~cycle.\n\nBS ingress/egress phases ($\\phi_{bi},\\phi_{be}$) were measured from\nthe lightcurves in quiescence in which it was possible to simultaneously\nidentify the eclipse of BS and the egress of CS. We measured the CS\ncontact and mid-egress phases and used the derived value of $\\Delta\\phi$\nto reconstruct the lightcurve of CS assuming that the flux and duration\nof its ingress feature are the same as in egress. Mid-ingress/egress\nphases of BS were measured in the lightcurves after removal of the CS\ncomponent, which provide and unblended, clean view of the BS ingress\nfeature (Fig.~\\ref{fig6}). \n%\n%%%%%%%%%%%%%%%%%%%%% FIGURE 6 %%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig06.ps,angle=-90,width=9.5cm,rheight=7cm}}\n \\caption{ Measuring the eclipse phases of the bright spot.\n (a) Lightcurve 8007. (b) The reconstructed central source lightcurve,\n shifted upwards by 1 mJy. (c) Lightcurve (a) after subtraction of the\n central source component, shifted downwards by 3 mJy. (d) The derivative\n of lightcurve (c), multiplied by a factor 2 and shifted downwards by 2 mJy.\n Dashed lines mark the mid-ingress and mid-egress phases of the bright\n spot and dotted lines mark the four contact phases of the compact\n central source. } \n\\label{fig6}\n\\end{figure}\n%\nThe eclipse parameters measured from the lightcurves in quiescence\nare listed in Table~\\ref{tab4}. The BS eclipse in lightcurve 7569 starts\nearlier and ends later than in the other lightcurves, indicating a\nrelatively larger disc radius at this epoch (see section~\\ref{geom}).\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TABLE 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table*}\n \\centering\n \\begin{minipage}{95mm}\n \\caption{Eclipse parameters from lightcurves in quiescence.} \\label{tab4}\n \\begin{tabular}{@{}lcccccc@{}}\ncycle & $\\phi_{bi}$ & $\\phi_{be}$ & $\\phi_{c3}$ & $\\phi_{c4}$ &\n$\\phi_{ce}$ & $\\Delta_{ce}$ \\\\ [1ex]\n7569 \t& $-0.061$ & +0.099 & +0.0480 & +0.0620 & +0.0550 & 0.014 \\\\\n8007 \t& $-0.055$ & +0.096 & +0.0495 & +0.0575 & +0.0540 & 0.008 \\\\\n8008 \t& $-0.055$ & +0.096: & +0.0490 & +0.0600 & +0.0550 & 0.011 \\\\\n8012\t& $-0.056$ & +0.095 & +0.0490 & +0.0600 & +0.0545 & 0.011 \\\\\n8016+8017 & $-0.054$ & +0.096 & +0.0510 & +0.0580 & +0.0540 & 0.007 \\\\\n\\end{tabular}\n\\end{minipage}\n\\end{table*}\n\n\n\\subsubsection {Mass ratio, inclination and disc radius} \\label{geom}\n\nMaking the usual assumption that the secondary star fills its Roche\nlobe and given the duration of the eclipse of the central parts of\nthe disc, $\\Delta\\phi$, there is a unique relation between the mass\nratio $q= M_2/M_1$ and the binary inclination $i$ (Bailey 1979;\nHorne 1985). From Table\\,\\ref{tab3}, the width of the eclipse in\nEX~Dra is $\\Delta\\phi= 0.1085$. This gives the constraint $q>0.64$,\nwith $q=0.64$ if $i=90\\degr$.\n\nWhen combined with the measured eclipse phases of the CS and BS, this\nrelation gives a unique solution for $q$, $i$, and $R_{bs}/R_{L1}$,\nwhere $R_{bs}$ is the distance from disc centre to the BS (usually taken\nto be the disc radius) and $R_{L1}$ is the distance from disc centre\nto the inner lagrangian point L1 (e.g., Smak 1971; Cook \\& Warner 1984). \nFig.\\,\\ref{fig7}(a) shows a diagram of ingress versus egress phases for\nthe measurements of the CS and BS in Tables~\\ref{tab3} and \\ref{tab4}.\nMeasurements of the CS ingress and egress are shown as the cluster of\nsmall diamonds around phases ($-0.054, +0.054$) in the lower portion of\nthe diagram. Eclipse phases of BS are indicated by crosses.\n%\n%%%%%%%%%%%%%%%%%%%%% FIGURE 7 %%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig07.ps,width=11.5cm,rheight=15cm}}\n \\caption{ Inferring the binary geometry from the ingress/egress phases\n of CS and BS. (a) Ingress-egress phases diagram. The observed phases\n of mid-ingress/egress of CS are marked with diamonds, those of BS\n with crosses. A diagonal dotted line depicts the line joining the\n component stars. Theoretical gas stream trajectories for three values\n of $q$ are plotted. The stream of matter passes through the position\n of BS for $q=0.72$. The squashed circles represent the accretion discs\n whose edges pass through the two distinct positions of the BS. For\n $q=0.72$, this yields disc radii of $R_{bs}= 0.50$ and $0.56\\;\n R_{L1}$. (b) The adopted geometry of the binary for $q=0.72$.\n The observed positions of CS and BS are shown with the theoretical\n gas stream trajectory and discs of radii $R_{bs}= 0.50$ and $0.56\\;\n R_{L1}$. The direction at which the bright spot is at maximum is\n indicated by an arrow. } \n\\label{fig7}\n\\end{figure}\n%\nTheoretical gas stream trajectories corresponding to a set of pairs \n$(i,q)$ are also shown. The trajectories were computed by solving the\nequations of motion in a coordinate system synchronously rotating with\nthe binary, using a 4th order Runge-Kutta algorithm (Press et al. 1986)\nand conserving the Jacobi integral constant to one part in $10^{6}$.\nThe correct mass ratio, and hence inclination, are those for which the calculated stream trajectory passes through the observed position of\nthe bright spot. \nThis yields $q= 0.72 \\pm 0.06$ and $i= 85^{+3}_{-2}$ degrees, where the\nuncertainties are taken from the standard deviation of the points about\nthe trajectory of best fit. Fig.~\\ref{fig7}(b) shows the geometry of\nthe binary system for $q=0.72$. For this mass ratio, the relative size\nof the primary Roche lobe is $R_{L1}/a= 0.534\\pm 0.009$, where $a$ is\nthe orbital separation.\n\nBS eclipse phases are clustered at two distinct positions along the\nbest-fit stream trajectory. The squashed circles in Fig.~\\ref{fig7}(a)\nrepresent the accretion discs whose edges pass through these positions\nfor the adopted mass ratio. This corresponds to disc radii of \n$R_{bs}/R_{L1}= (0.50\\pm 0.01)$ and $(0.56 \\pm 0.01)$ with the bright\nspot making angles of, respectively, $\\alpha_{bs}= 20\\degr \\pm 1\\degr$\nand $16\\degr \\pm 1\\degr$ with respect to the line joining both stars.\nCircles with these radii are depicted in Fig.~\\ref{fig7}(b).\nThe larger disc radius comes from measurements of BS phases just after\nthe end of an outburst (lightcurve 7569, end of outburst A) while the\nremaining points correspond to lightcurves well into quiescence\n(lightcurves 8007, 8008, 8012, 8016+8017). This result suggests that\nthe accretion disc of EX~Dra shrinks (by at least $\\simeq 12$ per cent)\nduring quiescence -- a similar behaviour to that found in other dwarf\nnovae (e.g., Smak 1984, 1991; Wood et~al. 1989).\nThe calculated radii are a factor of 2--3 larger than the radius expected\nfor zero-viscosity discs, $R_d/R_{L1}\\!=\\!0.19$ (Flannery 1975), but \nare smaller than the radius expected for pressureless discs,\n$R_d/R_{L1}\\!=\\!0.66$ (Paczy\\'{n}ski 1977).\n\nLightcurve 8074 gives the best phase coverage of the orbital hump in\nour dataset. The hump can be well described by a sinusoid of amplitude\n0.6 mJy and maximum at orbital phase $-0.17\\pm 0.01$ cycle. The \ndirection of hump maximum (i.e., maximum visibility of the bright spot)\nis indicated in Fig.~\\ref{fig7}(b) by an arrow; it is clearly different\nfrom the radial direction of the bright spot. If the hump maximum is\nnormal to the plane of the shock at the bright spot site then the\nshock lies in a direction between the stream trajectory and the edge\nof the disc, making an angle of $41\\degr \\pm 4\\degr$ with the latter.\n\n\n\\subsubsection{Masses and radii of the component stars}\n\nAn estimate of the binary parameters of EX~Dra may be obtained by\ncombining the inferred mass ratio $q$ with the empirical main sequence\nmass-radius relation of Smith \\& Dhillon (1998),\n\\begin{equation}\nR_2/R_\\odot = \\alpha\\;\\left( M_2/M_\\odot \\right)^\\beta \\;\\; ,\n\\label{zams}\n\\end{equation}\n%\nwhere $\\alpha= 0.91 \\pm 0.09$ and $\\beta= 0.75\\pm 0.04$. The latter \nassumption seems reasonably well justified by the good quality of the\nfit to the measured masses of secondary stars in CVs and of field main\nsequence stars.\n\nThe primary-secondary mass diagram for EX~Dra can be seen in \nFig.~\\ref{fig8}. The constraints from the mass ratio and the empirical\nmass-radius relation are shown as thick solid lines. We also plotted\nlines corresponding to the mass functions for a radial velocity of\nthe white dwarf of $K_1= 167\\; km\\,s^{-1}$ (Fiedler et~al. 1997) and\nfor a radial velocity of the secondary star of $K_2= 210\\;km\\,s^{-1}$\n(Billington et~al. 1996). The four relations are consistent at the\n1-$\\sigma$ level. \n%\n%%%%%%%%%%%%%%%%%%%%% FIGURE 8 %%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n\\centerline{\\psfig{figure=xfig08.ps,angle=-90,width=15.3cm,rheight=11cm}}\n \\caption{ Primary-secondary star mass diagram for EX~Dra. Thick solid\n lines show the constraints obtained from the inferred mass ratio of\n $q=0.72$ and the empirical mass-radius relation of Smith \\& Dhillon \n (1998) [SD98]. Solid lines illustrate the mass functions for a white dwarf\n radial velocity of $K_1= 167\\;km\\,s^{-1}$ (Fiedler et~al. 1997) and\n a radial velocity of the secondary star of $K_2= 210\\;km\\,s^{-1}$\n (Billington et~al. 1996). Dotted lines indicate the 1-$\\sigma$ limit\n on these relations. The gray cloud of points shows the confidence\n region and is the result of a $10^4$ points Monte Carlo simulation with\n the value of $q$ and the coefficients of the empirical mass-radius\n relation. } \n\\label{fig8}\n\\end{figure*}\n%\nA Monte Carlo propagation code was used to estimate\nthe errors in the calculated parameters. The values of the input\nparameters $q$ and ($\\alpha,\\beta)$ are independently varied according\nto Gaussian distributions with standard deviation equal to the \ncorresponding uncertainties. The results, together with their 1-$\\sigma$\nerrors, are listed in Table~\\ref{tab5}.\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TABLE 5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table}\n \\centering\n \\begin{minipage}{84mm}\n \\caption{Comparison of binary parameters.} \\label{tab5}\n \\begin{tabular}{@{}lcccc@{}}\nparameter & \\multicolumn{4}{c}{reference} \\\\ [-0.5ex]\n& this work & (1) & (2) & (3) \\\\ [1ex]\n$q$\t\t\t& $0.72\\pm 0.06$ & 0.80 & 0.75 & 0.73-0.97 \\\\\n$i$\t\t\t& $85\\degr$ ($+3\\degr$/$-2\\degr$) & 84.1 & 84.2 & 82.1 \\\\\n$M_1/M_\\odot$\t& $0.75\\pm 0.15$ & 0.66 & 0.75 & 0.70 \\\\\n$M_2/M_\\odot$\t& $0.54\\pm 0.10$ & 0.52 & 0.56 & 0.59 \\\\\n$R_1/R_\\odot$\t& $0.011\\pm 0.002$ & 0.011 & 0.013 \\\\\n$R_2/R_\\odot$\t& $0.57\\pm 0.04$ & & 0.57 & 0.59 \\\\\n$a/R_\\odot$\t& $1.61\\pm 0.10$ & & 1.63 & 1.58 \\\\\n$R_d/a$ (quies.) & $0.267\\pm 0.004$ & 0.21 & 0.27 \\\\\n$\\alpha_{bs}$ (quies.) & $20\\degr \\pm 1\\degr$ \\\\\n$R_{L1}/R_\\odot$ & $0.85\\pm 0.04$ & & 0.85 & 0.82 \\\\\n$K_1\\; (km\\;s^{-1})$ & $163\\pm 11$ & 167 & 167 & 176 \\\\\n$K_2\\; (km\\;s^{-1})$ & $224\\pm 17$ & 210 & 223 & 210 \\\\\n$v_2\\,\\sin i \\;(km\\;s^{-1})$ & $136\\pm 9$ & 140 & & 140 \\\\ [0.5ex]\n\\multicolumn{5}{l}{(1)= Billington et~al. (1996), (2)= Fiedler et~al. \n(1997),} \\\\\n\\multicolumn{5}{l}{(3)= Smith \\& Dhillon (1998).} \\\\\n\\end{tabular}\n\\end{minipage}\n\\end{table}\n% \nThe quoted $K_1, K_2$ and\n$v\\sin i$ are the predicted values of, respectively, the radial velocity\nof the primary and secondary stars and the secondary star rotational\nvelocity; $a$ is the binary separation, and the remaining parameters\nare self-explanatory. The cloud of points in Fig.~\\ref{fig8} was \nobtained from a set of $10^4$ trials using this code. The highest\nconcentration of points indicates the region of most probable solutions.\nTable~\\ref{tab5} also lists the estimated parameters of Billington \net~al. (1996), Fiedler et~al. (1997) and Smith \\& Dhillon (1998).\nOur model of the EX~Dra binary is in reasonably good agreement with\nthe models independently derived by those authors from spectroscopic\nmeasurements.\n\nWe now turn our attention to the compact central source. An estimate\nof its diameter can be obtained from the duration of its ingress/egress\nfeature in the lightcurve, $\\Delta_{cs}$, using the approximate relations\n(Ritter 1980),\n\\begin{equation}\nR_{cs}/a= \\pi z(q)\\; \\Delta_{cs} \\; \\sin\\theta \\; ,\n\\;\\;\\;\\;\\; \\cos\\theta= \\frac{a}{R_2} \\cos i \\; ,\n\\label{larg}\n\\end{equation}\n%\nwhere $R_{cs}$ and $R_2$ are the radii of the central source and of\nthe secondary star, respectively, and $z(q)$ is the distance (in units\nof $a$) from disc centre to the point tangent to the surface of the\nsecondary that marks the beginning/end of the eclipse of CS (Baptista \net~al. 1989). $z(q)$ is a slow varying function and is usually close\nto unity. In our case, for $q=0.72$ we have $z=0.924$.\n\nFor the following exercise we adopted the value of $\\Delta_{cs}= 0.0082$\ncycle inferred from the lightcurves of the low state (section~\\ref{phases}).\nWe note that the width of the CS ingress/egress feature is usually larger\nthan this in the lightcurves in quiescence (see Table~\\ref{tab4});\nfrom the mean $B$ lightcurve in quiescence of Fiedler et~al. (1997) \n(see their fig.\\,7) we estimate a width of the egress feature of 0.010\ncycle.\n\nAssuming that the compact central source is the white dwarf, the\nsubstitution of Kepler's third law into equation (\\ref{larg}) yields a\nrelation between the mass and the radius of the white dwarf than can be\ncombined with the Hamada-Salpeter (1961) mass-radius relation (c.f.\nNauenberg 1972) to eliminate $R_{cs}$ and solve for $M_1(q,\\Delta_{cs})$\n(e.g., Baptista et~al. 1998). This relation (plotted in Fig.~\\ref{fig8}\nas a dashed line) predicts unreasonably low white dwarf masses of $M_1\n\\simeq 0.2\\; M_\\odot$, in clear disagreement with the results in\nTable~\\ref{tab5}. The discrepancy is not alleviated by the use of a\nmass-radius relation for hot white dwarfs (Koester \\& Sh\\\"onberner 1986;\nVennes, Fontaine \\& Brassard 1995), the inclusion of possible spherical\ndistortion effects due to fast rotation of the white dwarf or the \nconsideration of strong limb-darkening effects (Wood \\& Horne 1990), \nor by adopting the larger value of $\\Delta_{cs}$ from the quiescent \nlightcurves. The measured $\\Delta_{cs}$ is simply too large for a \n$\\simeq 0.7 \\;M_\\odot$ white dwarf in a binary with the orbital period\nof EX~Dra. Together with the variability in flux and duration of the\ningress/egress feature this leads to the conclusion that the observed\ncompact central source is not a bare white dwarf.\n\nThe substitution of the parameters of Table~\\ref{tab5} into equation\n(\\ref{larg}) yields $R_{cs}(\\Delta_{cs}= 0.0082)= 0.23\\;a = 0.037\\; \nR_\\odot = 3.36\\; R_1$. Therefore, the white dwarf in EX~Dra seems\nsurrounded by an extended, variable atmosphere or boundary layer of at\nleast 3 times its radius. In this regard EX~Dra is similar to the long\nperiod, eclipsing dwarf nova IP~Peg -- where the white dwarf seems to\nbe wrapped in a thick boundary layer more than twice its radius (Wood\n\\& Crawford 1986) -- and is clearly different from the short-period\ndwarf novae OY~Car, Z~Cha and HT~Cas, where the central source seems\nto be a bare white dwarf (Wood \\& Horne 1990). This result suggests\nthat different physical conditions may exist in the inner disc regions\nof the short period and of the long period dwarf novae, possibly related\nto the distinct mass accretion rates of these groups, although the\nstatistics of eclipsing dwarf novae is still very low on both sides of\nthe CV period gap. From the derived parameters, we predict a duration\nof the ingress/egress of the white dwarf of $\\Delta_{wd}= 0.0024 \\pm\n0.0006$ cycle.\n\n\n\\subsection {Distance estimates}\n\nThe flux densities at mid-eclipse of the flat-bottomed lightcurves of\nthe low state (Fig.~\\ref{fig3}) yield an upper limit to the contribution\nof the secondary star that can be used to set a lower limit on the\ndistance to EX~Dra (e.g., Baptista, Steiner \\& Cieslinski 1994).\n\nWe find $F_{\\rm mid}(V)= 0.79\\pm 0.05$ mJy and $F_{\\rm mid}(R)= 1.56 \\pm\n0.03$ mJy, where the quoted values are the median of the fluxes in the\nphase range ($-0.02,+0.02$) cycle and the uncertainties were derived from\nthe median of the absolute deviations with respect to the median. This\ncorresponds to an apparent magnitude of $V_{\\rm mid}= 16.66\\pm 0.07$ mag\nand a color index of $(V-R)= +0.92\\pm 0.07$ mag. We estimated a reddening\nof $E(B-V)= 0.15\\; {\\rm mag}\\;kpc^{-1}\\; (A_v= 4.8\\times 10^{-4}\\; {\\rm\nmag}\\;pc^{-1})$ for EX~Dra from the galactic interstellar extinction contour\nmaps of Lucke (1978), which gives a color excess of $E(V-R)= 0.02$ mag \nfor a distance of $D=290\\;pc$ (see below). This leads to a corrected,\nintrinsic color index of $(V-R)_0= +0.90\\pm 0.07$ mag.\n\nA main sequence star with this color index has a spectral type \nM$0\\pm 2$, an absolute magnitude of $M_v= 9.2\\pm 0.6$ mag and an \neffective surface temperature of $T_{\\rm eff}= 3850\\pm 200\\;K$ \n(Schmidt-Kaler 1982; Pickles 1985). This spectral type is in good\nagreement with that inferred from the spectroscopy by Billington et~al.\n(1996) and Fiedler et~al. (1997). With the assumption that the observed\nproperties of the secondary star in EX~Dra are similar to those of a\nnormal main sequence star of same mass, we replace these values into\nthe equation,\n\\begin{equation}\n5\\,\\log D(pc)= V_{\\rm mid} - M_v + 5 - A_v\\, D(pc) \\;\\;\\; ,\n\\end{equation}\n%\nto find a photometric parallax distance of $D_{MS}= (290\\pm 80)\\;pc$, where\nthe quoted uncertainty is obtained from the propagation of errors in the \ninput parameters and do not account for possible systematic errors.\nIf we neglect the interstellar extinction, the inferred distance is\nreduced to $D=280\\pm 80\\;pc$. An alternative blackbody fit to the\nmid-eclipse fluxes including the interstellar extinction yields a\nsolid angle of $\\theta^2_{BB}= [(R_2/R_\\odot)/(D/kpc)]^2= 3.8\\pm 0.8$,\nan $T_{\\rm eff}= 3550\\pm 250\\;K$, and a distance of $D_{BB}= (290\\pm\n40)\\;pc$. The measured mid-eclipse fluxes and the best-fit main sequence\nand blackbody spectra are shown in the upper panel of Fig.~\\ref{fig9}.\n%\n%%%%%%%%%%%%%%%%%%%%% FIGURE 9 %%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\\psfig{figure=xfig09.ps,angle=-90,width=10cm,rheight=7cm}}\n \\caption{ Top: $V$ and $R$ mid-eclipse fluxes (open squares) and best-fit\n main sequence (solid) and blackbody (dashed) spectra. Dotted curves\n show normalized response functions of the $V$ and $R$ passbands. \n Horizontal bars show the calculated flux of each model in the \n corresponding passband and marks the full-width half-maximum of each\n passband. Bottom: the measured fluxes of the central source and the \n best-fit white dwarf atmosphere model. The notation is the same as above. } \n\\label{fig9}\n\\end{figure}\n\n\nAnother distance estimate can be obtained from the $V$ and $R$ flux\ndensities of the compact central source in the lightcurves of the low\nstate, since we also have an estimate of the physical dimension of this\nsource. The fluxes at egress, which are free from contamination of light\nfrom the bright spot, were obtained by integrating the derivative\nbetween the third and fourth contact phases (see section~\\ref{phases}).\nWe find $F_{cs}(V)= 0.55\\pm 0.05$ mJy and $F_{cs}(R)= 0.42\\pm 0.04$ mJy.\nWe fitted the observed flux densities from synthetic photometry with\nwhite dwarf atmosphere models (G\\\"ansicke, Beuermann \\& de Martino 1995)\nallowing for the effect of interstellar extinction as estimated above. \nThe best-fit model has $T_{cs}= (28\\pm 3)\\times 10^3\\;K,\\:\\log g= 8$ \nand $ \\theta^2_{cs}= (3.3\\pm 0.5) \\times 10^{-3}$. The measured central\nsource fluxes and best-fit white dwarf atmosphere model are shown in\nthe lower panel of Fig.~\\ref{fig9}.\n\nThe corresponding distance depends on the geometry and effective emitting\narea of the central source as seen by an observer on Earth. A spherical\ncentral source has an effective area of $A_{sp}= \\pi R^2_{cs}$\nas projected onto the plane of the sky. In this case, if the inner disc\nis optically thin, both hemispheres of the central source are seen \nand a distance of $D= 640\\pm 50\\;pc$ is obtained. If the inner disc is\nopaque the lower hemisphere of the central source is occulted and the\ndistance is reduced to $D= 450\\pm 40\\;pc$. Both values are in agreement\nwith the lower limit derived from the contribution of the secondary star.\n\nAlternatively, if we assume that the distance is $D=290\\;pc$, the\ninferred $\\theta^2_{cs}$ allow us to constrain the geometry of the central\nsource. At this distance the effective area of the central source is\nreduced to 21 per cent of $A_{sp}$. Since the equatorial diameter of\nthe central source is set by the width of its ingress/egress feature\nto be $2 R_{cs}$, this implies that the polar diameter is significantly\nsmaller than $R_{cs}$. Hence, the distance estimate from the flux of\nthe secondary star and that from the flux of the central source can be\nreconciled if the central source has a toroidal shape with an equatorial\ndiameter of $2\\times 0.037\\;R_\\odot$ and a vertical thickness of $0.012\\;\nR_\\odot$ (if the inner disc is optically thin) or $0.024\\;R_\\odot$ (if\nthe inner disc is opaque).\n\n\n\\section{Summary} \\label{final}\n\nThe results of the analysis of $V$ and $R$ high speed photometry of \nEX~Dra in quiescence and through outburst can be summarized as follows:\n\n\\begin{enumerate}\n\n\\item During the period of the observations EX~Dra showed outbursts\nwith typical amplitudes of $\\simeq 2.0$ mag, duration of $\\simeq 10$\ndays, and average time between outbursts of $20\\pm 3$ days. The observed\namplitudes are larger than those found by Billington et~al. (1996).\n\n\\item The lightcurves during outburst were grouped by outburst phase.\nThe analysis of these lightcurves indicates that the outbursts do not\nstart in the outer disc regions and, therefore, favours the disc \ninstability model. The disc expands during the rise to maximum (as\nindicated by the increasing width of the eclipse) and shrinks during\ndecline. The decrease in brightness at the later stages of the outburst\nis due to the fading of the light from the inner disc regions.\n\n\\item At the end of two outbursts the system was seen to go through a\nphase of lower brightness (named the low state), characterized by the\nfairly symmetric eclipse of a compact source at disc centre with little\nevidence of a bright spot at disc rim, and by an out-of-eclipse level\n$\\simeq 15$ per cent lower than the typical quiescent level.\n\n\\item New eclipse timings were measured from the lightcurves in\nquiescence and a revised ephemeris was derived. The residuals with\nrespect to the linear ephemeris show a clear cyclical behaviour and\ncan be well described by a sinusoid of amplitude 1.2 minutes and period\n$\\simeq 4$ years. This period variation is possibly related to a\nsolar-like magnetic activity cycle in the secondary star.\n\n\\item Eclipse phases of the compact central source and of the bright\nspot were used to derive the geometry of the binary. By constraining\nthe gas stream trajectory to pass through the observed position of the \nbright spot we find $q=0.72\\pm 0.06$ and $i= 85^{+3}_{-2}$ degrees.\n\n\\item The binary parameters were estimated by combining the measured\nmass ratio with the assumption that the secondary star in EX~Dra\nobeys the empirical main sequence mass-radius relation of Smith \\&\nDhillon (1998). The set of derived parameters in listed in \nTable~\\ref{tab5}.\n\n\\item The observed changes in the position of the bright spot with\ntime suggest that the accretion disc shrinks during quiescence by at\nleast $\\simeq 12$ per cent.\n\n\\item The phase of hump maximum is distinct from the radial direction\nof the bright spot. If the hump maximum is normal to the plane of the\nshock at the bright spot site then the shock lies in a direction between\nthe stream trajectory and the edge of the disc, making an angle of\n$41\\degr\\pm 4\\degr$ with the latter.\n\n\\item The white dwarf seems surrounded by an extended, variable atmosphere\nor boundary layer of at least 3 times its radius. From the derived\nparameters, a duration of the ingress/egress of the white dwarf of\n$\\Delta_{wd}= 0.0024\\pm 0.0006$ cycle is predicted.\n\n\\item The fluxes at mid-eclipse of the lightcurves of the low state\nyield an upper limit to the contribution of the secondary star and lead\nto a lower limit photometric parallax distance of $D_{MS}= 290\\pm 80\\;pc$.\n\n\\item The fluxes of the central source are well fitted by a white\ndwarf atmosphere model with $T_{cs}= (28\\pm 3)\\times 10^3\\;K ,\\: \\log g\n= 8$ and solid angle $\\theta^2_{cs}= [(R_{cs}/R_\\odot)/(D/kpc)]^2=\n(3.3\\pm 0.5) \\times 10^{-3}$. For a spherical central source, this leads\nto a distance of $D= 640\\pm 50\\;pc$ if the inner disc is optically thin.\nThe distance estimates from the mid-eclipse fluxes and from the fluxes\nof the central source can be reconciled if the central source has a\ntoroidal shape with an equatorial diameter of $2\\times 0.037\\;R_\\odot$ \nand a vertical thickness of $0.012\\; R_\\odot$ (if the inner disc is\noptically thin) or $0.024\\;R_\\odot$ (if the inner disc is opaque).\n\n\\end{enumerate}\n\nThe analysis of the set of lightcurves through outburst with eclipse\nmapping techniques yields an uneven opportunity to investigate the\nchanges in the structure of an outbursting accretion disc and is the\nsubject of another paper (Baptista \\& Catal\\'an 1999, 2000).\n\n\n\\section*{Acknowledgments}\n\nWe are grateful to Yvonne Unruh for valuable help in obtaining the data\nat JGT and to Boris G\\\"ansicke for kindly providing the white dwarf \natmosphere models.\n% and an anonymous referee for very useful comments that improved \n% the presentation of the paper.\nIn this research we have used, and acknowledge with thanks, data from\nthe AAVSO International Database and the VSNET that are based on\nobservations collected by variable star observers worldwide. \nRB acknowledges financial support from CNPq/Brazil through grant no.\n300\\,354/96-7. MSC acknowledges financial support from a PPARC\npost-doctoral grant during part of this work. This research was\npartially supported by PRONEX grant FAURGS/FINEP 7697.1003.00.\n\n\n\\begin{thebibliography}{99}\n\n\\bibitem{b1} Applegate J.H., 1992. ApJ, 385, 621\n\\bibitem{b3} Bade N., Hagen H.-J., Reimers D., 1989. 23rd Eslab Symp. ESA\n\t\tSP-296, p.883\n\\bibitem{b5} Bailey J., 1979. MNRAS, 187, 645\n\\bibitem{b7} Baptista R., Catal\\'an M.S., Horne K., Zilli D., 1998. MNRAS,\n\t\t300, 233\n\\bibitem{b9} Baptista R., Catal\\'an M.S., 1999. Cataclysmic Variables: a 60th\n\t\tBirthday Symp. in honour of Brian Warner, eds. P. Charles et~al.,\n\t\tNew Astronomy Reviews, in press (astro-ph/9905096).\n\\bibitem{b11} Baptista R., Catal\\'an M.S., 2000. in preparation\n\\bibitem{b13} Baptista R., Jablonski F.J., Steiner J.E., 1989. MNRAS, 241, 631\n\\bibitem{b15} Baptista R., Steiner J. E., Cieslinski D., 1994. ApJ, 433, 332\n\\bibitem{b17} Barwig H., Fiedler H., Reimers D., Bade N., 1993. in Compact\n\t\tStars in Binary Systems, IAU Symp. 165, ed. van Woerden H., p.89\n\\bibitem{b19} Bell S.A., Hilditch R.W., Edwin R.P., 1993. MNRAS, 260, 478\n\\bibitem{b21} Bessell M., 1983. PASP, 95, 480\n\\bibitem{b23} Billington I., Marsh T.R., Dhillon V.S., 1996. MNRAS 278, 673\n\\bibitem{b25} Cannizzo J.K., Wheeler J.C., Polidan R.S., 1986. ApJ, 301, 364\n\\bibitem{b27} Cook M.C., Warner B., 1984. MNRAS, 207, 705\n\\bibitem{b29} Fiedler H., Barwig H., Mantel K.-H., 1997. A\\&A, 327, 173\n\\bibitem{b31} Flannery B.P., 1975. MNRAS, 170, 325\n\\bibitem{b32} G\\\"ansicke B.T., Beuermann K., de Martino D., 1995. A\\&A 303, 127\n\\bibitem{b33} Horne K., 1985. MNRAS, 213, 129\n\\bibitem{b35} Koester D., Sh\\\"onberner D., 1986. A\\&A, 154, 125\n\\bibitem{b37} Lamla E., 1982. in Landolt-B\\\"{o}rnstein - Numerical Data and\n\t\tFunctional Relationships in Science and Technology, New Series,\n\t\tVol.\\,2, eds. K.\\,Schaifers \\& H.H.\\,Voigt, Springer-Verlag, Berlin\n\\bibitem{b39} Lucke P.B., 1978. A\\&A, 64, 367\n\\bibitem{b41} Massey P., Strobel K., Barnes J.V., Anderson E., 1988. ApJ,\n\t\t328, 315\n\\bibitem{b43} Massey P., Gronwall C., 1990. ApJ, 358, 344\n\\bibitem{b45} Nauenberg M., 1972. ApJ, 175, 417\n\\bibitem{b47} Paczy\\'{n}ski B., 1977. ApJ, 216, 822\n\\bibitem{b49} Pickles A.J., 1985. ApJS, 59, 33\n\\bibitem{b51} Richman H.R., Applegate J.H., Patterson J., 1994. PASP, 106, 1075\n\\bibitem{b53} Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T.,\n\t\t1986. Numerical Recipes, Cambridge University Press, Cambridge\n\\bibitem{b55} Ritter H., 1980. A\\&A, 86, 204\n\\bibitem{b57} Smak J., 1971. Acta Astr., 21, 15\n\\bibitem{b59} Smak J., 1984. Acta Astr., 34, 93\n\\bibitem{b61} Smith D.A., Dhillon V.S., 1998. MNRAS, 301, 767\n\\bibitem{b63} Schmidt-Kaler Th., 1982. in Landolt-B\\\"{o}rnstein - Numerical\n\t\tData and Functional Relationships in Science and Technology, New\n\t\tSeries, Vol.\\,2, eds. K.\\,Schaifers \\& H.H.\\,Voigt, Springer-Verlag,\n\t\tBerlin\n\\bibitem{b65} Vennes S., Fontaine G., Brassard P., 1995. A\\&A, 296, 117\n\\bibitem{b67} Warner B., 1995. Cataclysmic Variable Stars, Cambridge\n\t\tAstrophysics Series 28, Cambridge University Press, Cambridge\n\\bibitem{b69} Wood J.H., Crawford C.S., 1986. MNRAS, 222, 645\n\\bibitem{b71} Wood J.H., Horne K., Berriman G., Wade R., O'Donoghue D.,\n\t\tWarner B., 1986. MNRAS, 219, 629\n\\bibitem{b73} Wood J.H., Horne K., Berriman G., Wade R., 1989. ApJ, 341, 974\n\\bibitem{b75} Wood J.H., Horne K., 1990. MNRAS, 242, 609\n\\bibitem{b77} Wood J.H., Irwin M.J., Pringle J.E., 1985. MNRAS, 214, 475\n\n\\end{thebibliography}\n\n\\bsp\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002382.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{b1} Applegate J.H., 1992. ApJ, 385, 621\n\\bibitem{b3} Bade N., Hagen H.-J., Reimers D., 1989. 23rd Eslab Symp. ESA\n\t\tSP-296, p.883\n\\bibitem{b5} Bailey J., 1979. MNRAS, 187, 645\n\\bibitem{b7} Baptista R., Catal\\'an M.S., Horne K., Zilli D., 1998. MNRAS,\n\t\t300, 233\n\\bibitem{b9} Baptista R., Catal\\'an M.S., 1999. Cataclysmic Variables: a 60th\n\t\tBirthday Symp. in honour of Brian Warner, eds. P. Charles et~al.,\n\t\tNew Astronomy Reviews, in press (astro-ph/9905096).\n\\bibitem{b11} Baptista R., Catal\\'an M.S., 2000. in preparation\n\\bibitem{b13} Baptista R., Jablonski F.J., Steiner J.E., 1989. MNRAS, 241, 631\n\\bibitem{b15} Baptista R., Steiner J. E., Cieslinski D., 1994. ApJ, 433, 332\n\\bibitem{b17} Barwig H., Fiedler H., Reimers D., Bade N., 1993. in Compact\n\t\tStars in Binary Systems, IAU Symp. 165, ed. van Woerden H., p.89\n\\bibitem{b19} Bell S.A., Hilditch R.W., Edwin R.P., 1993. MNRAS, 260, 478\n\\bibitem{b21} Bessell M., 1983. PASP, 95, 480\n\\bibitem{b23} Billington I., Marsh T.R., Dhillon V.S., 1996. MNRAS 278, 673\n\\bibitem{b25} Cannizzo J.K., Wheeler J.C., Polidan R.S., 1986. ApJ, 301, 364\n\\bibitem{b27} Cook M.C., Warner B., 1984. MNRAS, 207, 705\n\\bibitem{b29} Fiedler H., Barwig H., Mantel K.-H., 1997. A\\&A, 327, 173\n\\bibitem{b31} Flannery B.P., 1975. MNRAS, 170, 325\n\\bibitem{b32} G\\\"ansicke B.T., Beuermann K., de Martino D., 1995. A\\&A 303, 127\n\\bibitem{b33} Horne K., 1985. MNRAS, 213, 129\n\\bibitem{b35} Koester D., Sh\\\"onberner D., 1986. A\\&A, 154, 125\n\\bibitem{b37} Lamla E., 1982. in Landolt-B\\\"{o}rnstein - Numerical Data and\n\t\tFunctional Relationships in Science and Technology, New Series,\n\t\tVol.\\,2, eds. K.\\,Schaifers \\& H.H.\\,Voigt, Springer-Verlag, Berlin\n\\bibitem{b39} Lucke P.B., 1978. A\\&A, 64, 367\n\\bibitem{b41} Massey P., Strobel K., Barnes J.V., Anderson E., 1988. ApJ,\n\t\t328, 315\n\\bibitem{b43} Massey P., Gronwall C., 1990. ApJ, 358, 344\n\\bibitem{b45} Nauenberg M., 1972. ApJ, 175, 417\n\\bibitem{b47} Paczy\\'{n}ski B., 1977. ApJ, 216, 822\n\\bibitem{b49} Pickles A.J., 1985. ApJS, 59, 33\n\\bibitem{b51} Richman H.R., Applegate J.H., Patterson J., 1994. PASP, 106, 1075\n\\bibitem{b53} Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T.,\n\t\t1986. Numerical Recipes, Cambridge University Press, Cambridge\n\\bibitem{b55} Ritter H., 1980. A\\&A, 86, 204\n\\bibitem{b57} Smak J., 1971. Acta Astr., 21, 15\n\\bibitem{b59} Smak J., 1984. Acta Astr., 34, 93\n\\bibitem{b61} Smith D.A., Dhillon V.S., 1998. MNRAS, 301, 767\n\\bibitem{b63} Schmidt-Kaler Th., 1982. in Landolt-B\\\"{o}rnstein - Numerical\n\t\tData and Functional Relationships in Science and Technology, New\n\t\tSeries, Vol.\\,2, eds. K.\\,Schaifers \\& H.H.\\,Voigt, Springer-Verlag,\n\t\tBerlin\n\\bibitem{b65} Vennes S., Fontaine G., Brassard P., 1995. A\\&A, 296, 117\n\\bibitem{b67} Warner B., 1995. Cataclysmic Variable Stars, Cambridge\n\t\tAstrophysics Series 28, Cambridge University Press, Cambridge\n\\bibitem{b69} Wood J.H., Crawford C.S., 1986. MNRAS, 222, 645\n\\bibitem{b71} Wood J.H., Horne K., Berriman G., Wade R., O'Donoghue D.,\n\t\tWarner B., 1986. MNRAS, 219, 629\n\\bibitem{b73} Wood J.H., Horne K., Berriman G., Wade R., 1989. ApJ, 341, 974\n\\bibitem{b75} Wood J.H., Horne K., 1990. MNRAS, 242, 609\n\\bibitem{b77} Wood J.H., Irwin M.J., Pringle J.E., 1985. MNRAS, 214, 475\n\n\\end{thebibliography}"
}
] |
astro-ph0002383
|
Predictions on the number of variable stars for the GAIA space mission and for surveys as the ground-based International Liquid Mirror Telescope
|
[
{
"author": "Laurent Eyer"
}
] |
Future space and ground-based survey programmes will produce an impressive amount of photometric data. The GAIA space mission will map the complete sky down to mag V=20 and produce time series for about 1 billion stars. Survey instruments as the International Liquid Mirror Telescope will observe slices of the sky down to magnitude V=23. In both experiments, the opportunity exists to discover a huge amount of variable stars. A prediction of the expected total number of variable stars and the number of variables in specific subgroups is given.
|
[
{
"name": "eyer2.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\n\\markboth{Eyer, Cuypers}{The number of variable stars for GAIA}\n\n\\pagestyle{myheadings}\n\n\\begin{document}\n\\title{Predictions on the number of variable stars for\n the GAIA space mission\n and for surveys as the ground-based\n International Liquid Mirror Telescope}\n\\author{Laurent Eyer}\n\\affil{Instituut voor Sterrenkunde, K.U.Leuven,\n%Celestijnenlaan 200B,\nB-3001 Heverlee, Belgium}\n\\author{Jan Cuypers}\n\\affil{Royal Observatory of Belgium, Ringlaan~3,\nB-1180 Brussel, Belgium}\n\n\\begin{abstract}\nFuture space and ground-based survey programmes will produce an impressive\namount of photometric data. The GAIA space mission will map the\ncomplete sky down to mag V=20 and produce time series for about 1\nbillion stars. Survey instruments as the International Liquid Mirror Telescope will\nobserve slices of the sky down to magnitude V=23.\nIn both experiments, the opportunity exists to discover a huge amount\nof variable stars. A prediction of\nthe expected total number of variable stars and the number of\nvariables in specific subgroups is given.\n\\end{abstract}\n\\vspace{-0.7truecm}\n\\section{The total number of variable stars} A first estimate of the\ntotal number of variable stars observable by GAIA was done by Eyer\n(1999). The star population used came from the star-count model of\nFigueras~et~al.~(1999) and the variability detection threshold was\nderived from the Hipparcos survey results. With the new\nqualifications of the GAIA mission, about 1 billion stars (up to\nmag~G$<$20) are expected to be observed, with about 18~million\nvariable stars, including about 5~million \"classic\" periodic\nvariables.\\\\\nVery different star counts are obtained according to the extinction\nlaws used (Figueras, private communication). Since the quality of the\nGAIA photometry in the crowded fields is still uncertain, we cannot\ndiscuss here the number of variables in dense clusters and\ngalaxies.\\\\\nAbout 2 to 3 millions eclipsing binaries will be observed, but their\ndetection probability will be studied in detail in the future. About\n300\\,000 stars with rotation induced variability can be expected as\nwell.\n\\section{The methods} For a specific interval of V-I, we computed the\nproportion of variables in the Hipparcos survey and we applied that\nrate to the number of stars obtained from the Figueras model\n(method~A). Surface densities were calculated, either from the\nHipparcos parallaxes or from the specific properties of the stars. We\nintegrated and removed the stars behind the bulge (method~B). We\nextrapolated the GCVS data (Kholopov et al., 1998) assuming detection\ncompleteness up to a certain magnitude and a magnitude limit for the\npopulation beyond which no more stars are present (method~C). We also\nanalysed the detection rates of the microlensing surveys (when\navailable) and scanned the literature.\n\\section{Pulsating variables} Method\nA and C estimate the number of $\\beta$ Cephei stars to be about 3000.\n15\\,000 SPB variables will be detected according to Method A.\nApplying method A and C gave about the same estimate for $\\delta$\nScuti stars: 60\\,000. However, it will be very difficult to analyse\nthe very reddened low amplitude variables. With\nmethod B even higher numbers as 240\\,000 $\\delta$~Scuti stars show up.\\\\\nWith a total number of RR Lyrae as given by Suntzeff et al. (1991)\nwe arrive at 70\\,000 observable RR~Lyrae (method~B). Using the OGLE\nand MACHO detection rates, we expect 15\\,000 to 40\\,000 RR Lyrae in\nthe bulge.\\\\\nAll galactic Cepheids are within the observational range of GAIA, if\nnot too obscured by interstellar extinction. Results of recent deep\nsurveys confirm the early estimates of a total of 2000 to 8000\nCepheids. With the help of the Fernie database (1995), we\nobtained (Method B) a density of 15-20\nCepheids/$\\mbox{kpc}^2$, leading to an estimate of 5\\,200--6\\,900\nobservable stars.\\\\\nEarly estimates gave in total 200\\,000 Mira and related long period\nvariables in the Galaxy. With\n500~Miras/$\\mbox{kpc}^2$, 140\\,000 to 170\\,000 Miras will be\nobservable. Method B gave us a density of 250-350 Semi-Regular\nvariables/$\\mbox{kpc}^2$ or a total of 100\\,000 observable SR\nstars.\\\\\nWe plan to calculate and analyse all categories of variables\nstars in more detail to arrive at reliable estimates of all\nobservable variable stars in the Galaxy.\n\\section{Variable stars in deep surveys} An example:\nThe International Liquid MirrorTelescope (ILMT).\\\\\n(see \\verb=http://vela.astro.ulg.ac.be/themes/telins/lmt/index_e.html=) \\\\\nAn international group of institutions are actively interested in\ndeveloping a 4-m class liquid mirror telescope. If the view of the\nILMT includes fields near the galactic center and all stars from R\nmagnitude 17 up to 20 can be measured with high precision ($\\leq$ 0.01\nmag), the project will yield a unique time series of about 2 million\nstars with a total of 500 measurements of each star during 5 years.\nAbout 10\\,000 new variable stars can be expected, including 6\\,000 faint\neclipsing binaries, 200 RR Lyrae and 300 long periodic variables.\n\\nopagebreak\n\n\\begin{references}\n\\reference Eyer, L. 1999, Balt. Ast., 8, 321\n\\reference Fernie, J.D., Beattie, B., Evans, N.R., \\& Seager, S. 1995, IBVS 4148\n\\reference Figueras, F. et al., 1999, Balt. Ast., 8, 291\n\\reference GAIA: \\verb=http://astro.estec.esa.nl/SA-general/Projects/GAIA/=\n\\reference HIPPARCOS: Hipparcos and Tycho catalogues, ESA SP-1200\n%\\reference ILMT: \\verb=http://vela.astro.ulg.ac.be/themes/telins/lmt/index_e.html=\n\\reference Kholopov, P.N., et al. 1998, GCVS, 4th Edition\n\\reference Suntzeff, N.B., Kinman, T.D., \\& Kraft, R.P. 1991, \\apj, 367, 528\n\\end{references}\n\\end{document}\n****************************************************************************************\n\n\n"
}
] |
[] |
astro-ph0002384
|
Quasar Clustering and the Lifetime of Quasars
|
[
{
"author": "Paul Martini\\altaffilmark{1} \\& David H. Weinberg"
}
] |
Although the population of luminous quasars rises and falls over a period of $\sim~10^9$ years, the typical lifetime of individual quasars is uncertain by several orders of magnitude. We show that quasar clustering measurements can substantially narrow the range of possible lifetimes with the assumption that luminous quasars reside in the most massive host halos. If quasars are long-lived, then they are rare phenomena that are highly biased with respect to the underlying dark matter, while if they are short-lived they reside in more typical halos that are less strongly clustered. For a given quasar lifetime, we calculate the minimum host halo mass by matching the observed space density of quasars, using the Press-Schechter approximation. We use the results of Mo \& White to calculate the clustering of these halos, and hence of the quasars they contain, as a function of quasar lifetime. A lifetime of $\tq = 4 \times 10^7$ years, the $e$-folding timescale of an Eddington luminosity black hole with accretion efficiency $\epsilon = 0.1$, corresponds to a quasar correlation length $r_0 \approx 10 \hmpc$ in low-density cosmological models at $z = 2 - 3$; this value is consistent with current clustering measurements, but these have large uncertainties. High-precision clustering measurements from the 2dF and Sloan quasar surveys will test our key assumption of a tight correlation between quasar luminosity and host halo mass, and if this assumption holds then they should determine $\tq$ to a factor of three or better. An accurate determination of the quasar lifetime will show whether supermassive black holes acquire most of their mass during high-luminosity accretion, and it will show whether the black holes in the nuclei of typical nearby galaxies were once the central engines of high-luminosity quasars.
|
[
{
"name": "martini.tex",
"string": "\\documentclass[preprint]{aastex}\n\\usepackage{epsf}\n\n\\shorttitle{Quasar Clustering and Lifetimes}\n\\shortauthors{Martini \\& Weinberg}\n\n\\begin{document}\n\n\\newcommand{\\mmin}{M_{\\rm min}}\n\\newcommand{\\beff}{b_{\\rm eff}}\n\\newcommand{\\hmpc}{h^{-1}{\\rm Mpc}}\n\\newcommand{\\tq}{t_Q}\n\\newcommand{\\tu}{t_U}\n\\newcommand{\\om}{\\Omega_M}\n\\newcommand{\\ol}{\\Omega_\\Lambda}\n\\newcommand{\\ob}{\\Omega_b}\n\\newcommand{\\neff}{n_{\\rm eff}}\n\\newcommand{\\ronem}{r_{1m}}\n\\newcommand{\\ltq}{{\\rm log}_{10} \\, t_Q}\n\n\\slugcomment{Accepted for publication in {\\it The Astrophysical Journal} }\n\n\\title{Quasar Clustering and the Lifetime of Quasars}\n\n\\author{Paul Martini\\altaffilmark{1} \\& David H. Weinberg}\n\n\\affil{Department of Astronomy, 140 W. 18th Ave., Ohio State University, \\\\\nColumbus, OH 43210 \\\\\nmartini@ociw.edu,dhw@astronomy.ohio-state.edu}\n\n\\altaffiltext{1}{Current Address: Carnegie Observatories, 813 Santa Barbara St., Pasadena, CA 91101}\n\n\\begin{abstract}\n\nAlthough the population of luminous quasars rises and falls over\na period of $\\sim~10^9$ years, the typical lifetime of individual quasars\nis uncertain by several orders of magnitude. We show that quasar\nclustering measurements can substantially narrow the range of\npossible lifetimes with the assumption that luminous quasars reside\nin the most massive host halos. If quasars are long-lived, then they\nare rare phenomena that are highly biased with respect to the underlying\ndark matter, while if they are short-lived they reside in more typical\nhalos that are less strongly clustered. For a given quasar lifetime,\nwe calculate the minimum host halo mass by matching\nthe observed space density of quasars, \nusing the Press-Schechter approximation.\nWe use the results of Mo \\& White to calculate the clustering of\nthese halos, and hence of the quasars they contain,\nas a function of quasar lifetime. \nA lifetime of $\\tq = 4 \\times 10^7$ years, the $e$-folding timescale of \nan Eddington luminosity black hole with accretion efficiency $\\epsilon = 0.1$, \ncorresponds to a quasar correlation length $r_0 \\approx 10 \\hmpc$ in \nlow-density cosmological models at $z = 2 - 3$; this value is consistent \nwith current clustering measurements, but these have large uncertainties. \nHigh-precision clustering measurements from the 2dF and Sloan quasar surveys \nwill test our key assumption of a tight correlation between quasar luminosity\nand host halo mass, and if this assumption holds then they should determine \n$\\tq$ to a factor of three or better. An accurate determination of the quasar \nlifetime will show whether supermassive black holes acquire most of their \nmass during high-luminosity accretion, and it will show whether the \nblack holes in the nuclei of typical nearby galaxies were once the central \nengines of high-luminosity quasars. \n\n\\end{abstract}\n\n\\keywords{galaxies: quasars -- cosmology: dark matter, large-scale structure of the universe}\n\n\\section{Introduction}\n\nMounting evidence for the existence of supermassive black holes in the\ncenters of nearby galaxies \n\\citep[recently reviewed by, e.g.,][]{richstone98}\nsupports the long-standing hypothesis that quasars are powered by\nblack hole accretion \\citep[e.g.,][]{salpeter64,zeldovich64,lyndenbell69}.\nHowever, one of the most basic properties of quasars, the typical\nquasar lifetime $\\tq$, remains uncertain by orders of magnitude.\nThe physics of gravitational accretion and radiation pressure provides\none natural timescale, the $e$-folding time \n$t_e=M_{\\rm BH}/\\dot{M} = 4 \\times 10^8\\, \\epsilon\\, l$ years of \na black hole accreting mass with a radiative efficiency\n$\\epsilon=L/\\dot{M}c^2$ and shining at a fraction $l=L/L_E$ of\nits Eddington luminosity \\citep{salpeter64}.\nBut while $\\epsilon \\sim 0.1$ and $l \\sim 1$ are plausible \nvalues for a quasar, it is possible that black holes accrete \nmuch of their mass while radiating at much lower efficiency,\nor at a small fraction of $L_E$.\nThe task of determining $\\tq$ must therefore be approached empirically.\n\nThe observed evolution of the quasar luminosity function imposes \na strong upper limit on $\\tq$ of about $10^9$ years, since the \nwhole quasar population rises and falls over roughly this interval \n\\citep[see, e.g.,][]{osmer98}.\nThe lifetime of individual quasars could be much shorter than the lifetime\nof the quasar population, however, and lower limits of $\\tq \\sim 10^5$ years\nrest on indirect arguments, such as the requirement that quasars maintain\ntheir ionizing luminosity long enough to explain the proximity effect\nin the Ly$\\alpha$ forest \\citep[e.g.,][]{bajtlik88,bechtold94}.\nA typical lifetime $\\tq \\sim 10^9$ years would imply that quasars are\nrare phenomena, arising in at most a small fraction of high-redshift\ngalaxies. Conversely, a lifetime as low as $\\tq \\sim 10^5$ years would imply\nthat quasars are quite common, suggesting that a large fraction of\npresent-day galaxies went through a brief quasar phase in their youth.\n\nThe comoving space density $\\Phi(z)$ of active quasars at redshift $z$\nis proportional to $\\tq n_H(z)$, where $n_H$ is the comoving space density\nof quasar hosts. ``Demographic'' studies of the local black\nhole population \\citep[e.g.,][]{mag98,salucci99,marel99}\nhave opened up one route to determining the typical quasar lifetime:\ncounting the present-day descendants of the quasar central engines\nin order to estimate $n_H(z)$ and thus constrain $\\tq$ by matching $\\Phi(z)$.\nRoughly speaking, the ubiquity of black holes in nearby galaxies\nsuggests that quasars are common and that $\\tq$ is likely in the \nrange $10^6$ -- $10^7$ \\citep[e.g.,][]{richstone98,haehnelt98,salucci99}.\nHowever, as \\citet{richstone98}\nemphasize, the lifetime estimated in this way depends crucially on \nthe way one links the mass of a present-day black hole to the \nluminosity of a high-redshift quasar, which in turn depends on assumptions\nabout the growth of black hole masses since the quasar epoch via\nmergers or low-efficiency accretion.\n\nIn this paper we propose an alternative route to the quasar lifetime,\nusing measurements of high-redshift quasar clustering.\nThe underlying idea goes back to the work of \\citet{kaiser84}\nand \\citet{bbks86}:\nin models of structure formation based on \ngravitational instability of Gaussian primordial fluctuations, the\nrare, massive objects are highly biased tracers of the underlying\nmass distribution, while more common objects are less strongly biased.\nTherefore, a longer quasar lifetime $\\tq$ should imply a more clustered\nquasar population, provided that luminous quasars reside in massive hosts.\nThe specific calculations that we present in this paper use the\nPress-Schechter (1974; hereafter PS) \napproximation for the mass function of dark matter\nhalos and the \\citet[hereafter MW]{mw96} and \\citet{jing98} \napproximations for the bias of these\nhalos as a function of mass. The path from clustering to quasar lifetime\nhas its own uncertainties; in particular, our predictions for quasar\nclustering will rely on the assumption that the luminosity of a quasar\nduring its active phase is a monotonically increasing function of the\nmass of its host dark matter halo. However, the assumptions in the\nclustering approach are at least very different from those in the black\nhole mass function approach, and they can be tested empirically by\ndetailed studies of quasar clustering as a function of luminosity and\nredshift. \n\nOur theoretical model of quasar clustering follows a general trend\nin which the study of quasar activity is embedded in the broader \ncontext of galaxy formation and gravitational growth of structure\n\\citep[e.g.,][]{efstathiou88,turner91,haehnelt93,katz94,haehnelt98,haiman98,\nmonaco00,kauffmann00}.\nThis paper also continues a theme that is prominent in recent work\non the clustering of Lyman-break galaxies, namely that the clustering\nof high-redshift objects is a good tool for understanding the physics\nof their formation and evolution \n\\citep[e.g.,][]{adelberger98,katz99,kolatt99,mmw99}.\nOur model of the quasar population is idealized, but by focusing\non a simple calculation with clearly defined predictions, we hope to\nhighlight the link between quasar lifetime and clustering strength.\nAfter presenting the theoretical results, we will draw some inferences\nfrom existing estimates of the quasar correlation length.\nHowever, our study is motivated mainly by the anticipation of vastly\nimproved measurements of quasar clustering from the 2dF \nand Sloan quasar surveys \\citep[see, e.g.,][]{boyle99,fan99,york00}.\nThese measurements can test various\nhypotheses about the origin of quasar activity, including our primary\nassumption of a monotonic relation between quasar luminosity and host \nhalo mass. If this assumption proves valid, then the first major\nphysical result to emerge from the 2dF and Sloan measurements of high-redshift\nquasar clustering will be a new determination of the typical quasar\nlifetime.\n\n\\section{Method} \\label{sec:meth}\n\n\\subsection{Overview} \\label{sec:over}\n\nWe adopt a simple model of the high-redshift quasar population that is,\ndoubtless, idealized, but which should be reasonably accurate for our purpose\nof computing clustering strength as a function of quasar lifetime.\nWe assume that all quasars reside in dark matter halos and that\na given halo hosts at most one active quasar at a time.\nThe first assumption is highly probable, since a dark matter collapse\nis necessary to seed the growth of a black hole, and the second\nshould be a fair approximation at high redshift, where the masses\nof large halos are comparable to the masses of individual galaxy\nhalos today.\n\nOur strongest and most important assumption is that the luminosity of\na quasar during its active phase is monotonically related to the mass\nof its host dark matter halo, and that all sufficiently massive halos\nhost an active quasar at some point. More precisely, we assume \nthat an absolute-magnitude limited sample of quasars at redshift $z$\nsamples the most massive halos present at that redshift,\nand that the probability that a halo above the minimum host mass $\\mmin$\nharbors an active quasar at any given time is $\\tq/t_H$, where\n$\\tq$ is the average quasar lifetime and $t_H$ is the halo lifetime.\nWe can therefore compute the value of $\\mmin$ for a quasar population\nwith comoving space density $\\Phi(z)$ from the condition\n\\begin{equation}\n\\Phi(z) = \\int_{M_{\\rm min}}^\\infty dM n(M) {\\tq \\over t_H} .\n\\label{eqn:phimatch}\n\\end{equation}\nWe compute $n(M)$ using the PS approximation, and we compute the\nbias of halos with $M>\\mmin$ using the MW approximation.\n\nA connection between quasar luminosity and host halo mass is\nplausible on theoretical grounds --- the cores of massive halos collapse \nearly, giving black holes time to grow, and these halos provide larger gas\nsupplies for fueling activity. It is also plausible on empirical\ngrounds --- local black hole masses are correlated with the host\nspheroid luminosity \\citep{mag98,marel99,salucci99},\nwhich in turn is correlated with stellar velocity dispersion \n\\citep{faber76}.\nA precisely monotonic relation is certainly an idealization, and we\nexplore the effects of relaxing this assumption in \\S \\ref{sec:sen}. \nThe assumption of an approximately monotonic relation can be tested\nempirically by searching for the predicted relation between clustering\nstrength and luminosity, as we discuss in \\S \\ref{sec:pros}.\n\nThe ubiquity of black holes in luminous local spheroids supports our\nassumption that all sufficiently massive halos go through a quasar phase.\nHowever, once the quasar space density declines at $z<2$, the occurrence\nof quasar activity must be determined by fueling rather than by\nthe mere existence of a massive black hole, so it is not plausible that all\nlarge halos host a {\\it low-redshift} quasar. We therefore apply\nour model only to the high-redshift quasar population, at $z \\geq 2$.\n\nWe implicitly assume that a quasar turns on at a random point in the\nlife of its host halo. In this sense, our model differs subtly from\nthat of \\citet{haehnelt98},\nwho assume that a quasar turns on when\nthe halo is formed, but this difference is unlikely to have a significant\neffect on the predicted clustering. \n\\citet{haehnelt98} pointed out that a longer quasar lifetime\nwould correspond to stronger quasar clustering because of the \nassociation with rarer peaks of the mass distribution, but they\ndid not calculate this relation in detail.\n\nBecause the quasar lifetime enters\nour calculation only through the probability $\\tq/t_H$ that a halo\nhosts an active quasar at a given time, it makes no difference whether\nthe quasar shines continuously or turns on and off repeatedly with a\nshort duty cycle (as argued recently by \\citealt{ciotti99}).\nFor our purposes, $\\tq$ is the total time that the\nquasar shines at close to its peak luminosity.\nWe also assume that quasars radiate isotropically, with a beaming\nfactor $f_B=1$, but because a smaller beaming factor simply changes\nthe conversion between observed surface density and intrinsic comoving space\ndensity, all of our results can be scaled to smaller average beaming\nfactors by replacing $\\tq$ with $f_B \\tq$.\n\n\\subsection{Notation} \\label{sec:note}\n\nAll of our calculations assume Gaussian primordial fluctuations.\nWe denote by $P(k)$ the power spectrum of these fluctuations\nas extrapolated to the present day ($z=0$) by linear theory.\nThe rms fluctuation of the linear density field on mass scale $M$ is\n\\begin{equation}\n\\sigma(M) = \\left[\\frac{1}{2 \\pi^2} \\int_0^{\\infty} dk \\; k^2 \\; P(k) \n\\widetilde{W}^2(kr)\\right]^{1/2}~,\n\\label{eqn:sigma}\n\\end{equation} \nwhere\n\\begin{equation}\n\\widetilde{W}(kr) = {3(kr\\sin kr - \\cos kr) \\over (kr)^3}, \\qquad\n r = \\left(3M \\over 4\\pi\\rho_0\\right)^{1/3}\n\\label{eqn:window}\n\\end{equation}\nis the Fourier transform of a spherical top hat containing average\nmass $M$. The mean density of the universe at $z=0$ is\n$\\rho_0 = 2.78\\times 10^{11}\\om h^2 \\;M_\\odot\\;{\\rm Mpc}^{-3}$,\nwith $h \\equiv H_0/(100\\;{\\rm km}\\;{\\rm s}^{-1}\\;{\\rm Mpc}^{-1})$.\nThe rms fluctuation can be considered as a function of either \nthe mass scale $M$ or the equivalent radius $r$.\nWe define the normalization of the power spectrum by the value of \n$\\sigma_8 \\equiv \\sigma(r=8\\hmpc)$.\n\nThe rms fluctuation of the linear density field at redshift $z$ is\n\\begin{equation}\n\\sigma(M,z) = \\sigma(M)D(z),\n\\label{eqn:sigmaz}\n\\end{equation}\nwhere $D(z)$ is \nthe linear growth factor $D(z)$, defined so that $D(z=0)=1$.\nThe general expression for the growth factor in terms of the scaled\nexpansion factor $y=(1+z)^{-1}$ is \n\\begin{equation}\n\\delta(y) = \\frac{5}{2}\\om {1 \\over y} {dy \\over d\\tau}\n \\int_0^y \\left({dy^\\prime \\over d\\tau}\\right)^{-3} dy^\\prime ,\n\\label{eqn:gfac}\n\\end{equation}\nwhere $D(y) = \\delta(y)$ for $\\om = 1$, $D(y) = \\delta(y)/\\delta(1)$ \nfor $\\om < 1$, and the dimensionless time variable is $\\tau=H_0 t$\n\\citep{heath77,carroll92}.\nIf the dominant energy components are pressureless matter and a\ncosmological constant with $\\Omega_\\Lambda=\\Lambda/3H_0^2$, then\nthe Friedmann equation implies\n\\begin{equation}\n\\left({dy \\over d\\tau}\\right)^2 = \n 1 + \\Omega_M\\left(y^{-1} - 1\\right) + \\Omega_\\Lambda\\left(y^2-1\\right).\n\\label{eqn:dydt}\n\\end{equation}\nFor an $\\om = 1$, $\\ol=0$ universe, $D(z)=(1+z)^{-1}$.\n\\citet[eq.~11.16]{peebles80} gives an exact analytic expression for\n$D(z)$ for the case $\\om<1$, $\\ol=0$, \nand \\citet[eq.~29]{carroll92} give an accurate analytic approximation for\n$\\Omega_\\Lambda \\neq 0$.\nIn our notation, $\\sigma(M)$ without any explicit $z$ always refers\nto the rms linear mass fluctuation on scale $M$ at $z=0$.\n\nAt any redshift, we can define a characteristic mass $M_*(z)$\nby the condition\n\\begin{equation}\n\\sigma\\left[M_*(z)\\right] = \\delta_c(z) = {\\delta_{c,0} \\over D(z)},\n\\label{eqn:mstar}\n\\end{equation}\nwhere $\\delta_c(z)$ is the threshold density for collapse of a \nhomogeneous spherical perturbation at redshift $z$.\nBecause we implicitly define the density field as ``existing'' at\n$z=0$, the collapse threshold $\\delta_c(z)$ increases with increasing\nredshift. For an $\\om=1$, $\\ol=0$ universe,\n$\\delta_{c,0} = 0.15(12\\pi)^{2/3} \\approx 1.69$\n(see, e.g., \\citealt{peebles80}, \\S 19).\nFor other models, we incorporate the dependence of $\\delta_{c,0}$ on\n$\\om$ in Appendix A of \\citet{nfw97}, but\nbecause $\\om$ approaches one at high redshift in all models\nthis correction to $\\delta_c$ is less than 2\\% in all of the cases that \nwe consider.\n\n\\subsection{From the Quasar Lifetime to the Minimum Halo Mass} \\label{sec:life}\n\nFor a specified quasar lifetime, we compute the minimum halo mass\nby matching the comoving number density $\\Phi(z)$ of observed quasars,\naccounting for the fact that only a fraction $\\tq/t_H$ of host halos\nwill have an active quasar at the time of observation.\nThe matching condition is equation~(\\ref{eqn:phimatch}), or,\nputting in explicit mass and redshift dependences,\n\\begin{equation}\n\\Phi(z) = \\int_{M_{\\rm min}}^\\infty dM {\\tq \\over t_H(M,z)} n(M,z).\n\\label{eqn:phimatch2}\n\\end{equation}\nIf $\\tq>t_H(M,z)$, we set the factor $\\tq/t_H$ to unity.\nFor the halo number density we use the PS approximation,\n\\begin{equation}\nn(M, z)\\;dM = - \\sqrt{\\frac{2}{\\pi}} \\frac{\\rho_0}{M} \n\t\t\\frac{\\delta_c(z)}{\\sigma^2(M)} \\frac{d\\sigma(M)}{dM} \\; \n\t\t{\\rm exp} \\left[ -\\frac{\\delta_c^2(z)}{2 \\sigma^2(M)} \\right]\n\t\tdM ,\n\\label{eqn:ps}\n\\end{equation}\nwhere $\\rho_0$ is the mean density of the universe at $z=0$,\n$\\sigma(M)$ is the rms fluctuation given by equation~(\\ref{eqn:sigma}),\nand $\\delta_c(z)$ is the critical density for collapse by redshift $z$.\n\nIn a gravitational clustering model of structure formation,\nhalos are constantly growing by accretion and mergers, so the\ndefinition of a ``halo lifetime'' is somewhat ambiguous.\nFor $\\om(z) \\approx 1$, a typical halo survives\nfor roughly a Hubble time\nbefore being incorporated into a substantially larger halo,\nsince the age of the universe at redshift $z$\nis also the characteristic dynamical time of objects forming at that redshift.\nThus, to a first approximation, one could simply substitute\n$t_H(M,z)=\\tu(z)$ in equation~(\\ref{eqn:ps}).\nWe can do somewhat better by using the extended Press-Schechter\nformalism \n\\citep[e.g.,][]{bond91,lc93}\nto calculate\nthe average halo lifetime, thereby accounting for the dependence\nof $t_H$ on the power spectrum shape and the halo mass.\nStructure grows more rapidly in a cosmology with a redder power\nspectrum, and more massive halos accrete mass more rapidly.\n\nEquation~(2.22) of \\citet{lc93} gives the probability that\na halo of mass $M_1$ existing at time $t_1$ will have been incorporated\ninto a new halo of mass greater than $M_2$ by time $t_2$:\n\\begin{eqnarray}\nP(S < S_2, \\omega_2 | S_1, \\omega_1) & = &\\frac{1}{2} \n \\frac{(\\omega_1 - 2 \\omega_2)}{\\omega_1} {\\rm exp} \n \\left[ \\frac{2 \\omega_2 (\\omega_1 - \\omega_2)}{S_1}\\right] \n \\left[ 1 - {\\rm erf} \\left( \\frac{S_2 (\\omega_1 - 2 \\omega_2) + S_1 \\omega_2}\n {\\sqrt{2 S_1 S_2 (S_1 - S_2)}} \\right) \\right] \\nonumber \\\\\n &&+ \\frac{1}{2} \\left[ 1 - {\\rm erf} \n \\left( \\frac{S_1 \\omega_2 - S_2 \\omega_1}{\\sqrt{2 S_1 S_2 (S_1 - S_2)}} \n \\right) \\right]~,\n \\label{eqn:lc}\n\\end{eqnarray}\nwhere $S_1 = \\sigma^2(M_1)$, $S_2 = \\sigma^2(M_2)$, $\\omega_1 = \\delta_c(t_1)$, \nand $\\omega_2 = \\delta_c(t_2)$. \nIn this equation, $\\omega$ plays the role of the ``time'' variable, with\n$\\omega_2<\\omega_1$ corresponding to $t_2>t_1$, and $S$ plays the role\nof the ``mass'' variable, with $S_2<S_1$ corresponding to $M_2>M_1$.\nFor a halo of mass $M$ existing at time $\\tu(z)$, we define the halo lifetime\nto be the median interval before such a halo is incorporated into a\nhalo of mass $2M$. Thus, $t_H(M,z) = \\hat{t}_S-\\tu(z)$, where $\\hat{t}_S$\nis the time at which the probability in equation~(\\ref{eqn:lc}) equals 0.5,\nfor $S_1=\\sigma^2(M)$ and $S_2=\\sigma^2(2M)$.\nClearly other plausible definitions of $t_H(M,z)$ are possible, \nand they would give answers different by factors of order unity.\nWith our definition, a black hole that lights up repeatedly \nis considered the ``same'' quasar as long as the mass of its host\nhalo remains the same within a factor of two.\nIf the host merges into a much larger halo and the black hole lights\nup again, it is considered a ``new'' quasar.\nWe show the halo lifetimes for different masses and power spectra when we\ndiscuss specific models below.\n\nFor comoving space densities $\\Phi(z)$, we adopt values based on the \nwork of \\citet{boyle90}, \\citet{hewett93}, and \\citet{who94}.\nSince observations constrain the number of objects per unit redshift\nper unit solid angle, the conversion to comoving space density\ndepends on the values of the cosmological parameters.\nWe provide the formulas for these conversions in the Appendix, and in Table A1 \nwe list our adopted values of $\\Phi(z)$ and the surface densities of objects \nto which these space densities correspond. In general, $\\Phi(z)$\nrepresents the space density of quasars above some absolute magnitude, \ncorresponding to a surface density above some apparent magnitude. \nIn \\S \\ref{sec:pros} we discuss how to scale our results to predict the \nclustering of samples with different measured surface densities. \n\n\\subsection{From Minimum Halo Mass to Clustering Length} \\label {sec:clust}\n\nHalos with $M>M_*$ are clustered more strongly than the underlying\ndistribution of mass. MW give an approximate formula,\n\\begin{equation}\nb(M, z) = 1 + \\frac{1}{\\delta_{c,0}} \n\t \\left[ \\frac{\\delta_c^2(z)}{\\sigma^2(M)} - 1 \\right],\n\\label{eqn:biasmw}\n\\end{equation}\nfor the bias factor of halos of mass $M$ at redshift $z$.\nOn large scales, the ratio of rms fluctuations in halo number\ndensity to rms fluctuations in mass should be $b(M,z)$.\nThis formula is derived from an extended Press-Schechter analysis,\nand it agrees fairly well with the results of N-body simulations\non scales where the rms mass fluctuations are less than unity.\nThe MW formula becomes less accurate for halos with $M<M_*$,\ni.e., $\\sigma(M)<\\delta_c(z)$, and \\citet{jing98} provides\nan empirical correction that fits the N-body results,\n\\begin{equation}\nb(M, z) = \\left( 1 + \\frac{1}{\\delta_{c,0}} \n\t \\left[ \\frac{\\delta_c^2(z)}{\\sigma^2(M)} - 1 \\right] \\right)\n \\left( \\frac{\\sigma^4(M)}{2\\,\\delta_c^4(z)} \n + 1 \\right)^{(0.06 - 0.02\\neff)}, \n\\label{eqn:bias}\n\\end{equation}\nwhere $\\neff=3-6\\,(d\\ln\\sigma/d\\ln M)$ \nis the effective index of the power spectrum on mass scale $M$.\n\nAccording to our model, the quasars at redshift $z$ only reside in \nhalos of mass $M>\\mmin$. The effective bias of these host halos\nis the bias factor~(\\ref{eqn:bias}) weighted by the number density\nand lifetime of the corresponding halos:\n\\begin{equation}\n\\beff(\\mmin,z) = \\left(\\int_{\\mmin}^{\\infty} dM\\;\n \\frac{b(M, z) n(M, z)}{t_H(M, z)}\\right) \n \\left(\\int_{\\mmin}^{\\infty} dM\\;\\frac{n(M, z)}{t_H(M, z)}\\right)^{-1}.\n\\label{eqn:beff}\n\\end{equation}\nBecause the halo number density drops steeply with increasing mass,\nthe effective bias is usually only slightly larger than the bias\nfactor at the minimum halo mass, $b(\\mmin,z)$.\n\nAs our measure of clustering amplitude, we use the radius $r_1$ of a top hat \nsphere in which the rms fluctuation $\\sigma_Q$ of quasar number counts \n(in excess\nof Poisson fluctuations) is unity. This quantity is similar to the \ncorrelation length $r_0$ at which the quasar correlation function \n$\\xi(r)$ is unity, but it can be\nmore robustly constrained observationally because it does not require\nfitting the scale-dependence of $\\xi(r)$. For a power law correlation\nfunction $\\xi(r)=(r/r_0)^{-1.8}$, $r_1\\approx 1.4 r_0$.\nWith our adopted approximation for the bias, $r_1$ is determined\nimplicitly by the condition\n\\begin{equation}\n\\sigma_Q(r_1,z) = \\beff(\\mmin, z)\\sigma(r_1)D(z) = 1,\n\\label{eqn:r1def}\n\\end{equation}\nwhere $\\sigma(r_1)$ is the rms linear mass fluctuation at $z=0$ in\nspheres of radius $r_1$. For a specified cosmology, mass power spectrum\n$P(k)$, quasar lifetime $\\tq$, and comoving space density $\\Phi(z)$,\nwe determine $r_1$ from equation~(\\ref{eqn:r1def}),\ncomputing $\\sigma(r)$ \nfrom equation~(\\ref{eqn:sigma}), $D(z)$ from equation~(\\ref{eqn:gfac}),\n$\\mmin$ from equation~(\\ref{eqn:phimatch2}), and $\\beff(\\mmin)$\nfrom equations~(\\ref{eqn:bias}) and~(\\ref{eqn:beff}).\n\n\n\\subsection{Results for Power Law Power Spectra} \\label{sec:plspec}\n\nModels with a power law power spectrum, $P(k) \\propto k^n$, provide\na useful illustration of our methods, since many steps of the calculation\ncan be done analytically.\nFor such models, the dependence of rms fluctuation on mass is also a\npower law,\n\\begin{equation}\n\\sigma(M) ~=~ {\\sigma(M,z) \\over D(z)} ~=~ \n {\\delta_{c,0} \\over D(z)} \\left[{M \\over M_*(z)}\\right]^{-(3+n)/6} ~=~\n \\delta_c(z) \\left[{M \\over M_*(z)}\\right]^{-(3+n)/6},\n\\label{eqn:sigmapl}\n\\end{equation}\nwhere $M_*(z)$ is the characteristic non-linear mass defined by\nequation~(\\ref{eqn:mstar}).\nWith this substitution, the PS mass function can be expressed as a\nfunction of $M_*(z)$ and the dimensionless mass variable $x=M/M_*(z)$.\nIntegrating to obtain the comoving number density of objects\nwith mass $M>\\mmin$ yields\n\\begin{equation}\nN(M>\\mmin) = \\sqrt{\\frac{2}{\\pi}} \\left(\\frac{n+3}{6}\\right) \n\t \\left(\\frac{\\rho_0}{M_*}\\right) \\int^{\\infty}_{x_{min}} dx\\; \n\t x^{\\frac{n-9}{6}} {\\rm exp}\\left[ -\\frac{1}{2} \n\t x^{\\frac{n+3}{3}} \\right]. \n\\label{eqn:psint}\n\\end{equation}\n\nFor power law models with $\\om=1$, the ratio of the halo\nlifetime $t_H(M,z)$ to the age of the universe at redshift $z$\ndepends only on $M/M_*(z)$ and has no separate dependence on redshift.\nFigure~\\ref{fig:lifepl} shows $t_H$ and the ratio $t_H/\\tu$ as a function\nof $M/M_*$ for power law models with $n=0$, $-1$, and $-2$.\nMore massive halos tend to accrete mass more quickly and therefore\nhave shorter median lifetimes. At a given value of $M/M_*$, the\nhalo lifetime is shorter for lower $n$ because a greater amount\nof large scale power causes the typical mass scale of non-linear\nstructure to grow more rapidly. Although the calculation of the\nmedian halo lifetime via equation~(\\ref{eqn:lc}) is moderately\ncomplicated, the median lifetime for large masses \nasymptotically approaches a constant value\n\\begin{equation}\nt_H(M,z) = \\left[2^{(3+n)/2}-1\\right]\\tu(z), \\qquad\n M \\gg M_*(z),~\\Omega_M=1,\n\\label{eqn:tsimple}\n\\end{equation}\n\\citep{lc93}.\nWe will find below that the predicted masses\nof quasar host halos are indeed in this asymptotic regime\nfor most plausible parameter choices.\nThe halo lifetime is longer for $\\om<1$ than for $\\om=1$\nbecause fluctuations grow more slowly in a low-density universe, \nbut $t_H$ still asymptotically approaches a constant value. \nThe dotted curves \nin Figure~\\ref{fig:lifepl} illustrate the case $n=-1$, $\\om=0.3$,\n$\\ol=0$. The cosmological parameters for all of our models with power law\npower spectra are summarized in Table~\\ref{tbl:pl}. \n\n\\begin{figure*}[t]\n\\centerline{\n\\epsfxsize=3.5truein\n\\epsfbox[65 165 550 730]{martini.f1.eps}\n}\n\\caption{\n\\footnotesize\nHalo lifetimes vs. $M/M_*$ for the power law cosmologies listed in \nTable~\\ref{tbl:pl}. Upper panels show the halo lifetimes in Gyr for \neach model at $z = 2$, 3, and 4. Lower panels show the ratio of the \nhalo lifetime to the age of the universe. This ratio is independent of \nredshift for the $\\om = 1$ models, but not for the $n = -1, \\om = 0.3$ \nmodel.\n} \\label{fig:lifepl}\n\\end{figure*}\n\n\\begin{center}\n\\begin{deluxetable}{lrccclll}\n\\tablenum{1}\n\\tablewidth{0pt}\n\\tablecaption{Power Law Model Parameters \\label{tbl:pl} }\n\\tablehead {\n \\colhead{} &\n \\colhead{} &\n \\colhead{$\\sigma_8$} &\n \\colhead{$h$} &\n \\colhead{$\\om$} &\n \\colhead{$M_* (z = 2)$} &\n \\colhead{$M_* (z = 3)$} &\n \\colhead{$M_* (z = 4)$} \\\\\n}\n\\startdata\n$n = 0$ &. . . . . . . & 0.5 & 1.0 & 1.0 & $5.87\\cdot 10^{12}$\n & $3.30\\cdot 10^{12}$ & $2.11\\cdot 10^{12}$ \\\\\n$n = -1$ &. . . . . . . & 0.5 & 1.0 & 1.0 & $5.80\\cdot 10^{12}$\n & $2.45\\cdot 10^{12}$ & $1.25\\cdot 10^{12}$ \\\\\n$n = -1$ &. . . . . . . & 1.0 & 1.0 & 0.3 & $5.44\\cdot 10^{12}$\n & $2.87\\cdot 10^{12}$ & $1.70\\cdot 10^{12}$ \\\\\n$n = -2$ &. . . . . . . & 0.5 & 1.0 & 1.0 & $5.59\\cdot 10^{8}$\n & $9.96\\cdot 10^7$ & $2.61\\cdot 10^{7}$ \\\\\n\\enddata\n\\tablecomments{Parameters of the four power law cosmological models \ndiscussed in \\S\\ref{sec:plspec}. Columns 1 - 4 list the power spectrum \nindex $n$, normalization $\\sigma_8$, scaled Hubble constant $h$, and \nmass density parameters $\\om$. \nColumns 5 - 7 list the values of $M_*$ (eq.~[\\ref{eqn:mstar}])\nat $z = 2$, 3, and 4, in units of $h^{-1} M_\\odot$.\n}\n\\end{deluxetable}\n\\end{center}\n\nThe power law scaling of the rms fluctuation amplitude,\nequation~(\\ref{eqn:sigmapl}), allows the bias\nformula~(\\ref{eqn:bias}) to be written\n\\begin{equation}\nb(M,z) = \\left(1 + {1 \\over \\delta_{c,0}}\n \\left\\{\\left[{M \\over M_*(z)}\\right]^{(3+n)/3}-1\\right\\} \\right) \n \\left( \\frac{1}{2} \\left[{M \\over M_*(z)}\\right]^{-2(3+n)/3}\n + 1 \\right)^{(0.06 - 0.02n)}. \n\\label{eqn:biaspl}\n\\end{equation}\nNote that the second factor is very close to one for $M \\geq M_*$. \nFigure~\\ref{fig:biaspl} shows the bias and the corresponding\nnumber-weighted effective bias (eq.~[\\ref{eqn:beff}]) as a \nfunction of $\\mmin/M_*$. For $\\mmin>M_*$, the \neffective bias is only slightly larger than $b(\\mmin)$, \nsince the number density of halos declines rapidly with\nincreasing $M$. As equation~(\\ref{eqn:biaspl}) shows,\nthe bias depends more strongly on $M$ for larger $n$.\nHowever, the exponentially falling tail of the mass function\nat high $M/M_*$ is much steeper for higher $n$, \nas one can see from equation~(\\ref{eqn:psint}).\nAs a result, the bias at fixed comoving number density is\nhigher for {\\it smaller} $n$ in the high $M/M_*$ regime \n(see Fig.~\\ref{fig:r1pl} below). \n\n\\begin{figure*}[t]\n\\centerline{\n\\epsfxsize=3.5truein\n\\epsfbox[65 165 550 730]{martini.f2.eps}\n}\n\\caption{\n\\footnotesize\nBias vs. $M/M_*$ for the power law models with $n = 0$ (solid), \n$-1$ (short-dashed), and $-2$ (long-dashed). Lower curves show $b(\\mmin)$ \ncomputed from equation~(\\ref{eqn:bias}), and upper curves show the \nnumber-weighted effective bias (eq.~[\\ref{eqn:beff}]). \n} \\label{fig:biaspl}\n\\end{figure*}\n\nUnder the (good) approximation that the halo lifetime is\ngiven by the asymptotic formula~(\\ref{eqn:tsimple}) in the\nmass range of interest, the halo lifetime can be moved outside\nof the integral~(\\ref{eqn:phimatch2}) for the number density\nof active quasars. The implied quasar lifetime as a function of \nminimum halo mass is then\n\\begin{equation}\n\\tq(\\mmin) = \\frac{t_H \\, \\Phi(z)}{N(M>\\mmin)}, \n\\label{eqn:tqpl}\n\\end{equation}\nwhere $N(M>\\mmin)$ is given by equation~(\\ref{eqn:psint}). For the \n$\\om = 0.3, n = -1$ model, we also use \nthe asymptotic value of $t_H$, though this is no longer given by \nequation~(\\ref{eqn:tsimple}).\nWe use a $P(k)$ normalization $\\sigma_8 = 0.5$ for the three\n$\\om=1$ models and $\\sigma_8 = 1.0$ for the $\\om=0.3$ model,\nin approximate agreement with the constraint on $\\sigma_8$ and $\\om$\nimplied by the observed mass function of rich galaxy clusters\n\\citep{white93,eke96}.\n\nEquation~(\\ref{eqn:tqpl}) implicitly determines $\\mmin/M_*(z)$ given $\\tq$.\nThe top panels of Figure~\\ref{fig:r1pl} show $\\mmin/M_*(z)$ as a \nfunction of $\\tq/\\tu$ for $z = 2$, 3 and 4 and a constant \ncomoving space density $\\Phi(z)=10^{-6} h^3$ Mpc$^{-3}$. \nFor the $\\om=1$ cases, where $t_Q/t_U$ depends only on $n$ and\n$\\mmin/M_*$, the redshift dependence of $\\mmin/M_*$ arises solely\nfrom the presence of $M_*$ in the number density formula~(\\ref{eqn:psint}).\nAs $M_*$ increases with decreasing redshift, the value of\n$x_{\\rm min}=\\mmin/M_*$ must decrease to keep $\\Phi(z)$ constant.\nSmaller values of $n$ lead to higher values of $\\mmin/M_*$ because\nof the gentler fall off of the mass function at large $M/M_*$. \nThe $n=-2$ curves become\nflat at the largest values of $\\tq/t_U$ because $\\tq$ begins to exceed\nthe halo lifetime $t_H$, implying that all halos above $\\mmin$ are\noccupied by quasars. The difference between the open and $\\om=1$\ncurves for $n=-1$ reflects mainly the larger values of $\\sigma_8$\nand $D(z)$ in the open model, which lead to a lower value of $\\rho_0/M_*$\nin the mass function~(\\ref{eqn:psint}) and therefore require a lower value \nof $\\mmin/M_*$ to compensate.\n\n\\begin{figure*}[t]\n\\centerline{\n\\epsfxsize=3.5truein\n\\epsfbox[65 165 550 730]{martini.f3.eps}\n}\n\\caption{\n\\footnotesize\nHalo mass, bias, and clustering length for the power law models, \nas a function of quasar lifetime. Top panels show the minimum mass $\\mmin$ \nrequired to obtain a space density $\\Phi(z) = 10^{-6} h^3$ Mpc$^{-3}$ for \na given value of $\\tq/\\tu$ at $z = 2$, 3 and 4. Middle panels show the \ncorresponding effective bias $\\beff$ for halos $\\mmin$. \nBottom panels show the clustering lengths $r_1$ as a function of $\\tq/\\tu$. \nThe clustering length is the radius of a top hat sphere in which rms number \ncount fluctuations (in excess of Poisson) are unity. For a power law \ncorrelation function $\\xi(r) = (r/r_0)^{-1.8}$, $r_1 \\approx 1.4 \\, r_0$. \n} \\label{fig:r1pl}\n\\end{figure*}\n\nThe middle panels of Figure~\\ref{fig:r1pl} show the effective bias\n$\\beff(\\mmin,z)$ for the power law models. As already remarked, the\nbias at fixed space density and $\\tq/t_U$ is higher for redder power\nspectra (smaller $n$) because of the much higher values of $\\mmin/M_*$,\ndespite the partially counterbalancing effect of the stronger\ndependence of bias on mass at larger $n$. Physically, the higher\nbias for redder spectra\nreflects the greater influence of the large scale environment\non the amplitude of small scale fluctuations.\nFor a given model, the bias \nincreases with increasing redshift, reflecting the increase in $\\mmin/M_*$; \nthe change, however, is quite modest.\n\nThe rms number count fluctuation on comoving scale $r$ is\n\\begin{equation}\n\\sigma_Q(r,z)=b_{\\rm eff}(\\mmin,z)\\sigma(r,z)=\n b_{\\rm eff}(\\mmin,z) \\sigma_8 D(z) \\left({r \\over 8\\hmpc}\\right)^{-(3+n)/2}.\n\\label{eqn:sigmaqpl}\n\\end{equation}\nThe quasar clustering length $r_1$ is the scale on which this rms\nfluctuation amplitude is unity,\n\\begin{equation}\nr_1 = 8\\hmpc\\,\\times\\, \\left[b_{\\rm eff}(\\mmin,z)\\sigma_8 D(z)\\right]^{2/(3+n)}.\n\\label{eqn:r1pl}\n\\end{equation}\nThe bottom panels of Figure~\\ref{fig:r1pl} present the main result of\nthis Section, the dependence of $r_1$ on \nquasar lifetime for our four power law models at $z=2$, 3 and 4. \nAs anticipated, the quasar clustering length shows a strong dependence\non quasar lifetime.\nThe relation between $r_1$ and $\\tq$ depends on the power spectrum\nindex $n$, so the shape of the power spectrum must be known\nfairly well to determine $\\tq$ from measurements of $r_1$.\nThe clustering at fixed $\\tq/t_U$ is substantially stronger in the\nopen $n=-1$ model than in the $\\om=1$ model because the\nunderlying mass distribution is more strongly clustered\n(larger $\\sigma_8$ and $D(z)$).\n\nFor a specified value of $\\om$, the cluster mass function imposes\na reasonably tight constraint on the normalization $\\sigma_8$.\nIt is nonetheless interesting to explore the sensitivity of the\npredicted quasar clustering to this normalization. More intuitive\nthan the $\\sigma_8$-dependence is the equivalent relation between\nthe quasar clustering length and the corresponding clustering length\nof the underlying mass distribution at the same redshift,\n\\begin{equation}\n\\ronem = 8\\hmpc\\,\\times\\, \\left[\\sigma_8 D(z)\\right]^{2/(3+n)}.\n\\label{eqn:r1m}\n\\end{equation}\nFigure~\\ref{fig:r1m} plots this relation at $z=3$ for the four power\nlaw cosmologies and $\\tq = \\tu$ (top curve), $0.1\\tu$, $0.01\\tu$, \nand $0.001\\tu$ (bottom curve), for\nvalues of $\\sigma_8$ ranging from $0.2$ to $2.0$.\nThe values of $\\ronem$ that correspond to the $\\sigma_8$ \nvalues in Table~\\ref{tbl:pl} are marked with open circles. \nIf the bias did not change with $\\ronem$, then the quasar clustering\nlength $r_1$ would grow in proportion to $\\ronem$, and the curves\nin Figure~\\ref{fig:r1m} would parallel the diagonal of the box,\nwhich has a slope of 1.0. However, increasing $\\ronem$ increases\n$M_*$ and therefore requires a lower value of $\\mmin/M_*$ to match\nthe quasar space density. The correspondingly lower bias partially\ncompensates for the larger $\\ronem$, making the curves in Figure~\\ref{fig:r1m}\nshallower than the box diagonal. For $n=0$ and large $\\tq/t_U$ (the\nhighest solid curve), the minimum mass $\\mmin$ lies far out on the tail\nof a steeply falling mass function. In this regime, a change in $M_*$\nrequires only a small change in $\\mmin/M_*$ to compensate, so there \nis little change in $\\beff$ with $\\ronem$, and the curves approach the\n$r_1 \\propto \\ronem$ lines that would apply for constant bias.\nA similar argument explains the steepening of all curves towards \nlow $\\ronem$, where the small values of $M_*$ put the value of $\\mmin$\nfurther out on the tail of the mass function.\n\n\\begin{figure*}[t]\n\\centerline{\n\\epsfxsize=3.5truein\n\\epsfbox[65 165 550 730]{martini.f4.eps}\n}\n\\caption{\n\\footnotesize\nThe dependence of the quasar clustering length $r_{1Q}$ on the mass \nclustering length $r_{1m}$, for the four power law models at $z = 3$. \nIn each case, the four lines show, from top to bottom, the lifetimes\n$\\tq = \\tu$, $0.1\\tu$, $0.01\\tu$, and $0.001\\tu$. \nResults are computed for normalizations running from $\\sigma_8 = 0.2$ to \n$\\sigma_8 = 2.0$. Open circles show \n$r_{1m}$ and $r_{1Q}$ for our standard choices of $\\sigma_8$, \nlisted in Table~\\ref{tbl:pl}. If bias were independent of $r_{1m}$, the \nlines would parallel the diagonal of the box, which has a slope of $1.0$. \n} \\label{fig:r1m}\n\\end{figure*}\n\n\\section{Results for Cold Dark Matter (CDM) Cosmologies} \\label{sec:cdm}\n\nThe results of \\S\\ref{sec:plspec} confirm our initial contention\nthat quasar clustering can provide a good diagnostic of the typical\nquasar lifetime. However, they show that the predicted clustering\nlength also depends on the shape of the mass power spectrum and on\nthe value of $\\om$, which influences the cluster normalization of\n$\\sigma_8$ at $z=0$ and (together with $\\ol$) determines the growth\nfactor $D(z)$. Accurate determination of $\\tq$ from measurements\nof quasar clustering therefore requires reasonably good knowledge\nof the underlying cosmology.\nFortunately, many lines of evidence now point towards a flat,\nlow-density model based on inflation and cold dark matter \n\\citep[see, e.g., the review by][]{bahcall99}. In particular, \nrecent studies of the power spectrum of the Ly$\\alpha$ forest\nimply that the matter power spectrum has the shape and amplitude\npredicted by COBE- and cluster-normalized CDM models with $\\om \\sim 0.4$\nat the redshifts and length scales relevant to the prediction\nof quasar clustering \\citep{croft99,weinberg99,mcdonald00,phillips00}.\n\nFor the power spectrum of our CDM models, we adopt \n$P(k) \\propto k^{n_p} \\, T^2(k)$ with scale-invariant ($n_p=1$)\nprimeval inflationary fluctuations and the transfer function parameterization\nof \\citet{bbks86},\n\\begin{equation} \nT(k) = \\frac{ {\\rm ln}(1 + 2.34 q)}{2.34 q} \\left[ 1 + 3.89 q + (16.1 q)^2 + \n (5.46 q)^3 + (6.71 q)^4 \\right]^{-1/4} .\n\\label{eqn:trans}\n\\end{equation}\n\n\\noindent\nHere $q = k/\\Gamma$ and $\\Gamma$, with units of $(\\hmpc)^{-1}$,\nis the CDM shape parameter, given approximately by\n$\\Gamma = \\om h \\exp(-\\ob-\\sqrt{2h}\\ob/\\om)$ \\citep{sugiyama95}.\nWe calculate $\\sigma(M)$ and $(d\\sigma/dM)$ by numerical integration\nof this power spectrum.\n\nWe consider five different CDM models with the parameters \nlisted in Table~\\ref{tbl:cdm}. These models are chosen to illustrate\na range of cosmological inputs and also to isolate the effects of \ndifferent parameters on quasar clustering predictions.\nThe $\\tau$CDM, OCDM, and $\\Lambda$CDM models have $\\Gamma=0.2$,\nin approximate agreement with the shape parameter estimated from\ngalaxy surveys \\citep[e.g.,][]{baugh93,peacock94}, \nand they have $\\sigma_8$\nvalues consistent with the cluster mass function constraints of \n\\citet{eke96}. The $\\tau$CDM and $\\Lambda$CDM models are \napproximately COBE-normalized. COBE normalization would imply\na lower $\\sigma_8$ for OCDM, but a slight increase in $n_p$ could\nraise $\\sigma_8$ without having a large impact on the shape of\n$P(k)$ at the relevant scales. The OCDM and $\\Lambda$CDM models\nare consistent with the Ly$\\alpha$ forest power spectrum measurements\nof \\citet{croft99}, but the $\\tau$CDM model is not.\nOCDM is inconsistent with the observed location of the first\nacoustic peak in the cosmic microwave background anisotropy\nspectrum \\citep[e.g.,][]{miller99,melchiorri99,tegmark00}, \nand of the three models, only $\\Lambda$CDM is consistent\nwith the Hubble diagram of Type Ia supernovae \\citep{riess98,perlmutter99}.\n\n\\begin{center}\n\\begin{deluxetable}{lccccclll}\n\\tablenum{2}\n\\tablewidth{0pt}\n\\tablecaption{CDM Model Parameters \\label{tbl:cdm} }\n\\tablehead {\n \\colhead{} &\n \\colhead{$\\sigma_8$} &\n \\colhead{$h$} &\n \\colhead{$\\om$} &\n \\colhead{$\\ol$} &\n \\colhead{$\\Gamma$} &\n \\colhead{$M_* (z = 2)$} &\n \\colhead{$M_* (z = 3)$} &\n \\colhead{$M_* (z = 4)$} \\\\\n}\n\\startdata\nSCDM & 0.5 & 0.5 & 1.0 & 0.0 & 0.5 & $3.58\\cdot 10^{9}$\n & $2.26\\cdot 10^8$ & $1.86\\cdot 10^7$ \\\\\n$\\tau$CDM & 0.5 & 0.5 & 1.0 & 0.0 & 0.2 & $9.44\\cdot 10^6$\n & $1.09\\cdot 10^5$ & $1.87\\cdot 10^3$ \\\\\nOCDM & 0.9 & 0.65 & 0.3 & 0.0 & 0.2 & $1.50\\cdot 10^{11}$\n & $2.70\\cdot 10^{10}$ & $5.60\\cdot 10^{9}$ \\\\\n$\\Lambda$CDM & 0.9 & 0.65 & 0.3 & 0.7 & 0.2 & $2.70\\cdot 10^{10}$\n & $2.03\\cdot 10^9$ & $1.91\\cdot 10^8$ \\\\\n$\\Lambda$CDM2 & 1.17 & 0.65 & 0.3 & 0.7 & 0.2 & $2.16\\cdot 10^{11}$\n & $2.34\\cdot 10^{10}$ & $3.10\\cdot 10^9$ \\\\\n\\enddata\n\\tablecomments{Parameters of the five CDM models discussed in \\S\\ref{sec:cdm}. \nColumn 1 lists the model name, columns 2 - 5 the power spectrum normalization \nand cosmological parameters, and column 6 the power spectrum shape \nparameter (see eq.~[\\ref{eqn:trans}]). \nColumns 7 - 9 list the values of $M_*$ \n(eq.~[\\ref{eqn:mstar}]) at $z = 2$, 3, and 4, in units of $h^{-1} M_\\odot$. \n}\n\\end{deluxetable}\n\\end{center}\n\nWe will use the comparison between the $\\tau$CDM and SCDM models,\nwith $\\Gamma=0.2$ and $\\Gamma=0.5$, respectively, to illustrate the \nimpact of power spectrum shape for fixed $\\om$ and $\\sigma_8$.\nThe SCDM model is cluster-normalized, but its $\\sigma_8=0.5$\nis well below the value $\\sigma_8 \\approx 1.2$ implied by COBE\nfor $n_p=1$, $\\Gamma=0.5$ \\citep[e.g.,][]{bunn97}.\nThe OCDM and $\\Lambda$CDM models have the same $P(k)$ shape and\nthe same $P(k)$ amplitude at $z=0$, but at high redshift the OCDM\nmodel has stronger fluctuations because of a larger $D(z)$.\nWe therefore include the model $\\Lambda$CDM2, which has $\\sigma_8$\nchosen to yield the same power\nspectrum amplitude as OCDM at $z=3$. Differences between OCDM and\n$\\Lambda$CDM2 isolate the impact of a cosmological constant for \nfixed high-redshift mass clustering.\n\nFigure~\\ref{fig:lifecdm} shows $t_H$ in Gyr (upper panels) and \n$t_H/\\tu$ (lower panels) as a function of $M/M_*$ for the CDM models at\n$z = 2$, 3, and 4. \nIn contrast to the power law models shown in Figure~\\ref{fig:lifepl}, \nthe ratio $t_H/t_U$ does not approach a constant value but instead increases\nat very large $M/M_*$. This increase can be understood with reference to \nthe power law case: the effective power law index \n$\\neff=3-6\\,(d\\ln\\sigma/d\\ln M)$ increases\nwith increasing mass in a CDM spectrum, and larger values of $\\neff$\ncorrespond to slower growth of mass scales (and larger $t_H/t_U$) as\nshown in Figure~\\ref{fig:lifepl}.\nThe difference between the SCDM and $\\tau$CDM curves in \nFigure~\\ref{fig:lifecdm} reflects the higher values of $\\neff$ \nfor the $\\Gamma=0.5$ power spectrum. The differences between the various \n$\\Gamma=0.2$ models largely reflect the differences in $M_*$, and\nhence the differences in $\\neff$ at fixed $M/M_*$, and they also reflect the\ndifferences in fluctuation growth rates.\n\n\\begin{figure*}[t]\n\\centerline{\n\\epsfxsize=3.5truein\n\\epsfbox[65 165 550 730]{martini.f5.eps}\n}\n\\caption{\n\\footnotesize\nHalo lifetime as a function of $M/M_*$, as in Figure~\\ref{fig:lifepl}, \nfor the CDM models with parameters listed in Table~\\ref{tbl:cdm}. \n} \\label{fig:lifecdm}\n\\end{figure*}\n\nFigure~\\ref{fig:biascdm} plots the effective bias against $\\mmin/M_*$\nfor the five CDM models at $z=3$. Figure~\\ref{fig:biaspl} showed\nthat the value of $\\beff$ at fixed $\\mmin/M_*$ is higher for larger $n$.\nThe lines in Figure~\\ref{fig:biascdm} curve upwards because $\\neff$\nincreases with mass scale, and to a good approximation the value of $\\beff$\nin the CDM models equals the value of $\\beff$ at the same $\\mmin/M_*$\nin a power-law model of index $\\neff(\\mmin)$.\nThe difference between SCDM and $\\tau$CDM in Figure~\\ref{fig:biascdm}\ntherefore reflects the higher $\\neff$ values in SCDM, and the \ndifferences among the other models reflect the different values of $M_*$,\nand hence the different values of $\\neff$ at fixed $\\mmin/M_*$.\n\n\\begin{figure*}[t]\n\\centerline{\n\\epsfxsize=3.5truein\n\\epsfbox[65 165 550 730]{martini.f6.eps}\n}\n\\caption{\n\\footnotesize\nEffective bias as a function of minimum halo mass, as in \nFigure~\\ref{fig:biaspl}, for the CDM models at $z = 3$. \n} \\label{fig:biascdm}\n\\end{figure*}\n\nThe top three panels of Figure~\\ref{fig:r1cdm} show the dependence of\n$\\mmin/M_*$ on $\\tq$ at $z = 2$, 3, and 4; the values of $M_*$\nare listed in Table~\\ref{tbl:cdm}.\nThe calculation of $\\mmin$ via\nequation~(\\ref{eqn:phimatch2}) incorporates both the dependence of \nhalo lifetime on mass and the influence of $\\om$ and $\\ol$ on the\nvalue of $\\Phi(z)$ inferred from the quasar\nsurface density (as discussed in the Appendix). \nThe two $\\om = 1$ models have the lowest values of $M_*$\nbecause of their lower $\\sigma_8$ and $D(z)$, so they\nrequire the largest $\\mmin/M_*$ to match the observed $\\Phi(z)$.\nThe value of $M_*$ is smaller for $\\Lambda$CDM than for OCDM because\n$D(z)$ is smaller for the flat model, so $\\Lambda$CDM requires\nlarger $\\mmin/M_*$. The higher normalization of the $\\Lambda$CDM2\nmodel largely removes this difference, since $\\sigma_8 D(z=3)$ is\nmatched to that of the OCDM model, but $\\Lambda$CDM2 still has a \nslightly lower $M_*$ because of the influence of $\\Omega_\\Lambda$\non $\\delta_c(z)$. As a result, the $\\mmin/M_*$ curve for\n$\\Lambda$CDM2 lies just above that of OCDM at $z=3$.\n\n\\begin{figure*}[t]\n\\centerline{\n\\epsfxsize=3.5truein\n\\epsfbox[65 165 550 730]{martini.f7.eps}\n}\n\\caption{\n\\footnotesize\nMinimum halo mass, effective bias, and clustering length as a function \nof $\\tq$, for the CDM models at $z = 2$, 3, and 4. \nFormat is the same as Figure~\\ref{fig:r1pl}. \n} \\label{fig:r1cdm}\n\\end{figure*}\n\nThe middle panels of Figure~\\ref{fig:r1cdm} show the effective\nbias values, which display the same relative dependence on $\\tq$\nand cosmology as the $\\mmin/M_*$ values. Because $\\mmin/M_* > 1$\nin all of the CDM models, even for $\\tq$ as low as $10^5$ years,\nthe MW bias formula~(\\ref{eqn:biasmw}) yields nearly identical\nresults to Jing's (\\citeyear{jing98}) corrected formula~(eq.~[\\ref{eqn:bias}]).\n\nThe bottom panels of Figure~\\ref{fig:r1cdm} present the main \nresults of this paper: the relation between the clustering length \n$r_1$ and the quasar lifetime $\\tq$ for CDM models at $z = 2$, 3, and 4. \nThe clustering length is an increasing function of quasar lifetime\nfor the reasons outlined in the Introduction and detailed in \n\\S\\ref{sec:meth}. A longer $\\tq$ implies that quasar host halos\nare rarer, more highly biased objects.\nThe change in the $r_1$ vs. $\\tq$ relation with redshift \nreflects the evolution of the quasar space density and of the\nunderlying mass fluctuations. For a given model and $\\tq$,\nthe predicted quasar clustering is weakest\nat $z = 3$, the peak of the quasar space density.\nThe smaller quasar abundance at $z=4$ implies a higher bias of\nthe host halo population, which more than compensates for\nthe slightly weaker mass clustering.\nThe clustering length grows between $z=3$ and $z=2$ because of\nboth the drop in quasar space density and the growth of mass clustering.\nThe $r_1$ vs. $\\tq$ relation becomes flat at the largest $\\tq$ for the \nSCDM model at $z = 4$ and for the $\\tau$CDM model at $z = 3$ and $4$,\nwhere $\\tq$ exceeds the halo lifetime $t_H(\\mmin)$ and\nthe value of $\\mmin$ required to match $\\Phi(z)$ \ntherefore becomes independent of $\\tq$.\n\nThe differences between models reflect the differences in bias\nfactors discussed above and the differences in the mass clustering.\nThere are also differences in the values of $\\Phi(z)$ inferred\nfrom the observed quasar surface density (see Appendix), but\nthese have relatively little effect.\nThe main separation in Figure~\\ref{fig:r1cdm} is between \nthe low-density models and the $\\om=1$ models, which have weaker\nmass clustering because of their lower values of $\\sigma_8$ and $D(z)$.\nThe $\\om=1$ models have larger bias factors, but these are not enough \nto compensate for the smaller mass fluctuations.\nThe $r_1$ vs. $\\tq$ relations are also shallower for the $\\om=1$ models,\nbecause the values of $\\mmin$ lie further out on the steep, high-mass tail\nof the mass function, where a smaller change in $\\mmin$ can make up\nfor the same change in $\\tq$.\nThe three low-density models yield very similar predictions.\n\nTo facilitate comparison of future observational results to our predictions, \nwe have fit polynomials of the form\n\\begin{equation}\nr_1 = \t\\left\\{ \\begin{array}{ll}\n\t a_0 + a_1 \\, \\ltq & {\\rm for} \\; \\ltq \\geq -1.5 \\\\\n\t a_0 + a_1 \\, \\ltq + a_2 \\, (\\ltq + 1.5)^2 & {\\rm for} \\; \\ltq < -1.5\\\\\n \\end{array}\n \\right.\n\\label{eqn:fits}\n\\end{equation}\nto each of the $r_1$ vs. $\\tq$ curves shown in Figure~\\ref{fig:r1cdm}. \nThe values of the coefficients are given in Table~\\ref{tbl:fits}, and \nthe coefficients $a_0$ and $a_1$ have the same value over the entire \nrange in $\\tq$. These fits are accurate to better than 3\\% in $r_1$ for \ngiven $t_Q$, or better than 10\\% in $\\tq$ given $r_1$, for all cases except \nthe SCDM and $\\tau$CDM models at $z = 4$, where the maximum errors are \n3\\% in $r_1$ given $\\tq$ and 20\\% in $\\tq$ for given $r_1$. \n\n\\begin{center}\n\\begin{deluxetable}{lccccccccccr}\n\\tablenum{3}\n\\tablewidth{0pt}\n\\tablecaption{$r_1$ vs. $\\tq$ fitting coefficients \\label{tbl:fits} }\n\\tablehead {\n \\colhead{Model} &\n \\colhead{$a_0$} &\n \\colhead{$a_1$} &\n \\colhead{$a_2$} &\n \\colhead{} &\n \\colhead{$a_0$} &\n \\colhead{$a_1$} &\n \\colhead{$a_2$} &\n \\colhead{} &\n \\colhead{$a_0$} &\n \\colhead{$a_1$} &\n \\colhead{$a_2$} \\\\\n}\n\\startdata\n & &$z = 2$& & & &$z=3$& & & &$z=4$ & \\\\\nSCDM & 12.47 & 2.437 & 0.1001 & & 10.62 & 1.932 & 0.0601 & & 11.26 &1.590 & -0.0042 \\\\\n$\\tau$CDM & 16.54 & 3.163 & 0.1662 & & 13.89 & 2.422 & 0.0882 & & 14.48 &1.964 & -0.0166 \\\\\nOCDM & 27.18 & 7.002 & 0.7798 & & 25.32 & 6.029 & 0.5347 & & 30.26 &5.457 & 0.1640 \\\\\n$\\Lambda$CDM & 26.79 & 6.173 & 0.4913 & & 23.48 & 4.974 & 0.3122 & & 26.12 &4.248 & 0.0823 \\\\\n$\\Lambda$CDM2 & 29.84 & 7.441 & 0.7465 & & 26.51 & 6.093 & 0.4840 & & 30.23 &5.274 & 0.1393 \\\\\n\\enddata\n\\tablecomments{\nCoefficients for polynomial fits (eq.~[\\ref{eqn:fits}]) to the \npredicted relations between quasar lifetime and clustering length shown in \nFigure~\\ref{fig:r1cdm}. Column 1 lists the model name, columns 2 - 4 the \ncoefficients for $z=2$, columns 5 - 7 the coefficients for $z=3$, and \ncolumns 8 - 10 the coefficients for $z=4$. \n}\n\\end{deluxetable}\n\\end{center}\n\n\\section{Discussion} \\label{sec:dis}\n\n\\subsection{Sensitivity to model details} \\label{sec:sen}\n\nAs already mentioned in \\S\\ref{sec:life}, the definition of a ``halo\nlifetime'' is somewhat ambiguous. We have so far adopted a definition of \n$t_H$ as the median time before a halo of mass $M$ is incorporated\ninto a halo of mass $2M$. If we increase this mass ratio from 2 to 5\n(a rather extreme value),\nthen the typical halo lifetimes in our CDM models increase\nby factors of $2-4$. \nSince it is the ratio $t_Q/t_H$\nthat enters our determination of $\\mmin$ (eq.~[\\ref{eqn:phimatch2}]),\nand hence fixes the bias factor, this change in $t_H$ would require\nan equal increase in $t_Q$ to maintain the same clustering length $r_1$.\nWe conclude that the ambiguity in halo lifetime definition \nintroduces a factor $\\sim 2$ uncertainty in the determination of\n$t_Q$ from clustering measurements, in the context of our model.\n\nWe have also assumed that quasar luminosity is perfectly correlated\nwith host halo mass, so that matching the space density of an\nabsolute-magnitude limited sample imposes a sharp cutoff in \nthe host mass distribution at $M=\\mmin$. If there is some scatter\nin the luminosity--host mass relation, then some halos with $M<\\mmin$\nwill host a quasar above the absolute-magnitude limit and some\nhalos with $M>\\mmin$ will not. We can model such an effect\nby introducing a soft cutoff into equation~(\\ref{eqn:phimatch2}): \n\\begin{equation}\n\\Phi(z) = \\int_{0}^{\\infty} dM\\;g(M)\\;\\frac{\\tq}{t_H(M, z)} n(M, z)\n\\end{equation}\nwith\n\\begin{equation}\ng(M) = \t\\left\\{ \\begin{array}{ll}\n\t0 & {\\rm for} \\; M < \\frac{\\mmin}{\\alpha} \\\\\n\t\\left( \\frac{\\alpha}{\\mmin (\\alpha^2 - 1)} \\right) M - \\frac{1}{\\alpha^2 - 1} & {\\rm for} \\; \\frac{\\mmin}{\\alpha} < M < \\alpha \\mmin \\\\\n\t1 & {\\rm for} \\; M > \\alpha \\mmin\n \\end{array}\n \\right.\n\\label{eqn:cut}\n\\end{equation}\nand $\\alpha > 1$. Adopting a soft cutoff slightly decreases \n$\\mmin$ and, more significantly, reduces the value of $\\beff$ by allowing \nsome quasars to reside in lower mass halos, which are less strongly biased.\nQuantitatively, we find that setting $\\alpha = 2$, which corresponds to \nincluding halos down to $M=\\mmin/2$,\ndecreases the clustering length by $\\la 6$\\% for the \nshortest quasar lifetimes and $\\la 10$\\% for the longest quasar \nlifetimes. Matching a fixed $r_1$ with an $\\alpha=2$\ncutoff requires lifetimes that are longer by a factor $\\sim 1-1.5$\nat short $\\tq$ and $\\sim 2-2.5$ at long $\\tq$.\nLonger lifetimes are more sensitive to scatter in the luminosity-host mass \nrelation because $\\beff$ depends more strongly on $\\mmin/M_*$ for these \nrarer objects. \nThe assumption of a perfectly monotonic relation between quasar\nluminosity and host mass leads to the smallest $\\tq$ for\na given $r_1$. Thus if any scatter does exist in this relation, our model \npredictions for $\\tq$ effectively become lower limits to the quasar \nlifetime. \n\nAnother simplification of our model is the assumption that a quasar is\neither ``on'' or ``off'' -- each quasar shines at luminosity $L$ for time\n$t_Q$, perhaps divided among several episodes of activity, and the rest\nof the time it is too faint to appear in a luminous quasar sample.\nMore realistically, variations in the accretion rate and\nradiative efficiency will cause the quasar luminosity to vary, especially\nif the black hole mass itself grows significantly during the \nluminous phase. Nonetheless, the maximum luminosity will still depend on \nthe maximum black hole mass. At a given time, the luminous quasar population\nwill include black holes shining at close to their maximum luminosity and\n``faded'' black holes of higher mass. Because the host halos lie on the\nsteeply falling tail of the mass function, the first component of the\npopulation always dominates over the second, and we therefore expect our\nclustering method to yield the time $t_Q$ for which a quasar shines within\na factor $\\sim 2$ of its peak luminosity. More strongly faded quasars are too\nrare to make much difference to the space density or effective bias.\n\nTo illustrate this point, we consider the model of \\citet{haehnelt98} in\nwhich a quasar hosted by a halo of mass $M$ has a luminosity history\n$L(t) = L_0(M)\\,{\\rm exp}(-t/t_Q)$, with a maximum luminosity \n$L_0(M) = \\alpha\\,M$ \nproportional to the halo mass. In this model, the time that a quasar shines \nabove the luminosity threshold $L_{\\rm min} = L_0 (\\mmin)$ of a survey is the\nvisibility time $t_Q' = t_Q\\,{\\rm ln}(M/\\mmin)$. We can calculate $\\mmin$ for a\ngiven space density by substituting $t_Q'$ for $t_Q$ in\nequation~(\\ref{eqn:phimatch2}), then calculate $\\beff(\\mmin)$ by\nmultiplying the integrands in the numerator and denominator of\nequation~(\\ref{eqn:beff}) by the visibility weighting factor \n${\\rm ln}(M/\\mmin)$.\nThe middle curves in Figure~\\ref{fig:lt} compare $r_1(t_Q)$ for\nthe on--off ({\\it solid line}) and exponential decay ({\\it dotted line})\nmodels, in the case of $\\Lambda$CDM at $z = 3$ with our standard $\\Phi(z)$.\nThe curves are remarkably similar, showing that the lifetime inferred from\nclustering assuming an on--off model would be close to the $e$-folding\ntimescale in an exponential decay model. The curves for the exponential\ndecay model are slightly shallower because at low $\\mmin$ (low $t_Q$) the\nmass function is not as steep, allowing faded quasars in more massive halos\nto make a larger contribution to $\\beff$ and thereby raise $r_1$. Although\nresults for a different functional form of $L(M,t)$ would differ in\ndetail, we would expect the lifetime inferred from clustering to be\nclose to the ``half-maximum'' width of the typical luminosity history, for\nthe general reasons discussed above.\n\n\\begin{figure*}[t]\n\\centerline{\n\\epsfxsize=3.5truein\n\\epsfbox[65 165 550 730]{martini.f8.eps}\n}\n\\caption{\n\\footnotesize\nClustering length vs. $\\tq$ for the $\\Lambda$CDM model at $z=3$ for \ntwo different models of quasar luminosity evolution at three different \nspace densities $\\Phi(z)$. The ``on -- off'' model ({\\it solid lines}) \nassumes the quasar luminosity is constant throughout its lifetime $\\tq$ \nand is the standard model we discuss in this paper. The central line \nshows results for the $\\Lambda$CDM model at $z = 3$ with our \nstandard $\\Phi(z)$. The other solid curves, related \nto the first by simple horizontal shifts, show results for space densities \ndifferent by factors of $10$ and $1/10$ (bottom and top).\nIn the exponential model ({\\it dotted lines}), the quasar luminosity starts at \nsome maximum luminosity proportional to the halo mass and decays with an \n$e$-folding timescale $\\tq$. The middle line again corresponds to our \nstandard $\\Phi(z)$, and the other two dotted curves show results for \nspace densities different by factors of $10$ and $1/10$ (bottom and top).\n} \\label{fig:lt}\n\\end{figure*}\n\nAs mentioned in \\S\\ref{sec:over}, we assume that quasars radiate isotropically. \nIf they radiate instead with an average beaming factor $f_B < 1$, then \nthe true value of $\\Phi(z)$ is larger than the observed value by a \nfactor $f_B^{-1}$. The implied lifetime for a given $r_1$ would therefore \nbe larger by a factor $f_B^{-1}$ as well. \n\n\n\\subsection{Interpretation of Existing Data} \\label{sec:data}\n\nAfter several attempts \\citep{osmer81, webster82}, quasar clustering was \nfirst detected by \\citet{shaver84}, and later by \\citet{shanks87} and \n\\citet{iovino88}. However, measurements of quasar clustering are\nstill hampered by small, sparse samples, and even the best studies\nto date yield detections with only several-$\\sigma$ significance.\nGiven the limitations of current data, it is not surprising that\ndifferent authors reach different conclusions about the strength of\nclustering and its evolution. Analyzing a combined sample of quasars\nwith $0.3<z<2.2$ from the Durham/AAT UVX Survey, \nthe CFHT survey, and the Large Bright Quasar Sample,\n\\citet{shanks94} and \\citet{croom96} find a reasonable fit to the data with\nan $\\om=1$ model that has $\\xi(r)=(r/r_0)^{-\\gamma}$, $\\gamma \\approx 1.8$,\nand a constant comoving correlation length $r_0=6\\hmpc$.\n\\citet{lafranca98} report a higher correlation length, \n$r_0=9.1 \\pm 2.0\\hmpc$ for a $\\gamma=1.8$ power law, in their\n$1.4 < z < 2.2$ sample.\n\nIf we adopt $r_0 \\approx 8\\hmpc$ at $z=2$ and a corresponding\n$r_1 \\approx 11\\hmpc$, then the implied quasar lifetime is \n$\\sim 10^{7.5}$ years for the $\\tau$CDM model and $\\sim 10^8$ years\nfor SCDM. The $r_0$ values quoted above are for $\\om=1$,\nand because quasar pair separations are measured in angle and redshift,\nthey should be increased by a factor $\\sim 1.5$ in an $\\om=0.3$, $\\ol=0.7$\nuniverse and a factor $\\sim 1.3$ in an $\\om=0.3$, $\\ol=0$ universe\n(roughly the inverse cube-roots of the volume ratios listed in \nTable A1). Adopting $r_1 \\approx 16\\hmpc$ implies a lifetime\n$t_Q \\sim 10^{7-7.5}$ years in our low-density models.\nHowever, these numbers must be considered highly uncertain because of the \nlimitations of current data and because the space densities of the various \nobservational samples do not necessarily match those assumed in our \nmodel predictions. \n\nAll of these measurements are based\nmainly on quasars with $z<2$. At higher redshift, \\citet{kundic97}\nand \\citet{stephens97} have investigated clustering in the\nPalomar Transit Grism Survey (PTGS; \\citealt{schneider94}).\nFitting a $\\gamma=1.8$ power law, \\citet{stephens97} find\n$r_0=17.5 \\pm 7.5\\hmpc$ for $z>2.7$. This high\ncorrelation length (inferred from the presence of three close\npairs in a sample of 90 quasars) could be a statistical fluke,\nbut in the context of our model it is tempting to see it as\na consequence of the high luminosity threshold of the PTGS\nsurvey, which might lead it to pick out the most strongly clustered members \nof the quasar population.\n\n\\subsection{Prospects} \\label{sec:pros}\n\nThe 2dF \\citep{boyle00,shanks00} and Sloan \\citep{york00} quasar surveys\nwill transform the study of quasar clustering over the next\nseveral years, yielding high-precision measurements for a wide\nrange of redshifts. These measurements will allow good determination\nof the typical quasar lifetime $\\tq$ in the context of the model \npresented here. They will also test the key assumption of this model, \nthe monotonic\nrelation between quasar luminosity and host halo mass, by\ncharacterizing the clustering as a function of redshift and,\nespecially, as a function of quasar absolute magnitude.\n\nFigure~\\ref{fig:lt} illustrates this test for the $\\Lambda$CDM model \nat $z=3$. Brighter quasars have a lower space density $\\Phi(z)$,\nso they should have a higher minimum host halo mass $\\mmin$, and,\nbecause of the higher bias of more massive halos, they should \nexhibit stronger clustering. Fainter, more numerous quasars\nshould exhibit weaker clustering. Figure~\\ref{fig:lt} shows \nthe predicted $r_1$ vs. $\\tq$ relation for samples with 1/10\nand 10 times the space density of our standard case (3.42 quasars\nper square degree per unit redshift; see Table~\\ref{tbl:qlf}).\nIn our standard on--off model ({\\it solid lines}), \na change in $\\Phi(z)$ in equation~(\\ref{eqn:phimatch2}) \ncan be exactly compensated by changing $\\tq$ by the same factor,\nso the solid curves in Figure~\\ref{fig:lt} are simply shifted horizontally\nrelative to each other. Our predictions in \nFigure~\\ref{fig:r1cdm} (see eq.~[\\ref{eqn:fits}]) can therefore be\ntransformed to any quasar space density by changing $\\tq$ in\nproportion to $\\Phi(z)$. In the exponential decay model ({\\it dotted lines}), \nthe scaling of $t_Q$ with $\\Phi(z)$ is no longer exact, though it \nis still a good approximation. \n\nIf there is a large dispersion in the relation between quasar luminosity\nand host halo mass, then the dependence of clustering strength on\nquasar space density will be much weaker than Figure~\\ref{fig:lt} predicts. \nDetection of the predicted trend between luminosity and clustering, or \ndefinitive demonstration of its absence, would itself provide an important\ninsight into the nature of quasar host halos.\nMore generally, the parameters of a model that incorporates scatter\n(such as the $\\alpha$ prescription of equation~[\\ref{eqn:cut}])\ncould be determined by matching the observed relation\nbetween $r_1$ and $\\Phi(z)$.\n\nIf the observations do support a tight correlation between luminosity\nand host halo mass, then the first property of quasars to emerge from \nthe 2dF and Sloan clustering studies will be the typical lifetime $\\tq$.\nFor the low-density models in Figure~\\ref{fig:r1cdm},\nthe slope of the correlation between $r_1$ and $\\log_{10}\\tq$ is $\\sim 10$,\nso a determination of $r_1$ with a precision of $2\\hmpc$ would\nconstrain $\\tq$ to a factor of $10^{0.2} \\approx 1.6$, for \na specified cosmology. By the time these quasar surveys are complete,\na variety of observations may have constrained cosmological\nparameters to the point that they contribute negligible uncertainty\nto this constraint. Instead, the uncertainty in $\\tq$ will probably\nbe dominated by the limitations of the quasar population model,\ne.g., the approximate nature of the\nassumptions that the quasar luminosity tracks the halo mass,\nthat there is only quasar per halo, and that the average lifetime $\\tq$\nis independent of quasar luminosity.\nThese assumptions can be tested empirically to some degree, but not\nperfectly.\nDespite these limitations, it seems realistic to hope that \n$\\tq$ can be constrained to a factor three or better by high-precision\nclustering measurements, a vast improvement over the current situation.\nIt is worth reiterating that our assumption of a perfectly monotonic\nrelation between luminosity and halo mass leads to the smallest $\\tq$\nfor an observed $r_1$, since with a shorter lifetime there are simply\nnot enough massive, highly biased halos to host the quasar population.\n\nA determination of $\\tq$ to a factor of three will be sufficient\nto address fundamental issues about the physics of quasars and\ngalactic nuclei. Comparison of $\\tq$ to the Salpeter timescale\nwill answer one of the most basic questions about supermassive\nblack holes: do they shine as they grow?\nIf $\\tq \\ga 4\\times 10^7$ years, the $e$-folding timescale\nfor $L \\sim L_E$, $\\epsilon \\sim 0.1$, then quasar black holes increase \ntheir mass by a substantial factor during their optically bright phase. \nIf $\\tq$ is much shorter than this, then the black holes must accrete most\nof their mass at low efficiency, or while shining at $L \\ll L_E$.\nA short lifetime could indicate an important role for advection \ndominated accretion (\\citet{narayan98} and references therein), or it \ncould indicate that black holes acquire much of their mass through\nmergers with other black holes, emitting binding energy in the form of \ngravitational waves rather than electromagnetic waves.\nA determination of $\\tq$ would also resolve the question\nof whether the black holes in the nuclei of local galaxies\nare the remnants of dead quasars.\nFor example, \\citet{richstone98} infer a lifetime $t_Q \\sim 10^6$ years by\nmatching the space density of local\nspheroids that host black holes of mass $M \\ga 4\\times 10^8 M_\\odot$ \nto the space density of high-redshift quasars\nof luminosity $L_E(M) \\ga 6 \\times 10^{46}\\;{\\rm erg}\\;{\\rm s}^{-1}$.\nIf clustering implies a much longer lifetime, then these numerous local \nblack holes may once have powered active nuclei, but they were not the engines\nof the luminous, rare quasars.\n\nWe have assumed in our model that quasar activity is a random \nevent in the life of the parent halo.\nQuasar activity might instead be triggered by a major merger,\nby a weaker ``fly-by'' interaction, or by the first burst of\nstar formation in the host galaxy.\nRegardless of the trigger mechanism, the lifetime will be the\ndominant factor in determining the strength of high-redshift quasar \nclustering, if our assumed link between luminosity\nand halo mass holds. However, different triggering mechanisms\nmight be diagnosed by more subtle clustering properties,\nsuch as features in the correlation function at small separations,\nor higher-order correlations. At low redshift, where the evolution\nof the quasar population is driven by fueling rather than by\nblack hole growth, the nature of the triggering mechanism might\nplay a major role in determining quasars' clustering properties.\nThe calculations presented here illustrate the promise of quasar\nclustering as a tool for testing ideas about quasar physics, a promise \nthat should be fulfilled by the large quasar surveys now underway. \n\n\\acknowledgments\nWe thank James Bullock, Alberto Conti, Jordi Miralda-Escud{\\'e}, \nPatrick Osmer, and Simon White for helpful discussions. \nWe also thank the referee for constructive suggestions, which led to \nour consideration of the exponential decay model in \\S~\\ref{sec:dis}. \nAs we were nearing completion of this work, we learned of a\nsimilar, independent study by Z. Haiman \\& L. Hui \n\\citep{haiman00}; our general conclusions are consistent with theirs, \nalthough the approaches are quite different in detail, precluding a \nprecise comparison of results. \nThis work was supported in part by NSF grant AST96-16822 and\nNASA grant NAG5-3525.\n\n\\appendix\n\n\\section{Converting from observed quasar numbers to $\\Phi(z)$} \n\nThe observed quantity that is measured in studies of quasar clustering and \nthe quasar space density is the number of sources brighter than a given \napparent magnitude $m$ per unit redshift per unit solid angle on the sky. \nThis surface density per unit redshift can be converted into a comoving space \ndensity of objects brighter than a given absolute magnitude $M$, \n\\begin{equation}\n\\Phi(z, < M) = \\frac{dN (< m)}{d\\Omega \\; dz} \\; \\frac{d\\Omega \\; dz}{dV_c(z)}, \n\\end{equation}\nwhere $dV_c(z)$ is the differential comoving volume element corresponding to \n$d\\Omega \\, dz$. \nFollowing the notation in \\citet{hogg99}, this volume element is \n\\begin{equation}\ndV_c(z) = D_H \\frac{D_M^2}{E(z)} d\\Omega dz, \n\\end{equation}\n\\noindent\nwhere $D_H = c/H_0$ is the Hubble distance, $D_M$ is the transverse \ncomoving distance, \n\\begin{equation}\nD_M = \t\\left\\{ \\begin{array}{ll}\n\tD_H \\, \\frac{1}{\\sqrt{\\Omega_k}} \\, {\\rm sinh}[\\sqrt{\\Omega_k}\\frac{D_c}{D_H} ] & {\\rm for} \\; \\Omega_k > 0 \\\\\n\tD_H \\int_{0}^{z} \\frac{dz'}{E(z')} & {\\rm for} \\; \\Omega_k = 0 \\\\\n\tD_H \\frac{1}{\\sqrt{|\\Omega_k}|} \\, {\\rm sin} [\\sqrt{|\\Omega_k|}\\frac{D_c}{D_H} ] & {\\rm for} \\; \\Omega_k < 0 \n\t\\end{array}\n\t\\right.\n\\end{equation}\n\\noindent \nand \n$E(z) = \\sqrt{\\om(1+z)^3 + \\Omega_k(1+z)^2 + \\ol}$, \nwhere $\\Omega_k = 1 - \\om - \\ol$. \nFor $\\om = 1$, $\\Omega_k = 0$, the differential comoving volume element is \n\\begin{equation}\ndV_C(z) = 4 \\, \\left(\\frac{c}{H_0}\\right)^3 \\; (1 + z)^{-3/2} \\; \\left[ 1 - \\frac{1}{\\sqrt{1 + z}} \\right]^2 \\, d\\Omega \\, dz\n\\end{equation}\nper steradian per unit redshift. \n\nThe fact that $dV_c(z)$ depends on the cosmological parameters means that \na given measured surface density of sources corresponds to a different \ncomoving space density for different cosmological model parameters. \nThe space density of quasars is commonly quoted for an $\\om = 1$ universe. \nTo convert this space density (in units of $h^3$ Mpc$^{-3}$) into the space \ndensity for a model with different values of $\\om$ and $\\ol$ requires a \ncorrection of the form\n\\begin{equation} \n\\Phi(z, \\om, \\ol) = \n\t\\Phi(z, \\om', \\ol') \n\t\\frac{f(z, \\om', \\ol')}\n\t{f(z, \\om, \\ol)}, \n\\end{equation}\nwhere\n\\begin{equation} \nf(z, \\om, \\ol) = \\frac{D_H \\, D_M^2}{E(z)}. \n\\label{eqn:f}\n\\end{equation}\nThis procedure converts the reported space density under one set of \ncosmological parameters back into the observed surface density and \nthen converts the surface density into the space density for the new \nset of cosmological parameters. In the notation of \\citet{pwro98}, \n$f(z, \\om, \\ol) = g \\times f^2$, where $f$ and $g$ are given by their \nequations (5) and (6), respectively. \n\n\\begin{center}\n\\begin{deluxetable}{lrcccc}\n\\tablenum{A1}\n\\tablewidth{0pt}\n\\tablecaption{Quasar Space and Surface Density \\label{tbl:qlf} }\n\\tablehead {\n \\colhead{$z$} &\n \\colhead{} &\n \\colhead{$\\Phi(z)$} &\n \\colhead{$\\frac{dN}{dz\\,d\\Omega}$} &\n \\colhead{$\\frac{f(1.0, 0.0)}{f(0.3, 0.0)}$} &\n \\colhead{$\\frac{f(1.0, 0.0)}{f(0.3, 0.7)}$} \\\\\n}\n\\startdata\n2 & . . . . . . . . . . . . . . . . & $1.889\\cdot 10^{-6}$ & 2.132 & 0.425 & 0.279 \\\\\n3 & . . . . . . . . . . . . . . . . & $3.331\\cdot 10^{-6}$ & 3.417 & 0.339 & 0.253 \\\\\n4 & . . . . . . . . . . . . . . . . & $3.200\\cdot 10^{-7}$ & 0.287 & 0.287 & 0.241 \\\\\n\\enddata\n\\tablecomments{Adopted values of the space density of quasars at \n$z = 2$, 3, and 4, \nand cosmological conversion factors. Values of $\\Phi(z)$ in column 2 are from \n\\citet{who94} (assuming $\\om = 1$) for quasars with $M_c < -24.5$ (absolute \ncontinuum flux at 1216 \\AA), converted from their adopted $h = 0.75$ to \n$h^3$ Mpc$^{-3}$. \nColumn 3 lists the abundance of quasars in number per square \ndegree per unit redshift to which the space density in column 2 \ncorresponds. Columns 4 and \n5 contain the ratios of the factors $f(\\om, \\ol)$ defined in \nequation~(\\ref{eqn:f}) needed to convert the space density in column 2, \nwhich is valid for $\\om = 1$, to space densities for the OCDM and \n$\\Lambda$CDM models, respectively. \n}\n\\end{deluxetable}\n\\end{center}\n\nIn Table~\\ref{tbl:qlf} we list the factors to convert the space density \nin column 2, which is listed for $\\om = 1, \\ol = 0$, \nto the corresponding space densities for $\\om = 0.3, \\ol = 0.0$ and \n$\\om = 0.3, \\ol = 0.7$. The factors in \nTable~\\ref{tbl:qlf} are all less than unity because the comoving volume \nelement is smallest in an $\\om = 1$ universe. \n\n\\begin{thebibliography}{}\n\n\\bibitem[Adelberger et al.(1998)]{adelberger98}\nAdelberger, K. L., Steidel, C. C., Giavalisco, M., Dickinson, M.,\nPettini, M., \\& Kellogg, M. 1998, \\apj, 505, 18\n\n\\bibitem[Bahcall et al.(1999)]{bahcall99}\nBahcall, N. A., Ostriker, J. P., Perlmutter, S., \\& Steinhardt, P. J. 1999,\nScience, 284, 1481\n\n\\bibitem[Baugh \\& Efstathiou(1993)]{baugh93}\nBaugh, C. M., \\& Efstathiou, G. 1993, \\mnras, 265, 145\n\n\\bibitem[Bajtlik, Duncan, \\& Ostriker(1988)]{bajtlik88}\nBajtlik, S., Duncan, R.C., \\& Ostriker, J.P. 1988, \\apj, 327, 570\n\n\\bibitem[Bardeen et al.(1986)]{bbks86} \nBardeen, J., Bond, J.R., Kaiser, N., \\& Szalay, A.S. 1986, \\apj, 304, 15\n\n\\bibitem[Bechtold(1994)]{bechtold94}\nBechtold, J., 1994, \\apjs, 91, 1\n\n\\bibitem[Blumenthal et al.(1984)]{blumenthal84}\nBlumenthal, G.R., Faber, S.M., Primack, J.R., \\& Rees, M.J. 1984, \n\\nat, 311, 517\n\n\\bibitem[Bond et al.(1991)]{bond91}\nBond, J. R., Cole, S., Efstathiou, G., \\& Kaiser, N. 1991, \\apj, 379, 440\n\n\\bibitem[Boyle et al.(1990)]{boyle90} \nBoyle, B.J., Fong, R., Shanks, T., \\& Peterson, B.A. 1990, \\mnras, 243, 1\n\n\\bibitem[Boyle et al.(1999)]{boyle99}\nBoyle, B. J., Smith, R.\nJ., Shanks, T., Croom, S. M. \\& Miller, L. 1999, in IAU Symp. 183:\nCosmological Parameters and the Evolution of the Universe, ed. K. Sato,\n(Kluwer: Dordrecht), p. 178\n\n\\bibitem[Boyle et al.(2000)]{boyle00}\nBoyle, B.J., Shanks, T., Croom, S.M., Smith, R.J., Miller, L., Loaring, N., \n\\& Heymans, C. 2000, \\mnras, {\\it in press} astro-ph/0005368\n\n\\bibitem[Bunn \\& White(1997)]{bunn97}\nBunn, E. F., \\& White, M. 1997, \\apj, 480, 6\n\n\\bibitem[Carroll, Press, \\& Turner(1992)]{carroll92}\nCarroll, S. M., Press, W. H., \\& Turner, E. L. 1992, \\araa, 30, 499\n\n\\bibitem[Ciotti \\& Ostriker(1999)]{ciotti99}\nCiotti, L., \\& Ostriker, J. P. 1999, \\apj, {\\it submitted}, astro-ph/9912064\n\n\\bibitem[Croft et al.(1999)]{croft99}\nCroft, R. A. C., Weinberg, D. H., Pettini, M., Katz, N., \\& Hernquist, L. 1999,\n\\apj, 520, 1\n\n\\bibitem[Croom \\& Shanks(1996)]{croom96} \nCroom, S.M. \\& Shanks, T. 1996, \\mnras, 281, 893\n\n\\bibitem[Efstathiou \\& Rees(1988)]{efstathiou88}\nEfstathiou, G. \\& Rees, M. J. 1988, \\mnras, 230, 5P\n\n\\bibitem[Eke, Cole, \\& Frenk(1996)]{eke96}\nEke, V. R., Cole, S., \\& Frenk, C. S. 1996, \\mnras, 282, 263\n\n\\bibitem[Faber \\& Jackson(1976)]{faber76}\nFaber, S. M. \\& Jackson, R. E. 1976, \\apj, 204, 668\n\n\\bibitem[Fan et al.(1999)]{fan99}\nFan, X., et al.\\ 1999, \\aj, 118, 1\n\n\\bibitem[Haehnelt \\& Rees(1993)]{haehnelt93} \nHaehnelt, M.G. \\& Rees, M.J. 1993, \\mnras, 263, 168\n\n\\bibitem[Haehnelt, Natarajan, \\& Rees(1998)]{haehnelt98}\nHaehnelt, M. G., Natarajan, P., \\& Rees, M. J. 1998, \\mnras, 300, 817\n\n\\bibitem[Haiman \\& Hui(2000)]{haiman00}\nHaiman, Z. \\& Hui, L. 2000, \\apj, submitted, astro-ph/0002190\n\n\\bibitem[Haiman \\& Loeb(1998)]{haiman98}\nHaiman, Z. \\& Loeb, A. 1998, \\apj, 503, 505\n\n\\bibitem[Heath(1977)]{heath77}\nHeath, D. J. 1977, \\mnras, 179, 351\n\n\\bibitem[Hewett, Foltz, \\& Chaffee(1993)]{hewett93}\nHewett, P.C., Foltz, C.B., \\& Chaffee, F.C. 1993, \\apj, 406, L43\n\n\\bibitem[Hogg(1999)]{hogg99} \nHogg, D.W. 1999, astro-ph/9905116\n\n\\bibitem[Iovino \\& Shaver(1988)]{iovino88}\nIovino, A. \\& Shaver, P.A. 1988, \\apj, 330, L13\n\n\\bibitem[Jing(1998)]{jing98}\nJing, Y.P. 1998, \\apj, 503, L9\n\n\\bibitem[Kaiser(1984)]{kaiser84}\nKaiser, N. 1984, \\apj, 294, L9\n\n\\bibitem[Katz, Hernquist, \\& Weinberg(1999)]{katz99}\nKatz, N., Hernquist, L., \\& Weinberg, D. H. 1999, \\apj, 523, 463\n\n\\bibitem[Katz et al.(1994)]{katz94}\nKatz, N., Quinn, T., Bertschinger, E., \\& Gelb, J. M. 1994,\n\\mnras, 270, L71\n\n\\bibitem[Kauffmann \\& Haehnelt(2000)]{kauffmann00}\nKauffmann, G., \\& Haehnelt, M. 2000, \\mnras, 311, 576\n\n\\bibitem[Kolatt et al.(1999)]{kolatt99}\nKolatt, T. S., et al. 1999, \\apjl, 523, L109 \n\n\\bibitem[Kundi\\'c(1997)]{kundic97} \nKundi\\'c, T. 1997, \\apj, 482, 631\n\n\\bibitem[La Franca et al.(1998)]{lafranca98}\nLa Franca, F., Andreani, P., \\& Cristiani, S. 1998, \\apj, 497, 529\n\n\\bibitem[Lacey \\& Cole(1993)]{lc93} \nLacey, C. \\& Cole, S. 1993, \\mnras, 262, 649 \n\n\\bibitem[Lynden-Bell(1969)]{lyndenbell69}\nLynden-Bell, D. 1969, Nature, 223, 690\n\n\\bibitem[Magorrian et al.(1998)]{mag98} \nMagorrian, J., et al. 1998, \\aj, 115, 2285\n\n\\bibitem[McDonald et al.(2000)]{mcdonald00}\nMcDonald, P., Miralda-Escud\\'e, J., Rauch, M., Sargent, W. L. W.,\nBarlow, T. A., Cen, R., \\& Ostriker, J. P. 2000, \\apj, submitted,\nastro-ph/9911196\n\n\\bibitem[Melchiorri et al.(1999)]{melchiorri99}\nMelchiorri, A. et al.\\ 1999, \\apjl, in press, astro-ph/9911445\n\n\\bibitem[Miller et al.(1999)]{miller99}\nMiller, A. D. et al.\\ 1999, \\apj, 524, L1\n\n\\bibitem[Mo \\& White(1996)]{mw96} \nMo, H.J. \\& White, S.D.M. 1996, \\mnras, 282, 347 (MW)\n\n\\bibitem[Mo, Mao, \\& White(1999)]{mmw99} \nMo, H.J., Mao, S., \\& White, S.D.M. 1999, \\mnras, 304, 175\n\n\\bibitem[Monaco, Salucci, \\& Danese(2000)]{monaco00}\nMonaco, P., Salucci, P., \\& Danese, L. 2000, \\mnras, 311, 279\n\n\\bibitem[Narayan, Mahadevan, \\& Quatert(1998)]{narayan98}\nNarayan, R., Mahadevan, R., \\& Quatert, E. 1998, in \nThe Theory of Black Hole Accretion Discs, \ned. M. A. Abramowicz, G. Bjornsson, \\& J. E. Pringle, \n(Cambridge University Press), 148\n\n\\bibitem[Navarro, Frenk, \\& White(1997)]{nfw97} \nNavarro, J.F., Frenk, C.S., \\& White, S.D.M. 1997, \\apj, 490, 493\n\n\\bibitem[Osmer(1981)]{osmer81} \nOsmer, P.S. 1981, \\apj, 247, 762\n\n\\bibitem[Osmer(1998)]{osmer98}\nOsmer, P. S. 1998, in \nASP Conference Series 146, The Young Universe,\ned. S. D'odorico, A. Fontana, E. Giallongo, (San Francisco: ASP), 1\n\n\\bibitem[Peacock \\& Dodds(1994)]{peacock94}\nPeacock, J. A., \\& Dodds, S. J. 1994, \\mnras, 267, 1020\n\n\\bibitem[Peebles(1980)]{peebles80}\nPeebles, P. J. E. 1980, The Large Scale Structure of the\nUniverse (Princeton: Princeton University Press)\n\n\\bibitem[Perlmutter et al.(1999)]{perlmutter99}\nPerlmutter, S., et al. 1999, \\apj, 517, 565\n\n\\bibitem[Phillips et al.(2000)]{phillips00}\nPhillips, J., Croft, R. A. C., Weinberg, D.H., Hernquist, L., Katz, N., \\&\nPettini, M. 2000, \\apj, submitted, astro-ph/0001089\n\n\\bibitem[Press \\& Schechter(1974)]{ps74} \nPress, W.H. \\& Schechter, P. 1974, \\apj, 187, 425 (PS)\n\n\\bibitem[Popowski et al.(1998)]{pwro98} \nPopowski, P.A., Weinberg, D.H., Ryden, B.S., \\& Osmer, P.S. 1998, \\apj, 498, 11\n\n\\bibitem[Richstone et al.(1998)]{richstone98}\nRichstone, D., et al.\\ 1998, Nature, 395 Supp, A14\n\n\\bibitem[Riess et al.(1998)]{riess98}\nRiess, A. G., et al.\\ 1998, \\aj, 116, 1009\n\n\\bibitem[Salucci et al.(1999)]{salucci99}\nSalucci, P., Szuszkiewicz, E., Monaco, P., \\& Danese, L. 1999, \\mnras,\n307, 637\n\n\\bibitem[Salpeter(1964)]{salpeter64}\nSalpeter, E. E. 1964, \\apj, 140, 796\n\n\\bibitem[Schneider, Schmidt, \\& Gunn(1994)]{schneider94}\nSchneider, D. P., Schmidt, M., \\& Gunn, J. E. 1994, \\aj, 107, 1245\n\n\\bibitem[Shanks \\& Boyle(1994)]{shanks94} \nShanks, T. \\& Boyle, B.J. 1994, \\mnras, 271, 753\n\n\\bibitem[Shanks et al.(1987)]{shanks87}\nShanks, T., Fong, R., Boyle, B.J., \\& Peterson, B.A. 1987, \\mnras, 227, 739\n\n\\bibitem[Shanks et al.(2000)]{shanks00}\nShanks, T., Boyle, B.J., Croom, S.M., Loaring, N., Miller, L., Smith, R.J.\n2000, in Clustering at High Redshift, eds. A. Mazure, O. LeFevre, V. Lebrun, \n{\\it in press}, astro-ph/0003206\n\n\\bibitem[Shaver(1984)]{shaver84}\nShaver, P.A. 1984, \\aap, 136, L9\n\n\\bibitem[Stephens et al.(1997)]{stephens97} \nStephens, A.W., Schneider, D.P., Schmidt, M., Gunn, J.E., \\& Weinberg, D.H. \n1997, \\aj, 114, 41\n\n\\bibitem[Sugiyama(1995)]{sugiyama95}\nSugiyama, N. 1995, \\apjs, 100, 281\n\n\\bibitem[Tegmark \\& Zaldarriaga(2000)]{tegmark00}\nTegmark, M. \\& Zaldarriaga, M. 2000, \\apj, {\\it in press}, astro-ph/0002091\n\n\\bibitem[Turner(1991)]{turner91}\nTurner, E. L. 1991, \\aj, 101, 5\n\n\\bibitem[van der Marel(1999)]{marel99}\nvan der Marel, R. P. 1999, \\aj, 117, 744\n\n\\bibitem[Warren, Hewett, \\& Osmer(1994)]{who94} \nWarren, S.J., Hewett, P.C., \\& Osmer, P.S. 1994, \\apj, 421, 412\n\n\\bibitem[Weinberg et al.(1999)]{weinberg99}\nWeinberg, D. H., Croft, R. A. C., Hernquist, L., Katz, N., \\& Pettini, M. 1999,\n\\apj, 522, 563\n\n\\bibitem[White, Efstathiou, \\& Frenk(1993)]{white93}\nWhite, S. D. M., Efstathiou, G. P., \\& Frenk, C. S. 1993, \\mnras, 262, 1023\n\n\\bibitem[Webster(1982)]{webster82}\nWebster, A. 1982, \\mnras, 199, 683\n\n\\bibitem[York et al.(2000)]{york00}\nYork, D., et al. 2000, \\aj, {\\it in press}\n\n\\bibitem[Zel'dovich \\& Novikov(1964)]{zeldovich64}\nZel'dovich, Ya. B. \\& Novikov, I.D. 1964, Sov. Phys. Dokl., 158, 811\n\n\\end{thebibliography}{}\n\n\\end{document}\n"
}
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[
{
"name": "astro-ph0002384.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Adelberger et al.(1998)]{adelberger98}\nAdelberger, K. L., Steidel, C. C., Giavalisco, M., Dickinson, M.,\nPettini, M., \\& Kellogg, M. 1998, \\apj, 505, 18\n\n\\bibitem[Bahcall et al.(1999)]{bahcall99}\nBahcall, N. A., Ostriker, J. P., Perlmutter, S., \\& Steinhardt, P. J. 1999,\nScience, 284, 1481\n\n\\bibitem[Baugh \\& Efstathiou(1993)]{baugh93}\nBaugh, C. M., \\& Efstathiou, G. 1993, \\mnras, 265, 145\n\n\\bibitem[Bajtlik, Duncan, \\& Ostriker(1988)]{bajtlik88}\nBajtlik, S., Duncan, R.C., \\& Ostriker, J.P. 1988, \\apj, 327, 570\n\n\\bibitem[Bardeen et al.(1986)]{bbks86} \nBardeen, J., Bond, J.R., Kaiser, N., \\& Szalay, A.S. 1986, \\apj, 304, 15\n\n\\bibitem[Bechtold(1994)]{bechtold94}\nBechtold, J., 1994, \\apjs, 91, 1\n\n\\bibitem[Blumenthal et al.(1984)]{blumenthal84}\nBlumenthal, G.R., Faber, S.M., Primack, J.R., \\& Rees, M.J. 1984, \n\\nat, 311, 517\n\n\\bibitem[Bond et al.(1991)]{bond91}\nBond, J. R., Cole, S., Efstathiou, G., \\& Kaiser, N. 1991, \\apj, 379, 440\n\n\\bibitem[Boyle et al.(1990)]{boyle90} \nBoyle, B.J., Fong, R., Shanks, T., \\& Peterson, B.A. 1990, \\mnras, 243, 1\n\n\\bibitem[Boyle et al.(1999)]{boyle99}\nBoyle, B. J., Smith, R.\nJ., Shanks, T., Croom, S. M. \\& Miller, L. 1999, in IAU Symp. 183:\nCosmological Parameters and the Evolution of the Universe, ed. K. Sato,\n(Kluwer: Dordrecht), p. 178\n\n\\bibitem[Boyle et al.(2000)]{boyle00}\nBoyle, B.J., Shanks, T., Croom, S.M., Smith, R.J., Miller, L., Loaring, N., \n\\& Heymans, C. 2000, \\mnras, {\\it in press} astro-ph/0005368\n\n\\bibitem[Bunn \\& White(1997)]{bunn97}\nBunn, E. F., \\& White, M. 1997, \\apj, 480, 6\n\n\\bibitem[Carroll, Press, \\& Turner(1992)]{carroll92}\nCarroll, S. M., Press, W. H., \\& Turner, E. L. 1992, \\araa, 30, 499\n\n\\bibitem[Ciotti \\& Ostriker(1999)]{ciotti99}\nCiotti, L., \\& Ostriker, J. P. 1999, \\apj, {\\it submitted}, astro-ph/9912064\n\n\\bibitem[Croft et al.(1999)]{croft99}\nCroft, R. A. C., Weinberg, D. H., Pettini, M., Katz, N., \\& Hernquist, L. 1999,\n\\apj, 520, 1\n\n\\bibitem[Croom \\& Shanks(1996)]{croom96} \nCroom, S.M. \\& Shanks, T. 1996, \\mnras, 281, 893\n\n\\bibitem[Efstathiou \\& Rees(1988)]{efstathiou88}\nEfstathiou, G. \\& Rees, M. J. 1988, \\mnras, 230, 5P\n\n\\bibitem[Eke, Cole, \\& Frenk(1996)]{eke96}\nEke, V. R., Cole, S., \\& Frenk, C. S. 1996, \\mnras, 282, 263\n\n\\bibitem[Faber \\& Jackson(1976)]{faber76}\nFaber, S. M. \\& Jackson, R. E. 1976, \\apj, 204, 668\n\n\\bibitem[Fan et al.(1999)]{fan99}\nFan, X., et al.\\ 1999, \\aj, 118, 1\n\n\\bibitem[Haehnelt \\& Rees(1993)]{haehnelt93} \nHaehnelt, M.G. \\& Rees, M.J. 1993, \\mnras, 263, 168\n\n\\bibitem[Haehnelt, Natarajan, \\& Rees(1998)]{haehnelt98}\nHaehnelt, M. G., Natarajan, P., \\& Rees, M. J. 1998, \\mnras, 300, 817\n\n\\bibitem[Haiman \\& Hui(2000)]{haiman00}\nHaiman, Z. \\& Hui, L. 2000, \\apj, submitted, astro-ph/0002190\n\n\\bibitem[Haiman \\& Loeb(1998)]{haiman98}\nHaiman, Z. \\& Loeb, A. 1998, \\apj, 503, 505\n\n\\bibitem[Heath(1977)]{heath77}\nHeath, D. J. 1977, \\mnras, 179, 351\n\n\\bibitem[Hewett, Foltz, \\& Chaffee(1993)]{hewett93}\nHewett, P.C., Foltz, C.B., \\& Chaffee, F.C. 1993, \\apj, 406, L43\n\n\\bibitem[Hogg(1999)]{hogg99} \nHogg, D.W. 1999, astro-ph/9905116\n\n\\bibitem[Iovino \\& Shaver(1988)]{iovino88}\nIovino, A. \\& Shaver, P.A. 1988, \\apj, 330, L13\n\n\\bibitem[Jing(1998)]{jing98}\nJing, Y.P. 1998, \\apj, 503, L9\n\n\\bibitem[Kaiser(1984)]{kaiser84}\nKaiser, N. 1984, \\apj, 294, L9\n\n\\bibitem[Katz, Hernquist, \\& Weinberg(1999)]{katz99}\nKatz, N., Hernquist, L., \\& Weinberg, D. H. 1999, \\apj, 523, 463\n\n\\bibitem[Katz et al.(1994)]{katz94}\nKatz, N., Quinn, T., Bertschinger, E., \\& Gelb, J. M. 1994,\n\\mnras, 270, L71\n\n\\bibitem[Kauffmann \\& Haehnelt(2000)]{kauffmann00}\nKauffmann, G., \\& Haehnelt, M. 2000, \\mnras, 311, 576\n\n\\bibitem[Kolatt et al.(1999)]{kolatt99}\nKolatt, T. S., et al. 1999, \\apjl, 523, L109 \n\n\\bibitem[Kundi\\'c(1997)]{kundic97} \nKundi\\'c, T. 1997, \\apj, 482, 631\n\n\\bibitem[La Franca et al.(1998)]{lafranca98}\nLa Franca, F., Andreani, P., \\& Cristiani, S. 1998, \\apj, 497, 529\n\n\\bibitem[Lacey \\& Cole(1993)]{lc93} \nLacey, C. \\& Cole, S. 1993, \\mnras, 262, 649 \n\n\\bibitem[Lynden-Bell(1969)]{lyndenbell69}\nLynden-Bell, D. 1969, Nature, 223, 690\n\n\\bibitem[Magorrian et al.(1998)]{mag98} \nMagorrian, J., et al. 1998, \\aj, 115, 2285\n\n\\bibitem[McDonald et al.(2000)]{mcdonald00}\nMcDonald, P., Miralda-Escud\\'e, J., Rauch, M., Sargent, W. L. W.,\nBarlow, T. A., Cen, R., \\& Ostriker, J. P. 2000, \\apj, submitted,\nastro-ph/9911196\n\n\\bibitem[Melchiorri et al.(1999)]{melchiorri99}\nMelchiorri, A. et al.\\ 1999, \\apjl, in press, astro-ph/9911445\n\n\\bibitem[Miller et al.(1999)]{miller99}\nMiller, A. D. et al.\\ 1999, \\apj, 524, L1\n\n\\bibitem[Mo \\& White(1996)]{mw96} \nMo, H.J. \\& White, S.D.M. 1996, \\mnras, 282, 347 (MW)\n\n\\bibitem[Mo, Mao, \\& White(1999)]{mmw99} \nMo, H.J., Mao, S., \\& White, S.D.M. 1999, \\mnras, 304, 175\n\n\\bibitem[Monaco, Salucci, \\& Danese(2000)]{monaco00}\nMonaco, P., Salucci, P., \\& Danese, L. 2000, \\mnras, 311, 279\n\n\\bibitem[Narayan, Mahadevan, \\& Quatert(1998)]{narayan98}\nNarayan, R., Mahadevan, R., \\& Quatert, E. 1998, in \nThe Theory of Black Hole Accretion Discs, \ned. M. A. Abramowicz, G. Bjornsson, \\& J. E. Pringle, \n(Cambridge University Press), 148\n\n\\bibitem[Navarro, Frenk, \\& White(1997)]{nfw97} \nNavarro, J.F., Frenk, C.S., \\& White, S.D.M. 1997, \\apj, 490, 493\n\n\\bibitem[Osmer(1981)]{osmer81} \nOsmer, P.S. 1981, \\apj, 247, 762\n\n\\bibitem[Osmer(1998)]{osmer98}\nOsmer, P. S. 1998, in \nASP Conference Series 146, The Young Universe,\ned. S. D'odorico, A. Fontana, E. Giallongo, (San Francisco: ASP), 1\n\n\\bibitem[Peacock \\& Dodds(1994)]{peacock94}\nPeacock, J. A., \\& Dodds, S. J. 1994, \\mnras, 267, 1020\n\n\\bibitem[Peebles(1980)]{peebles80}\nPeebles, P. J. E. 1980, The Large Scale Structure of the\nUniverse (Princeton: Princeton University Press)\n\n\\bibitem[Perlmutter et al.(1999)]{perlmutter99}\nPerlmutter, S., et al. 1999, \\apj, 517, 565\n\n\\bibitem[Phillips et al.(2000)]{phillips00}\nPhillips, J., Croft, R. A. C., Weinberg, D.H., Hernquist, L., Katz, N., \\&\nPettini, M. 2000, \\apj, submitted, astro-ph/0001089\n\n\\bibitem[Press \\& Schechter(1974)]{ps74} \nPress, W.H. \\& Schechter, P. 1974, \\apj, 187, 425 (PS)\n\n\\bibitem[Popowski et al.(1998)]{pwro98} \nPopowski, P.A., Weinberg, D.H., Ryden, B.S., \\& Osmer, P.S. 1998, \\apj, 498, 11\n\n\\bibitem[Richstone et al.(1998)]{richstone98}\nRichstone, D., et al.\\ 1998, Nature, 395 Supp, A14\n\n\\bibitem[Riess et al.(1998)]{riess98}\nRiess, A. G., et al.\\ 1998, \\aj, 116, 1009\n\n\\bibitem[Salucci et al.(1999)]{salucci99}\nSalucci, P., Szuszkiewicz, E., Monaco, P., \\& Danese, L. 1999, \\mnras,\n307, 637\n\n\\bibitem[Salpeter(1964)]{salpeter64}\nSalpeter, E. E. 1964, \\apj, 140, 796\n\n\\bibitem[Schneider, Schmidt, \\& Gunn(1994)]{schneider94}\nSchneider, D. P., Schmidt, M., \\& Gunn, J. E. 1994, \\aj, 107, 1245\n\n\\bibitem[Shanks \\& Boyle(1994)]{shanks94} \nShanks, T. \\& Boyle, B.J. 1994, \\mnras, 271, 753\n\n\\bibitem[Shanks et al.(1987)]{shanks87}\nShanks, T., Fong, R., Boyle, B.J., \\& Peterson, B.A. 1987, \\mnras, 227, 739\n\n\\bibitem[Shanks et al.(2000)]{shanks00}\nShanks, T., Boyle, B.J., Croom, S.M., Loaring, N., Miller, L., Smith, R.J.\n2000, in Clustering at High Redshift, eds. A. Mazure, O. LeFevre, V. Lebrun, \n{\\it in press}, astro-ph/0003206\n\n\\bibitem[Shaver(1984)]{shaver84}\nShaver, P.A. 1984, \\aap, 136, L9\n\n\\bibitem[Stephens et al.(1997)]{stephens97} \nStephens, A.W., Schneider, D.P., Schmidt, M., Gunn, J.E., \\& Weinberg, D.H. \n1997, \\aj, 114, 41\n\n\\bibitem[Sugiyama(1995)]{sugiyama95}\nSugiyama, N. 1995, \\apjs, 100, 281\n\n\\bibitem[Tegmark \\& Zaldarriaga(2000)]{tegmark00}\nTegmark, M. \\& Zaldarriaga, M. 2000, \\apj, {\\it in press}, astro-ph/0002091\n\n\\bibitem[Turner(1991)]{turner91}\nTurner, E. L. 1991, \\aj, 101, 5\n\n\\bibitem[van der Marel(1999)]{marel99}\nvan der Marel, R. P. 1999, \\aj, 117, 744\n\n\\bibitem[Warren, Hewett, \\& Osmer(1994)]{who94} \nWarren, S.J., Hewett, P.C., \\& Osmer, P.S. 1994, \\apj, 421, 412\n\n\\bibitem[Weinberg et al.(1999)]{weinberg99}\nWeinberg, D. H., Croft, R. A. C., Hernquist, L., Katz, N., \\& Pettini, M. 1999,\n\\apj, 522, 563\n\n\\bibitem[White, Efstathiou, \\& Frenk(1993)]{white93}\nWhite, S. D. M., Efstathiou, G. P., \\& Frenk, C. S. 1993, \\mnras, 262, 1023\n\n\\bibitem[Webster(1982)]{webster82}\nWebster, A. 1982, \\mnras, 199, 683\n\n\\bibitem[York et al.(2000)]{york00}\nYork, D., et al. 2000, \\aj, {\\it in press}\n\n\\bibitem[Zel'dovich \\& Novikov(1964)]{zeldovich64}\nZel'dovich, Ya. B. \\& Novikov, I.D. 1964, Sov. Phys. Dokl., 158, 811\n\n\\end{thebibliography}"
}
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astro-ph0002385
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WHERE DO COOLING FLOWS COOL?
|
[
{
"author": "Fabrizio Brighenti$^{1,2}$ and William G. Mathews$^1$"
}
] |
Typically $\sim 5$ percent of the total baryonic mass in luminous elliptical galaxies is in the form of cooled interstellar gas. Although the mass contributed by cooled gas is small relative to the mass of the old stellar system in these galaxies, it is almost certainly concentrated within the optical effective radius where it can influence the local dynamical mass. However, the mass of cooled gas cannot be confined to very small galactic radii ($r \lta 0.01r_e$) since its mass would greatly exceed that of known central mass concentrations in giant ellipticals, normally attributed to massive black holes. We explore the proposition that a population of very low mass, optically dark stars is created from the cooled gas. For a wide variety of assumed radial distributions for the interstellar cooling, we find that the mass of cooled gas contributes significantly ($\sim$30 percent) to stellar dynamical mass to light ratios which, as a result, are expected to vary with galactic radius. However, if the stars formed from cooled interstellar gas are optically luminous, their pertubation on the the mass to light ratio of the old stellar population may be reduced. Cooling mass dropout also perturbs the local apparent X-ray surface brightness distribution, often in a positive sense for centrally concentrated cooling. In general the computed X-ray surface brightness exceeds observed values within $r_e$, suggesting the presence of additional support by magnetic stresses or non-thermal pressure. The mass of cooled gas inside $r_e$ is sensitive to rate that old stars lose mass ${\dot M_*}$, but this rate is nearly independent of the initial mass function of the old stellar population.
