Clusters of Galaxies (Space Telescope Science Institute Symposium Series)

Collected in this volume are the review papers from the Space Telescope Science Institute symposium on Clusters of Galaxies held in May 1989. Fifteen experts in the field have presented summaries of our current understanding of the formation and evolution of clusters and their constituent galaxies. Subjects covered include the existence and importance of subclustering, models of the evolution of clusters and the intracluster medium, the effect of the cluster environment on galaxies, observations of high redshift clusters, and the use of clusters as tracers of large-scale structure. This book provides a timely focus for future observational and theoretical work on clusters of galaxies.

SPACE TELESCOPE SCIENCE INSTITUTE SYMPOSIUM SERIES: 4 Series Editor S. Michael Fall, Space Telescope Science Institute

CLUSTERS OF GALAXIES

SPACE TELESCOPE SCIENCE INSTITUTE

Other titles in the Space Telescope Science Institute Symposium Series 1

Stellar Populations Edited by C.A. Norman, A Renzini and, M. Tosi 1987 0 521 33380 6 2 Quasar Absorption Lines Edited by C. Blades, C.A. Norman and, D.Tumshek 1988 0 521 34561 8 3 The Formation and Evolution of Planetary Systems Edited by H.A. Weaver and L.Danly 1989 36633 X 4 Clusters of Galaxies Edited by W.R. Oegerle, MJ. Fitchett and L.Danly 1990 0 521 38462 1

CLUSTERS OF GALAXIES Proceedings of the Clusters of Galaxies Meeting Baltimore 1989 May 15-17

Edited by WILLIAM R. OEGERLE Space Telescope Science Institute MICHAEL J. FITCHETT Space Telescope Science Institute LAURA DANLY Space Telescope Science Institute

Published for the Space Telescope Science Institute

The right of the University of Cambridge to print and tell alt manner of book} was granted by Henry VIII in 1534. The University hat printed and published continuously since IS84.

CAMBRIDGE UNIVERSITY PRESS Cambridge New York Melbourne

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Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge CB2 1RP 40 West 20th Street, New York, NY 10011, USA 10 Stamford Road, Oakleigh, Melbourne 3166, Australia © Cambridge University Press 1990 First published 1990 Printed in Great Britain at the University Press, Cambridge British Library cataloguing in publication data Library of Congress cataloguing in publication data

ISBN 0 521 38462 1 hardback

CONTENTS Preface Participants

xi xiii

Chapter 1 Cosmology and Cluster Formation P. J. E. PEEBLES The Statistics of Clusters of Galaxies Biasing The Sequence of Creation Did Clusters Form From Gaussian Fluctuations? References Discussion — N. Bahcall, Chair

1 1 4 6 7 8 9

Chapter 2 Clusters of Galaxies: Structure, Infall, and Large-Scale Distribution M. J. GELLER Substructure: Does It Exist? Infall Patterns and Q The Large-Scale Distribution of Clusters (Groups) Conclusion References Discussion — N. Bahcall, Chair

25 25 31 34 36 38 40

Chapter 3 Cosmogony with Clusters of Galaxies A. CAVALIERE, S. COLAFRANCESCO Introduction Morphologies The Search for a Mass Function Local Luminosity Functions X-ray Clusters in Redshift Space Concluding Remarks References Discussion — A. Oemler, Chair

43 43 44 48 51 53 56 57 59

Chapter 4 Cosmogony and the Structure of Rich Clusters of Galaxies M. J. WEST Introduction Cluster Formation in Gravitational Instability Models Cluster Formation in the Explosion Scenario Cluster Formation with Dark Matter

65 65 68 90 95

viii

Contents

Summary References Discussion

—

A. Oemler, Chair

101 102 104

Chapter 5 The Dark Matter Distribution in Clusters M. J. FITCHETT Introduction Motivation Cluster Dynamics X-ray Constraints Substructure and the Mass Distribution Gravitational Lensing Conclusions References Discussion — A. Oemler, Chair

111 111 112 113 117 121 127 130 131 133

Chapter 6 T h e Effect of t h e Cluster Environment on Galaxies B. C. WHITMORE Introduction Possible Mechanisms The Morphology-Density Relation The Size of Galaxies in Clusters The Distribution of Mass for Galaxies in Clusters Summary References Discussion — 0 . Richter, Chair

139 139 140 144 151 156 161 164 167

Chapter 7 Evidence for Gas Deficiency in Cluster Galaxies M. P. HAYNES Introduction HI Deficiency in Clusters Observations of the Virgo Cluster Constraints on the Sweeping Mechanism Induced Star Formation Recent Results for Early Type Galaxies Summary and Conclusions References Discussion — O. Richter, Chair

177 177 179 181 183 187 188 190 192 194

Chapter 8 Properties of Galaxies in Groups and Clusters A. SANDAGE Introduction The Virgo Cluster Survey

201 201 202

Contents Survey of the Fornax Cluster and Loose Groups Field Survey for the Ratio of Dwarfs to Giants Variation of Effective Size and Surface Brightness with Absolute Magnitude for E and dE Galaxies Are There Transfigurations Along the Hubble Sequence? Galaxy Clusters Are Still Young References Discussion — W. Oegerle, Chair

ix 213 213 215 218 219 223 225

Chapter 9 Dynamical Evolution of Clusters of Galaxies D. RICHSTONE Introduction Physical Processes Evolution of Spherical Virialized Clusters Formation and Evolution of Subclusters Summary References Discussion — W. Oegerle, Chair

231 231 232 236 239 248 249 250

Chapter 10 Hot Gas in Clusters of Galaxies W. FORMAN, C. JONES Hot Gas In Galaxies, Groups, and Clusters Importance of Studies of the Hot Intracluster Medium Dynamical Classification of Clusters of Galaxies and the Role of the Central Galaxy The Origin of the Intracluster Medium Future Progress References Discussion — A. Meiksin, Chair

257 257 261 262 269 274 275 277

Chapter 11 Hydrodynamic Simulations of the Intracluster Medium A. E. EVRARD Introduction Theoretical Overview Numerical Details Not Another Coma Cluster The Hydrostatic Isothermal Model and Binding Mass Estimates Characteristics of the Ensemble Estimated Abundance Functions Summary and Discussion References Discussion — A. Meiksin, Chair

287 287 289 290 294 304 307 312 316 320 323

x

Contents

Chapter 12 Evolution of Clusters in the Hierarchical Scenario N. KAISER Introduction Self-Similar Clustering Allowed Range of Spectral Indices Application to Physically Plausible Spectra Optical Clusters X-ray Clusters References Discussion — M. Fall, Chair

327 327 328 330 332 332 333 336 336

Chapter IS Distant Clusters as Cosmological Laboratories J. E. GUNN Introduction Catalogs, Surveys and Outlook for the Future The Evolution of Cluster Galaxies The Implications of the Dynamics of Distant Clusters The Epoch of Galaxy Formation Parting Comments References Discussion — M. Fall, Chair

341 341 342 345 347 349 350 350 351

Chapter 14 Future Key Optical Observations of Galaxy Clusters J. P. HUCHRA Introduction Internal Properties of Clusters Connection to the Environment Clusters and Large-Scale Structure A Prescription for the Abell Blues Summary References Discussion — R. Burg, Chair

359 359 360 362 366 369 370 371 372

Chapter 15 Cluster Research with X-ray Observations R. GIACCONI, R. BURG Introduction X-ray Luminosity Function Interpretation of the Luminosity Function Future Surveys Summary References

377 377 379 384 385 394 394

PREFACE Clusters of galaxies are probably the largest gravitationally bound entities in the universe. They offer a laboratory for studying such diverse astrophysical problems as the form of the initial fluctuation spectrum, the evolution and formation of galaxies, environmental effects on galaxies, and the nature and quantity of dark matter in the universe, as well as providing tracers of the large-scale structure. The view that clusters are dynamically relaxed systems has been challenged by the demonstration of significant substructure in the galaxy and X-ray distribution within clusters (see the chapters herein by Geller, Cavaliere & Colafrancesco, Fitchett, Richstone, and Forman). There is, however, still some dissent on the reality of subclustering (see the discussion in West's chapter). New simulations of the formation and evolution of the dark matter and gas distributions in clusters are giving interesting results—their confrontation with observations may yield information on the nature of the initial density fluctuations required to form galaxies and enable us to solve some of the problems in this field (e.g., the so-called "^-discrepancy"). The simulations should also allow for better comparisons between theory and optical and X-ray observations (see the chapters by Cavaliere & Colafrancesco, Evrard and West). The abundance and velocity dispersions of rich clusters, and measurements of their clustering properties and peculiar motions may provide strong constraints on theories of galaxy formation (see the chapters by Kaiser, Peebles and West). The effect of the environment on galaxies in rich clusters and compact groups (eg. tidal and ram-pressure stripping of galaxy halos and the morphology—density relation) is discussed in the chapters by Whitmore, Haynes and Sandage. The discovery of 'luminous arcs' in several intermediate redshift clusters may lead to a better understanding of the dark matter distribution in clusters (see the chapter by Fitchett). The observations of high-redshift clusters are just beginning to provide clues to the evolution of clusters and their constituent galaxies (see Gunn's chapter). This book is a collection of review papers and discussions from the workshop entitled "Clusters of Galaxies" held at the Space Telescope Science Institute (ST Scl) during May 15-17, 1989. The workshop sought to bring together observers and theorists to discuss the observations, their interpretation, and the models of cluster formation and evolution. The program covered the dynamical state of clusters on the first day of the meeting, observations and theory of the influence of the cluster environment on galaxies during the second day, and the evolution of clusters on the third day. The meeting concluded with reviews of the key optical and X-ray observations that need to be obtained (reviews by Huchra and Giacconi & Burg, respectively). This book will appear in print just as the Hubble Space Telescope and the ROSAT X-ray telescope are launched. Several of the chapters herein discuss what should be investigated by these missions, and some predictions have been made. It would be very interesting indeed to hold this meeting again in five years time, and discuss the new results that we can only speculate on now. Many workers in the field contributed greatly to this meeting, either by the presentation of poster papers or the participation in the discussion sessions. The poster papers were were bound and distributed to workshop participants, and mailed to a number of Astronomy department libraries. One of the hallmarks of the ST Scl workshops is the large amount of time devoted to discussion after each talk. Discussion periods varied greatly in time, but averaged ~ 30 — 40 minutes each. We have painstakingly transcribed the discussions after each talk from audio tape, and they appear here at the end of each chapter. We hope that the discussions capture the true flavor of the

XII

meeting. The success of this workshop and the publication of it's proceedings are due to the efforts of many people at ST Scl. The local organizing committee, who set the scientific program, consisted of Neta Bahcall, Rich Burg, Holland Ford, Riccardo Giacconi, Colin Norman, Brad Whitmore, and the undersigned. The smooth running of the meeting was due to months of preparation by Barb Eller, who arranged for all the accomodations and food for more than 100 visitors, as well as taking care of endless details that we would never have dreamed of. Sarah Stevens-Rayburn and Rod Fansler took care of the finances (they kept us from deficit-spending). We thank the the Facilities department and the ST Scl Science Data Analysts for technical assistance in running the meeting. We thank Dave Paradise for making photographs of the figures. Finally, we thank Dorothy Whitman and Ron Meyers in our Publications department for editorial assistance, and especially Rob Miller for cheerfully and expertly making the numerous changes to the manuscripts to produce these proceedings.

Bill Oegerle Mike Fitchett Laura Danly

PARTICIPANTS Luis Aguilar James Annis Lee Armus John Bahcall Neta Bahcall Stephen Balbus Chantal Balkowski David Batuski Mark Bautz Timothy Beers Suketu Bhavsar Chris Blades Elihu Boldt Kirk Borne Gregory Bothun Richard Bower Richard Burg Jack Burns Chris Burrows Claude Canizares Alphonso Cavaliere Veronique Cayatte Stephane Chariot Dennis Cioffi Ray Cruddace Ruth Daly Laura Danly R. R. De Carvalho Herwig DeJonghe Van Dixon S. G. Djorgovski Megan Donahue Eli Dwek Joanne Eder A. C. Edge Jean Eilek Richard Elston August Evrard Michael Fall James Felten Harry Ferguson Michael Fitchett William Forman Bernard Fort Andrew Fruchter Margaret Geller Daniel Gerbal

Riccardo Giacconi Riccardo Giovanelli Daniel Golombek James Gunn Herbert Gursky Asao Habe Robert Hanisch Bill Harris Martha Haynes J. Patrick Henry Gary J. Hill John Hill Paul Hintzen John Huchra Walter Jaffe Fred Jaquin Robert Jedrzejewski Roman Juszkiewicz Nick Kaiser Neal Katz Stephen Kent Randy Kimball Anne Kinney Michael Kowalski Gerard Kriss Michael Kurtz Ofer Lahav Kenneth Lanzetta Tod Lauer Russel Lavery Ray Lucas Gerard Luppino Elliot Malumuth Eyal Maoz Bruno Marano A. Mazure Thomas McGlynn Brian McNamara Avery Meiksin Yannick Mellier Michael Merrifield Georges Meylan Richard Mushotzky Colin Norman William Oegerle Augustus Oemler R. P. Olowin

Frazer Owen Paolo Padovani James Peebles Vahe Petrosian Marc Postman Massimo Ramella George Rhee Douglas Richstone Otto Richter Rex Rivolo Hermann-Josef Roesser William Romanishin Vera Rubin Eduard Salvadore-Sole Allan Sandage Manuel Sanroma James Schombert Robert Schommer Ethan Schreier Patrick Seitzer William Snyder Noam Soker Mitchell Struble Alex Szalay Ed Smith Eric Smith Gustav Tammann Peter Teague Edgar Thomas Peter Thomas Chris Thompson Scott Tremaine Melville Ulmer C. Megan Urry Jacqueline VanGorkom Tiziana Ventura Duncan Walsh David Weinberg Michael West Raymond White Richard White Brad Whitmore Barbara Williams Michael Wise Gianni Zamorani Stephen Zepf Esther Zirbel

COSMOLOGY AND CLUSTER FORMATION

P. J. E. Peebles Joseph Henry Laboratories Princeton University Jadwin Hall Princeton NJ 08544

Abstract. I discuss some issues that arise in the attempt to understand what rich clusters of galaxies might teach us about cosmology. First, the mean mass per galaxy in a cluster, if applied to all bright galaxies, yields a mean mass density ~ 30 percent of the critical Einstein-de Sitter value. Is this because the mass per galaxy is biased low in clusters, or must we learn to live in a low density universe? Second, what is the sequence of creation? There are theories in which protoclusters form before galaxies, or after, or the two are more or less coeval. Third, can we imagine that clusters formed by gravitational instability out of Gaussian primeval density fluctuations? Or do the observations point to the non-Gaussian perturbations to be expected from cosmic strings, or explosions, or even some variants of inflation? These issues depend on a fourth: do we know the gross physical properties of clusters well enough to use them as constraints on cosmology? I argue that some are too well established to ignore. Their implications for the other issues are not so clear, but one can see signs of progress.

1. THE STATISTICS OF CLUSTERS OF GALAXIES To draw lessons for cosmology, we need not only the physical properties of individual clusters but also an understanding of how typical the numbers are. The issue here is whether the Abell catalog or any other now available is adequate for the purpose. There are known problems in the catalogs: they contain objects with suspiciously low velocity dispersions, and they miss systems whose X-ray properties might be consistent with massive clusters. Recently there has been considerable interest in the possible systematic errors this might introduce in estimates of cluster masses and spatial correlations (Sutherland 1988; Kaiser 1989; Dekel et al. 1989; Frenk et al. 1989). The points are well taken but I think the situation is not disastrous: if we take a balanced view, not attempting to push the data too hard, and taking care to look for supporting evidence from tests of reproducibility, we get some believable and useful measures. The cluster-galaxy cross correlation function, l+^cff(r), is the mean number density

2

P. J. E. Peebles

of galaxies as a function of distance r from a cluster, measured in units of the large-scale mean density. The fact that one finds consistent estimates of £Cg from different cluster distance classes (with reasonable choice of parameters in the luminosity function) is evidence that the typical richness of the cluster sample does not vary substantially with distance. The number of bright galaxies within the Abell radius r 0 = 1.5h~l Mpc (H = lOOh km sec" Mpc ) around a cluster is larger than expected for a homogeneous distribution by the factor

nVa

-4

The original estimate (Seldner and Peebles 1977) is N(< ra)/nVa = 360; the reanalysis by Lilje and Efstathiou (1988), which uses better cluster distances and galaxy luminosity function, is half that. I adopt the mean with twice the weight for the newer value:

(„

The scatter around the mean value of N(< ra) surely is large, even for a given nominal richness class, because richness estimates are compromised by groups and clusters seen in projection. The rms scatter in iV(< r) from cluster to cluster is measured by the cluster-galaxy-galaxy correlation function, £cgg (Fry and Peebles 1980). Estimates of £cgg should be reworked using the better current distance scales and luminosity function; the old result is 6N

((*(
(2)

This is substantial, but still it indicates that we can trust equation (1) to a factor of two for the overdensity of a typical richness class 1 cluster. We can compare equation (2) to the scatter in estimates of the velocity dispersion v for Abell clusters. The average over the estimates of v for the 54 R > 1 clusters in the Struble and Rood (1988) compilation is v2 = (950 km sec" 1 ) 2 ^ ± 0.68) .

(3)

The last factor is the fractional rms scatter in the estimates of u2 among the 54 clusters. The scatter surely has been inflated by the cosmological redshift differences of objects accidently close in projection (and perhaps suppressed by over-enthusiastic pruning of the tails of the velocity distribution). However, the coincidence of the fractional scatter in v and the bound for N (eq. [2]) is consistent with the assumption that the scatter in velocity dispersions is dominated by the scatter in masses of the clusters rather than measuring errors. Arguing for the same conclusion is the fact that most clusters are X-ray sources, and that where the X-ray gas temperature is known it is about what would be expected if the plasma and galaxies had the same temperature. For example, in Mushotzky's (1983) sample, clusters with X-ray temperature ~ 10 keV have galaxy line of sight velocity dispersions in the range 900 ± 300 km sec , compared to the expected value 800 km sec" 1 for equal temperatures. Part of the scatter surely comes from temperature differences between plasma and galaxies and from variations of temperature with position, but the key point for our purpose is that there is not a lot of room for spurious estimates of the typical cluster velocity dispersion.

Cosmology and Cluster Formation

S

As a final check, let us estimate the cosmological mean mass density from these numbers. Since the velocity dispersion in a cluster tends to drop with increasing distance from the center, and equation (3) surely has been somewhat inflated by random errors in the measurements of v, a reasonable estimate of the rms line of sight velocity dispersion at the Abell radius is 750 km sec . In the isothermal gas sphere model, this makes the mass within the Abell radius Md{< ra) = 2v*ra/G = 4 x lO 14 /*" 1 M 0 .

(4)

If galaxies traced the large-scale mass distribution, then the contrast in galaxy counts in equation (1) would be the same as the mass contrast:

ra) ^ M(< ra) nVa

pVa

"

With equation (4) this fixes the mean mass density, p, which translates to the cosmological density parameter ft ~ 0.4 . (5) The more direct way to get at this number is to find masses and luminosities of individual clusters. For example, Hughes (1989) finds for the Coma Cluster a mass to light ratio ~ 300A solar units. This multiplied by the mean luminosity density gives ft ~ 0.3, a commonly encountered number from this method. Very similar numbers follow from masses derived from luminous arcs (Grossman and Narayan 1989, Hammer and Rigault 1989). The value of this effective ft thus is secure, and the consistency with equation (5) is a positive check of equations (1) and (4). There are three notable results from these observations. First, there is a hard upper cutoff in cluster masses, as evidenced by the fact that the Struble-Rood (1987) catalog lists just one cluster with estimated v ~ three times the mean in equation (3). That is, Nature is adept at placing the mass in equation (4) into a radius of 1.5A Mpc, but quite reluctant to place three times that amount in the same volume. (The analogous effect for galaxies is the upper cutoff in circular velocity at r ~ 10 kpc at about twice that of our galaxy.) This cluster mass cutoff might be expected in theories for cluster formation out of Gaussian primeval density fluctuations, because the upper envelope of Gaussian fluctuations is tightly bounded. In cosmic string theories the effect is more problematic, because clusters are supposed to be seeded by loops that have a broad range of masses. However, Zurek (1988) argues that with suitable parameter choices the predicted spread in cluster masses may agree with the observations. Second, the mass Mj in equation (4) is at the upper end of the range of masses Mx of the X-ray producing gas (Jones and Foreman 1984). The fact that Mx typically is less than Mj illustrates the familiar point that clusters generally are dominated by dark mass. It will be interesting to see whether there are clusters in which the dynamical mass within the Abell radius may be accounted for by the mass needed to produce the X-rays. If so, then theories that assume the universe is dominated by weakly interacting matter initially well mixed with the baryons would a require considerable settling of the plasma, an effect that might be testable by the methods described at these Proceedings by Evrard. Third, as we have noted in equation (5), if the mean mass per galaxy in clusters applied to all galaxies, the mean mass density would be less than the simple (and currently fashionable) Einstein-de Sitter cosmology with negligibly small space curvature and cosmological constant. The possible relation to galaxy formation theories is discussed in Section II below.