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[
{
"name": "aasdropout2table.tex",
"string": "% file: aasdropout.tex \n%**********************AASTEX v4.0************************\n% ApJ Macro\n% DOCUMENT STYLE COMMANDS\n%\n% TWO-COLUMN PREPRINT SUBSTYLE\n%\\documentstyle[twocolumn,aas2pp4]{article}\n%\n% GENERAL ARTICLE STYLE\n%\\documentstyle[12pt]{article}\n%\n%\n% WORKING MANUSCRIPT STYLE (text extends over the full page)\n% AND STYLE FOR ELECTRONIC SUBMISSION\n%\\documentstyle[12pt,aasms4]{article}\n%\n% APJ PREPRINT STYLE (text is split into two half pages)\n%\\documentstyle[aaspp4]{article}\n%\n%\n%\n%\n%************************AASTEX v5.0***********************\n%\n%\n% AASTEX v5.0 commands:\n% DOCUMENT STYLE COMMANDS\n%\n% TWO-COLUMN PREPRINT SUBSTYLE\n\\documentclass[preprint2]{aastex}\n%\n% GENERAL ARTICLE STYLE\n%\\documentclass[preprint]{aastex}\n%\n%\n% WORKING MANUSCRIPT STYLE (text extends over the full page)\n% AND STYLE FOR ELECTRONIC SUBMISSION\n%\\documentclass[manuscript]{aastex}\n%\n% APJ PREPRINT STYLE (text is split into two half pages)\n%\\documentstyle[aaspp4]{article}\n\n\n% set up some macros (based on ``TEX by Example'' page 131):\n\\def\\stacksymbols #1#2#3#4{\\def\\theguybelow{#2}\n\t\\def\\verticalposition{\\lower#3pt}\n\t\\def\\spacingwithinsymbol{\\baselineskip0pt\\lineskip#4pt}\n\t\\mathrel{\\mathpalette\\intermediary#1}}\n\\def\\intermediary #1#2{\\verticalposition\\vbox{\\spacingwithinsymbol\n\t\\everycr={}\\tabskip0pt\n\t\\halign{$\\mathsurround0pt#1\\hfil##\\hfil$\\crcr#2\\crcr\n\t\t\\theguybelow\\crcr}}}\n\\def\\lta{\\stacksymbols{<}{\\sim}{2.5}{.2}}\n\\def\\gta{\\stacksymbols{>}{\\sim}{3}{.5}}\n\\def\\approxprop{\\stacksymbols{\\propto}{\\sim}{3}{.5}}\n\n%\n%\n\\begin{document}\n\n\\title{WHERE DO COOLING FLOWS COOL?}\n\n%\\title{DISTRIBUTED COOLING IN GALACTIC COOLING FLOWS -- \n%INFLUENCE ON X-RAY IMAGES AND MASS TO LIGHT RATIOS}\n\n%\\title{INFLUENCE OF COOLED INTERSTELLAR GAS \n%ON DYNAMICAL MASS TO LIGHT RATIOS OF ELLIPTICAL GALAXIES}\n\n%\n%\\title{WHERE DOES GAS COOL IN GALACTIC COOLING FLOWS?}\n\n%\\title{CONSTRAINTS ON THE ENDSTATE OF GAS THAT COOLS IN \n%GALACTIC COOLING FLOWS}\n\n%\\title{A CENSUS OF MASS DEPOSITED BY COOLING FLOWS \n%IN ELLIPTICAL GALAXIES}\n\n\\author{Fabrizio Brighenti$^{1,2}$ and William G. Mathews$^1$}\n\n\\affil{$^1$University of California Observatories/Lick Observatory,\nBoard of Studies in Astronomy and Astrophysics,\nUniversity of California, Santa Cruz, CA 95064\\\\\nmathews@lick.ucsc.edu}\n\n\\affil{$^2$Dipartimento di Astronomia,\nUniversit\\`a di Bologna,\nvia Ranzani 1,\nBologna 40127, Italy\\\\\nbrighenti@bo.astro.it}\n\n\n\n%\\vskip 2.in\n%\\noindent\n%Received:\n\n%\\noindent\n%PROOFS TO BE SENT TO:\n\n%\\noindent\n%Lick Observatory\n\n%\\noindent\n%Santa Cruz, CA 95064\n\n%\\noindent\n%$^1$UCO/Lick Observatory Bulletin No.\n\n\n\\vskip .2in\n\n\\begin{abstract}\n\nTypically $\\sim 5$ percent of the total baryonic mass in luminous\nelliptical galaxies is in the form of cooled interstellar gas.\nAlthough the mass contributed by cooled gas is small relative to the\nmass of the old stellar system in these galaxies, it is almost\ncertainly concentrated within the optical effective radius where it\ncan influence the local dynamical mass. However, the mass of cooled\ngas cannot be confined to very small galactic radii ($r \\lta 0.01r_e$)\nsince its mass would greatly exceed that of known central mass\nconcentrations in giant ellipticals, normally attributed to massive\nblack holes. We explore the \nproposition that a population of very low mass, optically\ndark stars is created from the cooled gas. For a wide variety of\nassumed radial distributions for the interstellar cooling, we find\nthat the mass of cooled gas contributes significantly ($\\sim$30\npercent) to stellar dynamical mass to light ratios which, as \na result, are expected to vary with galactic radius. \nHowever, if the stars formed from cooled interstellar gas are \noptically luminous, their pertubation on the the mass to light \nratio of the old stellar population may be reduced.\nCooling mass dropout also\nperturbs the local apparent X-ray surface brightness distribution,\noften in a positive sense for centrally concentrated cooling. In\ngeneral the computed X-ray surface brightness exceeds observed values\nwithin $r_e$, suggesting the presence of additional support by\nmagnetic stresses or non-thermal pressure. The mass of cooled gas\ninside $r_e$ is sensitive to rate that old stars lose mass ${\\dot\nM_*}$, but this rate is nearly independent of the initial mass\nfunction of the old stellar population.\n\n\\end{abstract}\n\n\\keywords{galaxies: elliptical and lenticular -- \ngalaxies: evolution --\ngalaxies: cooling flows --\ngalaxies: interstellar medium --\nx-rays: galaxies}\n\n\\section{INTRODUCTION}\n\nPerhaps the most perplexing and long-standing problem \nassociated with galactic and cluster cooling flows is the \nuncertain physical nature and spatial distribution \nof the gas that cools. \nThe apparent absence of large \nmasses of cooled gas in elliptical \ngalaxies has led some \nto argue that little or no cooling actually occurs \nand to postulate some source of heating that offsets \nthe radiative losses in X-ray emission. \nBut the energy required to balance \nradiative losses is prohibitively large and \nappropriate heating sources may not be universally \navailable.\nIf the expected radiative cooling actually occurs, \ntwo questions arise:\n(1) What is the nature of the objects \nthat condense from the hot gas? and \n(2) Where is most of the cooled mass located \nin the galaxy?\nRegarding the first question, \na variety of physical arguments support the \nhypothesis, or even the inevitability, \nof low mass star formation \n(Fabian, Nulsen \\& Canizares 1982; \nThomas 1986;\nCowie \\& Binney 1988;\nVedder, Trester, \\& Canizares 1988;\nSarazin \\& Ashe 1989;\nFerland, Fabian \\& Johnstone 1994; \nMathews \\& Brighenti 1999).\nHere we shall address the second question in the \ncontext of cooling flows in elliptical galaxies where \nthe known stellar mass and light profiles \nstrongly constrain the spatial distribution of cooled gas.\n\nWe adopt the generally accepted hypothesis that only \nstars of very low mass (e.g. $\\lta 0.1$ $M_{\\odot}$) \nform in cooling flows (e.g. Ferland, Fabian \\& Johnstone 1994), \nso that the mass to light ratio of the young stellar population \nformed from the cooling gas is essentially infinite.\nIn view of the difficulties we encounter with this \nhypothesis, described below, \nit seems more likely that the stellar population \nformed from cooled gas extends to somewhat more \nmassive stars that are optically luminous.\n\nOur gas dynamical models for the evolution of hot interstellar \ngas in giant ellipticals indicate that the origin \nof the gas varies with galactic radius.\nMost of the gas in the inner, optically luminous \nregions originates from the ejected envelopes of \nevolving stars; gas in the outer halo is supplied by \ncosmological secondary infall or tidal acquisitions from \nneighboring galaxies (Mathews \\& Brighenti 1998b). \nCircumgalactic gas around massive ellipticals is enriched \nby Type II supernovae that accompanied early star formation. \nThe variability of circumgalactic gas among luminous \nellipticals is responsible for some of the \nenormous dispersion in X-ray luminosity $L_x$ \namong ellipticals of similar \noptical luminosity $L_B$ (Mathews \\& Brighenti 1998a).\n\nSince the hot interstellar gas in a bright elliptical \nemits observable X-rays,\nit is clearly losing energy.\nHowever, as the gas loses energy \nit is compressed toward the galactic center by gravitational \nforces and $Pdv$ work maintains the high temperatures observed,\n$T \\sim 10^7$ K, producing a galactic cooling flow. \nThe positive interstellar temperature gradients typically observed\nwithin\na few effective radii are often cited as evidence of radiative\ncooling in a cooling flow,\nbut this cooling is due instead to the mixing\nof somewhat cooler, locally virialized gas ejected from stars\nwith hotter gas arriving from larger galactic\nradii (Mathews \\& Brighenti 1998b; Brighenti \\& Mathews 1998, \n1999a).\nIf large entropy fluctuations are present in the hot \ngas, catastrophic \ncooling can occur at any radius in the flow.\nRegions of low entropy (low temperature, high density) \nradiate more and cool sooner. \nThe amplitude distribution of entropy fluctuations \nin the interstellar gas \ndetermines the radius \nwhere cooling mass dropout occurs in the cooling flow. \nFor example, if the entropy in some region in the flow \nis only slightly less than in the ambient flow,\nthe differential radiative cooling will be \nsmall and the region will cool out of the flow \nat small galactic radii; conversely, localized regions with \nentropy much lower than the ambient flow \ncool rapidly and deposit their mass at large radii.\nSome possible sources of interstellar entropy variations are \nstellar winds, \nexplosions of Type Ia supernovae, non-uniform SNII heating \nat early times, and \nmergers with small, gas-rich galaxies. \n\nThe total rate that mass cools and drops out of the flow \nis closely related to the X-ray luminosity $L_x$.\nThe X-ray luminosity can be approximately expressed as the \nproduct of the total cooling rate ${\\dot M}$ and the \nenthalpy per gram in the hot gas, or \n$${\\dot M} = \\left({2 \\mu m_p \\over 5 k T}\\right) L_{x,bol}\n\\approx 2.5 M_{\\odot} {\\rm yr}^{-1}.$$\nHere we have used data from the giant Virgo elliptical \nNGC 4472: $T \\approx 1.3 \\times 10^7$ K; \n$L_x(0.5 - 4.5 ~{\\rm keV}) = 4.5 \\times 10^{41}$;\n$L_{x,bol} \\approx 1.6 L_x(0.5 - 4.5 ~{\\rm keV})$.\nIf $L_x$ and $T$ are reasonably constant over the Hubble time, \na mass $M_{cg} \\approx 3 \\times 10^{10}$ \n$M_{\\odot}$ of cold gas is expected to condense from the \nhot ISM somewhere within NGC 4472.\nAlthough this mass is very large, it is only about 4 percent \nof the total stellar mass in NGC 4472 today.\nThe mass that cools can therefore be ignored \nif it is widely distributed throughout the galactic volume.\nHowever, the central concentration of H$\\alpha$ emission \nin ellipticals (e.g. Macchetto et al. 1996) \nsuggests that the cooling \nis concentrated toward the galactic \ncenter where the interstellar density is highest \nand the bulk of the X-ray energy is emitted. \n\nThe motivation of this paper is to explore \na variety of options for the mass dropout profile of cooled \ngas in bright ellipticals appropriately constrained by \nthe known radial distributions of total stellar and \nnon-baryonic mass. \nThe radial mass dropout profile of cooled gas \ncannot be determined from first principles \nbecause the distribution and amplitude of \nthe entropy and magnetic fluctuations in the hot gas\nare unknown and difficult to evaluate \nfrom simple physical arguments.\nNevertheless, the total mass of cooled gas inside an \neffective (half-light) radius $r_e$ must be consistent \nwith the mass to light ratio determined from stellar velocities \nand with the total mass \ninferred from X-ray observations within $r_e$. \nAssuming that the stellar mass to light ratio is \nuniform with radius, the stellar mass $M_*(r)$ and the \nX-ray mass $M_x(r)$ appear to be in nearly perfect agreement \nfor two bright Virgo ellipticals \nin the range $0.1r_e \\lta r \\lta r_e$ \n(Brighenti \\& Mathews 1997a). \nBecause of \nconstraints on the mass distribution of cooled gas \nprovided by X-ray and stellar dynamical observations,\ngalactic cooling flows provide a critical venue for testing \nthe physics of mass deposition in cooling flows.\n\nThe mass of cold ($T \\lta 10^4$ K) gas $M_{cg}$ \nactually observed \nin ellipticals is many orders of magnitude less than \nthe total cooled mass estimated above. \nFor example, neither HI nor H$_2$ gas has been observed in NGC 4472, \nonly upper limits, $M_{cg} \\lta 10^7$ $M_{\\odot}$\n(Bregman, Roberts \\& Giovanelli 1988;\nBraine, Henkel \\& Wiklind 1988). \nIf stars form they must either be indistinguishable from \nthe old stellar population or non-luminous.\nWe explore here the possibility that most of the \ncooled gas forms dense baryonic clouds or stars \nthat are dark at optical and radio frequencies.\nThe very low mass stars advanced by \nFerland, Fabian \\& Johnstone (1994) \nsatisfy this invisibility criterion, \nwhile the star formation models of \nMathews \\& Brighenti (1999) indicate that \n(luminous) stars of mass $\\sim 1 - 2$ $M_{\\odot}$ can form \nin galactic cooling flows.\n\nX-ray studies indicate significant masses of \ncold, absorbing gas in cluster and galactic cooling flows \n(e.g. White et al. 1991; Allen et al. 1993;\nFabian et al. 1994; Allen \\& Fabian 1997; Buote 1999), \nbut these results are inconsistent with \nthe absence of radio frequency emission \nfrom the cold gas (Braine \\& Dupraz 1994; \nDonahue \\& Vogt 1997) and should \nbe regarded as controversial until this inconsistency is resolved. \nEven taken at face value, the total mass of cooled gas implied \nby the X-ray absorption in cluster cooling flows \nis typically only a small fraction of the \ntotal mass that should have cooled in a Hubble time\n(Allen \\& Fabian 1997;\nWise \\& Sarazin 1999), implying that most of the \ncooled gas may have formed stars. \nIf cooled gas forms into small stars,\nthese stars will have apogalatica near their point of origin \nwhere they will spend most of their orbital time. \nWe shall assume that the gas mass that cools and drops out of the \nflow contributes optically dark (stellar) \nmass at the radius where the cooling occurred. \n\nIn the following we describe \na series of gas dynamical calculations for the evolution of \nX-ray emitting interstellar gas over the Hubble time \nand investigate a variety \nof assumptions about the radial distribution of \noptically dark cooled gas.\nTo be specific,\nwe compare our models with \nthe well-observed massive elliptical NGC 4472.\nWe find that the mass of cooled gas contributes \nsignificantly to dynamical mass to light determinations \nwithin $r_e$ based on stellar velocities. \n\n\\section{KNOWN STELLAR AND DARK MASS DISTRIBUTION IN NGC 4472}\n\nThe E2 elliptical NGC 4472 is a luminous, slowly rotating \n[$(v/\\sigma)_* = 0.43$] galaxy in the Virgo cluster. \nWith an adopted distance $d = 17$ Mpc, its optical luminosity \nis $L_B = 7.89 \\times 10^{10}$ $L_{B\\odot}$ and its \nhalf light or effective radius \n$r_e = 1.733'$ is $8.57$ kpc (Faber et al. 1989).\nThe total stellar mass \n$M_{*t} = 7.26 \\times 10^{11}$ $M_{\\odot}$ is found \nfrom the \nmass to light ratio $M/L_B = 9.2$ determined by \nvan der Marel (1991) with a two-integral \nstellar distribution function.\nThis mass to light ratio is appropriate to the \ngalactic region within about 0.4$r_e$ where \nstellar velocities are well determined, \nalthough the mass determined from X-ray observations \nsuggests that $M/L_B$ remains constant to at least $r_e$\n(Brighenti \\& Mathews 1997a).\nIf $M/L_B$ is spatially constant, the stellar \nmass also has a de Vaucouleurs profile.\nWithin a central core or break radius \n$r_b = 2.41''$ ($200$ pc) the stellar density \nprofile flattens (Faber et al. 1997), but \nwe shall not consider this small feature here.\nNGC 4472 contains a central black \nhole of mass $M_{bh} = 2.9 \\times 10^9$ $M_{\\odot}$\n(Magorrian et al. 1998).\n\nThe total mass distribution in luminous ellipticals can \nmost easily be determined \nfrom the radial variation of density \nand temperature in the \nhot interstellar gas, assuming hydrostatic equilibrium.\nFigure 1 illustrates the interstellar density and temperature \nprofiles in NGC 4472.\nThe filled circles in Figure 1 \nare {\\it Einstein} HRI observations \n(Trinchieri, Fabbiano \\& Canizares 1986) and \nopen circles are ROSAT HRI and PSPC data \nfrom Irwin \\& Sarazin (1996) \n(also see Forman et al. 1993).\nThe $T(r)$ and $n(r)$ profiles have been fit with \nanalytic curves as described by Brighenti \\& Mathews \n(1997a).\n\nHydrostatic equilibrium in the hot interstellar gas \nis an excellent approximation \nsince the cooling flow velocity is very subsonic. \nThe total mass interior to radius $r$ determined from X-ray \nobservations is \n\\begin{equation}\nM_{x}(r) = - {k T(r) r \\over G \\mu m_p }\n\\left( {d \\log \\rho \\over d \\log r} + {d \\log T \\over d \\log r}\n+ {P_m \\over P} ~ {d \\log P_m \\over d \\log r} \\right)\n\\end{equation}\nwhere $m_p$ is the proton mass and $\\mu = 0.61$ is the \nmean molecular weight.\nThe last term, representing the possibility of\nmagnetic pressure $P_m = B^2/8 \\pi$, is negative\nif $d P_m / dr < 0$ as seems likely.\nIf the magnetic term is important but not included, \nthe total mass will be underestimated. \nAssuming $P_m = 0$,\nthe total mass $M_x(r)$ in NGC 4472 is shown \nwith a solid line in Figure 1b.\n\nIn the outer halo, $r \\gta r_e$,\nthe total mass is dominated by the dark halo. \nThe dark halo mass distribution in NGC 4472 \ncan be approximated with an NFW halo profile \n(Navarro, Frenk \\& White 1996) \nof virial mass $M_h = 4 \\times 10^{13}$ $M_{\\odot}$ \nalthough the \nobserved halo is somewhat less centrally peaked \nthan NFW (Brighenti \\& Mathews 1999a).\nWithin $r_e$ the contribution of the dark \nNFW halo mass \nin the model is small;\nfor example at $r < r_e/3$ the total mass to light ratio \nis $M/L_B = 10.18$, only 10 percent greater than the dynamic \nvalue 9.2 determined in $r \\lta 0.4r_e$. \n\nIt is remarkable that \nthe total mass found from the X-ray data $M_x(r)$ \nis nearly identical to the \nexpected dynamical mass $M_*(r)$ \n(based on stellar velocities and $M/L$)\nin the range $0.1r_e \\lta r \\lta r_e$ (Figure 1).\nAn almost identical agreement in this radius range is \nindicated by X-ray observations of another bright \nVirgo elliptical, NGC 4649 (Brighenti \\& Mathews 1997a). \nIn this important region the \nhot gas is confined by the {\\it stellar} potential.\nThe excellent agreement of the stellar and X-ray masses \nsupports the \nconsistency of two radically different mass determinations: \nfrom stellar velocities and from the radial equilibrium of \nhot interstellar gas.\nThe apparent agreement of the X-ray and stellar \nmasses in this range of galactic radii \nalso indicates that the hydrostatic \nsupport of the hot gas is not strongly influenced \nby local magnetic fields and rotation.\n\nHowever, it is not obvious why $M/L_B$ would be constant \nwith galactic radius, particularly when the cooling \ndropout mass is considered, and why the \nagreement between stellar dynamic and \nX-ray masses no longer obtains in the \ncentral regions $r \\lta 0.1 r_e$. \nIn this central region the total mass \nindicated by the X-ray observations in Figure 1 \nis considerably \nless than the expected mass based on an assumed \nde Vaucouleurs profile and constant mass to light ratio. \nThis type of deviation could be due to \nmagnetic or other non-thermal pressure in this region,\nto rotation, or \nto local cooling dropout in the hot interstellar gas. \nThe lower mean temperature in cooling regions lowers\nthe total apparent gas temperature and results in \nan underestimate of the total internal mass \n(equation 1). \n\nWe assume that currently available \n{\\it Einstein} and ROSAT observations are accurate \nin the central region of NGC 4472, $r \\lta 0.1 r_e$. \nThese observations have been reduced assuming \nno (non-Galactic) photoelectric absorption by low temperature \ngas in the central regions.\nIf X-ray absorption is \npresent, the true hot gas density would be \nmore centrally peaked than \nshown in Figure 1 and \nthe total mass indicated by the X-ray observations would \nincrease.\nBuote (1999) finds that two-temperature models fit the \nX-ray spectrum for NGC 4472 quite well.\nThe two temperatures do not necessarily need to be \nspatially mixed; they could also approximately represent \nthe range of the radial \ntemperature variation observed in NGC 4472. \nIn Buote's two temperature model, only the cooler component \n($T \\sim 0.7$ keV located in $r \\lta r_e$) \nrequires an absorption column $N_H = 2.9 \\times 10^{21}$ \ncm$^{-2}$ in excess of the Galactic value.\nHowever, the influence of cold gas having this column density \non the hot gas density plotted in Figure 1 is small.\nFor a worst case example, suppose that absorbing material \nwith column density $N_H = 2.9 \\times 10^{21}$\ncm$^{-2}$ \nis in a disk oriented perpendicular to the line of sight \nand that this disk \nabsorbs {\\it all} X-rays from the back side of the galaxy. \nThe radius of this disk would be $< 370$ pc if it contained \nthe maximum mass $M_{cg} \\sim 10^7$ $M_{\\odot}$ \nallowed by CO and HI observations \n(Bregman, Roberts \\& Giovanelli 1988;\nBraine, Henkel \\& Wiklind 1997) \nor 20 kpc if it contained \nall of the gas that has cooled, $M_{cg} = 3 \\times 10^{10}$\n$M_{\\odot}$.\nThe X-ray surface brightness \nwithin the opaque disk would be reduced by 2, \nbut the corresponding gas density would be lowered by only \n$2^{1/2} = 10^{0.15}$ since the volume emissivity \n$\\propto n^2$. \nSuch a small correction in the density (gradient) \ncould not account for the large mass \ndiscrepancy between the X-ray mass and the \nstellar dynamical mass shown in Figure 1 within 0.1$r_e$.\n\nThe densities and temperatures in Figure 1 \nwere determined from X-ray data \nassuming the abundance of the hot \ngas is uniformly solar. \nSince the gas is likely to be more metal rich at smaller \ngalactic radii (Matsushita 1997; Brighenti \\& Mathews 1999b),\nan allowance for this gradient would tend to lower \nthe derived density gradient and the internal mass, \n{\\it increasing} the discrepancy in $r \\lta 0.1~r_e$ \nin Figure 1 by a small amount.\nIn the following discussion we shall ignore the \nrelatively small possible influence of absorption or metallicity \ngradients on the results shown in Figure 1.\n\n\\section{HYDRODYNAMICAL MODELS}\n\nThe hydrodynamical models we use in this paper are similar \nto those in our recent papers (e.g. Brighenti \\& Mathews 1999a) \nso we provide only a brief review here. \nHot interstellar gas in ellipticals \nhas a dual origin: (i) mass loss from an evolving old stellar \npopulation and (ii) secondary infall into the overdensity \nperturbation that formed the galaxy group within which \nthe elliptical formed by early merging events.\nFor a given set of cosmological parameters, dark \nand baryonic matter flow toward an overdensity region.\nThe dark matter forms an NFW halo, growing in size with \ntime.\nSpherical geometry is assumed.\nWithin the accretion shock at time $t_* = 2$ Gyr, \nwhen enough baryons have accumulated,\nwe form the current de Vaucouleurs stellar profile and \nrelease the energy of all Type II supernovae according \nto a Salpeter IMF (slope: $x = 1.35$, mass limits: \n$m_{\\ell} = 0.08$ and $m_u = 100$ $M_{\\odot}$).\nAll stars greater than 8 $M_{\\odot}$ produce \nType II supernovae each \nof energy $E_{sn} = 10^{51}$ ergs.\nWe assume that \na fraction $\\epsilon_{sn} = 0.8$ of this energy is \ndelivered to the internal energy of the gas.\nWe have shown (Brighenti \\& Mathews 1999b) that \nsuch a galaxy formation scheme can work in a variety of \ncosmologies: flat or low density, \nwith or without a lambda term. \nThe evolution of gas within the optical\neffective radius $r_e$, of most interest \nhere, is insensitive to these cosmological parameters. \nFor simplicity therefore we \nassume a simple flat universe with $\\Omega = 1$, \n$H_o = 50$ km s$^{-1}$ \nMpc$^{-1}$ and $\\Omega_b = 0.05$.\nWe characterize the dark halo with an \nNFW profile (Navarro, Frenk \\& White 1996) having a \nvirial mass $M_h = 4 \\times 10^{13}$ $M_{\\odot}$ \nat the current time $t_n = 13$ Gyrs.\nThe models we discuss here are identical to the \nstandard model of (Brighenti \\& Mathews 1999a) except \nwe now use a finer central spatial zoning (65 pc for the \ninnermost zone), a SNII efficiency $\\epsilon_{sn} = 0.8$, \nand a mass ``dropout'' function $q(r)$ with more \nadjustable parameters (see below).\n\nOur objective is to seek \nsolutions of the gasdynamical equations \nincluding mass dropout that jointly satisfy several \nobservational constraints at time $t_n$:\n(i) the observed hot gas density, temperature \nand X-ray surface brightness profiles,\n(ii) the known dynamical mass in the galactic center \nusually attributed to a massive black hole,\n(iii) the apparent dynamical mass to light ratio \n$M/L_B = 9.2$ determined in $r \\lta 0.4r_e$,\nand\n(iv) an apparent internal mass $M_x(r)$ in $(0.1 - 1)r_e$ \nbased on Equation (1) that agrees with the \nconstant-$(M/L_B)$ de Vaucouleurs profile as shown in \nFigure 1. \n\nThe baryonic component in our models has a complex evolution.\nMuch of the initial \nbaryonic mass is consumed in creating the stellar system. \nWhen the Type II supernova energy is released, \na significant mass of gas is expelled as a galactic wind.\nAfter these early events, the \ninterstellar gas is re-established and sustained \nby stellar mass loss \nand by inflow of circumgalactic gas (secondary infall), most of \nwhich was previously enriched and expelled by SNII. \nWe assume that the stars form during a short epoch that \ncan be described by a single burst Salpeter IMF \nas discussed above.\nThe stellar mass loss rate for this IMF \nvaries as \n$\\dot{M_{*t}} = \\alpha_*(t) M_{*t}$ where\n$\\alpha_*(t) = 4.7 \\times 10^{-20} \n[t/(t_n - t_{*s})]^{-1.3}$ sec$^{-1}$.\nAlthough galactic stars form at $t_{*s} = 1$ Gyr, \ntheir mass loss contribution to the ambient \ninterstellar gas is assumed to begin at a later time,\n$t_* = 2$ Gyrs.\nSince galactic stars have been enriched \nby supernova ejecta, the single burst model cannot \nbe strictly correct, but our approximation \n$\\alpha_*(t < t_* ) = 0$ is \nconsistent with several early \nstarbursts closely spaced in time and allows for metal\nenrichment of old galactic stars that are not in\nthe first single-burst population.\nIf the de Vaucouleurs profile is a result of \nlargely dissipationless merging, \nsome or most of the \nstar formation must have occurred at a time $t_{*s}$ \nbefore the important merging events at $t_* = 2$ Gyrs.\nBy taking $t_{*s} < t_*$ we \nreduce by $\\sim 10^{10}$ $M_{\\odot}$ \nthe total amount of gas ejected by stars \nwithin the galactic potential. \nWe recognize the inconsistencies in these approximations \nof complex stellar formation and dynamical processes\nthat are poorly understood. \nHowever, once the galaxy is formed, we follow the \ninterstellar gas dynamical evolution in full detail,\nconserving mass and energy.\n\nContinued heating by Type Ia supernova is assumed to vary\ninversely with time, SNu$(t) =~$ SNu$(t_n)$$(t_n/t)$, \nwhere the current rate, SNu$(t_n) = 0.03$ SNIa \nper 100 yrs per $10^{10}$ $L_{B\\odot}$, is near \nthe lower limit of observed values,\nSNu$(t_n) = 0.06 \\pm 0.03(H/50)^2$ (Cappellaro et al. 1997), \nas required to maintain the low interstellar \niron abundance. \n\nFor the models discussed here \nthe equation of continuity includes a ``mass dropout'' term:\n$${ \\partial \\rho \\over \\partial t}\n+ {1 \\over r^2} { \\partial \\over \\partial r}\n\\left( r^2 \\rho u \\right) = \\alpha \\rho_*\n-q(r) {\\rho \\over t_{do}},$$\nwhere $t_{do} = 5 m_p k T / 2 \\mu \\rho \\Lambda$\nis the time for gas to cool locally by radiative \nlosses at constant pressure (see, e. g. Sarazin \\& Ashe 1989).\nThe cooling is assumed to be instantaneous \nwithout advection in the cooling flow, \ni.e. $t_{do} \\ll t_{flow} = r/v$, \nalthough in practice \nthis inequality may not always be satisfied. \nWhile this type of cooling dropout has been widely used in \npast models, there is no adequate physical \nmodel for mass dropout. \nClearly, the gas must cool somewhere -- the emission \nof X-rays indicates a large net energy (and mass) loss \nfrom the interstellar medium. \n\nWhen small regions of low entropy cool, the pressure \nremains constant since the sound crossing time \nis much less than the flow time. \nFollowing Fabian, Nulsen \\& Canizares (1982) and \nFerland, Fabian, \\& Johnstone (1994), we assume that \ncooled gas converts to a second population of \noptically dark, low mass stars. \nRegarding H$\\alpha$ emission as a tracer for \nthe cooling gas,\nMathews \\& Brighenti (1999) have shown that \nthe cooling occurs at a multitude ($\\sim 10^6$) of\ncooling sites distributed throughout the inner galaxy \nand that\nonly stars with mass $\\lta 1 - 2 M_{\\odot}$ can form at each \ncooling site. \nThis is supported by the observed absence of \nyoung massive stars and SNII in elliptical galaxies.\nNevertheless, in the following discussion \nwe assume that the maximum stellar mass \nin the dropout population is sufficiently \nlow that the optical light from these stars is \nunobservable.\nWe expect cooling and \nlow mass star formation to be concentrated \nwithin at least 2 kpc,\nwhich is the observed extent of H$\\alpha$ emission \nin NGC 4472 (Macchetto et al. 1996). \nWhile the region containing optical emission lines \nprovides a natural \nguideline for selecting the dropout profile,\nwe consider a wider range of constant or variable \ndropout coefficients $q(r)$ parameterized by \n\\begin{equation}\nq(r) = q_o \\exp(-r/r_{do})^m\n\\end{equation}\nwhich concentrates the cooling within radius $r_{do}$. \nNote that even when $q$ is constant, the mass dropout \nterm is spatially concentrated, $\\rho / t_{do} \\propto \n\\rho^2$.\n\n%\\section{HIGHLY CONCENTRATED AND WIDELY DISTRIBUTED MASS DROPOUT}\n%\\section{MODELS WITHOUT DROPOUT AND WITH WIDELY DISTRIBUTED DROPOUT}\n\\section{MODELS WITH ZERO OR CONSTANT q}\n\nIn a series of recent papers in this Journal \nwe have presented evolutionary cooling flow models \nfor NGC 4472 that agree quite well with \nthe observed distributions \nof interstellar gas density, temperature and metallicity \n(Brighenti \\& Mathews 1999a; 1999b), \nparticularly at intermediate and large radii.\nSince the total mass of cooled gas in these calculations \nwas only a few percent of the stellar mass, \nthe gravitational contribution of cooled gas was ignored,\neven in models including mass dropout.\nFor a better understanding of the inner galaxy,\nwe now include the gravity of all gas, \nboth hot and cold, except when specifically noted.\nIn this section we begin with models having \n$q = 0$ everywhere, so that cooling to low temperatures \noccurs in a small central region, \nthen we investigate \nmodels in which $q$ is constant throughout the cooling flow.\n\n\\subsection{{\\it Models Without Distributed Mass Dropout ($q =0$)}}\n\nWe begin by considering a perfectly homogeneous \ninterstellar flow in which all the gas reaches \nthe central computational zone ($r = 65$ pc) \nor its neighboring zones \nwhere it then cools to $T \\ll 10^7$ K.\nFor comparison \nwe discuss two cases: in Model 1 we ignore \nthe gravity of this cooled gas; in Model 2 (and \nsubsequent models) we include its gravitational influence \non the flow.\nThe mass of gas that cools into the central gridzone \nis dynamically equivalent to a massive black hole, \nbut we do not necessarily regard our \ncalculation as a realistic model for black hole formation.\nIn Figure 2a we illustrate the radial variation of gas \ndensity and temperature for Models 1 and 2 \nafter the interstellar gas has evolved to $t = t_n = 13$ Gyrs.\nSeveral global parameters for these and subsequent models\nare listed in Table 1.\n\nWhen the gravity of the cooled gas is considered (Model 2), \nthe interstellar gas \nwithin a few kpc of the galactic center is compressed \nand sharply heated in the local potential. \nSuch hot central thermal cores are not generally \nobserved (but see Colbert \\& Mushotzky 1998). \nThe central mass in both models, \n$M_{cent} = 4.65 \\times 10^{10}$ $M_{\\odot}$ is \nabout 16 times larger than the black hole mass found in NGC 4472, \n$M_{bh} = 2.9 \\times 10^9$ $M_{\\odot}$ (Magorrian et al. 1998). \nFor these reasons neither Model 1 nor 2 \nprovides a realistic interstellar mass distribution for this \ngalaxy. \n\nROSAT band X-ray surface brightness profiles $\\Sigma_x(R)$ \nfor Models 1 and 2 \nare shown in Figure 2b and the total ROSAT band luminosities \nare listed in Table 1.\nFor Model 1 the X-ray brightness peaks strongly \nin the galactic center, \ndiverging from the observations within about 3 kpc; \nit was just this sort \nof disagreement that initially led to \nthe assumption of distributed mass dropout in cooling flows\n(Thomas 1986; \nVedder, Trester, \\& Canizares 1988;\nSarazin \\& Ashe 1989).\nIf the efficiency of heating by early SNII were lowered, \nModels 1 and 2 could be made to agree better with \n$\\Sigma_x$ observations in $r \\gta 10$ kpc, \nbut the computed $\\Sigma_x$ would rise even further \nabove the observations within a few kpc.\nThe X-ray luminosities $L_x$ \nfor Models 1 and 2 listed in Table 1 are \nunreliable in part because of numerical inaccuracies caused \nby the extremely steep variation of gas temperature \nand density in the central 2 or 3 computational zones. \nThis numerical difficulty is common to all cooling flows \nthat proceed to the very center of the galaxy \nbefore cooling, for \nany reasonable central grid spacing. \nSince more $Pdv$ work is done on the flow in Model 2 \n(where the gravity of cooled gas is included), we \nexpect that $L_x$ should also be larger than for Model 1.\nThe opposite sense of the change in $L_x$ shown \nin Table 1 evidently results from numerical inaccuracies near \nthe central singularity where zone to zone \nvariations are no longer linear.\nIf the gas has not cooled before flowing \ninto the core ($\\lta 100$ pc), as in Models 1 and 2,\na significant fraction of the total X-ray emission \nshould come from this very \ncentral region, again in disagreement with observations.\n\nIn Models 1 and 2 a sphere of cold ($T = 10$ K), dense gas\naccumulates in the central gridzones and grows in mass and size over\nthe Hubble time. \nThis sphere is an unrealistic artifact of our\ncomputational assumptions. \nTherefore, to explore further the central\nnumerical difficulty with $L_x$ encountered in Models 1 and 2, we\nconsidered two additional models using higher spatial resolution\n(radius of central zone is only 15 pc), both of which include the\ngravitational influence of cooled gas. \nThe first model (Model 2.1) is \nsimilar to Model 2 with $q = 0$ in all zones. \nIn the second model \n(Model 2.2) we set $q = 0$ in all zones except the central zone where\n$q = 4$. \nModel 2.2 is the appropriate limit of the series\nof models discussed below in which the cooling dropout is more and\nmore centrally concentrated.\n\nWhile the flow in $r \\gta 1$ kpc is very similar \nin Models 2.1 and 2.2, the behaviour at smaller radii \nis quite different. \nFor example the flow parameters \nfor Model 2.1 at 100 pc and $t_n = 13$ Gyrs are: \n$T = 7.9 \\times 10^7$ K,\n$n = 1$ cm$^{-3}$,\nand \n$u = -320$ km s$^{-1}$. \nAt the same radius and time \nfor Model 2.2 the flow is quite different: \n$T = 6.3 \\times 10^7$ K,\n$n = 5$ cm$^{-3}$,\nand \n$u = -60$ km s$^{-1}$.\nAt projected radius $R = 100$ pc, the ROSAT X-ray \nsurface brightness in Model 2.2 is 20 times larger \nthan Model 2.1 and the total ROSAT X-ray luminosity \nintegrated over the entire cooling flow in Model 2.2 \nis larger by a factor 32.\nThe differences between these two models result from \nupstream propagation of information \nabout the central boundary conditions made possible \nby subsonic flow near the origin. \nFortunately, these numerical and physical \ndifficulties near the origin \ndo not arise in more realistic cooling flows \ndiscussed below in which $q > 0$ at larger galactic radii.\n\n\\subsection{{\\it True and Apparent Gas Density and Temperature}}\n\nWhile solutions of the gasdynamical equations provide the\ntemperature as a function of physical radius $T(r)$, \nthe observed temperature $T(R)$ is an\nemission-weighted mean temperature \nalong the line of sight at projected radius $R$.\nFor symmetric galaxies and at small galactic radii, these\ntwo temperatures are nearly identical because of the\nsteep radial variation in X-ray emissivity.\nThe variation of \ntemperature with physical radius $T(r,t_n)$ \nin the background flow is shown\nwith light solid lines in Figure 2a.\n\nIn the presence of spatially distributed \ncooling dropout, the local \ntemperature is an emission-weighted mean of the \nbackground (uncooled) gas and the cooling regions.\nCooling is assumed to occur at a large number \nof cooling sites where the gas remains \nin pressure equilibrium as it cools, apparently unrestricted \nby magnetic stresses (see Mathews \\& Brighenti 1999 for details).\nThe heavy solid lines in Figure 2a \nshow the mean apparent temperature $T_{eff}(r,t_n)$\nincluding contributions from locally cooling regions, \n\\begin{equation}\nT_{eff} = { T + q T \\Delta_1(T) \\over 1 + q \\Delta_0 (T) }\n\\end{equation}\nwhere $T$ is the background flow temperature and \nthe slowly-varying functions $\\Delta_i(T)$ are \nplotted in Brighenti \\& Mathews (1998).\nNote that the effective temperature is independent of the \nlocal gas density.\nThe temperature that is actually observed is an\naverage of $T_{eff}$ along the line\nof sight; this temperature $T_{eff}(R,t_n)$\nis shown with dotted lines in Figure 2a. \n\nSimilarly, \nthe apparent hot gas density is increased because of \nadditional emission from denser, cooling-out gas.\nThe observed electron density shown in the Figure 2a \nis found by Abel inversion of \nthe X-ray surface brightness distribution. \nWhen cooling sites are present, \nthe local emissivity into the ROSAT energy band is\n$$\\varepsilon_{\\Delta E} = (\\rho_{eff}/m_p)^2 \\Lambda_{\\Delta E}(T)$$\n$$= (\\rho/m_p)^2 \\Lambda_{\\Delta E}(T)\n[1 + q \\Delta_0(T)] ~~~ {\\rm ergs/sec~cm}^3.$$\nThe effective density is therefore\n\\begin{equation}\nn_{eff} = n [ 1 + q \\Delta_0(T)]^{1/2}\n\\end{equation}\nwhere $n$ is the electron density of the background,\nuncooled gas.\nThe observed (azimuthally-averaged)\ndensities in NGC 4472 plotted in Figure 2a \nshould be compared with $n_{eff}(r,t_n)$ shown with \nheavy solid lines. \n\n\\subsection{{\\it Distributed Mass Dropout with Constant $q$}}\n\nLacking an acceptable physical model for \nspatially distributed mass dropout \nin galactic cooling flows, we are at liberty to choose \nany variation for the dropout coefficient $q(r)$, appropriately \nconstrained {\\it a posteriori} \nby the known dynamical mass from stellar velocities, \nthe X-ray mass, the central black hole mass \nand the observed radial variation of hot gas density, \ntemperature and X-ray surface brightness.\nIt is natural to begin with constant $q$ solutions \nsimilar to those \nconsidered by Sarazin \\& Ashe (1989) in their steady state \ncooling flow solutions. \nFor simplicity we assume that the mass of cooled gas\nremains at the cooling site where it contributes to the\ngravitational potential.\n\nIn the central panels of Figure 2a we \nillustrate the hot interstellar gas density and temperature that \nresults after $t_n = 13$ Gyrs assuming uniform $q = 1$ \nand 4; \nthese are \nlisted in Table 1 as Models 3 and 4 respectively.\nWhen $q$ is a constant independent of radius, \nthe ratios of true to apparent \nvalues -- $n/n_{eff}$, $T/T_{eff}$ and $M_{tot}/M_x$ -- are \nalso approximately uniform with galactic radius.\nHere $M_{tot}(r)$ is the true total mass within $r$ and \n$M_x(r)$ is the value that would be determined from \nX-ray observations of the models \nby assuming hydrostatic equilibrium (as in Fig. 1).\nThe influence of constant-$q$ mass dropout \nis similar at all galactic radii since the \nfactors that convert background temperature and density \nto effective values in equations (3) and (4) depend \nonly on $T(r)$ which is slowly varying, not on $n(r)$.\nBecause of the enormous volume and time \navailable to gas dropping \nout at large $r$, the total mass of cooled gas (listed in \nTable 1) becomes very large in the outer galaxy.\nIn Figure 3 we compare the radial distribution of \nstellar and dark halo mass with the \ndistributed dropout mass that \nresults after 13 Gyrs with $q = 1$ and 4.\nThe de Vaucouleurs ``stellar'' mass profile in Figure 3 \nis constructed \nassuming uniform $M/L_B = 9.2$.\n\nAs $q$ increases from 1 to 4,\nthe background \nhot gas density (light solid lines in Fig. 2a) \ndecreases and its radial gradient flattens, \ncausing a rise in temperature to provide enough \npressure to support the cooling flow atmosphere.\nNote that the total dropped-out mass within \n$r_e/3$ decreases with larger $q$ (Figure 3 and Table 1).\nAlthough more overall cooling dropout occurs as $q$ increases,\nmost of this cooling occurs at very large $r$ \nand, somewhat paradoxically, less gas remains for dropout \ncloser to the galactic center, $r \\lta r_e$.\nHowever, the effective \n(i.e. apparent) density (heavy solid lines in Fig. 2a)\nis less sensitive to $q$.\nThe $q = 1$ solution (Model 3) is preferred for its \nfit to observed temperatures while the $q = 4$ solution (Model 4) \nagrees better with the observed density in $r \\lta 10$ kpc \nand almost exactly with the X-ray surface brightness \n(Fig. 2b).\n\nIn addition, the centrally concentrated \ndropped out mass in the $q = 1$ solution (Model 3) \ncontributes \na larger fraction of the dynamical mass in $r \\lta r_e/3$ \nand the total mass within the central gridzone\n($r = 65$ pc) is almost equal to the known mass of the\nblack hole in NGC 4472 (Table 1). \nEvidently, cooled masses in \nmodels with $q < 1$ would exceed the central dark mass observed. \n\nFor both values of $q$ considered, the dropped out mass \nlisted in Table 1 \ncontributes appreciably to the total mass within $r = r_e/3$.\nWhen both old stellar and dropout mass are included,\nthe $M/L_B$ values at $r_e/3$ shown in Table 1 -- 12.19 and 11.21 -- \nexceed both the dynamical value $M/L_B = 9.2$\nfound by van der Marel (1991) within $\\sim 0.4r_e$ \nand the value $M/L_B(r_e/3) = 10.18$ \nin our models which includes a \nsmall additional contribution of non-baryonic dark matter. \nTo quantify the influence of the dark baryonic dropout mass on \nthe mass to light ratio we include in Table 1 an entry for \n$$\\Delta_{m/l}(r_e/3) = \n{ (M/L_B)_{*,dh,do}(r_e/3) \\over (M/L_B)_{*,dh}(r_e/3)} - 1$$\n$$= {M_{*,dh,do}(r_e/3) \\over M_{*,dh}(r_e/3)} - 1$$\nwhere $M_{*,dh}(r_e/3) = 1.35 \\times 10^{11}$ \n$M_{\\odot}$ is the combined mass of \nluminous stars and dark halo matter at $r_e/3$ and \n$M_{*,dh,do}(r_e/3) = M_{tot}(r_e/3)$ also \nincludes the dropout mass within this radius.\nSince our computed total mass \n$M_{*,dh,do}(r_e/3)$ exceeds \nthe observed dynamical value 9.2 (and also 10.18), \nto be fully consistent we should have chosen \n${M/L_B}_* < 9.2$ for the old stellar population\n(see below), provided $M/L_B$ for stars produced from \nthe cooled gas is infinite as we have assumed.\n\nIf these constant $q$ models are physically appropriate, \nthe agreement between $M_x(r)$ and $M_*(r)$ \nin $(0.1 - 1)r_e$, as shown in Figure 1 \n(and for NGC 4649), \nis surprising since $M_x(r_e/3)$ and $M_{*,dh}(r_e/3)$ \ndiffer by 10 - 40 percent (Table 1) for the constant $q$ models. \nThis suggests that the mass to light ratio \nof the dropout stellar population is not infinite as \nwe have assumed, but comparable with that of \nthe old stellar population.\n\n\\section{MODELS WITH CENTRALLY CONCENTRATED DROPOUT}\n\nWe now seek evolutionary gasdynamical solutions with \nvariable dropout coefficients $q(r)$ \nthat strongly concentrate the mass dropout \nin the inner galaxy, $r \\lta r_e$.\nThe limited spatial extent of optical emission lines \nin the cores of bright ellipticals suggests that cooling dropout \noccurs well within $r_e$.\nFor example, the H$\\alpha$ + [NII] image of\nNGC 4472 is observed out to approximately $\\sim 0.25r_e$ or\n2 kpc (Macchetto et al. 1996).\nAs hot interstellar gas cools in \nthis region, its temperature pauses at $T \\sim 10^4$ K where\nthe gas is heated and ionized by stellar UV radiation. \nTherefore, \nwe consider parameters $r_{do}$ and $m$ in equation (2) \nthat concentrate the mass dropout in the central region, \nbut not at the very center as in Model 2. \n\nThe dropout parameters $q_o$, $r_{do}$ and $m$,\nare listed in Table 1 for Models 5, 6 and 7. \nThe mass dropout in these three models is progressively \nmore concentrated toward the galactic center.\nThe results for Model 5, for which the dropout scale length\nis very large, $r_{do} = 15$ kpc, are similar in most \nrespects to those of Model 4 except \nthe massive dropout in the outer galaxy is no longer present.\nIn particular, \nthe mass to light ratio at $r_e/3$ in Table 1 \nis very similar for Models 4 and 5.\n\nThe current \ninterstellar density and temperature variations for Model 6 \nwith $r_{do} = 2$ kpc are shown in Figure 2a \nand $\\Sigma_x(R)$ is plotted in Figure 2b. \nThe apparent density \nand $\\Sigma_x$ (heavy solid lines) are considerably \ngreater than observed values in $r \\lta 3$ kpc, \nalthough the projected apparent temperature is a reasonable \nfit to the NGC 4472 data.\nThe radial distribution of \ndropout mass for Model 6 is shown in Figure 3.\nFrom Table 1\nthe total (old stars, halo and dropout) mass to light ratio \nat $r_e/3$ is $M_{tot}/L_B = 13.03$, \n29 percent higher than van der Marel's value \nand 22 percent greater than the corresponding value for our \nbackground model galaxy. \n\nAlso shown in Figures 2a and 2b are similar results for \nModel 7 in which the mass dropout, now \napproximated with a Gaussian, is concentrated within \n$r_{do} = 800$ pc. \nModel 7 is constructed so that \nmost of the mass dropout occurs \nin $r \\lta 0.1r_e$, corresponding to the region of apparent \ndisagreement between $M_x$ and $M_*$ in Figure 1. \nIt is of interest that the gas density and $\\Sigma_x$ within \n1 kpc for Model 7, where the dropout is greatest, \nexceeds those of Model 2 in which there is no \ndropout at all. \nThis can be understood from the flow velocity distribution.\nFor Model 2 without distributed dropout the inward moving \ngas velocity increases through the entire region \nillustrated and shocks at $r \\ll 1$ kpc.\nIn the presence of dropout, the flow velocity \nat corresponding radii in Model 7 is much slower \nand reaches a maximum (negative) value \nnear $r = 1$ kpc then approaches zero subsonically at the origin.\nThe density and $\\Sigma_x$ \nenhancements in the background flow \nfor Model 7 at $r \\lta 3$ kpc \nare due to a local compression \nas the gas flows into slowly moving gas in the core. \nWithin about 3 kpc, both the background and apparent \ndensities exceed the observations by a larger factor than \nthose of Model 6 \nand $\\Sigma_x$ also peaks \nunrealistically in this same region (Fig. 2b).\nThe dropout mass for Model 7 shown in Figure 3 equals \nthat of the old population stellar mass \nat $r \\approx 1$ kpc ($0.12 r_e$).\nFor these reasons Model 7 seems less satisfactory than \nModel 6, but neither is as generally successful as Model 3 \n($q = 1$).\n\nAlthough increased mass dropout can decrease the X-ray surface \nbrightness $\\Sigma_x$, as when uniform $q$ increased from \n1 to 4 (Models 3 and 4 in Fig. 2b), this is not always the case. \nWhen the dropout is concentrated more toward the galactic \ncenter, $\\Sigma_x$ actually increases, as in the transition \nfrom Model 6 to 7.\n\nIt is interesting to determine the influence \nof distributed dropout on the total apparent \nmass $M_x(r)$ found from the model \nby assuming hydrostatic equilibrium (equation 1).\nDue to the contribution of low temperature cooling regions \nto the total X-ray emission, $T(r)$ and \ntherefore $M_x(r)$ is always lower \nthan the true mass $M_{*,dh}(r)$ in cooling dropout regions. \nA difference in this sense is apparent in Table 1 at \n$r = r_e/3$ for Models 3 - 7; \nthis is similar to the mass discrepancy \nin Figure 1 at $r \\lta 0.1 r_e$.\n\nThe high central apparent gas density and surface brightness\nfor Model 6 shown in Figures 2a and 2b\nare obvious problems for this model.\nHowever, the gas density can be reduced\nif a strong magnetic field \nor other non-thermal energy density \nis present in $r \\lta 0.25r_e = 2$ kpc. \nDynamically important magnetic fields\nmay also be required to fit the X-ray data\nof NGC 4636 (Brighenti \\& Mathews 1997a) and may be generally\nexpected in luminous ellipticals (Mathews \\& Brighenti 1997;\nGodon, Soker \\& White 1998).\nAdditional non-thermal pressure support \nis also implied for Model 6 since\nthe effect of central cooling dropout fails to\nlower the apparent mass $M_x(r)$ below the actual\nmass $M_{tot}$ as much as the observed\ndeviation shown in Figure 1.\nLike many bright ellipticals, NGC 4472 has a weak non-thermal\nradio source within the central $\\sim 4$ kpc,\nindicating $B \\sim 10 - 100$ $\\mu$G (Ekers \\& Kolanyi 1978). \n\nFor all calculated models in Table 1 with distributed dropout, \nthe total mass $M_{tot} = M_{*,dh,do}$ \nsignificantly exceeds the mass of the \nold stellar population plus dark halo $M_{*,dh}$ \nthroughout the inner galaxy,\nindicating that dropout material makes an important \nadditional contribution to the total mass.\nHowever, the apparent mass $M_x$ determined from equation (1) \nis less than $M_{tot}$ in the inner galaxy and, \nfor Model 6, can also be less than $M_{*}$.\nOf particular interest is the region \n$0.1 r_e \\lta r \\lta r_e$ \n(i.e., $-0.07 \\lta \\log r_{kpc} \\lta 0.93$) in Figure 1. \nAlthough the agreement in Figure 1 is excellent in this \nregion, for Models 6 and 7 the total mass is larger than \n$M_{*,dh}(r)$ and values of $\\Delta_{m/l}$ in Table 1 \nsuggest that the dropped out \nmass contributes 25 - 35 percent of the total \nmass in this region.\nTherefore, if the dropout mass is optically dark, \nthe true stellar mass to light ratio of the \nold stellar population \nmust be $M/L_B \\approx 6$ rather than the value $M/L_B = 9.2$ \nfound by van der Marel which includes the dropout mass. \n\nTo investigate such a possibly more self-consistent \nold stellar component, \nwe consider Model 8 based on the same $q(r)$ used in Model 6, but \nwith $M/L_B = 6$ for the old stellar population.\nFor additional consistency \nin Model 8, $\\alpha_*(t)$ is increased by the ratio of \nassumed stellar mass to light ratios 9.2/6 = 1.53 as described \nbelow; the total stellar mass ejected is identical\nto that in Model 6. \nFigure 3 illustrates the dropout mass profile for Model 8. \nThe apparent density, temperature and $\\Sigma_x$ \nprofiles for \nModel 8 shown in Figures 4a and 4b \nare very similar to those of Model 6, \nso this adjustment of the stellar $M/L_B$ has had \nlittle effect.\n\nThe radial mass profiles of Models 6 and 8 are \ncompared in Figure 5. \nIn this plot the open circles show the observed X-ray mass \n$M_x(r)$ for NGC 4472 using equation (1) and \nthe solid lines shows $M_x(r)$ based on equation (1) \nusing $n(r)$ and $T(r)$ from the models.\nThe dashed lines show $M_{tot}(r)$ and the dotted \nlines are the stellar mass $M_*(r)$ based on \na de Vaucouleurs profile with $M/L_B = 9.2$ in the \nupper panel (Model 6) and $M/L_B = 6$ in the lower panel \n(Model 8).\nThe superiority of Model 8 is evident from the \ncloser agreement between the \nX-ray mass data points for NGC 4472 and \nthe solid line for that model.\nThis agreement for Model 8 would be even closer\nin the range $\\log r \\approx 0.5 - 1$ if we had \nused a dark halo mass profile less centrally \npeaked than NFW.\nModel 8 may provide the most self-consistent \noverall fit to the mass\nconstraints for NGC 4472; \nif so, the old stars in NGC 4472 \nhave a mass to light ratio $M/L_B \\approx 6$, \nabout $\\sim 30$ percent lower than the mass to light \nratio determined from stellar dynamics.\n\nIn summary, none of our \nmodels is fully satisfactory in every respect. \nThe total mass to light ratio \n(including dropout mass) \nin $r \\lta r_e/3$ is 10 - 35 percent higher than \nthe value for the underlying galaxy.\nHowever, in Model 8 in which $M/L_B = 6$ for the \nold stars, the difference between the\nX-ray mass determined from the models and NGC 4472 \nis appreciably reduced.\nNevertheless, \nthe central apparent gas density \nand X-ray surface brightness in Model 8\nare still larger than observed, requiring additional\nnon-thermal support.\nThere is no independent theoretical justification \nfor the dropout profile $q(r)$ assumed in \nModels 6 and 8; \nas explained earlier, the dropout distribution depends on \nunknown interstellar entropy fluctuations. \nNevertheless, for all models considered here \nthe mass of cooled interstellar gas contributes \nsignificantly to the total mass \nand the dynamically determined mass to light ratio \nwithin the inner galaxy. \n\n%\\end{document}\n\\section{FINAL REMARKS AND CONCLUSIONS}\n\nIn this series of calculations \nwe have taken a census of all baryons involved in \nthe evolution of a large elliptical galaxy:\nthe original stellar component,\nthe interstellar medium, and -- of most interest -- the \nsmall but troublesome mass of hot gas \nthat cools over cosmic time.\nWe have shown that \nthe radial distribution of cooled interstellar gas \ninfluences dynamical and X-ray determinations of \nthe total interior mass and the radial profiles \nof apparent density, temperature and X-ray brightness of \nthe hot gas.\nIn our models, cooled gas is \nslowly deposited in the central galaxy \n$r \\lta r_e$ (see Figure 3) \nas indicated by the extent of observed H$\\alpha$ emission.\nSince there is little or no direct observational evidence for \nthe mass that has dropped out in ellipticals like NGC 4472, \nthe cooled mass must either \nbe dark at optical and radio frequencies \nor indistinguishable from the old stars.\nLow mass stars are an obvious and physically reasonable \nendstate for the cooled gas \n(Ferland, Fabian \\& Johnstone 1994; \nMathews \\& Brighenti 1999).\nWe also suppose that \nthe cooled gas remains at the dropout site \nwhere it contributes to the galactic potential.\n\n\\subsection{{\\it Reducing Stellar Mass Loss}}\n\nIn an attempt to reduce the influence of cooling and cooled \ngas on the models, we have altered many of the \nmodel parameters.\nThe chosen cosmology ($\\Omega = 1$; $\\Omega = 0.3$ \nand $\\Omega_{\\Lambda} = 0.7$, etc.) or \nthe baryon fraction $\\Omega_b$ have little \ninfluence on the total dropout mass.\nChanging the times when the stars and \nthe galactic potential form ($t_{*s}$ and $t_{*}$) or the \nspatial scale of the release of SNII energy \nwithin reasonable limits\nhave only a modest influence on the dropout mass \nthat accumulates by time $t_n = 13$ Gyrs. \nIncreasing the interval $t_{*s} - t_*$ between star and \ngalaxy formation does reduce the total dropout mass, \nbut this interval cannot be too large \nsince luminous ellipticals are observed at large redshifts.\nThe cooling dropout would not be dramatically reduced \nif massive ellipticals were all only \na few Gyrs old since most of the stellar mass loss \noccurs just after star formation; however, many or \nmost luminous ellipticals are thought to be very old. \n\nPerhaps the most effective way to preserve the excellent\nagreement between $M_{*}$ and $M_x$ in Figure 1\nin $0.1r_e \\lta r \\lta 1 r_e$, without constraining\nthe mass dropout profile $q(r)$, would be to reduce\nthe total mass that has cooled over cosmic time.\nThe most sensitive parameter influencing the cooled mass is \nthe specific rate of stellar mass loss, $\\alpha_*(t)$. \nAlthough the total mass of hot gas increases with \ntime due to the continued influx of secondary infalling gas, \nthe mass of hot gas within the optical galaxy \noriginates mostly from stellar mass loss and \nthe X-ray luminosity there scales as \n$L_x \\propto \\alpha_*(t) \\propto t^{-1.3}$ \n(Appendix B of Tsai \\& Mathews 1995).\nComputed models similar to those described here \nbut with arbitrarily reduced $\\alpha_*(t)$ \nfit the $n(r)$ and $\\Sigma_x(R)$ data rather well \nat time $t_n$ and produce much less cooling dropout. \nHowever, $\\alpha_*(t)$ cannot be lowered \nwithout also increasing the stellar mass.\nFor all reasonable power law initial mass functions, \n$\\alpha_*(t)$ varies inversely \nwith the stellar mass to light ratio:\n$$\\alpha_*(t) \\equiv { d M_* /dt \\over M_*}\n= \\left[{ d M_* /dt \\over L_B}\\right] {1 \\over (M_*/L_B)}\n\\propto {1 \\over (M_*/L_B)}.$$\nThe physical explanation for the constancy \nof $(d M_* /dt)/L_B$ is that both $L_B$ (dominated by\npost-main sequence stars) and $d M_* /dt$ depend on\nthe instantaneous rate that stars leave \nthe main sequence so this IMF-dependent factor \ncancels out (e.g. Renzini \\& Buzzoni 1986).\nTo illustrate this result,\nwe use the Renzini-Buzzoni procedure \nand plot in Figure 6 the relationship between \n$\\alpha_*$ and $M/L_B$ at time $t_n = 13$ Gyrs for 84 \npower law IMFs with slopes $x = $0.6, 0.8, 1.0, 1.2, 1.4, 1.6,\nand 1.8, each with lower and upper mass limits of \n$m_{\\ell} = $0.01, 0.032, 0.1, 0.32\nand $m_u = $10, 32, 100.\nThe remarkable linearity in Figure 6 shows \nthat the quantity in square brackets in the equation above \nis almost invariant to large \nchanges in the slope or mass limits for power law IMFs.\n\nTherefore, if $\\alpha_*(t)$ is reduced by 2 or 3 in an attempt \nto reduce the total dropout mass, \nthe stellar mass (and $M/L_B$) must be increased by the same \nfactor; as a result the total mass ejected, \n$\\int \\alpha_* M_* dt$, and the total dropout mass \ndo not change. \n\n\\subsection{{\\it Effect of Galactic Rotation}}\n\nAlthough massive ellipticals are not rotationally\nflattened, they do rotate significantly, \ne.g. $(v/\\sigma)_* = 0.43$ for NGC 4472 \n(Faber et al. 1997).\nIf the hot interstellar gas rotates\nin the same sense as the bulk of mass-losing stars, \nstars formed from the cooled gas\nshould form into a disk of scale $\\sim r_e$\n(Brighenti \\& Mathews 1997b), \nalthough the development of such disks is likely to be \nsuppressed by the mass dropout process. \nNevertheless, to the extent that the cooled gas has a disk-like \ndistribution, \nits global influence on the stellar\ndynamics in $r \\lta 0.4r_e$ would be less than if the\nsame dark mass were distributed spherically.\nRemarkably, there is \nno observational evidence at present for\nrotational flattening in the X-ray images of giant\nellipticals like NGC 4472.\n\n\\subsection{{\\it Non-Baryonic Dark Matter within $r_e$}}\n\nDynamical determinations of the mass to light ratio from \nstellar velocities reflect the entire mass within \nthe stellar orbits, including non-baryonic mass.\nThe NFW halo we use in our models for NGC 4472 agrees with \nX-ray observations in the extended halo but is \nslightly too massive \nnear $r \\sim r_e$ relative to the X-ray mass \n$M_x(r)$ observationally determined for NGC 4472. \nThis may indicate that dark halos are less \ncentrally peaked than NFW (see Kravtsov et al. 1998).\nThe mass of our NFW halo model contributes about 10 percent to \nthe dynamical mass to light ratio measured within $r_e/3$,\nbut the NFW profile is probably disturbed in this region. \nWhen the dominant baryonic mass in $r \\lta r_e$ compressed \nto form the de Vaucouleurs profile, we expect that the NFW \nhalo was dragged inward and distorted. \nHowever, the dark halo cores of the earlier \ngalactic condensations \nthat merged to form the elliptical may have expanded \ndue to starburst driven galactic winds. \nBecause of these various counteracting effects, \nthe small non-baryonic contribution \nto dynamical mass to light determinations is uncertain.\n\n\\subsection{{\\it Contribution of Dropout to ``Stellar'' $M/L$}}\n\nFor all models studied here -- based on a wide variety \nof mass dropout profiles $q(r)$ -- \nthe mass of cooled interstellar \ngas contributes substantially to the \ntotal mass within $\\sim 0.4r_e$ where \nthe stellar mass to light ratio is determined from \nstellar velocities.\nIf optically dark low mass stars form from the cooled gas, \nthe ``stellar'' mass to light ratios in the literature \nrefer to two distinct \nstellar populations having radically different initial \nmass functions and spatial distributions. \nThe stellar mass to light ratio of the original, optically luminous \nstellar population is lower than published values indicate. \n\nA complete solution of this problem \nrequires a better understanding of \nthe physics of star formation and the processes that \ncontrol the stellar IMF. \nWe have assumed here that a Salpeter \nIMF provides a satisfactory approximation to the \noriginal single-burst star formation at early times.\nYet we argue that the younger dropout IMF is strongly \nskewed toward low mass stars. \nThe IMF has evolved over time. \nIt is possible therefore that the early, more \nintense mass dropout resulted in \na more nearly Salpeter-like IMF, \nproducing a fraction of currently observed \nluminous stars in ellipticals. \nIf so, this early dropout would not contribute to the \nexcess dropout mass that we find in our models, \nbut would have already been included in the \noriginal de Vaucouleurs population.\nHigh density, metal enriched \nstellar cores in elliptical galaxies may have derived from \nnormal-IMF star formation from early, more intense \ninterstellar cooling. \nThis is similar to assumptions made for \ndissipative galactic core formation \nfrom the convergence of \ngas following major mergers (Mihos \\& Hernquist 1996).\nWhile such notions cannot be entirely dismissed,\nthe approximate universality of the de Vaucouleurs \nlight profile \namong ellipticals may argue against a dual formation process \nfor the radial distribution of luminous stars: \nviolent relaxation and cooling flow dropout.\n\nThroughout this discussion we have assumed that the stellar \npopulation formed from cooling flow dropout is optically dark. \nAlthough there is little or no evidence that normal massive \nOB stars (or SNII) are present in elliptical galaxies, \nit is possible that younger stars having masses up to \n$\\sim 1 - 2$ $M_{\\odot}$ are present and that \nsuch intermediate mass stars could form from the \ncooled gas (Mathews \\& Brighenti 1999).\nThis type of dropout stellar population \ncould contribute to the total optical light. \nIf the mass to light ratio of dropout and old stellar \npopulations are similar, the dropout \ncomponent could be difficult to detect by the means \nwe have discussed here and its perturbation on \nthe observed $M/L_B$ would be greatly lessened.\nIn this case the dropout population would introduce \nan additional radial light profile that would differ \nslightly from that of the old stellar population. \nThe dropout mass profiles in Figure 3 indicate that \nModels 4 and 6 would be rather difficult to detect \nagainst the background stellar light.\nIntermediate mass dropout stars could therefore \nprovide a satisfactory resolution to the problems \nwe have discussed here.\n\n\\subsection{{\\it Influence of Dropout on the Fundamental Plane}}\n\nThe ensemble of elliptical galaxies is known to have \nglobal parameters that deviate slightly from the assumptions \nof virial equilibrium and homologous structure.\nThe deviation of this fundamental plane relationship \nis in the sense that the dynamical mass to \nlight ratio increases with galactic mass,\n$M/L_B \\propto M^{0.24}$\n(Dressler et al. 1987; Djorgovski \\& Davis 1987).\nSuch a non-homologous deviation could in principle be produced \nby the small amount of cooled interstellar gas $M_{cg}$ \nprovided it increases appropriately with $M_*$. \nTo test this idea, we performed an identical hydrodynamic \ncalculation for an elliptical galaxy having a mass one fourth \nthat of NGC 4472. \nThe dark halo mass was also reduced by the same factor \nbut the cosmological environment \nand mass dropout distribution \nwere identical to those used for NGC 4472, \nscaled to a smaller $r_e$.\nWe found that the amount of mass dropout \n$M_{cg}$ is {\\it higher} in smaller ellipticals \nrelative to the total baryonic mass $M_*$. \nThis is opposite to the trend observed in the \nfundamental plane.\nHowever, if hot gas and dark matter in \nthe outer halos of smaller ellipticals \nis tidally stripped in group environments, \nas suggested by Mathews \\& Brighenti (1998b), \nthen the mass of cooled gas would be reduced and \nits effect on the fundamental plane would be reduced. \nNevertheless, explanations of the deviations of \nthe fundamental plane from virial scaling \nmust recognize the possible \nadditional influence of dropout \nmass, regardless of the trend of $M_{cg}/M_*$ with \n$M_*$.\n\n\\subsection{{\\it Conclusions}}\n\nUsing simple spherical gas-dynamical\nmodels for the evolution of interstellar gas \nand data from the well-observed elliptical\nNGC 4472, we reach the following conclusions:\n\n\\noindent\n(1) If the hot interstellar \ngas cools only in the very center of NGC 4472\nfor $\\sim 10$ Gyrs, the total accumulated mass there \nwould be $\\gta 10$ times larger than the \nmass of the central black hole\nobserved. If such large\nconcentrated masses were generally \npresent in bright ellipticals,\ninterstellar gas in $r \\lta 0.1r_e$ would be \ncompressed and heated to temperatures $> 1$ keV. \nSuch hot thermal cores are not generally observed.\nWe conclude that \nthe cooling dropout in massive \nellipticals must occur before the gas reaches\nthe galactic center.\nThe hypotheses of distributed \nmass dropout and low mass star formation \nwere proposed many years ago \n(Fabian, Nulsen \\& Canizares 1982; \nThomas 1986; \nCowie \\& Binney 1988;\nVedder, Trester, \\& Canizares 1988;\nSarazin \\& Ashe 1989;\nFerland, Fabian, \\& Johnstone 1994).\nHowever, these historical arguments were \ngenerally based on the notion that mass dropout would \nhelp reduce computed X-ray surface brightness \nprofiles at small projected radii, as required \nby the observations, but we have \nshown here that in some cases enhanced dropout \nat small galactic radii can cause \n$\\Sigma_x$ to increase, not decrease. \n(The total bolometric X-ray luminosity $L_x$ \nshould always be lower in distributed cooling models since the \nhot gas experiences only a fraction of the galactic \npotential.) \nThe best arguments for distributed cooling dropout \nare (i) limits on the central black hole mass and (ii) the \nabsence of rotational flattening in X-ray images.\n\n\\noindent\n(2) We have considered a wide variety of possible \nmass profiles for the radial deposition of \ncooled interstellar gas in NGC 4472. \nThe dropout mass is assumed to be optically dark, \nconsistent with the formation of very low mass stars. \nIn every case the (stellar plus dropout)\nmass to light ratio at $\\sim r_e/3$ significantly exceeds \nthe mass to light ratio determined from stellar velocities. \nIf the dropout mass is optically dark, dynamical \nmass to light ratios in luminous ellipticals \nshould be substantially enhanced by \ndark baryonic matter. \nIn this case \nthe true $M/L_B$ for luminous stars may be $\\sim 30$ percent \nsmaller than published values. \n\n\\noindent\n(3) The excellent agreement\nbetween the X-ray and ``stellar'' mass in NGC 4472\nshown in Figure 1 (and also NGC 4649) \nin the range $0.1r_e \\lta r \\lta 1 r_e$\nmay be a coincidence if our estimates \nof the cooling flow dropout mass are correct \nand if this mass is non-luminous.\n\n\\noindent\n(4) Dynamical mass to light determinations within $r_e$ refer \nto a superposition of two stellar populations: an old luminous \npopulation with a de Vaucouleurs galactic profile and \na younger population having a bottom-heavy IMF and \na different galactic mass profile.\nIf the younger population is optically dark,\nthe mass to light ratio is not likely to be\nconstant with galactic radius within $r_e$.\n\n\\noindent\n(5) It is not possible to reduce the total amount \nof mass deposited from the cooling flow simply by lowering \nthe specific rate of stellar mass loss\n$\\alpha_*(t) \\equiv (dM_*/dt)/M_*$.\nFor all reasonable power law initial mass functions \nwe show that $\\alpha_* \\propto (M_*/L_B)^{-1}$.\nFor given $L_B$, larger stellar masses $M_*(r)$ \nmust accompany lower values\nof $\\alpha_*$ so the total amount of mass\nejected from stars $\\propto \\int \\alpha_*(t)M_{*} dt$\nis nearly independent of the IMF.\n\n\\noindent\n(6) Among the models we consider, those with \ncentrally concentrated mass dropout perform best in\nminimizing the overall disagreement with the central $M/L_B$\nand the X-ray determined mass in $0.1r_e \\lta r \\lta 1 r_e$.\nConstant $q$ \nmodels in which the dropout is proportional to the\nlocal gas emissivity at every radius deposit less mass\nin $0.1r_e \\lta r \\lta 1 r_e$, but may have gas temperatures\nthat are too low ($q \\gta 4$) \nor central masses that are too large ($q \\lta 1$).\n\n\\noindent\n(7) Even in the presence of mass dropout, \nthe computed central interstellar gas \ndensities and X-ray surface brightnesses $\\Sigma_x(R)$ are \ngenerally too large. \nSuch deviations would be reduced if the hot gas \nis partially supported in $r \\lta 0.1r_e$ by \nmagnetic or other non-thermal pressure \nassociated with the extended radio source. \n\n\\noindent\n(8) If the stellar population formed from cooled interstellar \ngas extends to intermediate masses, \n$\\sim 1 - 2$ $M_{\\odot}$, its mass to light ratio may blend \nwith that of the older population. \nIn this case the dropout mass would already be represented \nin the de Vaucouleurs profile representing the \nstellar mass distribution in our models.\nDynamical determinations of \n$M/L_B$ would be a weighted mean of the two \npopulations. \nIf the dropout stellar population is luminous, \nsome of the difficulties we have discussed here would \nbe alleviated, but not those regarding $\\Sigma_x(R)$.\n\n\\noindent\n(9) If the influence of rotation and non-thermal pressure \ncan be understood, \nhigh resolution images of the central regions of \nelliptical galaxies using the {\\it Chandra} (AXAF) satellite \nmay detect the presence of dark baryonic dropout material \nand an accurate determination of the mass to light ratio \nof the old stellar population.\n\n\n\\acknowledgments\n\nThanks to Karl Gebhardt for providing useful\ninformation.\nStudies of the evolution of hot gas in elliptical galaxies \nat UC Santa Cruz are supported by\nNASA grant NAG 5-3060 and NSF grant AST-9802994 \nfor which we are very grateful. \nFB is supported\nin part by Grant MURST-Cofin 98.\n\n%\\clearpage\n\n%\\centerline{\\bf APPENDIX}\n%\\appendix\n\n\n%\\end{document}\n\n\n\n%\\clearpage \n\n\n\\begin{references}\n\\reference{head1988} Allen, S. W., Fabian, A. C.,\nJohnstone, R. M., White, D. A., Daines, S. J., \nEdge, A. C. \\& Stewart, G. C. 1993, MNRAS 262, 901\n\\reference{head1988} Allen, S. W. \\& Fabian, A. C. 1997,\nMNRAS 286, 583\n\\reference{head1988} Braine, J. \\& Dupraz, C. 1994, A\\&A \n283, 407\n\\reference{head1988} Braine, J., Henkel, C. \\& Wiklind, T. 1997, \nA\\&A 321, 765\n\\reference{head1988} Bregman, J. N., Roberts, M. S. \\& \nGiovanelli, R. 1988 ApJ 330, L93\n\\reference{head1988} Brighenti, F. \\& Mathews, W. G. 1997a, ApJ 486,\nL83 \n\\reference{head1988} Brighenti, F. \\& Mathews, W. G. 1997b, ApJ 490,\n592 \n\\reference{head1988} Brighenti, F. \\& Mathews, W. G. 1998 ApJ 495,\n239 \n\\reference{head1988} Brighenti, F. \\& Mathews, W. G. 1999a, ApJ 512,\n65 \n\\reference{head1988} Brighenti, F. \\& Mathews, W. G. 1999b, ApJ\n(in press) \n\\reference{head1988} Buote, D. A. 1999, MNRAS (submitted)\n\\reference{head1988} Cappellaro, E., Turatto, M., Tsvetkov, D. Yu.,\nBartunov, O. S., Pollas, C., Evans, R., \\& Hamuy, M. 1997, Astron. \\&\nAp. 322, 431\n\\reference{head1988} Colbert, E. \\& Mushotzky, R. F. 1998, \n(astro-ph/9809150)\n\\reference{head1988} Cowie, L. L. \\& Binney, J. 1988, ApJ 215, 723\n\\reference{head1988} Djorgovski, S. G. \\& Davis, M. 1987, ApJ 313, 59\n\\reference{head1988} Donahue, M. \\& Vogt, M. 1997, \nin {\\it Galactic and Cluster Cooling Flows}, ed. N. Soker,\nASP Conf. Series 115, 48\n\\reference{head1988} Dressler, A., Lynden-Bell, D., Burstein, D.,\nDavies, R. L., Faber, S. M., Terlevich, R. J., \n\\& Wegner, G. 1987, ApJ 313, 42\n\\reference{head1988} Ekers, R. \\& Kolanyi, C. 1978,\nA\\&A 67, 47\n\\reference{head1988} Faber, S. M., Wegner, G.,\nBurstein, D., Davies, R. L., Dressler, A., Lynden-bell, D. \n\\& Terlevich, R. J. 1989, ApJS 69, 763\n\\reference{head1988} Faber, S. M., Tremaine, S., \nAjhar, E. A., Byun, Y-I, Dressler, A., Gebhardt, K., \nGrillmair, C., Kormendy, J., Lauer, T. R., \\& Richstone, D. \n1997, AJ 114, 1771\n\\reference{head1988} Fabian, A. C., Nulsen, P. E. J. \\& \nCanizares, C. R. 1982, MNRAS 201, 933\n\\reference{head1988} Fabian, A. C., Arnaud, K. A.,\nBautz, M. W. \\& Tawara, Y. 1994, ApJ 436, L63\n\\reference{head1988} Ferland, G. J., Ferland, A. C. \\& \nJohnstone, R. M. 1994, MNRAS 266, 399\n\\reference{head1988} Forman, W., Jones, C., David, L., \nFranx, M., Makishima, K., \\& Ohashi, T. 1993, ApJ 418, L55\n\\reference{head1988} Godon, P., Soker, N. \\& White III, R. E. 1998,\nAJ 116, 37\n\\reference{head1988} Irwin, J. A. \\& Sarazin, C. L. 1996, ApJ, 471,\n683\n\\reference{head1988} Kravtsov, A. V., Klypin A. A., Bullock, J. S.\n\\& Primack, J. R. 1998, ApJ 502, 48\n\\reference{head1988} Macchetto, F., Pastoriza, M., Caon, N., \nSparks, W. B., Giavalisco, M., Bender, R. \\& Capaccioli, M. 1996,\nA\\&AS 120, 463\n\\reference{head1988} Magorrian, J., Tremaine, S., Richstone, D., \nBender, R., Bower, G., Dressler, A., Faber, S. M., Gebhardt, K.,\nGreen, R., Grillmair, C., Kormendy, J., \\& Lauer, T. 1998,\nAJ 115, 2285\n\\reference{head1988} Mathews, W. G. \\& Brighenti, F. 1997, ApJ 488,\n595\n\\reference{head1988} Mathews, W. G. \\& Brighenti, F. 1998a, ApJ 493,\nL9 \n\\reference{head1988} Mathews, W. G. \\& Brighenti, F. 1998b, ApJ 503,\nL15 \n\\reference{head1988} Mathews, W. G. \\& Brighenti, F. 1999, ApJ\n(submitted) \n\\reference{head1988} Matsushita, K. 1997, Ph.D. thesis, University of\nTokyo\n\\reference{head1988} Mihos, J. C. \\& Hernquist, L. 1996, \nApJ 464, 641\n\\reference{head1988} Navarro, J. F., Frenk, C. S., \\& White, S. D. M.\n1996,\nApJ, 462, 563\n\\reference{head1988} Renzini, A. \\& Buzzoni, A. 1986, \nin {\\it The Spectral Evolution of Galaxies} eds. C. Chiosi \\&\nA. Renzini (Reidel: Dordrecht), p. 195\n\\reference{head1988} Sarazin, C. L. \\& Ashe, G. A. 1989, \nApJ 345, 22\n\\reference{head1988} Thomas, P. A. 1986, MNRAS 220, 949\n\\reference{head1988} Trinchieri, G., Fabbiano, G., \\& \nCanizares, C. R. 1986, ApJ, 310, 637\n\\reference{head1988} Trinchieri, G., Fabbiano, G., \\&\nKim, D.-W. 1997, A\\&A 318, 361\n\\reference{head1988} Tsai, J. C. \\& Mathews, W. G. 1995,\nApJ 448, 84\n\\reference{head1988} van der Marel, R. P. 1991, MNRAS, 253, 710\n\\reference{head1988} Vedder, P. W., Trester, J. J., \\&\nCanizares, C. R. 1988, ApJ 332, 725\n\\reference{head11988} White, D. A., Fabian, A. C., \nJohnstone, R. M., Mushotzky, R. F., \\& Arnaud, K. A. 1991,\nMNRAS 252, 72\n\\reference{head1988} Wise, M. W. \\& Sarazin, C. L. 1999, \nApJ (submitted)\n\\end{references}\n\n%\\end{document}\n\n\n%\\makeatletter\n%\\def\\jnl@aj{AJ}\n%\\ifx\\revtex@jnl\\jnl@aj\\let\\tablebreak=\\nl\\fi\n%\\makeatother\n\n%\\footnotesize\n\\clearpage\n\n%this reduces vertical spacing (from Don Korycansky):\n%\\renewcommand\\baselinestretch{1.0}\n\n\\begin{deluxetable}{crccccccccccc}\n%\\scriptsize\n%\\rotate\n\\tabletypesize{\\scriptsize}\n\\tablewidth{60pc}\n%\\tablewidth{0pc}\n\\tablenum{1}\n\\tablecolumns{13}\n\\tablecaption{MASS DROPOUT MODELS FOR NGC 4472\\tablenotemark{a}}\n\\tablehead{\n\\colhead{Model} &\n\\colhead{$q_o$} &\n\\colhead{$r_{do}$} &\n\\colhead{$m$} &\n\\colhead{$M_{cg}$\\tablenotemark{b}} &\n\\colhead{$M_{cg}({r_e \\over 3})$\\tablenotemark{c}} &\n\\colhead{$M_{tot}({r_e \\over 3})$\\tablenotemark{d}} &\n\\colhead{$M_x({r_e \\over 3})$\\tablenotemark{e}} &\n\\colhead{${M_{tot}\\over L_B}({r_e \\over 3})\\tablenotemark{f}$} &\n\\colhead{$\\Delta_{m/l}({r_e \\over 3})\\tablenotemark{g}$} &\n\\colhead{$M_{cent}$\\tablenotemark{h}} &\n\\colhead{$L_{x,bck}^{ros}$\\tablenotemark{m}} &\n\\colhead{$L_{x,tot}^{ros}$\\tablenotemark{n}} \\cr\n\\colhead{} &\n\\colhead{} &\n\\colhead{(kpc)} &\n\\colhead{} &\n\\colhead{($10^{10} \\; M_{\\odot}$)} &\n\\colhead{($10^{10} \\; M_{\\odot}$)} &\n\\colhead{($10^{11} \\; M_{\\odot}$)} &\n\\colhead{($10^{11} \\; M_{\\odot}$)} &\n\\colhead{($M_{\\odot}/L_{B \\odot}$)} &\n\\colhead{} &\n\\colhead{($10^{10} \\; M_{\\odot}$)} &\n\\colhead{($10^{40}$~erg~s$^{-1}$)} &\n\\colhead{($10^{40}$~erg~s$^{-1}$)} \\cr\n}\n\\startdata\n1 & 0 & ... & ... & $4.64$ & 4.64 & $1.35\\tablenotemark{k} $\n& $1.36 $ & $13.70$ & 0.00 & $4.64 $ & 28.6 & 28.6 \\cr\n2 & 0 & ... & ... & $4.66$ & 4.66 & $1.81 $\n& $1.70$ & $ 13.71$ & 0.34 & $4.66 $ & 21.7 & 21.7 \\cr\n3 & 1 & ... & ... & $36.1 $\\tablenotemark{i}\n& $2.64 $ &\n$1.61 $ & $1.26 $ & $12.19 $& 0.19 & $0.254$ &\n18.7 & 36.4 \\cr\n4 & 4 & ... & ... & $81.1 $\\tablenotemark{j}\n& $1.36$ &\n$1.48 $ & $0.97 $ & $11.21$ & 0.10 & $ 0.013$ &\n8.8 & 42.6 \\cr\n5 & 4 & 15 & 1 & $4.65 $ & $1.55$\n& $1.50 $ &\n$1.01 $ & $11.36$ & 0.11 & $ 0.013$ & 13.9 & 27.7 \\cr\n6 & 4 & 2 & 1 & $4.65 $ & $3.76$ &\n$1.72 $ & $1.51 $ & $13.03$ & 0.27 & $ 0.015 $ &\n22.1 & 33.5 \\cr\n7 & 4 & 0.8 & 2 & $4.65 $ & $4.65$ &\n$1.81$ & $1.76$ & $13.71$ & 0.34 & $ 0.017$ &\n29.1 & 43.3 \\cr\n8\\tablenotemark{l} & 4 & 2 & 1 & $4.60 $ & $3.65$ &\n$1.29 $ & $1.17 $ & $9.74$ & 0.40 & $ 0.012 $ &\n20.0 & 28.1 \\cr\n\\enddata\n\\tablenotetext{a}{All masses evaluated at time $t_n = 13$ Gyrs.}\n\\tablenotetext{b}{Total cooled mass within 1 Mpc.}\n\\tablenotetext{c}{Mass of cooled gas within ${r_e/3} = 2.86$ kpc.}\n\\tablenotetext{d}{Total mass within ${r_e/3}$; $M_{*,dh}(r_3/3) = 1.36\n\\times 10^{11}$ $M_{\\odot}$.}\n\\tablenotetext{e}{Mass of cooled gas at ${r_e/3}$ evaluated using\nhydrostatic equilibrium.}\n\\tablenotetext{f}{$M{*,dh}/L_B = 10.18$ \nis the value for the stars and dark halo for Models 1-7.}\n\\tablenotetext{g}{Relative contribution of dropout mass \nto $M/L_B$ at $r_e/3$.}\n\\tablenotetext{h}{Mass cooled into central gridzone;\nthe central black hole in NGC 4472 has mass\n$M_{bh} = 0.29 \\times 10^{10}$ $M_{\\odot}$.}\n\\tablenotetext{i}{Mass within 100 kpc is $4.72 \\times 10^{10}$\n$M_{\\odot}$}\n\\tablenotetext{j}{Mass within 100 kpc is $4.96 \\times 10^{10}$\n$M_{\\odot}$}\n\\tablenotetext{k}{Mass of cooled gas is not included.}\n\\tablenotetext{l}{With lower $M/L_B$ for old stars.}\n\\tablenotetext{m}{ROSAT X-ray luminosity (0.2 - 2 keV) of \nbackground flow}\n\\tablenotetext{n}{Total ROSAT X-ray luminosity including \nemission from dropout}\n\\end{deluxetable}\n\n\\normalsize\n\n%***************Table 1 continued since \\rotate doesn't work********\n\n\\begin{deluxetable}{ccc}\n\\scriptsize\n\\tablewidth{15pc}\n\n\\tablenum{1}\n\\tablecolumns{3}\n\\tablecaption{MASS DROPOUT MODELS FOR NGC 4472 -- TABLE 1 CONTINUED\nHERE BECAUSE OF AASTEX BUG}\n\\tablehead{\n\\colhead{Model} &\n\\colhead{$L_{x,bck}^{ros}$\\tablenotemark{m}} &\n\\colhead{$L_{x,tot}^{ros}$\\tablenotemark{n}} \\cr\n\\colhead{} &\n\\colhead{($10^{40}$~erg~s$^{-1}$)} &\n\\colhead{($10^{40}$~erg~s$^{-1}$)} \\cr\n}\n\\startdata\n1 & 28.6 & 28.6 \\cr\n2 & 21.7 & 21.7 \\cr\n3 & 18.7 & 36.4 \\cr\n4 & 8.8 & 42.6 \\cr\n5 & 13.9 & 27.7 \\cr\n6 & 22.1 & 33.5 \\cr\n7 & 29.1 & 43.3 \\cr\n8 & 20.0 & 28.1 \\cr\n\\enddata\n\\end{deluxetable}\n\n\\normalsize\n\n\n%*******************************************************************\n\n%\\end{document}\n\\clearpage\n\n%for reference, this is the latex format used in figure captions \n%for the previous paper:\n\n\\vskip.1in\n\\figcaption[aasdropoutfig1.ps]{\n(a) Interstellar gas temperature and density in NGC 4472. \ntop: fit to ROSAT data for $T(R)$; bottom: fit to ROSAT\ndata for $n(r)$ (open circles) and {\\it Einstein} data (closed circles);\n(b) {\\it solid curve}: $M_x(r)$ determined from above data \nusing equation (1); \n{\\it long-dashed curve}: de Vaucouleurs \nmass profile $M_*(r)$ assuming $M_*/L_B = 9.2$.\n\\label{fig1}}\n\n\\vskip.1in\n\\figcaption[aasdropoutfig2.ps]{\n(a) Comparison of observed hot gas density and temperature \nin NGC 4472 with various hydrodynamical models at time \n$t_n = 13$ Gyrs.\nThe source of observed data in all panels is identical to \nthat in Figure 1.\n{\\it Light solid lines:} density and temperature of the \nbackground flow as functions of physical radius $r$;\n{\\it heavy solid lines:} apparent density and temperature \nas functions of $r$ including emission from cooling regions;\n{\\it dotted lines:} apparent gas temperature \nas function of projected \nradius, similar to the temperature data points.\n(b) Comparison of ROSAT and {\\it Einstein} \nX-ray surface brightness distributions in NGC 4472 \nwith various models. \n{\\it Light solid lines:} emission just from the \nbackground cooling flow; \n{\\it heavy solid lines:} combined emission from \nbackground and distributed cooling regions.\n\\label{fig2}}\n\n\\vskip.1in\n\\figcaption[aasdropoutfig3.ps]{\nBaryonic and non-baryonic mass distributions in NGC 4472.\n{\\it Light solid line:} de Vaucouleurs profile of \ndynamical mass based on $M/L_B = 9.2$;\n{\\it heavy solid line:} NFW dark halo profile for best fit \nto NGC 4472 data;\n{\\it short dashed line:} cooled dropout mass $M_{cg}$ for \nModel 1;\n{\\it long dashed line:} cooled dropout mass $M_{cg}$ for\nModel 4;\n{\\it dotted line:} cooled dropout mass $M_{cg}$ for\nModel 6;\n{\\it short dash-dotted line:} cooled dropout mass $M_{cg}$ for\nModel 7;\n{\\it long dash-dotted line:} cooled dropout mass $M_{cg}$ for\nModel 8.\n\\label{fig3}}\n\n\n\\vskip.1in\n\\figcaption[aasdropoutfig4.ps]{\n(a) Comparison of observed hot gas density and temperature\nin NGC 4472 with Model 8 at time\n$t_n = 13$ Gyrs. \nData and curve designations are identical to those in \nFigure 2a.\n(b) X-ray surface brightness profiles at $t_n = 13$ Gyrs \nfor Model 8.\nData and curve designations are identical to those in\nFigure 2b.\n\\label{fig4}}\n\n\\vskip.1in\n\\figcaption[aasdropoutfig5.ps]{\nMass profiles at $t_n = 13$ Gyrs for Model 6 (upper panel) \nand Model 8 (lower panel).\n{\\it Solid lines:} X-ray mass profiles $M_x(r)$\nderived from the computed models using equation (1);\n{\\it dashed lines:} actual mass profiles $M_{tot}(r)$\nfor each model;\n{\\it dotted curves:} de Vaucouleurs profiles $M_*(r)$\nbased on uniform mass to light ratios, \n$M/L_B = 9.2$ for Model 6 and $M/L_B = 6$ for Model 8.\n{\\it Circles:} data points show the \napparent mass distribution \n$M_x(r)$ using NGC 4472 observations and equation (1).\n\\label{fig5}}\n\n\\vskip.1in\n\\figcaption[aasdropoutfig6.ps]{\nPlot of the specific mass loss rate $\\alpha_*(t_n)$ (in sec$^{-1}$)\nagainst the mass to light ratio $M_*/L_B$ in solar units \nfor 84 power law initial mass functions with varying slopes and \nmass cutoffs as described in the text.\n\\label{fig6}}\n\n\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002386
|
Dust Emission from High Redshift QSOs
|
[
{
"author": "C. L. Carilli$^{1,2}$"
},
{
"author": "F. Bertoldi$^1$"
},
{
"author": "K.M. Menten$^1$"
},
{
"author": "M.P. Rupen$^2$"
},
{
"author": "E. Kreysa$^1$"
},
{
"author": "Xiaohui Fan$^3$"
},
{
"author": "Michael A. Strauss$^3$"
},
{
"author": "Donald P. Schneider$^4$"
},
{
"author": "A. Bertarini$^1$"
},
{
"author": "M.S. Yun$^2$"
},
{
"author": "R. Zylka$^1$"
}
] |
We present detections of emission at 250 GHz (1.2 mm) from two high redshift QSOs from the Sloan Digital Sky Survey sample using the bolometer array at the IRAM 30m telescope. The sources are SDSSp 015048.83+004126.2 at $z = 3.7$, and SDSSp J033829.31+002156.3 at $z = 5.0$, which is the third highest redshift QSO known, and the highest redshift mm emitting source yet identified. We also present deep radio continuum imaging of these two sources at 1.4 GHz using the Very Large Array. The combination of cm and mm observations indicate that the 250 GHz emission is most likely thermal dust emission, with implied dust masses $\approx 10^8$ M$_\odot$. We consider possible dust heating mechanisms, including UV emission from the active nucleus (AGN), and a massive starburst concurrent with the AGN, with implied star formation rates $> 10^3$ M$_\odot$ year$^{-1}$.
|
[
{
"name": "0338.tex",
"string": "\\documentstyle[12pt,aasms4,psfig]{article}\n%\\documentstyle[12pt,aasms4]{article}\n%\\documentstyle[emulateapj]{article}\n \n\\slugcomment{to appear in the Astrophysical Journal (Letters)} \n \n\\begin{document}\n \n\\title{Dust Emission from High Redshift QSOs}\n\n%the $z = 5$ QSO SDSS 0338+0021\n%and the $z = 3.7$ QSO SDSS 0150+0041}\n \n\\author{\nC. L. Carilli$^{1,2}$,\nF. Bertoldi$^1$,\nK.M. Menten$^1$,\nM.P. Rupen$^2$,\nE. Kreysa$^1$,\nXiaohui Fan$^3$,\nMichael A. Strauss$^3$,\nDonald P. Schneider$^4$,\nA. Bertarini$^1$,\nM.S. Yun$^2$,\nR. Zylka$^1$\n} \n\n\\affil{$^{1}$Max-Planck-Institut f\\\"{u}r Radioastronomie,\nAuf dem H\\\"ugel 69, D-53121 Bonn, Germany}\n\n\\affil{$^{2}$National Radio Astronomy Observatory, P.O. Box O,\nSocorro, NM 87801, USA }\n\n\\affil{$^{3}$Princeton University Observatory, Peyton Hall, Princeton,\nNJ 08544, USA}\n\n\\affil{$^{4}$Dept. of Astronomy, Pennsylvania State University, \nUniversity Park, PA 16802, USA} \n\n\\vskip 0.2in\n\\affil{ccarilli@nrao.edu} \n\n\\begin{abstract}\n\nWe present detections of emission at 250 GHz (1.2 mm) from two high\nredshift QSOs from the Sloan Digital Sky Survey sample using the\nbolometer array at the IRAM 30m telescope. The sources are \nSDSSp 015048.83+004126.2\nat $z = 3.7$, and SDSSp J033829.31+002156.3\nat $z = 5.0$, which \nis the third highest redshift QSO known, and the highest\nredshift mm emitting source yet identified. We also present deep\nradio continuum imaging of these two sources at 1.4 GHz using the Very\nLarge Array. The combination of cm and mm observations indicate that\nthe 250 GHz emission is most likely thermal dust emission, with\nimplied dust masses $\\approx 10^8$ M$_\\odot$. We consider possible\ndust heating mechanisms, including UV emission from the active nucleus\n(AGN), and a massive starburst concurrent with the AGN, with implied\nstar formation rates $> 10^3$ M$_\\odot$ year$^{-1}$.\n\n\\end{abstract}\n \n\\keywords{dust: galaxies ---\nradio continuum: galaxies --- infrared: galaxies ---\ngalaxies: starburst, evolution, active} \n\n\\section {Introduction}\n\nModern telescopes operating from radio through optical wavelengths are\ndetecting star forming galaxies out to redshifts $z > 4$ (Steidel et\nal. 1999, Bunker \\& van Breugel 2000, Adelberger \\& Steidel 2000). \nThese observations are pushing into the `dark\nages,' the epoch when the first stars and/or black holes may have\nformed (Rees 1999). Millimeter (mm) and submm\nobservations provide a powerful probe into this era due to the\nsharp rise of observed flux density with increasing frequency in the\nmodified Rayleigh-Jeans portion of the grey-body spectrum for thermal\ndust emission from galaxies. Millimeter and submm surveys thereby\nprovide a uniquely {\\it distance independent} sample of objects in the\nuniverse for $z > 0.5$ (Blain \\& Longair 1993). These surveys have\nrevealed a population of dusty, luminous star forming galaxies\nat high redshift which may correspond to forming spheroidal galaxies\n(Smail, Ivison, \\& Blain 1998, Hughes et al. 1998, Barger et\nal. 1998, Eales et al. 1998, Bertoldi et al. 2000). An interesting\nsub-sample of dust emitting sources at high redshift are active\ngalaxies, including powerful radio galaxies (Chini \\& Kr\\\"ugel 1994,\nHughes \\& Dunlop 1999, Cimatti et al. 1999, Best et al. 1999,\nPapadopoulos et al. 1999, Carilli et al. 2000), and optically selected\nQSOs (Omont et al. 1996a).\n\nIn an extensive survey at 240 GHz, Chini, \nKreysa, \\& Biermann (1989) found that the majority of $z < 1$ QSOs\nshow dust emission with dust masses $\\approx$ few$\\times 10^{7}$\nM$_\\odot$, comparable to normal spiral galaxies. \nThey argue that the dominant dust heating mechanism is\nradiation from the active nucleus (AGN), based primarily on spectral\nindices between mm and X-ray wavelengths. On the other hand, Sanders\net al. (1989) showed that the majority of radio quiet QSOs in the PG\nsample show spectral energy distributions from cm to submm wavelengths\nconsistent with star forming galaxies. However, they suggest that \nthis may be coincidental, since concurrent starbursts would\nrequire large star formation rates to power the dust emission, while\nit would require the\nabsorption of only a fraction of the AGN UV luminosity by dust.\n\nOmont et al. (1996a) extended the 240 GHz study of QSOs to high\nredshift by observing a sample of $z > 4$ QSOs from the Automatic\nPlate Measuring (APM) survey. They found that 6 of 16 sources show\ndust emission at 3 mJy or greater, with implied FIR luminosities\n$\\ge$ 10$^{13}$ L$_\\odot$, and dust masses $\\ge 10^8$ M$_\\odot$.\nFollow-up observations of three of these dust-emitting QSOs revealed\nCO emission as well, with implied molecular gas masses $\\approx$ few\n$10^{10}$ M$_\\odot$ (Guilloteau et al. 1997, 1999, Ohta et al. 1996,\nOmont et al. 1996b, Carilli, Menten, \\& Yun 1999). \nGiven the large dust and gas\nmasses, Omont et al. (1996a) made the circumstantial argument that the\ndominant dust heating mechanism may be star formation. Supporting\nevidence came from deep radio observations at 1.4 GHz, which showed\nthat the ratio of the radio continuum to submm continuum emission from\nthese sources is consistent with the well established \nradio-to-far IR \ncorrelation for low redshift star forming galaxies (Yun et al. 1999).\nAll these data\n(dust, CO, radio continuum) suggest that the host galaxies of these\nQSOs are gas-rich, and may be forming stars at a rate $\\ge$ 10$^3$\nM$_\\odot$ year$^{-1}$, although it remains unclear to what extent the\nAGN plays a role in heating the dust and powering the radio emission.\n\nWe have begun an extensive observational program \nat cm and mm wavelengths on a sample of high\nredshift QSOs from the Sloan Digital Sky Survey (SDSS; York\net al. 2000). The sample is the result of optical \nspectroscopy of objects of\nunusual color from the northern Galactic Cap and the Southern\nEquatorial Stripe, which has yielded 40 QSOs with $z \\ge 3.6$, \nincluding the four highest redshift QSOs known\n(Fan et al. 1999, Fan et al. 2000,\nSchneider et al. 2000). This sample presents an ideal opportunity to\ninvestigate the properties of the most distant QSOs and their host\ngalaxies. The SDSS sample spans a range of $M_B = -26.1 \\rm ~to~\n-28.8$, and a redshift range of 3.6 to 5.0. Comparative numbers for\nthe APM sample observed by Omont et al. (1996a) are\n$M_B = -26.8 \\rm ~to~ -28.5$, and $4.0 \\le z \\le 4.7$. \n\nOur observations of the SDSS QSO sample include sensitive radio\ncontinuum imaging at 1.4 GHz with the Very Large Array (VLA), and\nphotometry at 250 GHz using the Max-Planck Millimeter Bolometer array\n(MAMBO) at the IRAM 30m telescope. These observations are a factor\nthree more sensitive than previous studies of high redshift QSOs at\nthese wavelengths (Schmidt et al. 1995, Omont et al. 1996a), and are\nadequate to detect emission powered by star formation in the host\ngalaxies of the QSOs at the level seen in low redshift ultra-luminous\ninfrared galaxies (L$_{FIR}$ $\\ge$ 10$^{12}$ L$_\\odot$; Sanders and\nMirabel 1999). We will use these data to measure the correlations\nbetween optical, mm, and cm continuum properties, and optical emission\nline properties, and look for trends as a function of redshift. \n\nIn this letter we present the first two mm detections from this study.\nThe sources are SDSSp J033829.31+002156.3 (hereafter SDSS 0338+0021),\nand SDSSp J015048.83+004126.2 (hereafter SDSS 0150+0041); these\nobjects' names are their J2000 coordinates. They have $z = 5.00 \\pm\n0.04$ with $i^* = 19.96$, and $z = 3.67 \\pm 0.02$ with $i^* =18.20$\n(Fan et al. 1999). The absolute blue magnitudes of these quasars are\n--26.56 and --27.75, respectively, assuming H$_o$ = 50 km s$^{-1}$\nMpc$^{-1}$ and q$_o$ = 0.5. \nThese two sources were taken from the Fall survey sample\n(Fan et al. 1999), which covered a total area of 140 deg$^2$. \nNote that J0150+0041 is the second most lumininous QSO in the \ncombined Fall and Spring samples of Fan et al. (1999, 2000). \n \n\\section{Observations and Results}\n\nObservations were made using MAMBO (Kreysa et al. 1999) at\nthe IRAM 30m telescope in December 1999 and February 2000. \nMAMBO is a 37 element\nbolometer array sensitive between 190 and 315 GHz. \nThe half-power sensitivity range is 210 to 290 GHz, and\nthe effective central frequency for a typical\ndust emitting source at high redshift is 250 GHz. \nThe beam for the feed horn of each bolometer is\nmatched to the telescope beam of 10.6$''$, and the bolometers are\narranged in an hexagonal pattern with a beam separation of\n22$''$. Observations were made in standard on-off mode, with 2 Hz\nchopping of the secondary by 50$''$ in azimuth. \nThe data were reduced using\nIRAM's NIC and MOPSI software packages (Zylka 1998). \nPointing was monitored every hour, and was found to be\nrepeatable to within 2$''$. The sky opacity was monitored every\nhour, with zenith opacities between 0.23 and 0.36. Gain\ncalibration was performed using observations of Mars, Neptune, and\nUranus. We estimate a 20$\\%$ uncertainty in absolute flux\ndensity calibration based on these observations. The target sources\nwere centered on the central bolometer in the array (channel 1),\nand the temporally correlated variations of the sky signal (sky-noise) \ndetected in the remaining bolometers was subtracted from all the\nbolometer signals. The total on-target plus off-target observing time \nfor SDSS 0338+0021 was 108 min, while that for SDSS 0150+0041 was\n77 min. \n\nThe source SDSS 0338+0021 was detected with a flux density of\n$3.7 \\pm 0.5$mJy (Figure 1). At $z = 5.0$, 250 GHz corresponds to an\nemitted frequency of 1500 GHz, or a wavelength of 200 $\\mu$m.\nThe source SDSS 0150+0041 was detected at 250 GHz\nwith a flux density of $2.0 \\pm 0.4$ mJy (Figure 1). \nAt $z = 3.7$, 250 GHz corresponds to an emitted frequency of 1180 GHz,\nor a wavelength of 254 $\\mu$m. \nThe quoted errors in flux density do not\ninclude the $20\\%$ uncertainty in gain calibration. The sources \nwere not seen to vary dramatically ($\\le 30\\%$)\nbetween December 1999 and February 2000. \n\nAssuming a dust spectrum of the type seen in the low redshift starburst\ngalaxy Arp 220 (corresponding roughly to a modified black body\nspectrum of index 1.5 and temperature of 50 K), \nthe implied 60$\\mu$m luminosity (Rowan-Robinson et al. 1997) \nfor SDSS 0338+0021 is L$_{60} = 8.2 \\pm 1.0 \\times\n10^{12}$ L$_\\odot$, while that\nfor 0150+021 is L$_{60} = 5.0 \\pm 1.0 \\times 10^{12}$ L$_\\odot$.\nIncreasing the temperature to 100 K would increase the values of\nL$_{60}$ by a factor of about 3.5, while using the spectrum of M82 as\na template would increase the values by a factor of 1.5. \n\nThe 1.4 GHz VLA observations were made in the A \n(30 km) and BnA (mixed 30 km and 10 km) configurations\non July 8, August 14, September 30, and\nOctober 8, 1999, using a total bandwidth of 100 MHz with two\northogonal polarizations. Each source was observed for a total of 2\nhours, with short scans made over a large range in hour angle to\nimprove Fourier spacing coverage. Standard phase and amplitude\ncalibration were applied, as well as self-calibration using background\nsources in the telescope beam. The absolute flux density scale was set \nusing observations of 3C 48. The final images were generated using\nthe wide field imaging and deconvolution capabilities of the AIPS task\nIMAGR. The observed rms noise values on the images were within\n30$\\%$ of the expected theoretical noise. The Gaussian restoring CLEAN \nbeam was between 1.5$''$ and 2$''$ FWHM.\n\nNeither source was detected at 1.4 GHz. For SDSS 0338+0021 the\nobserved value at the source position was $37 \\pm 24$ $\\mu$Jy\nbeam$^{-1}$, and the peak in an 8$''$ box centered on the source\nposition was 60$\\mu$Jy beam$^{-1}$ located 3.4$''$ southwest of the\nsource position. At $z = 5.0$, 1.4 GHz corresponds to an emitted\nfrequency of 8.4 GHz. For SDSS 0150+0041 the observed value at the\nsource position was $-3.0 \\pm 19$ $\\mu$Jy beam$^{-1}$, and the peak in\nan 8$''$ box centered on the source position was 55$\\mu$Jy beam$^{-1}$\nlocated 2.8$''$ north of the source position. At $z = 3.7$, 1.4 GHz\ncorresponds to an emitted frequency of 6.6 GHz. We quote maximum and\nminimum values in an 8$''$ box in the eventuality that the dust\nemission is not centered on the QSO position (see discussion below).\nIn the analysis below we adopt an upper limit of 60$\\mu$Jy beam$^{-1}$\nfor both sources.\n\nAssuming a radio spectral index of --0.8, the 3$\\sigma$ upper limit to\nthe rest frame spectral luminosity at 5 GHz of SDSS 0338+0021 is $3.3\n\\times 10^{31}$ erg s$^{-1}$ Hz$^{-1}$, while that for 0150+0041 is\n$1.7 \\times 10^{31}$ erg s$^{-1}$ Hz$^{-1}$. These upper limits\nplace the sources in the\nradio quiet regime, using the division at $10^{33}$ erg s$^{-1}$\nHz$^{-1}$ at 5 GHz suggested by Miller et al. (1990). Note that\n90$\\%$ of optically selected \nhigh redshift QSOs are radio quiet according to this\ndefinition (Schmidt et al. 1995).\n \n\\section{Discussion}\n\nThe fact that the cm flux densities for these sources are at least two\norders of magnitude below the mm flux densities, and that the sources\ndo not appear to be highly variable at 250 GHz, argues that the mm\nsignal is thermal emission from warm dust. Adopting the relation\nbetween L$_{60}$ and dust mass for hyper-luminous infrared galaxies\n(i.e. galaxies with L$_{60}$ $\\ge 10^{13}$ L$_\\odot$), derived by\nRowan-Robinson (1999), the dust mass in SDSS 0338+0021 is $3.5 \\times\n10^8$ M$_\\odot$, while that in SDSS 0150+0021 is $2 \\times 10^8$\nM$_\\odot$. This gives gas masses of $10 \\times 10^{10}$ M$_\\odot$,\nand $6 \\times 10^{10}$ M$_\\odot$, respectively, using the\ndust-to-molecular gas mass ratio of 300 suggested by Rowan-Robinson\n(1999). Of course, such estimates using data at a single frequency\nare quite uncertain due to the lack of knowledge of\nthe dust temperature and emissivity law, \nand uncertainties in the gas-to-dust\nratio. We are currently searching for CO emission from these two\nsources to obtain a better understanding of the gas content of these\nQSOs.\n\nOmont et al. (1996a) found that dust emission\nseems to be correlated\nwith broad absorption line systems (BALs) in the APM QSO sample. \nThe source SDSS 0150+0041 has been classified as a\n`mini-BAL' by Fan et al. (1999). The source SDSS 0338+0021 \nalso shows strong and broad associated C IV absorption \nin high signal-to-noise spectra (Songaila et al. 1999). The\npresence of strong associated absorption\nis yet another indication of a rich gaseous\nenvironment in these systems. \n\nThe critical question when interpreting thermal dust emission from\nhigh redshift QSOs is whether the emission is powered by the AGN or\nstar formation. This question has been considered in great detail for\nultra- and hyper-luminous infrared galaxies (Sanders \\& Mirabel 1996,\nSanders et al. 1989, Genzel et al. 1998), and a review of this\nquestion can be found in Rowan-Robinson (1999). Dust emitting\nluminous QSOs, such\nas SDSS 0338+0021 and SDSS 0150+0041, comprise a subset of the ultra-\nand hyper-luminous infrared galaxies. \nIn QSOs, typically less than 30$\\%$ of the bolometric luminosity\nis emitted in the infrared. Using the blue luminosity bolometric\ncorrection factor of 16.5 derived for the PG QSO sample by\nSanders et al. (1989), the FIR luminosity of SDSS 0338+0021\naccounts for only 15$\\%$ of its bolometric luminosity,\nand the FIR emission of SDSS 0150+0041 comprises only\n3$\\%$ of its bolometric luminosity. \nIt is important to keep in mind that the FIR luminosity estimates\nare based on measurements at a single frequency, and hence have\nat least a factor two uncertainty (Adelberger \\& Steidel 2000), \nwhile the bolometric luminosity estimates require an extrapolation\nfrom the rest frame UV measurements into the blue, and hence have\ncomparable uncertainties.\nStill, it is likely that only a minor fraction of\nthe total AGN luminosity needs to be absorbed and re-emitted\nby dust to explain the FIR luminosity in both SDSS 0338+0021 and \nSDSS 0150+0041. \n\nAn important related point is that the IR emitting region has a\nminimum size of about 0.5 kpc for sources such as SDSS 0338+0021 and\nSDSS 0150+0041, as set by the far IR luminosity and assuming optically\nthick dust emission with a dust temperature of 50 K (Benford et\nal. 1999, Carilli et al. 1999). In the Sanders et al. (1989) model\nfor AGN-powered IR emission from QSOs, dust heating on kpc scales is\nfacilitated by assuming that the dust is distributed in a kpc-scale\nwarped disk, thereby allowing UV radiation from the AGN to illuminate\nthe outer regions of the disk. Detailed models by Andreani,\nFranceschini, and Granato (1999) and Willott et al. (1999) show that\nthe dust emission spectra from 3$\\mu$m to 30$\\mu$m can be \nexplained by such a model. \n\nThe alternative to dust heating by the AGN is to assume that there is\nactive star formation co-eval with the AGN in these systems. Omont et\nal. (1996) and Rowan-Robinson (1999) argue that star formation would\nbe a natural, although not required, consequence of the large gas\nmasses in these systems. Imaging of a few high redshift dust emitting\nAGN shows that in some cases the dust and CO emission come from\nregions that are separated from the location of the optical AGN by\ntens of kpc (Omont et al. 1999b, Papadopoulos et al. 2000, Carilli et\nal. 2000). Such a morphology argues strongly for a dust heating\nmechanism unrelated to UV emission from the AGN, at least in these\nsources. Lastly, Rowan-Robinson (1999) performed a detailed analysis\nof the spectral energy distributions (SEDs) of hyper-luminous infrared\ngalaxies and concluded that, although $\\ge 50\\%$ of these systems show\nevidence for an AGN in the optical spectra, the SEDs between 50$\\mu$m\nand 1mm are best explained by dust heated by star formation. Yun et\nal. (2000) have extended this argument to cm wavelengths and reach a\nsimilar conclusion. \n\nCarilli \\& Yun (2000) present a model for the expected behavior with\nredshift of the observed spectral index between cm and submm\nwavelengths for star forming galaxies, relying on the tight\nradio-to-far IR correlation found for nearby star forming galaxies\n(Condon 1992). \n%Implicit in these models is the assumption that the\n%radio-to-far IR correlation is unchanged with redshift (see Carilli\n%\\& Yun 1999 for a discussion of this issue). \nUsing the observed mm\nflux densities of SDSS 0150+0041 and SDSS 0338+0021, \nthese models predict flux densities\nat 1.4 GHz between 15 and 60 $\\mu$Jy for both sources. \nRadio images with a factor three better sensitivity are required to\ndetermine if these two sources have cm-to-mm SEDs\nconsistent with low redshift star forming galaxies. \n\nIf the dust and radio continuum emission is powered by star formation\nin SDSS 0338+0021 and SDSS 0150+0041, then the star formation rates in\nthese galaxies are high. Using the relation between L$_{60}$ and\ntotal star formation rate given in Rowan-Robinson (1999) for a $10^8$\nyear starburst assuming a standard Salpeter IMF, the implied rate for\nSDSS 0338+0021 is 2700 M$_\\odot$ year$^{-1}$, while that for SDSS\n0150+0041 is 1800 M$_\\odot$ year$^{-1}$. Note that the high redshift\nQSOs from the APM sample were detected at flux levels between 3mJy\nand 12mJy at 240 GHz (Omont et al. 1996a), hence the required star formation\nrates may be even larger in some systems. The implication is that we may\nbe witnessing the formation of a large fraction of the stars of the\nAGN host galaxy on a timescale $\\le 10^8$ years. \n\nMagnification by\ngravitational lensing would lower the required luminosities, bringing\nthe sources more in-line with known ultra-luminous infrared galaxies.\nTwo of the APM QSOs detected at 240 GHz by Omont et al. (1996a)\nshow possible evidence for gravitational lensing, while \ntwo other high redshift dust emitting QSOs, H1413+117 and APM\n08279+5255, are known to be gravitationally lensed (Barvainis et\nal. 1994, Downes et al. 1999). However, thus far there is\nno evidence for multiple imaging on arc-second scales for either SDSS\n0338+0021 or SDSS 0150+0041 in optical and near IR images (Fan et al.\n2000). Imaging at sub-arcsecond resolution is required to determine\nif these sources are gravitationally lensed.\n\nAn important question concerning the formation of objects in the\nuniverse is: which came first, black holes or stars (Rocca-Volmerange\net al. 1993)? If the dust emission is powered by a starburst in SDSS\n0338+0021 and SDSS 0150+0041, then the answer to the above question in\nsome systems may be: both. Co-eval starbursts and AGN at high\nredshift may not be surprising, since both may occur in violent galaxy\nmergers as predicted in models of structure formation via hierarchical\nclustering (Franceschini et al. 1999, Taniguchi, Ikeuchi, \\& Shioya\n1999, Blain et al. 1999, Kauffmann \\& Haehnelt 2000, Granato et\nal. 2000). To properly address the interesting question of \nAGN versus starburst dust heating in these high redshift QSOs\nrequires well sampled SEDs from cm to optical wavelengths, \nand perhaps most importantly, imaging of the mm and cm continuum, and\nCO emission, with sub-arcsecond resolution. \n\n\\vskip 0.2truein \n\nThe VLA is a facility of the National Radio\nAstronomy Observatory (NRAO), which is operated by Associated\nUniversities, Inc. under a cooperative agreement with the National\nScience Foundation.\nThis work was based on observations carried out with the IRAM 30 m\ntelescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and\nIGN (Spain). This research made use of the NASA/IPAC Extragalactic\nData Base (NED) which is operated by the Jet propulsion Lab, Caltech,\nunder contract with NASA. CC acknowledges support from the Alexander\nvon Humboldt Society. DPS acknowledges support from National Science\nFoundation Grant AST99-00703. XF and MAS acknowledge support from the\nResearch Corporation, NSF grant AST96-16901, and an Advisory Council\nScholarship.\n\n%\\vfill\\eject\n\n\\begin{references}\n\n\\reference{}Adelberger, K.L \\& Steidel, C.C. 2000, \nApJ, in press (astroph 0001126)\n\n\\reference{}Andreani, P., Franceschini, A., and Granato, G. 1999,\nMNRAS, 306, 161\n\n\\reference{}Barger, A., Cowie, L.L., Sanders, D.B., Fulton, E.,\nTaniguchi, Y., Sato, Y., Kawara, K., \\& Okuda, H. 1998, \nNature, 394, 248\n\n\\reference{}Barvainis, R., Tacconi, L., Antonucci, R., Alloin, D. and\nColeman, P. 1994, Nature, 371, 586\n\n\\reference{}Benford, D. J., Cox, P., Omont, A., Phillips, T. G.,\n\\&\\ McMahon, R. G. 1999, ApJ (letters), 518, 65\n\n\\reference{} Bertoldi, F. et al. 2000, in preparation\n\n\\reference{} Best, P. et al. 1999, MNRAS (letters), 301, 15\n\n\\reference{}Blain, A.W., \\&\\ Longair, M.S. 1993, MNRAS, 264, 509 \n\n\\reference{}Blain, A.W., Jameson, A., Smail, I., Longair, M.S., \nKneib, J.-P., and Ivison, R.J. 1999, MNRAS, 309, 715\n\n\\reference{}Bunker, A.J. and van Breugel, W.J.M. (eds) 1999, \n{\\sl The Hy-Redshift Universe} (PASP, San Francisco)\n\n\\reference{}Carilli, C. L. \\& Yun, \nM. S. 1999, ApJ, 513, L13\n \n\\reference{}Carilli, C. L., Menten, K.M. \\& Yun, \nM. S. 1999, ApJ (lettes), 521, L25\n\n\\reference{}Carilli, C. L. \\& Yun, \nM. S. 2000, ApJ, in press\n\n\\reference{}Carilli, C.L. et al. 2000, in preparation\n\n\\reference{} Carilli, C.L., Menten, K.M., Yun, M.S., Bertoldi, F.,\nOwen, F., \\& Dey, A. 1999, in {\\sl Scientific imperatives at \ncentimeter \\& meter wavelengths,} eds. M.P. van Haarlem \\& J.M. van\nder Hulst (NFRA, Dwingeloo)\n\n%\\reference{}Chapman, S.C., et al. 1999, MNRAS, in press (astroph 9909092)\n\n\\reference{}Chini, R., Kreysa, E., \\& Biermann, P.L. 1989, \nA\\&A, 219, 87\n\n\\reference{} Chini, R. \\& Kr\\\"ugel, E. 1994, A\\&A (letters), 288, 33\n\n\\reference{}Cimatti, A., Freudling, W., R\\\"ottgering, H., Ivison,\nR.J., \\& Mazzei, P. 1998, A\\&A, 329, 399\n\n\\reference{}Condon, J.J. 1992, ARAA, 30, 575\n\n%\\reference{}Downes, D. \\& Solomon, P. 1998, ApJ, 507, 615\n\n\\reference{}Downes, D., Neri, R., Wiklind, T., Wilner, D.J., and\nShaver, P.A. 1999, ApJ (letters), 513, 1\n\n\\reference{}Eales, S. et al. 1999, ApJ, 515, 518\n\n%\\reference{}Efstathiou, A., Rowan-Robinson, M., \\& Siebenmorgen, D. \n%2000, MNRAS, in press (astroph 9912252)\n\n\\reference{}Fan, X. et al. 1999, AJ, 118, 1\n\n\\reference{}Fan, X. et al. 2000, AJ, 119, 1\n\n\\reference{}Franceschini, A., Hasinger, G., Mayaji, T., \\& Malquori,\nD. 1999, MNRAS (letters), 310, 5\n\n\\reference{}Granato, G.L. et al. 2000, MNRAS, in press (astroph\n9911304) \n\n\\reference{}Guilloteau, S., Omont,A., \nMcMahon, R.G., Cox,P., \\& Petitjean,P. 1997, A\\&A, 328, L1\n\n\\reference{}Guilloteau, S., Omont,A., \nMcMahon, R.G., Cox,P., \\& Petitjean,P. 1999, A\\&A, 349, 363\n\n\\reference{} Hughes, D.H. et al. 1998, Nature, 394, 241\n\n\\reference{} Hughes, D.H. \\& Dunlop, J.S. 1999, in {\\sl Highly\nRedshifted Radio Lines}, eds. C. Carilli, S. Radford, K. Menten, \\&\nG. Langston (PASP, San Francisco), p. 103\n\n%\\reference{}Hu, E., McMahon, R.G., \\&\\ Egami, E. 1996, ApJ, 459, L53\n\n\\reference{}Kreysa, E. et al. 1999, SPIE, 3357, 319\n\n\\reference{}Kauffmann, G. \\& Haehnelt, M. 2000, MNRAS, 311, 576\n\n%\\reference{}Neugebauer, G. et al. 1987, ApJ (Supp), 615\n\n\\reference{}Ohta, K., Yamada, T., Nakanishi,\nK., Kohno, K., Akiyama, M., \\& Kawabe, R. 1996, Nature, 382, 426\n\n\\reference{}Omont, A., McMahon, R. G., Cox,\nP., Kreysa, E., Bergeron, J., Pajot, F., \\& Storrie-Lombardi,\nL.J. 1996a, A\\&A, 315, 1 \n\n\\reference{}Omont, A., Petitjean, P.,\nGuilloteau, S., McMahon, R. G., Solomon, P. M., \\& Pecontal, E. 1996b,\nNature, 382, 428\n\n\\reference{}Papadopoulos, P.P. et al. 2000, ApJ, 528, 626 (astroph\n9908286) \n\n\\reference{}Rees, M.J. 1999, in {\\sl After the Dark Ages},\neds. S. Holt \\& E. Smith (AIP, Washington), p. 13\n\n\\reference{}Rowan-Robinson, M. 1999, MNRAS, in press (astroph 9912286)\n\n\\reference{}Rowan-Robinson, M. et al. 1997, MNRAS, 298, 490\n\n\\reference{}Rocca-Volmerange, B., Guiderdoni, B., Dennefeld, M., \\&\nVan, Tran-Thanh 1993, {\\sl First Light in the Universe}, (Editions\nFrontieres, Cedex, France)\n\n\\reference{}Sanders, D.B. \\& Mirabel, I.F. 1996, ARAA, 34, 749\n\n\\reference{}Sanders, D.B., Phinney, E.S., Neugebauer, G., Soifer,\nB.T., \\& Matthews, K. 1989, ApJ, 347, 29\n\n\\reference{}Schmidt, M., van Gorkom, J.H., Schneider, D.P., \n\\& Gunn, J.E. 1995, AJ, 109, 473\n\n\\reference{}Schneider, D.P. et al. 2000, PASP, 112, 6\n\n\\reference{}Songaila, A., Hu, E.M., Cowie, L.L., \\& McMahon,\nR.G. 1999, ApJ (letters), 525, 5\n\n\\reference{}Steidel, C.C., Adelberger, K.L., Giavalisco, M.,\nDickinson, M., \\& Pettini, M. 1999, ApJ, 519, 1\n\n%\\reference{}Stocke, J.T., Morris, S.L., Weymann, R.J., and\n%Foltz, C.B. 1992, ApJ, 396, 487\n\n\\reference{}Taniguchi, Y., Ikeuchi, S., \\& Shioya, Y. 1999, ApJ\n(letters), 514, 9\n\n\\reference{}Willott, C.J., Rawlings, S., and Jarvis, M.J. 2000, MNRAS, \nin press (astroph 9910422)\n\n\\reference{}York, D.G. et al. 2000, AJ, submitted\n\n\\reference{}Yun, M.S., Carilli, C.L., Kawabe, R., Tutui, Y., Kohno,\nK. \\& Ohta, K. 2000, ApJ, in press\n\n\\reference{}Zylka, R. 1998, {\\sl MOPSI Users Manual}, (IRAM: Grenoble)\n\n\\end{references}\n\n\\newpage\n\n\\begin{figure}\n%\\vskip -1in\n%\\psfig{figure=carillif1.ps,width=4in}\n%\\psfig{figure=carillif2.ps,width=4in}\n\\caption{The time averaged, opacity corrected, sky-noise subtracted\nflux densities derived for 35 of the 37 bolometers (two channels\nwere disfunctional). \nThe thick line represents the time-averaged signal from the central, \non-source bolometer (channel 1). The thin solid line is the \nmean of the off-source bolometers, and \nthe dashed lines \nshow the 1$\\sigma$ noise envelope for the off-source bolometers. \nThe upper figure shows observations of SDSS 0338+0021 and the lower\nfigure shows observations of SDSS 0150+0041.\n}\n\\end{figure}\n\n\\begin{figure}\n\\vskip -0.5in\n\\psfig{figure=carillif1.ps,width=4in}\n\\psfig{figure=carillif2.ps,width=4in}\n\\end{figure}\n\n\\vfill\\eject \n\n\n\\end{document}\n\n\n%Preliminary results from our observations of approximately a quarter\n%of the SDSS sample indicate that between 20$\\%$ and 30$\\%$ of the\n%objects have flux densities $\\ge$ \n%$\\ge$ 2 mJy at 250 GHz. Observations of the\n%full sample will be completed in the Spring of 2000, and will provide\n%more accurate statistics for dust emission from high redshift QSOs. \n\n\n\\begin{figure}\n%\\vskip -1in\n\\psfig{figure=carillif1.ps,width=4in}\n\\psfig{figure=carillif2.ps,width=4in}\n\\caption{The time averaged, opacity corrected, sky-noise subtracted\nflux densities derived for 35 of the 37 bolometers (two channels\nwere disfunctional). \nThe thick line represents the time-averaged signal from the central, \non-source bolometer (channel 1).\nThe dashed lines \nshow the 1$\\sigma$ noise envelope for the off-source bolometers. \nThe upper figure is for SDSS 0338+0021 and the lower figure is\nfor SDSS 0150+0041.\n}\n\\end{figure}\n\n\\vfill\\eject \n\n\n\n\n\nradio flux densities of \nSDSS 0338+0021 \\& SDSS 0159+0041 are consistent with radio emission driven by\nextreme starbursts, comparable to hyperluminous IRAS galaxies\n(Rowan-Robinson 1999), with luminosities about an order of magnitude\nlarger than nearby ultraluminous starburst galaxies\n(Sanders \\& Mirabel 1996).\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nthe rest-frame far IR emission is simply re-cycled UV radiation from\nthe AGN, since \n\n\n\n$<$ 20$\\%$ of the bolometric luminosity of \n\n\n\n\n\n\n\n\n\n\n\nOmont et\nal. (1996a) have made the circumstantial argument that the occurrence\nof star formation is very likely in these objects, given the large\nreservoirs of gas \\& dust. A more direct diagnostic is comparing the\nobserved spectral index between cm \\& mm frequencies with that\nexpected for a starburst galaxy (Yun et al. 2000), \n\n This model is based on a sample\nof 17 low redshift star forming galaxies with well sampled cm-through-IR\nspectral energy distributions. The expected spectral index between\nobserved frequencies of 1.4 GHz \\& 350 GHz for a source at $z = 5.0$ is\n1.08$\\pm$0.13, while that for a source at $z = 3.7$ is 0.97$\\pm$0.12.\nAssuming a submm spectrum with a spectral index of +3.5 between 240\nGHz \\& 350 GHz leads to an observed value for SDSS 0150+0041 of $0.92 \\pm\n0.14$, while the 3$\\sigma$ lower limit for SDSS 0338+0021 is 0.92. Given\nthat we only have a lower limit to the cm-to-mm spectral index for\nSDSS 0338+0021, \\& a marginal cm detection of SDSS 0150+0041, this is clearly\nnot strong evidence that the observed dust and radio synchrotron\nemission from these two galaxies is powered by star formation (Chini\net al. 1989). These data simply show that the source spectra are at\nleast consistent with such a hypothesis. \nRadio imaging with a factor three\nbetter sensitivity is required to determine if these sources are\ninconsistent with the radio-far IR correlation for nearby starforming\ngalaxies.\n"
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astro-ph0002387
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"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentstyle[12pt]{article}\n\\def\\fnote#1#2{\\begingroup\\def\\thefootnote{#1}\\footnote{#2}\n\\endgroup}\n\n\\thispagestyle{empty}\n\n\\begin{document}\n\n\n\n\\hfill{UTTG-01-00}\n\n\n\\vspace{36pt}\n\n\\begin{center}\n{\\large{\\bf {\\em A Priori} Probability Distribution of the\nCosmological Constant}}\n\n\n\\vspace{36pt}\nSteven Weinberg\\fnote{*}{Electronic address:\nweinberg@physics.utexas.edu}\\\\\n{\\em Theory Group, Department of Physics, University of\nTexas\\\\\nAustin, TX, 78712}\n\\end{center}\n\n\\vspace{30pt}\n\n\\noindent\n{\\bf Abstract}\n\nIn calculations of the probability distribution for the\ncosmological constant, it has been previously assumed that\nthe {\\em a priori} probability distribution is essentially\nconstant in the very narrow range that is anthropically\nallowed. This assumption has recently been challenged.\nHere we identify large classes of theories in which\nthis assumption is justified.\n\n\\vfill\n\n\\baselineskip=24pt\n\\pagebreak\n\\setcounter{page}{1}\n\n\\begin{center}\nI. INTRODUCTION\n\\end{center}\n\nIn some theories of inflation$^1$ and of quantum\ncosmology$^2$\nthe observed big bang is just one of an\nensemble of expanding regions in which the cosmological\nconstant takes various different values. In such theories\nthere is a probability distribution for the cosmological\nconstant: the probability $d{\\cal P}(\\rho_V)$ that a\nscientific society in any of the expanding regions will\nobserve a vacuum energy between $\\rho_V$ and $\\rho_V+\\rho_V$\nis given by$^{3,4,5}$\n\\begin{equation}\nd {\\cal P}(\\rho_V)={\\cal P}_*(\\rho_V){\\cal N}(\\rho_V)d\n4\\rho_V\\;,\n\\end{equation}\nwhere ${\\cal P}_*(\\rho_V)d \\rho_V$ is the {\\em a priori}\nprobability that an expanding region will have a vacuum\nenergy between $\\rho_V$ and $\\rho_V+d\\rho_V$ (to be precise,\nweighted with the number of baryons in such regions), and\n${\\cal N}(\\rho_V)$ is proportional to the fraction of\nbaryons that wind up in galaxies. (The constant of\nproportionality in ${\\cal N}(\\rho_V)$ is independent of\n$\\rho_V$, because once a galaxy is formed the subsequent\nevolution of its stars, planets, and life is essentially\nunaffected by the vacuum energy.)\n\nThe factor ${\\cal N}(\\rho_V)$\n vanishes except for values of $\\rho_V$ that are very small\nby the standards of elementary particle physics, because for\n$\\rho_V$ large and positive there is a repulsive force that\nprevents the formation of galaxies$^6$ and hence of stars,\nwhile for $\\rho_V$ large and negative the universe\nrecollapses too fast for galaxies or stars to form.$^7$ The\nfraction of baryons that form galaxies has been\ncalculated$^5$ for $\\rho_V>0$ under reasonable astrophysical\nassumptions. On the other hand, we know little about the\n{\\em a priori} probability distribution\n${\\cal P}_*(\\rho_V)$. However, the range of values of\n$\\rho_V$ in which ${\\cal N}(\\rho_V)\\neq 0$ is so narrow\ncompared with the scales of energy density typical of\nparticle physics that it had seemed reasonable in earlier\nwork $^{4,5}$ to assume that ${\\cal P}_*(\\rho_V)$ is\nconstant within this range, so that $d {\\cal P}(\\rho_V)$\ncan be calculated as proportional to ${\\cal N}(\\rho_V)d\n\\rho_V$. In an interesting recent article,$^8$ Garriga and\nVilenkin have argued that this assumption (which they call\n``Weinberg's conjecture'') is generally not valid. This\nraises the problem of characterizing those theories in which\nthis assumption is valid and those in which it is not.\n\nIt is shown in Section II that this assumption is in fact\nvalid for a broad range of theories, in which the different\nregions are characterized by\ndifferent values of a scalar field that couples only to\nitself and gravitation. The deciding factor is how we\nimpose the flatness conditions on the scalar field potential\nthat are needed to ensure that the vacuum energy is now\nnearly time-independent. If the potential is flat because\nthe scalar field renormalization constant is very large,\nthen the {\\em a priori} probability distribution of the vacuum\nenergy is essentially constant within the anthropically\nallowed range, for scalar potentials of generic form. It is\nalso essentially constant for a large class of other\npotentials.\nSection III is a digression, showing that the same flatness\nconditions ensure tht the vacuum energy has been roughly\nconstant since the end of inflation. Section IV takes up\nthe sharp peaks in the\n{\\em\na priori} probability found in\ntheories of quantum cosmology and eternal inflation.\n\n\\vspace{12pt}\n\\begin{center}\nII. SLOWLY ROLLING SCALAR FIELD\n\\end{center}\n\nOne of the possibilities considered by Garriga and Vilenkin\nis a vacuum energy that depends on a homogeneous scalar\nfield $\\phi(t)$ whose present value is governed by some\nsmooth probability distribution. The vacuum energy is\n\\begin{equation}\n\\rho_V=V(\\phi)+\\frac{1}{2} \\dot{\\phi}^2\\;,\n\\end{equation}\n and the scalar field time-dependence is given by\n\\begin{equation}\n\\ddot{\\phi}+3H\\dot{\\phi}=-V'(\\phi)\\;,\n\\end{equation}\nwhere $H(t)$ is the Hubble fractional expansion rate,\n$V(\\phi)$ is the scalar field potential, dots denote\nderivatives with respect to time, and primes denote\nderivatives with respect to $\\phi$. Following Garriga and\nVilenkin,$^8$ we assume that at present the scalar field\nenergy appears like a cosmological constant because the\nfield $\\phi$ is now nearly constant in time, and that this\nscalar field energy now dominates the cosmic energy density.\nFor this to make sense it is necessary for the potential\n$V(\\phi)$ to satisfy certain flatness conditions. In the\nusual treatment of a slowly rolling\nscalar, one neglects the\ninertial term $\\ddot{\\phi}$ in Eq.~(3) as well as the\nkinetic energy term $\\dot{\\phi}^2/2$ in Eq.~(2). With the\ninertial term neglected, the condition that $V(\\phi)$ should\nchange little in a Hubble time $1/H$ is that$^9$\n\\begin{equation}\nV'^2(\\phi)\\ll 3 H^2 |V(\\phi)|\\;.\n\\end{equation}\nWith the scalar field energy dominating the total cosmic\nenergy density, the Friedmann equation gives\n\\begin{equation}\n|V(\\phi)|\\simeq \\rho_V \\simeq 3H^2/8\\pi G\\;,\n\\end{equation}\nso Eq.~(4) requires\n\\begin{equation}\n\\left|V'(\\phi)\\right|\\ll \\sqrt{8\\pi G}\\,\\rho_V\\;.\n\\end{equation}\n(The kinetic energy term $\\dot{\\phi}^2/2$ in Eq.~(2) can be\nneglected under the slightly weaker condition\n$$\n\\left|V'(\\phi)\\right|\\ll \\sqrt{18 H^2\n\\left|V(\\phi)\\right|}\\simeq\n\\sqrt{48\\pi G}\\,\\rho_V\\;,\n$$\nwhich is the flatness condition given by Garriga and\nVilenkin.) There is also a bound on the second derivative\nof the potential, needed in order for the inertial term to\nbe neglected. With the scalar field energy dominating the\ntotal cosmic\nenergy density, this condition requires that$^9$\n\\begin{equation}\n\\left|V''(\\phi)\\right|\\ll 8\\pi G\\rho_V\\;.\n\\end{equation}\n\n\n\n\n\n\nAs Garriga and Vilenkin correctly pointed out, the smallness\nof the slope of $V(\\phi)$ means that $\\phi$ may vary\nappreciably even when $\\rho_V\\simeq V(\\phi)$ is restricted\nto the very narrow anthropically allowed range of values in\nwhich galaxy formation is\nnon-negligible. They concluded that it would be possible\nfor the {\\em a priori} probability ${\\cal P}_*(\\rho_V)$ to\nvary appreciably in this range. In particular, Garriga and\nVilenkin assumed an {\\em a priori} probability distribution\nfor $\\phi$ that is constant in the anthropically allowed\nrange, in which case the {\\em a priori} probability\ndistribution for\n$\\rho_V$ is\n\\begin{equation}\n{\\cal P}_*(\\rho_V)\\propto 1/|V'(\\phi)|\n\\end{equation}\nwhich they said could vary appreciably in the anthropically\nallowed range.\n\nThough possible, this rapid variation is by no means the\ngeneric case. As already mentioned, the second as well as\nthe first derivative of the potential must be small, so\nthat the {\\em a\npriori} probability density (8) may change little in the\nanthropically allowed range. It all depends on how the\nflatness conditions are satisfied. There are two obvious\nways that one might try to make the potential sufficiently\nflat. Potentials of the first type are of the general form\n\\begin{equation}\nV(\\phi)=V_1 f(\\lambda\\phi)\\;,\n\\end{equation}\nwhere $V_1$ is some large energy density, in the range of\n$m_W^{4}$ to $G^{-2}$; the constant $\\lambda$ is very small:\nand $f(x)$ is some dimensionless function involving no very\nlarge or very small parameters.\nPotentials of the second type are of the general form\n\\begin{equation}\nV(\\phi)=V_1\\left[1-\\epsilon\\, g(\\lambda\\phi)\\right]\\;,\n\\end{equation}\nwhere $V_1$ is again some large energy density; $\\lambda$\nis here some fixed inverse mass, perhaps of order\n$\\sqrt{G}$; now it is $\\epsilon $ instead of $\\lambda$ that\nis very small; and $g(x)$ is some other dimensionless\nfunction involving no very large or very small parameters.\n\nFor potentials (9) of the first type, it is always possible\nto meet all observational conditions by taking $\\lambda$\nsufficiently small, provided that the function $f(x)$ has a\nsimple zero at a point $x=a$ of order unity, with\nderivatives at $a$ of order unity. Because $V_1$ is so\nlarge, the present value of $\\lambda\\phi$ must be very close\nto the assumed zero $a$ of $f(x)$. With $f'(a)$ and\n$f''(a)$ of order unity, the flatness conditions (6) and (7)\nare both satisfied if\n\\begin{equation}\n|\\lambda|\\ll \\left(\\frac{\\rho_V}{V_1}\\right)\\sqrt{8\\pi G}\\;.\n\\end{equation}\nGalaxy formation is only possible for $|V(\\phi)|$ less than\nan upper bound $V_{\\rm max}$ of the order of the mass\ndensity\nof the universe at the earliest time of galaxy\nformation,$^6$ which in the absence of fine tuning of the\ncosmological constant is very\nmuch less than $V_1$. The\nanthropically allowed range of $\\phi$ is therefore given by\n\\begin{equation}\n\\Delta \\phi\\equiv |\\phi-a/\\lambda|_{\\rm max}= \\frac{V_{\\rm\nmax}}{ |\\lambda f'(a)V_1|}\\;.\n\\end{equation}\nThe fractional change in the {\\em a priori} probability\ndensity $1/|V'(\\phi)|$ in this range is then\n\\begin{equation}\n\\left|\\frac{V''(\\phi)\\Delta\\phi}{V'(\\phi)}\\right|=\n\\left|\\frac{V_{\\rm max}}{V_1}\\right|\\left|\\frac{\nf''(a)}{f'^2(a)}\\right|\\;,\n\\end{equation}\nwith no dependence on $\\lambda$.\nAs long as the factor $f''(a)/f'^2(a)$ is roughly of order\nunity the fractional variation (13) in the {\\em a priori}\nprobability will be very small, as was assumed in references\n4 and 5.\n\n\nThis reasoning applies to potentials of the form\n$$\nV(\\phi)=V_1\\left[1-(\\lambda\\phi)^n\\right]\\;,\n$$\nwhich, as already noted by Garriga and Vilenkin, lead to an\n{\\em priori} probability distribution that is nearly\nconstant in the anthropically allowed range. (In this case\n$a=1$ and $f''(a)/f'^2(a)=(1-n)/n$.) But this reasoning\nalso applies to the ``washboard potential'' that was taken\nas a counterexample by Garriga and Vilenkin, which with no\nloss of generality can be put in the form:\n$$\nV(\\phi)=V_1\\left[1+\\alpha\\lambda\\phi+\\beta\\sin(\\lambda\\phi)\n\\right]\\;.\n$$\nThe zero point $a$ is here determined by the condition\n$$\n1+\\alpha a+\\beta\\sin a=0\\;,\n$$\nand the factor $f''(a)/f'^2(a)$ in Eq.~(13) is\n$$\n\\frac{f''(a)}{f'^2(a)}=\\frac{-\\beta\\sin a}{(\\alpha+\\beta\n\\cos a)^2}\\;.\n$$\nIf the flatness condition is satisfied by taking $\\lambda$\nsmall, with $\\alpha$ and $\\beta$ of order unity, as is\nassumed for potentials of the first kind, then the factor\n$f''(a)/f'^2(a)$ in Eq.~(13) is\nof order unity unless $\\alpha$ and $\\beta$ happen to be\nchosen so that\n$$\n\\left| 1+\\alpha\\cos^{-1}\\left(\\frac{-\n\\alpha}{\\beta}\\right)+\\beta\\sqrt{1-\n\\frac{\\alpha^2}{\\beta^2}}\\right|\\ll 1\\;.\n$$\nOf course it would be possible to impose this condition on\n$\\alpha$ and $\\beta$, but this is the kind of fine-tuning\nthat would be upset by adding a constant of order $V_1$ to\nthe potential. Aside from this exception, for all $\\alpha$\nand $\\beta$ of order unity the factor $f''(a)/f'^2(a)$ is of\norder unity, so the washboard potential also yields an {\\em\na priori} probability distribution for the vacuum energy\nthat is flat in the anthropically allowed range.\n\nIn contrast, for potentials (10) of the second kind the\nflatness conditions are not necessarily satisfied no matter\nhow small we take $\\epsilon$. Because the present vacuum\nenergy\nis much less than $V_1$, the present value of $\\phi$ must be\nvery close to a value $\\phi_\\epsilon$, satisfying\n\\begin{equation}\ng(\\lambda\\phi_\\epsilon)=1/\\epsilon\\;.\n\\end{equation}\nThis requires $\\lambda\\phi_\\epsilon$ to be near a\nsingularity\nof the function $g(x)$, perhaps at infinity, so it is not\nclear in general that such a potential would have small\nderivatives at $\\lambda\\phi_\\epsilon$ for any value of\n$\\epsilon$. For instance, for an exponential\n$g(x)=\\exp(x)$ we have $\\phi_\\epsilon=- \\ln\n\\epsilon/\\lambda$, and\n$V'(\\phi_\\epsilon)$ approaches an $\\epsilon$-independent\nvalue proportional to $\\lambda$, which is not small unless\nwe take\n$\\lambda$ very small, in which case have a potential of the\nfirst kind, for which as we have seen the {\\em a priori}\nprobability density (8) is flat in the anthropically allowed\nrange.\nThe flatness conditions {\\em are} satisfied for small\n$\\epsilon$ if $g(x)$ approaches a power $x^n$ for\n$x\\rightarrow \\infty$. In this case $\\phi_\\epsilon$ goes as\n$\\epsilon^{-1/n}$, so $V'(\\phi_\\epsilon)$ goes as\n$\\epsilon^{1/n}$ and\n$V''(\\phi_\\epsilon)$ goes as $\\epsilon^{2/n}$, both of which\ncan be made as small as we like by taking $\\epsilon$\nsufficiently small.\n\nIn particular, if the singularity in $g(x)$ at $x\\rightarrow\n\\infty$ consists only of poles in $1/x$ of various orders up\n to $n$\n(as is the case for a polynomial of order $n$) then the\nanthropically allowed range of $\\phi$ is\n\\begin{equation}\n\\Big|\\phi-\\phi_\\epsilon\\Big|_{\\rm max}\\approx\n\\frac{V_m}{V_1\\epsilon |g'(\\phi_\\epsilon)|}\\approx\n\\epsilon^{-1/n}\\left(\\frac{V_m}{V_1}\\right)\\;.\n\\end{equation}\nThe flatness conditions make this range much greater than\nthe Planck mass, but the fractional change in the {\\em a\npriori} probability density (8) in this range is still very\nsmall\n\\begin{equation}\n\\left|\\frac{V''(\\phi_\\epsilon)}{V'(\\phi_\\epsilon)}\\right|\n\\Big|\\phi-\\phi_\\epsilon\\Big|_{\\rm max}\\approx\n\\frac{V_m}{V_1}\\ll 1\\;.\n\\end{equation}\nTo have a large fractional change in the {\\em a priori}\nprobability distribution in the anthropically allowed range\nfor potentials of the second type that satisfy the flatness\nconditions, we need a function $g(x)$ that goes like a power\nas $x\\rightarrow \\infty$, but has a more complicated\nsingularity at $x=\\infty$ than just poles in $1/x$.\nAn example is provided by the washboard potential with\n$\\alpha$ and\n$\\beta$ very small and $\\lambda$ fixed, the case\nconsidered by Garriga and Vilenkin, for which $g(x)$ has an\nessential singularity at $x=\\infty$.\n\nIn summary, the {\\em a priori} probability is flat in the\nanthropically allowed range for several large classes of\npotentials,\nwhile it seems to be not flat only in exceptional cases.\n\nIt remains to consider whether the small parameters\n$\\lambda$\nor $\\epsilon$ in potentials respectively of the first or\nsecond kind could arise naturally. Garriga and Vilenkin\nargued that a term in a potential of what we have called the\nsecond kind with an over-all factor\n$\\epsilon\\ll 1$ could be naturally produced by instanton\neffects. On the other hand, for potentials of type 1 a\nsmall parameter $\\lambda$ could be naturally produced by the\nrunning of a\nfield-renormalization factor. The field $\\phi$ has a\nconventional ``canonical'' normalization, as shown by the\nfact that the term $\\dot{\\phi}^2/2$ in the vacuum energy (2)\nand the inertial term $\\ddot{\\phi}$ in the field equation\n(3) have coefficients unity. Factors dependent on the\nultraviolet cutoff will therefore be associated with\nexternal $\\phi$-lines. In order for the potential $V(\\phi)$\nto be expressed in a cut-off independent way in terms of\ncoupling parameters $g_\\mu$ renormalized at a wave-number\nscale $\\mu$, the field $\\phi$ must be accompanied with a\nfield-renormalization factor $Z_{\\mu}^{-1/2}$, which\nsatisfies a differential equation of the form\n\\begin{equation}\n\\mu\\frac{d Z_\\mu}{d\\mu}=\\gamma(g_\\mu)Z_\\mu\\;.\n\\end{equation}\nAt very large distances, the field $\\phi$ will therefore be\naccompanied with a factor\n\\begin{equation}\n\\lambda=Z^{-1/2}_0=\\exp\\left\\{\\frac{1}{2}\\int_0^{\\mu}\n\\frac{d\\mu'}{\\mu'}\\gamma(g_{\\mu'})\\right\\}Z^{-1/2}_\\mu\\;.\n\\end{equation}\nThe integral here only has to be reasonably large and\nnegative in order for $\\lambda$ to be extremely small.\n\n\n\n\n\\begin{center}\n{\\bf III. SLOW ROLLING IN THE EARLY UNIVERSE}\n\\end{center}\n\nWhen the cosmic energy density is dominated by the vacuum\nenergy, the flatness conditions (6) and (7) insure that the\nvacuum energy changes little in a Hubble time. But if the\nvacuum energy density is nearly time-independent, then from\nthe end of inflation until nearly the present it must have\nbeen much smaller than the energy density of matter and\nradiation, and under these conditions we are not able to\nneglect the inertial term $\\ddot{\\phi}$ in Eq.~(3). A\nseparate argument is needed to show that the vacuum energy\nis nearly constant at these early times. This is important\nbecause, although\nthere is no observational reason to require $V(\\phi)$ to be\nconstant at early times, it must have been less than the\nenergy of radiation at the time of nucleosynthesis in order\nnot to interfere with the successful prediction of light\nelement abundances, and therefore at this time must have\nbeen very much less than $V_1$, which we have supposed to be\nat least of order $m_W^4$. For potentials (9) of the first\nkind, this means that $\\phi$ must have been very close to\nits present value at the time of helium synthesis. Also,\nif $\\phi$ at the end of\ninflation were not the same as $\\phi$ at the time of galaxy\nformation, then a flat {\\em a priori} distribution for the\nfirst would not in general imply a flat {\\em a priori}\ndistribution for the second.\n\n\nAt times between the end of inflation and the recent past\nthe expansion rate behaved as $H=\\eta/t$, where $\\eta=2/3$\nor $\\eta =1/2$ during the eras of matter or radiation\ndominance, respectively. During this period, Eq.~(3) takes\nthe form\n\\begin{equation}\n\\ddot{\\phi}+\\frac{3\\eta}{t}\\dot{\\phi}=-V'(\\phi)\\;,\n\\end{equation}\nIf we tentatively assume that $\\phi$ is nearly constant,\nthen Eq.~(19) gives for its rate of change\n\\begin{equation}\n\\dot{\\phi}\\simeq-\\, \\frac{t\\,V'(\\phi)}{1+3\\eta}\\;.\n\\end{equation}\nThe change in the vacuum energy from the end of inflation\nto the present time $t_0$ is therefore\n\\begin{equation}\n\\Delta V\\simeq\\int_0^{t_0} V'(\\phi)\\,\\dot{\\phi}\\,dt\\simeq -\n\\,\\frac{V'^2(\\phi)t_0^2}{2(1+3\\eta)}\\;.\n\\end{equation}\nThe present time is roughly given by $t_0\\approx\n\\eta\\sqrt{3/8\\pi G\\rho_{V0}}$,\nso the fractional change in the vacuum energy density since\nthe end of inflation is\n\\begin{equation}\n\\left|\\frac{\\Delta V}{\\rho_{V0}}\\right|\\approx\n \\left(\\frac{3\\eta^2}{2(1+3\\eta)}\\right)\\,\\left(\n\\frac{V'^2(\\phi)}{8\\pi G \\rho_{V0}^2}\\right)\\;,\n\\end{equation}\na subscript zero as usual denoting the present instant.\nThe factor $3\\eta^2/2(1+3\\eta)$ is of order unity, so the\ninequality (6) tells us that the change in the vacuum\nenergy during the time since inflation has indeed been much\nless\nthan its present value.\n\n\n\n\\begin{center}\n{\\bf III. QUANTUM COSMOLOGY}\n\\end{center}\n\nIn some theories of quantum cosmology the wave function of\nthe universe is a superposition of terms, corresponding to\nuniverses with different (but time-independent) values for\nthe vacuum energy $\\rho_V$. It has been argued by Baum$^2$,\nHawking$^2$ and Coleman$^{10}$ that these terms are weighted\nwith a $\\rho_V$-dependent factor, that gives an {\\em a\npriori} probability distribution with an infinite peak at\n$\\rho_V=0$, but this claim has been challenged.$^{11}$ As\nalready acknowledged in references 4 and 5, if this peak at\n$\\rho_V=0$ is really present, then anthropic considerations\nare both inapplicable and unnecessary in solving the problem\nof the cosmological constant.\n\n\nGarriga and Vilenkin$^{8}$ have\nproposed a different sort of infinite peak, arising\nfrom a $\\rho_V$-dependent rate of nucleation of\nsub-universes operating over an infinite time.\nEven granting the existence of such a peak, it is not clear\nthat it really leaves a vanishing normalized probability\ndistribution at all other values of $\\rho_V$. For instance,\nthe nucleation rate might depend on the population of \nsub-universes already present, in such a way that the peaks in\nthe probability distribution are kept to a finite size.\nIf ${\\cal\nP}_*(\\rho_V)=0$\nexcept at the peak, then anthropic considerations are\nirrelevant and the cosmological constant problem is as bad\nas ever, since there is no known reason why the peak should\noccur in the very narrow range of $\\rho_V$ that is\nanthropically allowed. On the other hand, if there is a\nsmooth background in addition to a peak outside the\nanthropically allowed range of $\\rho_V$ then the peak is\nirrelevant, because no observers would ever\nmeasure such values of $\\rho_V$. In this case the\nprobability distribution of the cosmological constant can be\ncalculated using the methods of references 4 and 5.\n\n\n\\begin{center}\n{\\bf ACKNOWLEDGEMENTS}\n\\end{center}\n\n\nI am grateful for a useful correspondence with Alex\nVilenkin. This research was\nsupported in part by the\nRobert A. Welch\n Foundation and NSF Grant PHY-9511632.\n\n\\begin{center}\n{\\bf REFERENCES}\n\\end{center}\n\n\\begin{enumerate}\n\n\\item A. Vilenkin, {\\it Phys. Rev.} {\\bf D27}, 2848 (1983);\nA. D. Linde, {\\em Phys. Lett.} {\\bf B175}, 395 (1986).\n\n\\item E. Baum, {\\em Phys. Lett.} {\\bf B133}, 185 (1984); S.\nW. Hawking, in {\\em Shelter Island II - Proceedings of the\n1983 Shelter Island Conference on Quantum Field Theory and\nthe Fundamental Problems of Physics}, ed. R. Jackiw {\\em et\nal.} (MIT Press, Cambridge, 1995); {\\em Phys. Lett.} {\\bf\nB134}, 403 (1984); S. Coleman, {\\it Nucl. Phys.} {\\bf B\n307}, 867 (1988).\n\n\\item An equation of this type was given by A. Vilenkin,\n{\\em Phys. Rev. Lett.} {\\bf 74}, 846 (1995); and in {\\em\nCosmological Constant and the Evolution of the Universe}, K.\nSato, {\\em et al.}, ed. (Universal Academy Press, Tokyo,\n1996) (gr-qc/9512031), but it was not used in a calculation\nof the mean value or probability distribution of $\\rho_V$.\n\n\\item S. Weinberg, in {\\em Critical Dialogs in Cosmology},\ned. by N. Turok (World Scientific, Singapore, 1997).\n\n\\item H. Martel, P. Shapiro, and S. Weinberg, {\\em Ap. J.}\n{\\bf 492}, 29 (1998).\n\n\\item S. Weinberg, {\\em Phys. Rev. Lett.} {\\bf 59}, 2607\n(1987).\n\n\\item J. D. Barrow and F. J. Tipler, {\\it The Anthropic\nCosmological Principle} (Clarendon Press, Oxford, 1986).\n\n\\item J. Garriga and A. Vilenkin, Tufts University preprint\nastro-ph/9908115, to be published.\n\n\\item P. J. Steinhardt and M. S. Turner, {\\it Phys. Rev.}\n{\\bf D29}, 2162 (1984).\n\n\\item S. Coleman, {\\em Nucl. Phys.} {\\bf B 310}, 643 (1988).\n\n\\item W. Fischler, I. Klebanov, J. Polchinski, and L.\nSusskind, {\\em Nucl. Phys.} {\\bf B237}, 157 (1989).\n\n\\end{enumerate}\n\n\\end{document}\n\n"
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astro-ph0002388
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Star Formation and Chemical Evolution of Lyman-Break Galaxies
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"author": "Chenggang Shu"
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The number density and clustering properties of Lyman-break galaxies (LBGs) observed at redshift $z\sim 3$ are best explained by assuming that they are associated with the most massive haloes at $z\sim 3$ predicted in hierarchical models of structure formation. In this paper we study, under the same assumption, how star formation and chemical enrichment may have proceeded in the LBG population. A consistent model, in which the amount of cold gas available for star formation must be regulated, is suggested. It is found that gas cooling in dark haloes provides a natural regulation process. In this model, the star formation rate in an LBG host halo is roughly constant over about 1 Gyr. The predicted star formation rates and effective radii are consistent with observations. The metallicity of the gas associated with an LBG is roughly equal to the chemical yield, or about the order of $1 Z_{\odot}$ for a Salpeter IMF. The contribution to the total metals of LBGs is roughly consistent with that obtained from the observed cosmic star formation history. The model predicts a marked radial metallicity gradient in a galaxy, with the gas in the outer region having much lower metallicity. As a result, the metallicities for the damped Lyman-alpha absorption systems expected from the LBG population are low. Since LBG halos are filled with hot gas in this model, their contributions to the soft X-ray background and to the UV ionization background are calculated and discussed.