4

P. J. E. Peebles

Galaxy formation theories also are tested by the spatial clustering of clusters, as measured by the usual N-point correlation functions. As for any other statistic, the way to decide whether the cluster-cluster two-point function, £Cc, is reliably detected is to test for reproducibility of results from independent samples and from different ways of analyzing the same sample. The hope is that these different approaches are differently affected by systematic errors, so errors would be revealed as significant discrepancies in the statistic. Thus Mike Hauser and I decided that we had a believable detection of clustering because we found that the two-point angular function, wcc(0), in the Abell (1958) catalog scales with distance about as expected for a spatially homogeneous random process. Bahcall and Soneira (1983) introduced the use of the standard fitting form for the two-point function: (6) tcc(r) = (r cc /r)T 7 ~ 1.8 . The angular two-point function gives hrcc ~ 28 ± 7 Mpc (Hauser and Peebles 1973). Bahcall's (1988) estimate, based mainly on redshift samples, is 23±3 Mpc. The angular and redshift correlation functions use the same catalog but in different ways, that one might have expected would be differently affected by spurious clustering introduced in the discovery of the clusters. The rough consistency of these estimates of rcc thus argues for the reality of the clustering. The same comments apply to the deeper redshift sample of Postman (1989), which gives I9I4, and the X-ray selected sample of Lahav et al. (1989), which gives 19 ± 4 Mpc. The mean of these four estimates is r c c = 2 2 ± 4 / T 1 Mpc,

(7)

where I have taken the precaution of doubling the formal standard deviation of the mean. Dekel et al. (1989) argue that the clustering of Abell clusters may be an artifact of projection contamination. The case for contamination at some level is persuasive, but of course their model for the effect need not usefully approximate the way people actually discover clusters. My conclusion from the reproducibility of rcc is that projection effects are a second order correction, that there is a strong case for the reality of clustering at the level of equation (7). With the Hubble constant H = 50 km see" Mpc favoured by the biased cold dark matter theory (Frenk et al. 1989), the mass autocorrelation function vanishes at r ~ 70 Mpc, about 50 percent larger than rcc. Thus the cold dark matter theory does not directly contradict equation (7), but in some estimates the margin is uncomfortably close (Blumenthal, Dekel and Primack 1988).

2. BIASING As discussed above, the mean mass per galaxy in a great cluster is about 30% of the global mean for the Einstein-de Sitter model. This difference might be telling us something about cosmology, or about the formation and evolution of clusters. Two commonly cited processes after cluster assembly may change the mean mass per galaxy. Gas loss by stripping would lower the luminosities of cluster members and so increase the value of the mass per galaxy brighter than some fixed cutoff. This goes the wrong way if we want an Einstein-de Sitter universe. West and Richstone (1988) note that dynamical relaxation would tend to raise the galaxy concentration in the cluster center, and so lower the mean mass per galaxy, which is in the wanted direction. The traditional problem with this is that the same effect might have been expected to have

Cosmology and Cluster Formation

5

segregated giant galaxies from dwarfs, and to have driven the intracluster plasma out of the center of the cluster. Neither effect could be considered to be manifestly present in clusters: the plasma mass in some clusters is larger than the mass in the bright parts of galaxies, and, as discussed in these Proceedings by Sandage and by Haynes, clusters contain a high relative abundance of apparently low mass galaxies. Thus my impression of the evidence is that the low mass per galaxy in clusters probably was present at creation, as bias in galaxy formation, or because the mean density of the universe is low. In massive cosmic string theories, a cluster forms by gravitational accretion around a large cosmic string loop (Turok 1985). Since the large loops would come from a generation well removed from the progenitors of galaxies, it would be reasonable to expect that the positions of the large loops are not strongly correlated with the positions of galaxies. It would follow that the large loop on average collects a fair sample of mass and galaxies. Thus the low value of equation (5), if primeval, is a serious problem for massive cosmic string pictures with density parameter fi = 1. One way out is to suppose that some component of the dark mass has pressure high enough to resist accretion by the cluster; decaying dark matter is a possibility (e.g., Suto, Kodama and Sato 1987). In cosmic string theories with hot dark matter (neutrinos with mass of a few tens of electron volts, as discussed e.g., by Brandenberger, Perivolaropoulos and Stebbins 1989), galaxies would be assembled at low redshifts, and the biasing mechanism to be discussed next might be relevant. There has not yet been much discussion of the possibility of applying the cosmic string picture in a low density world model. In the biased galaxy formation picture, one argues that galaxies may have formed at higher than average efficiency in the generally overdense region of a protocluster (Frenk et al. 1989 and references therein), thus lowering the mean mass per cluster member. It may be possible to test this, because in a dense universe a massive cluster once formed continues to grow by gravitational accretion, as we see in virgocentric flow. In an Einstein-de Sitter universe, this accretion doubles the mass of a cluster from redshift z = 1 to the present. If the mass per galaxy were biased low within the cluster at formation, then it would be reasonable to expect that the cluster subsequently grew by accretion of material with a higher mass per galaxy. (This is required in the global average; it might be expected to apply to the galaxies in the immediate neighbourhood of a cluster because they would have formed at lower density and hence at lower efficiency than in the central parts of the cluster.) Since the material accreted at low redshifts would tend to be found in the outer parts of the cluster, the biasing picture would predict that the mass per galaxy increases with increasing distance from the cluster center. Measurements of cluster masses have greatly improved with the addition of Xray observations ( as discussed by Forman at this conference) and the observations of gravitationally lensed images (Grossman and Narayan 1989, Hammer and Rigaut 1989), but tests of the predicted radial variation of the ratio p(r)/n(r) of mass density to galaxy number density unfortunately still are limited by the relatively small range of radii of the observations. One could design a measurement of the ensemble average values of p(r) and n(r) as functions of radius r, using the equilibrium condition familiar from stellar dynamics, GM(< r)n _ d 2 + ? ! i / 2 _ 2 x /«v ( drUVr r ^ r V±) ' ' r2 where uj.(r) and Uj_(r) are the mean square values of the radial and one dimensional transverse galaxy velocities as functions of distance r from the cluster center, and

6

P. J. E. Peebles

n(r) is proportional to the cluster-galaxy cross correlation function (Cg(r) discussed above. It will be noted that individual clusters are not assumed to have any particular symmetry; equation (8) applies to the ensemble average under the assumption that the mean density is constant over a dynamical time. There is the usual problem that the velocity anisotropy is unknown. If vj^ were small, the mass would be smaller than is indicated by the isotropic case in equation (4), which means equation (4) would overestimate the mass per galaxy. The bias in the other direction is relatively small, saturating at circular orbits. That is, a low apparent mass per galaxy in the outer parts of clusters would be a significant and exceedingly interesting challenge for biasing. To apply equation (8), one would need a fair sample of galaxy redshifts around a fair sample of clusters. The practical problem is that a substantial fraction of the redshift measurements at large projected distances from a cluster center would be 'wasted' on background and foreground galaxies.

3. T H E S E Q U E N C E O F C R E A T I O N How did clusters form? Part of the answer was mentioned above: if the conventional understanding of gravity physics is correct, we know that clusters, being massive and not isolated from the field, are growing by the gravitational accretion of surrounding material. But the central parts could form in some other way. In pancake theories (Shandarin and Zel'dovich 1989), such as those involving massive neutrinos or baryoris with primeval adiabatic mass density fluctuations, the coherence length of the primeval mass distribution is large. This means the first generation would be protoclusters that fragment to form galaxies. The problem for this picture is field galaxies such as those in the Local Group (Peebles 1984a). It is difficult to imagine that these galaxies ever were part of a cluster. The local relative galaxy velocity dispersion is less than ~ 100 km sec" 1 , and the local mean flow is directed more or less toward the nearest cluster, a situation difficult to imagine if we were ejected from the cluster. Could the local galaxies have been produced in an unusually low mass protocluster or pancake? Arguing against this is the indication, from the small local relative velocities, that the Local Group is only now collapsing for the first time. That is, the direct evidence is that the Local Group is considerably younger than our galaxy. It is also worth noting that galaxy masses (measured within a fixed radius, m ~ t^r/Cr, where vc is the circular velocity in the disc, or the equivalent for ellipticals) and mass to infrared luminosities are quite similar in cluster members and the field. This suggests field and cluster galaxies formed under rather similar conditions, before clusters formed. If there were a sensible way to circumvent these simple points it would be good to know about it. Meanwhile, let us turn to hierarchical scenarios, where clusters form after the bulk of galaxy masses are assembled. In the biased cold dark matter theory, the numerical solutions of Frenk et al. (1989) indicate that clusters formed soon after the assembly of the galaxies they contain. This has the great advantage that it is easy to think of ways of producing the systematic difference between the early type galaxies that tend to appear in clusters and the late types that prefer the field. At the same time, the model is tested by the predicted differences between cluster and field galaxies. In particular, White et al. (1987) conclude that in the biased cold dark matter theory galaxies with larger circular velocities prefer denser regions. This certainly is not true in our immediate neighborhood, within distances ~ 400 km sec , where, as Tully (1989) emphasises, it is striking to see how strongly giant and dwarf galaxies alike avoid the local voids. White, Tully and Davis

Cosmology and Cluster Formation

7

(1988) find evidence for a segregation of galaxies with large and small vc by local density in deeper samples of Tully's Nearby Galaxy Catalog. It will be interesting to follow the discussion of tests of this effect in clusters: is the prediction consistent with the high abundance of dwarf cluster members discussed by Haynes and Sandage? In theories such as primeval baryon isocurvature (Peebles 1987) and massive cosmic strings (Turok 1985) protogalaxies form well before clusters, so one must find a way to develop the different abundance ratios of ellipticals to lenticulars in clusters and the field out of environmental effects. The one idea I know for how this might happen builds on the argument that discs have to be relatively late additions to galaxies even if the spheroids were assembled early: discs require a large collapse factor to spin up the material, which argues for late formation, and the fact that discs are fragile suggests that any that did manage to form early would tend to be destroyed by the high rate of accretion of debris onto galaxies at early epochs. If discs were added late, then it is easy to imagine that the character (or existence) of the disc would depend on the environment the galaxy finds itself in at low redshifts, for that determines the amount and state of the material available for accretion.

4. DID CLUSTERS FORM FROM GAUSSIAN FLUCTUATIONS? Since clusters are held together by gravity, the final step in the creation of a cluster must be controlled by gravity. In gravitational instability pictures, it usually is assumed that clusters grew by gravity out of primeval mass fluctuations that approximated a homogeneous and isotropic random Gaussian process. This Gaussian assumption certainly is one of the first cases to try because it is simple, and it follows in the simplest inflation models where homogeneity is perturbed by quantum fluctuations of an almost free field, which would be a Gaussian process. But people have devised schemes for producing non-Gaussian mass fluctuations out of inflation (Ortolan, Lucchin and Matarrese 1988; Peebles 1989); and it is of course possible that structure is not to be understood within the inflation scenario. In particular, the cosmic string (Turok 1985) and explosion (Weinberg, Ostriker, and Dekel 1989) pictures produce distinctly nonGaussian seeds. Thus it would be very helpful to know whether or not the large-scale structure of the universe is consistent with gravitational growth from Gaussian initial mass density fluctuations (Peebles 1984b). Let us consider the typical mass within the Abell radius in a rich cluster of galaxies. The answer to our question, whether this mass could have grown out of Gaussian initial fluctuations, depends on parameters that are not yet sufficiently well constrained, but still it is interesting to explore what would be needed. By the conventional estimates reviewed below, clusters could have grown out of Gaussian fluctuations if (1) the mass within the Abell radius were assembled at low redshifts, zt ~ 0.5, (2) the universe were Einstein-de Sitter, and (3) the present large-scale fluctuations in mass are down from the fluctuations in galaxy counts by the factor favored by Kaiser (1988): 6M 16N

. "B-tTf

6 1 6

~ ' -

(9

»

Each of these assumptions is under some challenge, which makes for an interesting situation. The standard way to analyze the development of rare mass concentrations by gravitational instability is described and applied by Kaiser and Davis (1985) and Efstathiou and Rees (1988). One considers the mass distribution in the early universe, when density fluctuations were supposed to be small, and one estimates the ratio v of the mass

8

P. J. E. Peebles

fluctuation needed to produce a prominent object such as a cluster to the rms fluctuation in mass on the same scale. If v is larger than 5 or so, then under the Gaussian assumption these prominent objects ought to be vanishingly rare, while they of course could be common under other distributions. The estimate of the ratio v is v = a ( l + zf)/a0

,

a > 1.5 .

(10)

Here zj is the redshift at which the mass observed within some fixed part of the cluster first became concentrated to a density large compared to the background. The observed mass defines a comoving volume in the early universe; cr0 is the rms fractional fluctuation in mass within this volume extrapolated to the present according to linear perturbation theory, a oc (1 + z) in an Einstein-de Sitter universe. The bound on the constant a is from the discussion of Peebles, Daly and Juszkiewicz (1989). Now let us estimate the quantities in equation (10). The mean mass of an Abell cluster within the Abell radius is given by equation (4). The comoving radius of a sphere that contains this mass in an Einstein de Sitter universe is ra = 7/T 1 Mpc .

(11)

The present mean square fluctuation in galaxy counts within a sphere of this radius is

This uses the power law form for the galaxy two-point correlation function, £gg = ( r o / r ) 1 7 7 , with ro = 5Ah~l Mpc. If we convert 8N/N to 6M/M using equation (9), with b = 1.6, we get o~o ~ 0.7. A lower bound zj > 0.5 for assembly of the mass seems safe, because at that redshift ~ 70 percent of the cluster members have the spectra characteristic of quiescent present day E and SO galaxies (Dressier and Gunn 1988), suggesting they already were in place in a dense environment. This gives v ~ 3.2, which is a reasonable number for rare peaks. However, if astronomical evidence forced zt up to 1.5, say, or b to the value b ~ 2.5 favored by some, it would be a serious problem for the Gaussian picture and an interesting clue to cluster formation. This research was supported in part by the National Science Foundation.

REFERENCES Abell, G. 0 . 1958, Ap. J. SuppL, 3, 211. Bahcall, N. A. 1988, Annual Reviews of Astronomy and Astrophysics, 26, 631. Bahcall, N. A. and Soneira, R. M. 1983, Ap. J., 270, 20. Blumenthal, G. R., Dekel, A. and Primack, J. R. 1988, Ap. J., 326, 539. Brandenberger, R. H., Perivolaropoulos, L. and Stebbins, A. 1989, Brown University, preprint PUB-701. Dekel, A., Blumenthal, G. R., Primack, J. R. and Oliver, S. 1988, Ap. J., 338, L5. Dressier, A. and Gunn, J. E. 1988, in Large-Scale Structures of the Universe, eds J. Audouze et al. (Dordrecht: Kluwer). Efstathiou, G. and Rees, M. 1988, M.N.R.A.S., 230, 5P.

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Prenk, C. S., White, S. D. M., Efstathiou, G. and Davis, M. 1989, preprint. Fry, J. N. and Peebles, P. J. E. 1980, Ap. J., 238, 785. Grossman, S. A. and Narayan, R. 1989, Seward observatory preprint 865. Hammer, F. and Rigaut, F. 1989, Astron and Astrophys., in press. Hauser, M. G. and Peebles, P. J. E. 1973, Ap. J., 185, 757. Hughes, J. P. 1989, Ap. J., 337, 21. Jones, C. and Foreman, W. 1984, Ap. J., 276, 38. Kaiser, N. 1988, M.N.R.A.S., 231, 149. Kaiser, N. 1989, in Large-Scale Motions in the Universe, eds. V. C. Rubin and G. V. Coyne (Princeton: Princeton University Press). Kaiser, N. and Davis, M. 1985, Ap. J., 297, 365. Lahav, 0., Edge, A. C , Fabian, A. C. and Putney, A. 1989, preprint. Lilje, P. B. and Efstathiou, G. 1988, M.N.R.A.S., 231, 635. Mushotzky, R. F. 1983, Physica Scripta, T7, 157. Ortolan, A., Lucchin, F. and Matarrese, S. 1988, Phys. Rev., 37. Peebles, P. J. E. 1984a, in Clusters and Groups of Galaxies eds. F. Mardirossian et al. (Dordrecht: Reidel), p. 495. Peebles, P. J. E. 1984b, Ap. J., 274, 1. Peebles, P. J. E. 1987, Nature, 327, 210. Peebles, P. J. E. 1989, in Large Scale Structure and Motions in the Universe, eds. M. Mezzetti et al. (Dordrecht: Kluwer), p. 119. Peebles, P. J. E., Daly, R. A. and Juszkiewicz, R. 1989, Ap. J., in press. Postman, M. 1989, private communication. Seldner, M. and Peebles, P. J. E. 1977, Ap. J., 215, 703. Shandarin, S. F. and Zel'dovich, Ya. B. 1989, Rev. Mod. Phys., 61, 185. Struble, M. F. and Rood, H. J. 1987, Ap. J. Suppl., 63, 543. Sutherland, W. 1988, M.N.R.A.S., 234, 159. Suto, Y., Kodama, H. and Sato, K. 1987, in Dark Matter in the Universe, eds. J. Kormendy and G. Knapp (Reidel: Dordrecht) p. 497. Tully, R. B. 1989, private communication. Turok, N. 1985, Phys. Rev. Lett, 42, 407. Weinberg, D.H., Ostriker, J.P. and Dekel, A., 1989, Ap. J., 336, 9. West, M. J. and Richstone, D. O. 1988, Ap. J., 335, 532. White, S. D. M., Davis, M., Efstathiou, G. and Frenk, C. S. 1987, Nature, 330, 451. White, S. D. M., Tully, R. B. and Davis, M. 1988, Ap. J., 333, L45. Zurek, W. H. 1988, Ap. J., 324, 19.

DISCUSSION John Bahcall: My name is Neta Bahcall. I'd like to ask a question with regard to your first view graph, Jim, where you were discussing the number of galaxies. How would you change your conclusions if there were a class of galaxies either which looked

10

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star-like or if it were true that faint galaxies, if their mass was not a monotonic function of optical luminosity and they were left out of the luminosity function, contained a lot more of the mass. Could either of those be a way out? Peebles: Yes, I think they could. Depending, of course, on how the numbers go for these faint or star-like objects. By the way, I've never heard of this person back there! Here is a statistic. The number of galaxies in the cluster relative to the mean expected is ~ 240. That applies to bright galaxies, giants which are easily detected. What would be the analogous statistic for dwarfs? There are those who would predict that the contrast would be considerably smaller, that the dwarfs are in the field. If that were true, then lowering the contrast raises the apparent density parameter so that the biasing game, of course, becomes considerably less problematic. So, that is an important way out. If dwarf galaxies were a better tracer of mass than giants and if dwarfs were less strongly clustered, then you would raise estimates of density parameter and relieve the problem of bias. OK? John Bahcall: Yes. Sandage: I think that way is not the way out, however; because we know from the field surveys that the dwarfs are concentrated in the regions where there are big galaxies. Several surveys are in progress and have been published to that extent and so, every time you see a void in big galaxies, you see the void in dwarfs. Peebles: You certainly see that in the neighborhood, and I was hoping to elicit that remark from you about other regions. Sandage: It's true every place we've looked. Peebles: Yes. And that is, as I tried to emphasize, a serious problem for some theories of galaxy formation, but not all. Djorgovski: Jim, I do not quite understand your objection to the top-down scenarios in which you claim a problem because galaxies have similar masses in the field and in clusters—somehow, that's hard to understand. First of all, that may not be true, there well might be systematic differences within a factor of two or more. But even so, one can imagine all manner of dissipative or self regulatory processes. Peebles: You make a really good point George. If the physical properties of the galaxy can be internally regulated, then the top-down scenario would be viable. The question is, can you imagine internal regulation determining the mass at which a galaxy ends up. If you can come up with such a mechanism, then I will have to back off from my arguments against top-down. But it doesn't sound so easy to me. A galaxy is an enormously large object and to imagine that such things as explosions can regulate the mass seems to me a little hard to imagine, but then of course one's imagination is limited. Come up with a mechanism, and then I will pull out some bets. Bhavsar: Your value of fi = 0.4 is determined from these regions which really are just a very small fraction, 5%, of the universe. So you are really taking a universal value based on just that, it could even be even much lower, it's definitely a very upper bound.

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Peebles: Well, I don't know. We will see how the West-Richstone mechanism, which we will be hearing about, comes about. If you can imagine that, indeed, relaxation has punched dark matter out of clusters without punching out the dwarfs or the plasma, then you can raise fi. I could be underestimating it and that would be good. A strong operation, of course, in the other direction is that one tends to suppress the luminosity of cluster members relative to the field by losing gas, that would push 0 in the opposite direction. You made another point, that I am discussing only a small minority of galaxies in concentrating on great clusters, and that is true. But of course one applies similar dynamical games to groups and even pairs of galaxies. One of the things that made me feel a little nervous about the prospects of being able to live in a dense universe is the fact that systematically, almost always, one finds that the density parameter is less than unity. That could be because of biases, but it really behooves us to come up with a self consistent mechanism, which I don't think we yet have for biasing. Fitchett: I just wondered if you know within the biased cold dark matter scenario on which physical scale you typically have a very large mass excess compared to luminosity? I am curious as to how far out we have to probe a cluster, to see if biased CDM is OK or not. Peebles: I cannot tell you in specific detail. I don't know whether the biased CDM people have looked at the effect that I was mentioning; namely, the mass as a function of the radius. I was arguing on more general physical grounds, and I would put it in this way. Assume that the universe is Einstein de-Sitter. Then, since a redshift of one, a cluster has grown in mass by a factor of two. Where will we put that extra material? Well we put it on the outskirts where the density is perhaps ten to hundred times the mean; that is, outside the Abell radius. I would look there for the increase of mass with radius. That, of course, is the tough part, but I think not impossible. I hope you will be discussing this, and I am looking forward to hearing about it. Huchra: Don't you have already some indication that the mass is not increasing with radius when you think about infall into superclusters? There is a fair amount of work, at least on the local supercluster that says that the Q that you get from the infall pattern, assuming mass traces light, is the same as what you get from the center of the cluster itself. So, that sort of argues, at least on a fifteen or twenty Mpc scale, that you are not in trouble or that you are, if you like the biased CDM scenario. Peebles: Yes, I agree. But you also start out with the fact that velocity dispersions tend to decrease with increasing distance from the center of the cluster which is in an unpromising direction. Huchra: Yes, but how much do they decrease? That is the question. Peebles: Do we know examples of where the velocity dispersion increases with increasing distance from the center. Beers: Yes. Peebles: Oh, what's its name?