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"name": "9137.tex",
"string": "\n%\\documentstyle{aa}\n\\documentclass[11pt,referee]{aa}\n\\usepackage{graphics}\n\n%\\documentstyle[referee]{mn}\n%\\newcommand{\\reference}{\\bibitem}\n%\n\\def\\beq{\\begin{equation}}\n\\def\\eeq{\\end{equation}}\n\\def\\bey{\\begin{eqnarray}}\n\\def\\eey{\\end{eqnarray}}\n\\def\\beqarray{\\begin{eqnarray}}\n\\def\\eeqarray{\\end{eqnarray}}\n\\def\\RM{\\rm}\n\\def\\cm{\\,{\\rm {cm}}}\n\\def\\mpc{\\,{\\rm {Mpc}}}\n\\def\\Mpc{\\,{\\rm {Mpc}}}\n\\def\\kpc{\\,{\\rm {kpc}}}\n\\def\\kpch{\\,{h^{-1}{\\rm kpc}}}\n\\def\\mpch{\\,h^{-1}{\\rm {Mpc}}}\n\\def\\kms{\\,{\\rm {km\\, s^{-1}}}}\n\\def\\msun{M_\\odot}\n\\def\\vcir{V_{\\rm c}}\n\\def\\v200{V_{200}}\n\\def\\mmw{{MMW}}\n\\def\\Md{M_d}\n\\def\\md{m_d}\n\\def\\Onow{\\Omega_0}\n\\def\\Lnow{\\Lambda_0}\n\\def\\Rd{R_d}\n\\def\\my{{\\rm M_\\odot yr^{-1}}}\n\n\\begin{document}\n\n \\thesaurus{( 11.01.2; % Galaxies: active\n 11.06.1; % Galaxies: formation\n 11.05.2)} % Galaxies: evolution\n\n\n\n%\n\\input epsf\n%\\input psfig\n\n%\n\\title\n{Star Formation and Chemical Evolution of Lyman-Break Galaxies}\n\n\\author{Chenggang Shu}\n\\offprints{C. Shu, cgshu@center.shao.ac.cn}\n \\institute{\n 1. Shanghai Astronomical Observatory, Chinese Academy of\nSciences, Shanghai 200030, P. R. China\\\\\n 2. Max-Planck-Institut f\\\"ur Astrophysik\n Karl-Schwarzschild-Strasse 1, 85748 Garching, Germany\\\\\n 3. National Astronomical Observatories, Chinese Academy of Sciences, P. R. China\\\\\n 4. Joint Lab of Optical Astronomy, Chinese Academy of Sciences, P. R. China}\n\n\\date{Accepted ........\n Received ........}\n%\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n%\\pubyear{1998}\n\n\\titlerunning{Star Formation and Chemical Evolution of LBGs}\n\n\\maketitle\n\\begin{abstract}\nThe number density and clustering properties of Lyman-break\ngalaxies (LBGs) observed at redshift $z\\sim 3$ are best explained\nby assuming that they are associated with the most massive haloes\nat $z\\sim 3$ predicted in hierarchical models of structure\nformation. In this paper we study, under the same assumption, how\nstar formation and chemical enrichment may have proceeded in the\nLBG population. A consistent model, in which the amount of cold\ngas available for star formation must be regulated, is suggested.\nIt is found that gas cooling in dark haloes provides a natural\nregulation process. In this model, the star formation rate in an\nLBG host halo is roughly constant over about 1 Gyr. The predicted\nstar formation rates and effective radii are consistent with\nobservations. The metallicity of the gas associated with an LBG is\nroughly equal to the chemical yield, or about the order of $1\nZ_{\\odot}$ for a Salpeter IMF. The contribution to the total\nmetals of LBGs is roughly consistent with that obtained from the\nobserved cosmic star formation history. The model predicts a\nmarked radial metallicity gradient in a galaxy, with the gas in\nthe outer region having much lower metallicity. As a result, the\nmetallicities for the damped Lyman-alpha absorption systems\nexpected from the LBG population are low. Since LBG halos are\nfilled with hot gas in this model, their contributions to the soft\nX-ray background and to the UV ionization background are\ncalculated and discussed.\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: LBGs - galaxies: formation - galaxies: star formation -\ngalaxies: chemical evolution\n\\end{keywords}\n\n\\section {Introduction}\n\nThe Lyman-break technique (e.g. Steidel, Pettini \\& Hamilton 1995)\nhas now been proved very successful in finding large numbers of\nstar forming galaxies at redshift $z\\sim 3$ (e.g. Steidel et al.\n1996, 1999b). The observed number density and clustering\nproperties of Lyman-break galaxies (hereafter LBGs, Steidel et al.\n1998; Giavalisco et al. 1998; Adelberger et al. 1998) are best\nexplained by assuming that they are associated with the most\nmassive haloes at $z\\sim 3$ predicted in hierarchical models of\nstructure formation (Mo \\& Fukugita 1996; Baugh, Cole \\& Frenk\n1998; Mo, Mao \\& White 1998b; Coles, et al. 1998; Governato, et\nal. 1998; Jing 1998; Jing \\& Suto 1998; Katz, et al. 1998;\nKauffmann, et al. 1998; Moscardini, et al. 1998; Peacock, et al.\n1998; Wechsler, et al. 1998). This assumption provides a framework\nfor predicting a variety of other observations for the LBG\npopulation. Steidel et al. (1999b and references therein) gave a\ngood summary of recent studies on this population including the\nluminosity functions, luminosity densities, color distribution,\nstar formation rates, clustering properties, and the differential\nevolution.\n\nAssuming that LBGs form when gas in dark haloes settles into\nrotationally supported discs or, in the case where the angular\nmomentum of the gas is small, settles at the self-gravitating\nradius, Mo, Mao \\& White (1998b) predict sizes, kinematics and\nstar formation rates and halo masses for LBGs, and find that the\nmodel predictions are consistent with the current (rather limited)\nobservational data; Steidel et al. (1999a) suggest that the total\nintegrated UV luminosity densities of LBGs are quite similar\nbetween redshift 3 and 4 although the slope of their luminosity\nfunction might have a large change in the faint-end.\n\nFurthermore, Steidel et al. (1999b) suggest that a ``typical\" LBG\nhave a star formation rate of about $65h_{50}^{-2}\\rm\n{M_{\\odot}yr^{-1}}$ for $\\Omega_{0}=1$ and the star formation time\nscale be the order of 1Gyr based on their values of E(B-V) as\npointed out by Pettini et al. (1997b) after adopting the reddening\nlaw of Calzetti (1997). Recently, Friaca \\& Terlevich (1999) use\ntheir chemodynamical model to propose that an early stage (the\nfirst Gyr) of intense star formation in the evolution of massive\nspheroids could be identified as LBGs.\n\nHowever, Sawicki \\& Yee (1998) argued that LBGs could be very\nyoung stellar populations with the age less than 0.2Gyr based on\nthe broadband optical and IR spectral energy distributions. This\nis also supported by the work of Ouchi \\& Yamada (1999) based on\nthe expected sub-mm emission and dust properties. It is worthy of\nnoting that the assumptions about the intrinsic LBG spectral shape\nand the reddening curve play important roles in these results.\n\nIn this paper, we study how star formation and chemical enrichment\nmay have proceeded in the LBG population. As we will demonstrate\nin Section 2, the observed star formation rate at $z\\sim 3$\nrequires a self-regulating process to keep the gas supply for a\nsufficiently long time. We will show (in Section 2) that such a\nprocess can be achieved by the balance between the energy feedback\nfrom star formation and gas cooling. Model predictions for the LBG\npopulation and further discussions about the results are presented\nin Section 3, a brief summary is given in Section 4.\n\nAs an illustration, we show theoretical results for a CDM model\nwith cosmological density parameter $\\Omega_{0}=0.3$, cosmological\nconstant $\\Omega_\\Lambda=0.7$. The power spectrum is assumed to be\nthat given in Bardeen et al. (1986), with shape parameter\n$\\Gamma=0.2$ and with normalization $\\sigma_{8}=1.0$. We denote\nthe mass fraction in baryons by $f_{\\rm B}=\\Omega_{\\rm\nB}/\\Omega_0$, where $\\Omega_{\\rm B}$ is the cosmic baryonic\ndensity parameter. According to the cosmic nucleosynthesis, the\ncurrently favoured value of $\\Omega_{\\rm B}$ is $\\Omega_{\\rm\nB}\\sim 0.019 h^{-2}$ (Burles \\& Tytler 1998), where $h$ is the\npresent Hubble constant in units of 100 $\\rm kms^{-1}Mpc^{-1}$,\nand so $f_{\\rm B}\\sim0.063 h^{-2}$. Whenever a numerical value of\n$h$ is needed, we take $h=0.7$. At the same time, we define\nparameter $t_\\star$ as the time scale for star formation in the\nLBG population throughout the paper.\n\n\\section {Models}\n\\subsection{Galaxy Formation}\n\n In this paper, we use the galaxy formation scenario described\nin Mo, Mao \\& White (1998a, hereafter MMWa) to model the LBG\npopulation. In this scenario, central galaxies are assumed to form\nin dark matter haloes when collapse of protogalactic gas is halted\neither by its angular momentum, or by fragmentation as it becomes\nself-gravitating (see Mo, Mao \\& White 1998b, hereafter MMWb, for\ndetails). As described in MMWb, the observed properties of LBGs\ncan be well reproduced if they are assumed to be the central\ngalaxies formed in the most massive haloes with relatively small\nspins at $z\\sim 3$. As in MMWb, we assume that gas in a dark halo\ninitially settles into a disk with exponential surface density\nprofile.\n\nWhen the collapsing gas is arrested by its spin, the central gas\nsurface density and the scale length of an exponential disk are\n\\beq\n \\Sigma_{0} \\approx 380h {\\rm M}_{\\odot}{\\rm\npc^{-2}}\\left({m_{\\rm d} \\over 0.05}\\right)\\left({\\lambda \\over\n0.05}\\right)^{-2} \\left({V_{c} \\over {\\rm 250kms}^{-1}}\\right)\n\\left[{H(z) \\over {H_{0}}}\\right], \\eeq and \\beq R_{\\rm d} \\approx\n8.8h^{-1}{\\rm kpc}\\left({{\\lambda} \\over\n{0.05}}\\right)\\left({{V_{c}} \\over {{\\rm 250kms}^{-1}}}\\right)\n\\left[{H(z) \\over {H_{0}}}\\right]^{-1}, \\eeq\n where $m_{\\rm d}$ is the fraction of halo mass that settles into\nthe disk, $V_{c}$ is the circular velocity of the halo, $\\lambda$\nis the dimensionless spin parameter, $H(z)$ is the Hubble constant\nat redshift $z$ and $H_{0}$ is its present value (see MMWa for\ndetails). Since $H(z)$ increases with $z$, for a given $V_c$ disks\nare less massive and smaller but have a higher surface density at\nhigher redshift. When $\\lambda$ is low and $m_{\\rm d}$ is high,\nthe collapsing gas will become self-gravitating and fragment to\nform stars before it settles into a rotationally supported disk.\nIn this case, we will take an effective spin $\\lambda\\propto\nm_{\\rm d}$ in calculating $\\Sigma_0$ and $R_{\\rm d}$.\n\nWe take the empirical law (Kennicutt 1998) of star formation rate\n(SFR) to model the star formation in high-redshift disks which is\n \\beq\\label{SFR_law}\n \\Sigma_{\\rm SFR} = a\n\\left({{\\Sigma_{\\rm gas}} \\over {{\\rm M}_{\\odot}{\\rm\npc^{-2}}}}\\right)^{b} {\\rm M}_{\\odot}{\\rm yr^{-1}}{\\rm pc^{-2}} ,\n\\eeq\n where\n \\beq a = {2.5 \\times 10^{-10}}, ~~~ b=1.4 \\eeq\n respectively. Here $\\Sigma_{\\rm SFR}$ is the SFR per unit area and\n$\\Sigma_{\\rm gas}$ is the gas surface density. Note that this star\nformation law was derived by averaging the star formation rate and\ncold gas density over large areas on spiral disks and over\nstarburst regions (Kennicutt 1998). We will apply this law\ndifferentially on a disk and also take into account the Toomre\ninstability criterion of star formation (Toomre 1964; see also\nBinney \\& Tremaine 1987).\n\nFor a given cosmogonic model, the mass function for dark matter\nhaloes at redshift $z$ can be estimated from the Press-Schechter\nformalism (Press \\& Schechter 1974): \\beq {\\rm d}N = -\\sqrt{2\n\\over \\pi}{\\rho_{0} \\over M}{\\delta_{c}(z) \\over \\Delta(R)} {{\\rm\nd}\\ln\\Delta(R) \\over {\\rm d}\\ln M}{\\exp}\\left[-{\\delta_{c}^{2}(z)\n\\over {2\\Delta^{2}(R)}}\\right]{{\\rm d} M \\over M}, \\eeq where\n$\\delta_{c}(z)=\\delta_{c}(0)(1+z)g(0)/g(z)$ with $g(z)$ being the\nlinear growth factor at $z$ and $\\delta_{c}(0)\\approx 1.686$,\n$\\Delta(R)$ is the linear $rms$ mass fluctuation in top-hat\nwindows of radius $R$ which is related to the halo mass $M$ by\n$M=(4\\pi/3){\\overline \\rho}_{0}R^{3}$, with ${\\overline\\rho}_{0}$\nbeing the mean mass density of the universe at $z=0$. The halo\nmass $M$ is related to halo circular velocity $V_c$ by\n$M=V_c^3/[10GH(z)]$. A detailed description of the PS formalism\nand the related cosmogonic issues can be found in the Appendix of\nMMWa.\n\nFrom the Press-Schechter formalism and the $\\lambda$-distribution\nwhich is a log-normal function with mean ${\\overline\n{\\ln\\lambda}}=\\ln 0.05$ and dispersion $\\sigma_{\\rm ln\n\\lambda}=0.5$ (see equation [15] in MMWa), we can generate Monte\nCarlo samples of the halo distributions in the $V_c$-$\\lambda$\nplane at a given redshift and, using the star formation law\noutlined above, assign a star formation rate to each halo. As in\nMMWb, we select LBGs as the galaxies with the highest star\nformation rate, so that the comoving number density for LBGs is\nequal to the observed value, $N_{\\rm LBG}=2.4 \\times\n10^{-3}h^{3}{\\rm Mpc^{-3}}$ for the assumed cosmology at $z=3$, as\ngiven in Adelberger et al. (1998). Here it is worth noting that\nthe model selection of LBGs we adopted is without the dust\nextinction being considered. This implies that the contribution of\nthe dust is assumed to be uniform. But in fact, it could be very\ndifferent from galaxies to galaxies. So, our selection of LBGs may\nnot have one-to-one correspondence with the observed LBGs (Baugh\net al. 1999), but the selection should be correct on average.\n\n\\subsection{Cooling-Regulated Star Formation}\n\nWhat regulates the amount of star-forming gas in a dark halo? In\nthe standard hierarchical scenario of galaxy formation (e.g. White\n\\& Rees 1978; White \\& Frenk 1991, hereafter WF), gas in a dark\nmatter halo is assumed to be shock heated to the virial\ntemperature,\n \\beq T=2.24 \\times 10^6{\\rm K} \\left({V_c\\over\n250{\\rm km\\,s^{-1}}}\\right)^2, \\eeq\n as the halo collapses and\nvirializes. The hot gas then cools and settles into the halo\ncentre to form stars. As suggested in WF, the amount of cold gas\navailable for star formation in a dark halo is either limited by\ngas infall or by gas cooling, depending on the mass of the halo.\nFor the massive haloes ($V_c\\ga 200 {\\rm km\\,s^{-1}}$) we are\ninterested here, gas cooling rate is smaller than gas-infall rate,\nand the supply of star-forming gas is limited by gas cooling (see\nWF for details). It is therefore likely that gas cooling is the\nmain process that constantly regulates the SFR in LBGs.\n\nTo have a quantitative assessment, let us compare different rates\ninvolved in the problem. Using equations (1)-(4) we can write the\nSFR as\n\\begin{eqnarray}\\label{MSFR}\n\\dot M_{\\star }= {2\\pi a\\Sigma_{0}^{b}R_{\\rm d}^{2} \\over b^{2}}\n\\approx 2.33\\times 10^{2}h^{-0.6}\\left({m_{\\rm d}\\over\n0.05}\\right)^{1.4} \\left({\\lambda \\over\n0.05}\\right)^{-0.8}\\left({V_{c}\\over {{\\rm 250\nkm\\,s^{-1}}}}\\right)^{3.4}\\left[{H(z) \\over {H_{0}}}\\right]^{-0.6}\n{\\rm M_{\\odot}\\,yr ^{-1}},\n\\end{eqnarray}\nwhere $m_{\\rm d}$ is the current gas content of the disk. The rate\nat which gas is consumed by star formation is therefore\n \\beq\n {\\dot M}_{\\rm SFR}=(1-R_{\\rm r}) {\\dot M}_\\star,\n \\eeq\n where $R_{\\rm r}$\nis the returned fraction of stellar mass into the ISM; we take\n$R_{\\rm r}=0.3$ for a Salpeter IMF (e.g. Madau et al. 1998).\nAccording to WF, the heating rate due to supernova explosions\nunder the approximation of instantaneous recycling can be written\nas\n \\beq {{\\rm d}E \\over {{\\rm d}t}}=\\epsilon_{0}\\dot\nM_{\\star}(700{\\rm km\\,s^{-1}})^{2},\n \\eeq\n where $\\epsilon_{0}$ is\nan efficiency parameter which is still very uncertain. We take it\nto be $0.02$ as in WF. The rate at which gas is heated up (to the\nvirial temperature) is therefore\n \\beq \\dot\nM_{\\rm heat}={0.8 \\over V_{c}^2}{{\\rm d}E \\over {\\rm d}t}\n \\eeq\nwhich is the same form as equation (9) of Kauffmann (1996; see\nalso Somerville 1997). At $z=3$ and for the cosmology considered\nhere, this rate can be written as\n \\beq\\label{Mheat} \\dot M_{\\rm\nheat} \\approx 29.2h^{-0.6} \\left({m_{d}\\over 0.05}\\right)^{1.4}\n\\left({\\lambda \\over 0.05}\\right)^{-0.8}\\left({V_{c}\\over {250{\\rm\nkm\\,s^{-1}}}}\\right)^{1.4} \\left[{H(z) \\over\n{H_{0}}}\\right]^{-0.6} {\\rm M_{\\odot}\\,yr^{-1}}.\n \\eeq\nComparing this equation with equations (7) and (8), we can find\nthat the rate for gas consumption due to star formation is much\nlarger than the rate of gas heating for LBG halos. Because LBGs\nare hosted by massive halos which have large circular velocities\n$V_{\\rm c}$, the halos are cooling dominated which is confirmed\nduring the detailed calculation below. Following WF we define a\nmass cooling rate by\n \\beq \\dot M_{\\rm cool}=4\\pi\\rho_{\\rm\ngas}(r_{\\rm cool})r_{\\rm cool}^{2} {{\\rm d}r_{\\rm cool}\\over {{\\rm\nd}t}}, \\eeq\n where $r_{\\rm cool}$ is the cooling radius and\n$\\rho_{\\rm gas}$ is the density profile of the hot gas in the\nhalo. For simplicity, we assume that $\\rho_{\\rm gas}(r)=f_{\\rm\nB}V_c^2/(4\\pi Gr^2)$, and we define $r_{\\rm cool}$ to be the\nradius at which the cooling time is equal to the age of the\nuniverse, which is similar to the time interval between major\nmergers of haloes (Lacey \\& Cole 1994). The density distribution\nof the halo mass here is assumed to be isothermal. However, it is\nthe NFW profile (Navarro, Frenk \\& White, 1997) in MMWb. Because\nthe difference of the resulted cooling rates between these two\ndifferent choices of density profiles is small (Zhao et al, 1999),\nand the major goal here is to show whether or not the\ncooling-regulated star formation can be valid, the adoption of\nisothermal profile will not influence the final result very much.\n\nUnder this definition, gas within the cooling radius can cool\neffectively before the halo merges into a larger system where it\nmay be heated up to the new virial temperature if it is not\nconverted into stars. Using the cooling function given by Binney\n\\& Tremaine (1987) where cooling function $\\Lambda \\approx\n10^{-23}\\rm ergs^{-1}cm^{3}$ in the range of $5\\times 10^{5}{\\rm\nK} \\la T \\la 2\\times 10^{7}{\\rm K}$ (and assuming gas with\nprimordial composition), the mass cooling rate can then be written\nas\n \\beq\\label{Mcool}\n \\dot M_{\\rm cool} \\approx 49.8\nh^{1/2}\\left({V_{c}\\over {{\\rm 250km\\,s^{-1}}}}\\right)^{2}\n\\left({f_{\\rm B}\\over {0.1}}\\right)^{3/2} {\\rm M_{\\odot}{\\rm\nyr}^{-1}}. \\eeq\n\nIf ${\\dot M}_\\star$ is smaller than ${\\dot M}_{\\rm cool}$, then\ncold gas will accumulate in the halo centre and lead to higher\nstar formation rate. If, on the other hand, ${\\dot M}_\\star >{\\dot\nM}_{\\rm cool}$, the amount of cold gas will be reduced by star\nformation and supernova heating, leading to a lower star formation\nrate. We therefore assume that there is a rough balance among\nthese three rates:\n \\beq\\label{balance} {\\dot M_{\\rm cool} \\approx {\\dot\nM_{\\rm heat} + \\left(1-R_{\\rm r}\\right) \\dot M_{\\star}}}.\n \\eeq\nIt should be noted that the cooling-regulated star formation\nprocess is only a reasonable hypothesis, and the real situation\nmust be much more complicated. For example, during a major merger\nof galactic haloes, the amount of gas that can cool must be much\nlarger than that given by the cooling argument, and the star\nformation may be in a short burst (e.g. Mihos \\& Hernquist 1996).\nHowever, such bursts are not expected to dominate the observed LBG\npopulation, because of their brief lifetimes. Thus, star formation\nrates in the majority of LBGs are expected to be regulated by\nequation (14) on average. As shown in MMWb, to match the observed\nnumber density of LBGs, the median value of $V_c$ is about\n$300\\kms$ in the present cosmogony. The typical star formation\nrate is of the order $100{\\rm M_{\\odot}\\,yr^{-1}}$. This is not\nvery different from the observed star formation rates, albeit dust\ndistinction in the observations may be difficult to quantify.\n\n\\begin{figure}\n\\epsfysize=9.5cm \\centerline{\\epsfbox{LBG01.ps}} \\caption{The\nvalue of $m_{\\rm d}$ required by the balance condition equation\n(14) as a function of halo circular velocity $V_{c}$ at $z=3$ for\n$\\lambda=0.035$ and $\\lambda=0.08$, assuming $f_{\\rm B}=0.1$ (see\ntext).}\n\\end{figure}\n\n Figure 1 shows the value of $m_{\\rm d}$ required by the balance\ncondition equation (14) as a function of halo circular velocity,\nassuming that $f_{\\rm B}=0.1$ and the left hand side exactly\nequals to the right hand ones in equation (14). Results are shown\nfor two choices of spin parameters, $\\lambda=0.035$ and 0.08,\ncorresponding to the 50 and 90 percent points of the $\\lambda$\ndistribution for the LBG population (MMWb). As one can see, for\nthe majority of LBG hosts, gas cooling indeed regulates the values\nof $m_{\\rm d}$ to the range from 0.02 to 0.04. So, we can\nreasonably choose $m_{\\rm d}=0.03$ for the LBG population as MMWb\ndid. Since the cooling time is approximately the age of the\nuniverse at $z \\sim 3$, cooling regulation ensures that star\nformation at the predicted rate can last over a large portion of a\nHubble time.\n\n\\section {MODEL PREDICTIONS FOR THE LBG POPULATION}\n\nSince the cooling regulation discussed above gives specific\npredictions of how star formation may have proceeded in LBGs, here\nwe use this model to predict the properties of the LBG population.\nThe condition in equation (14) implies that the star formation\nrate in a disk is equal to the rate of gas infall (due to a\nbalance between cooling and heating). Thus the evolution of the\ngas in the disk of an LBG host halo is described by the standard\nchemical evolution model with infall rate equal to star formation\nrate, i.e., the new infalling gas to the disk distributed radially\nin an exponential form with the scale length of $R_{\\rm d}/b\n\\approx 0.7R_{\\rm d}$, and the reheated gas removed decreases with\nthe increasing radius due to the decreasing SFR. Under the\ninstantaneous recycling approximation (Tinsley 1980), the gas\nmetallicity $Z$ is given by\n \\beq\\label{metallicity} Z =\ny(1-e^{-\\nu})+Z_{i},~~~ \\nu = {\\Sigma_{\\rm tot}\\over \\Sigma _{\\rm\ngas}}-1,\n \\eeq\nwhere $Z_{i}$ is the initial metallicity of the infalling gas,\n$y$ is the stellar chemical yield, $\\Sigma_{\\rm gas}$ is the gas\nsurface density (which is kept constant by gas infall) and\n$\\Sigma_{\\rm tot}$ is the total mass surface density, which\nincreases as star formation proceeds: \\beq {{\\rm d}\\Sigma_{\\rm\ntot} \\over {\\rm d}t}=(1-R_{\\rm r})\\Sigma_{\\rm SFR}. \\eeq Here the\nenrichment of the halo hot gases is not taken into account because\nthe amount of metals heated up to the halos by SNs is relatively\nsmaller than that of primordial gases.\n\n\n\\subsection{Individual Objects}\n\nFigure 2 shows the star formation rate as a function of halo\ncircular velocity $V_{c}$ and spin parameter $\\lambda$. As\nexpected, the predicted SFR increases with $V_c$ but decreases\nwith $\\lambda$ . As we can see from the figure, if we define\nsystems with ${\\rm SFR}\\ga 40 {\\rm M_{\\odot}\\,yr^{-1}}$ (which\nmatches the SFRs for the observed LBG population) to be LBGs, the\nmajority of their host haloes must have $V_c\\ga 200\\kms$ which are\ncooling dominated. This result is the same as that obtained by\nMMWb based on the observed number density and clustering of LBGs.\nThus, the star formation rate based on cooling argument is also\nconsistent with the observed number density and clustering.\nBecause SFR is higher in a system with smaller $\\lambda$, the LBG\npopulation are biased towards haloes with small spins, but given\nits relatively narrow distribution, this bias is not very strong.\n\n\\begin{figure}\n\\epsfysize=9.5cm \\centerline{\\epsfbox{LBG02.ps}}\n\\caption{Predicted SFR as a function of $V_{c}$ and $\\lambda$ in\nthe cooling-regulated model. (a) SFR vs $V_{c}$, for\n$\\lambda=$0.03, 0.05 and 0.1 (from top to bottom). (b) SFR vs\n$\\lambda$, for $V_{c}=$300, 200 and 100${\\rm km/s}$ (from top to\nbottom).}\n\\end{figure}\n\nThe predicted metallicity gradients on individual disks are shown\nin Figure 3 for two different choices of star formation time\nscale $t_\\star$ of 0.5Gyr and 1Gyr respectively, where we assume\nthat $y=Z_{\\odot}$ and $Z_{\\rm i}=0$ in order to make the\npredictions easily compare with observations. The metallicity\ngradients are negative in all cases. When radius is measured in\ndisk scale length, the predicted metallicity depends weakly on\n$V_c$ but strongly on $\\lambda$, and is higher for a longer star\nformation time. As one can see from equation (15), the largest\nmetallicity in the model is $Z=Z_i+y$. This metallicity can be\nachieved in the inner part of compact disks (with small $\\lambda$)\nwhen star formation time $t_\\star\\ga 1$ Gyr. The metallicity drops\nby a factor of $\\sim 2$ from its central value at $R\\sim 3 R_{\\rm\nd}$.\n\n\\begin{figure}\n\\epsfxsize=9cm \\centerline{\\epsfbox{LBG03.ps}} \\caption{The\nmetallicity gradients for LBGs for different star formation time\n$t_\\star$ assuming that $y=Z_{\\odot}$ and $Z_{\\rm i}=0$ (see\ntext). Full and dash lines show results for $V_{c}=300{\\rm\nkms^{-1}}$ and $150{\\rm kms^{-1}}$, respectively. From top to\nbottom, $\\lambda=0.03$ and 0.1; (a) $t_\\star=$0.5Gyr; (b)\n$t_\\star=$1Gyr}\n\\end{figure}\n\n\\subsection{LBG Population}\n\n Since the distribution of haloes with respect to\n$V_c$ and $\\lambda$ are known, we can generate Monte-Carlo samples\nof the halo distribution in the $V_c$-$\\lambda$ plane at any given\nredshift. We can then use the galaxy formation model (MMWb)\ndiscussed above to transform the halo population into an LBG\npopulation based on LBGs with highest SFRs which is the same as\nthat outlined in Sec. 2.\n\n\\begin{figure}\n\\epsfxsize=9.0cm \\centerline{\\epsfbox{LBG04.ps}} \\caption{The\npredicted metallicity distributions for LBG populations assuming\nthat $y=Z_{\\odot}$ and $Z_{\\rm i}=0$ in order to make the\npredictions easily compare with observations (see text). Results\nare shown for two star formation timescales $t_\\star=0.5$ Gyr\n(dash) and $t_\\star=1$ Gyr (solid), respectively (cf. equation\n(15)).}\n\\end{figure}\n\nWe define the typical metallicity of a galaxy as the one at its\neffective radius. Figure 4 shows the distribution of this\nmetallicity for two choices of the star formation time, $t_\\star\n=0.5$ Gyr and 1 Gyr. Just as the same reason as Figure 3 in last\nsection, we have assumed that $y=Z_{\\odot}$ and $Z_{\\rm i}=0$ in\norder to make the predictions easily compare with observations.\nThe median values of $(Z-Z_{i})/y$ are 0.60 and 0.84 for\n$t_\\star=0.5$ Gyr and 1 Gyr, respectively. The sharp truncation at\n$(Z-Z_{i})/y=1$ is due to the fact that this quantity has a\nmaximum value of 1 in the present chemical evolution model. It can\nbe inferred form Figure 3 that the range in $(Z-Z_{i})/y$\ndecreases with increasing star formation time. Thus, if gas infall\nlasts for a long enough time, the distribution in $(Z-Z_{i})/y$\nwill be very narrow near 1 and all LBGs will have metallicity\n$Z=Z_i+y$. According to the works of Tinsley (1980) and Maeder\n(1992), the stellar yield $y$ is the order of $Z_{\\odot}$ for the\nSalpeter IMF. If we adopt a stellar yield $y\\sim 0.5Z_{\\odot}$ and\n$Z_{i}=0.01Z_{\\odot}$, and if LBGs are not short bursts (e.g.\n$t_\\star \\ga 0.5$ Gyr) then their metallicity will be $Z\\ga 0.2\nZ_\\odot$ which is similar to that proposed by Pettini (1999).\n\n\\begin{figure}\n\\epsfysize=9.5cm \\centerline{\\epsfbox{LBG05.ps}} \\caption{The\npredicted effective-radius distribution for LBGs in the\ncooling-regulated scenario (solid), compared to the observed\ndistribution (dash).}\n\\end{figure}\n\nThe predicted distribution of effective radii for the LBG\npopulation is shown in Figure 5. The distribution is similar to\nthat of MMWb. The predicted range is $1.0\\la R_{\\rm eff}\\la 5.0\\,\nh^{-1} {\\rm kpc}$ with a median value of 2.5 $h^{-1}$kpc. Note\nthat the effective radii in the cooling-regulated model are\nindependent of the star formation time $t_\\star$ and $m_{\\rm d}$.\nThe model prediction is in agreement with the observational\nresults given by Pettini, et al. (1998), Lowenthal, et al. (1997)\nand Giavalisco et al. (1996) which are mentioned above.\n\nThe predicted SFR distribution of LBGs also resembles the\nprediction of MMWb except for a slight difference with MMWb, which\nis shown in Figure 6. The median values are 180${\\rm\nM}_{\\odot}~{\\rm yr}^{-1}$ for the model and spans from 100 to\n500${\\rm M}_{\\odot}~{\\rm yr}^{-1}$. To compare with observations,\nwe have to take into account the effect of dust. If we apply an\naverage factor of 3 in dust extinction, then the predictions\nclosely match the values derived from infrared observations by\nPettini, et al. (1998) although there might exist rare LBGs with\nvery high SFR.\n\n\\begin{figure}\n\\epsfysize=9.5cm \\centerline{\\epsfbox{LBG06.ps}} \\caption{The\npredicted SFR distribution for LBGs in the cooling-regulated\nscenario.}\n\\end{figure}\n\n\n\\subsection{Contribution To The Soft X-ray and UV Background}\n\nSince the virial temperature of LBG haloes are quite high, in the\nrange of $10^6-10^7$K, significant soft X-ray and hard UV photons\nmay be emitted as the halo hot gas cools. It is therefore\ninteresting to examine whether the LBG population can make\nsubstantial contribution to the soft X-ray and UV backgrounds.\n\nThe dominant cooling mechanism for hot gas with temperature $\\ga\n10^6$ K is the thermal bremsstrahlung. The bremsstrahlung\nemissivity is given by (e.g., Peebles 1993)\n \\beq\n j_{\\nu}=5.4\n\\times 10^{-39}n_{e}^{2}T^{-1/2}e^{-h\\nu / kT}{\\rm erg\\, cm^{-3}\\,\ns^{-1} \\,ster^{-1}\\,Hz^{-1}},\n \\eeq\nwhere $n_{e}$ (in ${\\rm cm}^{-3}$) is the electron density and $T$\n(in K) is the temperature given by equation (6). The total power\nemitted per unit volume is\n \\beq J=1.42 \\times 10^{-27} ~ T^{1/2}~\nn_{e}^{2} ~ {\\rm erg~cm^{-3}~s^{-1}}.\n \\eeq\nWe write the total luminosity $L_{\\rm b}$ in thermal\nbremsstrahlung as\n \\beq L_{\\rm b}=\\beta {\\dot M_{\\rm\ncool}}V_{c}^{2},\n \\eeq\nand we take $\\beta=2.5$ here as WF so that $L_{\\rm b}$ is equal to\nthe initial thermal energy in the cooling gas. Note that the value\nof $\\beta$ is quite uncertain because it depends on the detail\ndensity and temperature profiles of the hot gas. Substituting\nequation (13) into the above equation, we obtain the total soft\nX-ray luminosity for an LBG\n \\beq L_{\\rm sx}(V_c)\\approx 4.1 \\times\n10^{40} f_{\\rm soft} \\left({V_{c} \\over {\\rm\n250km/s}}\\right)^{4}\\left({f_{\\rm B} \\over 0.1}\\right)^{3/2} {\\rm\nerg ~ s^{-1}}, \\eeq where \\beq f_{\\rm soft} = {1 \\over kT}\n{\\int_{0.5(1+z)}^{2(1+z)}} e^{-E/kT} dE\n \\eeq\nis the fraction of total energy that falls into the ROSAT soft\nX-ray (0.5-2 keV) band. The contribution of the LBG population to\nthe soft X-ray background is then\n \\beq \\rho_{\\rm sx} = \\int\\int\ndV_c dV_{\\rm com} { n(z) L_{\\rm sx} \\over 4\\pi d_{L}^2} \\approx\n5.7 \\times10^{-8} \\left({f_{\\rm B} \\over 0.1}\\right)^{3/2} {\\rm\nerg ~s^{-1}cm^{-2}},\n \\eeq\nwhere $n(z)$ is the comoving number density of LBG haloes as a\nfunction of redshift $z$, $dV_{\\rm com}$ is the differential\ncomoving volume from $z$ to $z+dz$ and $d_{L}$ is the luminosity\ndistance. The integrate for $V_{\\rm c}$ is to sum up all selected\nLBGs with $V_{\\rm c}$ based on their highest SFRs. We have\nintegrated over redshift range from 3 to 4 where the number\ndensity of LBGs is nearly a constant (Steidel 1998a,b). This\ncontribution should be compared with the value derived from the\nROSAT observations (Hasinger et al. 1998) in the 0.5-2 keV band\n\\beq \\rho_{\\rm sx}\\approx 2.4\\times10^{-7}{\\rm\nerg\\,s^{-1}cm^{-2}}. \\eeq As we can see, the soft X-ray\ncontribution from LBGs could be a substantial fraction (about\n20\\%) of the total soft X-ray background.\n\nSimilarly we can calculate the contribution of LBGs to the UV\nbackground at $z=3$. We evaluate the UV background at 4 Ryd\n(1Ryd=13.6 eV) using nearly identical procedures, we find that\n\\beq i_{\\rm 4Ryd} \\approx 2.4\\times10^{-24}{ \\left({f_{\\rm B}\n\\over 0.1}\\right)^{3/2} {\\rm ergs^{-1}cm^{-2}Hz^{-1}ster^{-1}}},\n\\eeq which is much smaller than the UV background from AGNs,\n$i_{\\rm 4Ryd} \\sim 10^{-22}{\\rm ergs^{-1}cm^{-2}Hz^{-1}ster^{-1}}$\n(e.g. Miralda-Escude \\& Ostriker 1990).\n\n\\subsection{Contribution to the Total Metals}\n\nBased on the recent observational results of the cosmic star\nformation history, Pettini (1999) obtained a predicted total mass\nof metals produced at $z=2.5$. After combining results of all\ncontributors observed, he argued that there seems to exist a very\nserious ``missing metal\" problem, i.e., the predicted result is\nmuch higher than observed ones. So, it is interesting to evaluate\nthe total metals produced by LBGs in our model.\n\nAccording to the method we select LBGs to be the galaxies with\nhighest SFR and our chemical evolution model mentioned in Sec.\n3.2, we can calculate the total metal density produced by the LBG\npopulation at $z=3$ based on their observed comoving number\ndensity which is $N_{\\rm LBG}=2.4 \\times 10^{-3}h^{3}{\\rm\nMpc^{-3}}$ for the assumed cosmology (Adelberger et al. 1998).\nDefining that $\\Omega_{\\rm Z}$ is the metal density relative to\nthe critical density, we get that $\\Omega_{\\rm Z}$ of LBGs are\n$0.19\\Omega_{\\rm B}\\times y$ and $0.29\\Omega_{\\rm B}\\times y$ for\nstar formation time of 0.5Gyr and 1Gyr respectively, where $y$ is\nthe stellar yield which is the same as above. Because the virial\ntemperature of LBG halos are very high, a significant fraction of\nthe metal should be in hot phase. Comparing our results with that\nestimated by Pettini (1999) which is $0.08\\Omega_{\\rm B}\\times\nZ_{\\odot}$ (the cosmogony has been taken into account), we find\nthat there is no ``missing metal\" problem in our model.\n\n\\subsection{LBGs and Damped Lyman-Alpha Systems}\n\nDamped Lyman-alpha systems (DLSs) are another population of\nobjects that can be observed at similar redshift to LBGs. The DLSs\nare selected according to their high neutral HI column density\n($>10^{20.3}~{\\rm cm}^{-2}$), and are believed to be either\nhigh-redshift thick disk galaxies (Prochaska \\& Wolfe 1998) or\nmerging protogalactic clumps (Haehnelt, Steimetz \\& Rauch 1998).\nIn either case, to match the observed abundance of DLSs, most DLSs\nshould have circular velocity between $50\\kms$ to $200\\kms$, much\nsmaller than the median circular velocity of LBGs ($\\sim\n300\\kms$). Based on the PS formalism (equation (5)) and disk\ngalaxy formation scenario suggested by MMWa (equations (1) and\n(2)), we can estimate with the random inclination being taken into\naccount, that the fraction of absorbing cross-sections contributed\nby LBGs amounts to only about 5\\% of the total absorption\ncross-section assumed LBGs with highest SFRs. This means that only\na very small fraction of DLSs can be identified as LBGs.\n\nThe physical connection between LBGs and DLSs is still unclear,\nalthough the recent observation of Moller \\& Warren (1998) using\n$HST$ indicates that some DLSs could be associated with LBGs. In\nFigure 7, we show the predicted metallicity distribution for the\nsubset of DLSs which can be observed as LBGs. aGain, we have\nassumed that $y=Z_{\\odot}$ and $Z_{\\rm i}=0$ to let the\npredictions more easily compare to observations. As can be seen,\nthe DLSs generally have lower metallicity than LBGs, because they\nare biased towards the outer region of the host galaxies, where\nthe star formation activity is reduced. Notice, however, that the\nmetallicity of these DLSs could still be higher than most DLSs at\nthe same redshift, which typically have metallicity of $0.1\nZ_\\odot$ (Pettini, et al 1997a).\n\n\\begin{figure}\n\\epsfxsize=9.cm \\centerline{\\epsfbox{LBG07.ps}} \\caption{The\npredicted metallicity distribution for the DLSs expected from the\nLBG population (see text). Results are shown for two star\nformation timescales $t_\\star=0.5$ Gyr (dash) and $t_\\star=1$ Gyr\n(solid), respectively.}\n\\end{figure}\n\n\\section{SUMMARY}\n\nIn this paper, we have examined the star formation and chemical\nenrichment in Lyman break galaxies, assuming them to be the\ncentral galaxies of massive haloes at $z\\sim 3$ and using simple\nchemical evolution models. We found that gas cooling in dark\nhaloes provides a natural process which regulates the amount of\nstar forming gas. The predicted star formation rates and effective\nradii are consistent with observations. The metallicity of the gas\nassociated with an LBG is roughly equal to the chemical yield, or\nabout the order of $1 Z_{\\odot}$ for a Salpeter IMF. Because of\nthe relatively long star-formation time, the colours of these\ngalaxies should be redder than that of short starbursts. It is not\nclear whether this prediction is consistent with current (rather)\nlimited observations, because the interpretation of the\nobservational data depends strongly on the adopted dust reddening.\nStringent constraint can be obtained when full spectral\ninformation of the LBG population is carefully analyzed.\n\nThe model predicts a marked radial metallicity gradient in an LBG,\nwith the gas in the outer region having lower metallicity. As a\nresult, the metallicities for the damped Lyman-alpha absorption\nsystems expected from the LBG population are lower than those for\nthe LBGs themselves, although high metallicity is expected for a\nsmall number of sightlines going through the central regions of an\nLBG. At the same time, our modeled contribution to the total metal\nis roughly consistent with that obtained from the observed cosmic\nstar formation history, i.e., there might not exist so-called\n``missing metal\" problem although there could be more than half of\nthe metals to be in the hot phase. Finally, a prediction of our\nmodel is that LBG haloes are filled with hot gas. As a result,\nthese galaxies may have a non-negligible contribution to the soft\nX-ray background. The contribution of LBGs to the ionizing UV\nbackground is found to be small.\n\nThere are two basic assumptions in our work. One is that the LBG\npopulation is one-to-one associated with the most massive halos\nwhich are generated from the PS formalism, as done by MMWb;\nanother is that the timescale of star formation for LBG population\nis assumed to be the order of 1Gyr, which is suggested by Steidel\net al. (1999a,b, 1995). However, Baugh et al. (1999) recently\nargue that the prediction of the clustering properties of LBGs\nbased on this first simple assumption will be discrepancy with the\nresults of more detailed semi-analytic models. Still, the second\nwill lead to difficulty in reproducing the redshift evolution of\nbright galaxies (Kolatt et al. 1999). More detailed modelling done\nby Somerville (1997) suggest the collisional starbursts could be\nexpected to be an important effect in understanding the LBGs. So,\nfurther observations are required to investigate the intrinsic\nproperties of LBGs.\n\n\\section*{Acknowledgments}\n\nThis project is partly supported by the Chinese National Natural\nFoundation. I thank Dr. S. Mao, Dr. H. J. Mo and Prof. S. D. M.\nWhite for detailed discussions, and the useful help of anonymous\nreferee.\n\n%\\vfill\\eject\n\\begin{thebibliography}{}\n\\bibitem{} Adelberger,K.L., Steidel,C., $\\&$ Giavalisco,M., et al., 1998,\nApJ, 505, 18\n \\bibitem{} Bardeen, J.M., Bond,\nJ.R.,$\\&$ Kaiser, N., et al., 1986, ApJ, 304, 15\n\\bibitem{} Baugh,C.M., Cole,S.,$\\&$ Frenk,C.S.,1998,\npreprint(astro-ph/9808209)\n\\bibitem{} Baugh,C.M., Benson, \\& Cole,S., et al., 1999, MNRAS, 305, L21\n\\bibitem{} Binney,J. $\\&$ Tremaine,S., 1987,\nGalactic dynamics. Princeton Univ. Press, Princeton, NJ, P580\n\\bibitem{}Burles,S., \\& Tytler,D., 1998, ApJ, 507, 732\n\\bibitem{}Calzetti,D., 1997, AJ, 113, 162\n\\bibitem{} Coles,P., Lucchin,F.,\n$\\&$ Matarrese,S., 1998, MNRAS, 300, 183\n\\bibitem{} Cole,M. $\\&$ Lacey,C., 1996,\npreprint(astro-ph/9510147 v3)\n\\bibitem{} Friaca,A.C.S. \\&\nTerlevich,R.J., 1999, MNRAS, 305, 90\n\\bibitem{}\nGiavalisco,M., Steidel,C., $\\&$ Adelberger,K.L., 1998, ApJ, 503,\n543\n\\bibitem{} Giavalisco,M., Steidel,C.,\n$\\&$ Macchetto,F.D., 1996, ApJ, 470, 189\n\\bibitem{}Governato,F., Baugh,C.M., $\\&$ Frenk,C.S., et al., 1998,\nNature, 392, 359\n\\bibitem{} Haehnelt M., Steinmetz M., Rauch\nM.,1998, ApJ, 495, 647\n\\bibitem{} Hasinger,G., Burg,R., $\\&$\nGiacconi,R., et al., 1993, A$\\&$A, 275, 1\n\\bibitem{} Jing,Y.P.,\n1998, ApJ, 503, L9\n\\bibitem{} Jing,Y.P. $\\&$\nSuto,Y., 1998, 494, L5\n\\bibitem{}Kauffmann,G., 1996, MNRAS, 281, 475\n\\bibitem{}Kauffmann,G., Colberg,J.M., Diaferio,A., $\\&$ White,\nS.D.M., 1999, MNRAS, 303, 188\n\\bibitem{} Katz,N.,\nHernquist,L., $\\&$ Weinberg,D.H., et al., 1998,\npreprint(astro-ph/9806257)\n\\bibitem{} Kennicutt,R., 1998, ApJ, 498, 541\n\\bibitem{} Kolatt, et al., 1999, preprint (astro-ph/9906104)\n\\bibitem{} Lacey,C. $\\&$ Cole,S.,\n1994, MNRAS, 271, 676\n\\bibitem{}Lowenthal,J.D., Koo,D.C., $\\&$\nGuzman,R., et al, 1997, ApJ, 481, 673\n\\bibitem{} Madau,P.,\nPozzetti,L., $\\&$ Dickinson,M., 1998, ApJ, 499, 106\n\\bibitem{}\nMadau,P., Ferguson,H.C., $\\&$ Dickinson,M., et al., 1996, MNRAS,\n283, 1388\n\\bibitem{} Maeder,A., 1992, A$\\&$A, 264, 105\n\\bibitem{} Mihos,J.C. $\\&$ Hernquist,L., 1996, ApJ, 464, 641\n\\bibitem{} Miralda-Escude,J. \\& Ostriker.J.P., 1990, ApJ, 350, 1\n\\bibitem{} Mo, H.J. $\\&$ Fugugita,M., 1996, ApJ, 467, L9\n\\bibitem{} Mo, H.J., Mao, S., $\\&$ White, S.D.M., 1998a, MNRAS,\n295, 319(MMWa)\n\\bibitem{} Mo, H.J., Mao, S., $\\&$ White, S.D.M.,\n1998b, 1999, MNRAS, 304, 175 (MMWb)\n\\bibitem{} Moller,P. $\\&$ Warren,S.J., 1998, MNRAS, 299, 661\n\\bibitem{} Moscardini,L., Coles,P., $\\&$ Lucchin,F., et al.,\n1998, MNRAS, 299, 95\n\\bibitem{} Narvarro, J. F., Frenk, C. S., \\& White, S. D. M.,\n1997, ApJ, 490,493\n\\bibitem{} Ouchi,M. \\&\nYamada,T., 1999, ApJ, 517, L19\n\\bibitem{} Peacock,J.A., Jimenez,R., $\\&$ Dunlop,J.S., et al., 1998,\npreprint (astro-ph/9801184)\n\\bibitem{} Peebles,P.J.E., 1993,\nPrinciples of Physical Cosmology, Princeton Univ. Press,\nPrinceton, NJ, P577\n\\bibitem{} Pettini,M., 1999, preprint\n(astro-ph/9902173)\n\\bibitem{} Pettini,M., Smith,L.J., King,D.L.,\n$\\&$ Hunstead,R.W., 1997a, ApJ, 486, 665\n\\bibitem{} Pettini,M.,\nSteidel,C., Dickinson M., Kellogg,M., Giavolisco M., $\\&$\nAdelberger K.L., 1997b, preprint (astro-ph/9707200)\n\\bibitem{}\nPettini,M., Kellogg,M., $\\&$ Steidel,C., et al., 1998, ApJ, 508,\n539\n\\bibitem{}Press,W.H. $\\&$ Schechter,P., 1974,\nApJ, 187, 425 (PS)\n\\bibitem{} Prochaska,J.X. \\& Wolfe,A.M.,\n1998, ApJ, 507, 113\n\\bibitem{} Sawicki M., Yee\nH.K.C., 1998, AJ, 115, 1329\n\\bibitem{} Somerville,R.S., 1997,\nPhD Thesis\n\\bibitem{} Somerville,R.S., Primack,J.R., \\&\nFaber,S.M.,1999, MNRAS, 307, 15\n\\bibitem{}\nSteidel,C., Pettini,M., $\\&$ Hamilton,D., 1995, AJ, 110, 2519\n\\bibitem{}Steidel,C., Giavalisco,M., $\\&$ Pettini,M., et al.,\n1996, ApJ,462, L17\n\\bibitem{} Steidel,C., Adelberger,K.L., $\\&$\nDickison,M., et al., 1998, ApJ, 492, 428\n\\bibitem{} Steidel,C.,\nAdelberger,K.L., $\\&$ Giavalisco,M., et al., 1999a, ApJ, 519, 1\n\\bibitem{} Steidel,C., Adelberger,K.L., $\\&$\nDickison,M., et al., 1999b, preprint, (astro-ph/9812167)\n\\bibitem{} Tinsley,B.M., 1980, Fundam. Cosmic Phys., 5, 287\n\\bibitem{} Toomre,A., 1964, ApJ, 139, 1217\n\\bibitem{}\nWechsler,R.H.,Gross,M.A.K., $\\&$ Primack,J.R., et al., 1998, ApJ,\n509, 19\n\\bibitem{} White,S.D.M. $\\&$\nFrenk,C.S., 1991, ApJ, 379, 25 (WF)\n\\bibitem{} White,S.D.M. $\\&$\nRees,M.J., 1978, MNRAS, 183, 341\n\\bibitem{} Zhao, D., Shu, C., Song, G., \\& Zhao, J., 1999,\nsubmitted to ApJ\n\\end{thebibliography}{}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002388.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem{} Adelberger,K.L., Steidel,C., $\\&$ Giavalisco,M., et al., 1998,\nApJ, 505, 18\n \\bibitem{} Bardeen, J.M., Bond,\nJ.R.,$\\&$ Kaiser, N., et al., 1986, ApJ, 304, 15\n\\bibitem{} Baugh,C.M., Cole,S.,$\\&$ Frenk,C.S.,1998,\npreprint(astro-ph/9808209)\n\\bibitem{} Baugh,C.M., Benson, \\& Cole,S., et al., 1999, MNRAS, 305, L21\n\\bibitem{} Binney,J. $\\&$ Tremaine,S., 1987,\nGalactic dynamics. Princeton Univ. Press, Princeton, NJ, P580\n\\bibitem{}Burles,S., \\& Tytler,D., 1998, ApJ, 507, 732\n\\bibitem{}Calzetti,D., 1997, AJ, 113, 162\n\\bibitem{} Coles,P., Lucchin,F.,\n$\\&$ Matarrese,S., 1998, MNRAS, 300, 183\n\\bibitem{} Cole,M. $\\&$ Lacey,C., 1996,\npreprint(astro-ph/9510147 v3)\n\\bibitem{} Friaca,A.C.S. \\&\nTerlevich,R.J., 1999, MNRAS, 305, 90\n\\bibitem{}\nGiavalisco,M., Steidel,C., $\\&$ Adelberger,K.L., 1998, ApJ, 503,\n543\n\\bibitem{} Giavalisco,M., Steidel,C.,\n$\\&$ Macchetto,F.D., 1996, ApJ, 470, 189\n\\bibitem{}Governato,F., Baugh,C.M., $\\&$ Frenk,C.S., et al., 1998,\nNature, 392, 359\n\\bibitem{} Haehnelt M., Steinmetz M., Rauch\nM.,1998, ApJ, 495, 647\n\\bibitem{} Hasinger,G., Burg,R., $\\&$\nGiacconi,R., et al., 1993, A$\\&$A, 275, 1\n\\bibitem{} Jing,Y.P.,\n1998, ApJ, 503, L9\n\\bibitem{} Jing,Y.P. $\\&$\nSuto,Y., 1998, 494, L5\n\\bibitem{}Kauffmann,G., 1996, MNRAS, 281, 475\n\\bibitem{}Kauffmann,G., Colberg,J.M., Diaferio,A., $\\&$ White,\nS.D.M., 1999, MNRAS, 303, 188\n\\bibitem{} Katz,N.,\nHernquist,L., $\\&$ Weinberg,D.H., et al., 1998,\npreprint(astro-ph/9806257)\n\\bibitem{} Kennicutt,R., 1998, ApJ, 498, 541\n\\bibitem{} Kolatt, et al., 1999, preprint (astro-ph/9906104)\n\\bibitem{} Lacey,C. $\\&$ Cole,S.,\n1994, MNRAS, 271, 676\n\\bibitem{}Lowenthal,J.D., Koo,D.C., $\\&$\nGuzman,R., et al, 1997, ApJ, 481, 673\n\\bibitem{} Madau,P.,\nPozzetti,L., $\\&$ Dickinson,M., 1998, ApJ, 499, 106\n\\bibitem{}\nMadau,P., Ferguson,H.C., $\\&$ Dickinson,M., et al., 1996, MNRAS,\n283, 1388\n\\bibitem{} Maeder,A., 1992, A$\\&$A, 264, 105\n\\bibitem{} Mihos,J.C. $\\&$ Hernquist,L., 1996, ApJ, 464, 641\n\\bibitem{} Miralda-Escude,J. \\& Ostriker.J.P., 1990, ApJ, 350, 1\n\\bibitem{} Mo, H.J. $\\&$ Fugugita,M., 1996, ApJ, 467, L9\n\\bibitem{} Mo, H.J., Mao, S., $\\&$ White, S.D.M., 1998a, MNRAS,\n295, 319(MMWa)\n\\bibitem{} Mo, H.J., Mao, S., $\\&$ White, S.D.M.,\n1998b, 1999, MNRAS, 304, 175 (MMWb)\n\\bibitem{} Moller,P. $\\&$ Warren,S.J., 1998, MNRAS, 299, 661\n\\bibitem{} Moscardini,L., Coles,P., $\\&$ Lucchin,F., et al.,\n1998, MNRAS, 299, 95\n\\bibitem{} Narvarro, J. F., Frenk, C. S., \\& White, S. D. M.,\n1997, ApJ, 490,493\n\\bibitem{} Ouchi,M. \\&\nYamada,T., 1999, ApJ, 517, L19\n\\bibitem{} Peacock,J.A., Jimenez,R., $\\&$ Dunlop,J.S., et al., 1998,\npreprint (astro-ph/9801184)\n\\bibitem{} Peebles,P.J.E., 1993,\nPrinciples of Physical Cosmology, Princeton Univ. Press,\nPrinceton, NJ, P577\n\\bibitem{} Pettini,M., 1999, preprint\n(astro-ph/9902173)\n\\bibitem{} Pettini,M., Smith,L.J., King,D.L.,\n$\\&$ Hunstead,R.W., 1997a, ApJ, 486, 665\n\\bibitem{} Pettini,M.,\nSteidel,C., Dickinson M., Kellogg,M., Giavolisco M., $\\&$\nAdelberger K.L., 1997b, preprint (astro-ph/9707200)\n\\bibitem{}\nPettini,M., Kellogg,M., $\\&$ Steidel,C., et al., 1998, ApJ, 508,\n539\n\\bibitem{}Press,W.H. $\\&$ Schechter,P., 1974,\nApJ, 187, 425 (PS)\n\\bibitem{} Prochaska,J.X. \\& Wolfe,A.M.,\n1998, ApJ, 507, 113\n\\bibitem{} Sawicki M., Yee\nH.K.C., 1998, AJ, 115, 1329\n\\bibitem{} Somerville,R.S., 1997,\nPhD Thesis\n\\bibitem{} Somerville,R.S., Primack,J.R., \\&\nFaber,S.M.,1999, MNRAS, 307, 15\n\\bibitem{}\nSteidel,C., Pettini,M., $\\&$ Hamilton,D., 1995, AJ, 110, 2519\n\\bibitem{}Steidel,C., Giavalisco,M., $\\&$ Pettini,M., et al.,\n1996, ApJ,462, L17\n\\bibitem{} Steidel,C., Adelberger,K.L., $\\&$\nDickison,M., et al., 1998, ApJ, 492, 428\n\\bibitem{} Steidel,C.,\nAdelberger,K.L., $\\&$ Giavalisco,M., et al., 1999a, ApJ, 519, 1\n\\bibitem{} Steidel,C., Adelberger,K.L., $\\&$\nDickison,M., et al., 1999b, preprint, (astro-ph/9812167)\n\\bibitem{} Tinsley,B.M., 1980, Fundam. Cosmic Phys., 5, 287\n\\bibitem{} Toomre,A., 1964, ApJ, 139, 1217\n\\bibitem{}\nWechsler,R.H.,Gross,M.A.K., $\\&$ Primack,J.R., et al., 1998, ApJ,\n509, 19\n\\bibitem{} White,S.D.M. $\\&$\nFrenk,C.S., 1991, ApJ, 379, 25 (WF)\n\\bibitem{} White,S.D.M. $\\&$\nRees,M.J., 1978, MNRAS, 183, 341\n\\bibitem{} Zhao, D., Shu, C., Song, G., \\& Zhao, J., 1999,\nsubmitted to ApJ\n\\end{thebibliography}"
}
] |
astro-ph0002389
|
Formation of Intermediate-Mass Black Holes in Circumnuclear Regions of Galaxies
|
[
{
"author": "Yoshiaki {\\sc Taniguchi}"
},
{
"author": "Yasuhiro {\\sc Shioya}"
},
{
"author": "{Aramaki, Aoba, Sendai 980-8578}"
},
{
"author": "[6pt] Takeshi G. {\\sc Tsuru}"
},
{
"author": "{Kitashirakawa, Sakyo, Kyoto 606-8502}"
},
{
"author": "and"
},
{
"author": "Satoru {\\sc Ikeuchi}"
},
{
"author": "{Furo, Chikusa, Nagoya 464-8602}"
}
] |
[
{
"name": "astro-ph0002389.tex",
"string": "%-----------------------------------------------------------------------------\n% Authors: Taniguchi, Y., Shioya, Y., Tsuru, G. T., and Ikeuchi, S.\n%\n% Title: FORMATION OF INTERMEDIATE-MASS BLACK HOLES IN CIRCUMNUCLEAR REGIONS\n% OF GALAXIES\n%\n% CONTENTS:\n%\n% This file:\n% (1) Title Page\n% (2) Abstract & Key words \n% (3) Text & Acknowledgments\n% (4) References\n% \n% No Figure \n%-----------------------------------------------------------------------------\n\\documentstyle[PASJadd,12pt]{PASJ95}\n\\draft\n\\markboth{Y.\\ Taniguchi et al.}\n{Formation of Sub-Supermassive Black Holes}\n\n\\newcommand{\\vol}{}\n\\newcommand{\\no}{}\n\\newcommand{\\lett}{}\n\\newcommand{\\spage}{}\n\\newcommand{\\rdate}{}\n\\newcommand{\\adate}{}\n\n\\begin{document}\n\n\\title{Formation of Intermediate-Mass Black Holes in Circumnuclear \n Regions of Galaxies}\n\n\\author{Yoshiaki {\\sc Taniguchi}, Yasuhiro {\\sc Shioya} \\\\\n{\\it Astronomical Institute, Graduate School of Science, Tohoku University,}\\\\\n{\\it Aramaki, Aoba, Sendai 980-8578} \\\\\n{\\it E-mail (YT): tani@astr.tohoku.ac.jp}\n\\\\[6pt]\nTakeshi G. {\\sc Tsuru} \\\\\n{\\it Physics Department, Graduate School of Science, Kyoto University,} \\\\\n{\\it Kitashirakawa, Sakyo, Kyoto 606-8502} \\\\\nand \\\\\nSatoru {\\sc Ikeuchi} \\\\\n{\\it Physics Department, Graduate School of Science, Nagoya University,} \\\\\n{\\it Furo, Chikusa, Nagoya 464-8602}}\n%\n%----------------------------------------------------------------------------\n% Abstract \n%----------------------------------------------------------------------------\n%\n\\abst{\nRecent high-resolution X-ray imaging studies have discovered\npossible candidates of intermediate-mass black holes with masses\nof $M_\\bullet \\sim 10^{2-4} \\MO$ in circumnuclear regions\nof many (disk) galaxies. It is known that a large number of \nmassive stars are formed in a circumnuclear giant H {\\sc ii} region.\nTherefore, we propose that continual merger of compact remnants left from \nthese massive stars is responsible for the formation of such an \nintermediate-mass black hole within a timescale of $\\sim 10^9$ years.\nA necessary condition is that several hundreds of massive\nstars are formed in a compact region with a radius of a few pc.\n} \n%\n\\kword{black holes --- galaxies: starburst --- \ngalaxies: star clusters --- X-rays: sources}\n\n\\maketitle\n\\thispagestyle{headings}\n\n%-------------------------------------------------------------------------\n\n\\section{Introduction}\n\nRecent sensitive, high-resolution X-ray imaging studies have found\nunusually bright, compact X-ray sources in circumnuclear regions\nof many (disk) galaxies [Colbert \\& Mushotzky\n1999 (hereafter CM99), Okada et al. 1998;\nPtak \\& Griffiths 1999; Matsumoto \\& Tsuru 1999; Makishima et al. 2000].\nPrior to these observations, it has been known that some nearby galaxies\nhave luminous X-ray sources in their circumnuclear regions\n(Fabbiano \\& Trinchieri 1987; Kohmura et al. 1994; Petre et al. 1994;\nTakano et al. 1994; Colbert et al. 1995;\nReynolds et al. 1997; see for a review Fabbiano 1988).\nThe observational properties of such circumnuclear X-ray sources \nare summarized as follows (e.g., CM 99);\n1) ROSAT X-ray luminosities, $L_{\\rm X}$(0.2--2.4 keV)\n$\\sim 10^{37}$ -- $10^{40}$ ergs s$^{-1}$ with a mean of $3\\times 10^{39}$\nergs s$^{-1}$; note that some of them are also detected\nin the hard X ray and thus the total X-ray luminosities \nare higher by about one order of magnitude than the above values, \n2) the mean displacement between the location of the \ncompact X-ray source and the optical photometric center of the galaxy\nis $\\sim$ 390 pc, and 3) they are common; the detection rate of such \ncompact X-ray sources is $\\gtsim$ 50\\%.\n\nPossible origins of these sources are; 1) black hole X-ray binaries,\n2) low-luminosity AGN, 3) young X-ray luminous supernovae, or\n4) a new X-ray population (e.g., CM99). Since the Eddington\nluminosity of a 1.4 $\\MO$ accreting neutron star is \n$10^{38.3}$ ergs s$^{-1}$, the luminous compact X-ray sources\ncannot be explained by a single accreting neutron star.\nIf they are black hole X-ray binaries, their masses are\nestimated to be $M_\\bullet \\sim$ 10$^2$ -- 10$^4 \\MO$;\ni.e., intermediate-mass black holes (hereafter IMBHs).\nThis urges us to consider how such IMBHs can be formed in \ncircumnuclear regions of galaxies.\n\nOne of ideas may be that they are formed \nthrough the collapse of massive clouds (see Rees 1978).\nIn typical disk galaxies, gas clouds are present as a form of \ngiant molecular gas clouds; hereafter GMCs.\nA typical GMC has the following characteristics (e.g., Blitz 1993);\n1) the mass, $M_{\\rm GMC} \\simeq$ (1 -- 2) $\\times 10^5 \\MO$,\n2) the mean diameter, $D_{\\rm GMC} \\simeq 45$ pc,\n3) the volume, $V_{\\rm GMC} \\simeq 9.6 \\times 10^4$ pc$^3$,\n4) the average density of H$_2$, $\\overline{n}_{\\rm H_2} \\simeq 50$ cm$^{-3}$,\nand 5) the mean column density of H$_2$, \n$\\overline{N}_{\\rm H_2} \\simeq$ (3 -- 6) $\\times 10^{21}$ cm$^{-2}$.\nAlthough the typical kinetic temperature is $T_{\\rm kin} \\sim 10$ K,\nthe sound speed, $c_{\\rm s}$,\nis generally higher than the velocity dispersion\nderived from the kinetic temperature because the turbulence\nplays an important role in GMCs; therefore, $c_{\\rm s} \\sim 1$ km s$^{-1}$.\nIf a GMC is perturbed gravitationally by some physical mechanism,\nit is likely that it begins to experience fragmentation,\nresulting in the formation of sub-giant molecular clouds.\nSuch fragmentation could occur preferentially in denser parts of the GMC.\nSince a typical H$_2$ density and a typical kinetic temperature \nin such dense parts are $n_{\\rm H_2} \\sim 10^4$ cm$^{-3}$ and\n$T_{\\rm kin} \\sim$ 10 K, respectively, we obtain a Jeans' mass of\n$m_{\\rm J} \\sim \\lambda_{\\rm J}^3 \\rho_{\\rm H_2} \\sim 20 \\MO$ for\n$\\lambda_{\\rm J} = c_{\\rm s} (\\pi / G \\rho_{\\rm H_2})^{1/2}\n\\sim 0.36 ~ (c_{\\rm s}/{\\rm 0.3 ~ km ~ s^{-1}})$ pc and\n$\\rho_{\\rm H_2} = n_{\\rm H_2} m_{\\rm H_2}$\nwhere $m_{\\rm H_2}$ is the mass of a hydrogen molecule (Jeans 1929).\nTherefore, IMBHs may not be formed directly from such massive gas clouds.\n\nInstead, in this Letter, we propose that an IMBH is formed by \ncontinual merging \nof compact remnants (i.e., neutron stars and black holes)\nleft from massive stars in a giant H {\\sc ii} region. The reason for this\nis that giant H {\\sc ii} regions are often observed in circumnuclear \nregions of disk galaxies (e.g., Kennicutt, Keel, \\& Blaha 1989\nand references therein; see for the formation mechanism of such\ncircumnuclear giant H {\\sc ii} regions, Elmegreen 1994).\nWe also discuss some other proposed mechanisms responsible for\nthe formation of IMBHs. \n\n\\section {Proposed Model}\n\n\\subsection{Dynamical Relaxation of Massive-Star Compact Remnants}\n\nIt has been considered that \none plausible mechanism for the formation of\nsupermassive black holes (SMBHs) in galactic\nnuclei is to pile up compact remnants of massive stars born in nuclear regions\n(e.g., Spitzer \\& Saslaw 1966; Spitzer \\& Stone 1967, Spitzer 1969;\nSaslaw 1973; Begelman \\& Rees 1978; Weedman 1983; Norman \\& Scoville 1988;\nQuinlan \\& Shapiro 1989, 1990; Lee 1995; Taniguchi, Ikeuchi, \\& Shioya 1999).\nOn the analogy of this mechanism, we investigate the dynamical evolution of\ncompact remnants left from massive stars born in the core of a giant H {\\sc ii}\nregion in circumnuclear regions of galaxies.\n\nTypical masses of IMBHs lie in the range between \n$\\sim 10^2 \\MO$ and $\\sim 10^4 \\MO$ (CM99).\nTherefore, we investigate a possibility that an IMBH with \nmass of $10^3 \\MO$ can be formed from mergers of compact remnants\nleft in the core of a giant H {\\sc ii} region. \nWe consider a case that $N$ massive stars with masses higher\nthan 8 $\\MO$ are formed within a sphere with a radius of $r_{\\rm cl}$.\nHere it is noted that all such massive stars yield a compact remnant\nafter the supernova explosion while the core of \nstars with masses less massive than 8 $\\MO$ evolves into a white dwarf.\nIt is known that the mass of a neutron star\nis $\\approx 1.4 \\MO$ while that of\na stellar-size black hole is from a few $\\MO$ to $\\approx 10\n\\MO$; e.g., Brown \\& Bethe (1994) suggested that main-sequence stars\nwith $18 \\MO < m_* < 25 \\MO$ evolve to low-mass black holes\n($m_\\bullet \\simeq 1.5 \\MO$) while stars with $m_* > 25 \\MO$\nevolve to high-mass black holes ($m_\\bullet \\gtsim 10 \\MO$).\nHowever, the mass function for giant H {\\sc ii} regions has not yet\nbeen well known. Therefore, in the above estimate,\nwe have assumed for simplicity that all the compact\nremnants are black holes with a mass of 2 $\\MO$ and thus\n500 seed compact remnants are necessary to\nmake an IMBH with a mass of $10^3 \\MO$.\n\nAll the massive stars die within a timescale of $\\sim 10^7$ years \nand then a cluster of compact remnants will result in.\nThe candidates of IMBHs are observed in circumnuclear regions\nof galaxies (i.e., a typical radial distance is\n$R \\simeq $ a few 100 pc). At such a distance, the rotation \ncurve of galaxies may be described by the rigid rotation (e.g., Rubin et al.\n1985; cf. Sofue 1997); we assume that the rigid rotation continues \nup to a radius of $R$ = 1 kpc and reaches the maximum rotation velocity of \n$v_{\\rm rot}$ = 200 km s$^{-1}$.\nIf a giant H {\\sc ii} region is formed at $R$ = 100 pc,\nthe cluster of massive stars (and thus the cluster of compact \nremnants too) is influenced by the mass contained within $R$ = 100 pc. \nThis mass is estimated to be $M \\sim R v_{\\rm rot}^2 / G\n\\sim 9 \\times 10^6 R_{100}^3 \\MO$ where\n$R_{100}$ is the radial distance\nin units of 100 pc; note that $v_{\\rm rot} = 20 R_{100}$ km s$^{-1}$.\nThe radius of the remnant cluster can be estimated as the tidal radius,\n\n\\begin{equation}\nr_{\\rm cl} \\sim r_{\\rm tidal} \\sim R [N m_\\bullet/(2M)]^{1/3}\n\\sim 3.8 N_{500}^{1/3} m_{\\bullet, 2}^{1/3} ~~ {\\rm pc}\n\\end{equation}\nwhere $N_{500}$ is the number of compact remnants in units of 500 \nand $m_{\\bullet, 2}$ is the mass of a compact remnant in units of\n2 $\\MO$. In this case, the cluster can be relaxed dynamically \nwith a timescale of\n\n\\begin{equation}\n\\tau_{\\rm dyn} \\sim N^{1/2} G^{-1/2} r_{\\rm cl}^{3/2} m_\\bullet^{-1/2}\n\\sim 1.8 \\times 10^9 ~~ {\\rm y}.\n\\end{equation}\nSince this timescale is shorter than the age of galaxies,\nthis mechanism may be responsible for the formation of IMBHs in\ncircumnuclear regions of galaxies.\n\nIt is noted that the dynamical situation for a cluster of compact\nremnants considered here is completely different from both that\nfor a cluster of compact remnants in globular clusters (e.g.,\nKulkarni, Hut, \\& McMillan 1993) and that for a cluster of\ncompact remnants in the nuclear region\nof galaxies (e.g., Weedman 1983; Lee 1995 and references therein)\nbecause low-mass stars dominate the cluster gravitational potential\nfor the latter two cases. On the other hand, it is expected that\nmassive stars may be preferentially formed in the core. Since supernovae\ncould blow the gas resided originally in the core region, compact\nremnants themselves may dominate the cluster gravitational potential.\nFurthermore, lifetimes of OB stars are less than $\\sim 10^7$ years,\nbeing much shorter than the dynamical relaxation timescale \nestimated above. Therefore,\nthe star cluster evolves to a cluster of compact remnants quickly.\nSome black holes may be ejected from the cluster by the \ndynamical effect during the formation of black hole binaries through\nthe three-body encounters (Spitzer 1987; Kulkarni et al. 1993).\nHowever, this effect is negligible if $N \\gtsim 100$ \n(e.g., Binney \\& Tremaine 1987); this is indeed the case discussed here.\n\nThen we investigate what kind of massive star formation is necessary.\nWe estimate an average number density of gas,\n$n_{\\rm H} = M_{\\rm gas} / [(4 \\pi/3) r_{\\rm cl}^3 m_{\\rm H}]\n\\simeq 1 \\times 10^4$ cm$^{-3}$ where \n$M_{\\rm gas} = N m_* \\eta_{\\rm SF, 0.1}^{-1} = 5 \\times 10^4 \\MO$ \ngiven $m_* = 10 \\MO$ and \n$\\eta_{\\rm SF, 0.1}$ is the star formation efficiency \nin units of 0.1; i.e., 10\\% of the gas in the cloud is\nused to form massive stars. \nThis density is comparable to those in typical\ndense cores in star forming regions (e.g., $n_{\\rm H}\n\\sim 10^4$ cm$^{-3}$; e.g., Lada, Strom, \\& Myers 1993). \nNote that the gas mass lies in the observed range of $M_{\\rm GMC}$. \nThe mass volume density of massive stars is estimated as \n$ N m_* / [(4 \\pi/3) r_{\\rm cl}^3] \\simeq 22 \\MO$\npc$^{-3}$. This is lower by two orders of magnitude than\nthat of the compact star cluster R136a, whose \nhalf light radius is 1.7 pc, embedded in the\ncentral region of the 30 Dor nebula\nin Large Magellanic cloud; $5.5 \\times 10^4 \\MO$ pc$^{-3}$\n(Hunter et al. 1995). \nTherefore, the star formation properties as well as the star cluster \nproperties in our model are not unusual.\n\nFinally we mention which type of galaxies tends to have \nmore massive IMBHs. Using equations (1) and (2) together with\nthe relation $M \\sim R v_{\\rm rot}^2 / G$, we obtain\n\n\\begin{equation}\n\\tau_{\\rm dyn} \\sim {N \\over 2} ~ {R \\over v_{\\rm rot}} \n\\sim {N \\over 2} ~ {\\tau_{\\rm rot} \\over {2 \\pi}},\n\\end{equation}\nwhere $\\tau_{\\rm rot}$ is the rotation period. If the rigid rotation\nis achieved up to a radius of $R =$ 1 kpc as observed,\nthe dynamical timescale is independent of $R$ if $R \\leq 1$ kpc; \ni.e., any cluster of compact remnants left from the core of a giant\nH {\\sc ii} region within $R \\leq$ 1 kpc could evolve to an IMBH.\nSince any disk galaxy have been able to form such IMBHs during its\nlifetime, i.e., $\\sim 10^{10}$ years, the total number of IMBHs formed\nin its lifetime is estimated to be \n\n\\begin{equation}\nN \\sim 4 \\pi \\times \\left({{\\tau_{\\rm dyn}} \\over {\\tau_{\\rm rot}}}\\right) \n\\sim 4 \\times 10^3 \\left({{\\tau_{\\rm dyn}} \\over {10^{10} ~ {\\rm y}}}\\right)\n \\left({{\\tau_{\\rm rot}} \\over {3.1 \\times 10^{7} ~ {\\rm y}}}\\right)^{-1}.\n\\end{equation}\n\nMore importantly, the relation given in equation (3)\nimplies that galaxies with slower rigid-rotation velocities \n(i.e., late-type spirals) tend to have less massive IMBHs\nwhile those with higher rigid-rotation velocities (i.e.,\nearly-type spirals) tend to have more massive IMBHs. \nSince the survey conducted by CM99 is biased to late-type spirals,\nwe are unable to make this observational test. X-ray surveys will be \nrecommended for a sample of early-type spirals to test whether or not\nthis prediction is consistent with observation. \n\n\\subsection{Intermediate-mass Black Holes Supplied \nfrom Satellite Galaxies}\n\nWe have shown that an IMBH can be made through the merger of\ncompact remnants of massive stars born in a giant H {\\sc ii} region.\nSince any galaxies have satellite galaxies (e.g., Zaritsky et al. 1997) \nand giant H {\\sc ii} regions could be made in some gas-rich satellites\n(e.g., 30 Dor in LMC), it seems important to\ninvestigate a possibility that IMBHs can be supplied\nby minor mergers with satellite galaxies having IMBHs.\nM 32, one of the satellite galaxies of M 31, may have a \nsupermassive black hole with a mass of $\\sim 10^6 \\MO$\n(Dressler \\& Richstone 1988; see for a review Kormendy et al.\n1998). At present, there is no observational evidence\nfor the presence of IMBHs in any satellite galaxies.\nHowever, if some satellite galaxies had IMBHs in their\nnuclei, it could be possible that minor mergers with such satellites\nare responsible for the presence of IMBHs in circumnuclear regions\nof the host galaxies.\n\nWe estimate the frequency of occurrence of compact X-ray sources\nif all of them are attributed to the IMBHs supplied by minor mergers with\nnucleated satellite galaxies (see Taniguchi \\& Wada 1996).\nTremaine (1981) estimated that every galaxy would experience minor mergers with\nits satellite galaxies several times. Since a typical galaxy may have several\nsatellite galaxies, the probability of merger\nfor a satellite galaxy may be estimated to be $f_{\\rm merger} \\simeq 0.5$; i.e.,\nhalf of the satellite galaxies have already merged to a host galaxy, while the rest\nare still orbiting. Another important value is the number of nucleated\nsatellite galaxies. For example,\nM31 has two nucleated satellites (M32 and NGC 205), and a field S0 galaxy\nNGC 3115 has a nucleated dwarf (van den Bergh 1986).\nAlthough there has been no systematic search for nucleated satellite galaxies,\nit is likely that every galaxy has (or had) a few nucleated satellites.\nTherefore, for simplicity we assume $n_{\\rm sat} = 2$.\nIf we assume that the typical lifetime of the X-ray sources\nis $\\tau_{\\rm active} \\simeq 10^8$ years, we obtain an \nexpected frequency,\n\n\\begin{equation}\nP_{\\rm IMBH} \\simeq f_{\\rm merger} ~ n_{\\rm sat} ~ \\tau_{\\rm active} ~\n\\tau_{\\rm Hubble}^{-1} \\sim 0.01 n_{\\rm sat, 2} \\tau_{\\rm active, 8},\n\\end{equation}\nwhere $\\tau_{\\rm Hubble}$ is the Hubble time, $\\sim 10^{10}$ years,\n$n_{\\rm sat, 2}$ is the number of nucleated satellites in units of 2,\n$\\tau_{\\rm active, 8}$ is the duration of the active phase\nin units of $10^8$ years. Hence,\nif minor mergers with nucleated satellites are responsible for\nthe IMBHs in the circumnuclear regions of their host galaxies, \nit is statistically expected that hard X-ray sources\nare found in about 1 \\% of field disk galaxies.\nThis is significantly smaller than the observed frequency, $\\gtsim$\n50\\% (CM99).\n\nHowever, it seems possible that IMBHs can be formed through \nthe dynamical relaxation of cores of giant H {\\sc ii} regions\nin gas-rich satellite galaxies and they travel \nto circumnuclear regions of their host galaxies by minor mergers.\nThis case gives another expected frequency, \n\n\\begin{equation}\nP_{\\rm IMBH} \\simeq f_{\\rm merger} ~ n_{\\rm sat} ~ n_{\\rm IMBH} ~ \n\\tau_{\\rm active} ~ \\tau_{\\rm Hubble}^{-1}\n\\end{equation}\nwhere $n_{\\rm IMBH}$ is the number of IMBH in each satellite galaxy.\nSince the maximum number of IMBHs can be estimated as \n$n_{\\rm IMBH} \\sim \\tau_{\\rm Hubble} / \\tau_{\\rm dyn}$, we obtain\n \n\\begin{equation}\nP_{\\rm IMBH} \\simeq f_{\\rm merger} ~ n_{\\rm sat} ~ \n\\tau_{\\rm active} ~ \\tau_{\\rm dyn}^{-1} \\sim\n0.1 n_{\\rm sat, 2} \\tau_{\\rm active, 8} \\tau_{\\rm dyn, 9}^{-1}\n\\end{equation}\nwhere $\\tau_{\\rm dyn, 9}$ is the dynamical timescale in units of\n$10^9$ years. Note that $n_{\\rm sat}$ is not the number of nucleated\nsatellites but that of gas-rich satellites. However, for simplicity,\nwe adopt $n_{\\rm sat} = 2$ even in this estimate.\n\nIn summary, the frequency of occurrence of IMBHs supplied from\nsatellite galaxies lies in a range between 0.01 and 0.1.\nTherefore, we suggest that \nminor mergers may not explain the observed higher frequency of IMBHs\nunless $n_{\\rm sat} > 10$.\n\n\\section{Alternative Mechanisms}\n\nWe have shown that continual merging of compact remnants left from\nmassive stars in a giant H {\\sc ii} region formed in circumnuclear\nregions of galaxies may be responsible for the formation of an IMBH\nintermediate-mass black hole within a timescale of $\\sim 10^9$ years.\nA necessary condition is that several hundreds of massive\nstars are formed in a compact region with a radius of a few pc.\nIn this section, we discuss some alternative mechanisms responsible\nfor the formation of IMBHs.\n\n\\subsection{Bondi-type gas accretion onto a seed black hole}\n\nCompact remnants left from massive stars formed in the initial \nstar formation in a galaxy have been surviving for the galaxy age,\ni.e., $\\tau_{\\rm age} \\sim 10^{10}$ years. \nThey have been experiencing a number of encounters with gas clouds\nin the galaxy. Therefore, classical Bondi-type (Bondi 1952) gas accretion\nis the most probable accretion process for them (Yoshii 1981).\nThis gas accretion rate is given by\n$\\dot M_{\\rm Bondi} = 2~\\pi ~m_{\\rm H} ~ n_{\\rm H} ~ r_{\\rm a}^2 ~ v_{\\rm e}$,\nwhere $m_{\\rm H}$, $n_{\\rm H}$, $r_{\\rm a}$, and $v_{\\rm e}$ are \nthe mass of a hydrogen atom, the number density of the hydrogen atom,\nthe accretion radius defined as $r_{\\rm a} = G M_\\bullet v_{\\rm e}^{-2}$ \n($M_\\bullet$ is the mass of the seed compact remnant), \nand the effective relative velocity \nbetween the seed black hole and the ambient gas, respectively.\n\nSince the Bondi-type gas accretion is most important for \nthe low-velocity encounter, we adopt $v_{\\rm e} = 1$ km s$^{-1}$\nin order to estimate the maximum accretion rate\n(Yoshii 1981) although $v_{\\rm e}$ is realistically much higher\nthan this value.\nAdopting an average gas density of the interstellar medium,\n$n_{\\rm H} \\sim 1$ cm$^{-3}$, we obtain the total accreting mass\ndue to the Bondi-type accretion,\n\n\\begin{equation}\nM_{\\rm acc, Bondi} = {\\dot M}_{\\rm Bondi} ~ \\tau_{\\rm age} \n\\sim 3 \\times 10^{-2} M_{\\bullet, 1}^2\nn_{\\rm H, 1} v_{\\rm e, 1}^{-3} \\tau_{\\rm age, 10} ~ \\MO\n\\end{equation}\nwhere $M_{\\bullet, 1}$ is the mass of the seed compact remnant\nin units of $1 \\MO$, \n$n_{\\rm H, 1}$ is the average gas density in units of $1$ cm$^{-3}$,\n$v_{\\rm e, 1}$ is the orbital velocity with respect to the ambient gas\nin units of 1 km s$^{-1}$, and $\\tau_{\\rm age, 10}$ is the age of \nthe galaxy in units of $10^{10}$ years.\nEven if a black hole with a mass of 10 $\\MO$ was born \n$10^{10}$ years ago in the galaxy (see for the formation of \nblack holes with $m_\\bullet \\simeq 10 \\MO$, Brown \\& Bethe 1994), \nits accreting mass amounts only to a few $\\MO$.\nIt is expected that some black holes might encounter dense molecular\nclouds. However, the crossing time is as short as\n$\\tau_{\\rm cross} \\sim D_{\\rm GMC, 45} / v_{\\rm e, 1} \\sim\n4.5 \\times 10^7$ years where $D_{\\rm GMC, 45}$ is the mean\ndiameter of GMCs in units of 45 pc. \nIt is also noted that the age of a GMC may range between $\\sim 10^5$\nyears (the molecule formation time) and several times 10$^8$ years\n(e.g., Elmegreen 1985). Therefore, in the case of an encounter\nbetween a black hole and a GMC, we should adopt $\\tau_{\\rm age}\n\\sim 10^8$ years in equation (8). Therefore,\nthe mass growth is negligibly small\neven if $\\overline{n}_{\\rm H} \\sim 50$ cm$^{-3}$.\nHowever, if $v_{\\rm e} \\ll 1$ km s$^{-1}$, an IMBH could be formed\nthrough this accretion process.\nSince it seems unlikely that such a very slow encounter occurs\nfrequently, it is suggested that the Bondi-type gas accretion\nonto the seed black hole may not be responsible for the formation of\nan IMBH within the age of the galaxy.\n\n\\subsection{Disk-type gas accretion onto a seed black hole}\n\nNext we consider a case that a compact remnant is a black hole\nwith a mass of 1 $M_\\bullet$ and the disk-type gas accretion has been\noccurring at the Eddington accretion rate, \n${\\dot M}_{\\rm Disk} \\simeq 2.2 \\times 10^{-8} \\eta_{\\rm acc, 0.1} \nM_{\\bullet, 1} ~ \\MO ~ {\\rm y}^{-1}$\nwhere $\\eta_{\\rm acc}$ is the conversion efficiency from\nthe gravitational energy to the radiation in units of 0.1 (e.g., Rees 1984).\nThe seed black hole with a mass of 1 $\\MO$ can increase in mass and its\nmass is given by \n\n\\begin{equation}\nM_\\bullet(t_8) = \nM_{\\bullet, 1} e^{2.2 \\eta_{\\rm acc, 0.1} t_8} ~~ \\MO\n\\end{equation}\nwhere $t_8$ is the duration of the gas accretion in units of\n$10^8$ years.\nOne obtains $M_\\bullet = 10^2 \\MO$ at $t_8 = 2.09$,\n$M_\\bullet = 10^3 \\MO$ at $t_8 = 3.14$, and\n$M_\\bullet = 10^4 \\MO$ at $t_8 = 4.19$.\nTherefore, it seems that IMBHs could be easily formed by this mechanism.\n\nHowever, there is a serious problem in this model.\nThe star formation rate may be higher in earlier phases of\ngalaxy evolution. Even if we assume that massive stars\nhave been made continuously at a constant rate,\nthe number of compact remnants made during the last $10^9$ years\nis estimated to be $\\sim 10^7$ for a typical galaxy with mass of \n$10^{12} \\MO$ in which stars were formed with the Salpeter mass\nfunction (see Taniguchi et al. 1999).\nIf all these compact remnants have been\nexperiencing the disk accretion at the Eddington rate,\nwe would observe a lot of IMBHs in the galaxy if they have not\nyet merged into one SMBH. \nIf they were already merged into one SMBH, there would be\na very supermassive black hole with mass of $M_\\bullet \n\\sim 10^7 \\times 10^4 \\MO \\sim 10^{11} \\MO$ in some galaxies.\nTherefore, the idea described here may not be a \ndominant mechanism responsible for the formation of IMBHs.\n\n\\par\n\\vspace{1pc}\\par\n%\nWe would like to thank an anonymous referee for his/her many\nuseful comments and suggestions which improved this paper\nsignificantly.\nThis work was supported in part by the Ministry of Education, Science,\nSports and Culture in Japan under Grant Nos. 10044052, and 10304013.\n\n\\clearpage\n\\section*{References}\n%----------------------------------------------------------------------------\n% References \n%----------------------------------------------------------------------------\n\n\\re \nBlitz L.\\ 1993, in Protostars and Planets III, \ned E.H. Levy, J.I. Lunine (The University of Arizona \nPress, Tucson), p125\n\\re \nBegelman M.C., Rees M.J.\\ 1978, MNRAS, 185, 847\n\\re \nBinney J., Tremaine S.\\ 1987, Galactic Dynamics \n(Princeton University Press, Princeton), 492\n\\re \nBondi H.\\ 1952, MNRAS, 112, 195\n\\re \nBrown G.E., Bethe H.A.\\ 1994, ApJ, 423, 659\n\\re \nColbert E.J.M., Mushotzky R.F.\\ 1999, ApJ, 519, 89\n\\re \nColbert E.J.M., Petre R., Schlegel E.M., Ryder S.D.\\ \n1995, ApJ, 446, 177\n\\re \nDressler A., Richstone D.O.\\ 1988, ApJ, 324, 701\n\\re\nElmegreen B.G.\\ 1985, in Protostars and Planets, edited by D. C.\nBlack, and M. S. Matthews (The University of Arizona Press), 33\n\\re\nElmegreen B.G.\\ 1994, ApJ, 425, L73\n\\re\nFabbiano G.\\ 1988, ARA\\&A, 27, 87\n\\re\nFabbiano G., Trinchieri G.\\ 1987, ApJ, 315, 46\n\\re\nHunter D.A., Shaya E.J., Holtzman J.A., Light R.M., \nO'Neil E.J., Lynds R.\\ 1995, ApJ, 448, 179\n\\re\nJeans J.H. 1929, Astronomy and Cosmogony, 2nd ed. \nCambridge, Eng.: (Cambridge University Press, Cambridge)\n\\re\nKennicutt R.C.\\ Jr, Keel W.C., Blaha C.A.\\ 1989, \nAJ, 97, 1022\n\\re\nKohmura Y., et al.\\ 1994, PASJ, 46, L157\n\\re\nKormendy J., Bender R., Evans A.S., Richstone D.\\ 1998, \nAJ, 115, 1823\n\\re\nKulkarni S.R., Hut P., McMillan S.\\ 1993, Nature, 364, 421\n\\re\nLada E.A., Strom K.M., Myers P.C.\\ 1993, \nin Protostars and Planets III, ed E.H. Levy, J.I. Lunine \n(The University of Arizona Press, Tucson), p245\n\\re\nLee H.M.\\ 1995, MNRAS, 272, 605\n\\re\nMakishima K., et al. 2000, ApJ, submitted (astro-ph/0001009)\n\\re \nMatsumoto H., Tsuru T.G.\\ 1999, PASJ, 51, 321\n\\re\nMushotzky R. F., Done C., Pounds K. A.\\ 1993, ARA\\&A, 31, 717\n\\re\nNorman C., Scoville, N.\\ 1988, ApJ, 332, 124\n\\re\nOkada K., Dotani T., Makishima K., Mitsuda K., Mihara T.\\ \n1998, PASJ, 50, 25\n\\re\nPetre R., Okada K., Mihara T., Makishima K., Colbert E.J.M.\\ \n1994, PASJ, 46, L115\n\\re\nPtak A., Griffiths R.\\ 1999, ApJ, 517, L85\n\\re\nRees M.J.\\ 1978, Observatory, 98, 210\n\\re\nRees M.J.\\ 1984, ARA\\&A, 22, 471\n\\re\nReynolds C.S., Loan A.J., Fabian A.C., Makishima K., \nBrandt W.N., Mizuno T.\\ 1997, MNRAS, 286, 349\n\\re\nRubin V.C., Burstein D., Ford W.K.\\ Jr, Thonnard N.\\ \n1985, ApJ, 289, 81\n\\re\nQuinlan G.D., Shapiro S.L.\\ 1989, ApJ, 343, 725\n\\re \nQuinlan G.D., Shapiro S.L.\\ 1990, ApJ, 356, 483\n\\re\nSalpeter, E.E. 1955, ApJ, 121, 161\n\\re\nSaslaw W.C.\\ 1973, PASP, 85, 5\n\\re\nSofue Y.\\ 1997, PASJ, 49 17\n\\re\nSpitzer L.\\ 1969, ApJ, 158, L139\n\\re\nSpitzer L.\\ 1987, Dynamical Evolution of Globular Clusters \n(Princeton University Press, Princeton), ch3\n\\re\nSpitzer L., Saslaw W.C.\\ 1966, ApJ, 143, 400\n\\re\nSpitzer L., Stone, M.E.\\ 1967, ApJ, 147, 519\n\\re\nStevens I.R., Strickland D.K., Wills K.A. MNRAS, 308, L23\n\\re\nTakano M., Mitsuda K., Fukazawa Y., Nagase F. 1994, \nApJ, 436, L47\n\\re\nTaniguchi Y., Ikeuchi S., Shioya Y.\\ 1999, ApJ, 514, L9\n\\re\nTaniguchi Y., Wada K.\\ 1996, ApJ, 469, 581\n\\re\nTremaine S. 1981, in The Structure and Evolution of Normal Galaxies, \ned S.M. Fall, D. Lynden-Bell (Cambridge University\nPress, Cambridge), p67\n\\re\nvan den Bergh S.\\ 1986, AJ, 91, 271\n\\re\nWeedman D.W.\\ 1983, ApJ, 266, 479\n\\re\nYoshii Y.\\ 1981, A\\&A, 97, 280\n\\re\nZaritsky D., Smith R., Frenk C., White S.D.M. 1997,\nApJ, 478, 39\n\n\\end{document}\n%----------------------------------------------------------------------------\n\n\n\n\n\n"
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astro-ph0002390
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High-Resolution Near-Infrared Imaging of the Powerful Radio Galaxy 3C 324 at $z$ = 1.21 with the Subaru Telescope
|
[
{
"author": "Toru {\\sc Yamada}"
},
{
"author": "Masaru {\\sc Kajisawa}"
},
{
"author": "Ichi {\\sc Tanaka}"
},
{
"author": "{Sendai, Miyagi 980-8578}"
},
{
"author": "%"
},
{
"author": "Toshinori {\\sc Maihara}"
},
{
"author": "Fumihide {\\sc Iwamuro}"
},
{
"author": "Hiroshi {\\sc Terada}"
},
{
"author": "Miwa {\\sc Goto}"
},
{
"author": "Kentaro {\\sc Motohara}"
},
{
"author": "Hirohisa {\\sc Tanabe}"
},
{
"author": "Tomoyuki {\\sc Taguchi}"
},
{
"author": "Ryuji {\\sc Hata}"
},
{
"author": "{Kyoto 606-8502}"
},
{
"author": "Masanori {\\sc Iye}"
},
{
"author": "Masatoshi {\\sc Imanishi}"
},
{
"author": "Yoshihiro {\\sc Chikada} Michitoshi {\\sc Yoshida}"
},
{
"author": "{National Astronomical Observatory, 2-21-1, Osawa, Mitaka,}"
},
{
"author": "{Tokyo 181-8588, Japan}"
},
{
"author": "Chris {\\sc Simpson}"
},
{
"author": "Toshiyuki {\\sc Sasaki}"
},
{
"author": "George {\\sc Kosugi}"
},
{
"author": "Tomonori {\\sc Usuda}"
},
{
"author": "Koji {\\sc Omata}"
},
{
"author": "Katsumi {\\sc Imi}"
},
{
"author": "{Subaru Telescope, National Astronomical Observatory of Japan,}"
},
{
"author": "{650 North Aohoku Place, Hilo, HI 96720, U.S.A. }"
},
{
"author": "\\vspace{2.0cm}"
}
] |
[
{
"name": "3C324_RG_ver2b.tex",
"string": "%\n\\documentstyle[PASJadd, psfig]{PASJ95}\n%\n% PASJ LaTex \n%\n%\\draft\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\markboth{T.\\ Yamada et al.}\n{Radio galaxy at z=1.2}\n\n\\newcommand{\\vol}{999}\n\\newcommand{\\no}{1}\n\\newcommand{\\lett}{}\n\\newcommand{\\spage}{1}\n\\newcommand{\\rdate}{1999 September 30}\n\\newcommand{\\adate}{1999 November 30 }\n\n\\begin{document}\n\n\\title{High-Resolution Near-Infrared Imaging of the Powerful Radio Galaxy 3C 324 at $z$ = 1.21 with the Subaru Telescope}\n\n\\author{Toru {\\sc Yamada}, Masaru {\\sc Kajisawa}, Ichi {\\sc Tanaka} \\\\\n{\\it Astronomical Institute, Tohoku University, Aoba-ku, } \\\\\n{\\it Sendai, Miyagi 980-8578} \\\\\n{\\it E--mail(TY): yamada@astr.tohoku.ac.jp } \\\\\n%\n \\\\\nToshinori {\\sc Maihara}, Fumihide {\\sc Iwamuro}, Hiroshi {\\sc Terada}, Miwa {\\sc Goto}, Kentaro {\\sc Motohara}, \\\\\nHirohisa {\\sc Tanabe}, Tomoyuki {\\sc Taguchi}, Ryuji {\\sc Hata} \\\\\n{\\it Department of Physics, Faculty of Science, Kyoto University, Sakyo-ku,} \\\\\n{\\it Kyoto 606-8502} \\\\\n%\n \\\\\nMasanori {\\sc Iye}, Masatoshi {\\sc Imanishi}, Yoshihiro {\\sc Chikada} Michitoshi {\\sc Yoshida} \\\\\n{\\it National Astronomical Observatory, 2-21-1, Osawa, Mitaka,} \\\\\n{\\it Tokyo 181-8588, Japan} \\\\\n%\n \\\\\nChris {\\sc Simpson}, Toshiyuki {\\sc Sasaki}, George {\\sc Kosugi}, Tomonori {\\sc Usuda} \\\\\nKoji {\\sc Omata}, Katsumi {\\sc Imi} \\\\\n{\\it Subaru Telescope, National Astronomical Observatory of Japan,} \\\\\n{\\it 650 North Aohoku Place, Hilo, HI 96720, U.S.A. }\\\\\n\\vspace{2.0cm}\n }\n\n\\abst{\n We have obtained high-resolution $K^\\prime$-band images of the powerful $z=1.206$ radio galaxy 3C 324 with the Subaru telescope under seeing conditions of 0$^{\\prime\\prime}$.3--0$^{\\prime\\prime}$.4. We clearly resolved the galaxy and directly compared it to the optical images obtained with the Hubble Space Telescope. The host galaxy of 3C 324 is revealed to be a moderately luminous elliptical galaxy with a smooth light profile. The effective radius of the galaxy, as determined by profile fitting, is 1.3$\\pm$ 0$^{\\prime\\prime}$.1 (1.2 kpc), which is significantly smaller than the value of 2$^{\\prime\\prime}$.2 published in Best et al.\\ (1998, MNRAS, 292, 758). The peak of the $K^\\prime$-band light coincides with the position of the radio core, which implies that the powerful AGN lies at the nucleus of the host galaxy. The peak also coincides with the gap in the optical knotty structures which may be a dust lane hiding the UV-optical emission of the AGN from our line of sight; it is very likely that we are seeing the obscuring structure almost edge-on. We clearly detected the `aligned component' in the $K^\\prime$-band image by subtracting a model elliptical galaxy from the observed image. The red $R_{{\\rm F702W}}-K$ color of the outer region of the galaxy avoiding the aligned component indicates that the near infrared light of the host galaxy is dominated by an old stellar population. }\n%\n\\kword{galaxies: active --- galaxies: evolution\n --- galaxies: elliptical and lenticular, cD --- galaxies: individual:\n(3C 324)}\n%\n\\setcounter{page}{1}\n\\maketitle\n\\thispagestyle{headings}\n\n{ \\it To be appear in PASJ vol. 52, 2000}\n\n\n%%%%\n\n%\n\\clearpage\n\n%\n\\section{Introduction}\n\n Powerful radio galaxies provide one of the most exciting opportunities to trace the evolution of galaxies and their activity over the history of the Universe. There is a rapid evolution of the power of active galactic nuclei (AGN), such as quasars and radio galaxies, toward $z\\sim3$, and such evolution may reflect some aspects of the phenomena of galaxy formation and evolution. Powerful radio galaxies have an advantage over quasars in studying the structures in hosts since they are not swamped by the bright nucler light.\n\n One of the most striking properties of high-redshift powerful radio galaxies (HzPRGs) is the `alignment effect' observed in their optical images (McCarthy et al. 1987; Chambers et al. 1987; Rigler et al. 1992). Rest-frame ultraviolet (UV) radiation tends to have an elongated structure aligned with the radio-jet axis.\n The origin of this aligned UV radiation is still not clear; while the scattered non-thermal radiation contributes to the observed UV flux, at least to some extent, in many radio galaxies, the stellar photospheric emission and/or the nebular continuum emission has also been observed in some sources (e.g., Cimatti et al. 1996). In any case, UV emission is very likely to be the {\\it consequence} of nuclear activity, and near-infrared observations may be more essential to reveal the true host-galaxy structure.\n\n 3C 324 at $z=1.206$ has been extensively studied as one of the `proto-typical' objects which show the optical alignment effect. Its total radio power at 5 GHz is large, log $P_{\\rm 5 GHz}$= 27.75 ($H_0$ = 50 km s$^{-1}$Mpc$^{-1}$, $q_0$ = 0.5; hereafter we use this set of cosmological parameters unless noted), which implies the existence of a very powerful AGN. Indeed, Cimatti et al. (1996) detected a broad Mg {\\sc II} $\\lambda$ 2800 \\AA\\ emission line in the polarized spectrum, and thus established that 3C 324 hosts a quasar obscured by dust. The radio source has two distinct radio lobes with a separation of $\\sim 11$$^{\\prime\\prime}$ (95 kpc at $z=1.206$; Fernini et al. 1993; Best et al. 1998b) at a position angle of 71$^\\circ$ (Dunlop, Peacock 1993). Best et al. (1998b) detected a plausible radio core at frequencies of 8.2 and 4.7 GHz. Hubble Space Telescope (HST) WFPC2 observations with the ${\\rm F702W}$ and ${\\rm F791W}$ filters (Longair et al. 1995; Dickinson et al. 1995; Best et al. 1997, 1998a) revealed in detail the elongated patchy structure of the rest-frame UV emission, which is collinear with the radio axis. The radio core is located in a gap between the two central optical knots (Best et al. 1998b), which suggests that this gap is due to a dust lane which obscures the active nucleus. The existence of a significant amount of dust is supported by the detection of sub-mm radiation which is not associated with the synchrotron radiation (Best et al. 1998c).\n\n At near-infrared (NIR) wavelengths, previous ground-based observations under $\\sim$ 1$^{\\prime\\prime}$ seeing conditions have detected the red host galaxy (Dunlop, Peacock 1993; Dickinson et al. 1995; Best et al. 1997, 1998a). Dunlop and Peacock (1993) showed that the host galaxy has a somewhat elongated structure whose position angle (PA) is $\\sim 75^\\circ$, closely aligned with the radio axis. Best et al. (1998a) argued that the galaxy is as bright as $K=16.99$ mag (9$^{\\prime\\prime}$ aperture) and has a light profile well represented by a de Vaucouleurs law with an effective radius of 2$^{\\prime\\prime}$.2 (19 kpc). Dickinson et al. (1995) pointed out that the $K$-band light peak coinsides with the gap of the optical knots. It has been known that 3C 324 is located in a galaxy cluster (Dickinson et al. 1997; Kajisawa et al. 1999 and references therein) and is the brightest galaxy in the cluster at z = 1.21. \n\n We have observed 3C 324 with the Subaru telescope equipped with the Cooled Infrared Spectrograph and Camera for OHS (CISCO: Motohara et al. 1998), which provides a $\\sim 2$$^{\\prime\\prime}$ $\\times 2$$^{\\prime\\prime}$ field of view at a sampling of 0$^{\\prime\\prime}$.116 pixel$^{-1}$. The observations were made during the telescope commissioning period and good image quality with 0$^{\\prime\\prime}$.3--0$^{\\prime\\prime}$.4 seeing (FWHM of stellar images) was achieved. In this paper, we investigate the NIR properties of the host galaxy of 3C 324. Thanks to the high spatial resolution, we can directly compare the light distribution in the optical images obtained with the deep HST observations without seriously degrading the HST data. In section 2, we briefly describe the observations and the data reduction. We show the light distribution and color map of the host galaxy in section 3 and discuss its properties as a brightest cluster galaxy in section 4. We present our conclusions in section 5. \n\n\\section{Observations and Data Reduction}\n\n The observations were made under stable weather condition on 1999 April 2 (UT), during the telescope commissioning period. In total, we observed the field for $\\sim 1$ hour to investigate the luminosity function of the cluster galaxies (Kajisawa et al. 1999), with a typical seeing of $\\ltsim$ 0$^{\\prime\\prime}$.5. For this paper, we extracted only the images taken in good seeing quality (FWHM $<$ 0$^{\\prime\\prime}$.37). The total net exposure time of the resultant image is 800 s and the r.m.s. noise level per pixel corresponds to a $K$-band surface brightness of $\\mu_K$=21.4 mag arcsec$^{-2}$. \n\n A description of the reduction procedure is given in Kajisawa et al. (1999). Since there were small variations of the bias level from frame to frame, we developed a procedure to construct a flatfield frame after removing the bias residual. Otherwise, we followed the standard procedures in reducing NIR imaging data. The flux values were calibrated to those in the $K$ band by using the data of faint UKIRT standard star FS 27 ($K^\\prime - K \\sim 0.01$ mag) observed immediately after 3C 324 at a similar zenith distance. Using the model spectra of an old passively evolving galaxy at $z =1.2$ and the transmission curve of the CISCO $K^\\prime$ filter, we estimate the color of 3C~324 to be $K^\\prime - K \\sim 0.1$ mag. We then applied this correction to the photometric calibration, although there may be an uncertainty of $\\sim 0.1$ mag, since the true color term of the telescope and instrument has not been well defined at this stage.\n\n We compare the NIR image with the deep WFPC2 images of the field of 3C 324. We retrieved the calibrated ${\\rm F702W}$ and ${\\rm F450W}$ images (PI: M. Dickinson; PID 5465 and 6553, respectively;see also Dickinson et al. 1995) from the Space Telescope Science Institute data archive. The total exposure times of these images are 64800 s (${\\rm F702W}$) and 15000 s (${\\rm F450W}$), and the ${\\rm F702W}$ image is much deeper than that analyzed in Longair et al. (1995), Best et al. (1997), and Best et al. (1998b). We use $B_{{\\rm F450W}}$ and $R_{{\\rm F702W}}$ to denote the magnitudes measured in the STMAG system (HST Data Handbook Vol.1). STMAG is defined as $m_{ST} = -21.10-2.5 {\\rm log} f_\\lambda$ where $f_\\lambda$ is expressed\nin erg cm$^{-2}$ s$^{-1}$ \\AA $^{-1}$.\n\n\n\\section{Light Distribution in the Host Galaxy}\n\n\\subsection{Images}\n\n Figure 1a shows the observed $K^\\prime$ image of a 17$^{\\prime\\prime}$ $\\times$ 17$^{\\prime\\prime}$ field centered on 3C 324. The host galaxy is clearly detected as a bright spheroidal galaxy, and surrounding objects which may be other cluster members are resolved. The total magnitude (MAG BEST value of the SExtractor output; Bertin, Arnouts 1996) of the host galaxy, obtained after separating the close companions, is $K=17.3$ mag. Figure 1b shows a contour map of the $K^\\prime$-band surface brightness distribution. For a comparison, we also show the original HST images taken in ${\\rm F702W}$ and the ${\\rm F450W}$ filters in figures 1c and 1d, respectively. While the optical images show elongated knotty structures, the light distribution in the $K^\\prime$-band image of the galaxy is fairly smooth and round.\n\n Figure 2 shows the combined color image. The WFPC2 images were smoothed with a Gaussian kernel to match the FWHM of the stellar images to those of the Subaru $K^\\prime$ image. The difference in the light distribution between the optical and NIR images is clearly seen. The peak of the NIR light clearly coincides with the gap in the optical structures, and thus also coincides with the position of the radio core (Best et al. 1998b), which implies that the powerful AGN indeed lies at the nucleus of the host galaxy. The gap in the optical structure may be due to a dust lane which hides the UV-optical emission of the AGN from direct view; it is very likely that we are seeing the obscuring structure from almost edge-on.\n\n\\subsection{Light Distribution and Near-Infrared Alignment Effect}\n\nIn order to investigate the intrinsic light profile of the host galaxy, we have to correct for contamination by the nearby companions. We removed them by replacing the pixels within 10-pixel (diameter) apertures centered on each object by an interpolation of the surrounding region. The surface brightness contours of the resultant image are shown in figure 3; any contamination by the close companions was removed well. The one-dimensional light profile obtained by isophotal-ellipse fitting to the resultant image is shown in figure 4. For a comparison, we also plot the light profile of a star in the same frame normalized at the peak.\n\n The galaxy has a smooth and regular light distribution, and the profile can be approximated by a de Vaucouleurs law with an effective semi-major axis (SMA) of 1$^{\\prime\\prime}$.3$\\pm$ 0$^{\\prime\\prime}$.1 (11.2 kpc) and an effective surface brightness of $\\mu_K$=20.3$\\pm 0.2$ mag arcsec$^{-2}$, except for the central region affected by the effects of seeing and the outer region where sky noise dominates. We show the result of the fitting that was made for the SMA between 4 and 25 pixels (0$^{\\prime\\prime}$.46--2$^{\\prime\\prime}$.88). The position angle of the fitted isophotal ellipse at large radius (at $\\mu_K \\gtsim 21$ mag arcsec$^{-2}$) is $\\sim 90^\\circ$, similar to the position angle of the optical structures ($\\sim 100^\\circ$, Longair et al. 1995) and also close to that of the radio axis ($\\sim 71^\\circ$); there is therefore a weak alignment effect also in the $K^\\prime$-band image. The effective radius evaluated in our profile fitting is significantly smaller than the value of 2$^{\\prime\\prime}$.2 published in Best et al. (1998a). This may be due to the relatively large seeing size of the UKIRT image and contamination by the close companions shown in figure 1a.\n\n Since the fit with the de Vaucouleurs law shown in figure 4 is not perfect, and it may overestimate the surface brightness at large radius (consequently, overestimate the effective radius), we also performed a curve of growth analysis. The SMA of the ellipse that contains a half of the total flux is 0$^{\\prime\\prime}$.8, smaller than the value obtained in the light-profile fitting. The disagreement may be due to a contribution by the obscured AGN at the center of the galaxy and/or to the component that causes the alignment effect. We find that $\\sim 25$\\% of the total flux comes from the region within the central 0$^{\\prime\\prime}$.37 (= FWHM) SMA elliptical aperture. If the flux within this aperture is completely dominated by the AGN component alone, the half-light semi-major axis could be as large as $\\sim 1$$^{\\prime\\prime}$.1.\n\n In order to evaluate the contribution from the `aligned component', we compared the observed $K^\\prime$-band image with models of a smooth elliptical galaxy with an ideal de Vaucouleurs profile constructed by using the IRAF ARTDATA package. We consider the two limiting cases: (i) the host galaxy indeed has an effective SMA of 0$^{\\prime\\prime}$.8 and the apparent large effective SMA is due to the contribution by the extended `aligned' component, and (ii) the surface brightness at SMA $\\sim 1$$^{\\prime\\prime}$.3 is dominated by the host galaxy and the disagreement with the half-light SMA may be due to the contribution by the nuclear (point source) component and/or to an intrinsic light profile which deviates from a de Vaucouleurs law at large radius. For the first case, we construct a model galaxy with an effective SMA of 0$^{\\prime\\prime}$.8 and the same position angle and ellipticity as the observed best-fit ellipse at SMA = 0$^{\\prime\\prime}$.8. The model is convolved with a Moffat point spread function with FWHM of 0$^{\\prime\\prime}$.37 and normalized to the observed galaxy flux within a central 2-pixel-radius circle. For the second case, we use a model with SMA = 1$^{\\prime\\prime}$.3, normalized to the observations at the effective SMA. We then subtract the model images from the data to investigate the residual `aligned component' in the resultant images. These two limiting cases should bracket the range of the possible strengths of the aligned component.\n\n Figures 5 and 6 show the results. In panels (a) and (b) of both figures, we show the observed $K^\\prime$-band image after removing the close companions (equivalent to figure 4) and the image of the adopted model galaxy to be subtracted from the observed one. In panels (c) and (d), we show the resultant images after subtraction and a version of these images smoothed with a 3-pixel boxcar. For a comparison, in panels (e) and (f) we show the HST images smoothed with a Gaussian kernel to the spatial resolution of the Subaru $K^\\prime$-band image. The crosses show the position of the light peak in the $K^\\prime$-band image. In both cases, an aligned component is seen whose morphology shows excellent agreement with the optical images. As expected, it is more conspicuous for the case of the model with an effective SMA = 0$^{\\prime\\prime}$.8. The peak surface brightness of the residuals is $\\sim 10$--$20$\\% of the host galaxy peak in the case of SMA=0$^{\\prime\\prime}$.8 and a few \\% for the case of SMA = 1$^{\\prime\\prime}$.3.\n\n It is difficult to tell which case is true from the observed data. The subtraction of the host galaxy seems to be good, but not perfect, in both cases. There is some diffuse positive residual in the northeastern part of the galaxy in figures 5c and 5d, which suggests that the galaxy may be more extended than the SMA = 0$^{\\prime\\prime}$.8 de Vaucouleurs profile, although it could be residuals from the subtracted close companion. At the same time, the counts in the northwestern part of the residual image are negative which may suggest the existence of a nuclear component. Although the residual appears to be fairly flat in figures 6c and 6d, the counts become negative at SMA $\\gtsim 2$$^{\\prime\\prime}$, consistent with the fact that the half-light SMA is smaller than the effective radius obtained from the profile fitting.\n\n What is the origin of the aligned component seen in the $K^\\prime$-band image? If it is the continuum emission associated with the rest-frame UV light seen in the HST images, we may constrain its nature by investigating the spectral energy distribution of the component. Alternatively, there is a possibility that it is dominated by the line emission of [S {\\sc III}] $\\lambda$9532 \\AA . Rawlings et al. (1991) shows that the [S {\\sc III}] emission line sometimes account for $\\sim 10\\%$ of the observed broad-band flux although there may be some variation in the [S {\\sc III}] line strength among the powerful radio galaxies and the uncertainty in their line flux measurements seems to be somwhat large (15--50\\%; their table 2).\n\n\\subsection{Two-Color Diagram}\n\n In order to constrain the origin of the NIR light, we also investigate the spatially resolved spectral energy distribution of the objects assuming that the $K^\\prime$-band aligned component is dominated by the continuum emission. The degraded HST images, whose seeing was matched to that of the $K^\\prime$-band image, are used for the purpose. We show the twelve positions where the photometry was performed with the used aperture (2-pixels radius) superposed on the $K^\\prime$-band image in figure 7, and the resultant two-color diagram is shown in figure 8. \\#1 corresponds to the peak of the $K^\\prime$-band light distribution or the gap in the optical structure. \\#2--\\#5 sample the colors of the outer part of the host galaxy less contaminated by the UV-optical structure. \\#6--\\#9 correspond to the four knots in the optical images and \\#10--\\#12 are located at the positions of companion galaxies. The peaks of the knotty structures on the western side of the galaxy are slightly ($\\sim 2$ pix) different between the ${\\rm F450W}$ and ${\\rm F702W}$ images and we put the aperture on the ${\\rm F450W}$ peak. The sky level was determined well outside of the galaxy and was assumed to be constant over the galaxy in each band. The r.m.s. fluctuation of the sky level was evaluated with the same size of aperture over the 17$^{\\prime\\prime}$ by 17$^{\\prime\\prime}$ field avoiding the detected objects. We provide $2 \\sigma$ upper limits for positions \\#5, \\#10, and \\#12 in the $B_{{\\rm F450W}}$ image.\n\n For a comparison, the colors of model galaxies with various ages observed at z = 1.2 are also plotted in figure 7. These models were calculated by using GISSEL 96 (Bruzual, Charlot 1993) with a Salpeter IMF and solar metallicity. We have also plotted the colors of a quasar at $z = 1.21$ mimicked by a power-law with $\\alpha=-0.7$ ($f_\\nu \\propto \\nu^\\alpha$; Cristiani, Vio 1990). The effect of reddening evaluated using the Galactic extinction curve (Cardelli et al. 1989) as well as the Calzetti's formula (Calzetti 1997) for $E(B-V)=0.3$, is indicated by the arrows. \n\n The host galaxy has a very red $R_{{\\rm F702W}}-K$ color, as expected for the oldest passively evolving galaxies. It is thus likely that the bulk of the infrared light from the host galaxy comes from an old stellar population at an age of $\\sim 2--4$ Gyr. It seems difficult to explain the observed red color by dust reddening alone, since a huge amount of reddening, $E(B-V) \\sim 1$ mag, is needed, while at least one of the apertures, \\#4, is located in the outer region of the galaxy away from the putative dust lane (see figures 2 and 8). On the other hand, the observed $B_{{\\rm F450W}}-R_{{\\rm F702W}}$ colors at all positions in the host galaxy are considerably bluer than in the passive evolution models. These colors are better represented by the mildly evolving model with ongoing star formation. Ongoing star-formation activity is naturally expected from the existence of a significant amount of dust ($\\sim 10^8$ $M_\\odot$, Best et al. 1998c). The bulk of the stars is, however, formed at a very early stage, even in such a mild-evolution model, and only a very small amount of star formation activity remains at the observed epoch. Alternatively, the blue $B_{{\\rm F450W}}-R_{{\\rm F702W}}$ color may be due to a small amount of contamination by the `aligned' component, even at the outer region of the galaxies. The three companion galaxies (apertures \\#10--\\#12) have colors that are rather consistent with the old passively evolving models.\n\n The $R_{{\\rm F702W}}-K$ colors at positions \\#2 and \\#5, namely the southwestern side of the galaxy, are redder than those at \\#3 and \\#4 (the northeastern side). This may be due to reddening by asymmetrically-distributed dust. Alternatively, there is an excess of $K^\\prime$-band light at $\\sim 1$$^{\\prime\\prime}$ south of the nucleus (see figures 5d and 6d) which may be another red cluster member seen {\\it behind} the host of 3C 324, and therefore further reddened by dust in the radio galaxy.\n\n At position \\#1, there may be a contribution from reddened AGN light. Indeed, the colors of \\#1 are also consistent with those of an AGN reddened by $E(B-V) \\sim 0.6$, and it is difficult to distinguish between the mild evolution model and the reddened AGN in the two-color diagram. Spectroscopic observations are needed to resolve this issue; the redshifted 4000 \\AA\\ break may be observed at $\\sim 9000$ \\AA\\ if the stellar light dominates. \n\n The observed colors of the optical knots, \\#6--\\#9, are redder than the AGN and star-formation models. However, they agree well with the AGN spectrum reddened by $E(B-V) \\sim 0.15$. Note that the effect of the underlying host galaxy on the $K^\\prime$-band magnitude is negligible at positions \\#8 and \\#9 (figure 2). This agreement implies that scattered light from the hidden nuclear source provides a significant fraction of the observed flux. In fact, Cimatti et al. (1996) measured the polarization degree, $\\sim 10 \\%$ at 4000--8000 \\AA . Since the structures at \\#8 and \\#9 are well separated from the host galaxy, they must be clouds of material formed as a consequence of the jet activity. Although Cimatti et al. (1996) argue that \\#9 may be a blue star-forming companion galaxy, the identical colors of \\#8 and \\#9 suggest that they have the same origin, which is a consequence of the AGN activity.\n\n At \\#6 and \\#7, we must correct for the contribution from the host galaxy to obtain the colors of the `aligned' components, which we show by the open triangles denoted by \\#6A and \\#7A in figure 7. We performed photometry on the $K^\\prime$-band image after removing the model host galaxy as described above. The $B_{{\\rm F450W}}$- and $R_{{\\rm F702W}}$-band magnitudes of the aligned component were obtained by subtracting the contribution from the host galaxy ($\\sim 10--25 \\%$) from the observed flux; we evaluate the host contribution assuming the $R_{{\\rm F702W}}-K$ and $B_{{\\rm F450W}}-K$ colors at \\#1. The $R_{{\\rm F702W}}-K$ colors at \\#6A and \\#7A are much bluer than those at \\#8 and \\#9, suggesting that the emission mechanism might be different between the knotty structure inside and outside the host galaxy.\n\n Assuming that the light of the optical knots is dominated by scattered radiation, the scattering mechanism can be determined from the observed spectra (e.g., Cimatti et al. 1996 and references therein). In the case of electron scattering, the observed spectrum has the same shape as the incident spectrum. Scattering by optically thin dust predicts a `blued' spectrum (Cimatti et al. 1993).\n%\n%With optically thick dust, the scattered light may have similar\n%spectrum with the incident %one at $\\lambda_{rest} > 2300$ \\AA\\ but\n%may be redder at the shorter wavelength. Since the %{\\rm F450W} filter\n%samples the wavelength range of $\\lambda_{rest} = 1900$ to 2200 \\AA\\\n%at z=1.20%6, we may be able to discriminate these three possibilities\n%from the two-color diagram assu%ming the shape of the incident\n%spectrum. \n%\n We assume an incident spectrum represented by an $\\alpha = -0.7$ power-law. Models for scattering by optically thin dust predict that the reprocessed spectrum is bluer than the incident one, and to be a flat spectrum, $f_\\nu \\sim$ constant (Cimatti et al. 1993). The observed $B_{{\\rm F450W}}-R_{{\\rm F702W}}$ and $R_{{\\rm F702W}}-K$ colors at \\#8 and \\#9 coincide with those of the incident spectrum (figure 7) with a small amount of reddening. On the other hand, a large amount of reddening is needed to match with the flat spectrum, and we must demand a rather peculiar distribution of dust in the knots at \\#8 and \\#9 (i.e., optically thin to nuclear light but with a large reddening along the line of sight). Electron scattering with a relatively small amount of reddening along the line of sight seems to be favored in explaining the colors at \\#8 and \\#9.\n\nOn the other hand, while the corrected $R_{{\\rm F702W}}-K$ colors at \\#6 and \\#7 are as blue as the flat spectrum, the $B_{{\\rm F450W}}-R_{{\\rm F702W}}$ colors are $\\sim 1$ mag redder than the model predictions. It seems to be difficult to explain the observed color at \\#6 and \\#7 by the simple electron- or thin-dust scattering models. We compare the colors at \\#6A and \\#7A with the predictions of nebular continuum emission (e.g., Aller 1987; Dickson et al. 1995). We consider two rather extreme cases: (i) N(He$^+$)/N(H$^+$) = 0.1 and N(He$^{++}$)/N(H$^+$) = 0 (`NC1' in figure 7), and (ii) N(He$^+$)/N(H$^+$) = 0. and N(He$^{++}$)/N(H$^+$) = 0.1 (`NC2'). An electron temperature, $T_{\\rm e}$, of 10000 K is assumed. The colors become $\\sim 0.1--0.3$ mag and $\\sim 0.2--0.4$ mag bluer in $B_{{\\rm F450W}}-R_{{\\rm F702W}}$ and $R_{{\\rm F702W}}-K$, respectively, if we consider the case with $T_{\\rm e}$=20000 K. The observed colors can be explained by nebular emission with a small amount of reddening, or by a mixture of the nebular emission and the flat spectrum. If the observed light at \\#6 and \\#7 is dominated by nebular continuum emission, we can predict the fluxes of the hydrogen recombination lines. Under Case B, the flux of the H$\\beta$ line is predicted to be $\\sim 1--2 \\times 10^{-16}$ erg s$^{-1}$ cm$^{-2}$ within a 0$^{\\prime\\prime}$.4 aperture, depending on the ionization structure of helium.\n\n Cimatti et al. (1996) estimated that unpolarized radiation contributes 50--70 \\% of the optical flux within a 3$^{\\prime\\prime}$.8 by 1$^{\\prime\\prime}$ aperture. Although they argued that this could be due to photospheric emission from OB stars, we note that it can be explain by nebular continuum emission at positions \\#6 and \\#7. In fact, the amount of reddening required to explain the observed $B_{{\\rm F450W}}-R_{{\\rm F702W}}$ color of the optical knots predicts far too red a $R_{{\\rm F702W}}-K$ color ($R_{{\\rm F702W}}-K$ $\\sim 5.5$--6); the observed optical continuum emission of the `aligned' component cannot be dominated by a reddened starburst at \\#6 and \\#7.\n\n\\section{Properties as a Brightest Cluster Galaxy}\n\nIn this section, we discuss the near-infrared photometric properties of the 3C 324 host galaxy as the brightest cluster galaxy (BCG).\n\nArag\\'on-Salamanca et al. (1998) showed that BCGs at $z = 0$--0.9 have luminosities consistent with the no-evolution prediction, while other giant ellipticals have some brightening as expected for passive evolution. Since the no-evolution model is unphysical because the galaxies must dim with cosmic time as the stars age, they argue that some merging has occurred in the BCGs since that epoch. Since the expected luminosity difference between no-evolution and passive evolution models increased with the redshift, the 3C 324 host galaxy could put stronger constraints on the issue.\n\nFigures 9a and 9b show the apparent rest-frame $K$-band magnitudes of the BCGs in a 50-kpc aperture against redshift following Arag\\'on-Salamanca et al. (1998). We plot the 3C 324 host galaxy by the star; the applied $k$-correction is $-0.69$ mag, which has been evaluated from Kodama and Arimoto's (1997) model spectrum of a giant elliptical galaxy. Clearly, it lies at the extension of the sequence of BCGs at $z = 0$--0.9 and this behavior is not consistent with the prediction of the passive evolution models. If $q_0=0.5$ is assumed, the 3C 324 host galaxy is even less luminous than the no-evolution prediction. The intrinsic luminosity is fainter than this since there is a contamination by the aligned component although it may be smaller than 0.1 mag (10\\%). The 3C 324 host may also experience merging or assembly events that have doubled its stellar mass since the observed epoch. \n\n We also plot the other three BCGs and candidates at $z> 1$, namely the two spectroscopically confirmed brightest red galaxies in the regions of the CIG J0848+4453 at $z=1.27$ (ID 65 with $K=18.11$; Stanford et al. 1997), RX J0848.9+4452 at $z=1.26$ (ID 1 with $K=16.72$; Rosati et al. 1999), and the object ``G1'' with $K=17.23$ in the cluster near B2 1335+28 at $z \\sim 1.1$ (Tanaka et al. 1999). Note that the magnitude values quoted from Stanford et al. (1997) and Rosati et al. (1999) are those with 2$^{\\prime\\prime}$.4 and 2$^{\\prime\\prime}$ apertures, respectively, and they\nshould be brighter in the 50-kpc aperture; a correction of $\\sim -0.6$ mag (assuming the same light profile as the 3C 324 host galaxy) may be needed for a direct comparison with other data. The applied $k$-correction is $-0.68$ mag at $z=1.26$ and 1.27 and $-0.70$ mag at $z=1.1$. The apparent magnitudes of the BCGs from Stanford et al. and Tanaka et al. are fainter than the predictions of the passive evolution models for both the $q_0=0$ and $q_0=0.5$ cases.\n\n%f we plot the 3C 324 in the $K$-$z$ Hubble diagram of the powerful radio galaxies (e.g., Simpson et al. 1991) , it lies just on the line.\n\n%{\\bf K-band Kormendy Relation ?? TBF}\n\n\\section{Conclusions}\n\n The host galaxy of the powerful radio galaxy 3C 324 was observed with the Subaru telescope under good seeing conditions. The host galaxy is clearly resolved and seen to be a spheroidal galaxy well approximated by a de Vaucouleurs profile. The effective (half-light) radius evaluated from profile fitting is 1$^{\\prime\\prime}$.3 (11.2 kpc), which is about half the value previously published in the literature, while a curve of growth analysis produces a value of 0$^{\\prime\\prime}$.8. After subtraction of the model galaxies, we clearly detect the `aligned component' in the $K^\\prime$-band image. The disagreement between the effective radius obtained in the profile fitting and the half-light radius in the growth-curve analysis may be due to this `aligned component' and/or to a contribution from the obscured AGN.\n\nThe peak of the $K^\\prime$-band light coincides with the position of the radio core, which strongly implies that the engine of the powerful radio sources is indeed hosted at the nucleus of the giant elliptical galaxy. The NIR peak also corresponds to the gap in the rest-frame UV emission, which may be due to a dust lane. It is very likely that we see the obscuring structure from an almost edge-on view. \n\n The host galaxy has a very red $R_{{\\rm F702W}}-K$ color and the near-infrared light of the galaxy is likely to be dominated by an old stellar population, while the relatively blue $B_{{\\rm F450W}}-R_{{\\rm F702W}}$ color suggests that there may be some small amount of star-formation activity.\n\nThe colors of the 'aligned' components located inside the host galaxy, which are obtained after subtracting the host component, may be explained by nebular continuum emission with a small amount of a dust while those outside the host galaxy are better modeled by optically-thin dust scattering of the nuclear light.\n\n\n\\vspace{0.5cm}\n\nThe authors are indebted to all members of the Subaru Observatory, NAOJ, Japan. We thank Nobuo Arimoto for kindly providing the Kodama and Arimoto evolutionary synthesis models. TY thanks Takashi Murayama for useful discussions. We thank Dr. Marc Dickinson, the referee, for the invaluable comments. This research was supported by grants-in-aid for scientific research of the Ministry of Education, Science, Sports and Culture (08740181, 09740168). This work was also supported by the Foundation for the Promotion of Astronomy of Japan. This work is based in part on observations with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute, U.S.A., which is operated by AURA, Inc.\\ under NASA contract NAS5--26555. The Image Reduction and Analysis Facility (IRAF) used in this paper is distributed by National Optical Astronomy Observatories. U.S.A., operated by the Association of Universities for Research in Astronomy, Inc., under contact to the U.S.A. National Science Foundation.\n\\clearpage\n\n\\section*{References}\n\\small\n\n%\n%\\bibitem[Aragon-Salamanca Ellis Couch \\& Carter 1993]{1993MNRAS.262..764A} \n%Aragon-Salamanca, A. , Ellis, R. S., Couch, W. J. \\& Carter, D. 1993,\n%\\mnras, 262, 764\n\n\\re\nAller, L. 1987, Physics of Thermal Gaseous Nebulae, Astrophys. Space Sci. Library Vol.112, (Leidel, Dordrecht)\n\n\\re\nAragon-Salamanca A. , Baugh C. M. \\& Kauffmann G. 1998, MNRAS \n297, 427\n\n\\re\nBertin E., Arnouts S. 1996, A\\&AS 117, 393\n\n%bibitem[Best Bailer Longair \\& Riley 1995]{1995MNRAS.275.1171B} Best, P. \n%N., Bailer, D. M., Longair, M. S. \\& Riley, J. M. 1995, MNRAS, 275, 1171 \n\n%\\bibitem[Best Longair \\& Rottgering 1996]{1996MNRAS.280L...9B} Best, P. N., \n%Longair, M. S. \\& R\\\"ottgering, H. J. A. 1996, MNRAS, 280, L9 \n\n\\re \nBest P. N. Longair M. S., R\\\"oettgering J. H. A. 1997, MNRAS\n292, 758\n\n\\re\nBest P. N., Longair M. S., R\\\"oettgering, H. J. A. 1998a, MNRAS\n295, 549\n\n\\re\nBest P. N., Carilli C. L., Garrington S. T., Longair M. S.,\nRottgering H. J. A. 1998b, MNRAS 299, 357\n\n\\re\nBest P. N., R\\\"oettgering H. J. A., Bremer M.N., Amatti A., Mack K.-H., Miley G.K., Pentericci L., Tilanus R.P.J., van der Warf P.P., 1998c, MNRAS 301, L15 \n\n\\re\nBruzual A. G., Charlot S. 1993, ApJ 405, 538\n\n\\re\nCalzetti D. 1997, The Ultraviolet Universe at Low and High Redshift : Probing the Progress of Galaxy Evolution, ed. W. H. Waller et al. (Amrican Institute of Physics: New York), 403\n\n\\re\nCardelli J. A., Clayton G. C., Mathis J. S. 1989, ApJ 345, 245 \n\n\\re\nChambers K. C., Miley G. K., van Breugel W. 1987, Nature 329, 604\n\n\\re\nCimatti A., di Serego-Alighieri S., Fosbury R. A. E., Salvati \nM., Taylor D. 1993, MNRAS 264, 421 \n\n\\re\nCimatti A. , Dey A. , Van Breugel W., Antonucci R., Spinrad \nH. 1996, ApJ 465, 145\n\n\\re\nCristiani S., Vio R. 1990, A\\&A 227, 385\n\n\\re\nDickinson M., Day A., Spinrad H., 1995, Galaxies in the Young Universe, eds. H. Hippelein, K. Meisenheimer, \\& H.-J. Roser (Springer Verlag: Berlin), 164. \n\n\\re\nDickinson M. 1997, The Early Universe with the VLT. ed. \nJ. Bergeron (Springer Verlag: Berlin), 274\n\n\\re\nDickson R., Tadhunter C., Shaw M., Clark N., Morganti R. 1995,\nMNRAS 273, L29\n\n\\re\nDunlop J. S., Peacock J. A. 1993, MNRAS 263, 936\n\n\\re\nFernini I. , Burns J. O., Bridle A. H., Perley R. A. 1993, AJ\n105, 1690\n\n\\re\nHST Data Handbook, Ver3.1 1998, http://www.stsci.edu/documents/data-handbook.html\n\n\\re\nKajisawa M, et al. 1999, PASJ in press.\n\n\\re\nKodama T., Arimoto N. 1997, A\\&A 320, 41\n\n\\re\nLongair M. S., Best P. N., R\\\"ottgering H. J. A. 1995, MNRAS\n275, L47\n\n\\re\nMcCarthy P. J., van Breugel W. , Spinrad H., Djorgovski, S. 1987, ApJL 321, L29 \n\n\\re\n%Motohara K., Maihara T., Iwamuro F., Oya S., Imanishi M., Terada H, Goto M., Iwai J.,\n% Tanabe H., Tuskamoto H., Sekiguchi K. 1998, 3354, 659\nMotohara K., et al. 1998, Proc. SPIE 3354, 659\n\n\\re\nRigler M. A., Lilly S. J., Stockton A., Hammer F., Le Fevre O. 1992, ApJ 385, 61 \n\n\\re\nRosati P., Stanford S. A., Eisenhardt P. R., Elston R., Spinrad \nH., Stern D., Dey A. 1999, AJ 118, 76\n\n%\\re\n%Sawicki, M. \\& Yee, H. K. C. 1998, AJ 115, 1329\n\n\\re\nStanford S. A., Elston R., Eisenhardt P. R., Spinrad H., Stern D., Dey A. 1997, AJ 114, 2232\n\n\\re\nTanaka I. , Yamada T. , Arag\\'on-Salamanca A. , Kodama T. , Ohta \nK., Miyaji T., Arimoto N. 1999, ApJ in press.\n\n%\\clearpage\n\n% Fig.1\n\\begin{fv}{1}{18pc}%\n{$K^\\prime$ images of 3C 324 taken with the Subaru telescope (panel a) and the isophotal contour map for the image after boxcar smoothing with 3$\\times$3 pixels (panel b). The lowest contour in panel (b) corresponds to the 1$\\sigma$ noise level of the sky {\\it before} the smoothing; the contour interval is 0.5 mag arcsec$^{-2}$. The images HST/WFPC2 taken in the ${\\rm F702W}$ (panel c) and the ${\\rm F450W}$ filters (panel d) are also shown. The box spans 17$^{\\prime\\prime}$ in panels (a), (c), and (d) and 10$^{\\prime\\prime}$ in the panel (b). }\n\\end{fv}\n\n\\begin{fv}{2}{18pc}%\n{Combined $B_{{\\rm F450W}}R_{{\\rm F702W}}K^\\prime$ three-color image of 3C 324. The optical images taken with HST have been Gaussian-smoothed to match the PSF to that of the $K^\\prime$-band image.}\n\\end{fv}\n\n\\begin{fv}{3}{18pc}%\n{Contour map of the $K^\\prime$ image of 3C 324 after removing the close companions. The levels of the contours are the same as in figure 1b. The box spans 5$^{\\prime\\prime}$. }\n\\end{fv}\n\n\\begin{fv}{4}{18pc}%\n{One-dimensional light profile of the 3C 324 host after removing the close companions. The light profile of a star in the frame is also shown with crosses. The horizontal bar indicates a radius of twice the half width of the half maximum. The dashed line shows the best-fit de Vaucouleurs profile, fitted between 4-25 pix (0$^{\\prime\\prime}$.46--2$^{\\prime\\prime}$.88). }\n\\end{fv}\n\n\\begin{fv}{5}{18pc}%\n{Observed $K^\\prime$-band image after removing of the close companions (panel (a)) and the image of the adopted model galaxy with an effective semi-major axis of 0$^{\\prime\\prime}$.8 is shown in (b). The resultant image after subtraction of the model host in shown in (c) and a boxcar-smoothed version of this is shown in (d). A NIR alignment effect is clearly detected. For comparison, we show the Gaussian-smoothed HST images in panels (e) and (f). The crosses show the position of the light peak in the $K^\\prime$-band image. }\n\\end{fv}\n\n\\begin{fv}{6}{18pc}%\n{ Same as figure 5 but for the model with an effective semi-major axis of 1$^{\\prime\\prime}$.3. }\n\\end{fv}\n\n\\begin{fv}{7}{18pc}%\n{Positions and apertures (2-pixel radius) for the photometry presented in figure 8.}\n\\end{fv}\n\n\\begin{fv}{8}{18pc}%\n{Two-color diagram of the various positions (\\#1--\\#12) shown in figure 7. The colors of the `aligned' component after subtracting the host galaxy models with $r_{\\rm e}=0$$^{\\prime\\prime}$.8 (upper ones) and $r_{\\rm e}=1$$^{\\prime\\prime}$.3 (lower ones) are also plotted by the open triangles, denoted as 6A and 7A. The tracks of the passive evolution model with a 1-Gyr initial starburst (long dashed line) and the mild evolution model with an exponential star-formation decaying time scale of 0.5 Gyr (short dashed line) with various ages are shown for comparison. The solid tick marks on the tracks correspond to ages of 2, 2.5, 3, 3.5, and 4 Gyr; the reddest one is the oldest. The colors of constant star-formation models at ages of 0.01 Gyr and 0,1 Gyr are shown by the crosses. The colors of power-law spectra with $\\alpha=-0.7$ and $\\alpha = 0$ are also indicated by the star labeled `AGN' and the asterisk labeled as `$f_\\nu$ = const.', respectively. NC1 and NC2 refer the colors of the nebular thermal continuum emission (see text for the detail). The arrow shows the effect of reddening calculated using the galactic extinction curve by Cardelli et al.(1989) as well as the Calzetti's (1997) formula for starburst galaxies with $E(B-V)=0.3$. }\n\\end{fv}\n\n\\begin{fv}{9}{18pc}%\n{$k$-corrected apparent magnitude of the 3C 324 host galaxy (star) shown together with those of the brightest cluster galaxies studied in Arag\\'on-Salamanca et al. (1998) (filled circles) and those in the clusters at $z > 1$ (open circles; see text). Prediction of the case of no evolution as well as the passive evolution models are shown for $H_0$ = 50 km s$^{-1}$ Mpc$^{-1}$ and $q_0$ = 0.5 (panel a) and 0.0 (panel b).}\n\\end{fv}\n\n\\clearpage\n\n\n\\begin{figure} \n\\psfig{file=fig1.ps,width=1.0\\textwidth}\n\\caption[fig1.ps]{} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure} \n\\psfig{file=fig2.ps,width=1.0\\textwidth}\n\\caption[fig2.ps]{} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure} \n\\psfig{file=fig3.ps,width=1.0\\textwidth}\n\\caption[fig3.ps]{} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure} \n\\psfig{file=fig4.ps,width=1.0\\textwidth}\n\\caption[fig4.ps]{} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure} \n\\psfig{file=fig5.ps,width=1.0\\textwidth}\n\\caption[fig5.ps]{} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure} \n\\psfig{file=fig6.ps,width=1.0\\textwidth}\n\\caption[fig6.ps]{} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure} \n\\psfig{file=fig7.ps,width=1.0\\textwidth}\n\\caption[fig7.ps]{} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure} \n\\psfig{file=fig8.ps,width=1.0\\textwidth}\n\\caption[fig8.ps]{} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure} \n\\psfig{file=fig9a.ps,width=1.0\\textwidth}\n\\caption[fig9a.ps]{} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure} \n\\psfig{file=fig9b.ps,width=1.0\\textwidth}\n\\caption[fig9b.ps]{} \n\\end{figure}\n\n\\end{document}\n"
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"name": "astro-ph0002390.extracted_bib",
"string": "\\bibitem[Aragon-Salamanca Ellis Couch \\& Carter 1993]{1993MNRAS.262..764A} \n%Aragon-Salamanca, A. , Ellis, R. S., Couch, W. J. \\& Carter, D. 1993,\n%\\mnras, 262, 764\n\n\\re\nAller, L. 1987, Physics of Thermal Gaseous Nebulae, Astrophys. Space Sci. Library Vol.112, (Leidel, Dordrecht)\n\n\\re\nAragon-Salamanca A. , Baugh C. M. \\& Kauffmann G. 1998, MNRAS \n297, 427\n\n\\re\nBertin E., Arnouts S. 1996, A\\&AS 117, 393\n\n%bibitem[Best Bailer Longair \\& Riley 1995]{1995MNRAS.275.1171B} Best, P. \n%N., Bailer, D. M., Longair, M. S. \\& Riley, J. M. 1995, MNRAS, 275, 1171 \n\n%\n\\bibitem[Best Longair \\& Rottgering 1996]{1996MNRAS.280L...9B} Best, P. N., \n%Longair, M. S. \\& R\\\"ottgering, H. J. A. 1996, MNRAS, 280, L9 \n\n\\re \nBest P. N. Longair M. S., R\\\"oettgering J. H. A. 1997, MNRAS\n292, 758\n\n\\re\nBest P. N., Longair M. S., R\\\"oettgering, H. J. A. 1998a, MNRAS\n295, 549\n\n\\re\nBest P. N., Carilli C. L., Garrington S. T., Longair M. S.,\nRottgering H. J. A. 1998b, MNRAS 299, 357\n\n\\re\nBest P. N., R\\\"oettgering H. J. A., Bremer M.N., Amatti A., Mack K.-H., Miley G.K., Pentericci L., Tilanus R.P.J., van der Warf P.P., 1998c, MNRAS 301, L15 \n\n\\re\nBruzual A. G., Charlot S. 1993, ApJ 405, 538\n\n\\re\nCalzetti D. 1997, The Ultraviolet Universe at Low and High Redshift : Probing the Progress of Galaxy Evolution, ed. W. H. Waller et al. (Amrican Institute of Physics: New York), 403\n\n\\re\nCardelli J. A., Clayton G. C., Mathis J. S. 1989, ApJ 345, 245 \n\n\\re\nChambers K. C., Miley G. K., van Breugel W. 1987, Nature 329, 604\n\n\\re\nCimatti A., di Serego-Alighieri S., Fosbury R. A. E., Salvati \nM., Taylor D. 1993, MNRAS 264, 421 \n\n\\re\nCimatti A. , Dey A. , Van Breugel W., Antonucci R., Spinrad \nH. 1996, ApJ 465, 145\n\n\\re\nCristiani S., Vio R. 1990, A\\&A 227, 385\n\n\\re\nDickinson M., Day A., Spinrad H., 1995, Galaxies in the Young Universe, eds. H. Hippelein, K. Meisenheimer, \\& H.-J. Roser (Springer Verlag: Berlin), 164. \n\n\\re\nDickinson M. 1997, The Early Universe with the VLT. ed. \nJ. Bergeron (Springer Verlag: Berlin), 274\n\n\\re\nDickson R., Tadhunter C., Shaw M., Clark N., Morganti R. 1995,\nMNRAS 273, L29\n\n\\re\nDunlop J. S., Peacock J. A. 1993, MNRAS 263, 936\n\n\\re\nFernini I. , Burns J. O., Bridle A. H., Perley R. A. 1993, AJ\n105, 1690\n\n\\re\nHST Data Handbook, Ver3.1 1998, http://www.stsci.edu/documents/data-handbook.html\n\n\\re\nKajisawa M, et al. 1999, PASJ in press.\n\n\\re\nKodama T., Arimoto N. 1997, A\\&A 320, 41\n\n\\re\nLongair M. S., Best P. N., R\\\"ottgering H. J. A. 1995, MNRAS\n275, L47\n\n\\re\nMcCarthy P. J., van Breugel W. , Spinrad H., Djorgovski, S. 1987, ApJL 321, L29 \n\n\\re\n%Motohara K., Maihara T., Iwamuro F., Oya S., Imanishi M., Terada H, Goto M., Iwai J.,\n% Tanabe H., Tuskamoto H., Sekiguchi K. 1998, 3354, 659\nMotohara K., et al. 1998, Proc. SPIE 3354, 659\n\n\\re\nRigler M. A., Lilly S. J., Stockton A., Hammer F., Le Fevre O. 1992, ApJ 385, 61 \n\n\\re\nRosati P., Stanford S. A., Eisenhardt P. R., Elston R., Spinrad \nH., Stern D., Dey A. 1999, AJ 118, 76\n\n%\\re\n%Sawicki, M. \\& Yee, H. K. C. 1998, AJ 115, 1329\n\n\\re\nStanford S. A., Elston R., Eisenhardt P. R., Spinrad H., Stern D., Dey A. 1997, AJ 114, 2232\n\n\\re\nTanaka I. , Yamada T. , Arag\\'on-Salamanca A. , Kodama T. , Ohta \nK., Miyaji T., Arimoto N. 1999, ApJ in press.\n\n%\\clearpage\n\n% Fig.1\n\\begin{fv}{1}{18pc}%\n{$K^\\prime$ images of 3C 324 taken with the Subaru telescope (panel a) and the isophotal contour map for the image after boxcar smoothing with 3$\\times$3 pixels (panel b). The lowest contour in panel (b) corresponds to the 1$\\sigma$ noise level of the sky {\\it before} the smoothing; the contour interval is 0.5 mag arcsec$^{-2}$. The images HST/WFPC2 taken in the ${\\rm F702W}$ (panel c) and the ${\\rm F450W}$ filters (panel d) are also shown. The box spans 17$^{\\prime\\prime}$ in panels (a), (c), and (d) and 10$^{\\prime\\prime}$ in the panel (b). }\n"
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"name": "dyopaper.tex",
"string": "\n\\documentstyle[a4wide,12pt,epsf]{article}\n\\textheight 8.5in\n\\textwidth 6in\n\\pagestyle{empty}\n\\topmargin -0.25truein\n\\oddsidemargin 0.30truein\n\\evensidemargin 0.30truein\\raggedbottom\n\\parindent=3pc\n\\baselineskip=12pt\n\\begin{document}\n% TH FORMAT\n\\begin{flushright}\n\\baselineskip=12pt\n%{SUSX-TH-99-005}\\\\\n{RHCPP00-1T}\\\\\n{astro-ph/0002391}\\\\\n{MARCH 2000}\n\\end{flushright}\n\n\\begin{center}\n%\\vglue 0.5cm\n{\\Large \\bf A New Dark Matter Model for Galaxies\n\\\\}\n\\vglue 0.35 cm\n{ \nGeorge V. Kraniotis $^{\\spadesuit}$ \\footnote\n {G.Kraniotis@rhbnc.ac.uk}and Steven B. Whitehouse$^{\\spadesuit}$ \\footnote{\nSbwphysics@aol.com}\\\\}\n\n\n\n{$\\spadesuit$ {\\it \nCentre for Particle Physics,\\\\\nRoyal Holloway College, University of London, \\\\\nEgham, Surrey, TW20-0EX, U.K\\\\}}\n\\baselineskip=12pt\n\n\\vglue 0.25cm\nABSTRACT\n\\end{center}\n%\\vglue 0.5cm\n{\\rightskip=3pc\n\\leftskip=3pc\n\\noindent\n\\baselineskip=20pt\nIn this paper a new theory of Dark Matter is proposed.\nExperimental analysis of several Galaxies show how the \nnon-gravitational contribution to galactic Velocity Rotation \nCurves can be interpreted as that due to the Cosmological Constant $\\Lambda$. \nThe experimentally determined values \nfor $\\Lambda$ are found \nto be consistent with those expected from Cosmological Constraints.\nThe Cosmological Constant is interpreted as leading to a constant energy \ndensity which in turn can be used to partly address \nthe energy deficit problem (Dark Energy) of the Universe.\nThe work presented here leads to the conclusion that the \nCosmological Constant is negative and that the universe is de-accelerating.\nThis is in clear contradiction to the Type Ia Supernovae results which support \nan accelerating universe.}\n\n\\vfill\\eject\n\\setcounter{page}{1}\n\\pagestyle{plain}\n\\baselineskip=14pt\n\t\n\n\n\\section{Dark Matter}\n\nThe problem of missing or Dark Matter, namely that there is insufficient \nmaterial in the form of stars to hold galaxies and clusters together, \nhas been known since the pioneering work of Bessel, Zwicky and most recently \nRubin \\cite{VERA}.\\\\\n\\\\\nThe existence of non-luminous \nDark Matter was first inferred in 1984 by Fredrich Bessel from \ngravitational effects on positional measurements of Sirius and \nProcyon. In 1933, Zwicky concluded that the velocity dispersion in Rich \nClusters of galaxies required 10 to 100 times more mass to keep them \nbound than could be accounted for by luminous galaxies themselves.\\\\\n\\\\\nFinally, Trimble \\cite{TRIMBLE} noted that the majority of galactic rotation curves, \nat large radii, remain flat or even rise well \noutside the radius of the luminous astronomical object.\\\\\n\\\\\nThe missing Dark Matter has been traditionally explained in terms of\nDark Matter Halo's \\cite{SCIAMA}, although none of the Dark Matter\nHalo models have been very successful in explaining the experimental \ndata \\cite{ITALY,VAN}.\\\\\n\\\\\nThis paper will describe the missing matter (Dark Energy) in terms of a\nCosmological Constant which leads to a constant energy density.\\\\\n\\\\ \nThe experimental determination of galactic velocity rotation curves (VRC) has \nbeen\none of the most important approaches used to estimate the\n\"local\" mass (energy) density of the Universe. Several sets of data from\nVRC's will be analysed and the contribution due to the Cosmogical \nConstant determined.\\\\\n\n\n\n\\section{Constaints on the value of the Cosmological Constant}\nIt is interesting to estimate the allowed range of values for the \nCosmological Constant within the constraints of General Relativity \nand observational astronomy, (for a comprehensive review, see \nBahcall et.al. \\cite{PAUL}).\\\\\n\\\\\nStarting from a General Relativity point of view, the \nFriedman energy equation is given by:\n\\begin{equation}\n1=\\frac{8 \\pi G_N}{3}\\frac{\\rho_{matter}}{H^2}-\\frac{k c^2}{R^2 H^2}+\n\\frac{c^2 \\Lambda}{3 H^2},\n\\label{FRIEDMAN}\n\\end{equation}\\\\\nwhere the Hubble Constant is denoted by $H$, \nthe curvature term by $k$ and\n$G_N$ denotes the Newton gravitational constant.\nEq.(\\ref{FRIEDMAN}) can be rewritten as\n\\begin{equation}\n1=\\Omega_{m}+\\Omega_k+\\Omega_{\\Lambda}\n\\end{equation}\nHere the relative contributions to the energy density of the universe \nare given by, the mass, curvature and Cosmological Constant.\\\\\n\\\\\nIf we assume that the curvature contribution is \nsmall:\n\\begin{equation}\n1=\\Omega_{Matter}+\\Omega_{\\Lambda}\n\\label{TTT}\n\\end{equation}\\\\\n\\\\\nIn order to satisfy equation (\\ref{TTT}), it was surprising to \ndiscover that only a narrow range of values for the \nobserved Cosmological Parameters were allowed.\nA \"reasonable\" set of parameters consistent with observation are:\n\\begin{equation}\nH_O=100Km s^{-1} Mpc^{-1}, \\;\n\\rho_{matter}=5 \\times 10^{-30} g cm^{-3}, \\;\n\\frac{\\Omega_{\\Lambda}}{\\Omega_{matter}}=4.3 \n\\end{equation}\\\\\n\\\\\nand $\\Omega_{Matter}+\\Omega_{\\Lambda}=1.4$ (here we assume a \nsmall value for the curvature $\\sim 0.4$. (For an\nauthoritative review of the matter/energy sources of the universe, \nsee Turner \\cite{turner}).\\\\\n\\\\\nIt was found that observational constraints placed upon the range of \nvalues \nfor the cosmological parameters lead to a surprisingly narrow \nrange of possible values for the Cosmological Constant, the range \nbeing given by:\n\\begin{equation}\n10^{-56} < |\\Lambda| < 5\\times10^{-55} cm^{-2}.\n\\end{equation}\\\\\n\\\\\n\n\n\n\n\\section{Experimental Results}\n\n\n\n\n\n%The galaxies studied, the radii of the galaxies and the value for the \n%Cosmological Constant are shown \\cite{KENT} below in Table 1.\n\n\n\n\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\\hline\\hline\n${\\rm Galaxy}$ & ${\\rm Radius}$ \n& ${\\rm Cosmological\\; Constant}$ \n\\\\ \\hline\\hline\nNGC 2403&20Kpc & $\\Lambda_{NGC 2403}=3.6\\times 10^{-55}cm^{-2}$ \\\\ \\hline\nNGC 4258&50 Kpc & $\\Lambda_{NGC 4258}=5.5\\times 10^{-55}cm^{-2}$ \\\\ \\hline\nNGC 5033&40 Kpc & $\\Lambda_{NGC 5033}=1.0 \\times 10^{-55}cm^{-2}$ \\\\ \\hline\nNGC 5055&50 Kpc & $\\Lambda_{NGC 5055}=1.4\\times 10^{-55}cm^{-2}$ \\\\ \\hline\nNGC 2903& 30 Kpc &$\\Lambda_{NGC 2903}=3.8\\times 10^{-55}cm^{-2}$ \\\\ \\hline \nNGC 3198& 50 Kpc &$\\Lambda_{NGC 3198}=5.0\\times 10^{-56} cm^{-2}$ \\\\ \\hline\n\\hline\\hline\n\\end{tabular}\n\\end{center}\n\\caption{Absolute values of the Cosmological Constant \nare shown above.}\n\\end{table}\n\nIt was shown \\cite{SWGK}, within the Weak Field Approximation, \nthat the Cosmological Constant at large radii could be determined \nfrom galactic velocity \nrotation curves. This contribution is given by:\n\\begin{equation}\nv^2_{\\Lambda}(r)=v^2_{obs}(r)-v^2_{mass}(r), {\\rm \\;\\;\\;leading\\; to,} \n\\label{vel}\n\\end{equation}\n\\begin{equation}\nv^2_{\\Lambda}/r=\\frac{c^2 \\Lambda r}{3},\\;\\;\\;\n{\\rm at \\;large \\;r}\n\\end{equation}\nThe results obtained by this analysis are shown in Table 1.\\\\\n\\\\\nThe experimental values obtained for the Cosmological Constant \nfall within the range determined from General Relativity \nand observational constraints. While the initial results are promising, \na thorough and systematic analysis of galactic rotation curves \nneeds to be undertaken in order to confirm the trend.\\\\\n\\\\\nPrevious results \\cite{SWGK} reported for the value of the \nCosmological Constant were 100 to 1000 times the \"allowed value\". This \nsystematic error arose for two main reasons: the first by not taking \nthe gradient of the curves at sufficiently large radii and the second by \nthe lack of access to \"real\" experimental data leading to \ncrude data analysis.\\\\\n\\\\\nThe results presented in this paper suffer from the second problem, i.e. all \nthe gradients were obtained from the data in the \npublished literature and not from raw experimental data\ni.e. M33 Corbelli $\\&$ Salucci \\cite{ITALY}, NGC 3198 \\cite{HOL} and all \nothers from \\cite{KENT}. \\\\\n\\\\\nHowever \nexperience has taught us that a cursory look at \nrotation curves will determine which galaxies are candidates for \nexplanation by a Cosmological Constant and which are not. \nGalaxies where the velocity rotation curve remains flat or rises \nat large radii, are immediate candidates.\nNGC 3198 is a good example, \nwhereas others such as M33 \\cite{ITALY} has clearly not relaxed to \nthe Cosmological background, even at many times the galactic radii. A \nfull explanation for M33 has to be sought in a different direction.\\\\\n\\\\\nFinally, a simple calculation of the effective mass density due to the \nCosmological Constant in NGC 3198, \n\\begin{equation}\n\\rho_{eff}=-\\frac{c^2 \\Lambda}{4\\pi G_N}\n\\end{equation}\nleads to a value of $5.4\\times 10^{-29} g cm^{-3}$ which is \ncomparable to the HI mass density \\cite{PAOLO} \nat the outer disk of NGC 3198 galaxy. This is further confirmation \nthat the Cosmological Constant effect can be seen at galactic scale \nlengths.\n%As Trimble \n%\\cite{TRIMBLE}\n%noted\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\section{Accelerating or Decelerating Universe?}\n\nRecently there has been great interest in the Type Ia Supernovae results \nof Perlmutter et al \\cite{SUPERN} which suggest that the universe \nis accelerating.\\\\\n\\\\\nIn this section we will show that the Weak Field Approximation \ncoupled with galactic velocity rotation curve data inevitably lead to a \nnegative Cosmological Constant.\\\\\n\\\\\nThe equation for the VRC is given \\cite{SWGK} by\n\\footnote{In Ref.\\cite{SWGK} eq.(15), there was a typographical sign error \nfor one of the terms and also the negative pressure effect associated with \n$\\Lambda$ was not fully appreciated.}\n\\begin{equation}\n-\\frac{v^2}{r}=-\\frac{G m}{r^2}+\\frac{c^2 \\Lambda}{3} r\n\\label{improv}\n\\end{equation}\nWe note that Eq.(\\ref{improv}) is only strictly true for small and \nlarge radii, however it will serve to illustrate our \narguments.\\\\\n\\\\\nUsing the Newtonian limit \nof Einstein field equations we derived \nequation (\\ref{improv}). It is important to realize that \nthe Cosmological Constant obeys the equation of state given by, \n\\begin{equation}\nP_{\\Lambda}=-c^2 \\rho_{\\Lambda},\n\\end{equation}\nwhere $P_{\\Lambda}$ is the pressure term due to $\\Lambda$.\nTaking the Newtonial limit in the \nabsence of matter, $T_{\\mu\\nu}=0$, the differential equation for \nthe static \nNewtonian potential becomes\n\\begin{equation} \n\\nabla^2 \\Phi=-c^2 \\Lambda\n\\label{potential}\n\\end{equation}\nleading to, \n\\begin{equation}\n\\rho_{eff}=\\rho_{\\Lambda}+\\frac{3 P_{\\Lambda}}{c^2}=-2\\rho_{\\Lambda}\n\\end{equation}\n\\\\\nIf we arbitrary set $\\Phi=0$ at the origin, then in spherical \ncoordinates (\\ref{potential}) has the solution \n$\\Phi=-\\frac{c^2 \\Lambda}{6}r^2$ \\cite{SIROHA}. Thus, the Cosmological \nConstant leads \nto the following correction to the Newtonial potential \n\\begin{equation}\n\\Phi=-\\frac{Gm}{r}-\\frac{c^2 \\Lambda}{6}r^2\n\\end{equation}\nAt small galactic radii the velocity versus radius contribution is \nwell known and follows Newtonian physics. For large radii a negative \nCosmological Constant gives a positive contribution to the \nVRC which is what is actually observed.\nOn the other hand the effect of a positive Cosmological Constant \nwould be to lower the rotation curve below that due \nto matter alone. \\\\\n\\\\\nThe above simple argument, based on observational astronomy, \nallows only a negative Cosmological Constant as a possible explanation \nfor the galactic velocity rotation curve data.\nThis is in clear disagreement with the Type Ia supernovae results \n\\cite{SUPERN}. However, given the uncertainties in the determination \nof the deceleration parameter, $q_0$, derived from supernovae data \n\\cite{SUPERN} the approach \noutlined above has certain merits worth consideration. \\\\\n\\\\\nIn summary these are , the \nCosmological Constant is determined from $direct$ measurement \nunlike the Supernovae results, the experimentally determined value \nis the correct \norder of magnitude as that required from cosmological constraints, and \nfinally a negative Cosmological Constant is consistent, and indeed \na natural physical explanation , for the observed galactic \nvelocity rotation \ncurve data.\\\\\n\\\\\nFinally, observations of global clusters of stars constrain \nthe age of the universe and consequently place an observational limit \non a negative Cosmological Constant \\cite{OHA} of , \n\\begin{equation}\n|\\Lambda| \\leq 2.2 \\times 10^{-56} cm^{-2}.\n\\label{limit}\n\\end{equation}\nNote, the Cosmological Constant derived from \nglobal cluster constraints is in agreement with the \nexperimentally determined value derived from \ngalactic velocity rotation curve data.\n\n\n\n\\subsection{Experimental Tests-Dark Matter Halo vs Cosmological Constant }\nIt would be of some interest if it was possible to experimentally \ndistinguish between the contribution of Dark Matter Halo's and Dark Energy \n(Cosmological Constant) to galactic rotation curves.\\\\\n\\\\\nWe know that Dark Matter predicts a variation of mass at large radii given by\n\\cite{KOLBE},\n\\begin{equation}\nM_{DM}(r)\\propto r\n\\end{equation}\nwhile for Dark Energy due to a Cosmological \nConstant,\n\\begin{equation} \nM_{\\Lambda}(r)\\propto r^3[\\rho_{\\Lambda}+(3 P_{\\Lambda}/c^2)].\n\\end{equation}\\\\\n\\\\\nWith these different types of predictive variations it should be \npossible to design experimental tests to distinguish between the \ntwo phenomena.\n\n\\section{Quark Hadron Phase transition}\n\nIn this section which is of more speculative nature, working \nwithin the Extended Large Number Hypothesis, and using the \nexperimentally determined Cosmological Constant, we will demonstrate \nhow the energy density for the Quark - Hadron can be estimated.\\\\\n\\\\\nHowever, it is useful to put into context the significance of the \nCosmological Constant for many seemingly disparate \nbranches of Physics. The figure 1 below shows the Cosmological Constant \nat the epicentre of Physics.\\\\\n\\\\\nThe diagram demonstrates a dichotomy whereby several branches of Physics \nneed a non-zero Cosmological Constant in order to explain key \nphysical phenomena, whilst in others a non-zero value \npresents a fundamental problem.\\\\\n\\\\\n\\begin{figure}[h]\n\\epsfxsize=4.2in\n\\epsfysize=3.3in\n\\epsffile{lambdaco.eps}\n\\caption{$\\Lambda$ at the epicentre of Physics}\n\\end{figure}\n\nIt is also noted here that while fundamental \ntheories of Particle Physics such as \n the Standard Model, Quantum Field Theory and \nString Theory have many major predictive successes they all have \nproblem with a high vacuum energy density. \nOn the other hand while the Extended LNH is formulated from a naive \ntheory \\cite{ZELDO} it appears to correctly predict \nthe correct vacuum energy density and other cosmological parameters.\nThe Extended LNH relates the value of the Cosmological Constant to \nthe effective mass given by:\n\\begin{equation}\n|\\Lambda|=\\frac{G_N^2 m^6_{eff}}{h^4}=\\frac{c^6 L_s^4}{h^6}m^{6}_{eff}\n\\label{constant}\n\\end{equation}\nMatthews \\cite{MATTHEWS} pointed out that when using the Extended LNH to \ndetermine today's cosmological parameters, the mass of the \nproton originally suggested by Dirac should be replaced by \nthe energy density of the last phase transition of the \nUniverse : Quark - Hadron.\\\\\n\\\\\nNote that in equation (\\ref{constant}) there are no \nfree parameters, $L_s$ is normalised to the \ngravitational constant and corresponds to \nthe fundamental length of \nString Theory.\\\\\n\\\\\nUsing equation (\\ref{constant}) and the Cosmological Constant determined from NGC 5033, the effective mass is given by \n\\begin{equation}\nm_{Effective}=332 MeV\n\\end{equation}\nWe will associate this value with the Quark - Hadron phase \ntransition energy. (Other experimentally determined \nCosmological Constant data give $m_{QH}$ in the range 295 - 410 MeV).\nThe experimentally determined value within the LNH predicts the \ncorrect order of magnitude for the phase transition.\\\\\n\\\\\nThe above result poses the question that it might be possible to gain \ninsights on the quantum mechanical origin of the Universe, \nas Dirac \\cite{NUMBER,DIRAC,LARGE} suggested, from direct observation of \nthe present day Universe.\\\\\n\\\\\nFinally, does the Cosmological Constant \nprovide the key to the integration of the various Physics \ndisciplines as Figure 1 suggests?\\\\\n\\\\\n\n\n\\section{Discussion}\n\nAnalysis of the galactic rotation curves \nshow that the missing Galactic Dark Matter \ncan be explained in terms of a Cosmological Constant.\\\\\n\\\\\nThis contribution can be considered a prime \ncandidate for the \"Dark Energy\" which is smoothly distributed \nthroughout space, and \ncontributes approximately $70\\%$ to the mass/energy of \nthe Universe \\cite{turner}.\\\\\n\\\\ \nHowever, in order to support this thesis for the Cosmological Constant, \nthorough and systematic analysis of galactic velocity rotation \ndata needs to take place.\\\\\n\\\\\nIt was shown how, within the Weak Field Approximation, \nthat VRC data inevitably \nlead to a negative value for the Cosmological Constant in direct \ndisagreement with the type Ia Supernovae data. Nevertheless, given \nthe uncertainties in determining the \ndeceleration parameter $q_0$ \\cite{HOYLE}, from the \nredshift-magnitude \nHubble diagram using Type Ia supernovae as standard candles, we believe \nour approach is worth further consideration.\\\\\n\\\\\nThe experimental values determined for the \nCosmological Constant are shown to lie within an \nacceptable range. These values, used within the Extended Large \nNumber Hypothesis, predict values for \nthe Quark-Hadron phase transition energy \nin the range 295-410 MeV.\\\\\n\\\\\nIt would be remarkable, if proved correct, that the \nCosmological Constant could be directly \ndetermined from the analysis of galactic velocity rotation curves.\\\\\n\\\\\nEqually remarkable, if proved correct, is the idea \nthat astronomical observations can shed light on the \nlast quantum mechanical phase transition of the Universe, namely the \nQuark-Hadron.\\\\\n\\\\\n\n\n\n\n\n\n\n\n\n\\section{Acknowledgements}\n\nWe would like to thank Paolo Salucci for \ninvaluable discussions on \nCosmological and Astronomical aspects related to this work and Alexander \nLove for useful comments on the manuscript. We also thank J. Hargreaves \nand D. Bailin for suggestions and \nuseful discussions.\\\\\n\\\\\nWe also would like to thank Deja Whitehouse for proof \nreading this document.\\\\\n\\\\\nGeorge Kraniotis was supported for this work by PPARC.\n\n\n\\begin{thebibliography}{99}\n\\bibitem{VERA} V. Rubin, A. Waterman, J. Kenney, astro-ph/9904050\n\\bibitem{TRIMBLE} Trimble, Ann. Rev. Astron. Astrophysics, 1981, 25, 425,72\n\\bibitem{SCIAMA} D. Sciama, Modern Cosmology and the Dark Matter Problem, \nCambridge University Press, 1995\n\\bibitem{ITALY} E. Corbelli $\\&$ Paolo Salucci, \naccepted by Mon. Not. R. Astron. Soc., Astro-ph/9909252\n\\bibitem{VAN}S. van Albada $\\&$ R.Sancisi, Phil. Trans. R. Soc. Lond., \nA320, (1986),P447\n\\bibitem{PAUL} N. Bahcall, J. Ostriker, S. Perlmutter, P. Steinhardt, \nastro-ph/9906463\n\\bibitem{turner} Turner, Astro-ph/9904051\n\\bibitem{HOL} T.S. Van Albada, J.N. Bahcall, K. Begeman and \nR. Sanscisi, Astrophysical Journal,295(1985)305\n\\bibitem{ZELDO}Ya.B .Zel'dovich, Usp. Fiz. Nauk 95, 209 (1968)\n\\bibitem{SWGK}S. B. Whitehouse $\\&$ G. V. Kraniotis, astro-ph/9911485\n\\bibitem{SUPERN}S. Perlmutter et. al., Astro-ph/9812133, \nDecember 1998. (Type 1a Supernovae)\n\\bibitem{KENT} S.M. Kent, Astr.J.93(1987)81\n%\\bibitem{PAOLO} A. Borrelli $\\&$ P. Salucci, astro-ph/0001082\n\\bibitem{PAOLO} P. Salucci, private communication; K.G. Begeman, \nAstron. Astrophys.223(1989)47\n\\bibitem{SIROHA} H.C.Ohanian $\\&$ R. Ruffini, Gravitation $\\&$ Spacetime, \nW.W.Norton $\\&$ Company, 1996\n\\bibitem{HOYLE} A.G. Riess, \nA.V. Filippenko, W. Li, B. P. Schmidt, \nastro-ph/9907038, accepted by the Astronomical Journal;\nF. Hoyle, G. Burbidge and J. V. Narlikar, \n``{\\it A different Approach to Cosmology}'', Cambridge University Press, \nCambridge, 2000; ``{\\it How will it end?}'',New Scientist, 17 July 1999,page 4\n\\bibitem{OHA} S.M. Carrol, W.H. Press and E.L. Turner, Ann. Rev. Astron.\nAstrophys.30(1992)499\n\\bibitem{KOLBE} E. W. Kolb $\\&$ M.S. Turner, ``{\\it The Early Universe}'',\nFrontiers in Physics;v. 69, Addison-Wesley (1990)\n\\bibitem{MATTHEWS} R.Matthews, Astronomy $\\&$ Geophysics, \nVol 33, no. 6, (1998), 19-20\n\\bibitem{NUMBER} P. Dirac, Proc. Roy. Soc. A165, 198 (1939)\n\\bibitem{DIRAC} P.Dirac, Proc. R. Soc. Lond., A 338, (1974), 439\n\\bibitem{LARGE} P.Dirac, Proc. R. Soc. Lond., A 365, (1978), 19\n\n\\end{thebibliography}\n\n%\\newpage\n%\\begin{figure}\n%\\epsfxsize=6.5in\n%\\epsfysize=7.5in\n%\\epsffile{TWO.nb.eps}\n%\\epsffile{cosmola.eps}\n%\\caption{$\\Lambda$ at the epicentre of Physics}\n%\\end{figure}\n\n\n\n\n\\end{document}\n\n\n\n\n"
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[
{
"name": "astro-ph0002391.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{VERA} V. Rubin, A. Waterman, J. Kenney, astro-ph/9904050\n\\bibitem{TRIMBLE} Trimble, Ann. Rev. Astron. Astrophysics, 1981, 25, 425,72\n\\bibitem{SCIAMA} D. Sciama, Modern Cosmology and the Dark Matter Problem, \nCambridge University Press, 1995\n\\bibitem{ITALY} E. Corbelli $\\&$ Paolo Salucci, \naccepted by Mon. Not. R. Astron. Soc., Astro-ph/9909252\n\\bibitem{VAN}S. van Albada $\\&$ R.Sancisi, Phil. Trans. R. Soc. Lond., \nA320, (1986),P447\n\\bibitem{PAUL} N. Bahcall, J. Ostriker, S. Perlmutter, P. Steinhardt, \nastro-ph/9906463\n\\bibitem{turner} Turner, Astro-ph/9904051\n\\bibitem{HOL} T.S. Van Albada, J.N. Bahcall, K. Begeman and \nR. Sanscisi, Astrophysical Journal,295(1985)305\n\\bibitem{ZELDO}Ya.B .Zel'dovich, Usp. Fiz. Nauk 95, 209 (1968)\n\\bibitem{SWGK}S. B. Whitehouse $\\&$ G. V. Kraniotis, astro-ph/9911485\n\\bibitem{SUPERN}S. Perlmutter et. al., Astro-ph/9812133, \nDecember 1998. (Type 1a Supernovae)\n\\bibitem{KENT} S.M. Kent, Astr.J.93(1987)81\n%\\bibitem{PAOLO} A. Borrelli $\\&$ P. Salucci, astro-ph/0001082\n\\bibitem{PAOLO} P. Salucci, private communication; K.G. Begeman, \nAstron. Astrophys.223(1989)47\n\\bibitem{SIROHA} H.C.Ohanian $\\&$ R. Ruffini, Gravitation $\\&$ Spacetime, \nW.W.Norton $\\&$ Company, 1996\n\\bibitem{HOYLE} A.G. Riess, \nA.V. Filippenko, W. Li, B. P. Schmidt, \nastro-ph/9907038, accepted by the Astronomical Journal;\nF. Hoyle, G. Burbidge and J. V. Narlikar, \n``{\\it A different Approach to Cosmology}'', Cambridge University Press, \nCambridge, 2000; ``{\\it How will it end?}'',New Scientist, 17 July 1999,page 4\n\\bibitem{OHA} S.M. Carrol, W.H. Press and E.L. Turner, Ann. Rev. Astron.\nAstrophys.30(1992)499\n\\bibitem{KOLBE} E. W. Kolb $\\&$ M.S. Turner, ``{\\it The Early Universe}'',\nFrontiers in Physics;v. 69, Addison-Wesley (1990)\n\\bibitem{MATTHEWS} R.Matthews, Astronomy $\\&$ Geophysics, \nVol 33, no. 6, (1998), 19-20\n\\bibitem{NUMBER} P. Dirac, Proc. Roy. Soc. A165, 198 (1939)\n\\bibitem{DIRAC} P.Dirac, Proc. R. Soc. Lond., A 338, (1974), 439\n\\bibitem{LARGE} P.Dirac, Proc. R. Soc. Lond., A 365, (1978), 19\n\n\\end{thebibliography}"
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astro-ph0002392
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The role of outflows and star formation efficiency in the evolution of early-type cluster galaxies
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"author": "Ignacio Ferreras \\& Joseph Silk"
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A phenomenological model for chemical enrichment in early-type galaxies is presented, in which the process of star formation is reduced to a set of four parameters: star formation efficiency ($\ceff$), fraction of ejected gas in outflows ($\bout$), formation redshift ($z_F$) and infall timescale ($\tau_f$). Out of these four parameters, only variations of $\bout$ or $\ceff$ can account for the color-magnitude relation. A range of outflows results in a metallicity sequence, whereas a range of star formation efficiencies will yield a mixed age + metallicity sequence. The age-metallicity degeneracy complicates the issue of determining which mechanism contributes the most (i.e. outflows versus efficiency). However, the determination of the slope of the correlation between mass-to-light ratio and mass in clusters at moderate or high redshift will allow us to disentangle age and metallicity.