12

P. J. E. Peebles

Beers: Abell 194. Peebles: Thank you. Tremaine: I would have thought there was a fairly natural way to get some mass segregation in clusters in a hierarchical clustering picture. The experience with people doing mergers of two clumps, say two galaxies, has generally been that the stuff which starts off in the centers of the two clumps remains in the center of the merger remnant after the collapse is over. Basically, because it's high density it can survive for a long time. That means that any sort of mass segregation that you can get is largely preserved in the process of going from a galaxy say to a cluster. And we know that there is mass segregation in galaxies because the light is in the middle and the dark halo is around the outside so it is quite natural that, at least to some degree that will persist all the way up to groups and clusters. Peebles: I'm not sure whether you're giving the West-Richstone line. Maybe they will want to comment on this. There is indeed biasing on the scale of individual galaxies. But, if you take a region which contains many galaxies, I am not so sure that the effect would operate outside the scale that contains the mass of one galaxy. There surely is biasing in the sense that the center of a galaxy is dominated by baryonic matter. But we are looking for biasing on the scale of many galaxies. I presume, also, that when you have relaxation of the sort that rearranges material on scales large compared to the distances between galaxies, then you run into the potential problem that the same relaxation that punches out the dark matter might tend to punch out the dwarf companions. Tremaine: I think that's true if the dwarf companions started out distributed like the dark matter. Peebles: That's what I had in mind. Yes. Tremaine: Yes, but what I am suggesting is different from West and Richstone in that it doesn't rely on any sort of mass segregation. Peebles: This sounds more like biased galaxy formation in which you form, before a cluster, a concentration of massive galaxies. Is that the case? Tremaine: Yes. It would require, I think, that you have a well defined hierarchy of things collapsing in a well-defined way. Peebles: Then there might be the hazard of running into the observation that Sandage mentioned that one does see many dwarfs intermingled with the giants in the clusters. Maybe Richstone or West should respond to this one. I have been kind of dumping on them. West: I think that Scott Tremaine was describing initially the mechanism that we find. Just a general comment, I think that the segregation is probably very robust in the sense that if the galaxies start with dark halos around them, then what we can show is that subsequent subclusters merge. We do expect the luminous material to end up

Cosmology and Cluster Formation

13

in the highest density regions. And even if the galaxies do not begin with dark halos, we expect to get pretty much the same effect. This rapid segregation which is able to survive the subsequent generations of collapse, appears to be a very robust effect. Peebles: In your letter to me in response to my vitriolic complaint about this mechanism, you had some well-reasoned arguments why one should not be concerned about the absence of segregation of dwarfs and giants. Maybe you would like to repeat those. West: In terms of mass segregation, it is not clear that we really observe significant mass segregation in most clusters. Doug talked about a heat transfer mechanism whereby it is not clear that just because massive galaxies may become strongly clustered, this would necessarily puff up the intermediate and lighter mass galaxies as well, because there's a heat exchange going on. Peebles: Did that argument work for the plasma? West: That's not clear. I'll have to think about that some more. Unknown: I don't see how that would work with the plasma. Peebles: So, what do you do about the plasma? Richstone: I think the two arguments that you have raised against this model are good arguments. That is, the question of whether you can get the low mass galaxy distribution right and the question of the flow of galaxies at large radii near clusters. John mentioned one particular case of Virgocentric flow. The flip side of the argument, it seems to me, is unless we have made a mistake and so has everybody else whose simulations we have looked at, it is hard to avoid something like this happening, in a bottom-up scenario. Peebles: I wonder if you were willing to lower the mass of the galaxies relative to the dark component you could avoid this happening. Richstone: The most interesting part of the argument is the result that fi is big. If you do that then you are agreeing with us in the final conclusion, although not with the process by which we get to it. Peebles: I'll have to think about that. (Laughter) Bahcall: May be we'll take some questions related directly to the topic so then we can move to some other topic. Fitchett: I just have a comment about this problem of mass segregation. Mike West and I have talked about this. There is a test you can possibly do using luminous arcs. When you calculate the mass interior to a luminous arc and get the mass to light ratio in that region it is typical of the mass to light ratio in the cluster. Now if mass segregation has occurred so that there is a luminous central component and a huge extended halo you would expect a larger mass to light ratio within the luminous arc - the arc probes the mass interior to a tube through the cluster, which includes mass in the outer halo. So, in a sense, the fact that you actually get just the right mass to

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light ratio tells you that there might not be this huge halo around the cluster. Now this requires some calculations. Another problem is that since the clusters observed to have luminous arcs are at high redshift.there may not have been sufficient time for the effect to have occurred - we'd need to look at the simulations. Looking further out in the cluster for distorted galaxies would help. Peebles: Could I ask Michael, what is the maximum impact parameter at which luminous arcs have been detected? Fitchett: This is interesting. Tony Tyson told me that he thinks that distorted galaxies actually cut off forming at about a Mpc. He doesn't see these distorted galaxies. You need a high surface density to form a luminous arc so typical luminous arcs are only ~ 200 kpc from the center of the cluster. So you are only probing a small region, but I don't know what the mass is in the tube under the segregation hypothesis. Peebles: It's a good point. If you can be precise enough about this tube, it might be an important probe of the mass distribution at large radii. Fitchett: Exactly, what we need are density profiles. We need to get together and discuss this. Huchra: This in fact is something that I want to throw in real quick, where ST is going to be able to do some very nice things by looking at the shapes of galaxies as a function of radius in rich clusters. Peebles: Incidentally, it will be able to tell us perhaps whether disks have formed at a redshift of one, which would be nice to know. Huchra: Jim, I have a perverse comment to make, which is you show NGC 6946 and said there were no dwarfs around it. For those of you in the audience who are not observers, NGC6946 is pretty badly buried in the galactic plane. Finding dwarfs around it is non-trivial. Peebles: It is awfully close, John. Even though I'm a theorist I can look at that picture, and I see that galaxy sprawling across the page—the big page. (Laughter) It would be easy to see something a factor of ten less luminous. Sandage: That scale is so small that if you go out three or four galaxy radii, you would have to go out that far to find the dwarfs. And there are dwarfs around it. Peebles: Perhaps there are—but not in the Tully atlas. Sandage: He only has things that he can either measure redshifts for or are brighter than a certain magnitude. Peebles: There are lots of background objects, of course. Sandage: Not at low surface brightness. No. There is a very strong surface brightnessabsolute magnitude morphology relation.

Cosmology and Cluster Formation

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Peebles: So, these are neaxby, at a couple of hundred kilometers per second. We have to be careful because this void is not very big, so there's lots of background stuff, that isn't very far away. Sandage: dwarfs.

You have to go out to around a Mpc around any galaxy to say it has no

Peebles: Well, you don't have to go that far around M31. Sandage: Well, you have to go around that far in the local group. Peebles: We have the Magellanic cloud. Neta Bahcall: On a similar note in the CFA Survey, when you see the little close void right in front of Coma and the CFA Survey now goes much deeper, all of the bright galaxies keep sitting right around that shell and you get no faint galaxies inside that void.

Huchra: Three. Neta Bahcall: Oh you have three now? It is a very high density. Huchra: In fact the three there might just be members of Coma that appear to lie in the void because of the velocity dispersion of Coma. Neta Bahcall: Jim, can I ask a slightly different question on a different topic. In the isocurvature baryonic model one of the nice statements that you always say is that we stick only with "what you see is what you get." Now, if you go to an fi of 0.4 now for the clusters and if you believe, at least in the classic nucleosynthesis, are you out of that nice statement? Do you have to add non baryonic dark matter? Peebles: Yes. I guess I would deviate from the "what you see is what you get" line and argue that I would bet that fl estimated from clusters is biased high because of stripping that has lowered the luminosity of galaxies in clusters relative to the field and so biased upward the mass per galaxy. So I would go with an fl down to around 0.1 to 0.2 in that theory, arguing for a little anti-biasing, so as to speak, in clusters. Weinberg: Regarding the question of where the mass to light mass ratio changes over, Adrian Melott has told me that from his N-body simulations, he finds that in fact the mass to light ratio is basically constant out to a scale of something like 8-10 Mpc, and then suddenly changes. So, the notion, that we would see a slow, continuous change, if he is right, is not necessarily so. Peebles: It certainly is true that if the radius were that large you would be very hard pressed to detect it. Weinberg: On your last view graph, I want to add the possibility that gaussian fluctuations in an open universe would also do fine as well as explosions and cosmic strings. And, do we really know enough about the clusters at a redshift of 0.5 to know that they aren't simply 50% less massive than the ones today, in which case that would

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be sort of exactly what something like cold dark matter would predict. Peebles: I don't know whether cold dark matter would predict that the central parts of these clusters, which are, after all, very dense would be that much less massive at a redshift of a half or whether they would say no, you are pasting on the material on the outskirts. Of course, the direct way to test is measure the velocity dispersion of galaxies either directly or through their X-ray temperature at a redshift of a half. One certainly knows of examples of clusters of that redshift that have high velocity dispersions. I don't think one knows yet what the systematics of galaxy velocity dispersions are at high redshift but it certainly is testable. Postman: Just to respond to that. I know that the 8 or 9 high redshift clusters in the Gunn and Dressier example, where they do have spectroscopy, typically show dispersions of between 900 and, in one case, as high as 3,000 kilometers per second. So, they are certainly comparable with dispersions now. Peebles: Yes. And then the debate becomes, are these the rare exceptions that were discovered because one was looking for something. It has to be. Evrard: Following up on David's point on the point of measuring the mass to light ratio as a function of radius, what you really want to do is to measure the mass at over densities of about ten to hundred. And there you are not going to be able to count on virial or hydrostatic equilibrium. So, your mass estimates are going to be highly model dependent as David pointed out—that means, you've got to do it for various cosmologies and see what the model dependence actually is. The second point is that your assassination of b = 2.5 CDM on the last view graph sounds to me to be a bit premature because we know that using abundance arguments is a very dangerous thing. Abundances are exponentially sensitive to some power of the mass or some power of velocity dispersion or temperature, so slight errors in those quantities can make a large difference in abundance. Peebles: Good points both of them. I am not convinced that we can trust the prediction of spherical collapse models to say that at a density contrast of say ten we are not yet close to virial equilibrium. It's a point that I would like to address more carefully myself. My instincts say I don't trust the spherical model much beyond a density contrast of a few because surely things are going to get highly non-spherical, and once you have gone non-spherical surely you are going to develop transverse motions, and once you have done that I can imagine a rough balance of kinetic and potential energy, so I am a little bit more optimistic than you about applying measures of mass to light ratio at a density contrast of ten to thirty, but of course we will check that by exhaustive N-body simulations. As for my assassination, of course, I meant it, but I also was hoping to stimulate remarks such as yours, which are good. The predictions are exponentially sensitive—you need to know whether this number (i/) is really 3, or 4, or is it 5 or 6. And, as you say, that's a very small change in parameters to yield the dramatic difference in conclusions. So we have to ask, can you really keep this number down. Evrard: Yes but you must remember that number is dependent upon the mass scale at which you are measuring a. So that if you go to high redshift you just reduce the

Cosmology and Cluster Formation

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mass scale a bit. So instead of going up to 5 or 6, you can keep it around 3 or 4. Peebles: Yes, that's right. But then I hope I was being very conservative in the way I applied this. The Abell radius is way up there in density contrast. I only went to a redshift of a half where we see lots of clusters with high velocity dispersions, so am I not being pretty conservative? You see all these clusters at redshift of a half. They look pretty normal. Evrard : The main point being used is that the velocity dispersions or X-ray temperatures are very large at high redshifts, but you can get a high velocity dispersion for a smaller mass. (A loud buzzer goes off) Something's wrong. (Everyone starts laughing) Peebles: OK. Let me come down to this debate. The Fire Alarm. I see it works. Let me come down to your final provocative remark, Gus. You can imagine having a high velocity dispersion at a low mass. That's quite true. Then the question is whether you can now evolve that into a large mass and a low velocity dispersion. Evrard: Well, no. I wouldn't say a large mass and a low velocity dispersion. Peebles: Well, that's the direction you want, isn't it? You want to have the velocity dispersion high and the mass low relative to now. Evrard: Well, I think the velocity dispersions are sufficiently uncertain at high redshifts that we really don't know that we need them higher. We see clusters today with velocity dispersions around 1400 kilometers per second, a few. Peebles: Remember I am using 750 here. Daly: And also there is X-ray data on clusters that look very similar optically and have the same velocity dispersion, and the X-ray profiles are virtually identical. Also, to come back to your abundance arguments, some of these arguments are based on the use of one cluster, at redshift 0.5 and there are probably many thousands. Evrard: Well, the abundance is sensitive to exponential statistics. Juszkiewicz: I would like to comment on that. I things are exponentially sensitive, you can inherently something that looks like a 5 sigma fluctuation and luck. It's a problem of the model. Why can I not use model?

think that despite the fact that talk of the models. So if you see it shouldn't be there, its tough gaussian statistics for a gaussian

Evrard: It's just that a certain amount of error in the measurement of velocity dispersion or temperature can allow a reasonably wide range of v. So you can say 5 a but what you really mean is 3-6
to 10

.

Evrard: Well you only see a few of these objects. It's hard to estimate their true abundance.

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Weinberg: I was reading the abstract to Carlos Frenk's Poster and he says that in his N-body simulations; he finds almost nothing (3-D things) with velocity dispersions of 1200 kilometers per second. But when he tries to observe the simulation in the way one looks for clusters of galaxies and measures velocity dispersions, he finds plenty. And I can't imagine that it's easier to get velocity dispersions right at a redshift of .5 than it is very nearby. Peebles: Can you imagine this bias extending to the X-ray temperatures? Unknown: No, sir. Do we know the X-ray temperatures? Peebles: I tried to emphasize that X-ray temperatures, at least at low redshift, agree remarkably well with velocity dispersions. I think its crazy to argue that the velocity dispersions are out of line, or am I out of line? Daly: And even the X-ray luminosities, if you see things that appear to have large velocity dispersion but really don't, and then you go and look at them in X-ray and you see large X-ray luminosities due to thermal bremsstrahlung, then that's a deep potential well and that argues that the velocity dispersions are real. Giacconi: A certain contempt for the data is useful to theory, but I am wondering now whether we are going too fast here. You have ignored the large dispersion here between X-ray temperatures and the measurement of the mass and visible light. Can you really do that? The second point is that the X-ray luminosity is not related directly and simply to the mass. It has to do with many other things. Peebles: You could be right, but I am not trying to deny that there is missing mass. One knows that one needs dark mass in order to account for dynamics. At least, that's what I hoped to say. But, here is the comparison I am making. Velocity dispersions and measurements of X-ray temperatures have a correlation that I think won't go away and I think this is telling us that you can trust these numbers. Edge: If people would like to turn to page 56, Figure 3 of the poster book (laughter), you will find a similar plot with data from EXOSAT with much smaller dispersion. Peebles: And what is your conclusion? Edge: It is a very tight correlation. N e t a Bahcall: I'd like to mention some recent work by Carlos Frenk. He has used simulations of cold dark matter to see how much projections affect the data. He claims that many of the rich clusters are really not rich but are a result of various projection effects. In addition you have uncertainties or discrepancies in the velocity dispersion. However, there are different ways of estimating the projection effect. What we know from the data when we look at X-ray clusters, for example, which really have nothing to do with projection effects, is that you get various excellent agreements with various optical observations. There is some recent work done by Ofer Lahav and collaborators on using X-ray clusters of galaxies, for example, to determine the cluster correlation

Cosmology and Cluster Formation

19

function on which much recent but wrong work on contamination was done. He shows that there is a very strong agreement between the X-ray observations and the earlier results that Jim summarized here of the optical observations. Again, showing the contaminations cannot really effect either the velocity dispersion or the large structure to a great extent. Maybe Ofer also can mention that a little bit. Giacconi: Let me ask my question again. It is basically this correspondence between the temperature in gas and the temperature of the galaxies that you are basing the fact there is only a small range of ratios between the luminous mass and the virial mass and the dark mass? Peebles: No. My purpose is to get the mass of a cluster within the Abell radius because for many purposes in cosmology what you need is a mass. I wish to derive that mass from a velocity dispersion for galaxies. I wish to check that velocity dispersion against an X-ray temperature just to see whether such problems as those that Neta mentioned which were raised by Carlos Frenk could be operative. Could it be that many clusters are accidental projections of groups? Giacconi: No. I think that statement is correct. On the other hand, to get the mass directly, you must keep in mind that we do find that the scale height, for instance, for X-rays is typically twice that of the galaxies. Right? There's the real problem. Peebles: Is it a problem in estimating the mass, say within the Abell radius? For that I need hydrostatic support. I need to know what temperature, and I need to know the gradient in density. Giacconi: But you know that is wrong, too. You know that those equilibrium models do not represent what's there. They represent 10% of what's there. Peebles: I don't care how much plasma there is there for this argument. What is the giant gravitational acceleration at the Abell radius? That's what I want to know. Let me review the logic. For many clusters we have velocity dispersions that if they're taken at face value give you secure masses. Should you take these velocity dispersions at face value? Well, one argument is that where you can check them against X-ray temperatures, you get not dissimilar results. Unknown: I would be surprised, if that's better than a factor of two given the uncertainties about whether the X-ray gas is isothermal or adiabatic. Peebles: But it is a coincidence that, in fact, if you treat the galaxies as an isothermal that is to say isotropic distribution you get on the average about the same temperature as for the plasma, which surely is isotropic. Unknown: It's not the isotropy, it's the run of temperature. The temperature of the galaxies in many cases is at least dropping at an increasing radius, then you have to take that into account. Daly: It is also interesting that the number count of galaxies within the Abell radius is very tightly correlated with the total X-ray luminosity.

20

P. J. E. Peebles

Peebles: Another good point indicating that it is hard to see why they could have been heavily polluted by accidental projections. Neta Bahcall: Ofer, would you like to say something on your X-ray cluster result? Lah&y.: I can only agree that in relation to largescale structure I believe the X-ray clusters are the right thing to measure because then there is no problem of identification. The X-ray emitting region is very small, about 1 Mpc or so and the physics there is well understood, so it seems to be much easier really to take a selection of X-ray clusters, at least in the future with ROSAT, and then to repeat the calculation of the correlation function. I have made a modest attempt, using existing data from HEAO-1, Einstein and Exosat, where surely there aren't contamination effects and there is less of a problem with absorbtion in the galactic plane. I find it interesting to get such a good agreement with optical determinations of the correlation length. Neta Bahcall: I think that's a very strong answer to various contamination effects, not that there are no contamination effects at all in optical clusters. It is just a question of their influence on the main result. Like Jim mentioned, many other tests have been done before, like the proper scaling of the correlation function with depth, that checked out very well. This cannot happen if you have contamination. The X-ray clusters are a very nice clean way for checking that result because it is such a different method. Giacconi: I would like to follow that up. It is clear that in X-rays, the X-ray luminosity has a range of 100 for a given richness class. Therefore, it is a very poor measurement of mass. Right? Temperature, may relate to mass and since we do find problems, of a factor of at least 2 in scale height for instance, we do not find equal temperatures nor do we find what you might expect from the profile in the measurement of the spectrum. So I think that that you can't use those things to within a factor of 2 or more. Unknown: The fact that the temperatures come out reasonable tells you that the gas is being held by the same gravity that is holding in the galaxies. Peebles: That's what I want. Unknown: But it doesn't tell you that the mass to light ratio of visible matter to better than a factor of 2 to 2-1/2. It doesn't calibrate the scale so that your 0.4 is right. It could still be one or some other number. Neta Bahcall: I think there was a nice result that either Richard or Riccardo might talk about later in the week of using X-ray clusters of galaxies. Again we are looking there at very clean things and we can't argue much about contamination. What you see when you look at different cluster richnesses is quite a different luminosity function. I find this very impressive as it really tells you in that optical clusters of richness 2 are different to those of richness 1 and richness 0. Peebles: That's what we were taught to believe ten years ago. Burg: (showing a plot) These are luminosity functions for the Abell clusters that we did using the Einstein database, and these are all detections and upper-bounds that we found. This work was done with Riccardo and Bill and Christine Forman. You

Cosmology and Cluster Formation

21

can see that within each richness class there is a variance in the X-ray luminosity of roughly a factor of 100 and that the X-ray emission has a total variance of roughly a factor of 1,000. The richness 2 clusters have nearly 7 times the average luminosity of the richness 0 and if you fit these with Schecter functions you can see that when we plot L* versus the average number of galaxies for the richness class that there is a very tight correlation. You can see clearly that the richness 2 clusters are systematically brighter by a very, very large factor. In fact, the dependence is slightly larger than linear. Neta Bahcall: I think that really goes against the claim that Frenk was going to make here that the richness 2 clusters are more likely to be projection effects. Evrard: I would just like to ask the observers how much of the scatter could be coming from the central regions? Burg: (Laughter). 20-30% of the total luminosity of clusters. We chiefly knew where the clusters were, we knew the ratio of the clusters. We used a one Mpc physical radius to measure the X-ray luminosity. In fact, many of the problems that X-ray luminosity functions and X-ray log N-log S functions had in the past are due to use of nonmetric apertures, so most of the problems that you can imagine, for instance, the cooling flows, become much smaller in this treatment. Neta Bahcall: Any more questions? I think those new X-ray results that Richard showed, are really very exciting because they re-iterate some of the problems that we had before, causing us to focus in a different way. Beers: At least in the Einstein database, this concerns me a little bit. Yes, there are some advantages of using the X-ray information. But certainly for high redshift clusters, you have fewer X-ray photons than you have detectable galaxies. Neta Bahcall: I think that this cluster sample doesn't go to very high redshift. They are mostly nearby clusters, and I think that the situation is not that bad there. You see the problem with the optical galaxies, especially when you go to poor clusters is that it's quantized and then you have background corrections and so on. You don't have much of those problems in the X-rays, and I assume that the signal to noise is still much higher than you have in the galaxy counts. Unknown: The question is if we are taking a very large radii for clusters which are not very far away, can you get the total fluxes very well, given the background problems? Giacconi: Yes, our method is very simple. We don't integrate until the signal to noise is nice. We integrate to a fixed physical radius. At most what happens is that you don't have a detection, you have an upper limit. But you do it properly. So, it doesn't matter. Burg: This is an imaging detector we are using so the background is taken from the adjacent areas. This is done with the Einstein IPC. Djorgovski: Can we switch back to the topic of Jim's talk? (Laughter). One of the deadliest classes of observations for simple cold dark matter and biasing is the observation that dwarfs do not fill the voids. They follow the large scale structure. Is

22

P. J. E. Peebles

there any way to wiggle out of that or is that a really crucial observation? Peebles: Of course, I wish I knew, and I can't answer you because I haven't looked at all possible models. Huchra: You have to ask a theorist who likes cold dark matter. Peebles: And I'm sure you will find it's alright (laughter). That is uncalled for and I withdraw it! Under the biasing picture, surely you would expect that the galaxy that forms in a low density region has a stigma attached to it. There's the challenge—find the stigma. Djorgovski: If I make those significantly fainter they all drop out of the optical catalog and all of the Redshift surveys are based on optical catalogs. I may have to discontinuously change the luminosity functions, but I don't know that I have to change it by more than a magnitude or so. Peebles: I showed you this map of a nearby galaxy catalog. For that very reason, you have to go much more than a magnitude. Bothun: I think I can clarify this about dwarfs and voids. Laughter. You have a point because a proper test hasn't been done yet, as dwarfs are extremely hard to find— they're of extremely low surface brightness; you cannot get a velocity of them unless they have HI. A test for voids as a function of surface brightness has been carried out, one finds that the low surface brightness galaxies do not fill the void. However, that is not a collection of dwarf galaxies. The only test for dwarf galaxies was carried out in one part of the sky was done by Gus Oemler and collaborators, and they found that in fact that dwarfs do not fill the void. But this is only an isolated instance in an isolated part of the sky. A proper test has not been done yet, and a proper test would be extremely difficult because most of the dwarfs that you really want to see require you to Malin-ize plates or to look very hard. You can't get redshifts by guilt by association. So I think it's a mistake to say that this test has been done yet. Peebles: That's a fair remark. As you emphasize we have selected places where one has examined the dwarfs and one hasn't, yet, examined all possibilities. Sandage: I would like to take the opposite tack! (laughter) We did a strip survey which crosses the supergalactic plane and we've also gone up to 45 degrees which crosses the Ursa Major cloud, and these are very nearby regions and what we are looking for are dwarf ellipticals where you surely can tell what the absolute magnitude is from the surface brightness absolute magnitude relation. Now that is somewhat controversial, but I'll talk about that tomorrow why there should be no controversy. And from that surface brightness test of the distance, we don't find any dwarfs except in conjunction with the bright standard galaxies. So I think the test has been made, and I don't think you have to have redshifts in order to show that. Bothun: I'm not going to dispute that, but that's inside a local supercluster. You just take the Southern Sky Region Survey and Northern Sky Region Survey and look at all these small scale voids between 3,000 and 5,000 kilometers a second—that's where you want to make this test. That hasn't been done yet. I agree with you. In the local

Cosmology and Cluster Formation

23

supercluster, there's a high degree of association, of dwarfs, with luminous galaxies, independent of what the larger scale 6p/p is. But in voids in redshift surveys that are beyond 3,000 kilometers a second, I don't see that this test has been done yet. Peebles: You're asking now about the southern sky where there are no rich clusters, you will see segregation. Bothun: The only thing that I am saying is that you can pick out voids very easily in redshift surveys. Then you may want to ask the following question—Can I find dwarf galaxies that fill those voids? Peebles: The question has been addressed in some cases. Bothun: My point is that can't be done yet in any great detail other than in the local supercluster. It can be done as a function of surface brightness, but you are talking about things that have distance moduli such that dwarf galaxies are incredibly faint and have apparent magnitude of 18 or 19. Neta Bahcall: You have some work on that now in the Bootes void. What are you finding? Bothun: Those aren't dwarfs. The Bootes void is at a redshift of 0.05. Again, you can't do that with dwarfs. You have a whole redshift survey of 750 objects detected by the IRAS faint source Survey in the Bootes void. Neta Bahcall: And those are what, low surface brightness galaxies? Bothun: They're just low luminosity galaxies. They aren't dwarfs. You can't find dwarfs beyond 3,000 kilometers per second very easily. Peebles: And then, I guess, the question becomes how many voids do you have to sample before you are convinced of the absence of segregation of giants from dwarfs. Bothun: Well, more than one, I would think. (Laughter). Peebles: Have we sampled more than one? We discussed the local Virgo cluster and its surroundings. We have discussed our immediate neighborhood, and we have discussed the fact that when the deep CFA survey was done to 15.5, the nearby galaxies fell along the surfaces outlined by the bright 14.5 redshift survey. Non negligible evidence, I would say. Bothun: done yet.

I'm not saying they are in the voids, I'm only saying the test hasn't been

Peebles: I'm saying that the evidence for absence of segregation is not negligible. Is that fair? Bothun: Yes.

CLUSTERS OF GALAXIES: STRUCTURE, INFALL, AND LARGE-SCALE DISTRIBUTION

Margaret J. Geller Center for Astrophysics 60 Garden St. Cambridge, MA 02138

Abstract. Clusters of galaxies are interesting both as individual dynamical "units" and as tracers of large-scale structure. Although we have made progress in understanding both issues, many profoundly nagging questions remain. Here I review three aspects of cluster research where I think further investigation might yield some answers. In Section 1, I discuss the controversial issue of substructure and its importance in individual systems. Section 2 is a discussion of the infall region. Study of these regions might yield a cosmological test. Section 3 is a discussion of the problems and the promise of clusters as tracers of large-scale structure. Section 4 contains some suggestions for further investigation.

1. SUBSTRUCTURE: DOES IT EXIST? Some clusters are regular, apparently relaxed, nearly spherically symmetric systems which can be characterized by a few global parameters. The azimuthally averaged surface density profiles for these systems vary approximately as /i(r) = /xo[l + (r/re) 2 ]" 1 .

(1)

Rood et al. (1972) first made explicit use of this model for an analysis of data for the Coma cluster. The corresponding space density is p(r) = po[l + ( r / r c ) 2 ] " 3 / 2

(2)

where r c is the core radius of the cluster and fi0 = 2rcpo. If a is the line-of-sight velocity dispersion, and p0 is the central density, 4*Gporc2 = 9(72.

(3)

A fit of Equation (1) and a measurement of the central line-of-sight velocity dispersion thus yield a central mass density under the assumption that the galaxies in the cluster trace the matter distribution. Another model frequently fitted to cluster surface density distributions is the de Vaucouleurs law (1948) |i(r) = fioexpi-imir/re)1/4).

(4)

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M. J. Geller

usually used to describe the surface brightness profiles of elliptical galaxies. This profile has a central cusp. Nearly every aspect of the application of Equation (1) or (4) to the data has been subject to scrutiny and debate. One current issue is the existence of the flat core indicative of dynamical relaxation. Tonry (1985) emphasizes that continuing infall or a large number of galaxies on radial orbits produces a cusp in the surface density distribution. In fact, Beers and Tonry (1986) argue that the surface density profiles in the cores of many rich clusters (r ;S 0.25A"1 Mpc; the Hubble constant H = lOOh km s - 1 Mpc throughout) are well approximated by an r power law (or, equivalently, by a de Vaucouleurs law with re ~ 3A Mpc). The apparently flat cores could be artifacts introduced by misidentification of the cluster center. It is difficult to resolve this issue with data currently available because the number of galaxies in the core is generally not large enough for clear discrimination among the models. However, the argument for cusps is consistent with the idea that many of the multiple nuclei of cDs are actually cluster members on radial orbits. A recent analysis (Merrifield and Kent 1990) of deep CCD images of 29 clusters, each containing a cD, supports the existence of a central cusp in these systems. In spite of the subtleties of fitting and interpreting surface density profiles for rich clusters, the values of the physical parameters in Equation (3) give a zero-order feeling for the properties of these systems. From his maps of 12 rich clusters, Dressier (1978) derived a mean core radius of 0.25/i Mpc. (Note that two of the clusters in this sample (A2029 and A154) have central cusps.) A more recent analysis (Colless 1987) of maps of 14 more rich clusters yields essentially the same result. The dispersion in r c ~ 0.07 h~l Mpc. The typical central number density of galaxies with M £ M* + 2.5 (M* is the characteristic luminosity in the Schechter (1976) form for the galaxy luminosity function) is ~ 10 3 ± 0 ' 6 /i 3 galaxies/Mpc 3 (Dressier 1978). A redshift survey of a rich clusters now frequently includes £ 50 velocity measurements. Dressier and Shectman (1988) measured 1268 velocities in the fields of 15 rich clusters; Colless (1987) measured 604 velocities in 14 more clusters with the fiber-optic facility at the Anglo-Australian Telescope. These large velocity samples enable much more sophisticated studies of cluster kinematics than have been possible previously. In many cases there is evidence of structure in the velocity distribution. Although one can now do more than calculate a straightforward velocity dispersion for many systems, it is instructive to look at the distribution of velocity dispersions for clusters which have £ 10 velocity measurements. Figure 1 shows the distribution (solid histogram) of line-of-sight velocity dispersions within the central l.bh~ Mpc for 65 Abell (1958) clusters (Zabludoff, Huchra, and Geller 1990). The median velocity dispersion is 744 km s . The dashed histogram is the distribution of velocity dispersions for the 25 clusters which contain a cD galaxy. The median dispersion is 773 km s . A K-S test does not differentiate between the two distributions in Figure 1. With the 'typical' values of the core radius (r c = 0.25/i -1 Mpc) and line-of-sight velocity dispersion (a = 750 km s ), Equation (3) yields an estimate of the central mass density, po = 1.4 x 10 h MQ/MJ>C . The central luminosity density is about 4.5 X 1 0 1 2 / J ~ 2 L 0 / M p c 3 (in the B band; see e.g., Dressier 1978). Thus the massto-light ratio for the cluster core is ~ 300/i MQ/LQ, again at B. This value for the mass-to-light ratio in the core of a typical rich cluster is a example of the 'missing mass' or dark matter problem originally discovered by Zwicky (1933) in his application of the virial theorem to the Coma cluster. This value of the mass-to-light ratio is within the range obtained in detailed studies of rich systems.

Structure, Infall, and Large-Scale Distribution I

i

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27 1

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n = 65 °r. mm = 744 km s"'

18

n (cD) = 25 (7,. r i (cD) = 773 km s"'

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16

14 — to

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200

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1200

Figure 1. Histogram of line-of-sight velocity dispersions for 65 rich clusters (solid line) and for the 25 clusters containing a cD galaxy (dashed line). For ~ 25 well-studied systems (Colless 1987; Chapman, Geller, and Huchra 1987; Chapman, Geller, and Huchra 1988; Postman, Geller, and Huchra 1988; Kent and Gunn 1982; Kent and Sargent 1983), the B(0) mass-to-light ratio within ~ l.5h~l Mpc of the cluster center ranges from l80h MQ/LQ to 850h MQ/LQ. The median mass-to-light ratio, M/L#(o) = 500 ± lOO/i M0/L0. If characteristic of the universe as a whole, the median mass-to-light ratio implies that the universal mean mass density, fi = 0.2e . (Note that these results are within one standard deviation of the one obtained by analyzing catalogs of small groups. For groups in the CfA redshift survey, the median M/L 5 ( 0 ) = 186 implies Q = 0.13e ± 0 9 (Ramella, Geller, and Huchra 1989)). N-body simulations reveal the complexity of the evolution of a spherically symmetric system of discrete masses (White 1976; Cavaliere et al. 1986; Cavaliere 1990; West 1990). These models show that the morphology of a cluster and the timescale for its evolution are tied to the details of the initial configuration. If most of the matter in the system is initially attached to individual galaxies, discreteness effects are important. During the initial expansion, galaxies form groups or subclusters which gradually coalesce during the collapse. If groups form only on small scales, the dynamical timescale for cluster evolution is essentially unaffected. However, correlations in the initial conditions can often lead to the formation of large lumps which have a substantial effect on the rate of evolution of the cluster (Cavaliere et al. 1986). Non-linear dynamics amplifies the discreteness affects and leads to a broad distri-

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M. J. Geller

bution of cluster morphologies and evolutionary timescales. For example, in about 30% of the simulations by Cavaliere et al. two large clumps form. These clumps effectively drain potential energy from the system as a whole. Thus the radius of the entire system at maximum expansion is significantly larger than in the uniform case (or, equivalently, where substructure occurs only on a scale small compared with the entire system). Subclustering can delay overall contraction and virialization by as much as a factor of ~ 6 over the canonical timescale (~ (Gp)~^'^). Even among systems as dense and massive as the Coma cluster, the simulations by Cavaliere et al. (1986) suggest that after a Hubble time only one-third will actually be relaxed, virialized systems. Another third are bimodal and the rest are messier. The fraction of lumpy clusters should remain large for two or three Hubble times. The message of these simulations is clear: detailed study of the structure of rich clusters can provide clues to their formation and evolution. Another examination of the structure of rich clusters produced in N-body simulations (West, Oemler, and Dekel 1987; West 1990) provides a less promising message. West et al. argue that the amount of substructure in the inner regions (R£ 2h~^ Mpc) of rich clusters is insensitive to the range of initial conditions appropriate for pancake, hierarchical, and hybrid models. West et al. address the thorny issue of evaluating the significance of substructure in simulated clusters and in the 55 cluster maps of Dressier (1980); they conclude that the importance of substructure in clusters may have been exaggerated in previous analyses based on surface density distributions (e.g., Geller and Beers 1982). West et al. argue that most clusters today are relaxed systems. The reasons for the disagreement between the conclusions of West et al. and those of Cavaliere et al. remain unclear even after some discussion at this symposium. The results of the simulations by Cavaliere et al. are in strikingly good correspondence with recent detailed X-ray and optical observations of clusters. Only ~ 20% of the clusters observed with the Einstein Observatory are smooth; most of the X-ray surface brightness distributions have clumps ranging in scale from 100 kpc to 1 Mpc. In fact, the observation of X-ray double clusters (Forman et al. 1981; Forman and Jones 1982) reawakened interest in quantifying the complexity of rich clusters from optical data. In Dressler's (1980; 1980b) sample of 65 clusters, 40% show more than one statistically significant peak in the surface number density of galaxies (Geller and Beers 1982). Baier (1978) independently reached the conclusion that substructure in clusters is common. The uncertainty in the fraction of clusters with sub condensations is large because the biases in the selection of the cluster sample may be large and because the detection of structure in a particular cluster is limited by the number of galaxies in the survey. Sensitivity to structure is also a function of the cluster geometry and of the orientation of the system with respect to the line-of-sight. Without redshift data, superposed foreground and/or background groups can give the appearance of substructure. On the other hand, redshift data may resolve structure which is not obvious in the distribution of galaxies on the sky. The recent availability of large redshift samples enormously increases the possibility of resolving the general issue of substructure in clusters. The studies by Colless (1987) and by Dressier and Shectman (1988b) both underscore the importance of substructure. Colless' surveys cover the inner r ;& lh~* Mpc of 14 clusters. Of these 14 systems, at most 6 show no evidence of substructure. Two systems are convincingly double and the remaining 6 show hints of substructure in the velocity and/or surface density distribution. Dressier and Shectman (1988b) develop a statistic for evaluating the

Structure, Infall, and Large-Scale Distribution

29

significance of substructure in the velocity distributions of the 15 clusters which they survey out to a radius of ~ \.bh~^ Mpc. Of these systems, 4 show no convincing velocity substructure (data show that one of these, A754, is actually double — see below), 3 have obvious structure on the sky which is confirmed by analysis of the velocity data, and the other 8 have £ 20% of the cluster population in a subgroup. The results of both of these surveys are consistent with the claims of Geller and Beers (1982). Many clusters of galaxies are dynamically young; they retain the clumpy structure which is present in N-body simulations (and presumably in real systems) at early stages in cluster evolution. At present, three pieces of observational evidence point to the importance of substructure at the current epoch: X-ray surface brightness profiles, photometric and velocity surveys of clusters, and the robustness of the morphology-local density relation. The fraction of X-ray clusters with smooth surface brightness profiles (~ 20%) is roughly consistent with the fraction of clusters in extensive velocity surveys (Colless 1987; Dressier and Shectman 1988) which appear to be genuinely relaxed systems. However, agreement in the abundance of clumpy clusters may be fortuitous — the cluster samples are not complete in any sense. The observation that the morphology-density relation holds for both these regular and for irregular clusters argues further for the reality of subclumps as physical units rather than mere statistical fluctuations. With these statistics (of admittedly small samples) in mind, it is instructive to examine a few of the systems with substructure. The literature contains extensive discussions of more regular systems like Coma (Kent and Gunn 1982; but see Fitchett and Webster 1987) and Perseus (Kent and Sargent 1983). Figure 2 (Geller and Beers 1982) shows isopleths for two of relaxed systems identified among the clusters surveyed by Dressier and Shectman (1988a, b).

Figure 2. Isopleths for two relaxed clusters (from Geller and Beers 1982; see that paper for quantitative details). The contours are linearly spaced. The "messier" systems which have apparent substructure potentially offer more clues to the early development of clustering. Figure 3 shows two systems which have obvious structure on the sky. Redshift surveys (Dressier and Shectman 1988) confirm the physical reality of these substructures. Figure 4 shows isopleths for two more

SO

M. J. Geller

systems in which the structure on the sky is probably not statistically significant. However, the redshift data of Dressier and Shectman (1988) show that there are physically separate clumps centered close to the peaks in the surface density maps.

Figure 3. Isopleths for two rich clusters with obvious structure in their surface density distributions (Geller and Beers 1982).

04 h 28 m 0

Figure 4. Isopleths for two rich clusters where redshift surveys (Dressier and Shectman 1988) reveal significant substructure. The subclumps are centered on the apparent peaks in these surface density distributions. The surface density distributions alone are insufficient to substantiate the substructure. Substructure is apparent in other systems. About 20% of the clusters in the samples of Colless (1987) and Dressier and Shectman (1988) have two components separated on the sky, in redshift, or both. In at least one of these systems, A754, double structure

Structure, Infall, and Large-Scale Distribution

SI

is required to fit the highly flattened and asymmetric X-ray surface brightness profile (Fabricant et al. 1986; Dressier and Shectman 1988). The Centaurus cluster, surveyed by Lucey et al. (1986) is an additional superposition of two components along the line-of-sight. The impact of substructure on the determination of mass-to-light ratios has not yet been investigated in adequate detail. It is clear that the effects can be important in some cases. One example is the Centaurus cluster where, from the parameters given by Lucey et al. (1986), the mass-to-light ratio would be overestimated by about a factor of two in ignorance of the double structure. The case for A548 is discussed by Shectman and Dressier (1988b). More detailed examination of the structure of individual systems shows some of the effects that the resolution of substructure has on our understanding of the physics of these systems. The examples briefly discussed so far show that (1) structure is present in both high and low density systems, (2) in some cases resolution of substructure can affect estimates of the cluster mass-to-light ratio, and (3) the structure of some "individual" systems clouds the distinction between clusters and superclusters and could affect the statistics of the large-scale distribution of rich clusters. Although the above discussion is not a survey of homogeneous data acquired for well-defined samples, there are some hints about the kinds of results which might be obtained from more extensive surveys. At the current epoch, we observe substructure in both high and low density systems. We also observe relaxed high density systems. The range of morphologies at fixed density and the coeval appearance of substructure over a wide range of densities are predicted by N-body simulations in which discreteness effects are important at early epochs. According to the models of Cavaliere et al. (1986), the fraction of clusters which retain structure places a constraint on the initial distribution of dark material in the cluster. A dominant, smooth component suppresses the development and persistence of significant structures; the evolutionary timescale is completely determined by the density of the dominant smooth component. In this case, clusters of a particular density should all have nearly the same morphology, contrary to the developing observational situation. From well defined optical surveys (photometric and redshift) we could evaluate the fraction of clusters which retain substructure as a function of the density of the systems (taking account of the limits to resolution caused by sampling effects). X-ray data will surely become increasingly important in understanding the dynamics of clusters of galaxies. The Einstein data support the indications from optical data that only the minority of clusters are relaxed systems at the current epoch. Even clusters which contain cD galaxies show a wide variety of X-ray morphologies. These data together with the similarity of the distributions of velocity dispersions for cD- and non-cD-clusters are consistent with the suggestion that giant galaxies begin to form in subclusters present at early epochs. The presence of a cD does not imply that the system is "globally" relaxed.

2. INFALL PATTERNS AND ft Surveys of clusters of galaxies are generally limited to the dense central region. With our increasing ability to measure large numbers of redshifts, it is now feasible to examine the infall region (within ~ 5h~ Mpc of a cluster center) for clusters other than Virgo. Analysis of Virgo infall has, of course, provided one of the few large-scale dynamical limits on the value of the cosmological mean mass density, fl (Davis et al.