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"name": "ferrerasi.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Ferreras \\& Silk}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\n\\def\\bout{B_{\\rm out}}\n\\def\\ceff{C_{\\rm eff}}\n\\def\\simlt{\\mathrel{\\hbox to 0pt{\\lower 3.5pt\\hbox{$\\mathchar\"218$}\\hss}\n \\raise 1.5pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\simgt{\\mathrel{\\hbox to 0pt{\\lower 3.5pt\\hbox{$\\mathchar\"218$}\\hss}\n \\raise 1.5pt\\hbox{$\\mathchar\"13E$}}}\n\n\\begin{document}\n\n\\title{The role of outflows and star formation efficiency in the evolution\nof early-type cluster galaxies}\n\\author{Ignacio Ferreras \\& Joseph Silk}\n\\affil{Nuclear \\& Astrophysics Laboratory, Keble Road, Oxford OX1 3RH, U.K.}\n\n\\begin{abstract}\nA phenomenological model for chemical enrichment in early-type galaxies\nis presented, in which the process of star formation is reduced to a set\nof four parameters: star formation efficiency ($\\ceff$), fraction\nof ejected gas in outflows ($\\bout$), formation redshift ($z_F$) and\ninfall timescale ($\\tau_f$). Out of these four parameters, only variations\nof $\\bout$ or $\\ceff$ can account for the color-magnitude relation.\nA range of outflows results in a metallicity sequence, whereas a\nrange of star formation efficiencies will yield a mixed age + metallicity\nsequence. The age-metallicity degeneracy complicates the issue of\ndetermining which mechanism contributes the most (i.e. outflows \nversus efficiency). However, the determination of the slope of the \ncorrelation between mass-to-light ratio and mass in clusters at moderate \nor high redshift will allow us to disentangle age and metallicity.\n\\end{abstract}\n\n%\\begin{keywords}\n%galaxies: evolution --- galaxies: formation --- \n%galaxies: elliptical --- galaxies: clusters.\n%\\end{keywords}\n\n\\section{Introduction}\nOne of the long-standing problems in astrophysics is the process of star\nformation in galaxies. The standard scenario assumes stars to form \nfrom gas that falls in the potential wells of dark matter halos. \nSubsequent interacting or merging stages among galaxies might trigger\nadditional bursts of star formation. The complex nature of star formation\nmakes this problem rather an untractable one from an analytical point\nof view, so that the best approach towards understanding the distribution\nof stellar populations in galaxies requires a heavy use of rough \napproximations and all-too-often dangerous generalizations. \nIt is the purpose of current phenomenological models describing the \nformation and evolution of the stellar component in galaxies to \nreveal the mechanisms which describe the wide range of galaxy colors \nand luminosities as well as their connection to morphology.\nThe current status of the determination of the ages of the stellar \npopulations in galaxies is rather controversial due to the\ndegeneracy between age and metallicity (Worthey 1994). Observations of \nearly-type galaxies by two different groups using similar techniques\ntargeting narrow spectral indices to infer a luminosity-weighted\nage give contradictory results. While Trager et al. (2000) find\na large age spread in the sample of field and group early-type systems\nof Gonz\\'alez (1993), Kuntschner (2000) reports a large metallicity\nspread in Fornax cluster ellipticals. So far, any observational\nmeasurement of age is plagued by many degeneracies which render a direct\nestimate uncertain. An alternative approach modelling the formation\nand chemical enrichment of the stellar component of galaxies\nis needed in order to reveal the actual scenario of galaxy formation.\n\n\\begin{figure}\n \\epsfxsize=2.6in\n\\begin{center}\n \\leavevmode\n \\epsffile{ferrerasi_f1.eps}\n\\end{center}\n\\vskip -0.3truein\n \\caption{Gas ({\\sl top}) and metallicity ({\\sl bottom}) evolution\nof two models: one with a series of short bursts ({\\sl thin line})\nand another with a single, more extended burst. The inset shows\nthe evolution of $U-V$ color in the rest frame. \n}\\label{f1}\n\\end{figure}\n\n\\section{Modelling chemical enrichment}\nThe model presented here describes the process of star formation\nin early-type galaxies in terms of four parameters: star formation\nefficiency ($\\ceff$), ejected gas fraction in outflows ($\\bout$),\nformation redshift ($z_F$) and infall timescale ($\\tau_f$).\nThe latter two parameters refer to the epoch ($t = t(z_F)$) \nat maximum and spread of a Gaussian profile for the\ninfalling gas, i.e.:\n\\begin{equation}\nf(t) \\propto e^{-\\left(t-t(z_F)\\right)^2/2\\tau_f^2}\n\\end{equation}\nThis gas will be turned into stars according to a\nlinear Schmidt-type law, where the proportionality constant is\nthe star formation efficiency parameter. The model is described in\nmore detail in Ferreras \\& Silk (2000a,b). This generic description \nallows us to include multi-burst scenarios in galaxies undergoing\nseveral merging stages with enough gas to fuel star formation\nat each merging event. Figure~1 shows a comparison between two star\nformation histories: one with three equally strong starburst events \nand a second one as a simplification to the former using our\napproach. The top panel shows the evolution of the gas mass --- which\nis proportional to the star formation rate. The bottom panel\nshows the evolution of the metallicity and the top inset traces\nthe evolution of rest frame $U-V$ color for both scenarios.\nOne can see that at times after the last bursting episode,\nthe evolution in both cases is roughly undistinguishable. Hence,\nwe conclude that our four-parameter model can account not only for a\nstandard ``monolithic'' scenario but also for multi-burst formation\nhistories. Furthermore, a Gaussian profile for infall avoids the\noverproduction of low metallicity stars. In fact, a suitable choice \nof infall parameters ($\\tau_f$,$z_F$) can reproduce the local \nmetallicity distribution of stars (Rocha-Pinto \\& Maciel 1996).\n\n\\begin{figure}\n \\epsfxsize=3.5in\n\\begin{center}\n \\leavevmode\n \\epsffile{ferrerasi_f2.eps}\n\\end{center}\n\\vskip-0.3truein\n \\caption{Evolution of the color-magnitude relation observed in Coma\n(Bower, Lucey \\& Ellis (1992) projected to moderate redshift using both\nan outflow-driven sequence ($B_{out}$, {\\sl left}) and an efficiency-driven\nsequence ($C_{eff}$, {\\sl right}). The shaded area corresponds to the\nobservations of cluster Cl0016+16 ($z=0.55$, Ellis et al. 1997).\n}\\label{f2}\n\\end{figure}\n\nFor a given set of four parameters ($\\bout$,$\\ceff$,$z_F$,$\\tau_f$) \nwe can trace a star formation history and convolve it in age and \nmetallicity with the simple stellar populations of Bruzual \\& Charlot\n(in preparation). Hereafter a closed cosmology ($\\Omega_m=0.3$, \n$\\Omega_\\Lambda =0.7$, $H_0=60$ km s$^{-1}$ Mpc$^{-1}$),\nand a hybrid Initial Mass Function between Scalo and Salpeter \n(Ferreras \\& Silk 2000b) are used. Out of these four parameters, \nwe find only $\\bout$ and\n$\\ceff$ can generate the range of observed $U-V$ colors in nearby\nearly-type cluster galaxies (Bower, Lucey \\& Ellis 1992). Hence, \nthe luminosity sequence of these systems could be explained either\nby a range of outflows ($\\bout$-sequence), by a range of star formation\nefficiencies ($\\ceff$-sequence), or by some combination thereof.\nFigure~2 shows the predicted color-magnitude relation (CMR) of \nComa galaxies at the redshift of cluster Cl0016+16 \n($z=0.55$, Ellis et al. 1997) assuming a $\\bout$-sequence \n({\\sl left}) or a $\\ceff$-sequence ({\\sl right}), and a range\nof infall parameters ($z_F$,$\\tau_f$). A sequence driven by\n$\\ceff$ results in an age spread for the stellar populations. This\ncauses the remarkable departure of the predictions from the\nobserved CMR (shaded area) for extended star formation histories\n($z_F=10$, $\\tau_f=2$ Gyr). However, because of the age-metallicity\ndegeneracy, we find that quite a large range of the parameters \nagree with the observations within error bars. Hence, we cannot use \nphotometric measurements of moderate redshift clusters in order\nto determine whether age ($\\ceff$) or metallicity ($\\bout$)\ndrive the CMR.\n\n\\section{$M/L$ ratio as tracer of age evolution}\nOne of the most age-sensitive observables is the mass-to-light\nratio. Hence, the predicted evolution of $M/L$ with lookback\ntime should be different for sequences driven by age or\nby metallicity. We consider the evolution with redshift \nof the slope of the correlation\nbetween $M/L$ in rest frame $B$-band and {\\sl stellar} mass.\nThis slope change is parametrized by $\\eta_B$ defined as follows:\n\\begin{equation}\n\\eta_B(z) \\equiv \\left.\\frac{\\Delta\\log M/L_B}{\\Delta\\log M}\\right|_{z} -\n\t\\left.\\frac{\\Delta\\log M/L_B}{\\Delta\\log M}\\right|_{z=0}\n\\end{equation}\nFor a $\\bout$-sequence (driven by outflows), the range of luminosities is \nrelated by a spread in metallicities. As we evolve the cluster to \nhigher redshifts, the mass-to-light ratio will decrease uniformly\nacross the luminosity sequence because of lookback time, and there\nwill also be a relative change of $M/L$ among early-type galaxies \ncaused by its very weak metallicity dependence,\nwhich makes the decrease in mass-to-light ratio slighly larger in\ngalaxies with a higher metallicity, thereby flattening the slope\nof $M/L$ vs $M$ (i.e. $\\eta_B\\simlt 0$). On the other hand,\na $\\ceff$-sequence (driven by efficiency) will introduce a significant\nage spread which varies with galaxy mass, so that $M/L$ at the \nfainter end (which has a lower efficiency and thus a larger age \nspread) will decrease more than the bright end, steepening the\nslope (i.e. $\\eta_B > 0$, see figure~5 in Ferreras \\& Silk 2000b).\n\nThis behavior makes the study of the evolution of $M/L$ with\nredshift a suitable candidate to infer the star formation\nhistory of early-type cluster galaxies. Unfortunately, this\nobservable still poses a long string of uncertainties which prevent it\nfrom establishing a clearcut way of breaking the degeneracy between\nage and metallicity: mass-to-light ratios require time-consuming \nspectral observations in order to measure velocity dispersions,\nand can only be achieved with 10m class telescopes for clusters\nat moderate and high redshifts. Furthermore, the measured $M/L$ ratios\n(inferred from observations of velocity dispersions, \nsurface brightnesses and galaxy sizes) rely on a set of assumptions \nabout the structure of the galaxy. Any correlation between galaxy \nstructure and mass or luminosity will add systematic errors which are \nhard to estimate. However, alternative age-dependent observables \nsuch as Balmer spectral indices are also plagued by model-dependent \nuncertainties. Despite all these caveats, the study of the evolution \nof $M/L$ with lookback time is still one of the best methods to determine \nthe stellar demography in galaxies.\n\n\\begin{references}\n\\reference Bower, R.~G., Lucey, J.~R. \\& Ellis, R.~S. 1992, \\mnras, 254, 601 \n\\reference Ferreras, I. \\& Silk, J. 2000a, \\apj, March 20, astro-ph/9910385\n\\reference Ferreras, I. \\& Silk, J. 2000b, \\mnras, in press\n\\reference Gonz\\'alez, J.~J. 1993, Ph.D. thesis, University of California\n\\reference Kuntschner, H. 2000, \\mnras, in press (astro-ph/0001210)\n\\reference Rocha-Pinto, H.~J. \\& Maciel, W.~J. 1996, \\mnras, 279, 447\n\\reference Trager, S.~C., et al. 2000, \\aj, in press (astro-ph/0001072)\n\\reference Van Dokkum, P.~G., et al. 1998, \\apj, 504, L17\n\\reference Worthey, G. 1994, \\apjs, 95, 107\n\\end{references}\n\n\n\\end{document}\n"
}
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astro-ph0002393
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\noindent Gigahertz Peaked Spectrum (GPS) sources form a key element in the study of the onset and evolution of radio-loud AGN, since they are most likely the young counterparts of extended radio sources. Here we discuss space-VLBI observations of GPS sources, which enable us to obtain unprecedented angular resolution at frequencies near their spectral turnovers. Observed peak brightness temperatures of $10^{10.5-11}$ Kelvin indicate that synchrotron self absorption is responsible for their spectral turnovers. This is in close agreement with previous size $-$ spectral turnover statistics for GPS sources. The combination of these new space-VLBI observations with ground-based VLBI observations taken at an earlier epoch, confirm the young ages for the most compact GPS galaxies of several hundred years.
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[
{
"name": "snellen.tex",
"string": "\\documentstyle[11pt,psfig,vsopsymp]{article}\n\\pagestyle{myheadings}\n\\setcounter{page}{100}\n\\begin{document}\n%=======================================================================\n% Edit the following, adding first author's name and short title\n%=======================================================================\n\n\\markboth{\\hfill Snellen et al.}{Space-VLBI observations of \nyoung radio sources \\hfill}\n\n%=======================================================================\n% Paper title \n\\centerline{\\LARGE\\bf \n A study of young radio-loud AGN \n}\\medskip\n\\centerline{\\LARGE\\bf using space-VLBI}\\bigskip\n%=======================================================================\n% Author list.\n% Authors may use their given name or their initials, either is okay.\n%=======================================================================\n\\renewcommand{\\thefootnote}{\\fnsymbol{footnote}}\n\\centerline{\\sc \nIgnas Snellen$^1$\n\\footnote{This research was supported by the European Commission, \nTMR Programme, Research Network Contract ERBFMRXCT96-0034 ``CERES'', and\nthe TMR Access to Large-scale Facilities programme under contract No. \nERBFMGECT950012}, \nWolfgang Tschager$^2$, Richard Schilizzi$^{3,2}$\n}\\medskip\n\\centerline{\\sc \nHuub R\\\"ottgering$^2$ \\& George Miley$^2$\n}\\medskip\n\n\n\n%=======================================================================\n% Please type the institute affiliations of all authors here.\n% If all authors are from the same institution, the superscript $^1$ is \n% not required in the author list and affiliation.\n%=======================================================================\n\\centerline{\\it\n$^1$ Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK}\n\\centerline{\\it\n$^2$ Sterrewacht Leiden, Postbus 9513, 2300 RA Leiden, The Netherlands}\n\n\\centerline{\\it\n$^3$ Joint Institute for VLBI in Europe, Postbus 2, 7990 AA, Dwingeloo,}\n\\centerline{\\it The Netherlands}\n\n\n%=======================================================================\n% Abstract\n%=======================================================================\n\\begin{abstract} \\noindent \nGigahertz Peaked Spectrum (GPS) sources form a key element in the \nstudy of the onset and evolution of radio-loud AGN, since they are most likely \nthe young counterparts of extended radio sources.\nHere we discuss space-VLBI observations of GPS sources, which enable us \nto obtain unprecedented angular resolution at frequencies near their\nspectral turnovers. Observed peak brightness temperatures of $10^{10.5-11}$\nKelvin indicate that synchrotron self absorption is responsible for \ntheir spectral turnovers. This is in close agreement with previous size $-$ \nspectral turnover statistics for GPS sources. The combination of these\nnew space-VLBI observations with ground-based VLBI observations taken at an\nearlier epoch, confirm the young ages for the \nmost compact GPS galaxies of several hundred years.\n\\end{abstract}\n\n\\keywords{}\n\n\\sources{0108+388, 2021+614}\n\n\n\\section{Young radio-loud AGN}\n\nAlthough radio-loud Active Galactic Nuclei (AGN) have been studied\nfor several decades, still not much is known about their birth\nand subsequent evolution. The recent identification of a class of \nvery young radio sources can be considered as a major breakthrough\nin this respect, since it has opened many unique opportunities for \nradio source evolution studies.\n\nUnfortunately, the nomenclature and use of acronyms in this \nfield of research is rather confusing. This is mainly caused by\nthe different ways in which young radio sources are selected.\nSelection of young sources is made in two ways, the first based \non their broadband radio spectra, and the second based on their\ncompact morphology. \nA convex shaped spectrum, peaking at about 1 GHz \ndistinguishes young radio sources from other classes of compact radio sources.\nIn this case they are called Gigahertz Peaked Spectrum ({\\bf GPS}) radio\nsources (eg. O'Dea etal. 1991, O'Dea 1998). Similar objects, which are\ntypically an order of magnitude larger in size, have their spectral turnovers \nshifted to the $10 - 100$ MHz regime, causing them to be dominated at cm \nwavelengths by the optically thin parts of their spectra. \nThese are called Compact Steep Spectrum ({\\bf CSS}) radio\nsources to distinguish them from the general population of extended \nsteep spectrum sources (eg. Fanti et al. 1991). \n\nOn the other hand, young radio sources are found in multi-frequency VLBI\nsurveys, in which they can be recognised by compact jet/lobe-like\nstructures on both sides of their central core. They are called \nCompact Symmetric Objects ({\\bf CSO}, Wilkinson et al. 1994). \nTheir double sided structures\nclearly distinguish them from the large majority of compact sources\nshowing one-sided core-jet morphologies. This implies that the luminosities\nof CSO are unlikely to be substantially enhanced by Doppler boosting. \nLarger versions\nof CSOs are subsequently called Medium Symmetric Objects ({\\bf MSO}) and \nLarge Symmetric Objects ({\\bf LSO}).\n\nThe overlap between the classes of CSO and GPS galaxies is large and we \nbelieve that they can be considered to be identical objects.\nHowever, note that a substantial fraction of GPS sources are optically \nidentified with high redshift quasars, which in general show core-jet \nstructures (Stanghellini et al. 1997). \nThe relationship between GPS quasars and GPS galaxies/CSO\nis not clear and under debate (Snellen et al. 1999). \nWe therefore believe it is wise to\nrestrict evolution studies to GPS galaxies and CSOs.\n\n\\subsection*{Evidence for youth}\n\nAlthough it was always speculated that GPS sources were young objects,\nonly recently has strong evidence been found to support this \nhypothesis. Monitoring several GPS sources over a decade or more using\nVLBI, allowed Owsianik \\& Conway (1998) and Owsianik, Conway \\& \nPolatidis (1998) to \nmeasure the hotspot advance speeds of several \nprototype GPS sources to be $\\sim 0.1h^{-1}c$. These imply dynamical \nages of typically $10^{2-3}$ years. \n\nAdditional proof for youth comes from analysis of the overall radio\nspectra of the somewhat larger CSS sources. Murgia et al (1999) show that \ntheir spectra can be fitted with synchrotron aging models, implying \nages of typically $10^{3-5}$ years.\n\nThe work of these authors shows that GPS/CSO sources are very young and most \nlikely \nthe progenitors of large, extended radio sources. This makes them\nkey objects for radio source evolution studies.\n\n\n\\subsection*{Tools for radio source evolution studies}\n\nSeveral authors have used number count statistics and \nlinear size distributions to constrain the luminosity evolution\nof radio sources (Fanti et al. 1995; Readhead et al. 1996, O'Dea \\& \nBaum 1997). All these studies find an excess of young \nobjects in relation to the number of old, extended radio sources.\nThis over-abundance of GPS and CSS sources has generally been explained by\nassuming that a radio source significantly decreases in luminosity over its \nlifetime. In this way, sources are more likely to \ncontribute to flux density limited samples at young than at old age, causing \nthe apparent excess.\n\nHowever, in addition to their over-abundance, GPS galaxies are found to be \nsignificantly \nmore biased towards high redshift than large extended radio galaxies (Snellen \\& Schilizzi, 2000). \nThis is puzzling since classes of sources representing similar objects at \ndifferent stages of their evolution are expected to have similar birth \nfunctions and redshift distributions. Furthermore, it suggests that the \ninterpretation of their number count statistics, which are averaged over a \nlarge redshift range, is not so straightforward.\nWe have postulated a simple evolution scenario which can resolve these \npuzzles. We argue that the luminosity evolution of a \nradio-loud AGN\nduring its first $10^5$ years is qualitatively very different from that \nduring the rest of its lifetime. This may be caused by a turnover\nin the density profile of the interstellar/intergalactic medium \nat the core-radius of the host galaxy, resulting in an increase in\nluminosity for young, and a decrease in luminosity for old radio-loud AGN \nwith time. Such a luminosity evolution results in a \nflatter collective luminosity function for the young objects, \ncausing their bias towards higher \nredshifts, and their over-abundance at bright flux density levels (Snellen et al. 2000).\n\nAn alternative explanation is that GPS sources are indeed young AGN, but \nmainly short-lived objects, which will never evolve into extended radio sources\n(Readhead et al. 1994). In that case, the two populations are not \ndirectly connected, and no similar cosmological evolution or redshift \ndistribution is necessary.\n\n\\section{Space-VLBI observations of GPS sources}\n\nIn general, the angular resolution of VLBI observations at a \ncertain observing frequency is limited by the size of the earth.\nThe combination of ground VLBI stations with the Japanese satellite \nHALCA (part of the VLBI Space Observatory Programme \n VSOP), achieves a resolution typically 3 times higher than this\n($\\sim 1.5$ mas and $\\sim 0.5$ mas at 1.6 and 5 GHz respectively).\nIn particular, the study of GPS sources benefits from VSOP, since observing at\na higher frequency to achieve a similar resolution is often not an option,\n because of their steep fall-off in flux density towards high frequency.\nFurthermore, their physical properties are most interesting around their \nspectral turnover, where differences in spectral indices within the source \nare more prominent than at high frequency.\n\nWe have been awarded VSOP observing time for 11 and 8 of the brightest\nand most compact GPS sources at 5.0 and 1.6 GHz respectively. \nDetails and status of the observations are listed in Table \\ref{table1}.\nAt the time of writing, all targets at 5 GHz, and \n6 of the 8 sources at 1.6 GHz have been observed.\n\n\n\\begin{table}\n\\caption{Status of VSOP observations. \\label{table1} }\n\\hskip 1cm\n\\begin{tabular}{|lllcc|} \\hline\nName & id & z & Date of Obs & Date of Obs\\\\\n & & & 5 GHz & 1.6 GHz \\\\ \\hline\n0108+388&Gal& 0.669&1999.08.06 &1999.08.05 \\\\\n0248+430&QSO& 1.316&1999.02.15 &1999.08.18 \\\\\n0552+398&QSO& 2.370&1999.03.23 &1999.01.15 \\\\\n0615+820&QSO& 0.710&1999.09.18 & tbd \\\\\n0646+600&QSO& 0.460&1999.09.20 &1999.09.27 \\\\ \n1333+459&QSO& 2.450&1998.06.22 &1999.05.28 \\\\\n1404+286&Gal& 0.077&1998.06.30 & tbd \\\\ \n2021+614&Gal& 0.227&1997.11.16 &1999.09.28 \\\\ \\hline\n1550+582&QSO& 1.324&1998.07.02 & -- \\\\\n1622+665&Gal& 0.201&1998.05.24 & -- \\\\\n0636+680&QSO& 3.180&1999.09.19 & -- \\\\ \\hline\n\\end{tabular}\n\\end{table}\n\n\n\\subsection*{First results and discussion}\n\n\\begin{figure}\n\\vspace{170mm}\n\\special{psfile=snellen_fig1.ps hoffset=-40 voffset=-80 hscale=70 vscale=70}\n\\caption{\\label{fig1} VSOP observations of 0108+388 at 5 GHz. The upper left\npanel shows the VLBA only image, the upper right panel shows the VLBA+HALCA\nimage, and the lower panel shows some of the fringes of the VLBA antennas\nand the VLA to HALCA.}\n\\end{figure}\n\n\nA large fraction of the sources have now been imaged.\nSome examples are shown in figures \\ref{fig1} and \\ref{fig2}.\nAdditional observations have been taken at 15 GHz with the VLBA to\nmatch the 5 GHz VSOP data in resolution, which will allow detailed \nspectral decompositions of the objects. In particular, this may\nsched new light on the nature of the GPS quasars and the role of Doppler \nboosting in these sources.\n\nOne of the first results of \nthese observations are the high brightness temperatures observed\nof typically $10^{10.5-11}$ Kelvin. This indicates that these objects\nmust be near their synchrotron self absorption (SSA) turnover at the \nobserved frequency, making it very likely that indeed SSA is the cause of \ntheir spectral peaks. This is in agreement with the statistical arguments\nof Snellen et al. (2000), who found that among samples of GPS and CSS sources,\nthe ratio of component size, as derived from the spectral peak assuming SSA,\nand overall angular size, are constant and very similar to \nthose found for large\nextended radio sources. This not only implies self-similar evolution,\nbut also provides strong \nevidence for SSA. Note however, that several authors argue \nthat free-free\nabsorption can not be ruled out for the smallest GPS galaxies \n(Kameno et al., this volume; Marr et al., this volume)\n\n\\begin{figure}\n\\vspace{80mm}\n\\special{psfile=snellen_fig2.ps hoffset=-37 voffset=265 hscale=52 vscale=52\nangle=270}\n\\caption{\\label{fig2} VSOP observations of 2021+614 at 1.6 and 5 GHz. \nThe dotted lines connect the two dominant features at 5 GHz with their \nposition at 1.6 GHz. Note the importance of sufficient resolution near\nthe spectral turnover frequency, where the differences in spectral index\nbetween the components are most prominent.} \n\\end{figure}\n\n\nA valuable spin-off from these high angular resolution VSOP observations\ncome from their comparison with ground-based VLBI images taken at an \nearlier epoch. Following the method of Owsianik \\& Conway (1998), we \nuse these to derive dynamical ages for GPS sources.\nIn this way, we find that the two dominant components at 5 GHz of 2021+614 (fig \\ref{fig2}),\nhave a larger separation at the epoch of the VSOP observations, compared to \ndata from Conway et al. (1994) taken in 1982 and 1987. \nThe increase in separation indicates\na hotspot advance speed of $\\sim 0.1$c, which implies an age of $\\sim 400$\nyears for these components (Tschager et al. 2000). Preliminary analysis \nof 0108+388 (fig \\ref{fig1}) shows an advance speed of 15 $\\mu as$/yr, \nconsistent with what is found by Owsianik, Conway \\& Polatidis \n(1998; 9 $\\mu as/yr$).\nThese observations confirm the young ages of a few hundred years for \nthe most compact GPS galaxies.\n\n\\section{Summary}\n\nGPS galaxies and CSO are now identified as classes of young radio sources.\nThey form a key element in the investigation of the evolution of \nradio-loud AGN.\nWe report on VSOP observations of 11 and 8 bright GPS sources\nat 5.0 and 1.6 GHz frequency respectively.\nFirst analysis indicates high brightness temperatures consistent with\nsynchrotron self absorption as the cause of their spectral turnover.\nComparison with ground-based VLBI datasets taken at earlier epochs confirm\nthe very young ages for the most compact GPS galaxies of a few hundred\nyears.\n\n\n\\acknowledgements\n\nWe gratefully acknowledge the VSOP Project, which is led by the\nJapanese Institute of Space and Astronautical Science in cooperation\nwith many organizations and radio telescopes around the world.\n\n\n\\begin{references}\n\n\\newref Conway J.E., Myers S.T., Pearson T.J., Readhead C.S., Unwin S.C.,\n\\& Xu W., 1994, \\apj, 425, 568\n\\newref Fanti R., Fanti C., Schilizzi R.T., Spencer R.E., Nan Rendong, \n Parma P., Van Breugel W.J.M., Venturi T., 1990, A\\&A, 231, 333\n\n\\newref Fanti C., Fanti R., Dallacasa D., Schilizzi R.T., Spencer R.E.,\n Stanghellini C., 1995, A\\&A, 302, 317\n\\newref Kameno et al., this volume\n\\newref Marr et al., this volume\n\\newref Murgia M., Fanti C., Fanti R., Gregorini L., Klein U., \n Mack K-H., Vigotti M., 1999, A\\&A, 345, 769\n\\newref O'Dea C.P., Baum S.A., Stanghellini C., 1991, ApJ, 380, 66\n\\newref O'Dea C.P., Baum S.A., 1997, AJ, 113, 148\n\n\\newref O'Dea C.P., 1998, PASP, 110, 493\n\\newref Owsianik I., Conway J.E., 1998, A\\&A, 337, 69\n\n\\newref Owsianik I., Conway, J.E., Polatidis, A.G., 1998, A\\&A, 336, L37\n\\newref Readhead A.C.S, Xu W., Pearson T.J., 1994, in Compact\n Extragalactic Radio Sources, eds Zensus \\& Kellerman, p19 \n\n\\newref Readhead A.C.S., Taylor G.B., Xu W., \n Pearson T.J., Wilkinson P.N., 1996, ApJ, 460, 634\n\\newref Snellen I.A.G., Schilizzi R.T., Bremer M.N, Miley G.K., de Bruyn A.G.,\n R\\\"ottgering H.J.A., 1999a, MNRAS, 307, 149 \n\\newref Snellen I.A.G., \\& Schilizzi R.T., proc. of `Lifecycles of Radio \n Galaxies' workshop, ed J. Biretta et al., to appear in New Astronomy Reviews. \n\\newref Snellen I.A.G., Schilizzi R.T., Miley G.K., de Bruyn A.G.,\nBremer, M.N. \\& R\\\"ottgering H.J.A., 2000, \\mnras, submitted\n\\newref Stanghellini C., O'Dea C.P., Baum S.A., Dallacasa D., Fanti R., \n Fanti C., 1997a, A\\&A, 325, 943\n\\newref Tschager W., Schilizzi R.T., R\\\"ottgering, H.J.A., Snellen I.A.G., \nMiley, G.K., 2000, submitted to A\\&A\n\\newref Wilkinson P.N., Polatidis A.G., Readhead A.C.S., Xu W., Pearson T.J.,\n 1994, ApJ, 432, L87\n\\end{references}\n\n\\end{document}\n\n\n\n\n\n\n"
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astro-ph0002394
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Innermost stable circular orbits around strange stars\\ and kHz QPOs in low-mass X-ray binaries
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[
{
"author": "J. L. Zdunik \\inst{1}"
},
{
"author": "P. Haensel\\inst{1,2}"
},
{
"author": "D. Gondek-Rosi{\\'n}ska\\inst{1}"
},
{
"author": "E. Gourgoulhon\\inst{2}"
}
] |
% Exact calculations of innermost stable circular orbit (ISCO) around rotating strange stars are performed within the framework of general relativity. Equations of state (EOS) of strange quark matter based on the MIT Bag Model with massive strange quarks and lowest order QCD interactions, are used. The presence of a solid crust of normal matter on rotating, mass accreting strange stars in LMXBs is taken into account. It is found that, contrary to neutron stars, above some minimum mass (which for the considered equations of state ranged from $1.4~{M}_\odot$ to $1.6~{M_\odot}$) a gap always separates the ISCO and stellar surface, independently of the strange star rotation rate. For a given baryon mass of strange star, we calculate the ISCO frequency as function of stellar rotation frequency, from static to Keplerian configuration. For masses close to the maximum mass of static configurations the ISCO frequencies for static and Keplerian configurations are similar. However, for masses significantly lower than the maximum mass of static configurations, the minimum value of the ISCO frequency is reached in the Keplerian limit. Presence of a solid crust increases the ISCO frequency for the Keplerian configuration by about ten percent compared to that for a bare strange star of the same mass. For standard parameters of strange quark matter EOS, resulting in a maximum static mass of $1.8~{M}_\odot$, the ISCO frequency for $\ga 1.4~{M}_\odot$ strange stars always exceeds 1.07~kHz (the upper QPO frequency reported for 4U 1820-30). We give an example of strange quark matter model, which yields maximum static mass of $2.3~{M}_\odot$, and for which the ISCO frequency of 1.07 kHz is allowed at stellar rotation rates 200-300 Hz, provided the strange star mass exceeds 2.2 ${M}_\odot$. For this EOS even lower value $\nu_{ISCO}\simeq 1$~kHz is reached near the Keplerian limit, for a broad range of stellar masses. While reproducing $\nu_{ISCO}=1.07$ kHz at slow rotation rates requires tuning of strange quark matter parameters, no such a tuning is required to reproduce orbital frequencies around strange stars equal to highest observed upper QPO frequencies. \keywords{dense matter -- equation of state -- gravitation -- stars: neutron -- X-rays: stars}
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[
{
"name": "zdunik2.tex",
"string": "%\n% in this version also changes to 1.33 in main section\n% changes marked by bold face (\\chng)\n% to remove bf simply define\n\\def\\chng{}\n%\\def\\chng{\\bf}\n\\def\\Nf{N^{\\varphi}}\n\\def\\nums{\\nu_{\\rm ms}}\n\\def\\mcr{M_{\\rm crust}}\n\\def\\msol{{\\rm M}_{\\odot}}\n\\def\\nurot{\\nu_{\\rm rot}}\n\\documentclass{aa}\n%\\documentclass[referee]{aa}\n\\usepackage{graphicx}\n%\n\\begin{document}\n%\n%\n% Petites macros\n%\n\\newcommand{\\ddp}[2]{\\frac{\\partial #1}{\\partial #2}}\n\\newcommand{\\ddps}[2]{\\frac{\\partial^2 #1}{\\partial #2 ^2}}\n\n%\\thesaurus{02.04.01, 08.14.1, 08.16.6, 02.07.01}\n\\thesaurus{06(02.04.1, 02.05.2, 02.07.1, 08.14.1, 13.25.5)}\n\\title{Innermost stable circular orbits around strange stars\\\\\n and kHz QPOs in low-mass X-ray binaries }\n\\author{J. L. Zdunik \\inst{1}\n \\and\nP. Haensel\\inst{1,2}\n \\and\nD. Gondek-Rosi{\\'n}ska\\inst{1}\n \\and\nE. Gourgoulhon\\inst{2}\n}\n%\n\\institute{N. Copernicus Astronomical Center, Polish\n Academy of Sciences, Bartycka 18, PL-00-716 Warszawa, Poland\n\\and\nD\\'epartement d'Astrophysique Relativiste et de Cosmologie\n-- UMR 8629 du CNRS, Observatoire de Paris, F-92195 Meudon Cedex,\nFrance\\\\\n%\n{\\em jlz@camk.edu.pl, haensel@camk.edu.pl, dorota@camk.edu.pl,\n Eric.Gourgoulhon@obspm.fr}}\n\\offprints{J.L. Zdunik}\n%\n\\date{received/accepted}\n%\n\\titlerunning{Innermost stable orbits around strange stars and QPOs}\n\\authorrunning{J.L.~Zdunik et al.}\n\\maketitle\n%\\markboth{}\n%\n\\begin{abstract}\n%\nExact calculations of innermost stable circular orbit (ISCO)\naround rotating strange stars are performed within the framework\nof general relativity. Equations of state (EOS) of strange quark\nmatter based on the MIT Bag Model with massive strange quarks and\nlowest order QCD interactions, are used. The presence of a solid crust\nof normal matter on rotating, mass accreting strange stars in\nLMXBs is taken into account. It is found that, contrary to neutron\nstars, above some minimum mass (which for the\nconsidered equations of state ranged from $1.4~{\\rm M}_\\odot$\nto $1.6~{\\rm M_\\odot}$)\n a gap always separates the ISCO and stellar surface,\nindependently of the strange star rotation rate.\nFor a given baryon mass of strange star, we calculate the ISCO frequency\nas function of stellar rotation frequency, from static to Keplerian\nconfiguration. For masses close to the maximum mass of\nstatic configurations the ISCO frequencies for static\nand Keplerian configurations are similar. However, for masses\nsignificantly lower than the maximum mass of static configurations,\nthe minimum value of the ISCO frequency is reached in the Keplerian limit.\n Presence of a\nsolid crust increases the ISCO frequency for the Keplerian configuration\nby about ten percent compared to that for a bare strange star of the\nsame mass. For standard parameters of strange quark matter EOS,\nresulting in a maximum static mass of $1.8~{\\rm M}_\\odot$,\nthe ISCO frequency for $\\ga 1.4~{\\rm M}_\\odot$ strange stars always exceeds\n1.07~kHz (the upper QPO frequency reported for 4U 1820-30).\nWe give an example of\nstrange quark matter model, which yields maximum static mass of\n$2.3~{\\rm M}_\\odot$, and for which the ISCO frequency of 1.07 kHz\n is allowed at stellar rotation rates\n200-300 Hz, provided the strange star mass exceeds 2.2 ${\\rm\nM}_\\odot$. For this EOS\n even lower value $\\nu_{\\rm ISCO}\\simeq 1$~kHz is\nreached near the\nKeplerian limit,\nfor a broad range of stellar masses.\n While reproducing $\\nu_{\\rm\nISCO}=1.07$ kHz at slow rotation rates requires tuning of\nstrange quark matter parameters, no such a tuning is required to\nreproduce orbital frequencies around strange stars equal to\nhighest observed upper QPO frequencies.\n\n\\keywords{dense matter -- equation of state -- gravitation \n-- stars: neutron -- X-rays: stars}\n\n\\end{abstract}\n%\n\\section{Introduction}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\nObservations of quasi periodic oscillations (QPOs) in the X-ray\nfluxes from low-mass X-ray binaries (LMXB), which are believed to\nbe due to the orbital motion of matter in an accretion disk,\n raised hopes concerning observational constraints on the equation of\n state (EOS) of matter at supranuclear densities (Kaaret et al. 1997,\n Klu{\\'z}niak 1998,\nZhang et al. 1998,\n Miller et al. 1998, Thampan et al. 1999, Schaab \\&\nWeigel 1999).\n General relativity predicts the existence of the\nmarginally stable (MS) orbit, within which no stable circular\nmotion is possible. This implies the existence of the innermost\nstable circular orbit (ISCO) around neutron stars.\n The frequency of the ISCO is\nan upper bound on the frequency of stable orbital motion around\nneutron stars. Whether the ISCO is separated from neutron star\nsurface by a gap, or its radius coincides with stellar equatorial\nradius, depends on the star mass and on the EOS of neutron star\nmatter. On the other hand, accreting neutron stars in LMXBs are\nexpected to be rotating, and this influences both neutron star\nstructure and the ISCO. Therefore, in order to attempt to use\nobserved frequencies of QPOs to constrain the EOS of dense matter,\none has to calculate the ISCO as a function of stellar mass and\nstellar rotation frequency. Such a procedure is based on the\nassumption that the observed upper QPO frequency is due to orbital\nmotion, and that the effects of magnetic field, accretion, and\nradiation drag on the matter flow can be neglected.\n\nA basic assumption of the present paper is that the frequency of the\nupper kHz QPO is the orbital frequency of the inner edge of an\naccretion disk surrounding the compact object, which will be identified\nwith the ISCO. This is the leading interpretation of the QPOs. However,\nalternative models of the kHz QPOs were also proposed. In a model of\nAlpar \\& Yilmaz (1997) the kHz QPOs are explained in terms of\nwave packets of sound waves in the inner disk. In a series of papers,\nTitarchuk and collaborators propose a model in which the QPOs result\nfrom radial oscillations of the plasma in the boundary layer, i.e.\nin the region between the ISCO and stellar surface\n(see Titarchuk \\& Osherovich 1999 and references therein).\nThese alternative\nmodels will not be considered in our study.\n\n%%%%%%%%%%%%%%%%%fig1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*} %1\n \\resizebox{\\hsize}{!}{\\includegraphics[angle=-90]{zdunik1.eps}}\n\\caption{ The radius of the ISCO (dotted line), equatorial radius\nof a bare strange star (solid line), equatorial radius of a\nstrange star with maximally thick solid crust (long-dashed line),\nversus rotation frequency of strange star. Thin short-dashed line\ncorresponds to slow-rotation approximation of Klu{\\'z}niak \\&\nWagoner (1985). Calculations were performed for the SQM1 EOS of\nstrange matter (see the text). Figures correspond to stellar\nmodels with fixed total baryon number,\n equal to that of a static star of gravitational mass\nof $1.2,~1.4,~1.6, 1.75~{\\rm M}_\\odot$. Maximum mass for static\nstrange stars is $1.8~{\\rm M}_\\odot$ } \\label{fig1}\n\\end{figure*}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nIn the present paper we describe results of exact calculations of\nthe ISCO, under the assumption that the compact object is not a\nneutron star, but a strange star. A strange star is\n composed of self-bound quark matter,\n which at zero pressure would constitute a real ground state of matter (strange\n matter), with energy per unit\nbaryon number lower than that of $^{56}{\\rm Fe}$ crystal (Witten\n1984, Farhi \\& Jaffe 1984, Haensel et al. 1986, Alcock et al.\n1986; for a recent review of physics and astrophysics of strange\nmatter, see Madsen 1999). Recently, strange stars were invoked by several\nauthors in the context of modeling of observational properties of\nsome X-ray and gamma-ray sources (Bombaci 1997, Cheng et al. 1998,\nDai \\& Lu 1998, Li et al. 1999). First study of possibility\nof existence of strange stars in LMXBs exhibiting kHz QPOs was restricted\nto slow-rotation approximation for the ISCO, neglected the effect of\nrotation on the strange star structure, and used simplified EOS of strange\nmatter, with massless, non-interacting quarks (Bulik et al. 1999\n). Very recently, the ISCOs around bare strange stars were calculated,\nassuming a simplified EOS of strange matter, for\nthe limiting case of rotation at Keplerian frequency (Stergioulas\net al. 1999). In both these studies the possible presence of the solid crust on\nthe strange star surface was not taken into account.\n\n In principle, a strange star could be covered\n by a thin crust of normal matter, a possibility which is\nparticularly natural in the case of LMXB. The problem of formation\nand structure of a crust on an accreting strange star was\nstudied by Haensel \\& Zdunik (1991)(see also Miralda-Escud{\\'e}\net al. 1990). Because of its low mass, typically $\\la 10^{-5}~{\\rm\nM}_\\odot$, the effect of the crust on the exterior spacetime is\nnegligible. However, it determines the location of the star\nsurface, due to its finite thickness of $\\sim 200-300~$m. The\nmatter distribution within the strange core, relevant for the\nexterior metric of rotating strange star, is characterized by a\nvery flat density profile: for a massive strange star, density at\nthe stellar center is typically only 2-3 times larger than that at\nthe outer edge of the strange core. This has to be contrasted with\nthe density distribution within a massive neutron star, which\ndecreases continuously from $\\sim 10^{15}~{\\rm g~cm^{-3}}$ at the\ncenter to a few ${\\rm g~cm^{-3}}$ at the surface.\n The differences between the density profiles of a strange star\nand a neutron star result from the\nbasic difference in the EOS of their interiors.\nIn the case of a rapidly rotating compact object (situation relevant to\n LMXB), the differences between matter distributions within neutron star\n and strange star\nmay be expected to imply differences in the spacetime exterior\nto the compact object, and in particular, differences in\nthe properties of the ISCO.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{ISCOs around strange stars for\nstandard MIT Bag Model of strange matter}\n%\nOur EOS of strange matter, composed of massless u, d quarks, and\nmassive s quarks, is based on the MIT Bag Model. It involves three\nbasic parameters: the bag constant, $B$, the mass of the strange\nquarks, $m_{\\rm s}$, and the QCD coupling constant, $\\alpha_{\\rm\nc}$ (Farhi \\& Jaffe 1984, Haensel et al. 1986, Alcock et al.\n1986). Our basic EOS corresponds to standard values of the Bag\nModel parameters for strange matter: $B=56~{\\rm MeV/fm^3}$,\n$m_{\\rm s}=200~{\\rm MeV/c^2}$, and $\\alpha_{\\rm c}=0.2$ (Farhi \\&\nJaffe 1984, Haensel et al. 1986, Alcock et al. 1986). This EOS of\nstrange quark matter will be hereafter referred to as SQM1. It\nyields energy per unit baryon number at zero pressure $E_0=918.8\n~{\\rm MeV} <E(^{56}{\\rm Fe})=930.4~$MeV. For the SQM1 EOS maximum\nallowable mass for static strange star models is $M_{\\rm\nmax}^{\\rm stat}=1.8~{\\rm M_\\odot}$.\n\n\nThe general relativistic models of stationary rotating strange stars\nhave been calculated by means of the multi-domain spectral method,\ndeveloped recently by Bonazzola et al. (1998). Details of the\ncalculation method, specifically adapted for rotating strange stars, may be\nfound in Gourgoulhon et al. (1999). Having calculated a particular\nstationary rotating strange star model, and its exterior\nspacetime, we determine the frequency of a particle in stable\ncircular orbit in the equatorial plane, $\\nu_{\\rm\norb}(r)$, where $r$ is the radial coordinate of the orbit. By\ntesting the stability of orbital motion, we determine the radius of\nthe innermost, marginally stable orbit, $R_{\\rm ms}$, and its\nfrequency $\\nu_{\\rm ms}$ (see, e.g., Datta et al. 1998, for\nthe equations to be solved). Our numerical code calculating the ISCO\nhas been successfully tested by comparing our results\nfor the polytropic $\\gamma=2$ EOS with those obtained by\nCook et al. (1994a). Let us notice that the high precision of our\nnumerical method makes it particularly suitable for the\ndetermination of $R_{\\rm ms}$, which requires calculation of\nsecond derivatives of metric functions: these latter are better\nevaluated by the spectral method we employ than by means of finite\ndifferences.\n\n\n No orbital motion is possible for $r<R_{\\rm ms}$.\nThe values of $R_{\\rm ms}$ and $\\nu_{\\rm ms}$ for particles\ncorotating with strange star differ from those for counterrotating ones.\nIn the present paper we restricted ourselves to the corotating\ncase, relevant for the LMXB. We neglect the effect of magnetic field,\naccretion, and radiation drag on the location of the ISCO, which\nis justified for $B\\la 10^{8}~$G and ${\\dot M}\\ll {\\dot M}_{\\rm\nEdd}$.\n\nLet us consider a strange star, rotating at a frequency $\\nu_{\\rm\nrot}$, with equatorial radius $R_{\\rm eq}$. If $R_{\\rm ms}>R_{\\rm\neq}$, then stable orbits exist for $r>R_{\\rm ms}$; the ISCO has\nthen the radius $R_{\\rm ms}$ and the frequency $\\nu_{\\rm ms}$, and\nthere is a gap of width $R_{\\rm ms}-R_{\\rm eq}$ between the ISCO\nand the strange star surface. However, if $R_{\\rm ms}<R_{\\rm\neq}$, then $R_{\\rm ISCO}=R_{\\rm eq}$, $\\nu_{\\rm ISCO}= \\nu_{\\rm\norb}(R_{\\rm eq})$; and the accretion disk extends then down to the\nstrange star surface (or, more precisely, joins stellar surface\nvia a boundary layer).\n\nWhile the exterior spacetime\n is practically not influenced by the presence\nof a solid crust on the strange star surface, the value of $R_{\\rm eq}$ is\naffected by it.\nNeutrons are\nabsorbed by strange matter, and therefore the density at the\nbottom of the crust, $\\rho_{\\rm bott.cr.}$,\n cannot be higher than $\\rho_{\\rm n-drip}\\simeq\n4\\times 10^{11}~{\\rm g~cm^{-3}}$ (lower values of $\\rho_{\\rm\nbott.cr.}$ were discussed by Huang \\& Lu 1997). The equatorial\nthickness of the crust, $t_{\\rm eq}$, which we calculate,\ncorresponds to $\\rho_{\\rm bott.cr.} =\\rho_{\\rm n-drip}$, and is\ntherefore an upper bound on $t_{\\rm eq}$. At a fixed baryon\nnumber, rotation increases $t_{\\rm eq}$, as compared to the value\nfor a static strange star, $t_0$. Dependence of $t_{\\rm eq}$ on\n$\\nu_{\\rm rot}$ is well described by a formula $t_{\\rm\neq}(\\nu_{\\rm rot})=t_0\\cdot [1+0.7 (\\nu_{\\rm rot}/\\nu_{\\rm\nK})^2]$, where $\\nu_{\\rm K}$ is the Keplerian (mass shedding)\nfrequency of strange star. For rotating strange stars our formula\nfor $t_{\\rm eq}$ reproduces numerical results of Glendenning \\&\nWeber (1992) within better than 2\\% in all cases considered by\nthese authors.\n It is obvious that the bare strange star rotating\nat Keplerian limit would be unstable if we added a crust of \nnonzero thickness due to the increase of the radius, leaving the\nmass and the angular momentum practically unaltered. Thus at a\nfixed baryon mass of rotating strange star, the presence of the\ncrust implies a decrease of the Keplerian frequency. Knowing the\ndependence of the radius of the strange core and rotational\nfrequency on the stellar angular momentum one can estimate the\npoint of the Keplerian instability for a strange star with crust.\n%\n%%%%%%%%%%%%%%%%%fig2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure} %2\n \\resizebox{\\hsize}{!}{\\includegraphics[angle=-90]{zdunik2.eps}}\n\\caption{Frequency of the ISCO versus the rotation frequency of strange\nstar, for the same SQM1 EOS of strange matter.\nDash-dotted line was obtained for a simplified\n SQM0 model of strange matter with massless, noninteracting quarks\n (see the text). Each curve corresponds to a fixed\nbaryon mass, equal to that of a static strange star of\ngravitational mass indicated by a label.\nAlong each curve, angular momentum increases from $J=0$ (static\nconfiguration) to $J_{\\rm max}$ (Keplerian limit). Filled circles\n correspond to Keplerian configurations of strange stars with\n crust. Segments below the filled circles can be reached\nonly by the bare\n strange stars.}\n \\label{fig2}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\nLet us consider first rotating strange stars for the SQM1 EOS, which\ncorresponds to the ``standard set'' of the Bag Model parameters for\nstrange matter. A sample of our results for sequences of\nrotating strange star models with fixed baryon number are presented in Fig. 1.\n\n The form of Fig. 1 is analogous to that constructed by Miller et al.\n(1998) for neutron stars, and therefore is suitable for discussion\nof the differences between neutron stars and strange stars. For\nstrange stars with static mass $M\\ga 1.4~{\\rm M}_\\odot$, we have\nalways $R_{\\rm ms}>R_{\\rm eq}$, for any $\\nu_{\\rm rot}$. So, for\n$M\\ga 1.4~{\\rm M}_\\odot$ the gap between strange star surface\n(with or without solid crust) and the ISCO exists at any strange\nstar rotation rate. Even for lower $M$, the gap, which disappears\nat moderate rotation rates, reappears at $\\sim$ 1 kHz frequency\nof rotation; this is visualized by the $M=1.2~{\\rm M}_\\odot$ case\nin Fig. 1. At $\\nu_{\\rm rot}= \\nu_{\\rm K}$, the ISCO is always\nseparated from the strange star surface by a gap. Clearly, these\nfeatures of the ISCO around strange stars are quite different from\nthose obtained by Miller et al. (1998) for neutron stars with\nthe FPS EOS (see their Fig. 1). Note that the existence of a gap\n($R_{\\rm ms}>R_{\\rm eq}$) is expected to lead to a qualitatively\ndifferent spectrum of X-ray radiation from LMXB, compared to the\nno-gap case (Klu{\\'z}niak et al. 1990).\n\n\n%%%%%%%%%%%%%%%%%fig3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*} %3\n \\resizebox{\\hsize}{!}{\\includegraphics[angle=-90]{zdunik3.eps}}\n\\caption{ The radius of the ISCO (dotted line), equatorial radius\nof bare strange star (solid line), equatorial radius of\nstrange with a solid crust (long-dashed line),\nversus rotation frequency of strange star, for the SQM2 EOS of\nstrange quark matter (see the text). Thin short-dashed line\ncorresponds to slow-rotation approximation of Klu{\\'z}niak \\&\nWagoner (1985). Figures correspond to stellar models with fixed\ntotal baryon number,\n equal to that of a static star of the gravitational mass\nof $1.6,~1.8,~2.0,~2.25~{\\rm M}_\\odot$. Maximum mass of static\nstrange stars is $2.3~{\\rm M_\\odot}$} \\label{fig3}\n\\end{figure*}\n%\n\nConstraints on EOS of dense matter, resulting from the\nkHz QPOs observations, were initially derived within the slow-rotation\napproximation,\nin which $R_{\\rm ms}\\simeq R_{\\rm ms}^{\\rm s.r.}=6GM/c^2\\cdot[1-(2/3)^{3/2}j]$,\n $j\\equiv Jc/GM^2$, and $J$ is stellar angular momentum (Klu{\\'z}niak\n\\& Wagoner 1985). However as pointed out by Shibata \\& Sasaki\n(1998), the mass quadrupole moment is as important as the angular\nmomentum in determining the ISCO. Indeed as we can see in Fig. 1,\nslow rotation approximation yields $R_{\\rm ms}^{\\rm s.r.}$, which\nin the case of $M=1.4~{\\rm M}_\\odot$ diverges from exact $R_{\\rm\nms}$ for $\\nu_{\\rm rot} \\ga 500~$Hz. Moreover, for rotating\nstrange stars\n $R_{\\rm ms}^{\\rm s.r.}$ leads always to\ndisappearance of the gap at sufficiently high $\\nu_{\\rm rot}$,\n in contrast to exact calculation.\n\nA quantity of particular interest in the context of the interpretation of\nobserved kHz QPOs in LMXB, is the\nmaximum frequency of the stable circular orbit at a given $\\nu_{\\rm rot}$,\n which we identify here with that of the ISCO. In principle, both\n$\\nu_{\\rm ISCO}$ and $\\nu_{\\rm rot}$ are observable (measurable)\nquantities, which can be thus used for confronting stellar models\nwith observations. In Fig. 2 we present curves $\\nu_{\\rm\nISCO}(\\nu_{\\rm rot})$ for the SQM1 EOS. As in Fig. 1, baryon\nmasses are fixed along each curve, while labels correspond to\ngravitational mass of non-rotating strange star.\n\nIn all cases, displayed in Fig. 2, gap between stellar surface and\nISCO exists, and therefore $\\nu_{\\rm ISCO}=\\nu_{\\rm ms}$. The\ndash-dotted line was calculated for a simplified EOS, with\nmassless, non-interacting quarks ($m_{\\rm s}=0$, $\\alpha_{\\rm\nc}=0$, $B=56~{\\rm MeV/fm^3}$), hereafter referred to as SQM0 (such\na type of the EOS of strange quark matter was used in Bulik et al.\n1999). For $\\nu_{\\rm rot} \\ga 500~$Hz, neglecting strange quark\nmass (and, to a smaller extent, neglecting QCD interactions) leads\nto a rather severe underestimate of $\\nu_{\\rm ISCO}$ for rapidly\nrotating strange stars (by 200 Hz at $\\nu_{\\rm rot}=1~$kHz). As we\nstressed before, presence of the solid crust does not influence\nthe space-time outside rotating strange strange star. However,\nsolid crust decreases (by about 10\\%) the value of $J_{\\rm max}$\nof strange stars of a given baryon mass. Complete curves in Fig. 2\ncorrespond to bare strange stars. Rotating configurations with\ncrust terminate at filled dots, corresponding to the Keplerian\nlimit in the presence of the crust. The effect of the presence of\nthe crust on the value of $\\nu_{\\rm ISCO}$ at $\\nu_{\\rm K}$ turns\nout to be significant, which is due to the steepness of the\n$\\nu_{\\rm ISCO}(\\nu_{\\rm rot})$ curve for bare strange stars at\n$J\\simeq J_{\\rm max}$. For $J$ approaching $J_{\\rm max}$ bare\nstrange star undergoes strong deformation with increasing $J$.\nThis deformation in turn implies strong decrease of $\\nu_{\\rm\nISCO}$ with increasing rotation frequency. Consequently, the\nvalues of $\\nu_{\\rm ISCO}$ for maximally rotating strange stars\nwith crust is about hundred Hz higher than for bare strange stars.\nThis effect increases\n with decreasing strange star mass. At fixed $B$, the\neffect is stronger for the EOS which produces less compact strange\nstars of a given mass. Therefore, it is strongest for the SQM0\nEOS with massless, noninteracting quarks, where maximally rotating\nconfigurations of $1.4~{\\rm M}_\\odot$ with crust have the ISCO\nfrequency of 1.1 kHz, to be compared with less than 1 kHz for\nmaximally rotating bare strange stars.\n\nThe problem of an appropriate parametrization of the one-parameter family\nof rotating strange stars with fixed baryon mass deserves a comment.\nThese configurations may be labeled by the value of the total\nangular momentum $J$, which changes from $J=0$ in the static case to\n $J_{\\rm max}$ at the Keplerian limit. As one can see in Fig.2,\nfor bare strange stars, Keplerian configuration is not that with\nmaximum $\\nu_{\\rm rot}$. The reason is that for very rapidly\nrotating strange stars the increase of the total angular momentum\nresults mainly in the oblateness of the configurations leading to\nthe significant increase of the equatorial radius without an\nincrease of $\\nurot$ (or even with a decrease of $\\nurot$ very\nclose to $J_{\\rm max}$). As a consequence at fixed baryon mass the\nKeplerian configurations is reached not due to the increase of\n$\\nurot$ but because of the increase of the equatorial radius\nrelated to the deformation of the star. It is worth noticing that\nthe difference between $\\nu_{\\rm rot,max}$ and $\\nu_{\\rm K}$ is of\nthe order of one percent. The existence of this difference\n implies that for $J\\simeq J_{\\rm max}$\n it is in principle possible to spin up\nthe strange star by the angular momentum loss. Such a situation was\npreviously discussed in the case of supramassive neutron stars\n(Cook et al. 1994b) and supramassive\nstrange stars (Gourgoulhon et al. 1999).\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Confronting the standard MIT Bag Model of strange matter with\nQPO observations}\n%\n\nLet us pass now to the confrontation of our results for strange\nstars with observations of the QPOs. Nearly twenty LMXBs,\nexhibiting QPOs, have been observed (van der Klis 2000). The\nupper-peak frequency, $\\nu^{\\rm u.p.}_{\\rm QPO}$, is usually\ninterpreted as the frequency of the orbital motion around a\nneutron star. The most general observational constraint on a\nneutron star in LMXB is thus $\\nu^{\\rm u.p.}_{\\rm QPO} \\le\n\\nu_{\\rm ISCO}$. Highest observed $\\nu^{\\rm u.p.}_{\\rm\nQPO}$ is {\\chng $1329\\pm 4$ Hz in 4U 0614+09 (van Straaten et al. \\cite{Straaten}). \nCondition $\\nu_{\\rm ISCO}\\ge 1.33$~kHz is satisfied by nearly all strange star\nmodels displayed in Fig. 2 (except those rotating very close to \nthe Keplerian frequency and slowly rotating maximum mass model). \nIn particular for the spin frequency of the star $\\nu_{\\rm spin}=312$~Hz\n(Ford et al. \\cite{Ford97}, van Straaten et al. \\cite{Straaten}) all\nstellar configurations for SQM1 model of strange matter are allowed.} \n\nFor neutron stars, condition $\\nu_{\\rm ISCO}\\ge 1.2$~kHz \n{\\chng (considered by Thampan et al. 1999 as the highest \n$\\nu^{\\rm u.p.}_{\\rm QPO}$)}\neliminates stellar masses below some limit, ranging from \n$0.6~{\\rm M_\\odot}$ for\nstiff EOS to $1.4~{\\rm M_\\odot}$ for soft EOS (Thampan et al.\n1999). In this case the innermost allowed orbit is defined by the\nradius of the star and corresponds to the Keplerian frequency\nat the surface $\\nu_{\\rm K}$. {\\chng This conclusion would be stronger \nin the case of $\\nu^{\\rm u.p.}_{\\rm QPO}=1.33$~kHz excluding the\nsoftest EOS and shifting the above mass limits to a little higher values\n(see Fig 1. in the paper by Thampan et al. 1999).} \nSuch a constraint does not apply to bare strange stars, for which in\nthe limit of $M\\ll {\\rm M_\\odot}$ one gets $\\nu_{\\rm K}\\simeq\n(G\\rho_{\\rm sm}/3\\pi)^{1/2}= 0.841\\cdot (\\rho_{\\rm\nsm,14})^{1/2}$~kHz, where $\\rho_{\\rm sm,14}$ is the density of\nstrange matter at zero pressure, in the units of $10^{14}~{\\rm\ng/cm^3}$. For reasonably high values of $\\rho_{\\rm sm}$, in\nparticular for those considered in the present paper, one gets\n{\\chng $\\nu_{\\rm K}>1.33$~kHz } for low-mass, \nslowly rotating bare strange stars.\nIn the case of strange stars with crust, condition $\\nu_{\\rm\nK}>1.33$~kHz turns out to be violated for $M\\la 0.4~{\\rm M}_\\odot$.\n\n\nThe behavior of QPOs in 4U 1820-30 has been interpreted as\nevidence for $\\nu^{\\rm u.p.}_{\\rm QPO}=\\nu_{\\rm ms}$ in this LMXB\n(Kaaret et al. 1999, and references therein). Accepting such an\ninterpretation of $\\nu^{\\rm u.p}_{\\rm QPO}= 1.07$ kHz implies\nstrong constraints on neutron star model, and therefore, on the\nneutron star EOS\n(Klu{\\'z}niak 1998, Miller et al. 1998). Only a few existing EOS\nof neutron star matter allow simultaneously for $R_{\\rm eq}<R_{\\rm ms}$ and\n$\\nu_{\\rm ms}=1.07~$kHz. It is clear from Fig. 2 that\nSQM1 models of strange stars cannot give $\\nu_{\\rm ISCO}$ as\nlow as 1.07 kHz at slow rotation rates. In the case of the SQM0\nEOS one is able to get such low $\\nu_{\\rm ISCO}$ for bare strange\nstars of $M\\la 1.4~{\\rm M}_\\odot$ rotating close to Keplerian\nfrequency; we confirm in this way result of Stergioulas et al.\n(1999). However, as we see in Fig. 2, passing to an EOS which at\nthe same value of $B$ includes effects of strange quark mass and\nof lowest order QCD interaction increases the values of $\\nu_{\\rm\nISCO}$ of bare strange stars at high rotation rates to such\nextent, that the value of $1.07$~kHz cannot be\nreproduced.The presence of solid crust on rotating\nstrange stars described by the ``standard strange matter EOS''\nSQM1 excludes $\\nu_{\\rm ISCO}(\\nu_{\\rm K})$ lower than 1.2 kHz. In\nthe case of the simplest SQM0 EOS the value of $\\nu_{\\rm\nISCO}(\\nu_{\\rm K})$ is increased by the presence of the crust a little\nabove 1.07 kHz. Generally, the presence of the crust on rotating\nstrange star with standard strange matter EOS, such as SQM1 (or\nSQM0) excludes possibility of getting $\\nu_{\\rm ISCO}$ as low as\n1.07 kHz for any possible rotation rates.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{MIT Bag Model of strange matter consistent with\nQPO observations}\n%\n\nIn order to get $\\nu_{\\rm ISCO}$ as low as 1.07 kHz at slow and moderate\nrotation rates, one has\nto consider a specific set of the MIT Bag Model parameters,\n characterized by significantly lower values of both $B$ and\n$m_{\\rm s}$, and higher value of $\\alpha_{\\rm c}$, than those\ncharacteristic of the SQM1 model. In this way one is able to\nincrease significantly the value of $M_{\\rm max}^{\\rm stat}$, and\nget ISCO frequencies as low as 1 kHz at slow rotation rates.\nFor such a choice of EOS it is also relatively easy to\nget $\\nu_{\\rm ISCO}\\la 1$~kHz for a broad range of masses of\nconfigurations rotating close to the Keplerian limit\n (see below). An example of\nsuch an EOS, hereafter referred to as the SQM2, was obtained assuming\n$B=40~{\\rm MeV/fm^3}$, $m_{\\rm s}=100~{\\rm MeV/c^2}$, and\n$\\alpha_{\\rm c}=0.6$. At zero pressure, the SQM2 model yields\nenergy per unit baryon number $E_0=874.2$~ MeV. Let us stress\nthat despite the relatively low value of $B$, the standard condition\nthat neutrons do not fuse (coagulate) spontaneously into\nstrangelets (droplets of quark matter), is satisfied by this\nmodel. Maximum mass of static strange stars for the SQM2 EOS is $2.3~{\\rm\nM}_\\odot$.\n\n%%%%%%%%%%%%%%%%%fig4%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure} %4\n \\resizebox{\\hsize}{!}{\\includegraphics[angle=-90]{zdunik4.eps}}\n\\caption{Frequency of ISCO versus rotation frequency of strange star\n for the SQM2 EOS of strange matter (see the text).\nLines correspond to stellar\nmodels with fixed total baryon number,\n equal to that of a static star of the gravitational mass\nof $1.6,~1.8,~2.0, ~2.25~{\\rm M}_\\odot$,\n Lower thin horizontal line:\n upper-peak frequency observed in 4U 1820-30, 1.07~kHz. \nUpper horizontal line:\n maximum upper-peak frequency observed in the QPOs\nin LMXBs, 1.33~kHz. Keplerian configurations for strange stars with crust\nare indicated by filled circles. Segments of curves below filled circles\ncorrespond to bare strange stars. Maximum mass for static strange stars\nis 2.3~${\\rm M}_\\odot$. } \\label{fig4}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\n\nOur SQM2 model is a rather extreme one, as far as the\nvalues of the $B$, $m_{\\rm s}$, and $\\alpha_{\\rm c}$ parameters\nare concerned. Canonical value of $B$, resulting from fitting\nhadronic masses, is $59~{\\rm MeV/fm^3}$ (De Grand et al. 1975),\nsignificantly higher than $B=40~{\\rm MeV/fm^3}$ used in the SQM2\nmodel. On the other hand, $m_{\\rm s} = 100~{\\rm MeV/c^2}$ of the\nSQM2 model is on the lower side of usually considered $m_{\\rm s}$\nvalues (Farhi \\& Jaffe 1984, Madsen 1999). Finally, $\\alpha_{\\rm\nc}=0.6$ is on the upper side of the interval of the $\\alpha_{\\rm\nc}$ values considered in the strange matter calculations\n(Farhi \\& Jaffe 1984).\n\nOur results for the SQM2 EOS, analogous to those displayed in Fig.~1\nand Fig. 2 for the SQM1 EOS, are shown in Fig.~3 and Fig.~4.\nThe main differences between these models can be explained by the\nscaling laws with the bag constant, discussed in\nSect. 5. The features of $R_{\\rm ms}$ and radius\nof the rotating strange star of given mass for SQM1 model corresponds to\nthe star SQM2 with the mass larger by the\nfactor $\\sim (B_1/B_2)^{1/2}$.\n As one can see in Fig.~4, slowly rotating strange stars\n can have ISCO frequencies as low as $1-1.1$ kHz,\nprovided their mass is sufficiently high, $M\\simeq 2.2-2.3~\\msol$\njust because maximum allowable mass\nfor static strange stars is sufficiently high. Moreover,\nfor bare strange stars,\nthe ISCO frequency below 1~kHz can also be reached for\n very rapid rotation close to the Keplerian limit. Less massive is\nbare strange star, lower is the ISCO frequency reached at the\nKeplerian limit. The presence of the solid crust makes\nthe window (subset) of rapidly rotating configurations\nallowing for\n$\\nu_{\\rm ISCO}=1.07$~kHz significantly narrower.\n These configurations are very close to the Keplerian ones.\nNotice that the SQM2 EOS is simultaneously consistent with\n$\\nu_{\\rm ISCO}\\ge 1.33$~kHz, provided the strange star mass $M\\la 1.8~{\\rm\nM}_\\odot$.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Discussion and conclusion}\n%\nThe features of ISCOs around rapidly rotating\nstrange stars, described\nin the present paper\n for a particular choice of strange matter EOS, are actually\ngeneric.\nThe MIT Bag Model EOS of strange quark matter depends on $B$, $m_{\\rm s}$,\nand $\\alpha_{\\rm c}$ in a way, which implies specific scaling properties\nwith respect to change of $B$ (Haensel et al. 1986, Zdunik \\& Haensel 1990).\n As a consequence, the global parameters of rotating strange stars scale with\nsome power of $B$, which allows one to determine the values of $M$,\n$R_{\\rm eq}$, $R_{\\rm ms}$, etc., for $B$, $\\alpha_{\\rm c}$, and\n$m_{\\rm s}$, from those calculated\n for $B_0$, $\\alpha_{\\rm c}$ and strange quark mass\n $m_{\\rm s}(B_0/B)^{1/4}$. All length-type quantities\n(stellar radius, thickness of the\ncrust and radius of the ISCO) scale as\n$B^{-1/2}$, and all frequencies ($\\nu_{\\rm ISCO}$, $\\nu_{\\rm rot}$)\nscale as\n $B^{1/2}$, e.g.,\n$\\nu_{\\rm ISCO}[B]=\\nu_{\\rm ISCO}[B_0]\\cdot (B/B_0)^{1/2}$ and\n$R_{\\rm ms}[B]=R_{\\rm ms}[B_0]\\cdot (B/B_0)^{-1/2}$. Thus, for\nother values of $B$ the patterns of lines in Figs. 1-4 do not\nchange, provided one rescales the axes and stellar masses.\n\nOur calculations show that the properties of the ISCOs around strange stars\ndiffer from those around neutron stars.\nA generic property is the existence of the\ngap between the ISCO and the stellar surface, for both slowly and rapidly\nrotating strange stars.\n\nThe highest observed QPO frequency of {\\chng 1.33 kHz in 4U\n0614+91} can be easily interpreted as an orbital frequency around\nstrange star based on the standard SQM1 EOS of strange matter,\nwith no significant constraint on strange star mass and rotation\nrate. In the case of the SQM2 EOS, the orbital origin of the {\\chng 1.33\nkHz QPO implies $M\\la 1.8~{\\rm M}_\\odot$ at rotation frequencies\n$\\sim 300$~Hz}, while frequencies close to the mass shedding limit are\nexcluded. \n\nThe value of the ISCO frequency at the\nKeplerian limit is significantly influenced by the presence of a\ncrust on the strange star\nsurface, which increases this frequency\n by about hundred Hz compared to the value for\na bare strange star of the same mass.\nAs one expects the presence of\na crust on a strange star in a LMXB, we conclude that only\nslowly rotating strange\nstars with mass above $2.2~{\\rm M}_\\odot$ seem to be consistent\nwith $\\nu_{\\rm ISCO}=1.07$~kHz. This excludes EOS of strange matter\ncorresponding to the standard bag model parameters, and can be\nsatisfied only by choosing a set of parameters quite different\nfrom the standard one.\n\n\nThe numerical results discussed in the present paper show that\nconsistency of the ISCOs around slowly rotating strange stars\n with orbital-motion\ninterpretation of QPOs in LMXBs can be achieved only with a\nsubstantial tuning of the MIT Bag Model parameters of strange\nmatter.\nOur SQM2 EOS is a result of such a tuning. For this EOS,\nthe condition $\\nu_{\\rm ISCO}\\simeq 1$~kHz is satisfied not only\nfor slowly rotating massive models with $M\\ga 2.2~{\\rm M}_\\odot$,\nbut also for a broad range of masses of configurations close to\nthe Keplerian limit.\nIn contrast to $\\nu_{\\rm ISCO}$ at low rotation rate,\nwhich decreases with increasing baryon mass, the ISCO frequency at the\nKeplerian limit decreases with decreasing baryon mass of rotating\nstrange star.\n\n\n%\n%\n\\begin{acknowledgements}\nDuring his stay at DARC, Observatoire de Paris, P. Haensel was\nsupported by the PAST professorship of French MENRT. This research\nwas partially supported by the KBN grants No. 2P03D.014.13, 2P03D.021.17.\nThe numerical calculations have been performed on computers purchased\nthanks to a special grant from the SPM and SDU departments of\nCNRS. We are very grateful to the referee, P. Kaaret, for helpful\ncomments and suggestions, which influenced the final version of\nthe present paper.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{} % (do not forget {})\n\n\\bibitem[1986]{Alcock86}\nAlcock C., Farhi C.E., Olinto A., 1986, ApJ 310, 261\n\n\\bibitem[1997]{Alpar97}\nAlpar M.A., Yilmaz, A., 1997, New Astronomy 2, 225\n\n\n\\bibitem[1997]{Bombaci97}\nBombaci I., 1997, Phys. Rev. C 55, 1587\n\n%\\bibitem[1993]{bona93}\n%Bonazzola S., Gourgoulhon E., Salgado M., Marck J.A., 1993, A\\&A\n%278, 421\n\n\n\\bibitem[1998]{Bona98}\nBonazzola S., Gourgoulhon E., Marck J.A., 1998, Phys. Rev. D 58,\n104020\n\n\n\\bibitem[1999]{Bulik99}\nBulik T., Gondek-Rosi{\\'n}ska D., Klu{\\'z}niak W. 1999, A\\&A 344,\nL71\n\n\n\\bibitem[1998]{Cheng98}\nCheng K.S., Dai Z.G., Wei D.M., Lu T., 1998,\n Science 280, 407\n\n\n\\bibitem[1994]{CST94a}\nCook G.B., Shapiro S.L., Teukolsky S.A., 1994a, ApJ 422, 227\n\n\\bibitem[1994]{CST94b}\nCook G.B., Shapiro S.L., Teukolsky S.A., 1994b, ApJ 424, 823\n\n\\bibitem[1998]{Dai98}\nDai Z.G., Lu T., 1998, Phys. Rev. Lett. 81, 4301\n\n\\bibitem[1998]{Datta98}\nDatta D., Thampan A.V., Bombaci I., 1998, A\\&A 334, 943\n\n\n\\bibitem[1975]{DeGrand75}\nDe Grand T., Jaffe R.L., Johnson K., Kiskis J., 1975, Phys. Rev. D\n12, 2060\n\n\\bibitem[1984]{FJ84}\nFarhi E., Jaffe R.L., 1984, Phys. Rev. D 30, 2379\n\n\\bibitem[1997]{Ford97}\nFord E.C., Kaaret P., Tavani M., et al., 1997, ApJ 475, L123\n\n\\bibitem[1992]{GW92}\nGlendenning N.K., Weber F., 1992, ApJ 400, 647\n\n%\\bibitem[1997]{Glend97}\n%Glendenning N.K., 1997,\n%Compact Stars: Nuclear Physics, Particle Physics and General\n%Relativity, Springer, New York\n\n\\bibitem[1999]{Gour99}\n%Gourgoulhon E., Haensel P., Livine R., Paluch E.,Bonazzola S., Marck J.A., \nGourgoulhon E., Haensel P., Livine R., et al., \n1999, A\\&A 349, 851\n\n\\bibitem[1991]{HZ91}\nHaensel P., Zdunik J.L., 1991, Nucl. Phys. B (Proc. Suppl.) 24B,\n139\n\n\\bibitem[1986]{HZS86}\nHaensel P., Zdunik J.L., Schaeffer R., 1986, A\\&A 160, 121\n\n\\bibitem[1997]{HuangL97}\nHuang Y.F., Lu T., 1997, A\\&A 325, 189\n\n\\bibitem[1997]{Kaaret97}\nKaaret P., Ford E.C., Chen K., 1997, ApJ 480, L27\n\n\\bibitem[1999]{Kaaret99}\n%Kaaret P., Piraino S., Bloser P.F., Ford E.C., Grindlay J.E.,\n%Santangelo A., Smale A.P., Zhang W., 1999, ApJ 520, L37\nKaaret P., Piraino S., Bloser P.F., et al., 1999, ApJ 520, L37\n\n\\bibitem[1998]{Kluzniak98}\nKlu{\\'z}niak W., 1998, ApJ 509, L37\n\n\\bibitem[1985]{KluzniakWag85}\nKlu{\\'z}niak W., Wagoner R.V., 1985, ApJ 297, 548\n\n\\bibitem[1990]{Kluzniak90}\nKlu{\\'z}niak W., Michelson P., Wagoner R.V., 1990, ApJ 358, 538\n\n\\bibitem[1999]{Li99}\nLi X.-D., Bombaci I., Dey M., Dey J., van den Heuvel E.P.J., 1999,\nPhys. Rev. Lett. 83, 3776\n\n\n\\bibitem[1999]{Madsen99}\nMadsen J., 1999,\nin Hadrons in Dense Matter and Hadrosynthesis, Lecture Notes in\nPhysics, Cleymans~J. (ed.). Springer-Verlag, p.162\n\n\\bibitem[1998]{Miller98}\nMiller M.C., Lamb F.K., Cook G.B., 1998, ApJ 509, 793\n\n\n\\bibitem[1990]{Miralda90}\nMiralda-Escud{\\'e} J., Haensel P., Paczy{\\'n}ski B., 1990, ApJ\n362, 572\n\n\n\\bibitem[1999]{Schaab99}\nSchaab C., Weigel M.K., 1999, MNRAS 308, 718\n\n\\bibitem[1998]{Shibata99}\nShibata M., Sasaki M., 1998, Phys. Rev D58, 104011\n\n\\bibitem[1999]{Sterg99}\nStergioulas N., Klu{\\'z}niak W., Bulik T., 1999,\nA\\&A 352, L116\n\n\\bibitem[1999]{Thampan99}\nThampan A.V., Bhattacharya D., Datta D., 1999, MNRAS 302, L69\n\n\\bibitem[1999]{Titarch99}\nTitarchuk, L., Osherovich, V., 1999, ApJ 518, L95\n\n\\bibitem[1998]{VdKlis00}\nvan der Klis M., 2000,\nto appear in the Proceedings of the Third William Fairbank Meeting,\nRome June 29-July 4, 1998. E-print: astro-ph/9812392\n\n\\bibitem[2000]{Straaten}\nvan Straaten S., Ford E., van der Klis M., M\\'endez M., Kareet\nP., 2000, E-print: astro-ph/0001480\n\n\\bibitem[1984]{Witt84}\nWitten E., 1984, Phys. Rev. D 30, 272\n\n\n\\bibitem[1990]{Zdunik90}\nZdunik J.L., Haensel P., 1990, Phys. Rev. D 42, 710\n\n\n%\\bibitem[1997]{Zhang97} Zhang et al. 1997 IAUC 6541\n\n\\bibitem[1998]{Zhang98}\nZhang W., Strohmayer T.E., Swank J.H., 1998, ApJ 482, L167\n\n\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002394.extracted_bib",
"string": "\\begin{thebibliography}{} % (do not forget {})\n\n\\bibitem[1986]{Alcock86}\nAlcock C., Farhi C.E., Olinto A., 1986, ApJ 310, 261\n\n\\bibitem[1997]{Alpar97}\nAlpar M.A., Yilmaz, A., 1997, New Astronomy 2, 225\n\n\n\\bibitem[1997]{Bombaci97}\nBombaci I., 1997, Phys. Rev. C 55, 1587\n\n%\\bibitem[1993]{bona93}\n%Bonazzola S., Gourgoulhon E., Salgado M., Marck J.A., 1993, A\\&A\n%278, 421\n\n\n\\bibitem[1998]{Bona98}\nBonazzola S., Gourgoulhon E., Marck J.A., 1998, Phys. Rev. D 58,\n104020\n\n\n\\bibitem[1999]{Bulik99}\nBulik T., Gondek-Rosi{\\'n}ska D., Klu{\\'z}niak W. 1999, A\\&A 344,\nL71\n\n\n\\bibitem[1998]{Cheng98}\nCheng K.S., Dai Z.G., Wei D.M., Lu T., 1998,\n Science 280, 407\n\n\n\\bibitem[1994]{CST94a}\nCook G.B., Shapiro S.L., Teukolsky S.A., 1994a, ApJ 422, 227\n\n\\bibitem[1994]{CST94b}\nCook G.B., Shapiro S.L., Teukolsky S.A., 1994b, ApJ 424, 823\n\n\\bibitem[1998]{Dai98}\nDai Z.G., Lu T., 1998, Phys. Rev. Lett. 81, 4301\n\n\\bibitem[1998]{Datta98}\nDatta D., Thampan A.V., Bombaci I., 1998, A\\&A 334, 943\n\n\n\\bibitem[1975]{DeGrand75}\nDe Grand T., Jaffe R.L., Johnson K., Kiskis J., 1975, Phys. Rev. D\n12, 2060\n\n\\bibitem[1984]{FJ84}\nFarhi E., Jaffe R.L., 1984, Phys. Rev. D 30, 2379\n\n\\bibitem[1997]{Ford97}\nFord E.C., Kaaret P., Tavani M., et al., 1997, ApJ 475, L123\n\n\\bibitem[1992]{GW92}\nGlendenning N.K., Weber F., 1992, ApJ 400, 647\n\n%\\bibitem[1997]{Glend97}\n%Glendenning N.K., 1997,\n%Compact Stars: Nuclear Physics, Particle Physics and General\n%Relativity, Springer, New York\n\n\\bibitem[1999]{Gour99}\n%Gourgoulhon E., Haensel P., Livine R., Paluch E.,Bonazzola S., Marck J.A., \nGourgoulhon E., Haensel P., Livine R., et al., \n1999, A\\&A 349, 851\n\n\\bibitem[1991]{HZ91}\nHaensel P., Zdunik J.L., 1991, Nucl. Phys. B (Proc. Suppl.) 24B,\n139\n\n\\bibitem[1986]{HZS86}\nHaensel P., Zdunik J.L., Schaeffer R., 1986, A\\&A 160, 121\n\n\\bibitem[1997]{HuangL97}\nHuang Y.F., Lu T., 1997, A\\&A 325, 189\n\n\\bibitem[1997]{Kaaret97}\nKaaret P., Ford E.C., Chen K., 1997, ApJ 480, L27\n\n\\bibitem[1999]{Kaaret99}\n%Kaaret P., Piraino S., Bloser P.F., Ford E.C., Grindlay J.E.,\n%Santangelo A., Smale A.P., Zhang W., 1999, ApJ 520, L37\nKaaret P., Piraino S., Bloser P.F., et al., 1999, ApJ 520, L37\n\n\\bibitem[1998]{Kluzniak98}\nKlu{\\'z}niak W., 1998, ApJ 509, L37\n\n\\bibitem[1985]{KluzniakWag85}\nKlu{\\'z}niak W., Wagoner R.V., 1985, ApJ 297, 548\n\n\\bibitem[1990]{Kluzniak90}\nKlu{\\'z}niak W., Michelson P., Wagoner R.V., 1990, ApJ 358, 538\n\n\\bibitem[1999]{Li99}\nLi X.-D., Bombaci I., Dey M., Dey J., van den Heuvel E.P.J., 1999,\nPhys. Rev. Lett. 83, 3776\n\n\n\\bibitem[1999]{Madsen99}\nMadsen J., 1999,\nin Hadrons in Dense Matter and Hadrosynthesis, Lecture Notes in\nPhysics, Cleymans~J. (ed.). Springer-Verlag, p.162\n\n\\bibitem[1998]{Miller98}\nMiller M.C., Lamb F.K., Cook G.B., 1998, ApJ 509, 793\n\n\n\\bibitem[1990]{Miralda90}\nMiralda-Escud{\\'e} J., Haensel P., Paczy{\\'n}ski B., 1990, ApJ\n362, 572\n\n\n\\bibitem[1999]{Schaab99}\nSchaab C., Weigel M.K., 1999, MNRAS 308, 718\n\n\\bibitem[1998]{Shibata99}\nShibata M., Sasaki M., 1998, Phys. Rev D58, 104011\n\n\\bibitem[1999]{Sterg99}\nStergioulas N., Klu{\\'z}niak W., Bulik T., 1999,\nA\\&A 352, L116\n\n\\bibitem[1999]{Thampan99}\nThampan A.V., Bhattacharya D., Datta D., 1999, MNRAS 302, L69\n\n\\bibitem[1999]{Titarch99}\nTitarchuk, L., Osherovich, V., 1999, ApJ 518, L95\n\n\\bibitem[1998]{VdKlis00}\nvan der Klis M., 2000,\nto appear in the Proceedings of the Third William Fairbank Meeting,\nRome June 29-July 4, 1998. E-print: astro-ph/9812392\n\n\\bibitem[2000]{Straaten}\nvan Straaten S., Ford E., van der Klis M., M\\'endez M., Kareet\nP., 2000, E-print: astro-ph/0001480\n\n\\bibitem[1984]{Witt84}\nWitten E., 1984, Phys. Rev. D 30, 272\n\n\n\\bibitem[1990]{Zdunik90}\nZdunik J.L., Haensel P., 1990, Phys. Rev. D 42, 710\n\n\n%\\bibitem[1997]{Zhang97} Zhang et al. 1997 IAUC 6541\n\n\\bibitem[1998]{Zhang98}\nZhang W., Strohmayer T.E., Swank J.H., 1998, ApJ 482, L167\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002395
|
Properties of spherical galaxies and clusters with an NFW density profile
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{
"author": "\\L"
}
] |
Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high resolution cosmological $N$-body simulations by Navarro, Frenk \& White. We adopt three models for the internal kinematics: isotropic velocities, constant anisotropy and increasingly radial Osipkov-Merritt anisotropy. Analytical solutions are found for the radial dependence of the mass, gravitational potential, velocity dispersion, energy and virial ratio and we test their variability with the concentration parameter describing the density profile and amount of velocity anisotropy. We also compute structural parameters, such as half-mass radius, effective radius and various measures of concentration. Finally, we derive projected quantities, the surface mass density and line-of-sight as well as aperture velocity dispersion, all of which can be directly applied in observational tests of current scenarios of structure formation. On the mass scales of galaxies, if constant mass-to-light is assumed, the NFW surface density profile is found to fit well Hubble-Reynolds laws. It is also well fitted by S\'ersic $R^{1/m}$ laws, for $m \simeq 3$, but in a much narrower range of $m$ and with much larger effective radii than are observed. Assuming in turn reasonable values of the effective radius, the mass density profiles imply a mass-to-light ratio that increases outwards at all radii.
|
[
{
"name": "proper1.tex",
"string": "%\\documentstyle[referee]{mn}\n% final version\n\\documentstyle{mn}\n\\input{epsf}\n\\input{rotate}\n\n\\title[Properties of galaxies and clusters]{Properties of\nspherical galaxies and clusters with an NFW density profile}\n\n\\author[Ewa L. {\\L}okas and Gary A. Mamon]{Ewa L. {\\L}okas$^1$ and Gary A.\n Mamon$^{2,3}$\\\\ $^1$Copernicus Astronomical Center, Bartycka 18,\n 00--716 Warsaw, Poland\\\\ $^2$Institut d'Astrophysique de Paris\n (CNRS UPR 341), 98 bis Bd Arago, F--75014 Paris, France \\\\ $^3$DAEC\n (CNRS UMR 8631), Observatoire de Paris,\n Place Jules Janssen, F--92195 Meudon, France}\n\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\nUsing the standard dynamical theory of spherical systems, we\ncalculate the properties of spherical galaxies and clusters whose density\nprofiles obey the universal form first obtained in high resolution\ncosmological $N$-body simulations by Navarro, Frenk \\& White.\nWe adopt three models for the internal kinematics: isotropic\nvelocities, constant anisotropy and increasingly radial Osipkov-Merritt\nanisotropy.\nAnalytical solutions are found for the radial\ndependence of the mass, gravitational\npotential, velocity dispersion, energy and virial ratio and we test their\nvariability with the concentration parameter describing the density\nprofile and amount of velocity anisotropy.\nWe also compute structural parameters, such as half-mass radius,\neffective radius and various measures of concentration. Finally, we derive\nprojected quantities, the surface mass density and line-of-sight as well\nas aperture velocity dispersion, all of which can be directly applied in\nobservational tests of current scenarios of structure formation.\n\nOn the mass scales of galaxies, if constant mass-to-light is assumed, the\nNFW surface density profile is found to fit well Hubble-Reynolds\nlaws. It is also well fitted by S\\'ersic $R^{1/m}$ laws, for $m \\simeq 3$,\nbut in a much narrower range of $m$ and with much larger effective radii\nthan are observed. Assuming in turn reasonable values of the effective\nradius, the mass density profiles imply a mass-to-light ratio that\nincreases outwards at all radii.\n\n\\end{abstract}\n\n\\begin{keywords}\nmethods: analytical -- galaxies: clusters: general -- large--scale\nstructure of Universe\n\\end{keywords}\n\n\\section{Introduction}\n\nA universal profile of dark matter haloes was introduced as a result\nof high-resolution $N$-body simulations performed by Navarro, Frenk \\&\nWhite (1995, 1996, 1997, hereafter NFW) for power-law as well as CDM\ninitial power spectra of density fluctuations. NFW found that in a\nlarge range of masses the density profiles of dark haloes can be fitted\nwith a simple formula with only one fitting parameter. The density profile\nsteepens from $r^{-1}$ near the centre of the halo to $r^{-3}$ at large\ndistances. The NFW profile has been confirmed in cosmological simulations\nby Cole \\& Lacey (1996), Tormen, Bouchet \\& White (1997), Huss, Jain \\&\nSteinmetz (1999a), Jing (2000), Bullock et al. (1999), while Huss, Jain \\&\nSteinmetz (1999b) have shown that the NFW profile also arises from\nnon-cosmological initial conditions. It is worthwhile noting that some\n(but not all) recent very high resolution cosmological simulations produce\nsteeper density profiles, with inner slopes $\\simeq -1.5$ (Fukushige \\&\nMakino 1997, Moore et al. 1998, Ghigna et al. 1999, see also Jing \\& Suto\n2000). The density profiles in the cosmological simulations also display\nconsiderable scatter (Avila-Reese et al. 1999, Bullock et al. 1999), and\nAvila-Reese et al. find that the outer slopes of galaxy size haloes are\nsteeper than the NFW slope of $-3$ when selected within clusters ($-4$)\nand slightly shallower within groups ($-2.7$). Although the exact\nproperties of dark matter haloes are still under debate, the NFW profile is\npresently considered to provide the reference frame for any further\nnumerical research on density profiles of dark haloes.\n\nSimple cosmological derivations of the density profiles of bound\nobjects are difficult, essentially because one needs to work in the\nnon-linear regime of the growth of gravitational instabilities.\nNevertheless, using the spherical top-hat model of Gunn \\& Gott\n(1972), density profiles typically varying as $r^{-9/4}$ were derived by\nGott (1975), Gunn (1977), Fillmore \\& Goldreich (1984) and Bertschinger\n(1985). Hoffman \\& Shaham (1985) applied the spherical infall model to the\nhierarchical clustering scenario and predicted that the density profiles of\nhaloes should depend on $\\Omega$ as well as the initial power spectrum of\ndensity fluctuations. However, for $\\Omega=1$ they obtained power-law\nprofiles in contradiction with the steepening slopes found in the current\n$N$-body simulations described above. In a recent study, \\L okas (2000)\nhas improved the model of Hoffman \\& Shaham\n(1985) by a generalization of the initial density distribution, the\nintroduction of a cut-off in this distribution at half the inter-peak\nseparation and by a proper calculation of the collapse factor. The\nimproved model reproduces the changing slope of the density profile and its\ndependence on halo mass and the type of cosmological power spectrum found by\nNFW. The NFW profile is also reproduced in studies taking into account\nthe merging mechanism (see Lacey \\& Cole 1993) in the halo formation\nscenario (e.g. Salvador-Sol\\'{e}, Solanes \\& Manrique 1998, Avila-Reese,\nFirmani \\& Hernandez 1998). Therefore the numerical and analytical\nconsiderations seem to converge on the statement that the density\nprofiles of dark matter haloes are indeed well described by the universal\nformula proposed by NFW.\n\nThe ultimate test of both the analytical and numerical results must come\nfrom the observations of density profiles of galaxies and\ngalaxy clusters. Three recent studies of clusters (Carlberg et al. 1997,\nAdami et al. 1998, van der Marel et al. 2000) claim good agreement between\ncluster observations and the NFW mass density profile. But for galaxies,\nthe situation is less satisfying. Flores \\& Primack (1994) show that the\nNFW profile is incompatible with the rotation curves of spiral galaxies,\nwhile Kravtsov et al. (1998) estimate that the inner slope of the density\nprofile of dwarf irregular and LSB galaxies is $-0.3$ instead of $-1$.\nHowever, these conclusions were obtained with a number of assumptions and\napproximations concerning the very unclear issues of biasing,\nnon-sphericity of objects and so on. Besides, as pointed out by van den\nBosch et al. (2000), Swaters, Madore \\& Trewhella (2000) and van den Bosch\n\\& Swaters (2000), the observed rotation curves of these galaxies are too\nuncertain to discriminate between cores and cusps.\n\nThe main motivation for this research is to explore analytically\nthe physical properties of objects with NFW density profiles.\nThe aim is to check whether these properties are acceptable from the\nphysical point of view and thus to test the validity of density profiles\nobtained in cosmological $N$-body simulations. Additionally, this paper\npresents formulae for observable quantities that can be used for\ncomparisons between the theoretical predictions (such as the NFW profile)\nand observations.\n\nThe paper is organized as follows: after a short presentation of\nthe universal formula for the density profile proposed by NFW, in\nSection~2 we describe physical properties of spherical systems following\nfrom this density profile. Section~3 is devoted to a simple comparison between\nthe projected NFW density profile and the surface brightness of elliptical\ngalaxies. A more thorough comparison is beyond the scope of the present\npaper and will be given elsewhere (Mamon \\& {\\L}okas, in preparation).\nThe discussion follows in Section~4.\n\n\\section{Properties of the NFW model}\n\n\\subsection{Basic properties}\n\nNFW established that the density profiles of dark\nmatter haloes in high resolution cosmological simulations for a wide range\nof masses and for different initial power spectra of density fluctuations\nare well fitted by the formula\n\\begin{equation} \\label{c1}\n \\frac{\\rho(r)}{\\rho_c^0} = \\frac{\\delta_{\\rm char}}{(r/r_{\\rm\n s})\\,(1+r/r_{\\rm s})^{2}}\n\\end{equation}\nwith a single fitting parameter $\\delta_{\\rm char}$, the characteristic\ndensity. The so-called scale radius $r_{\\rm s}$ is defined by\n\\begin{equation} \\label{c2}\n r_{\\rm s} = \\frac{r_{v}}{c} \\ ,\n\\end{equation}\nwhere $r_{v}$ is the virial radius usually defined as the distance from the\ncentre of the halo within which the mean density is $v$ times the\npresent critical density, $\\rho_c^0$. The value of the virial\noverdensity $v$ is often assumed to be $v=178$, a number predicted\nby the simplest version of the spherical model for $\\Omega=1$. For other\ncosmological models it can be lower by a factor of 2 or more\n(Lacey \\& Cole 1993, Eke, Cole \\& Frenk 1996). However, according\nto the improved spherical infall model (\\L okas 2000) $v$ can be as low\nas 30 even for $\\Omega=1$. In the following, $v$ is kept as a free parameter.\n\nThe quantity $c$ introduced in equation (\\ref{c2})\nis the concentration parameter, which is related to the\ncharacteristic density by\n\\begin{equation} \\label{c3}\n \\delta_{\\rm char} = \\frac{v \\,c^3 g(c)}{3} \\ ,\n\\end{equation}\nwhere\n\\begin{equation} \\label{c4}\n g(c) = \\frac{1}{\\ln (1+c) - c/(1+c)} \\ .\n\\end{equation}\nThe concentration parameter will be used hereafter as the only parameter\ndescribing the shape of density profile. From cosmological\n$N$-body simulations (Navarro et al. 1997, Jing 2000, Bullock et\nal. 1999, Jing \\& Suto 2000), extended Press-Schechter theory (Navarro et\nal. 1997, Salvador-Sol\\'e, Solanes \\& Manrique 1998), and the spherical\ninfall model (\\L okas 2000), we know that $c$ depends on the mass of\nobject and the form of the initial power spectrum of density fluctuations.\nFor all initial power spectra, the observed trend is for lower\nconcentration parameter in higher mass objects, with $4 < c < 22$ in\ncosmological simulations with CDM initial power spectra and $c$ up to 90\nfor the less realistic scale-free power spectra. More precisely, in the\n$\\Lambda$CDM cosmology, $c=5$ corresponds to the masses of clusters of\ngalaxies, while $c=10$ corresponds to the masses of bright galaxies.\n\nIt is convenient to express the distance from the centre of the object in\nunits of the virial radius $r_{v}$:\n\\begin{equation} \\label{c5}\n s=\\frac{r}{r_{v}}\n\\end{equation}\nand the density profile of equation (\\ref{c1}) then becomes\n\\begin{equation} \\label{c6}\n \\frac{\\rho(s)}{\\rho_c^0} = \\frac{v \\,c^2 g(c)}{3 \\,s\\,(1+ c\n s)^2} \\ .\n\\end{equation}\n\nThe mass of the halo is usually defined as the mass within the virial\nradius:\n\\begin{equation} \\label{c7}\n M_v = \\frac{4}{3} \\,\\pi \\,r_{v}^3\\, v \\,\\rho_c^0 \\ .\n\\end{equation}\nThe distribution of mass in units of the virial mass follows from\nequation (\\ref{c6}):\n\\begin{equation} \\label{c8}\n \\frac{M(s)}{M_v} = g(c) \\left[ \\ln (1+c s) - \\frac{c s}{1 + c\n s} \\right]\n\\end{equation}\nand we see that it diverges at large $s$, which is a disadvantage of the\nmodel from a physical point of view.\n\nThe gravitational potential associated with the density distribution\n(\\ref{c6}) is\n\\begin{equation} \\label{c9}\n \\frac{\\Phi(s)}{V_v^2} = - g(c) \\,\\frac{\\ln (1 + c s)}{s} \\ ,\n\\end{equation}\nwhere $V_v$ is the circular velocity at $r=r_v$:\n\\begin{equation} \\label{c10}\n V_v^2 = V^2(r_v) = \\frac{G M_v}{r_v}\n = \\frac{4}{3} \\,\\pi \\,G \\,r_{v}^2 \\,v \\,\\rho_c^0 \\ .\n\\end{equation}\nHence, from equation~(\\ref{c9}) we see that\nthe gravitational potential at the centre, $\\Phi(0) = - c g(c)\nV_v^2$, is finite.\n\nEquations (\\ref{c8}) and (\\ref{c10}) lead to a circular\nvelocity that obeys\n\\begin{equation} \\label{c12}\n \\frac{V^2(s)}{V_v^2} = \\frac{g(c)}{s} \\left[ \\ln (1+c s) -\n \\frac{c s}{1 + c s} \\right] \\ .\n\\end{equation}\nEquations~(\\ref{c8}), (\\ref{c9}) and (\\ref{c12}) were first derived by Cole\n\\& Lacey (1996).\n\nThe radial velocity dispersion $\\sigma_{\\rm r}(r)$ can be obtained by\nsolving the Jeans equation\n\\begin{equation} \\label{c13}\n \\frac{1}{\\rho} \\frac{\\rm d}{{\\rm d} r} (\\rho \\sigma_{\\rm r}^2) +\n 2 \\beta \\frac{\\sigma_{\\rm r}^2}{r} = -\\frac{{\\rm d} \\Phi}{{\\rm d} r} \\ ,\n\\end{equation}\nwhere $\\beta=1-\\sigma_\\theta^2(r)/\\sigma_{\\rm r}^2(r)$ is a measure of\nthe anisotropy in the velocity distribution. In the simplest case of\nisotropic orbits, $\\sigma_\\theta(r)=\\sigma_{\\rm\nr}(r)$ and $\\beta=0$. This value of $\\beta$ is also close to the results of\n$N$-body simulations: Cole \\& Lacey (1996) and Thomas et al. (1998) show\nthat, in a variety of cosmological models, the ratio\n$\\sigma_\\theta/\\sigma_{\\rm r}$ is not far from unity and decreases slowly\nwith distance from the centre to reach $\\simeq 0.8$ at the virial\nradius. However, Huss, Jain \\& Steinmetz (1999a) find\n$\\sigma_\\theta/\\sigma_{\\rm r} \\simeq 0.6$ at $r_v$.\n\nFirst we consider the case of $\\beta$=const.\nThen the solution to the equation (\\ref{c13}) with the condition of\n$\\sigma_{\\rm r} \\rightarrow 0$ at $s \\rightarrow \\infty$ is\n\\begin{eqnarray}\n \\frac{\\sigma_{\\rm r}^2}{V_v^2} (s, \\beta={\\rm const})\n &=& g(c) (1+c s)^2 s^{1-2 \\beta}\n \\nonumber \\\\\n &\\hspace{-2cm} \\times & \\hspace{-1.4cm} \\int_{s}^\\infty\n \\left[ \\frac{s^{2 \\beta - 3} \\ln (1+c\n s)}{(1+c s)^2} - \\frac{c s^{2 \\beta-2}}{(1+c s)^3} \\right] {\\rm d} s .\n \\label{c13a}\n\\end{eqnarray}\nFor $\\beta=0$, 0.5 and 1, reasonably simple analytical solutions to this\nequation can be found:\n\\begin{eqnarray}\n \\frac{\\sigma_{\\rm r}^2}{V_v^2} (s, \\beta=0)\n &=& \\frac{1}{2} c^2 \\,g(c) \\,s\n \\,(1 + c s)^2 \\ [\\pi^2 - \\ln (c s) - \\frac{1}{c s} \\nonumber \\\\\n &\\hspace{-2.8cm} - & \\hspace{-1.7cm} \\frac{1}{(1+c s)^2} -\\frac{6}{1+c s}\n + \\left(1 +\\frac{1}{c^2 s^2} - \\frac{4}{c s}\n - \\frac{2}{1+c s} \\right) \\nonumber \\\\\n &\\hspace{-2.8cm} \\times & \\hspace{-1.7cm} \\ln (1+c s)\n + 3 \\ln^2 (1+c s) + 6 \\, {\\rm Li}_2(-c s) ] \\ ,\n \\label{c14}\n\\end{eqnarray}\n\\begin{eqnarray}\n \\frac{\\sigma_{\\rm r}^2}{V_v^2} (s, \\beta=0.5)\n &=& c \\, g(c) \\, (1 + c s)^2\n [- \\frac{\\pi^2}{3} +\\frac{1}{2(1+c s)^2} \\nonumber \\\\\n &\\hspace{-2.8cm} + & \\hspace{-1.7cm} \\frac{2}{1+c s}\n +\\frac{\\ln (1+c s)}{c s} + \\frac{\\ln\n (1+c s)}{1+c s} \\nonumber \\\\\n &\\hspace{-2.8cm} - & \\hspace{-1.7cm} \\ln^2 (1+c s)\n - 2 {\\rm Li}_2 (-c s)] , \\label{c14a}\n\\end{eqnarray}\n\\begin{eqnarray}\n \\frac{\\sigma_{\\rm r}^2}{V_v^2} (s, \\beta=1)\n &=& g(c) \\, (1 + c s)^2\n \\frac{1}{s} \\left[ \\frac{\\pi^2}{6} - \\frac{1}{2(1+ c s)^2} \\right.\n \\nonumber \\\\\n &\\hspace{-2.8cm} - & \\hspace{-1.7cm} \\left. \\frac{1}{1+c s}\n - \\frac{\\ln (1+c s)}{1+c s} + \\frac{\\ln^2 (1+c s)}{2} +\n {\\rm Li}_2 (-c s) \\right]. \\label{c14b}\n\\end{eqnarray}\n\nIn the above expressions ${\\rm Li}_2 (x)$ is the dilogarithm, a special\nfunction which can be conveniently dealt with using \\emph{Mathematica}\npackages. Otherwise, it can be approximated by\n\\begin{equation} \\label{dilog}\n {\\rm Li}_2 (x) = \\int_x^0 \\!{\\ln(1-t){\\rm d}t \\over t}\n \\simeq x \\left [1\\!+\\!10^{-0.5}(- x)^{0.62/0.7} \\right ]^{-0.7} .\n\\end{equation}\nThe fit is accurate to better than 1.5\\% in the range $-100 < x < 0$.\n\nWe included the predictions for $\\beta=1$ just as a limiting case. In fact\nsuch a model with purely radial orbits and NFW density profile is not\nphysical since its distribution function is not everywhere non-negative. As\npointed out by e.g. Richstone \\& Tremaine (1984, see also \\L okas \\&\nHoffman 2000), such velocity anisotropy requires the inner density profile\nto be $r^{-2}$ or steeper for the model to be physical.\n\nA more realistic description of velocity anisotropy is provided by a model\nproposed by Osipkov (1979) and Merritt (1985) with $\\beta$ dependent on\ndistance from the centre of the object\n\\begin{equation} \\label{c14c}\n \\beta_{\\rm OM} = \\frac{s^2}{s^2 + s_{\\rm a}^2}\n\\end{equation}\nwhere $s_{\\rm a}$ is the anisotropy radius determining the transition\nfrom isotropic orbits inside to radial orbits outside.\nAs mentioned above, the results of $N$-body simulations suggest\n$\\sigma_{\\theta}/\\sigma_{\\rm r} \\simeq 0.8$ and therefore $\\beta \\simeq 0.36$\nat $s=1$, which gives $s_{\\rm a} \\simeq 4/3$, a value that we adopt here\nfor all numerical calculations.\n\nFor the Osipkov-Merritt model the solution to the Jeans equation (with\nthe same boundary condition as before) reads\n\\begin{eqnarray}\n \\frac{\\sigma_{\\rm r}^2}{V_v^2} (s, \\beta_{\\rm OM})\n &=& \\frac{g(c) s (1+c s)^2}{s^2 + s_{\\rm a}^2} \\nonumber \\\\\n &\\hspace{-2.5cm} \\times & \\hspace{-1.5cm} \\int_{s}^\\infty\n \\left[ \\frac{(s^2 + s_{\\rm a}^2) \\ln (1+c s)}{s^3 (1+c s)^2}\n - \\frac{c (s^2 + s_{\\rm a}^2)}{s^2 (1+c s)^3} \\right] {\\rm d} s\n \\label{c14d}\n\\end{eqnarray}\nand the integration gives\n\\begin{eqnarray}\n \\frac{\\sigma_{\\rm r}^2}{V_v^2} (s, \\beta_{\\rm OM})\n &=& \\frac{g(c) s (1+c s)^2}{2 (s^2 + s_{\\rm a}^2)}\n \\nonumber \\\\\n &\\hspace{-3.5cm} \\times & \\hspace{-2cm}\n \\left\\{ -\\frac{c s_{\\rm a}^2}{s} - c^2 s_{\\rm a}^2 \\ln (c s)\n + c^2 s_{\\rm a}^2 \\ln (1+c s)\n \\left( 1 +\\frac{1}{c^2 s^2} - \\frac{4}{c s} \\right) \\right. \\nonumber \\\\\n &\\hspace{-3.5cm} - & \\hspace{-2cm} (1+ c^2 s_{\\rm a}^2)\n \\left[ \\frac{1}{(1+c s)^2} + \\frac{2 \\ln (1+c s)}{1+c s} \\right]\n \\label{c14e} \\\\\n &\\hspace{-3.5cm} + & \\hspace{-2cm} \\left. (1+3 c^2 s_{\\rm a}^2)\n \\left[ \\frac{\\pi^2}{3} - \\frac{2}{1+c s} + \\ln^2 (1+c s)\n + 2 {\\rm Li}_2(-c s) \\right] \\right\\} . \\nonumber\n\\end{eqnarray}\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 560]{sig1.ps}\n\\end{center}\n \\caption{Radial velocity dispersion profile (in units of the\n circular velocity at the virial radius), given by in isotropic model,\n equation (\\ref{c14}), for three different values of the concentration\n parameter $c$ (upper panel) and for the four considered anisotropy\n models with $c=10$ (lower panel).}\n\\label{sig}\n\\end{figure}\n\nFigure~\\ref{sig} shows the radial dependence of the radial velocity\ndispersion. The upper panel of the Figure presents how the results depend on\nthe concentration parameter in the isotropic case, while the lower panel\ncompares predictions for different anisotropy models with $c=10$.\n\n\n\\subsection{The energy distributions}\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 560]{tws2.ps}\n\\end{center}\n \\caption{The radial dependence\n of the virial ratio in the isotropic model (eqs.\n [\\ref{c15}] and [\\ref{c17}]) for three different values of the\n concentration parameter (upper panel) and for the four considered\n anisotropy models with $c=10$ (lower panel).}\n\\label{tws}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 310]{twc1.ps}\n\\end{center}\n \\caption{Dependence on the concentration parameter\n of the virial ratio at the virial radius for the four considered\n anisotropy models.}\n\\label{twc}\n\\end{figure}\n\n\nThe potential energy associated with the mass distribution of equation\n(\\ref{c8}) is\n{\\samepage\n\\begin{eqnarray}\n W(s) &=& - \\frac{1}{r_v} \\int_0^s \\frac{G M(s)}{s}\n \\frac{{\\rm d} M(s)}{{\\rm d} s} {\\rm d} s \\nonumber \\\\\n &=& - W_\\infty \\left[ 1-\\frac{1}{(1+c s)^2}\n - \\frac{2 \\ln (1+c s)}{1+c s} \\right] \\ , \\label{c15}\n\\end{eqnarray}\n}\nwhere\n\\begin{equation} \\label{c16}\n W_\\infty = - \\lim_{s \\rightarrow \\infty} W(s) =\n \\frac{c g^2(c) G M_v^2}{2 r_v} .\n\\end{equation}\nThe kinetic energy for arbitrary $\\beta$ is given by\n\\begin{equation} \\label{c16a}\n T(s, \\beta) = 2 \\pi \\,r_v^3\n \\,\\int_0^s (3 - 2 \\beta) \\rho (s) \\sigma_{\\rm\n r}^2(s, \\beta) \\,s^2\\, {\\rm d} s .\n\\end{equation}\nFor the three cases of $\\beta$=0, 0.5 and 1, we obtain respectively\n\\begin{eqnarray}\n T(s, \\beta=0) &=&\n \\frac{1}{2} W_\\infty \\{ -3 + \\frac{3}{1+c s} - 2 \\ln (1+c s)\n \\nonumber \\\\\n &\\hspace{-2.8cm} + & \\hspace{-1.7cm} c s [5 + 3 \\ln (1+ c s)]\n - c^2 s^2 [7 + 6 \\ln (1+ c s)]\n \\nonumber \\\\\n &\\hspace{-2.8cm} + & \\hspace{-1.7cm} c^3 s^3 [\\pi^2 - \\ln c - \\ln s +\n \\ln (1+c s) \\nonumber \\\\\n &\\hspace{-2.8cm} + & \\hspace{-1.7cm} 3 \\ln^2 (1+c s) +\n 6 {\\rm Li}_2 (-c s)] \\} \\ ,\n \\label{c17}\n\\end{eqnarray}\n\\begin{eqnarray}\n T(s, \\beta=0.5) &=&\n \\frac{1}{3} W_\\infty \\{ -3 + \\frac{3}{1+c s} - 3 \\ln (1+c s)\n \\nonumber \\\\\n &\\hspace{-2.8cm} + & \\hspace{-1.7cm}\n 6 c s [1 + \\ln (1+ c s)] - c^2 s^2 [\\pi^2\n \\nonumber \\\\\n &\\hspace{-2.8cm} + & \\hspace{-1.7cm} 3 \\ln^2 (1+c s)\n + 6 {\\rm Li}_2 (-c s)] \\} \\ ,\n \\label{c17a}\n\\end{eqnarray}\n\\begin{eqnarray}\n T(s, \\beta=1) &=&\n \\frac{1}{2} W_\\infty \\{ - 2 \\ln (1+c s)\n + c s [\\frac{\\pi^2}{3} - \\frac{1}{1+ c s}\n \\nonumber \\\\\n &\\hspace{-2.8cm} + & \\hspace{-1.7cm} \\ln^2 (1+c s)\n + 2 {\\rm Li}_2 (-c s)] \\} ,\n \\label{c17b}\n\\end{eqnarray}\nwhere we have used in each case the corresponding expression for\n$\\sigma_{\\rm r}^2(s, \\beta)$ from equations (\\ref{c14})-(\\ref{c14b}). For the\nOsipkov-Merritt model the calculation has to be done numerically.\n\nThe results for the potential and kinetic energy (\\ref{c15})-(\\ref{c17b})\nlead to a virial ratio $\\lim_{s \\rightarrow \\infty} 2 T/|W| = 1$\nfor any value of $c$, in agreement with the virial theorem.\nFigure~\\ref{tws} shows how the virial ratio depends on distance for three\ndifferent values of the concentration parameter in the isotropic case (upper\npanel) and compares the ratios obtained for different $\\beta$ with $c=10$\n(lower panel). At low radii, the virial ratio is large, especially for low\nconcentration parameters and models with much anisotropy. However, as\ndemonstrated by Figure~\\ref{twc}, at the virial radius $r_v (s\\!=\\!1)$,\n$2T/|W|$ is still greater than unity and grows with the amount of\nanisotropy in the model. We see that the virial theorem is better\nsatisfied at $s=1$ for objects with larger concentration parameters, as\n$\\lim_{c \\rightarrow \\infty} 2 T/|W| (s=1) = 1$.\nSince objects of smaller mass have larger concentration parameters, they\nare closer to dynamical equilibrium.\n\nThe scalar virial theorem we referred to above is expected to be satisfied\nfor self-gravitating systems in steady state. In more realistic\nsituations, the system is never isolated and experiences an external\ngravitational field; there is also continuous infall of matter. We may\nconclude from the results above that objects with NFW density\nprofiles and different velocity distributions are close to dynamical\nequilibrium. However, the virial ratio cannot be used to define the\nboundary of the virialized object.\n\n\\subsection{Structural parameters}\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 310]{rhgamma.ps}\n\\end{center}\n\\caption{Dependence on the concentration parameter of the half-mass\nradius, scaled to the virial radius (thicker lower solid line, see\neq.~[\\ref{rhfit}]) and $\\gamma$ for the four anisotropy models\n(eq.~[\\ref{gammadef2}], four upper lines).}\n\\label{rhgamma}\n\\end{figure}\n\n\nA useful quantity is the half-mass radius. Unfortunately, the\ndivergence of the mass of the NFW profile forces one to define the\nhalf-mass radius within a cutoff radius $r_{\\rm cut}$. The most natural\nchoice is $r_{\\rm cut} = r_v$, since the density distribution is only\nreliable out to the virial radius. With $r_{\\rm cut} = r_v$, the\nhalf-mass radius $r_{\\rm h}$ satisfies the following relation for\nthe mass of dimensionless radius:\n\\begin{equation}\n M\\left({r_{\\rm h}\\over r_v}\\right) = {M(1)\\over 2} \\ .\n\\end{equation}\nNumerical values of $r_{\\rm h}/r_v$ are easily obtained using\nequation (\\ref{c8}) and over the range $1 < c < 100$ they can be\napproximated to better than 2\\% accuracy by\n\\begin{eqnarray} \\label{rhfit}\n {r_{\\rm h} \\over r_v} &=& 0.6082 - 0.1843\\,\\log c \\nonumber \\\\\n & & \\mbox{} - 0.1011\\,\\log^2 c\n + 0.03918\\,\\log^3 c \\ .\n\\end{eqnarray}\nThe lowest thick solid line in Figure~\\ref{rhgamma} shows how\n$r_{\\rm h}/r_v$ decreases with increasing concentration parameter.\n\nIt is useful to estimate the concentration $\\gamma$ of a dynamical system,\nsuch that\n\\begin{equation} \\label{gammadef}\n \\left\\langle \\sigma^2 \\right \\rangle = \\gamma {G M \\over r_{\\rm h}} \\ ,\n\\end{equation}\nwhere $\\langle \\sigma^2 \\rangle =\\langle \\sigma_{\\rm r}^2 + \\sigma_{\\theta}^2\n+ \\sigma_{\\phi}^2 \\rangle $ is the mass weighted mean-square velocity\ndispersion. As first noted by Spitzer (1969) for polytropes, many\nrealistic density profiles have $\\gamma = 0.4$. For example, it is easy\nto show that for the Hernquist (1990) model with $\\beta=0$, $\\gamma\n= (1+\\sqrt{2})/6 \\simeq 0.403$ (Mamon 2000).\n\nUsing equation~(\\ref{gammadef}) and limiting again the mass to $r_{\\rm cut} =\nr_v$, we define $\\gamma$ with\n\\begin{equation} \\label{gammadef2}\n \\gamma = {r_{\\rm h}\\,\\left \\langle \\sigma^2\n \\right\\rangle_{r \\leq r_v} \\over G M(1)} = 2\\,{r_{\\rm h}\\,T(1, \\beta)\n \\over G M^2(1)} \\ ,\n\\end{equation}\nwhere we made use of\n\\begin{equation} \\label{tvssigmav}\n T(x, \\beta) = {1 \\over 2}\\,M(x)\\,\\left\\langle \\sigma^2\n \\right\\rangle_{r \\leq x\\,r_v} \\ .\n\\end{equation}\nThe values of $\\gamma$ for different velocity anisotropy models, derived\nfrom equations~(\\ref{c7}), (\\ref{c8}), (\\ref{c16}), (\\ref{c16})-(\\ref{c17b}),\n(\\ref{rhfit}), and (\\ref{gammadef2}) are shown in Figure~\\ref{rhgamma}\nand in the case of $\\beta=0$ yield numbers closest to 0.4: $\\gamma = 0.56$\nfor $c = 5$ and $\\gamma = 0.51$ for $c = 10$. Thus the NFW model produces\n$\\gamma$s that are higher than the canonical value of 0.4, especially if more\nvelocity anisotropy is assumed. This may be caused by the ill-defined\ncutoff radius.\n\nIn models with homogeneous cores, the central density, the core radius\n$r_{\\rm c}$ and the central 3-D velocity dispersion $\\sigma^2 (0)$ are\nrelated through\n\\begin{equation}\n 4\\pi G\\rho(0) r_{\\rm c}^2 = \\frac{1}{3} \\eta \\,\\sigma^2 (0) \\ .\n\\end{equation}\nKing (1966) models have $\\eta = 9$.\nIn models with cuspy cores, we propose the scaling relation\n\\begin{equation}\n 4\\pi G\\rho(r_{\\rm s}) r_{\\rm s}^2 =\n \\frac{1}{3} \\eta \\left \\langle \\sigma^2 \\right\\rangle_{r < r_{\\rm s}} \\ .\n\\end{equation}\nUsing equations~(\\ref{c2}), (\\ref{c6}) and (\\ref{c7}), one has\n$4 \\pi G \\rho(r_{\\rm s}) r_{\\rm s}^2 = c\\,g(c)\\,V_v^2/4$ and from\nequation~(\\ref{tvssigmav}) for $x = 1/c$\none obtains\n\\begin{equation}\n \\eta = \\frac{3 c g(c) V_v^2 M(1/c)}{8 T(1/c, \\beta)} \\ .\n\\end{equation}\nFor different velocity anisotropy models we then have\n\\begin{equation}\n \\eta (\\beta=0) = \\frac{3(2 \\ln 2 - 1)}{2(\\pi^2 - 7 - 8 \\ln 2\n + 6 \\ln^2 2)} \\simeq 2.797 ,\n\\end{equation}\n\\begin{equation}\n \\eta (\\beta=0.5) = \\frac{9(1 - 2 \\ln 2)}{4(\\pi^2 - 9 - 6 \\ln 2\n + 6 \\ln^2 2)} \\simeq 2.138 ,\n\\end{equation}\n\\begin{equation}\n \\eta (\\beta=1) = \\frac{9(2 \\ln 2 - 1)}{2(\\pi^2 - 3 - 12 \\ln 2\n + 6 \\ln^2 2)} \\simeq 1.212 ,\n\\end{equation}\nwhere we have used equations~(\\ref{c8}) and (\\ref{c17})-(\\ref{c17b}), and\nthe fact that ${\\rm Li}_2(-1) = -\\pi^2/12$. Note that $\\eta$ is independent\nof $c$ in all cases with $\\beta=$const. For the Osipkov-Merritt model $\\eta$\nis no longer a constant but we find $1.902 < \\eta < 2.797$ in the range\n$1 < c < 100$ with the limiting cases of $\\eta \\rightarrow \\eta(\\beta=1)$ for\n$c \\rightarrow 0$ and $\\eta \\rightarrow \\eta(\\beta=0)$ for\n$c \\rightarrow \\infty$. Such limiting behaviour is due to the fact that\nfor large $c$ the integration of $T(1/c, \\beta)$, equation (\\ref{c16a}),\nprobes only the range of $s$ where $\\beta$ is close to zero, while for\nsmall $c$ the integral is dominated by contribution from large $s$ where\n$\\beta$ is close to unity.\n\nFinally, we consider the structural parameter\n\\begin{equation}\n \\hbox{WUM} = {W(s) \\over M(s) \\Phi(0)}\n\\end{equation}\nbrought forward by Seidov \\& Skvirsky (2000) with the motivation of WUM\nbeing constant for different self-gravitating objects of simple geometry.\nUsing equations (\\ref{c8}), (\\ref{c9}) and (\\ref{c15}) we find that for\nthe NFW model\n\\begin{equation}\n \\hbox{WUM} = \\frac{ c s (2 + c s) - 2 (1+ c s) \\ln (1+c s)}{2 (1+ c s)\n [- c s + (1+ c s) \\ln (1+ c s)]}\n\\end{equation}\nso the parameter turns out to be a function of $c s = r/r_{\\rm s}$ only.\nIt grows with $s$ from zero at $s \\rightarrow 0$ reaching a maximum\nvalue of $0.196$ at $r/r_{\\rm s}=4.62$ and decreases\nto zero again as $s \\rightarrow \\infty$. The values of this parameter at\nthe virial radius are $0.196$, $0.187$ and $0.125$ respectively for $c=5,\n10$ and $100$.\n\n\\subsection{The distribution function}\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 310]{df.ps}\n\\end{center}\n \\caption{The distribution function for isotropic model (eq. [\\ref{c26}])\n for three different values of the concentration parameter.}\n\\label{df}\n\\end{figure}\n\nA quantity of great dynamical importance is the distribution function. For\na spherical system with an isotropic velocity tensor, the distribution\nfunction depends on the phase-space coordinates only through the energy\n(e.g. Binney \\& Tremaine 1987), and can be derived through the Eddington\n(1916) formula (e.g. Binney \\& Tremaine 1987):\n\\begin{equation} \\label{c26}\n f({\\cal E}) = \\frac{1}{\\sqrt{8} \\pi^2} \\left [\\int_{0}^{{\\cal E}}\n \\frac{{\\rm d}^2 \\rho}{{\\rm d} \\Psi^2} \\frac{{\\rm d}\n \\Psi}{\\sqrt{{\\cal E} - \\Psi}} + \\frac{1}{{\\cal E}^{1/2}}\n \\left ( \\frac{{\\rm d} \\rho}{{\\rm d}\\Psi}\\right)_{\\Psi=0}\\right ] \\ ,\n\\end{equation}\nwhere ${\\cal E}$ and $\\Psi$ are the conventionally defined relative\nenergy and potential; here ${\\cal E} = -E$, where $E$ is the total\nenergy per unit mass and $\\Psi = -\\Phi$, where $\\Phi$ is given by\nequation (\\ref{c9}).\n\n\nIt is easy to show that, given equations (\\ref{c6}) and (\\ref{c9}), the\nsecond term in brackets in equation~(\\ref{c26}) is zero.\nThe simplest way to perform the integration of the first term is to\nintroduce dimensionless variables\n$\\widetilde{\\Psi} = \\Psi/C_1$ and $\\widetilde{\\rho} = \\rho/C_2$,\nwhere $C_1 = g(c)\\,V_v^2$ and $C_2 = c^2 g(c) M_v/(4 \\pi r_v^3)$. Then\nthe integration variable should be changed to $s$ and the limit of integration\ncorresponding to $\\cal E$ found numerically for each $\\cal E$ by solving\nequation $\\Psi(s)=\\cal E$. Otherwise, with a few percent accuracy, the\nintegration in (\\ref{c26}) can be done directly with an approximation\n$s_{\\rm apx } = -1.75 \\ln (\\widetilde{\\Psi}/c)/\\widetilde{\\Psi}$.\n\nThe calculations of the distribution function are usually performed in\nunits such that $G=M=R_{\\rm e}=1$ (Binney \\& Tremaine 1987), where $M$ is\nthe total mass of the system and $R_{\\rm e}$ is its effective radius.\nSince in the case of NFW profile the total mass is infinite a reasonable\nchoice seems to be to put $M_v = 1$. The effective radius is not well\ndefined either but can be approximated as $r_v/2$ (see the next\nsection). Therefore we choose the units so that $G = M_v = r_v/2 = 1$\nand arrive at the numerical results shown in Figure~\\ref{df}. This choice\nof normalization is equivalent to measuring $f$ in units of $\\sqrt{8} M_v\n/(r_v V_v)^3$ and $E$ in units of $V_v^2$.\n\nFigure~\\ref{df} proves that the distribution function turns out to be\nsimilar to the distribution functions obtained from other density\nprofiles (see e.g. Figure 4-12 in Binney \\& Tremaine 1987), except that\nthe NFW distribution functions do not display the cutoff at nearly unbound\nenergies characteristic of King (1966) models. The results\nshown in Figure~\\ref{df} indicate a proper behaviour of the\ndistribution function (it is nowhere negative). Quantitative comparisons\nwith other models should, however, be made with caution because of the\naforementioned problem with normalization. Distribution functions for\nmore realistic velocity dispersion models, like the Osipkov-Merritt model,\nwere recently considered in detail by Widrow (2000).\n\n\\subsection{Projected distributions}\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 560]{losvd1.ps}\n\\end{center}\n \\caption{Upper panel: radial dependence of the line-of-sight\n velocity dispersion for isotropic orbits (eq. [\\ref{c24}]) on the\n projected radius for three values of the concentration parameter.\n Lower panel:\n comparison of the line-of-sight velocity dispersion profiles for\n four anisotropy models calculated with $c=10$.}\n\\label{losvd}\n\\end{figure}\n\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 560]{sap1.ps}\n\\end{center}\n \\caption{Upper panel: radial profiles of the aperture velocity\n dispersion in the isotropic model for three concentration parameters.\n Lower panel:\n comparison of the aperture velocity dispersions for four anisotropy\n models calculated with $c=10$.}\n\\label{sap}\n\\end{figure}\n\nOf primary importance for comparisons with observations are the\nprojected distributions. The surface mass density of an object is\nobtained by integrating the density along the line of sight:\n%{\\samepage\n\\begin{eqnarray}\n \\Sigma_M(R) \\!\\!\\!\\!&=& \\!\\!\\!\\!\n 2\\, \\int_{R}^{\\infty}\n \\frac{r \\,\\rho(r)}{(r^2 - R^2)^{1/2}} \\,{\\rm d} r \\nonumber \\\\\n &=& \\!\\!\\!\\!\\frac{c^2\\,g(c)}{2\\pi}\\,\\frac{M_v}{r_v^2}\\,\n \\frac{1 - |c^2{\\widetilde R}^2 - 1|^{-1/2} C^{-1} [1/(c\\widetilde\n R)]}{(c^2{\\widetilde R}^2 -1)^2} ,\n\\label{c20}\n\\end{eqnarray}\n%}\nwhere\n\\begin{equation} \\label{c20a}\n C^{-1} (x) = \\left\\{\n \\begin{array}{ll}\n \\cos^{-1} (x) & \\mbox{if $R > r_{\\rm s}$} \\\\\n \\cosh^{-1} (x) & \\mbox{if $R < r_{\\rm s}$ .}\n \\end{array}\n \\right.\n\\end{equation}\nIn the above expressions $R$ is the projected radius and ${\\widetilde\nR}=R/r_v$. For the singular case $R = r_{\\rm s}$ the $\\widetilde\nR$-dependent expression in equation (\\ref{c20}) equals $1/3$ and we have\n$\\Sigma_M(R) = c^2 g(c) M_v/(6 \\pi r_v^2)$ .\nAn analytical formula equivalent to equation (\\ref{c20}) was derived\nindependently by Bartelmann (1996).\n\nThe projected mass is then given by\n\\begin{eqnarray}\n M_{\\rm p}(R) \\!\\!\\!\\!&=&\\!\\!\\!\\!\n 2 \\pi \\int_{0}^{R} R\\,\\Sigma_M(R) \\,{\\rm d} R \\nonumber \\\\\n &=& \\!\\!\\!\\! g(c) \\,M_v\n \\left[\\frac{C^{-1} [1/(c\\widetilde R)]}\n {|c^2{\\widetilde R}^2 -1|^{1/2}} + \\ln\n \\left ( \\frac{c\\widetilde R}{2}\\right)\\right] \\ , \\label{c21}\n\\end{eqnarray}\nwhich is logarithmically divergent at large ${\\widetilde R}$. $C^{-1}(x)$\nis again given by equation (\\ref{c20a}).\n\n\nAnother important projected quantity is the line-of-sight velocity\ndispersion which for a spherical non-rotating system\nis (Binney \\& Mamon 1982)\n\\begin{equation} \\label{c24}\n \\sigma_{\\rm los}^2 (R) = \\frac{2}{\\Sigma_M(R)} \\int_{R}^{\\infty}\n \\left( 1-\\beta \\frac{R^2}{r^2} \\right) \\frac{\\rho \\,\n \\sigma_{\\rm r}^2 (r, \\beta) \\,r}{\\sqrt{r^2 - R^2}} \\,{\\rm d} r \\ ,\n\\end{equation}\nwhere $\\Sigma_M(R)$ is given by equation (\\ref{c20}) and the radial\nvelocity dispersions $\\sigma_{\\rm r}(r, \\beta)$ for our four models are\ngiven by equations (\\ref{c14})-(\\ref{c14b}) and (\\ref{c14e}).\nFor circular orbits, $\\sigma_{\\rm r}=0$, and one has\n\\begin{equation} \\label{c25}\n \\sigma_{\\rm los}^2 (R) = \\frac{1}{\\Sigma_M(R)} \\int_{R}^{\\infty}\n \\left( \\frac{R}{r} \\right)^2 \\frac{\\rho \\,V^2 \\,r}{\\sqrt{r^2 -\n R^2}}\\, {\\rm d} r \\ ,\n\\end{equation}\nwhere $V$ is the circular velocity given by equations (\\ref{c10}) and\n(\\ref{c12}). The upper panel of Figure~\\ref{losvd} shows the profiles of\nline-of-sight velocity dispersion (with isotropic orbits), obtained\nthrough numerical integration of equation (\\ref{c24}) for different\nconcentration parameters. The lower panel of Figure~\\ref{losvd} compares\nthe radial profiles of line-of-sight velocity dispersions obtained\nfor $c=10$ for different velocity anisotropy models.\n\nFor more distant or intrinsically small galaxies, as well as for groups\nand clusters, spectroscopic observations are often limited to a single\nlarge aperture centred on the object.\nThe mean velocity dispersion within an aperture (hereafter,\naperture velocity dispersion) is\n\\begin{equation} \\label{c28}\n \\sigma_{\\rm ap}^2 (R) = \\frac{S^2(R)}{M_{\\rm p}(R)}\n\\end{equation}\nwhere\n\\begin{equation} \\label{c29}\n S^2(R) = 2 \\pi \\int_0^R \\Sigma_M(P) \\sigma_{\\rm los}^2 (P) P {\\rm d} P.\n\\end{equation}\nIn the above expressions $R$ is the radius of the aperture,\n$\\Sigma_M(P)$ is the surface mass distribution, equation (\\ref{c20}),\nand $M_{\\rm p}(R)$ is the projected mass given by equation (\\ref{c21}).\n\nInserting the expression for $\\sigma_{\\rm los}$ (eq.~[\\ref{c24}])\ninto equation (\\ref{c29}), we obtain a double integral, which after inversion\nof the order of integration is reduced to an easily computable single\nintegral:\n\\begin{eqnarray}\n S^2(R) &=& c^2 \\,g(c) \\,M_v \\left\\{ \\int_0^\\infty\n \\frac{\\sigma_{\\rm r}^2(s, \\beta)\\, s}{(1+c\n s)^2} \\, \\left(1-\\frac{2 \\beta}{3} \\right) {\\rm d} s \\right.\n \\nonumber \\\\\n &\\hspace{-2cm} + & \\hspace{-1.4cm}\n \\left. \\int_{\\widetilde R}^\\infty \\frac{\\sigma_{\\rm\n r}^2(s, \\beta) \\,({s^2 - {\\widetilde R}^2})^{1/2}}{(1+c s)^2} \\left[\n \\frac{\\beta({\\widetilde R}^2 + 2 s^2)}{3 s^2} - 1 \\right] {\\rm d} s\n \\right\\} , \\label{c30}\n\\end{eqnarray}\nwhere as before, $\\widetilde R=R/r_v$, $s=r/r_v$ and $\\sigma_{\\rm\nr}^2 (s, \\beta)$ for different $\\beta$ are given by\nequations~(\\ref{c14})-(\\ref{c14b}) and (\\ref{c14e}).\nAnalogous expression for circular orbits can be obtained from (\\ref{c30})\nby replacing $\\sigma_{\\rm r}^2$ by $V^2$, keeping only the terms\nproportional to $\\beta$ and dividing by $(-2 \\beta)$.\n\nFigure~\\ref{sap} displays the radial profiles of aperture velocity\ndispersion, computed numerically from equation~(\\ref{c30}). From the upper\npanel of the Figure we see that in the isotropic case the dependence of the\nresults on the concentration parameter is rather strong and monotonic for\na given $R$. The lower panel of the Figure compares the predictions for\ndifferent velocity anisotropy models.\n\n\\section{Comparison with observations}\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[90 40 550 779]{gamis.ps}\n\\end{center}\n \\caption{Radial profiles of the surface mass density,\n given by equation (\\ref{c20}), (upper panel) and the\n projected mass, equation (\\ref{c21}), (lower panel)\n for three different values of the concentration parameter.\n Hubble-Reynolds fits from equation~(\\ref{c32}) are shown as\n thin curves ($R_{\\rm HR}/r_v = 0.119$, $0.0640$ and\n $0.00743$ for $c=5, 10$ and $100$, respectively).\n For $c=100$, the NFW surface mass density is virtually\n indistinguishable from the best-fitting Hubble-Reynolds law.}\n\\label{is}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 310]{aec.ps}\n\\end{center}\n \\caption{The dependence of the effective radius, defined in equation\n (\\ref{c22}), on the concentration parameter, with various choices of\n ${\\widetilde R}_{\\rm cut}$.}\n\\label{aec}\n\\end{figure}\n\nComparisons of the surface mass density to surface brightness\nobservations are usually performed with the assumption of constant\nmass-to-light ratio $\\Upsilon = {\\rm const}$.\nThis assumption is not likely to be physical, because of the different\nphysics involved in the assemblies of the dark matter and baryonic components\nof galaxies. In particular, the baryons in elliptical galaxies may well\nsettle at an early epoch, within a\nradius that is the lower of the radius with virial overdensity $v \\simeq\n200$ and the radius at which gas can cool to form molecular clouds and later\nstars. The baryons in ellipticals will then sit today in a region of\noverdensity $v \\gg 200$, and one then expects $\\Upsilon$ to rise with $r$,\nat least at large radii.\n\nNevertheless, for simplicity, we check whether the observations of elliptical\ngalaxies are consistent with the idea that stars are distributed\nwithin elliptical galaxies according to the NFW density profile,\ncharacterized by a virial radius where the mean overdensity is 200.\nSuch a situation may arise if the dark matter were negligible within\nelliptical galaxies or distributed precisely like the luminous matter.\nIn a forthcoming paper (Mamon \\& {\\L}okas, in preparation), we will check\nin more detail whether the observations of elliptical galaxies are\ncompatible or not with NFW density profiles for the mass distribution.\n\nFor constant mass-to-light ratio we have $\\Sigma_M(R) =\n\\Upsilon I(R)$, where $I$ is the surface brightness. The radial profiles of\n$I = \\Sigma_M/\\Upsilon$ and $M_{\\rm p}$ are shown in Figure~\\ref{is}. Both\nquantities are normalized to their values at the virial radius.\nFigure~\\ref{is} shows that the surface mass density depends weakly on the\nconcentration parameter, especially at larger distances from the centre.\n\nSince the surface mass density (eq. [\\ref{c20}]) behaves as $1/R^2$ at\nlarge distances, one may therefore compare it with the Hubble-Reynolds\nformula (Reynolds 1913), which was the first model used to describe the\nsurface brightness profiles of elliptical galaxies:\n\\begin{equation} \\label{c32}\n I_{\\rm HR} (R) = \\frac{I_0}{(1+R/R_{\\rm HR})^2} \\ .\n\\end{equation}\n$R_{\\rm HR}$ is the characteristic radius of the distribution,\nwhere the surface brightness falls to one-quarter of its central value.\nThe thin curves of Figure~\\ref{is} show that the surface mass density of\nthe NFW model (eq.~[\\ref{c20}]) is very well fitted by\nequation~(\\ref{c32}) and the best-fit values of ${\\widetilde R}_{\\rm HR}\n= R_{\\rm HR}/r_v$ are $0.119$, $0.0640$ and $0.00743$ respectively for\n$c=5, 10$ and $100$.\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=9cm\n \\epsfbox{gamde.ps}\n\\end{center}\n \\caption{Upper panel: surface brightness profiles (eq.\n [\\ref{c20}]) for three concentration parameters and ${\\widetilde\n R}_{\\rm cut}=1$. Lower panel: the dependence of the surface\n brightness profiles on the cut-off $\\widetilde R_{\\rm cut}$ for $c=10$\n and ${\\widetilde R}_{\\rm cut} = 3$, 3.5, 4, 4.5, and 5 (bottom\n to top curves). In both panels, the $R^{1/4}$ law (eq. [\\ref{c23}])\n is shown as long dashed lines. The vertical lines\n represent the virial radius (for the three concentration parameters in\n the upper panel and for the 5 values of $\\widetilde R_{\\rm cut}$ in\n the lower panel, with $\\widetilde R_{\\rm cut}$ increasing from right\n to left). The circles are the data points for the galaxy NGC 3379.}\n\\label{de}\n\\end{figure}\n\n\nThe surface brightness profiles of astrophysical objects are often scaled\nwith the effective radius, which we denote $R_{\\rm e}$,\nwhere the projected luminosity is half the total luminosity. Given the\ndivergence of the projected mass, we are forced again to introduce a cut-off\nat some scale $R_{\\rm cut} = {\\widetilde R}_{\\rm cut}\\,r_v$. We then have\n\\begin{equation} \\label{c22}\n M_{\\rm p}({R_{\\rm e}}) = M_{\\rm p}({R}_{\\rm cut})/2 \\ .\n\\end{equation}\nFigure~\\ref{aec} shows the effective radius,\ncalculated numerically from equations (\\ref{c21}) and (\\ref{c22}).\nFor $\\widetilde R_{\\rm cut} = 1$, a useful approximation, good to better\nthan 2\\% relative accuracy, is:\n{\\samepage\n\\begin{eqnarray}\n R_{\\rm e} / r_v &=& 0.5565 - 0.1941\\,\\log c \\nonumber \\\\\n & & \\mbox{} - 0.0756\\,\\log^2 c + 0.0331\\,\\log^3 c \\ .\n\\end{eqnarray}\n}\n\nThe prediction for the surface brightness $I = \\Sigma_M/\\Upsilon$ with\n$\\Sigma_M$ given by equation (\\ref{c20}) expressed in terms of\nthe effective radius and the corresponding effective brightness $I_{\\rm e}\n= I(R_{\\rm e})$ is shown in the upper panel of Figure~\\ref{de} for\ndifferent values of the concentration parameter $c$. For comparison, we\nalso show the de Vaucouleurs (1948) $R^{1/4}$ law describing the observed\nsurface brightness distribution in giant elliptical galaxies:\n\\begin{equation} \\label{c23}\n I(R) = I_{\\rm e} \\exp\\{-b\\,[(R/R_{\\rm e})^{1/4}-1]\\} \\ ,\n\\end{equation}\nwhere $b = 7.67$. Clearly, the NFW surface brightness profiles are poorly\nfitted by the $R^{1/4}$ law, when using $R_{\\rm cut} = r_v$ to define the\neffective radius of the NFW profile.\n\n\\begin{figure*}\n\\begin{center}\n \\leavevmode\n \\setbox100=\\hbox{\\epsfxsize=12cm\\epsffile{sersic.ps}}\n \\setbox101=\\vbox{\\rotr{100}}\n \\hbox{\\box101}\n\\end{center}\n \\caption{Comparisons of $c=10$ projected NFW models\n (using eq.~[\\ref{c20}]) to S\\'ersic models (eq.~[\\ref{c31}]).\n The curves represent the NFW models\n (for equally spaced values of $\\widetilde R_{\\rm cut}$ within\n the interval indicated in each plot,\n with $\\widetilde R_{\\rm cut}$ increasing upwards on the left portion\n of each plot). The S\\'ersic law is shown as long dashed lines.\n The vertical lines represent the virial radius (with\n $\\widetilde R_{\\rm cut}$ increasing from right to left). }\n\\label{sersic10}\n\\end{figure*}\n\nThe lower panel of Figure~\\ref{de} shows how the results depend on the\nchoice of cut-off for $c=10$ and $\\widetilde R_{\\rm cut} = 3$, 3.5, 4,\n4.5, and 5. At first glance, it seems that the NFW profile is well\nfitted by the $R^{1/4}$ law, especially for $\\widetilde R_{\\rm cut} \\simeq\n4$. However, the range of surface mass densities where the fit is\nexcellent is roughly $10^2$, and the fit is adequate for a range smaller\nthan $10^3$. In contrast, the surface brightness profile of the nearby\ngiant elliptical galaxy NGC~3379 (M~105) follows the $R^{1/4}$ law in a\nrange of 10 magnitudes (de Vaucouleurs \\& Capaccioli 1979), i.e. a factor\n$10^4$ in intensity.\n\nIn order to see how good is the de Vaucouleurs's fit in this case in both\npanels of Figure~\\ref{de} we plotted a number of data points equally\nspaced in $R^{1/4}$. Since de Vaucouleurs \\& Capaccioli (1979) do not\nprovide the error bars for their data, the error bars shown in the Figure\nwere taken from Goudfrooij et al. (1994). The excess of the data above the\n$R^{1/4}$ law for small $R$ was already noted by de Vaucouleurs \\&\nCapaccioli (1979). The error bars are negligible for $R < R_{\\rm e}$ and\nsmaller than 15\\% out to $2.5 R_{\\rm e}$, the maximum distance from the\ncentre reached in the data of Goudfrooij et al. (1994).\n\nAccording to de Vaucouleurs \\& Capaccioli (1979), in this galaxy the\n$R^{1/4}$ surface brightness profile extends to $R_{\\rm lim} =\n7.5\\,R_{\\rm e} = 26.4\\,\\rm kpc$, given a distance of 12.4 Mpc to NGC 3379\n(Salaris \\& Cassisi 1998). Within $R_{\\rm lim}$, de Vaucouleurs \\&\nCapaccioli (1979) report a blue magnitude, corrected for galactic\nextinction of $B = 10.10$, yielding a total blue luminosity of $2.2\\times\n10^{10}\\,L_\\odot$, hence a blue luminosity density of $2.8 \\times 10^5\n\\,L_\\odot\\,\\rm kpc^{-3}$. Since the mass within $R_{\\rm lim}$ must be\ngreater than the mass in stars, we infer that within this radius,\n$\\Upsilon_B > 8$ (the typical mass to blue luminosity ratio for old\nstellar populations), yielding an overdensity of the galaxy, relative to\nthe critical density $\\rho_c$ of $v > 1.6\\times 10^4/(H_0/70\\,\\rm km\n\\,s^{-1} \\, Mpc^{-1})^2$. Therefore, since $v \\gg 100$ (the value at\n$r_v$), we conclude that $R_{\\rm lim} \\ll r_v$, hence $R_{\\rm e} \\ll\nr_v/7.5$. In contrast, with $\\widetilde R_{\\rm cut} = 1$, the effective\nradius of the NFW model ($c=10$) is $\\simeq 0.3\\,r_v$ (Figure~\\ref{aec}).\nThis discrepancy in $R_{\\rm e}/r_v$ between NFW and $R^{1/4}$ law gets\neven worse if one adopts $\\widetilde R_{\\rm cut} = 4$, which provides the\nbest fits of the NFW surface mass density to the $R^{1/4}$ law: indeed,\nFigure~\\ref{aec} indicates $R_{\\rm e} \\simeq 0.8 \\,r_v$\nfor the NFW model.\n\nIn summary, the NFW surface mass density profile resembles an $R^{1/4}$\nlaw in a fairly wide range of radii, but 1) one has to resort to an\nabnormally large effective radius, very close to the virial radius, and\nassume that the effective radius measures half the projected light (or\nmass) within 4 times the virial radius, and 2) the fit is good in\na considerably\nsmaller range of radii than is observed in the nearby giant elliptical\nNGC~3379.\n\nThe generalization of the $R^{1/4}$ law into an $R^{1/m}$ law, first\nproposed by S\\'ersic (1968), is known to fit the surface brightness profiles\nof elliptical galaxies within a much larger mass range than the de\nVaucouleurs law (Caon, Capaccioli \\& D'Onofrio 1993). The surface brightness\nof the S\\'ersic profile is\n\\begin{equation} \\label{c31}\n I(R) = I_{\\rm e} \\exp\\{-b(m)\\,[(R/R_{\\rm e})^{1/m}-1]\\} \\ ,\n\\end{equation}\nwhere $b(m)$ is tabulated by Ciotti (1991), who gives the empirical relation\n$b(m) \\simeq 2\\,m-0.324$, good to 0.1\\% relative accuracy. The de\nVaucouleurs law is reproduced for $m=4$, while $m=1$ corresponds\nto an exponential law as in spiral disks.\n\nIn Figure~\\ref{sersic10}, we plot the NFW surface\nbrightness $I =\\Sigma_M/\\Upsilon$, with $\\Sigma_M$ given by\nequation~(\\ref{c20}) and $c=10$, as a function of $(R/R_{\\rm e})^{1/m}$\nfor various values of the S\\'ersic parameter $m$. We compare them to the\nS\\'ersic profiles given by the straight dashed lines. The agreement is\ngood for all values of $m$, within ranges of $I/I_{\\rm e}$ that increase\nwith increasing $m$. Comparison of the plots for different $m$ shows that\nthe S\\'ersic models with lower $m$ generally agree better with the NFW\nsurface brightness for smaller radii, while those with larger $m$ are in\nbetter agreement at larger radii, closer to the virial radius. Overall,\nthe NFW profile matches best the $m=3$ S\\'ersic law, over a factor of\n$10^3$ in intensity (7.5 magnitudes).\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 310]{fitser.ps}\n\\end{center}\n \\caption{The best fitting parameters of the S\\'ersic law, eq.\n (\\ref{c31}), as functions of concentration: $1/m$ (dashed line) and\n $R_{\\rm e}/r_v$ (solid line).}\n\\label{fitser}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n \\leavevmode\n \\epsfxsize=8cm\n \\epsfbox[50 50 340 310]{nfwser.ps}\n\\end{center}\n \\caption{Comparison of the projected NFW density profile, eq.\n (\\ref{c20}), and the best fitting S\\'ersic law, eq. (\\ref{c31}).}\n\\label{nfwser}\n\\end{figure}\n\nFor a more quantitative comparison, we performed\ntwo-parameter fits of the S\\'ersic models (\\ref{c31}) to the projected NFW\nformula (\\ref{c20}). The NFW profile was sampled in the range of $0.01 <\n\\widetilde R < 1$ with a given $c$. The fitted S\\'ersic parameters\n$1/m$ and $R_{\\rm e}/r_v$ obtained for different $c$ are shown in\nFigure~\\ref{fitser}. Figure~\\ref{nfwser} compares the two projected\nprofiles for $c=10$. The best-fit parameters of the S\\'ersic model in\nthis case are $m=3.07$ and $R_{\\rm e}/r_v=0.55$.\n\nWhile Caon et al. (1993) find similar ranges of agreement between observed\nprofiles and S\\'ersic laws, this range in intensity is still smaller than\nthe range of $10^4$ found for NGC~3379 by de Vaucouleurs \\& Capaccioli\n(1979). Moreover, while Caon et al. (1993) find that the best fitting\nS\\'ersic models for elliptical galaxies have indices spanning a wide\nrange, from $m=2$ for faint ellipticals to $m=10$ for bright ellipticals,\nthe S\\'ersic laws that match the NFW models span a much smaller range,\nroughly $m = 3\\pm0.5$ ($2.71 < m < 3.41$ for $5 < c < 15$, see\nFigure~\\ref{fitser}). Moreover, the problem of very high values of\n$R_{\\rm e}/r_v$ ($0.46 < R_{\\rm e}/r_v < 0.81$ for $5 < c < 15$, see\nFigure~\\ref{fitser}), remains in the fits of S\\'ersic profiles to\nprojected NFW models.\n\n\n\n\\section{Discussion}\n\nThe main disadvantage of the NFW model is the logarithmic divergence of\nits mass (and luminosity for constant mass-to-light ratio). In\ncontrast, the Jaffe (1983) and Hernquist (1990) models converge in mass,\nand their properties can be expressed in units of their asymptotic mass.\nFor the NFW model, one is restricted to a mass at a physical radius such\nas the virial radius. This mass divergence also complicates the analysis\nof surface brightness profiles, which involve the effective radius where\nthe aperture luminosity is half its asymptotic value. However,\nindependently of the radial cut-off introduced to define the effective\nradius, the projected NFW density profile is consistent with constant\nmass-to-light ratio, given the observed S\\'ersic profiles of elliptical\ngalaxies, but only in a limited range of radii, with unusually high values\nof $R_{\\rm e}$ and in a smaller interval of S\\'ersic shape parameters than\nobserved. On the other hand, the Hernquist (1990) model, whose density\nprofile scales as $r^{-4}$ at large radii, produces better fits to the\n$R^{1/4}$ law.\n\nThe upper panel of Figure~\\ref{de} suggests that, for reasonable\neffective radii, if indeed dark matter follows the NFW profile, the\nmass-to-light ratio, $\\Upsilon$, is not constant but increases with radius,\nnot only in the outer regions, as is inferred from the\ncommonly accepted picture of galaxies embedded in more spatially extended\ndark haloes, but also in the inner regions. This is at odds with the\nobserved kinematics of ellipticals that Bertola et al. (1993) inferred\nfrom observations of ionised and neutral gas around specific ellipticals.\nMoreover, increasing $\\Upsilon$ throughout the galaxy implies radial\nvelocity anisotropy throughout elliptical galaxies, whereas violent\nrelaxation should cause isotropic cores.\\footnote{Note that recent, state\nof the art observations and modelling by Saglia et al. (2000) and Gebhardt\net al. (2000) do not strongly constrain the gravitational potentials of\nelliptical galaxies, although NFW potentials may turn out to be\ninconsistent with the current data. On the other hand, Kronawitter et al.\n(2000) are able to rule out constant $\\Upsilon$ for some elliptical\ngalaxies.} Thus it appears difficult to reconcile the photometry and\nkinematics of elliptical galaxies with NFW models. In a forthcoming paper\n(Mamon \\& {\\L}okas, in preparation), we will omit the assumption of mass\nfollows light in a more detailed assessment of the compatibility of the\nobservations of elliptical galaxies with the NFW model.\n\nThe results presented in this paper can be directly applied to the\nanalysis of the mass and light distribution in clusters of galaxies. A\nstandard procedure to do it is to measure the surface brightness and the\nlight-of-sight velocity dispersion and assuming some form of velocity\ndistribution or mass-to-light ratio calculate the luminosity density and\nthe velocity dispersion by solving the Abel integral equations (\\ref{c20})\nand (\\ref{c24}) and the Jeans equation (Binney \\& Mamon 1982, Tonry 1983,\nSolanes \\& Salvador-Sol\\'{e} 1990, Dejonghe \\& Merritt 1992). The\nresults of this procedure are uncertain because it involves derivatives of\nobserved quantities which are usually noisy. One also experiences a\ndegeneracy because different models fit the data equally well\n(Merritt 1987). Instead of solving the Abel equations one can also model\nthe luminosity density and velocity dispersion with simple functions and\nfit their parameters so that they reproduce their projected counterparts\n(Carlberg et al. 1997).\n\nOur results are useful for the simpler approach of assuming realistic\nforms of the density distribution, velocity distribution and mass-to-light\nratio. Here we provide the tools for modelling the NFW density profile\nwith different velocity distributions and constant\nmass-to-light ratio ($\\Upsilon={\\rm const}$), and obtain exact predictions\nfor the surface brightness and the line-of-sight as well as aperture\nvelocity dispersion that can be directly compared to observations.\n\n\\section*{Acknowledgements}\n\nWe thank Daniel Gerbal and Bernard Fort for useful conversations, and an\nanonymous referee for helpful comments. EL\\L \\\nacknowledges hospitality of Institut d'Astrophysique de Paris, where\npart of this work was done. This research was partially supported by the\nPolish State Committee for Scientific Research grant No. 2P03D00813 and\n2P03D02319 as well as the Jumelage program Astronomie France Pologne of\nCNRS/PAN.\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[]{amkb} Adami C., Mazure A., Katgert P., Biviano A., 1998, A\\&A,\n 336, 63\n\\bibitem[]{afh98} Avila-Reese V., Firmani C., Hernandez X., 1998, ApJ, 505,\n 37\n\\bibitem[]{afh99} Avila-Reese V., Firmani C., Klypin A., Kravtsov A. V.,\n 1999, MNRAS, 310, 527\n\\bibitem[]{b96} Bartelmann M., 1996, A\\&A, 313, 697\n\\bibitem[]{bpms93} Bertola F., Pizzella A., Persic M., Salucci P., 1993,\n ApJ, 416, L45\n\\bibitem[]{be} Bertschinger E., 1985, ApJS, 58, 39\n\\bibitem[]{bm} Binney J., Mamon G. A., 1982, MNRAS, 200, 361\n\\bibitem[]{bt} Binney J., Tremaine S., 1987, Galactic Dynamics. Princeton\n Univ. Press, Princeton, chap. 4.4.3\n\\bibitem[]{bu} Bullock J. S., Kolatt T. S., Sigad Y., Somerville R. S.,\n Kravtsov A. V., Klypin A. A., Primack J. R., Dekel A., 1999,\n submitted to MNRAS, astro-ph/9908159\n\\bibitem[]{ccdo} Caon N., Capaccioli M., D'Onofrio M., 1993, MNRAS, 265,\n 1013\n\\bibitem[]{c} Carlberg R. G. et al., 1997, ApJ, L13\n\\bibitem[]{ci} Ciotti L., 1991, A\\&A, 249, 99\n\\bibitem[]{cl} Cole S., Lacey C., 1996, MNRAS, 281, 716\n\\bibitem[]{dm92} Dejonghe H., Merritt D., 1992, ApJ, 391, 531\n\\bibitem[]{dv} de Vaucouleurs G., 1948, Ann. Ap. 11, 247\n\\bibitem[]{dvc79} de Vaucouleurs G., Capaccioli M., 1979, ApJS, 40, 699\n\\bibitem[]{edd16} Eddington A. S., 1916, MNRAS, 76, 572\n\\bibitem[]{ecf} Eke V. R., Cole S., Frenk C.S., 1996, MNRAS, 282, 263\n\\bibitem[]{fg} Fillmore J. A., Goldreich P., 1984, 281, 1\n\\bibitem[]{fp} Flores R. A., Primack J. R., 1994, ApJ, 427, L1\n\\bibitem[]{fm} Fukushige T., Makino J., 1997, ApJ, 477, L9\n\\bibitem[]{geb} Gebhardt K. et al., 2000, AJ, 119, 1157\n\\bibitem[]{gmglqs} Ghigna S., Moore B., Governato F., Lake G., Quinn T.,\n Stadel J., 1999, submitted to ApJ, astro-ph/9910166\n\\bibitem[]{go} Gott J. R., 1975, ApJ, 201, 296\n\\bibitem[]{ghj} Goudfrooij P., Hansen L., J\\o rgensen H. E.,\n N\\o rgaard-Nielsen H. U., de Jong T., van den Hoek L. B., 1994, A\\&AS,\n 104, 179\n\\bibitem[]{gu} Gunn J. E., 1977, ApJ, 218, 592\n\\bibitem[]{gg} Gunn J. E., Gott J. R., 1972, ApJ, 176, 1\n\\bibitem[]{h} Hernquist L., 1990, ApJ, 356, 359\n\\bibitem[]{hs} Hoffman Y., Shaham J., 1985, ApJ, 297, 16\n\\bibitem[]{hjs1} Huss A., Jain B., Steinmetz M., 1999a, MNRAS, 308,\n1011\n\\bibitem[]{hjs2} Huss A., Jain B., Steinmetz M., 1999b, ApJ, 517, 64\n\\bibitem[]{j} Jaffe W., 1983, MNRAS, 202, 995\n\\bibitem[]{j99} Jing Y. P., 2000, ApJ, 535, 30\n\\bibitem[]{js} Jing Y. P., Suto Y., 2000, ApJ, 529, L69\n\\bibitem[]{k66} King I. R., 1966, AJ, 71, 64\n\\bibitem[]{kkbp} Kravtsov A. V., Klypin A. A., Bullock J. S., Primack J.\n R., 1998, ApJ, 502, 48\n\\bibitem[]{kronawitter} Kronawitter A., Saglia R. P., Gerhard O., Bender\n R., 2000, A\\&AS, 144, 53\n\\bibitem[]{lc} Lacey C., Cole S., 1993, MNRAS, 262, 627\n\\bibitem[]{lo} \\L okas E. L., 2000, MNRAS, 311, 423\n\\bibitem[]{lh} \\L okas E. L., Hoffman Y., 2000, ApJL, in press,\n astro-ph/0005566\n\\bibitem[]{m00} Mamon G. A., 2000, in Combes F. et al., eds, Proc. XVth IAP\nMeeting, Dynamics of Galaxies: From the Early Universe to the Present. ASP\nConference Series, 197, 377, astro-ph/9911333\n%\\bibitem[]{ml01} Mamon G. A., {\\L}okas E. L., in preparation\n\\bibitem[]{merritt85} Merritt D., 1985, AJ, 90, 1027\n\\bibitem[]{merritt87} Merritt D., 1987, ApJ, 313, 121\n\\bibitem[]{mgqsl} Moore B., Governato F., Quinn T., Stadel J., Lake G.,\n 1998, ApJ, 499, L5\n\\bibitem[]{nfw0} Navarro J. F., Frenk C. S., White S. D. M., 1995, MNRAS,\n 275, 720\n\\bibitem[]{nfw1} Navarro J. F., Frenk C. S., White S. D. M., 1996, ApJ,\n 462, 563\n\\bibitem[]{nfw2} Navarro J. F., Frenk C. S., White S. D. M., 1997, ApJ,\n 490, 493\n\\bibitem[]{osip} Osipkov L. P., 1979, PAZh, 5, 77\n\\bibitem[]{r13} Reynolds J. H., 1913, MNRAS, 74, 132\n\\bibitem[]{rt} Richstone D. O., Tremaine S., 1984, ApJ, 286, 27\n\\bibitem[]{saglia00} Saglia R. P., Kronawitter A., Gerhard O.,\nBender R., 2000, AJ, 119, 153\n\\bibitem[]{sc98} Salaris M., Cassisi S., 1998, MNRAS, 298, 166\n\\bibitem[]{ssm} Salvador-Sol\\'{e} E., Solanes J. M., Manrique A., 1998,\n ApJ, 499, 542\n\\bibitem[]{ss2} Seidov Z. F., Skvirsky P. I., 2000, preprint,\n astro-ph/0003064\n\\bibitem[]{s} S\\'ersic J. L., 1968, Atlas de Galaxies Australes,\nObservatorio Astronomico, Cordoba\n\\bibitem[]{ss} Solanes J. M., Salvador-Sol\\'{e} E., 1990, A\\&A, 234, 93\n\\bibitem[]{sp} Spitzer L., 1969, ApJ, 158, L139\n\\bibitem[]{smt} Swaters R. A., Madore B. F., Trewhella M., 2000, ApJL,\n 531, 107\n\\bibitem[]{thomas} Thomas P. A. et al., 1998, MNRAS, 296, 1061\n\\bibitem[]{t} Tonry J. L., 1983, ApJ, 266, 58\n\\bibitem[]{tbw} Tormen G., Bouchet F. R., White S. D. M., 1997, MNRAS,\n 286, 865\n\\bibitem[]{vdbs} van den Bosch F. C., Swaters R. A., 2000, submitted to AJ,\n astro-ph/0006048\n\\bibitem[]{vdb} van den Bosch F. C., Robertson B. E., Dalcanton J. J.,\n de Blok W. J. G., 2000, AJ, 119, 1579\n\\bibitem[]{vdm} van der Marel R. P., Magorrian J., Carlberg R. G., Yee H.\n K. C., Ellingson E. 2000, AJ, 119, 2038\n\\bibitem[]{wid} Widrow L. M., 2000, submitted to ApJ, astro-ph/0003302\n\n\\end{thebibliography}\n\n\\end{document}"
}
] |
[
{
"name": "astro-ph0002395.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[]{amkb} Adami C., Mazure A., Katgert P., Biviano A., 1998, A\\&A,\n 336, 63\n\\bibitem[]{afh98} Avila-Reese V., Firmani C., Hernandez X., 1998, ApJ, 505,\n 37\n\\bibitem[]{afh99} Avila-Reese V., Firmani C., Klypin A., Kravtsov A. V.,\n 1999, MNRAS, 310, 527\n\\bibitem[]{b96} Bartelmann M., 1996, A\\&A, 313, 697\n\\bibitem[]{bpms93} Bertola F., Pizzella A., Persic M., Salucci P., 1993,\n ApJ, 416, L45\n\\bibitem[]{be} Bertschinger E., 1985, ApJS, 58, 39\n\\bibitem[]{bm} Binney J., Mamon G. A., 1982, MNRAS, 200, 361\n\\bibitem[]{bt} Binney J., Tremaine S., 1987, Galactic Dynamics. Princeton\n Univ. Press, Princeton, chap. 4.4.3\n\\bibitem[]{bu} Bullock J. S., Kolatt T. S., Sigad Y., Somerville R. S.,\n Kravtsov A. V., Klypin A. A., Primack J. R., Dekel A., 1999,\n submitted to MNRAS, astro-ph/9908159\n\\bibitem[]{ccdo} Caon N., Capaccioli M., D'Onofrio M., 1993, MNRAS, 265,\n 1013\n\\bibitem[]{c} Carlberg R. G. et al., 1997, ApJ, L13\n\\bibitem[]{ci} Ciotti L., 1991, A\\&A, 249, 99\n\\bibitem[]{cl} Cole S., Lacey C., 1996, MNRAS, 281, 716\n\\bibitem[]{dm92} Dejonghe H., Merritt D., 1992, ApJ, 391, 531\n\\bibitem[]{dv} de Vaucouleurs G., 1948, Ann. Ap. 11, 247\n\\bibitem[]{dvc79} de Vaucouleurs G., Capaccioli M., 1979, ApJS, 40, 699\n\\bibitem[]{edd16} Eddington A. S., 1916, MNRAS, 76, 572\n\\bibitem[]{ecf} Eke V. R., Cole S., Frenk C.S., 1996, MNRAS, 282, 263\n\\bibitem[]{fg} Fillmore J. A., Goldreich P., 1984, 281, 1\n\\bibitem[]{fp} Flores R. A., Primack J. R., 1994, ApJ, 427, L1\n\\bibitem[]{fm} Fukushige T., Makino J., 1997, ApJ, 477, L9\n\\bibitem[]{geb} Gebhardt K. et al., 2000, AJ, 119, 1157\n\\bibitem[]{gmglqs} Ghigna S., Moore B., Governato F., Lake G., Quinn T.,\n Stadel J., 1999, submitted to ApJ, astro-ph/9910166\n\\bibitem[]{go} Gott J. R., 1975, ApJ, 201, 296\n\\bibitem[]{ghj} Goudfrooij P., Hansen L., J\\o rgensen H. E.,\n N\\o rgaard-Nielsen H. U., de Jong T., van den Hoek L. B., 1994, A\\&AS,\n 104, 179\n\\bibitem[]{gu} Gunn J. E., 1977, ApJ, 218, 592\n\\bibitem[]{gg} Gunn J. E., Gott J. R., 1972, ApJ, 176, 1\n\\bibitem[]{h} Hernquist L., 1990, ApJ, 356, 359\n\\bibitem[]{hs} Hoffman Y., Shaham J., 1985, ApJ, 297, 16\n\\bibitem[]{hjs1} Huss A., Jain B., Steinmetz M., 1999a, MNRAS, 308,\n1011\n\\bibitem[]{hjs2} Huss A., Jain B., Steinmetz M., 1999b, ApJ, 517, 64\n\\bibitem[]{j} Jaffe W., 1983, MNRAS, 202, 995\n\\bibitem[]{j99} Jing Y. P., 2000, ApJ, 535, 30\n\\bibitem[]{js} Jing Y. P., Suto Y., 2000, ApJ, 529, L69\n\\bibitem[]{k66} King I. R., 1966, AJ, 71, 64\n\\bibitem[]{kkbp} Kravtsov A. V., Klypin A. A., Bullock J. S., Primack J.\n R., 1998, ApJ, 502, 48\n\\bibitem[]{kronawitter} Kronawitter A., Saglia R. P., Gerhard O., Bender\n R., 2000, A\\&AS, 144, 53\n\\bibitem[]{lc} Lacey C., Cole S., 1993, MNRAS, 262, 627\n\\bibitem[]{lo} \\L okas E. L., 2000, MNRAS, 311, 423\n\\bibitem[]{lh} \\L okas E. L., Hoffman Y., 2000, ApJL, in press,\n astro-ph/0005566\n\\bibitem[]{m00} Mamon G. A., 2000, in Combes F. et al., eds, Proc. XVth IAP\nMeeting, Dynamics of Galaxies: From the Early Universe to the Present. ASP\nConference Series, 197, 377, astro-ph/9911333\n%\\bibitem[]{ml01} Mamon G. A., {\\L}okas E. L., in preparation\n\\bibitem[]{merritt85} Merritt D., 1985, AJ, 90, 1027\n\\bibitem[]{merritt87} Merritt D., 1987, ApJ, 313, 121\n\\bibitem[]{mgqsl} Moore B., Governato F., Quinn T., Stadel J., Lake G.,\n 1998, ApJ, 499, L5\n\\bibitem[]{nfw0} Navarro J. F., Frenk C. S., White S. D. M., 1995, MNRAS,\n 275, 720\n\\bibitem[]{nfw1} Navarro J. F., Frenk C. S., White S. D. M., 1996, ApJ,\n 462, 563\n\\bibitem[]{nfw2} Navarro J. F., Frenk C. S., White S. D. M., 1997, ApJ,\n 490, 493\n\\bibitem[]{osip} Osipkov L. P., 1979, PAZh, 5, 77\n\\bibitem[]{r13} Reynolds J. H., 1913, MNRAS, 74, 132\n\\bibitem[]{rt} Richstone D. O., Tremaine S., 1984, ApJ, 286, 27\n\\bibitem[]{saglia00} Saglia R. P., Kronawitter A., Gerhard O.,\nBender R., 2000, AJ, 119, 153\n\\bibitem[]{sc98} Salaris M., Cassisi S., 1998, MNRAS, 298, 166\n\\bibitem[]{ssm} Salvador-Sol\\'{e} E., Solanes J. M., Manrique A., 1998,\n ApJ, 499, 542\n\\bibitem[]{ss2} Seidov Z. F., Skvirsky P. I., 2000, preprint,\n astro-ph/0003064\n\\bibitem[]{s} S\\'ersic J. L., 1968, Atlas de Galaxies Australes,\nObservatorio Astronomico, Cordoba\n\\bibitem[]{ss} Solanes J. M., Salvador-Sol\\'{e} E., 1990, A\\&A, 234, 93\n\\bibitem[]{sp} Spitzer L., 1969, ApJ, 158, L139\n\\bibitem[]{smt} Swaters R. A., Madore B. F., Trewhella M., 2000, ApJL,\n 531, 107\n\\bibitem[]{thomas} Thomas P. A. et al., 1998, MNRAS, 296, 1061\n\\bibitem[]{t} Tonry J. L., 1983, ApJ, 266, 58\n\\bibitem[]{tbw} Tormen G., Bouchet F. R., White S. D. M., 1997, MNRAS,\n 286, 865\n\\bibitem[]{vdbs} van den Bosch F. C., Swaters R. A., 2000, submitted to AJ,\n astro-ph/0006048\n\\bibitem[]{vdb} van den Bosch F. C., Robertson B. E., Dalcanton J. J.,\n de Blok W. J. G., 2000, AJ, 119, 1579\n\\bibitem[]{vdm} van der Marel R. P., Magorrian J., Carlberg R. G., Yee H.\n K. C., Ellingson E. 2000, AJ, 119, 2038\n\\bibitem[]{wid} Widrow L. M., 2000, submitted to ApJ, astro-ph/0003302\n\n\\end{thebibliography}"
}
] |
astro-ph0002396
|
The spectral variations of the O-type runaway supergiant HD 188209 \author[G. Israelian et al.] {G.~Israelian,$^1$ A.~Herrero,$^1$ F.~Musaev,$^2$ A.~Kaufer,$^3$ A.~Galeev$^{4,2},$ G.~Galazutdinov$^2$\cr and E.~Santolaya-Rey$^1$\\ $^1$Insituto de Astrofisica de Canarias, E-38200 La Laguna, Tenerife, Canary Islands, Spain\\ $^2$Special Astrophysical Observatory of the Russian AS, Nizhnij Arkhyz 357147, Russia\\ $^3$ ESO, Karl-Schwarzschild-Str. 2, D-85748, Garching, Germany\\ $^4$ Department of Astronomy, Kazan State University, Kazan, Kremlevskaja Str., 420008, Russia}
|
[
{
"author": "G.~Israelian"
},
{
"author": "$^1$ A.~Herrero"
},
{
"author": "$^1$ F.~Musaev"
},
{
"author": "$^2$ A.~Kaufer"
},
{
"author": "$^3$ A.~Galeev$^{4,2}"
},
{
"author": "$ G.~Galazutdinov$^2$\\cr and E.~Santolaya-Rey$^1$"
},
{
"author": "$^1$Insituto de Astrofisica de Canarias"
},
{
"author": "E-38200 La Laguna"
},
{
"author": "Tenerife"
},
{
"author": "Canary Islands"
},
{
"author": "Spain"
},
{
"author": "$^2$Special Astrophysical Observatory of the Russian AS"
},
{
"author": "Nizhnij Arkhyz 357147"
},
{
"author": "Russia"
},
{
"author": "$^3$ ESO"
},
{
"author": "Karl-Schwarzschild-Str. 2"
},
{
"author": "D-85748"
},
{
"author": "Garching"
},
{
"author": "Germany"
},
{
"author": "$^4$ Department of Astronomy"
},
{
"author": "Kazan"
},
{
"author": "Kremlevskaja Str."