32

M. J. Geller

1980; Davis and Huchra 1982; Huchra 1985; Yahil 1985; Davis and Peebles 1983). Here I argue that study of the infall patterns around clusters holds promise for limiting the value of ft and for testing the assumption that light traces mass in the infall region (Ostriker et al. 1988; Regos and Geller (1989). Shectman (1982) was one of the first to recognize that limits on ft can be obtained from study of these regions and Kaiser (1987), who does not expressly consider cosmological tests, simulates the form of infall patterns in redshift space. In the linear regime, the peculiar velocity, vp induced by a spherical density enhancement A inside radius r is

i

- -lrt»A

(5)

(Gunn 1978; Peebles 1976; 1980). Regos and Geller (1989) show that the peculiar velocity can be written to arbitrary order as a separable function of ft and A:

£ * "06P(A),

(6)

where p(A) is a power series in A. In redshift space, high density caustic surfaces define the infall pattern (Kaiser 1987). Figure 5a is a schematic of the geometry in real space. The labels 0 , C, and G denote the observer, the center-of-mass of the cluster, and a galaxy, respectively.. Ro is the distance to the cluster. The angle 9 is the angular separation on the sky between a galaxy and the cluster center. The angle is the polar angle subtended by the position of the galaxy at the cluster center. Figure 5b shows the pattern which would be marked by test particles which trace the mass distribution (i.e., not necessarily the pattern marked by the galaxies) in redshift space. The curves are the caustics. The arrows indicate the direction of increasing phase space density. The simple model of Figure 6 qualitatively explains the appearance of the caustics in Figure 5b. The plot shows the observed velocity as a function of r for fixed 9 and 0< 9 < 90°. For the shell presently turning around (up = 0) at rturn, the observed velocity cz = HoRoCOs(0). The extremal velocity cz m j n defines the caustic surface. This velocity can correspond to only two values of r. For cz > czmin, there are three corresponding values of r. The caustics thus represent the boundary of the triplevalued region. Outside the caustics, the solutions are single-valued; inside they are triple-valued. For an optimal comparison of the data with an infall model, we need a complete redshift survey which extends to sufficiently large angular radius from the cluster center. Few (if any) such samples exist. However, there are at least four systems with sufficient data to make a preliminary and demonstrative comparison: A539, A1656 (Coma), A1367, and A2670. Figure 7 shows the azimuthally averaged data (Ostriker et al. 1988; Huchra et al. 1990; Sharpies et al. 1988) for these systems (see Regos and Geller (1989) for a complete description of the construction of these plots). The redshift samples shown are not magnitude limited; they include all the available data. In each cluster we use the observed angular distribution for a magnitude limited sample of galaxies to obtain an estimate of the spatial distribution. We assume spherical symmetry. With an estimate of the mean galaxy density in the field (de Lapparent, Geller, and Huchra 1989), we can take the observed galaxy number density enhancement as the matter density enhancement A(r). In so doing, we tacitly assume that the galaxies trace the matter distribution. Given A(r) we can calculate the caustics as a

Structure, In/all, and Large-Scale Distribution

S3

TURN (H0R0 cos 9)

9

9 'mm

a)

^intersect

b)

Figure 5. a). The geometry of a cluster of galaxies where 0, C, and G are the observer, the cluster center and a galaxy, respectively. Ro is the distance to the cluster center, b). A cluster in redshift space. The curves A and B are the caustics and the arrows denote the direction of increasing phase space density. function of il from Equation (6). Note that for a particular A(r) the amplitude of the caustics is a function of Si only. The caustics in Figure 7 are marked with the relevant value of fi. For a given Si, variation in the form of A(r) changes the form of the caustics. Thus, in principle, by fitting the caustics to the data, we could test the assumption that the galaxies trace the matter distribution. For all four clusters in Figure 7, the density of points (galaxies) in redshift space drops substantially outside the caustics for Si ~ 0.2 — 0.5. Given the assumptions, the data appear to be consistent with low values of Si. In the data, the caustics are not apparent near the turnaround radius (where the predicted caustics meet). In this region the infall velocities are small and the density contrast associated with the caustics is not observable. These preliminary comparisons indicate that it is probably worthwhile to carry out magnitude limited redshift surveys (deep enough to include £ 100 galaxies in the infall region) which cover the infall region in a judiciously chosen set of clusters. The estimates of Si obtained by fitting the caustics are independent of those derived from the cluster core and apply to a larger spatial scale (~ 1 — bh Mpc). Fitting the caustics to sufficiently dense data could also provide constraints on the relative distribution of dark and light-emitting matter in the region. The technique is limited by some of the

34

M. J. Geller

N O

Figure 6. Observed velocity, cz, as a function ofr for fixed 0 in the range 0< 0 < 90°. problems which plague analysis of the core region. Substructure (groups) in the infall region are a problem as is asymmetry of the system. These problems might be amenable to treatment with N-body simulations.

3. THE LARGE-SCALE DISTRIBUTION OF CLUSTERS (GROUPS) On the largest scale, clusters of galaxies could be convenient markers of large-scale structure in the distribution of galaxies. However, the results of statistical analyses of existing catalogs remain poorly understood. So far several groups have used the language of correlation functions (Peebles 1980) to describe the cluster distribution. Bahcall and Soneira (1983) calculated the two-point correlation function for the Hoessel, Gunn, and Thuan (1980) sample of 104 nearby Abell clusters. Postman, Geller, and Huchra (1986) calculated the cluster correlation function for a variety of other samples drawn from both the Abell and Zwicky catalogs, and Shectman (1985) analyzed a sample of clusters drawn from the Shane-Wirtanen counts (1967). More recently Huchra et al. (1990) observed and analyzed a sample of 145 Abell (richness R> 0) clusters at high galactic latitude and with distance class D<6. For all of these samples a straightforward calculation of the correlation function yields a result consistent with the power law form

~ (ro/r) 1.8

(7)

Structure, In/all, and Large-Scale Distribution

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Figure 7. The observed distribution of galaxies in redshift space for a) A539, b) Coma, c) A1367, and d) A2670. The curves are the caustics predicted from the observed A(r) for the indicated values of fl. Note the low density of points outside the caustics for Cl ~ 0.2 — 0.5 in all cases. The caustics appear to be detectable in the region outside the virialized core and inside the turnaround radius where the upper and lower caustic meet. where the amplitude r o lies in the range

^ ^ " ^ p c $ r o $ 24A~1Mpc.

(8)

In general, the lower values of r o are for samples which contain less rich systems. For a sample of ~150 clusters, the uncertainty in r o is ~ 50%. Even given this substantial uncertainty, the results in Equation (8) are inconsistent with the predictions of the standard cold dark matter models with biased galaxy formation (White et al. 1987). The models predict a significantly smaller amplitude, ro ~ 11 A" 1 Mpc. The discrepancy between the model predictions and the data has been an incentive to search for problems in the cluster catalogs and in the methods of analysis (Sutherland 1988; Soltan 1988; Lucey 1983). There is no shortage of problems, but their effect on the results remains hard to gauge because samples are small and non-uniform. Problems include (1) clusters in the catalog which should not be included, (2) erroneous mean redshifts, (3) clusters missing from the catalogs and (4) limited samples. Some of the clusters in the catalogs are superpositions along the line-of-sight: a system, if present, is actually too poor to meet the Abell's selection criteria. Several investigators (Sutherland 1988; Dekel

36

M. J. Geller

et al. 1989) have attempted to correct the catalogs for this superposition problem. The correction procedure lowers the value of r o largely because the correction algorithm removes clusters in dense regions from the sample. Observations indicate that superposition is a problem but that the correction procedures which account for overlap of neighboring clusters are probably overly simplistic. For example, in a complete sample of 31 R>1 Abell clusters with velocities cz < 15,000 km s""1, at least two are superpositions of groups (and/or foreground galaxies) along the line-of-sight. Neither of these systems has a close neighbor which is also a cluster in the catalog (Zabludoff, Geller, and Huchra 1990). Erroneous mean redshifts also arise from the superposition problem with somewhat surprising frequency; in fact, there appears to be a bias in the Abell catalog toward superpositions and toward identifying concentrations of galaxies on the sky which appear to be associated with an apparently bright galaxy (which may well be foreground). It is dangerous to base cluster redshifts on a single redshift measurement and the danger, of course increases with redshift! It seems that the only reliable approach to these problems is well-defined sampling of the redshift distribution in the direction of each cluster. The flip side of the superposition problem is the failure to identify systems which show up as fingers in complete redshift surveys (Ramella, Geller, and Huchral1989). In the first two slices of the CfA redshift survey there are 2 R = 1 clusters; there are 4 groups (including the 2 Abell clusters) which have physical properties indistinguishable from those of Abell R = 1 systems. Although the rich clusters selected by Abell are apparently biased tracers of the distribution of individual galaxies, groups of galaxies selected from complete redshift surveys do appear to trace the structure in the galaxy distribution (Ramella, Geller, and Huchra 1990). Figure 8a shows the distribution of galaxies in the first two slices of the CfA redshift survey extension. These slices cover the declination range 26.5° < 6 < 38.5°. Figure 8b shows the distribution of group centers in the two slices. Note that the group centers trace the large-scale features visible in the galaxy distribution of Figure 8a. Perhaps not surprisingly the correlation function for the 128 groups is consistent with the correlation function for the galaxy distribution (Ramella, Geller, and Huchra 1990). It would be valuable to have model predictions of the correlation function for groups selected from N-body simulations in the same way that they are selected from the data.

4. CONCLUSION In principle clusters of galaxies offer probes of the development of large-scale structure on scales from a fraction of a Megaparsec to hundreds of Megaparsecs. However, on each scale there are profound, but clearly defined issues which could be at least partially resolved by a combination of well-designed observations and models. On scales ^ lh Mpc, the internal dynamics of individual clusters can provide insight into their history. There are a number of systems which clearly have substructure. Controversy centers Figure 8. (opposite page) a) A cone diagram for galaxies in the declination range 26.5° < 8 < 38.5° and with cz < 12,000 km s~l. b). A cone diagram showing the distribution of the centers of 128 groups in the same declination slice. The crosses denote the Abell clusters in the region, all of which are detected by the group-finding algorithm.

Structure, Infall, and Large-Scak Distribution

right ascension

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37

38

M. J. Geller

on the abundance of such systems. The obvious solution to the problem is observation of a well-defined set of systems. On scales of lh~* to 5h~* Mpc, the infall regions associated with rich clusters could provide limits on fi and on the relative distributions of dark and light-emitting matter. Here the data are sparse, to say the least. Some pilot projects would be worthwhile here. Analysis of simulations could be used to see whether substructure and other asymmetries are insurmountable complications. Mpc, the investigation of clusters as tracers of the large-scale On scales £ 5h matter distribution is important. The problems in the construction of cluster catalogs can only be solved with focused (and large) observational programs. One route which might prove powerful is the use of cluster catalogs derived from surveys in the X-ray (see, for example, Lahav et al. 1989). Soon the ROSAT survey should provide a catalog of several thousand rich cluster X-ray sources at redshifts £ 0 . 1 . With a complete redshift survey to this depth one could evaluate the X-ray selection which should be less subject to superposition biases than selection based on galaxy surface density. Future X-ray missions could then be used to map the large-scale cluster distribution as a function of epoch (see Geller 1990 for a more complete discussion). This research is supported in part by NASA grant NAGW-201, the Smithsonian Scholarly Studies Program, and the Digital Equipment Corporation.

REFERENCES Abell, G.O. 1958, Ap.J. Suppl., 3, 211. Bahcall, N.A. and Soneira, R.M. 1983, Ap.J., 270, 20. Baier, F.W. 1978, Astron. Nach., 299, 311. Beers, T.C. and Tonry, J.L., 1986, Ap.J., 300, 557. Cavaliere, A., Santangelo, P., Tarquini, G., and Vittorio, N. 1986, Ap.J., 305, 651. Cavaliere, A. 1990, this volume. Chapman, G.N.F., Geller, M.J., and Huchra, J.P. 1987, A.J., 94, 571. Chapman, G.N.F., Geller, M.J., and Huchra, J.P. 1988, A.J., 95, 999. Colless, M. M. 1987, Ph.D. Thesis, University of Cambridge Davis, M. and Huchra, J.P. 1982, Ap.J., 254, 437. Davis, M., Tonry, J., Huchra, J.P., and Latham, D.W. 1980, Ap.J.Lett.,238, L113. Davis, M. and Peebles, P.J.E. 1983, Ann. Rev. Astron. Ap., 21, 109. Dekel, A., Blumenthal, G.R., Primack, J.R., and Olivier, S. 1989, Ap.J. Lett, 302, LI. Dressier, A. 1979 Ap.J., 231, 659. Dressier, A. 1980, Ap.J. Suppl, 42, 565. Dressier, A. \980&,Ap.J., 236, 351. Dressier, A. and Shectman, S. 1988, A.J., 95, 284 Dressier, A. and Shectman, S. 1988b, A.J., 95, 985. Fabricant, D., Beers, T . C , Geller, M.J., Gorenstein, P., Huchra, J.P., and Kurtz, M.J. 1986, Ap.J., in press. Fitchett, M. and Webster, R. 1987, Ap.J., 317, 653. Forman, W. and Jones, C. 1982, Ann. Rev. Astr. Astrophys., 20, 547. Forman,W.,Bechtold, J., Blair, W., Giacconi, R., Van Speybroeck,L., and Jones, C. 1981, Ap.J. (Letters), 243, L133. Geller, M.J. and Beers, T.C. 1982, P.A.S.P., 94, 421.

Structure, Infall, and Large-Scale Distribution

39

Geller, M. J. 1990, in NASA Symposium High-Energy Astrophysics in the 21st Century, Taos, New Mexico (in preparation). Gunn, J.E. 1978 in Observational Cosmology, 8 Saas Fee Course, L. Martinet and M. Mayor, eds. (Sauverny: Geneva Observatory) Hoessel, J.G., Gunn, J.E., and Thuan, T.X. 1980, Ap.J., 241, 486. Huchra, J.P. 1985 in The Virgo Cluster, eds. O.-G. Richter and B. Binggeli (Munich: European Southern Observatory) p. 181 Huchra, J.P., Geller, M.J. et al. 1990, in preparation. Huchra, J.P., Henry, J.P., Postman, M., and Geller, M.J. 1990, Ap.J., in press. Kaiser, N. 1987, M.N.R.A.S., 227, 1. Kent, S.M. and Gunn, J.E. 1982, Ap.J., 87, 945. Kent, S.M. and Sargent, W.L.W. 1983, A.J., 88, 697. Lahav, 0., Edge, A.C., Fabian, A.C., and Putney, A. 1990, M.N.R.A.S., in press. Lapparent, V.de, Geller, M.J., and Huchra, J.P. 1989, Ap.J., 343, 1. Lucey, J.R. 1983, M.N.R.A.S., 204, 33. Lucey, J.R., Currie, M.J., and Dickens, R.J. 1986, M.N.R.A.S., 221, 453. Merrifield, M. and Kent, S. 1990, Ap.J., submitted. Ostriker, E.C., Huchra, J.P., Geller, M.J., and Kurtz, M.J. 1988, A.J., 96, 1775. Peebles, P.J.E. 1976, Ap.J., 205, 318. Peebles, P.J.E. 1980, The Large-Scale Structure of the Universe (Princeton University Press) Postman, M., Geller, M.J., and Huchra, J.P. 1986 A.J., 91, 1267 Postman, M., Geller, M.J., and Huchra, J.P. 1988, A.J., 95, 267. Ramella, M., Geller, M.J., and Huchra, J.P. 1989, Ap.J., 344, 57. Ramella, M., Geller, M.J., and Huchra, J.P. 1990, Ap.J., in press. Regos, E. and Geller, M.J. 1989, A.J., 98, 755. Rood, H.J., Page, T. Kintner, E.C., and King, I.R. 1972, Ap.J., 175, 627. Schechter, P.L. 1976, Ap.J., 203, 297. Sharpies, R.M., Ellis, R.M., and Gray, P.M. 1988, M.N.R.A.S., 231, 479. Shectman, S.A. 1982, Ap.J., 262, 9. Shectman, S.A. 1985, Ap.J. Suppl., 57, 77. Soltan, A. 1988 M.N.R.A.S., 231, 309. Sutherland, W. 1988, M.N.R.A.S., 234, 159. Tonry, J.R. 1985, Ap.J., 279, 13. Vaucouleurs, G. de 1948, Ann. d'Astrophysique, 11, 247. West, M., 1990, this volume. West, M., Dekel, A., and Oemler, A. 1987, 'it Ap.J., 316, 1. White, S.D.M. 1976, M.N.R.A.S., 174, 19. White, S.D.M. 1976a, M.N.R.A.S., 177, 717. White, S.D.M. 1982, in Morphology and Dynamics of Galaxies, ed. L. Martinet and M.Mayor (Sauverny: Geneva Observatory), p. 289 White, S.D.M., Frenk, C.S., Davis, M., and Efstathiou, G. 1987, Ap.J., 313, 505. Yahil, A., Walker, D., and Rowan-Robinson, M. 1986, Ap.J. (Letters), 5, 84. Yahil, A. in The Virgo Cluster, eds. O.-G. Richter and B. Binggeli (Munich: European Southern Observatory) p. 359. Zabludoff, A.I., Huchra, J.P., and Geller, M.J., 1990, Ap.J. Suppl, in press. Zabludoff, A.I., Geller, M.J., and Huchra, J.P. 1990, in preparation.

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Zwicky, F. 1933, Helv. Phys. Acta, 6, 110. Zwicky, F.,Herzog, W., Wild, P, Karpowicz, M. and Kowal, C. 1961-1968, Catalog of Galaxies and of Clusters of Galaxies, (Pasadena: California Institute of Technology)

DISCUSSION Unknown: In your two isothermal sphere models for A754, one of them is reasonably centered on the cD. Do you know from your data that it can't have zero core radius? Geller: Yes. I think you need something with a finite core radius. You need two spheres with finite core radii. Peebles: What redshifts are there known in A754? Geller: There are a hundred redshifts which have been measured. I forgot to mention that. Thank you very much. These were measured by Dressier and Shectman. Now Dressier and Shectman made redshift surveys for 15 clusters and in 11 of the 15 they find substructure in the redshift distribution; however, not in this case, nor did we. The clumps, if they are really there, are at the same velocity. J . Bahcall: Margaret, for Einstein observations of a deep sample of Abell clusters, what fraction are found to be X-ray sources? Similarly, when the Einstein serendipitous Survey was made, what fraction of X-ray sources, which later turned out to be what looked like rich clusters, were not in AbelPs catalog? Geller: Well, I really don't know the answer. I don't know the numbers, but a large fraction of Abell clusters which were looked at with Einstein turned out to be X-ray clusters. N . Bahcall: Let me give you a quantitative answer. We have looked at that together with Maccacaro, using the medium deep Einstein survey, and we looked at it two ways. One is to look at all the nearby Abell clusters, and to see how many of them are detected at luminosities that correspond to richness class 0 and above - and the answer is that for all of the nearest 25 or 30 clusters, that's where we can detect them for sure with Einstein, they were all detected as X-ray sources. And the other way around, which I think is more interesting, is has Abell missed any clusters among those nearby ones? The nearby sample. Has he missed any that are clusters but were not called a cluster by him. We looked at all the serendipitous big surveys for extended X-ray sources. Then we went back to the plates and looked to see if there was a really rich cluster that should have been seen by Abell but was not. And the answer was that we found none like that. We found many that were poor clusters, less than richness 0, but there were none that, when we looked at them, corresponded to richness class 1 and above that should have been included in Abell. And that gives you a completeness that is consistent with what Richard said of about 80% or so.

Structure, Infall, and Large-Scale Distribution

J^l

Kaiser: But can someone tell me, what would be the scatter in X-ray luminosity at richness class one? N. Bahcall: The luminosity is very broad, but you still can answer the question are there any rich clusters that have been missed? Just looking at anything that is extended in X-rays, going back to the plate, and seeing if there is a rich cluster that should have been in Abell, for the nearby sample I am talking of, and is missed - and the answer is none, within the statistics of the area that was covered. Kaiser: So are you saying that the groups that Margaret is finding that she said should be clusters have really tiny luminosities ? N. Bahcall: When John showed me before, two of these clusters were at 16.5 hours and that is below the limit of the Abell catalog in latitude, and we've not seen now where they are. Geller: No, they are Abell clusters. N. Bahcall: One has to look at the completeness of latitude and longitude, etc. Geller: At 16 1/2 hours, they are Abell clusters. I will mark which ones they are, but they are not outside Abell's limit, as far as I know. They are not particularly on the edges of the survey. The only thing at the onset is that the two richness class 1 clusters in the survey - they were not detected in the X-ray. Burg: There are very rich clusters that have very low X-ray luminosity. For example, those X-ray luminosities may be consistent with some of the elliptical galaxies within the cluster, so it is possible to have very rich clusters with very low gas emission. Geller: So there could be a large dispersion. The point is that you can select systems from a redshift survey where you can measure various properties and they are indistinguishable on the basis of the redshift survey as we understand clusters. Now the question is to go back and look to see whether they are indistinguishable or not based on their X-ray properties. And I think that the fair answer to that question is that we really don't know the answer to that question. Beers: I just wanted to mention at the end of Margaret's talk that they are better ways of estimating dispersion that are not as dominated by interlopers as what people usually use. And if anyone is curious about what these estimators are, they can look at the poster I have here. I should also emphasise that there is a gut reaction that we need larger redshift surveys. I agree in detail but I would emphasize that once we get 200 velocities per cluster the interesting questions are still going to come down to what's happening with 10 or 20 velocities in a particular region of a cluster, so we shouldn't fool ourselves that all the problems will go away by simply having large numbers of velocities, but should think long and hard about what we are going to do with information on a small scale. We need some more ideas.

COSMOGONY WITH CLUSTERS OF GALAXIES

A. Cavaliere Astrofisica, Dip. di Fisica II Universita di Roma, Italy S. Colafrancesco Dip. di Astronomia, Universita di Padova, Italy.

Abstract. We attempt to bring together N-body simulations, analytical mass distribution functions, scaling laws and numerical computations of luminosity functions, that describe from different angles the hierarchical formation and evolution of groups and clusters of galaxies. The results are discussed in the light of the existing local observations in the optical and X-ray bands, and in the perspective of preliminary evidence and expected data from X-ray surveys at medium redshifts.

1. INTRODUCTION Clusters of galaxies contribute to cosmogony from three main directions: their individual morphologies and substructures may still preserve remnants of initial conditions before collapse; their local statistics may be informative about sites and dynamics of the collapse process; their distribution in redshift should reflect the clustering in action. Because their gravitational potential wells hold a large amount of hot intracluster plasma (ICP, with temperature T ~ 108 K, density n ~ 10~ 3 cm" 3 , and mass M even larger than that in stars), the clusters emit powerfully in the X-ray band with Lx ~ 10 — 10 erg/s; see Cavaliere et al. 1971, Sarazin 1988. Some of this output is in high excitation emission lines, but most is in optically thin thermal Bremsstrahlung: Lx oc hMT1/2 a g2pMv ,

(1)

related by the latter expression to the dynamical variables: mass M, density /?, and galaxy velocity dispersion v under conditions of virial equilibrium; here, g(M, t) is the ICP mass fraction M/M. Such emission density a n 2 T 1 ' 2 offers another means, in addition to optical observations, for mapping physical clumps within the local objects. The associated emissivity also offers the means for fast surveys of clusters or groups at z ~ 0.5 — 1, in principle out to the redshift where the hot ICP forms. This talk, more than reviewing the few established points in this developing field, is intended to discuss a number of open and pressing issues.

44

A. Cavaliere and S. Colafrancesco

2. MORPHOLOGIES The ICP is in fair equilibrium with the gravitational potential over scales of Mpcs, (cf. Cavaliere 1980, Sarazin 1988). This is due to its fast relaxation (the sound crossing time matches the cluster's dynamical time) and to its slow cooling (apart from cooling flows localized within the densest central regions, cf. Fabian 1988). To lowest order, the ICP is in hydrostatic equilibrium, implying a scale height close to that of the galaxies. In cases where spherical symmetry applies, such as A2255 or Coma, analytical models provide useful parametrizations for the runs of density and temperature and hence of the surface brightness out to several Mpcs (for example, the so called /?-model, cf. Cavaliere 1980, Sarazin 1988). On the other hand, maps by X-ray telescopes (see, e.g., Forman and Jones 1982, Arnaud et al. 1987) and optical studies {e.g., those of Geller and Beers 1982, Binggeli et al. 1987) have stressed the morphological variance occurring even within the set of the rich clusters, with clumpy and irregular shapes apparent in many objects: examples are provided by A194 or A2151 up to such extreme cases as A1367, but even in Coma there is evidence of weak inner asymmetry (see, e.g., Fitchett and Webster 1987, Mellier et al. 1988). To match the observational resolution, the theoretical tool required is constituted by N-body simulations like those of Peebles 1970, White 1976, Cavaliere et al. 1986, Evrard (this Workshop). These can follow in time and in three dimensions the nonlinear stage of the gravitational instability, starting from a field of small fluctuations in the total density present at recombination. The diffuse baryons constituting the ICP with its X-ray emission may be included using coupled hydrostatic or hydrodynamic modules, to produce simulated brightness maps resolved down to galactic scales. Such simulations naturally fit in the Hierarchical Clustering Scenario (HCS, cf. Peebles 1980, Dekel 1989), the most definite and least unsatisfactory cosmogony to date, where the gravitational instability proceeds bottom up with minor help by dissipation: galaxies are assembled into groups, these into poor and eventually into rich clusters. In the simplest version of the HCS, the initial overdensities 8 on a mass scale M follow a Gaussian distribution p(8\M) with a power-law dispersion a oc M~a. The field may be Fourier represented by random-phased components with power spectrum (\6^\ ) oc kn, extending longward from subgalactic masses; then the relationship a = (n + 3)/6 holds. Many results carry over at the lowest order to the specific CDM model (cf. Davis and Peebles 1983), with its spectrum n(M) gently curving from n ~ — 2 in the galaxy range toward n ~ — 1 for the rich clusters. Past the linear regime where 8(z) oc (1 + z) holds for £2 = 1, the non-linear stage is the domain of the N-body simulations, whose results may be outlined in terms of a tuning fork diagram. This starts with two parallel and interacting sequences, namely I) overall condensation: the expansion detaches from the Hubble flow and halts, recollapse follows; II) internal subclustering: clumps of a few galaxies single out, merge into larger and larger units to form a few large clumps that fall together. Eventually, these two branches join when the systems violently relax and approach spherical configurations, with weak asymmetries petering out. Meanwhile, the collapse process goes on with accretion or infall onto the dominant condensations of some or much surrounding matter (depending on £20) both in diffuse form or in weaker, slower substructures. Similar events occur on smaller scales in the preceeding subclusters. Sequence I may be described also with an analytical model (Gunn and Gott 1972) of a spherical uniform region, collapsing on the time scale tc oc M ' \E\ ' oc 6 ' that governs both the linear and the non-linear regimes. For typical fluctuations along the

Cosmogony with Clusters of Galaxies

^5

hierarchy corresponding to 6 ~ a and virializing at a given redshift z, canonical scaling laws (Peebles 1974, White 1982) are as follows: the density scales like the universal background, p oc p\j{z)\ the size

Rc oc M J 5 + ^ 6 , the specific energy while the mass scales like

^

a

^1-n)^

M c (z)oc(l + * ) - 1 / ° .

(2)

Values of the index n in the range —3 < n < 1 preserve with increasing mass a sequential increase of the specific energies and of the collapse epochs. Such a sequential development, however, is much too rigid to account for the observed spreads in galaxy and cluster formation epochs: e.g., Coma is considerably more massive than Virgo, yet it looks more relaxed. So variances and dispersions are of crucial importance for a HCS to work. One kind of dispersion is embodied in the distribution p(6\M) for the overall linear overdensities. The N-body simulations add specific information concerning the nonlinear effects of small-scale inhomogeneity in the initial conditions, corresponding to sequence II with its feedback onto sequence I. Numerically one can follow how the gravitational instability amplifies statistical inhomogeneities or fine-grained correlations in the initial conditions to form macroscopic substructures, and how the feedback of extensive subclustering slows down the overall collapse. In fact, in a numerical ensemble of protoclusters of a given mass Cavaliere et al. 1986 found the effective collapse times to span a wide range (by factors up to ~ 5), the more clumpy objects being generally more delayed; this converts to a broad morphological range at the present epoch. Equivalently, the variance of the mass distribution at a given epoch may be enhanced over and above the contribution from the linear p(6\M). In fact, some runs in the ensemble were found to hang on in unevolved configurations similar to A1367 for many canonical crossing times when other runs, differing only in the realization of the initial noise, were already well relaxed. Such sparse, unevolved configurations as represented in Figure 1, where the definition of a "core radius" loses meaning, approached the frequency of the well relaxed ones at epochs corresponding to the present. At moderate look-back time they were considerably more frequent in the simulations: in the real world, they may require planned searches even in X-rays. Bimodal configurations constitute a limiting inhomogeneity. These developed in a fair percentage (another £ 1/3) of the runs by Cavaliere et al. 1986 often with a long lifetime, providing models for such objects as A548 traced by Geller and Beers 1982, and A754 discussed by Fabricant et al. 1986. As noted by Fitchett 1988, with definite knowledge of the dynamics of bimodal systems (see Figure 2) it should be possible to determine subcluster masses from a large sample of bimodal clusters with velocity differences measured between the components. In the rest of the ensemble, the amount of mass in any subclump was quite less than 50% and the contrasts were much smaller. X-ray mapping of such substructures is favoured by two circumstances: the ICP is a continuous medium in local equilibrium, as opposed to discrete galaxies with their small numbers and possibly anisotropic velocities; in addition, the emission density oc n selects or stresses physical ICP density bumps out of random galaxy superpositions. These circumstances may help sorting out substructures that optical tracings signal but sometimes spectroscopic evidence does

46

A. Cavaliere and S. Colafrancesco

•:«v" :t

J»"

I

I

"' I

Figure 1. A cluster of intermediate age from the simulations of Cavaliere et al. 1986. Frame size: 8 Mpc. Some outlying emission of low surface brightness is swamped by the background noise. not confirm, as discussed by Geller 1988, Dressier and Shectman 1988, Oegerle et al. 1989. The simulations outlined above started from approximately white-noise initial distributions corresponding to n ~ 0, which yields a realistic upper bound to the variance. West et al. 1988 have evolved initial conditions from power-law spectra with n values down to —2, close to the opposite bound within the HCS. At the present epoch (in principle defined by the universal clock provided by the time dependent galaxy correlation function as suggested by Davis and Peebles 1983, in practice contending with wiggles in the computed slope and uncertainties in the observed correlation length by factors ~ 2, cf. Geller 1988) they found a larger proportion of centrally smooth systems, but also rich substructure exterior to a few Mpcs. In comparing results from different spectra but with a fixed amplitude at 10 M Q , various effects of n(M) should be discerned: n smaller on nearly galactic scales means less initial noise to seed substructures; smaller n on group scales implies specific energy increasing more steeply with M, resulting in faster erosion of clumps (beginning with the inner ones), but also in less effective mergings between comparable subclumps; n smaller on cluster scales implies - apart from any substructure feedback - closer time scales for the collapses and, faster evolution. AH that may balance to weaken the branch II and to stress the accretion-like mode onto a dominant core. On the other hand, a lack of substructure in simulated clusters could be caused by miscalibration of the simulation time to an epoch in our future, as noted by Fitchett 1988. In the balance, the morphologies derived from simulations implementing the canonical HCS may agree with the observations, given "enough" fine scale inhomogeneity in the initial conditions. But many specific questions remain open for numerical experiments: What minimal amount of initial noise is needed to generate the morphological variance and substructures as observed locally? The answer requires determining the cosmic time of the simulations (including bias effects) to better that 25%, and calibrating the initial perturbations as for their profile, power spectrum (e.g., by the elegant method of Bertschinger 1987), and dark matter content. What shapes and brightness are to be expected for the distant condensations, which the X-ray survey planned from

Cosmogony with Clusters of Galaxies

s. a

IB.

e

is. e

20. e

23. a

3e. e

35. e

TiriE _ _ _=L0BEl;

=L0BE2

TIME _=LOBE1; _ .=BIL0BE; _

=L0BE2

.=BIL0BE;

CO

Figure 2. Dimensions (separation and sizes, unit: 0.8 Mpc) and 3D velocities (relative and internal dispersions, unit: 2100 km/s) for the two dominant clumps during a bimodal configuration. Time unit: 1/3 Gyr. ROSAT (c/. Triimper 1988) may catch in the making? The answer depends again on whether a merging or an accretion-like evolution prevailed, with a large dispersion in

48

A. Cavaliere and S. Colafrancesco

the former case. We are testing the following evolutionary scenario: the design of the (transient but often long lived) cluster structure ought to be imprinted by the granularity of the total mass on small scales. In the subsequent evolution much of the matter may be stripped away and diffused throughout the system, little affecting the forming substructure. But the final distribution of the optical M/Lo may settle under the effects of slow dissipation (cf. Evrard 1987 vs. West and Richstone 1988) and of continuing infall of darker matter from the environment. In the next Sections, statistical implications of infall will be explored.

3. THE SEARCH FOR A MASS FUNCTION Another outcome from N-body experiments is a mass distribution for the clumps: the indication by Efstathiou et al. 1988 that N(M) -> Af~2 at the low end, albeit close to their resolution limit, is interesting as it puts considerable strain on theories of hierarchical clustering that suggest flatter slopes. Models of hierarchical clustering that attempt to include non-linear collapses end up in mass distribution functions (MFs) of Schechter-like form (3) N(M,z)dM oc p(z)M~1(z) f(m)dm, f(m) = m " r c" 1 " 6 with the mass m normalized to a unit proportional to Mc. This general structure is that expected on dimensional grounds, and the form of f(rn) quantifies the notion of a wide distribution with considerable weight (modulated by F < 2) at the high-M end before a cutoff (modulated by 0 ^ 1). In fact, Press and Schechter (1974) obtained a MF of the above form with F, 0 specified in terms of initial conditions, based on a two-step derivation. A golden rule N(M, z)MdM = —dF is assumed to relate the mass density of clumps just in the range M — M + dM with the differential of the fractional mass in all objects gone non-linear by the redshift z. An ansatz for F suggests adding up the independent volumes of size Re, and mass Ms oc pRg, wherein the mean overdensity exceeds a threshold of non-linearity 6C ^ 1: F(Ms,z)

oc p f°°dv e-" 2 /2 .

(4)

JVc

The mass appears explicitly only in the limit vc = 6c/
Cosmogony with Clusters of Galaxies

^9

Closer to dynamics is the other ansatz taking up the expectation that collapses ought to start at definite peaks in the density field rather than occurring in random overdense volumes. Such collapses ought to be governed by the topology and the average geometry of peaks in a noisy background as discussed by Doroshkevich 1970, and by Bardeen et al. 1986 (similar, by the way, to the bidimensional effect illustrated by Figure 2). In terms of the peak density Afp after smoothing over a length R8 the mass fraction is given by

j™v

Mp{v) M{v,t) .

(5)

The full expression of Afp(v), given by Bardeen et al. 1986, describes a dearth of small, isolated maxima, and in the important range v ~ 1—0.2 it declines approximately like up exp[—u/2], with p ~ 1.5. The MF derived with the use of the golden rule or its equivalents as indicated by Bardeen et al. 1986 or used by Bond 1989, is still of the form of Equation (3) but flatter, if anything, than Press-Schechter's result down to M ~ 10~ 2 M c : in this range the slope may be approximated with T ~ 2 — a(p + 1). This implies N -> M~lb for CDM, assuming M ~ M8. Actually, the range of gravitational influence for a peak is sensitive to its height (Doroshkevich 1970, Ryden 1988, Scaramella 1988), and the mass that can infall from the surrounding, simply connected region onto a primary peak asymptotes to M ~ M8v^a. For v & \ the index a is close to 1/2, implying small masses; but for v > 1, a may be up to & 2/(n + 3), setting to halos an upper limit approached in conditions of extreme coherence, i.e., in a homogeneous isotropic, high density background with noise maximally smoothed over scales larger than Rs during the collapse. Then at given 6 = 6C, the high-// halos would asymptote to M = Ms m , with the upper limit corresponding to 3e*a = 1. So in the limit of instantaneous collapse and infall, the MF suggested by a simple peak theory for the cores (here to mean the central few Mpcs), or for the halos, looks unrealistic at either small or large M. But the infall develops t'n time and the build up of high-f halos may compete with new cores collapsing on the current scale tc ~ Mc/Mc. To progress, we propose to break the limit of instantaneous collapse and introduce explicit secular changes. A dynamical approach may be started from rewriting comoving MFs of the class given by Equation (3) in the form dN/dt = N/T+ - N/T-

(6)

that contains an M-independent time scale r_ = Mc (the number of lower M produced during tc is considerable in absolute terms but small relative to N(M))\ and destruction of previous generations on the scale r_, which dominates at the low end. Guided changes of these time scales modulate the MF. For example, the formal limit of long persistence or large T_ tilts the MF towards N(M) —• M at the low end. In general, the shape and time scales for MFs of the form of Equation (3) are linked by the following relationship:

50

A. Cavaliere and S. Colafrancesco dlnN/dlnM = - 2 - tc/t dlnN/dlnt .

(7)

Equation (6) - at variance with the Press-Schechter approach - represents the MF at a given z and low M as a superposition of objects produced mainly with M J£ Afc(z,) at previous epochs z,-, which partly survive reshuffling into larger clumps. But survivors grow by progressive infall from the local environment, and are shifted toward higher masses. The MF may then be tilted to a steeper slope, depending on a finite accretion rate of the once leading masses. Figure 3 represents the effects of contmuing infall from regions with signal (peak) to noise ratio S/N £ 1 onto the cores formed at earlier times t,-, computed using N(M,t)dM = = f/

Jim Jim

dt dti{ dMi(dN/dt)i .

(8)

The collapsed mass fraction including halos increases, with a steeper distribution, up to Fp ~ 0.9 when Daa = 1 (where D is the effective dimensionality—see later) and n->-1.8.

-5

-10

-2

-1 0 Log M/M o

Figure 3. The mass functions for cores collapsed at density peaks (dashed line), and for maximal halos (continuous line), are compared with that from the full Press-Schechter theory (dotted line). Here and in the following: CDM spectrum, threshold Se = 1.33, Qo = 1. Here we adopt b/B = 1.5.

Cosmogony with Clusters of Galaxies

51

The number of low mass objects may be increased by additional cores arising from constructive superpositions of smaller sub-threshold volumes: an upper bound may be estimated granting priority to the peak collapses, but adding a maximal collapse chance Fps/2 to overdense random spheres in all the truly residual volume. This means using the golden rule F = Fp(M) + (1 — Fp)Fps(M)/2. A large infall may dominate the statistics of added collapses in the MF. To fix the realistic size of the halos Cavaliere and Colafrancesco (1989, in preparation) first re-interpret in terms of energy-like conditions the geometrical S/N £ 1 definition of a gravitational range. Thus the asymptote is seen to be set by any breakdown of the homogeneity, isotropy and high density conditions in the environment of the accreting objects; such breakdowns are implied by the transient cellular structure delineated by Doroshkevich (1970) and by Shandarin and Zeldovich (1989) on the basis of quasilinear deformations rather than linear overdensities. By the time taken for the potential associated with a peak to draw mass inflows from large radii, other potentials on comparable scales (albeit in their quasilinear regime) exert a long-A forcing (% oc 6%k~*) of the flows into filaments or sheets (with intervening voids), setting to infall an effective dimensionality D < 3 on large scales. The upper limit is decreased to Daa < 1 if on halo scales n > —OAD holds. A limit Daa £> 1/2 holds in subcritical conditions. The shape of the leading edge of the MF, on the other hand, is very sensitive to the selection of these objects. To demonstrate this sensitivity, consider that linear bias in the simple form a oc b~ < 1 competes with non-linear delays introduced by small-scale substructures: to lowest order, this may be represented with a dispersion increased by a factor B i£ 1, to yield a cutoff oc exp[—(6/B)2m2a/2]. In addition, given the average collapse threshold 6C, soft clipping of the kind envisaged by Szalay 1988 and by Bonometto and Borgani 1989 may further soften the cutoff. 4. LOCAL LUMINOSITY FUNCTIONS Over and above the complexities in determining the parameters F (slope) and 0 (cutoff) in the basic form of Equation (3), one general point that emerges is that the local MF will contain some time-integrated information relevant to cosmogony, especially when effects of finite time are important. The next question is, how these features are reflected in the luminosity functions (LFs). In the optical band, the mass-to-luminosity ratios show an apparent increasing trend M/Lo ~ Me with a slope e ~ 0.3, cf. Hoffman et al. 1982; such a trend is consistent with an overall density at the critical value. This implies some steepening of the optical LF relative to the MF, namely

N(L0) oc 4-r+0/d-0.

(9)

The result for the core LF falls short of existing data for groups (see Figure 4), but only marginally considering that the actual uncertainties may be larger than the formal errors (Figure 4). In X-rays, instead, a flattening is expected because Equation (1) yields M/Lx oc g~ M~ ' . For the LF of cores localized around peaks the flattening is considerable: N{LX) = N(M)dLx/dM -+ L"?, (10) with 7 = 0.75(F + 0.3) that takes on the value ~ 1.4 for CDM. Compared with the observations by Johnson et al. 1983, and Kowalski et al. 1984, this is too flat - see

52

A. Cavaliere and S. Colafrancesco

-5

-

2

.3

L V /1O 1 3 L G Figure 4. 7Vie optical luminosity functions for cores collapsed at peaks with M/L = 200 (dashed line) is compared with that for halos (Daa = 1, continuous line), assuming a considerable mass fraction to be visible with M/L oc M"'3 (see discussion in the text). Data points from Bahcall 1979, with the rich cluster luminosities shifted as shown by the triangles to convert to luminosities at given contrast. Figure 5. Note that the X-ray emission tends to enhance the inner regions, so that the mass sampled is not necessarily the same as in the optical. We are examining the "visibility" of the halos, and the prospects are as follows. In the optical, halos to be relevant must be flatter than p oc r~^ + e (which is likely, cf. Ryden 1988 and references therein), and old, so as to stand out against the background. In X-rays, where the background is essentially given, the brightness distribution may remain marginal in spite of a ICP disposition flatter than that of the galaxies (the /? models again); in any case, low brightness halos in the local objects call for wide

Cosmogony with Clusters of Galaxies

53

apertures. On the other hand, accreting halos may cause a secular increase of the central h (t); similar increasing trends are seen in N-body experiments, but they are sensitive to physical, and also to numerical, dissipation. Note that a further flattening of the X-ray LF may be associated with a varying ICP fraction. Indications that MjM = g ^ constant holds, come from comparing galaxies accessible to detailed X-ray mappings that contain or retain only a small ICP mass compared with the mass in stars M/M* & 10 (c/. Fabbiano 1988), with rich clusters where the ratio is quite large, up to values ~ 5 (Blumenthal et al. 1984). Clearly at some intermediate scale or formation epoch more diffuse baryons (relative to those bound into stars) are to be differentially produced, retained or engulfed in the deepening and enlarging potential wells. Because stars, once formed under a reasonable IMF, return on average £> 1/2 of their mass in diffuse baryons, engulfing or infall is bound to dominate eventually, and is likely to concern "failed" galaxies. Considerable dilution by material of primeval composition is required anyway to maintain the definitely subsolar composition observed in the ICP, starting from the high yields of leading stellar evolutionary models (cf. reviews by Matteucci 1989, Giannone and Angeletti 1989). Quantitative indications for M in the range from groups to clusters are obtained by David et al. 1989 (and concurringly by Oemler, private communication), who find the ratio within a fixed radius to increase by a factor ~ 4. Now, there may be a size dependence g(M) or an epoch dependence g(t). A limit to a pure size dependence q(M) ex MJJ is given by n ~ 0.3. In fact, the total X-ray luminosity follows Lx oc M ' + ** oc JV^ ' (where JV^ = number of galaxies within the Abell radius, see Kaiser 1986); comparing with the data collations by Bahcall 1979b, Mushotzky 1984, the resulting upper bound is n £> 0.4. A size dependence g oc M * would further flatten the slope of the X-ray LF by an additional 0.2.