},
{
"author": "420008"
}
] |
{ We report spectral time series of the late O-type runaway supergiant HD 188209. Radial velocity variations of photospheric absorption lines with a possible quasi-period $\sim$ 6.4 days have been detected in high-resolution echelle spectra. Night-to-night variations in the position and strength of the central emission reversal of the \Ha~profile occuring over ill-defined time-scales have been observed. The fundamental parameters of the star have been derived using state-of-the-art plane--parallel and unified non-LTE model atmospheres, these last including the mass-loss rate. The derived helium abundance is moderately enhanced with respect to solar, and the stellar masses are lower than those predicted by the evolutionary models. The binary nature of this star is not suggested either from {Hipparcos\/} photometry or from radial velocity curves. }
|
[
{
"name": "hd18.tex",
"string": "\\documentstyle[psfig]{mn}\n%\\def\\baselinestretch{2}\n\\topmargin -1cm\n\\newcommand{\\HI} {H\\,{\\sc i}}\n\\newcommand{\\HII} {H\\,{\\sc ii}}\n\\newcommand{\\HeI} {He\\,{\\sc i}}\n\\newcommand{\\HeII} {He\\,{\\sc ii}}\n\\newcommand{\\NII} {N\\,{\\sc ii}}\n\\newcommand{\\NIII} {N\\,{\\sc iii}}\n\\newcommand{\\NIV} {N\\,{\\sc iv}}\n\\newcommand{\\NV} {N\\,{\\sc v}}\n\\newcommand{\\CII} {C\\,{\\sc ii}}\n\\newcommand{\\CIII} {C\\,{\\sc iii}}\n\\newcommand{\\CIV} {C\\,{\\sc iv}}\n\\newcommand{\\CV} {C\\,{\\sc v}}\n\\newcommand{\\OII} {O\\,{\\sc ii}}\n\\newcommand{\\OIII} {O\\,{\\sc iii}}\n\\newcommand{\\OIV} {O\\,{\\sc iv}}\n\\newcommand{\\OV} {O\\,{\\sc v}}\n\\newcommand{\\SiIII} {Si\\,{\\sc iii}}\n\\newcommand{\\SiII} {Si\\,{\\sc ii}}\n\\newcommand{\\SiIV} {Si\\,{\\sc iv}}\n\\newcommand{\\MgII} {Mg\\,{\\sc ii}\\,}\n\\newcommand{\\FeII} {Fe\\,{\\sc ii}\\,}\n\\newcommand{\\FeI} {Fe\\,{\\sc i}\\,}\n\\newcommand{\\SrII} {Sr\\,{\\sc ii}\\,}\n\\newcommand{\\TiII} {Ti\\,{\\sc ii}\\,}\n\\newcommand{\\CaII} {Ca\\,{\\sc ii}\\,}\n\\newcommand{\\SII} {S\\,{\\sc ii}\\,}\n\\newcommand{\\NeI} {Ne\\,{\\sc i}\\,}\n\\newcommand{\\NaI} {Na\\,{\\sc i}\\,}\n%\n\\newcommand{\\teff}{$T_{\\rm eff}$}\n\\newcommand{\\g} {$\\log g$}\n\\newcommand{\\Mv} {$M_{\\rm v}$}\n\\newcommand{\\eps} {$\\epsilon$}\n\\newcommand{\\Vr} {$V_{\\rm r}${\\thinspace}sin{\\thinspace}$i$}\n\\newcommand{\\Vrot} {$V_{\\rm r}$}\n\\newcommand{\\Vi} {$V_{\\infty}$}\n\\newcommand{\\lMp} {log \\.M}\n%\n\\newcommand{\\Hep} {H${\\epsilon}$}\n\\newcommand{\\Hd} {H${\\rm \\delta}$}\n\\newcommand{\\Hg} {H${\\rm \\gamma}$}\n\\newcommand{\\Hb} {H${\\rm \\beta}$}\n\\newcommand{\\Ha} {H${\\rm \\alpha}$}\n%\n\\newcommand{\\Rsun} {$R_{\\odot}$}\n\\newcommand{\\Msun} {$M_{\\odot}$}\n\\newcommand{\\R} {$R/R_{\\odot}$}\n\\newcommand{\\M} {$M/M_{\\odot}$}\n\\newcommand{\\lgg} {$\\log (g/g_{\\odot})$}\n\\newcommand{\\lL} {$\\log (L/L_{\\odot})$}\n\\newcommand{\\Lum} {$(L/L_{\\odot})$}\n\\newcommand{\\lT} {$\\log (T_{\\rm eff}/T_{\\odot})$}\n\\newcommand{\\lR} {$\\log (R/R_{\\odot})$}\n\\newcommand{\\lM} {$\\log (M/M_{\\odot})$}\n\\newcommand{\\lan} {$\\lambda$}\n%\n\\newcommand{\\dlR} {${\\rm \\Delta}$ ($\\log (R/R_{\\odot}))$}\n\\newcommand{\\dlM} {${\\rm \\Delta}$ ($\\log (M/M_{\\odot}))$}\n\\newcommand{\\dR} {${\\rm \\Delta}$ (($R/R_{\\odot}))$}\n\\newcommand{\\dM} {${\\rm \\Delta}$ (($M/M_{\\odot}))$}\n%\n\\newcommand{\\Ms} {$M_{\\rm s}$}\n\\newcommand{\\es} {$\\epsilon_{\\rm s}$}\n\\newcommand{\\Mo} {$M_{\\rm 0}$}\n\\newcommand{\\Mev} {$M_{\\rm ev}$} \n\\newcommand{\\eev} {$\\epsilon_{\\rm ev}$}\n\\newcommand{\\DM} {$\\Delta M$} \n\\newcommand{\\diM} {$\\delta M$} \n\\newcommand{\\gev} {log $g_{\\rm ev}$}\n%\n\\newcommand{\\MO} {$M_{\\rm O}$}\n\\newcommand{\\Mx} {$M_{\\rm x}$}\n\\title[The spectral variations of the O-type runaway supergiant HD 188209]\n{The spectral variations of the O-type runaway supergiant HD 188209\n\\author[G. Israelian et al.]\n{G.~Israelian,$^1$\n A.~Herrero,$^1$ \n F.~Musaev,$^2$\n A.~Kaufer,$^3$\n A.~Galeev$^{4,2},$\n G.~Galazutdinov$^2$\\cr and E.~Santolaya-Rey$^1$\\\\\n $^1$Insituto de Astrofisica de Canarias, E-38200 La Laguna, Tenerife,\n Canary Islands, Spain\\\\\n $^2$Special Astrophysical Observatory of the Russian AS, Nizhnij Arkhyz\n 357147, Russia\\\\\n $^3$ ESO, Karl-Schwarzschild-Str. 2, D-85748, Garching, Germany\\\\\n $^4$ Department of Astronomy, Kazan State University, Kazan, Kremlevskaja Str.,\n 420008, Russia}}\n\\date{}\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\begin{document}\n\\label{firstpage}\n\\maketitle\n\\begin{abstract}\n{\nWe report spectral time series of the late O-type runaway supergiant \nHD 188209. Radial velocity variations of photospheric absorption \nlines with a possible quasi-period $\\sim$ 6.4 days have been detected in \nhigh-resolution echelle spectra. \nNight-to-night variations in the \nposition and strength of the central emission reversal of the \n\\Ha~profile occuring over \nill-defined time-scales have been observed. The fundamental parameters \nof the star have been derived using state-of-the-art plane--parallel and \nunified non-LTE model atmospheres, these last including the mass-loss rate. \nThe derived helium abundance is moderately enhanced with respect to solar, \nand the stellar masses are lower than those predicted by the evolutionary models.\nThe binary nature of this star is not suggested either from {\\it Hipparcos\\/}\nphotometry or from radial velocity curves.\n} \n\\end{abstract}\n\n\n\n\\begin{keywords}\nStars: individual :HD 188209-- Stars: mass-loss -- Stars: early-type \n-- Stars: supergiants -- Physical data and processes: line profiles\n\\end{keywords}\n\n\n\\section{Introduction}\n\n\n\nRunaway O stars have been defined \nas a group by Blaauw (1961), who introduced the term {\\it runaway} \nto describe the space motions of AE Aur and $\\mu$ Col.\nBlaauw (1961) has also suggested that\nsuch stars were ejected in the breakup of binary systems in \nsupernova explosions by their companions. In later evolutionary\nstages, the initial secondary appears as a most massive star\nand transfers matter to the compact companion (the initial\nprimary) making the system appear as a massive X-ray binary\n(van den Heuvel 1976). \nGiven the possibility of the binary nature of runaway stars,\nit appears to be an important task to measure the radial velocity (RV)\nvariations of the photospheric lines. Systematic searches \nfor RV variations have been made in order to assess the\nbinary frequency of O stars (e.g. Garmany, Conti \\& Massey 1980; \nStone 1982, Gies 1987). In many cases the amplitude of RV variations is \nquite large, and the additional presence of a clear periodicity \nimmediately suggests a binary nature for the system. \nHowever, there are stars which show more complicated RV curves, \nand the interpretation of their spectral variability is not \nstraightforward. HD 188209 (O9.5Iab) is one of those objects. \nGarmany et al. (1980) have concluded from three spectra that this \nstar is probably not a binary, and that the RV variations must be \nattributed to atmospheric motions. This conclusion was supported\nby Musaev \\& Chentsov (1988). However, based on 21 measurements \nStone (1982) has concluded that HD 188209 can be considered\nas a spectroscopic binary with a period 57 days and small \nsemiamplitude. More recently, Fullerton, Gies \\& Bolton (1996) \nincluded HD 188209 in a large sample of stars investigated on\nthe presence of line profile variability (LPV) and found \nLPVs only in \\HeI~5876 \\AA. However, they did not flag \nHD 188209 as a velocity variable (their Table 10). \n\nThe binarity of many\nO supergiants has been proposed recently by Thaller (1997).\nThe fact that binaries have a higher incidence and an H$\\alpha$\nemission strength in post-MS stages may indicate that wind\ninteractions are a common source of emission in massive stars.\nIn other words, even in cases where RV measurements are not\navailable, the presence of \\Ha~emission in\na spectrum could be linked with colliding winds. One needs to study\norbital phase variations in the \\Ha~profile in order\nto be sure that the latter is due to colliding winds instead of\nsome other mechanism. Note that HD 188209 is an X-ray source\ndetected by {\\it ROSAT} (Berghoefer, Schmitt \\& Cassinelli 1996). \n\nIn this paper we focus on the high-resolution spectroscopic data\nof HD 188209. Our observations can possibly account for \nthe small semi-amplitudes and eccentric orbits of this binary \ncandidate since they have been accumulated at different \nperiods over a long baseline. \n\n\\section{Observations}\n\nThe observations have been carried out in different runs (Table 1) using \nthe the Coud\\'{e} Echelle Spectrometer (Musaev 1993) at the 1-m telescope\nof the Special Astrophysical Observatory of the Russian Academy of\nScience. Most of the spectra have a signal-to-noise ratio\nS/N$\\ge$100 per resolution element, and an average resolution \n$R = $ 40000 in the wavelength region 4400--7000 \\AA. Preliminary \nreduction of the echelle spectra CCD images was made using \nthe {\\sc dech} code (Galazutdinov 1992), which allows\nthe flat-field division, bias/background subtraction, one-dimensional \nspectrum extraction from two-dimensional images, \nexcision of cosmic-ray features, spectrum addition, \ncorrection for diffuse light, etc. Numerous bias, flat-field\nhave been obtained every night. Each image was subject to a\nbias-frame subtraction and flat-field division using nightly\nmeans. Comparison exposures of a Th-Ar lamp were taken for each \nstellar spectrum. The control measurements of interstellar \\CaII~\nand \\NaI~D lines revealed a small scatter of 0.8 $~{\\rm km}~{\\rm s}^{-1}$ \n(1 $\\sigma$). However, the 1 $\\sigma$ dispersion of the velocity\nof the DIB was 1.5 $~{\\rm km}~{\\rm s}^{-1}$. These interstellar\nlines have been used to align all the spectra in the time series\naccurately. As an indicator of the overall\nprecision of our measurements we have adopted 1 $\\sigma$ \ndispersion 1.5 $~{\\rm km}~{\\rm s}^{-1}$ of the velocity of the DIB. \nAll stellar absorption lines exhibited variations about their\nrespective mean velocities at least 2-3 times the dispersion \nof the DIB velocities. The mean rms obtained from different \ndispersion curves was at least 0.003 \\AA. The Coud\\'{e} Echelle \nSpectrograph was not a subject to mechanical and/or thermal instabilities. \n\n We used a 580$\\times$530 (pixel size 24 $\\times$ 18 $\\mu$m)\nCCD camera in all runs except 8 and 9. The last run was carried out \nusing the Coud\\'{e} Echelle Spectrograph (Musaev, 1999) at the 2-m \ntelescope located in Terskol (North Caucasus, Russia). The CCD used in\nlast two runs had a larger matrix (WI 1242$\\times$1152 pixel with\npixel size 22.5 $\\times$ 22.5 $\\mu$m) allowing a coverage in a \nsingle exposure of the region $\\sim$ 3500--10100 \\AA\\ with almost \nthe same resolution. \n \n\\def\\baselinestretch{1}\n\n\\begin{table}\n\\caption{Journal of Observations. The second column gives the universal \nplus exposure time and in third column is the spectral region. \nThe S/N ratio is given at 6600 \\AA.}\n\\begin{flushleft}\n\\begin{tabular}{lllrr}\n\\hline\\noalign{\\smallskip}\nRun & Date & UT + EXP & Region & S/N \\\\\n &(dd.mm.yy)& & (\\AA) & \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n\n1 & 14.06.93 & 20h 35m+30m & 4800--7500 & 100 \\\\\n & 07.07.93 & 20h 40m+30m & 4420--6710 & 100 \\\\\n & 08.07.93 & 19h 25m+20m & 4350--4510 & 200 \\\\\n & & & 6540--6720 & \\\\\n2 & 04.09.93 & 21h 53m+30m & 4350--4510 & 200 \\\\\n & & & 6540--6720 & \\\\\n & 05.09.93 & 23h 55m+20m & 4350--4510 & 200 \\\\\n & & & 6540--6720 & \\\\\n & 06.09.93 & 20h 40m+20m & 4350--4510 & 200\\\\\n & & & 6540--6720 & \\\\\n & 07.09.93 & 20h 07m+45m & 4350--4510 & 200 \\\\\n & & & 6540--6720 & \\\\\n & 09.09.93 & 22h 40m+45m & 4350--4510 & 200 \\\\\n & & & 6540--6720 & \\\\\n3 & 07.10.93 & 17h 46m+60m & 4370--6720 & 150 \\\\\n & 08.10.93 & 17h 35m+60m & 4370--6720 & 150 \\\\\n & 09.10.93 & 17h 40m+60m & 4370--6720 & 150 \\\\\n & 10.10.93 & 18h 32m+60m & 4370--6720 & 150 \\\\\n4 & 31.10.93 & 16h 22m+30m & 4330--4520 & 200 \\\\\n & & & 6540--6720 & \\\\\n & 01.11.93 & 20h 32m+30m & 4330--4520 & 200 \\\\\n & & & 6540--6720 & \\\\\n & 02.11.93 & 16h 18m+45m & 4400--6800 & 100 \\\\\n5 & 24.11.93 & 17h 56m+45m & 4420--7000 & 100 \\\\\n & 25.11.93 & 17h 02m+60m & 4420--7000 & 150 \\\\\n & 27.11.93 & 19h 15m+60m & 4420--7000 & 150 \\\\\n & 28.11.93 & 16h 50m+60m & 4420--7000 & 150 \\\\\n & 29.11.93 & 16h 41m+60m & 4420--7000 & 150 \\\\\n & 30.11.93 & 15h 50m+60m & 4420--7000 & 150 \\\\\n & 02.12.93 & 16h 22m+60m & 4420--7000 & 150 \\\\\n & 05.12.93 & 17h 08m+60m & 4420--7000 & 150 \\\\\n6 & 16.09.94 & 17h 27m+60m & 4420--7000 & 150 \\\\\n & 17.09.94 & 17h 26m+60m & 4420--7000 & 150 \\\\\n & 18.09.94 & 17h 18m+60m & 4420--7000 & 150 \\\\\n & 19.09.94 & 17h 36m+60m & 4420--7000 & 150 \\\\\n & 20.09.94 & 21h 21m+60m & 4420--7000 & 150 \\\\\n & 21.09.94 & 18h 01m+60m & 4420--7000 & 150 \\\\\n7 & 13.10.94 & 17h 00m+60m & 4350--6710 & 150 \\\\\n & 15.10.94 & 16h 40m+60m & 4350--6710 & 150 \\\\\n & 16.10.94 & 20h 20m+60m & 4350--6710 & 150 \\\\\n & 17.10.94 & 18h 01m+60m & 4350--6710 & 150 \\\\\n & 25.10.94 & 18h 00m+60m & 4350--6710 & 150 \\\\\n & 27.10.94 & 19h 06m+40m & 4350--6710 & 100 \\\\\n & 29.10.94 & 16h 36m+40m & 4350--6710 & 100 \\\\\n8 & 15.05.97 & 00h 35m+45m & 3380--10060 & 200 \\\\\n & 15.05.97 & 21h 56m+60m & 3380--10060 & 250 \\\\\n & 16.05.97 & 21h 09m+60m & 3380--10060 & 250 \\\\\n & 30.08.97 & 19h 03m+30m & 4420--6800 & 100 \\\\\n9 & 08.03.98 & 02h40m+30m & 3560--10060 & 200 \\\\\n & 09.03.98 & 01h50m+45m & 3560--10060 & 250 \\\\\n & 10.03.98 & 02h02m+45m & 3560--10060 & 250 \\\\\n & 11.03.98 & 01h32m+20m & 3560--10060 & 200 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\end{table}\n\n\n\\begin{figure*}\n\\vbox{\\psfig{file=fig1.ps,width=17.5cm,height=11.0cm,angle=270}}\n\\caption[]{ {\\it Hipparcos} photometry of HD 188\\,209.}\n\\end{figure*}\n\n\\def\\baselinestretch{2}\n\n\\section{Photometry}\n\nThe photometry of HD 188209 obtained with\n{\\it Hipparcos} (ESA 1997) is presented in Figure 1. \nThe approximate response curve for the Hp$_{\\rm dc}$ passband (see\nvan Leeuwen et al. 1997) is very extended with a maximum at\n$\\sim$ 4500 \\AA. Our observations did not reveal a strong\nvariability in the equivalent widths of the\nstrongest lines in the spectrum of HD 188209, which suggests \nthat the variations detected by {\\it Hipparcos}\nin the Hp$_{\\rm dc}$ band are due to changes in the \ncontinuum flux. The mean value of Hp$_{\\rm dc}$=5.605 has a \nstandard deviation 0.0155. The level of photometric variability is \nsignificant and cannot be ascribed to standard errors in the\nHp$_{\\rm dc}$ magnitude of the order of 0.005 (van Leeuwen et al. 1997).\nTests on the periodicity of the photometric variations were\nperformed but no convincing period has been found. However, \nconsidering the large gaps in different {\\it Hipparcos} measurements\nwe cannot definitely rule out short-term photometric periodicity.\n\n\n\\section{Fundamental Parameters of HD~188209}\n\n\\subsection{Plane--parallel analysis}\n\nTo analyse the spectrum of HD 188209 we first determine the \nrotational velocity from the \nwidth of 11 metal lines of C, N, O, Si, Mg and Ca, adopting\na Gaussian instrumental profile with a FWHM of 0.13 \\AA.\nThe resulting value was a projected rotational velocity\nof 82.0 $\\pm$ 8.5 km~s$^{-1}$, in good agreement with \nthe value of 87$~{\\rm km}~{\\rm s}^{-1}$ reported by Penny (1996),\nand between those given by Conti and Ebbets (1977) and\nHowarth et al. (1997) who give 70 and 92$~{\\rm km}~{\\rm s}^{-1}$,\nrespectively. \n\nThe method followed in determining the stellar parameters from the\nspectrum using NLTE, plane--parallel hydrostatic model atmospheres\nhas been described in detail by Herrero et al. (1992, and \nreferences therein). Briefly, we determine, at a fixed helium \nabundance, the gravity that best fits the different \nH and He profiles at a given temperature for a set of temperatures.\nIf the abundance is right, the lines in the \\teff --\\g~ diagram\nwill ideally cross at a point, giving the stellar \\teff~ and \\g. Usually,\nthey form an intersection region, whose central point is taken as\ngiving the stellar parameters, and whose limits give the adopted error.\nIf the lines do not cross at any point, the helium abundance is changed.\nThe helium abundance giving the smaller intersection region for all\nprofiles is the one selected. The center of the intersection region is \ntaken again as that giving the stellar parameters.\n\nRecently, McErlean, Lennon \\& Dufton~\\cite{mc98} and Smith \\& Howarth~ \n\\cite{sh98} have shown that different \\HeI~ lines give different\nhelium abundances in the region of the \\teff -- \\g~ diagram\noccupied by HD 188209. They attribute this to the effect\nof microturbulence and show that a value of around 10 km s$^{-1}$\nis appropriate for bringing most of the \\HeI~ lines into agreement.\n Thus, we adopt \nthis value for HD 188209 and carry out the analysis in the way \ndescribed above.\n\n\\def\\baselinestretch{1}\n\n\\begin{figure*}\n\\label{spfit}\n\\psfig{{figure=fig2.ps,width=18.5cm,height=22cm}}\n\\caption[] {The fit to the HD 188209 lines using unified models.\na) \\Hg ; b) \\HeI~ 4471; c) \\HeI~ 4387;\nd) \\HeI~ 4922; e) \\HeII~ 4200, and f) \\HeII~ 4541 \\AA (see text for details).}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\label{spfit}\n\\psfig{{figure=fig3.ps}}\n\\caption[] {The fit to the HD 188209 lines using unified models.\na) \\Hg ; b) \\HeI~ 4471; c) \\HeI~ 4387;\nd) \\HeI~ 4922; e) \\HeII~ 4200, and f) \\HeII~ 4541 \\AA (see text for details).}\n\\end{figure*}\n\n\\def\\baselinestretch{2}\n\nWith this method we have determined the stellar parameters of HD 188209.\nWe obtained \\teff= 31\\,500 K $\\pm ^{1000}_{500}$, \\g= 3.0 $\\pm 0.1$\n(uncorrected for centrifugal force; because of the low rotational velocity\nwe neglect this small correction here) and \\eps= 0.12 $\\pm 0.03$\n(the abundance of helium\nwith respect to the total abundance of hydrogen plus helium, by number;\nthe solar abundance is \\eps= 0.09). The final fits for the H and He\nlines are shown in Figure 2.\n\nThe larger errors towards higher temperatures is due to a small difference\nin the two spectrograms available for \\HeII~4541 \\AA. Using the \nsecond one, we would have obtained a \\teff~ of 32\\,000 K, all other\nparameters remaining the same. For this reason, we have enlarged\nthe error bar in this direction. Remember that the errors given are\nformal errors, in the sense that they express the uncertainty\nin the fit using the models described above.\n \nAs has been show by Herrero \\cite{h94} the metal opacity in the\nUV (line blocking) could also affect the value of the parameters \ndetermined. However, at the relatively low temperature of HD 188209\nthe effect would be minor, moving \\teff~ towards higher temperatures\nwithin the error box.\n\nWith the stellar parameters given above we can determine the\nradius, luminosity and mass of HD 188209 as described in Herrero \net al. (1992). For \\Mv = $-$6.0 mag ($M_{\\rm bol}$ = $-$9.0 mag) \ngiven by Howarth \\& Prinja (1989) we obtain \\R = 20.9, \\lL = 5.59 \nand \\M = 16.6. The errors are again as in Herrero et al. (1992): \n$\\pm$0.06 in \\lR, $\\pm$0.16 in \\lL~ and $\\pm$0.22 in \\lM.\n\nHD 188209 does not formally show the helium discrepancy, as the solar\nhelium abundance is within the error bars. However, it shows\nthe mass discrepancy: the mass derived from the plane--parallel\nspectroscopic analysis is, even including the error bars, much\nlower than the one derived from the evolutionary tracks\nfrom Schaller et al. \\cite{sch92}.\n\n\\subsection{Unified model analysis}\n\nAfter having the parameters from the plane--parallel analysis, we\ncan try to use a spherical, non-hydrostatic model\natmosphere in order to improve the already derived \nparameters and also to obtain the mass-loss rate. In a supergiant\nlike HD 188209 this can have an important impact on the\nfinal parameters. Usually, it is also assumed that this will\ncontribute to the reduction in the mass discrepancy.\n\nThe unified code we use is that recently developed by Santolaya--Rey,\nPuls \\& Herrero \\cite{sph97}. The reader will find all the details \ntherein, but for our present purposes we mention that the code uses\nspherical geometry, with a $\\beta$--velocity field, and treats\nthe wind and the photosphere in a unified way. It also makes\nuse of the NLTE-Hopf functions. Stark broadening is included in the\nformal solution, and the model atoms are the same as in the\nplane--parallel case (slightly adapted for the new program).\n\nWe begin by estimating the mass-loss rate from the \\Ha~profile,\nand then, with this mass-loss rate, we try again to find the\nbest gravity (from the \\Hg~wings), effective temperature \nand He abundance (from the He ionization equilibrium).\nWith the new parameters, we again try to fit the \\Ha~ by \nvarying the mass-loss rate, and so on. In the whole process \nwe take the wind terminal velocity from Haser (1995), who\ngives 1700 km s$^{-1}$. Note that Howarth et al. (1997), give a\nsimilar value of 1650 km s$^{-1}$. \n\nWe have used for the analysis the same lines as in Fig. 2, but have\nincluded \\HeI~4471 \\AA\\ instead of \\Hb (that improved as does \\Hg)\nto show the dilution effect (see below). \nIn Fig. 3 we show the fit of the \\Hg, \\HeI~and \\HeII~lines.\nThe adopted parameters are now \\teff = 31\\,500 K, \\g = 3.00\nand \\eps= 0.12, i.e. the same parameters as in the plane--parallel case,\neven for the gravity (again adopting a microturbulent velocity of 10 \nkm s$^{-1}$). Thus, the unified models do not contribute\nin this case to changes in the mass discrepancy\nfound with the plane--parallel models (nor in the He abundance).\nWe can also see in Fig. 3 \nthat the \\HeI~4471 line shows the well known dilution effect\nmentioned by Voels et al. \\cite{vo89}, although the other He lines fit \nperfectly well. This effect merits an explanation.\n\nThe fitting of the \\Ha~profile needed \nto derive the mass-loss rate cannot be done properly.\nThe profile is highly variable, and we have adopted a qualitative\napproach: we have simply tried to give upper and lower limits to\nthe mass-loss rate. As an example, we illustrate the procedure\nin Fig. 4, where we show one of the profiles with\nvarious mass-loss rates for the stellar parameters given above.\nThe theoretical mass-loss rate values shown in Fig. 4\nare \\lMp = $-$5.70, $-$5.80 and $-$5.90 (with \\.M in \\Msun /yr). \nThis situation is\nsimilar to that found by Herrero et al. \\cite{h95} for Cygnus X--1.\nThe profile shown cannot be adopted as either an average or a \nrepresentative one, as the profile varies a lot. The figure is only\nfor illustrative purposes. An average logarithmic mass-loss rate for \nHD~188209 would be between $-$6.0 and $-$5.7. These values are \nalso in agreement with the profiles in Fig. 3, where\nthe adopted mass-loss rate was \\lMp =$-$5.80 \n(corresponding to 1.58 10$^{-6}$ \\Msun /yr). We should point out\nthat other values of the mass-loss rate give worse\nfits to the \\Hg~and \\HeI~lines, by strongly modifying the\nline cores.\n\n\n\\section{Radial velocity variations of the absorption lines}\n\n\\def\\baselinestretch{1}\n\n\\begin{figure}\n\\label{halfa}\n\\vbox{\\psfig{figure=fig4.ps,width=8.0cm,height=7.0cm}}\n\\caption[]{The \\Ha~profiles of HD 188209 observed on 1993 \nSeptember 7 enclosed by\ndifferent theoretical profiles calculated for \\lMp = $-$5.70, $-$5.80 and\n$-$5.90 (dotted, dashed and dash--dotted lines, respectively)\nfor the parameters given in text. The selected observed \n\\Ha~profile is neither an average nor \nrepresentative, and the figure merely illustrates the approach we\nhave followed.}\n\\end{figure}\n\n\\begin{figure}\n\\vbox{\\psfig{file=fig5.ps,width=9.5cm,height=8.0cm,angle=90}}\n\\caption[]{Mean radial velocities of different groups of lines\nversus TEE. A linear fit (0.1527,-17.05) provides a non-parametric \ncorrelation coefficient 0.73.}\n\\end{figure}\n\n\\begin{figure}\n\\vbox{\\psfig{file=fig6.ps,width=9.5cm,height=8.0cm,angle=90}}\n\\caption[]{Standard deviations of mean radial velocities of\ndifferent groups of lines versus TEE. A linear fit ($-$0.049,8.474) \nprovides a non-parametric correlation coefficient 0.76.}\n\\end{figure}\n\n\\def\\baselinestretch{2}\n\n\nThe radial velocity variations in stars can have instrumental, internal\n(atmospheric) and/or external (Keplerian) origin. Instrumental effects\nin our measurements are minimized due to the high resolution and high\nS/N of the data presented. The internal accuracy achieved for the\nwavelength calibrations is of the order 1.5 ${\\rm km}~{\\rm s}^{-1}$ as\nderived from the scatter of measured radial velocities of interstellar \nand telluric lines in the spectra. Note that all former studies \nof HD 188209 (except\nfor five spectra obtained by Fullerton et al. 1996) were based on \nthe photographic spectra. Atmospheric pulsations of early-type stars\nhave been the subject of extensive studies (e.g. Burki 1978; Bohannan\n\\& Garmany 1978, Kaufer et al. 1997, Fullerton et al. 1996) \nand have been reviewed by Baade (1988, 1998). \nGies (1987) has compared the velocity distribution and binary frequency\namong 195 Galactic O-type stars (cluster and association, field and runaway)\nand found a deficiency of spectroscopic binaries among field stars \n(and especially among the runaway).\nThe most comprehensive radial velocity studies of OB and BA supergiants\nto date are those of Fullerton et al. (1996) and Kaufer et al. (1996; 1997). \nRadial pulsation periods with P$\\leq$5$^{\\rm d}$ have been predicted\nfor O-type supergiants (Burki 1978; de Jager 1980; Levy et al. 1984). The \npresence of pulsations or random motions in stellar atmospheres results in\ncomplex velocity curves for different spectral lines due to \nstratification effects (Abt 1957). This is in contrast to Keplerian\nmotions where all the lines vary synchronously with time (Ebbets 1979;\nGarmany et al. 1980). However, in many cases the amplitude \nof the RV variations does not exceed 25--30~${\\rm km}~{\\rm s}^{-1}$,\nand it is very difficult to distinguish whether these variations\nare of an internal or an external nature. Additional difficulty comes\nfrom the possible presence of non-radial pulsations (NRP). Variable profiles\n(LPVs) have been detected in many narrow-line supergiants (e.g. Baade 1988; \nKaufer et al. 1997; Fullerton et al. 1996) and in some cases they\ncorrespond to the radial velocity variations measured in photographic\nspectra. However, in contrast to broad-line supergiants, clear evidence\nof NRPs in narrow- and intermediate-line O-type supergiants has not \nyet been found. Although LPVs are a common occurrence among the O-type\nstars, some of them (like HD 34656; Fullerton, Gies \\& Bolton 1991)\nshow a variability which consists of cyclical fluctuations in radial\nvelocity due to pulsations in a fundamental mode. \n\n\\def\\baselinestretch{1}\n\n\\begin{figure*}\n\\vbox{\\psfig{file=period.ps,width=17.5cm,height=16.0cm,angle=0}}\n\\caption[]{Lomb-Scargle (top panel) and CLEAN periodograms of the \naverage RV for each date obtained by averaging the RVs \nof all the groups.}\n\\end{figure*}\n\n\\begin{figure*}\n\\vbox{\\psfig{file=fig7.ps,width=15.5cm,height=13.0cm,angle=0}}\n\\vbox{\\psfig{file=fig8.ps,width=15.5cm,height=13.0cm,angle=0}}\n\\caption[]{The fitting of a sin curve to folded data for a period\n6.4 days. The curve is derived for RV=$-$9.8+4.17$\\sin$\n[2$\\pi$(JD-318.629)/6.406].}\n\\end{figure*}\n\n\\def\\baselinestretch{2}\n \nCareful inspection of our time series showed that all\nabsorption lines varied in position over the course of a day. \nWe have detected a few asymmetric profiles of He lines but there were \nno signatures of moving features. It is however possible that the S/N ratio \nof our data is not high enough to trace LPVs. Small \ndistortions in profile shape are typically less than 1\\% of the \ncontinuum strength and a minimum S/N ratio required would be \nat least 300 (Fullerton et al. 1996). \n\n\n\\subsection{The velocity-excitation relationship}\n\nWe have selected unblended lines by utilizing theoretical synthetic \nspectra computed for the model atmosphere of HD 188209 and measured RVs \nby fitting a Gaussian to \nthe line profile. The following groups of lines have been selected:\n\\HeI~(4921, 4471, 4713, 5015, 5047, 5876, 6678 \\AA), \\HeII~(5411,\n 4541, 4686 \\AA), \\SiIV~(4654, 4631 \\AA), \\CIII~(4650, 4647, 5696 \\AA), \n\\SiIII~(4567, 4552, 4574 \\AA), \\CIV~(5801, 5811 \\AA), \n\\NIII~(4514, 4510, 4518, 4523 \\AA), \\OII~4661 \\AA\\ and\n\\MgII~4481 \\AA. \nThe average RVs computed for each of these groups of lines are listed \nin Table 2. It is normally assumed that lines of different total excitation\nenergy (TEE, ionization energy plus excitation energy of the\nlower level) form in different layers of the atmosphere (Hutchings 1976). \nHowever, it is not clear whether the stratification\nexists in a dynamically active, pulsating atmosphere. One can \nassume that the time scale of dynamical processes (pulsations,\nstochastic motions etc.) is much less than the time necessary for\nthe establishment of radiative equilibrium. Thus, while pulsating, \nthe atmosphere is supposed to pass through a chain of hydrostatic stages.\nThe assumption that TEE correlates with line formation depths\ncan be tested as well. We applied our plane--parallel models to\ncompute formation depths of the line cores of the \\HeI~and \\HeII~lines.\nIt appeared that the core of the strong \\HeII~4686 \\AA\\ line forms\nmuch closer to the surface (at column mass $\\sim$ 0.01 g\\,cm$^{-2}$) \nthan any of the \\HeI~lines. However, this was not the case with the\ntwo other \\HeII~lines (5411 and 4541 \\AA) we used in our study. \nSimilar tests have been carried out for other groups of lines \nbut assuming an LTE line formation. These exercises suggest \nthat before combining lines in different groups and computing \ntheir average RVs, one has to be sure (of course under the \nassumption that our plane--parallel models are applicable) that their\ndepths of formation are similar. \n\n\\def\\baselinestretch{1} \n\n \n\\begin{table*}\n\\caption{ Radial velocities of different groups of lines.}\n\\begin{flushleft}\n\\begin{tabular}{lllllllllrr}\n\\hline\\noalign{\\smallskip}\nDate & He\\,{\\sc i} & He\\,{\\sc ii} & Si\\,{\\sc iv} & C\\,{\\sc iii} & Si\\,{\\sc iii} & C\\,{\\sc iv} &\nN\\,{\\sc iii} & O\\,{\\sc ii} 4661 \\AA\\ & Mg\\,{\\sc ii} 4481 \\AA\\ \\\\\nTEE (eV) & 21 & 75 & 57 & 54 & 35 & 85 & 57 & 36 & 8.5 \\\\\n\\noalign{\\smallskip}\n\\hline\\noalign{\\smallskip}\n2449176.36 & $-$12.3 & $-$11.2 & $-$6.3 & $-$8.1 & $-$15.9 & $-$13.2 & $-$8.4 &\n$-$26.4 & $-$19.4 \\\\\n2449268.24 & $-$5.9 & $-$1.4 & 6.9 & $-$4.9 & $-$13.8 & $-$2.9 & $-$5.6 & $-$18.8 & $-$1.3 \\\\\n2449269.23 & $-$10.9 & $-$2.1 & $-$0.3 & $-$11.7 & $-$15.1 & $-$4.8 & $-$8.0 & $-$24.1 & $-$15.3 \\\\\n2449270.24 & $-$10.3 & $-$8.1 & 5.5 & $-$7.5 & $-$11.7 & $-$0.1 & $-$6.8 & $-$12.8 & $-$11.6 \\\\\n2449271.27 & $-$15.7 & $-$16.5 & $-$7.6 & $-$17.4 & $-$35.5 & $-$16.9 & $-$12.3 &\n$-$18.2 & $-$14.9 \\\\\n2449294.18 &~ 7.9 &~ 11.1 &~ 6.4 & $-$0.7 & $-$4.6 & $-$1.5 &~ 2.4 & $-$4.4 & $-$0.6 \\\\\n2449316.25 & $-$17.3 & $-$6.5 & $-$1.6 & $-$13.7 & $-$25.3 & $-$0.7 & $-$10.8 &\n$-$22.7 & $-$4.3 \\\\\n2449317.21 & $-$17.2 & $-$12.9 & $-$13.5 & $-$10.4 & $-$22.5 & $-$14.7 & $-$12.2 &\n$-$24.9 & $-$20.9 \\\\\n2449319.30 & $-$4.5 & $-$1.6 &~ 3.3 &~ 3.1 & $-$17.1 & $-$6.1 & $-$5.6 & $-$15.7 & $-$5.4 \\\\\n2449320.20 & $-$8.5 &~ 2.4 &~ 1.5 & $-$1.4 & $-$23.0 & $-$6.0 & $-$1.3 & $-$27.6 & $-$12.2 \\\\\n2449321.20 & $-$2.6 &~ 2.7 &~ 8.4 &~ 1.2 & $-$3.9 & $-$0.2 &~ 0.1 &\n$-$14.9 & $-$6.5 \\\\\n2449322.16 & $-$16.0 & $-$7.5 & $-$3.5 & $-$9.1 & $-$16.3 & $-$11.9 & $-$11.5 &\n$-$28.5 & $-$38.1 \\\\\n2449324.18 & $-$14.8 & $-$5.2 & $-$7.1 & $-$9.9 & $-$20.9 & $-$5.8 & $-$10.6 &\n$-$33.5 & $-$36.2 \\\\\n2449327.21 & $-$1.3 & $-$1.6 &~ 8.6 & $-$3.7 &~ 1.4 &~ 1.6 & $-$3.7 & $-$20.5 & $-$35.8 \\\\\n2449612.23 & $-$15.3 & $-$11.1 & $-$13.9 & $-$11.7 & $-$22.7 & $-$11.5 & $-$11.9 &\n$-$17.2 & $-$18.8 \\\\\n2449613.23 & $-$10.6 & $-$6.2 & $-$7.9 & $-$8.6 & $-$12.7 & $-$5.6 & $-$6.2 & $-$15.8 & $-$11.0 \\\\\n2449614.22 & $-$14.5 & $-$8.7 & $-$8.2 & $-$10.4 & $-$19.6 & $-$6.6 & $-$8.5 &\n$-$16.9 & $-$9.6 \\\\\n2449615.23 & $-$9.2 & $-$4.7 & $-$1.6 & $-$12.3 & $-$16.7 & $-$4.9 & $-$6.4 & $-$15.7 & $-$22.9 \\\\\n2449616.39 & $-$10.2 & $-$6.4 & $-$5.4 & $-$8.7 & $-$16.2 & $-$4.6 & $-$5.2 & $-$14.2 & $-$20.0 \\\\\n2449617.25 & $-$15.6 & $-$7.6 & $-$9.4 & $-$11.5 & $-$23.8 & $-$10.4 & $-$10.7 &\n$-$23.2 & $-$18.2 \\\\\n2449639.21 & $-$0.5 &~ 0.3 &~ 2.3 & $-$0.4 & $-$8.7 & $-$1.4 &~ 0.2 & $-$13.9 & $-$6.5 \\\\\n2449641.19 & $-$2.0 &~ 3.7 & $-$1.1 & $-$4.1 & $-$6.3 & $-$4.1 & $-$3.4 & $-$10.1 & $-$9.5 \\\\\n2449642.35 & $-$9.7 & $-$3.1 & $-$3.1 & $-$5.9 & $-$17.2 & $-$7.1 & $-$5.9 & $-$16.3 & $-$14.9 \\\\\n2449643.25 & $-$6.1 & $-$2.7 & $-$1.2 & $-$6.9 & $-$14.9 & $-$1.6 & $-$5.0 & $-$6.4 & $-$18.0 \\\\\n2449651.25 & $-$13.4 & $-$13.3 & $-$8.3 & $-$12.3 & $-$19.9 & $-$10.5 & $-$11.8 &\n$-$23.1 & $-$18.3 \\\\\n2449653.30 & $-$6.4 & $-$0.2 & $-$5.5 & $-$6.4 & $-$9.9 & $-$8.5 & $-$7.2 & $-$25.0 & $-$11.5 \\\\\n2449655.19 & $-$8.2 & $-$4.3 & $-$3.6 & $-$7.5 & $-$3.4 & $-$3.3 & $-$7.8 & $-$15.7 & $-$9.7 \\\\\n2450583.52 & $-$11.6 & $-$7.5 & $-$7.0 & $-$16.0 & $-$15.6 & $-$9.1 & $-$11.3 &\n$-$16.4 & $-$13.9 \\\\\n2450584.41 & $-$13.4 & $-$5.8 & $-$10.8 & $-$11.6 & $-$15.9 & $-$5.6 & $-$11.4 & $-$19.9 & $-$15.3 \\\\\n2450585.38 & $-$19.2 & $-$16.9 & $-$13.9 & $-$14.6 & $-$24.9 & $-$8.9 & $-$14.2 & $-$25.3 & $-$31.4 \\\\\n2450691.25 & $-$7.6 & $-$8.6 & $-$3.2 &~ 5.6 & $-$8.9 & $-$7.1 & $-$4.8 &~ 1.6 & $-$5.9 \\\\\n2450880.61 & $-$6.5 & $-$4.6 & $-$3.5 & $-$7.8 & $-$11.1 & $-$5.4 & $-$7.8 & $-$8.8 & $-$17.9 \\\\\n2450881.58 & $-$14.4 & $-$9.6 & $-$7.3 & $-$13.1 & $-$14.2 & $-$6.2 & $-$12.1 & $-$17.3 & $-$23.0 \\\\\n2450882.58 & $-$11.0 & $-$4.3 & $-$4.2 & $-$7.7 & $-$13.6 & $-$1.2 & $-$7.3 & $-$17.0 & $-$13.3 \\\\\n2450883.56 & $-$9.1 & $-$5.2 & $-$4.8 & $-$4.6 & $-$12.9 & $-$2.9 & $-$2.7 & $-$15.3 & $-$11.4 \\\\\nMean~ & $-$9.6 & $-$5.1 & $-$3.4 & $-$7.7 & $-$15.2 & $-$6.0 & $-$7.3 & $-$17.8 & $-$15.5 \\\\\nStdv &~ 5.8 &~ 5.7 &~ 6.1 &~ 5.3 &~ 7.3 &~ 4.4 &~ 4.1 &~ 7.2 &~ 9.3 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\end{table*}\n\n\n\n\\begin{figure*}\n\\vbox{\\psfig{file=fig9.ps,width=17.5cm,height=16.0cm,angle=270}}\n\\caption[]{The variety of \\Ha~profiles observed in different runs. \nA vertical dashed line indicates zero velocity.}\n\\end{figure*}\n\n\\def\\baselinestretch{2}\n\n\nThe velocity--excitation relationship found for many hot \nsupergiants (Hutchings 1976) exists also in HD 188209.\nIn Figs. 5 and 6 we present plots of mean RV versus TEE \nand standard deviations of the mean RV versus TEE for \nthe different groups of lines computed for all dates (the last \ntwo lines in Table 2). These plots exclude a pure Keplerian\nmotion as the only cause of the RV variations. Pulsations and\nstochastic motions (intrinsic wind variations caused by some\nhydrodynamical instabilities) in the wind can bring to the \nRV variations as well. If we suppose that stochastic \nvariations are not important, then the existence of a standard \ndeviation-TEE relationship would suggest that deeper layers\nin the atmosphere pulsate with smaller amplitudes. The \namplitude of pulsations increases when approaching\nto the surface. \n\n\n\\subsection{The periodicity of the radial velocity variations}\n\nThe period search was carried out with help of \nthe {\\sc period} package (Dhillon \\& Privett 1997)\nof the {\\sc starlink} software. The following strategy was applied when\nlooking for a periodic signal in the RV curves of different groups of lines.\nDue to the large gaps (especially between runs 5 and 6) in our observations,\nwe first decided to study each of the runs 5, 6 and 7 separately. \nThe {\\sc clean} algorithm (Roberts et al. 1987) was employed to cover a \nspace of loop gains from 0.2 to 0.6 and the number of iterations from \n10 to few hundreds. The convergence of the periodograms was achieved for \nthe majority of groups of lines in all three runs. \nThe mean frequency suggested by most of the groups in \nall three runs is 0.44$\\pm$0.05 days$^{-1}$ (2.24 days). However, this \nperiod is very close to the Nyquist frequency \n(1/(2$\\times$Smallest Data Interval)) of the data and might be\nmisleading. \n \nWe have also looked for periodic signals in the combined data of all \ngroups obtained in all runs (Table 2). The maximum and minimum \nfrequencies were set to 100 and 0, respectively. A {\\sc clean} analysis of \nthe time series of the majority of groups revealed a frequency \nof 0.51$\\pm$0.1 days$^{-1}$ (1.95 days). The gain factor was 0.1 at \nthe first iteration, then was decreased by 15-20 % at each new\niteration until stabilization. The average RV for each date \nobtained by averaging the RVs of all the groups revealed a \nfrequency of 0.47$\\pm$0.12 days$^{-1}$ (2.1 days). \nAgain, both frequencies are very close to the Nyquist frequency and we\nshould discard them. We must point out that our periodograms did not show\nany peaks at frequencies smaller than 0.4 days$^{-1}$. The next strongest \npeak which appeared in our periodograms was near 0.156$\\pm$0.15 days$^{-1}$\n(6.4 days). Clearly this period is not affected by sampling.\nWe have also analysed the RV data using the Lomb-Scargle method\n(Lomb 1976, Scargle 1982) which allows to compute statistical\nprobability of peaks in periodograms. To ensure reliable significance\nvalues, the minimum number of permutations was set 100. The probability that\nthe period is not equal to 6.4 days was always less than 30 $\\%$. The\npeak at 6.4 days appears in all periodograms but given its significance\nvalue, we cannot definitely rule out its non-physical nature. \nIn Figs. 7 and 8 we show the {\\sc clean} and the {\\sc lomb-scargle}\nperiodograms and the fitting of a sin curve to folded data, respectively. \n\n\\def\\baselinestretch{1}\n\n\\begin{figure*}\n\\vbox{\\psfig{file=fig10.ps,width=17.5cm,height=16.0cm,angle=270}}\n\\caption[]{The radial velocities of blue and red absorption components\nversus residual intensity of the central emission.}\n\\end{figure*}\n\n\\def\\baselinestretch{2}\n\n\n\\section{Variability of H$\\alpha$}\n\nAll hot supergiants have variable \\Ha~profiles in their\nspectra (Rosendahl 1973). The shape of the \\Ha~may vary from P Cyg to \ninverse P Cyg, double-peaked, pure absorption and/or emission \n(Ebbets 1982) with typical time-scales of the order of days. \nThe nature of this variability is not yet understood. \nThe existence of variable asymmetric outflows/infalls of\nmatter and some corotating structures related to surface \ninhomogenities and possible magnetic fields have been proposed for \nBA-type (Kaufer et al. 1996) and O-type (Fullerton et al. 1996; \nKaper et al. 1997) supergiants.\nIn addition, there have been detailed studies of the rotating\ngiant loop in $\\beta$ Orionis (Israelian, Chentsov \\& Musaev 1997) \nand the corotating spiral structures in HD 64760 and HD 93521 \n(Howarth et al. 1998; Fullerton et al. 1997). It is of course \nvery difficult to distinguish binary systems from single \nstars without understanding the nature of \\Ha~variability. \nAs Thaller (1997) suggests, the \\Ha~can suffer some peculiar\nvariability due to the colliding winds in a binary system. \n\nThe time evolution of \\Ha~profiles in three different runs is shown \nin Figure 9. The average \\Ha~profile consists of three components, \na central emission accompanied by blue and red absorptions.\nWe have not observed a single \\Ha~profile without a central \nreversal. The emission is not always centered exactly on the rest \nwavelength but is varying. It may approach the continuum level, \ngo above it and decrease rapidly in strength. Apparently\nthe time-scale of the \\Ha~variability is at least one day. \nThe 5$^{\\rm th}$ run has been divided into two parts\n(runs 5a \\& 5b) with four successive nights in each. \nThe \\Ha~variability is observed over a wide range from \nabout $-$400 to 200~${\\rm km}~{\\rm s}^{-1}$. \n \nWe have already seen in Section 4.2 that our spherical unified \nmodels can account for the central reversal (or at least set\nupper and lower limits of the mass-loss). Thus, we know that\nthe central emission forms in the expanding envelope and accounts\nfor the filling-in effect observed in \\Ha, \\Hb~and some other lines.\nThe filling-in effect observed in \\Hb~ correlated perfectly with\nthe strength of the \\Ha~central reversal. The \\Ha~ wings \noriginate deep in the atmosphere, whereas the central reversal comes\nfrom the thin layers of the envelope. One cannot use the term\n``underlying photospheric absorption line'' since the central\nreversal is not emitted by a detached layer far from the \nphotosphere. It is important to stress that we deal with a\n$single$ line formed in a $unified$ model atmosphere. \nA variable amount of incipient emission can be due to density \n(or radius) variations in the outer\natmosphere. However, these variations are not expected to produce\nan asymmetry as long as we deal with spherically symmetric\nmass-loss. Our observations indicate that the velocity of the\ncentral emission varies as well. We $do$ expect RV \nvariations in the central emission (the upper atmosphere) since we know that\nthe RVs of all absorption lines vary. The amplitude of the RV variations \nof \\MgII~4481 \\AA\\ can reach 30$~{\\rm km}~{\\rm s}^{-1}$ (Table 2) and\n40$~{\\rm km}~{\\rm s}^{-1}$ in \\Hb. Thus, it is not unusual for the\namplitude of RV variations of the \\Ha~central emission to reach \n50$~{\\rm km}~{\\rm s}^{-1}$. \nA period analysis of the RV curves of the central emission resulted in the \ndetection of quasi-periodic variability with a frequency\n0.42$\\pm$0.14 d$^{-1}$ (2.35 days). It turns out that the RV \ncurves of all groups of lines vary in phase. However, the RV curve \nof the \\Ha~was shifted half phase relative to all groups. \n\nWe have measured the RVs of the blue and red absorption components\nof the \\Ha~and plotted them against the residual intensity of the central\nemission reversal. This plot (Fig. 10) shows a correlation\nwith a large scatter due to the RV variations of the central reversal.\nThis kind of correlation can be expected when the central reversal\nis moving up and down relative to a local continuum. We found similar\ncorrelations between the RV of the central emission and the residual\nintensities of the red and blue absorptions.\nApparently all the changes observed in the\n\\Ha~wings at velocities $v \\leq -$ 100$~{\\rm km}~{\\rm s}^{-1}$ and \n$v \\geq$ +100$~{\\rm km}~{\\rm s}^{-1}$ are due to the variations\nof the central reversal. We do not anticipate such large\nRV variations deep in the atmosphere where these wings are formed. \nThe conclusion is that the overall shape of the \\Ha~is determined by the \ncentral emission. \n\nWe have performed a period search of the integrated equivalent width \n(EW) of the \\Ha~data set and found a maximum in power at frequency \n0.22 day$^{-1}$. Figures 11 and 12 show the phase diagram for the\nperiod 4.41 days and a grey-scale representation of the phase \nspectrum, respectively. A phase spectrum represents a two-dimensional\ncase of the {\\sc clean} algorithm where each velocity bin of the \n\\Ha~is treated as a time series of the \\Ha~intensity. \n\n\\def\\baselinestretch{1}\n\n\\begin{figure}\n\\vbox{\\psfig{file=fig11.ps,width=8.5cm,angle=270}}\n\\caption[]{The phase diagram of the EWs of \\Ha.}\n\\end{figure}\n\n\n \n\\begin{figure}\n\\label{dyn}\n\\psfig{figure=fig12.ps,width=8.0cm}\n\\caption[]{Dynamical phase spectrum of \\Ha.}\n\\end{figure}\n\n\n\\def\\baselinestretch{2}\n\n\n\\section{Discussion}\n\nOur target belongs to the group of stars for which the existence of\na compact companion has been proposed in the literature. \nThe task of disproving or confirming the binary nature of the system \ncan be tackled only if sufficiently accurate analysed \nobservational data are available. In this paper we used state-of-the-art \nmodels of atmospheres to determine the fundamental parameters of\nHD 188209.\n\nTo establish the presence of a possible companion we have studied\nthe RVs of absorption lines by combining them in different groups. \nFourier analysis based on the iterative {\\sc clean} \nalgorithm was used to search for periodic variability. \nUnfortunately the time coverage of runs 1--4 and 8--9 was too\nsparse to set constraints on their time-dependent behaviour. \nFor this reason we first analysed a few runs separately and\nthen utilized the {\\sc clean} algorithm to search for periods in\na whole data set. The highest peak in the Fourier power spectrum \nwas centered near the frequency 0.156 day$^{-1}$ (6.4 days). \n\nThe 6.4 days period can be due to the binary nature of the system\nif one assumes very small and unlikely values for the mass ratio (q$\\le$0.1). \nTaking the values derived in this article (\\M = 16.6, \\R =20.9)\nand assuming q=0.1, we obtain for the Roche radius and\nfor the major semi-axis of the binary orbit \n15 \\Rsun~and 25 \\Rsun, respectively. This simple \nestimate shows that an O supergiant can hardly fit \nwithin the orbit because its Roche radius would be less than \nthe stellar radius. Even if it would fit, the tides in such a\ntight binary would be very strong making the star \nto speed up quickly until the rotation period matches the orbit. \nEven if we assume that the system is very young, it's \nhard to explain that the putative orbital period is 2 times \nshorter than the rotational period (13 days). \nThe second difficulty with the binary interpretation comes\nfrom the variability of H$\\alpha$. A TVS (temporal variance spectrum,\nshowing the extent and distribution of statistically significant \nprofile variability) has been computed recently \n(Baade 1998b, Kaper et al. 1998) for 15 spectroscopic binaries and\nit was found that all they show a characteristic double-peaked \nprofile. This is due to two H$\\alpha$ absorption/emission profiles\nmoving in a composite spectra. In our case the H$\\alpha$ profile \nis splitted because of the central emission coming from the lower\nwind. The last argument comes from the clear relations between\nexcitation energies and radial velocity amplitude and excitation energy\nand mean radial velocities and from the model atmosphere atmosphere \ncalculations. The latter is a good discriminant between\ninternal variations (pulsations \\& wind instabilities) and \nKeplerian motions. In a binary system one would expect all lines to\nhave the same amplitude independent on their TEE. \n\nIt has been known for a long time (Abt 1957) that the quasi-periodicity \nin hot supergiants might be ascribed to radial pulsations. \nA simple relation (Burki 1978; de Jager 1980) can be used to estimate \nthe period of radial pulsation,\n\\begin{equation}\n\\log P_{\\rm fund} = 10.93 - 0.5\\log (M/M_{\\odot}) - 0.38M_{\\rm bol} - 3 \\log \nT_{\\rm eff}\n\\end{equation}\nUsing the values of parameters obtained in Section 4 we arrive\nat $P_{\\rm fund}$=1.75 d. \nNote that the form of the relation (1)\ndepends on the stellar evolutionary models and the input parameters;\nboth are subject to large errors. In particular, note that we\nfound no large differences in the parameters determined with \nplane--parallel and unified model atmospheres. Nevertheless, Levy et al. (1984)\nhave pointed out that periods a factor of 1.5 longer than the\ncorresponding periods of the radial pulsations can be ascribed to\nnon-radial pulsations. This means that a factor of two difference \nbetween the evolutionary and the spectroscopic masses can easily\nresult in the mis-identification of the pulsating mode.\nAnother difficulty has been pointed by the referee of the article.\nA more sophisticated approach shows (Unno et al. 1979) that f-mode \npulsation (which is the lowest-frequency mode supported by radial \npulsation) periods are about 10 times larger than the one suggested\nby a period-luminosity relation. In any case, the theoretical \nperiod of 1.75 days is very close to the Nyquist frequency of our\ndata which means that we have a little chance to identify it in \nour data set even if it exists.\n\nOur data not allow to distinguish between pulsations and\nstochastic variations of the stellar wind. It is also \nquite possible that we have a combination of both effects. \n \nNote that the projected rotational period \nof this star ($\\sim$ 13 d) is much longer than any of the quasi-periods \nfound in this paper (but of course our runs do not cover a whole\nrotation cycle). The surface features (if any) will always be\nvisible on the projected disc of the star independently of the inclination\nangle. Thus, any periods due to the rotation of these features must \ncorrespond directly to the rotation period. We do not find any\npeaks in the power spectra at $\\sim$13 d and this leads us to discard\nrotational modulation as a possible explanation of the RV variations \nreported here. \n\nThe quality and the sampling of our data do not\nallow a careful study of the line asymmetries, moving components\n(if later exists) and/or long-term spectroscopic variability to be made.\nIt is quite possible that the non-sinusoidal character of the RV curve\nfor 6.4 days period (Fig 8)\nis caused by some disturbances due to the NRPs and/or moving features\nin the profiles plus any stochastic instabilities of the wind. \nNew monitoring with much higher S/N may allow NRPs, multimode \npulsations and clearly separate a sinusoidal curve of the radial \npulsations to be revealed. However, we found convincing \nevidence that the atmospheric motions cannot be ascribed solely \nto Keplerian motions and probably are not of a binary origin. \n\n \n\\section*{Acknowledgments}\n \nWe thank D.~Baade, O.~Pols and Pablo Rodriguez for their useful comments. \nA.~G. thanks the Canadian Astronomical Society for the travel grant \nto SAO, and I.~Bikmaev for helpful discussions. We wish to thank \nthe anonymous referee for his careful reading of the manuscript and \nseveral constructive suggestions. \n\n \n\n\\begin{thebibliography}{}\n\n\\bibitem[1957]{} Abt, H. A. 1957, ApJ, 126, 138\n\\bibitem[1988]{} Baade, D. 1988, in O Stars and Wolf-Rayet\nStars, eds. Conti, P. and Underhill, A., SP-NASA, Washington DC, p.199\n\\bibitem[1998b]{} Baade, D. 1998a, in Cyclical Variability in Stellar\nWinds, eds. Kaper, L. and Fullerton, A., ESO Astrophysics Symposia,\nSpringer, p. 196 \n\\bibitem[1998b]{} Baade, D. 1998b, private communication\n\\bibitem[1996]{} Berghoefer, T., Schmitt, T., Cassinelli, J. \n1996, A\\&AS, 118, 481 \n\\bibitem[1961]{} Blaauw, A. 1961, Bull. Astr. Inst. Nether., 15, 265\n\\bibitem[1978]{} Bohannan, B., and Garmany, C. D. 1978, ApJ, 223. 908 \n\\bibitem[1978]{} Burki, G. 1978, A\\&A, 65, 357\n\\bibitem[1977]{} Conti, P. \\& Ebbets, D. 1977, ApJ, 213, 438\n\\bibitem[1997]{} Dhillon, V. S. \\& Privett, G. J. 1997, \n{\\em PERIOD, A Time-Series Analaysis Package}, Stralink Project,\nRutherford Appleton Laboratory \n\\bibitem[1979]{} Ebbets, D. 1979, ApJ, 227, 510\n\\bibitem[1982]{} Ebbets, D. 1982, ApJS, 48, 399\n\\bibitem[1997]{} ESA 1997, The Hipparcos Catalogue, ESA SP-1200\n\\bibitem[1991]{} Fullerton, A. W., Gies, D. R., Bolton, C. T.\n1991, ApJ, 368, L35\n\\bibitem[1996]{} Fullerton, A. W., Gies, D. R., Bolton, C. T.\n1996, ApJS, 103, 475\n\\bibitem[1997]{} Fullerton, A. W., Massa, D. L., Prinja, R. K., \nOwocki, S. P., Cranmer, S. R. 1997, A\\&A, 327, 699\n\\bibitem[1992]{} Galazutdinov H. A. 1992, Preprint of the Special\nAstrophysical Observatory of Russian Academy of Science No. 92\n\\bibitem[1980]{} Garmany, C., D., Conti, P. S., Massey, P. 1980,\nApJ, 242, 1063\n\\bibitem[1987]{} Gies, D. R. 1987, ApJS, 64, 545\n\\bibitem[1995]{} Haser, S. M. 1995, PhD thesis, Ludwig-Maximillians-\nUniversit\\\"{a}t M\\\"{u}nchen \n\\bibitem[1994]{h94}\nHerrero, A., 1994, Sp. Sc. Rev. 66, 137 \n\\bibitem[1995]{h95}\nHerrero A., Kudritzki R. P., Gabler, R., et al., 1995, A\\&A 297, 556\n\\bibitem[1992]{h92}\nHerrero A., Kudritzki R. P., Vilchez J. M., et al., 1992, A\\&A 261, 209\n\\bibitem[1985]{} van den Heuvel, E. P. J. 1976, in Eggleton, P. \ned., IAU Symp. 73, Structure and Evolution of Close Binary Systems,\nDordrecht, Reidel, p. 263\n\\bibitem[1989]{} Howarth, I. D., Prinja, R. K. 1989, ApJS, 69, 527 \n\\bibitem[1997]{} Howarth, I. D., Siebert, K. W., Hussain, G. A. J., and\nPrinja, R. K. 1997, MNRAS, 284, 265\n\\bibitem[1998]{} Howarth, I. D., Townsend, R. H. D., Clayton, M. J.,\nFullerton, A. W., Gies, D. R., Massa, D., Prinja, R. K., Reid, A. H. N.\n 1998, MNRAS, 296, 949\n\\bibitem[1976]{} Hutchings, J. B. 1976, ApJ, 203, 438\n\\bibitem[1997]{} Israelian, G., Chentsov, E. and Musaev, F. 1997, MNRAS,\n290, 521\n\\bibitem[1980]{} de Jager C. 1980 The Brightest Stars, Kluwer Dordrecht\n\\bibitem[1997]{} Kaper, L. et al. 1997, A\\&A, 327, 281\n\\bibitem[1998]{} Kaper, L. et al. 1998, in Cyclical Variability in \nStellar Winds, eds. Kaper, L. and Fullerton, A., ESO Astrophysics \nSymposia, Springer, p. 103\n\\bibitem[1997]{} Kaufer A., Stahl O., Wolf B., Fullerton A., \nG\\\"{a}ng T., Gummersbach C. A., Jankovics I., Kov\\'{a}cs J., Mandel H., \nPeitz J., Rivinius Th., Szeifert Th. 1997, A\\&A, 320, 273\n\\bibitem[1996]{} Kaufer A., Stahl O., Wolf B., G\\\"{a}ng T.,\nGummersbach C. A., Kov\\'{a}cs J., Mandel H., Szeifert, Th. 1996, A\\&A, 305, 887 \n\\bibitem[1997]{} van Leeuwen, F. et al. 1997, A\\&A, 323, L61\n\\bibitem[1984]{} Levy, D., Maeder, A., No\\\"{e}ls, and Gabriel, M. 1984, A\\&A, 133, 307\n\\bibitem[1976]{} Lomb, N. R. 1976, Ap. \\& Sp. Sc., 39, 447\n\\bibitem[1998]{mc98}\nMcErlean, N., Lennon, D.J., Dufton, P., 1998, A\\&A, 329, 613\n\\bibitem[1993]{} Musaev F. 1993, Pis'ma v AZh, 19, 776\n\\bibitem[1993]{} Musaev F. 1999, Pis'ma v AZh, in press\n\\bibitem[1988]{} Musaev F., and Chentsov, E. L. 1988, Soviet. Astron.\nLetters, 14, 226\n\\bibitem[1996]{} Penny, L. R. 1996, ApJ, 463, 737\n\\bibitem[1987]{} Roberts, D. H., Leh\\'{a}r, J., Dreher, J. W. 1987, AJ, 93, 968\n\\bibitem[1973]{} Rosendahl, J. D. 1973, ApJ, 186, 909\n\\bibitem[1997]{sph97}\nSantolaya--Rey, A.E., Puls, J., Herrero, A. 1997, A\\&A 323, 488\n\\bibitem[1982]{} Scargle, J.D. 1982, ApJ, 263, 835\n\\bibitem[1992]{sch92}\nSchaller, G., Schaerer, D., Meynet, G., Maeder, A., 1992, A\\&AS 96, 269\n\\bibitem[1998]{sh98}\nSmith, K., Howarth, I. D. 1998, MNRAS, 299, 114\n\\bibitem[1982]{} Stone, R. C. 1982, ApJ, 261, 208\n\\bibitem[1997]{} Thaller, M. 1997, ApJ, 487, 380\n\\bibitem[1979]{} Unno, W., Osaki, Y., Ando, H. and Shibahasi, H. 1979,\nNon-radial Oscillations of Stars, Univ. Tokyo Press, Tokyo\n \\bibitem[1989]{vo89}\nVoels, S.A., Bohannan, B., Abbott, D.C., Hummer, D.G., 1989, ApJ 340, 1073\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002396.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1957]{} Abt, H. A. 1957, ApJ, 126, 138\n\\bibitem[1988]{} Baade, D. 1988, in O Stars and Wolf-Rayet\nStars, eds. Conti, P. and Underhill, A., SP-NASA, Washington DC, p.199\n\\bibitem[1998b]{} Baade, D. 1998a, in Cyclical Variability in Stellar\nWinds, eds. Kaper, L. and Fullerton, A., ESO Astrophysics Symposia,\nSpringer, p. 196 \n\\bibitem[1998b]{} Baade, D. 1998b, private communication\n\\bibitem[1996]{} Berghoefer, T., Schmitt, T., Cassinelli, J. \n1996, A\\&AS, 118, 481 \n\\bibitem[1961]{} Blaauw, A. 1961, Bull. Astr. Inst. Nether., 15, 265\n\\bibitem[1978]{} Bohannan, B., and Garmany, C. D. 1978, ApJ, 223. 908 \n\\bibitem[1978]{} Burki, G. 1978, A\\&A, 65, 357\n\\bibitem[1977]{} Conti, P. \\& Ebbets, D. 1977, ApJ, 213, 438\n\\bibitem[1997]{} Dhillon, V. S. \\& Privett, G. J. 1997, \n{\\em PERIOD, A Time-Series Analaysis Package}, Stralink Project,\nRutherford Appleton Laboratory \n\\bibitem[1979]{} Ebbets, D. 1979, ApJ, 227, 510\n\\bibitem[1982]{} Ebbets, D. 1982, ApJS, 48, 399\n\\bibitem[1997]{} ESA 1997, The Hipparcos Catalogue, ESA SP-1200\n\\bibitem[1991]{} Fullerton, A. W., Gies, D. R., Bolton, C. T.\n1991, ApJ, 368, L35\n\\bibitem[1996]{} Fullerton, A. W., Gies, D. R., Bolton, C. T.\n1996, ApJS, 103, 475\n\\bibitem[1997]{} Fullerton, A. W., Massa, D. L., Prinja, R. K., \nOwocki, S. P., Cranmer, S. R. 1997, A\\&A, 327, 699\n\\bibitem[1992]{} Galazutdinov H. A. 1992, Preprint of the Special\nAstrophysical Observatory of Russian Academy of Science No. 92\n\\bibitem[1980]{} Garmany, C., D., Conti, P. S., Massey, P. 1980,\nApJ, 242, 1063\n\\bibitem[1987]{} Gies, D. R. 1987, ApJS, 64, 545\n\\bibitem[1995]{} Haser, S. M. 1995, PhD thesis, Ludwig-Maximillians-\nUniversit\\\"{a}t M\\\"{u}nchen \n\\bibitem[1994]{h94}\nHerrero, A., 1994, Sp. Sc. Rev. 66, 137 \n\\bibitem[1995]{h95}\nHerrero A., Kudritzki R. P., Gabler, R., et al., 1995, A\\&A 297, 556\n\\bibitem[1992]{h92}\nHerrero A., Kudritzki R. P., Vilchez J. M., et al., 1992, A\\&A 261, 209\n\\bibitem[1985]{} van den Heuvel, E. P. J. 1976, in Eggleton, P. \ned., IAU Symp. 73, Structure and Evolution of Close Binary Systems,\nDordrecht, Reidel, p. 263\n\\bibitem[1989]{} Howarth, I. D., Prinja, R. K. 1989, ApJS, 69, 527 \n\\bibitem[1997]{} Howarth, I. D., Siebert, K. W., Hussain, G. A. J., and\nPrinja, R. K. 1997, MNRAS, 284, 265\n\\bibitem[1998]{} Howarth, I. D., Townsend, R. H. D., Clayton, M. J.,\nFullerton, A. W., Gies, D. R., Massa, D., Prinja, R. K., Reid, A. H. N.\n 1998, MNRAS, 296, 949\n\\bibitem[1976]{} Hutchings, J. B. 1976, ApJ, 203, 438\n\\bibitem[1997]{} Israelian, G., Chentsov, E. and Musaev, F. 1997, MNRAS,\n290, 521\n\\bibitem[1980]{} de Jager C. 1980 The Brightest Stars, Kluwer Dordrecht\n\\bibitem[1997]{} Kaper, L. et al. 1997, A\\&A, 327, 281\n\\bibitem[1998]{} Kaper, L. et al. 1998, in Cyclical Variability in \nStellar Winds, eds. Kaper, L. and Fullerton, A., ESO Astrophysics \nSymposia, Springer, p. 103\n\\bibitem[1997]{} Kaufer A., Stahl O., Wolf B., Fullerton A., \nG\\\"{a}ng T., Gummersbach C. A., Jankovics I., Kov\\'{a}cs J., Mandel H., \nPeitz J., Rivinius Th., Szeifert Th. 1997, A\\&A, 320, 273\n\\bibitem[1996]{} Kaufer A., Stahl O., Wolf B., G\\\"{a}ng T.,\nGummersbach C. A., Kov\\'{a}cs J., Mandel H., Szeifert, Th. 1996, A\\&A, 305, 887 \n\\bibitem[1997]{} van Leeuwen, F. et al. 1997, A\\&A, 323, L61\n\\bibitem[1984]{} Levy, D., Maeder, A., No\\\"{e}ls, and Gabriel, M. 1984, A\\&A, 133, 307\n\\bibitem[1976]{} Lomb, N. R. 1976, Ap. \\& Sp. Sc., 39, 447\n\\bibitem[1998]{mc98}\nMcErlean, N., Lennon, D.J., Dufton, P., 1998, A\\&A, 329, 613\n\\bibitem[1993]{} Musaev F. 1993, Pis'ma v AZh, 19, 776\n\\bibitem[1993]{} Musaev F. 1999, Pis'ma v AZh, in press\n\\bibitem[1988]{} Musaev F., and Chentsov, E. L. 1988, Soviet. Astron.\nLetters, 14, 226\n\\bibitem[1996]{} Penny, L. R. 1996, ApJ, 463, 737\n\\bibitem[1987]{} Roberts, D. H., Leh\\'{a}r, J., Dreher, J. W. 1987, AJ, 93, 968\n\\bibitem[1973]{} Rosendahl, J. D. 1973, ApJ, 186, 909\n\\bibitem[1997]{sph97}\nSantolaya--Rey, A.E., Puls, J., Herrero, A. 1997, A\\&A 323, 488\n\\bibitem[1982]{} Scargle, J.D. 1982, ApJ, 263, 835\n\\bibitem[1992]{sch92}\nSchaller, G., Schaerer, D., Meynet, G., Maeder, A., 1992, A\\&AS 96, 269\n\\bibitem[1998]{sh98}\nSmith, K., Howarth, I. D. 1998, MNRAS, 299, 114\n\\bibitem[1982]{} Stone, R. C. 1982, ApJ, 261, 208\n\\bibitem[1997]{} Thaller, M. 1997, ApJ, 487, 380\n\\bibitem[1979]{} Unno, W., Osaki, Y., Ando, H. and Shibahasi, H. 1979,\nNon-radial Oscillations of Stars, Univ. Tokyo Press, Tokyo\n \\bibitem[1989]{vo89}\nVoels, S.A., Bohannan, B., Abbott, D.C., Hummer, D.G., 1989, ApJ 340, 1073\n\n\\end{thebibliography}"
}
] |
astro-ph0002397
|
Observational constraints on the spectral index\\ of the cosmological curvature perturbation
|
[
{
"author": "$^1$ David H.~Lyth"
},
{
"author": "$^2$ Laura Covi"
}
] |
We evaluate the observational constraints on the spectral index $n$, in the context of the $\Lambda$CDM hypothesis which represents the simplest viable cosmology. We first take $n$ to be practically scale-independent. Ignoring reionization, we find at a nominal 2-$\sigma$ level $n\simeq 1.0 \pm 0.1$. If we make the more realisitic assumption that reionization occurs when a fraction $f\sim 10^{-5}$ to $1$ of the matter has collapsed, the 2-$\sigma$ lower bound is unchanged while the 1-$\sigma$ bound rises slightly. These constraints are compared with the prediction of various inflation models. Then we investigate the two-parameter scale-dependent spectral index, predicted by running-mass inflation models, and find that present data allow significant scale-dependence of $n$, which occurs in a physically reasonable regime of parameter space.
|
[
{
"name": "p99nB.tex",
"string": "\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% p99n.tex\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\documentstyle[prd,aps,floats]{revtex}\n%\\documentstyle[prl,aps,preprint]{revtex}\n\n\\begin{document}\n\\preprint{astro-ph/0002397}\n\\draft\n\\tighten\n\n% Remove this and closure after abstract, plus preprint number,\n% in electronic submission\n%\n\\input epsf\n\n\n\\def\\la{\\mathrel{\\mathpalette\\fun <}}\n\\def\\ga{\\mathrelbe {\\mathpalette\\fun >}}\n\\def\\fun#1#2{\\lower3.6pt\\vbox{\\baselineskip0pt\\lineskip.9pt\n \\ialign{$\\mathsurround=0pt#1\\hfill##\\hfil$\\crcr#2\\crcr\\sim\\crcr}}}\n\n\\renewcommand\\({\\left(}\n\\renewcommand\\){\\right)}\n\\renewcommand\\[{\\left[}\n\\renewcommand\\]{\\right]}\n\n\\newcommand\\del{{\\mbox {\\boldmath $\\nabla$}}}\n\n\\newcommand\\eq[1]{Eq.~(\\ref{#1})}\n\\newcommand\\eqs[2]{Eqs.~(\\ref{#1}) and (\\ref{#2})}\n\\newcommand\\eqss[3]{Eqs.~(\\ref{#1}), (\\ref{#2}) and 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p}}\n\\def\\ko{K^0}\n\\def\\kb{\\bar{K^0}}\n\\def\\al{\\alpha}\n\\def\\ab{\\bar{\\alpha}}\n\n\\def\\calm{{\\cal M}}\n\\def\\calp{{\\cal P}}\n\\def\\calr{{\\cal R}}\n\\def\\calpr{{\\calp_\\calr}}\n\n\\newcommand\\bfa{{\\bf a}}\n\\newcommand\\bfb{{\\bf b}}\n\\newcommand\\bfc{{\\bf c}}\n\\newcommand\\bfd{{\\bf d}}\n\\newcommand\\bfe{{\\bf e}}\n\\newcommand\\bff{{\\bf f}}\n\\newcommand\\bfg{{\\bf g}}\n\\newcommand\\bfh{{\\bf h}}\n\\newcommand\\bfi{{\\bf i}}\n\\newcommand\\bfj{{\\bf j}}\n\\newcommand\\bfk{{\\bf k}}\n\\newcommand\\bfl{{\\bf l}}\n\\newcommand\\bfm{{\\bf m}}\n\\newcommand\\bfn{{\\bf n}}\n\\newcommand\\bfo{{\\bf o}}\n\\newcommand\\bfp{{\\bf p}}\n\\newcommand\\bfq{{\\bf q}}\n\\newcommand\\bfr{{\\bf r}}\n\\newcommand\\bfs{{\\bf s}}\n\\newcommand\\bft{{\\bf t}}\n\\newcommand\\bfu{{\\bf u}}\n\\newcommand\\bfv{{\\bf v}}\n\\newcommand\\bfw{{\\bf w}}\n\\newcommand\\bfx{{\\bf x}}\n\\newcommand\\bfy{{\\bf y}}\n\\newcommand\\bfz{{\\bf z}}\n\n\\newcommand\\sub[1]{_{\\rm #1}}\n\\newcommand\\su[1]{^{\\rm #1}}\n\n\\newcommand\\supk{^{(K) }}\n\\newcommand\\supf{^{(f) }}\n\\newcommand\\supw{^{(W) }}\n\\newcommand\\Tr{{\\rm Tr}\\,}\n\n\\newcommand\\msinf{M\\sub{inf}}\n\\newcommand\\phicob{\\phi\\sub{COBE}}\n\\newcommand\\delmult{\\Delta V_{\\chi\\widetilde\\chi{\\rm f}}}\n\\newcommand\\mgrav{m_{3/2}(t)}\n\\newcommand\\mgravsq{m_{3/2}(t)}\n\\newcommand\\mgravvac{m_{3/2}}\n\n\\newcommand\\cpeak{\\sqrt{\\widetilde C_{\\rm peak}}}\n\\newcommand\\cpeako{\\sqrt{\\widetilde C_{\\rm peak}^{(0)}}}\n\\newcommand\\omb{\\Omega\\sub b}\n\\newcommand\\ncobe{N\\sub{COBE}}\n\\newcommand\\vev[1]{\\langle{#1}\\rangle}\n%\\twocolumn[\\hsize\\textwidth\\columnwidth\\hsize\\csname\n%@twocolumnfalse\\endcsname]\n\n\\title{Observational constraints on the spectral index\\\\ of the cosmological\ncurvature perturbation }\n\\author{$^1$ David H.~Lyth, $^2$ Laura Covi}\n\\address{$^1$Physics Department, Lancaster University\nLancaster LA1 4YB, Great Britain}\n\\address{$^2$DESY Theory Group, Notkestrasse 85, D-22603 Hamburg, Germany}\n%\\date{February 2000} \n\\maketitle\n\\begin{abstract}\n We evaluate the observational constraints on the spectral index $n$,\nin the context of the $\\Lambda$CDM hypothesis which represents the\n simplest viable cosmology. We first take \n $n$ to be practically scale-independent. Ignoring reionization,\nwe find at a nominal 2-$\\sigma$ level\n $n\\simeq 1.0 \\pm 0.1$. If we make\n the more realisitic assumption that \n reionization occurs when a fraction $f\\sim 10^{-5}$ to $1$\n of the matter has collapsed, \nthe 2-$\\sigma$ lower bound is unchanged while the 1-$\\sigma$ bound rises\nslightly. These constraints are \n compared with the \nprediction of various inflation models. Then we\n investigate the two-parameter scale-dependent spectral\nindex, predicted by running-mass inflation models, and find\n that present data allow significant scale-dependence\nof $n$, which occurs in a physically reasonable\nregime of parameter space.\n\\end{abstract}\n\n\\pacs{PACS numbers: 98.80.Cq \\hfill astro-ph/0002397}\n\n\\section{Introduction}\n\nIt is generally supposed that structure in the Universe originates\nfrom a primordial gaussian curvature perturbation, generated\nby slow-roll inflation. The spectrum $\\calpr(k)$ of the curvature\nperturbation is the point\nof contact between observation and models of inflation. It is given\nin terms of the inflaton potential $V(\\phi)$ by\\footnote\n{As usual, $\\mpl=2.4\\times 10^{18}\\GeV$ is the Planck mass, \n$a$ is the scale factor and $H=\\dot a/a$ is the Hubble parameter, and\n$k/a$ is the wavenumber. We assume the usual slow-roll conditions\n$\\mpl^2|V''/V|\\ll 1$ and $\\mpl^2(V'/V)^2\\ll1$, leading to \n$3H\\dot\\phi\\simeq -V'$.}\n\\be\n\\frac4{25}\\calpr(k)\n = \\frac1{75\\pi^2\\mpl^6}\\frac{V^3}{V'^2} \\,,\n\\label{delh}\n\\ee\nwhere the \n potential and its derivatives are\n evaluated at the epoch of horizon exit\n$k=aH$. To work out the value of $\\phi$ at this epoch one uses\nthe relation\n\\be\n\\ln(k\\sub{end}/k)\\equiv N(k)\n=\\mpl^{-2}\\int^\\phi_{\\phi\\sub{end}} (V/V') \\diff\\phi\n\\,,\n\\label{Nofv}\n\\ee\n where $N(k)$ is actually the number\nof $e$-folds from horizon exit to the end of slow-roll inflation.\nAt the scale explored by the COBE measurement of the cosmic microwave\nbackground (cmb) anisotropy, \n $N(k\\sub{COBE})$ depends on the expansion of the Universe after inflation\nin the manner specified by \\eq{Ncobe} below.\n\nGiven this prediction, the\n observed\n large-scale normalization $\\calp_\\calr^{1/2}\\simeq 10^{-5}$ provides a \nstrong \nconstraint on models of inflation.\nTaking that for granted, we are here interested in the scale-dependence of\nthe spectrum, defined by the, in general, scale-dependent spectral \nindex $n$;\n\\be\nn(k)-1\\equiv \\frac {\\diff \\ln \\calpr}{ \\diff \\ln k}\n\\,.\n\\ee\nAccording to most inflation models, $n$ has negligible variation on\ncosmological scales so that $\\calpr\\propto k^{n-1}$, but\nwe shall also discuss an interesting class of models giving\na different scale-dependence.\n\n{}From \\eqs{delh}{Nofv},\n\\bea\nn-1 &=& 2\\mpl^2 (V''/V)-3\\mpl^2 (V'/V)^2 \n\\,,\n\\label{nofv}\n\\eea\nand in almost all models of inflation, \\eq{nofv} is well approximated by\n\\be\nn-1=2\\mpl^2(V''/V)\n\\label{nofvapprox}\n\\,.\n\\ee\nWe see that the spectral index \n measures the {\\em shape} of the inflaton potential $V(\\phi)$,\nbeing independent of its overall normalization. For this reason, \nit is a powerful discriminator between models of inflation.\n\nThe observational constraints on \nthe spectral index have been studied by many authors, but \na new investigation is justified for two reasons.\nOn the observational side, the \n cosmological parameters are at last being pinned down, \n as is the height of the first peak in the spectrum the cmb \nanisotropy.\nNo study has yet been given which takes on board these observational\ndevelopments, while at the same time taking on board the crucial\ninfluence of the reionization epoch on the peak height.\n On the theory\nside, it is known that the spectral index may be strongly\nscale-dependent if the inflaton has a gauge coupling, leading\nto what are called running-mass models. The quite specific, two-parameter\n prediction for \nthe scale dependence of the spectral index in these models\n has not been compared with\npresently available data.\n\n\\section{The observational constraints on the parameters of the\n$\\Lambda$CDM model}\nObservations of various types \n indicate that we live in a low density \nUniverse, which is at least approximately flat \n\\cite{likely,url,boom,ten,maxima}.\n In the interest of simplicity\nwe therefore adopt the \n $\\Lambda$CDM model, defined by the\nrequirements that the Universe is exactly flat, and that the \nnon-baryonic dark matter is cold with negligible interaction.\nEssentially exact flatness is predicted by inflation, unless one invokes\na special kind of model, or special initial conditions.\nAlso, there is no clear \n motivation to modify the cold dark matter hypothesis.\\footnote\n{In particular, the rotation curves of dwarf galaxies may be\ncompatible with cold dark matter \\cite{dwarf}.}\nWe shall constrain the parameters of the $\\Lambda$CDM model, including\nthe spectral index, by performing a least-squares fit to \n key observational quantities.\n\n\\subsection{The parameters}\nThe $\\Lambda$CDM model is defined by the spectrum\n$\\calpr(k)$ of the\nprimordial curvature perturbation, and \n the four parameters that are\nneeded to translate this spectrum into spectra for\nthe matter density perturbation and the cmb anisotropy.\nThe four parameters are the\n Hubble constant $h$ (in units of \n$100\\km\\sunit^{-1}\\Mpc^{-1}$),\n the total matter density parameter $\\Omega_0$, the \nbaryon density parameter $\\omb$, and the \nreionization redshift $z\\sub R$. As we shall describe, \n $z\\sub R$ is estimated by assuming that reionization occurs when some\nfixed fraction $f$ of the matter collapses.\nWithin the reasonable range $f\\sim 10^{-4}$ to $1$, the main results\nare insensitive to the precise value of $f$.\n\nThe spectrum is conveniently specified by its value at a scale explored\nby COBE, and the spectral index $n(k)$.\nWe shall consider the usual case of a constant spectral index,\nand the case of running mass models where $n(k)$ is given by\na two-parameter expression. Since $\\calpr(k\\sub{COBE})$ is determined\nvery accurately by the COBE data (\\eq{cobe1} below) we fix its value.\nExcluding $z\\sub R$ and $\\calpr(k_{COBE})$,\n the $\\Lambda$CDM model is specified by\nfour parameters in the case of a constant spectral index, or by five\nparameters in the case of running mass inflation models.\n\n\\subsection{The data}\nTo compare the $\\Lambda$CDM model with observation, we \ntake as our starting point a \nstudy performed a few years ago \\cite{llvw}. \nWe consider the same seven observational quantities as in the earlier\nwork, since they still summarize most of the relevant\ndata. Of these quantities, three are\n the cosmological quantities\n$h$, $\\Omega_0$, $\\Omega\\sub B$, which we are also taking as free\nparameters. The crucial difference between the present situation and \nthe earlier one is that observation is beginning to pin down\n$h$ and $\\Omega_0$. Judging by the spread of measurements,\nthe systematic error, while still important, is no longer completely\ndominant compared with the random error. At least at some\ncrude level, it therefore makes sense to pretend that the errors are all\nrandom, and to perform a least squares fit.\nThe adopted values and errors\nare given in Table 1, and summarized below. In common with earlier\ninvestigations, we take the errors\nto be uncorrelated.\n\n\\paragraph{Hubble constant}\nOn the basis of observations that have\nnothing to do with large scale structure\nit seems very likely \\cite{likely} that $h$ is in the range $0.5$ to $0.8$. \nWe therefore\nadopt, at notionally the 2-$\\sigma$ level, the value\n $h=0.65\\pm 0.15$, corresponding to $h=0.65\\pm 0.075$\nat the notional 1-$\\sigma$ level. \n\n\\paragraph{The matter density}\nThe case of the total density parameter $\\Omega_0$ is similar\nto that of the Hubble parameter. On the basis of observations that \nhave nothing to do with large scale structure,\n it seems very likely \\cite{likely} that $\\Omega_0$\nlies between $0.2$ and $0.5$, and \n we adopt at the notional 1-$\\sigma$ level\nthe value $\\Omega_0 = 0.35 \\pm 0.075$. \n\n\\paragraph{The baryon density}\nAs described for instance in \\cite{osw,subir}, the baryon density\nparameter $\\Omega\\sub b$\nhas two likely ranges. At the 1-$\\sigma$ level, these are estimated\nin \\cite{osw} to be $\\Omega\\sub b h^2 =.019\\pm .002 $ and \n$\\Omega\\sub b h^2 =.007\\pm.0015$. \nWe adopt the high $\\Omega\\sub b$ range, which\nis generally regarded as the most likely, though our conclusions would\nbe much the same if we were to adopt the low range.\n\n\\paragraph{The rms density perturbation at $8h^{-1}\\Mpc$}\nPrimarily through the abundance of rich galaxy clusters,\n a useful constraint on the primordial spectrum is provided by\nthe rms density contrast, in a comoving sphere with present radius\n $R\\sim 10h^{-1}\\Mpc$, at redshift $z=0$ to a few.\n The constrained quantity is conventionally taken to be the present,\nlinearly evolved rms density contrast at $R=8h^{-1}\\Mpc$,\n denoted by $\\sigma_8$.\nA recent estimate \\cite{vl} based on low-redshift clusters\ngives at 1-$\\sigma$\n\\bea\n\\sigma_8 &=& \\widetilde \\sigma_8 \\Omega_0^{-0.47} \\\\\n\\widetilde \\sigma_8 &=& .560\\pm .059\n\\,.\n\\eea\nThis constrains the primordial curvature perturbation on \nthe scale $k\\sim k_8\\equiv (8h^{-1}\\Mpc)^{-1}$.\n\n\\paragraph{The shape parameter}\nThe slope of the galaxy correlation function on scales of order\n$1h^{-1}$ to $100h^{-1}\\Mpc$ \n is conveniently specified by a shape parameter \\cite{llvw}\n$\\widetilde \\Gamma$,\ndefined by\n\\bea\n\\widetilde \\Gamma &=& \\Gamma - 0.28(n_8^{-1}-1) \\\\\n \\Gamma &=& \n \\Omega_0 h \\exp(-\\Omega\\sub B -\\Omega\\sub B/\\Omega_0)\n\\,.\n\\eea\n(The quantity $\\Gamma$ determines, to an excellent approximation, the\nshape of the \nmatter transfer function on scales $k^{-1}\\sim 1$ to $100h^{-1}\\Mpc$,\nwhile the second term accounts for the scale dependence of the \nprimordial spectrum.\nFor definiteness, we evaluate $n$ at\n$k=k_8$, in the case that $n$ has significant scale\ndependence.)\nA fit reported in\n \\cite{llvw} gives $\\widetilde \\Gamma = .23$ with a $15\\%$ uncertainty\nat 2-$\\sigma$. A more recent fit with more data\n \\cite{will} gives $\\widetilde \\Gamma=.20 $ to $.25$, depending on the\nassumed velocity dispersion, but with $15\\%$ statistical\nuncertainty at the 1-$\\sigma$ level.\\footnote\n{See Table 3 of \\cite{will}; in the present\ncontext one should focus on the last three rows of the Table.}\nWe therefore adopt $\\widetilde\\Gamma=.23$, with $15\\%$ uncertainty\nat 1-$\\sigma$.\n\n\\paragraph{The COBE normalization of the spectrum}\nTo a good approximation, the\n spectrum $C_\\ell$ of the cmb anisotropy at large $\\ell$\nis sensitive to the\nprimordial spectrum on the corresponding scale at the particle\nhorizon, \n\\bea\nk(\\ell,\\Omega_0) &=& \\frac{\\ell}{x\\sub{hor}(\\Omega_0)} \\label{kofell}\\\\\nx\\sub{hor}&\\equiv& 2H_0^{-1} \\Omega_0^{-1/2} \\( 1+0.084\\ln\\Omega_0 \\)\n\\label{xhor}\n\\,.\n\\eea\nThe COBE measurements cover the range $2\\leq \\ell \\lsim 30$, and \nthey constrain $\\calpr(k)$ on the corresponding scales.\nInstead of $\\calpr$, it is usual in this context to consider a quantity\n$\\delta_H$, which is of direct interest for studies of \nstructure formation and is defined by\n\\bea\n\\delta_H(k) &\\equiv\n&\\frac25 \\frac{ g(\\Omega_0)}{\\Omega_0} \\calpr^{1/2}(k) \\label{delhdef}\\\\\ng(\\Omega_0)&\\equiv&\\frac52 \\Omega_0 \\(\\frac 1{70}+\\frac{209\\Omega_0}{140}\n-\\frac{\\Omega_0^2}{140} + \\Omega_0^{4/7} \\)^{-1}\n\\,.\n\\eea\nThe factor $g/\\Omega_0$, normalized to 1 at $\\Omega_0=1$,\n represents the $\\Omega_0$-dependence of the \npresent, linearly evolved, density contrast after pulling out\nthe scale-dependent transfer function and $\\calpr$. Equivalently, \n$a(\\Omega)g(\\Omega)$ \nis the time-dependence of the density contrast after matter domination.\n\n According to the\nordinary (as opposed to 'integrated') Sachs-Wolfe approximation\n\\be\n C_\\ell=\\frac{4 \\pi}{25}\n \\int^\\infty_0 \\frac{\\diff k}k j_\\ell^2\\( k x\\sub{hor} \\)\n\\calpr(k)\n\\,.\n\\ee\nIn the regime $\\ell\\gg 1$, it\n satisfies \\eq{kofell} because $j_\\ell^2$ peaks when its argument\nis equal to $\\ell$.\nIn the $\\Lambda$CDM model, the Sachs-Wolfe approximation is quite\ngood in COBE regime, but still the quality of the \ndata justify using the full (linear) calculation, given for instance by the\noutput of the CMBfast package \\cite{CMBfast}.\n\nConsider first the case\n $n=1$ (scale-independent spectrum).\nIn the Sachs-Wolfe approximation, the value of $\\calpr$\nobtained by fitting the COBE data is independent\nof the cosmological parameters $h$,\n$\\Omega_0$ and $\\Omega\\sub b$.\nUsing instead the full calculation, a fit to the data by \n Bunn and White \\cite{bw} gives\n\\bea\n\\delta_H &=&\\Omega_0^{-0.785 -0.05 \\ln\\Omega_0} \n \\widetilde \\delta_H \\nonumber\\\\\n10^5\\widetilde \\delta_H &=& 1.94\\pm 0.08 \\label{cobe1}\n\\,,\n\\eea\nAs expected, the \n corresponding spectrum of the curvature perturbation\nhas only mild dependence on $\\Omega_0$\n($\\calpr\\propto \\Omega_0^{-0.03}$).\n\nConsider next the case of a scale-independent spectral index $n\\neq 1$.\nDropping an insignificant term quadratic in $n-1$, the\n fit of Bunn and White \\cite{bw} handles the $n$-dependence by assuming\nthat \\eq{cobe1} holds at a 'pivot' scale $k\\sub{COBE}$ which is\nindependent of $\\Omega_0$.\\footnote\n{Keeping the quadratic term, the 'pivot' scale at which \\eq{cobe1} holds\nis dependent on $n$, but still independent of $\\Omega_0$.\nA related fit by Bunn, Liddle and White \\cite{blw} keeps a cross-term\nin $(n-1)$ and $\\Omega_0$, which makes the 'pivot' scale increase\nwith $\\Omega_0^{-1}$, though not as strongly as in \\eq{kcobeofom}\nbelow.}\n\\be\nk\\sub{COBE} \\equiv 6.6H_0\n\\,,.\n\\label{kcobe}\n\\ee\nInsofar as the approximation \\eq{kofell} is valid, this corresponds\nto fixing $C_\\ell$ at an $\\Omega_0$-dependent value of $\\ell$, which is\n $\\ell=13$ for $\\Omega_0$, and $\\ell=22$ \nfor our central value $\\Omega_0=.35$.\n\nIn the case of a scale-independent $n$, an alternative fit is provided\nby the CMBfast package, which chooses $\\calpr(k)$ to fit an\n$n$-independent best-fit value of $C_{10}$. As expected, the \n output of CMBfast is in good agreement with the\n Bunn-White fit. Even better agreement is obtained\nusing \n\\be\nk\\sub{COBE}(\\Omega_0)\\equiv 13.2/x\\sub{hor}\n\\,,\n\\label{kcobeofom}\n\\ee\nwhich reduces to \\eq{kcobe} for $\\Omega_0=1$. Insofar as \\eq{kofell} is\nvalid, this $\\Omega_0$-dependent pivot for $k$ corresponds to an \n$\\Omega_0$-independent pivot for $\\ell$, namely $\\ell=13$.\n\nWe are also interested in the \n scale-dependent $n$\n predicted by the running-mass inflation models.\nHowever, as \n the range of scales explored by COBE corresponds to only\n$\\Delta N\\simeq 2$, with the central values of $\\ell $ the most important,\nwe can take the variation of $n$ to be negligible on these scales.\n\nGuided by these considerations, \nwe have adopted three slightly different versions\nof the COBE normalization, chosen for convenience according to the context.\n When calculating \n$\\widetilde \\Gamma$ and $\\widetilde \\sigma_8$, we\nin all cases\nfixed $\\delta_H$ at the central value given by \\eq{cobe1}, at\nthe Bunn-White pivot point $k\\sub{COBE}$.\nWhen calculating the height of the first peak in the cmb anisotropy,\n in the case of \n the running-mass model, we used\n\\eq{kofell}, with $\\delta_H$ again fixed at the central\nvalue given by \\eq{cobe1} but now\nevaluated at the slightly more accurate\npivot point $k\\sub{COBE}(\\Omega_0)$.\nFinally, when evaluating the peak height in the case of scale-independent $n$,\nwe used a linear fit to the output of CMBfast.\nExplicit expressions for the peak height will be given after\nconsidering the effect of reionization.\n\n\\paragraph{The peak height}\nThe model under consideration predicts a peak in the cmb anisotropy at\n$\\ell\\simeq 210$ to $230$, and \npresently available data \\cite{url,boom,ten,maxima} confirm the \nexistence of a peak at about this position.\nWe adopt as a crucial observational quantity \n$\\widetilde C\\sub{peak}$, defined as the maximum value of \n\\be\n\\widetilde C_\\ell \\equiv \\ell(\\ell +1) C_\\ell/2\\pi\n\\,.\n\\ee\nPresently available data give conflicting estimates\n\\cite{url,boom,ten,maxima}\n of $\\cpeak$, with central values in the range 70 to\n$90\\muK$.\n We adopt\n$(80\\pm 10)\\muK$ with the uncertainty taken to be at 1-$\\sigma$.\n\n\\subsection{Reionization}\nThe effect of reionization on the cmb anisotropy is determined by the\noptical depth $\\tau$. \n We assume sudden, complete reionization\nat redshift $z\\sub R$, so that the optical depth $\\tau$ is given by\n\\cite{peacock,abook}\n\\be\n\\tau= 0.035\\frac{\\omb}{\\Omega_0} h \\( \\sqrt{\\Omega_0(1+z\\sub R)^3 +1\n-\\Omega_0} -1 \\)\n\\,.\n\\ee\n\nIn previous investigations, $z\\sub R$ has \n been regarded as a free parameter, usually fixed at zero or some\nother value. In this investigation, we instead take on board that fact that\n $z\\sub R$ can be estimated, in terms of the parameters that we are varying\nplus assumed astrophysics. Indeed,\nit is usually supposed that reionization occurs at an early epoch,\nwhen some fraction\n $f$ of the matter has \ncollapsed, into objects with mass very roughly $M=10^6\\msun$.\nEstimates of $f$ are in the range \\cite{llreion}\n\\be\n10^{-4.4}\\lsim f\\lsim 1\n\\label{fest}\n\\,.\n\\ee\nIn the case $f\\ll 1$, the \n Press-Schechter approximation gives the estimate \n\\be\n1+z\\sub R \\simeq\\frac{\\sqrt2 \\sigma(M)}{\\delta\\sub c g(\\Omega_0)}\n{\\,\\rm erfc}^{-1}(f)\n\\hspace{4em}(f\\ll 1)\n\\label{fll1}\n\\,.\n\\ee\nHere $\\sigma(M)$ is the present, linearly evolved,\n rms density contrast with top-hat smoothing, \n and $\\delta\\sub c=1.7$ is the overdensity required\nfor gravitational collapse. \n( $g$ is the suppression factor of the linearly\nevolved density contrast at the present epoch, which does not apply\nat the epoch of reionization.)\nIn the case $f\\sim 1$, one can justify only the \nrough estimate\n\\be\n1+z\\sub R \\sim \\frac{ \\sigma(M)}{g(\\Omega_0)}\n\\hspace{4em}(f\\sim 1)\n\\,.\n\\ee\n(This estimate is not very different from the one that would be obtained\nby using $f=1$ in \\eq{fll1}.)\n\nIn our fits, we fix $f$ at different values in the above range,\nand find that the most important results are not very sensitive to $f$\neven though the corresponding values of $z\\sub R$ can be quite high.\n\n\\subsection{The predicted peak height}\n\nThe CMBfast package \\cite{CMBfast} gives $C_\\ell$, \nfor \n given values of the parameters with $n$ taken to be \nscale-independent.\nFollowing \\cite{martin}, we parameterize the \nCMBfast output at the first peak in the form\n\\be\n\\cpeak = \\cpeako \\(\\frac{220}{10}\\)^{\\nu/2}\n\\,,\n\\label{eq:cpeak}\n\\ee\nwhere \n\\be\n\\nu \\equiv a_n(n-1)\n + a_h \\ln(h/0.65) + a_0\\ln(\\Omega_0/0.35)\n+a\\sub b h^2(\\omb - {\\omb}^{(0)}) -0.65f(\\tau)\\tau\n\\,.\n\\ee\n $\\cpeako$ is the value of $\\cpeak$\nevaluated with each term of $\\nu$ equal to zero.\nThe \ncoefficients for the high choice $\\omb^{(0)}h^2=0.019$ are \n$a_n=0.88$, $a_h= -0.37$, $a_0=-0.16$,\n$a\\sub b= 5.4$, and $\\cpeako=77.5\\muK$. The formula\nreproduces the CMBfast results within 10\\% for a 1-$\\sigma$\nvariation of the \ncosmological parameters, $h, \\Omega_0$ and $ \\omb$,\nand $n\\sub{COBE}=1.0\\pm 0.05$. \nWith the function $f(\\tau)$ set equal to 1, the \n term $-0.65 \\tau$ is equivalent to multiplying\n$\\cpeak$ by the usual factor $\\exp(-\\tau)$. \nWe use the following formula, which \nwas obtained by fitting the output of CMBfast, and is\naccurate to a few percent over the interesting range of $\\tau$;\n\\be\nf=1- 0.165 \\tau/(0.4+\\tau)\n\\,.\n\\ee\n\nFor the running-mass model, we start with the above estimate for $n=1$,\nand adjust it using \\eq{kofell}. Adopting the COBE\nnormalization mentioned earlier, this adjustment is\n\\be\n\\frac{\\cpeak}{\n\\sqrt{\\widetilde C\\sub{peak}\\su{(n=1)}}\n} = \\frac{\\delta_H(k(\\ell,\\Omega_0))}{\\delta_H(k\\sub{COBE}(\\Omega_0))}\n\\,.\n\\label{peakpresc}\n\\ee\nIn the case of constant $n$, this prescription\n corresponds to the previous one with $a_n=0.91$, in good agreement\nwith the output of CMBfast.\n\n\\section{Constant spectral index}\n\n\\subsection{The observational constraints}\nMost models of inflation make $n$ roughly scale-independent, over the\ncosmologically interesting range. We therefore begin by considering \nthe case that $n$ is exactly scale-independent.\n The resulting bound\non $n$ is shown in Figure 1. In the left-hand panel we make the traditional\nassumption that reionization occurs at some fixed redshift $z\\sub R$.\nIn the right-hand panel we make the more reasonable assumption, that it \noccurs when some fixed fraction $f$ of the matter collapses, in a\nreasonable range $10^{-4.5}<f<1$. The bounds in the latter case\nare relatively insensitive to $f$, because the corresponding range\nof $z\\sub R$ is narrower; everywhere on the displayed curves, $z\\sub R$\nis within (usually well within) the range $8$ to $36$. \nDetails of the fit for $z\\sub R=20$ are given in \nTable 1. Practically the same fit is obtained if instead we fix $f$ at\n$10^{-1.9}$.\n\nThe least-squares fits were performed with the CERN minuit package,\nand the quoted error bars invokes the usual parabolic approximation\n(i.e., it they are the diagonal elements of the error matrix). The\nexact error bars given by the same package agree to better than\n10\\%. For $z\\sub R$, our results are similar to those obtained in \n\\cite{dick},\nbut more precise because of improvements in our knowledge of the cosmological\nparameters; they are also similar to those obtained in\n \\cite{ruth}, if we take the errors to be the ones given by the error\nmatrix. (We do not know why the exact \n error bars in \\cite{ruth} are about three times bigger, in conflict with\nboth our work and that of \\cite{dick}.)\n \nAfter we completed this work, \n the BOOMeranG \\cite{boom} and MAXIMA \\cite{maxima} measurements of\nthe cmb anisotropy appeared, both of which extend to the second\n acoustic peak. Fits to these data \\cite{boomfit,maximafit}\n seem to again give a similar\nconstraint on $n$, but the values for $\\Omega\\sub b$, $\\Omega\\sub c$\nand $h$ outside our adopted 2-$\\sigma$ range. \nAt the time of writing, the new cmb data have not been included in a fit\nof the type that we are performing (i.e., with \nwith strong prior requirements on the cosmological parameters,\nas well as on the \nsmall-scale data $\\widetilde\\sigma_8$ and $\\widetilde \\Gamma$).\n\n\\begin{figure}\n\\centering\n\\leavevmode\\epsfysize=6.5cm \\epsfbox{n-zR.eps} \n\\epsfysize=6.5cm \\epsfbox{n-f.eps}\\\\\n\\caption{The nominal 1- and 2-$\\sigma$ bounds on $n$.\nIn the left-hand panel, the reionization redshift\n $z\\sub R$ is fixed. In the right-hand panel, reionization is assumed to \noccur when a fixed fraction $f$ of matter collapses \n(corresponding reionization redshift, not shown, is roughly in the range $10$\nto $35$).\nA result $n>1$ would rule out most known models of inflation,\n a result $n>.93$ would rule out 'new' inflation with a cubic potential;\nthese cases are indicated by horizontal lines. \n}\n\\end{figure}\n\n\\subsection{Models of inflation giving $n<1$}\nAlthough the quality and quantity of data are insufficient for a \nproper statistical analysis, these bounds on $n$ are very striking\nwhen compared with theoretical expectations.\nThese expectations \\cite{treview,abook} are summarized\\footnote\n{This Table excludes the running-mass models to be discussed later,\nand a recently-proposed model \\cite{ewan00} giving $(n-1)/2= -2/N$.\nIt also excludes the ad hoc 'chaotic inflation' potentials\n$V\\propto \\phi^p$, which give $n-1=-(2+p)/(2N)$ with a \nsignificant gravitational\ncontribution to the cmb anisotropy.}\n in Tables 2\nand 3, and we now discuss them \nbeginning with the usual case $n<1$ (red spectrum). Details of the models\nand references are given in \\cite{treview}.\n \nThe simplest prediction is for a potential of the form\\footnote\n{In this expression and in \\eqs{pot}{runpot}, the \n remaining terms are supposed to be negligible, and \n$V_0$ is supposed to dominate,\nwhile cosmological scales leave the horizon.}\n\\be\nV=V_0-\\frac12 m^2\\phi^2 + \\cdots\n\\,,\n\\label{invq}\n\\ee\nleading to $n-1=-2\\mpl^2 m^2/V_0$.\nThis is the form that one expects if $\\phi$ is a string modulus\n(Modular Inflation), or\na pseudo-Goldstone boson (Natural Inflation), or the radial part\nof a massive field spontaneously breaking a symmetry (Topological\nInflation). The vacuum expectation value (vev) of $\\phi$ in these\nmodels is expected to be of order $\\mpl$ or less, while the potential\n\\eq{invq} gives \n$\\vev{\\phi}\\sim (1-n)^{-1/2}\\mpl$.\nTherefore, the \n present bound $n\\gsim 0.9$ is already beginning to disfavor these models.\nThe potential \\eq{invq} may however give $n$ very close to 1 if the potential\nsteepens after cosmological scales leave the horizon, for instance in an\ninverted \nhybrid inflation model.\n\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{|c|c|ccc|ccc|}\n& $n$ & $\\omb h^2$ & $\\Omega_0$ & $h$ \n&$\\widetilde \\Gamma$ & $\\widetilde \\sigma_8$ & $\\cpeak$ \\\\[4pt]\ndata & --- & $0.019$ & $0.35$ & $0.65$ &\n $0.23$ & $0.56$ & $80\\muK$ \\\\[4pt]\nerror & --- & 0.002 & 0.075 & 0.075 & 0.035 & 0.059 & $10\\muK$\n \\\\[4pt]\nfit & $1.064$ & $0.019$ & $0.34$ & $0.63$\n & 0.19 & 0.59 & $77\\muK$ \\\\[4pt]\nerror & 0.077 & 0.002 & 0.06 & 0.06 & --- & --- & --- \\\\[4pt]\n$\\chi^2$ & --- & $9\\times10^{-5}$ & $3\\times 10^{-2}$ & 0.1 &\n $1.3$ & $0.2$ & $0.1$ \\\\[4pt]\n\\end{tabular}\n\\label{table1}\n\\caption{Fit of the $\\Lambda$CDM model to presently available data,\nwith $z\\sub R=20$.\nThe spectral index $n$ is a parameter of the model, and so are\nthe next three quantities. Every quantity except $n$ is \na data point, with the value and uncertainty listed in\nthe first two rows. The result of the least-squares fit is given in the\nlines three to five. All uncertainties are at the nominal 1-$\\sigma$\nlevel. The total $\\chi^2$ is 1.8 for two degrees of freedom.}\n\\end{center}\n\\end{table}\n\n\n\\begin{table}\n\\begin{center}\n\\label{table2}\n\\caption{Predictions for the spectral index $n(k)$.\nWavenumber $k$ is related to number of $e$-folds $N$\nby $d\\ln k=-dN$. \nConstants $q$ and $Q$ are positive, \nand $p$ can have either sign.}\n\\begin{tabular}{|lll|}\nComments \n& $V(\\phi)/V_0$ & $\\frac12 (n-1)$ \\\\[4pt] \\hline\nMass term & $1\\pm\\frac12 \\frac{m^2}{V_0} \\phi^2$ \n& $\\pm \\mpl^2 m^2/V_0$ \n\\\\[4pt]\n$p$ integer $\\leq -1$ or $\\geq 3$ \n & $1+|c|\\phi^p$ &\n$\\frac{p-1}{p-2}\\frac1{N\\sub{max}-N}$ \\\\[4pt]\nSpont. broken susy &\n$1+|c| \\ln\\frac\\phi Q$ & $-\\frac1{2N} $ \\\\[4pt]\nVarious models & $1- e^{-q\\phi}$ & $-\\frac1 N$ \\\\[4pt]\n$p>2$ or $-\\infty<p<1$ & $1-|c|\\phi^p$ &\n$-\\(\\frac{p-1}{p-2} \\) \\frac1 N$ \n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\\begin{table}\n\\begin{center}\n\\label{table3}\n\\caption{ Predictions for the spectral index $n$,\n for some potentials of the form\n$V_0(1 +c \\phi^p)$ with {\\em negative} $c$.\nThe case $p\\to 0$ corresponds to the potential $V_0(1+c\\ln\\frac{\\phi}Q)$,\n and the case\n$p\\to -\\infty$ corresponds to $V_0(1-e^{-q\\phi})$.\nThe parameter $\\ncobe<60$ depends on the cosmology after inflation.}\n\\begin{tabular}{|cll|}\n$p$ & $n$ & \\\\ \n & $\\ncobe=50$ & $\\ncobe=20$ \\\\ \\hline\n$p\\to 0$ & $0.98$ & $0.95$ \\\\\n$p=-2$ & $0.97$ & $0.93$ \\\\\n$p\\to \\pm \\infty$ & $0.96$ & $0.90$ \\\\\n$p=4$ & $0.94$ & $ 0.85$ \\\\\n$p=3$ & $0.92$ & $ 0.80$ \\\\ \n\\end{tabular}\n\\end{center}\n\\end{table}\n\nOf the remaining models of Table 2, those giving a red spectrum\n involve a potential basically of the form\n\\be\nV=V_0\\( 1+c \\phi^p + \\cdots \\)\n\\,,\n\\label{pot}\n\\ee\nwith $c$ {\\em negative} and $p$ {\\em not} in the range $1\\leq p \\leq 2$.\n( 'New' inflation corresponds\nto $p$ an integer $\\geq 3$, while mutated hybrid inflation models\n account for the\nrest of the range.\nThe logarithmic and exponential potentials in Table 2\n may be regarded as the limits\nrespectively $p\\to 0$ and $p\\to - \\infty$.)\n With this form, the prediction is\n\\be\nn-1=-\\(\\frac{p-1}{p-2} \\) \\frac 2 N\n\\,.\n\\label{pred}\n\\ee\nFor the moment, we ignore the mild scale-dependence and set\n$N=\\ncobe$.\n\n Depending on the history of the Universe, \n\\be\nN\\sub{COBE} \\simeq 60 - \\ln(10^{16}\\GeV/V^{1/4}) - \\frac13\\ln(V^{1/4}/T\\sub{\nreh})\n-%\\Delta N\nN_0\n\\, .\n\\label{Ncobe}\n\\ee\nIn this expression, $T\\sub{reh}$ is the reheat temperature, \nwhile the final contribution $-N_0$ (negative in all reasonable cosmologies)\n encodes our ignorance about\nwhat happens between the end of inflation and nucleosynthesis.\nLet us pause to discuss this ignorance.\nIn the present context, we are defining $T\\sub{reh}$\n as the temperature when the Universe {\\em first}\nbecomes radiation dominated after inflation. In the conventional\ncosmology, radiation domination persists until the present matter\ndominated era begins, long after nucleosynthesis. If this is the case,\nand if also slow-roll inflation gives way promptly to matter domination\nas is the case in most models,\nthen $N_0=0$.\\footnote{In some inflation models, slow-roll is followed \nby an extended era\nof fast-roll giving $N_0$ of order a few; for simplicity we ignore\nthat possibility in the present discussion.}\n In this conventional case, $N\\sub{COBE}$ is largely determined by \n$V_0^{1/4}$, and hence by the model of inflation. It is certainly in the range\n$32$ to $60$ (lower limit corresponding to $V_0^{1/4}=100\\GeV$) and\nmuch more likely in the range $40$ to $60$ (lower limit corresponding to\n$V_0^{1/4}\\sim 10^{10}\\GeV$ and $T\\sub{reh}\\sim 100\\GeV$).\n\nHowever, the conventional cosmology need not be correct. In particular,\nthe initial radiation-dominated era may give way to matter domination\nby a late-decaying particle, and most crucially there may be an era\nof thermal inflation \\cite{thermal} during the transition. \nThis unconventional cosmology, with its huge entropy dilution after\ninflation, is indeed demanded in many inflation models, if\n gravitinos created from the vacuum fluctuation \\cite{gravitino}\npersists to late times \\cite{latetime}.\nEven one bout of thermal inflation will give $N_0\\sim 10$ and additional\nbout(s) cannot be ruled out. Thus, from the theoretical viewpoint, \n$N\\sub{COBE}$ can be anywhere in the range $0$ to $60$.\n\nLet us discuss the prediction \\eq{pred}, excluding for simplicity the\nranges $0<p<1$ and $2<p<3$ (recall that the straightforward\n'new' inflation models make $p$ an integer $\\geq3$).\nTaking the maximum value $\\ncobe\\simeq 60$, we learn that\n $n<0.93$ for $p=3$ (the lowest prediction), and $n<0.95$ for $p=4$.\nLooking at the right-hand panel of Figure 1, we see that at \nnominal 1-$\\sigma$ level,\nthe former case is ruled out, though it is still allowed\nat the 2-$\\sigma$ level.\nStronger results hold in the if $\\ncobe < 60$. Looking at things another\nway, a lower bound on $n$ gives a lower bound on $\\ncobe$,\n\\be\n\\ncobe >\\frac{p-1}{p-2}\\,\\frac2{1-n} \\\\\n\\,.\n\\ee\nEven with present data, the 2-$\\sigma$ result $n\\gsim .9$ gives\n$\\ncobe\\gsim 40$ for $p=3$, and $\\ncobe\\gsim20$ for $p\\gg 3$.\n\nThe scale dependence given by \\eq{pred} is\n\\be\n\\frac{\\diff n}{\\diff \\ln k} = -\\frac12\\(\\frac{p-2}{p-1}\\) \\(n-1\\)^2\n<0\n\\label{scaledep1}\n\\,.\n\\ee\nOver the cosmological\nrange of scales $\\ln(k/k\\sub{COBE})$ is at most a few, and in particular\n $\\ln(8^{-1} h\\Mpc^{-1}/k\\sub{COBE})\\simeq 4$, corresponding to\n\\be\n\\Delta n\\equiv\nn_8-n\\sub{COBE} = -.02 \\(\\frac{p-2}{p-1} \\) \\(\\frac{n-1}{0.1}\\)^2\n<0\n\\,.\n\\label{scaledep2}\n\\ee\nTaking $n = 0.9$ to saturate the present bound,\nthis gives \n $|\\Delta n|<0.02$\nwith $p\\geq 3$, and \n$|\\Delta n|<0.04$ with $p\\leq 0$.\nEven in the latter case, the change in $n$ is hardly\n significant with present data.\n\n\\subsection{Models giving $n>1$}\n\nKnown models \n giving $n>1$ (blue spectrum) are all of the \nhybrid inflation type. The simplest case is $V=V_0+\\frac12m^2\\phi^2$;\nit gives the scale-independent prediction $n-1=2\\mpl^2m^2/V_0$,\nwhich may be either close to 1 or well above 1.\n\nThe other cases\ninvolve a potential of the form $\nV=V_0\\( 1+c\\phi^p \\)$ with {\\em positive} $c$, and $p$ an integer\n$\\geq 3$ or $\\leq -1$.\n There is a maximum (early-time) value\nfor $N$, and the prediction\n\\be\nn-1 = \\frac{p-1}{p-2} \\frac1{N\\sub{max} - N}\n\\,.\n\\ee\nBarring the fine-tuning $N\\sub{COBE}\\simeq N\\sub{max}$,\nthis gives $n-1\\ll 0.04$, which is compatible with the \nobservational bound. \nThe scale-dependence of $n$ in these models is still given by \n\\eqs{scaledep1}{scaledep2}; it may be observationally significant\nonly in the fine-tuned case $N\\sub{COBE}\\simeq N\\sub{max}$,\nwhich we have not investigated. \n\n\\section{The running mass models}\n\n\\subsection{The potential}\nWe have also done fits with the \n scale-dependent spectral index,\n predicted in inflation models with a running inflaton mass\n \\cite{st97,st97bis,clr98,cl98,c98,rs}. In these models,\nbased on softly broken supersymmetry,\none-loop corrections to the tree-level potential are taken into\naccount, by evaluating the inflaton mass-squared\n $m^2(\\ln (Q))$ at the renormalization \nscale $Q\\simeq \\phi$,\\footnote\n{The choice $Q\\simeq \\phi$ is to be made in the regime\nwhere $\\phi$ is bigger than the relevant masses. When $Q$ falls below \nthe relevant masses, \n $m^2(Q)$ becomes practically scale-independent (the mass 'stops running').\nWe have a running mass model if inflation takes place in the former\nregime, which happens in some interesting cases \\cite{cl98,c98},\nincluding that of a gauge coupling.}\n\\be\nV=V_0 + {1\\over 2} m^2(\\ln(Q)) \\phi^2 + \\cdots\n\\,.\n\\label{runpot}\n\\ee\n\nOver any small range of $\\phi$, \nit is a good approximation to take the running mass to be a \nlinear function of $\\ln\\phi$.\nThis is equivalent to choosing the renormalization scale to be \nwithin the range, and then adding the loop correction explicitly,\n\\be\nV=V_0 +\\frac12m^2(\\ln Q)\\phi^2 -\\frac 12 c(\\ln Q) \\frac{V_0}{\\mpl^2}\n\\phi^2 \\ln(\\phi/Q)\n\\,.\n\\label{vlin1}\n\\ee\nThe dimensionless quantity $c$ specifies the strength of the coupling.\nLet us discuss its likely magnitude, taking for definiteness\n $Q=\\phi\\sub{COBE}$.\n\nIt has been shown \\cite{cl98} that the linear approximation\nis very good over the range of $\\phi$ corresponding to horizon exit\nfor scales between $k\\sub{COBE}$ and $8h^{-1}\\Mpc$. We shall want\nto estimate the reionization epoch, which involves a\n scale of order $k\\sub{reion}^{-1}\\sim\n10^{-2}\\Mpc$ (enclosing the relevant mass of order\n$10^6\\msun$). Since only a crude estimate of the reionization\nepoch is needed, we shall assume that the linear approximation is\nadequate down to this `reionization scale'. In other words,\nwe assume that it is adequate for $\\phi$ between $\\phi\\sub{COBE}$\nand $\\phi\\sub{reion}$, the subscripts denoting the value of $\\phi$\nwhen the relevant scale leaves the horizon.\nWithin this range, we it is convenient to write \\eq{vlin}\nin the form \\cite{cl98}\n\\be\nV=V_0-\\frac12 \\frac{V_0}{\\mpl^2} c\\phi^2\\( \\ln\\frac{\\phi}{\\phi_*}\n-\\frac12 \\) \n\\,,\n\\label{vlin}\n\\ee\n so that\n\\be\nV'=- \\frac{V_0}{\\mpl^2} c\\phi \\ln\\frac{\\phi}{\\phi_*}\n\\,.\n\\ee\nIn these expressions, the constants $c$ and $\\phi_*$ both depend on the \nrenormalization scale\n$Q$, which can be chosen \n anywhere in the range corresponding to cosmological\nscales (say $Q=\\phi\\sub{COBE}$).\n The dimensionful constant $\\phi_*$ is related to \n the mass-squared by\n\\be\n\\ln(\\phi_*/Q) = {m^2(Q)\\mpl^2\\over c(Q) V_0} -\\frac12\n\\,.\n\\label{mofphi}\n\\ee\nNote that the limit of no running, $c \\rightarrow 0$, corresponds to\nfinite $ c |\\ln(\\phi/\\phi_*)| $, so that \\eq{vlin} in that\nlimit gives back \\eq{runpot} with a constant mass.\n\nIn general, the point $\\phi=\\phi_*$ may be far\n outside the regime\nwhere the linear approximation \\eq{vlin} applies.\n However, in simple models the cosmological \nregime is sufficiently close to that point \nthat the linear approximation \nis approximately valid there. \nIn that case, we can trust the \n \\eq{vlin} and its derivatives for $\\phi=\\phi_*$; \nsince $V'$ vanishes at that point,\n there are four\nclearly distinct models of inflation as shown in\nFigure \\ref{models}. The labeling (i), (ii), (iii) and (iv)\nis the one introduced \nin \\cite{cl98}.\nIn Models (i) and (ii), \n $c$ is positive and the potential\nhas a maximum near $\\phi_*$,\nwhile in Models (iii) and (iv),\n$c$ is negative and there is a minimum.\nIn Models (i) and (iv),\n $\\phi$ moves towards the origin, while in Models\n(ii) and (iii) the opposite is true.\nEven if \\eq{vlin} is not valid near $\\phi=\\phi_*$, \nthis fourfold classification of models, according to the sign of $c$ and\nthe direction of motion of $\\phi$, is still useful.\n\nLet us discuss the likely magnitude of $c$, assuming that \n a single coupling dominates the loop correction.\n The value of $c$ is conveniently obtained\n from the well-known\nRGE for $\\diff m^2/\\diff (\\ln Q)$.\n If a gauge coupling dominates one finds\n\\cite{st97bis}\n\\be\n\\frac{V_0 c}{\\mpl^2} = \\frac{2 C}\\pi \\alpha \\widetilde m^2\n\\,.\n\\label{c-def}\n\\ee\nHere, $C$ is a positive group-theoretic number of order 1, \n $\\alpha$ is the gauge coupling, and \n $\\widetilde m$ is the gaugino mass.\n We see that\n {\\em if the loop correction comes from a single gauge\ncoupling, $c$ is positive}, corresponding to Model (i) or Model\n(ii). If a Yukawa coupling dominates, one finds \\cite{c98} (for\nnegligible supersymmetry breaking trilinear coupling)\n\\be\n\\frac{V_0 c}{\\mpl^2} = - {D\\over 16\\pi^2} |\\lambda |^2 m^2_{loop}\n\\,,\n\\ee\nwhere $D$ is a positive constant counting the number of \nscalar particles interacting with the inflaton, $m^2\\sub{loop}$ \nis their common susy breaking mass-squared, and \n$\\lambda$ is their common Yukawa coupling.\n In this case, $c$ can be of either\nsign. \n\nTo complete our estimate of $c$, we \n need the gaugino or scalar mass. \n The traditional\nhypothesis is that soft supersymmetry breaking is gravity-mediated,\nand in the context of inflation this means that the scale\n$M\\sub S$ of supersymmetry\nbreaking will be roughly $V_0^{1/4}$. (As usual we are defining \n$M\\sub S\\equiv \\sqrt F$, where $F$ is the auxiliary field responsible\nfor spontaneous supersymmetry breaking in the hidden sector.\n We also assume that there is no accurate cancelation\nin the formula $V=|F|^2-3\\mpl^2m_{3/2}^2$, which is the case in most\nsupersymmetric inflation models \\cite{treview}.)\nWith gravity-mediated susy breaking, typical values of the \n masses are $\\widetilde m^2\\sim |m\\sub{loop}^2|\\sim V_0/\\mpl^2$,\nwhich makes $|c|$ of order of the coupling strength\n $\\alpha$ or $|\\lambda|^2$. At least in the case of a gauge coupling, one\nthen expects\n\\be\n|c|\\sim 10^{-1}\\mbox{ to }10^{-2}\n\\,.\n\\ee\nIn special versions of gravity-mediated susy breaking,\n the masses could be much smaller, leading to $|c|\\ll 1$. In that case,\nthe mass would hardly run, and the spectral index would be practically\nscale-independent. With gauge-mediated\nsusy breaking, the masses could be much bigger; this\n would not\nlead to a model of inflation\n(unless the coupling is suppressed) because\nit would not satisfy the slow-roll requirement\n$|c|\\lsim 1$. \n\n\\subsection{The spectrum and the spectral index}\n\nUsing \n\\eq{Nofv} we find\n\\bea\ns e^{c\\Delta N(k)} &=& c \\ln(\\phi_*/\\phi)\\label{sigma}\\\\\n\\Delta N(k)&\\equiv& N\\sub{COBE} - N(k)\n\\equiv \\ln(k/k\\sub{COBE})\n\\,,\n\\eea\nwhere \n$s$ is an integration constant.\\footnote\n{In an earlier paper \\cite{cl98}\nwe used $\\sigma\\equiv s e^{cN\\sub{COBE}}$, \nbut $s$ is more convenient.}\n \\eq{nofvapprox} then gives\n\\be\n{n(k)-1\\over 2} = \ns e^{c\\Delta N(k)} - c \\label{runpred}\n\\,.\n\\ee\nSome lines of fixed $n\\sub{COBE}$ in the plane $s$ versus $c$\nare shown in the left-hand panel of Figure \\ref{s-c-f1}.\nIn order to evaluate \\eq{peakpresc}, we also need the variation of\n$\\delta_H$ which comes from integrating this expression,\n\\be\n\\frac{\\delta_H(k)}{\\delta_H(k\\sub{COBE})}\n=\\exp\\[ \\frac sc \\(e^{c\\Delta N}-1\\)-c\\Delta N \\]\n\\,.\n\\ee\n\nWe are mostly interested in cosmological scales between $k\\sub{COBE}$\nand $k_8$, corresponding to $0\\lsim \\Delta N\\lsim 4$.\nIn this range the scale-dependence of $n$ is approximately linear\n(taking $|c|\\lsim 1$)\nand the variation $\\Delta n\\equiv n_8-n\\sub{COBE}$ is given approximately\nby\n\\be\n\\Delta n \\simeq 4\n\\frac{\\diff n}{\\diff \\ln k}\\simeq 8sc\n\\,.\n\\label{scaledep3}\n\\ee\nIn contrast with the prediction \n \\eqs{scaledep1}{scaledep2} of the earlier models we considered,\n$\\Delta n$ is positive. Also in contrast with those models,\nit is not tied to the magnitude of $|n-1|$, and (as we shall see)\n may be significant even with present data, for physically reasonable\nvalues of the parameters.\n In the right-hand panel of \n Figure \\ref{s-c-f1},\nwe show the branches\nof the hyperbola $8sc=\\Delta n$, for the reference\nvalue\n$\\Delta n=0.04$.\n Within\nthe hyperbola, the scale-dependence of $n$ is probably \ntoo small to be significant\nwith present data.\n\n\\begin{figure}\n\\centering\n\\leavevmode\\epsfysize=6.5cm \\epsfbox{i-ii.eps}\n\\epsfysize=6.5cm \\epsfbox{iii-iv.eps}\\\\\n\\caption[sc-fig1]{Sketches of the potential for the different models\nin the case an extremum exists: the right panel shows the inflaton \nbehavior for Models (i) and (ii), while the left panel shows\nModels (iii) and (iv).}\n\\label{models}\n\\end{figure}\n\nThe spectral index \\eq{runpred} depends on the coupling $c$,\nwhich we already discussed, and the integration constant $s$.\nTo satisfy the slow-roll conditions $\\mpl^2|V''/V|\\ll 1$ and\n$\\mpl^2(V'/V)^2\\ll1 $,\n both $c$ and $s$ \nmust be at most of order 1 in magnitude.\nSignificant additional \n constraints on $s$ follow, if we make the reasonable\nassumptions that\n the mass continues to run to the end of \nslow-roll inflation, and that \n the linear approximation\n remains {\\em roughly} valid. Indeed, setting \n$\\Delta N=N\\sub{COBE}$, \\eq{sigma} becomes\n$\ns=e^{-c\\ncobe}c\\ln(\\phi_*/\\phi\\sub{end})$.\nDiscounting the possibility that \n the end of inflation is very fine-tuned, to occur close to the\nmaximum or minimum of the potential, this \ngives a lower bound \n\\be\n|s|\\gsim e^{-c\\ncobe}|c|\n\\,.\n\\label{sb1}\n\\ee\nIn the case of positive $c$ (Models (i) and (ii)),\n we also obtain a significant upper bound\nby \nsetting $\\Delta N=\\ncobe$ in \\eq{runpred}, and remembering\nthat slow-roll requires\n $|n-1|\\lsim 1$;\n\\be\n|s|\\lsim e^{-cN\\sub{COBE}}\\hspace{2em}(c>1)\n\\,.\n\\label{sb2}\n\\ee\nIn the simplest case, that \nslow-roll \ninflation \n ends when $n-1$ actually becomes of order 1, this bound becomes\nan actual estimate,\n $|s|\\sim e^{-cN\\sub{COBE}}$.\n\n In the case of \nModels (i) and (iv), \nthe mass may cease to run before the end of slow-roll inflation\n(but after cosmological scales leave the horizon, \n or the running mass model\nwould not apply) at some point $N\\sub{run}$.\n In this somewhat fine-tuned situation,\n$\\ncobe$ in the above estimates should\nbe replaced $\\ncobe-N\\sub{run}$, which may be much less than $\\ncobe$.\nIn the case of Model (iv), this leads to a weaker \n lower bound\n\\be\ns\\gsim |c|\\hspace{3em}(c<0)\n\\,.\n\\label{sb3}\n\\ee\nIn the case of Model (i) it leads to a weaker\nupper bound\n\\be\ns\\lsim 1\\hspace{3em}(c>0)\n\\,.\n\\label{sb4}\n\\ee\nIn the left-hand panel of Figure \\ref{s-c-f1},\nwe show the bounds relevant to the \nchoice of parameter's ranges, i.e. the \nlower bound \\eq{sb1}, the upper bound \\eq{sb2}\nand the weak lower bound \\eq{sb3}.\n\n\\subsection{The magnitude of the spectrum}\nAlthough it is not directly relevant for our investigation of the spectral\nindex, we should mention the constraint on the running mass model that comes\nfrom the observed magnitude $\\calpr^{1/2}\\simeq 10^{-5}$ of the spectrum.\n{}From \\eq{delh}, \n\\be\n\\frac4{25}\\calpr=\n \\frac{V_0}{\\phi_*^2\\mpl^2}\\exp\\(\\frac\n{2s}c \\)\\frac1{|s|^2} \n\\,.\n\\label{cobenorm}\n\\ee\nThis prediction \n involves $V_0$ and $\\phi_*$, in addition to the parameters $c$\nand $s$ that determine the spectral index.\n\nThe simplest thing is to again assume gravity-mediated susy breaking,\nwith the ultra-violet cutoff at the traditional scale around $\\mpl$,\nand the same supersymmetry breaking scale\n during inflation as in the true vacuum so that\n $V_0^{1/4}\\sim 10^{10}\\GeV$. \nIn this scenario, one expects\n $|m^2(Q)|\\sim V_0/\\mpl^2$ at $Q\\sim \\mpl$.\nAs Stewart pointed out in the first paper\non the subject, with this very traditional set of assumptions,\n\\eq{cobenorm} can give the correct COBE normalization, with \n $|c|$ in the physically favored range $10^{-1}$ to $10^{-2}$.\\footnote\n{At the crudest level, one can verify this using\nthe linear approximation \\eq{vlin}\n all the way up to the $\\phi\\sim\\mpl$, corresponding to \n$\\ln(\\mpl/\\phi_*)\\sim 1/c\\sim 10$ to $100$. Proper calculations\n\\cite{st97bis,clr98,cl98}\nusing the RGE's lead to the same conclusion.}\n\nIt is remarkable that \n the most traditional set of assumptions can give a model with the \ncorrect COBE normalization, and, as we shall see, with \na viable spectral index.\nIf one relaxes these assumptions, \n there is much more freedom in choosing\n $V_0$ and $\\phi_*$. Such\n freedom\nmay be very welcome, in coping with the difficulty of implementing\n inflation in the context of large extra dimensions \\cite{large}.\n\n\\subsection{Observational constraints on the running mass models}\n\n\n\\begin{figure}[t]\n\\centering\n\\leavevmode\n\\epsfysize=7.5cm \\epsfbox{s-c-th-f1.eps}\n\\epsfysize=7.5cm \\epsfbox{s-c-data-f1.eps}\n\\caption[sc-fig2]{\nThe parameter space for the running mass model.\nIn the left-hand panel we show the straight lines \ncorresponding to $n\\sub{COBE}=1.2$, $1.0$ and $0.8$. \nAlso shown in the left-hand panel are the lower bound \\eq{sb1},\nthe upper bound \\eq{sb2}, and (diagonal line in upper right quadrant)\nthe weak lower bound \\eq{sb3}. (The weak upper bound \\eq{sb4} is off the \nscale.) As explained in the text, these curves \ndefine the theoretically reasonable region of the parameter space.\nIn the right-hand panel, we show the region allowed by observation,\nin the case that reionization occurs when $f\\simeq 1$.\nNote that the allowed region is parallel to the fixed $n_{COBE}$\nlines around $n_{COBE}\\simeq 1$, as one would expect.\nTo show the scale-dependence of the prediction for $n$, we also show in \nthis panel the branches\nof the hyperbola $8sc=\\Delta n\\equiv n_8-n\\sub{COBE}$, for the reference\nvalue $\\Delta n=0.04$.}\n\\label{s-c-f1}\n\\end{figure}\n\nExtremizing with respect to all other parameters, we have calculated\n$\\chi^2$ in the $s$ vs. $c$ plane and obtained contour levels\nfor $\\chi^2$ equal to the minimum value plus\n$2.41$ and $5.99$ respectively, \ncorresponding nominally to the 70\\% and 95\\% confidence level in \ntwo variables. (The\n$\\chi^2$ function presents actually two nearly degenerate minima in the \nallowed region, one in the positive and one in the negative quadrants \n(Models (i) and (iii)), separated by a very low barrier, but we assume\nthat the usual quadratic estimate of the probability content is not very \nfar from the true value.)\n\nThe allowed region is shown in the right-hand panel of \nFigure \\ref{s-c-f1}, for\n the case that \n reionization occurs when $f\\simeq 1$.\nFor $c=0$ or $s = 0$ the constant $n$ result is recovered with\n$n-1= -2 c$ or $ 2s$; our plots give in this case a slightly larger \nallowed interval with respect to the two sigma value in the previous\nsection, due to the mismatch between the statistical one variable and\ntwo variables 95\\% CL contours.\n This allowed region is not too different\nfrom the one that we estimated\nearlier \\cite{cl98}, by imposing the crude requirement\n$|n-1| < 0.2 $ at both the COBE scale and the low scale \ncorresponding to $N_{COBE} - 10$.\n(Note that in the earlier work we used the less convenient\nvariable $\\sigma\\equiv s\\exp(c\\ncobe)$, instead of $s$.)\n%We can assume that the freedom in changing the cosmological \n%parameters is in some way compensating the more accurate \n%prescription we are using here.\n\nThe allowed region for Models (ii) \n and (iv) lies inside the\nhyperbola corresponding to $\\Delta n=.04$,\nwhich means that their scale-dependence is hardly significant\n at the level of present data.\nIn contrast, the allowed region for Models (i) and (iii)\n extends to $\\Delta n\\geq 0.2$, representing an extremely significant\nscale-dependence even with present data.\nTo demonstrate this, we show in Figures \\ref{n8ncobe} and \n\\ref{n8ncobe3} the allowed regions for Models (i) and (iii)\nin the $n_8$ versus $n\\sub{COBE}$ plane. \nIn the case of Model (iii), \nthe theoretical bounds on the\nparameters restrict the parameter space to a small corner of\nthe allowed region, within which $n$ has \n negligible variation.\n In contrast, there is no significant theoretical restriction on\nthe parameters in the case of Model (i), and $n$ has significant variation\nin a physically reasonable regime of parameter space.\nIn both cases, \n a lower value of the fraction of \ncollapsed matter $f$ just reduces the allowed region\nat large n, without affecting significantly the allowed scale-dependence\nof n. \n\n In the case of Model (i), a further observational constraint comes\nfrom the requirement that the\n density perturbation on scales leaving the horizon at the {\\em end}\nof inflation, should be small enough to avoid dangerous black hole\nformation. The linear approximation is not adequate\non such small scales, and one should instead evaluate the running\nmass using the RGE. The simplest assumption is that the RGE\ncorresponds to a single gauge coupling, either with or without asymptotic\nfreedom \\cite{clr98}. The black hole constraint has been evaluated for these\ncases \\cite{lgl}. \nThe constraint amounts more or less to an upper bound on\n$n\\sub{COBE}$, typically in the range $1.1$ to $1.3$ depending on the\nchoices of $N\\sub{COBE}$ and other parameters. Such a bound\nsignificantly reduces the allowed region of parameter space, \nbut still leaves a region where $n$ has a strong variation.\n\n\\begin{figure}[t]\n\\centering\n\\leavevmode\\epsfysize=7.5cm \\epsfbox{new-n8ncobe-f1.eps}\n\\epsfysize=7.5cm \\epsfbox{new-n8ncobe-f2.2.eps}\n\\caption[n8-ncobe]{Allowed region in the $n_{COBE}-1$ \nvs $n_8-1$ plane at 95\\% CL (solid line) and 70\\% CL (dashed line)\nfor positive $s$ and $c$ (Model (i)). The two panels correspond\nto different hypotheses about the reionization epoch.\nIn the right panel, it is assumed that \nreionization occurs when a fraction\n $f = 10^{-2.2}$ of the matter has collapsed into bound structures,\nwhile in the left panel the fraction is taken to be $f\\sim 1$. \n}\n\\label{n8ncobe}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\leavevmode\\epsfysize=7.5cm \\epsfbox{new-n8ncobe-f1-iii.eps}\n\\epsfysize=7.5cm \\epsfbox{new-n8ncobe-f2.2-iii.eps}\n\\caption[n8-ncobe2]{Allowed region in the $n_{COBE}-1$ \nvs $n_8-1$ plane for negative $s$ and $c$ (Model (iii)). \nAgain the two panels\ncorrespond to different reionization epoch hypothesis, as in \nFig.\\ref{n8ncobe}. \n The allowed region is below the dotted line $n_8=n\\sub{COBE}$,\nand above the solid (dashed) line at 95\\% (70\\%) confidence level.\nThese lines do not depend on the value of \n$N_{COBE}$.\nThe line $s=c e^{c N_{COBE}}$ is also drawn for \n$N_{COBE}=50$. The theoretically favored\nregime $|s| \\geq |c| e^{c N_{COBE}} $ is the\nsector between this line and the $n_8=n_{COBE}$ line.\nThe region of positive\n$n_8-1$ and/or $n\\sub{COBE}-1$ is not shown, since it corresponds to\n$|c| \\gg |s| e^{-c N_{COBE}} $.}\n\\label{n8ncobe3}\n\\end{figure}\n\n\n\\section{Conclusion}\n\nIn the context of the $\\Lambda$CDM model, we \n have evaluated the observational constraint on the spectral index \n$n(k)$.\nThis constraint comes from \n a range of data, including the height of the first peak in the\n cmb anisotropy, which we take to be\n$80\\pm 10\\mu$K (nominal 1-$\\sigma$). \nReionization is assumed to occur when some fixed fraction $f$ of the \nmatter collapses, and the most important results are insensitive\nto this fraction in the reasonable range $10^{-4}\\lsim f\\lsim 1$.\n\nWe first considered the case that $n$ \n has negligible scale dependence, comparing the observational bound with\nthe prediction of various models of inflation.\nA significant improvement in the 2-$\\sigma$ lower bound, which may well occur\nwith the advent of slightly better measurements of the cmb anisotropy,\nwill become a serious discriminator between models of inflation.\nEven the present bound has serious implications if, as is very\npossible, late-time gravitino creation or some other \nphenomenon requires an era of thermal inflation\nafter the usual inflation.\n\nWe also considered the running mass models of inflation,\n where the spectral\nindex can have significant scale-dependence. Because of this\nscale dependence, it is in this case crucial to fix not the epoch \nof reionization, but the fraction $f$ of matter\nthat has collapsed at that epoch. We presented results for the choice\n$f=1$ (corresponding to $z\\sub R\\simeq 13$ if the spectral index has\n negligible scale-dependence), and for a perhaps more reasonable\nchoice $ f=10^{-2.2}$.\n In the running-mass models, the\n scale-dependent spectral index $n(k)$ is given by $n-1=s \\exp(c\\Delta N)\n-c$, where $\\Delta N=\\ln(k\\sub{COBE}/k)$. The parameters in this expression\ncan be of either sign, leading to four different models of inflation.\nBarring fine-tuning, one expects $s$ to be in the range\n$|c|e^{-cN\\sub{COBE}}\\lsim |s|\\lsim e^{-cN\\sub{COBE}}$.\nThe parameter $c$ depends on the nature of the soft supersymmetry\nbreaking, but in \n the simplest case of \n gravity-mediation it becomes a dimensionless coupling strength,\npresumably of order \n$ 10^{-1}$ to $10^{-2}$ in magnitude.\n\nWithout worrying about the origin of the parameters\n $c$ and $s$, \nwe have investigated the observational constraints on them.\n In the case $c,s>0$ (referred to as Model (i)) we find that \n$n$ can have a significant variation on\ncosmological scales, with \n $n-1$ passing through zero signaling a minimum of the spectrum\nof the primordial curvature perturbation.\nIn a future paper, we shall exhibit the \npossible effect of this scale-dependence\n on the cmb anisotropy, at and above the first peak.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section*{Acknowledgments}\nWe thank Pedro Ferreira and Andrew Liddle and Martin White\nfor useful discussions.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\renewcommand\\pl[3]{Phys. Lett. {\\bf #1}, #2 (#3)}\n\\newcommand\\np[3]{Nucl. Phys. {\\bf #1}, #2 (#3)}\n\\newcommand\\pr[3]{Phys. Rep. {\\bf #1}, #2 (#3)}\n\\renewcommand\\prl[3]{Phys. Rev. Lett. {\\bf #1}, #2 (#3)}\n\\renewcommand\\prd[3]{Phys. Rev. D{\\bf #1}, #2 (#3)}\n\\newcommand\\ptp[3]{Prog. Theor. Phys. {\\bf #1}, #2 (#3)}\n\\newcommand\\rpp[3]{Rep. on Prog. in Phys. {\\bf #1}, #2, (#3)}\n\\newcommand\\jhep[2]{JHEP #1 (19#2)}\n\\newcommand\\grg[3]{Gen. Rel. Grav. {\\bf #1}, #2, (#3)}\n\\newcommand\\mnras[3]{MNRAS {\\bf #1}, #2, (#3)}\n\\newcommand\\apjl[3]{Astrophys. J. Lett. MNRAS {\\bf #1}, #2, (#3)}\n\n\\begin{references}\n\\bibitem{likely} M. S. Turner, astro-ph/9904051; W. L. Freedman,\nastro-ph/9905222; N. A. Bahcall, J. P. Ostriker, S. Perlmutter and P.\nJ. Steinhardt, astro-ph/9906463.\n\\bibitem{dwarf} F. C. van den Bosch and R. A. Swaters, astro-ph/0006048.\n\\bibitem{llvw} A. R. Liddle, D. H. Lyth, P. T. P. Viana and M. White,\n\\mnras{282}{281}{1996}.\n\\bibitem{osw} K. A. Olive, G. Steigman and T. P. Walker, \nastro-ph/9905320.\n\\bibitem{subir} S. Sarkar, \\rpp{59}{1493}{1996}.\n\\bibitem{vl} P. T. P. Viana and A. R. Liddle, astro-ph/9902245.\n\\bibitem{will} W. Sutherland et. al., astro-ph/9901189.\n\\bibitem{bw} E. F. Bunn and M. White, Astrophys. J. 480, 6 (1997).\n\\bibitem{blw} E. F. Bunn, A. R. Liddle and M. White, \\prd{54}{5917R}{1996}.\n\\bibitem{url}\n {\\tt http://imogen.princeton.edu/$\\sim$page/where\\_is\\_peak.html}.\n\\bibitem{boom}\nP. De Bernardis et. al., Nature {\\bf 404}, 955 (2000)\n\\bibitem{ten}\nD. L. Harrison et. al., astro-ph/0004357.\n\\bibitem{maxima} S. Hanany et al., astro-ph/0005123.\n\\bibitem{peacock} J. A. Peacock, {\\em Cosmological physics},\nCambridge University Press (1999).\n\\bibitem{abook} A. R. Liddle and D. H. Lyth,\n{\\em Cosmological Inflation and Large--Scale Structure},\n Cambridge University Press (1999).\n\\bibitem{llreion} A. R. Liddle and D. H. Lyth, \\mnras{273}{1177}{1995}.\n\\bibitem{gbl} L. M. Griffiths, D. Barbosa and A. R. Liddle,\nastro-ph/9812125.\n\\bibitem{CMBfast} \n{\\tt http://www.sns.ias.edu/$\\sim$matiasz/CMBfast/CMBfast.html}.\n\\bibitem{martin} M. White, Phys.Rev. D {\\bf 53} 3011 (1996).\n\\bibitem{dick} J. R. Bond and A. H. Jaffe, astro-ph/9809043, published in\nPhilosophical Transactions of the Royal Society of London A, \n{\\it Discussion Meeting on \nLarge Scale Structure in the Universe}, Royal Society, London, March 1998. \n\\bibitem{ruth} B. Novosyadlyj et. al., astro-ph/9912511.\n\\bibitem{treview}D. H. Lyth and A. Riotto, Phys. Rept. 314 1 (1999).\n\\bibitem{thermal} D. H. Lyth and E. D. Stewart, Phys.Rev. D{\\bf 53} \n1784 (1996).\n\\bibitem{gravitino}\n R. Kallosh, L. Kofman, A. \n Linde and A. Van Proeyen,\n \\prd{61}{103503}{2000}; G. F. Giudice, I. Tkachev and A. Riotto,\n\\jhep{9908:009}{99}; D. H. Lyth, \\pl{469B}{69}{1999}\nand hep-ph/9911257.\n\\bibitem{latetime} D. H. Lyth, \\pl{476B}{356}{2000} and\n hep-ph/0003120.\n\\bibitem{gorski} K. M. Gorski et. al., \\apjl{464}{L11}{1996}.\n\\bibitem{st97} E. D. Stewart Phys. Lett. {\\bf 391B}, 34 (1997).\n\\bibitem{st97bis} E. D. Stewart Phys. Rev. D{\\bf 56}, 2019 (1997).\n\\bibitem{clr98} L. Covi, D. H. Lyth and L. Roszkowski \nPhys. Rev. D{\\bf 60}, 023509 (1999).\n\\bibitem{cl98} L. Covi and D. H. Lyth Phys. Rev. D{\\bf 59}, 063515\n(1999).\n\\bibitem{c98} L. Covi Phys. Rev. D{\\bf 60}, 023513 (1999).\n\\bibitem{rs} G. German, G. Ross and S. Sarkar,\n\\pl{B469}{46}{1999}.\n\\bibitem{large} See for instance D. H. Lyth, \\pl{B466}{85}{1999}\n\\bibitem{lgl}\nS. M. Leach, I. J. Grivell and A. R. Liddle,\nastro-ph/0004296.\n\\bibitem{boomfit} A. E. Lange {\\it at al.}, astro-ph/0005004. \n\\bibitem{maximafit} A. Balbi {\\it et al.}, astro-ph/0005124.\n\\bibitem{ewan00} E. D. Stewart and J. D. Cohn, astro-ph/0002214. \n\\end{references}\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002397.extracted_bib",
"string": "\\bibitem{#1}\\hspace{1cm}#1\\hspace{1cm}}\n\\newcommand{\\dlabel}[1]{\\label{#1} \\ \\ \\ \\ \\ \\ \\ \\ #1\\ \\ \\ \\ \\ \\ \\ \\ }\n\\def\\dcite#1{[#1]}\n\n\\def\\dslash{\\not{\\hbox{\\kern-2pt $\\partial$}}}\n\\def\\Dslash{\\not{\\hbox{\\kern-4pt $D$}}}\n\\def\\Oslash{\\not{\\hbox{\\kern-4pt $O$}}}\n\\def\\Qslash{\\not{\\hbox{\\kern-4pt $Q$}}}\n\\def\\pslash{\\not{\\hbox{\\kern-2.3pt $p$}}}\n\\def\\kslash{\\not{\\hbox{\\kern-2.3pt $k$}}}\n\\def\\qslash{\\not{\\hbox{\\kern-2.3pt $q$}}}\n\n%\n \\newtoks\\slashfraction\n \\slashfraction={.13}\n \\def\\slash#1{\\setbox0\\hbox{$ #1 $}\n \\setbox0\\hbox to \\the\\slashfraction\\wd0{\\hss \\box0}/\\box0 }\n \n% EXAMPLE OF HOW TO USE IT\n% $\\slash D$\n% {\\slashfraction={.075} $\\slash{\\cal A}$}\n% $\\slash B$\n% $\\slash a$\n% {\\slashfraction={.09} $\\slash p$}\n% $\\slash q$\n\n\\def\\ee{\n\\bibitem{likely} M. S. Turner, astro-ph/9904051; W. L. Freedman,\nastro-ph/9905222; N. A. Bahcall, J. P. Ostriker, S. Perlmutter and P.\nJ. Steinhardt, astro-ph/9906463.\n\n\\bibitem{dwarf} F. C. van den Bosch and R. A. Swaters, astro-ph/0006048.\n\n\\bibitem{llvw} A. R. Liddle, D. H. Lyth, P. T. P. Viana and M. White,\n\\mnras{282}{281}{1996}.\n\n\\bibitem{osw} K. A. Olive, G. Steigman and T. P. Walker, \nastro-ph/9905320.\n\n\\bibitem{subir} S. Sarkar, \\rpp{59}{1493}{1996}.\n\n\\bibitem{vl} P. T. P. Viana and A. R. Liddle, astro-ph/9902245.\n\n\\bibitem{will} W. Sutherland et. al., astro-ph/9901189.\n\n\\bibitem{bw} E. F. Bunn and M. White, Astrophys. J. 480, 6 (1997).\n\n\\bibitem{blw} E. F. Bunn, A. R. Liddle and M. White, \\prd{54}{5917R}{1996}.\n\n\\bibitem{url}\n {\\tt http://imogen.princeton.edu/$\\sim$page/where\\_is\\_peak.html}.\n\n\\bibitem{boom}\nP. De Bernardis et. al., Nature {\\bf 404}, 955 (2000)\n\n\\bibitem{ten}\nD. L. Harrison et. al., astro-ph/0004357.\n\n\\bibitem{maxima} S. Hanany et al., astro-ph/0005123.\n\n\\bibitem{peacock} J. A. Peacock, {\\em Cosmological physics},\nCambridge University Press (1999).\n\n\\bibitem{abook} A. R. Liddle and D. H. Lyth,\n{\\em Cosmological Inflation and Large--Scale Structure},\n Cambridge University Press (1999).\n\n\\bibitem{llreion} A. R. Liddle and D. H. Lyth, \\mnras{273}{1177}{1995}.\n\n\\bibitem{gbl} L. M. Griffiths, D. Barbosa and A. R. Liddle,\nastro-ph/9812125.\n\n\\bibitem{CMBfast} \n{\\tt http://www.sns.ias.edu/$\\sim$matiasz/CMBfast/CMBfast.html}.\n\n\\bibitem{martin} M. White, Phys.Rev. D {\\bf 53} 3011 (1996).\n\n\\bibitem{dick} J. R. Bond and A. H. Jaffe, astro-ph/9809043, published in\nPhilosophical Transactions of the Royal Society of London A, \n{\\it Discussion Meeting on \nLarge Scale Structure in the Universe}, Royal Society, London, March 1998. \n\n\\bibitem{ruth} B. Novosyadlyj et. al., astro-ph/9912511.\n\n\\bibitem{treview}D. H. Lyth and A. Riotto, Phys. Rept. 314 1 (1999).\n\n\\bibitem{thermal} D. H. Lyth and E. D. Stewart, Phys.Rev. D{\\bf 53} \n1784 (1996).\n\n\\bibitem{gravitino}\n R. Kallosh, L. Kofman, A. \n Linde and A. Van Proeyen,\n \\prd{61}{103503}{2000}; G. F. Giudice, I. Tkachev and A. Riotto,\n\\jhep{9908:009}{99}; D. H. Lyth, \\pl{469B}{69}{1999}\nand hep-ph/9911257.\n\n\\bibitem{latetime} D. H. Lyth, \\pl{476B}{356}{2000} and\n hep-ph/0003120.\n\n\\bibitem{gorski} K. M. Gorski et. al., \\apjl{464}{L11}{1996}.\n\n\\bibitem{st97} E. D. Stewart Phys. Lett. {\\bf 391B}, 34 (1997).\n\n\\bibitem{st97bis} E. D. Stewart Phys. Rev. D{\\bf 56}, 2019 (1997).\n\n\\bibitem{clr98} L. Covi, D. H. Lyth and L. Roszkowski \nPhys. Rev. D{\\bf 60}, 023509 (1999).\n\n\\bibitem{cl98} L. Covi and D. H. Lyth Phys. Rev. D{\\bf 59}, 063515\n(1999).\n\n\\bibitem{c98} L. Covi Phys. Rev. D{\\bf 60}, 023513 (1999).\n\n\\bibitem{rs} G. German, G. Ross and S. Sarkar,\n\\pl{B469}{46}{1999}.\n\n\\bibitem{large} See for instance D. H. Lyth, \\pl{B466}{85}{1999}\n\n\\bibitem{lgl}\nS. M. Leach, I. J. Grivell and A. R. Liddle,\nastro-ph/0004296.\n\n\\bibitem{boomfit} A. E. Lange {\\it at al.}, astro-ph/0005004. \n\n\\bibitem{maximafit} A. Balbi {\\it et al.}, astro-ph/0005124.\n\n\\bibitem{ewan00} E. D. Stewart and J. D. Cohn, astro-ph/0002214. \n"
}
] |
astro-ph0002398
|
OH Zeeman Magnetic Field Detections Toward Five Supernova Remnants Using the VLA
|
[
{
"author": "C. L. Brogan\\altaffilmark{1}"
},
{
"author": "D. A. Frail\\altaffilmark{2}"
},
{
"author": "W. M. Goss\\altaffilmark{2}"
},
{
"author": "and T. H. Troland\\altaffilmark{1}"
}
] |
We have observed the OH (1720 MHz) line in five galactic SNRs with the VLA to measure their magnetic field strengths using the Zeeman effect. We detected all 12 of the bright ($S_{\nu} > 200$ mJy) OH (1720 MHz) masers previously detected by \markcite{Fra96}Frail et al. (1996) and \markcite{Gre}Green et al. (1997) and measured significant magnetic fields (i.e. $ > 3\sigma$) in ten of them. Assuming that the ``thermal'' Zeeman equation can be used to estimate $\mid\vec{B}\mid$ for OH masers, our estimated fields range from 0.2 to 2 mG. These magnetic field strengths are consistent with the hypothesis that ambient molecular cloud magnetic fields are compressed via the SNR shock to the observed values. Magnetic fields of this magnitude exert a considerable influence on the properties of the cloud with the magnetic pressures ($10^{-7} - 10^{-9}$ erg \cc\/) exceeding the pressure in the ISM or even the thermal pressure of the hot gas interior to the remnant. This study brings the number of galactic SNRs with OH (1720 MHz) Zeeman detections to ten.