5. X-RAY CLUSTERS IN REDSHIFT SPACE The ICP content may have a primary epoch dependence, g(t). The issue is best discussed in comparison with a reference baseline, provided by non-evolutionary cluster sources distributed homogeneously in look-back time. To represent empirically the X-ray local data one can use a Schechter-like function, N(Lx)dLx

oc A f - ^ - T e " * it

(11)

with Lx normalized to a unit proportional to Lc oc pc Mc ; the slope consistent with the data by Johnson et al. 1983, Kowalski et al. 1984 is 7 ~ 1.7 - see Figure 5. If one assumes the LFs at higher z to be invariant with constant normalizations Mc and Lc, the expected number counts and z- distributions are as given in Figures 6 and 7. Note how - given the evolution, no evolution in this particular case - both these integrals over the distant LFs depend on their shape because the objects observed in a flux-limited survey "slide" down the LF with increasing redshift. Can we expect the invariant case to be realistic? Actually, any HCS for the formation of cosmic structure implies strong changes outside the local environment; specifically, it implies strong changes of the density-evolution type along with some luminosity antievolution (Kaiser 1986). This is because the HCS holds the same amount of mass to be reshuffled into larger and larger units along the cosmic arrow of time. As we look back, we expect to see more numerous, smaller units, that are also denser and cooler, see Equation (2). Thus the opposite behaviours of p(z), M(z) tend to cancel each

54

A. Cavaliere and S. Colafrancesco

o

-8

-10

Figure 5. The local X-ray luminosity function fitted with the empirical Schechter-like function given in eq. 11: 0 = 1 and 7 = 1.7 (dotted curve). We also show the LF for cores collapsed around peaks (dashed curve). Here and in the following figures. b/B = 1. Data points from Kowalski et al. 1984- Luminosity unit: 10 erg/s in the range 2 — 6 keV; vertical unit: # Mpc~ 3 /10 44 erg s~l. other out of the X-ray emission, and if a = constant is assumed, one expects a weakly decreasing Lc(z) <x (1 + z)( 5 + 7n )/ 2 ("+ ; 0. Correspondingly, the comoving LF behaves scale-invariantly as given by N(Lx,z) K

oc M-\z)L-\z)

/ ( / ) oc (1 + zf

= [7 + 5 7 + 7n( 7 - l)]/2(n + 3)

(12)

(Cavaliere and Colafrancesco 1988). Figures 6 and 7 include representations of number

Cosmogony with Clusters of Galaxies

55

Eh

A

-2

-1

Log F/F_ 12

Figure 6. Integral counts of X-ray clusters for representative evolutions of the empirical Schechter-like local LF of previous figure: A) homogeneous distribution in redshift; B) scale-invariant evolution of the luminosity function, corresponding to the approximate Equation 12; C) epoch-dependent ICP content g(z) ~ (1 -f z ) ~ 1 2 . Curve D) shows instead the scale-invariant evolution of the LF for peaks. Preliminary counts from the EMSS of Gioia et al. (1988) are also shown. Flux unit: 10 erg/s cm in the range 0.3 - 3.5 keV; counts: # sr'1. counts and ^-distributions under these conditions. To what extent does the scale-invariant limit hold? Actually, we have already mentioned indications that the ICP content may vary or change. Within the limits derived in the previous Section for a pure size dependence, the alteration to the scaleinvariant evolution is small. Epoch dependence can be effectively tested at z ^ 0.5. Cavaliere and Colafrancesco 1988 considered an average dependence g(z) oc (1+z)" 3 ^/ 2 . In the limit of constant time-rate £ = 1, it follows that g (z) oc p~ (z) cancels the dependence p(z) from the emission and gives way to the strong decrease of Mc(z). The result is the addition to the exponent K in the previous equation of a negative AK = —3£(7 — 1), which implies counts considerably flatter, and z-distributions cut off faster than by the mere sliding down the LF. Figures 6 and 7 illustrate the difference between these alternatives, computed numerically to include relevant details. Cavaliere and Colafrancesco 1988 discuss the robustness of these behaviours of the counts and zdistributions: in particular, it is plain that a flatter shape of the LF may well flatten the counts at medium and low fluxes, but cannot sharpen the decline in the z-distribution. Note that an epoch dependence g(z) converts to an apparent size dependence, since groups and clusters of richness 0 are on average smaller and older as well: on the basis of Mc(z) from Equation (2), the equivalence is given by rj = 3a£/2 ~ 0.3. To wit, typical groups formed at z ~ 2.5 would have an ICP content smaller by (1 + z)~ 1 °/( n + 3 ) compared with rich clusters, in accord with the result of David et al. 1989.

56

A. Cavaliere and S. Colafrancesco 1

1

1

1

! ^ a)

,

_r

c -1 i...

"1

->—I

—1_

-

b)

D ....... r-

—L_J

I

j 1

.5

1

1

11

B i

i

i

1.5

Figure 7. The redshift distributions corresponding to Figure 6, to the flux level of 10" 1 3 erg/s cm2. Refinements of the selection procedure for cluster sources from the EMMS (Gioia et al. 1987), or the new survey planned from ROSAT, will discriminate between these evolutionary patterns.

6. CONCLUDING REMARKS Epoch dependence of the ICP content may be expected in a biased HCS. This is because stellar time scales may well start and govern the first build up of the ICP, in regions of high total overdensity where galaxies can condense and star formation is efficient. But with the progress of the clustering, the deeper and larger potential wells accrete or engulf regions originally underdense on large scales; there galaxy formation is delayed and star generations are hindered by sub-threshold conditions, so that the content in diffuse baryons of primeval composition remains high. After such failed galaxies are engulfed into the hot ICP, star formation activity is permitted to resume only in localized cooling flows. A dearth of early ICP will maintain the cooling time comparable to the age, and so preclude early pervasive cooling flows with a large soft X-ray emission. It also implies

Cosmogony with Clusters of Galaxies

57

statistical Sunyaev-Zel'dovich effects somewhat less than the canonical estimate, cf. Cole and Kaiser 1988, because the dearth would be already effective at z ~ 0.5. The other implication is a metal abundance diluted toward us, in particular a decreasing equivalent width of the Fe lines. To sum up, we have stressed that linear perturbation theory may be well defined (e.g., the CDM spectrum depends specifically on the normalization o~o[8Mpc] = b ) but non-linear dynamics introduces many complexities. Some of these are welcome, like the increased variance that within the HCS may yield in priciple a range of morphologies as wide as observed. But specific models with little power on small scales, like CDM, may have a hard time in achieving this. This is an area still open to calibrated N-body experiments. As for the luminosity functions, these complexities require more parameters to enter the theories, to reflect such important features as sites and actual masses of successful collapses (including secondary infall), or the feedback of internal substructure and ambient geometry (including the effective dimensionality of the collapses). At the bright end of the luminosity function, where today rich clusters lie, the effects of non-linear variance or soft clipping may counteract those of linear bias: the relative abundances of these rare objects are particularly sensitive to the balance. Here stands another crucial knot for ensemble N-body experiments to disentangle. At the faint end, for poor clusters and groups, we see requirements for steeper luminosity functions especially in X-rays, relative to the predictions by a simple peak theory. A concurring indication for the mass function comes from the N-body experiments. Added collapses (and persistence), or added age-dependent mass, constitute possible solutions. We have explored effects of infall, which is inevitable with gravitational instability, and is now directly observable around rich clusters (see Regos and Geller 1989). Infall is conceivably enhanced by spectra flat towards small masses in a flat universe. The associated steepening effect looks interesting for the MF, possibly also for the optical LF, but not necessarily so in X-rays, unless numerical experiments prove flat brightness distributions or a stimulated increase of the ICP central densities. We end by noting that delays associated with non-linear dynamics (and bias) may further enhance the appreciable amount of groups still forming today in the timeresolved picture we propose. In these terms one could understand the finding by Hickson et al. 1988 of a population of compact, but dynamically unevolved groups. We are grateful for many discussions to S. Matarrese and N. Vittorio, and especially to R. Scaramella for fruitful exchanges.

REFERENCES Arnaud, K.A., Johnstone, R.M., Fabian, A.C., Crawford, C.S., Nulsen, P.E.J., Shafer, R.A., and Mushotzky, R.F. 1987, M.N.R.A.S., 227, 241. Bahcall, N.A. 1979, Ap. J., 232, 689. Bahcall, N.A. 1979b, Ap. J. Lett., 232, L83. Bardeen, J.M., Bond, J.R., Kaiser, N., and Szalay, A.S. 1986, Ap. J., 304, 15. Bertschinger, E. 1987, Ap. J. Lett, 323, L103. Binggeli, B., Tammann, G.A., and Sandage, A. 1987, A.J., 94, 251. Blumenthal, G.R., Faber, S.M., Primack, J.R., and Rees, M.J. 1984, Nature, 311, 517. Bond, J.R. 1989, in Large Scale Motions in the Universe, Rubin V.C. and Coyne G. eds., Princeton: Princeton University Press, p. 465.

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Bonometto, S., and Borgani, S., 1989, preprint. Cavaliere, A., Gursky, H., and Tucker, W.H 1971, Nature, 231, 437. Cavaliere, A., Santangelo, P., Tarquini, G., and Vittorio, N. 1986, Ap. J., 305, 651. Cavaliere, A. 1980, in X-ray Astronomy, R. Giacconi and G. Setti eds., Dordrecht: Reidel, p.217. Cavaliere, A., and Colafrancesco, S. 1988, Ap. J., 331, 660. — 1989, in Large Scale Structure and Motions in the Universe, M. Mezzetti et al. eds., Dordrecht: Reidel, p.73. Cole, S., and Kaiser, N. 1988, M.N.R.A.S., 233, 637. David, L.P., Arnaud, K.A., Forman, W., and Jones, C. 1989, preprint. Davis, M., and Peebles, P.J.E. 1983, Ap. J., 267, 465. Dekel, A. 1989, in Large Scale Motions in the Universe, Rubin V.C. and Coyne G. eds., Princeton: Princeton University Press, p. 465. Doroshkevich, A.G., 1970, Astrophysica, 6, 320. Dressier, A., and Shectman, S.A. 1988, A.J., 95, 985. Efstathiou, G., Frenk, C.S., White, S.D.M., and Davis, M. 1988, M.N.R.A.S., 235, 715. Evrard, A.E. 1987, Ap. J., 316, 36. Fabian, A.C. 1988, in Hot Thin Plasmas in Astrophysics, R. Pallavicini ed., Dordrecht: Kluwer, p.293. Fabbiano, G., 1988, preprint. Fitchett, M.J. 1988, in Proc. of the Minnesota Astrophysics Lecture Series Large Scale Structure and Its Relation to Clusters of Galaxies. Fitchett, M.J., and Webster, R. 1987, Ap. J., 317, 653. Forman, W., and Jones, C. 1982, Ann. Rev. Astr. Ap., 20, 547. Geller, M.J. 1988, in Saas Fee Lectures, Large-Scale Structure in the Universe, Martinet L. and Major M. eds., Sauverny: Geneva Observatory, p.69. Geller, M.J., and Beers, T.C. 1982, P.A.S.P., 94, 421. Giannone, P., and, Angeletti, L. 1989, preprint. Gioia, I.M., Maccacaro, T., Morris, S.L., Schild, R.E., Stocke, J.T., and Wolter, A. 1988, in High Redshift and Primeval Galaxies, J. Bergeron et al. eds., Paris: E. Frontiers, p.231. Gunn, J.E., and Gott, J.R. 1972, Ap. J. 176, 1. Gott, J.R., and Turner, E.L. 1977, Ap. J., 216, 357. Hickson, P., Kindl, E., and Huchra, J.P. 1988, Ap. J., 331, 64. Hoffman, Y., Shaham, J., and Shaviv, G., 1982, Ap. J.. 262, 413. Johnson, M.W., Cruddace, R.G., Ulmer, M.P., Kowalski, M.P., and Wood, K.S. 1983, Ap. J., 266, 425. Kaiser, N. 1986, M.N.R.A.S. 222, 323. Kowalski, M.P., Ulmer, M.P., Cruddace, R.G., and Wood, K.S. 1984, Ap. J. Suppl., 56, 403. Lucchin, F., 1988, Morphological Cosmology, P. Flin ed., Lecture Notes in Physics, 332, p. 284. Matteucci, F. 1989, preprint. Mellier, Y., Mathez, G., Mazure, A., Chauvineau, B., and Proust, D. 1988, A. A. 199, 67. Mushotzky, R.F. 1984, Physica Scripta, T7, 157. Oegerle, W.R., Fitchett, M.J., and Hoessel, J.G. 1989, A.J., 97, 627.

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Peebles, P.J. 1974, Ap. J. Lett. 189, L51. Peebles, P.J. 1980, The Large Scale Structure of the Universe, Princeton: Princeton University Press. Press, W.H., and Schechter, P. 1974, Ap. J., 187, 425. Regos, E., and Geller, M. 1989, A. J., 98, 755. Ryden, B.S., 1988, Ap. J., 333, 78. Sarazin, C.L. 1988, X-ray Emission from Clusters of Galaxies, Cambridge: Cambridge University Press. Scaramella, R. 1988, Ph.D. Thesis at S.I.S.S.A. Schaeffer, R., and Silk, J., 1988, Ap. J., 332, 1. Shandarin, S.F., and Zel'dovich, Ya. B., 1989, Rev. Mod. Phys., 61, 185. Szalay, A., 1988, Ap. J., 333, 21. Triimper, J. 1988, in Hot Thin Plasmas in Astrophysics, R. Pallavicini ed., Dordrecht: Kluwer, p.355. West, M.J., Oemler, A., and Dekel, A. 1988, Ap. J., 327, 1. West, M.J., and Richstone, D.O. 1988, Ap. J., 335, 532. White, S.D.M. 1982, in Morphology and Dynamics of Galaxies, Martinet L. and Mayor M. eds., Geneva: Geneva Observatory, p. 289.

DISCUSSION Peebles: You showed us the results of N-body simulations in which you reproduced remarkably well the bimodal structures seen now in some clusters, both in the X-ray and galaxy counts. How would such an object look at a redshift of 1? Cavaliere: I would say, more fragmented and more sparse. Peebles: What is the effect of that as an X-ray source? Cavaliere: That depends on the brightness selection or brightness bias. Giacconi: The answer is certainly yes. The subclumps are denser and of higher surface brightness. Cavaliere: Not always, there is a point here which I would like to stress. These are bimodal configurations at earlier times. Felten: Would you say what the time sequence is in these plots? Cavaliere: Yes. We are seeing here three different projections at two different times. These are at three time units, and twenty-three time units, like ten Gyr from the beginning. The other question was, how that would be observable in X-rays? And this comes back to the figure that I show you (see Figure 2). So it is true, Riccardo, that

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a typical condensation would have a large surface-brightness, but the point that I am trying to make is that there is a large variance, so along with some typical condensations there are also many marginal ones. Those are subjected to what I call the brightness bias, which is strong because it is nonlinear, proportional to the density squared. So one is almost certainly bound to underestimate observationally the number of objects at earlier times in X-rays. Not to mention the other point that the amount of gas relative to the dynamical mass may have been less at those times than it is now: that is a separate issue. Fitchett: Many people have claimed that the bimodal structures that we have seen in simulation are well described by a linear orbit model. Is this actually accurate or do your structures persist for so long at maximum expansion that this doesn't fit? Cavaliere: We produced a number of plots which illustrate the run of the relative velocities of the two components. We found that in a typical bimodal run these are not badly off the data for A98, for example. We never published these results. Fitchett: I wanted to make the point that what is interesting is that the relative velocities observed for known bimodal clusters are small, and if you are observing these systems at a random orientation and time you would expect to see some large velocities. Cavaliere: So you mean that an interesting point is the velocity vs. time. That's right, I'll try to dig out those results for the Proceedings. Sandage: In both Virgo and in Coma we have evidence for substructure and it is very strong optical evidence. What is the X-ray distribution? Is it spherically symmetric about a center, or do you have two lobes? Cavaliere: Do you mean the observed or simulated X-ray distribution? Sandage: The observed. Cavaliere: There are people in the audience that know this more directly than me, but I just mention that there is a slight hint of an ellipticity in the Coma distribution of X-ray luminosity. As for the simulations, I stress the following point. In some numerical runs, it happens that even when you don't have a very strong bimodal configuration and you have only a hint of dumpiness at very early times, later on when the thing appears at a first look as a sphere, if you go to examine the simulated X-ray maps you will still find a trace of inner asymmetry. It is usually weak, ellipses with axial ratios 1.5 to 1 or something like that. Sandage: Why is it in Virgo where we have very strong evidence for two clusters the X-ray emission is spherically symmetric only about one. Cavaliere: Can some X-ray observer comment on Virgo? Mushotzky: There is X-ray emission centered around 4472. The surface brightness is low enough that it can't be that far away from the galaxy. The main emission is centered around M87 and the surface brightness is high enough to be well mapped out to a large angular scale.

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Sandage: How about in Coma? Mushotzky: In Coma, as Cavaliere said, it's elliptical and I don't remember exactly, but it is roughly about 0.6 elliptical. And then again, the angular scale is such that the Einstein data is not mapped as far out as the galaxies. Rhee: I have a question about the theoretical prediction of the frequency of occurrence of substructure in clusters, because from what I heard this morning, it is about 40% or less. And it seems that West using a rather rigorous approach starting with Gaussian fluctuations and then fixing the normalization using the amplitude and slope of the correlation function doesn't find evidence for the substructure today and yet you do, in your simulations, using rather more simple initial conditions. And I was wondering how simple your results are. There are things you didn't mention such as how you start your simulation at l/6th of the turn-around radius with 500 particles, and what I meant about the initial conditions is how sensitive are your results to those two parameters? Cavaliere: When speaking about substructure, I think that we must divide the subject into two parts: large scale substructure, with separations of the order of megaparsecs or more, and probably here everybody agrees that such things do exist in the simulations and do exist in the real world! And the small scales, very sensitive to the initial conditions, as I said. Now, here there are a number of contrasting facts. First of all, observationally there have been contrasting claims: Margaret Geller this morning has reviewed this matter and I will say no more on that. As for the simulations, there are discrepancies also there. Now, when you take n ~ 0 initial condition, simple random extraction from a uniform sphere, you overplay the small scale non-uniformities, that is, you put much power on small scales. So the small scale dumpiness in these simulations is emphasized. On the other hand, looking at the simulations by Efstathiou et al. or by West et al. , even they have some small scale substructure. Now, the point is semantic to some extent. That is, what do you define as substructure, what level of Ap//>, or mass of the largest subclumps compared to the total mass, do you call substructure? Even the substructures appearing in white-noise simulations, apart from bimodals, often consist of clumps with mass much smaller than the total, of order 10 % or so. So, this involves a threshold in a continuous distribution depending on n—some small scale substructure arises in all simulations and the thing that really varies is the contrast. The average mass fraction in the second largest clumps or so is enhanced in simulations with n ~ 0. My summary of the numerical experiments is that the merging mode of evolution is emphasized by initial white noise, while accretion of small subclumps onto a dominant one prevails for spectra flatter toward low masses. Oemler: Wouldn't it be fair to say that you have found more of the sort of binary structures for separations of the Mpc scale or so, than we found in our simulations? Cavaliere: Do you have a statistics? How many of your simulations do show bimodals? Oemler: Not many — 5 or 10% . Cavaliere: Whereas we have on the order of 20-30%. Another point is, how do you gauge the present time in your simulations. Oemler: It's normalized by the correlation function.

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Cavaliere: Do you notice in your simulation that the proportion of bimodals is strongly decreasing with time? Oemler: What's the answer to that, Mike? West: I'm going to address this in my talk. Oemler: Maybe we should wait until after Mike talks to answer that. Peebles: Could I ask how you handle the dark mass? Cavaliere: As a matter of fact, the dark matter is not included in these particular simulations. Peebles: Would it not worry you, for example, that the number of particles in those very small clumps is not large, perhaps 10. And, therefore, two body relaxation might be excessively over emphasized in the simulations as well as in the real world. Cavaliere: The two body relaxation should be coped with anyway by the appropriate choice of the softening length. This is generally on the order of 30 kpc for our simulations. Peebles: If you doubled the number of particles, would you reproduce the structure or would it look different? Cavaliere: We tried that, with the E4 simulation for example, and the structure persisted. There might be another point to consider—the settling of the galaxies relative to the dark matter caused by dynamical friction or energy absorbed into internal degrees already mentioned here. That might be a possible way of making more compact cores and hence a more visible X-ray emission. However, the amount of baryons relative to dark matter then is a very crucial parameter, the effect in the general potential would be very different if that fraction changed. Huchra: One thing that I want to say sort of in response to Allan's question but also in reference to people who like to make X-ray maps of clusters. If you look at the Virgo cluster there are indeed two very dense clumps of galaxies—one centered on M87, one centered on 4472. They have roughly, within a factor of 2, the same total luminosity in galaxies. But one is a relatively strong extended X-ray source and the other isn't. The one that isn't has a velocity dispersion of only about 450 or 500 kilometers per second, the one around 4472, whereas the one around M87 is 300 or 400 kilometers per second higher, about 800 kilometers per second. And the X-ray emission is going as a relatively strong power of the temperature, and the velocity dispersion is a measure of the temperature, which is what a lot of people are saying. I don't think it's crazy to say that this could mean that low velocity dispersion clumps like you might see in your simulations don't show up in X-rays because the temperature for the velocity dispersion is just too low. Cavaliere: Yes. Let me point out on my maps, what is mapped here is the total emission, but what you say is obviously very true once we are in an observational window. For instance it would be interesting to compare ROSAT with Einstein and see

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what the difference is. Sandage: May I ask you if it is fair to say that any cluster that you see clumps or subclusters, that cluster is in the epoch of its formation. Cavaliere: Well, that is a very interesting point. That is related to the problem of how we normalize a luminosity function in the presence of increased dispersion. I mean that if the collapse times have a large dispersion, then what you get is a rather soft cutoff at high masses. Now, what you call a critical mass or mass being non-linear now, that is observationally influenced very much by the dispersion of your actual luminosity function. So, I would respond that indeed if an object has a very clumpy appearance, that particular object should be near the time of its formation or on the way to recollapse down for its first time, but still far from the virialization or the violent relaxation for the object as a whole. Sandage: And also, don't parts of a given cluster collapse at different rates? So, those parts that have the lowest density initially will take a lot longer to collapse, so it may be that you have an old core that was high density to begin with and then later you are having all these things raining down, which are now the spirals, which will then give you the morphology density relation. Cavaliere: As a matter of fact, if you take seriously the peak approach, you have the central peak collapsing, and then a lot of mass infalling onto it in a halo, especially with flat power on small scales in a critical universe. That infall is gradual, in fact it might take up to a few Hubble times for those objects collapsing now. Sandage: And is still going on? Cavaliere: Still going on, probably in many clusters. Some direct evidence has been mentioned Geller. Considering the distribution of halo masses, that is even more influenced by the point that I was mentioning before: the spread, or variance, is even longer for the halos than for the cores, so you are quite right. Giacconi: I wanted to go back to something that you mentioned, namely the evidence for lack of clusters at z > 0.5. Cavaliere: Please do not quote me as accepting that as final. I consider it as an intriguing but preliminary result. Giacconi: But you know those data are incorrect because they have not been corrected for the exposure time. So that in fact real data could be very different. In addition it was very difficult to detect any clusters with z > 0.5 on the visual optical material that was used to identify clusters. So, I believe the discussion about the evolution of mass of the gas is very interesting, but I think the data on which you base your comparison is nonexistent (laughter). Cavaliere: Riccardo, I fully appreciate your view. I consider those counts as a normalization, if you allow me. (laughter) But it is well understood that on ROSAT with a carefully planned survey can solve the issue and say whether there is any real dearth at z > 0.5 or not. So those results provide a motivation, if you like, for looking

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the corner and predicting what will be observed eventually. Henry: Can I make a comment on that? We are analysing the extended medium survey again, and I guess the point that Riccardo is making is that the survey detects objects at fixed angular size bins so you get different variable fractions of the emission at different redshifts, so the number count is going to be very hard to interpret and for that reason we are looking at just the luminosity function in a narrow redshift range, which will at least eliminate this problem. And, in fact, the first results we got (I didn't get a chance to discuss them yet), if anything, are a lot lower than the low redshift luminosity function. Djorgovski: What's the redshift? Henry:

0.3-0.4

COSMOGONY AND THE STRUCTURE OF RICH CLUSTERS OF GALAXIES

Michael J. West Department of Astronomy University of Michigan Ann Arbor, MI 48109

Abstract. N-body simulations of the formation of clusters of galaxies allow a detailed, quantitative comparison of theory with observations, from which one can begin to address two fundamental and related questions: Can the observed properties of rich clusters of galaxies tell us something about the cosmological initial conditions? Can we use N-body simulations of clusters to test/constrain theories for the formation of the large-scale structure of the universe?