|
[
{
"name": "ms1720.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n%\\documentstyle[12pt,aaspp4]{article}\n\\documentstyle[12pt,aas2pp4]{article}\n\n\\begin{document}\n\\lefthead{Brogan et al.}\n\\righthead{Magnetic Fields Toward Five SNR}\n\n\\small\n% LaTeX definitions.\n\\newcommand\\HII{H\\,{\\sc ii}}\n\\newcommand\\HI{H\\,{\\sc i}}\n\\newcommand\\OI{[O\\,{\\sc i}] 63 $\\mu$m}\n\\newcommand\\CII{[C\\,{\\sc ii}] 158 $\\mu$m}\n\\newcommand\\CI{[C\\,{\\sc i}] 370 $\\mu$m} \n\\newcommand\\SiII{[Si\\,{\\sc ii}] 35 $\\mu$m}\n\\newcommand\\Hi{H110$\\alpha$}\n\\newcommand\\He{He110$\\alpha$}\n\\newcommand\\Ca{C110$\\alpha$}\n\\newcommand\\kms{km~s$^{-1}$}\n\\newcommand\\cmt{cm$^{-2}$}\n\\newcommand\\cc{cm$^{-3}$}\n\\newcommand\\CeO{C$^{18}$O}\n\\newcommand\\tCO{$^{12}$CO}\n\\newcommand\\thCO{$^{13}$CO}\n\\newcommand\\Blos{$B_{los}$}\n\\newcommand\\Bth{$B_{\\theta}$}\n\\newcommand\\Bm{$B_{m}$}\n\\newcommand\\Bvm{$\\mid\\vec{B}\\mid$}\n\\newcommand\\BS{$B_S$}\n\\newcommand\\Bscrit{$B_{S,crit}$}\n\\newcommand\\Bw{$B_W$}\n\\newcommand\\mum{$\\mu$m}\n\\newcommand\\muG{$\\mu$G}\n\\newcommand\\thi{$\\tau_{HI}$}\n\\newcommand\\toh{$\\tau_{OH67}$}\n\\newcommand\\tmin{$\\tau_{min}$}\n\\newcommand\\tmax{$\\tau_{max}$}\n\\newcommand\\dv{$\\Delta v_{FWHM}$}\n\\newcommand\\va{$v_A$}\n\\newcommand\\Np{$N_p$}\n\\newcommand\\np{$n_p$}\n\\newcommand\\gtsim{\\raisebox{-.5ex}{$\\;\\stackrel{>}{\\sim}\\;$}}\n\\newcommand\\We{${\\cal W}$}\n\\newcommand\\Ms{${\\cal M}_S$}\n\\newcommand\\Mw{${\\cal M}_w$}\n\\newcommand\\Te{${\\cal T}$}\n\\newcommand\\Ps{${\\cal P}_s$}\n\\newcommand\\Ra{${\\cal R}$}\n\\newcommand\\Da{${\\cal D}$}\n\\newcommand\\xb{$x_b$}\n\\newcommand\\xbt{$x_b^2$}\n\n\\title{OH Zeeman Magnetic Field Detections Toward Five Supernova Remnants Using the VLA}\n\n\\author{C. L. Brogan\\altaffilmark{1}, D. A. Frail\\altaffilmark{2}, W. M. Goss\\altaffilmark{2},\nand T. H. Troland\\altaffilmark{1}}\n\\altaffiltext{1}{University of Kentucky, Department of Physics \\& Astronomy, \nLexington, KY 40506-0055}\n\\altaffiltext{2}{National Radio Astronomy Observatory, P. O. Box O, 1003 Lopezville Road, Socorro, \nNM 87801}\n\n\\authoremail{brogan@pa.uky.edu} \n\n\\begin{abstract}\n\\small\n\nWe have observed the OH (1720 MHz) line in five galactic SNRs with the VLA to measure their\nmagnetic field strengths using the Zeeman effect. We detected all 12 of the bright ($S_{\\nu} >\n200$ mJy) OH (1720 MHz) masers previously detected by \\markcite{Fra96}Frail et al. (1996) and\n\\markcite{Gre}Green et al. (1997) and measured significant magnetic fields (i.e. $ >\n3\\sigma$) in ten of them. Assuming that the ``thermal'' Zeeman equation can be used to\nestimate $\\mid\\vec{B}\\mid$ for OH masers, our estimated fields range from 0.2 to 2 mG. These\nmagnetic field strengths are consistent with the hypothesis that ambient molecular cloud\nmagnetic fields are compressed via the SNR shock to the observed values. Magnetic fields of\nthis magnitude exert a considerable influence on the properties of the cloud with the magnetic\npressures ($10^{-7} - 10^{-9}$ erg \\cc\\/) exceeding the pressure in the ISM or even the thermal\npressure of the hot gas interior to the remnant. This study brings the number of galactic SNRs\nwith OH (1720 MHz) Zeeman detections to ten.\n\n\n\\end{abstract}\n\n\\keywords\\small{ISM:clouds --- ISM:individual (W51, G349.7+0.2, CTB37A, CTB33, G357.7$-$0.1) ---\nISM:magnetic fields --- masers --- polarization --- radio lines:ISM}\n\\topmargin -0.5in\n\\textheight9.0in\n\n\\section{INTRODUCTION}\n\nMagnetic fields can moderate the impact that a shock has on a molecular cloud. In the absence\nof a field, a supernova blast wave will heat, compress and fragment the cloud and may\nultimately destroy it (\\markcite{Kle}Klein, McKee \\& Colella 1994). The inclusion of a field\nmitigates these effects, limiting compression and stabilizing it against fragmentation,\nallowing the cloud to survive, perhaps to trigger a future generation of star formation\n(\\markcite{Mie}Miesch \\& Zweibel 1994; \\markcite{MacL}MacLow et al. 1994).\n\nIt has long been known that supernova remnants (SNRs) possess magnetic fields. Observations of\nsynchrotron radiation have established that the {\\it direction} of the magnetic field in young\nSNRs like Cas A is predominately parallel to the shock normal (i.e. radial), whereas for older\nremnants the fields are perpendicular (e.g. \\markcite{Dic}Dickel et al. 1991;\n\\markcite{Mil}Milne 1990). The latter geometry likely originates from the compression of the\nambient interstellar field, while Rayleigh-Taylor instabilities are invoked to explain the\nradial fields in young SNRs (\\markcite{Jun}Jun \\& Norman 1996). Until recently, estimates of\nthe {\\it strength} of the magnetic fields in SNRs had to rely on the somewhat dubious\nequipartition approximation. This situation has changed with the re-discovery of shock-excited\nOH (1720 MHz) maser emission in SNRs (\\markcite{Fra94}Frail, Goss \\& Slysh 1994).\n\nIn a series of recent papers, the satellite line of the OH molecule at 1720.53 MHz has been\nused as a powerful probe of SNR-molecular cloud interactions. OH (1720 MHz) masers are found\nin $\\sim $20 SNRs, or 10\\% of the known SNRs in our Galaxy (see \\markcite{Kor}Koralesky et al.\n1998 and references therein). This maser line is inverted through collisions with H$_2$\n($n\\sim$~few$\\times{10}^4$ cm$^{-3}$ and T$\\sim $80 K) behind C-type shocks propagating into\nmolecular clouds (\\markcite{Rea99}Reach \\& Rho 1999, \\markcite{Fra98}Frail \\& Mitchell 1998).\nThe geometry of the shock is well constrained since strong maser amplification can only occur\nwhen the shock front is viewed edge on (\\markcite{Cla97}Claussen et al. 1997). These\nobservational statements are well-supported by theoretical modeling of the OH (1720 MHz)\nexcitation (\\markcite{Loc}Lockett, Gauthier \\& Elitzur 1998; \\markcite{War99}Wardle,\nYusef-Zadeh, \\& Geballe 1999; \\markcite{Wardle}Wardle 1999).\n\nOne advantage of observing the OH (1720 MHz) maser line is that it allows for a measurement of\nthe strength of the magnetic field via Zeeman splitting (e.g. \\markcite{Tro}Troland \\& Heiles\n1982). In this case, when the observed splitting is small compared to the line width, V $=\nZC$\\Bvm\\/\\thinspace{dI/d$\\nu$}, where \\Bvm\\/ is the the total magnetic field strength, Z is the\nZeeman splitting coefficient, and $C$ is a constant which depends on the angle between the line\nof sight and $\\vec{B}$ (the possible forms of $C$ will be discussed in \\S 4.1). For now we\nwill denote the combination of $C$\\Bvm\\/ as \\Bth\\/.\n\nThis method has already been used to successfully measure the magnetic field strength in the\npost-shock gas behind five SNRs (Sgr A East, W44, W28, G32.8$-0.1$, and G346.6$-$0.2), yielding\nvalues for \\Bth\\/ between 0.1 to 4 mG (\\markcite{Yus96}Yusef-Zadeh et al. 1996,\n\\markcite{Cla97}Claussen et al. 1997, \\markcite{Kor}Koralesky et al. 1998). With these\npromising results in mind, we have performed 1720 MHz Zeeman studies toward five more of the 17 SNRs\nfound in surveys by \\markcite{Fra96}Frail et al. (1996) and \\markcite{Gre}Green et al. (1997)\nto contain OH (1720 MHz) masers using the NRAO\\footnote{The National Radio Astronomy\nObservatory is a facility of the National Science Foundation operated under a cooperative\nagreement by Associated Universities, Inc.} VLA. Only SNRs with bright masers (I$>$200 mJy)\nand no previous high resolution Stokes V observations were chosen.\n\n\n\n\\section{OBSERVATIONS} \n\n\\placetable{tab1}\n\n\n\n\\begin{deluxetable}{lcccccrc}\n\\tablewidth{40pc}\n\\tablecaption{\\footnotesize Observational Parameters with the VLA}\n\\tablehead{\n\\colhead{SNR} & \\colhead{R. A.$~^a$} & \\colhead{Decl.$~^a$} & \\colhead{$V_{lsr}$} & \n\\colhead{$t_{source}$} & \\colhead{Beam} & \\colhead{P. A.} & \\colhead{$\\sigma_{rms}~^b$} \\\\\n\\colhead{} & \\colhead{(B1950)} & \\colhead{(B1950)} & \n\\colhead{(km s$^{-1}$)} & \\colhead{(hours)} & \\colhead{($\\arcsec$ x $\\arcsec$)} & \n\\colhead{($\\arcdeg$)} & \\colhead{(mJy)} } \n\\footnotesize\\startdata\nW51C (2IF) & 19 20 35.0 & +14 09 00.0 & +64.0 & 3.3 & 1.4 x 1.2 & $-$40 & 6.6 \\\\\n~~~~~~~~~~(PA)$^c$ & 19 20 35.0 & +14 09 00.0 & +70.0 & 1.6 & 1.6 x 1.3 & +55 & 6.5 \\\\\nG349.7+0.2 & 17 14 36.0 & $-$37 22 00.0 & +16.0 & 2.6 & 3.4 x 1.3 & +08 & 7.2 \\\\\nCTB37A (I)& 17 11 00.0 & $-$38 30 00.0 & $-$64.0 & 4.9 & 3.9 x 1.2 & $-$14 & 5.4 \\\\\n~~~~~~~~~~~(II) & 17 11 00.0 & $-$38 30 00.0 & $-$22.0 & 4.0 & 4.2 x 2.3 & +23 & 5.5 \\\\\nCTB33 & 16 32 14.0 & $-$47 31 00.0 & $-$70.0 & 2.1 & 8.0 x 1.1 & +67 & 10.2 \\\\\nG357.7$-$0.1 & 17 36 56.0& $-$30 56 00.0 & $-$12.0 & 5.1 & 3.0 x 1.2 & +18 & 5.2\\enddata \n\\tablenotetext{a} {Units of right ascension are hours, minutes, and seconds, and \nunits of declination are degrees, arcminutes, and arcseconds.} \n\\tablenotetext{b} {rms noise in an individual channel.}\n\\tablenotetext{c} {W51C (PA) data have a velocity resolution of 0.56 \\kms\\/ while all other data have \nvelocity resolution of 0.27 \\kms\\/.}\n\\label{tab1}\n\\end{deluxetable}\n\nWe observed five SNRs (W51, G349.7+0.2, CTB37A, CTB33, and G357.7$-$0.1) at 1720 MHz with the\nVLA in A configuration. The key observing parameters for each SNR are given in Table 1. All\nof the SNRs were observed in ``2IF mode'' (recording both right (RCP) and left (LCP) circular\npolarization) with a 0.1953 MHz (34.0 \\kms\\/) bandwidth divided into 127 channels. Due to this\nnarrow bandwidth, CTB37A had to be observed with two different center frequencies (-22 \\kms\\/\nand -64 \\kms\\/) in order to obtain data for its two different OH (1720 MHz) maser populations.\nThe observations were conducted on June 22, July 6, 8, 12, 15, September 13, and October 24,\n1999. The OH data were Hanning smoothed online, and the resulting velocity resolution is 0.27\n\\kms\\/. We observed both senses of circular polarization simultaneously and since Zeeman\nobservations are very sensitive to small variations in the bandpass, a front-end transfer\nswitch was used to periodically switch the sense of circular polarization passing through each\ntelescope's IF system.\n\nThe AIPS (Astronomical Image Processing System) package of the NRAO was used for the\ncalibration, imaging, and cleaning of the OH (1720 MHz) data sets. The RCP and LCP data were\ncalibrated separately and later combined during the imaging process to make Stokes I$=$(RCP +\nLCP)/2 and Stokes V$=$(RCP $-$ LCP)/2 data sets. Bandpass correction was applied only to the I\ndata sets since bandpass effects cancel to first order in the V data. Line data sets were\ncreated by estimating and removing the continuum emission in the UV plane using the AIPS task\nUVLSF. The strongest maser channel in each line data set was then self-calibrated and the\nsolutions were applied to each channel. Subsequent magnetic field estimates were performed\nusing the MIRIAD (Multichannel Image Reconstruction Image Analysis and Display) processing\npackage from BIMA. The rms noise per spectral channel obtained for each SNR is summarized in\nTable 1.\n\n\n\n\\begin{deluxetable}{lcccrccc}\n\\tablewidth{40pc}\n\\tablecaption{\\footnotesize Fitted Parameters of OH (1720 MHz)\nMasers}\n\\tablehead{\n\\colhead{SNR} & \\colhead{Feature} & \\colhead{R. A.$~^a$} & \\colhead{Decl.$~^a$} & \n\\colhead{$S_{peak}~^b$} & \\colhead{$v_{lsr}~^c$} & \\colhead{$\\Delta v_{FWHM}~^d$} & \n\\colhead{$\\theta_{max}$} \\\\\n\\colhead{} & \\colhead{} & \\colhead{(B1950)} & \\colhead{(B1950)} & \n\\colhead{(mJy)} & \\colhead{(km s$^{-1}$)} & \\colhead{(km s$^{-1}$)} & \n\\colhead{($\\arcsec$)} } \n\\footnotesize \\startdata\nW51C ........& 1 & 19 20 35.9 & +14 09 53.6 & 2710 & +72.0 & 0.9 & 0.7 \\\\\n& 2 & 19 20 36.4 & +14 09 50.3 & 4760 & +69.1 & 1.2 & 0.1 \\\\\nG349.7+0.2 ..& 1 & 17 14 36.0 & $-$37 23 01.9 & 770 & +16.2 & 1.1 & 1.6\\\\\n& 2 & 17 14 36.9 & $-$37 22 52.8 & 1800 & +15.2 & 0.3 & 1.0 \\\\\n& 3 & 17 14 37.5 & $-$37 23 14.7 & 1060 & +16.7 & 0.6 & 0.9 \\\\\nCTB37A ......& 1 & 17 10 51.8 & $-$38 28 51.7 & 410 & $-$66.2 & 0.7 & 0.6 \\\\\n& 2 & 17 10 56.8 & $-$38 28 56.7 & 730 &$-$63.7 & 0.5 & 0.3 \\\\\n& 3 & 17 10 59.3 & $-$38 31 19.2 & 470 &$-$63.5 & 1.5 & 0.2 \\\\\n& 4 & 17 11 01.4 & $-$38 37 32.9 & 220 &$-$65.3 & 1.1 & 0.7 \\\\\n& 5 & 17 11 09.0 & $-$38 25 51.3 & 400 &$-$21.5 & 0.9 & 1.7 \\\\\nCTB33 .......& 1 & 16 32 06.2 & $-$47 29 53.2 & 250 & $-$71.8 & 1.0 & 1.7 \\\\\nG357.7$-$0.1 ..& 1 & 17 36 54.6 & $-$30 56 07.6 & 400 & $-$12.3 & 0.6 & 0.8\\enddata\n\\tablenotetext{a} {Units of right ascension are hours, minutes, and seconds, and \nunits of declination are degrees, arcminutes, and arcseconds.} \n\\tablenotetext{b} {Errors in the peak flux range from 4 to 8 mJy.}\n\\tablenotetext{c} {Errors in $v_{lsr}$ range from 0.02 to 0.002 \\kms\\/.}\n\\tablenotetext{d} {Errors in $\\Delta v_{FWHM}$ range from 0.05 to 0.003 \\kms\\/, and \nthe values shown have been deconvolved from the finite channel width (0.27 \\kms\\/).}\n\\label{tab2}\n\\end{deluxetable}\n\nAfter imaging, each of the bright maser spots was fit with a 2-D Gaussian using the AIPS task\nJMFIT. None of these fits showed convincing evidence that the individual maser spots are\nresolved at the resolutions shown in Table 1; therefore, we regard the maximum sizes reported\nby JMFIT to be upper limits. The positions, peak flux densities, and an upper limit to the\nmaser spot sizes are reported in Table 2. In addition, the Stokes I spectrum at the peak pixel\nof each maser spot was fit with a single Gaussian in the spectral domain using GIPSY, to obtain\neach maser's center velocity ($v$) and linewidth ($\\Delta v_{FWHM}$). These estimates of\n$\\Delta v_{FWHM}$ were then corrected for the finite channel width of the the data (0.27\n\\kms\\/). These deconvolved $\\Delta v_{FWHM}$ and center velocities are also reported in Table\n2. The absolute position errors of these data are $\\sim 0.1\\arcsec$, while the relative\nposition errors (compared to other masers in the field) are $\\sim 0.02\\arcsec$.\n\nIn addition, W51 was observed on August 3, 1999 in ``PA mode'' (recording all Stokes\nparameters) with a 0.1953 MHz bandwidth, and 64 channels. This correlator setup resulted in a\nvelocity resolution of $\\sim 0.54$ \\kms\\/ after Hanning smoothing. The details of this\nobservation can also be found in Table 1. These data were calibrated in the same manner\ndescribed above, with the exception of the polarization calibration. The absolute polarization\ncalibration was carried out by extrapolating 3C48 data from seven previous 20 cm polarimetry\nobservations to yield a position angle of P.A.$=13\\arcdeg$ for this calibrator at 1720 MHz.\nThe error in this estimate ($\\sim 5\\arcdeg$) will also apply to the position angles derived\nfrom these data.\n\n\\placetable{tab2}\n\n\\section{RESULTS}\n\n\\subsection{General Maser Properties}\n\n\n\n\\begin{deluxetable}{lcc}\n\\tablewidth{20pc}\n\\tablecaption{\\footnotesize Magnetic Fields}\n\\tablehead{\n\\colhead{SNR} & \\colhead{Feature} & \\colhead{$B_{\\theta}~^a$} \\\\\n\\colhead{} & \\colhead{} & \\colhead{(mG)} } \n\\footnotesize \\startdata\nW51C ...........& 1 & +1.5 $\\pm$ 0.05 \\\\\n& 2 & +1.9 $\\pm$ 0.10 \\\\\nG349.7+0.2 ...& 1 & complex~$^b$\\\\\n& 2 & $\\lesssim 0.1~^c$ \\\\\n& 3 & $-0.35 ~\\pm$ 0.05\\\\\nCTB37A ........& 1 & $-0.5 ~\\pm$ 0.10\\\\\n& 2 & +0.22 $\\pm$ 0.05\\\\\n& 3 & $-0.60 ~\\pm$ 0.09\\\\\n& 4 & +1.5 $\\pm$ 0.20\\\\\n& 5 & $-0.8 ~\\pm$ 0.10\\\\\nCTB33 .........& 1 & +1.1 $\\pm$ 0.30 \\\\\nG357.7$-$0.1 ....& 1 & +0.7 $\\pm$ 0.12 \\enddata\n\\tablenotetext{a} {These \\Bth\\/ field estimates were calculated using the thermal Zeeman equation\nand may {\\em overestimate} the maser fields according to the maser theory of Elitzur\n(1998). The correction cannot be determined exactly but is probably on the order of $(0.5 -\n0.2)\\times$\\Bth\\/, therefore these values should be viewed as upper limits. See \\S 4.1 for further\ndiscussion.}\n\\tablenotetext{b} {Stokes V profile is complex, probably indicative of blending.}\n\\tablenotetext{c} {Upper limit to \\Bth\\/ based on S/N of data. See also \\S 3.2.2.}\n\\label{tab3}\n\\end{deluxetable}\n\nFrom the five observed SNRs, we detected all 12 bright OH (1720 MHz) masers (S $>$ 200 mJy)\npreviously known from the surveys of \\markcite{Fra96}Frail et al. (1996) and\n\\markcite{Gre}Green et al. (1997). Table 2 summarizes the fitted parameters of these maser\nfeatures. Of these, ten show classical S-shaped Stokes V profiles (e.g.\n\\markcite{Eli98}Elitzur 1998), one shows a complicated Stokes V profile, and one shows no\ndiscernible V signal despite its $\\sim 1800$ mJy peak flux density. The observed masers have\ntypical deconvolved line widths of $\\sim 0.8$ \\kms\\/, spanning the range from 0.3 to 1.5\n\\kms\\/. In addition, none of the observed OH (1720 MHz) masers appear to have undergone\nsignificant changes in flux density or position since the detection experiments were performed\nin 1994. As noted in \\S 2, none of the maser spots have been resolved at the resolutions\nlisted in Table 1. This may be due, in part, to the low declination, and hence elliptical\nsynthesized beam shapes observed for four of the five SNRs. Using the upper limits on the\nmaser spot sizes listed in Table 2, lower limits on the brightness temperatures of these masers\nrange from $4 \\times 10^4$ K to $10^8$ K. \n\nUsing the thermal Zeeman expression (V $=ZC$\\Bvm\\/\\thinspace{$d$I$/d\\nu$}) with $Z=0.6536$ Hz\n\\muG\\/$^{-1}$ for OH at 1720 MHz, the derivative of Stokes I was fitted to Stokes V in a least\nsquare fitting routine as described by \\markcite{Cla97}Claussen et al (1997), to obtain the\ncombination $C$\\Bvm\\/=\\Bth\\/. The validity of the thermal Zeeman formulation for the magnetic field\nin masers along with the $\\theta$ dependence and magnitude of $C$ is discussed in \\S 4.1. Magnetic\nfields were detected toward all five SNR at greater than the 3$\\sigma$ level. The fitted magnetic\nfield strengths (\\Bth\\/), and their associated $1\\sigma$ errors are summarized in Table 3, while\ncomments on individual sources appear in \\S 3.2. The detected \\Bth\\/ fields range from 0.2 to 2 mG.\nUnlike W28 and W44, where the fields were found to be uniform in both magnitude and direction\n(\\markcite{Cla97}Claussen et al. 1997), CTB37A shows a complicated magnetic field morphology. In\nthis source \\Bth\\/ changes by a factor of seven and reverses sign on a length scale of $\\sim 3$ pc.\n\n\\placetable{tab3}\n\n\n\\subsection{Individual Sources}\n\n\\subsubsection{W51}\n\n\\placefigure{figu1}\n\n\n\nW51 is composed of two \\HII\\/ region complexes (W51A and W51B), as well as the SNR W51C and is\nlocated at the tangent point of the Sagittarius arm at $\\ell=49\\arcdeg$ corresponding to a\ndistance of $\\sim 6$ kpc (\\markcite{Koo95}Koo, Kim, \\& Seward 1995). A continuum image of W51\nat 330 MHz from \\markcite{Sub}Subrahmanyan \\& Goss (1995) is shown in Figure 1 with the two W51\nOH (1720 MHz) masers superposed. The spectral index of W51C is difficult to calculate due to\ncontamination from the W51B \\HII\\/ regions, but \\markcite{Sub}Subrahmanyan \\& Goss (1995)\nestimate that $\\alpha = -0.2$ ($S=\\nu^{\\alpha}$).\n\n\\begin{figure}[ht]\n\\epsfxsize=8.5cm \\epsfbox{fig1.eps}\n\\figcaption[Filename]{\\footnotesize W51 VLA 330 MHz continuum image from Subrahmanyan \\& Goss (1995) with\ncontours at (0.02, 0.12, 0.22, 0.32, 0.42, 0.52, 0.62, 0.72, 0.82) $\\times$ 2.46 Jy beam$^{-1}$\n. The resolution of this image is $\\sim 1\\arcmin$. The locations of the two W51C OH (1720\nMHz) masers are indicated by the white (+) symbols\\label{figu1}.}\n\\end{figure}\n\n\\begin{figure}[ht]\n\n\\epsfxsize=9.0cm \\epsfbox{fig2.eps}\n\\figcaption[Filename]{\\footnotesize Fits of \\Bth\\/ for W51 OH (1720 MHz) maser features (1) and (2). The upper\npanels show the VLA Stokes I profiles ({\\em solid histogram}), and the bottom panels show the\nVLA Stokes V profiles ({\\em solid histogram}) with the fitted derivative of Stokes I shown as\nsmooth dotted curves. The value of \\Bth\\/ fit for each position and its calculated error are\ngiven at the top of each plot\\label{figu2}.}\n\\end{figure}\n\nBased on the absorption of X-ray emission from W51C toward W51B, \\markcite{Koo95}Koo et al.\n(1995) suggest that W51C must be located behind W51B. \\markcite{Koo97a}\\markcite{Koo97b}Koo \\&\nMoon (1997a, 1997b) observed high velocity (HV) \\HI\\/, CO(1$-$0), and CO(2$-$1) emission\nbetween $+85$ and $+120$ \\kms\\/ to the east of W51B where it overlaps W51C (see Fig. 1). They\ninterpret this HV gas as arising from a shock interaction between W51C and a molecular cloud\n(located between W51C and W51B, or possibly the backside of the W51B complex itself). They\nshow that the HV \\HI\\/ is located toward the western edge of the centrally bright X-ray\nemitting region of W51C in an arc-shape, while the shocked CO gas is located slightly east of\nthe HV \\HI\\/ emission. The two OH (1720 MHz) masers reported in this work (and\n\\markcite{Gre}Green et al. 1997) are located toward the NE end of the shocked CO/\\HI\\/ arc\nstructure and $\\sim 2\\arcmin$ SW of the \\HII\\/ region G49.2-0.3 (see Fig. 1) at velocities of\n$\\sim 70$ \\kms\\/. From the coincidence of these OH (1720 MHz) masers with the shocked gas and\ntheir angular separation from G49.2$-$0.3 ($\\sim 3.5$ pc for $d=6$ kpc), \\markcite{Gre}Green et\nal. (1997) argue that they are associated with the W51C SNR shock.\n\n\\placefigure{figu2}\n\\placefigure{figu3}\n\n\n\n\n\\begin{figure}[ht]\n\n\\epsfxsize=5.0cm \\epsfbox{fig3.eps}\n\\figcaption[Filename]{\\footnotesize VLA Stokes Q and U linear polarization profiles ({\\em upper panel}) and\nStokes V circular polarization profile ({\\em lower panel}) for W51C OH (1720 MHz) maser feature\n(2). Note that the spectral resolution of these data are only 0.56 \\kms\\/ \nwhile the spectra displayed in Fig. 2 (and all other Figures) have a resolution of 0.27 \\kms\\/\\label{figu3}.}\n\\end{figure}\n\nFits of \\Bth\\/ for the two W51C OH (1720 MHz) masers are shown in Figure 2. The values of\n\\Bth\\/ for these masers are 1.5 and 1.9 mG for features 1 and 2, respectively (see Tables 2 and\n3). The W51C masers were also observed in PA mode, providing images of all four Stokes\nparameters (I, V, Q, U), with 0.54 \\kms\\/ velocity resolution. Toward the strongest W51C OH\nmaser (feature 2), Stokes Q and U signals were detected at 15$\\sigma$ and 17$\\sigma$,\nrespectively. A profile showing Stokes Q and U toward this maser is shown in Figure 3. Using\nStokes Q and U values of Q $= 0.10$ Jy beam$^{-1}$ and U $= -0.11$ Jy beam$^{-1}$, we obtain a\nlinear polarization percentage of 3.5\\% and a P.A. of $-25^{\\circ}$ for the linear polarization \nvector.\n\n\n\\subsubsection{G349.7+0.2}\n\n\\placefigure{figu4}\n\n\\begin{figure}[ht] \n\\epsfxsize=8.5cm \\epsfbox{fig4.xv.ps}\n\\figcaption[Filename]{\\footnotesize G349.7+0.2 20 cm VLA continuum image with contours at (0.05, 0.15, 0.25,\n0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95) $\\times$ 63 mJy beam$^{-1}$. This image is composed\nof archival VLA data from A, B, C, and D configurations. The resolution is $5\\arcsec \\times\n2\\arcsec$ (P.A. = 0.6\\arcdeg) and the peak flux density is 63 mJy beam$^{-1}$ with an rms\nnoise of $\\sim 1$ mJy beam$^{-1}$. The locations of the three G349.7+0.2 OH (1720 MHz) masers\nwith $S_{\\nu}> 200$ mJy are indicated by the black (+) symbols\\label{figu4}.} \n\\end{figure}\n\n\n\\begin{figure}[ht]\n\n\\epsfxsize=5.0cm \\epsfbox{fig5.eps} \n\\figcaption[Filename]{\\footnotesize Fit of \\Bth\\/ for G349.7+0.2 OH (1720 MHz) maser feature (3). The\nupper panels show the VLA Stokes I profiles ({\\em solid histogram}), and the bottom panels show the\nVLA Stokes V profiles ({\\em solid histogram}) with the fitted derivative of Stokes I shown as smooth\ndotted curves. The value of \\Bth\\/ fit for each position and its calculated error are given at the\ntop of each plot\\label{figu5}.}\n\\end{figure}\n\nG349.7+0.2 is one of the most luminous SNR's in the galaxy (after Cas A and the Crab;\n\\markcite{Shaa}Shaver et al. 1985a), if it is located at a distance of $\\sim 22$ kpc\n(\\markcite{Fra96}Frail et al. 1996). The spectral index of G349.7+0.2 was estimated by\n\\markcite{Shaa}Shaver et al. (1985a) to be $\\sim -0.5$, typical of shell type remnants. This\nSNR contains three bright maser features along with several weaker features within $\\sim\n1\\arcmin$ (6 pc) near the center of the remnant. The positions of the brightest masers are\nshown on a continuum image of G349.7+0.2 in Figure 4. This continuum image is a compilation of\n18 and 20 cm data from the VLA archive, and contains data from all four configurations (A, B,\nC, and D). It is the most sensitive and highest resolution continuum image of this SNR to\ndate, with a resolution of $5\\arcsec \\times 2\\arcsec$ (P.A.$=0.6\\arcdeg$) and rms noise of\n$\\sim 1$ mJy beam$^{-1}$.\n\n\\placefigure{figu5}\n\nOnly G349.7+0.2 OH(3) (OH maser feature 3) has a significant magnetic field detection with \\Bth\\/$ =\n0.35$ mG. The \\Bth\\/ fit for this feature is shown in Figure 5. Maser features 1 and 2 are the\nonly bright (S $>$ 200 mJy) OH (1720 MHz) masers in our sample for which we were unable to detect a\nsignificant \\Bth\\/. G349.7+0.2 OH(1) exhibits a complicated Stokes V spectrum that is indicative of\nblending. Therefore, it is possible that improved velocity and/or angular resolution would lead to\na \\Bth\\/ detection for this maser. G349.7+0.2 OH(2) shows no hint of any Stokes V signal despite\nits 1800 mJy flux density. The S/N of these data alone suggest that \\Bth\\/$ < 0.1$ mG, however,\nthis maser is also the narrowest maser in our sample ($\\Delta v_{FWHM}=0.3$ \\kms\\/). Therefore, it\nis possible that if the Stokes V was not resolved in velocity, \\Bth\\/ for \nG349.7+0.2 OH(2) could be $\\sim 0.3$ mG.\n\n\n\\subsubsection{CTB37A}\n\nCTB37A, also known as G348.5+0.1, is estimated to lie at a distance of $\\sim 11$ kpc\n(\\markcite{Fra96}Frail et al. 1996). \\markcite{Kas}Kassim, Baum, \\& Weiler (1991) estimate\nits spectral index to be $\\sim -0.5$ based on flux density measurements ranging from 80 MHz to\n14.7 GHz. A 21 cm continuum map of CTB37A from \\markcite{Kas}Kassim et al. (1991) is\ndisplayed in Figure 6 with the OH (1720 MHz) masers superposed. CTB37A contains two\nkinematically distinct sets of OH (1720 MHz) masers. One group at $\\sim -22$ \\kms\\/ is located\ntoward the north end of CTB37A, while the others have velocities of $\\sim -65$ \\kms\\/ and are\nlocated near the center and southern parts of the source. \\markcite{Kas}Kassim et al. (1991)\npropose that the extension of continuum emission seen to the east of CTB37A (see Fig. 6) is a\nseparate SNR which they name G348.5$-$0.0. It was further proposed by \\markcite{Fra96}Frail et\nal. (1996) that the $\\sim -22$ \\kms\\/ masers originate from this second SNR.\n\n\\placefigure{figu6}\n\\begin{figure}[t]\n\\epsfxsize=8.5cm \\epsfbox{fig6.eps }\n\\figcaption[Filename]{\\footnotesize CTB37A 20 cm VLA continuum image from Kassim et al. (1991) with contours\nat (0.01, 0.12, 0.23, 0.34, 0.45, 0.56, 0.66, 0.76 0.87) $\\times$ 0.427 Jy beam$^{-1}$. The\nbeam is $33\\arcsec \\times 18\\arcsec$ (P.A.$=5\\arcdeg$). The (+) symbols mark the locations of\nthe $\\sim -65$ \\kms\\/ OH (1720 MHz) maser features, while the locations of the $\\sim -22$\n\\kms\\/ OH (1720 MHz) maser features are marked with ($\\times$) symbols\\label{figu6}.}\n\\end{figure}\n\nCTB37A, also known as G348.5+0.1, is estimated to lie at a distance of $\\sim 11$ kpc\n(\\markcite{Fra96}Frail et al. 1996). \\markcite{Kas}Kassim, Baum, \\& Weiler (1991) estimate\nits spectral index to be $\\sim -0.5$ based on flux density measurements ranging from 80 MHz to\n14.7 GHz. A 21 cm continuum map of CTB37A from \\markcite{Kas}Kassim et al. (1991) is\ndisplayed in Figure 6 with the OH (1720 MHz) masers superposed. CTB37A contains two\nkinematically distinct sets of OH (1720 MHz) masers. One group at $\\sim -22$ \\kms\\/ is located\ntoward the north end of CTB37A, while the others have velocities of $\\sim -65$ \\kms\\/ and are\nlocated near the center and southern parts of the source. \\markcite{Kas}Kassim et al. (1991)\npropose that the extension of continuum emission seen to the east of CTB37A (see Fig. 6) is a\nseparate SNR which they name G348.5$-$0.0. It was further proposed by \\markcite{Fra96}Frail et\nal. (1996) that the $\\sim -22$ \\kms\\/ masers originate from this second SNR.\n\n\n\n\\begin{figure}[ht]\n\\epsfxsize=8.5cm \\epsfbox{fig7I.eps}\n\\figcaption[Filename]{\\footnotesize Fits of \\Bth\\/ for CTB37A OH (1720 MHz) maser features (1 - 5). Note that\nfeatures (1-4) correspond to the $\\sim -65$ \\kms\\/ masers, while feature (5) is the single strong $\\sim\n-22$ \\kms\\/ maser. The upper panels show the VLA Stokes I profiles ({\\em solid histogram}), and the\nbottom panels show the VLA Stokes V profiles ({\\em solid histogram}) with the fitted derivative of\nStokes I shown as smooth dotted curves. The value of \\Bth\\/ fit for each position and its\ncalculated error are given at the top of each plot\\label{figu7}.}\n\\end{figure}\n\n%\\clearpage\n\n\\addtocounter{figure}{-1}\n\\begin{figure}[ht]\n\n\\epsfxsize=4.5cm \\epsfbox{fig7e.eps}\n\\figcaption[Filename]{\\footnotesize Continued...}\n\\end{figure}\n\nAs noted at the beginning of this section, the \\Bth\\/ of the $\\sim -65$ \\kms\\/ OH (1720 MHz)\nmasers have the unusual property that they change direction along the line of site over length\nscales as small as $1\\arcmin$ ($\\sim 3$ pc). In addition, the magnitude of \\Bth\\/ changes by a\nfactor of seven between CTB37A OH(2) and CTB37A OH(4) from $\\sim 0.2$ mG to $\\sim 1.5$ mG.\nFits of \\Bth\\/ for these four $\\sim -65$ \\kms\\/ masers are shown in Figure 7. The only strong\n$\\sim -22$ \\kms\\/ OH maser has \\Bth\\/$= -0.8$ mG and the fit for this maser feature (CTB37A\nOH(5)) is also shown in Fig. 7.\n\nReynoso \\& Mangum (1999, in prep.) have detected CO(1-0) emission toward CTB37A with $\\sim\n1\\arcmin$ resolution using the Kitt Peak 12m telescope. Their maps show two distinct CO\nclouds, one at $\\sim -22$ \\kms\\/ in the northern part of CTB37A, and another at $\\sim -65$\n\\kms\\/ which is concentrated to the northwest and middle of the source. Both CO clouds are\ncoincident spatially and in velocity with our two groups of OH (1720 MHz) masers.\n\n\\placefigure{figu7}\n\nAs noted at the beginning of this section, the \\Bth\\/ of the $\\sim -65$ \\kms\\/ OH (1720 MHz)\nmasers have the unusual property that they change direction along the line of site over length\nscales as small as $1\\arcmin$ ($\\sim 3$ pc). In addition, the magnitude of \\Bth\\/ changes by a\nfactor of seven between CTB37A OH(2) and CTB37A OH(4) from $\\sim 0.2$ mG to $\\sim 1.5$ mG.\nFits of \\Bth\\/ for these four $\\sim -65$ \\kms\\/ masers are shown in Figure 7. The only strong\n$\\sim -22$ \\kms\\/ OH maser has \\Bth\\/$= -0.8$ mG and the fit for this maser feature (CTB37A\nOH(5)) is also shown in Fig. 7.\n\nReynoso \\& Mangum (1999, in prep.) have detected CO(1-0) emission toward CTB37A with $\\sim\n1\\arcmin$ resolution using the Kitt Peak 12m telescope. Their maps show two distinct CO\nclouds, one at $\\sim -22$ \\kms\\/ in the northern part of CTB37A, and another at $\\sim -65$\n\\kms\\/ which is concentrated to the northwest and middle of the source. Both CO clouds are\ncoincident spatially and in velocity with our two groups of OH (1720 MHz) masers.\n\n\\subsubsection{CTB33}\n\n\\placefigure{figu8}\n\n\nThe SNR in CTB33 is also known as G337.0$-$0.1, and was estimated to lie at a distance of $\\sim 11$\nkpc by \\markcite{Sarma}Sarma et al. (1997) using \\HI\\/ absorption data from the ATCA (Australia\nTelescope Compact Array). These authors also find that CTB33 has a spectral index of $\\sim -0.6$,\ntypical of shell type SNRs. The locations of the two bright OH (1720 MHz) masers from\n\\markcite{Fra96}Frail et al. (1996) are shown on Figure 8 superposed on a 1380 MHz CTB33 continuum\nimage (\\markcite{Sarma}Sarma et al. 1997). However, \\markcite{Sarma}Sarma et al. (1997) present\nevidence that the southern most CTB33 maser is probably associated with the \\HII\\/ region\nG336.9$-$0.2. Our OH (1720 MHz) results are consistent with this suggestion since this maser\nfeature has been resolved into at least four different velocity components, each of which show\ncomplicated Stokes V spectra typical of \\HII\\/ region masers (i.e. no ``S'' shaped Zeeman pattern;\nsee \\markcite{Eli98}Elitzur 1998). For this reason only the centrally located CTB33 maser (CTB33\nOH(1)) has been included in Tables 2 and 3. The \\Bth\\/ detected for this maser is 1.1 mG, but the\nrange of channels over which the fit was performed had to be limited to obtain a reasonable fit (see\nFig. 9). Therefore, this detection should be considered tentative. Such a suppression of part of\nthe Stokes V signal may be the result of blending of the maser line in velocity space since this\nmaser is fairly wide (\\dv\\/$\\sim 1$ \\kms\\/, also see \\markcite{Rob}Roberts et al. 1993), but could also\nsimply be a result of poor S/N.\n\n\\begin{figure}[ht]\n\\epsfxsize=8.5cm \\epsfbox{fig8.eps}\n\\figcaption[Filename]{\\footnotesize CTB33 1375 MHz ATCA continuum image from Sarma et al. (1997) with\ncontours at (0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) $\\times$ 0.090 Jy beam$^{-1}$. The resolution\nof this image is $\\sim 12\\arcsec$. The locations of the two CTB33 OH (1720 MHz) masers with\n$S_{\\nu}> 200$ mJy are indicated by the black (+) symbols\\label{figu8}.}\n\\end{figure}\n\n\\begin{figure}[ht]\n\n\\epsfxsize=5.0cm \\epsfbox{fig9.eps}\n\\figcaption[Filename]{\\footnotesize Fit of \\Bth\\/ for CTB33 OH (1720 MHz) maser feature (1). The upper panels\nshow the VLA Stokes I profiles ({\\em solid histogram}), and the bottom panels show the VLA Stokes V\nprofiles ({\\em solid histogram}) with the fitted derivative of Stokes I shown as smooth dotted\ncurves. The value of \\Bth\\/ fit for each position and its calculated error are given at the top of\neach plot. The solid portion of the Stokes I histogram ({\\em upper panel}) shows the velocity\nrange used in the fit\\label{figu9}.}\n\\end{figure}\n\n\\placefigure{figu9}\n\n\\markcite{Cor}Corbel et al. (1999) have detected a number of molecular clouds toward CTB33 in\nCO($J=1-0$) and CO($J=2-1$) emission using the SEST telescope. In particular, they find a\ngiant molecular cloud at a velocity of $\\sim -71$ \\kms\\/ ($\\Delta v=11$ \\kms\\/) with an\napproximate size of 67 pc and a mass of $4\\times 10^6$ M$_{\\sun}$. The velocity of this\nmolecular cloud is in excellent agreement with the velocity of CTB33 OH(1) ($-71.8$ \\kms\\/) and\nmay well be the origin of the SNR/molecular cloud interaction needed to pump the maser (see \\S\n1 \\& \\S 4.2). These authors also suggest that the SNR must lie on the near-side of the $\\sim\n-71$ \\kms\\/ GMC based on comparison of their CO data (and its implied extinction) with the\nX-ray data from \\markcite{Woo}Woods et al. (1999).\n\n\\placefigure{figu10}\n\\begin{figure}[ht]\n\\epsfxsize=8.5cm \\epsfbox{fig10.eps}\n\\figcaption[Filename]{\\footnotesize Similar to Figure 8, but in J2000 coordinates with contours at (0.4, 0.6,\n0.8) $\\times$ 0.090 Jy beam$^{-1}$. The IPN and BeppoSAX error boxes are superposed showing\nthe location of SGR1627$-$41\\label{figu10}.}\n\\end{figure}\n\nThe CTB33 SNR is coincident with the site of a recently discovered Soft Gamma ray Repeater\n(SGR1627$-$41; see \\markcite{Hur}Hurley et al. 1999). The location of the SGR has been\nconstrained by the 3rd Interplanetary Network (IPN: {\\em Ulysses}, KONUS-WIND and BATSE) along\nwith the detection of a presumably related BeppoSAX X-ray source to lie within the error boxes\nshown in Figure 10 on a simplified contour image of CTB33 (\\markcite{Sarma}Sarma et al. 1997;\n\\markcite{Hur}Hurley et al. 1999; \\markcite{Woo}Woods et al. 1999). Current theories for the\nnature of SGR's suggest that they arise from strongly magnetized neutron stars or `magnetars',\nand that the outbursts are the result of crustquakes on the surface of the neutron star\n(\\markcite{Tho}Thompson \\& Duncan 1995). The discovery of SGR1627$-$41, marks only the fourth\nsuch source to be detected.\n\nAll of the previously known SGRs have been associated with young SNRs (although SGR1900+14 lies\nclose to, but not inside its associated SNR; see \\markcite{Hur}Hurley et al. 1999 and\nreferences therein). For this reason, despite the inexact correspondence between the\nIPN/BeppoSAX error boxes and the extent of CTB33 ($95\\arcsec$) proposed by\n\\markcite{Sarma}Sarma et al. (1997), SGR1627$-$41 has been assumed to be the progenitor of\nCTB33. For this reason, a number of authors (\\markcite{Hur}Hurley et al. 1999;\n\\markcite{Cor}Corbel et al. 1999) have estimated that SGR1627$-$41 must have a transverse\nvelocity of more than $\\sim 1,000$ \\kms\\/ if CTB33's age is $\\lesssim 5,000$ years. Although\nthese velocities are not unreasonable (\\markcite{Lyn}Lyne \\& Lorimer 1994), the location of the\nmaser CTB33 OH(1) suggests that CTB33 actually extends farther west as shown in Figure 10, and\nhas a `blowout' morphology toward the NE and SW. Such a morphology would not be unexpected in\na region populated by \\HII\\/ regions that could have effectively cleared such cavities (see\n\\markcite{Jon}Jones et al. 1998). Therefore, an increase in the estimated size of CTB33 would\nplace the IPN/BeppoSAX error boxes and the OH (1720 MHz) maser much closer to the center of\nCTB33, rather than at its outskirts, with a substantial reduction in the estimate for the\ntransverse velocity of SGR1627$-$41. Future molecular, or high resolution, low-frequency\ncontinuum data toward CTB33 may help resolve this issue.\n\n\n\n\\subsubsection{G357.7$-$0.1 (Tornado)}\n\n\\placefigure{figu11}\n\nG357.7$-$0.1 is an unusual SNR candidate located near the galactic center with a non-thermal\nspectral index in the range $-0.5 < \\alpha < -1.0$ (\\markcite{Ste}Stewart et al. 1994). It\nhas been variously considered to be everything from an extragalactic head-tail or double lobed\nsource (\\markcite{Wei}Weiler \\& Panagia 1980; \\markcite{Cas}Caswell et al. 1989) to a new\nclass of galactic head-tail object (\\markcite{Bec}Becker \\& Helfand 1985; \\markcite{Hel}Helfand\n\\& Becker 1985; see also \\markcite{Gra}Gray 1994). Another intriguing suggestion is that\nG357.7$-$0.1 is powered by an object ejected from the nearby SNR (G359.0-0.9) which lies only\n$1\\arcmin$ from the symmetry axis of G357.7$-$0.1. This scenario, however, would require such\na `runaway' pulsar or X-ray binary to have a transverse velocity $\\ga 2,000$ \\kms\\/ which is\nconsidered unlikely (\\markcite{Gra}Gray 1994). The discovery of a OH (1720 MHz) maser\ncoincident with G357.7$-$0.1 has renewed speculation that it is, in fact, a galactic SNR\n(\\markcite{Fra96}Frail et al. 1996).\n\n\n\nThe odd morphology of G357.7$-$0.1 has earned it the name `Tornado'. The reason for this\nmoniker can be seen in the greyscale continuum images of G357.7$-$0.1 shown in Figure 11 (see\nalso, \\markcite{Shaa}Shaver et al. 1985a; \\markcite{Bec}Becker \\& Helfand 1985). Figure 11a\nwas created from archival VLA data at $\\sim 6$ cm from both C and D configuration data. The\nresulting image has a resolution of $13.4\\arcsec \\times 6.7\\arcsec$ (P.A. = 23.8\\arcdeg) and\nan rms of $\\sim 0.6$ mJy beam$^{-1}$. The data used to create the image in Figure 11b were\ncompiled from 18 cm and 20 cm VLA archive data from all four VLA configurations. The resulting\nimage is one of the most sensitive and highest resolution images of this source to date with an\nrms of $\\sim 1.5$ mJy beam$^{-1}$ and resolution of $11\\arcsec.6 \\times 8\\arcsec.1$ (P.A. =\n26.2\\arcdeg; see also \\markcite{Shaa}Shaver et al. 1985a; \\markcite{Bec}Becker \\& Helfand\n1985; \\markcite{Yus99b}Yusef-Zadeh 1999b). Comparison of the peak flux densities in Figs. 11a\n($S_{6{\\rm cm}}=$77 mJy beam$^{-1}$) and 11b ($S_{20{\\rm cm}}=$145 mJy beam$^{-1}$) confirms\nthat the spectral index of G357.7$-$0.1 is $\\approx -0.5$.\n\n\\begin{figure}[ht]\n\\epsfxsize=9.0cm \\epsfbox{fig11.xv.ps}\n\\figcaption[Filename]{\\footnotesize Greyscale continuum images of G357.7$-$0.1 composed of archival \nVLA data showing its spiral morphology. a) 6 cm image with a resolution of $13\\arcsec.4 \\times\n6\\arcsec.7$ (P.A. = 23.8\\arcdeg) and a peak flux density of 77 mJy beam$^{-1}$ with an rms\nnoise of $\\sim 0.6$ mJy beam$^{-1}$. b) Same as a) but at 20 cm. The resolution of the 20 cm\nimage is $11\\arcsec.6 \\times 8\\arcsec.1$ (P.A. = 26.2\\arcdeg) and the peak flux is 145 mJy\nbeam$^{-1}$ with an rms noise of $\\sim 1.5$ mJy beam$^{-1}$\\label{figu11}.}\n\\end{figure}\n%\\clearpage\n\n\\begin{figure}[ht]\n\\epsfxsize=8.5cm \\epsfbox{fig12.xv.ps}\n\\figcaption[Filename]{\\footnotesize Similar to Figure 11b, but with contours at (0.05, 0.15, 0.25, \n0.35, 0.45, 0.55, 0.65, 0.75, 0.85) $\\times$ 145 mJy beam$^{-1}$. The location of \nG357.7-0.1 OH (1720 MHz) maser feature (1) is marked by an ($\\times$) symbol\\label{figu12}.}\n\\end{figure}\n\n\n\\begin{figure}[ht]\n\n\\epsfxsize=5.0cm \\epsfbox{fig13.eps}\n\\figcaption[Filename]{\\footnotesize Fit of \\Bth\\/ for G357.7$-$0.1 OH (1720 MHz) maser feature (1). \nThe upper\npanels show the VLA Stokes I profiles ({\\em solid histogram}), and the bottom panels show the VLA\nStokes V profiles ({\\em solid histogram}) with the fitted derivative of Stokes I shown as smooth\ndotted curves. The value of \\Bth\\/ fit for each position and its calculated error are given at the\ntop of each plot. The solid portion of the Stokes I histogram ({\\em upper panel}) shows the\nvelocity range used in the fit\\label{figu13}.}\n\\end{figure}\n\\clearpage\n\n\nA compact source at the western edge of G357.7$-$0.1 is also apparent in Figs. 11a and b (also\nobserved by \\markcite{Shab}Shaver et al. (1985b); see also \\markcite{Ste}Stewart et al. 1994,\nand references therein). We obtain flux densities of $70\\pm 4$ mJy and $69\\pm 12$ mJy for this\ncompact source at 6 cm and 20 cm respectively, confirming that this source has a flat spectrum\nas suggested by \\markcite{Shab}Shaver et al. 1985b. At the resolution of the 18 cm A-array\ndata ($4\\arcsec.5 \\times 3\\arcsec.4$) this source is extended and has a diameter of $\\sim\n6\\arcsec$ with a possible extension to the east (toward the SNR). The exact nature of this\nsource remains unknown. \\markcite{Shab}Shaver et al. (1985b) cite its flat spectral index at\nradio wavelengths as evidence that it is an unrelated \\HII\\/ region. Alternatively,\n\\markcite{Shu}Shull, Fesen, \\& Saken (1989) suggest that it could be a pulsar which is\ninteracting with the SNR shell and is responsible for the peculiar morphology of G357.7$-$0.1\nsimilar to CTB 80. Higher resolution continuum observations or recombination line observations\nof this compact source are needed to determine its nature.\n\n\n\n\\placefigure{figu12}\n\\placefigure{figu13}\n\nFigure 12 shows the 20 cm image (similar to Fig. 11b) with the single G357.7$-$0.1 OH (1720 MHz)\nmaser superposed. The fit of this maser's \\Bth\\/ $= 0.7$ mG is shown in Figure 13. For this maser\nfeature, only the high velocity side of the line could be adequately fit by the derivative of Stokes\nI. As mentioned for CTB33 OH(1), a suppression of part of the Stokes V signal can be due to the\npresence of more than one velocity component, but the narrowness of this line (\\dv\\/$\\sim 0.6$\n\\kms\\/) makes either an inability to fully resolve the Stokes V pattern or poor S/N more probable\nexplanations. In the absence of better data, this detection should be regarded as tentative.\n\\markcite{Yus99b}Yusef-Zadeh et al. (1999b) also observed G357.7$-$0.1 at 1720 MHz with the VLA in\nA-configuration during an OH (1720 MHz) survey of the Galactic center. With their short integration\ntime (rms $\\sim 12$ mJy), they were able to place an upper limit on \\Bth\\/ for G357.7$-$0.1 OH(1) of\n2 mG, consistent with our 0.7 mG detection. In addition, these authors detected extended OH (1720\nMHz) emission toward G357.7$-$0.1 with the VLA in D-configuration ($114\\arcsec \\times 38\\arcsec$\nresolution). These authors note that this extended emission may originate from low-gain masers\ngiven the lack of OH (1720 MHz) absorption toward this source.\n\nLinear polarization images of the synchrotron emission from G357.7$-$0.1 at 5.8 GHz by\n\\markcite{Ste}Stewart et al. (1994) show that the plane-of-sky magnetic field vectors lie\ncircumferentially to the vertical bands of continuum emission (best seen in Fig. 11). These\nauthors note that this morphology is suggestive of a spiral magnetic field structure in the\nSNR. It is also interesting to note that the \\markcite{Ste}Stewart et al. images indicate a\nlack of linear polarization at the location of the OH (1720 MHz) maser, as might be expected if\n$\\vec{B}$ were nearly along the line of sight.\n\n\\section{DISCUSSION}\n\n\\subsection{Implications from 1720 MHz Maser Theory}\n\nWe have assumed until now that magnetic fields can be calculated from the Zeeman effect in masers using\nthe same formalism that has been developed for thermal radiation (i.e. \\markcite{Tro}Troland \\& Heiles\n1982 and \\Bth\\/ in Table 3). However, stimulated emission is intrinsically different from spontaneous\nemission or absorption (see \\markcite{Eli96}Elitzur 1996), so it is not unreasonable to imagine that a\nmaser's polarization properties are different from those of thermal emission. A common variable in any\npolarization study is the ratio of the line splitting ($\\Delta\\nu_B=Z\\mid\\vec{B}\\mid$) to the Doppler\nwidth ($\\Delta\\nu_D$) which we will denote $x_B$. In what follows we assume this ratio is small ($x_B\n<< 1$) since we do not resolve the line splitting in our Stokes I spectra (i.e. the splitting is only\ndetected in Stokes V). In this section we review the results of several theoretical maser polarization\nstudies for the case $x_B<<1$ (\\markcite{Eli96}\\markcite{Eli98}Elitzur 1996, 1998; and\n\\markcite{Ned92}Nedoluha \\& Watson 1992) and compare the implications and predictions of these studies\nto the currently available OH (1720 MHz) Zeeman data. These comparisons have not proven sufficient to\ndiscern exactly how the total maser magnetic field strength \\Bvm\\/ scales with our thermal estimates\n\\Bth\\/ (Table 3), but have led to a number of related conclusions which are described below.\n\nOne recent analytical study of the polarization properties of masers by \\markcite{Eli98}Elitzur (1998)\nhas suggested that the usual thermal Zeeman formulation, V $=ZC$\\Bvm\\/\\thinspace{$d$I$/d\\nu$} with $C$ a\nconstant, may not be valid for unsaturated masers. Unfortunately, a key uncertainty in the study of\nmasers is that their degree of saturation cannot be observed directly. However, \\markcite{Eli98}Elitzur\n(1998) also proposes that a maser's saturation state can be revealed by the ratio of its Stokes V\nprofile to the derivative of Stokes I (i.e. \\Ra\\/$=$V/($d$I$/d\\nu$)). This is a consequence of the\nfact that maser amplification during unsaturated maser growth is exponential, causing a narrowing of the\nmaser line. Under these circumstances, Elitzur (1998) predicts that \\Ra\\/$=ZC$\\Bvm\\/ is not a constant\n(i.e. $C \\neq$ constant) and instead assumes a Gaussian absorption shape.\n\nA test of this prediction was performed for the \\Ra\\/ profiles of W51C feature 2 (dynamic range = 720:1)\nand the highest dynamic range maser in the \\markcite{Cla97}Claussen et al. (1999) VLBA study of W28\n(W28 F39 [A]; dynamic range = 60:1). Note, that the VLBA OH maser data have three times the spectral\nresolution of the VLA data. The \\Ra\\/ profiles for both of these masers are relatively flat (to within\ntheir rms) and show no evidence of the Gaussian absorption shape predicted for unsaturated maser\nemission. We conclude however, that while these \\Ra\\/ profiles are indicative of saturated maser\nemission, this test is somewhat impractical for real data. The derivative of I passes through zero at\nline center by definition, and toward the line wings as well depending on the rms of the spectra. A\nmore useful variation of this test is to investigate the linear dependence of Stokes V as a function of\n$d$I$/d\\nu$ since this test does not suffer from the discontinuities that are inevitable with the \\Ra\\/\ntest. The resulting V vs. $d$I$/d\\nu$ plots reveal the straight lines expected from saturated emission\n(i.e. $ZC$\\Bvm\\/= constant) for W51C OH(2) and W28 F39 [A] along with several more of the masers in\nthis study (i.e. G349.7$+$0.2 OH(3), CTB37A OH(1-5)), but remain inconclusive for the lowest S/N masers\n(i.e. CTB33 OH(1)).\n\nAnother perspective on a maser's degree of saturation can be gained by comparing an upper limit for its\noptical depth ($\\tau_{max}$) assuming that it {\\em is} unsaturated, with a lower limit ($\\tau_{min}$)\nbased on the flatness of its observed \\Ra\\/ ratio. For unsaturated masers, $T_b = T_xexp(\\tau_{max})$\n(where $\\tau_{max}$ is the maser's optical depth at line center and $T_x$ is the excitation temperature;\nsee \\markcite{Eli98}Elitzur 1998 for details). As mentioned above, the lower limit depends on the\nconfidence with which a flat \\Ra\\/ profile can be determined, so that $\\tau_{min} =\n\\epsilon^{-1}$ln\\Da\\/, where $\\epsilon$ is the dynamic range of the observations and \\Da\\/ is\n$\\sigma_{B_{\\theta}}/$\\Bth\\/ (\\markcite{Eli98}Elitzur 1998). \\markcite{Eli98}Elitzur (1998) notes that\nwhenever these two limits are inconsistent ($\\tau_{min} > \\tau_{max}$), the maser must be saturated.\nThis `inconsistency' was found to be true for every maser in our sample, indicating that OH (1720 MHz)\nmasers may indeed be saturated. This was also found to be the case in a OH (1720 MHz) maser study of\nthe galactic center by \\markcite{Yus99a}Yusef-Zadeh et al. (1999a). We point out, however, that we\nhave only been able to calculate a lower limit for $T_{b}$ since the maser spots are not resolved at the\npresent resolutions. This means that if the true values of $T_{b}$ (and hence $\\tau_{max}$) are large\nenough, the apparent saturated maser inconsistencies ($\\tau_{min} > \\tau_{max}$) could disappear.\nHowever, the sizes found for OH (1720 MHz) masers in the W28 and W44 VLBA observations of Claussen et\nal. (1999) $\\sim 50 - 180$ mas, if typical, imply that the majority of masers in this study would still\nhave $\\tau_{min} > \\tau_{max}$ as required for saturated maser emission.\n\n\nEven if these masers are likely to be saturated, a second intrinsic uncertainty in performing Zeeman\nanalysis on OH masers is the value that should be taken for the constant ``$C$'' in V$ =\nZC$\\Bvm\\/\\thinspace{{\\rm I}$'$}. According to \\markcite{Eli98}Elitzur (1998), this constant is modified\nfrom its thermal value: $C_{th}=cos\\thinspace{\\theta}$ to $C_m=8/(3pcos\\thinspace{\\theta})$ for\nsaturated masers, where $\\theta$ is the angle between the magnetic field vector and the line-of-sight.\nThis solution to the maser polarization problem takes into account the fact that a photon generated via\nstimulated emission does not necessarily have the same polarization as the parent photon, and that the\nradiation is beamed. The parameter $p$ in this formulation depends on the geometry of the masing\nregion, with $p=1$ or 2 for filamentary or planar geometry respectively. Notice that in addition to the\nfactor of $8/(3p)$ difference between the thermal and maser equations for $\\mid\\vec{B}\\mid$, they also\nhave a completely different dependence on $cos{\\thinspace \\theta}$. That is, while thermal radiation\nsamples \\Blos\\/$=\\mid\\vec{B}\\mid cos{\\thinspace \\theta}$, masers sample\n\\Bm\\/$\\propto\\mid\\vec{B}\\mid/cos{\\thinspace \\theta}$ according to the Elitzur model. Therefore, this\nmodel suggests that the magnetic field needed to produce a maser's Stokes V signal is {\\em less} than\nthe field needed to produce a comparable signal from thermal radiation (i.e. $C_m > C_{th}$). For\nexample, using \\Bvm\\/ = (\\Bth\\//$C_m$), the Elitzur (1998) model predicts \\Bvm\\/ = $0.3p$\\Bth\\/ for\n$\\theta = 35\\arcdeg$, and \\Bvm\\/ = $0.1p$\\Bth\\/ for $\\theta = 75\\arcdeg$.\n\nIdeally, the Stokes parameters U, Q, and V should only depend on $\\theta$ and \\Bvm\\/. Therefore, if\nanalytic expressions for the Stokes parameters are known, it should be possible to calculate\n$\\theta$ and \\Bvm\\/ explicitly. According to \\markcite{Eli96}Elitzur (1996), the analytic\nexpression for the linear polarization fraction ($\\mid q\\mid =({\\rm Q}^2 + {\\rm U}^2)^{1/2}$/I) has\nthe approximate form \n\\begin{equation}\nq\\approx \\left[1- \\left(\\frac{2}{3\\thinspace{sin^2\\thinspace{\\theta}}}\\right)\\right], \n\\end{equation}\nas long as $x_B << 1$. Therefore, if the linear polarization fraction is known, Eq. [1] can\nprovide an estimate for $\\theta$ and hence the magnitude of $C_m$. For the case of W51C OH(2),\nwhere we have measured $q=3.5$\\% (\\S 3.2.1), we obtain $\\theta \\approx 56\\arcdeg$ and $C_m\\approx\n5/p$. Consequently, in the Elitzur model, W51C OH(2) has $\\mid\\vec{B}\\mid\\approx (0.4 \\times p)$ mG\ncompared to its estimated thermal \\Bth\\/ value of 1.9 mG (where\n$p =$ 1 or 2).\n\nUnfortunately, this technique can only produce accurate results if the ``total'' linear polarized\nintensity is measured. The more extensive Stokes Q and U observations of OH (1720 MHz) masers in W28\nand W44 (\\markcite{Cla97}Claussen et al. 1997), indicate that $q$ only ranges from 0.5\\% to 22\\% for\nall 30 of the masers with positive Q and U detections. In fact, the linear polarization of the masers\nin W28 and W44 is quite low with average values of $4\\pm 5$\\% and $10\\pm 5$\\% respectively , similar to\nthat found for W51C OH(2) ($\\pm$ gives the standard deviation of the distribution). It would be\nquite remarkable if $q$, and hence the angle between the line-of-sight and the magnetic field\n($\\theta$), were so similar in three different SNRs. Indeed it would be more natural for the polarized\nintensity of these masers to be more widely varied as is the case for SiO masers (see for example\n\\markcite{MacI}McIntosh \\& Predmore 1993). There are at least two other effects in addition to the\nviewing angle ($\\theta$) which can decrease the magnitude of $q$. These are 1) Faraday depolarization\nwithin the masing region and 2) curvature of the magnetic field lines within the masing region causing\ncancellation within the beam (i.e. MHD waves, see \\markcite{Eli92}Elitzur 1992).\n\nFaraday rotation can only be a significant factor if the Faraday rotation sizescale is smaller\nthan the length scale of the masing region (see \\markcite{Eli92}Elitzur 1992 for details).\nFrom \\markcite{Eli92}Elitzur (1992) the Faraday rotation sizescale is $\\ell_F=2\\times\n10^{16}(\\lambda^2n_e$\\Blos\\/)$^{-1}$ where $\\lambda$ is the observing frequency in cm, $n_e$ is\nthe electron density in \\cc\\/, and \\Blos\\/ is the magnitude of the magnetic field along the\nline of sight in Gauss. Theoretical modeling of OH (1720 MHz) masers by \\markcite{Loc}Lockett\net al. (1999) and Wardle (1999) suggest that the ionization fraction needed to produced a\nlarge enough column of OH for strong maser action is in the range $10^{-7}\\lesssim\n\\chi_e\\lesssim 10^{-5}$. These authors also find that the density in the masing region must\nlie in the range $1\\times 10^4$ \\cc\\/ $\\lesssim n_{H_2} \\lesssim 5\\times 10^5$ \\cc\\/. Given\nour average magnetic field detection of \\Bth\\/$\\sim 1$ mG, the Faraday rotation length scale\ncan be written\n\\footnotesize\\begin{equation}\\footnotesize\n\\ell_F=6.2\\times 10^{17}\\left[ \\left(\\frac {n_{H_2}}{10^5~{\\rm cm^{-3}}}\\right)\\left(\\frac \n{\\chi_e}{10^{-6}}\\right)\\left(\\frac {B_{los}}{1~{\\rm mG}}\\right)\\right] ^{-1}~{\\rm cm}.\n\\end{equation}\\small\nThis $\\ell_F$ estimate is only three times larger than the OH (1720 MHz) maser gain length\nestimated by \\markcite{Loc}Lockett et al. (1999) of $\\sim 2\\times 10^{17}$ cm, implying that Faraday\ndepolarization may contribute to the low linear polarization intensities observed by\n\\markcite{Cla97}Claussen et al (1997). The decrease of polarization intensity with increasing $J$ in\nSiO masers is also thought to be a consequence of such Faraday depolarization (\\markcite{MacI}McIntosh\n\\& Predmore 1993; or \\markcite{Wall97}Wallin \\& Watson 1997 for an opposing view). Unfortunately,\nthe magnitude of such depolarization is difficult to quantify and quite model dependent (see e.g.\nWallin \\& Watson 1997).\n\nIn addition, some evidence of tangling in the magnetic field lines may be indicated from the\nten-fold increase in \\Bth\\/ measured toward W28 F39 [A] with the VLBA ($\\sim 2$ mG) compared to\nthe average value measured throughout W28 with the VLA ($\\sim 0.2$ mG; \\markcite{Cla99}Claussen\net al. 1999). However, this particular spot did not have a positive VLA \\Bth\\/ detection (due\nto the presence of multiple spatial components at the lower resolution) so a direct comparison\nis not possible. More VLA vs. VLBA magnetic field strength comparisons are needed to\ndetermine whether this apparent increase in \\Bth\\/ with higher resolution is real and/or\ncommon.\n\nThese examples suggest that the linear polarization intensities observed toward W51C, W28, and W44 could\nbe reduced from their `true' values by one or both of these effects, making the calculation of $\\theta$\ndirectly from $q$ unreliable. Alternatively, using the condition that $q^2 + v^2 \\leq 1$, (where\n$v=$V/I), it is possible to obtain the following constraint on $\\theta$ at the frequency of the peak in\nStokes V, $16(x_B)^2\\lesssim cos^2\\thinspace{\\theta}\\lesssim 2/3$ as long as $x_B < 0.2$ (see Elitzur\n1996 for details). This means that the angle between $\\vec{B}$ and the line of sight must be greater\nthan $\\sim 35\\arcdeg$ in order for polarized emission to be observed at all (see also\n\\markcite{Gol}Goldreich, Keeley, \\& Kwan 1973). This lower limit on $\\theta$ ($\\sim 35\\arcdeg$),\nsuggests that the magnetic field values reported in Table 3 (\\Bth\\/) are {\\em overestimated} by factors\nof at least 1.5 ($p=2$). The upper bound on $\\theta$ cannot be accurately calculated from these data\nsince it depends on $x_B$ ($Z$\\Bth\\//$\\Delta\\nu_D$) and our current spectral resolution (0.27 \\kms\\/;\nthe highest available with the VLA in 2IF mode) is insufficient to resolve line splittings with $x_B <\n0.2$. However, since \\Bth\\/ is an {\\em upper limit} on the total field strength (\\Bvm\\/), a useful\nlimit on $x_B$ can be made by taking the average value of \\Bth\\//\\dv\\/ using data from Tables 2 and 3,\nin which case $x_B\\lesssim 0.12$ on the average and $\\theta\\lesssim 61\\arcdeg$. This upper limit to\n$\\theta$ suggests that the average total field strength is \\Bvm\\/$\\gtrsim 0.2p$\\Bth\\/, i.e. the thermal\napproximation (\\Bth\\/ in Table 3) {\\em overestimates} the maser field (\\Bvm\\/) by less than a factor of\n$C_m\\sim 5/p$.\n\n\nIt is important to note, however, that the analytic expressions formulated by Elitzur are controversial\nand that other maser studies have reached different conclusions. For example, the numerical simulations\nof \\markcite{Ned92}Nedoluha \\& Watson (1992) suggest that if $x_B << 1$ and the maser is not {\\em\nstrongly} saturated, the thermal Zeeman relationship is a good approximation (i.e. $C_m\\sim 1$).\nUnfortunately, it is quite difficult to compare the two methods since the Elitzur model is an analytical\ntreatment, while the Nedoluha \\& Watson (1992) result arises from a numerical simulation. Also notable\nis the \\markcite{Ned90}Nedoluha \\& Watson (1990) finding that it is very difficult to produce linear\npolarization in masers unless they are at least {\\em partially saturated}. It is impossible to make any\nquantitative statements on this issue with the data presented here since we only attempted linear\npolarization measurements toward one of our sources (W51C). However, the \\markcite{Cla97}Claussen et\nal. (1997) OH (1720 MHz) maser study of all four Stokes parameters toward the SNRs W28, W44, and IC443\ncontains a total of 49 masers with $S_{\\nu}>200$ mJy. About $60\\%$ of these have positive Q and/or U\ndetections. In addition, all 13 of the Claussen et al. (1997) masers with $3\\sigma$ \\Bth\\/ detections\nalso have positive Stokes Q and/or U detections. These comparisons suggest that in the Nedoluha \\&\nWatson model strong OH (1720 MHz) masers are also likely to be at least partially saturated.\n\nAn additional observational test offered by maser theory is to check whether there is any correlation\nbetween the linear polarization position angle (P.A.) and the SNR shock front in the vicinity of a\nmaser spot. Several studies have suggested that OH (1720 MHz) masers must arise in shocks which are\npropagating transverse to the line of sight (\\markcite{Loc}Lockett et al. 1999; \\markcite{Wardle}Wardle\n1999; \\markcite{Fra98}Frail \\& Mitchell 1998; \\markcite{Cla97}Claussen et al. 1997). It is also likely\nthat the magnetic field vector lies preferentially in the plane parallel to the shock front since only\nthis component can be amplified by shock compression. In addition, the linear polarization P.A. for\nmasers, unlike that of thermal dust emission, can be either parallel or perpendicular to the direction\nof the magnetic field in the plane of the sky. This difference occurs because the asymmetry of dust\ngrains removes one degree of freedom. For these reasons, we might expect the observed P.A. of the\nlinear polarization to be either parallel or perpendicular to the shock front. Of course such a\ncomparison is only meaningful if significant Faraday rotation of the P.A. has not occurred either\nbecause the Faraday depolarization is insignificant or because the P.A. of the linear polarization is\nunaffected by it. A lack of {\\em net} P.A. rotation in the presence of depolarization is suggested by\nElitzur (1992) and the SiO maser observations of McIntosh \\& Predmore (1993), although Wallin \\& Watson\n(1997) present an alternate viewpoint based on numerical simulations.\n\nFor the case of W44 region E, the linear polarization angle is $\\sim -28\\arcdeg$\n(\\markcite{Cla97}Claussen et al. 1997) and the OH (1720 MHz) masers are also distributed along a line\nwhich is oriented NW/SE at about the same angle. Further indication of the orientation of the shock\nfront comes from CO ($J=3-2$) observations by \\markcite{Fra98}Frail \\& Mitchell (1998) which show a\nridge of shocked CO emission parallel to the line of masers. This example suggests that there is a\ncorrelation between OH (1720 MHz) linear polarization position angles and the orientation of the shock\nfront. The presence of such a correlation could argue against the possibility of significant Faraday\nrotation within the SNRs or may result from Faraday depolarization without significant net rotation.\nIn any case, additional linear polarization measurements in conjunction with molecular observations of OH\n(1720 MHz) maser regions are needed to confirm this connection.\n\nThese comparisons between observation and theory of OH (1720 MHz) masers have led to the following\nconclusions: (1) It is likely that OH (1720 MHz) masers are saturated based on their flat \\Ra\\/\nprofiles (determined directly and from estimates of maser optical depths; \\markcite{Eli98}Elitzur 1998).\nThis conclusion is also supported by the high incidence of linear polarization in these masers\n(\\markcite{Ned92}Nedoluha \\& Watson 1992; \\markcite{Cla97}Claussen et al. 1997). (2) The linear\npolarization intensities of OH (1720 MHz) masers (needed to calculate \\Bvm\\/ in the Elitzur model) may\nbe significantly reduced from their intrinsic values by Faraday rotation and/or by tangling in the\nmagnetic field lines. This also means that it is impossible to calculate the reduction of \\Bvm\\/\ncompared to \\Bth\\/ using these data directly (\\Bvm\\/ $\\propto$ \\Bth\\/$cos{\\thinspace \\theta}$).\nHowever, for angles between 35$\\arcdeg$ and 75$\\arcdeg$, the Elitzur model predicts that the total\nmagnetic field strength should range from \\Bvm\\/ = (0.3 $-$ 0.1)p\\Bth\\/ (where $p=1$ or 2 for\nfilamentary or planar geometry respectively). Alternatively the numerical simulations of Nedoluha \\&\nWatson (1992) suggest that this correction factor is essentially unity. (3) It may be possible to predict the\ndirection of the shock in which an OH (1720 MHz) maser arises from the position angle of its observed\nlinear polarization (as long as the P.A. is not significantly rotated by Faraday rotation).\n\n\\subsection{Magnetic Fields in Shocked Molecular Gas} \n\nIn this study we have reported ten new measurements of OH (1720 MHz) Zeeman magnetic field strengths in\nfive galactic SNRs. Previous studies of this type (\\markcite{Cla97}Claussen et al. 1997;\n\\markcite{Kor}Koralesky et al. 1998; \\markcite{Yus96}Yusef-Zadeh et al. 1996) have measured \\Bth\\/ in\nan additional five SNRs. The magnitude of \\Bth\\/ in all of these SNRs (including those measured here)\nhave typical values between 0.1 and 4 mG. However, as the discussion in \\S 4.1 demonstrates, the\nconversion factor between thermal estimates of \\Bth\\/ and the true maser field \\Bvm\\/ is uncertain.\nTherefore, although we will continue to reference our measured fields \\Bth\\/ (Table 3), it should be\nkept in mind that \\Bth\\/ could be an upper limit that overestimates the true field by less than a factor\nof five.\n\nMaser theory suggests that OH (1720 MHz) masers originate in shocked molecular clouds (e.g.\n\\markcite{Loc}Lockett et al. 1999; \\markcite{Wardle}Wardle 1999). If so, the measurements\nreported here of \\Bth\\/ (and in the references cited above) must originate in post-shock gas.\nThese theories suggest that OH (1720 MHz) masers can only be pumped efficiently for densities\nin the range $1\\times 10^4$ \\cc\\/ $\\lesssim n_{H_2} \\lesssim 5\\times 10^5$ \\cc\\/ and\ntemperatures in the range 50 K $\\lesssim T \\lesssim$ 125 K (see \\markcite{Loc}Lockett et al.\n1999). Indeed, when independent measurements of the conditions in the post-shock gas have been\nmade (see \\markcite{Fra98}Frail \\& Mitchell; \\markcite{Rea98}\\markcite{Rea99}Reach \\& Rho 1998,\n1999) the gas properties are in agreement with these theoretical expectations.\n\nIt remains an open question how magnetic fields of these strengths are generated; i.e. shock\ncompression vs. turbulent amplification (\\markcite{Jun}Jun \\& Norman 1996). In what follows\nwe will show that compression of the existing ambient molecular cloud field is all that is\nrequired to produce the observed field strengths. One further argument against significant\nturbulent amplification of the fields is the likelihood of destroying the maser action due to\nloss of velocity coherence in a turbulent velocity field.\n\nA number of Zeeman studies have been undertaken in the past decade to detect magnetic fields in\nmolecular clouds for the purpose of studying star formation (e.g. \\markcite{Rob}Roberts et al.\n1993; \\markcite{Bro} Brogan et al. 1999). In a recent review by \\markcite{Cru}Crutcher (1999)\nof the existing data for star forming regions, the magnetic field was found to scale with\ndensity as $\\mid\\vec{B}\\mid \\propto n^{0.47}$. \\markcite{Cru}Crutcher notes that there are two\npossible physical interpretations for this relationship: (1) Such a relationship between\n$\\mid\\vec{B}\\mid$ and $n$ has been predicted by \\markcite{Fie}Fiedler \\& Mouschovias (1993)\nbased on studies of ambipolar diffusion; (2) A similar relation is suggested by the observed\ninvariance of the Alfv\\'enic Mach number $m_A = \\sqrt 3\\sigma/V_A \\approx 1$ in molecular\nclouds, where $V_A=\\mid\\vec{B}\\mid/4\\pi\\rho^{1/2}$ and $\\sigma = \\Delta v/(8\\ln 2)^{1/2}$ (see\n\\markcite{Ber}Bertoldi \\& McKee 1992; \\markcite{Zwe}Zweibel \\& McKee 1995). This invariance\nimplies $\\mid\\vec{B}\\mid \\propto \\Delta v\\sqrt\\rho$.\n\n\\begin{figure}[ht]\n\\epsfxsize=8.5cm \\epsfbox{fig14.eps}\n\\figcaption[Filename]{\\footnotesize Plot of \\Bth\\/$ \\propto n^{0.47}$ (Crutcher 1999; solid thick line) with the \nOH (1720 MHz) maser's \\Bth\\/ parameter space superposed. The two dashed lines show the $1\\sigma$ \nerrors on the fit obtained by Crutcher\\label{figu14}.}\n\\end{figure}\n\n\\placefigure{figu14}\n\nFor the range of gas densities expected in OH (1720 MHz) maser regions ($1\\times 10^4$ \\cc\\/\n$\\lesssim n_{H_2} \\lesssim 5\\times 10^5$ \\cc\\/; \\markcite{Loc}Lockett et al. 1999), the range\nof magnetic fields predicted by the relation $\\mid\\vec{B}\\mid \\propto n^{0.47}$ is 75 \\muG\\/ to\n475 \\muG\\/. Clearly the OH (1720 MHz) \\Bth\\/ measurements reported in this work (Table 3) are\ngreater than those predicted by \\markcite{Cru}Crutcher's relation (see also Figure 14).\nHowever, there is a great deal of uncertainty in this statement since \\markcite{Cru}Crutcher\nconsiders \\Blos\\/ (\\Blos\\/$=\\mid\\vec{B}\\mid cos{\\thinspace \\theta}$) which {\\em underestimates}\nthe field by factors of $\\sim 2$ while our determination of \\Bth\\/ could {\\em overestimate} the\nfield by as much as a factor of five according to the Elitzur model (see \\S 4.1).\n\nIf we assume, however, that the two types of magnetic field measurements (molecular cloud vs.\nOH (1720 MHz) masers) are approximately comparable (i.e. the thermal Zeeman equation is valid\nfor masers) it may not be surprising that their magnitudes are different. This is because\ntheory and observations suggest that OH (1720 MHz) masers do not originate in undisturbed\n``normal'' molecular clouds, but rather have experienced a shock (see above). If this is the\ncase, the \\markcite{Ber}Bertoldi \\& McKee interpretation for the scaling of $\\mid\\vec{B}\\mid$\n($\\propto \\Delta v\\sqrt\\rho$) suggests that OH (1720 MHz) masing regions simply have larger\nlinewidths for a given density than unshocked molecular clouds. If we set $V_A=\\sqrt 3\\sigma$\nas suggested by \\markcite{Ber}Bertoldi and McKee (1992), then $\\mid\\vec{B}\\mid=0.4 \\Delta v\nn_{p}^{1/2}$ where $n_{p}$ is the proton density in \\cc\\/ and the line width ($\\Delta v$) is in\n\\kms\\/. For the case of the W51C OH (1720 MHz) masers, we can take $\\Delta v = 10$ \\kms\\/\nbased on the CO observations of \\markcite{Koo99}Koo (1999), and $n_{p} = 1\\times 10^5$ \\cc\\/\nfrom the typical density needed to excite OH (1720 MHz) masers (\\markcite{Loc}Lockett et al.\n1999; Wardle et al. 1999). With these estimates, the implied magnetic field strength is\n\\Bvm\\/$=1.3$ mG, in close agreement with the \\Bth\\/ values observed toward W51C.\n\nAlternatively, if the \\Bth\\/'s measured in OH (1720 MHz) masers should be reduced by factors of\n$\\lesssim 5$ (i.e. Elitzur's maser polarization model), the fields estimated from OH (1720 MHz)\nmasers are in agreement with the values predicted by \\markcite{Cru}Crutcher's relation. In\nthis case, the magnetic fields in masing regions and molecular clouds follow the same scaling\nwith density without shock amplification of the field, i.e. no $\\Delta v$ dependence. Such\nagreement might be expected if the observed scaling were the result of ambipolar diffusion in\nboth types of regions. Clearly convergence on our understanding of the nature of maser\npolarization (and hence \\Bvm\\/) is needed to distinguish between the two possibilities.\n\nIn a radiative shock, compression of the gas follows the relation $\\eta = \\sqrt 2V_s/V_{Ao}$,\nwhere $V_{Ao}$ is the Alfv\\'en velocity in the pre-shock gas (see \\markcite{Dra}Draine \\& McKee\n1993). Using the relation $B_o\\propto n_o^{1/2}$, it can be shown that $V_{Ao}\\simeq 2$ \\kms\\/\n(see also \\markcite{Hei}Heiles et al. 1993). Thus for reasonable shock velocities (10 - 50\n\\kms\\/; \\markcite{Loc}Lockett et al. 1999; \\markcite{Fra98}Frail \\& Mitchell 1998), $\\eta = 7\n- 35$. This compression is sufficient to enhance $B_o$ to \\Bth\\/ without invoking turbulent\nenhancement of the magnetic field, assuming that $B_{ps}/B_o = \\eta$ (see\n\\markcite{Che}Chevalier 1999; \\markcite{Fra98}Frail \\& Mitchell 1998). For example, if we take\na typical shock speed of $V_s \\sim 25$ \\kms\\/ and typical values of $B_o \\sim 70$ \\muG\\/ for\nmolecular clouds of density $n_o \\sim 5 \\times 10^3$ \\cc\\/ (\\markcite{Fra98}Frail \\& Mitchell\n1998; \\markcite{Wardle}Wardle 1999; \\markcite{Cru}Crutcher 1999), $\\eta \\approx 18$ and\n$B_{ps}\\sim 1.2$ mG -- in close agreement with the observed values of \\Bth\\/. This\ndemonstration shows that typical cloud and shock parameters can lead to enhancement of the\npre-shock magnetic fields to the observed values of \\Bth\\/.\n\n\n\n\\subsection{Energetics Implied by Observed \\Bth\\/}\n\nUsing the thermal Zeeman equation, we have detected magnetic fields (\\Bth\\/) between 0.2 and 2 mG\n(Table 3) in OH (1720 MHz) masers associated with five galactic SNRs. However, as described in \\S\n4.1 these thermal field strengths may {\\em overestimate} the ``true'' field strength \\Bvm\\/ by a\nfactor between $\\sim 2-5$ (i.e Elitzur 1998). Alternatively, other theoretical studies suggest\nthat \\Bth\\/ is a good approximation to \\Bvm\\/ (i.e. Nedoluha \\& Watson 1992). For this reason,\nalong with our inability to calculate the exact correction factor in the Elitzur model, we have\nchosen to use \\Bth\\/ in the calculations below. However, the fact that \\Bth\\/ could be an upper\nlimit to the magnetic field strength should be kept in mind.\n\nRegardless of the exact details of the \\Bth\\/ to \\Bvm\\/ conversion\nor the origin of these fields (argued to be shock compression of the ambient field above), it is\nclear that the OH (1720 MHz) fields are strong (compared to those found in dark clouds $\\sim 30$\n\\muG\\/, for example). This is an important finding since the magnetic field plays a key role in\nmany aspects of the SNR/molecular cloud interaction including : (1) As noted above, the magnetic\nfield determines and, in fact, limits the amount of shock compression in the post-shock gas. (2)\nMagnetic support may help stabilize the post-shock cloud, via the magnetic force acting on ions\nperpendicular to the magnetic field lines. (3) In the model of \\markcite{Loc}Lockett et al.\n(1999), heating by ambipolar diffusion is needed to extend the length of time the post-shock gas\nspends at temperatures favorable to OH (1720 MHz) maser inversion. Ambipolar diffusion is also\nthought to be the method by which subcritical clouds dissipate their magnetic energy and form stars\n(\\markcite{Cio}Ciolek \\& Mouschovias 1995). Given the many roles that the magnetic field can play\nin the evolution of a shocked cloud, we estimate the magnetic energy compared to other energy\nsources within the region below.\n\nFrom the values of \\Bth\\/ listed in Table 3 the magnetic pressure ($P_{B_{ps}}=B_{ps}^2/8\\pi$), in\nthe post-shock gas of the five SNRs studied here, ranges from $10^{-7}$ to $10^{-9}$ erg \\cc\\/.\nThese values are large compared to both $P_{ISM}$ ($\\sim 5 \\times 10^{-13}$ erg \\cc\\/) and\n$P_{thermal}$ of the hot X-ray emitting gas interior to the remnant, $\\sim 2 \\times 10^{-10}$ erg\n\\cc\\/ (\\markcite{Kul}Kulkarni \\& Heiles 1988; \\markcite{Fra98}Frail \\& Mitchell 1998;\n\\markcite{Cla97}Claussen et al. 1997). From the X-ray observations of \\markcite{Koo95}Koo et al.\n(1995) of W51C ($n_e=0.3$ \\cc\\/; $T_e = 3 \\times 10^6$ K), we can estimate directly that\n$P_{thermal} = 2n_ekT_e \\approx 3 \\times 10^{-10}$ erg \\cc\\/ for this SNR. The ram pressure of the\nshock can also be compared to $P_{B_{ps}}$ since they should be approximately equal if the field\nstrengths are proportional to the amount of shock compression, i.e. $B_{ps}^2/8\\pi = \\rho _oV_s^2$.\nFor example, using the values of $n_o$ and $V_s$ estimated in \\S 4.2 ($n_o=5 \\times 10^3$ \\cc\\/ and\n$V_s=25$ \\kms\\/), $\\rho _o V_s^2 = 5 \\times 10^{-8}$ erg \\cc\\/. The equivalent magnetic pressure\nfor W51C OH(1) (\\Bth\\/$=1.5$ mG) is $9 \\times 10^{-8}$ erg \\cc\\/, in close agreement with the\nestimated ram pressure. Therefore, the magnetic pressure in the post-shock gas dominates over the\nthermal pressure of the SNR but is approximately equal to its ram pressure. The fact that the ram\npressure is almost three orders of magnitude larger than the thermal pressure of the shock indicates\nthat this SNR is in the radiative phase as expected for SNRs with OH (1720 MHz) masers.\n\n\n\n\\section{SUMMARY AND CONCLUSIONS}\n\nWe have observed the OH (1720 MHz) line in five galactic SNRs to measure their magnetic field strengths\nusing the Zeeman effect. We detected all 12 of the bright ($S_{\\nu} > 200$ mJy) OH (1720 MHz) masers\npreviously observed by \\markcite{Fra96}Frail et al. (1996) and \\markcite{Gre}Green et al. (1997) and\nmeasured significant magnetic fields (i.e. $ > 3\\sigma$) in ten of them. The estimated field\nstrengths, which we denote \\Bth\\/, range from 0.2 to 2 mG and are in good agreement with those measured\nin the five other SNR (0.1 - 4 mG) for which Zeeman OH (1720 MHz) maser studies exist (Koralesky et al.\n1997 and references therein). In these studies, the field strengths were calculated using the thermal\nZeeman equation for Zeeman splitting less $<<$ the line width (i.e. V\n$=Z$\\Bth\\/\\thinspace{$d$I$/d\\nu$}). In this formula, the total field strength (\\Bvm\\/) is related to\n\\Bth\\/ by \\Bvm\\/=\\Bth\\//$C_m$ where $C_m$ is a function of the viewing angle $\\theta$\n($C_m=cos\\thinspace{\\theta}$ for thermal emission). However, there exists some controversy about the\n$\\theta$ dependence of $C_m$ for saturated masers and whether it is even a constant for unsaturated\nmasers (see \\S 4.1). For example, in the Elitzur (1998) model $C_m\\propto 1/(cos\\thinspace{\\theta})$\nfor masers. {\\em From comparison of these data with maser polarization studies we conclude that these\nOH (1720 MHz) masers are likely to be saturated and that $C_m\\lesssim 5$, i.e. the \\Bth\\/ values\nreported in Table 3, overestimate the actual field strengths (\\Bvm\\/) by less than a factor of five.}\n\nWe estimate that these magnetic field strengths are consistent with the hypothesis that ambient\nmolecular cloud B-fields are compressed via the SNR shock to the observed values (\\S 4.2). Indeed,\nfield strengths of this magnitude exert a considerable influence on the properties of the shocked\ncloud. For example the magnetic pressures estimated from the values of \\Bth\\/ listed in Table 3\n($10^{-7} - 10^{-9}$ erg \\cc\\/) far exceed the pressure in the ISM or even the thermal pressure of\nthe hot gas interior to the remnant (\\S 4.3). We also find that this range of magnetic pressures is\nin very good agreement with the ram pressure expected from C-type radiative shocks.\n\nIn \\S 4.2 and \\S 4.3 we show that there is excellent agreement between our values of \\Bth\\/ and\nthose implied by shock compression and ram pressure using typical values from the literature.\nIt is somewhat difficult to maintain this agreement if \\Bth\\/ should be reduced by as much as a\nfactor of $\\lesssim 5$ (i.e. Elitzur's maser polarization model \\S 4.1), although there is\nprobably sufficient uncertainty in the parameters to allow such fine-tuning. We also show that\nthe observed values of \\Bth\\/ for OH (1720 MHz) masers are greater than those observed in\nmolecular clouds for the same range of densities (\\markcite{Cru}Crutcher 1999). It is possible\nthat this difference is due the intrinsic physical nature of the $\\mid\\vec{B}\\mid \\propto\nn^{1/2}$ relation (\\S 4.2) or may be the result of overestimating the maser B-fields (\\S 4.1).\n\nIn the future, knowledge of the field strength could be used in conjunction with molecular data\nto study the physics of these molecular shocks in more detail. In one such study\n\\markcite{Fra98}Frail \\& Mitchell (1998) mapped the distribution of molecular gas in the\nvicinity of several masers spots in W28 and W44 with the JCMT. These observations revealed\nthat the OH masers are preferentially located along the edges of thin filaments or clumps of\nmolecular gas, suggesting compression of the gas by the passing shock. In addition to this\nmorphological evidence, the density, temperature and velocity dispersion of the gas at these\nlocations suggested that the OH (1720 MHz) masers originate in post-shock gas. Combining the\nVLA and JCMT data they were able to show directly that the magnetic pressure dominates over the\nthermal pressure in the post-shock gas, balancing against the ram pressure of the gas entering\nthe shock wave (i.e. B$_{ps}^2/8\\pi=\\rho_\\circ{\\rm V}_s^2$). Thus OH (1720 MHz) measurements\nof \\Bth\\/ lead to constraints on the physics of these molecular shocks that are difficult to\nobtain any other way. When used in conjunction with molecular observations, it should be\npossible to fully specify the properties (i.e. geometry, density, temperature, velocity) of\nC-type shocks.\n\n\\acknowledgments\n\nC. Brogan would like to thank NASA/EPSCoR for fellowship support through the Kentucky Space\nGrant Consortium, as well as, summer student support from NRAO. We would also like to thank M.\nElitzur and G. Nedoluha for useful discussions on maser theory and M. Claussen for providing\nhis VLBA W28 data and useful comments on the manuscript. In addition, we thank the anonymous \nreferee for many useful suggestions.\n\n\n\n\\begin{references}\\footnotesize\n\n\\reference{Bec} Becker, R. H., \\& Helfand, D. J. \\ 1985, Nature, 313, 115\n\n\\reference{Ber} Bertoldi, F., \\& McKee, C. F. \\ 1992, \\apj, 395, 140\n\n\\reference{Bro} Brogan, C. L., Troland, T. H., Roberts, D. A., \\& Crutcher, R. M. \\ 1999, ApJ, 515, 304\n\n\\reference{Cas} Caswell, J. L., Kesteven, M. J., Bedding, T. R., \\& Turtle, A. J. \\ 1989 \nProc. Astron. Soc. Aust., 8, 184\n\n\\reference{Che} Chevalier, R. A. \\ 1999, ApJ, 511, 798\n\n\\reference{Cio} Ciolek, G. E. \\& Mouschovias, T. Ch. \\ 1995, \\apj, 454, 194\n\n\\reference{Cla97} Claussen, M. J., Frail, D. A., Goss, W. M., \\& Gaume, R. A. \\ 1997, ApJ, 489, 143\n\n\\reference{Cla99} Claussen, M. J., Frail, D. A., Goss, W. M., \\& Desai, K. \\ 1999, ApJ, 522, 349\n\n\\reference{Cor} Corbel, S., Chapuis, C., Dame, T. M., \\& Durouchoux, P. \\ 1999, ApJ, in press\n\n\\reference{Cru} Crutcher, R. M. \\ 1999, \\apj, 520, 706\n\n\\reference{Dic} Dickel, J. R., van Breugel, W. J. M., \\& Strom, R. G. \\ 1991, AJ, 101, 2151\n\n\\reference{Dra} Draine, B. T., \\& McKee, C. F. \\ 1993, ARA\\&A, 31, 373\n\n\\reference{Eli92} Elitzur, M., \\ 1992 Astronomical Masers (Dordrecht:Kluwer), 6.8\n\n\\reference{Eli96} Elitzur, M. \\ 1996, \\apj, 457, 415\n\n\\reference{Eli98} Elitzur, M. \\ 1998, \\apj, 504, 390\n\n\\reference{Fie} Fiedler, R. A., \\& Mouschovias, T. Ch. \\ 1993, \\apj, 415, 680\n\n\\reference{Fra94} Frail, D. A., Goss, W. M., \\& Slysh, V. I. 1994, ApJ, 424, L111\n\n\\reference{Fra96} Frail, D. A., Goss, W. M., Reynoso, E. M., Giacani, E. B., Green, A. J.,\n\\& Otrupcek, R. \\ 1996, AJ, 111, 1651\n\n\\reference{Fra98} Frail, D. A., \\& Mitchell, G. F. 1998, ApJ, 508, 690\n\n\\reference{Gol} Goldreich, P., Keeley, D. A., \\& Kwan, J. Y. \\ 1973, ApJ, 179, 111 \n\n\\reference{Gra} Gray, A. D. \\ 1994, \\mnras, 270, 835\n\n\\reference{Gre} Green, A. J., Frail, D. A., Goss, W. M., \\& Otrupcek, R. \\ 1997, AJ, 114, 2058\n\n\\reference{Hei} Heiles, C., Goodman, A. A., McKee, C. F., \\& Zweibel, E. G.\\ 1993, \nProtostars and Planets III, ed. E.H. Levy \\& J. I. Lunine (Tucson: Unv. of \nArizona Press), 279167-181\n\n\\reference{Hel} Helfand, d. J. \\& Becker, R. H. \\ 1985, Nature, 313, 118\n\n\\reference{Hur} Hurley, K., Kouveliotou, C., Woods, P., Mazets, E., Golenetskii, S., Frederiks, D. D., \nCline, T., \\& Van Paradijs, J. \\ 1999, \\apj, 519, L143\n\n\\reference{Jon} Jones, T. w., Rudnick, L., Jun, B., Borkowski, K. J., Dubner, G., Frail, D. A., \nKang, H., Kassim, N. E., \\& McCray, R. \\ 1998, PASP, 110, 125\n\n\\reference{Jun} Jun, B. \\& Norman, M. L. \\ 1996, ApJ, 472, 245\n\n\\reference{Kas} Kassim, N. E., Baum, S. A., \\& Weiler, K. W. \\ 1991, \\apj, 374, 212\n\n\\reference{Kle} Klein, R. I., McKee, C. F. \\& Colella, P. \\ 1994, \\apj, 420, 213 \n\n\\reference{Koo95} Koo, B. -C., Kim, K. -T., \\& Seward, F. D. \\ 1995, \\apj, 447, 211\n\n\\reference{Koo97a} Koo, B. -C., \\& Moon, D. -S., \\ 1997a, \\apj, 475, 194\n\n\\reference{Koo97b} Koo, B. -C., \\& Moon, D. -S., \\ 1997b, \\apj, 485, 263\n\n\\reference{Koo99} Koo, B. -C. \\ 1999, ApJ, 518, 760\n\n\\reference{Kor} Koralesky, B., Frail, D. A., Goss, W. M., Claussen, M. J, \\& Green, A. \nJ. \\ 1998, AJ, 116, 1323\n\n\\reference{Kul} Kulkarni, S. R., \\& Heiles, C. \\ 1988, Galactic \\& Extragalactic Radio Astronomy \n(2nd edition) Berlin and New York, Springer-Verlag, 95\n\n\\reference{Loc} Lockett, P., Gauthier, E., \\& Elitzur, M. \\ 1999, ApJ, 511, 235\n\n\\reference{Lyn} Lyne, A. G., \\& Lorimer, D. R. \\ 1994, Nature, 369, 127\n\n\\reference{MacI} McIntosh, G. C., \\& Predmore, C. R. \\ 1993, ApJ, 404, L71\n\n\\reference{MacL} MacLow, M.-M., McKee, C. F., Klein, R. I., Stone, J. M., \\& Norman, M. \nL., \\ 1994, ApJ, 433, 757\n\n%\\reference{McK92} McKee, C. F., \\& Zweibel, E. G. \\ 1992, \\apj, 399, 551\n\n%\\reference{McK95} McKee, C. F., \\& Zweibel, E. G. \\ 1995, \\apj, 440, 686\n\n\\reference{Mie} Miesch, M. S. \\& Zweibel, E. G. \\ 1994, \\apj, 432, 622\n\n\\reference{Mil} Milne, D. K. \\ 1990, in Proc. 140th IAU Symp., Galactic and Intergalactic Magnetic\nFields, Beck, B., Kronberg, P. P., \\& Wielebinski, R., ed., 67\n\n\\reference{Ned90} Nedoluha, G. E., \\& Watson, W. D. \\ 1990, \\apj, ApJ, 354, 660\n\n\\reference{Ned92} Nedoluha, G. E., \\& Watson, W. D. \\ 1992, \\apj, ApJ, 384, 185\n\n\\reference{Rea98} Reach, W. T., \\& Rho, J. \\ 1998, \\apj, 507, L93\n\n\\reference{Rea99} Reach, W. T., \\& Rho, J. \\ 1999, \\apj, 511, 836\n\n\\reference{Rob} Roberts, D. A., Crutcher, R. M., Troland, T. H., \\& Goss, W. M. \\ 1993, ApJ, 412, 675\n\n\\reference{Sar} Sarma, A. P., Goss, W. M., Green, A. J., \\& Frail, D. A. \\ 1997, 483, 335\n \n\\reference{Shaa} Shaver, P. A., Salter, C. J., Patnaik, A. R., van Gorkom, J. H. \\& Hunt, G. C. \n\\ 1985a, Nature, 313, 113\n\n\\reference{Shab} Shaver, P. A., Pottasch, S. R., Patnaik, A. R., van Gorkom, J. H. \\& Hunt, G. C. \n\\ 1985b, A\\&A, 147, L23\n\n\\reference{Shu} Shull, M. J., Fesen, R. A., \\& Saken, J. M. \\ 1989, \\apj, 346, 860\n\n\\reference{Ste} Stewart, R. T., Haynes, R. F., Gray, A. D., \\& Reich, W. \\ 1994, \\apjl, 432, L39\n\n\\reference{Sub} Subrahmanyan, R., \\& Goss, W. M. \\ 1995, MNRAS, 275, 755\n\n\\reference{Tho} Thompson., C., \\& Duncan, R. C. \\ 1995, MNRAS, 275, 255\n\n\\reference{Tro} Troland, T. H., \\& Heiles, C. \\ 1982, ApJ, 260, L19\n\n\\reference{Wall97} Wallin, B. K., \\& Watson, W. D. \\ 1997, ApJ, 481, 832\n\n\\reference{War99} Wardle, M., Yusef-Zadeh, F. \\& Geballe, T. R. \\ 1999, in ASP Conf. Series, \nVol. 186. The Central Parsecs, Falcke, H., Cotera, A., Duschl, W. J., Melia, F. \\& Rieke, M. J., \ned., 432\n\n\\reference{Wardle} Wardle, M., \\ 1999, ApJ, 527, L109\n\n\\reference{Wei} Weiler, K. W., \\& Panagia, N. \\ 1980, A\\&A, 90, 269\n\n%\\reference{Whi} Whiteoak, J. B. Z. \\& Green, A. J. \\ 1996, \\aaps, 118, 329\n\n\\reference{Woo} Woods, P., Kouveliotou, C., Van Paradijs, J. Hurley, K., Kippen, R. M., \nFinger, M. H., Briggs, M. S., Dieters, S., \\& Fishman, G. J. \\ 1999, \\apj, 519, L139 \n\n\\reference{Yus96} Yusef-Zadeh, F., Roberts, D. A., Goss, W. M., Frail, D. A., \\& Green, A. J. \n\\ 1996, ApJ, 466, L25\n\n\\reference{Yus99a} Yusef-Zadeh, F., Roberts, D. A., Goss, W. M., Frail, D. A., \\& Green, A. J. \n\\ 1999a, ApJ, 512, 230\n\n\\reference{Yus99b} Yusef-Zadeh, F., Goss, W. M., Roberts, D. A., Robinson, B. \\& Frail, D. A. \n\\ 1999b, ApJ, in press\n\n\\reference{Zwe} Zweibel, E. G., \\& McKee, C. F. \\ 1995, \\apj, 439, 779\n\n\n \n\\end{references}\n\n\n\n\n\n\n\\end{document}\n"
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astro-ph0002399
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The Detection of the Diffuse Interstellar Bands in Dusty Starburst Galaxies
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[
{
"author": "Timothy M. Heckman$^1$"
}
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We report the detection of the Diffuse Interstellar Bands (``$DIBs$'') in the optical spectra of seven far-infrared-selected starburst galaxies. The $\lambda$6283.9 \AA\ and $\lambda$ 5780.5 \AA\ features are detected with equivalent widths of $\sim$ 0.4 to 1 \AA\ and 0.1 to 0.6 \AA\ respectively. In the two starbursts with the highest quality spectra (M82 and NGC2146), four other weaker $DIBs$ at $\lambda$ 5797.0 \AA, 6010.1 \AA, 6203.1 \AA, and 6613.6 \AA\ are detected with equivalent widths of $\sim$ 0.1 \AA. The region over which the $DIBs$ can be detected ranges from $\sim$ 1 kpc in the less powerful starbursts, to several kpc in the more powerful ones. The gas producing the $DIBs$ is more kinematically quiescent on-average than the gas producing the strongly-blueshifted $NaI\lambda\lambda$5890,5896 absorption in the same starbursts. We show that the $DIBs$ in these intense starbursts are remarkably similar to those in our Galaxy: the relative strengths of the features detected are similar, and the equivalent widths follow the same dependence as Galactic $DIBs$ on $E(B-V)$ and $NaI$ column density. While the ISM in starbursts is heated by a photon and cosmic ray bath that is $\sim$ 10$^3$ times more intense than in the diffuse ISM of the Milky Way, the gas densities and pressures are also correspondingly larger in starbursts. This ``homology'' may help explain the strikingly similar $DIB$ properties.
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[
{
"name": "dib.tex",
"string": "%\\documentstyle[aasms4,12pt,epsf]{article}\n%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[12pt,aaspp4,psfig]{article}\n\\def\\fnsiz{\\footnotesize} \n%\\tighten\n%\\eqsecnum\n \n\\lefthead{T. Heckman et al.}\n\\righthead{Absorption-Lines in Galactic Winds}\n \n\\slugcomment{.}\n \n\\begin{document}\n\n\\title{The Detection of the Diffuse Interstellar Bands in \nDusty Starburst Galaxies}\n\n\\author{Timothy M. Heckman$^1$}\n\\affil{Department of Physics and Astronomy, Johns Hopkins\nUniversity, Homewood Campus, 3400 North Charles Street, Baltimore, MD 21218}\n\\author{Matthew D. Lehnert$^1$}\n\\affil{Max-Plank-Institut f\\\"ur extraterrestrische Physik, Postfach 1603,\nD-85740 Garching, Germany}\n\n\\parindent=0em\n\\vspace{4cm}\n \n1. Visiting astronomers, Kitt Peak National Observatory and Cerro Tololo\nInteramerican Observatory, NOAO,\noperated by AURA, Inc. under cooperative agreement with the\nNational Science Foundation.\n\n\\newpage\n\\parindent=2em\n\n\\begin{abstract}\nWe report the detection of the Diffuse Interstellar Bands (``$DIBs$'') in\nthe optical spectra of seven far-infrared-selected starburst galaxies.\nThe $\\lambda$6283.9 \\AA\\ and $\\lambda$ 5780.5 \\AA\\\nfeatures are detected\nwith equivalent widths of $\\sim$ 0.4 to 1 \\AA\\ and 0.1 to 0.6 \\AA\\ respectively.\nIn the two starbursts with the highest quality spectra\n(M82 and NGC2146), four other weaker $DIBs$ at \n$\\lambda$ 5797.0 \\AA, 6010.1 \\AA, 6203.1 \\AA,\nand 6613.6 \\AA\\\nare detected with equivalent widths of $\\sim$ 0.1 \\AA. The region over\nwhich the $DIBs$ can be detected ranges from $\\sim$ 1 kpc in the less\npowerful starbursts, to several kpc in the more powerful ones.\nThe gas producing the $DIBs$ is more kinematically quiescent on-average\nthan the gas producing the strongly-blueshifted $NaI\\lambda\\lambda$5890,5896\nabsorption in the same starbursts. We show that the $DIBs$ in these intense\nstarbursts are remarkably similar to those in our Galaxy: the relative\nstrengths of the features detected are similar, and the equivalent widths\nfollow the same dependence as Galactic $DIBs$ on $E(B-V)$ and $NaI$ column\ndensity. While the ISM in starbursts is heated by a photon and cosmic\nray bath that is $\\sim$ 10$^3$ times more intense than in the diffuse\nISM of the Milky Way, the gas densities and pressures are also\ncorrespondingly larger in starbursts. This ``homology'' may help\nexplain the strikingly similar $DIB$ properties.\n\\end{abstract}\n\n\\keywords{\nGalaxies: Starburst -- Galaxies: Nuclei -- Galaxies: ISM -- ISM: Molecules\n-- ISM: Dust,Extinction -- Line: Identification}\n\n\\newpage\n\n\\section{Introduction}\n\nThe Diffuse Interstellar Bands (``$DIBs$'') have been studied for over 60 years,\nsince Merrill (1934) first established their origin in the interstellar medium.\nDespite decades of intensive investigation, the identity of the carrier or\ncarriers of\nthe $DIBs$ has not been established (see the comprehensive\nreview by Herbig 1995). The \nmost likely candidates are large\ncarbon-rich molecules (e.g. Sonnentrucker et al 1997), perhaps\nPolycyclic Aromatic Hydrocarbons (PAH's - Salama et al 1999).\nThe strongest and best-studied $DIBs$ in the optical spectrum are known\nempirically to trace the $HI$ phase of the ISM, with\nstrengths that correlate well with the line-of-sight color excess $E(B-V)$,\nthe $HI$ column density, and the $NaI$ column density as probed with the\n$NaI \\lambda\\lambda$5890,5896 (``$NaD$'') doublet (see Herbig 1993).\n\nTo date, $DIBs$ have been observed almost exclusively in our own Galaxy,\nand to a limited extent in the Magellanic Clouds (Morgan 1987).\nSupernova 1986G in NGC 5128 (Cen A) allowed the detection of\n$DIBs$ produced within the famous dusty gas disk in this elliptical\ngalaxy (di Serego Alighieri \\& Ponz 1987). Most recently, \nGallagher \\& Smith (1999) have reported the possible discovery\nof the $DIB$ at $\\lambda$6283.9 \\AA\\ in the spectra of two\n``super starclusters'' near the\nnucleus of the prototypical starburst galaxy M 82. This is intriguing,\nsince it suggests that the $DIB$ carriers are present at a normal level\neven in the ISM of an intense starburst, in which the ambient radiation\nintensity and gas pressure are orders-of-magnitude higher than\nin the diffuse gas in the Milky Way disk (e.g. Colbert et al 1999).\n\nWe have recently analyzed the properties of the interstellar $NaD$ absorption-\nline in the spectra of 18 high-luminosity, infrared-selected (dusty) starbursts\n(Heckman et al. 2000 - hereafter HLSA).\nIn the course of this analysis, we examined the 7 starbursts with\nthe highest quality spectra for the presence of $DIBs$ (section 2). As we report\nin section 3 below,\nwe have detected one or both of the\n$\\lambda$6283.9 \\AA\\ and \n$\\lambda$5780.5 \\AA\\ $DIB$ features (normally the two strongest $DIBs$ in the\noptical spectral region) in all seven cases.\nWe have also been able\nto map the spatial distribution of the $DIBs$. \nThese data allow us to directly compare the properties\nof the $DIBs$ in the ISM of\nthese extreme starbursts to sight-lines in the Galaxy having similar\ngas column density and reddening (section 4).\n\n\\section{Observations \\& Data Analysis}\n\nDetails concerning the following are given in HLSA, so we only summarize\nthe most salient points here.\n\nThe starburst sample presented here is a subset of the 32 galaxies observed\nby HLSA. The HLSA sample itself was selected from two far-infrared-bright\nsamples: the Armus, Heckman, \\& Miley (1989) sample of galaxies\nwith very warm far-IR colors and the Lehnert \\& Heckman (1995) sample\nof far-IR-bright disk galaxies seen at high inclination. The combined\nsample is representative of the far-IR-galaxy phenomenon, but is not complete.\n\nHLSA found that the $NaD$ line was of predominantly interstellar origin\nin 18 of the 32 galaxies, while cool stars contributed significantly\nto the line in the other 14 cases. \nThe plethora of weak\nabsorption features in the spectra of cool stars greatly complicate\nthe detection of the $DIBs$, while the strength of $DIBs$\nin our Galaxy correlate strongly with the ISM $NaI$ column density. Thus,\nthe galaxies in the present paper were drawn exclusively from the\n18 ``interstellar-dominated'' objects in HLSA.\nWe then selected the objects in HLSA having the\nhighest signal-to-noise spectra obtained with\na resolution better than $\\sim$ 100 km s$^{-1}$\n(see below). This results in a sample of 7 galaxies, as listed in\nTable 1.\n\nThe observations were undertaken in 1993 and 1994\nusing two different facilities: the 4-meter Blanco Telescope with the\nCassegrain Spectrograph at $CTIO$ and the 4-meter Mayall Telescope with the\nRC Spectrograph at $KPNO$. The spectral resolution ranged from 1.1 \\AA\\\nFWHM in the $KPNO$ data to 1.8 \\AA\\ FWHM in the $CTIO$ data. Details regarding\nspectrograph configurations\nare listed in Table 2 of HLSA. \n\nThe spectra were all processed using the standard {\\it LONGSLIT} package\nin $IRAF$ (bias-subtracted, flat-fielded using spectra of a quartz-lamp,\ngeometrically-rectified and wavelength-calibrated using a $HeNeAr$ arc lamp,\nand then sky-subtracted). See HLSA for details. No explicit correction was\nmade for the presence of weak telluric absorption-features, but these\nare not a problem for our analysis. The strongest feature of relevance\nis the O$_2$ band from $\\sim$ 6276 to 6284 \\AA\\ (e.g. Figure 2a in\nBenvenuti \\& Porceddu 1989). Fortunately,\nthe redshifts\nof our galaxies are sufficient to move the $\\lambda$6283.9 \\AA\\ $DIB$ out\nfrom under this feature.\n\nThe spectra were analyzed using the interactive {\\it SPLOT} spectral fitting\npackage in $IRAF$. In all cases, a one-dimensional ``nuclear'' spectrum was\nextracted, covering a region with a size set by the slit width and summed over\n5 pixels\nin the spatial direction (the resulting aperture is typically 2 by 4 arcsec).\nThe\ncorresponding linear size of the projected aperture is generally a few hundred\nparsecs to a few kpc in these galaxies (median diameter 600 pc).\nThis is a reasonable match to the typical sizes of powerful starbursts\nlike these (e.g. Meurer et al 1997; Lehnert \\& Heckman 1996). Prior\nto further analysis, each 1-D spectrum was normalized to unit intensity by\nfitting it with, and then dividing it by, a low-order polynomial. \nSimilar one-dimensional spectra for off-\nnuclear regions were extracted over the spatial region with adequate signal-\nto-noise in the continuum for each galaxy.\n\nIt is essential to remove the myriad absorption features due to cool stars\nfrom the spectra before searching for the relatively weak $DIB$ features. We \nhave therefore used the average spectrum of several Galactic K giant stars as a \ntemplate. After redshifting the normalized stellar template to the galaxy\nrest-frame,\nwe have iteratively scaled and subtracted the template from the normalized\ngalaxy spectrum until the residuals in the difference spectrum were minimized\nin the spectral regions that exclude potentially detectable interstellar\nfeatures. \nThe scale factors found for the stellar template\nimply that cool stars typically contribute 20 to 30\\% of the continuum light\nat $\\sim$ 6000\\AA. This is consistent with both the less rigorous estimates\nreported\nin HLSA for these galaxies, and with theoretical\nexpectations for red supergiants in a mature metal-rich starburst\n(Bruzual \\& Charlot 1993; Leitherer et al 1999). \nTo compensate\nfor the effects of the continuum subtraction,\nwe added back an equivalent amount of featureless continuum.\nThus, the depths and equivalent widths of the $DIBs$ in the original\ndata are preserved by our analysis.\nAs an example, we show the spectrum of the nucleus of M82 before and after\nthe subtraction of a suitably-scaled K-star spectrum in Figure 1.\nThese final processed spectra are shown in Figures 2 and 3.\n\nWe have estimated the uncertainties in our measurements in two ways.\nFirst, we compared \nthe measurements for the four galaxies in the sample for which we have more\nthan one independent spectrum (taken at a different position angle).\nSecond, we have calculated the rms noise in the cool-star-subtracted spectra\nand used this to calculate the implied uncertainties (assuming standard\nerror propogation for Poissonian noise). We report these uncertainties\nin Tables 1 through 3.\n\n\\section{Results}\n\n\\subsection{The Identified Features}\n\nThe two most conspicuous $DIBs$ along typical sight-lines in the ISM of\nour Galaxy are the strong, relatively narrow features at\n$\\lambda$6283.9 \\AA\\ and\n$\\lambda$5780.5 \\AA\\ (Herbig 1995). In all but one case, both features are\nwithin the\nwavelength coverage of our spectra. The next strongest $DIBs$ in the Milky\nWay in the relevant spectral region are at 5797.0 \\AA, 6010.1 \\AA, 6203.1 \\AA,\nand 6613.6 \\AA. We have searched for all these features in our spectra.\n\nWe turn our attention first to the $\\lambda$6283.9 \\AA\\ feature, which is \nthe strongest feature in the Milky Way, and is not seriously confused by\nstellar photospheric lines in the starburst spectra.\nAs can be seen in Figure 2, the $\\lambda$6283.9 $DIB$ is detected in 6 of the\n7 starburst nuclei (Table 1).\nThe only exception is NGC 6240, where the feature would\nlie within the blue shoulder of the very strong and broad [OI]$\\lambda$6300\nnebular emission-line, making it very difficult to detect. \nIn the other six cases, the equivalent\nwidth of this $DIB$ ranges from $\\sim$ 0.4 to 0.9 \\AA\\, with a normalized\nresidual intensity at line-center of 0.83 to 0.94.\nThese values correspond to some of \nthe strongest features seen along sight-lines in the ISM of the Milky Way\n(e.g. Chlewicki et al 1986; Benvenuti \\& Porceddu 1989).\n\nWeaker absorption due to the $\\lambda$5780.5 $DIB$\nis definitely present in three of the seven members of our sample \n(NGC2146, M82, and NGC6240), and possibly present in three more\n(NGC1614, NGC1808, and NGC3256).\nNo measurement can be made\nin IRAS10565+2448, since \nthe feature lies just outside our spectral passband. In the five cases\nin which both features are detected,\nthe $\\lambda$5780.5 $DIB$ is typically about 25\\% as strong as\nthe $\\lambda$6283.9 feature, compared to a mean value of about 45\\%\nalong comparably-reddened lines-of-sight in the Milky Way\n(Chlewicki et al 1986; Benvenuti \\& Porceddu 1989). \nWe emphasize that the measurement \nof the\n$\\lambda$5780.5 $DIB$ is difficult in our spectra owing to its proximity to the \ncomparably\nstrong\nstellar photospheric CrI+CuI$\\lambda$5782 feature (with which it is badly\nblended). We estimate that this introduces an uncertainty\nof $\\pm$ 50 m\\AA\\ in the quoted equivalent widths (which is generally larger\nthan the formal measurement uncertainties estimated above).\n\nThe two starburst nuclei with the strongest $\\lambda$6283.9 \\AA\\ $DIB$ feature\nare NGC 2146 and M82. These two spectra also have the\nhighest signal-to-noise and (along with IRAS10565+2448) have the best\nspectral resolution and broadest wavelength coverage in our sample.\nIn these two spectra, several other weaker $DIB$ features can be identified,\nnamely those at 5797.0 \\AA, 6010.1 \\AA, 6203.1 \\AA,\nand 6613.6 \\AA\\ (Figure 3).\nThe equivalent widths of these features are $\\sim$100\nm\\AA\\, or typically 10 to 15\\% as large as those of the\n$\\lambda$6283.9 \\AA\\ feature. These relative strengths agree reasonably well\nwith Galactic $DIBs$ (Chlewicki et al 1986; Benvenuti \\& Porceddu 1989;\nHerbig 1995).\nWe summarize this information in Table 2, and note that similarly-weak\nfeatures could be present in the noisier spectra of the other five\nmembers of our sample.\n\n\\subsection{Kinematics}\n\nWe have measured the width and centroid of the $\\lambda$6283.9 \\AA\\ $DIB$\n feature\nin all cases but NGC 6240 (where we have instead used the $\\lambda$5780.5 \n\\AA\\ $DIB$).\nThe measured line widths (Table 3) range from $\\sim$ 5 to 9 \\AA. The intrinsic\nwidth of the $\\lambda$6283.9 ($\\lambda$5780.5) $DIB$ in the Milky Way is $\\sim$\n4 (2) \\AA\\ (Herbig 1995).\nTaking our instrumental resolution into account,\nthe implied Doppler broadening of the $DIBs$ due to macroscopic motions\nin the starburst ISM ranges from FWHM 160 to 430 km s$^{-1}$. In\nfour of the seven cases,\nthese Doppler widths are smaller than the widths of\nthe $NaD$ doublet (by 25 to 60\\%). In NGC1808, NGC2146 and M82, the $DIB$\n$NaD$ lines have the roughly the same Doppler widths.\nInterestingly, HLSA find that these are the three cases in the present sample in\nwhich the nuclear $NaD$ lines do not show significant blueshifts with respect\nto the galaxy systemic velocity ($v_{sys}$). \n\nThe centroids of the $DIBs$ are within $\\sim$ 100 km\ns$^{-1}$ of $v_{sys}$. However, in all four cases with strongly\nblueshifted\n$NaD$ lines (NGC1614, NGC3256, IRAS10565+2448, and NGC6240), the $DIBs$\nare mildly blueshifted (by $\\sim$ 50 to 110 km s$^{-1}$) with velocities\nthat are intermediate between $v_{NaD}$ and $v_{sys}$. The velocities\nof the $DIB$ and $NaD$ absorbers roughly agree with one another \n(and lie close to $v_{sys}$) in the other three\ncases. This kinematic information is summarized in Table 3.\n\nTaken together, these results suggest that \nthe $DIBs$ trace gas that is more quiescent on-average than that probed by\nthe $NaD$ line. That is, the $NaD$ absorption in the four ``outflow''\nnuclei is probably produced by\na combination of quiescent material ($v \\sim v_{sys}$\nwith smaller Doppler width) and disturbed,\noutflowing material. \nThe bulk of the $DIB$ absorption would be associated with the former,\nand this component would dominate both the $NaD$ and $DIB$ absorption\nin the three other cases in our sample.\n\n\\subsection{Spatial Extent}\n\nWe have used our long-slit data to map the \nextra-nuclear spatial extent of the $DIBs$\nin these galaxies.\nAs listed in Table 1, these sizes\nrange from\n$\\sim$ 1 to 6 kpc. The absorbing region is larger\n(3 to 6 kpc) in the more powerful starbursts (NGC1614, NGC3256,\nIRAS10565+2448, and NGC6240, with $logL_{bol}$ = 11.3 to 12.0 $L_{\\odot}$),\nand smaller (0.9 to 1.8 kpc) in the less powerful cases\n(NGC1808, NGC2146, and M82, with $logL_{bol}$ = 10.5 to 10.7 $L_{\\odot}$).\nIn the nearby (less powerful) starbursts, these sizes reflect the\nextent of the absorbing material. In the more distant (more powerful)\nstarbursts, these sizes are lower limits set by the\nregion with adequate signal-to-noise\nin the stellar continuum.\n\n\\section{Discussion}\n\n\\subsection{Comparison to Galactic DIBs}\n\nThe strengths of the prominent Galactic $DIBs$ correlate well\nwith the column densities of both $HI$ and $NaI$ \nand with the reddening\nalong the line-of-sight\n(e.g. Chlewicki et al 1986; Herbig 1993).\nThis implies\nthat the $DIB$ carrier is most plausibly associated with the cool\natomic phase of the ISM. We can use the data discussed in HLSA\nto estimate the values for $N_{NaI}$ and $E(B-V)$ in our sample\nof seven starbursts, to see if the $DIBs$ in our starburst sample\nobey the same empirical relations\ndefined by the ISM of the Milky Way.\n\nWe follow HLSA and derive estimates for $N_{NaI}$ using the average\nof the values obtained from \nthe classical ``doublet ratio'' method (Spitzer 1968) and the\nvariant described by Hammann et al (1997). We estimate the line-of-sight\nreddening to the stellar continuum using \nthe observed colors\ncompared to \ntheoretical models for a starburst stellar population\n(Leitherer et al 1999; see HLSA for details). We list\nthe results in Table 1.\n\nOur best-measured $DIB$ by-far is the strong $\\lambda$6283.9 feature.\nThe data compiled by Chlewicki et al (1986) and Benvenuti \\& Porceddu (1989)\nshow that the mean ratio of the equivalent width of this feature\nand the color excess is $<W_{6284}/E(B-V)>$ = 1.2 \\AA\\ for heavily-reddened\nGalactic sight-lines. For our small starburst sample we find a similar result:\n$<W_{6284}/E(B-V)>$ = 0.8 \\AA. This is shown\nin Figure 4 where we have plotted\n$W_{6284}$ {\\it vs.} $E(B-V)$ for a large sample of Galactic sight-lines\nusing the extensive data compled by Herbig (1993). To compare our starburst data\ndirectly to this Galactic data we have converted the values given by\nHerbig (1993) for the equivalent width of the $\\lambda$5780.5\n\\AA\\ $DIB$ into estimated values for $W_{6284}$ assuming that the mean\nratio measured by Chlewicki et al (1986) and Benvenuti \\& Porceddu (1989)\napplies ($W_{6284}/W_{5780}$ = 2.2). In Figure 5 we have likewise\nplotted $W_{6284}$ {\\it vs.} $N_{NaI}$ for both the Galactic data\nand our starburst data. The starbursts lie at the high-end of \nthe relationship defined by $DIBs$ in the\nMilky Way. \n\n\\subsection{Relationship to the $\\lambda$2175 \\AA\\ Dust Feature}\n\nOver the years, there has been considerable speculation as\nto a possible connection between the $DIBs$ and the strong and broad\nfeature at $\\lambda$2175 \\AA\\ in the Galactic extinction curve\n(see Benvenuti \\& Porceddu 1989). In this context, the detection\nof strong $DIBs$ in starburst spectra is noteworthy. As shown\nby Calzetti et al (1994), the $\\lambda$2175 feature is extremely\n(undetectably) weak in the UV spectra of starbursts. This\nimplies that the carriers of the $DIBs$ and the $\\lambda$2175 feature\nmust be quite distinct (in agreement with the conclusions\nof Benvenuti \\& Porceddu (1989) for the Galactic ISM).\n\n\\subsection{Speculations}\n\nOn the face of it, the above results may seem surprising given\nthe extreme differences between the physical\nconditions in the ISM of intense starbursts and our own Galactic disk.\nThe strong starbursts in our sample have bolometric surface\nbrightnesses of $\\Sigma_{bol} \\sim 10^{10}$ to $10^{11}$ L$_{\\odot}$ \nkpc$^{-2}$\n(e.g. Meurer et al. 1997), typical star-formation rates per unit area of\n$\\Sigma_{SFR} \\sim$ 10 M$_{\\odot}$ year$^{-1}$ kpc$^{-2}$, and surface\nmass densities in gas and stars of\n$\\Sigma_{gas} \\sim \\Sigma_{stars} \\sim$ 10$^9$ M$_{\\odot}$ kpc$^{-2}$ (e.g.\nKennicutt 1998).\nThese\nare roughly 10$^3$ ($\\Sigma_{SFR}$), 10$^2$ ($\\Sigma_{gas}$) and\n10$^1$ ($\\Sigma_{stars}$) times larger than the\ncorresponding values in the disks of normal galaxies.\nThese values for $\\Sigma_{bol}$ \ncorrespond to a radiant energy density inside the star-forming region that\nis roughly 10$^3$ times the value in the ISM of the Milky Way (and see\nColbert et al 1999 for direct measurements of this quantity). \nThe rate of mechanical energy deposition\n(supernova heating) per unit volume in these starbursts is of-order 10$^3$\ntimes\nhigher than in the ISM of our Galaxy (e.g. Heckman, Armus, \\& Miley 1990),\nas is the cosmic ray heating rate (Suchkov, Allen, \\& Heckman 1993).\nFinally,\nsimple considerations of hydrostatic equilibrium imply correspondingly\nhigh pressures in the ISM: $P \\sim G \\Sigma_g\n\\Sigma_{tot} \\sim$ few $\\times$ 10$^{-9}$ dyne cm$^{-2}$ (P/k $\\sim$\nfew $\\times$ 10$^7$ K cm$^{-3}$, or several thousand times the value\nin the local ISM in the Milky Way). These high pressures have been\nconfirmed observationally (e.g. Heckman, Armus, \\& Miley 1990;\nColbert et al 1999).\n\nThe interesting result of the above is that despite the extreme conditions\nprevailing inside these starbursts,\nthe dimensionless ratio of the\nISM pressure\nto the energy density in UV photons (or cosmic rays) is quite similar\nin starbursts and the disk of the Milky Way. This would in turn imply\nthat (for a given ISM temperature) the ratio of the number densities\nof the gas particles and UV\nphotons (or cosmic rays) would also be similar to their values in the\nlocal ISM. Wang, Heckman, \\& Lehnert (1998) have discussed the evidence\nthat this analysis is correct for the diffuse ionized medium in starbursts\nand the disks of normal late-type galaxies. \n\nThis ``homologous'' behavior of the ISM in regions spanning over\nthree orders-of-magnitude in heating and cooling rates per particle\nmay help to explain why the ratio of the column\ndensity of $DIB$ carriers to that of both $Na$ atoms (Figure 5) and dust grains \n(Figure 4) appears so similar in extreme starbursts and the ISM of our\nown Galaxy. In the absence of a well-understood origin for the $DIBs$,\nfurther speculation seems premature.\n\n\\section{Summary}\nDespite over six decades of investigation, the nature and origin of\nthe Diffuse Interstellar Bands remain a mystery (Herbig 1995). We have\npresented evidence that - far from being a possibly pathological\nproperty of the local ISM in our Galaxy - $DIBs$ are probably ubiquitous\nin the spectra of far-infrared-bright (dusty) starbursts.\n\nIn our own Galaxy, the two most conspicuous $DIBs$ are the features\nat $\\lambda$6283.9 \\AA\\ and $\\lambda$5780.5 \\AA. \nWe have detected one or both of these two $DIBs$ in all seven starbursts selected\non the basis of strong interstellar $NaI\\lambda\\lambda$5790,5796 ($NaD$)\nabsorption from the larger starburst sample studied by Heckman et\nal (2000 - HLSA). The equivalent widths of these features are\n$\\sim$ 400 to 900 m\\AA\\ and $\\sim$ 100 to 400 m\\AA\\ for the\n$\\lambda$6280.9 and $\\lambda$5780.5 features respectively. These roughly\ncorrespond to the greatest $DIB$\n strengths observed in the Milky Way\n(Herbig 1993;\nChlewicki et al 1986).\nIn two members of our sample (M82 and NGC2146) the spectra are of\nhigh enough signal-to-noise to detect four other weaker $DIBs$\n(at 5797.0 \\AA, 6010.1 \\AA, 6203.1 \\AA, \nand 6613.6 \\AA). These have typical equivalent widths of $\\sim$ 100 m\\AA.\nThe relative strengths of these $DIBs$ are rather similar to those\nin the Milky Way (Herbig 1995; Chlewicki et al 1986;\nBenvenuti \\& Porceddu 1989).\n\nThe $DIBs$ can be mapped over an extensive region in and around the\nnuclear starbursts. In the moderately powerful starbursts\n($L_{bol}$ = few $\\times$ 10$^{10}$ L$_{\\odot}$), this region is\n$\\sim$ 1 kpc in size {\\it vs.} several kpc in the more powerful\nstarbursts ($L_{bol}$ = few $\\times$ 10$^{11}$ L$_{\\odot}$). The kinematics\nof the gas producing the $DIBs$ is evidently more quiescent than that\nproducing the $NaD$ absorption studied by HLSA. In the four starbursts\nwith broad and strongly blueshifted $NaD$ lines, the $DIBs$ are less\nDoppler-broadened and much less blueshifted ($v_{DIB}$ - $v_{sys}$\n$\\sim$ -100 km s$^{-1}$).\n\nIn the Milky Way, the $DIBs$ are known to trace a dusty atomic phase\nof the ISM, since their equivalent widths correlate strongly with\nthe $HI$ column density, the $NaI$ column density, and the reddening\nparameter $E(B-V)$ (Herbig 1995 and references therein). We show that\nthese starburst $DIBs$ obey the same trends with $N_{NaI}$ and\n$E(B-V)$ (e.g. $W_{6284} \\sim$ 1.2 $E(B-V)$ \\AA\\ at log$N_{NaI}\n\\sim$ 14 cm$^{-2}$). Thus, the abundance of the $DIB$ carrier(s) relative\nto $Na$ atoms and dust grains appears to be very similar in intense\nstarbursts and the diffuse ISM of our own Galaxy.\n\nThis seems surprising, given the thousand-fold greater energy density in \nphotons and cosmic rays in the ISM of an intense starburst\n(e.g. Colbert et al 1999; Suchkov, Allen, \\& Heckman 1993). However,\nthe gas pressures and densities in the starburst ISM are correspondingly\nlarger as well (e.g. Heckman, Armus, \\& Miley 1990). Thus, such\nkey dimensionless ratios as gas/photon density and\ngas-pressure/radiant-energy-density are similar in the ISM of starbursts\nand the disks of normal spiral galaxies (Wang, Heckman, \\& Lehnert\n1998). This apparent ``homology'' may help explain the strikingly\nsimilar $DIB$ properties.\n\nFinally, we point out that starbursts apparently produce strong $DIBs$\nwithout producing a detectable $\\lambda$2175 \\AA\\ dust feature\nin their UV spectra (Calzetti et al 1994). This underscores the\nquite distinct origin of the two types of features.\n\n\n\\acknowledgements\n\n\nWe thank David Neufeld, Ken Sembach, and Don York for useful conversations\nat various stages of this project. The partial support\nof this project by NASA grant NAGW-3138 is acknowledged.\n \n\\begin{thebibliography}{}\n\n\\bibitem[]{}\nArmus, L., Heckman, T., \\& Miley, G. 1989, ApJ, 347, 727\n\\bibitem[]{}\nBenvenuti, P., \\& Porceddu, I. 1989, A\\&A, 223, 329\n\\bibitem[]{}\nBruzual, A.G. \\& Charlot, S.1993, ApJ, 405, 538\n\\bibitem[]{}\nCalzetti, D., Kinney, A., \\& Storchi-Bergmann, T. 1994, ApJ, 429, 582\n\\bibitem[]{}\nChlewicki, G., van der Zwet, G., van Ijzendoorn, I., \\& Greenberg, M. 1986,\nApJ, 305, 455\n\\bibitem[]{}\nColbert, J, Malkan, M.,\n Clegg, P., Cox, P.,\n Fischer, J., Lord, S.,\n Luhman, M., Satyapal, S.,\n Smith, H., Spinoglio, L.,\n Stacey, G., \\& Unger, S. 1999, ApJ, 511, 721\n\\bibitem[]{}\ndi Serego Alighieri, S., \\& Ponz, J. 1987, in `ESO Workshop on the SN1987A',\ned. I.J. Danziger, ESO Conf. Workshop Proc. No. 26, Garching Bei Munchen: ESO,\np. 545 \n\\bibitem[]{}\nGallagher, J. \\& Smith, L. 1999, MNRAS, 304, 540\n\\bibitem[]{}\nHamann, F., Barlow, T., Junkkarinen, V., \\& Burbidge, E.M. 1997, ApJ, 478, 80\n\\bibitem[]{}\nHeckman, T. M., Armus, L., \\& Miley, G. K. 1990, ApJS, 74, 833\n\\bibitem[]{}\nHeckman, T., Lehnert, M., Strickland, D., \\& Armus, L. 2000 (HLSA),\nsubmitted to ApJ\n\\bibitem[]{}\nHerbig, G. 1993, ApJ, 407, 142\n\\bibitem[]{}\nHerbig, G. 1995, ARA\\&A, 33, 19\n\\bibitem[]{}\nKennicutt, R. 1998, ApJ, 498, 541\n\\bibitem[]{}\nLehnert, M.., \\& Heckman, T. 1995, ApJS, 97, 89\n\\bibitem[]{}\nLehnert, M.., \\& Heckman, T. 1996, ApJ, 472, 546\n\\bibitem[]{}\nLeitherer, C., Schaerer, D., Goldader, J., Gonzalez-Delgado, R.,\nRobert, C., Kune, D., De Mello, D., Devost, D., \\& Heckman, T. 1999, ApJS,\n123, 3\n\\bibitem[]{}\nMerrill, P. 1934, PASP, 46, 206\n\\bibitem[]{}\nMeurer, G., Heckman, T., Leitherer, C., Lowenthal, J.,\n\\& Lehnert, M. 1997, AJ, 114, 54\n\\bibitem[]{}\nMorgan, D. 1987, QJRAS, 28, 328\n\\bibitem[]{}\nSalama, F., Galazutdinov, G. A.,\n Krelstrokowski, J., Allamandola, L. J.,\n\\& Musaev, F. A. 1999, ApJ, 526, 265\n\\bibitem[]{}\nSonnentrucker, P., Cami, J.,\n Ehrenfreund, P., \\& Foing, B. H. 1997, A\\&A, 327, 1215\n\\bibitem[]{}\nSpitzer, L. 1968, ``Diffuse Matter in Space'', (Interscience:\nNew York)\n\\bibitem[]{}\nSuchkov, A., Allen, R., \\& Heckman, T. 1993, ApJ, 413, 542\n\\bibitem[]{}\nWang, J., Heckman, T., \\& Lehnert, M. 1998, ApJ, 509, 93\n\n\\end{thebibliography}\n\n% table1 = sample properties\n\\include{tab1}\n\nNote. Col. (2) The equivalent width of the $\\lambda$6283.9 $DIB$\nin m\\AA.\nCol. (3) The equivalent width of the $\\lambda$5780.5 $DIB$\nin m\\AA. The uncertainty is due primarily\nto the accuracy with which contamination by the stellar photospheric\nCrI+CuI$\\lambda$5782 can be removed. We estimate this leads to an uncertainty\nof $\\pm$50m\\AA. The detection of this $DIB$ is therefore only tentative\nin NGC1614, NGC1808, and NGC3256 (indicated by a colon).\nCol. (4) The angular size (in arcsec) over which the $\\lambda$6283.9 $DIB$\nis detectable (the $\\lambda$5780.5 $DIB$ was used in NGC6240).\nCol. (5) The corresponding physical size (in kpc), for our adopted\n$H_0$ = 70 km s$^{-1}$ Mpc$^{-1}$.\nCol. (6) The estimated color excess along the line-of-sight to the\nstellar continuum, based on the observed continuum color and a model\nstarburst spectral energy distribution (Leitherer et al 1999; see HLSA\nfor details).\nCol. (7) The logarithm of the estimated column density of $NaI$ atoms\n(cm$^{-2}$). These were derived using the standard doublet ratio technique\n(Spitzer 1968) and its variant in Hammann et al (1997). See HLSA for\ndetails. Based on an intercomparison of the values obtained by different\ntechniques, we estimate the uncertainty to be $\\pm$0.2 dex.\n\n\n% table 2 = all detected DIBs\n\\include{tab2}\n\n% table 3 = kinematics\n\\include{tab3}\n\nNote. Col. (2) The Doppler broadening (full-width-at-half maximum) in\nkm s$^{-1}$ for the $\\lambda$6283.9 $DIB$ (the $\\lambda$5780.5 $DIB$ was used in\nNGC6240). These widths have been corrected for the intrinsic width\nof the DIB feature (see text) and for the instrumental resolution\nof the spectrograph (see HLSA). The raw, measured line widths\nand their associated uncertainties (in \\AA) are given in parantheses.\nCol. (3) The full-width-at-half-maximum in km s$^{-1}$ of the members of the\n$NaI\\lambda\\lambda$5890,5896 doublet ($NaD$). Uncertainties are $\\pm$20 km\ns$^{-1}$. Taken from HLSA.\nCol. (4) The heliocentric galaxy systemic velocity.\nApproximate uncertainties range\nfrom $\\pm$10 km s$^{-1}$ for NGC1808, NGC2146, and M82 to\n$\\pm$50 km s$^{-1}$ for NGC1614 and NGC3256, to $\\pm$100 km s$^{-1}$\nfor NGC6240 and IRAS10565+2448.\nSee HLSA and references therein.\nCol. (5) The heliocentric velocity of the $\\lambda$6283.9 $DIB$\n(the $\\lambda$5780.5 $DIB$ was used in NGC6240). The measurement\nuncertainties are $\\pm$30 km s$^{-1}$ for NGC2146 and M82,\n$\\pm$50 km s$^{-1}$ for NGC1614, NGC1808, and NGC3256, and\n$\\pm$80 km s$^{-1}$ for IRAS10565+2448 and NGC6240. These do not\ninclude any uncertainties in the true value of the rest wavelength for\nthe $DIB$.\nCol. (6) The heliocentric velocity of the $NaD$ doublet taken\nfrom HLSA. Uncertainties are $\\pm$20 km s$^{-1}$.\n\n\\newpage\n\n\\figcaption []\n{The spectrum of the nucleus of M82 before (top) and after (bottom)\nthe subtraction of the scaled spectrum of K giant star. This\nsubtraction removes the stellar photospheric absorption features\nwhose presence complicates the detection and measurement of\nthe $DIBs$ in our sample of starbursts. See text for details.}\n\n\\figcaption []\n{Spectra of the $DIB$ at $\\lambda_{rest}$ =\n6283.9 \\AA\\ in six starburst nuclei and of the $DIB$ at $\\lambda_{rest}$ =\n5780.5 \\AA\\ in NGC6240 (denoted by tick marks). These spectra have been\nnormalised to unit intensity, cleaned of photospheric absorption-lines\ndue to cool stars by subtraction of a suitably-normalized spectrum\nof a K giant star, and then diluted by the addition of featureless\ncontinuum equal in strength to the subtracted starlight. See Figure 1 for\nan example of the effect of K-star subtraction on the spectrum of M82.\nThe absorption feature at $\\lambda_{observed} \\sim$ \n6278 \\AA\\ in NGC1808, NGC2146, and M82 is telluric O$_2$. See\ntext for details.}\n\n\\figcaption []\n{Spectra of the nuclei of NGC2146 and M82 showing other\n$DIBs$. The spectra have been processed as\ndescribed in Figure 2 (see text).\nThe detected features are indicated by\nfive tick marks denoting the $DIBs$ at $\\lambda_{rest}$ = 5780.5 \\AA\\,\n5797.0 \\AA, 6010.1 \\AA, 6203.1 \\AA, and 6283.9 \\AA.\nThe unmarked absorption feature at $\\lambda_{observed} \\sim$ \n6278 \\AA\\ is telluric O$_2$. \nSee Table 2.}\n\n\\figcaption []\n{The equivalent width of the Diffuse Interstellar Band at\n$\\lambda_{rest}$ =6283.9 \\AA\\ (in m\\AA) is plotted {\\it vs.} the\ncolor excess $E(B-V)$ for a large sample of Galactic stars\n(hollow points) and our starburst nuclei (larger solid points).\nThe Galactic data come from Benvenuti \\& Porceddu (1989),\nChlewicki et al (1986), and Herbig (1993). Since Herbig gave\nonly the equivalent widths for the weaker $DIB$ at $\\lambda$5780.5 \\AA\\,\nwe have converted these values to $W_{6284}$ assuming the mean\nratio measured by Benvenuti \\& Porceddu (1989) and \nChlewicki et al (1986): $<W_{6284}/W_{5780}>$ = 2.2. We have\ndone likewise for NGC6240 in which the $\\lambda$ 6283.9\nfeature is buried under a strong and broad [OI]$\\lambda$6300\nnebular emission-line (see Figure 3). Note that the starburst\nnuclei lie along the relationship defined by the Galactic sight-lines.}\n\n\\figcaption []\n{The logarithm of the equivalent width of the Diffuse Interstellar Band at\n$\\lambda_{rest}$ =6283.9 \\AA\\ (in m\\AA) is plotted {\\it vs.} the\nlogarithm of the $NaI$ column density or a large sample of Galactic stars\n(hollow points) and our starburst nuclei (larger solid points).\nThe Galactic data come from Herbig (1993). Since Herbig gave\nonly the equivalent widths for the weaker $DIB$ at $\\lambda$5780.5 \\AA\\,\nwe have converted these values to $W_{6284}$ assuming the mean\nratio measured by Benvenuti \\& Porceddu (1989) and \nChlewicki et al (1986): $<W_{6284}/W_{5780}>$ = 2.2. We have\ndone likewise for NGC6240 in which the $\\lambda$ 6283.9\nfeature is buried under a strong and broad [OI]$\\lambda$6300\nnebular emission-line (see Figure 3). Note that the starburst\nnuclei lie at the upper end of the \nrelationship defined by the Galactic sight-lines.}\n\n\\end{document}\n"
},
{
"name": "tab1.tex",
"string": "\\begin{deluxetable}{lcccccc}\n\\tablecolumns{7}\n\\tablewidth{0pt}\n\\tablenum{1}\n\\tablecaption{Basic Properties}\n\\tablehead{\n\\colhead{Galaxy}&\\colhead{$W_{6284}$}&\\colhead{$W_{5780}$}&\n\\colhead{Ang. Size}&\\colhead{Size}&\\colhead{$E(B-V)$}&\\colhead{log$N_{NaI}$} \\\\\n\\colhead{(1)}&\\colhead{(2)}&\n\\colhead{(3)}&\\colhead{(4)}&\n\\colhead{(5)}&\\colhead{(6)}&\n\\colhead{(7)}}\n\\startdata\nNGC1614 & 940$\\pm$40 & 100: & 11 & 3.5 & 0.9 & 14.1 \\nl\nNGC1808 & 550$\\pm$40 & 140: & 17 & 1.2 & 0.9 & 14.3 \\nl\nNGC2146 & 940$\\pm$30 & 360 & 28 & 1.8 & 0.9 & 13.8 \\nl\nM82 & 880$\\pm$30 & 240 & 55 & 0.9 & 1.0 & 13.9 \\nl\nNGC3256 & 370$\\pm$40 & 100: & 18 & 3.0 & 0.6 & 13.8 \\nl\nIRAS10565+2448 & 530$\\pm$90 & ... & 5 & 4.5 & 0.7 & 14.0 \\nl\nNGC6240 & ... & 640$\\pm$70 & 12 & 6.0 & 1.2 & 13.9 \\nl\n\\enddata\n\\end{deluxetable} \n"
},
{
"name": "tab2.tex",
"string": "\\begin{deluxetable}{lccccccc}\n\\tablecolumns{8}\n\\tablewidth{0pt}\n\\tablenum{2}\n\\tablecaption{Weaker DIBs}\n\\tablehead{\n\\colhead{Galaxy}&\\colhead{$W_{5780}$}&\\colhead{$W_{5797}$}&\n\\colhead{$W_{6010}$}&\\colhead{$W_{6203}$}&\\colhead{$W_{6283}$}&\n\\colhead{$W_{6613}$}&\\colhead{$\\Delta$}\\\\\n\\colhead{(1)}&\\colhead{(2)}&\n\\colhead{(3)}&\\colhead{(4)}&\n\\colhead{(5)}&\\colhead{(6)}&\n\\colhead{(7)}&\\colhead{(8)}}\n\\startdata\nNGC2146 & 360 & 100 & 130 & 160 & 910 & 120 & 30 \\nl\nM82 & 240 & 70 & 110 & 120 & 880 & 120 & 30 \\nl\n\\enddata\n\\tablecomments{\nSee Figure 2. All equivalent widths are given in m\\AA.\nCol. (8) Uncertainties in m\\AA.}\n\\end{deluxetable}\n"
},
{
"name": "tab3.tex",
"string": "\\begin{deluxetable}{lccccc}\n\\tablecolumns{6}\n\\tablewidth{0pt}\n\\tablenum{3}\n\\tablecaption{Kinematic Properties}\n\\tablehead{\n\\colhead{Galaxy}&\\colhead{$\\Delta$$v_{DIB}$}&\\colhead{$\\Delta$$v_{NaD}$}&\n\\colhead{$v_{sys}$}&\\colhead{$v_{DIB}$}&\\colhead{$v_{NaD}$} \\\\\n\\colhead{(1)}&\\colhead{(2)}&\n\\colhead{(3)}&\\colhead{(4)}&\n\\colhead{(5)}&\\colhead{(6)}}\n\\startdata\nNGC1614 & 300(7.7$\\pm$0.6) & 420 & 4760 & 4657 & 4636 \\nl\nNGC1808 & 240(6.7$\\pm$0.6) & 300 & 1001 & 1040 & 1013 \\nl\nNGC2146 & 160(5.3$\\pm$0.4) & 140 & 916 & 932 & 930 \\nl\nM82 & 160(5.3$\\pm$0.4) & 170 & 214 & 268 & 204 \\nl\nNGC3256 & 220(6.4$\\pm$0.6) & 550 & 2801 & 2755 & 2489 \\nl\nIRAS10565+2448 & 370(9.3$\\pm$1.0) & 500 & 12923 & 12840 & 12717 \\nl\nNGC6240 & 430(8.9$\\pm$1.0) & 600 & 7339 & 7232 & 7049 \\nl\n\\enddata\n\\end{deluxetable} \n"
}
] |
[
{
"name": "astro-ph0002399.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[]{}\nArmus, L., Heckman, T., \\& Miley, G. 1989, ApJ, 347, 727\n\\bibitem[]{}\nBenvenuti, P., \\& Porceddu, I. 1989, A\\&A, 223, 329\n\\bibitem[]{}\nBruzual, A.G. \\& Charlot, S.1993, ApJ, 405, 538\n\\bibitem[]{}\nCalzetti, D., Kinney, A., \\& Storchi-Bergmann, T. 1994, ApJ, 429, 582\n\\bibitem[]{}\nChlewicki, G., van der Zwet, G., van Ijzendoorn, I., \\& Greenberg, M. 1986,\nApJ, 305, 455\n\\bibitem[]{}\nColbert, J, Malkan, M.,\n Clegg, P., Cox, P.,\n Fischer, J., Lord, S.,\n Luhman, M., Satyapal, S.,\n Smith, H., Spinoglio, L.,\n Stacey, G., \\& Unger, S. 1999, ApJ, 511, 721\n\\bibitem[]{}\ndi Serego Alighieri, S., \\& Ponz, J. 1987, in `ESO Workshop on the SN1987A',\ned. I.J. Danziger, ESO Conf. Workshop Proc. No. 26, Garching Bei Munchen: ESO,\np. 545 \n\\bibitem[]{}\nGallagher, J. \\& Smith, L. 1999, MNRAS, 304, 540\n\\bibitem[]{}\nHamann, F., Barlow, T., Junkkarinen, V., \\& Burbidge, E.M. 1997, ApJ, 478, 80\n\\bibitem[]{}\nHeckman, T. M., Armus, L., \\& Miley, G. K. 1990, ApJS, 74, 833\n\\bibitem[]{}\nHeckman, T., Lehnert, M., Strickland, D., \\& Armus, L. 2000 (HLSA),\nsubmitted to ApJ\n\\bibitem[]{}\nHerbig, G. 1993, ApJ, 407, 142\n\\bibitem[]{}\nHerbig, G. 1995, ARA\\&A, 33, 19\n\\bibitem[]{}\nKennicutt, R. 1998, ApJ, 498, 541\n\\bibitem[]{}\nLehnert, M.., \\& Heckman, T. 1995, ApJS, 97, 89\n\\bibitem[]{}\nLehnert, M.., \\& Heckman, T. 1996, ApJ, 472, 546\n\\bibitem[]{}\nLeitherer, C., Schaerer, D., Goldader, J., Gonzalez-Delgado, R.,\nRobert, C., Kune, D., De Mello, D., Devost, D., \\& Heckman, T. 1999, ApJS,\n123, 3\n\\bibitem[]{}\nMerrill, P. 1934, PASP, 46, 206\n\\bibitem[]{}\nMeurer, G., Heckman, T., Leitherer, C., Lowenthal, J.,\n\\& Lehnert, M. 1997, AJ, 114, 54\n\\bibitem[]{}\nMorgan, D. 1987, QJRAS, 28, 328\n\\bibitem[]{}\nSalama, F., Galazutdinov, G. A.,\n Krelstrokowski, J., Allamandola, L. J.,\n\\& Musaev, F. A. 1999, ApJ, 526, 265\n\\bibitem[]{}\nSonnentrucker, P., Cami, J.,\n Ehrenfreund, P., \\& Foing, B. H. 1997, A\\&A, 327, 1215\n\\bibitem[]{}\nSpitzer, L. 1968, ``Diffuse Matter in Space'', (Interscience:\nNew York)\n\\bibitem[]{}\nSuchkov, A., Allen, R., \\& Heckman, T. 1993, ApJ, 413, 542\n\\bibitem[]{}\nWang, J., Heckman, T., \\& Lehnert, M. 1998, ApJ, 509, 93\n\n\\end{thebibliography}"
}
] |
astro-ph0002400
|
Cosmic Equation of State, Quintessence and Decaying Dark Matter
|
[
{
"author": "Houri Ziaeepour"
}
] |
If CDM particles decay and their lifetime is comparable to the age of the Universe, they can modify its equation of state. By comparing the results of numerical simulations with high redshift SN-Ia observations, we show that this hypothesis is consistent with present data. Fitting the simplest quintessence models with constant $w_q$ to the data leads to $w_q \lesssim -1$. We show that a universe with a cosmological constant or quintessence matter with $w_q \sim -1$ and a decaying Dark Matter has an effective $w_q < -1$ and fits SN data better than stable CDM or quintessence models with $w_q > -1$.
|
[
{
"name": "ustate.tex",
"string": "%\\documentclass[11pt]{article}\n\\documentclass[referee]{aa}\n%\\documentclass[final]{aa}\n\\usepackage{epsfig}\n\\usepackage{amssymb}\n\\pagestyle{plain}\n\n%------------------------------------------------------------------------\n%--- style parameters for page. defined LaTeX book p 163\n\\oddsidemargin -1cm % origine: 1in\n\\evensidemargin -1cm % origine: 1in\n\\marginparwidth 0cm\n\\marginparsep 0cm\n\\topmargin -1cm\n\\headheight 0cm\n\\headsep 0cm\n\\textheight 26cm\n\\textwidth 17cm\n\\topskip 2cm\n\n%--- style parameters for paragraph. defined in LaTeX book p 155\n\\parindent 0pt\n\\parskip 1.3ex\n\n%=========================================================================\n\\def\\etal{{\\it et al.}}\n% A useful Journal macro\n\\def\\Journal#1#2#3#4{{#1} {\\bf #2}, #3 (#4)}\n\n\\def\\AA{\\em A.\\& A.}\n\\def\\APJ{\\em ApJ.}\n\\def\\AST{\\em Astron. J.}\n\\def\\APP{\\em Astropart. Phys.}\n\\def\\CPC{\\em Comp. Phys. Com.}\n\\def\\EJP{{\\em Europ. J. Phys.} C}\n\\def\\GEN{}\n\\def\\IMP{\\em Int. J. Mod. Phys.}\n\\def\\IMP{\\em Int. J. Mod. Phys.}\n\\def\\JHE{\\em J. High Ener. Phys.}\n\\def\\JPG{\\em J. Phys. G: Nucl. Part. Phys.}\n\\def\\JPg{\\em J. Phys. G}\n\\def\\JPL{\\em JETPhys. Lett.}\n\\def\\JPT{\\em Sov. Phys. JETP}\n\\def\\MPA{{\\em Mod. Phys.} A}\n\\def\\MRA{\\em MNRAS}\n\\def\\NAT{\\em Nature}\n\\def\\NCA{\\em Nuovo Cimento}\n\\def\\NPB{{\\em Nucl. Phys.} B}\n\\def\\PLB{{\\em Phys. Lett.} B}\n\\def\\PRL{\\em Phys. Rev. Lett.}\n\\def\\PRD{{\\em Phys. Rev.} D}\n\\def\\PRV{\\em Phys. Rev.}\n\\def\\PRE{\\em Phys. Rep.}\n\\def\\SCI{\\em Science}\n\\def\\SSR{\\em Space Sci. Rev.}\n\\def\\ZPC{{\\em Z. Phys.} C}\n\n% Some other macros used in the sample text\n\\def\\st{\\scriptstyle}\n\\def\\sst{\\scriptscriptstyle}\n\\def\\epp{\\epsilon^{\\prime}}\n\\def\\vep{\\varepsilon}\n\\def\\ra{\\rightarrow}\n\\def\\ppg{\\pi^+\\pi^-\\gamma}\n\\def\\vp{{\\bf p}}\n\\def\\ko{K^0}\n\\def\\kb{\\bar{K^0}}\n\\def\\al{\\alpha}\n\\def\\ab{\\bar{\\alpha}}\n\\def\\be{\\begin{equation}}\n\\def\\ee{\\end{equation}}\n\\def\\bea{\\begin{eqnarray}}\n\\def\\eea{\\end{eqnarray}}\n\\def\\CPbar{\\hbox{{\\rm CP}\\hskip-1.80em{/}}}%temp replacemt due to no font\n\n%\\renewcommand{\\thefootnote}{\\fnsymbol{footnot}}\n\n\\begin{document}\n \\thesaurus{12 % A&A Section 6: Form. struct. and evolut. of stars\n (12.04.1; % Cosmogony,\n 12.03.04;\n 02.05.1)} % Stars: structure of.\n\n\\title{Cosmic Equation of State, Quintessence and Decaying Dark Matter}\n\\author{Houri Ziaeepour}\n\\institute{ESO, Schwarzchildstrasse 2, 85748, Garching b. M\\\"{u}nchen, Germany\n\\footnote{Present Address: 03, impasse de la Grande Boucherie,\nF-67000, Strasbourg, France.}}\n\n\\date{Received ......; accepted ......}\n\\maketitle\n\n%\\begin{center}\n%\\Large \\bf {Cosmic Equation of State, Quintessence and Decaying Dark Matter\\\\}\n%\\end{center} \n\n%\\begin{center}\n%{\\it Houri Ziaeepour\\\\\n%{ESO, Schwarzchildstrasse 2, 85748, Garching b. M\\\"{u}nchen, Germany\n%\\footnote{Present Address: 03, impasse de la Grande Boucherie,\n%F-67000, Strasbourg, France.}\\\\\n%Email: {\\tt houri@eso.org}}}\n%\\end{center}\n\n\\begin {abstract}\nIf CDM particles decay and their lifetime is comparable to the age of the \nUniverse, they can modify its equation of state. By comparing the results \nof numerical simulations with high redshift SN-Ia observations, we show that \nthis hypothesis is consistent with present data. Fitting the simplest \nquintessence models with constant $w_q$ to the data leads to \n$w_q \\lesssim -1$. We show that a universe \nwith a cosmological constant or quintessence matter with $w_q \\sim -1$ and \na decaying Dark Matter has an effective $w_q < -1$ and fits SN data better \nthan stable CDM or quintessence models with $w_q > -1$.\n\\end {abstract}\n\nThere are at least two motivations for the existence of a Decaying Dark Matter \n(DDM). If R-parity in SUSY models is not strictly conserved, the LSP which \nis one of the best candidates of DM can decay to Standard Model \nparticles Banks \\etal~\\cite{banks}. Violation of this symmetry is one of the \nmany ways \nfor providing neutrinos with very small mass and large mixing angle.\\\\\nAnother motivation is the search for sources of Ultra High Energy Cosmic \nRays (UHECRs)(see Yoshida \\& Dai~\\cite {crrev} for review of their \ndetection and Blandford~\\cite{stdsrc} and Bhattacharjee \\& Sigl~\\cite{revorg} \nrespectively for conventional and exotic sources). In this case, DDM \nmust be composed of ultra heavy particles with $M_{DM} \\sim 10^{22}-10^{25} \neV$. In a recent work Ziaeepour~\\cite{wimpzilla} we have shown that the \nlifetime of \nUHDM (Ultra Heavy Dark Matter) can be relatively short, i.e. $\\tau \\sim 10 - \n100 \\tau_0$ where \n$\\tau_0$ is the age of the Universe. Here we compare the prediction of this \nsimulation for the Cosmic Equation of State (CES) with the observation of high \nredshift SN-Ia.\\\\\nFor details of the simulation we refer the reader to \nZiaeepour~\\cite{wimpzilla}. In \nsummary, the decay of UHDM is assumed to be like the hadronization of two \ngluon jets. The decay remnants interact with cosmic backgrounds, notably CMB, \nIR, and relic neutrinos, lose their energy and leave a high energy \nbackground of stable species e.i. $e^\\pm$, $p^\\pm$, $\\nu$, $\\bar \\nu$, and \n$\\gamma$. We solve the Einstein-Boltzmann equations to determine the energy \nspectrum of remnants. Results of Ziaeepour~\\cite{wimpzilla} show that \nin a homogeneous universe, even the short lifetime mentioned above can not \nexplain the observed flux of UHECRs. The clumping of DM in the Galactic Halo \nhowever limits the possible age/contribution. These parameters are degenerate \nand we can not separate them. For simplicity, we assume that CDM is entirely \ncomposed of DDM and limit the lifetime. Fig. \\ref{fig:t00} shows the \nevolution of energy density $T^{00}(z) \\equiv \\rho (z)$ at low and \nmedium redshifts in a flat universe with and without a cosmological constant. \nAs expected, the effect of DDM is more significant in a matter dominated \nuniverse i.e. when $\\Lambda = 0$. For a given cosmology, the lifetime of \nDDM is the only parameter that significantly affects the evolution of $\\rho$. \nFor the same lifetime, the difference between $M_{DM} = 10^{12} eV$ and \n$M_{DM} = 10^{24} eV$ cases is only $\\approx 0.4\\%$. Consequently, in the \nfollowing we neglect the effect of the DM mass.\n\\begin{figure}[t]\n\\begin{center}\n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm}\n%\\vskip 2.5cm\n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm}\n\\psfig{figure=t00.eps,height=5cm}\n\\caption{Energy density of the Universe. Solid line $\\Omega_{\\Lambda}^{eq} = \\Omega_{\\Lambda} = 0.7$ and stable DM; dashed line the same cosmology with $\\tau = 5 \\tau_0$; dash dot line $\\Lambda = 0$ and stable DM; dot line $\\Lambda = 0$ and $\\tau = 5 \\tau_0$. Dependence on the mass of DM is negligible.\\label{fig:t00}}\n\\end{center}\n\\end{figure}\nFor the same cosmological model and initial conditions, if DM decays, matter \ndensity at $z = 0$ is smaller than when it is stable because decay remnants \nremain highly relativistic even after losing part of their energy. Their \ndensity dilutes more rapidly with the expansion of the Universe than CDM and \ndecreases the total matter density. Consequently, relative \ncontribution of cosmological constant increases. This process mimics a \nquintessence model i.e. a changing cosmological constant Peebles \\& \nRatra~\\cite{quinorg}, Zlatev, Wang \\& Steinhardt~\\cite{tracker} (see Sahni \n\\& Starobinsky~\\cite{quinrev} for recent review). However, the equation of \nstate of this model has an exponent $w_q < -1$ which is in contrast with the \nprediction of scalar field models with positive potential (see appendix for \nan approximative analytical proof).\\\\\nThe most direct way for determination of cosmological densities and equation \nof state is the observation of SN-Ia's as standard candles. It is \nbased on the measurement of apparent magnitude of the maximum of SNs \nlightcurve Perlmutter \\etal~\\cite{snmeasur}~\\cite{snproj}, Riess A. \\etal\n~\\cite{snmeasur1}. After correction for various \nobservational and intrinsic variations like K-correction, width-luminosity \nrelation, reddening and Galactic extinction, it is assumed that their \nmagnitude \nis universal. Therefore the difference in apparent magnitude is only related \nto difference in distance and consequently to cosmological parameters.\\\\\nThe apparent magnitude of an object $m (z)$ is related to its absolute \nmagnitude $M$:\n\\be\nm (z) = M + 25 + 5 \\log D_L\n\\ee\nwhere $D_L$ is the Hubble-constant-free luminosity distance:\n\\be\nD_L = \\frac {(z + 1)}{\\sqrt{|\\Omega_R|}} {\\mathcal S} \\biggl (\\sqrt{|\\Omega_R|} \n\\int_{0}^{z} \\frac {dz'}{E (z')}\\biggr ) \\label {Dl}\\\\\n\\ee\n\\be\n{\\mathcal S}(x) = \n%\\begin {cases}\n\\begin {tabular}{ll}\n$\\sinh (x)$ & $\\Omega_R > 0$,\\\\ \n$x$ & $\\Omega_R = 0$,\\\\\n$\\sin (x)$ & $\\Omega_R < 0$.\n\\end {tabular}\n%\\end {cases}\n\\ee\n\\bea\nE (z) & = & \\frac {H (z)}{H_0}. \\label {ez}\\\\\nH^2 (z) & = & \\frac {8\\pi G}{3} T^{00} (z) + \\frac {\\Lambda}{3}. \\label {hz}\n\\eea\nHere we only consider flat cosmologies.\\\\\nWe use the published results of the Supernova Cosmology Project, Perlmutter \n\\etal~\\cite{snproj} for high redshift and Calan-Tololo sample, Hamuy \n\\etal~\\cite{tololo} for low redshift \nsupernovas and compare them with our simulation. From these data \nsets we eliminate 4 SNs with largest residue and stretch as explained in \nPerlmutter \\etal~\\cite{snproj} (i.e. we use objects used in their fit B).\\\\\nMinimum-$\\chi^2$ fit method is applied to the data to extract the parameters \nof the cosmological models. In all fits described in this letter we consider \n$M$ as a free parameter and minimize the $\\chi^2$ with respect to it. Its \nvariation in our fits stays in the acceptable range of $\\pm 0.17$, \nPerlmutter \\etal~\\cite{snmeasur}.\\\\\nWe have restricted our calculation to a range of \nparameters close to the best fit of Perlmutter \\etal~\\cite{snproj} i.e. \n$2.38 \\times 10^{-11} \\leqslant \\rho_\\Lambda \\equiv \\frac {\\Lambda}{8\\pi G} \n\\leqslant 3.17 \\times 10^{-11}eV^4$. The reason why we use $\\rho_\\Lambda$ \nrather than $\\Omega_\\Lambda$ is that the latter quantity depends on the \nequation of state and the lifetime of the Dark Matter. The range of \n$\\rho_\\Lambda$ given here is equivalent to $0.6\\leqslant \\Omega_{\\Lambda}^{eq} \n\\leqslant 0.8$ for a stable CDM and $H_0 = 70$ $km$ $Mpc^{-1} \\sec^{-1}$ (we use \n$\\Omega_{\\Lambda}^{eq}$ notation to distinguish between this quantity and real \n$\\Omega_\\Lambda$).\\\\\nFig.\\ref{fig:bestres} shows the residues of the best fit to DDM simulation. \nAlthough up to \n$1$-$\\sigma$ uncertainty all models with stable or decaying DM with $5 \\tau_0 \n\\lesssim \\tau \\lesssim 50 \\tau_0$ and $0.68\\lesssim \\Omega_{\\Lambda}^{eq} \n\\lesssim 0.72$ are compatible with the data, a decaying DM with $\\tau \\sim 5 \n\\tau_0$ systematically fits the data better than stable DM with the same \n$\\Omega_{\\Lambda}^{eq}$. Models with $\\Lambda = 0$ are ruled \nout with more than $99\\%$ confidence level.\\\\\n\\begin{figure}[t]\n\\begin{center}\n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm}\n%\\vskip 2.5cm\n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm}\n\\psfig{figure=bestres.eps,width=10cm}\n\\caption{Best fit residues with $\\Omega_{\\Lambda}^{eq} = 0.7$, $\\tau = 5 \n\\tau_0$. It leads to $\\Omega_{\\Lambda} = 0.73$. The curves correspond to \nresidue for stable DM with $\\Omega_{\\Lambda}^{eq} = \\Omega_{\\Lambda} = 0.7$ \n(doted); $\\Lambda = 0$ and $\\tau = 5 \\tau_0$ (dashed); $\\Lambda = 0$, stable \nDM (dash-dot).\\label{fig:bestres}}\n\\end{center}\n\\end{figure}\nIn fitting the results of DM decay simulation to the data we have directly \nused the \nequation (\\ref{hz}) without defining any analytical form for the evolution of \n$T^{00}(z)$. It is not usually the way data is fitted to cosmological \nmodels Perlmutter \\etal~\\cite{snmeasur},~\\cite{snmeasur1}, Garnavich \n\\etal~\\cite{coseq}. Consequently, we have also fitted an analytical \nmodel to the simulation for $z < 1$ as it is the redshift range of the \navailable data. It includes a stable DM and a quintessence matter. Its \nevolution equation is:\n\\be\nH^2 (z) = \\frac {8\\pi G}{3} (T^{00}_{st} + \\Omega_q (z + 1)^{3 (w_q + 1)}). \\label {quineq}\n\\ee\nThe term $T^{00}_{st}$ is obtained from our simulation when DM is stable. \nIn addition to CDM, it includes a small contribution from hot components i.e \nCMB and relic neutrinos. For a given $\\Omega_{\\Lambda}^{eq}$ and \n$\\tau$, the quintessence term is fitted to $T^{00} - T^{00}_{st} + \n\\frac {\\Lambda}{8\\pi G}$.\n\\footnote{The exact equivalent model should have \nthe same form as (\\ref {quinanal}). However, it is easy to verify that in \nthis case, the minimization of $\\chi^2$ has a trivial solution with $w_q = \n-1$, $\\Omega_q = 0$. Only one equation remains for non-trivial solutions and \nit depends on both $w_q$ and $\\Omega_q$. Consequently, there are infinite \nnumber of solutions.\\\\\nThe model we have used here generates a very good equivalent model to DDM with \nless than $2\\%$ error (Because CDM and quintessence terms are not fitted \ntogether, $\\Omega$ is not exactly $1$).\\label {foot}}\nThe results of this fit are $\\Omega_q$ and $w_q$ \nwhich characterize an equivalent quintessence model for the corresponding \nDDM. The analytical model fits the simulation extremely good and the \nabsolute value of relative residues is less than $0.2\\%$. Results for models \nin the $1$-$\\sigma$ distance of the best fit is summarized in \nTable \\ref{tab:quineq}.\\\\ \n\\begin{table}[t]\n\\caption{Cosmological parameters from simulation of a decaying DM and \nparameters of the equivalent quintessence model. $H_0$ is in $km$ $Mpc^{-1}\n\\sec^{-1}$.\\label{tab:quineq}}\n\\vspace{0.2cm}\n\\begin{center}\n\\footnotesize\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n &\n\\multicolumn {3}{c|}{Stable DM} & \n\\multicolumn {3}{c|}{$\\tau = 50 \\tau_0$} & \n\\multicolumn {3}{c|}{$\\tau = 5 \\tau_0$} \\\\\n\\hline\n &\n\\raisebox{0pt}[13pt][7pt]{$\\Omega_{\\Lambda}^{eq} = 0.68$} &\n\\raisebox{0pt}[13pt][7pt]{$\\Omega_{\\Lambda}^{eq} = 0.7$} &\n\\raisebox{0pt}[13pt][7pt]{$\\Omega_{\\Lambda}^{eq} = 0.72$} &\n\\raisebox{0pt}[13pt][7pt]{$\\Omega_{\\Lambda}^{eq} = 0.68$} &\n\\raisebox{0pt}[13pt][7pt]{$\\Omega_{\\Lambda}^{eq} = 0.7$} &\n\\raisebox{0pt}[13pt][7pt]{$\\Omega_{\\Lambda}^{eq} = 0.72$} &\n\\raisebox{0pt}[13pt][7pt]{$\\Omega_{\\Lambda}^{eq} = 0.68$} &\n\\raisebox{0pt}[13pt][7pt]{$\\Omega_{\\Lambda}^{eq} = 0.7$} &\n\\raisebox{0pt}[13pt][7pt]{$\\Omega_{\\Lambda}^{eq} = 0.72$}\\\\\n\\hline\n\\raisebox{0pt}[12pt][6pt]{$H_0$} \n & \\raisebox{0pt}[12pt][6pt]{$69.953$}\n & \\raisebox{0pt}[12pt][6pt]{$69.951$} & \\raisebox{0pt}[12pt][6pt]{$69.949$}\n & \\raisebox{0pt}[12pt][6pt]{$69.779$} & \\raisebox{0pt}[12pt][6pt]{$69.789$}\n & \\raisebox{0pt}[12pt][6pt]{$69.801$} & \\raisebox{0pt}[12pt][6pt]{$68.301$}\n & \\raisebox{0pt}[12pt][6pt]{$68.415$} & \\raisebox{0pt}[12pt][6pt]{$68.550$}\\\\\n\\hline\n\\raisebox{0pt}[12pt][6pt]{$\\Omega_{\\Lambda}$}\n & \\raisebox{0pt}[12pt][6pt]{$0.681$}\n & \\raisebox{0pt}[12pt][6pt]{$0.701$} & \\raisebox{0pt}[12pt][6pt]{$0.721$}\n & \\raisebox{0pt}[12pt][6pt]{$0.684$} & \\raisebox{0pt}[12pt][6pt]{$0.704$}\n & \\raisebox{0pt}[12pt][6pt]{$0.724$} & \\raisebox{0pt}[12pt][6pt]{$0.714$}\n & \\raisebox{0pt}[12pt][6pt]{$0.733$} & \\raisebox{0pt}[12pt][6pt]{$0.751$}\\\\\n\\hline\n\\raisebox{0pt}[12pt][6pt]{$\\Omega_q$}\n & \\raisebox{0pt}[12pt][6pt]{-}\n & \\raisebox{0pt}[12pt][6pt]{-} & \\raisebox{0pt}[12pt][6pt]{-}\n & \\raisebox{0pt}[12pt][6pt]{$0.679$} & \\raisebox{0pt}[12pt][6pt]{$0.700$}\n & \\raisebox{0pt}[12pt][6pt]{$0.720$} & \\raisebox{0pt}[12pt][6pt]{$0.667$}\n & \\raisebox{0pt}[12pt][6pt]{$0.689$} & \\raisebox{0pt}[12pt][6pt]{$0.711$}\\\\\n\\hline\n\\raisebox{0pt}[12pt][6pt]{$w_q$}\n & \\raisebox{0pt}[12pt][6pt]{-}\n & \\raisebox{0pt}[12pt][6pt]{-} & \\raisebox{0pt}[12pt][6pt]{-}\n & \\raisebox{0pt}[12pt][6pt]{$-1.0066$} & \\raisebox{0pt}[12pt][6pt]{$-1.0060$}\n & \\raisebox{0pt}[12pt][6pt]{$-1.0055$} & \\raisebox{0pt}[12pt][6pt]{$-1.0732$}\n & \\raisebox{0pt}[12pt][6pt]{$-1.0658$} & \\raisebox{0pt}[12pt][6pt]{$-1.0590$}\\\\\n\\hline\n\\raisebox{0pt}[12pt][6pt]{$\\chi^2$}\n & \\raisebox{0pt}[12pt][6pt]{$62.36$}\n & \\raisebox{0pt}[12pt][6pt]{$62.23$} & \\raisebox{0pt}[12pt][6pt]{$62.21$}\n & \\raisebox{0pt}[12pt][6pt]{$62.34$} & \\raisebox{0pt}[12pt][6pt]{$62.22$}\n & \\raisebox{0pt}[12pt][6pt]{$62.21$} & \\raisebox{0pt}[12pt][6pt]{$62.22$}\n & \\raisebox{0pt}[12pt][6pt]{$62.15$} & \\raisebox{0pt}[12pt][6pt]{$62.20$}\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\nIn the next step, we fit an analytical model to the SN-Ia data. Its evolution \nequation is the following:\n\\be\nH^2 (z) = \\frac {8\\pi G}{3} ((1 - \\Omega_q) (z + 1)^3 + \n\\Omega_q (z + 1)^{3 (w_q + 1)}). \\label {quinanal}\n\\ee\nThe aim for this exercise is to compare DDM equivalent quintessence models \nwith the data.\\\\\nFig.\\ref{fig:quindata} shows the $\\chi^2$ of these fits as a function of \n$w_q$ for various values of $\\Omega_q$. The reason behind using $\\chi^2$ \nrather than confidence level is that it directly shows the goodness-of-fit. \nAs with available data all relevant models are compatible up to $1$-$\\sigma$, \nthe error analysis is less important than goodness-of-fit and its behavior in \nthe parameter-space.\\\\\nModels presented in Fig.\\ref{fig:quindata} have the same $\\Omega_q$ as \nequivalent quintessence models obtained \nfrom DDM and listed in Tab.\\ref{tab:quineq}. These latter models are shown \ntoo. In spite of statistical closeness of all fits, the systematic tendency \nof the minimum of $\\chi^2$ to $w_q < -1$ when $\\Omega_q < 0.75$ is evident. \nThe minimum of models with $\\Omega_q > 0.75$ has $w_q > -1$, but the fit is \nworse than former cases. Between DDM models, one with $\\Omega_q = 0.71$ is \nvery close to the best fit of (\\ref{quinanal}) models with the same \n$\\Omega_q$. \nRegarding errors however, all these models, except $\\Omega_q = 0.8$ are \n$1$-$\\sigma$ compatible with the data.\\\\\n\\begin{figure}[t]\n\\begin{center}\n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm}\n%\\vskip 2.5cm\n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm}\n\\psfig{figure=quindata.eps,width=12cm}\n\\caption{$\\chi^2$-fit of models defined in (\\ref{quinanal}) as a function of \n$w_q$ for $\\Omega_q = 0.67$ (dashed), $\\Omega_q = 0.69$ (dash-dot), \n$\\Omega_q = 0.71$ (solid) and $\\Omega_q = 0.8$ (dotted). The $\\chi^2$ of \nequivalent quintessence models to DDMs with $\\tau = 5 \\tau_0$ and same $\\Omega_q$ is also shown. Except $\\Omega_q = 0.8$ model, others are all the best fit \nto DDM. For $\\Omega_q = 0.8$, a stable DM fits the data better, but the fit is \npoorer than former models.\\label{fig:quindata}}\n\\end{center}\n\\end{figure}\nOne has to remark that $\\Omega_q$ and $w_q$ are not completely independent \n(see Footnote \\ref{foot}) and models with smaller $\\Omega_q$ and smaller \n$w_q$ has even smaller $\\chi^2$. In fact the best fit corresponds to \n$\\Omega_q = 0.5$, $w_q = -2.6$ with $\\chi^2 = 61.33$. The rejection of these \nmodels however is based on physical grounds. In fact, if the quintessence \nmatter is a \nscalar field, to make such a model, not only its potential must be negative, \nbut also its kinetic energy must be comparable to the absolute value of the \npotential and this is in contradiction with very slow variation of the field. \nIn addition, these models are unstable against perturbations. It is however \npossible to make models with $w_q < -1$, but they need unconventional kinetic \nterm Caldwell~\\cite {negqw}.\\\\ \nThese results are compatible with the analysis performed by Garnavich \n\\etal~\\cite {coseq}. However, based on null energy \ncondition Wald~\\cite {wald}, they only consider models with $w_q \\geqslant -1$. This \ncondition should be satisfied by non-interacting matter and by total \nenergy-momentum tensor. As our example of a decaying matter shows, a \ncomponent or an equivalent component of energy-momentum tensor can have \n$w_q < -1$ when interactions are present.\\\\\nIn conclusion, we have shown that a flat cosmological model including a \ndecaying dark matter with $\\tau \\sim 5 \\tau_0$ and a cosmological constant \nor a quintessence matter with $w_q \\sim -1$ at $z < 1$ and $\\Omega_q \\sim \n0.7$ fits the SN-Ia data better than models with a stable DM or $w_q > -1$.\\\\\nThe effect of a decaying dark matter on the Cosmic Equation of State (CES) \nis a distinctive signature that can hardly be mimicked by other phenomena, \ne.g. conventional sources of Cosmic Rays. It is an independent mean for \nverifying the hypothesis of a decaying UHDM. In fact if a decaying DM \naffects CES significantly, it must be very heavy. Our simulation of a decaying \nDM with $M \\sim 10^{12} eV$ and $\\tau = 5 \\tau_0$ leads to an \nover-production by a few orders of magnitude of $\\gamma$-ray background at \n$E \\sim 10^{9}-10^{11} eV$ with respect to EGRET observation Sreekumar \n\\etal~\\cite{egret}. \nConsequently, such a DM must have a lifetime much longer than $5 \\tau_0$. \nHowever, in this case it can not leave a significant effect on CES.\\\\\nThe only other alternative for making a \nquintessence term in CES with $w_q$ sightly smaller than $-1$, is a scalar \nfield with a negative potential. Nevertheless, as most of quintessence models \noriginate from SUSY, the potential should be strictly positive. Even if a \nnegative potential or unconventional models are not a prohibiting conditions, \nthey rule out a large number of candidates.\\\\\nPresent SN-Ia data is too scarce to distinguish with high precision between \nvarious models. However, our results are encouraging and give the hope that \nSN-Ia observations will help to better understand the nature of the Dark \nMatter in addition to cosmology of the Universe.\n\n{\\bf Appendix:} Here we use an approximative solution of (\\ref {hz}) to find \nan analytical expression for the equivalent quintessence model of a cosmology \nwith DDM and a cosmological constant. With a good precision the total density \nof such models can be written as the following:\n\\be\n\\frac {\\rho (z)}{{\\rho}_c} \\approx {\\Omega}_M (1 + z)^3 \\exp \n(\\frac {{\\tau}_0 - t}\n{\\tau}) + {\\Omega}_{Hot} (1 + z)^4 + {\\Omega}_M (1 + z)^4 \\biggl (1 - \n\\exp (\\frac {{\\tau}_0 - t}{\\tau}) \\biggr ) + {\\Omega}_{\\Lambda}. \\label {totdens}\n\\ee\nWe assume a flat cosmology i.e. ${\\Omega}_M + {\\Omega}_{\\Lambda} = 1$ (ignoring the hot part). \n${\\rho}_c$ is the present critical density. If DM is stable and we neglect the \ncontribution of HDM, the expansion factor $a (t)$ is:\n\\be\n\\frac {a (t)}{a ({\\tau}_0)} = \\biggl [ \\frac {(B \\exp (\\alpha (t - \n{\\tau}_0)) - 1)^2}{4AB \\exp (\\alpha (t - {\\tau}_0))}\\biggr ]^{\\frac {1}{3}} \n\\equiv \\frac {1}{1 + z}. \\label {at}\n\\ee\n\\bea\nA & \\equiv & \\frac {{\\Omega}_{\\Lambda}}{1 - {\\Omega}_{\\Lambda}}, \\\\\nB & \\equiv & \\frac {1 + \\sqrt {{\\Omega}_{\\Lambda}}}{1 - \n\\sqrt {{\\Omega}_{\\Lambda}}}, \\\\\n\\alpha & \\equiv & 3 H_0 \\sqrt {{\\Omega}_{\\Lambda}}.\n\\eea\nUsing (\\ref {at}) as an approximation for $\\frac {a (t)}{a ({\\tau}_0)}$ when \nDM slowly decays, (\\ref {totdens}) takes the following form:\n\\bea\n\\frac {\\rho (z)}{{\\rho}_c} & \\approx & {\\Omega}_M (1 + z)^3 C^{-\\frac {1}\n{\\alpha \\tau}} + {\\Omega}_{Hot} (1 + z)^4 + {\\Omega}_M (1 + z)^4 (1 - \nC^{-\\frac {1}{\\alpha \\tau}}) + {\\Omega}_{\\Lambda}. \\label {totdens1}\\\\\nC & \\equiv & \\frac {1}{B} \\biggl (1 + \\frac {4A}{(1 + z)^3} - \\sqrt {(1 + \\frac {4A}{(1 + z)^3})^2 - 1} \\biggr).\n\\eea\nFor a slowly decaying DDM, $\\alpha \\tau >> 1$ and (\\ref {totdens1}) becomes:\n\\bea\n\\frac {\\rho (z)}{{\\rho}_c} & \\approx & {\\Omega}_M (1 + z)^3 + {\\Omega}_{Hot} \n(1 + z)^4 + {\\Omega}_q (1 + z)^{3 {\\gamma}_q}, \\label {totdens2} \\\\\n{\\Omega}_q (1 + z)^{3 {\\gamma}_q} & \\equiv & {\\Omega}_{\\Lambda} (1 + \n\\frac {{\\Omega}_M}{\\alpha \\tau {\\Omega}_{\\Lambda}} z (1 + z)^3 \\ln C). \n\\label {qeqdef}\n\\eea\nEquation (\\ref {qeqdef}) is the definition of equivalent quintessence matter. \nAfter its linearization:\n\\be\nw_q \\equiv {\\gamma}_q - 1 \\approx \\frac {{\\Omega}_M (1 + 4 A)(1 - \\sqrt {2 A})}\n{3 \\alpha \\tau {\\Omega}_{\\Lambda} B} - 1.\n\\ee\nIt is easy to see that in this approximation $w_q < -1$ if ${\\Omega}_{\\Lambda} > \\frac {1}{3}$.\n\n\\begin{thebibliography}{}\n\\bibitem [1995]{banks} Banks T., Grossman Y., Nardi E. \\& Nir Y., hep-ph/9505248.\n\\bibitem [1998]{revorg} Bhattacharjee P. \\& Sigl G., astro-ph/9811011.\n\\bibitem [1999]{stdsrc} Blandford R. astro-ph/9906026.\n\\bibitem [1999]{negqw} Caldwell R.R., astro-ph/9908168, Chiba T., Okabe T. \\& Yamaguchi M., astro-ph/9912463.\n\\bibitem [1998]{coseq} Garnavich P., \\etal, astro-ph/9806396.\n\\bibitem [1996]{tololo} Hamuy M., \\etal, \\Journal {\\AST}{112}{2391}{1996}.\n\\bibitem [1988]{quinorg} Peebles P.J.E. \\& Ratra B., \\Journal {\\APJ}{325}{L17}{1988}, Ratra B. \\& Peebles P.J.E., \\Journal {\\PRD}{37}{3406}{1988}.\n\\bibitem [1997]{snmeasur} Perlmutter S. \\etal, \\Journal {\\APJ}{483}{565}{1997} \n\\bibitem [1999]{snproj} Perlmutter S. \\etal, \\Journal {\\APJ}{517}{565}{1999}.\n\\bibitem [1998]{snmeasur1} Riess A., \\etal \\Journal {\\AST}{116}{1009}{1998}.\n\\bibitem [1999]{quinrev} Sahni V. \\& Starobinsky A.A., astro-ph/9904398.\n\\bibitem [1998]{egret} Sreekumar P., \\etal, \\Journal {\\APJ}{494}{523}{1998}.\n\\bibitem [1984]{wald} Wald R.M., {\\it General Relativity}, University of Chicago Press, 1984.\n\\bibitem [1998]{crrev} Yoshida Sh. \\& Dai H., \\Journal {\\JPG}{24}{905}{1998}.\n\\bibitem [2000]{wimpzilla} Ziaeepour H., astro-ph/0001137, submitted.\n\\bibitem [1999]{tracker} Zlatev I., Wang L. \\& Steinhardt P.J., \\Journal {\\PRL}{82}{896}{1999}, Steinhardt P.J., Wang L. \\& Zlatev I., \\Journal {\\PRD}{59}{123504}{1999}.\n\n\\end{thebibliography}\n\\end {document}\n"
}
] |
[
{
"name": "astro-ph0002400.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem [1995]{banks} Banks T., Grossman Y., Nardi E. \\& Nir Y., hep-ph/9505248.\n\\bibitem [1998]{revorg} Bhattacharjee P. \\& Sigl G., astro-ph/9811011.\n\\bibitem [1999]{stdsrc} Blandford R. astro-ph/9906026.\n\\bibitem [1999]{negqw} Caldwell R.R., astro-ph/9908168, Chiba T., Okabe T. \\& Yamaguchi M., astro-ph/9912463.\n\\bibitem [1998]{coseq} Garnavich P., \\etal, astro-ph/9806396.\n\\bibitem [1996]{tololo} Hamuy M., \\etal, \\Journal {\\AST}{112}{2391}{1996}.\n\\bibitem [1988]{quinorg} Peebles P.J.E. \\& Ratra B., \\Journal {\\APJ}{325}{L17}{1988}, Ratra B. \\& Peebles P.J.E., \\Journal {\\PRD}{37}{3406}{1988}.\n\\bibitem [1997]{snmeasur} Perlmutter S. \\etal, \\Journal {\\APJ}{483}{565}{1997} \n\\bibitem [1999]{snproj} Perlmutter S. \\etal, \\Journal {\\APJ}{517}{565}{1999}.\n\\bibitem [1998]{snmeasur1} Riess A., \\etal \\Journal {\\AST}{116}{1009}{1998}.\n\\bibitem [1999]{quinrev} Sahni V. \\& Starobinsky A.A., astro-ph/9904398.\n\\bibitem [1998]{egret} Sreekumar P., \\etal, \\Journal {\\APJ}{494}{523}{1998}.\n\\bibitem [1984]{wald} Wald R.M., {\\it General Relativity}, University of Chicago Press, 1984.\n\\bibitem [1998]{crrev} Yoshida Sh. \\& Dai H., \\Journal {\\JPG}{24}{905}{1998}.\n\\bibitem [2000]{wimpzilla} Ziaeepour H., astro-ph/0001137, submitted.\n\\bibitem [1999]{tracker} Zlatev I., Wang L. \\& Steinhardt P.J., \\Journal {\\PRL}{82}{896}{1999}, Steinhardt P.J., Wang L. \\& Zlatev I., \\Journal {\\PRD}{59}{123504}{1999}.\n\n\\end{thebibliography}"
}
] |
astro-ph0002401
|
Gravitational Lenses With More Than Four Images: \\ I. Classification of Caustics
|
[
{
"author": "Charles R. Keeton$^{1}$"
},
{
"author": "Shude Mao$^{2,3}$"
},
{
"author": "and Hans J. Witt$^{4}$"
}
] |
We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextuple and octuple lenses are likely to be rare because they require special lens configurations, but a full calculation of the likelihood will have to include both the existence of lenses with multiple lens galaxies and the strong magnification bias that affects sextuple and octuple lenses. At optical wavelengths these lenses would probably appear as partial or complete Einstein rings, but at radio wavelengths the individual images could probably be resolved.
|
[
{
"name": "paper.tex",
"string": "\n\\documentstyle[12pt,aaspp4,flushrt]{article}\n\\input epsf\n\n\\newcommand\\g{\\gamma}\n\\newcommand\\th{\\theta}\n\\newcommand\\s{\\sigma}\n\\newcommand\\e{\\varepsilon}\n\\renewcommand\\t{\\theta}\n\\newcommand\\tg{\\t_\\g}\n\\newcommand\\cg{c_\\g}\n\\newcommand\\rc{r_{\\rm crit}}\n\\newcommand\\uc{u_{\\rm caus}}\n\\newcommand\\vc{v_{\\rm caus}}\n\\newcommand\\M{{\\cal M}}\n\\newcommand\\bSIS{b_{\\rm SIS}}\n\n\\newcommand\\x{{\\vec x}}\n\\newcommand\\uu{{\\vec u}}\n\n\\newcommand\\refeq[1]{eq.~(\\ref{eq:#1})}\n\\newcommand\\refEq[1]{Eq.~(\\ref{eq:#1})}\n\\newcommand\\refeqs[2]{eqs.~(\\ref{eq:#1}) and (\\ref{eq:#2})}\n\\newcommand\\refEqs[2]{Eqs.~(\\ref{eq:#1}) and (\\ref{eq:#2})}\n\n\\begin{document}\n\n\\title{Gravitational Lenses With More Than Four Images: \\\\\n I. Classification of Caustics}\n\\author{Charles R. Keeton$^{1}$, Shude Mao$^{2,3}$,\n and Hans J. Witt$^{4}$}\n\\affil{$^{1}$ Steward Observatory, University of Arizona, Tucson, AZ 85721, USA}\n%\\affil{email: ckeeton@as.arizona.edu}\n\\affil{$^{2}$ Univ. of Manchester, Jodrell Bank Observatory,\n Macclesfield, Cheshire SK11 9DL, UK}\n%\\affil{email: smao@jb.man.ac.uk}\n\\affil{$^{3}$ Max-Planck-Institut f\\\"ur Astrophysik,\n Karl-Schwarzschild-Strasse 1, 85740 Garching, Germany}\n\\affil{$^{4}$ Astrophysikalisches Institut Potsdam, An der Sternwarte 16,\n 14482 Potsdam, Germany}\n\n\\bigskip\n\\bigskip\n\\centerline{Accepted for publication in {\\it The Astrophysical Journal\\/}}\n\n\\begin{abstract}\nWe study the problem of gravitational lensing by an isothermal\nelliptical density galaxy in the presence of a tidal perturbation.\nWhen the perturbation is fairly strong and oriented near the\ngalaxy's minor axis, the lens can produce image configurations with\nsix or even eight highly magnified images lying approximately on a\ncircle. We classify the caustic structures in the model and\nidentify the range of models that can produce such lenses. Sextuple\nand octuple lenses are likely to be rare because they require\nspecial lens configurations, but a full calculation of the\nlikelihood will have to include both the existence of lenses with\nmultiple lens galaxies and the strong magnification bias that\naffects sextuple and octuple lenses. At optical wavelengths these\nlenses would probably appear as partial or complete Einstein rings,\nbut at radio wavelengths the individual images could probably be\nresolved.\n\\end{abstract}\n\n\n\\section{Introduction}\n\nThe first gravitational lens to be discovered, Q~0957+561, has a\nsimple double image configuration (Walsh, Carswell \\& Weymann\n1979). It was quickly followed by the first four-image lens,\nPG~1115+080 (Weymann et al.\\ 1980). Together with Einstein ring\nlenses produced by extended sources (e.g.\\ MG~1131+0456, Hewitt et\nal.\\ 1988), double and quadruple lenses nearly exhaust the list of\nconfigurations in the more than 50 known strong gravitational\nlenses.\\footnote{For a summary, see\nhttp://cfa-www.harvard.edu/glensdata.} The only exceptions are\n2016+112, which has three images and appears to require the rare\nand complicated situation of two lens galaxies at different\nredshifts (Lawrence et al.\\ 1984; Nair \\& Garrett 1997), and\nB~1933+503, which has ten images that can be nicely explained as a\ncombination of three distinct sources, two of which are\nquadruply-imaged and one of which is doubly-imaged (Sykes et al.\\\n1998).\n\nTheoretical studies have shown, though, that lenses with more than\nfour images of a single source can exist. Schneider, Ehlers \\&\nFalco (1992) gave a mathematical analysis of caustic structures that\nyield additional images. Kochanek \\& Apostolakis (1988) surveyed\nmodels with two spherical galaxies at different redshifts and found\nthat they can produce up to seven images. Witt \\& Mao (2000) found\nexamples of models with an elliptical density galaxy and an external\nshear that can produce up to eight images, but they did not do a\nfull survey of the models. Lenses with more than four images would\nbe not only interesting to observe, but also very useful in\ndetermining the lensing mass distribution using the numerous\nconstraints.\n\nIn this paper we present a systematic classification of the\ncaustics and image configurations for lenses consisting of an\nisothermal elliptical density galaxy and a tidal perturbation. We\nshow examples of lensing cross sections and magnification\ndistributions for different image numbers. In a forthcoming paper\nwe will study the observability of lenses with double, quadruple,\nsextuple, and octuple image configurations. The outline of this\npaper is as follows. In \\S 2 we review basic lens theory and the\nsingular isothermal ellipsoid (SIE) and external shear lens models.\nIn \\S 3 we present an analytic classification of the caustics in a\nlens model with an SIE galaxy and a tidal perturbation approximated\nas an external shear. In \\S 4 we study the stability of the\ncaustics by adding a small core radius to the galaxy and letting\nthe perturbation be produced by a neighboring galaxy or group.\nFinally, in \\S 5 we discuss some of the observational consequences\nand applications of our results.\n\n\\section{Methods}\n\n\\subsection{Basic lens theory}\n\nThe theory of gravitational lensing is discussed in detail by\nSchneider et al.\\ (1992); here we summarize the features central\nto our analysis. The mapping between a source at angular position\n$\\uu$ on the sky and an image at angular position $\\x$ is given\nby the lens equation,\n\\begin{equation}\n \\uu = \\x - \\nabla\\phi(\\x)\\,, \\label{eq:lens}\n\\end{equation}\nwhere the lensing potential $\\phi$ is the projected gravitational\npotential of the lens mass. The potential is determined by the\ntwo-dimensional Poisson equation $\\nabla^2\\phi(\\x) =\n2\\Sigma(\\x)/\\Sigma_{\\rm cr}$, where $\\Sigma$ is the projected\nsurface mass distribution of the lens and the critical surface\ndensity for lensing is\n\\begin{equation}\n \\Sigma_{\\rm cr} = {c^2 \\over 4 \\pi G}\\,{D_{\\rm os} \\over\n D_{\\rm ol} D_{\\rm ls}}\\ , \\label{eq:sigcr}\n\\end{equation}\nwhere $D_{\\rm ol}$ and $D_{\\rm os}$ are angular diameter distances\nfrom the observer to the lens and source, respectively, and\n$D_{\\rm ls}$ is the angular diameter distance from the lens to the\nsource. For a point source at $\\uu$, there is an image at each root\n$\\x_i$ of the lens equation (\\ref{eq:lens}).\n\nThe brightnesses of the images are determined by the magnification\ntensor\n\\begin{equation}\n \\M(\\x) \\equiv \\left({\\partial\\uu \\over \\partial \\x}\\right)^{-1}\n = \\left[\\matrix{\n 1-\\phi_{,xx}(\\x) & -\\phi_{,xy}(\\x) \\cr\n -\\phi_{,xy}(\\x) & 1-\\phi_{,yy}(\\x) \\cr\n }\\right]^{-1} , \\label{eq:mu}\n\\end{equation}\nwhere subscripts denote partial differentiation, $\\phi_{,ij} =\n\\partial^2\\phi / \\partial x_i \\partial x_j$. The magnification of a\npoint image at position $\\x$ is given by $|\\det\\M(\\x)|$. In general there\nare several curves in the image plane along which the magnification\ntensor is singular and the magnification is infinite ($\\det\\M^{-1}\n= 0$). These are called ``critical curves,'' and they map to\n``caustics'' in the source plane. Caustics mark discontinuities in\nthe number of images, which leads to the key idea for our analysis:\nin order to determine the number of images produced by a lens\nmodel, it is sufficient to examine the caustics. If we know that a\nsource arbitrarily far from the lens produces only one image, then\nwe can imagine moving the source around and noting when it crosses\na caustic to keep track of the total number of images. We discuss\nexamples in \\S 3.2.\n\n\\subsection{Model components}\n\nWe model a galaxy as a singular isothermal ellipsoid, because this\nmodel is not only analytically tractable but also consistent with\nmodels of individual lenses, lens statistics, stellar dynamics,\nand X-ray galaxies (e.g.\\ Fabbiano 1989; Maoz \\& Rix 1993; Kochanek\n1995, 1996; Grogin \\& Narayan 1996; Rix et al.\\ 1997). If we take\nthe ellipsoid to be oblate with intrinsic axis ratio $q_3$ then\nits three-dimensional density distribution is\n\\begin{equation}\n \\rho = {\\s^2 \\over 2\\pi G q_3}\\,{\\e_3 \\over \\sin^{-1}\\e_3}\\,\n {1 \\over R^2 + z^2/q_3^2}\\,,\n\\end{equation}\nwhere $G$ is the gravitational constant, $\\s$ is the velocity\ndispersion and $\\e_3 = \\sqrt{1-q_3^2}$ the eccentricity of the mass\ndistribution, and $(R, z)$ are usual cylindrical coordinates. For\nlensing we need the projected mass distribution. Choosing\ncoordinates with the projected major axis along the $x$-axis, the\nprojected surface density distribution is\n\\begin{eqnarray}\n {\\Sigma \\over \\Sigma_{\\rm cr}} &=& {b_I \\over 2 q}\\,\n {1 \\over \\sqrt{x^2+y^2/q^2}}\\ , \\\\\n \\mbox{where}\\quad\n b_I &=& 4\\pi\\,{\\e_3 \\over \\sin^{-1}\\e_3}\\,\\left({\\s \\over\n c}\\right)^2\\,{D_{\\rm ls} \\over D_{\\rm os}}\\ . \\label{eq:bI}\n\\end{eqnarray}\nThe projected axis ratio $q$ depends on the intrinsic axis ratio\nand the inclination angle $i$ (where $i=0^\\circ$ is face-on and\n$i=90^\\circ$ is edge-on),\n\\begin{equation}\n q = \\sqrt{q_3^2\\,\\sin^2 i + \\cos^2 i}\\,.\n\\end{equation}\nThe lensing properties of the isothermal ellipsoid have been given\nby Kassiola \\& Kovner (1993), Kormann, Schneider \\& Bartelmann\n(1994), and Keeton \\& Kochanek (1998). The lensing potential $\\phi$\nand the deflection angle $(\\phi_{,x},\\phi_{,y})$ are\n\\begin{eqnarray}\n \\phi &=& x\\,\\phi_{,x} + y\\,\\phi_{,y}\\,, \\label{eq:SIE}\\\\\n \\phi_{,x} &=& {b_I \\over \\sqrt{1-q^2}}\\,\\tan ^{-1}\\left(\\sqrt{1-q^2 \\over q^2 x^2 + y^2}\\,x\\right)\\,, \\nonumber\\\\\n \\phi_{,y} &=& {b_I \\over \\sqrt{1-q^2}}\\,\\tanh^{-1}\\left(\\sqrt{1-q^2 \\over q^2 x^2 + y^2}\\,y\\right)\\,.\n \\nonumber\n\\end{eqnarray}\n\nIn the limit of a spherically symmetric mass distribution (a\nsingular isothermal sphere, or SIS), the tangential critical curve\nis a circle with radius\n\\begin{equation}\n \\bSIS = 4\\pi\\,\\left({\\s \\over c}\\right)^2\\,{D_{\\rm ls}\n \\over D_{\\rm os}}\n \\label{eq:bSIS}\n\\end{equation}\n(in angular units); the maximum separation between images is $\\approx\n2\\bSIS$. This ``critical radius'' therefore serves as a natural\nlength scale in the lensing analysis, and we use it this way below.\nTypically $\\bSIS \\sim 0.2\\arcsec$--$3\\arcsec$ for galaxy-scale\nlenses.\n\nIn \\S 3 we study models with a tidal perturbation approximated as\nan external shear. The potential and deflection angle for an\nexternal shear are\n\\begin{eqnarray}\n \\phi &=& -{1\\over2} \\g r^2 \\cos 2(\\t-\\tg)\\,, \\label{eq:shear} \\\\\n \\phi_{,x} &=& - \\g r \\cos(\\t-2\\tg) = -\\g x \\cos 2\\tg - \\g y \\sin 2\\tg \\nonumber\\,, \\\\\n \\phi_{,y} &=& \\phantom{-} \\g r \\sin(\\t-2\\tg) = -\\g x \\sin 2\\tg + \\g y \\cos 2\\tg \\nonumber\\,,\n\\end{eqnarray}\nwhere $\\g$ is the strength of the shear and $\\tg$ is its direction\nangle, which is equal to the angle between the major axis of the\ngalaxy and the shear axis because we have aligned the galaxy with\nthe $x$-axis. Note that a shear described by $(\\g,\\tg)$ is\nequivalent to one described by $(-\\g,\\tg+\\pi/2)$; we avoid this\nambiguity by considering only shears with $\\g>0$ to be physical.\n\n\n\n\\section{Galaxy+Shear Models}\n\nA common lens system features a galaxy that is well modeled as an\nisothermal ellipsoid, plus a perturbation from objects at the same\nredshift as the lens galaxy (e.g.\\ neighboring galaxies, or a group\nor cluster) or objects along the line of sight. For examples, see\nHogg \\& Blandford (1994), Keeton, Kochanek \\& Seljak (1997),\nKundi\\'c et al.\\ (1997ab), Witt \\& Mao (1997), Tonry (1998), and\nTonry \\& Kochanek (1999). To lowest order, the perturbation can be\napproximated as an external shear as in \\refeq{shear}. We begin by\nstudying such galaxy+shear lens models because they admit a\ncomplete analytic treatment. In \\S 4.2 we consider models in which\nthe perturbation is instead produced by a discrete object like a\ngalaxy or group.\n\n\\subsection{Critical curves and caustics}\n\nTo obtain a galaxy+shear lens model we merely add the lensing\npotentials in \\refeqs{SIE}{shear}. The magnification from the joint\nmodel has a simple analytic form,\n\\begin{eqnarray}\n \\det\\M^{-1} = 1 - \\g^2 - \\sqrt{2}\\,{b_I \\over r}\\,\n {1 + \\g \\cos 2(\\t-\\tg) \\over \\sqrt{ (1+q^2) - (1-q^2)\\cos 2\\t }}\\,.\n \\label{eq:mag}\n\\end{eqnarray}\nThis lens model has a single critical curve, or curve of infinite\nmagnification. From \\refeq{mag} we can easily find a polar\nparametric form for this curve,\n\\begin{equation}\n \\rc(\\t) = {\\sqrt{2}\\, b_I \\over 1-\\g^2}\\,\n {1 + \\g \\cos 2(\\t-\\tg) \\over \\sqrt{ (1+q^2) - (1-q^2)\\cos 2\\t }}\\,.\n \\label{eq:crit}\n\\end{equation}\nThe corresponding caustic is found by mapping the critical curve\nto the source plane with the lens equation (\\ref{eq:lens}). The\ncaustic can be written in a cartesian parametric form,\n\\begin{eqnarray}\n \\uc(\\t) &=& \\left[ \\cos\\t + \\g \\cos(\\t-2\\tg) \\right] \\rc(\\t)\n - {b_I \\over \\sqrt{1-q^2}}\\,\\tan^{-1}\\left(\\xi\\,\\cos\\t\\right)\\,,\n \\label{eq:astr}\\\\\n \\vc(\\t) &=& \\left[ \\sin\\t - \\g \\sin(\\t-2\\tg) \\right] \\rc(\\t)\n - {b_I \\over \\sqrt{1-q^2}}\\,\\tanh^{-1}\\left(\\xi\\,\\sin\\t\\right)\\,,\n \\nonumber\\\\\n \\mbox{where}\\quad\n \\xi &=& \\left[ 2(1-q^2) \\over (1+q^2) - (1-q^2)\\cos 2\\t \\right]^{1/2} .\n \\nonumber\n\\end{eqnarray}\nNote that in \\refeq{crit} the parameter $\\t$ is interpreted as the\npolar angle, but in \\refeq{astr} $\\t$ is simply a parameter that\nruns from 0 to $2\\pi$.\n\nThe caustic is continuous but not smooth; in general it has four or\nmore cusps. (See examples in \\S 3.2.) We can find a simple equation\nthat gives the location of the cusps. Consider the parametric\nderivatives of the caustic,\n\\begin{eqnarray}\n \\left[ \\matrix{ d\\uc/d\\t \\cr d\\vc/d\\t } \\right]\n &=& - b_I\\,\\xi\\,{ 3\\g\\sin2(\\t-\\tg) +\n (1+\\g\\cos2(\\t-\\tg))\\xi^2\\sin\\t\\cos\\t \\over (1-\\g^2)\\sqrt{1-q^2} }\n \\nonumber\\\\\n && \\quad \\times \\left[ \\matrix{ \\cos\\t + \\g\\cos(\\t-2\\tg) \\cr\n \\sin\\t - \\g\\sin(\\t-2\\tg) } \\right] . \\label{eq:astrderiv}\n\\end{eqnarray}\nAt a cusp the caustic stops and changes direction, so both\n$d\\uc/d\\t$ and $d\\vc/d\\t$ vanish (and at least one of them changes\nsign). The only way for both derivatives to vanish simultaneously\nis for the common multiplicative factor in \\refeq{astrderiv} to\nvanish. We can simplify this to find that the condition for a cusp\nis\n\\begin{equation}\n \\g \\sin 2(\\t-\\tg) \\Bigl[ 3(1+q^2) - 2(1-q^2) \\cos 2\\t \\Bigr]\n + (1-q^2)(\\sin 2\\t + \\g \\sin 2\\tg) = 0\\,. \\label{eq:cusps}\n\\end{equation}\n\nIf our model galaxy were non-singular, the lens model would have a\nsecond critical curve and caustic. Since it is singular, however,\nthe second critical curve collapses to a point at the origin, and\nthe corresponding caustic is considered to be a ``pseudo-caustic.''\nThe pseudo-caustic has the cartesian parametric form\n\\begin{eqnarray}\n u_{\\rm pseudo}(\\t) &=&\n - {b_I \\over \\sqrt{1-q^2}}\\,\\tan^{-1}\\left(\\xi\\,\\cos\\t\\right)\\,,\n \\label{eq:pseudo} \\\\\n v_{\\rm pseudo}(\\t) &=&\n - {b_I \\over \\sqrt{1-q^2}}\\,\\tanh^{-1}\\left(\\xi\\,\\sin\\t\\right)\\,,\n \\nonumber\n\\end{eqnarray}\nwhere again $0 \\le \\t \\le 2\\pi$, and $\\xi$ is the same as in\n\\refeq{astr}. Note that the pseudo-caustic does not depend on the\nshear.\n\n\\subsection{Examples}\n\nFigure 1 shows typical caustics and pseudo-caustics for\ngalaxy+shear lens models, plotted using $\\bSIS$ from \\refeq{bSIS}\nas the natural length scale. In general the pseudo-caustic is\nsmooth, while the true caustic has cusps that give it a diamond or\nastroid shape. As discussed in \\S 2.1, the caustics indicate where\nthe number of images changes. A source outside both the caustic and\nthe pseudo-caustic produces one image. When the source crosses to\nthe inside of the pseudo-caustic it gains one additional image,\nwhich is faint, close to the galaxy center, and distorted radially\nrelative to the galaxy; the pseudo-caustic is sometimes labeled the\n``radial caustic'' because of the nature of the distortions. When\nthe source crosses to the inside of the astroid caustic it gains\ntwo more images, which are bright, close to the corresponding\ncritical curve, and distorted tangentially relative to the galaxy;\nhence this caustic is sometimes labeled the ``tangential caustic.''\nThe presence of the pseudo-caustic and the tangential caustic means\nthat the number of images in these models is either one, two, or\nfour depending on the location of the source. All of these features\nare generic to singular lens models that are not axisymmetric (see\nSchneider et al.\\ 1992).\n\nThe size and shape of the astroid caustic are determined by the net\nquadrupole moment of the lens model. When the galaxy and shear are\naligned ($\\tg = 0^\\circ$, e.g.\\ Figure 1a), the individual\nquadrupoles from the galaxy ellipticity and the shear combine to\nproduce a larger astroid caustic than produced by either one alone.\nIn other words, the area where sources produce 4-image lenses is\nlarger. Mild misalignment between the ellipticity and shear twists\nthe caustic (e.g.\\ Figure 1b). As the shear becomes more misaligned\n(e.g.\\ Figure 1c), the quadupole from the shear partially cancels\nthe quadrupole from the ellipticity; this is why Figure 1c has the\nsmallest astroid caustic despite having the largest shear. We\nreturn to this point in the discussion (\\S 5).\n\nFigure 2 shows that when the shear is nearly orthogonal to the\nellipticity ($\\tg \\simeq 90^\\circ$), it can nearly cancel the\neffects of the ellipticity to produce a caustic that is quite\nsmall. Nevertheless, the caustic is very interesting because it\nshows qualitatively new features not seen in Figure 1. (Similar\nexamples can be found in Witt \\& Mao 2000.) The caustic folds over\non itself in features called ``swallowtails'' (see Schneider et\nal.\\ 1992). Because the number of images increases by two when the\nsource crosses the caustic, a source inside a swallowtail produces\nsix images (e.g.\\ Figure 2b). The swallowtails are sensitive to the\nangle between the ellipticity and shear. They grow larger as the\nmisalignment increases, until with near perfect misalignment the\nswallowtails overlap (e.g.\\ Figure 2c). The region of the source\nplane where swallowtails overlap corresponds to sources that\nproduce eight images. In other words, the interaction of the\nellipticity and shear makes it possible to have new image\nconfigurations with six or even eight images.\n\nNot all combinations of ellipticity and shear can produce these new\nimage configurations. Figure 3 shows caustics for three cases where\nthe shear is orthogonal to the ellipticity ($\\tg=90^\\circ$). If the\nshear is small (Figure 3a), the system is dominated by the\nellipticity and any swallowtails that exist are small. If the shear\nis large (Figure 3c), the system is dominated by the shear and\nagain any swallowtails are small. For a given ellipticity, only a\nnarrow range of orthogonal shears can produce overlapping\nswallowtails (Figure 3b). In \\S 3.3 we discuss in detail the range\nof models that can produce 6- and 8-image configurations.\n\n\\subsection{Models that can produce more than 4 images}\n\nAppendices A and B give a mathematical analysis of the range of\nmodels that have swallowtails and thus can produce 6- or 8-image\nlenses; we summarize the results here. We use the presence of\nswallowtails in the caustic to indicate that a model can produce\nmore than four images. This approach does not directly indicate\nthe probability of observing a lens with more than four images.\nEstimating this probability requires detailed computations of\nlensing cross sections and magnification distributions for\nrealistic sets of lens environments. We discuss these issues\nbriefly in \\S 5 and plan to study them in more detail in a\nforthcoming paper. For now we seek to delineate the conditions\nunder which a lens can produce more than four images.\n\nFigures 4--6 show the envelope of swallowtail models in the\n$(q,\\g)$ plane for different values of the shear angle $\\tg$. When\nthe shear is orthogonal to the ellipticity (Figure 4), the envelope\nencloses small shears for modestly flattened galaxies ($q \\lesssim\n1$) and larger shears for more flattened galaxies ($q \\ll 1$).\nSwallowtails can exist for $\\g$ arbitrarily small and $q$\narbitrarily close to unity (ellipticity arbitrarily small),\nprovided that the shear and ellipticity are in the narrow band\nwhere they properly balance each other. A relatively broad band of\nthe swallowtail models also have overlapping swallowtails and thus\ncan produce 8-image lenses.\n\nIf $\\tg$ changes by even a few degrees away from perfect\nmisalignment, however, the envelope pinches off at the\nhigh-$q$/low-$\\g$ end (Figure 5). In other words, obtaining\nswallowtails requires more ellipticity and shear. Also, the range\nof models with overlapping swallowtails quickly disappears (not\nshown). From these results we conclude that 6- and 8-image lenses\nproduced by small tidal perturbations (e.g.\\ $\\g \\sim 0.1$) are\nlikely to be very rare because they require a special combination\nof galaxy axis ratio and shear misalignment angle. However, with\nstronger perturbations the range of swallowtail models is\nconsiderably larger. Thus we predict that even though 6- or 8-image\nlenses may still be rare, they are more likely to occur when the\nperturbation is strong (such as a second galaxy near the primary\nlens galaxy) than when the perturbation is weak. Since strong\nperturbations may not be well approximated by the external shear\nmodel, in \\S 4.2 we study models using a full treatment of a\nperturbation from a nearby galaxy or group.\n\nThe mathematical analysis does reveal that swallowtails can exist\nfor smaller shear misalignments; while the results are formally\ninteresting, they are physically implausible because they require\nhighly flattened galaxies and very large shears (Figure 6). For\n$\\tg \\sim 60^\\circ$, there are two envelopes that are comparable in\nsize.\\footnote{The second envelope exists even for larger\nmisalignments, as indicated by Figure 12 in Appendix A. However, it\nis too small to be seen in Figure 5.} For $45^\\circ < \\tg <\n50.45^\\circ$ ($0 > \\cos2\\tg > -1/\\sqrt{28}$, see eq.~\\ref{eq:a6}),\none of the envelopes stretches to arbitrarily large shears. For\n$39.55^\\circ < \\tg < 45^\\circ$ ($1/\\sqrt{28} > \\cos2\\tg > 0$), the\nfinite envelope disappears but the infinite one remains. This\nenvelope finally disappears for $\\tg < 39.55^\\circ$ ($\\cos2\\tg >\n1/\\sqrt{28}$). With the strong perturbations required by these\nenvelopes, however, the simple shear approximation almost certainly\nbreaks down. Thus this analysis is probably not fully valid, but it\ndoes suggest features to look for when studying models with very\nstrong perturbations, such as interacting galaxies.\n\n\n\n\\section{Stability of the Caustics}\n\n\\subsection{Non-singular lens models}\n\nAlthough we have studied singular lens models for analytic\nconvenience, real galaxies may have a small but finite core radius.\nIt is important to understand whether swallowtails are robust under\nthe addition of a core radius. Adding a core radius adds one faint\nimage near the center of the galaxy for any configuration with more\nthan one image, so the total number of images is always odd (see\nSchneider et al.\\ 1992). Figure 7 shows generalizations of the\ncaustics in Figures 2b and 2c to a finite core radius $s$, using\nthe lensing properties of a softened isothermal ellipsoid given by\nKeeton \\& Kochanek (1998). The swallowtails shrink as $s$ increases\n-- probably because when we increase $s$ with $\\bSIS$ held fixed,\nwe decrease the galaxy mass and hence reduce the contribution of\nthe ellipticity to the potential. However, no convincing case of a\nfaint central image has been observed, and this limits the core\nradius ($s/\\bSIS \\lesssim 0.1$, see Wallington \\& Narayan 1993;\nKochanek 1996) and suggests that lens galaxies are quite cuspy. The\npresence of such small cores would not significantly affect our\nresults.\n\n\\subsection{Two-galaxy models}\n\nAs discussed in \\S 3.3, the galaxy+shear models suggest that the\nperturbation must be relatively strong in order to produce\nswallowtails. For such strong perturbations, the external shear\napproximation may not be justified, so in this section we examine a\nsimple model in which the perturbation is produced by a second mass\ndistribution representing a neighboring galaxy or group. We again\nuse a singular isothermal mass distribution for the perturber, but\nfor simplicity we assume it is spherical.\n\nThe perturber is described by three physical parameters: its\nvelocity dispersion $\\s_2$ (or equivalently its critical radius\n$b_{\\rm SIS,2}$ given by eq.~\\ref{eq:bSIS}),\\footnote{In this\nsection we use a subscript 1 to denote the main lens galaxy and a\nsubscript 2 to denote the perturber. We continue to use the\ncritical radius $b_{\\rm SIS,1}$ of the main lens galaxy as the\nnatural scale length.} and its position relative to the lens\ngalaxy, given by the projected distance $d$ from the galaxy center\nand the angle $\\tg$ from the lens galaxy's major axis. To\ngeneralize the galaxy+shear models, it is convenient to\ncharacterize the perturber not by its velocity dispersion $\\s_2$\nbut rather by the strength of the perturbation. To lowest order,\nthe perturbation is equivalent to an external shear with strength\n\\begin{equation}\n \\g = {b_{\\rm SIS,2}/(2d) \\over 1 - b_{\\rm SIS,2}/(2d)}\\ .\n\\end{equation}\nIt is important to understand what this strength means. All\nperturbers with a given strength $\\g$ are equivalent to each other\nand to an external shear of strength $\\g$ -- {\\it to second order\nin the potential\\/}. The differences enter only in terms of third\norder and higher. Nevertheless, we show here that the differences\nare important.\n\nWe note that since the perturbation strength $\\g$ is a combination\nof the velocity dispersion and distance, perturbers with a given\nstrength but different distances must have different velocity\ndispersions,\n\\begin{equation}\n \\left({\\s_2 \\over \\s_1}\\right)^2 = {b_{\\rm SIS,2} \\over b_{\\rm SIS,1}}\n = 2\\,{d \\over b_{\\rm SIS,1}}\\,{\\g \\over 1+\\g}\\ . \\label{eq:sigrat}\n\\end{equation}\nIn other words, the more distant the perturber is, the more massive\nit has to be, and vice versa.\n\nThe top panels in Figure 8 show the caustics for a galaxy+shear\nmodel with $q=0.5$ and $\\tg=90^\\circ$. They are similar to Figure 3\nbut include more values of $\\g$. The other panels in Figure 8 show\nthe generalization to two-galaxy models, using the same values of\n$\\g$ and distances $d/b_{\\rm SIS,1} = 5, 10, 20, 40$. Note that the\ngalaxy+shear models in the top panel are equivalent to two-galaxy\nmodels with $d \\to \\infty$. Figure 9 is similar, but shows the\ncaustic structures for $\\tg=88^\\circ$. From \\refeq{sigrat}, the\nmodels in Figures 8 and 9 have perturbers that range in mass from\nthe scale of a galaxy to that of a cluster.\n\nThe examples show two important effects. First, the swallowtails\ntend to be {\\it larger\\/} in two-galaxy models than in equivalent\ngalaxy+shear models, and they grow as the distance $d$ decreases.\nThe various models differ only in higher order terms, but those\nterms apparently strengthen the perturber's effects. Equivalently,\nthe range of models that produce swallowtails is larger. Second, in\ngalaxy+shear models the symmetry of the shear implies that there\nare always two identical swallowtails. By contrast, in two-galaxy\nmodels one of the swallowtails is often quite large, while the\nother is either small or absent. As a result, the area in the\nsource plane where swallowtails overlap is small or absent, so the\nmodels have a limited ability to produce 8-image lenses.\n\nWe conclude from these examples that the qualitative features we\nsaw in the galaxy+shear models are stable when we change the source\nof the perturbation. In fact, the range of swallowtail models seems\nto {\\it increase\\/} with more realistic treatments of strong or\nclose perturbations. However, it appears that the overlapping\nswallowtails required to produce octuple lenses are rare and not\nvery stable.\n\n\n\n\\section{Summary and Discussion}\n\nWe have studied the lensing properties of an isothermal elliptical\ndensity galaxy in the presence of a tidal perturbation to classify\nthe caustic structures and identify different image configurations.\nIn most cases the models have a simple caustic structure\ncorresponding to standard 2-image and 4-image lens configurations.\nHowever, when the tidal shear has a magnitude and direction\nappropriate to partially cancel the effects of the galaxy's\nellipticity, the caustics develop complicated swallowtail features\nthat correspond to 6- and 8-image configurations that have not yet\nbeen observed. We gave a complete analytic treatment of the case of\na singular galaxy with a perturbation modeled as an external shear,\nbut we showed that the caustic structures are stable when one adds\na small core radius or uses a more realistic treatment of the\nperturbation. In fact, the swallowtail caustic structures are\ngenerally bigger with the more realistic perturbation than with the\nshear approximation, which may enhance the likelihood of observing\nlenses with more than four images.\n\nOur analysis has several observational consequences. First,\nsextuple and octuple lenses are likely to be rare because they\nrequire special lens configurations. In fact, they will probably be\nfound only when there is a second galaxy close enough to the lens\ngalaxy to provide a strong perturbation. While this situation is\nuncommon, it is not exceedingly rare: at least five lenses\\footnote{\nB~1127+385 (Koopmans et al.\\ 1999), B~1359+154 (Rusin et al.\\ 1999),\nB~1608+656 (Koopmans \\& Fassnacht 1999), 2016+112 (see Nair \\&\nGarrett 1997 and references therein), and B~2114+022 (Augusto,\nWilkinson \\& Browne 1996; Jackson et al.\\ 1998).} appear to have\nmultiple lens galaxies within the Einstein radius. Still, to\nquantify the likelihood of finding a sextuple or octuple lens,\nit is necessary to compute the lensing cross sections for various\ncombinations of the galaxy axis ratio $q$ and the shear amplitude\n$\\g$ and misalignment angle $\\tg$. Figure 10 shows cross sections\nfor $q=0.5$, $\\g=0.22$, and three values of $\\tg$ that correspond\nto the cases shown in Figure 2. The configurations with more images\nhave smaller cross sections and thus smaller probabilities for\nbeing observed. However they also have significantly higher\nmagnifications, which means that magnification bias will be\nimportant (e.g.\\ Turner 1980; Turner, Ostriker \\& Gott 1984).\nMagnification bias will mitigate the effects of small cross\nsections to increase the likelihood of observing a sextuple or\noctuple lens. Clearly a realistic prediction of the lensing\nprobabilities will require computation of cross sections and\nmagnification bias for many combinations of $(q,\\g,\\tg)$ weighted\nby realistic populations of lens galaxies and perturbers. We\nplan to address these issues of observability in a forthcoming\npaper, both in the context of current surveys and of the Next\nGeneration Space Telescope, where large numbers of lenses are\nexpected (e.g.\\ Barkana \\& Loeb 1999).\n\nSecond, if discovered the sextuple and octuple lenses that we have\ndescribed will be easy to identify because the lensed images lie\napproximately on a circle (see Figure 2). Any lens with more than\nfour images that do not trace a circle must not be of the type\ndescribed here. Indeed, in B~1933+503 there are ten images not on a\ncircle, and it is thought that they must be associated with three\ndifferent sources (Sykes et al.\\ 1998). In B~1359+154 there are six\nradio sources with four sources in a standard quadruple lens\nconfiguration, plus two sources inside the configuration whose\ninterpretation is not clear (Myers et al.\\ 1999). Although\nobservations and models suggest that there may be multiple lens\ngalaxies (Rusin et al.\\ 1999), the fact that the six sources do not\nfollow a circle suggests that lens cannot be explained by\nswallowtails produced by the lens galaxies.\n\nThird, observed sextuple or octuple lenses would be very useful for\nconstraining models of the lensing mass distribution. The ``extra''\nimages beyond the standard two or four would provide additional\nposition and flux constraints. Even better, the sensitivity of the\ncaustic structures to the lens galaxy ellipticity and the shear\namplitude and misalignment angle means that the mere existence of\nsix or more images should place strong constraints on those\nproperties of the model. As a result, a sextuple or octuple lens\ncould represent a wonderful ability to break the common degeneracy\nbetween the lens galaxy shape and the shear from the surrounding\nenvironment (see Keeton et al.\\ 2000a). Such a lens might even\nserve as the long-sought ``golden lens'' for measuring the Hubble\nconstant $H_0$ (see Schechter 2000) provided that a time delay\ncould be measured, although the time delay might be relatively\nshort (a few days) because the images are all close to the critical\ncurve.\n\nThese applications are predicated on the ability to resolve the\nindividual images, and this ability might be limited when we\ninclude the effects of finite source size. Figure 11 shows that the\nsource does not have to be very large before the images smear into\na partial or complete Einstein ring. This happens for $R_{\\rm\nsrc}/\\bSIS \\sim 0.01$, where typically $\\bSIS \\sim\n1\\arcsec$--$3\\arcsec$ for galaxy-scale lenses. Radio surveys can\nachieve sub-milli-arcsecond resolution with VLBI or VLBA mapping\n(e.g.\\ the CLASS survey, see Browne 2000 and references therein),\nso they should still be able to resolve individual images and thus\nfind lenses amenable to these applications. By contrast, optical\nsurveys (such as the Sloan Digital Sky Survey, see Gunn et al.\\\n1998 and Fischer et al.\\ 1999, or the Next Generation Space\nTelescope, see Barkana \\& Loeb 1999) are more likely find partial\nor complete Einstein rings. Still, new techniques for modeling\nEinstein rings show that they are very useful for constraining not\nonly the lens model but also the intrinsic shape of the source\n(Keeton, Kochanek \\& McLeod 2000b).\n\nFinally, our study may be relevant for the so-called ellipticity\n``crisis,'' where lens galaxies are inferred to have larger\nellipticities than the observed early-type galaxies (see Kochanek\n1996 and references therein). From Figure 1, it is clear that the\ncaustic structures are the largest when the shear is aligned with\nthe major axis of the lensing galaxy so the ellipticity and shear\nact coherently; conversely, the caustic structures are the smallest\nwhen the shear is orthogonal to the major axis since the shear\npartially cancels the lens ellipticity. Observationally, this means\nthat for a sample of quadruple lenses the shear may preferentially\nlie along the galaxy major axis; a good example is B~1422+231 (Hogg\n\\& Blandford 1994). The presence of an aligned shear is difficult\nto infer from lens models due to a degeneracy in the lens equation\n(see Witt 1996): naive lens models simply imply a model ellipticity\nequivalent to the combination of the true ellipticity and the\nshear. This effect may generate a bias toward larger inferred\nellipticities for lens galaxies, although a full account of this\nbias awaits further investigations.\n\n\n\\acknowledgements\n{\\it Acknowledgements.\\/} We thank Peter Schneider for helpful\ndiscussions, and the anonymous referee for prompt and helpful\ncomments that improved the discussion.\n\n\n\\appendix\n\n\\section{Models that can produce at least 6 images}\n\nIn this Appendix we compute the range of galaxy+shear models (see\n\\S 3) that can produce at least six images. Because the caustics\ndetermine the image number, finding models that can yield at least\nsix images is equivalent to finding models in which the caustic has\nswallowtails. We saw in \\S 3.2 that in models without swallowtails\nthe caustic has four cusps, while in models with swallowtails the\ncaustic has more than four cusps. Thus to identify models with\nswallowtails it is sufficient to find models that have more than\nthe standard four solutions to the cusp equation (\\ref{eq:cusps}).\n\nIn other words, the envelope bounding the region in parameter space\nwhere models have swallowtails is located where the cusp equation\ndevelops additional pairs of solutions. If the cusp equation\n(\\ref{eq:cusps}) is written as $f(\\t)=0$, the place where\nadditional solutions appear is defined by\n\\begin{equation}\n f(\\t) = 0 \\qquad\\mbox{and}\\qquad\n {\\partial f(\\t) \\over \\partial \\t} = 0\\,.\n \\end{equation}\nThese equations yield two polynomials in $\\sin 2\\t$ and $\\cos 2\\t$,\nso we can use the resultant method (e.g.\\ Walker 1955; Erdl \\&\nSchneider 1993) to eliminate $\\t$. We find that the envelope is\ngiven by roots of the equation\n\\begin{equation}\n F(\\g,\\tg,q) \\equiv \\sum_{i=0}^6 a_i(\\tg,q)\\, (1-q^2)^{6-i}\\, \\g^i = 0\\,,\n \\label{eq:F}\n\\end{equation}\nwhere the coefficients $a_i(\\tg,q)$ are:\n\\begin{eqnarray}\na_0 &=& 1 \\nonumber\\\\\na_1 &=& 18\\cg(1+q^2) \\nonumber\\\\\na_2 &=& (1+q^4)(74+49\\cg^2)-40q^2+334\\cg^2q^2 \\nonumber\\\\\na_3 &=& 12\\cg(1+q^2) \\Bigl[ (1+q^4)(29+4\\cg^2)+50q^2+64\\cg^2q^2 \\Bigr] \\nonumber\\\\\na_4 &=& 16\\cg^4(1-q^2)^2 (1+34q^2+q^4)\n +2\\cg^2(7+58q^2+7q^4)(43+22q^2+43q^4) \\nonumber\\\\\n & & -3(1+380q^2-2058q^4+380q^6+q^8) \\nonumber\\\\\na_5 &=& 6\\cg(1+q^2) \\Bigl[ 4\\cg^2(1-q^2)^2(19+358q^2+19q^4)\n -1-500q^2+4890q^4-500q^6-q^8 \\Bigr] \\nonumber\\\\\na_6 &=& 128\\cg^4(1-q^2)^4(1+34q^2+q^4)\n - 3\\cg^2(1-q^2)^2(1+644q^2-6906q^4+644q^6+q^8) \\nonumber\\\\\n & & + 36 q^2(1+34q^2+q^4)^2\n\\label{eq:a}\n\\end{eqnarray}\nwith $\\cg=\\cos 2\\tg$. For any set of parameters $(\\g,\\tg,q)$, $F>0$\nmeans that the caustic does not have swallowtails, while $F<0$\nmeans that the caustic does have swallowtails. Thus each pair of\nsolutions to $F=0$ gives an envelope bounding a region in parameter\nspace in which swallowtails occur.\n\nFor $\\tg=0^\\circ$ and $90^\\circ$ we have $\\cg=+1$ and $-1$ and the\nenvelope equation simplifies to\n\\begin{equation}\n F(\\g,\\tg,q) = \\Bigl[ 1-q^2\\pm\\g(5+ q^2) \\Bigr]^3\\,\n \\Bigl[ 1-q^2\\pm\\g(1+5q^2) \\Bigr]^3 = 0\\,.\n\\end{equation}\nWith $\\cg=+1$ there are no solutions, and hence no models with\nswallowtails. With $\\cg=-1$ the envelope of swallowtail models is\n\\begin{equation}\n {1-q^2 \\over 5+q^2} < \\g < {1-q^2 \\over 1+5q^2}\\,.\n \\label{eq:t90}\n\\end{equation}\n\nMore generally, for given values of $\\tg$ and $q$ the envelope\nequation (\\ref{eq:F}) is a 6th order polynomial in $\\g$ whose roots\nare easy to find numerically. Before using a root finder, however,\nwe should understand how many roots to expect and what their\ngeneral ranges are. This requires that we examine how the\npolynomial $F$ depends on location in the $(q,\\tg)$ plane. First\nconsider how the number of roots changes as $q$ varies. Additional\npairs of roots appear when $F=0$ and $\\partial F / \\partial q = 0$,\nwhich can be combined using the resultant method to eliminate $\\g$\nand obtain the condition\n\\begin{eqnarray}\n G(\\cg,q) &\\equiv& 32(1-q^2)^2(1+970q^2+q^4)\\cg^4 - (7-986q^2+7q^4)^2 \\nonumber\\\\\n && + \\Bigl[ 17(1+q^8)+60196(q^2+q^6)+824358q^4 \\Bigr] \\cg^2 \\quad =\\quad 0,\n \\label{eq:G}\n\\end{eqnarray}\nwhere again $\\cg = \\cos 2\\tg$. This is a second order polynomial in\n$\\cg^2$, so its solution is\n\\begin{eqnarray}\n \\cg^2 = {1 \\over 64(1-q^2)^2(1+970q^2+q^4)} &\\Biggl[ &\n 17(1+q^8)+60196(q^2+q^6)+824358q^4 \\nonumber\\\\\n && +81(1+q^2)\\sqrt{1+322q^2+q^4}\\quad \\Biggr]\\ .\n \\label{eq:qroots}\n\\end{eqnarray}\n(The second solution of the quadratic equation is unphysical\nbecause it has $c_\\g^2<0$.) The right-hand side of \\refeq{qroots}\nis between 0 and 1 for all $0 \\le q \\le 1$, so there is always a\nphysical solution; in fact, there are two solutions, one for\n$\\cg>0$ and one for $\\cg<0$. The two solutions intersect when\n$\\cg=0$, which occurs at $q=\\sqrt{7/(493+90\\sqrt{30})}=0.0843$.\nNext, consider the behavior of the polynomial $F$ for large $\\g$,\nwhich is controlled by the coefficient $a_6$. If $a_6>0$ then $F>0$\nfor large $\\g$, so there are no swallowtails for large $\\g$.\nHowever, if $a_6<0$ then $F<0$ for large $\\g$, so there are\nswallowtails for arbitrarily large $\\g$. Thus the behavior of the\npolynomial changes qualitatively when $a_6$ changes sign. Since\n$a_6$ is a quadratic polynomial in $\\cg^2$ (see eq.~\\ref{eq:a}), it\nis easy to find that $a_6=0$ if\n\\begin{eqnarray}\n \\cg^2 = {3 \\over 256(1-q^2)^2(1+34q^2+q^4)} &\\Biggl[ &\n (1+644q^2-6906q^4+644q^6+q^8) \\nonumber\\\\\n && \\pm(1-253q^2-253q^4+q^6)\\sqrt{1-254q^2+q^4}\\quad \\Biggr]\\ .\n \\label{eq:a6}\n\\end{eqnarray}\nThe right-hand side is real for $|q| \\le 8-3\\sqrt{7} = 0.0627$, and\nat this point it has $\\cg=\\pm1/\\sqrt{28}$ or $\\tg=39.55^\\circ$ and\n$50.45^\\circ$.\n\nWith these results we can understand the $(q,\\tg)$ plane as shown\nin Figure 12. The curves given by \\refeqs{qroots}{a6} define nine\ndifferent regions where the swallowtail envelopes (the parameter\nregions with $F<0$) have the following properties:\n\\begin{eqnarray}\n \\mbox{none} &:& \\mbox{no envelopes } \\nonumber\\\\\n 1+ &:& \\mbox{one envelope, with $\\g>0$ } \\nonumber\\\\\n 2+ &:& \\mbox{two envelopes, both with $\\g>0$ } \\nonumber\\\\\n 1+,1- &:& \\mbox{two envelopes, one with $\\g>0$ and one with $\\g<0$ } \\nonumber\\\\\n 1+,\\infty &:& \\mbox{one finite envelope with $\\g>0$, and envelopes with $\\g\\to\\pm\\infty$ } \\nonumber\\\\\n 1- &:& \\mbox{one envelope, with $\\g<0$ } \\nonumber\\\\\n 2- &:& \\mbox{two envelopes, both with $\\g<0$ } \\nonumber\\\\\n 1-,1+ &:& \\mbox{two envelopes, one with $\\g<0$ and one with $\\g>0$ } \\nonumber\\\\\n 1-,\\infty &:& \\mbox{one finite envelope with $\\g<0$, and envelopes with $\\g\\to\\pm\\infty$ } \\nonumber\n\\end{eqnarray}\nNegative shear is unphysical (see \\S 2.2), so we are interested\nonly in envelopes with $\\g>0$, which occur in six of the nine\nregions: $(1+)$; $(2+)$; $(1+,1-)$; $(1+,\\infty)$; $(1-,1+)$; and\n$(1-,\\infty)$.\n\nWith this detailed knowledge of the $(q,\\tg)$ plane, we can use a\nnumerical root finder with \\refeq{F} to obtain the envelope of\nswallowtail models. The results are shown and discussed in \\S 3.3.\nIn particular, Figures 4--6 show envelopes in the $(q,\\g)$ plane\nfor different values of $\\tg$. Each envelope corresponds to a\nparticular horizontal line in Figure 11. Each point where this line\ncrosses a curve in the $(q,\\tg)$ plane corresponds to a cusp in the\nenvelope in the $(q,\\g)$ plane.\n\n\\section{Models that can produce 8 images}\n\nWe can also ask what range of swallowtail models produce\noverlapping swallowtails that bound 8-image regions (e.g.\\ Figure\n3b). We cannot answer this question analytically for arbitrary\nvalues of the shear angle $\\tg$. However, from the examples in \\S\n3.2 we expect that overlapping swallowtails occur only when the\nshear is nearly orthogonal to the galaxy, and the case with\n$\\tg=90^\\circ$ can be studied analytically. When $\\tg=90^\\circ$ the\nsystem has reflection symmetry, so the points on the caustic with\n$\\t=0$ and $\\t=\\pi/2$ are always cusps, no matter how convoluted\nthe rest of the curve is. (These cusps are indicated in Figure 3.)\nMoreover, the $\\t=0$ cusp always opens to the left, and the\n$\\t=\\pi/2$ cusp always opens downward. Label the $\\t=0$ cusp\nposition $(u_H,0)$ and the $\\t=\\pi/2$ cusp position $(0,v_V)$ (H\nfor horizontal, V for vertical). From Figure 3 we see that there\nare overlapping swallowtails only if $u_H$ and $v_V$ are both\npositive. (If one is positive and one negative then there are\nswallowtails that do not overlap.) We can use \\refeq{astr} to\nrewrite the conditions $u_H > 0$ as follows:\n\\begin{eqnarray}\n u_H>0 \\ \\Longleftrightarrow\\ \\g<\\g_H(q) &\\equiv& {1-E_H(q) \\over 1+E_H(q)}\\,,\n \\label{eq:gH} \\\\\n \\mbox{where}\\quad E_H(q) &\\equiv&\n {q \\over \\sqrt{1-q^2}}\\,\\tan^{-1}\\left({\\sqrt{1-q^2} \\over q}\\right)\\,.\n \\nonumber\n\\end{eqnarray}\nWe can similarly rewrite the condition $v_V > 0$:\n\\begin{eqnarray}\n v_V>0 \\ \\Longleftrightarrow\\ \\g>\\g_V(q) &\\equiv& {E_V(q)-1 \\over E_V(q)+1}\\,,\n \\label{eq:gV} \\\\\n \\mbox{where}\\quad E_V(q) &\\equiv&\n {1 \\over \\sqrt{1-q^2}}\\,\\tanh^{-1}\\left(\\sqrt{1-q^2}\\right)\\,.\n \\nonumber\n\\end{eqnarray}\nFor any galaxy axis ratio $0 \\le q \\le 1$, these functions satisfy\n$\\g_V(q) \\le \\g_H(q)$. Thus the condition for overlapping\nswallowtails is $\\g_V(q) < \\g < \\g_H(q)$, and this result is shown\nin Figure 4.\n\n\n\n\\begin{references}\n\\reference{au96} Augusto, P., Wilkinson, P. N., Browne, I. W. A. 1996,\n\tin Kochanek, C.S. Hewitt, J.N. (eds.),\n IAU 173, Melbourne, Astrophys. Applications \n of Gravitational Lensing, Kluwer, 399\n\\reference{bl99} Barkana, R., \\& Loeb, A. 1999, preprint astro-ph/9906398\n\\reference{br00} Browne, I. W. A. 2000, in Gravitational Lensing: Recent\n Progress and Future Goals, ASP conference series, eds. T. G. Brainerd \\&\n C. S. Kochanek, in press\n\\reference{ep93} Erdl, H., \\& Schneider, P. 1993, \\aap, 268, 453\n\\reference{f89} Fabbiano, G. 1989, \\araa, 27, 87\n\\reference{fi99} Fischer, P., et al. 1999, preprint astro-ph/9912119\n\\reference{gn96} Grogin, N. A., \\& Narayan, R. 1996, \\apj, 464, 92;\n erratum, 1996, \\apj, 473, 570\n\\reference{GW95} Gunn, J. E., et al. 1998, \\aj, 116, 3040\n\\reference{he88} Hewitt, J. N., Turner, E. L., Schneider, D. P.,\n Burke, B. F., \\& Langston, G. I. 1988, \\nat, 333, 537\n\\reference{hb94} Hogg, D. W., \\& Blandford, R. D. 1994, \\mnras, 268, 889\n\\reference{j98} Jackson, N., Helbig, P., Browne, I., Fassnacht, C. D.,\n Koopmans, L., Marlow, D., \\& Wilkinson, P. N. 1998, \\aap, 334, L33\n\\reference{KK93} Kassiola A., \\& Kovner, I. 1993, \\apj, 417, 450\n\\reference{kk98} Keeton, C. R., \\& Kochanek C. S. 1998, \\apj, 495, 157\n\\reference{kks97} Keeton, C. R., Kochanek, C. S., \\& Seljak, U. 1997,\n \\apj, 482, 604\n\\reference{k00a} Keeton, C. R., Falco, E. E., Impey, C. D., Kochanek, C. S.,\n Leh\\'ar, J., McLeod, B. A., Rix, H.-W., Mu\\~noz, J. A., \\& Peng, C. Y.\n 2000a, preprint astro-ph/0001500\n\\reference{k00b} Keeton, C. R., Kochanek, C. S., \\& McLeod, B. A. 2000b,\n in preparation\n\\reference{ko95} Kochanek, C. S. 1995, \\apj, 445, 559\n\\reference{ko96b} Kochanek, C. S. 1996, \\apj, 473, 595\n\\reference{ka88} Kochanek, C. S., \\& Apostolakis, J. 1988, \\mnras, 235, 1073\n\\reference{kf99} Koopmans, L. V. E., \\& Fassnacht, C. D. 1999, \\apj, 527, 513\n\\reference{kp99} Koopmans, L. V. E., et al. 1999, \\mnras, 303, 727\n\\reference{KSB94a} Kormann, R., Schneider, P., \\& Bartelmann M. 1994,\n A\\&A, 284, 285\n\\reference{kc} Kundi\\'c, T., Cohen, J. G., Blandford, R. D., \\&\n Lubin, L. M. 1997a, \\aj, 114, 507\n\\reference{kc2} Kundi\\'c, T., Hogg, D. W., Blandford, R. D., Cohen, J. G.,\n Lubin, L. M., \\& Larkin, J. E. 1997b, \\aj, 114, 2276\n\\reference{law84} Lawrence, C. R., Schneider, D. P., Schmidet, M.,\n Bennett, C. L., Hewitt, J. N., Burke, B. F., Turner, E. L., \\& Gunn, J. E.\n 1984, Science, 223, 46\n\\reference{mr93} Maoz, D., \\& Rix, H.-W. 1993, \\apj, 416, 425\n\\reference{my99} Myers, S. T., et al. 1999, \\aj, 117, 2565\n\\reference{n97} Nair, S., \\& Garrett, M. A. 1997, \\mnras, 284, 58\n\\reference{r97} Rix, H.-W., de Zeeuw, P. T., Carollo, C. M., Cretton, N., \\&\n van der Marel, R. P. 1997, \\apj, 488, 702\n\\reference{ru99} Rusin, D., Hall, P. B., Nichol, R. C., Marlow, D. R.,\n Richards, A. M. S., \\& Myers, S. T. 1999, preprint astro-ph/9911420\n\\reference{s00} Schechter, P. L. 2000, in Gravitational Lensing: Recent\n Progress and Future Goals, ASP conference series, eds. T. G. Brainerd \\&\n C. S. Kochanek, in press (also preprint astro-ph/9909466)\n\\reference{SEF} Schneider, P., Ehlers, J., \\& Falco, E. E. 1992, Gravitational\n Lenses (New York: Springer)\n\\reference{s98} Sykes, C. M., et al. 1998, \\mnras, 301, 310\n\\reference{t99} Tonry, J. L. 1998, \\aj, 115, 1\n\\reference{tk99} Tonry, J. L., \\& Kochanek, C. S. 1999, \\aj, 117, 2034\n\\reference{tu80} Turner, E. L. 1980, \\apj, 242, L135\n\\reference{tog84} Turner, E. L., Ostriker, J. P., \\& Gott, J. R. 1984,\n \\apj, 284, 1\n\\reference{wal55} Walker, R. J. 1955, Algebraic Curves\n (Oxford University Press)\n\\reference{wal55} Wallington, S., \\& Narayan, R. 1993, \\apj, 403, 517\n\\reference{wal79} Walsh, D., Carswell, R. F., \\& Weymann, R. J. 1979,\n \\nat, 279, 381\n\\reference{we80} Weymann, R. J., et al. 1980, \\nat, 285, 641\n\\reference{W96} Witt, H. J. 1996, \\apj, 472, L1\n\\reference{WM97} Witt, H. J., \\& Mao, S. 1997, \\mnras, 291, 211\n\\reference{WM00} Witt, H. J., \\& Mao, S. 2000, \\mnras, 311, 689\n\\end{references}\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% FIGURES %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\newpage\n\n\\begin{figure}\n\\centerline{\\epsfysize=6.5in \\epsfbox{fig1.ps}}\n\\caption{Sample caustics and pseudo-caustics for models with a\nsingular isothermal ellipsoid galaxy and an external shear. The\nsmooth elongated curves are the pseudo-caustics and the\ndiamond-shaped curves are the astroid caustics. All panels have a\ngalaxy with a projected axis ratio $q=0.5$ and a shear whose\nmagnitude $\\g$ and direction $\\tg$ are indicated. The axes are\nlabeled in terms of the natural lensing length scale $b_{\\rm SIS}$\nfrom \\refeq{bSIS}.}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfysize=6.0in \\epsfbox{fig2.ps}}\n\\caption{Examples of ``swallowtail'' caustics produced when the\nellipticity and shear are nearly orthogonal. The left-hand panels\nshow the tangential caustics and sample source positions; the\npseudo-caustics are larger than the frames. The right-hand panels\nshow the corresponding tangential critical curves and image\npositions. All models have $q=0.5$ and $\\g=0.22$ and the specified\nshear direction $\\tg$. The points show that a source inside the\nastroid but outside the swallowtails produces 4 images (case a);\na source inside a swallowtail produces 6 images (case b); and a\nsource inside overlapping swallowtails produces 8 images (case c).\nThe total magnification of the sample images in cases a, b, and c\nis 76.8, 178.3, and 266.2, respectively.}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfysize=6.5in \\epsfbox{fig3.ps}}\n\\caption{The dependence of swallowtails on the shear. All models\nhave $q=0.5$ and an orthogonal shear ($\\tg=90^\\circ$) with the\nspecified magnitude $\\g$. The points indicate the cusps with $\\t=0$\n(on the horizontal axis) and $\\t=\\pi/2$ (on the vertical axis); see\nAppendix B for details.}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfxsize=6.0in \\epsfbox{fig4.ps}}\n\\caption{The envelope of galaxy+shear models that can produce at\nleast 6 images in the $(q,\\g)$ plane, for a shear orthogonal to the\nlens galaxy ($\\tg=90^\\circ$). Models in the cross-hatched region\nhave overlapping swallowtails and can produce up to 8 images.\nModels in the shaded region have non-overlapping swallowtails and\ncan produce up to 6 images. Models outside the shaded region do not\nhave swallowtails and can produce at most 4 images. The curves\nbounding these regions are given by eqs.~(\\ref{eq:t90}), (\\ref{eq:gH}),\nand (\\ref{eq:gV}) in Appendices A and B. The three filled points\nindicate the locations of the three sample models shown in Figure 3.}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfxsize=6.0in \\epsfbox{fig5.ps}}\n\\caption{Similar to Figure 4, but for different values of the shear\nangle near $\\tg \\simeq 90^\\circ$. Only the swallowtail envelope is\nshown (not the envelope for overlapping swallowtails). The outer\nenvelope corresponds to $\\tg=90^\\circ$, and moving inward the line\ntype alternates as $\\tg$ decreases by $2^\\circ$.}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfxsize=6.0in \\epsfbox{fig6.ps}}\n\\caption{Similar to Figure 4, but for values of the shear angle\nnear $\\tg \\simeq 45^\\circ$. Note that the vertical axes are\n$\\log\\g$ instead of $\\g$. For $\\tg > 50.45^\\circ$ there are two\nclosed envelopes. For $50.45^\\circ > \\tg > 45^\\circ$ there is one\nclosed envelope and one envelope that extends to $\\g \\to +\\infty$.\nFor $45^\\circ > \\tg > 39.55^\\circ$ there is only the envelope that\nextends to infinity. For $\\tg < 39.55^\\circ$ there is no envelope.\n(Also see Figure 12 in Appendix A.)}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfxsize=6.0in \\epsfbox{fig7.ps}}\n\\caption{The dependence of swallowtails on the galaxy core radius\n$s$. All models have $q=0.5$ and $\\g=0.22$. The top panels show\nmodels with $\\tg=88^\\circ$, while the bottom panels show models\nwith $\\tg=90^\\circ$. For comparison, Figures 2b and 2c show the\nsame models in the limit $s=0$.}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfxsize=6.5in \\epsfbox{fig8a.ps}}\n\\centerline{\\epsfxsize=6.5in \\epsfbox{fig8b.ps}}\n\\caption{The caustics for a galaxy with $q=0.5$ perturbed by an\nexternal shear (top panels), and by a singular isothermal sphere at\nangle $\\tg=90^\\circ$ and distance $d$ (bottom panels). The strength\nof the perturbation is given by $\\g$. Each frame is $0.6\\,b_{\\rm\nSIS,1}$ on a side. In some cases with large $\\g$ and small $d$, the\ncaustics of the main lens galaxy and the perturber merge and become\nlarger than the frames.}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfxsize=6.5in \\epsfbox{fig9a.ps}}\n\\centerline{\\epsfxsize=6.5in \\epsfbox{fig9b.ps}}\n\\caption{Similar to Figure 8, but for $\\tg=88^\\circ$. \nEach frame is $0.6\\,b_{\\rm SIS,1}$ on a side.\n}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfxsize=5.0in \\epsfbox{fig10.ps}}\n\\caption{Differential cross sections (in units of $b_{\\rm SIS}^2$)\nvs.\\ logarithm of magnification $A$ for 2-, 4-, 6-, and 8-image\nlenses produced by galaxy+shear lens models. The cross-sections are\ncomputed for a point source in a square with side-length of\n$5\\,\\bSIS$. The lens galaxy axis ratio is $q=0.5$, the shear\namplitude is $\\g=0.22$, and the shear direction is indicated; the\ncases correspond to those shown in Figure 2.}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfxsize=6.0in \\epsfbox{fig11.ps}}\n\\caption{Sample images for a source with finite radius $R_{\\rm\nsrc}$. The lens model and source position are the same as in Figure\n2b. The images are distorted tangentially relative to the lens\ngalaxy, and as the source gets bigger they smear out into an\nEinstein ring.}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\epsfxsize=6.0in \\epsfbox{fig12.ps}}\n\\caption{The $(q,\\tg)$ plane for galaxy+shear models. The inset\nshows a closeup of the region with $q$ small and $\\tg \\simeq\n45^\\circ$. The solid curves show solutions to \\refeq{qroots},\nwhile the dotted curves show solutions to \\refeq{a6}. The solid\ncurves intersect at $\\tg=45^\\circ$ and\n$q=\\radical\"270370{7/(493+90\\radical\"270370{30})}=0.0843$.\nThe dotted curves meet the solid curves at\n$q=8-3\\radical\"270370{7}=0.0627$ and $\\cg=\\pm1/\\radical\"270370{28}$\nor $\\tg=39.55^\\circ$ and $50.45^\\circ$. The curves divide the plane\ninto nine regions. Each region has a distinct set of envelopes\ncontaining swallowtail models, as explained in Appendix A.}\n\\end{figure}\n\n\\end{document}\n\n"
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astro-ph0002402
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Intrinsic constraints on very high energy emission in gamma-ray loud blazars
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{
"author": "Jian-Min Wang"
}
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Photons with very high energy up to TeV (VHE) emitted from active galactic nuclei (AGNs) provide some invaluable information of the origin of $\gam$-ray emission. Although 66 blazars have been detected by {EGRET}, only three low redshift X-ray selected BL Lacs (Mrk 421, Mrk 501, and 1ES 2344+514) are conclusive TeV emitters (PKS 2155-304 is a potential TeV emitter) since VHE photons may be absorbed by cosmological background infrared photons ({external} absorption). Based on the ``mirror'' effect of clouds in broad line region, we argue that there is an {intrinsic} mechanism for the deficiency of TeV emission in blazars. Employing the observable quantities we derive the pair production optical depth $\tgg(\eps_{obs})$ due to the interaction of VHE photons with the reflected synchrotron photons by electron Thomson scattering in broad line region. This sets a more strong constraints on very high energy emission, and provides a sensitive upper limit of Doppler factor of the relativistic bulk motion. It has been suggested to distinguish the {intrinsic} absorption from the {external} by the observation on variation of multiwavelegenth continuum. \keywords{radiation mechanism: nonthermal - gamma rays: theory}
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"name": "vhe.tex",
"string": "%version from 12, Feb., 2000.\n\\documentstyle[emulateapj]{article}\n \n\\def\\al{\\alpha}\n\\def\\cd{{\\cal{D}}}\n\\def\\dl{d_{\\rm L}}\n\\def\\dt{\\Delta t_{\\rm obs}}\n\\def\\eps{\\epsilon}\n\\def\\epsg{\\epsilon_{\\gamma}}\n\\def\\epsp{{\\epsilon^{\\prime}}}\n\\def\\epspp{{\\epsilon^{\\prime \\prime}}}\n\\def\\gam{\\gamma}\n\\def\\Gam{\\Gamma}\n\\def\\lslc{L_{\\rm S}/L_{\\rm C}}\n\\def\\lssc{{l_{\\rm ssc}}}\n\\def\\lrsc{{l_{\\rm rsc}}}\n\\def\\np{n^{\\prime}}\n\\def\\npp{{n^{\\prime \\prime}}}\n\\def\\nucp{{\\nu_{\\rm c}^{\\prime}}}\n\\def\\nursc{{\\nu_{\\rm rsc}}}\n\\def\\nusp{{\\nu_{\\rm s}^{\\prime}}}\n\\def\\rblr{{R_{_{\\rm BLR}}}}\n\\def\\siggg{\\sigma_{\\gamma \\gamma}}\n\\def\\st{\\sigma_{_{\\rm T}}}\n\\def\\tblr{\\tau_{_{\\rm BLR}}}\n\\def\\tgg{\\tau_{\\gamma \\gamma}}\n\\def\\tggrsc{\\tgg^{\\rm rsc}(\\eps_{\\rm obs})}\n\\def\\ubb{u_{_{\\rm B}}}\n\\def\\ubp{$u_{\\rm B}^{\\prime}$}\n\\def\\usyn{u_{_{\\rm syn}}}\n\\def\\usynp{u_{\\rm syn}^{\\prime}}\n\\def\\veps{\\varepsilon}\n\\def\\xssa{x_{\\rm ssa}}\n\n\\slugcomment{To Appear in The Astrophysical Journal 538, No1. 20 July Issue, \n2000}\n\n\n\\begin{document}\n \n\\title{Intrinsic constraints on very high energy emission\nin gamma-ray loud blazars }\n\\author{Jian-Min Wang}\n\\affil{Laboratory of Cosmic Ray and High Energy Astrophysics,\nInstitute of High Energy Physics, Chinese Academy of Sciences,\nBeijing 100039, and Beijing\nAstrophysical Center (CAS-PKU.BAC), Beijing 100871, P.R. China,\nE-mail: wangjm@astrosv1.ihep.ac.cn}\n \n\\begin{abstract}\n\nPhotons with very high energy up to TeV (VHE) emitted from active galactic \nnuclei (AGNs) provide some invaluable information of the origin of $\\gam$-ray\nemission. Although 66 blazars have been detected by {\\it EGRET}, only\nthree low redshift X-ray selected BL Lacs (Mrk 421, Mrk 501, and 1ES 2344+514)\nare conclusive TeV emitters (PKS 2155-304 is a potential TeV emitter)\nsince VHE photons may be absorbed by cosmological background infrared photons\n({\\it external} absorption). Based on the ``mirror'' effect of clouds \nin broad line region, we argue that there is an {\\it intrinsic} mechanism \nfor the deficiency of TeV emission in blazars. Employing the observable\nquantities\nwe derive the pair production optical depth $\\tgg(\\eps_{\\rm obs})$ due to \nthe interaction of VHE photons with the reflected synchrotron photons by \nelectron Thomson scattering in broad line region. This sets a more strong \nconstraints on very high energy emission, and provides a sensitive upper \nlimit of Doppler factor of the relativistic bulk motion. It has been suggested \nto distinguish the {\\it intrinsic} absorption from the {\\it external} by the \nobservation on variation of multiwavelegenth continuum.\n\\keywords{radiation mechanism: nonthermal - gamma rays: theory}\n\\end{abstract}\n\n\\section{Introduction}\nClearly, the high energy $\\gam$-ray emission is an important piece\nin the blazar puzzle because the $\\gam$-ray observations of blazars \nprovide a new probe of dense radiation field released through \naccretion onto a supermassive black \nhole in the central engine (Bregman 1990). The Energetic Gamma Ray Experiment\nTelescope ({\\it EGRET}) which works in the 0.1--10GeV energy \ndomain has now detected \nand identified 66 extragalactic sources in 3th catalog (Mukherjee et al 1999). \nAll these objects are\nblazar-type AGNs whose relativistic jets are assumed to be close\nto the line of sight to the observer. It seems unambiguous that the intense\ngamma-ray emission is related with highly relativistic jet.\n\nIt has been generally accepted that the luminous gamma-ray emission\nis radiated from inverse Compton, but the problem of seed photons remains\nopen for debate. The following arguments have been proposed: \n(1) synchrotron photons in jet (inhomogeneous model of synchrotron self \nCompton) (Maraschi, Ghisellini \\& Celotti 1992); (2) optical and ultraviolet \nphotons directly from the accretion disk (Dermer \\& Schlikeiser\n1993); (3) diffusive photons in broad line region (BLR) (Sikora, Begelman\n\\& Rees 1994, Blandford \\& Levinson 1995); (4) the reflected synchrotron\nphotons by electron mirror in broad line region, namely, the reflected\nsynchrotron inverse Compton (RSC) (Ghisellini \\& Madau 1996). \nThese mechanisms may operate in different kinds of objects,\nhowever there is not yet a consensus on how these mechanisms work. Also\nit is not clear where the $\\gam$-ray emission is taking place largely\nbecause of uncertainties of soft radiation field in the central engine. \n\nOn the other hand, VHE observations (Kerrick et al 1995, Chadwick \net al 1999, Roberts et al 1999, Aharonian et al 1999) are making \nattempts to explore the radiation\nmechanism because they may provide some restrictive constraints\n(Begelman, Rees \\& Sikora 1994, Mastichiadis \\& Kirk 1997, Tavecchio, \nMaraschi \\& Ghisellini 1998, Coppi \\& Aharonian 1999, Harwit, Protheroe \nand Biermann 1999).\nBased on the simple version of SSC model, Stecker, de Jager \\& Salamon (1996)\npredicted a large number of low redshift X-ray selected BL Lacs as TeV\ncandidates, taking into account that the presence of intergalactic \ninfrared radiation field including cosmic background leads to strong \nabsorption of TeV photons from cosmological emitters (Stecker \n\\& de Jager 1998). It is suggested to form an extended pair halo in \ncosmological distance due to the {\\it external} absorption\n(Aharonian, Coppi, \\& Voelk 1994). However, so far only three X-ray selected \nBL Lacs have been found to be TeV emitters by Whipple telescope ($E>300$GeV),\nin addition, photons higher than 0.3TeV in the X-ray-selected PKS 2155-304 \nwith redshift $z=0.116$ has been detected photons 0.3TeV by Durham Mrk 6 \ntelescope \n(Chadwick et al 1999). The recent measurements of intergalactic infrared \nfield is quite different from the previous observations (Madau et al 1998, \nSteidel 1998). Although this {\\it external} absorption is definitely \nimportant, the critical redshift $z_{c}$\nbeyond which cosmological back ground radiation and intergalactic infrared\nfields will absorb VHE photons remains uncertain. \nEspecially the recent VHE observations show \nthat Mrk 501 emits 25 TeV photons (Aharonian et al 1999). Evidently this \nsuggests that the {\\it external} \nabsorption can not efficiently attenuate the VHE photons from reaching us \nacross distances of 100 Mpc. It is highly desired to accurately probe the \nstar formation rate in order to determine the critical redshift $z_{c}$.\n\nThus it seems significant to study the {\\it intrinsic} mechanism \nfor the deficiency of TeV photons from $\\gamma$-ray loud AGNs disregarding \nthe absorption by intergalactic infrared radiation field. A larger Lorentz\nfactor of the jet implies higher density of the external photons in the\nblob, if the reflection of clouds in broad line region works,\nand therefore stronger absorption of high energy $\\gamma$-rays\n(Celotti, Fabian \\& Rees 1998). Here we argue based on the hypothesis \nof Ghisellini \n\\& Madau (1996) that the energy density of reflected synchrotron photon \nis high enough for pair production via interaction of gamma-ray photons \nby inverse Compton scattering with reflected synchrotron photons \nif the bulk velocity is high enough. Further we apply the present \nconstraint to the representative individual objects, Mrk 421 and 3C 279. \n\n\\section{Constraints on VHE}\nGhisellini \\& Madau (1996) have calculated the energy density of reflected \nsynchrotron (Rsy) emission, and compared with the other reflected components. \nThey draw a conclusion that the energy density of Rsy component dominates \nover 10 times of that of reflected component of accretion disk radiation. In \nthis section we make an attempt to use the observables quantities\nto express the intrinsic constraints on very high energy emission.\nThe overall $\\nu F_{\\nu}$ spectrum of blazars shows that there are\ntwo power peaks: the first is low energy one between IR/soft X-ray band,\nand the second is high energy one\npeaking in the MeV/GeV range (von Montigny et al 1995, Sambruna, Maraschi \n\\& Urry 1996, Comastri et al 1997, Kubo et al 1998). This characteristic\ncan be explained by the simple context of one-zone homogeneous SSC or EC\nmodel. The low energy peak denoted $\\nu_{\\rm s}$ is caused by synchrotron \nradiation of relativistic electrons, and the second peak denoted $\\nu_{\\rm c}$,\nor $\\nursc$ results from the Compton scattering off the synchrotron or\nreflected synchrotron photons by the same population of electrons, \nrespectively. We take the two peaks and their corresponding\nfluxes as four observable quantities.\n\nFrom the RSC model the magnetic field $B$ can be approximately expressed\nby the observational quantities. The observed frequency of synchrotron \nphoton is $\\nu_{\\rm s}=\\cd \\nu_0 \\gamma_{\\rm b}^2B$ ($\\nu_0=2.8\\times 10^6$), \nand the frequency of reflected synchrotron Compton photons reads \n$\\nursc=\\cd (2\\Gam)^2\\gamma_{\\rm b}^4\\nu_0B$, and we can get the \nestimation of magnetic field $B$\n\\begin{equation}\nB=\\frac{(2\\Gam \\nu_{\\rm s})^2}{\\cd \\nu_0 \\nursc}\n \\approx \\frac{\\cd \\nu_{\\rm s}^2}{\\nu_0\\nursc},\n\\end{equation}\nwhile in pure SSC model the magnetic field is approximately as\n$B=\\nu_{\\rm s}^2/(\\cd\\nu_0\\nu_{\\rm c})$, \nwhere $\\nu_{\\rm c}$ is the frequency of photons emitted by SSC. The Doppler\nfactor $\\cd=1/\\Gam [1-\\mu(1-\\Gam^{-2})^{1/2}]$, where $\\mu=\\cos \\theta$ is the \ncosine of the orientated angle of jet relative to the observer.\nEquation (1) is similar to the model of\nSikora, Begelman \\& Rees (1994) (also see Sambruna, Maraschi \\& Urry 1996).\nComparing with the above two formula, we learn that RSC model needs stronger\nmagnetic field than SSC model does whereas the energy of relativistic \nelectrons is lower in RSC model than in SSC model.\nThe reflected synchrotron Compton (RSC) mainly depends on two parameters:\nthe reflection albedo, namely, the Thomson scattering optical depth\n($\\tblr$), and the Lorentz factor $\\Gamma$ of the relativistic jet. \n\n\\subsection{Reflected Synchrotron Compton Emission}\nIn the case of power-law distribution of electrons, $N=N_0\\gam^{-\\al}$, \n($\\gam_{\\rm min}\\leq \\gam \\leq \\gam_{\\rm max}$), where $N$ is the number\ndensity of relativistic electrons, and $\\gam$ is the Lorentz factor of \nelectron, the synchrotron emission coefficiency is approximately given by \n$\\veps_{\\nu}=c_5(\\al)N_0B^{1+\\al \\over 2}(\\nu/2c_1)^{1-\\al \\over 2}$. \nHere $c_1=6.27\\times 10^{18}$, and\n$c_5(\\al)$ is tabulated in Pacholczyk (1970) within the frequency range\n$\\nu_1\\leq \\nu \\leq \\nu_2$, where \n$\\nu_{1,2}=\\nu_0B(\\gam^2_{\\rm min},\\gamma^2_{\\rm max})$.\nThe average energy density per frequency $u^{\\prime}_{\\rm syn,\\nu^{\\prime}}$\nin a region with dimension $s$\nin the jet comoving frame can be obtained\n\\begin{equation}\nu^{\\prime}_{\\rm syn,\\nu^{\\prime}}=4\\pi c^{-1} c_5(\\al)N_TB^{1+\\al \\over 2}\n \\left(\\frac{\\nu^{\\prime}}{2c_1}\\right)^{1-\\al \\over 2},\n\\end{equation}\nwhere $N_T=N_0s$. The number density of synchrotron photons can be obtained by\n\\begin{equation}\nn^{'}_{\\epsp}=n_0(\\al)N_TB^{1+\\al \\over 2}\\epsp^{-{1+\\al \\over 2}},\n\\end{equation}\nand $n_0(\\al)$ reads\n$$\nn_0(\\al)=\\frac{4\\pi c_5(\\al)}{hc}\n \\left(\\frac{2hc_1}{m_ec^2}\\right)^{\\al-1 \\over 2},\n$$\nhere $h$ is Planck constant, and $\\epsp=h\\nu'/m_ec^2$. \nWe have employed relationship $n_{\\epsp}=n_{\\nu'}d\\nu'/d\\epsp$ to derive\nequation (3).\nThe mean energy density is expressed by\n\\begin{equation}\n\\usynp\\approx \\frac{8\\pi c_5(\\al)}{(3-\\al)c(2c_1)^{1-\\al \\over 2}}\n N_TB^{1+\\al \\over 2}\\nu_2^{\\prime^{3-\\al \\over 2}},\n\\end{equation}\nfor $\\al< 3$. Defining $\\lssc$ as\n\\begin{equation}\n\\lssc=\\frac{L_{\\rm s}}{L_{\\rm ssc}}=\\frac{u^{\\prime}_{\\rm B}}{\\usynp},\n\\end{equation}\nwe have\n\\begin{equation}\nN_T=\\frac{(3-\\al)c(2c_1)^{1-\\al \\over 2}}{64\\pi^2c_5(\\al)\\lssc}\n B^{3-\\al \\over 2}{\\nusp}^{\\al-3 \\over 2},\n\\end{equation}\nwhere $\\nusp$ denotes $\\nu_2^{\\prime}$. \n\nSince the opening angle of jet ($\\pi/\\Gam^2$) is much less than $2\\pi$, \nit is then reasonable to assume that the BLR reflection approximates to \nplane mirror with thickness $\\Delta R_{\\rm BLR}$ and electron number\ndensity $n_e$.\nThe distance distribution of reflected synchrotron photons has been\ndiscussed by Ghisellini \\& Madau (1996). The angular distribution has \nnot been issued. Since the thickness of mirror\nis zero, the energy density of reflected synchrotron emission \nsharply increases when blob is close to the mirror. In fact if we drop\nthe assumption of zero-thickness of mirror, this characteristic\nwill disappear. We will deal with this sophisticate model in future.\nBecause the reflected synchrotron emission is isotropic\nin observer's frame, the blob receives the reflected photon beamed\nwithin a solid angle $\\pi/\\Gam^2$. The \nsubsequent section will pay attention to this effects.\nNeglecting the angle-dependent distribution of reflected photon field,\nwe approximate the Doppler factor $\\cd \\approx 2\\Gam$ ($\\theta \\approx 0$). \nFor simplicity, we assume the mirror (reflecting clouds in broad\nline region) has Thomson scattering optical depth \n$\\tblr=\\st n_e\\Delta \\rblr \\approx \\st n_e \\rblr$. The received\nphoton density $\\npp(\\epspp)$ in the jet comoving frame can be then\napproximately written as\n\\begin{eqnarray}\n\\npp(\\epspp)&\\approx &(2\\Gam)^2\\tblr n_0(\\al)N_TB^{1+\\al \\over 2}\n {\\epsp}^{-{1+\\al \\over 2}}\\nonumber \\\\\n & = &(2\\Gam)^{3+\\al}\\tblr n_0(\\al)N_TB^{1+\\al \\over 2}\n {\\epspp}^{-{1+\\al\\over 2}},\n\\end{eqnarray}\nwhere we use $\\epspp=(2\\Gam)^2\\epsp$ (there are two Doppler shifts due to\nmirror effects). The convenient form of\ncross section of photon-photon collision is (Coppi \\& Blandford 1990)\n\\begin{equation}\n\\siggg=\\frac{\\st}{5\\eps}\\delta\\left(\\eps_0-\\frac{1}{\\eps}\\right),\n\\end{equation}\nwhere $\\delta$ is the usual $\\delta$-function. This approximation is\nonly valid for case of isotropic radiation field. The Rsy component is seen\nby the blob within the solid angle \n$\\Delta \\Omega \\approx 2\\pi(1-\\cos\\Gam^{-1})\\approx \\pi/\\Gam^2$. Although\nthe cross section of photon-photon interaction holds, the interacting\npossibility among photons reduces by a factor of \n$\\Delta \\Omega/4\\pi=1/(2\\Gam)^2$ due to the beaming effects, which \neffectively reduces the opacity. Thus the pair production optical depth \nfor photon with energy $\\epsg$ reads\n\\begin{eqnarray}\n\\tgg^{\\rm rsc}(\\epsg)&=&\\frac{0.2\\st s}{(2\\Gam)^2}\n \\int \\epsg^{-1}\\npp(\\epspp)\\delta(\\epspp-\\epsg^{-1})\n\t d\\epspp \\nonumber\\\\\n &=&(2\\Gam)^{1+\\al}\\tblr \\tgg^0(\\epsg),\n\\end{eqnarray}\nhere $\\tgg^0(\\epsg)$ is\n\\begin{equation}\n\\tgg^0(\\epsg)=0.2\\st s n_0(\\al)N_T B^{\\al+1 \\over 2}\\epsg^{\\al-1 \\over 2}.\n\\end{equation}\nWe will show the validity of the above approximation in the next subsection.\nSupposing that RSC operates efficiently\nin $\\gamma$-ray loud blazars, we can get $\\lrsc$ from the observations\n\\begin{equation}\n\\lrsc=\\frac{L_{\\rm s}}{L_{\\rm rsc}}\n =\\frac{u^{\\prime}_{\\rm B}}{(2\\Gam)^2\\tblr \\usynp}\n =\\frac{\\lssc}{(2\\Gam)^2\\tblr}.\n\\end{equation}\nFrom equation (11) we have\n\\begin{equation}\n\\tblr=\\frac{\\lssc}{(2\\Gam)^2\\lrsc},\n\\end{equation}\nand \n\\begin{equation}\n\\tgg^{\\rm rsc}(\\epsg)=\n (2\\Gam)^{\\al-1}\\left(\\frac{\\lssc}{\\lrsc}\\right)\\tgg^0(\\epsg).\n\\end{equation}\nFrom equation (11) we know that the observed $\\lrsc$ represents the\nreflection ratio and Doppler factor of jet motion as long as the\nCompton catastrophe does not occur. If we set $\\lrsc\\approx \\lssc$,\nwe get $\\tblr\\approx \\Gam^{-2}=0.01$ for $\\Gam=10$. This value is the\nlowest one in the model of Sikora, Begelman \\& Rees (1994) who suggest\n$\\tblr=0.1\\sim 0.01$. In fact we can roughly adopt $\\tblr$ as the covering\nfactor which is usually taken to be 0.1 in fitting the broad emission \nline by photoionization model.\n\nInserting $B$ and $N_T$ [eqs(1) and (6)] into \n$\\tgg^0$ (Eq. 10), and letting\n$\\epsg=\\eps_{\\rm obs}/\\cd$ and $s=c\\cd \\dt$, \nwe have the pair production optical depth for $\\eps_{\\rm obs}$\nin the observer's frame\n\\begin{eqnarray}\n\\tggrsc& =&K_{\\alpha}\\frac{\\nu_{\\rm s}^{5+\\al \\over 2}}{\\nu^2_{\\rm rsc}}\n (2\\Gam)^{3+\\al} \\cd^{1-\\al} \\eps_{\\rm obs}^{\\al-1 \\over 2}\n l^{-1}_{\\rm rsc}\\dt\\nonumber\\\\\n &\\approx& K_{\\alpha}\\frac{\\nu_{\\rm s}^{5+\\al \\over 2}}{\\nu^2_{\\rm rsc}}\n \\cd^4 \\eps_{\\rm obs}^{\\al-1 \\over 2} \\lrsc^{-1}\\dt,\n\\end{eqnarray}\nwhere $K_{\\alpha}=\\frac{(3-\\al)\\st c}{80\\pi h \\nu_0^2}\n \\left(\\frac{h}{m_ec^2}\\right)^{\\al-1 \\over 2}$\n($K_{\\alpha}=7.9\\times 10^{-18}$ for $\\alpha=2.4$).\nThere are five observational parameters: $\\nu_{\\rm s}$, $\\nu_{\\rm rsc}$,\n$\\al$, $\\dt$ and $\\lrsc$; and the unknown Doppler factor $\\cd$.\nFor the typical value of parameters, $\\al=2.4$, \n$\\nu_{\\rm s}=4.0\\times 10^{14}$Hz, and $\\nu_{\\rm rsc}=1.0\\times 10^{25}$Hz,\n$\\dt=1$~day, and $\\cd=10$, we have\n\\begin{eqnarray}\n\\tggrsc&=&1.9~l^{-1}_{\\rm rsc}\\cd_{10}^4\n \\left(\\frac{\\eps_{\\rm obs}}{{\\rm TeV}}\\right)^{0.7}\n \\left(\\frac{\\dt}{{\\rm day}}\\right)\\nonumber\\\\\n & &\\left(\\frac{\\nu_{\\rm s}}{4.0\\times 10^{14}{\\rm Hz}}\\right)^{3.7}\n \\left(\\frac{\\nu_{\\rm rsc}}{10^{25}{\\rm Hz}}\\right)^{-2},\n\\end{eqnarray}\nwhere $\\cd_{10}=\\cd/10$. Figure 1 shows the opacity due to pair production\nof photons with very high energy encountering with the reflected synchrotron\nphotons. The equation (15) tells us the constraints on VHE from jet:\n(1) smaller $\\lrsc$, i.e. stronger reflection, will leads to the absorption \nof TeV photons. This parameter represents the energy density reflected by \nthe BLR cloud including the bulk relativistic motion. \nFrom this estimation we know that TeV photon will be absorbed by the\nreflected synchrotron photons provided that $\\lrsc<1.9$.\n(2) $\\tgg$ is sensitive to $\\nu_{\\rm s}$ and $\\nu_{\\rm rsc}$.\n(3) $\\tgg$ is proportional to $\\cd^4$, in contrast to the usual down-limit \n(see Mattox et al 1993, and Dondi \\& Ghisellini 1995), providing the upper \nlimit Doppler factor of bulk motion from $\\tgg\\leq 1$, \n\\begin{eqnarray}\n\\cd &\\leq &8.5~l^{1/4}_{\\rm rsc}\n \\left(\\frac{\\eps_{\\rm obs}}{{\\rm TeV}}\\right)^{-0.175}\n \\left(\\frac{\\dt}{{\\rm day}}\\right)^{-0.25}\\nonumber\\\\\n & &\\left(\\frac{\\nu_{\\rm s}}{4.0\\times10^{14}{\\rm Hz}}\\right)^{-0.925}\n \\left(\\frac{\\nu_{\\rm rsc}}{10^{25}{\\rm Hz}}\\right)^{0.5}.\n\\end{eqnarray}\nThis is a new constraint, which is expressed by the observational quantities.\nIt lends us a simple and efficient way to select TeV candidates from known\nblazars in term of their known characteristics. \n\n\\subsection{Angular Distribution of Reflected Photons}\nThe received photons reflected by BLR in comoving frame is anisotropic, \ntherefore, the pair opacity should be carefully treated.\nWe have made important approximations that the BLR is thought to be\na plane mirror and treated the photon-photon interaction in an\napproximate way. Now let us show the validity of this approximation.\nWe adopt the geometry shown in Fig 1c of Ghisellin \\& Madau (1996).\nThey show that the energy density of reflected synchrotron\nphoton strongly depends on the location of emitting blob.\nWe should admit that the aximal symmetry holds in the reflected synchrotron\nemission. We approximate the Thomson scattering event by\nisotropic scattering with cross section $\\st$ and neglect\nrecoil, which is a very good approximation when $\\eps_s \\ll 1$.\nThe angular distribution of reflected synchrotron emission\nis given by $n_{\\rm ph}(\\eps_s, \\mu, r_0)=n_0 f(\\mu,r_0)\\eps_s^{-q}$ ($n_0$\nis a constant), the\nfunction $f(\\mu, r_0)$ determines the angular distribution of reflected\nsynchrotron photons (Ghisellini \\& Madau 1996)\n\\begin{equation}\nf(\\mu,r_0)=\\cd^2(\\mu)g(\\mu,r_0),\n\\end{equation}\nwhere \n$g(\\mu,r_0)=\\left[\\left(1-r_0^2+r_0^2\\mu^2\\right)^{1/2}-r_0\\mu\\right]^{-2}$,\nand $r_0=R_{\\gam}/\\rblr \\in (0,1)$, where $R_{\\gam}$ is the distance of\nblob to the center. Figure 2 shows the angular distribution in blob comoving \nframe. It can be seen that the geometry effect of reflecting mirror isotropizes\nthe radiation at some degrees, but the beaming effect still dominates. It is\nstill a good approximation that the radiation is beamed with a cone of\nsolid angle $\\pi/\\Gam^2$. \nThus the pair opacity can be written as (Gould \\& Schr\\'eder 1967)\n\\begin{equation}\n\\tgg(\\epsg)=2\\pi\\rblr \\int_0^1 dr_0 \\int_{-1}^1d\\mu (1-\\mu)\\int_{\\eps_c}\n n_{\\rm ph}\\siggg d \\eps_s,\n\\end{equation}\nwhere $\\eps_c=2/(1-\\mu)\\epsg$ and the photon-photon cross section\n$\\siggg$ reads\n\\begin{equation}\n\\siggg =\\frac{3\\st}{16}(1-\\beta^2)\\left[(3-\\beta^4)\\ln\\left(\n \\frac{1+\\beta}{1-\\beta}\\right)-2\\beta (2-\\beta^2)\\right],\n\\end{equation}\nwhere $\\beta$ is the speed of the electron and positron in the center of\nmomentum frame $\\beta=\\left[1-2/\\epsg \\eps_s(1-\\mu)\\right]^{1/2}$.\nPerforming the integral we have\n\\begin{equation}\n\\tgg=n_0\\st\\rblr \\epsg^{q-1}A(q),\n\\end{equation}\nwhere $A(q)$ reads\n\\begin{equation}\nA(q)=2^{3-q}\\pi A_0(q)\\int_{-1}^1d\\mu(1-\\mu)^qA_1(\\mu),\n\\end{equation}\nwith\n\\begin{equation}\nA_0(q)=\\int_0^1d\\beta (1-\\beta^2)^{q-2}\\beta \\siggg(\\beta),\n\\end{equation}\nand $A_1(\\mu)=\\int_0^1f(\\mu,r_0)dr_0$ is the integral of $f(\\mu,r_0)$ over \nthe entire broad line region, which can be evaluated as\n\\begin{eqnarray}\nA_1&=&\\sqrt{1-\\mu^2}\\nonumber\\\\\n & &\\left\\{\\cos \\theta_0 \\ln \\left[\n \\frac{\\tan {\\phi_1 \\over 2}}{\\tan {\\phi_2 \\over 2}}\\right]\n +\\sin \\theta_0 \\ln \\left[\\frac{\\sin \\phi_1}{\\sin \\phi_2}\\right]\n \\right\\},\n\\end{eqnarray}\nwith $\\phi_1=\\pi/2-\\theta_0$, $\\phi_2=\\arccos \\sqrt{1-\\mu^2}-\\theta_0$,\nand $\\theta_0=\\arcsin \\sqrt{1-\\mu^2}$.\nThe function $A(q)$ is plotted in Fig 3. Since the beamed radiation\nfield reduces the effective cross section of photon-photon interaction\nby a factor $1/(2\\Gam)^2$, it would be convenient to check our\napproximation by the quantity $(2\\Gam)^2A(q)$. We can easily find that it is\nclose to 0.3$\\sim$0.4 when $q \\sim 1.7$, suggesting our approximation is \naccurate enough. It should be pointed out that the present treatments of\nreflected synchrotron radiation can be conveniently extended to the inclusion\nof the radiation from the secondary electrons if we further study the pair \ncascade in the future. \n\n\\subsection{The Dimension of External Absorption}\nThe last two subsections are devoted to the {\\it internal} absorption of TeV\nphotons, the developments of pair cascade due to the present mechanism\nwill be treated in a preparing paper (Wang, Zhou \\& Cheng 2000).\nHowever it would be useful to compare the dimensions and radiation of\nthe pair cloud due to the {\\it internal} absorption and the pair halo\nsuggested by Aharonian, Coppi, \\& Veolk (1994), who argue the formation of \npair halo due to the interaction of TeV photons from AGNs with infrared\nphotons of cosmological background radiation. This {\\it external}\nabsorption produces pairs, which are quickly isotropized by an ambient\nrandom magnetic field, forming a extended halo of pairs with typical \ndimension of ($R>1$Mpc). Without specific mechanism we know that \nthe time scale of halo formation is of about $10^6$ yr. Usually this \nabsorption is regarded as the main mechanism of deficiency of TeV \nemission from {\\it EGRET}-loud blazars (Stecker \\& de Jager 1998). \nLet us simply estimate the scale of pair halo before it is isotropized \nby the ambient magnetic field. Assuming the intergalactic magnetic\nfield $B=10^{-9}$ Gauss, then the mean free path of pair electrons in\nhalo reads\n\\begin{equation}\n\\lambda_{\\rm e}\\approx 1.0 \\left(\\frac{E}{1.0{\\rm TeV}}\\right)^{0.5}\n \\left(\\frac{B}{10^{-9}{\\rm G}}\\right)^{-0.5} ~{\\rm Kpc},\n\\end{equation}\nThe initial halo is of such a dimension, which is much larger than\nthat of {\\rm intrinsic} absorption case. Aharonian, Coppi, \\& Volk\n(1994) have suggested some signatures of such an extended halo,\nespecially for the light curves in high energy bands (Coppi \\&\nAharonian 1999).\nAnyway this is much larger than that of the present {\\rm internal} \npair cloud. Thus it is easier to distinguish the two cases.\n\n\\section{Applications}\nWe have set a new constraint on the very high energy emission in term\nof observable quantities. As the applications of the present model, \nwe would like to address some properties of very high energy from blazars.\n\n\\subsection{Broadband Continuum and Mirror}\nThe broadband continuum of blazars show attractive features which indicate\nthe different processes powering the objects.\nThe ratio $L_{\\gam}/L_{\\rm op}$\nof $\\gam$-ray luminosity to optical in flat spectrum radio quasars (FSRQs)\nis quite different from that in BL Lacs (Dondi \\& Ghisellini 1995).\nComastri et al (1997) confirmed this result in a more larger samples\nand found this mean ratio\nis roughly of unity in BL Lacs and $L_{\\gam}/L_{\\rm op}\\approx 30$,\nnamely $l_{\\rm rsc}\\approx 0.03$ in FSRQs. \nGhisellini et al (1993), using the classical limit of SSC model,\nshow that there is a systematical difference in Doppler factors $\\cd$ between\nBL Lacs and core-dominated quasars, $\\langle \\log \\cd \\rangle=0.12$ for \nBL Lacs and $\\langle \\log \\cd \\rangle=0.74$ for core-dominated quasars. \nThese differences have been confirmed by G\\\"uijosa \\& Daly (1996) who assume\nthat the particles and magnetic field are in equipartition.\nThis difference would lead to more prominent difference of reflected \nsynchrotron photon energy density, suggesting a different mechanism in \nthese objects. The two systematically different features in\n$\\lrsc$ and Doppler factor $\\cd$ strongly suggest that the different \nmechanism of $\\gam$-ray \nradiation may operate in these objects. From eq.(15) it is believed that\nthe deficiency of TeV emission in radio-loud quasars may be {\\it intrinsic}\ndue to the present mechanism. \n\n\\subsection{On Mrk 421 and 3C 279}\nWhipple observatory had ever searched for TeV gamma-ray emission for 15\nEGRET-AGNs with low redshift, but only Mrk 421 has positive signal(Kerrick et\nal 1995). Even at present stage only three X-ray selected BL Lacs have been\nreported as TeV emitters, Mrk 421, Mrk 501 and\n1ES2344+514 (Cataness et al 1997), and PKS 2155-304 is a potential TeV\nemittor (Chadwick et al 1999).\nWe can apply the present model to the two representative sources:\nMrk 421 and 3C 279 for specific illustration.\n\n{\\it Mrk 421:} This is an X-ray selected BL Lac object, and has been\ndetected GeV $\\gam$-ray emission by EGRET (Lin et al 1992), and the first\nTeV emission by Whipple (Punch et al 1992). It has been extensively and\nfrequently observed by telescopes from radio to TeV bands(Kerrick et al 1995,\nMacomb et al 1995, Takahashi et al 1996, Krennrich et al 1999).\nTeV observations of Mrk 421 by Whipple show that the TeV photon did\nnot flare much more dramatically than the X-rays, suggesting that the \nenhanced high-energy electrons were scattering off a part of the \nsynchrotron spectral energy distribution that remained constant \n(Takahashi et al 1996). Roughly\nspeaking this object satisfies the energy equipartition for the two\npower peaks(Zdziarski \\& Krolik 1993, Macomb et al 1995), suggesting\n$\\lssc\\approx 1$ (Macomb et al 1995), and pure SSC model agrees with the \nobservations (Krennrich et al 1999), suggesting $\\lrsc\\gg 1$. This \nindicates the RSC process is not important. The\nsynchrotron component peaks in luminosity at UV to soft X-ray energies\nand continues into KeV X-rays(Maraschi, Ghisellini \\& Celotti 1994).\nThe gamma-ray emission extends from 50 MeV to an astounding TeV. Data\ncombined over several periods (Lin et al 1992) reveal a hard GeV\nspectrum ($\\al_{\\rm GeV}\\approx 0.7$) by EGRET and a steeper one at TeV\nenergies ($\\al_{\\rm TeV}\\approx 1.30$) from the Whipple observatory\n(Schubnell et al 1994), implying a spectral break. \nThe multiwavelegenth spectrum shows that\n$\\nu_{\\rm s}=3\\times 10^{16}$Hz, $\\nu_{\\rm rsc}=6.5\\times 10^{25}$Hz,\nand $\\alpha=2.0$ (Macomb et al 1995, Kubo et al 1998). The shortest\ntimescale of $\\gam$-ray variability is about $\\dt \\approx 20$ minutes \n(Gaidos et al 1996). If we take $\\cd=10$ and $\\lrsc=1$, we have \n$\\tggrsc=5.0\\times 10^5$ for TeV photons. This means $\\lrsc \\gg 1$,\nwhich is consistent with pure SSC model. From this we can estimate the \nscattering medium $\\tblr=2.0\\times 10^{-4}$ [$\\tggrsc=1$]\nwhen we take $\\lrsc=5.\\times 10^{-5}$ and $2\\Gam=10$,\nsuggesting the mirror effects can be ruled out in this object.\nThis result agrees to the absence of any evident emission lines in Mrk 421.\nInterestingly, Celotti, Fabian \\& Rees (1998) have suggested from rapid \nTeV variability of Mrk 421\nthat its accretion rate is lower than $10^{-2}\\sim 10^{-3}$ Eddington rate.\nThey thus propose that advection-dominated accretion flow or ion pressure \nsupported tori (Ichimaru 1977, Rees et al 1982, Narayan \\& Yi 1994) may \npower the luminosity. \n\n{\\it 3C 279:} This is a typical FSRQ. The first Whipple observation shows \nnegative signal in TeV\n(Kerrick et al 1995), however the multiwavelength simultaneous\nobservations by {\\it EGRET}, {\\it ASCA}, {\\it RXTE}, {\\it ROSAT}, {\\it IUE}\n in 1996 January-February\nshow an intensive flare with very flat spectrum in {\\it EGRET} band (Wehrle\net al 1998), showing $\\lrsc\\approx 10^{-1}$ \nat the high state of $\\gam$-ray emission. It has been argued that\nRSC may explain the 1996 gamma-ray flare (Wehrle et al 1998). \nThe observed flare show that\nthe synchrotron emission peaks at $\\nu_{\\rm s}=5.0\\times 10^{12}$Hz,\n$\\nu_{\\rm rsc}=1.0\\times 10^{23}$Hz, $\\lrsc=0.1$, and $\\dt=$8hr\n(Wehrle et al 1998). If we take \n$\\cd=10$, then we have $\\tggrsc=3.2$. Therefore it is expected that\nno TeV emission occurs in this object. However it is interesting to note\nthat this is due to the {\\it intrinsic} mechanism. We hope that\nthere will be some effects due to the presence of pair production in \nthe VHE flare (Wang, Zhou \\& Cheng 2000). \nThe Q1633+382 (Mattox et al 1993) is quite similar to 3C 279, but it\nshows much smaller $\\lrsc < 10^{-2}$. The strong reflected synchrotron\nphotons as seed photons may appear in this object, however its redshift\n($z=0.181$)\nis too large to detect VHE photons due to the absorptions of back ground \nphotons. Here we suggest that the deficiency of VHE emission may be\n{\\it intrinsic}. It is expected to make simultaneous\nobservations at other bands to test its light curves in order to \nreach a decision.\n\n\\section{Conclusions and discussions}\n\nThe present paper focuses our attention on the effects of BLR mirror on the\nattenuation of $\\gam$-ray in blazars. The mirror effect mainly depends \non two parameters: Lorentz factor of the \nbulk motion ($\\Gamma$) and the Thomson scattering depth ($\\tblr$) of \nbroad line region.\nBased on the calculations, we would like to draw the conclusions:\n\n1) The parameters $\\lrsc$ and Doppler factor $\\cd$ in FSRQs are systematically \ngreater than that in BL Lacs. This will cause the more stronger \n``{\\it intrinsic}'' absorption of VHE photons in FSRQs than that in BL Lacs.\nIt is predicted that there is general absence of very high energy emission\nin FSRQs, owning to the attenuation of VHE photons by the BLR reflection of\nsynchrotron emission. \n\n2) The mirror model provides a new constraint on relativistic bulk motion.\nThat {\\it intrinsic} absorption of TeV photons may operate in\nsome objects, especially in FSRQs. This constraint is cause by the motion\nof blob itself.\n\nAlthough the origin of $\\gam$-ray emission in blazars still remains open,\nVHE observations sets strong constraints on blazar's radiation mechanism. \nThese constraints are:\n(1) brightness temperature exceeding the Kellermann-Pauliny-Toth (Begelman \net al 1994), (2) multiwavelength light curves based on the homogeneous\nmodel (Mastichiadis \\& Kirk 1997), (3) high energy variations in X-ray\nand $\\gam$-ray including interaction with background IR radiation (Coppi\n\\& Aharonian 1999). These constraints are mainly based on SSC model. \nThe deficiency of VHE photons from high redshift $\\gamma$-ray loud blazars\nmay be explained by the interaction of the cosmic background radiation\nfields with the VHE photons. However the possible alternative mechanism\nmay be due to the {\\it intrinsic} attenuation by the reflected synchrotron\nphotons. Three BL Lac objects have been found to show $H\\alpha$ and $H\\beta$\nemission, indicating the existence of broad line region in these objects\n(Vermeulen et al 1995, Corbett et al 1996), even Mrk 421 has been detected \nweak luminosity of a broad emission line (Morgani, Ulrich \\& Tadhunter 1992). \nThe increasing evidence of the presence of broad emission lines\nin BL Lacs lends the possibility that the reflected external photons might\nbe the main source of seed photon in this kind of blazars. Distinguishing \nthe two different mechanisms might be traced by \nthe following-up observations in other wavebands because a pair \ncascade process may be developed, forming a pair halos in the {\\it external}\nabsorption (Aharonian, Coppi \\& Voelk 1994).\nSuch an extended halo due to {\\it external} absorption may be of very \nlong variable timescale at least $\\sim 10^3$ yr (corresponding to one\nmean free path) [see equation (24)]. \nHowever if the {\\it intrinsic} absorption works in the central\nengine, the time-dependent synchrotron self-Compton model including\npair cascade (Wang, Zhou \\& Cheng 2000) could predict\nthe interesting spectrum and light curves, which may interpret the variations\nof PKS 2155-304 (Urry et al 1997). \nThe other radiative properties of such an extended pair halo are needed to\nbe studied in order to distinguish the {\\it intrinsic} absorption\nfrom the {\\it external} one.\n\n\\acknowledgements{\nThe author is very grateful to the anonymous referee for the physical\ninsight of comments and suggestions, especially on the discussions on\nthe angular distribution of reflected synchrotron photons and its\neffects on the opacity of pair production. I thank C.-C. Wang and F.-J. Lu\nfor their careful reading of the manuscript and interesting discussions.\nThe simulating discussions with Y.-Y. Zhou, T.-P. Li, M. Wu and \nB.-F. Liu are gratefully acknowledged. This research is supported by \n'Hundred Talents Program of CAS' and Natural Science\nFoundation of China under Grant No. 19803002.}\n\n\n\\begin{thebibliography}{}\n\\bibitem[]{}Aharonian, F.A., Coppi, P.S. \\& Voelk, H.J., 1994, \\apj, 423, L5\n\\bibitem[]{}Aharonian, F.A., et al for the HEGRA collaboration 1999, \\aap,\n 349, 29 \n\\bibitem[]{}Begelman, M., Rees, M.J. \\& Sikora, M., 1994, \\apj, 429, L57\n\\bibitem[]{}Blandford, R.D. \\& Levinson, A., 1995, \\apj, 441, 79\n%\\bibitem[]{}Bradbury, S.M. et al, 1997, \\aap, 320, L5\n\\bibitem[]{}Bregman, J., 1990, \\aapr, 2, 125\n%\\bibitem[]{}Cataness, M., et al, 1997, \\apj, 480, 562 \n\\bibitem[]{}Cataness, M., et al, 1997, \\apj, 487, L143 \n%\\bibitem[]{}Cataness, M., et al, 1998, \\apj, 501, 616 \n\\bibitem[]{}Chadwick, P.M., et al 1999, \\apj, 513, 161\n\\bibitem[]{}Celotti, A., Fabian, A.C. \\& Rees, M.J., 1998, \\mnras, 293, 239\n\\bibitem[]{}Comastri, A., Fossati, G., Ghisellini, G. \\& Molendi, S., 1997\n \\apj, 480, 534\n\\bibitem[]{}Coppi, P.S. \\& Aharonian, F., 1999, ApJ, 521, L33\n\\bibitem[]{}Coppi, P.S. \\& Blandford, R.D., 1990, \\mnras, 245, 453\n\\bibitem[]{}Corbett, E.A., Robinson, A., Axon, D.J., Hough, J.H., Jeffries,\nR.D., Thurston, M.R. \\& Young, S., 1996, \\mnras, 281, 737 \n\\bibitem[]{}Dermer, C.D. \\& Schlikeiser, R., 1993, \\apj, 416, 458\n\\bibitem[]{}Dondi, L. \\& Ghisellini, G., 1995, \\mnras, 273, 583\n%\\bibitem[]{}Fazio, G.G. \\& Stecker, F.W., 1970, \\nat, 226, 135\n%\\bibitem[]{}Fichtel, C.E., et al, 1994, \\apjs, 94, 551\n\\bibitem[]{}Harwit, M., Protheroe, R.J., \\& Biermann, P.L., \\apj, 524, 91 \n\\bibitem[]{}Gaidos, J.A., et al, 1996, \\nat, 383, 319\n\\bibitem[]{}Ghisellini, G. \\& Madau, P., 1996, \\mnras, 280, 67\n%\\bibitem[]{}Ghisellini, G., Maraschi, L. \\& Treves, A., 1985, \\aap, 146, 204\n\\bibitem[]{}Ghisellini, G., Padovani, P., Celotti, A., Maraschi, L., 1993,\n \\apj, 407, 65\n\\bibitem[]{}Gould, R.J. \\& Schr\\'eder, G.P., 1967, Phys. Rev., 155, 1404\n\\bibitem[]{}G\\\"uijosa, A. \\& Daly, R.A., 1996, \\apj, 461, 600\n\\bibitem[]{}Ichimaru, S., 1977, ApJ, 214, 840\n%\\bibitem[]{}Jelly, J.V., 1966, \\nat, 211, 472\n\\bibitem[]{}Kerrick, A.D., et al, 1995, \\apj, 452, 588\n%\\bibitem[]{}Kniffen, D.A., 1993, \\apj, 411, 133\n\\bibitem[]{}Krennrich, F. et al, 1999, \\apj, 511, 149\n\\bibitem[]{}Kubo, H. et al, 1998, \\apj, 504, 693\n\\bibitem[]{}Lin, Y.C., et al, 1992, \\apj, 401, L61\n%\\bibitem[]{}Lin. Y.C., et al, 1994, in AIP Conf. Proc. 304, Second Compton\n%Symposium, ed. C.E. Fichtel, N. Gehrels \\& J.P. Norris (New York: AIP), 582\n\\bibitem[]{}Macomb, D.J. et al, 1995, \\apj, 449, L99\n\\bibitem[]{}Madau, P., Pozzetti, L., \\& Dickinson, M., 1998, \\apj, 498, 106\n\\bibitem[]{}Maraschi, L., Ghisellini, G. \\& Celotti, A., 1992, \\apj, 397, L5\n\\bibitem[]{}Maraschi, L., Ghisellini, G. \\& Celotti, A., 1994, in\nMultiwavelength continuum emission of AGN. ed. T.J.-L. Courvoisier \\& A.\nBleche (Dordrecht: Kluwer), 221\n\\bibitem[]{}Mastichiadis, A. \\& Kirk, J.G., 1997, \\aap, 320, 19\n\\bibitem[]{}Mattox, J.R., et al, 1993, \\apj, 410, 609\n\\bibitem[]{}Morgani, R., Ulrich, M.-H., Tadhunter, C.N., 1992, \\mnras, 254, 546\n\\bibitem[]{}Mukherjee, R., Hartman, R.C., Lin, Y.C. \\& Sreekumar, P., 1999,\n \\baas, 31, 699\n\\bibitem[]{}Narayan, R. \\& Yi, I., 1994, \\apj, 412, L13\n\\bibitem[]{}Pacholczyk, A.G., 1970, Radio astrophysics, Freeman (San Francisco)\n%\\bibitem[]{}Pian, E., et al, 1998, \\apj, 492, L17\n\\bibitem[]{}Punch, M. et al, 1992, \\nat, 358, 477\n%\\item[]{}Quinn, J. et al, 1996, \\apj, 456, L83\n%\\bibitem[]{}Readhead, T., 1994, \\apj, 426, 51\n\\bibitem[]{}Rees, M.J., Begelman, M.C., Blandford, R.D., \\& Phinney, E.S.,\n1982, \\nat, 295, 17\n\\bibitem[]{}Roberts, M.D., et al, 1999, \\aap, 343, 691 \n%\\bibitem[]{}Sambruna, R.M., 1997, \\apj, 487, 536\n\\bibitem[]{}Sambruna, R.M., Maraschi, L. \\& Urry, M.C., 1996, \\apj, 463, 444\n\\bibitem[]{}Schubnell, M., et al, 1994, in AIP Conf. Proc. 304, Second Compton\nSymposium, ed. C.E. Fichtel, N. Gehrels \\& J.P. Norris (New York: AIP), 602\n\\bibitem[]{}Sikora, M., Begelman, M. \\& Rees, M.J., 1994, \\apj, 421, 153\n%\\bibitem[]{}Sitko, M. \\& Junkkarinen, V.T., 1985, \\pasp, 97, 158\n\\bibitem[]{}Stecker, F.W. \\& de Jager, O.C., 1998, \\aap, 476, 712\n\\bibitem[]{}Stecker, F.W., de Jager, O.C. \\& Salamon, M.H., 1996, \n \\apj, 473, L75\n\\bibitem[]{}Steidel, C.C, et al, 1998, in A. Banday et al. eds. Evolution of\nLarge Scale Structure, to be published.\n\\bibitem[]{}Takahashi, F., et al , 1996, \\apj, 470, L89\n\\bibitem[]{}Tavecchio, F., Maraschi, L. \\& Ghisellini, G., 1998, \n \\apj, 509, 608\n%\\bibitem[]{}Ulrich, M.-H., 1981, \\aap, 103, L1\n\\bibitem[]{}Urry, C.M. et al , 1997, \\apj, 486, 799\n\\bibitem[]{}Vermeulen, R.C., et al, 1995, \\apj, 452, L5\n\\bibitem[]{}von Montigny, C. et al, 1995, \\apj, 440, 525\n\\bibitem[]{}Wang, J.-M., Zhou, Y.-Y. \\& Cheng, K.S., 2000, in preparation\n\\bibitem[]{}Wehrle, A.W., et al, 1998, \\apj, 497, 178\n\\bibitem[]{}Zdziaski, A.A. \\& Krolik, J.H., 1993, \\apj, 409, L33\n%\\bibitem[]{}Zhou, Y.-Y., Lu, Y.-J., Wang, T.-G., Yu.K.N., \\& Young, E.C.M.,\n% 1997, \\apj, 484, L47\n\\end{thebibliography}\n\n\n\\newpage\n\\begin{figure}\n\\vspace{7.5cm}\n\\epsscale{9.0}\n\\plotfiddle{fig1.ps}{190pt}{-90}{75}{85}{-295}{560}\n\\vspace{-30mm}\n\\caption{The opacity of pair production vs the ratio of two peak fluxes\nin the continuum of blazars. We set $\\cd=10$, $\\dt=1$day, \n$\\nu_{\\rm s}=4.0\\times 10^{14}$Hz, and $\\nursc=10^{25}$Hz.\nThe lines from the below to upper\nare corresponding to the opacity of very high energy photon with \n$\\eps_{\\rm obs}=1.0,3.5,6.0,8.5$TeV, respectively.}\n\\label{fig1}\n\\end{figure} \n\n\\newpage\n\\begin{figure}\n\\vspace{7.5cm}\n\\epsscale{9.0}\n\\plotfiddle{fig2.ps}{190pt}{-90}{75}{85}{-295}{560}\n\\vspace{-30mm}\n\\caption{The angular distribution of reflected synchrotron photons.\nThe location is $r_0=0.9$. The solid line represents the function\nof angular distribution $f(\\mu,r_0)$.}\n\\label{fig2}\n\\end{figure} \n\n\\newpage\n\\begin{figure}\n\\vspace{7.5cm}\n\\epsscale{9.0}\n\\plotfiddle{fig3.ps}{190pt}{-90}{75}{85}{-295}{560}\n\\vspace{-30mm}\n\\caption{The plot of $A(q)$ vs $q$ (eq. 21). We multiply $A(q)$ by\nthe factor $(2\\Gam)^2$ in order to see the reduced cross section of\nphoton-photon interaction in anisotropic radiation field. We take\n$\\Gam=10$.}\n\\label{fig3}\n\\end{figure} \n\n\\end{document}\n"
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{
"name": "astro-ph0002402.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[]{}Aharonian, F.A., Coppi, P.S. \\& Voelk, H.J., 1994, \\apj, 423, L5\n\\bibitem[]{}Aharonian, F.A., et al for the HEGRA collaboration 1999, \\aap,\n 349, 29 \n\\bibitem[]{}Begelman, M., Rees, M.J. \\& Sikora, M., 1994, \\apj, 429, L57\n\\bibitem[]{}Blandford, R.D. \\& Levinson, A., 1995, \\apj, 441, 79\n%\\bibitem[]{}Bradbury, S.M. et al, 1997, \\aap, 320, L5\n\\bibitem[]{}Bregman, J., 1990, \\aapr, 2, 125\n%\\bibitem[]{}Cataness, M., et al, 1997, \\apj, 480, 562 \n\\bibitem[]{}Cataness, M., et al, 1997, \\apj, 487, L143 \n%\\bibitem[]{}Cataness, M., et al, 1998, \\apj, 501, 616 \n\\bibitem[]{}Chadwick, P.M., et al 1999, \\apj, 513, 161\n\\bibitem[]{}Celotti, A., Fabian, A.C. \\& Rees, M.J., 1998, \\mnras, 293, 239\n\\bibitem[]{}Comastri, A., Fossati, G., Ghisellini, G. \\& Molendi, S., 1997\n \\apj, 480, 534\n\\bibitem[]{}Coppi, P.S. \\& Aharonian, F., 1999, ApJ, 521, L33\n\\bibitem[]{}Coppi, P.S. \\& Blandford, R.D., 1990, \\mnras, 245, 453\n\\bibitem[]{}Corbett, E.A., Robinson, A., Axon, D.J., Hough, J.H., Jeffries,\nR.D., Thurston, M.R. \\& Young, S., 1996, \\mnras, 281, 737 \n\\bibitem[]{}Dermer, C.D. \\& Schlikeiser, R., 1993, \\apj, 416, 458\n\\bibitem[]{}Dondi, L. \\& Ghisellini, G., 1995, \\mnras, 273, 583\n%\\bibitem[]{}Fazio, G.G. \\& Stecker, F.W., 1970, \\nat, 226, 135\n%\\bibitem[]{}Fichtel, C.E., et al, 1994, \\apjs, 94, 551\n\\bibitem[]{}Harwit, M., Protheroe, R.J., \\& Biermann, P.L., \\apj, 524, 91 \n\\bibitem[]{}Gaidos, J.A., et al, 1996, \\nat, 383, 319\n\\bibitem[]{}Ghisellini, G. \\& Madau, P., 1996, \\mnras, 280, 67\n%\\bibitem[]{}Ghisellini, G., Maraschi, L. \\& Treves, A., 1985, \\aap, 146, 204\n\\bibitem[]{}Ghisellini, G., Padovani, P., Celotti, A., Maraschi, L., 1993,\n \\apj, 407, 65\n\\bibitem[]{}Gould, R.J. \\& Schr\\'eder, G.P., 1967, Phys. Rev., 155, 1404\n\\bibitem[]{}G\\\"uijosa, A. \\& Daly, R.A., 1996, \\apj, 461, 600\n\\bibitem[]{}Ichimaru, S., 1977, ApJ, 214, 840\n%\\bibitem[]{}Jelly, J.V., 1966, \\nat, 211, 472\n\\bibitem[]{}Kerrick, A.D., et al, 1995, \\apj, 452, 588\n%\\bibitem[]{}Kniffen, D.A., 1993, \\apj, 411, 133\n\\bibitem[]{}Krennrich, F. et al, 1999, \\apj, 511, 149\n\\bibitem[]{}Kubo, H. et al, 1998, \\apj, 504, 693\n\\bibitem[]{}Lin, Y.C., et al, 1992, \\apj, 401, L61\n%\\bibitem[]{}Lin. Y.C., et al, 1994, in AIP Conf. Proc. 304, Second Compton\n%Symposium, ed. C.E. Fichtel, N. Gehrels \\& J.P. Norris (New York: AIP), 582\n\\bibitem[]{}Macomb, D.J. et al, 1995, \\apj, 449, L99\n\\bibitem[]{}Madau, P., Pozzetti, L., \\& Dickinson, M., 1998, \\apj, 498, 106\n\\bibitem[]{}Maraschi, L., Ghisellini, G. \\& Celotti, A., 1992, \\apj, 397, L5\n\\bibitem[]{}Maraschi, L., Ghisellini, G. \\& Celotti, A., 1994, in\nMultiwavelength continuum emission of AGN. ed. T.J.-L. Courvoisier \\& A.\nBleche (Dordrecht: Kluwer), 221\n\\bibitem[]{}Mastichiadis, A. \\& Kirk, J.G., 1997, \\aap, 320, 19\n\\bibitem[]{}Mattox, J.R., et al, 1993, \\apj, 410, 609\n\\bibitem[]{}Morgani, R., Ulrich, M.-H., Tadhunter, C.N., 1992, \\mnras, 254, 546\n\\bibitem[]{}Mukherjee, R., Hartman, R.C., Lin, Y.C. \\& Sreekumar, P., 1999,\n \\baas, 31, 699\n\\bibitem[]{}Narayan, R. \\& Yi, I., 1994, \\apj, 412, L13\n\\bibitem[]{}Pacholczyk, A.G., 1970, Radio astrophysics, Freeman (San Francisco)\n%\\bibitem[]{}Pian, E., et al, 1998, \\apj, 492, L17\n\\bibitem[]{}Punch, M. et al, 1992, \\nat, 358, 477\n%\\item[]{}Quinn, J. et al, 1996, \\apj, 456, L83\n%\\bibitem[]{}Readhead, T., 1994, \\apj, 426, 51\n\\bibitem[]{}Rees, M.J., Begelman, M.C., Blandford, R.D., \\& Phinney, E.S.,\n1982, \\nat, 295, 17\n\\bibitem[]{}Roberts, M.D., et al, 1999, \\aap, 343, 691 \n%\\bibitem[]{}Sambruna, R.M., 1997, \\apj, 487, 536\n\\bibitem[]{}Sambruna, R.M., Maraschi, L. \\& Urry, M.C., 1996, \\apj, 463, 444\n\\bibitem[]{}Schubnell, M., et al, 1994, in AIP Conf. Proc. 304, Second Compton\nSymposium, ed. C.E. Fichtel, N. Gehrels \\& J.P. Norris (New York: AIP), 602\n\\bibitem[]{}Sikora, M., Begelman, M. \\& Rees, M.J., 1994, \\apj, 421, 153\n%\\bibitem[]{}Sitko, M. \\& Junkkarinen, V.T., 1985, \\pasp, 97, 158\n\\bibitem[]{}Stecker, F.W. \\& de Jager, O.C., 1998, \\aap, 476, 712\n\\bibitem[]{}Stecker, F.W., de Jager, O.C. \\& Salamon, M.H., 1996, \n \\apj, 473, L75\n\\bibitem[]{}Steidel, C.C, et al, 1998, in A. Banday et al. eds. Evolution of\nLarge Scale Structure, to be published.\n\\bibitem[]{}Takahashi, F., et al , 1996, \\apj, 470, L89\n\\bibitem[]{}Tavecchio, F., Maraschi, L. \\& Ghisellini, G., 1998, \n \\apj, 509, 608\n%\\bibitem[]{}Ulrich, M.-H., 1981, \\aap, 103, L1\n\\bibitem[]{}Urry, C.M. et al , 1997, \\apj, 486, 799\n\\bibitem[]{}Vermeulen, R.C., et al, 1995, \\apj, 452, L5\n\\bibitem[]{}von Montigny, C. et al, 1995, \\apj, 440, 525\n\\bibitem[]{}Wang, J.-M., Zhou, Y.-Y. \\& Cheng, K.S., 2000, in preparation\n\\bibitem[]{}Wehrle, A.W., et al, 1998, \\apj, 497, 178\n\\bibitem[]{}Zdziaski, A.A. \\& Krolik, J.H., 1993, \\apj, 409, L33\n%\\bibitem[]{}Zhou, Y.-Y., Lu, Y.-J., Wang, T.-G., Yu.K.N., \\& Young, E.C.M.,\n% 1997, \\apj, 484, L47\n\\end{thebibliography}"
}
] |
astro-ph0002403
|
ISO far-infrared observations of rich galaxy clusters\thanks{ Based on observations with ISO, an ESA project with instruments founded by ESA member states (especially the PI countries: France, Germany, the Netherlands, and the United Kingdom) and with the participation of ISAS and NASA}
|
[
{
"author": "L. Hansen\\inst{1}"
},
{
"author": "H.E. J{\\o}rgensen\\inst{1}"
},
{
"author": "H.U. N{\\o}rgaard-Nielsen\\inst{2}"
},
{
"author": "K. Pedersen\\inst{2}"
},
{
"author": "P. Goudfrooij\\inst{3,4}"
},
{
"author": "M.J.D. Linden-V{\\o}rnle\\inst{1,2}"
}
] |
In a series of papers we investigate far-infrared emission from rich galaxy clusters. Maps have been obtained by ISO at $60\mu {m}$, $100\mu {m}$, $135\mu {m}$, and $200\mu {m} $ using the PHT-C camera. Ground based imaging and spectroscopy were also acquired. Here we present the results for the cooling flow cluster S\'{e}rsic\,159-03. An infrared source coincident with the dominant cD galaxy is found. Some off-center sources are also present, but without any obvious counterparts.
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[
{
"name": "Sersic.tex",
"string": "%\n% Accepted by A&A February 21, 2000\n%\n\\documentclass[]{aa} \n%\n\\input epsf.tex\n%\n\\topmargin -30pt \n%\\topmargin 27pt \n%\n\\title{ISO far-infrared observations of rich galaxy clusters\\thanks{\nBased on observations with ISO, an ESA project with instruments founded by\nESA member states (especially the PI countries: France, Germany, the\nNetherlands, and the United Kingdom) and with the participation of ISAS\nand NASA}\n}\n\\subtitle{II. \\object{S\\'{e}rsic\\,159-03}}\n%\n%\n\\author{L. Hansen\\inst{1} \n\\and H.E. J{\\o}rgensen\\inst{1}\n\\and H.U. N{\\o}rgaard-Nielsen\\inst{2}\n\\and K. Pedersen\\inst{2}\n\\and P. Goudfrooij\\inst{3,4} \n\\and M.J.D. Linden-V{\\o}rnle\\inst{1,2}\n}\n%\n\\institute{\nCopenhagen University Observatory,\nJuliane Maries Vej 30,\nDK-2100 Copenhagen, Denmark\n\\and \nDanish Space Research Institute,\nJuliane Maries Vej 30,\nDK-2100 Copenhagen, Denmark\n\\and \nSpace Telescope Science Institute,\n3700 San Martin Drive, Baltimore, \nMD 21218, USA \n\\and\nAffiliated to the Astrophysics Division, Space Science Department,\nEuropean Space Agency}\n%\n\\offprints{L. Hansen}\n\\mail{leif@astro.ku.dk}\n\\authorrunning{Hansen et al.}\n\\titlerunning{S\\'{e}rsic\\,159-03}\n%\n%\\date{DRAFT; \\today}\n\\date{Received date; accepted date}\n\n\\begin{document}\n%\n\\thesaurus{03 % Section 3: Extragalactic Astronomy\n(11.03.4 S\\'{e}rsic\\,159-03 % Galaxies: clusters: individual: S\\'{e}rsic\\,159-03\n 13.09.1) % Infrared: galaxies\n } \n\\maketitle\n%\n\\begin{abstract}\nIn a series of papers we investigate far-infrared emission from rich galaxy \nclusters. Maps have been obtained by ISO at $60\\mu {\\rm m}$, $100\\mu {\\rm m}$, \n$135\\mu {\\rm m}$, and $200\\mu {\\rm m} $ using the PHT-C camera. Ground based\nimaging and spectroscopy were also acquired. Here we present the results\nfor the cooling flow cluster S\\'{e}rsic\\,159-03. An infrared source coincident\nwith the dominant cD galaxy is found. Some off-center sources are also\npresent, but without any obvious counterparts.\n\\end{abstract}\n%\n\\keywords{ \n galaxies: clusters: individual: S\\'{e}rsic\\,159-03 -- \n infrared: galaxies\n }\n%\n%\n\\section{Introduction}\n\\label{introduction}\n%\nThe first paper in this series (Hansen et al. \\cite{han99}, paper{\\sc \\,i})\npresented infrared data for the Abell\\,2670 cluster. We identified 3 \nfar-infrared sources apparently related to star forming galaxies in the\ncluster. The present paper concerns the rich cluster S\\'{e}rsic\\,159-03. \n%\nThe central part of the S\\'{e}rsic\\,159-03 cluster was mapped by the\nInfrared Space Observatory (ISO) satellite, using the PHT-C camera \n(Lemke et al. \\cite{lem96}) at $60\\mu {\\rm m}$, $100\\mu {\\rm m}$,\n$135\\mu {\\rm m}$, and $200\\mu {\\rm m} $. The observations were performed\ntwice with slightly different position angles which gives an opportunity \nto do independent detections and to study possible instrumental effects.\n\nThe S\\'{e}rsic\\,159-03 cluster (Abell S1101, z=0.0564) is of richness class 0, \nBautz-Morgan type{\\sc \\,iii} with a central dominant cD galaxy \n(Abell et al. \\cite{abe89}). A cooling flow is \npresent, and Allen and Fabian (\\cite{all97}) found a mass deposition rate of\n${\\rm \\dot{M} = 231^{+11}_{-10} ~M_{\\sun} ~yr^{-1}}$ from ROSAT PSPC data. \nThe cooling flow is centered on the cD~galaxy which exhibits nebular\nline emission. Crawford and Fabian (\\cite{cra92}) obtained optical spectra\nand found from line-ratio diagrams that the ratios obtained along the slit\nbridged the gap between class{\\sc \\,i} and class{\\sc \\,ii} in the scheme of \nHeckman et al. (\\cite{hec89}). Their spectra had position angle $90\\degr$. \nWest of the center they discovered a detached\nfilament of emission having extreme class{\\sc \\,ii} characteristics. They\nargued that the different line ratios are due to changes in ionization\nproperties. Below in Fig.~\\ref{emission} we show the extent of the \nnebular emission.\nIn a subsequent paper Crawford and Fabian (\\cite{cra93}) included IUE data\nto obtain the optical-ultraviolet continuum. They announced that a strong\nLy$\\alpha$ line is present in the IUE spectrum.\n\n%\n\\section{Observations}\n\\label{observations}\n%\n\\subsection{The ISO data}\n\\label{ISOobs}\n%\nA rectangular area centered on the cD galaxy of S\\'{e}rsic\\,159-03\nwas mapped by ISO May 7, 1996 on revolution 173. The projected Z-axis of the\nspacecraft had a position angle of $54 \\fdg 4$ on the sky (measured from north \nthrough east). The observation\nwas repeated June 4, 1996, during revolution 200, but this time with position \nangle $69 \\fdg 5$. The observing mode was PHT\\,32 as for Abell\\,2670\n(paper{\\sc \\,i}). The 9 pixel C100 detector was used for \n$60\\mu {\\rm m} $ and $100\\mu {\\rm m} $ to map an area of\n$10 \\farcm 0 \\times 3 \\farcm 8$. For $135\\mu {\\rm m} $ and \n$200\\mu {\\rm m} $ the 4 pixel C200 detector was applied to cover a mapped \narea of $11 \\farcm 0 \\times 4 \\farcm 6$. The target dedicated times were\n1467 seconds for C100 and 1852 seconds for C200. \n\n\\begin{figure}\n% Constructed by /home/leif/diskb/Sersic/programmes/FigPIA.pro\n \\epsfxsize=8.7cm\n \\epsfbox{Fig_1.eps}\n \\caption[]{\nThe brightness maps for the four pass-bands are shown for revolutions 173 \nand 200. Maximum brightness is dark. The maps are all centered on \nthe dominant cD galaxy, but the revolution 200 maps are rotated $15 \\degr$\ncounter-clockwise on the sky with respect to the revolution 173 maps. \nThe C100 maps (left) cover $10 \\farcm 0 \\times 3 \\farcm 8$ while the C200\nmaps (right) cover $11 \\farcm 0 \\times 4 \\farcm 6$. The features\nmarked with numbers in the $60\\mu {\\rm m} $ maps are regarded as real\nsources. An optical image of the field is shown in Fig.~\\ref{field}\n }\n \\label{PIAim}\n\\end{figure}\n%\n\\begin{table*}\n\\caption[]{\nParameters describing the spectroscopy\n}\n\\begin{flushleft}\n\\begin{tabular}{l l l l l l }\n\\hline\nGrism & P.A. & exp. & slit & $\\Delta \\lambda$ & range \\\\\n & & min. & arcsec & \\AA & \\AA \\\\\n\\hline\n\\#8 & $21\\degr$ & 40 & 1.5 & 4 & 5900-8300 \\\\\n\\#8 & $270\\degr$ & 40 & 1.5 & 4 & 5900-8300 \\\\\n\\#10 & $21\\degr$ & 45 & 1.5 & 24 & 3500-8800 \\\\\n\\#10 & $270\\degr$ & 30 & 1.5 & 24 & 3500-8800 \\\\\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\label{spectro}\n\\end{table*}\n%\n%\nAs described in paper{\\sc \\,i} we apply the ISOPHOT Interactive Analysis \nsoftware\\footnote {The ISOPHOT data presented in this paper was reduced using \nPIA, which is a joint development by the ESA Astrophysics Division and the \nISOPHOT consortium.} (PIA) for the reduction work. We also perform parallel\nreductions using our own least squares reduction procedure \n(LSQ, cf. paper{\\sc \\,i}).\nAlthough LSQ does not use sophisticated methods to correct for various \neffects -- e.g. glitches from cosmic rays are simply discarded -- we find \nit valuable for comparisons with the PIA reductions when evaluating the \nreality of features visible in the frames. The conclusion is that the PIA \nreduced images presented here (Fig.~\\ref{PIAim}) do not contain noticeable \nartifacts from glitches. As in paper{\\sc \\,i} we present the data maps \nwith pixel sizes $15 \\arcsec \\times 46 \\arcsec$ for C100 and \n$30 \\arcsec \\times 92 \\arcsec$ for C200, but the instrumental resolution\nis only about $50 \\arcsec$ for C100 and $95 \\arcsec$ for C200 (paper{\\sc \\,i}).\nThe uncertainty of the maps increases towards the left and right borders due \nto the way the mapping was performed.\n\n\n\\subsection{Optical data}\n\\label{opt_obs}\n%\n\\begin{figure}\n \\epsfxsize=8.7cm\n \\epsfbox{Fig_2.eps}\n \\caption[]{\n%\n% The image has been displayed in IRAF and the ISO-fields drawn with markers.\n% The image was grabbed with `xv' and converted to FITS (field.fts). Objects\n% were marked using `Fig_field_over.pro'. The output is `field_mrk.fts' which\n% is converted to POSTSCRIPT using `xv'. The result is `field.eps'.\n%\nAn optical image of the central part of S\\'{e}rsic\\,159-03. North is up and \neast to the left. The areas covered by the two C200 mappings are shown. \nFor comparisons the map shown by Fig.~\\ref{PIAim} should be rotated \ncounter-clockwise by $54 \\fdg 4$ for revolution 173 and $69 \\fdg 5$ for\nrevolution 200. The numbers mark the approximate positions of off-center\nsources\n }\n \\label{field}\n\\end{figure}\n%\nOptical imaging and spectroscopy were performed September 1996 using \nthe DFOSC instrument\non the Danish 1.54m telescope at La~Silla. The field around the central cD \ngalaxy is shown in Fig.~\\ref{field}. The image was obtained by adding \nexposures in B (45 min), V (30 min), and Gunn\\,I (30 min). \nThe distribution of B-I colour for a $70\\arcsec \\times 70\\arcsec$ area \ncovering the central parts of the dominant cD galaxy is given in \nFig.~\\ref{B_I}. \n%\n\\begin{figure}\n% Constructed by ......................\n \\epsfxsize=8.7cm\n \\epsfbox{Fig_3.eps}\n \\caption[]{\nThe B-I colour distribution of the central part of the cD galaxy with\ncontours of the optical surface brightness overlayed (logarithmic scale). \nDark depicts the\nbluest colour. The upper left object is bluer than the cD galaxy by\n$\\Delta $(B-V)=-0.61 or $\\Delta $(B-I)=-1.17. The field is \n$70\\arcsec \\times 70\\arcsec$. North is up and east to the left\n }\n \\label{B_I}\n\\end{figure}\n%\n\n%\nIn order to image the distribution of the nebular emission we obtained narrow\nband exposures through a filter ($\\lambda 6908$, FWHM\\ =\\,98\\,{\\AA}, 1 hour)\ncovering the redshifted H$\\alpha$+[N\\,{\\sc ii}] lines and an off-band filter\n($\\lambda 6801$, FWHM\\,=\\,98\\,{\\AA}, 1 hour). After scaling and subtraction \na H$\\alpha$+[N\\,{\\sc ii}] image is obtained. The central part of this image is\nshown in Fig.~\\ref{emission}.\n%\n\\begin{figure}\n% Constructed by /home/leif/diskb/Sersic/programmes/H_alpha.pro\n \\epsfxsize=8.7cm\n \\epsfbox{Fig_4.eps}\n \\caption[]{\nThe image of H$\\alpha$+[N\\,{\\sc ii}] nebular emission overlayed with\ncontours of the optical image. Same field as Fig.~\\ref{B_I}. \nA filament of emission points from the nucleus along\nposition angle $\\approx 20\\degr$ flaring towards north some $5\\arcsec$\nfrom the center. Emission towards the southwest is also seen. The filament\ndiscovered by Crawford and Fabian (\\cite{cra92}) is clearly visible\npointing outwards between $6\\arcsec$ and $13\\arcsec$ west of the center.\nIf the image is smoothed faint emission becomes evident all the way from \nthe center to the filament. Other faint filaments become visible as well,\ne.g. one associated with the blue object seen in the contours in the upper\nleft part of the figure\n }\n \\label{emission}\n\\end{figure}\n%\n\n\nDetails about the spectroscopy are found in Table~\\ref{spectro}. The slit\nwas positioned on the cD nucleus with two different position angles. \nP.A.=$270\\degr$ covers the western filament, and P.A.=$21\\degr$ passes\nthe object in the upper left corner of Fig.~\\ref{emission} and covers the\njet-like emission to the northeast and southwest.\n\n\n\\section{Results}\n\\label{results}\n%\nThe general brightness distribution in the maps is described most easily\nfor the C200 maps. The $135\\mu {\\rm m} $ and $200\\mu {\\rm m} $ maps\nare rather similar. An enhancement is seen at the center in all four maps\nconcordant with the position of the cD. A maximum is present in the upper left \ncorners. After rotating the revolution 200 maps $15 \\degr$ into coincidence \nwith the rev.~173 maps we find these maxima to overlap suggesting the presence\nof one or more real sources. Similarly there are maxima in the upper right \ncorners. Their positions and relative brightness in the maps can be\nunderstood if a source is present in the upper right corner of the rev.~200\nmaps, but just outside the rev.~173 field. A third characteristic feature\nis the brightness minimum to the lower left (i.e. south) of the center of \nthe C200 maps. Again, when we compare the maps after rotation the reality\nof this minimum is confirmed. We conclude that the brightness distribution seen \nin the C200 maps is real.\n\nThe C100 maps have the advantage of better resolution which improves the\npossibility of identifying optical counterparts. However,\nthe reality of the peaks in the $100\\mu {\\rm m} $ maps is not convincing\nwhen the maps are compared after rotation. Generally the peaks occur at\ndifferent locations. Even the central source is doubtful: The rev.~200\nmap shows a weak enhancement slightly displaced to the right of the center,\nbut the rev.~173 map shows a minimum at the same location. \n\nA comparison between the $60\\mu {\\rm m} $ maps is more successful. Both \nshow a central enhancement (C100-1) although slightly displaced to the \nright (north) in the rev.~173 map. The maximum brightness (object C100-2) \noccurs in both maps\nnear the upper left corners and overlap after rotation. In Fig.~\\ref{field}\nthe approximate positions of overlap is marked by numbers for the off-center\nsources. The rev.~200 map has a peak (C100-3) in the upper \nright corner which may be related to the source present in the C200 \nmaps. Furthermore, the peak (C100-4) in the right part of the \nrev.~200 $60\\mu {\\rm m} $ map overlaps with an enhancement in the \nrev.~173 map. There are disagreements as well, however. The peak\nobvious in the rev.~173 map below C100-4 (confirmed by the LSQ reductions) is\nnot visible in the rev.~200 map. We conclude that the $60\\mu {\\rm m} $\nsources C100-1, C100-2, C100-3, and C100-4 are likely to be real, but that \nthe present reduction software still produces artifacts calling for \ncaution in the interpretation.\n\nIn paper{\\sc \\,i} we found that aperture photometry of the faint sources \nsuffers significantly from the uncertainty in\nthe evaluation of the background level. We therefore prefer to position,\nscale and subtract the PSF from the maps. The success in removing the\nsource is then evaluated by eye. By varying the scaling we estimate the\nmaximum and minimum acceptable flux. The median and its deviation from the \nlimits are given in Table~\\ref{fluxes} for our identified infrared sources.\nWe assume that the two sources in the upper corners of the C200 maps are \nidentical to C100-2 and C100-3. The reality of C100-1 at $100\\mu {\\rm m} $ \nmay be questionable. C100-3 is outside the field in the rev.~173 map. \n%\n\\begin{table*}\n\\caption[]{\nSource fluxes determined from the PIA images (Jy) by positioning, scaling, and\nsubtracting the PSF. The quoted uncertainties are {\\em not} statistical, but\nare subjectively evaluated limits\n}\n\\begin{flushleft}\n\\begin{tabular}{l l l l l l }\n\\hline\nobject & \n$60\\mu{\\rm m}$ & $100\\mu{\\rm m}$ & $135\\mu{\\rm m}$ & $200\\mu{\\rm m}$ & rev. \\\\\n\\hline\nC100-1 & $0.05\\pm0.03$ & $~~~~~~-~~~~$ & $0.05\\pm0.04$ & $0.07\\pm0.04$ & 173 \\\\\n & $0.05\\pm0.02$ & $0.04\\pm0.02$ & $0.07\\pm0.05$ & $0.11\\pm0.05$ & 200 \\\\\n\\hline\nC100-2 & $0.22\\pm0.04$ & $~~~~~~-~~~~$ & $0.22\\pm0.06$ & $0.07\\pm0.04$ & 173 \\\\\n & $0.27\\pm0.06$ & $~~~~~~-~~~~$ & $0.30\\pm0.10$ & $0.12\\pm0.05$ & 200 \\\\\n\\hline\nC100-3 & $~~~~~~-~~~~$ & $~~~~~~-~~~~$ & $~~~~~~-~~~~$ & $~~~~~~-~~~~$ & 173 \\\\\n & $0.12\\pm0.05$ & $~~~~~~-~~~~$ & $0.25\\pm0.05$ & $0.12\\pm0.05$ & 200 \\\\\n\\hline\nC100-4 & $0.11\\pm0.04$ & $~~~~~~-~~~~$ & $~~~~~~-~~~~$ & $~~~~~~-~~~~$ & 173 \\\\\n & $0.10\\pm0.03$ & $~~~~~~-~~~~$ & $~~~~~~-~~~~$ & $~~~~~~-~~~~$ & 200 \\\\\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\label{fluxes}\n\\end{table*}\n\n\\section{Discussion}\n\\label{discussion}\n%\n\\subsection{The cD galaxy}\n\\label{cD}\n%\nThe central infrared source, C100-1, is detected in all maps except at \n$100\\mu {\\rm m} $. The measured fluxes in the two independent observations\nalso agree within the limits. We therefore regard the source as real. \nA comparison with the list of Jura et al. (\\cite{jur87}) shows that the\nluminosity of S\\'{e}rsic\\,159-03 at $60\\mu{\\rm m}$ is larger than other \nearly type galaxies detected by IRAS by an order of magnitude or more,\nexcept the extraordinarily bright galaxy NGC\\,1275 which is the center of the\nPerseus cluster cooling flow, and which is undergoing an encounter \nwith an other galaxy (e.g. N{\\o}rgaard-Nielsen et al., \\cite{noe93}).\n\nIn a previous paper (Hansen~et~al.~\\cite{han95}) we presented a model for the\ninfrared emission from Hydra~A measured by IRAS. We assumed that most of the\nmass cooling out of the cluster gas ends up in low mass stars forming in the\nflow. We further assumed that dust grains were able to grow in the cool \npre-stellar clouds converting a fraction $y$ of the mass into grains. If\nthe mechanism is effective we expect $y \\approx 1$\\%. After a star has formed \nthe remaining material is dispersed in the hot cluster gas. If a fraction $f$ \nis recycled to the hot phase a dust mass of $y \\times f \\times {\\rm \\dot{M}}$ \nis continuously injected into the cluster gas. At forehand we expect $f$ to\nbe approximately $1-50$\\%. The grains are destroyed by sputtering on a time \nscale $\\tau_{\\rm d}$, and a steady state is obtained. At any time a dust mass \nof ${\\rm M_{d}}\\,=~y \\times f \\times {\\rm \\dot{M}} \\times \\tau_{\\rm d}$\nis present. The grains are heated by hot electrons (in the inner galaxy the\nphoton field may also be important), and the infrared emission can be \nevaluated. The present data do not allow testing of more elaborate\nmodels having radial distributions of e.g. the dust temperature. We therefore\nonly make a simple estimate using mean values.\n\nFor Hydra~A we found that $y\\,=~1\\%$ and $f\\,=~11\\%$ reproduced the observed\nIRAS flux. In Table~\\ref{model} giving calculated fluxes we repeat the \ncalculations for S\\'{e}rsic\\,159-03, but with $f$ reduced to 2\\%. \nConsidering the crude model and the uncertainty of the measurements we find\nthe agreement with the observed values in Table~\\ref{fluxes} satisfactory.\nThis result has some significance although $f$ has been used as a free\nparameter to obtain concordance. If a value of $f$ much larger than unity\nhad been necessary to fit the observations the model would have had to be \nrejected. Also, a value significantly lower than 1\\% would have made the \nmodel unconvincing.\n%\n\\begin{table*}\n\\caption[]{\nMass deposition rate, temperature and cooling radius for the cluster gas \n(Allen and Fabian \\cite{all97}). Predicted infrared fluxes from dust grains\nare given for a simple model. The model assumes the presence of dust in\nthe gas as a by-product of star formation in the flow. The calculated dust\ntemperature and total dust mass are also given\n}\n\\begin{flushleft}\n\\begin{tabular}{l l l l l l l l l}\n\\hline\n${\\rm \\dot{M}}$ & ${\\rm T_{x-ray}}$ & ${\\rm R_{cool}}$ &\n$60\\mu{\\rm m}$ & $100\\mu{\\rm m}$ & $135\\mu{\\rm m}$ & $200\\mu{\\rm m}$ &\n${\\rm T_{dust}}$ & ${\\rm M_{dust}}$ \\\\\n${\\rm M_{\\sun} ~yr^{-1}}$ & keV & arcmin & Jy & Jy & Jy & Jy & \nK & ${\\rm M_{\\sun}}$ \\\\\n\\hline\n231 & 2.9 & 1.89 & 0.05 & 0.07 & 0.06 & 0.03 & 40 & $1.4\\,10^{6}$ \\\\\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\label{model}\n\\end{table*}\n%\n\nA possible disagreement with the model is, however, the small extent of the\nsource. One would expect the infrared emission to show some distribution\nwithin the cooling radius which is $1 \\farcm 89$. Although the resolution at\n$60\\mu{\\rm m}$ is $50 \\arcsec$ C100-1 is indistinguishable from a point source\nin all our measurements. The reason could be that (1) the star formation\nis concentrated to the center (as seems to be the case for Hydra~A, see Hansen\net al.~\\cite{han95}), (2) the model does not apply, or (3) instrumental\neffects prevents detection of a faint, extended distribution of FIR\nemission. \n\nAlternative possibilities are that C100-1 is related to the active nucleus\nas inferred by the presence of a radio source (Large et al. \\cite{lar81},\nWright et al. \\cite{wri94}), or that dust has been introduced into the \nsystem by a recent merger event. A hint may be that all three measurable\nimages of the revolution 173 maps show a tendency to be displaced from the\ncenter by $\\approx 10 \\arcsec$ to the north where nebular line emission \nis seen (Fig.~\\ref{emission}). The cD galaxy shows no signs of dust lanes, but\nexhibits a constant distribution in colour (Fig.~\\ref{B_I}). There are,\nhowever, two objects in the upper left part of Fig.~\\ref{B_I} which are\nbluer than the cD. The brightest and bluest of these looks disturbed\npossibly due to tidal interaction. The spectra taken with P.A.\\,=~$21\\degr$\ncover the object and contain emission lines. The emission is weak in\nFig.~\\ref{emission} because the lines are shifted away from the peak \ntransmission of the filter. Relative to the cD we find the velocity of the\nobject to be $+1800\\pm 200\\,{\\rm km~s^{-1}}$. The galaxy may have plumped\nthrough the cD and contains young stars.\n\nThe origin of the optical filaments in Fig.~\\ref{emission} is a puzzle.\nIt may be captured material from mergers, related to radio plasma, or\nconnected to the cooling flow. The relative velocities do not support any\nparticular model. The velocities have been measured from our spectra, and \nthey are quite low as seen from Table~\\ref{velo}. \n%\n\\begin{table*}\n\\caption[]{\nVelocities of optical filaments relative to the nuclear \\\\\nemission of the cD galaxy (z\\,=~0.0568)\n }\n\\begin{flushleft}\n\\begin{tabular}{l c c}\n\\hline\nfilament & rel. vel. \\\\\n\\hline\nP.A. $21\\degr$ north & $-30\\pm30$ & ${\\rm km~s^{-1}}$ \\\\\nP.A. $21\\degr$ south & $-110\\pm60$ & -- \\\\\nP.A. $270\\degr$ west & $-120\\pm20$ & -- \\\\\n\\hline\n\\end{tabular}\n\\end{flushleft}\n\\label{velo}\n\\end{table*}\n%\nDonahue and Voit (\\cite{don93}) obtained spectra of the nuclear emission \nfrom the S\\'{e}rsic\\,159-03 cD galaxy. They argued that the lack of \n[Ca\\,{\\sc ii}] $\\lambda 7291$ emission indicates that Ca is depleted onto \ndust grains. We have added all our spectra of the center together and all of \nthe filaments. No [Ca\\,{\\sc ii}] emission was visible in any of the two\nresulting spectra. We then shifted the [N\\,{\\sc ii}]$\\lambda 6583$ to\nthe expected position of [Ca\\,{\\sc ii}] and added the shifted line after\nscaling with various constants. In this way we find that no [Ca\\,{\\sc ii}]\nemission stronger than 0.20 times [N\\,{\\sc ii}]$\\lambda 6583$ is present.\nFigure~1 of Donahue and Voit (\\cite{don93}) predicts (from ionization\ncalculations) that this ratio should \nnever be smaller than 0.24. Although marginal compared to the case of\nHydra~A the discrepancy can be explained by the \ncondensation of Ca onto grains in accord with Donahue and Voit's result.\n\nThe presence of dust in the nebular gas does not necessarily exclude \nthat it originates from the cooling cluster gas. Dust may grow in dense, cool\nclouds in connection with star formation. For the nebular gas in Hydra~A\nDonahue and Voit (\\cite{don93}) found a much tighter limit on the \n[Ca\\,{\\sc ii}] line strongly suggesting the presence of dust. In Hydra~A\nthe nebular gas is concentrated to a central disk-like structure of\nseveral kpc where vigorous star formation has taken place, and\nHansen~et~al.~(\\cite{han95}) argue that it is a result of the cooling flow\n(see also McNamara, \\cite{mcn95}). In S\\'{e}rsic\\,159-03 the extended nature \nof the filaments and the presence of the blue, star forming object is more \nin favour of a merger scenario, however.\n%\n\n\\subsection{Off-center infrared sources}\n\\label{non_central}\n%\nThere are no striking optical identifications to the off-center sources.\nThe position of C100-2 is relatively well determined by the overlap of the\ntwo observations. The nearest object visible in Fig.~\\ref{field} is \n$\\approx 0 \\farcm 5 $ to the south-west, is unresolved \nand of blue colour. It is not a known QSO (no QSO is closer than \n$30 \\arcmin$ in the NASA/IPAC Extragalactic Database\\footnote {The \nNASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion \nLaboratory, California Institute of Technology, under contract with the \nNational Aeronautics and Space Administration }),\nand it is just outside the overlap of the two observations. There are several \nfaint optical objects in the area of C100-3, but no show up in our data with \ncharacteristics\nfavouring a candidateship. The difficulties in pointing out candidates\nare even more pronounced for C100-4 which agrees poorly with the nearest faint\nobjects in Fig.~\\ref{field}. However, C100-4 is also the most uncertain of\nthe sources as it is only visible at $60\\mu {\\rm m} $.\n\n%\n\\section{Conclusion}\n\\label{conclusion}\n%\nThe availability of two observations covering essentially the same field\nat several wavelengths allows us to identify 4 faint ($\\approx 0.1$~Jy)\nfar-infrared sources with some confidence. A central source, C100-1, is \nattributed to the cD galaxy which contains optical filaments, but our\noptical images do not reveal significant evidence of dust lanes. \nThe fluxes measured for C100-1 are of the same\norder of magnitude as expected from dust related to star formation in\nthe cooling flow. For the non-central sources we cannot point out any \nparticular optical candidates\nin contrast to the results from the Abell\\,2670 field (paper{\\sc \\,i}) where\ngalaxies with enhanced star formation were found coincident with the\ninfrared sources.\n\n\\acknowledgements\n{This work has been supported by The Danish Board for Astronomical Research.\n}\n\n%\n\\begin{thebibliography}{}\n%\n \\bibitem[1989]{abe89}\n Abell G.O., Corwin H.G., Olowin R.P., 1989, ApJS 70, 1\n \\bibitem[1997]{all97}\n Allen S.W., Fabian A.C., 1997, MNRAS 286, 583\n \\bibitem[1992]{cra92}\n Crawford C.S., Fabian A.C., 1992, MNRAS 259, 265\n \\bibitem[1993]{cra93}\n Crawford C.S., Fabian A.C., 1993, MNRAS 265, 431\n \\bibitem[1993]{don93}\n Donahue M., Voit G.M., 1993, ApJ 414, L17\n \\bibitem[1995]{han95}\n Hansen L., J{\\o}rgensen H.E., N{\\o}rgaard-Nielsen H.U., 1995, A\\&A 297, 13\n \\bibitem[1999]{han99}\n Hansen L., J{\\o}rgensen H.E., N{\\o}rgaard-Nielsen H.U., Pedersen K.,\n Goudfrooij P., Linden-V{\\o}rnle M.J.D., 1999,\n A\\&A 349, 406 (paper{\\sc \\,i})\n \\bibitem[1989]{hec89}\n Heckman T.M., Baum S.A., van Breugel W.J.M., McCarthy P., 1989, ApJ 338, 48\n \\bibitem[1987]{jur87}\n Jura M., Kim D.W., Knapp G.R., Guhathakurta P., 1987, ApJ 312, L11\n \\bibitem[1981]{lar81}\n Large M.I., Mills B.Y., Little A.G., Crawford D.F., Sutton J.M., \n 1981, MNRAS 194, 693\n \\bibitem[1996]{lem96}\n Lemke D. et al., 1996, A\\&A 315, L64\n \\bibitem[1995]{mcn95}\n McNamara B.R., 1995, ApJ 443, 77\n \\bibitem[1993]{noe93}\n N{\\o}rgaard-Nielsen H.U., Goudfrooij P., J{\\o}rgensen H.E., Hansen L.,\n 1993, A\\&A 279, 61\n \\bibitem[1994]{wri94}\n Wright A.E., Griffith M.R., Burke B.F., Ekers R.D., 1994, ApJS 91, 111\n%\n\\end{thebibliography}\n%\n\n\\end{document} \n\n"
}
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[
{
"name": "astro-ph0002403.extracted_bib",
"string": "\\begin{thebibliography}{}\n%\n \\bibitem[1989]{abe89}\n Abell G.O., Corwin H.G., Olowin R.P., 1989, ApJS 70, 1\n \\bibitem[1997]{all97}\n Allen S.W., Fabian A.C., 1997, MNRAS 286, 583\n \\bibitem[1992]{cra92}\n Crawford C.S., Fabian A.C., 1992, MNRAS 259, 265\n \\bibitem[1993]{cra93}\n Crawford C.S., Fabian A.C., 1993, MNRAS 265, 431\n \\bibitem[1993]{don93}\n Donahue M., Voit G.M., 1993, ApJ 414, L17\n \\bibitem[1995]{han95}\n Hansen L., J{\\o}rgensen H.E., N{\\o}rgaard-Nielsen H.U., 1995, A\\&A 297, 13\n \\bibitem[1999]{han99}\n Hansen L., J{\\o}rgensen H.E., N{\\o}rgaard-Nielsen H.U., Pedersen K.,\n Goudfrooij P., Linden-V{\\o}rnle M.J.D., 1999,\n A\\&A 349, 406 (paper{\\sc \\,i})\n \\bibitem[1989]{hec89}\n Heckman T.M., Baum S.A., van Breugel W.J.M., McCarthy P., 1989, ApJ 338, 48\n \\bibitem[1987]{jur87}\n Jura M., Kim D.W., Knapp G.R., Guhathakurta P., 1987, ApJ 312, L11\n \\bibitem[1981]{lar81}\n Large M.I., Mills B.Y., Little A.G., Crawford D.F., Sutton J.M., \n 1981, MNRAS 194, 693\n \\bibitem[1996]{lem96}\n Lemke D. et al., 1996, A\\&A 315, L64\n \\bibitem[1995]{mcn95}\n McNamara B.R., 1995, ApJ 443, 77\n \\bibitem[1993]{noe93}\n N{\\o}rgaard-Nielsen H.U., Goudfrooij P., J{\\o}rgensen H.E., Hansen L.,\n 1993, A\\&A 279, 61\n \\bibitem[1994]{wri94}\n Wright A.E., Griffith M.R., Burke B.F., Ekers R.D., 1994, ApJS 91, 111\n%\n\\end{thebibliography}"
}
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astro-ph0002404
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The Nature of Composite LINER/H\,II Galaxies, As Revealed from High-Resolution VLA Observations
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"author": "Mercedes E. Filho"
}
] |
A sample of 37 nearby galaxies displaying composite LINER/H~II and pure H~II spectra was observed with the VLA in an investigation of the nature of their weak radio emission. The resulting radio contour maps overlaid on optical galaxy images are presented here, together with an extensive literature list and discussion of the individual galaxies. Radio morphological data permit assessment of the ``classical AGN'' contribution to the global activity observed in these ``transition'' LINER galaxies. One in five of the latter objects display clear AGN characteristics: these occur exclusively in bulge-dominated hosts.
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"name": "ms.tex",
"string": "% VERSION MEF JULY 7\n% EDITED BY PDB JULY 7\n% EDITED MEF JULY 12\n% more editing pdb, july 13-14\n% EDITED MEF JULY 15\n% more editing PDB, July 18-19\n% VERSION MEF JULY 21 with PDB's July 20th stuff\n% more editing PDB July 25, MEF (tables)\n% polishing PDB July 26\n% MEF July 27 with PDB's STUFF\n% EDITED + 3 TRANSITION OBJECTS (SEP 16) (suppressed)\n% EDITED + PBCOR (SEP 17) \n% EDITED NEW VERSION (OCT. 11)\n% EDITED (OCT. 28) PICTURES INSERTED\n% NEW INTRODUCTION \n% MORE EDITING PDB/MEF NOVEMBER 26\n% EDITED LCH, Nov. 30 1999\n% LAST POLISHING PDB, MEF DEC.8\n% Few more typos fixed, LCH, Dec. 8 1999\n% REVISED FEB. 7TH 2000\n% REVISED FEB. 11TH 2000\n% VERSION 50944 - FINAL VERSION FEB. 14TH 2000\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[11pt,aaspp4,tighten]{article}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\def\\gtaprx {\\lower .1ex\\hbox{\\rlap{\\raise .6ex\\hbox{\\hskip .3ex\n {\\ifmmode{\\scriptscriptstyle >}\\else\n {$\\scriptscriptstyle >$}\\fi}}}\n \\kern -.4ex{\\ifmmode{\\scriptscriptstyle \\sim}\\else\n {$\\scriptscriptstyle\\sim$}\\fi}}}\n\\def\\ltaprx {\\lower .1ex\\hbox{\\rlap{\\raise .6ex\\hbox{\\hskip .3ex\n {\\ifmmode{\\scriptscriptstyle <}\\else\n {$\\scriptscriptstyle <$}\\fi}}}\n \\kern -.4ex{\\ifmmode{\\scriptscriptstyle \\sim}\\else\n {$\\scriptscriptstyle\\sim$}\\fi}}}\n\\def\\etal {et al. }\n\\def\\littleprime{\\ifmmode{\\scriptscriptstyle \\prime }\n \\else{\\hbox{$\\scriptscriptstyle \\prime$ }}\\fi}\n\\def\\littless{\\ifmmode{\\scriptscriptstyle s }\n \\else{\\hbox{$\\scriptscriptstyle s $ }}\\fi}\n\\def\\littlemm{\\ifmmode{\\scriptscriptstyle m }\n \\else{\\hbox{$\\scriptscriptstyle m $ }}\\fi}\n\\def\\littlehh{\\ifmmode{\\scriptscriptstyle h }\n \\else{\\hbox{$\\scriptscriptstyle h $ }}\\fi}\n\\def\\littlecirc{\\ifmmode{\\scriptscriptstyle \\circ }\n \\else{\\hbox{$\\scriptscriptstyle \\circ $ }}\\fi}\n\\def\\rasec{\\raise .9ex \\hbox{\\littless}}\n\\def\\arcsec{\\raise .9ex\n \\hbox{\\littleprime\\hskip-3pt\\littleprime\\hskip-3pt}}\n\\def\\ramin{\\raise .9ex \\hbox{\\littlemm}}\n\\def\\arcmin{\\raise .9ex \\hbox{\\littleprime}}\n\\def\\hrs{\\raise .9ex \\hbox{\\littlehh}}\n\\def\\deg{\\hbox{$^\\circ$}}\n\\def\\degree{\\raise .9ex \\hbox{\\littlecirc}}\n\\def\\magpoint{\\hbox to 2pt{}\\rlap{\\hskip -.5ex \\arcmm}.\\hbox to 2pt{}}\n\\def\\arcsspoint{\\hbox to 1pt{}\\rlap{\\arcss}.\\hbox to 2pt{}}\n\\def\\arcsecpoint{\\hbox to 1pt{}\\rlap{\\arcsec}.\\hbox to 2pt{}}\n\\def\\arcminpoint{\\hbox to 1pt{}\\rlap{\\arcmin}.\\hbox to 2pt{}}\n\\def\\degreepoint{\\hbox to 1pt{}\\rlap{\\degree}.\\hbox to 2pt{}}\n\n\\slugcomment{Accepted by {\\it The Astrophysical Journal Supplements}.}\n\n\\begin{document}\n\n\\title{The Nature of Composite LINER/H\\,II Galaxies, As Revealed from \nHigh-Resolution VLA Observations}\n\n\\author{Mercedes E. Filho}\n\\affil{Lisbon Observatory and Kapteyn Astronomical Institute}\n\\authoraddr{P.O.~Box 800, NL--9700 AV Groningen, The~Netherlands}\n%%\\email{Mercedes Esteves Filho (mercedes@astro.rug.nl)}\n\n\\author{Peter D. Barthel}\n\\affil{Kapteyn Astronomical Institute}\n\\authoraddr{P.O.~Box 800, NL--9700 AV Groningen, The~Netherlands}\n\n\\author{Luis C. Ho}\n\\affil{Observatories of the Carnegie Institution of Washington}\n\\authoraddr{813 Santa Barbara Street, Pasadena, CA 91101, USA}\n\n\n\\begin{abstract}\n\nA sample of 37 nearby galaxies displaying composite LINER/H~II and pure\nH~II spectra was observed with the VLA in an investigation of the nature\nof their weak radio emission. The resulting radio contour maps overlaid\non optical galaxy images are presented here, together with an\nextensive literature list and discussion of the individual galaxies.\nRadio morphological data permit assessment of the ``classical AGN''\ncontribution to the global activity observed in these ``transition'' LINER\ngalaxies. One in five of the latter objects display clear AGN\ncharacteristics: these occur exclusively in bulge-dominated hosts.\n\n\\end{abstract}\n\n\\keywords{galaxies: active --- galaxies: nuclei --- galaxies: Seyfert --- \nradio continuum: galaxies}\n\n\\section{Introduction}\n\nLINER galaxies are a class of active galaxies characterized by the presence of \nstrong, nuclear, low-ionization emission lines (Heckman 1980). Like \nSeyfert nuclei, LINERs emit much stronger optical low-ionization forbidden \nlines compared to H~II nuclei, whose line emission is powered by \nphotoionization from young massive stars, but LINERs have a characteristically\nlower ionization state than Seyferts. In a recent optical survey of nearly \n500 nearby galaxies, Ho, Filippenko, \\& Sargent (1995, 1997a, 1997b) find that\n$\\sim$20\\% of all galaxies brighter than $B_T$ = 12.5\\,mag display\nLINER-type spectra. An additional 13\\% of the objects show spectra \nintermediate between those of ``pure'' LINERs and ``pure'' H\\,II nuclei. \nHo, Filippenko, \\& Sargent (1993; see also Ho 1996) dubbed this class as \n``transition objects,'' and they hypothesized that these might be composite \nsystems in which the optical signal of a weak active nucleus (the LINER \ncomponent) has been spatially blended by circumnuclear star-forming regions \n(the H~II component).\n\nModels have shown that photoionization by hot stars are able to reproduce the\noptical spectra of LINERs (Terlevich \\& Melnick 1985), especially those of \nthe transition-type variety (Shields 1992; Filippenko \\& Terlevich 1992). \nOther researchers have advocated shock-wave heating as a viable excitation \nmechanism for LINERs (Fosbury \\etal 1978; Heckman 1980; Dopita \\& Sutherland \n1995). At the same time, an increasing body of evidence suggests that a \nsignificant fraction of LINERs do contain irrefutable AGN characteristics \n(see reviews by Filippenko 1996 and Ho 1999b). Radio surveys, in particular, \nhave shown that many LINERs exhibit weak nuclear radio emission (Heckman 1980;\nSadler, Jenkins, \\& Kotanyi 1989; Wrobel \\& Heeschen 1991; Slee \\etal 1994; \nFalcke, Wilson, \\& Ho 1997; Van Dyk \\& Ho 1998). As discussed in detail by\nHo (1999a), weak nuclear radio emission in early-type (elliptical and S0) \ngalaxies is most likely related to accretion-driven energy production in these \nobjects, but at a very low level compared to powerful radio galaxies, which \nare also usually hosted by early-type systems. \n\nRadio observations provide an expecially attractive tool to further our \nunderstanding of the LINER phenomenon. Since radio frequencies are not plagued\nby dust obscuration and photoelectric absorption, high-resolution radio\nobservations potentially offer the cleanest and most efficient method to\nisolate an AGN core. Although radio emission also arises from supernova\nremnants and H\\,II regions, AGN cores can be identified through their \nhigh degree of central concentration, small angular size, flat spectral \nindices, and high brightness temperatures.\n\nGiven that LINERs are so numerous, they may be the most common type of\nAGN known. Their large space densities could make a major impact on the faint \nend of the local AGN luminosity function, which in turn has ramifications for \nmany astrophysical issues ranging from the cosmological evolution of AGN to\nthe contribution of AGN to the cosmic X-ray background. We are\ntherefore conducting high-resolution radio observations of selected\nLINER samples in order to investigate the interrelation between LINERs\nand classical AGN. For the present paper --- the first in a series ---\nwe have concentrated on transition-type LINERs. We report on sensitive \nVery Large Array (VLA)\\footnote{The VLA is a facility of the National Radio \nAstronomy Observatory (NRAO) which is a facility of the National Science \nFoundation operated under cooperative agreement by Associated Universities, \nInc.} C-array observations of a sample of 25 such transition LINERs at \n8.4\\,GHz. The resulting images, having angular resolution of about \n2\\arcsecpoint5, allow us to assess the strength and spatial distribution of \nthe nuclear radio emission. For comparison, we have also observed a small\nsample of 12 pure H\\,II nuclei. \n\nIn the following discussion and in upcoming papers, we adopt a\nHubble constant of H$_{0}$ = 75~km~s$^{-1}$~Mpc$^{-1}$.\n\n\\section{Sample Selection}\n\nThe sample of 25 transition LINER/H\\,II galaxies and 12 pure H\\,II\nnuclei was extracted from the original magnitude-limited Palomar survey of \n486 bright northern galaxies (Ho \\etal 1995), following the classification \ncriteria outlined in Ho et al. (1997a). The Palomar sample contains 65 \ntransition nuclei (Ho et al. 1997a), from which we chose a subset of 25 that \nhad little or no arcsec-scale resolution radio continuum data published, and\nthat fell within the observation window assigned to us by the VLA. In \naddition, we selected for comparison a small sample of 12 pure H\\,II nuclei \n(out of 206 such objects in the full Palomar sample). These were chosen to\nmimic the Hubble type distribution of the sample of transition objects, \nagain taking into consideration scheduling constraints.\nWe are not aware of any strong biases introduced by our sample selection. \n\nTable~1 lists the 37 sample objects. In addition to the optical positions of \nthe galaxies (columns 3 and 4), this table lists their distance (column~5) \nand their Hubble type (column~6). The Hubble types and distances are taken \nfrom Ho \\etal (1997a). The ``reference'' column (7), together with Table~2,\nsupplies references to earlier radio studies; it is readily apparent that\nseveral of the sample objects are well-studied objects, while some are\nnot. We will discuss our observational results in light of these existing \ndata in Section~4. The sample galaxies span a wide range of Hubble types, but \nthe majority are spirals.\n\n\\medskip \\centerline{\\bf -- TABLEs~1/2: Sample of transition LINER\n galaxies and H\\,II nuclei --}\n\n\\section {Observations and Data Reduction}\n\nThe resulting sample of 25 composite LINER/H\\,II and 12 pure H\\,II galaxies was\nobserved with the X-band (8.4\\,GHz) system of the VLA in two\nobserving sessions, on 1997 August~21 and August~25. The array was in its\nC-configuration, yielding a typical resolution of 2\\arcsecpoint5. Two\nbands of 50\\,MHz each were combined, yielding a total bandwidth of\n100\\,MHz. Snapshot observations combining two scans of 8--9~minutes\neach, at different hour angles, were obtained in order to improve the\nshape of the synthesized beam.\n\nSecondary phase and amplitude calibrators were observed before and after\neach scan. The primary calibrator was 3C\\,286, with appropriate\nbaseline constraints, and the adopted 8.4\\,GHz flux densities, as provided\nby the VLA staff, were 5.22~Jy and 5.20~Jy, at IF1 and IF2, respectively. \nThe calibration uncertainty is dominated by the uncertainty in the\nabsolute flux density of the primary calibrator, which is a few percent. \nThe array performed well: judging from the calibration sources,\nthe antenna phase and amplitude calibration appeared stable to within a\nfew percent. \n\nThe radio data are of high quality, and there was no need for\nextensive flagging of discrepant points. Reduction of the data was\nperformed using standard NRAO AIPS (version 15OCT98) image processing\nroutines. AIPS task IMAGR was employed to Fourier transform the\nmeasured visibilities and obtain CLEAN (H\\\"ogbom 1974; Clark 1980) maps of the sources. \nFull-resolution\nmaps, having synthesized beams of roughly 2\\arcsecpoint5, and tapered\nmaps, having beams between about 5\\arcsec~and 12\\arcsec, were\nmade. This proved useful to detect weak low surface brightness\nemission. As a rule of thumb, 1\\arcsec~corresponds to 50--100~pc for the \ntypical distances involved. Most images reach\nthe theoretical noise level of $\\sim 0.04$~mJy/beam (Perley, Schwab, \\& Bridle \n1989) to within a factor of two. Self-calibration was employed in\nthe analysis of two of the stronger sources (NGC\\,4552 and NGC\\,5354), \nleading to considerable improvements.\n\n\\section {Results}\n\n\\subsection {Radio Maps}\n\nNoting that a non-detection should be taken to imply no correlated flux\ndensity in excess of 0.5~mJy on the arcsec scale, radio contour maps of\nthe detected galaxies are presented in Figures 1--7, at the end of the\npaper. The radio maps are overlayed on optical images taken from the\nDigitized Sky Survey (DSS). In a number of cases only the\nhigh-resolution map (typical beamsize 2\\arcsecpoint5) or the\nlow-resolution map (typical beamsize 7\\arcsec~-- 10\\arcsec) are shown. \nUnrelated background radio sources were found in several fields; their\nnumber is entirely as expected given the size of the primary beam and\nthe sensitivity of the observations. In cases of large distances from\nthe field center, primary beam corrections were applied. Some of the\nbackground sources have been identified using NED (NASA/IPAC\nExtragalactic Database) and the Cambridge APM (Automatic Plate\nMeasuring) facility. Where possible, we have included them by their\nname in the tables below. Previously uncatalogued background sources\nare designated by their sky orientation with respect to the field center\nfor the relevant galaxy. All maps use contouring according to CLEV\n$\\times $ (--3, 3, 6, ..., MLEV) mJy/beam where MLEV are powers $3\n\\times 2^{\\rm n}$ up to a maximum of 96 and CLEV is the typical noise\nlevel on each radio map (see Table~3). \n\nTable~3 lists the various map parameters, with the following column\nheadings: the source name (1), the applied taper (2), the resulting\nrestoring beam (3), the position angle of the beam (4), the image noise \nlevel (5), and the relevant figure number (6). The H\\,II nuclei \nappear at the bottom of the table.\n\n\\medskip \\centerline{\\bf -- TABLE~3: Radio map parameters --}\n\nGiven that good phase stability was obtained, as judged from the VLA phase\ncalibrators, the astrometric accuracy of our overlay procedure must be\ndominated by the DSS accuracy, which is known to be about 0.6\\arcsec~ \n(V\\'eron-Cetty \\& V\\'eron 1996). This is born out by the images of several\nunresolved and slightly resolved nuclei (NGC\\,4552, NGC\\,5354, \nNGC\\,5838, NGC\\,5846) which appear accurate to within a few tenths of an arcsec. \n\n\\subsection {Comments on Individual Galaxies}\n\nWith reference to the images in the Appendix, we proceed by discussing\nthe results of our VLA imaging in the light of earlier studies of the\nsample objects. This discussion also deals with the detected background\nsources and includes important bibliographic information. We will\nfrequently compare our measurements with sample galaxy flux densities\nobtained within the VLA 1.4\\,GHz NVSS and FIRST surveys, having typical\nresolution of 45\\arcsec~ and 5\\arcsec, respectively (Condon \\etal 1998a;\nBecker, White, \\& Helfand 1995), as well as with the Green Bank 20~cm\nand 6~cm surveys, having typical resolution of $\\sim$700\\arcsec~and\n3\\arcminpoint5, respectively (White \\& Becker 1992, WB92 hereafter;\nBecker, White, \\& Edwards 1991, BWE91 hereafter). \n\n{\\bf IC\\,520 :} No compact structure was seen in this object, not even\non the tapered map. It was also not detected in the NVSS. However,\nCondon (1987) reports a detection at 1.49\\,GHz: at\n0\\arcminpoint8~resolution, he measured a 3.1~mJy radio source. \n\n{\\bf NGC\\,2541 :} We did not detect compact structure, not even on the\ntapered map. This source was also not detected in the FIRST or in the\nNVSS survey. However, Condon (1987) reports a possible detection at \n1.49\\,GHz, 0\\arcminpoint8~resolution, of a 3.2~mJy source, slightly\nextended to the SW relative to the optical position of the galaxy.\n\n{\\bf NGC\\,2985 :} We detect a 1.9~mJy source. At\n2\\arcsecpoint5~resolution, the source is slightly extended in the N-S\ndirection, along the orientation of the optical galaxy. The tapered map\nshows a 2.7~mJy core and about 1~mJy weak low surface brightness\nemission to the SW. The object was also detected in the NVSS: 44.1~mJy. \nAt 1.49\\,GHz, 1\\arcminpoint0~resolution, Condon (1987) measured a total\nflux of 61.9~mJy: the radio emission of NGC\\,2985 must be extended over\ntens of arcseconds. \n\n{\\bf NGC\\,3593 :} On both the untapered and tapered maps we measure\nabout 20~mJy of diffuse, 45\\arcsec~E-W elongated emission, oriented\nalong the major axis of the host of this H\\,II nucleus. NVSS measured\n87~mJy emission, WB92 measured 132~mJy (hence the radio source exceeds\none arcminute in size), whereas BWE91 measured 53~mJy. The 1.4\\,GHz,\n5\\arcsec~resolution map of Condon \\etal (1990) shows an E-W oriented\nsource of 63.4~mJy: these and our VLA data imply a steep-spectrum\nradio source.\n\nWe also detect an unrelated 10.6~mJy source, 3\\arcmin~to the N, extended\ntowards the E. As judged from the APM survey, the POSS plates show an as \nyet unclassified nonstellar source at this position: background source\nNGC\\,3593N is most likely a weak distant radio galaxy.\n\n{\\bf NGC\\,3627, M\\,66 :} This interacting galaxy belongs to the Leo\ntriplet. The 8.4\\,GHz maps show a 2\\arcmin~triple source aligned with\nthe inner bar of the optical galaxy. The outer radio components are\nrelated to star formation in the disk of the galaxy (Urbanik, Gr\\\"ave, \n\\& Klein 1985). We measure 3.9~mJy integrated emission in the compact central\ncomponent, while $\\sim$25~mJy are distributed in the NW and SE components.\nFrom comparison with low-resolution surveys (NVSS: 324.9~mJy; WB92:\n434~mJy; BWE91: 141~mJy) we infer that most of the radio emission of\nthis steep-spectrum radio source is resolved out by our observations.\nThe triple radio structure was also observed by Saikia \\etal (1994),\nat 5\\,GHz with 2\\arcsec~resolution. Combining our data with the Saikia\n\\etal (1994) and the Hummel \\etal (1987) data, we conclude that the\nnuclear radio source in NGC3627 must be of variable, flat-spectrum\nnature. More recently, high resolution (0\\arcsecpoint15) 15\\,GHz\nobservations detected an unresolved 1.4~mJy core (N. Nagar, private\ncommunication).\n\n{\\bf NGC\\,3628 :} Like NGC\\,3627, this galaxy also belongs to the Leo\ntriplet. Our 8.4\\,GHz full-resolution map shows some extended emission\nto the N and an eastern extension that is roughly aligned with the\nprojected disk of the galaxy. The nuclear region is clearly resolved. \nThe total flux density on our low-resolution map is about 70~mJy, 70$\\%$\nof which is in $\\sim$15\\arcsec~diffuse emission. The NVSS measured\n292~mJy whereas WB92, at lower resolution, detected 402~mJy, indicating\nresolved large-scale emission. At 1.4\\,GHz Condon \\etal (1990) measured\n203~mJy and 205~mJy at 5\\arcsec~and 1\\arcsecpoint5~resolution,\nrespectively. These and our data imply a steep-spectrum radio source,\nin agreement with the results from the Effelsberg 100m telescope\n(Schlickeiser, Werner, \\& Wielebinski 1984). Carral, Turner, \\& Ho\n(1990) observed this object at 15\\,GHz using the VLA in A-array and\nmeasured a total flux of 23~mJy. These authors sampled the innermost\npart of the source and obtain a $\\sim4$\\arcsec~string of a dozen\ncomponents aligned with the major axis of the galaxy, that they suggest\ncould be star-forming regions in the disk. \n\n{\\bf NGC\\,3675 :} We detect about 1.5~mJy of low surface brightness\nemission on our tapered maps. NVSS detected a 48.9~mJy source, whereas\nFIRST measured 8.04~mJy: the source must be strongly resolved. \n1.49\\,GHz VLA D-array observations (Condon 1987; Gioia \\& Fabbiano 1987)\ndetected a $\\sim$50~mJy source, oriented N-S, along the major axis of\nthe optical galaxy. Condon, Frayer, \\& Broderick (1991) report a flux\ndensity of 27~mJy at 4.85\\,GHz and a steep spectral index between 4.8\nand 1.4\\,GHz. \n\n{\\bf NGC\\,3681 :} We did not detect a radio source on the untapered or\ntapered maps. In contrast, NVSS measured a weak source of about\n4.2~mJy -- at much lower resolution.\n\n{\\bf NGC\\,3684 :} This H\\,II nucleus had no radio source detected,\neither on the untapered or on the tapered maps, but NVSS detected a\n15.9~mJy source. The radio emission of NGC\\,3684 must be diffuse.\n\nWe do, however, detect a partially resolved 18.1~mJy background\nsource, 3\\arcmin~to the SW, which APM identifies with a 19.5 mag\nstellar-like object. Further identification is still lacking.\n\n{\\bf NGC\\,4013 :} We detect a moderately resolved 1.1~mJy core and a small\nextension to the NE, parallel to the projected disk of this edge-on\ngalaxy. There is an additional 3~mJy of weak disk emission. On the\nbasis of the widely different NVSS and FIRST detections (40.5 vs. \n11.9~mJy), this disk emission must extend tens of arcseconds. Hummel,\nBeck, \\& Dettmar (1991) present 10\\arcsec~resolution 5\\,GHz data of\nNGC\\,4013 (UGC\\,6963) which show both the prominent core and the\nextended disk emission. Recent high resolution (0\\arcsecpoint15) 15\\,GHz\nobservations did not detect NGC\\,4013 above a 10$\\sigma$ limit of 1~mJy\n(N.~Nagar, private communication).\n\nWe also detect a slightly resolved 3.8~mJy background source,\n2\\arcmin~to the far SE. This source is also clearly seen in the map of\nCondon (1987). The APM facility reveals a 19.6 mag stellar-like object,\nwhich lacks further identification as yet. \n\n{\\bf NGC\\,4100 :} We detect about 7~mJy of low surface brightness\nemission associated with this H\\,II nucleus. The tapered map shows a\nslight extension to the SE along the major axis of the optical\ngalaxy. NVSS detected a 50.3~mJy source and FIRST detected 17.8~mJy,\nindicating resolution effects.\n\n{\\bf NGC\\,4217 :} We detect about 22~mJy, distributed along\n$\\sim$1\\arcminpoint5~of the projected galactic disk of this H\\,II\nnucleus. From low-resolution observations (NVSS: 123~mJy; WB92:\n139~mJy; BWE91: 40~mJy) we conclude that NGC\\,4217 harbours extended\nlow surface brightness radio emission, which must have a steep radio\nspectrum.\n \n{\\bf NGC\\,4245 :} No radio source associated with this H\\,II nucleus\nwas detected on the untapered or tapered maps. Neither NVSS nor FIRST\nhas detected this object at 1.4\\,GHz.\n\n{\\bf NGC\\,4321, M\\,100 :} We detect about 16~mJy of low surface\nbrightness emission in the nuclear region of this well-known grand\ndesign spiral in the Virgo cluster. The tapered map shows emission\nslightly extended to the NW. NVSS detected 87~mJy, while WB92 measured\n323~mJy and BWE91 87~mJy. At 1.49\\,GHz, 0\\arcminpoint9~resolution\nCondon (1987) measured 180\\,mJy total flux in a $\\sim $ 3\\arcmin\n$\\times $ 2\\arcmin region. At 4.9\\,GHz, 1\\arcsecpoint5~resolution\nCollison \\etal (1994) detect a ring-like structure coincident with our\nmain feature. At 8.5\\,GHz, 0\\arcsecpoint2 resolution, these authors\ndetect two unresolved sources, having peaks of 0.37~mJy/beam (E) and\n0.22\\,mJy/beam (W), respectively. The eastern radio source is\ncoincident with their 4.9\\,GHz main component while the one to the W\nis coincident with the optical nucleus and has a flat spectrum\n(Collison \\etal 1994).\n\nWe also detect an unresolved source, 1.5\\arcmin~to the SE, with 1.3~mJy\nintegrated flux, apparently located near the middle of the southern\nspiral arm of the galaxy. It is clearly visible on the NGC\\,4321 map. \nWe have identified this object with SN\\,1979C (Weiler \\etal 1981). \nCollison \\etal (1994) measured 2~mJy for this SN\\,1979C, at 4.9\\,GHz. \n\n{\\bf NGC\\,4369, Mrk\\,439 :} We detect 3.8~mJy of low surface brightness\ndisk emission associated with this H\\,II nucleus. On the basis of\nwidely different NVSS and FIRST detections (24.3 vs. 4.67\\,~mJy), this\ndisk emission must extend over tens of arcsec. The Condon \\etal (1990)\n1.49\\,GHz image, at 15\\arcsec~resolution, shows a 18.3~mJy source with\nextended emission to the E. \n\n{\\bf NGC\\,4405, IC\\,788 :} No compact emission was detected in the\nuntapered or tapered maps. NVSS detected weak (4.5~mJy) emission for\nthis H\\,II galaxy. \n\nWe did, however, detect a partially resolved 10.1~mJy source,\n2\\arcmin~SW of the NGC\\,4405 target position. As judged from the APM,\nthe POSS plates show a 19.2 mag stellar-like object at this position,\nwhich we subsequently identify as the $z=1.929$ QSO, LBQS\\,1223+1626\n(e.g., Hewett, Foltz, \\& Chaffee 1995). \n\n{\\bf NGC\\,4414 :} We detect $\\sim$29~mJy of low surface brightness\nemission, distributed along $\\sim$1\\arcminpoint5, in a structure aligned\nwith the galaxy's major axis. NVSS detected a 242~mJy source while\nFIRST detected a double-peaked source with 44 and 64~mJy components. \nThe Condon (1983), 1.465\\,GHz, 12\\arcsecpoint5~resolution map and the\nCondon (1987), 1.49\\,GHz, 1\\arcminpoint0~resolution map show comparable\nN-S structure, measuring $\\sim$0.22~Jy. Using this last value plus the\n78~mJy measured at 4.85\\,GHz, 15\\arcsec~resolution, Condon \\etal (1991)\nobtain a steep spectral index. \n\n{\\bf NGC\\,4424 :} On the tapered map we detect a resolved $\\sim$1~mJy core \nplus 1.5~mJy weak low surface brightness emission to the E along the\nprojected disk of this candidate merger galaxy (Kenney \\etal 1996). \nNVSS detected a weak 4.5~mJy source. Our full-resolution data show the\ncore of this H\\,II nucleus to be somewhat resolved. This is borne out of\nour recent high resolution\n(0\\arcsecpoint25) 8.4\\,GHz observations which did not detect NGC\\,4424 above\na 3$\\sigma$ limit of 0.2~mJy.\n\nWe also detect an unrelated, slightly resolved 13.3~mJy source,\n2\\arcminpoint5~to the SE. The APM identifies it with a 20.2 mag\nstellar-like object. Further properties of this background source\nremain as yet unknown. \n\n{\\bf NGC\\,4470 :} We detect $\\sim$3~mJy of weak low surface\nbrightness emission, extending 30\\arcsec~along the galaxy major \naxis. NVSS detected 17.1 mJy associated with this H\\,II nucleus.\n\nWe also detect an unrelated, resolved 16.0~mJy radio source,\n1\\arcminpoint5~to the NE of NGC\\,4470, which is not identified on the\nPOSS plate (APM). We identify this object with the radio source\nTXS\\,1227+081 (Douglas \\etal 1996), which has as yet no optical\nidentification.\n\n{\\bf NGC\\,4552, M\\,89 :} We detect about 77~mJy in a strong core plus \npossibly a jet-like structure to the NE. NVSS\ndetected a 103~mJy source. Since BWE91 measured 64~mJy at 5\\,GHz, the\nradio source in NGC\\,4552 must have a relatively flat radio spectrum,\nwhich is in agreement with findings by Condon \\etal (1991). The radio\nsource appears to be variable (Wrobel \\& Heeschen 1984; Ekers, Fanti, \\&\nMiley 1983; Sramek 1975a, 1975b; Ekers \\& Ekers 1973). Our recent\nsubarcsec resolution 8.4\\,GHz images have confirmed this object's compactness. \n\n{\\bf NGC\\,4643 :} No compact radio structure was detected on the\nuntapered or the tapered maps. NVSS also did not detect this source. \nHowever, we have detected several very weak sources ($\\sim$1~mJy) on the\ntapered maps, some of which may be due to weak diffuse disk emission. \n\n{\\bf NGC\\,4710 :} We detect about 6~mJy of weak disk emission\nassociated with this H\\,II nucleus. NVSS measured a 19.3~mJy source.\nAt 1.49\\,GHz, Condon \\etal (1990) measure 17.2~mJy and 14.7~mJy at 15\nand 5\\arcsec~resolution, respectively. The data imply a resolved\nsteep-spectrum radio source.\n\nWe also detect a 4.8~mJy resolved background source, 2.5\\arcmin~to the\nE of NGC\\,4710. No indentification could be found on the POSS.\n\n{\\bf NGC\\,4713 :} We detect $\\sim$1.2~mJy weak low surface brightness disk\nemission on our tapered maps. NVSS measured a 46.9~mJy source: our \nobservations must have resolved out much of the flux.\n\n{\\bf NGC\\,4800 :} We detect about 1.2~mJy of weak low surface brightness\nemission, stretching $\\sim30$\\arcsec~along the galaxy major axis. NVSS\ndetected a 23.5~mJy source and FIRST 12.2~mJy. Therefore, our\nobservations are resolving out much of the emission of this H\\,II\nnucleus. \n\n{\\bf NGC\\,4826 , M\\,64:} We detect about 21~mJy of low surface\nbrightness emission. The central region on the full-resolution map (not\npresented here) shows a double-peaked component, which can be compared\nto the complex inner triple structure of the 15 and 5\\,GHz,\n2\\arcsec~resolution maps of Turner \\& Ho (1994). Combining the data\nindicates that this is a steep spectrum source. NVSS detected a 101~mJy\nsource and BWE91 detected a 56~mJy source. The 1.49\\,GHz,\n1\\arcminpoint0~resolution data of Condon \\etal (1998b) and Condon (1987)\nshow a $\\sim$100~mJy source, as do the data of Gioia \\& Fabbiano (1987)\nat 40\\arcsec~resolution. \n\n{\\bf NGC\\,4845 :} On our tapered maps we detect a 2~mJy core and some\nemission to the N, perpendicular to the galaxy major axis, plus 10~mJy\nof $\\sim20$\\arcsec~elongated disk emission. NVSS detected a 43.8~mJy\nsource associated with this H\\,II nucleus. The data of Condon \\etal\n(1990) imply resolution effects on the 10~arcsec scale. \n\n{\\bf NGC\\,5012 :} We detect some very weak ($\\sim$1~mJy) features\nnear the target phase center. NVSS detected a 31.4~mJy source, but \nas FIRST did not detect it, we must be dealing with extended low\nsurface brightness emission.\n\n{\\bf NGC\\,5354 :} We detect an unresolved 11.7~mJy core. NVSS and\nFIRST detected a 8.4 and 8.0~mJy source, respectively, implying that the\nNGC\\,5354 radio source is unresolved at a resolution of 5\\arcsec. The\n4.85\\,GHz, 15\\arcsec~resolution maps of Condon \\etal (1991) show 7~mJy\nemission, implying that the nuclear radio source has an inverted\nspectrum. Our recent\nsubarcsec resolution 8.4\\,GHz images have confirmed this object's compactness. \n\n\nPaired galaxy NGC\\,5353 is also detected, 1\\arcminpoint25~to the S,\nwith a 26.7~mJy core. Condon \\etal (1991) measure 29~mJy at 4.85\\,GHz,\n15\\arcsec~resolution, implying that NGC\\,5353 also hosts a flat\nspectrum radio source.\n\n{\\bf NGC\\,5656 :} We detect $\\sim$1~mJy of weak low surface brightness\nemission, stretching over $\\sim$25\\arcsec~along the major axis of the\ngalaxy. NVSS detected a 22~mJy source.\n\n{\\bf NGC\\,5678 :} We detect about 8.5~mJy of low surface brightness\nemission stretching over $\\sim$1\\arcminpoint2~along the major axis of\nthe galaxy. The tapered map shows what could be a double-peaked source,\nsimilar to the 6\\arcsec~resolution, 1.4\\,GHz map of Condon (1983). NVSS\ndetected a 112~mJy source while BWE91 measured 68~mJy. The NVSS and\nBWE91 results, combined with Condon (1983) reporting 109~mJy at\n1.4\\,GHz, imply a steep spectrum source. \n\n{\\bf NGC\\,5838 :} We have detected a slightly resolved 2.2~mJy source. \nNVSS detected 3.0~mJy, while Wrobel \\& Heeschen (1991) report a 2 mJy\nsource (5\\,GHz, 5\\arcsec~resolution): the nuclear radio source in\nNGC\\,5838 must have a flat radio spectrum. Our recent\nsubarcsec resolution 8.4\\,GHz images have confirmed this object's compactness. \n\n \nThere is also an unrelated, unresolved 1.3~mJy source, about\n1\\arcminpoint5~to the S of NGC\\,5838. The POSS plates reveal an 18.4\nmag star-like object at that position, for which as yet no redshift is\navailable. \n\n{\\bf NGC\\,5846 :} We have detected a partially resolved 7.1~mJy source. \nNVSS measured a 22~mJy source. 1.4\\,GHz VLA observations by\nM\\\"ollenhoff, Hummel, \\& Bender (1992) measured an unresolved core of\n9~mJy plus 10~mJy of additional diffuse emission: NGC\\,5846 must possess\na compact flat-spectrum core component. Our recent\nsubarcsec resolution 8.4\\,GHz images have confirmed this object's compactness. \n\n \n{\\bf NGC\\,5879 :} No radio structure was detected on the untapered or\nthe tapered maps. NVSS detected a 21~mJy source, which hence must arise \nin an extended low surface brightness region.\n\nHowever, we did detect a 292.1~mJy, slightly resolved background\nsource, about 2\\arcmin~NE of our target. It shows up only on the POSS\nred plate as a noise-like source. We have identified this source as\nQSO 1508+5714, at a redshift of 4.301 (Hook \\etal 1995). It is in the\nWENSS (Rengelink \\etal 1997) and in BWE91 (282~mJy) as well as in WB92\n(149~mJy). Patnaik \\etal (1992) have observed the source with the VLA\nA-array at 8.5\\,GHz and measured 153~mJy: 1508+5714 must be a variable \nflat-spectrum quasar.\n \n{\\bf NGC\\,5921 :} We have detected a very weak 0.5~mJy core and some\nadditional weak extended emission. At 1.49\\,GHz and 0\\arcminpoint9\nresolution, Condon (1987) measured a 20.8~mJy source with an\nadditional 2.8~mJy eastern component which we do not detect at\n8.4\\,GHz. All emission must be of low surface brightness nature.\n\n{\\bf NGC\\,6384 :} Following the NVSS non-detection, we also do not\ndetect (compact) radio emission from NGC\\,6384. However, Condon\n(1987), at 1.49\\,GHz and 1\\arcminpoint2~resolution, found the radio\nsource, having $\\sim$ 35~mJy, to be very extended.\n\n{\\bf NGC\\,6482 :} We have not detected this source at 8.4\\,GHz and\nneither did NVSS.\n\nWe did, however, detect a slightly resolved 23.6~mJy background\nsource, about 3\\arcmin~to the S of NGC\\,6482. On the full-resolution\nmap this source is slightly extended. The POSS plates show a 20.9 mag\nstellar object. We have identified this source with the radio source\n1749+2302 included in GB6, with 26~mJy flux density.\n\n{\\bf NGC\\,6503 :} We do not detect radio emission from this galaxy on\nthe full-resolution or on the tapered maps. 1.4\\,GHz data (NVSS and Condon\n1987) indicate a NW-SE extended $\\sim$40~mJy source, which\nconsequently must be diffuse.\n \nWe also detect a background source, about 6\\arcmin~to the SW. Due to\nthe large distance from the phase center, which implies a large and uncertain\nprimary beam correction, we cannot assess the flux density of this\nsource. The source appears as a 16.9 mag stellar-like object on the POSS\nplates. We have identified this object with the BL Lacertae source\n1749+701 at redshift 0.77 (Hughes, Aller, \\& Aller 1992). This object has been\nextensively observed at other radio-frequencies and is included in the\nWENSS (Rengelink \\etal 1997) as well as BWE91 and WB92. The only other\n8.5\\,GHz measurement of this source comes from Patnaik \\etal (1992). They\nmeasure 558~mJy with the VLA A-array. \n\nTable~4 summarizes the properties of the background sources, including\nthe previously identified, as well as the new, identifications. Tabulated \n8.4\\,GHz fluxes have been corrected for primary beam attenuation. \n\n\\medskip \\centerline{\\bf -- TABLE~4: Field/background sources --}\n\n\\subsection {Radio Source Parameters}\n\nFor each galaxy with a 8.4\\,GHz detection, we list in Table~5 the radio\nsource parameters, measured both from the full-resolution and the\ntapered maps. Peak and integrated values (columns~3 and 6), as well as \nwell as sky positions of bidimensional gaussian fits (columns~4 and 5)\nare tabulated. These values were obtained using the AIPS task IMFIT. \nAs we are often dealing with resolved and/or asymmetric emission, such \nmeasurements are often inaccurate and must represent lower limits. \nIn such cases, we have estimated the integrated\n8.4\\,GHz flux density from inspection of the map and the relevant clean\ncomponent file and we have given it the prefix ``$\\geq$'' (column~6). \nAlso, given the fact that we have fitted single gaussian to the brightest\nsource components, the accuracy of the radio peak positions is judged to be\n\\ltaprx1\\arcsec~(see images). For NGC\\,3627, the quoted peak and integrated \nvalue are of the central core. In parentheses we include the total flux \nof the three components (see Section~4.2). \n\n\n\n \n\n\\medskip \n\\centerline{\\bf -- TABLE~5: Radio parameters of detected sources --}\n\nFrom a quick comparison with the integrated NVSS 1.4\\,GHz flux\ndensities, it is found that in many cases the high-resolution\nobservations must have resolved a substantial fraction of the emission. \nThis can be quantified by examination of the spectral index values. \nTable~6 lists spectral indices $\\alpha^{8.4}_{1.4}$ ($S_{\\nu } \\propto\n\\nu ^{-\\alpha}$) (column~5), obtained by combining the NVSS flux \ndensities (column~2)\nand the integrated 8.4\\,GHz flux densities (column~3) taken from Table~5. \nDue to the fact that the NVSS beam\n(45\\arcsec) exceeds the 8.4\\,GHz beam (7\\arcsec--10\\arcsec) by a\nsubstantial factor, these spectral index values should be considered\nas upper limits. It indeed\nappears that in most of these cases the radio emission was documented to\nbe extended over tens of arcseconds. \nWe also compile calculated NVSS radio luminosities (column~4) for the \n37 galaxies under consideration. \nAgain, for NGC\\,3627 quoted values refer to\nthe compact core except when in parentheses, in which case the values refer \nto all three source components. \n\n\n\n\\medskip \\centerline{\\bf -- TABLE~6: summary --}\n\nMost sample galaxies are seen to display steep spectral indices, as\ncommonly found for star-forming late-type galaxies (Condon 1992). The\nfollowing objects have flat ($\\alpha \\leq 0.6$) spectra: NGC\\,4552,\nNGC\\,5354, NGC\\,5838 and NGC\\,5846 and the H\\,II nucleus in NGC\\,4424. \nWe will return to this issue in the next Section. \n\n\\section {Discussion}\n\nOur VLA imaging observations have yielded X-band detections of 27 of the\n37 sample galaxies. These 27 include NGC\\,4643 and NGC\\,5012, which\nwere marginally detected. As for the non-detections, they are equally\ndistributed over the transition LINERs and the H\\,II nuclei. It appears\nthat non-detection at X-band, at a resolution of\n2\\arcsecpoint5--12\\arcsec, correlates with 1.4\\,GHz (NVSS) weakness\nand/or low surface brightness. Table~6 indicates that the NVSS radio\nluminosity distributions of the subsamples are comparable. The\nintegrated 1.4\\,GHz radio luminosities imply that the sample sources\nspan the usual luminosity range for nearby galaxies (10$^{26}$ --\n10$^{30.5}$ erg s$^{-1}$ Hz$^{-1}$; see, e.g., Condon 1987, 1992). \nWith the exception of NGC\\,4424 (see Section~4.2), none of the H\\,II \nnuclei display compact nuclear emission and/or a flat radio spectrum.\nThis is in strong contrast to the transition LINER galaxies.\n\nPurely based on the radio morphology, the transition LINER objects can\nbe divided into two categories. The first is made up of galaxies\ndisplaying extended, steep-spectrum, low surface brightness radio\nemission, usually tracing the optical isophotes of the host galaxy. The\nsecond category refers to objects that, in addition to extended\nemission, also show compact nuclear radio emission. The first category displays\nradio morphologies that are consistent with their being due to\nlarge-scale star formation; in several cases the radio morphology is\nseen to trace the H\\,II regions in the host. However, we stress that\nthe presence of a very weak nuclear component in these objects may still \nbe masked by the more dominant radio emission from star-forming regions. \nThe second category, which we will refer to in the following as AGN\ncandidates, is comprised of NGC\\,3627, NGC\\,4552, NGC\\,5354,\nNGC\\,5838, and NGC\\,5846. The last four of these are characterized with\na flat radio spectral index between 1.4 and 8.4 GHz (see end of Section~4.3). \nJudging from high-resolution observations which isolate the nuclear\nemission, the compact nucleus of NGC\\,3627 also displays a flat radio\nspectrum (see Section~4.2). These AGN candidates are on average more\nluminous than the non-AGN and, as we shall see below, their hosts\nare early rather than late-type galaxies. While at first sight the H\\,II nucleus\nNGC\\,4424 also belongs in this AGN candidate class, the radio image (Fig.~3d)\nshows it to be resolved. Higher resolution observations\nrecently carried out by us indeed resolve all the nuclear emission in \nNGC\\,4424 (see Section~4.2), in contrast to the AGN candidates \nfrom the transition LINER sample. As such there is a clear separation between\nthe non-AGN and AGN candidate classes. \n\nApparently, galaxies with composite LINER and star-formation spectra\nseparate out into objects with and without a clear signature of an\nAGN, that is to say, a compact, flat-spectrum radio source. The prime\nquestion to address, of course, is whether the optical spectra of\nthese classes differ in any way. Deferring the full analysis of this\nissue to another paper, we here just note that the class of AGN\ncandidates indeed displays somewhat stronger [N~II] and [S~II] lines\nin their optical spectra. As we will demonstrate in the forthcoming\npaper in this series, the behavior of the so called $u$-parameter,\nwhich measures the radio/far-IR ratio, also supports the weak AGN\nclassification. However, like in the case of Seyfert galaxies showing\na $\\sim$30\\% incidence rate of compact radio cores (e.g., Norris et\nal. 1990), there is not a one-to-one correspondence between compact\nradio emission and nuclear activity. We conclude that the radio\nproperties permit to isolate AGN candidates among the sample of\ntransition LINERs, although the absence of radio cores cannot be used to \nargue against their being AGN. These conclusions strongly support the \nhypothesis which resulted from the VLA observations of transition LINER\nNGC\\,7331 by Cowan et al. (1994).\n\nInspection of Table~6 readily shows that these AGN candidates are\nhosted by rather early-type galaxies (E--Sb). The relevant radio core\nluminosities L$_{\\rm 8.4\\,GHz}$ range from $\\sim$ 10$^{26.2}$ --\n10$^{28.5}$ erg s$^{-1}$ Hz$^{-1}$, which is several orders of\nmagnitude less than the core luminosities in FR\\,I or FR\\,II type\n(Fanaroff \\& Riley 1974) radio galaxies and quasars, and in the range\nof the weakest radio cores in Seyfert galaxies (Giuricin et al.\n1996). This, then, implies that weak LINER AGN preferentially occur\nin bulge-dominated hosts, not necessarily just in ellipticals,\nconsistent with statistical results from other lines of evidence (Ho\net al. 1997b; Ho 1999b). This is in agreement with the case of\nSeyfert galaxies, for which the radio core emission was also found to\nbe stronger in early-type hosts (Giuricin et al. 1996). As such,\nthese weak AGN differ from the more powerful FR\\,I radio galaxies,\nwhich are commonly associated with elliptical galaxies, not seldom\nbrightest cluster galaxies (Zirbel \\& Baum 1995). They exceed the\nvery weak nuclear source in the nearby transition LINER NGC\\,7331\n(Cowan et al. 1994) by a factor of $\\sim 15$, and are comparable in\nstrength to the well-known variable radio core of the LINER nucleus in\nM\\,81 (e.g., Ho et al. 1999). Hence, it must be concluded that at least some \nweak LINER AGN reveal themselves by low-power radio cores. This supports\nthe analysis of Ho (1999a), who proposed that the weak nuclear radio\nsources (radio power 10$^{26}$ -- 10$^{29}$ erg s$^{-1}$ Hz$^{-1}$) in\nnearby elliptical and S0 galaxies are the low-luminosity counterparts\nof more powerful AGN.\n\nFinally, it is intriguing that the transition LINER in the elliptical\ngalaxy NGC\\,6482 remained undetected in our observations (as well as in\nthe NVSS). Given that NGC 6482 is the most distant object in our\nsample, our non-detection would still allow a $\\leq 10^{27}$ erg\ns$^{-1}$ Hz$^{-1}$ compact radio source to reside in this object. \n\nFull analysis of our sample, including optical emission-line and infrared\nluminosities, will be presented in forthcoming papers. To address the\nphysical origin behind the findings presented here will be the challenge\nfor future work. \n\n\\section{Conclusions}\n\nA sample of composite LINER/H\\,II galaxies and pure H\\,II nuclei was\nstudied using the VLA (C-array) at 8.4\\,GHz. On the basis of their\nradio morphological properties, the composite sources can be divided\ninto objects with low surface brightness emission confined mainly to\nthe plane of the galaxy and objects displaying compact nuclear\ncomponents. The former\nobjects are similar in radio morphology to the H\\,II nuclei in our\nsample, whereas the latter show morphologies consistent with AGN. All\nfive of the LINER AGN are hosted by bulge-dominated galaxies (Hubble\ntype E--Sb), and four of them show flat spectral indices between 8.4 and\n1.4\\,GHz. In terms of radio luminosity, the present LINER AGN populate\nthe range of low core radio luminosities, which implies that classical AGN \nof low luminosity exist in a wide range of galaxy types.\n\n\\acknowledgments\n\nM.~E.~F. is supported by grant PRAXIS XXI/BD/15830/98 from the \nFunda\\c c\\~ao para a Ci\\^encia e Tecnologia, Minist\\'erio da Ci\\^encia e\nTecnologia, Portugal. P.~D.~B. acknowledges a visitor's grant from the\nSpace Telescope Science Institute, where a large part of this paper\ncould be written. L.~C.~H. is partly funded by NASA grant NAG 5-3556,\nand by NASA grants GO-06837.01-95A and AR-07527.02-96A from the Space\nTelescope Science Institute (operated by AURA, Inc., under NASA contract\nNAS5-26555). We want to thank Neil Nagar for providing us with \nsome of his preliminary results.\n\nThis research was supported in part by the European\nCommission TMR Programme, Research Network Contract ERBFMRXCT96-0034\n``CERES.'' We made extensive use of the APM (Automatic Plate Measuring)\nFacility, run by the Institute of Astronomy in Cambridge, the STScI DSS\n(Digitized Sky Survey), produced under US government grant NAGW -- 2166,\nand NED (NASA/IPAC Extragalactic Database), which is operated by the Jet\nPropulsion Laboratory, California Institute of Technology, under\ncontract with NASA. \n\n\\begin{references}\n\n\\reference{}\nBecker, R.~H., White, R.~L., \\& Edwards, A.~L. 1991, \n\\apjs, 75, 1\n\n\\reference{}\nBecker, R.~H., White, R.~L., \\& Helfand, D.~J. 1995,\n\\apj, 450, 559\n\n\\reference{}\nCarral, P., Turner, J.~L., \\& Ho, P.~T.~P. 1990, \\apj, 362, 434\n\n\\reference{}\nClark, B.~G., 1980, \\aap, 89, 377\n\n%Clark, R.~N., 1980, PASP, 92, 221\n\n\\reference{}\nCollison, P.~M., Saikia, D.~J., Pedlar, A., Axon, D.~J., \\& Unger, S.~W. 1994,\n\\mnras, 268, 203\n \n\\reference{}\nCondon, J.~J. 1983, \\apjs, 53, 459\n\n\\reference{}\nCondon, J.~J. 1987, \\apjs, 63, 485\n\n\\reference{}\nCondon, J.~J. 1992, ARA\\&A, 30, 575\n\n\\reference{}\nCondon, J.~J., \\& Broderick, J.~J. 1988, \\aj, 96, 30\n\n\\reference{}\nCondon, J.~J., Condon, M.~A., Gisler, G., \\& Puschell, J.~J. 1982, \n\\apj, 252, 102\n\n\\reference{}\nCondon, J.~J., Cotton, W.~D., Greisen, E.~W., Yin, Q.~F., \nPerley, R.~A., Taylor, G.~B., \\& Broderick, J.~J. 1998a, \\aj, 115, 1693\n\n\\reference{}\nCondon, J.~J., Frayer, D.~T., \\& Broderick, J.~J. 1991,\n\\aj, 101, 362\n\n\\reference{}\nCondon, J.~J., Helou, G., Sanders, D.~B., \\& Soifer, B.~T. 1990, \n\\apjs, 73 359\n\n\\reference{}\nCondon, J.~J., Yin, Q.~F., Thuan, T.~X., \\& Boller, Th. 1998b,\n\\aj, 116, 2682\n\n\\reference{}\nCowan, J.~J., Romanishin, W., \\& Branch, D. 1994, \\apj, 436, L139\n\n\\reference{}\nDopita, M.~A., \\& Sutherland, R.~S. 1995, \\apj, 102, 161\n\n\\reference{}\nDouglas, J.~N., Bash, F. N., Bozyan, F.~A., Torrence, G.~W., \\& \nWolfe, C. 1996, \\aj, 111, 1945\n\n\\reference{}\nDressel, L.~L., \\& Condon, J.~J. 1978, \\apjs, 36, 53\n\n\\reference{}\nDumke, M.~K., Krause, M., Wielebinski, R., \\& Klein, U. 1995,\n\\aap, 302, 691\n\n\\reference{}\nEkers, R.~D., \\& Ekers, J.~A. 1973, \\aap, 24, 247\n\n\\reference{}\nEkers, R.~D., Fanti, R., \\& Miley, G.~K. 1983, \\aap, 120, 297\n\n\\reference{}\nFabbiano, G., Gioia, I.~M., \\& Trinchieri, G. 1989, \\apj, 347, 127\n\n\\reference{}\nFalcke, H., Wilson, A.~S., \\& Ho, L.~C. 1997, in Relativistic\nJets in AGN, ed. M. Sikora \\& M. Ostrowski, 13\n\n\\reference{}\nFanaroff, B.~L., \\& Riley, J.~M. 1974, \\mnras, 167, 31P\n\n\\reference{}\nFilippenko, A.~V 1996, in The Physics of LINERs in View of Recent Observations, \ned. M. Eracleous et al. (San Francisco: ASP), 17\n\n\\reference{}\nFilippenko, A.~V., \\& Terlevich, R. 1992, \\apj, 397, L79\n\n\\reference{}\nFosbury, R.~A.~E., Melbold, U., Goss, W.~M., \\& Dopita, M.~A. 1978, MNRAS, 183,\n549\n\n\\reference{}\nGioia, I.~M., \\& Fabbiano, G. 1987, \\apjs, 63, 771\n\n\\reference{}\nGiuricin, G., Fadda, D., \\& Mezzetti, M. 1996, \\apj, 468, 475\n\n\\reference{}\nGregory, P.~C., \\& Condon, J.~J. 1991,\n\\apjs, 75, 1011\n\n\\reference{}\nHaynes, M., \\& Sramek, R.~A. 1975, \\aj, 80, 673\n\n\\reference{}\nHeckman, T.~M. 1980, \\aap, 87, 152\n\n\\reference{}\nHeckman, T.~M., Balick, B., \\& Crane, P.~C. 1980, \\aaps, 40, 295\n\n\\reference{}\nHewett, P.~C., Foltz, C.~B., \\& Chaffee, F.~H. 1995, \\aj, 109, 1498\n\n\\reference{}\nHo, L.~C. 1996, in The Physics of LINERs in View of Recent Observations, \ned. M. Eracleous et al. (San Francisco: ASP), 103\n\n\\reference{}\nHo, L.~C. 1999a, \\apj, 510, 631 \n\n\\reference{}\nHo, L.~C. 1999b, Advances in Space Research, 23 (5-6), 813\n\n\\reference{}\nHo, L.~C., Filippenko, A.~V., \\& Sargent, W.~L.~W. 1993, \\apj, 417, 63\n\n\\reference{}\nHo, L.~C., Filippenko, A.~V., \\& Sargent, W.~L.~W. 1995, \\apjs, 98, 477\n\n\\reference{}\nHo, L.~C., Filippenko, A.~V., \\& Sargent, W.~L.~W. 1997a, \\apjs, 112, 315\n\n\\reference{}\nHo, L.~C., Filippenko, A.~V., \\& Sargent, W.~L.~W. 1997b, \\apj, 487, 568\n\n\\reference{}\nHo, L.~C., Van Dyk, S.~D., Pooley, G.~G., Sramek, R.~A., \\& Weiler, K.~W. 1999,\n\\aj, 118, 843\n\n\\reference{}\nH\\\"ogbom, J.~A., 1974, \\aaps, 15, 417\n\n\\reference{}\nHook, I.~M., McMahon, R.~G., Patnaik, A.~R., Browne, I.~W.~A., Wilkinson, \nP.~N., Irwin, M.~J.,\\& Hazard, C. 1995, \\mnras, 273, L63\n\n\\reference{}\nHughes, P.~A., Aller, H.~D., \\& Aller, M.~F. 1992, \\apj, 396, 469\n\n\\reference{}\nHummel, E. 1980, \\aaps, 41, 151\n\n\\reference{}\nHummel, E., Beck, R., \\& Dettmar, R.-J. 1991,\n\\aaps, 87, 309\n\n\\reference{}\nHummel, E., \\& Kotanyi, C.~G. 1982, \\aap, 106, 183\n \n\\reference{}\nHummel, E., van der Hulst, J.~M., Keel, W.~C., \\& Kennicutt, R.~C., Jr.\n1987, \\aaps, 70, 517\n\n\\reference{}\nJenkins, C.~R. 1982, \\mnras, 200, 705\n\n\\reference{}\nJones, D.~L., Terzian, Y., \\& Sramek, R.~A. 1981a, \\apj, 246, 28\n\n\\reference{}\nJones, D.~L., Terzian, Y., \\& Sramek, R.~A. 1981b, \\apj, 247, L57\n\n\\reference{}\nKenney, J.~D.~P., Koopmann, R.~A., Rubin, V.~C., \\& Young, J.~S. 1996,\n\\aj, 111, 152\n\n\\reference{}\nKlein, U., \\& Emerson, D.~T. 1981, \\aap, 94, 29\n\n\\reference{}\nM\\\"ollenhoff, C., Hummel, E., \\& Bender, R. 1992,\n\\aap, 255, 35\n\n\\reference{}\nNiklas, S., Klein, U., Braine, J., \\& Wielebinski, R. 1995,\n\\aaps, 114, 21\n\n\\reference{}\nNorris, R.~P., Allen, D.~A., Sramek, R.~A., Kesteven, M.~J., \\& Troup, E.~R. \n1990, \n\\apj, 359, 291\n\n\\reference{}\nPatnaik, A.~R., Browne, I.~W.~A., Wilkinson, P.~N., \\& Wrobel, J.~M. 1992, \n\\mnras, 254, 655\n\n\\reference{}\nPerley, R.~A., Schwab, F.~R., \\& Bridle, A.~H. 1989, in Synthesis Imaging in \nRadio Astronomy: A Collection of Lectures from the Third NRAO Synthesis\nImaging Summer School (San Francisco: ASP), 6\n\n\\reference{}\nRengelink, R.~B., Tang, Y., de Bruyn, A.~G., Miley, G.~K., Bremer, M.~N., \nR\\\"ottgering, H.~J.~A., \\& Bremer, M.~A.~R. 1997, \\aaps, 124, 259\n\n\\reference{}\nReuter, H.-P., Krause, M., Wielebinski, R., \\& Lesch, H. 1991,\n\\aap, 248, 12 \n\n\n\\reference{}\nSadler, E.~M., Jenkins, C.~R., \\& Kotanyi, C.~G. 1989, \\mnras, 240, 591\n\n\\reference{}\nSaikia, D.~J., Pedlar, A., Unger, S.~W., \\& Axon, D.~J. 1994,\n\\mnras, 270, 46\n\n\\reference{}\nSchlickeiser, R., Werner, W., \\& Wielebinski, R. 1984, \\aap, 140, 227\n\n\\reference{}\nShields, J. C. 1992, \\apj, 399, L27\n\n\\reference{}\nSlee, O.~B., Sadler, E.~M., Reynolds, J.~E., \\& Ekers, R.~D. 1994,\n\\mnras, 269, 928\n\n\\reference{}\nSramek, R.~A. 1975a, \\aj, 80, 771\n\n \\reference{}\nSramek, R.~A. 1975b, \\apj, 198, L13\n\n\\reference{}\nTerlevich, R., \\& Melnick, J. 1985, \\mnras, 213, 841\n\n\\reference{}\nTurner, K.~C., Helou, G., \\& Terzian, Y. 1988, PASP, 100, 452\n\n\\reference{}\nTurner, J.~L., \\& Ho, P.~T.~P. 1994,\n\\apj, 421, 122\n\n\\reference{}\nUrbanik, M., Gr\\\"ave, R., \\& Klein, U. 1985, \\aap, 152, 291\n\n\\reference{}\nUrbanik, M., Klein, U., \\& Gr\\\"ave, R. 1986, \\aap, 166, 107\n\n\\reference{}\nvan Breugel, W.~J.~M., Schilizzi, R.~T., Hummel, E., \\& Kapahi, V.~K. 1981, \n\\aap, 96, 310\n\n\\reference{}\nvan der Hulst, J.~M., Crane, \\& P.~C., Keel, W.~C. 1981, \\aj, 86, 1175\n\n\\reference{}\nvan der Kruit, P.~C. 1973a, \\aap, 29, 231\n\n\\reference{}\nvan der Kruit, P.~C. 1973b, \\aap, 29, 249\n\n\\reference{}\nVan Dyk, S.~D., \\& Ho, L.~C. 1998, in IAU Symp. 184, The Central Regions of\nthe Galaxy and Galaxies, ed. Y. Sofue (Dordrecht: Kluwer), 489\n\n\\reference{}\nV\\'eron-Cetty, M.-P., \\& V\\'eron, P. 1996, \\aaps, 115, 97\n\n\\reference{}\nVila, M.~B., Pedlar, A., Davies, R.~D., Hummel, E., \\& Axon, D.~J. 1990, \n\\mnras, 242, 379\n\n\\reference{}\nWeiler, K.~W., van der Hulst, J.~M., Sramek, R.~A., \\& Panagia, N. 1981,\n\\apj, 243, L151\n\n\\reference{}\nWhite, R.~L., \\& Becker, R.~J. 1992,\n\\apjs, 79, 331\n\n\\reference{}\nWrobel, J.~M., \\& Heeschen, D.~S. 1984, \\apj, 287, 41\n\n\\reference{}\nWrobel, J.~M., \\& Heeschen, D.~S. 1991,\n\\aj, 101, 148\n\n\\reference{}\nZirbel, E.~L., \\& Baum, S.~A. 1995, \\apj, 448, 521 \n \n\\end{references}\n\n\\clearpage \n\n% TABLE 1\n%\\setcounter{table}{0}\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{l c c c c c c r}\n\\tableline\n\\tableline\n\nGalaxy & Other & R.A.(J2000) & Dec(J2000) & D & & Hubble Type & Reference \\\\\n & name & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ}$ $^{'}$ $^{''}$ & Mpc & & & \\\\\n\\tableline \nIC\\,520 & & 08 53 42.3 & +73 29 29 & 47.0 & & SAB(rs)ab? & 26\\\\\nNGC\\,2541 & & 08 14 40.2 & +49 03 42 & 10.6 & & SA(s)cd & 26,41\\\\\nNGC\\,2985 & & 09 50 20.9 & +72 16 44 & 22.4 & & (R')SA(rs)ab & 1,2,5,26,41,42 \\\\\nNGC\\,3627 & M\\,66 & 11 20 14.9 & +12 59 21 & 6.6 & & SAB(s)b & 1,5,6,11,13,14\\\\\n & & & & & & & 17,24,26,28,41,44\\\\\nNGC\\,3628 & & 11 20 16.2 & +13 35 22 & 7.7 & & SAb pec spin & 1,4,5,11,13,14,16\\\\\n &&&&&&& 17,18,19,24,26,30\\\\\n &&&&&&& 34,36,38,41,44,45\\\\\nNGC\\,3675 & & 11 26 08.0 & +43 34 58 & 12.8 & & SA(s)b & 1,3,17,25,26,41\\\\\n &&&&&&& 42,47\\\\\nNGC\\,3681 & & 11 26 29.4 & +16 51 51 & 24.2 & & SAB(r)bc & 1\\\\\nNGC\\,4013 & & 11 58 31.1 & +43 56 50 & 17.0 & & SAb spin & 1,3,15,26,41\\\\\nNGC\\,4321 & M\\,100& 12 22 54.8 & +15 49 20 & 16.8 & & SAB(s)bc & 1,5,7,11,13,14,17\\\\\n &&&&&&& 18,20,22,24,26,27\\\\\n &&&&&&& 35,36,41,47\\\\\nNGC\\,4414 & & 12 26 27.2 & +31 13 24 & 16.8 & & SA(rs)c? & 1,3,5,11,13,14\\\\\n &&&&&&& 17,18,24,26,31,36\\\\\nNGC\\,4552 & M\\,89 & 12 35 39.9 & +12 33 25 & 9.7 & & E & 1,13,14,17,22,29\\\\\n &&&&&&& 37,38,39,41,43,44\\\\\nNGC\\,4643 & & 12 43 20.2 & +01 58 41 & 16.8& & SB(rs)0/a & 21,24,41\\\\\nNGC\\,4713 & & 12 49 57.8 & +05 18 39 & 25.7 & & SAB(rs)d & 1\\\\\nNGC\\,4826 & M\\,64 & 12 56 44.2 & +21 41 05 & 17.9 & & (R)SA(rs)ab & 1,2,8,13,14,17,24,25\\\\\n &&&&&&& 26,36,40,41,44,46\\\\\nNGC\\,5012 & &13 11 36.8 & +22 54 56 & 4.1 & & SAB(rs)c & 1\\\\\nNGC\\,5354 && 13 53 26.7 & +40 18 09 & 32.8 & & SA0 spin & 1,3,12,17,32,41,44\\\\\nNGC\\,5656 && 14 30 25.5 & +35 19 17 & 42.6 & & SAab & 1\\\\\nNGC\\,5678 && 14 32 05.2 & +57 55 23 & 35.6 & & SAB(rs)b & 1,13,14,17,18,31\\\\\nNGC\\,5838 && 15 05 26.5 & +02 06 01 & 28.5 & & SA0$^{-}$ & 1\\\\\nNGC\\,5846 && 15 06 29.2 & +01 36 21 & 28.5 & & E0$^{-}$ & 1,9,10,12,41\\\\\nNGC\\,5879 && 15 09 47.1 & +57 00 05 & 16.8 & & SA(rs)bc? & 1,41\\\\\nNGC\\,5921 && 15 21 56.3 & +05 04 11 & 25.2 & & SB(r)bc & 1,24,26,41\\\\\nNGC\\,6384 && 17 32 24.5 & +07 03 37 & 26.6 & & SAB(r)bc & 5,17,24,26,41\\\\\nNGC\\,6482 && 17 51 48.9 & +23 04 20 & 52.3 & & E: & \\nodata \\\\\nNGC\\,6503 && 17 49 27.5 & +70 08 41 & 6.1 & & SA(s)cd & 1,5,26,41,42\\\\\n\n\\tableline\n\\end{tabular}\n\\end{center}\n\\setcounter{table}{0}\n\\caption{Sample sources -- the 25 transition LINERs.}\n\\end{table}\n\n\\clearpage\n\n% TABLE 1 - (cont.)\n%\\setcounter{table}{0}\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{l c c c c c c r}\n\n\\tableline\n\\tableline\n\n\nGalaxy & Other & R.A.(J2000) & Dec(J2000) & D & & Hubble Type & Reference \\\\\n & name & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ}$ $^{'}$ $^{''}$ & Mpc & & & \\\\\n\\tableline\nNGC\\,3593 & & 11 14 36.0 & +12 49 06 & 5.5 & & SA(S)0/a: & 1,5,11,13,14,17\\\\\n & & & & & & & 18,24,26,33,41\\\\\nNGC\\,3684 & & 11 27 11.1 & +17 01 49 & 23.4 & & SA(rs)bc & 1\\\\\nNGC\\,4100 & & 12 06 08.1 & +49 34 59 & 17.0 & & (R')SA(rs)bc & 1,3,5,26,41,42\\\\\nNGC\\,4217 & & 12 15 50.7 & +47 05 37 & 17.0 & & SAb spin & 1,3,5,11,13,14\\\\\n &&&&&&& 15,17,26,41\\\\\nNGC\\,4245 & & 12 17 36.7 & +29 36 29 & 9.7 & & SB(r)0/a & \\nodata\\\\\nNGC\\,4369 & Mrk\\,439 & 12 24 36.1 & +39 22 58 & 21.6 & & (R)SA(rs)a & 1,3,18,41\\\\\nNGC\\,4405 & IC\\,788 & 12 26 07.1 & +16 10 51 & 31.5 & & SA(rs)0: & 1\\\\\nNGC\\,4424 & & 12 27 11.4 & +09 25 15 & 16.8 & & SA(s)a: & 1\\\\\nNGC\\,4470 & & 12 29 37.9 & +07 49 25 & 31.4 & & Sa ? & 1\\\\\nNGC\\,4710 & & 12 49 38.9 & +15 09 55 & 16.8 & & SA(r)0+? spin & 1,12,15,18,32,36\\\\\n &&&&&&& 41,43\\\\\nNGC\\,4800 && 12 54 38.0 & +46 31 52 & 15.2 & & SA(rs)b & 1,3,41\\\\\nNGC\\,4845 & & 12 58 01.3 & +01 34 30& 15.6 & & SA(s)ab spin & 1,18\\\\\n\\tableline\n \n\\end{tabular}\n\\end{center}\n\\setcounter{table}{0}\n\\caption{Sample sources -- the 12 H\\,II nuclei (cont.).}\n\\end{table}\n\n\n%Table 2\n\\begin{table}\n\\small\n\\begin{center}\n\\begin{tabular}[h]{ll|ll}\n\\tableline\n\\tableline\nNo. & Reference & No. & Reference \\\\\n\\tableline\n\n1 & Condon \\etal 1998a & 25 & Gioia \\& Fabbiano 1987 \\\\\n2 & Condon \\etal 1998b & 26 & Condon 1987 \\\\\n3 & Becker \\etal 1995 & 27 & Urbanik \\etal 1986\\\\\n4 & Dumke \\etal 1995 & 28 & Urbanik \\etal 1985\\\\\n5 & Niklas \\etal 1995 & 29 & Wrobel \\& Heeschen 1984\\\\\n6 & Saikia \\etal 1994 & 30 & Schlickeiser et al. 1984\\\\\n7 & Collison \\etal 1994 & 31 & Condon 1983\\\\\n8 & Turner \\& Ho 1994 & 32 & Hummel \\& Kotanyi 1982\\\\\n9 & Slee \\etal 1994 & 33 & Jenkins \\etal 1982 \\\\\n10 & M\\\"ollenhoff \\etal 1992 & 34 & Condon \\etal 1982\\\\\n11 & White \\& Becker 1992 & 35 & Weiler \\etal 1981\\\\\n12 & Wrobel \\& Heeschen 1991 & 36 & van der Hulst \\etal 1981\\\\\n13 & Becker \\etal 1991 & 37 & van Breugel \\etal 1981\\\\\n14 & Gregory \\& Condon 1991 & 38 & Jones \\etal 1981a\\\\\n15 & Hummel \\etal 1991 & 39 & Jones \\etal 1981b\\\\\n16 & Reuter \\etal 1991 & 40 & Klein \\& Emerson 1981\\\\\n17 & Condon \\etal 1991 & 41 & Hummel \\etal 1980\\\\\n18 & Condon \\etal 1990 & 42 & Heckman \\etal 1980 \\\\\n19 & Carral \\etal 1990 & 43 & Dressel \\& Condon 1978 \\\\\n20 & Vila \\etal 1990 & 44 & Sramek 1975a \\\\\n21 & Fabbiano \\etal 1989 & 45 & Haynes \\& Sramek 1975\\\\\n22 & Turner \\etal 1988 & 46 & van der Kruit 1973a\\\\\n23 & Condon \\& Broderick 1988 & 47 & van der Kruit 1973b\\\\ \n24 & Hummel \\etal 1987 & & \\\\\n\n\\tableline \n\\end{tabular}\n\\end{center}\n\\setcounter{table}{1}\n\\caption{References for the radio data (see Table~1).}\n\\end{table}\n\n\n\\clearpage\n\n\n%TABLE 3\n\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{lccrcr}\n\\tableline\n\\tableline\n\nGalaxy & Taper & Beamsize & PA & $rms$ & Fig. No. \\\\\n & K$\\lambda $ & arcsec$^2$ & $^{\\circ }$ & mJy/beam & \\\\ \n\\tableline \nNGC\\,2985 & 0 & 2.98 $\\times $ 2.15 & $-$7.19 & 0.08 & \\\\\n & 20 & 9.30 $\\times $ 7.20 & $-$84.28 & 0.09 & 1a\\\\\nNGC\\,3627 & 0 & 2.55 $\\times $ 2.29 & $-$25.24 & 0.10 & \\\\\n & 15 & 10.96 $\\times $ 9.93 & $-$64.54 & 0.25 & 1c\\\\\t \nNGC\\,3628 & 0 & 2.54 $\\times $ 2.30 & $-$14.68 & 0.45 & \\\\\n & 20 & 8.78 $\\times $ 7.48 & $-$76.82 & 0.80 & 1d\\\\\nNGC\\,3675 & 25 & 7.27 $\\times $ 5.81 & 71.04 & 0.09 & 2a\\\\\nNGC\\,4013 & 0 & 2.52 $\\times $ 2.26 & $-$19.39 & 0.07 & \\\\\n & 30 & 5.90 $\\times $ 5.26 & 77.17 & 0.09 & 2b\\\\\nNGC\\,4321 & 0 & 2.52 $\\times $ 2.33 & $-$11.27 & 0.07 & \\\\\n & 30 & 7.25 $\\times $ 5.14 & $-$89.95 & 0.08 & 3a\\\\\nNGC\\,4414 & 0 & 2.43 $\\times $ 2.32 & $-$37.18 & 0.08 &\\\\\n & 10 & 18.70 $\\times $ 17.70 & $-$62.41 & 0.15 & 3c\\\\\nNGC\\,4552 & 0 & 2.93 $\\times $ 2.54 & 11.27 & 0.08 & 4b\\\\\nNGC\\,4643 & 15 & 12.04 $\\times $ 11.13 & 52.57 & 0.07 & 4c\\\\\nNGC\\,4713 & 15 & 12.12 $\\times $ 10.95 & 44.22 & 0.08 & 5a\\\\\nNGC\\,4826 & 0 & 2.76 $\\times $ 2.29 & $-$6.23 & 0.08 & \\\\\n & 20 & 9.62 $\\times $ 8.26 & 62.33 & 0.10 & 5c\\\\\nNGC\\,5012 & 15 & 11.59 $\\times $ 11.18 & 74.66 & 0.08 & 6a\\\\\nNGC\\,5354 & 0 & 2.84 $\\times $ 2.37 & $-$42.75 & 0.06 & 6b \\\\\n \nNGC\\,5656 & 20 & 9.54 $\\times $ 8.39 & 75.33 & 0.08 & 6c\\\\\nNGC\\,5678 & 0 & 2.99 $\\times $ 2.21 & $-$27.47 & 0.07 &\\\\\n & 15 & 11.09 $\\times $ 10.75 & $-$34.43 & 0.10 & 6d\\\\\nNGC\\,5838 & 0 & 3.13 $\\times $ 2.43 & 1.94 & 0.07 & \\\\\n & 35 & 5.62 $\\times $ 5.23 & 51.83 & 0.07 & 7a\\\\\nNGC\\,5846 & 0 & 3.13 $\\times $ 2.49 & 3.94 & 0.07 &\\\\\n & 30 & 7.06 $\\times $ 5.67 & 68.01 & 0.07 & 7b\\\\\nNGC\\,5921 & 20 & 7.12 $\\times $ 5.63 & 67.8 & 0.06 & 7c \\\\\n\\tableline\n\\tableline\n\nGalaxy & Taper & Beamsize & PA & $rms$ & Fig. No. \\\\\n & K$\\lambda $ & arcsec$^2$ & $^{\\circ }$ & mJy/beam & \\\\ \n\\tableline\n\nNGC\\,3593 & 0 & 2.58 $\\times $ 2.36 & $-$17.94 & 0.09 & \\\\ \n & 20 & 9.70 $\\times $ 7.17 & $-$80.16 & 0.15 & 1b \\\\\nNGC\\,4100 & 0 & 2.61 $\\times $ 2.35 & $-$29.79 & 0.07 & \\\\\n & 20 & 7.83 $\\times $ 7.40 & 84.07 & 0.08 & 2c \\\\\nNGC\\,4217 & 20 & 7.30 $\\times $ 5.41 & 76.75 & 0.09 & 2d\\\\\nNGC\\,4369 & 0 & 2.48 $\\times $ 2.34 & $-$14.62 & 0.07 & \\\\\n & 30 & 6.94 $\\times $ 5.51 & 88.71 & 0.10 & 3b \\\\\nNGC\\,4424 & 0 & 3.00 $\\times $ 2.46 & 12.14 & 0.09 & \\\\\n & 30 & 7.21 $\\times $ 5.60 & 76.27 & 0.07 & 3d\\\\\nNGC\\,4470 & 15 & 9.95 $\\times $ 7.99 & 59.70 & 0.07 & 4a\\\\\nNGC\\,4710 & 0 & 2.86 $\\times $ 2.48 & 3.88 & 0.10 &\\\\\n & 30 & 5.50 $\\times $ 5.16 & 72.46 & 0.08 & 4d\\\\\nNGC\\,4800 & 30 & 5.28 $\\times $ 5.15 & $-$82.56 & 0.10 & 5b\\\\\nNGC\\,4845 & 0 & 3.27 $\\times $ 2.44 & 15.08 & 0.08 & \\\\\n & 30 & 7.08 $\\times $ 5.69 & 64.51 & 0.10 & 5d \\\\\n\n\\tableline\n\\end{tabular}\n\\end{center}\n\\setcounter{table}{2}\n\\caption {Map parameters of the detected sources. The H\\,II nuclei appear\nbelow the transition LINERs.}\n\\end{table}\n\n\\clearpage \n\n\n\n%TABLE 4\n\n\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{lcccccrr}\n\\tableline\n\\tableline\n\n\nField Source & R.A.(J2000) & Dec(J2000) & z & NVSS & F$_{\\rm 8.4}^{\\rm int}$ & $\\alpha ^{\\rm 8.4}_{\\rm 1.4}$ & \nReference \\\\\n & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ }$ $^{'}$ $^{''}$ & & mJy & mJy & & \\\\ \n\\tableline\n\nNGC\\,3593N & 11 14 37.20 & +12 52 15.0 & \\nodata & 18.7 & 10.6 & 0.3 & \\nodata\\\\\nNGC\\,3684SW & 11 27 02.42 & +16 58 34.8 & \\nodata & 41.4 & 18.1 & 0.5 & \\nodata\\\\\nNGC\\,4013SE & 11 58 38.61 & +43 55 05.5 & \\nodata & \\nodata & 3.8 & \\nodata & \\nodata\\\\\nSN\\,1979C & 12 22 58.67 & +15 47 51.6 & 0.0052 & \\nodata & 1.3 & \\nodata & Weiler \\etal 1981 \\\\\nLBQS\\,1223+1626 & 12 25 59.09 & +16 10 21.2 & 1.9290 & 8.9 & 10.1 & $-$0.1 & Hewett \\etal 1995 \\\\\nNGC\\,4424SE & 12 27 19.83 & +09 23 03.0 & \\nodata & 11.0 & 13.3 & $-$0.1 & \\nodata \\\\\nTXS\\,1227+081 & 12 29 47.64 & +07 50 26.7 & \\nodata & 110.9 & 16.0 & 1.1 & Douglas \\etal 1996 \\\\\nNGC\\,4710E & 12 49 48.63 & +15 09 33.3 & \\nodata & 4.1 & 4.8 & $-$0.1& \\nodata \\\\ \nNGC\\,5353 & 13 53 26.69 & +40 16 58.7 & 0.0077 & 41.0 & 26.7 & 0.2 & Hummel \\& Kotanyi 1982\\\\\nNGC\\,5838S & 12 05 28.11 & +02 04 16.2 & \\nodata & 7.5 & 1.3 & 1.0 & \\nodata \\\\ \n87GB\\,1508+5714 & 15 10 02.97 & +57 02 43.6 & 4.3010 & 202.4 & 292.1 & $-$0.2 & Hook \\etal 1995 \\\\\n87GB\\,1749+2302 & 17 51 49.10 & +23 01 26.7 & 0.7700 & 45.3 & 23.6 & 0.4 & Becker \\etal 1991 \\\\\nBL\\,1749+701 & 17 48 32.87 & +70 05 52.5 & \\nodata & 735.6 & \\nodata & \\nodata & Hughes \\etal 1992 \\\\\n\n\\tableline \n\\end{tabular}\n\\end{center}\n\\setcounter{table}{3}\n\\caption{The field source parameters. The integrated 8.4\\,GHz flux densities \n(column~6) have been corrected for primary beam attenuation.}\n\\end{table}\n\n\\clearpage\n\n%TABLE 5\n\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{lccc cr}\n\\tableline\n\\tableline\nGalaxy & Taper & F$_{\\rm max}$ & R.A.(J2000) & Dec(J2000) & F$_{\\rm int}$ \\\\\n & K$\\lambda $ & mJy/beam & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ }$ $^{'}$ $^{''}$ & mJy \\\\ \n\\tableline \n\nNGC\\,2985 & 0 & 1.07 & 09 50 22.1 & +72 16 44 & $\\geq$1.9\\\\\n & 20 & 1.30 & 09 50 22.0 & +72 16 44 & $\\geq$2.7 \\\\\t\nNGC\\,3627 & 0 & 1.30 & 11 20 15.0 & +12 59 30 & 3.7 ($\\geq$22.1) \\\\\n & 15 & 2.99 & 11 20 15.1 & +12 59 31 & 3.9 ($\\geq$25.7)\\\\\nNGC\\,3628 & 0 & 15.31 & 11 20 17.0 & +13 35 20 & 61.4 \\\\\n & 20 & 41.07 & 11 20 17.0 & +13 35 19 & 69.1\\\\\nNGC\\,3675 & 25 & 0.37 & 11 26 08.7 & +43 35 01 & $\\geq$1.3 \\\\\n\nNGC\\,4013 & 0 & 1.08 & 11 58 31.4 & +43 56 51 & $\\geq$3.8 \\\\\n & 30 & 2.28 & 11 58 31.4 & +43 56 51 & $\\geq$4.1 \\\\\nNGC\\,4321 & 0 & 0.34 & 12 22 55.4 & +15 49 21 & 7.5\\\\\n & 30 & 1.64 & 12 22 55.3 & +15 49 21 & 15.7\\\\\nNGC\\,4414 & 0 & 0.65 & 12 26 27.5 & +31 13 40 & 2.3 \\\\\n & 10 & 3.72 & 12 26 26.7 & +31 13 42 & 29.4\\\\\nNGC\\,4552 & 0 & 76.51 & 12 35 39.8 & +12 33 23 & 76.8 \\\\\n \nNGC\\,4643 & 15 & \\nodata & \\nodata & \\nodata & $\\sim$1 \\\\\nNGC\\,4713 & 15 & 0.32 & 12 49 58.4 & +05 18 39 & $\\geq$1.2\\\\\nNGC\\,4826 & 0 & 1.8 & 12 56 43.4 & +21 41 01 & 18.9\\\\\n & 20 & 4.03 & 12 56 43.7 & +21 41 00 & 21.1\\\\\nNGC\\,5012 & 15 & \\nodata& \\nodata & \\nodata & $\\sim$1 \\\\\nNGC\\,5354 & 0 & 11.61 & 13 53 26.7 & +40 18 10 & 11.7 \\\\\n \nNGC\\,5656 & 20 & 0.40 & 14 30 26.9 & +35 19 25 & $\\geq$0.7\\\\\nNGC\\,5678 & 0 & 0.74 & 14 32 05.9 & +57 54 51 & $\\geq$2.0 \\\\\n & 15 & 1.31 & 14 32 05.5 & +57 54 51 & $\\geq$8.6\\\\\n\nNGC\\,5838 & 0 & 1.85 & 15 05 26.3 & +02 05 57 & 2.1\\\\\n & 35 & 1.88 & 15 05 26.3 & +02 05 57 & 2.2 \\\\\n\nNGC\\,5846 & 0 & 6.03 & 15 06 29.3 & +01 36 21 & 6.4 \\\\\n & 30 & 6.36 & 15 06 29.3 & +01 36 21 & 7.1\\\\\n\nNGC\\,5921 & 20 & 0.46 & 15 21 56.4 & +05 04 14 & $\\geq$0.8 \\\\\n\\tableline\n\\tableline\n\nGalaxy & Taper & F$_{\\rm max}$ & R.A.(J2000) & Dec(J2000) & F$_{\\rm int}$ \\\\\n & K$\\lambda $ & mJy/beam & $^{h}$ $^{m}$ $^{s}$ & $^{\\circ }$ ' '' & mJy \\\\ \n\\tableline \n\nNGC\\,3593 & 0 & 1.82 & 11 14 36.4 & +12 49 06 & 16.4 \\\\ \n & 20 & 4.79 & 11 14 36.6 & +12 49 05 & 20.0 \\\\\nNGC\\,4100 & 0 & 0.93 & 12 06 08.6 & +49 34 58 & $\\geq$3.9 \\\\\n & 20 & 3.58 & 12 06 08.4 & +49 34 59 & $\\geq$7.3 \\\\\nNGC\\,4217 & 20 & 0.55 & 12 15 51.0 & +47 05 29 & $\\geq$22.0 \\\\\nNGC\\,4369 & 0 & 0.31 & 12 24 36.3 & +39 22 56 & 1.3 \\\\\n & 30 & 1.31 & 12 24 36.3 & +39 22 57 & 3.8 \\\\\nNGC\\,4424 & 0 & 0.60 & 12 27 11.2 & +09 25 17 & 2.0 \\\\\n & 30 & 0.80 & 12 27 11.7 & +09 25 17 & 2.5 \\\\\n\nNGC\\,4470 & 15 & 0.38 & 12 29 37.8 & +07 49 24 & $\\geq$2.6 \\\\\nNGC\\,4710 & 0 & 0.71 & 12 49 38.9 & +15 09 59 & $\\geq$6.0 \\\\\n & 30 & 1.64 & 12 49 39.0 & +15 09 58 & 6.1 \\\\\nNGC\\,4800 & 30 & 0.36 & 12 54 37.8 & +46 31 52 & $\\geq$1.2 \\\\\nNGC\\,4845 & 0 & 1.76 & 12 58 01.2 & +01 34 32 & $\\geq$9.9 \\\\\n & 30 & 5.15 & 12 58 01.1 & +01 34 32 & 12.5 \\\\\n\n\n\\tableline \n\\end{tabular}\n\\end{center}\n\\setcounter{table}{4}\n\\caption{The 8.4\\,GHz radio parameters of the detected sources. The \nH\\,II nuclei appear below the transition LINERs.}\n\\end{table}\n\n\\clearpage\n\n\n%TABLE 6\n\n\\begin{table}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}[h]{l c r c r c}\n\\tableline\n\\tableline\n\nGalaxy & NVSS & F$_{\\rm 8.4}^{\\rm int}$ & Log L$_{\\rm 1.4}^{\\rm tot}$ & \n$\\alpha_{\\rm 1.4}^{\\rm 8.4}$ & Hubble Type \\\\\n & mJy & mJy & erg s$^{-1}$ Hz$^{-1}$ & & \\\\\n\\tableline \nIC\\,520 & \\nodata & \\nodata & \\nodata & \\nodata & SAB(rs)ab?\\\\\nNGC\\,2541 & \\nodata & \\nodata & \\nodata & \\nodata & SA(s)cd \\\\\nNGC\\,2985 & 44.1 & 2.7 & 28.4 & 1.6 & (R')SA(rs)ab \\\\\nNGC\\,3627 & 324.9 & 3.9 (25.7) & 28.2 & 2.5 (1.5) & SAB(s)b \\\\\nNGC\\,3628 & 291.7 & 69.1 & 28.3 & 0.8 & SAb pec spin \\\\ \nNGC\\,3675 & 48.9 & 1.3 & 27.9 & 2.0 & SA(s)b \\\\\nNGC\\,3681 & 4.2 & \\nodata & 27.5 & \\nodata & SAB(r)bc \\\\\nNGC\\,4013 & 40.5 & 4.1 & 28.2 & 1.3 & SAb spin \\\\\nNGC\\,4321 & 87.1 & 15.7 & 28.5 & 1.0 & SAB(s)bc\\\\\nNGC\\,4414 & 242.2 & 29.4 & 28.4 & 1.2 & SA(rs)c? \\\\\nNGC\\,4552 & 103.1 & 76.8 & 28.5 & 0.2 & E \\\\\nNGC\\,4643 & \\nodata & $\\sim$1 & \\nodata & \\nodata & SB(rs)0/a \\\\\nNGC\\,4713 & 46.9 & 1.2 & 28.3 & 2.0 & SAB(rs)d \\\\\nNGC\\,4826 & 101.1 & 21.1 & 27.3 & 0.9 & (R)SA(rs)ab\\\\\nNGC\\,5012 & 31.4 & $\\sim$1 & 28.8 & \\nodata & SAB(rs)c \\\\\nNGC\\,5354 & 8.4 & 11.7 & 28.0 & $-$0.2 & SA0 spin \\\\\nNGC\\,5656 & 22.0 & 0.7 & 28.7 & 2.0 & SAab \\\\\nNGC\\,5678 & 111.5 & 8.6 & 29.2 & 1.4 & SAB(rs)b \\\\\nNGC\\,5838 & 3.0 & 2.2 & 27.5 & 0.2 & SA0$^{-}$ \\\\\nNGC\\,5846 & 22.1 & 7.1 & 28.3 & 0.6 & E0$^{-}$ \\\\\nNGC\\,5879 & 21.1 & \\nodata & 27.9 & \\nodata & SA(rs)bc?\\\\\nNGC\\,5921 & 24.2 & 0.8 & 28.3 & 1.9 & SB(r)bc\\\\\nNGC\\,6384 & \\nodata & \\nodata & \\nodata & \\nodata & SAB(r)bc\\\\\nNGC\\,6482 & \\nodata & \\nodata & \\nodata & \\nodata & E: \\\\\nNGC\\,6503 & 40.0 & \\nodata & 27.3 & \\nodata & SA(s)cd\\\\\n\n\\tableline\n\\tableline\nGalaxy & NVSS & F$_{\\rm 8.4}^{\\rm int}$ & Log L$_{\\rm 1.4}^{\\rm tot}$& \n$\\alpha_{\\rm 1.4}^{\\rm 8.4}$ & Hubble Type \\\\\n & mJy & mJy & erg s$^{-1}$ Hz$^{-1}$ & & \\\\\n\\tableline \n \nNGC\\,3593 & 87.3 & 20.0 & 27.5 & 0.8 & SA(S)0/a: \\\\\nNGC\\,3684 & 15.9 & \\nodata & 28.0 & \\nodata & SA(rs)bc \\\\\nNGC\\,4100 & 50.3 & 7.3 & 28.2 & 1.1 & (R')SA(rs)bc \\\\\nNGC\\,4217 & 122.8 & 22.0 & 28.6 & 1.0& SAb spin \\\\\nNGC\\,4245 & \\nodata & \\nodata & \\nodata & \\nodata & SB(r)0/a \\\\\nNGC\\,4369 & 24.3 & 3.8 & 28.1 & 1.0 & (R)SA(rs)a \\\\\nNGC\\,4405 & 4.5 & \\nodata & 27.7 & \\nodata & SA(rs)0: \\\\\nNGC\\,4424 & 4.5 & 2.5 & 27.2 & 0.3 & SA(s)a: \\\\\nNGC\\,4470 & 17.1 & 2.6 & 28.3 & 1.1 & Sa ? \\\\\nNGC\\,4710 & 19.3 & 6.1 & 27.8 & 0.7 & SA(r)0+? spin \\\\\nNGC\\,4800 & 23.5 & 1.2 & 27.8 & 1.7 & SA(rs)b \\\\\nNGC\\,4845 & 43.8 & 12.5 & 28.1 & 0.7 & SA(s)ab spin \\\\\n\n\\tableline\n\\end{tabular}\n\\end{center}\n\\setcounter{table}{5}\n\\caption{Summary of the detected sources. The H\\,II nuclei appear\n below the transition LINERs. All tabulated spectral index values are upper\nlimits (see Section~4.3).}\n\\end{table}\n\n\n\n\n\\clearpage\n\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f1a.ps}\n(a) \n\\epsfxsize=7.3cm\n\\raisebox{1.4cm}{\n\\epsffile{f1b.ps}\n(b)\n}\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{1}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f1c.ps}\n(c)\n\\epsfxsize=7.3cm\n\\raisebox{1.4cm}{\n\\epsffile{f1d.ps}\n(d)\n}\n}\n\n\\caption{Radio emission (contours) superimposed on optical images from \nthe Digitized Sky Survey (greyscale). Contour levels are CLEV $\\times$ \n(--3, 3, 6, 12, 24, 48, 96), where CLEV is the $rms$ noise level (see Table~3). \nThe grey scale levels are arbitrary. The size of the restoring \nbeam is given in parentheses after each object name (see Table~3).\n{\\bf (a)} NGC\\,2985 (9\\arcsecpoint30 $\\times$ 7\\arcsecpoint20), {\\bf (b)} \nNGC\\,3593 (9\\arcsecpoint70 $\\times$ 7\\arcsecpoint17), {\\bf (c)} NGC\\,3627 (10\\arcsecpoint96 $\\times$ 9\\arcsecpoint93) and {\\bf (d)} NGC\\,3628 \n(8\\arcsecpoint78 $\\times$ 7\\arcsecpoint48). NGC\\,3593 is an H\\,II nucleus. }\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f2a.ps}\n(a)\n\\epsfxsize=7.3cm\n\\raisebox{1.8cm}{\n\\epsffile{f2b.ps}\n(b)\n}\n}\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{2}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f2c.ps}\n(c)\n\\epsfxsize=7.3cm\n\\raisebox{1cm}{\n\\epsffile{f2d.ps}\n(d)\n}\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,3675 (7\\arcsecpoint27 $\\times$ 5\\arcsecpoint81), {\\bf (b)} NGC\\,4013\n(5\\arcsecpoint90 $\\times$ 5\\arcsecpoint26), {\\bf (c)} NGC\\,4100 (7\\arcsecpoint83 $\\times$ 7\\arcsecpoint40) and {\\bf (d)}\nNGC\\,4217 (7\\arcsecpoint30 $\\times$ 5\\arcsecpoint41). NGC\\,4100 and NGC\\,4217 are H\\,II nuclei.}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\raisebox{0.1cm}{\n\\epsffile{f3a.ps}\n(a)\n}\n\\epsfxsize=7.3cm\n\\epsffile{f3b.ps}\n(b)\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{3}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f3c.ps}\n(c)\n\\raisebox{1.6cm}{\n\\epsfxsize=7.3cm\n\\epsffile{f3d.ps}\n(d)\n}\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,4321 (7\\arcsecpoint25 $\\times$ 5\\arcsecpoint14), {\\bf (b)} NGC\\,4369\n(6\\arcsecpoint94 $\\times$ 5\\arcsecpoint51), {\\bf (c)} NGC\\,4414 (18\\arcsecpoint17 $\\times$ 17\\arcsecpoint70) and {\\bf (d)} NGC\\,4424\n(7\\arcsecpoint21 $\\times$ 5\\arcsecpoint60). NGC\\,4369 and NGC\\,4424 are H\\,II nuclei.}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f4a.ps}\n(a)\n\\epsfxsize=7.3cm\n\\raisebox{0.4cm}{\n\\epsffile{f4b.ps}\n(b)\n}\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{4}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\raisebox{1.8cm}{\n\\epsffile{f4c.ps}\n(c)\n}\n\\epsfxsize=7.3cm\n\\epsffile{f4d.ps}\n(d)\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,4470 (9\\arcsecpoint95 $\\times$ 7\\arcsecpoint99), {\\bf (b)} NGC\\,4552\n(2\\arcsecpoint93 $\\times$ 2\\arcsecpoint54), {\\bf (c)} NGC\\,4643 (12\\arcsecpoint04 $\\times$ 11\\arcsecpoint13) and {\\bf (d)}\nNGC\\,4710 (5\\arcsecpoint50 $\\times$ 5\\arcsecpoint16). NGC\\,4470 and NGC\\,4710 are H\\,II nuclei.}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\raisebox{1cm}{\n\\epsffile{f5a.ps}\n(a)\n}\n\\epsfxsize=7.3cm\n\\epsffile{f5b.ps}\n(b)\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{5}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f5c.ps}\n(c)\n\\epsfxsize=7.3cm\n\\raisebox{0.6cm}{\n\\epsffile{f5d.ps}\n(d)\n}\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,4713 (12\\arcsecpoint12 $\\times$ 10\\arcsecpoint95), {\\bf (b)} NGC\\,4800\n(5\\arcsecpoint28 $\\times$ 5\\arcsecpoint15), {\\bf (c)} NGC\\,4826 (9\\arcsecpoint62 $\\times$ 8\\arcsecpoint26) and {\\bf (d)} NGC\\,4845\n(7\\arcsecpoint08 $\\times$ 5\\arcsecpoint69). NGC\\,4845 is an H\\,II nucleus.}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f6a.ps}\n(a)\n\\epsfxsize=7.3cm\n\\raisebox{1.1cm}{\n\\epsffile{f6b.ps}\n(b)\n}\n}\n\n\\end{figure}\n\n\n\\begin{figure}\n\\figurenum{6}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\raisebox{0.6cm}{\n\\epsffile{f6c.ps}\n(c)\n}\n\\epsfxsize=7.3cm\n\\epsffile{f6d.ps}\n(d)\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,5012 (11\\arcsecpoint59 $\\times$ 11\\arcsecpoint18), {\\bf (b)} NGC\\,5354\n(2\\arcsecpoint84 $\\times$ 2\\arcsecpoint37), {\\bf (c)} NGC\\,5656 (9\\arcsecpoint54 $\\times$ 8\\arcsecpoint39) and {\\bf (d)} NGC\\,5678\n(11\\arcsecpoint09 $\\times$ 10\\arcsecpoint75).}\n\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\leavevmode\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f7a.ps}\n(a)\n\\epsfxsize=7.3cm\n\\raisebox{0.3cm}{\n\\epsffile{f7b.ps}\n(b)\n}\n}\n\\end{figure}\n\n\\begin{figure}\n\\figurenum{7}\n\\centerline{\n\\epsfxsize=7.3cm\n\\epsffile{f7c.ps}\n(c)\n}\n\n\\caption{As in Figure~1. {\\bf (a)} NGC\\,5838 (5\\arcsecpoint62 $\\times$ 5\\arcsecpoint23), {\\bf (b)} NGC\\,5846\n(7\\arcsecpoint06 $\\times$ 5\\arcsecpoint67) and {\\bf (c)} NGC\\,5921 (7\\arcsecpoint12 $\\times$ 5\\arcsecpoint63).}\n\n\\end{figure}\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[] |
astro-ph0002405
|
Recovering the Topology of the Initial Density Fluctuations Using the {\em IRAS} Point Source Catalogue Redshift Survey
|
[
{
"author": "A. Canavezes"
},
{
"author": "$^1$ J. Sharpe"
},
{
"author": "$^2$"
},
{
"author": "$^1$ Centro de Astrof\\'{i}sica da Universidade do Porto"
},
{
"author": "Rua das Estrelas s/n"
},
{
"author": "4150 Porto"
},
{
"author": "Portugal"
},
{
"author": "$^2$ Imperial College of Science Technology and Medicine"
},
{
"author": "Blackett Laboratory"
},
{
"author": "Prince Consort Road"
},
{
"author": "London SW7 2BZ"
},
{
"author": "UK"
}
] |
We apply the reconstruction technique of Nusser \& Dekel (1992) to the recently available Point Source Catalogue Redshift Survey (PSCz) in order to subtract the phase correlations that are expected to develop in the mild non-linear regime of gravitational evolution. We study the evolution of isodensity contours defined using an adaptive smoothing algorithm in order to minimize the problems derived from the non-comutivity of operators. We study the genus curves of these isodensity contours and concentrate on the evolution of the amplitude drops, a meta-statistic able to quatify the level of phase-correlation present in the field. In order to test the method and to quatify the level of statistical uncertainty, we apply the method to a set of mock PSCz catalogues derived from the N-body simulations of two 'standard' CDM models, kindly granted to us by the Virgo consortium. We find the method to be reliable in recovering the right amplitude drops. When applied to PSCz the level of phase correlations observed is very low on all scales ranging from $5\lu$ to $60\lu$, providing support to the theory that structure originated from gaussian initial conditions.
|
[
{
"name": "reconstruction.tex",
"string": "\\label{rec}\n\nThe {\\em IRAS} Point Source Catalogue Redshift Survey \\cite{Sa99} lends itself to topological studies because of its high sampling densities and large volume. It countains approximately $15000$ galaxies to the full depth of the PSC ($0.6 Jy$). Its sky coverage is $84.1$ per cent, where only the zone of avoidance is excluded, here defined as an infrared background exceeding $25 \\rm{MJy sr}^{-1}$ at $100\\mu\\rm{m}$, and a few unobserved or contaminated patches at higher latitude. The excluded regions are coded in an angular mask, as shown in Fig. \\ref{figMask}. Canavezes et al. \\shortcite{Ca98} analysed the topology of PSCz and showed that it is consistent with the topology of CDM models: The genus curves retain the w-shape characteristic of random-phase density fields even at small smoothing lengths, where non-linear evolution has already generated significant skewness of the 1-point PDF. These non-linearities are, however, detected by a depressed amplitude of the genus curves - amplitude drops - consistent with those detected for the CDM models. Above $10 \\lu$ strong phase correlations were not detected in PSCz and those that were detected at smaller scales are expected in the framework of mildly non-linear gravitational evolution. This supports the hypothesis that structure grew from random-phase initial conditions.\n\n\\begin{figure*}\n\\bc\n\\resizebox{14cm}{!}{\\includegraphics{plots/aitoffcrop.eps}}\n\\caption\n{Sky coverage of the PSCz survey in an aitoff projection. The dots represent the galaxies in the survey, the shaded regions are unobserved and comprise the angular mask. The galactic centre lies in the centre of the plot.\n\\label{figMask}}\n\\ec\n\\end{figure*}\n\nIn this paper we attempt to subtract these phase correlations by reversing gravity. If it is true that structure does indeed originate in random-phase fluctuations, then reversing gravitational evolution should provide us with an initial density fluctuation field free from phase correlations on any scale.\n\nThere are several methods to achieve this goal. Nusser \\& Dekel \\shortcite{ND92}, showed how to express the Zel'dovich approximation in a set of Eulerian coordinates and reverse it to obtain a reconstructed density field. They tested the method with N-body simulations and found satisfactory results. Recently, some improvements have been made on the original method (e.g. Gramann \\shortcite{Gr93}). Nusser, Dekel \\& Yahil \\shortcite{Nu95} applied the Nusser \\& Dekel \\shortcite{ND92} approximation to the $1.2$ Jy $IRAS$ redshift survey to recover the 1-point probability distribution function of the initial density field. Their results were consistent with Gaussian initial conditions. The PSCz presents us with an unprecedented number of resolution elements and should constitute therefore the best available data set on which to apply a reconstruction technique. \n\nThe method we choose to follow here is the quasi-linear method proposed by Nusser \\& Dekel \\shortcite{ND92}. In section \\ref{recmethod} we describe this method; In section \\ref{recdenmaps} we describe the construction of the density maps used as the input of the {\\em time-machine} and describe our error estimates; Section \\ref{recnbody} is devoted to testing the method using N-body simulations of a CDM model and in section \\ref{recpscz} we apply the method to the PSCz and present our results.\n\n\\section{THE RECONSTRUCTION METHOD}\n\\label{recmethod}\n\nThe reconstruction method we follow is based on two premises: The velocity field is, when smoothed on a scale of a few Mpc, irrotational, and the Zel'dovich approximation is accurate over the mildly non-linear regime. \n\nOur first step is to try to express the Zel'dovich approximation in a set of Eulerian coordinates.\n\nGiven an initial comoving position $\\bf{q}$ for a given particle, a final position $\\bf{x}(\\bf{q},t)$ will have the form\n\\be \n{\\bf x}({\\bf q},t)={\\bf q}+P({\\bf q},t).\n\\ee\nThe Zel'dovich approximation states that the displacement term $P({\\bf q},t)$ can be written as a product of two functions, each a function only of one of the variables ${\\bf q}$ or $t$, i.e., we can separate the variables $q$ and $t$:\n\\be\n{\\bf x}({\\bf q},t)={\\bf q}+D(t)\\Psi({\\bf q}).\n\\ee\nThis is simply a linear approximation with respect to the particle displacements rather than density. Particles in the Zel'dovich approximation follow straight lines:\n\\be\n{\\bf v}({\\bf q},t)=a(t)\\frac{d{\\bf x}}{dt}=a(t)\\dot{D}(t)\\Psi({\\bf q}).\n\\ee\nThe density fluctuation is given by\n\\be\n\\delta({\\bf q},t)=\\bar{\\rho}/J({\\bf q},t)-1,\n\\ee\nwhere $J({\\bf q},t)$ is the Jacobian of the coordinate transformation ${\\bf q}\\rightarrow {\\bf x}$.\n\nAs long as second order terms in $\\delta$ and ${\\bf v}$ are negligible, $\\delta(t) \\propto D(t)$, where $D(t)$ is the growing mode solution in linear perturbation theory (see e.g. Peebles \\shortcite{Pe80}).\n\nUnlike linear theory, where the density at a given position evolves according to the linear growth rate, under the Zel'dovich approximation infinite density can develop in a finite time as a result of the convergence of particle trajectories into a {\\em pancake}. in order to integrate a density field back in time, Nusser \\& Dekel \\shortcite{ND92} found the differential equation in Eulerian space which contains the Zel'dovich approximation. This is derived from the standard equation of motion of dust particles in an expanding Universe (e.g. Peebles \\shortcite{Pe80}):\n\\be\n\\frac{d{\\bf v}}{dt} + H{\\bf v}=-\\frac{1}{a}\\nabla\\Phi_{g} .\n\\label{eqmotion}\n\\ee\nHere ${\\bf v}$ stands for the {\\em peculiar} velocity of the particle, i.e., ${\\bf v}=a(t)\\frac{d{\\bf x}}{dt}$, where ${\\bf x}$ are the comoving positions; $\\nabla=\\left( \\partial /\\partial x,\\partial/\\partial y,\\partial /\\partial z \\right)$ and $\\Phi_{g}$ is the gravitational potential which is related to the local density fluctuation via the Poisson equation\n\\be\n\\nabla^{2}\\Phi_{g}=\\frac{3}{2}H^{2}\\Omega a^{2} \\delta .\n\\label{poisson}\n\\ee\n\nUsing the normalized variables $\\theta$ and $\\varphi_{g}$ defined thus:\n\\begin{eqnarray}\n\\theta({\\bf x},t)&\\equiv &\\frac{{\\bf v}({\\bf x},t)}{a\\dot{D}}={\\bf \\psi}({\\bf q}) \\label{renormtheta}\n\\\\\n\\phi_{g}({\\bf x},t)&\\equiv & \\frac{\\Phi_{g}({\\bf x},t)}{a^{2}\\dot{D}} \\label{renormphi} ,\n\\end{eqnarray}\nequations \\ref{eqmotion} and \\ref{poisson} reduce to\n\\be\n\\dot{\\theta} + \\frac{3H\\Omega}{2f(\\Omega)}\\theta=-\\nabla\\varphi_{g} ,\n\\label{motiontheta}\n\\ee\nwhere $f(\\Omega)\\equiv \\dot{D}/HD \\sim \\Omega^{0.6}$ \\cite{Pe80}.\n\nNotice that the Zel'dovich approximation is contained in \\ref{renormtheta}, which is to say \n\\be\n\\dot{\\theta}=0\n\\label{zeld}\n\\ee\n along the trajectory of a given particle, i.e., along a line of constant ${\\bf q}$. Hence, \\ref{motiontheta} is reduced, under the Zel'dovich approximation, to\n\\be\n\\frac{3H\\Omega}{2f(\\Omega)}\\theta=-\\nabla\\varphi_{g} .\n\\ee\n$\\theta$ is therefore the gradient of a potential:\n\\be\n\\theta=-\\nabla\\varphi_{v},\n\\label{gradient}\n\\ee\nwith\n\\be \n\\phi_{v}=\\frac{2f(\\Omega)}{3H\\Omega}\\varphi_{g} + F(t) .\n\\ee\nWe can obviously set $F(t)\\equiv 0$ since $\\theta$ is the only physical (measurable) quantity.\n\nEquation \\ref{zeld} can now be expanded in Eulerian coordinates:\n\\begin{eqnarray}\n\\frac{d\\theta}{dt}=0&\\Leftrightarrow & \\left[ \\frac{\\partial}{\\partial t} + \\frac{d{\\bf x}}{dt}\\cdot \\nabla \\right] \\theta({\\bf x},t) = 0 \\nonumber \\\\\n& \\Leftrightarrow & \\frac{\\partial \\theta}{\\partial t} + \\dot{D}(t) {\\bf \\psi}({\\bf q}) \\cdot \\nabla \\theta=0 \\nonumber \\\\\n& \\Leftrightarrow & \\frac{\\partial \\theta}{\\partial t} + \\dot{D} \\left( \\theta\\cdot \\nabla \\right) \\theta =0 .\n\\end{eqnarray}\nMaking use of the identity $\\left( \\theta\\cdot \\nabla \\right) \\theta = 1/2 \\left( \\nabla \\theta \\right) ^{2} - \\theta \\wedge \\left( \\nabla \\wedge \\theta \\right) $, taking into account the irrotationality of $\\theta$, and substituting \\ref{gradient} we arrive at\n\\begin{eqnarray}\n-\\nabla \\frac{\\partial \\varphi_{v}}{\\partial t} + \\dot{D}\\frac{1}{2} \\left(\\nabla \\theta\\right)^{2} = 0 & \\Leftrightarrow & -\\nabla \\left[ \\frac{\\partial \\varphi_{v}}{\\partial t} + \\frac{\\dot{D}}{2} \\left(\\nabla \\varphi\\right)^{2} \\right] = 0 \\nonumber \\\\\n& \\Leftrightarrow & \\frac{\\partial \\varphi_{v}}{\\partial t} + \\frac{\\dot{D}}{2} \\left( \\nabla \\varphi_{v}\\right) ^{2} = F(t) .\n\\end{eqnarray}\nAgain, because only gradients of $\\varphi_{v}$ have a physical meaning, we can take $F(t)$ to be zero. We finally arrive at the equation:\n\\be\n\\frac{\\partial \\varphi_{v}}{\\partial D} + \\frac{1}{2} \\left( \\nabla \\varphi_{v}\\right) ^{2} =0 .\n\\label{motion}\n\\ee \n\nThis is the differential equation which expresses the Zel'dovich approximation in Eulerian coordinates. Knowing $\\varphi_{v}$ at any time enables us to compute $\\varphi_{v}$ at any other time simply by integrating \\ref{motion} forwards or backwards.\n\nThe first step is to calculate $\\varphi_{v}$ at the present time. That can be easily achieved using Poisson's equation, which in Fourier space reads:\n\\be\n-k^{2} \\tilde{\\Phi}_{g}=\\frac{3}{2}H^{2}\\Omega a^{2} \\tilde{\\delta} ,\n\\ee\nwhere the tildes denote the Fourier transforms. Using \\ref{renormphi} we arrive at:\n\\be\n-Dk^{2}\\tilde{\\varphi}_{v}=\\tilde{\\delta} .\n\\label{potenti}\n\\ee\nSo, in order to obtain the velocity potential of a given smooth density field with periodic boundary conditions, we first transform it to Fourier space using some FFT code, we then divide the obtained field by $-k^{2}$ (normalizing D to unity at present), and then transform back to real space to obtain $\\varphi_{v}$. $\\varphi_{v}$ is then integrated back in time in the most trivial way: At every step, we calculate $1/2 \\left( \\nabla \\varphi_{v} \\right) ^{2}$ from the potential field; this is then used as a first order Taylor correction to predict the value of $\\varphi_{v}$ at the next step. Once a suitable number of integration steps has been performed, we use equation \\ref{potenti} again to obtain the value of $\\delta$ at the corresponding value of $D$.\n\nFor our application - topology, we expect the exact number of integrations\nto be irrelevant. After a certain number of iterations we expect to reach the linear\nregime in all scales, which means that the genus curves of the density fields will no longer change. This particular characteristic of the genus can in fact be useful to test the convergence of the method. We obtained several reconstructed density fields for different values of the number of integration steps, and found the topologies to converge. This result is shown is Fig. \\ref{convergence}.\n\n\\section{CONSTRUCTION OF THE DENSITY MAPS}\n\\label{recdenmaps}\n\nThe construction of the density maps we follow is, to a large extent, equivalent to the method followed by Canavezes et al. \\shortcite{Ca98}. We employ the same fit for the PSCz selection function $s(z)$:\n\\be\ns(z)=\\frac{\\psi}{z^{\\alpha}\\left( 1+\\left( \\frac{z}{z^{\\star}}\\right) ^{\\gamma} \\right)^{\\beta/\\gamma}} ,\n\\ee\nwith the parameters shown in Table \\ref{tab1} \\cite{Sp98a}, and estimate the density $\\rho(r)$ by\n\\be\n\\rho(r)\\propto\\frac{m(r)}{s(r)} ,\n\\ee\n\n\\begin{table}\n\\bc\n\\caption{Parameters of the selection function of PSCz.\\label{tab1}}\n\\vspace{0.5cm}\n\n\\begin{tabular}{ccc}\n$\\alpha$ & $\\beta$ & $\\gamma$ \\\\\n$0.991^{+0.068}_{-0.073}$ \n& $3.445^{+0.173}_{-0.158}$ \n& $1.925^{+0.162}_{-0.153}$ \\\\\n\\\\\n$z^{\\star}$ & $\\psi \\;\\;[h^3{\\rm Mpc}^{-3}]$ & \\\\\n$0.02534^{+0.00130}_{-0.00116}$ \n&$(141.3\\pm 2.4 ) \\times 10^{-6}$ & \\\\\n\\end{tabular}\n\\ec\n\\end{table}\n\n\\begin{table}\n\\bc\n\\caption{The smoothing lengths adopted for the topological analysis of the PSCz\nsurvey. Listed are the adopted survey depth $R_{\\rm max}$, the\nresulting number\n$N_{\\rm res}$ of resolution elements and the number $N_{\\rm gal}$ \nof galaxies inside the survey volume.\n\\label{tab2}\n}\n\\vspace{0.5cm}\n\\begin{tabular}{c|c|r|r|r}\n$\\lambda\\;\\;[\\lu]$ & $R_{\\rm max}\\;\\;[\\lu]$ &\n$N_{\\rm res}$ & $N_{\\rm gal}$ \\\\\n 5& 34.92& 215.5& 2295\\\\\n 6& 47.16& 307.3& 3550\\\\\n 7& 58.35& 366.3& 4928\\\\\n 8& 68.58& 398.5& 5909\\\\\n10& 86.91& 415.3& 7510\\\\\n12& 103.19& 402.3& 8775\\\\\n14& 118.04& 379.2& 9681\\\\\n16& 131.81& 353.7& 10356\\\\\n20& 156.96& 305.8& 11309\\\\\n24& 179.79& 266.0& 11968\\\\\n28& 200.97& 233.9& 12496\\\\\n32& 221.79& 210.6& 12833\\\\\n40& 263.44& 180.7& 13339\\\\\n48& 305.09& 162.4& 13684\\\\\n50& 315.50& 158.9& 13748\\\\\n56& 346.73& 150.2& 13924\\\\\n\\end{tabular}\n\\ec\n\\end{table}\n\n\nwhere $m(r)$ is the discrete point distribution. However, the angular mask needs to be treated with care. Because the structure we can see behind the mask will have a significant effect on the evolution of structure on the whole observable area, we need to resort to some sort of filling, prior to using the time-machine. \n\nWe consider two different types of filling: One, a random filling, in which fake objects are placed randomly over the masked region with an average number density equal to the average number density of the whole survey (weighted by the selection function); And another, a {\\em cloning}, in which fake objects are placed randomly in each bin, but with an average number density equal to the average number density of the neighbouring observable bins, again weighted by the selection function. \n\nOn both cases, we create a box containing a sphere of radius $R_{max}$ as defined in Table \\ref{tab2}. $R_{max}$ is the maximum distance up to which the average distance between two neighbouring galaxies in PSCz is smaller than the adopted smoothing length. The size of the box will then be $\\frac{2}{\\sqrt{3}}Rmax$. Although boundary conditions are not periodic, we smooth the density field in Fourier space assuming periodic boundary conditions. We consider this to be preferable to zero padding, as this would create an artificial boundary that would eventually affect the gravitational time-machine.\n\nWe then apply the Zel'dovich time-machine on the box thus obtained for both filling techniques. In the subsequent topological analysis, we limit ourselves to the sphere inside the box with radius $R_{max}$. \n\n\\subsection*{Smoothing Procedure}\n\nIdeally, one would want to apply the operator {\\em time-reverse} directly upon the unsmoothed density field obtained from PSCz, and only then smooth it on a range of scales to be able to calculate its genus curve. However, in order to obtain meaningful results, we need a smooth field {\\em a priori}. This poses a very important problem: These operators ({\\em time-reverse} and {\\em smoothing}) do not in general commute. In other words, the topology of the final density field can be significantly different whether the smoothing operation is performed before or after applying the {\\em time-machine} to our original field.\n\nTo illustrate this point, let us consider a Gaussian random density field smoothed on some scale $\\lambda$. After applying the {\\em time-machine} this density field will still be Gaussian. However, if we are to naively calculate its genus curve choosing for isodensity contours the same isodensity contours defined {\\em prior} to applying te {\\em time-machine}, we would wrongly conclude that the field is not Gaussian. In order to circumvent this problem we would be forced to smooth the final field once again on a larger scale, thus reducing considerably the statistical significance of our results.\n\nThere is, however, an alternative way to solve this dilemma: One can try to find a smoothing operator that comutes with our reconstruction operator.\n\nHow can we look for such a smoothing operator? One way of ensuring this is to find an operator that does not change the density field if applied once again at a latter stage. By other words, if we ensure that our final density field remains the same regardless of how many times we perform the smoothing operation throughout the time-reversing process, then it is because these two operators do indeed comute. A class of such operators are the adaptive smoothing operators. By adaptive smoothing, we understand a {\\em local} smoothing of variable smoothing length according to the local structure. There are several types of adaptive smoothing. The ideal adaptive smoothing operator ensures that the total mass enclosed by isodensity contours remains constant throughout the time-reversing process. A simplified version assumes spherical symmetry. At each point we employ a smoothing length $\\lambda$ such that $\\lambda^{3}\\propto 1/\\rho=1/\\left( \\rho_{0}+\\delta \\right)$. The proportionality constant defines the characteristic smoothing length, which is the smoothing length employed when the overdensity $\\delta$ vanishes. For highly dense regions, a smaller value of $\\lambda$ will be chosen, whereas voids will be smoothed with a larger value of $\\lambda$.\n\nWhen we apply the time-machine operator on a map smoothed in this way, the isodensity contours around a cluster will move, but the total mass enclosed by them will remain approximately constant, as long as the spherical symmetry hypothesis is a good approximation. \n\nIn our application to the PSCz we use a spherically symmetric adaptive smoothing algorithm. We start by creating a set of maps obtained from the original map (this might be either the PSCz data or simulation data) by smoothing it on a range of scales around a given characteristic scale $l_{0}$, using Gaussian filters of the form\n\\be\nG_{\\lambda}(x)=\\frac{1}{\\pi^{3/2}\\lambda^{3}} e^{-x^{2}/\\lambda^{2}}\n\\ee\nwhere $\\lambda$ varies around $l_{0}$. We then look for the appropriate value of $\\lambda$ at each position $x$ by enforcing the equation\n\\be\n(1+\\delta_{\\lambda})\\lambda^{3}=l_{0}^{3} ,\n\\ee \nwhere $\\delta_{\\lambda}$ is the density contrast when the original map is smoothed on a scale $\\lambda$. This ensures that the mass enclosed on a sphere of radius $\\lambda$ is, to first order in a Taylor expansion, constant throughout the whole map.\n\n\n\\subsection*{Error Estimates}\n\nThere are three different sources of error that enter our results: Shot noise, cosmic variance and the errors associated with the Zel'dovich approximation itself.\n\nThe most accurate and realistic way of estimating these errors, which ultimately enter the genus curves of the reconstructed PSCz density fields, is to analyse the topology of fake PSCz catalogues drawn from N-body simulations of some {\\em standard} CDM model. Since we intend to test the validity of the Zel'dovich time-machine with N-body simulations, it seems reasonable to extent this philosophy to the calculation of the statistical errors themselves. This is achieved by seeking a galaxy number density field with a Poisson distribution, whose expectation value is identical to the density field of the N-body simulation multiplied by the PSCz selection function. This is equivalent to {\\em observing} the density field of the N-body simulation in a similar way to the way PSCz observes the density field of the real Universe. This galaxy number density field is then divided by the PSCz selection function again to obtain a \"PSCZ-noisy\" distance-independent estimate of the real galaxy number density. Each of the {\\em mock} PSCz catalogues is adaptively smoothed using the algorithm described above and then used as input in the Zel'dovich time-machine. The genus curves of the reconstructed fields are calculated and the variance obtained over 10 mock PSCz catalogues is used as the statistical error estimate. \n\n\n\\section{TESTING THE METHOD WITH N-BODY SIMULATIONS OF CDM MODELS.}\n\\label{recnbody}\n\nAs we mentioned previously, we intend to test the regime of validity of the Zel'dovich time-machine by means of an N-body simulation of a CDM model. We apply the time-machine on the present density field drawn from the simulation and compare the density field thus obtained with the density field drawn from the original test-mass positions used as input in the simulation. More specifically, we need only to compare the topologies of the reconstructed and original fields through their genus curves.\n\nFor this purpose, we use two N-body simulations corresponding to two cold dark matter models, kindly provided by the Virgo consortium \\cite{Col97,Je97}.The simulations have been performed with an AP$^{3}$M-SPH code \nnamed {\\small HYDRA} \\cite{Cou95}. Here we consider the SCDM model and the $\\tau$CDM model, which parameters are shown in Table \\ref{modelparameters}. Because this simulations contain CDM on periodic boxes of size $239.5\\lu$ and use such a large number of particles, they constitute an ideal ground for this test.\n\n\\begin{table}\n\\bc\n\\caption{Parameters of the examined CDM models. The simulations have\nbeen done by the \nVirgo collaboration.\\label{modelparameters}\n}\n\\begin{tabular}{l|c|c|c|c|}\n\\multicolumn{1}{l|}{ }& $\\tau$CDM & $\\Lambda$CDM\n\\vspace{0.1cm}\\\\ \n\\multicolumn{1}{l|}{Number of particles } & $256^{3}$ & $256\n^{3}$ \\\\\n\\multicolumn{1}{l|}{Box size$[\\lu]$ } & $239.5$ & $239.5$\\\\\n$z_{start}$& $50$ & $30$ & \\\\\n$\\Omega_{0}$ & $1.0$ & $0.3$ \\\\\n$\\Omega_{\\Lambda}$& $0.0$ & $0.7$\\\\\n \\multicolumn{1}{l|}{Hubble constant $h$} & $0.5$ & $0.7$\\\\\n$\\Gamma$ & 0.21 & 0.21 \\\\\n$\\sigma_{8}$ & $0.60$ & $0.90$ \\\\\n \\multicolumn{1}{l|}{Mass per particle [$10^{10}h^{-1}M_{\\odot}$]} & $22.7$ &$5.8$ & \\\\\n\n\\end{tabular}\n\\ec\n\\end{table}\n\nWe start by binning the particles in cells of side length $2\\lu$ and smooth further on some characteristic smoothing length $\\lambda$, using the adaptive smoothing algorithm described in section \\ref{recdenmaps}, in an analogous procedure to the way we treat the PSCz galaxies. This \"double\" smoothing is required in the real Universe in order to minimize shot noise effects, but it is also necessary in order to eliminate severe non-linearities since the Zel'dovich time-machine is expected not to work over such regimes. It is also needed to smooth out regions of orbit-crossing.\n\nThe next step is to calculate the genus curves of both the original density field that is used as input in the simulation, smoothed in the same manner as described above, and the reconstructed density field obtained after applying the Zel'dovich time-machine to the present density field smoothed in the same way. In order to compare both genus curves we compute their amplitudes and their amplitude drops. It is very important to note that if we are to obtain gaussianized versions of the density fields at the present time, they will not have, in principle, the same genus amplitudes as the density fields themselves, even when these are in the Gaussian regime. This is so because of the very nature of adaptive smoothing. When a given density field is smoothed adaptively its genus curve will have a different shape and amplitude than the shape and amplitude of the genus curve of the same field when this is smoothed with a constant Gaussian window. We need to be extremely careful not to draw the wrong conclusions about the Gaussian or non-Gaussian nature of our density fields. After applying the time-machine, however, the amplitude of fluctuations will be reduced significantly. In fact they will be reduced to such an extent as to make the field look almost homogeneous. This means that the isodensity contours on adaptively smoothed maps will be very close to the isodensity contours on maps smoothed using a constant Gaussian window. Hence, it is possible to calculate amplitude drops and determine the Gaussian (or non-Gaussian) nature of our density maps {\\em after} applying the Zel'dovich time-machine, i.e., to determine the Gaussian (or non-Gaussian) nature of the {\\em reconstructed} fields.\n\nIn order to test the convergence of the reconstruction method, we obtained several reconstructed density fields for diffent values of the total number of integration steps, as mentioned in \\ref{recmethod}. Fig. \\ref{convergence} shows a particular slice of the reconstructed density fields at different integration steps when the method is applied to the maps at $z=0$ obtained from the $\\tau$CDM simulation by smoothing on characteristic lengths of $8\\lu$ and $10\\lu$. As it is evident from this Figure, the topology of the density fields is undistinguishable for values of $z$ greater than $4$ on smoothing scales of both $8\\lu$ and $10\\lu$. Only the amplitude of the density fluctuations changes, indicating that we are now in the linear regime. In Fig. \\ref{convscater} this is made even clearer. Here we show a point-by-point comparison of the reconstructed $\\tau$CDM density fields at redshifts $z=4$ and $z=9$, for the characteristic smoothing lengths of $8\\lu$ and $10\\lu$. We only show one in eight of all points, chosen randomly. It is obvious from this plot that the shape of fluctuations did not change from $z=4$ to $z=9$, for either of the smoothing lengths adopted. It is also obvious that the amplitude of fluctuations was reduced by a factor of $2$, as it is expected in the linear regime (notice that in the linear regime the growing mode of fluctuations varies as $1/(1+z)$). Hence, our time-machine shows the correct assimptotic behaviour.\n\n\\begin{figure*}\n\\bc\n\\resizebox{6cm}{!}{\\includegraphics{plots/d8tcdmcrop_test50.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d10tcdmcrop_test50.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d8tcdmcrop_test80.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d10tcdmcrop_test80.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d8tcdmcrop_test90.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/d10tcdmcrop_test90.eps}}\n\\caption{A particular slice of the reconstructed fields for the $\\tau$CDM simulation for different values of $z$. The left panels show the fields smoothed adaptively with a characteristic smoothing length of $8\\lu$, whereas the panels on the right show the fields smoothed with a characteristic smoothing length of $10\\lu$ \\label{convergence}}\n\\ec\n\\end{figure*}\n\n\\begin{figure*}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/d8tcdm_scater.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/d10tcdm_scater.eps}}\n\n\\caption{ Point-by-point comparison of the reconstructed $\\tau$CDM density field at redshift $z=4$ and the reconstructed $\\tau$CDM density field at redshift $z=9$, when the adopted characteristic smoothing lengths are of $8\\lu$ and $10\\lu$. \\label{convscater}}\n\\ec\n\\end{figure*}\n\n\\begin{figure*}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/cont8tcdm_now.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/cont8tcdm_back80.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/cont8tcdm_orig.eps}}\n\n\\caption{Isodensity contours of the $\\tau$CDM simulation. The characteristic smoothing length adopted was $8\\lu$. The separation between contour levels is $0.2/(1+z)$. The zero contour is heavy; positive contours are solid; negative contours are dashed. \\label{nbodycontours}}\n\\ec\n\\end{figure*}\n\n\\subsection*{Results} \n\nFigure \\ref{nbodycontours} shows the isodensity contours obtained for the SCDM simulation and the $\\tau$CDM simulation, when the fields are adaptively smoothed on a characteristic scale of $5\\lu$ in a comoving box of size $240\\lu$. The first row shows the fields at the present time. The second row shows the fields after applying the Zel'dovich time-machine back to a redshift of 10 and the third row shows the original fields used as input in the simulations. In each panel the thick line represents the contour where the density contrast is zero. Dashed lines represent contours of negative density contrast whereas solid lines represent positive density contrasts. The contour spacing is $0.2/(1+z)$. Because this is normalized to the linear reconstruction case where $\\delta\\propto 1/(1+z)$, the linear theory reconstruction density maps look exactly like the present day maps (first row), albeit their much lower fluctuation amplitude. From the contours on both the reconstructed maps and the original maps we notice that their fluctuation amplitudes are larger than the fluctuation amplitude of a linearly reconstructed map. This result is expected because fluctuations will grow faster at the later stages of evolution, in the mildly non-linear regime. It is obvious from Fig. \\ref{nbodycontours} that the Zel'dovich time-machine is able to change the rank order of isodensity contours. This means that the genus curves will also be changed. In fact we can predict, just by looking at Fig. \\ref{nbodycontours} that the amplitude of the genus curves will increase after applying the Zel'dovich time-machine, as it is expected.\n\n\\begin{figure*}\n\\bc\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm_exp5.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm00_exp5.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm00_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm_exp14.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gscdm00_exp14.eps}}\n\n\\caption{Genus curves for the SCDM model, at selected smoothing lengths. The left column shows the genus curves of the reconstructed field (thick solid lines) and of the randomized version of that field (thin solid lines), whereas the right column shows the genus curves of the original density field used as input for the N-body simulations. The dashed and dotted lines are the best fit random-phase curves to each of the fields. \\label{SCDMgenus}}\n\\ec \n\\end{figure*}\n\n\n\\begin{figure*}\n\\bc\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm_exp5.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm00_exp5.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm00_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm_exp14.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gtcdm00_exp14.eps}}\n\n\\caption{Genus curves for the $\\tau$CDM model, at selected smoothing lengths. The left column shows the genus curves of the reconstructed field (thick solid lines) and of the randomized version of that field (thin solid lines), whereas the right column shows the genus curves of the original density field used as input for the N-body simulations. The dashed and dotted lines are the best fit random-phase curves to each of the fields.\\label{TCDMgenus}}\n\\ec\n\\end{figure*}\n\\begin{figure}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/recdropmodels.eps}}\n\\caption{Amplitude drops measured for the reconstructed SCDM simulation and $\\tau$CDM simulation. Also show for comparison are the amplitude drops measured for the simulations at $z=0$\\label{recdropbody}.}\n\\ec\n\\end{figure}\n\\begin{figure}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/recampmodels.eps}}\n\\caption{Genus amplitudes measured for the reconstructed SCDM simulation and $\\tau$CDM simulation. Also shown are the genus amplitudes of the original fields\\label{recampbody}.}\n\\ec\n\\end{figure}\n\n\n\nFigures \\ref{SCDMgenus} and \\ref{TCDMgenus} show the genus curves obtained for the SCDM model and the $\\tau$CDM model respectively, at selected characteristic smoothing lengths, namely at $5\\lu$, $8\\lu$ and $14\\lu$. We restrict our analysis to this range of smoothing lengths, as we know {\\em a priori} that the Zel'dovich time-machine is only relevant in the mildly non-linear regime. In both figures, the first column shows the genus curves of the reconstructed field and its randomized counterpart, whereas the second column shows the genus curves of the original fields, used as input for the simulations. We deliberately do not show the genus curves of the present day {\\em adaptively smoothed} density fields, since, as we argued in the previous chapter, the isodensity contours are, at this stage, different from the isodensity contours of the fields smoothed using a constant kernel.\n\nIt is striking in Fig. \\ref{SCDMgenus} and Fig. \\ref{TCDMgenus} the consistency between the genus curves of the reconstructed field and of its randomized counterpart. This is particularly true for the genus amplitudes, which indicates that there is very little phase correlation in the reconstructed fields on all scales, as it is expected from Gaussian initial conditions. With regard to the genus amplitudes {\\em per se}, we find consistency with the genus amplitudes of the original density fields, although we notice a tendency for these to be slightly higher in the reconstructed fields. These means that the second moment of the power spectrum is recovered slightly {\\em in excess}. This becomes more important as we approach the smaller scales, which is to say as the system becomes more non-linear.\n\nIt is also interesting to notice a depression at high values of $\\nu$ on the genus curves of the reconstructed fields. We find this depression to be present in all cases, both for the Virgo simulations and the PSCz data. We expect this to be a particular feature of the reconstruction technique, i.e., ultimately dependent on the Zel'dovich approximation itself. At high values of $\\nu$ the regime is considerably non-linear and so we expect the Zel'dovich approximation to perform rather poorly. This problem is enhanced by the fact that the density fields have been smoothed adaptively. Nevertheless, we do not expect this feature to affect our results considerably as the calculation of the amplitude of the genus curves is restricted to the range $-1<\\nu<1$.\n\nNote that there is no sampling noise in these density fields. The tremble in the genus curves is ultimately due to cosmic variance.\n\nIn Fig. \\ref{recdropbody} we plot the amplitude drops obtained for the reconstructed SCDM model and for the reconstructed $\\tau$CDM model as a function of smoothing length. Also shown are the amplitude drops obtained for the models at $z=0$ \\cite{Ca98}. In all scales, the values obtained for the reconstructed fields are closer to unity than those of the present-day fields. This indicates that the Zel'dovich time-machine is a good tool in recovering Gaussian initial density fields. However, at small scales, we detect a slight departure from the expected value of unity, even for the reconstructed fields. This is not surprising since at this scales non-linearities become strong. The degree of strength of the non-linearities depends on the particular model. As we see from Fig. \\ref{recdropbody} they are more important in the $\\tau$CDM model than in the SCDM model, in agreement to what was found by Canavezes et al. \\shortcite{Ca98}.\n\nFig. \\ref{recampbody} shows the genus amplitudes of the reconstructed fields for both the SCDM model and the $\\tau$CDM model, together with the genus amplitudes of the original fields. In the case of the $\\tau$CDM model the agreement between the original genus amplitude and the genus amplitude of the reconstructed field, is striking, in particular when we consider scales above $\\sim 7\\lu$. For the SCDM model the agreement is not as good. The reconstructed genus amplitudes appear to be slightly higher than the true original ones.\n\nThese results indicate that the Zel'dovich time-machine is effective in recovering the right genus amplitude {\\em drops} on scales larger than $\\sim 8\\lu$, although recovered amplitudes cannot be considered reliable in the strict sense of the word. \n\n\n\n\\section{RECOVERING THE INITIAL DENSITY FIELD FROM PSCZ}\n\\label{recpscz}\n\nAs mentioned previously, one of the difficulties in using the PSCz in an attempt to recover the initial density fluctuations in the Universe, is the fact that the masked region can make up to $\\sim 20\\%$ of the whole observable area. Since this region will have a definite gravitational influence on the observable area when we attempt to reconstruct to original density field, some sort of filling is essential. As mentioned in \\ref{recdenmaps} we employ two different techniques: The random filling and the cloning. Fig. \\ref{randcloned} shows how the two different fillings appear to the eye. On the upper panel we show the map where the mask has been filled randomly and on the lower panel we show the map where the mask has been cloned. Although it is impossible to the eye to recognize any significant difference, we will be able to detect some noticeable differences on the topologies of the reconstructed density fields.\n\n\\begin{figure*}\n\\bc\n\\resizebox{6cm}{!}{\\includegraphics{plots/gcloned_exp6.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/grand_exp6.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gcloned_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/grand_exp8.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gcloned_exp12.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/grand_exp12.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/gcloned_exp16.eps}}\n\\resizebox{6cm}{!}{\\includegraphics{plots/grand_exp16.eps}}\n\\caption{Genus curves of the reconstructed PSCz fields. \\label{PSCzgenus}}\n\\ec\n\\end{figure*}\n\\begin{figure*}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/randomcrop.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/clonedcrop.eps}}\n\\caption{Aitoff projections of PSCz galaxies and filled masks.In the upper panel the mask is filled randomly whereas in the lower panel the mask is filled using a cloning technique.\\label{randcloned}}\n\\ec\n\\end{figure*}\n\\begin{figure*}\n\\bc\n\\resizebox{10cm}{!}{\\includegraphics{plots/droppscznow.eps}}\n\\caption{The amplitude drop $R$ measured for PSCz. Also shown are the results\nobtained by Vogeley et al.$1994$ for the CfA survey. Here the \nerrors are taken to be the uncertainty Vogeley et al.$1994$ report \nfor mock catalogues extracted from a LCDM model\\label{drpscznow}}\n\\ec\n\\end{figure*}\n\\begin{figure*}\n\\bc\n\\resizebox{8cm}{!}{\\includegraphics{plots/dropcloned.eps}}\n\\resizebox{8cm}{!}{\\includegraphics{plots/droprandom.eps}}\n\\caption{The amplitude drops measured for the reconstructed PSCz density fields. In the upper panel the mask has been cloned, whereas in the lower panel the mask has been filled randomly. Also shown are the amplitude drops obtained for the reconstructed N-body simulations. \\label{psczdrops}}\n\\ec\n\\end{figure*}\n\n\\subsection*{Results \\& Discussion} \n\nFig. \\ref{PSCzgenus} shows the genus curves obtained for the reconstructed PSCz fields. On the first column we plot the genus curves of the fields for which the mask has been filled using a cloning technique, and on the second column we plot the genus curves of the fields where the mask has been filled randomly. The thick solid lines refer to the reconstructed PSCz fields {\\em proper}, whereas the thin solid lines refer to the randomized versions of those fields,i.e., the fields obtained from the reconstructed density fields by randomizing phases in Fourier space subject to the reality constraint $\\delta_{{\\bf k}}=\\delta_{-{\\bf k}}^{\\ast}$ and keeping the same power spectrum. The dotted and dashed lines are the best fitting random-phase curves to both the reconstructed PSCz density fields and their randomized versions.\n\nIt is striking to notice the proximity between genus curves, even at small smoothing lengths. The statistical errors drawn from the N-body simulation are not shown in Fig. \\ref{PSCzgenus} because of the high degree of correlation between the points in the genus curves.\n\nIndependently of whether the mask has been randomly filled or cloned, the recovered genus curves seem consistent with random-phase Gaussian fluctuations because the amplitude drops appear small. However, the amplitude themselves seem to depend on the mask filling technique.\n\n\nIn Fig. \\ref{psczdrops} we plot the amplitude drops obtained for the reconstructed PSCz density fields, as a function of smoothing length, as well as the error bars drawn from the $\\tau$CDM model following the method outlined in chapter \\ref{recdenmaps}. The amplitude drops of the reconstructed N-body simulations are also shown for comparison.\n\nIn contrast with Fig. \\ref{drpscznow}, where phase correlations were found for PSCz at small smoothing lengths, the reconstructed PSCz fields do not show any significant phase correlations on scales ranging from $5\\lu$ to $14\\lu$. This reinforces the hypothesis that density fluctuation originate from random-phase Gaussian initial conditions. \n \n\n\n\n\n"
},
{
"name": "zeld.tex",
"string": " \n\n\\documentstyle[epsfig]{mn}\n%\n% Preamble\n%\n\n\n\\newcommand{\\iras} {{\\it IRAS \\/}}\n\\newcommand{\\et} {{\\em et al.}}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bea}{\\begin{eqnarray}}\n\\newcommand{\\eea}{\\end{eqnarray}}\n\\newcommand{\\bc}{\\begin{center}}\n\\newcommand{\\ec}{\\end{center}}\n\\newcommand{\\ol}[1]{ {\\overline{#1}}}\n\\newcommand{\\lu}{\\,h^{-1}{\\rm Mpc}}\n\\renewcommand{\\vec}[1]{ {\\bmath #1} } \n\\newcommand{\\dd}{{\\rm d}}\n\\newcommand{\\ls}{\\raisebox{-.8ex}{$\\buildrel{\\textstyle<}\\over\\sim$}}\n\\newcommand{\\props}{\\raisebox{-.8ex}{$\\buildrel{\\textstyle\\propto}\\over\\sim$}}\n\\newcommand{\\gs}{\\raisebox{-.8ex}{$\\buildrel{\\textstyle>}\\over\\sim$}}\n\n\n\\title{Recovering the Topology of the Initial Density Fluctuations Using the {\\em IRAS} Point Source Catalogue Redshift Survey}\n\n\n\\author[A. Canavezes J. Sharpe]{A. Canavezes,$^1$ J. Sharpe,$^2$ \\\\\n$^1$ Centro de Astrof\\'{i}sica da Universidade do Porto, Rua das Estrelas s/n, 4150 Porto, Portugal\\\\\n$^2$ Imperial College of Science Technology and Medicine, Blackett Laboratory, Prince Consort Road, London SW7 2BZ, UK}\n\n\\begin{document}\n\\maketitle\n\n\\begin{abstract}\n\nWe apply the reconstruction technique of Nusser \\& Dekel (1992) to the recently available Point Source Catalogue Redshift Survey (PSCz) in order to subtract the phase correlations that are expected to develop in the mild non-linear regime of gravitational evolution. We study the evolution of isodensity contours defined using an adaptive smoothing algorithm in order to minimize the problems derived from the non-comutivity of operators. We study the genus curves of these isodensity contours and concentrate on the evolution of the amplitude drops, a meta-statistic able to quatify the level of phase-correlation present in the field. In order to test the method and to quatify the level of statistical uncertainty, we apply the method to a set of mock PSCz catalogues derived from the N-body simulations of two 'standard' CDM models, kindly granted to us by the Virgo consortium. We find the method to be reliable in recovering the right amplitude drops. When applied to PSCz the level of phase correlations observed is very low on all scales ranging from $5\\lu$ to $60\\lu$, providing support to the theory that structure originated from gaussian initial conditions.\n\n\\end{abstract}\n \n\\begin{keywords}\ngalaxies:clusters:general -- cosmology:observations -- cosmology:large-scale-structure of the Universe\n\\end{keywords}\n\n\\section*{INTRODUCTION}\n\n \\input{reconstruction.tex}\n\n\\section*{AKNOWLEDGEMENTS}\n\nWe are grateful to the Virgo consortium (J. Colberg, H. Couchman, G. Efstathiou, C. S. Frenk, A. Jenkins, A. Nelson, J. Peacock, F. Pearce, P. Thomas and S. D. M. White) for provinding simulation data ahead of publication. AC aknowledges the support of FCT (Portugal).\n\n\\bibliography{zeld}\n\n\n \n\\end{document}\n\n\n"
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[
{
"name": "zeld.bbl",
"string": "\\begin{thebibliography}{}\n\n\n\n\n\n\\bibitem[\\protect\\citename{Canavezes et al. }1998]{Ca98}\nCanavezes A., Springel V., Oliver S. J., Rowan-Robinson M., Keeble O., White S. D. M., Saunders W., Efstathiou G., Frenk C., McMahon R. G., Maddox S., Sutherland w., Tadros H., 1998, MNRAS, 297, 777\n \n\\bibitem[\\protect\\citename{Colberg et al. }1997]{Col97}\nColberg J.~M., White S.~D.~M., Jenkins A., Pearce F.~R., Frenk C.~S.,\nThomas P.~A., Hutchings R., Couchman H.~M.~P., Peacock J.~A.,\nEfstathiou G.~P., Nelson A.~H., 1997, in Hamilton D., ed, Ringberg Workshop,\nLarge-scale structure in the Universe. Cluver, Dordrecht, in press\n\n\\bibitem[\\protect\\citename{Couchman \\& Pearce }1995]{Cou95}\nCouchman H. M. P., Thomas P. A., Pearce F. R., 1995, ApJ, 452, 797\n\n\\bibitem[\\protect\\citename{Dekel et al. }1993]{De93}\nDekel A., Bertschinger E., Yahil A., Strauss M.~A., Davis M., Huchra\nJ.~P., 1993, ApJ, 412, 1\n\n\\bibitem[\\protect\\citename{Gramann }1993]{Gr93}\nGramann M., 1993, ApJ,405, 449\n\n\n\\bibitem[\\protect\\citename{Jenkins et al. }1997]{Je97}\nJenkins A. R., Frenk C. S., Pearce F. R., Thomas P. A.,\nColberg J. M., White S. D. M., Couchman H. M. P.,\nPeacock J. A., Efstathiou G. P., Nelson A. H., \n1997, ApJ, submitted\n\n\n\\bibitem[\\protect\\citename{Nusser \\& Davies }1994]{Nu94}\nNusser A., Davis M., 1994, ApJ, 421, L1 \n\n\\bibitem[\\protect\\citename{Nusser \\& Dekel }1992]{ND92}\nNusser A.,Dekel A, 1992, ApJ, 391, 443\n\n\\bibitem[\\protect\\citename{Nusser, Dekel \\& Yahil }1995]{Nu95}\nNusser A., Dekel A., Yahil A., 1995, ApJ, 449, 439\n\n\n\\bibitem[\\protect\\citename{Peebles }1980]{Pe80}\nPeebles J., 1980, {\\em Large Scale Struture of the Universe}, Princeton University Press\n\n\n\\bibitem[\\protect\\citename{Saunders et al. }1999]{Sa99}\nSaunders W. et al., 1999, MNRAS, submited, astro-ph/0001117 \n\n\n\\bibitem[\\protect\\citename{Springel \\& White }1998]{Sp98a}\nSpringel V., White S. D. M., 1998, MNRAS, in press\n\n\n\\bibitem[\\protect\\citename{Vogeley et al. }1994]{Vo94}\nVogeley M. S., Park C., Geller M. J., Huchra J.P., Gott J. R., 1994, ApJ, 420, 525\n\n\n\\end{thebibliography}\n"
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