1. INTRODUCTION A wide range of theories have been proposed to explain the origin of galaxies, clusters of galaxies, and the large-scale structure of the universe. Broadly speaking, these can be divided into two classes. Most currently popular models for the formation of structure in the universe are based on the idea of gravitational instability in an expanding universe, in which it is assumed that structure has grown gravitationally from small-amplitude, Gaussian primordial density fluctuations. A second class of cosmogonic scenarios, which will be referred to here as non-Gaussian models, appeal to other processes besides simple gravitational clustering as the driving force behind the genesis of structure. Within the basic framework of the gravitational instability picture, there are several rival theoretical scenarios that are viable at present. Depending on the the details of the cosmological initial conditions and dominant mass component of the universe, the sequence of formation of structure may have proceeded in quite different ways. If, for instance, the universe is dominated by weakly interacting, non-baryonic particles (i.e., cold dark matter, hereafter CDM) then the formation of structure is expected to proceed hierarchically from small to large scales, with galaxy and cluster formation preceding the collapse of superclusters. A similar hierarchical scenario would arise in a baryondominated universe if the primordial fluctuations were isothermal (e.g., Peebles 1980). If, on the other hand, the universe is baryon-dominated and the initial perturbations were adiabatic, or if the mass density of the universe is dominated by massive neutrinos,

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then small-scale fluctuations would have been erased prior to recombination by photon diffusion or by free streaming of the neutrinos. In this case the sequence of formation of structure would proceed from large to small scales, with the collapse of superclustersized pancakes occurring first, followed by their fragmentation to produce galaxies and clusters {e.g., Zel'dovich, Einasto, and Shandarin 1982). Hybrids of these different scenarios are also possible {e.g., Dekel 1983; Dekel and Aarseth 1984). Among non-Gaussian models, the two most popular at present are the explosion scenario {e.g., Ostriker and Cowie 1981; Ikeuchi 1981) and the cosmic string model {e.g., Zel'dovich 1980; Vilenkin 1985; Albrecht and Turok 1985). In the explosion scenario, it is assumed that there was an early generation of some unknown sort of "seed" objects which exploded at high redshifts. The ensuing shock waves would have swept up surrounding material into thin, dense, expanding shells which might have subsequently cooled and fragmented to produce a new generation of seed objects that also exploded, resulting in an amplification process that could conceivably lead to the formation of very large scale structures, with the most likely sites for the formation of rich clusters being the points where shells intersect. In cosmic string scenarios, the primordial perturbations are assumed to have been correlated, rather than uncorrelated as in gravitational instability models. Cosmic strings which might have arisen in the early universe could accrete surrounding matter to produce clusters and the largescale structure. Other non-Gaussian scenarios have also been proposed, such as the generation of structure by primordial turbulence or by radiation pressure. Discriminating between the various scenarios that have been proposed for the origin of the large-scale structure is one of the major goals of modern cosmology. Attempts to confront these theories with observations have generally tended to concentrate on largescale objects such as superclusters and voids, since these are believed to be relatively unevolved at present and hence still likely to retain some information about the initial conditions from whence they arose. However, as this article will attempt to show, rich clusters of galaxies can also provide a powerful means of testing theories for the origin of the large-scale structure. Rich clusters offer several advantages which are summarized below:

1.1 Advantages • Rich clusters have been studied for decades and so are a fairly well-observed class of objects for which a large body of observational data exists. Although it would seem that, ideally, the best way to learn about the origin of the large-scale structure of the universe would be to map the large-scale galaxy distribution using extensive redshift surveys, gathering the many redshifts needed for such an approach is very difficult and time-consuming. Furthermore, with existing samples such as the CfA and Southern Sky Redshift surveys, it is not clear that we even have a fair sample yet of what the large-scale structure is really like, since features can be seen in the galaxy distribution having sizes which span the surveyed volumes. • Clusters are believed to be dynamically young systems. This is based on such observations as their relatively low mean densities {6p/p ?« 200 within an Abell radius compared, say, to the typical mean densities of individual galaxies, which are generally two or more orders of magnitude greater) and the frequency with which substructure may appear within clusters. Because they are likely to be dynamically young and because dissipation has probably not played an important role in their

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formation, there is a chance that the observed properties of rich clusters might still reflect some traces of the initial conditions at the time of their formation and could therefore provide a useful probe of conditions at, say, the recombination epoch. • Since rich clusters can be identified to redshifts as great as z ~ 1, it should be possible to examine the ways in which clusters and clustering evolve with time, which could provide further important constraints on cosmogonic scenarios. There are, however, also some disadvantages: 1.2 Disadvantages • Although dynamically young, clusters of galaxies are nevertheless non-linear systems today, having already collapsed and probably virialized. Consequently there is no guarantee that any traces of the initial conditions which might have been present at the time of cluster formation have not already been erased by subsequent dynamical evolution. • Because clusters are highly non-linear systems today, studies of cluster formation are generally not amenable to analytic methods such as the simple linear theory that has been developed to describe the growth of structure in an expanding universe (e.g., Peebles 1980). Consequently, one must resort to N-body simulations, with all their inherent benefits and limitations (see Efstathiou et al. 1985 for a discussion), in order to extrapolate the evolution of structure from some assumed set of primordial conditions in the linear regime into the non-linear phase of clustering. A fairly large number of numerical simulations of clusters of galaxies have been performed to date. These can be roughly divided into three types: 1) Simulations of isolated clusters. These simulations focus on the expansion, turn around, and collapse phases of cluster formation, while essentially ignoring any surrounding cosmology. They usually assume very simple initial conditions, such as a spherical "top hat" sort of perturbation. Owing largely to their simplicity these were the earliest sorts of cluster simulations that were performed, with Aarseth pioneering much of this work (e.g., Aarseth 1963, 1966, 1969). Other well-known studies have also been done by Peebles (1970), White (1976), Cavaliere et al. (1986), and others. 2) Cosmological simulations. Large-scale cosmological simulations have become very popular in the last few years as a means of comparing the predictions of various theories with observations. Simulations have now been performed for most of the cosmological scenarios discussed earlier (e.^., Aarseth, Gott, and Turner 1979; Efstathiou and Eastwood 1981; Centrella and Melott 1983; Frenk, White, and Davis 1983; Klypin and Shandarin 1983; Dekel and Aarseth 1984; Albrecht and Turok 1985; Davis et al. 1985; Saarinen, Dekel, and Carr 1987; Bennet and Bouchet 1988; Weinberg, Dekel, and Ostriker 1989, and others). Such simulations allowed White, Davis, and Frenk (1984), for example, to argue that a neutrino- dominated universe could be ruled out because it would produce clusters which are much larger than those observed. Unfortunately, resolution on the scale of clusters in most large-scale cosmological simulations is usually too poor to permit a detailed study of the formation and systematic properties of clusters. This is because the dynamical range

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of such large-scale simulations is quite limited; one is attempting to simulate the mass distribution in a large volume of space using a limited number of particles and consequently each individual particle must be rather massive. 3) Large-scale cluster distribution. Such simulations are not intended for examining the properties of individual clusters per se, rather, these are studies of the largescale clustering properties of clusters, as reflected by the cluster-cluster correlation function and the morphology of superclusters (e.g., Barnes et al. 1985; Batuski, Melott, and Burns 1987; White et al. 1987; Weinberg, Ostriker, and Dekel 1989). Such studies have suggested, for example, that most simple gravitational instability scenarios may have difficulty accounting for the very large-scale structure indicated by recent observations. The above list is by no means meant to be complete, but rather is intended simply to give some idea of the sorts of cluster simulations that have been done to date. As a means of illustrating in more detail just what can be learned from comparing N-body simulations of clusters with observations, the following sections discuss several numerical studies of cluster formation that have been done in various collaborations between Dekel, Oemler, Richstone, Weinberg, and West. In what follows, many of the results will be presented in a rather qualitative way, however, more detailed, quantitative discussions can be found in the original papers cited below.

2. CLUSTER FORMATION IN GRAVITATIONAL INSTABILITY MODELS In a series of papers, Avishai Dekel, Gus Oemler, and I have performed simulations of the formation of clusters of galaxies in a wide range of cosmogonic scenarios within the framework of the gravitational instability picture (West, Dekel, and Oemler 1987, 1989; West, Oemler, and Dekel 1988, 1989). Our goal was to examine the systematic properties of these simulated clusters, with the hope that some differences could be found between clusters formed from different initial conditions. If such differences exist, then comparing the properties of the simulated clusters with those of observed rich clusters might allow one to place constraints on cosmogonic models or perhaps even rule out one or more of the competing scenarios. We assume that in the early universe there was a power-law spectrum of density fluctuations,


(1)

where 6^ are the Fourier components of the dimensionless density contrast 6p/p. An equivalent way of expressing this perturbation spectrum is in terms of the root-meansquare fluctuations in spheres containing on average mass M,

£ oc AH3*")/6.

(2)

Thus, provided n > —3, smaller-scale fluctuations will have higher initial amplitudes than larger-scale perturbations and hence should collapse earlier. A power-spectrum index n = 0 is equivalent to Poisson fluctuations, while smaller values of n correspond to relatively more power on large scales. If density fluctuations were initially present on all scales, then a hierarchical sequence of formation of structure is expected to occur. We performed simulations of hierarchical clustering scenarios with power-spectrum indices of n = 0 , - 1 , and —2. We also ran simulations of the pancake scenario in which

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the initial fluctuation spectrum possessed a coherence length with all small-scale perturbations erased below a critical scale and an n = 0 spectrum on larger scales. Hybrid models were also simulated in which the initial fluctuation spectrum had a coherence length identical to that of the pancake simulations, but with the amplitudes of smallscale fluctuations reduced rather than completely damped out. And although we did not explicitly simulate the cold dark matter scenario, the CDM spectrum (which cannot be represented by a single power-law over a wide range of scales) has an effective slope of n « 0 or —1 on the scale of rich clusters, and so as a reasonable approximation to cluster formation in CDM, one can use our hierarchical clustering simulations beginning from a power-law spectrum with n = 0 or n = - 1 . The different forms that the initial fluctuation spectrum can take are illustrated schematically in Figure 1. All the simulations assumed an Einstein-de Sitter (Ct = 1) universe. However, to check for any sensitivity of cluster properties on this assumption we repeated the n = 0 hierarchical clustering simulations for the case of an open universe (Uo = 0.15).

Hierarchical

Pancake T

T

OJO

00

O

o

t

t

\ o

o

log M

log M -»

Figure 1. Schematic representation of initial fluctuation spectra for different gravitational instability scenarios. In order to generate cluster simulations with sufficiently high resolution so as to allow a detailed comparison of the systematic properties of clusters formed in different scenarios with observations, a novel approach for increasing the dynamical range was used in which the clusters were simulated in two separate stages. In the first stage, low-

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resolution, large-scale simulations of the different theoretical scenarios were performed to find the locations where clusters formed for a given set of initial conditions. Then, in the second stage, high-resolution simulations were performed of the individual clusters that had been identified. In this way it is possible to efficiently achieve a much higher degree of resolution on the scales of clusters than would generally be possible with large-scale cosmological simulations.

2.1 Large-Scale Cosmological Simulations The initial conditions for the simulations were generated by superposing plane waves of random phase and direction to produce a particular spectrum of density fluctuations. As an economical measure, each simulation was first evolved in the very linear regime using the ZePdovich (1970) approximation, after which the full N-body simulation was begun. This is a technique that is commonly used for cosmological simulations such as these. Representative large-scale simulations of different scenarios are shown in Figures 2a-d, at those stages corresponding to the present epoch (see discussion below). As expected, the pancake simulation exhibits the pronounced pattern of large-scale filaments expected in that model. The n = 0 hierarchical simulation, on the other hand, shows a very clumpy appearance but no large-scale, coherent features. However, the n = — 2 scenario, which possesses much more large-scale power, shows coherent structure spanning several tens of Mpc. Clustering is much less developed in the n = 0 open universe simulation than in the corresponding case for fi = 1, since the growth of structure eventually halts in open cosmologies. To determine that stage of the simulations that corresponds to the present epoch, the particle two-point correlation function was compared with the observed galaxygalaxy correlation function. The correlation function for two representative simulations are shown in Figure 3. For the pancake scenario, the slope of the correlation function increases with time, and matches the observed galaxy-galaxy correlation function slope of -1.8 at only one stage, which provides a means of uniquely specifying the present epoch in these simulations. Furthermore, equating the correlation length of the simulations with the observed galaxy-galaxy correlation length of r0 w 5h Mpc provides a means of converting from simulation to physical units. With this scaling, the simulated volumes have diameters of ~ 100 h Mpc. For the case of hierarchical clustering, on the other hand, the slope of the two-point correlation function does not change with time but rather only increases in amplitude. Such self-similar growth is exactly what one would expect for the growth of structure from a power-law initial fluctuation spectrum in an Einstein-de Sitter universe, since unlike the pancake scenario, there is no preferred scale imprinted on the initial power-spectrum. Thus, we chose as the present epoch that stage in the hierarchical simulations when the correlation length is the same as that at the present epoch in the pancake simulations. As it turns out, cluster properties appear to be quite insensitive to the particular choice of present epoch.

2.2 High-Resolution Cluster Simulations Rich clusters were identified in the large-scale cosmological simulations using a simple cluster-finding algorithm that identifies clumps of particles that correspond to Abell clusters of richness classes 1 or 2. Then, using the same initial conditions as before but now with a greater density of particles, a smaller volume with radius of ~ 23ft

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Cosmogony and the Structure of Rich Clusters of Galaxies

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of the density profiles of rich clusters might depend on the form of the initial spectrum of density fluctuations (e.g., Fillmore and Goldreich 1984; Hoffman and Shaham 1985), and thus cluster density profiles might provide an interesting test of the cosmological initial conditions. Figure 5 shows the projected surface mass density profiles obtained for all clusters in various gravitational instability scenarios. It is striking that, although the clusters have formed in quite different ways, their density profiles appear nonetheless to be quite similar. Quantitative measurements of the shapes of these profiles confirm their similarity. Hence, it seems that the density profiles are insensitive to the initial conditions. Only profiles of clusters formed in an open universe (not shown here) differ, appearing significantly steeper in their inner regions. We interpret the similarity of profiles of clusters formed in quite different scenarios as a consequence of violent relaxation during cluster collapse, which is an efficient means of erasing traces of the initial conditions. Similar results have been obtained by van Albada (1982) and Villumsen (1984) for stellar systems. However, it is important to note that quite different results have been obtained by Quinn, Salmon, and Zurek (1986) and Efstathiou et al. (1988), who found that the density profiles of bound objects in their simulations beginning from different initial fluctuation spectra did in fact show a rather strong dependence on the initial conditions. Why these various studies produce such discrepant results is not clear, although there are several possible explanations. One possibility is that West, Dekel, and Oemler (1987) looked at systems of much lower mean overdensities (appropriate for rich clusters) than those of Quinn, Salmon, and Zurek (1986) and Efstathiou et al. (1988), who focused on higher density systems comparable to galactic halos. Second, according to standard lore, structure should evolve in a self-similar way from a scale-free initial fluctuation spectrum in a flat universe, and therefore one would expect galactic halos and galaxy clusters to be indistinguishable from one another except for a change of scale. However, the fact is that individual objects do not grow in an entirely self-similar manner but rather pass through several well-defined stages of evolution. Hence, it is entirely possible that systems of different dynamical ages will not necessarily exhibit similar properties. Specifically, the density profile which results from cluster collapse and violent relaxation may be altered by later secondary infall of outlying material, so that the density profile at later times may differ from that at earlier epochs. In hierarchical scenarios, the higher densities of galaxy halos imply that they must have collapsed at correspondingly earlier epochs than clusters and thus have had longer to accrete a significant fraction of their total mass by infall. Clusters of galaxies, on the other hand, because they are dynamically young may still reflect the universal density profile that results from violent relaxation. And, of course, a third possibility is that the different numerical results may simply be a consequence of the different ways in which the initial conditions were generated and the simulations performed by each group. Resolving this discrepancy would be an important step towards a better understanding of the relationship between density profiles and the cosmological initial conditions, as would a detailed numerical study of the competing effects of violent relaxation and secondary infall. Does the universal density profile of the simulated clusters agree with the observed density profiles of rich clusters? To answer this question we determined profiles for 27 Abell clusters for which reliable data are available. These are shown in Figure 5. In general, the observed profiles exhibit the same general shape as the profiles of the simulated clusters. This may be telling us something very interesting about the distributions of luminous and non-luminous matter in clusters of galaxies. If one takes

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2.4 Velocity Dispersion Profiles Another property worth examining is the run of velocity dispersion with radius in both the simulated and observed clusters. Figure 6 shows a comparison of the mean line-of-sight velocity dispersion profiles of the simulated clusters in different scenarios. Once again the cluster profiles are all remarkably similar, with the exception of those clusters formed in an open universe. To compare the simulation results with observations, Figure 6 also shows the composite velocity dispersion profile for a sample of 15 clusters taken from studies by West, Dekel, and Oemler (1987) and Dressier and Shectman (1988). Within the rather considerable scatter, the theoretical velocity dispersion profiles certainly appear to be consistent (or perhaps more fairly stated, at least not inconsistent with the observa-

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2.5 Subclustering Substructure in clusters of galaxies might provide a very useful means of probing the initial fluctuation spectrum. The basic idea behind this approach is quite simple. In the gravitational instability picture, the amount of small-scale clustering (i.e., binaries, small groups of galaxies, etc.) that develops will naturally depend on the amount of small-scale power present in the initial fluctuation spectrum. Thus, in pancake scenarios one would expect to find negligible small-scale structure since all small-scale perturbations were erased from the initial fluctuation spectrum prior to recombination, whereas in hierarchical scenarios one would expect to find a good deal of small-scale clustering. One way in which this small-scale clustering may manifest itself is in the form

Cosmogony and the Structure of Rich Clusters of Galaxies

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of substructure within clusters. West, Oemler, and Dekel (1988) attempted to quantify the amount of subclustering which occurs in clusters and their surroundings to see if this could indeed provide a useful diagnostic of the cosmological initial conditions. While this approach sounds straightforward in principle, in practice developing tests to objectively search for substructure and assessing the statistical significance of the results are quite difficult tasks. Numerous studies have claimed to detect substructure within rich clusters (e.g., Geller and Beers 1982; Dressier and Shectman 1988; Fitchett and Webster 1988; Mellier et al. 1988, and many others). However, based on three different tests that we developed, West, Oemler, and Dekel (1988) claimed to find little evidence of significant substructure within the inner regions of most of their simulated clusters. We then applied these same statistical tests to the observational data published by Dressier (1980) and also found little significant substructure in the inner regions of most of these clusters within, say, ~ 1 — 2 h~ Mpc of their centers. Similar results have also been obtained recently by West and Bothun (1989), who applied a different set of statistical tests using both the projected galaxy distribution and available velocity information. It is important to emphasize that clumps can often be seen in the projected galaxy distribution but in many cases these are consistent with what would be expected from simple Poisson noise and hence do not represent genuine dynamical entities. West, Oemler, and Dekel (1988) argued that the lack of significant substructure in the inner regions of most clusters is once again a consequence of violent relaxation, which acts to quickly obliterate any trace of substructure that might otherwise have been present. A similar conclusion has been reached by Efstathiou et al. (1988). We would argue that the lack of significant substructure in the inner regions of most Abell clusters implies that they are most likely dynamically relaxed systems at present. Although we found little substructure in the inner regions of most rich clusters, we did find that the amount of small-scale structure present in the regions immediately surrounding clusters can provide a sensitive test of cosmogony, with those scenarios originating from initial fluctuation spectra with more small-scale power showing the greatest amount of small-scale clustering in the cluster environs. I would like to digress here for a moment to discuss an important point regarding the interpretation of substructure. It is often argued that the (supposed) frequent occurrence of substructure implies that many rich clusters have formed only recently or are perhaps still forming today. However, it is important to remember that other equally plausible interpretations of apparent substructure are also possible. As emphasized by West and Bothun (1989), when discussing substructure in the context of cluster formation, it is essential to make a distinction between different types of "substructure" that might be observed: 1) those subclusters which are the surviving vestiges of smaller systems of galaxies that may have recently merged to produce a rich cluster and, thus, represent a genuine signal of recent cluster formation, 2) those subclusters which presently reside within an otherwise relaxed cluster, for example secondary infall of some bound group presently undergoing tidal disruption within the cluster (see the article by Fitchett in this volume for further discussion of this possibility), 3) those groups of galaxies which are bound to the cluster but still outside the cluster confines, destined to fall in at some later time, and 4) apparent subclustering in the form of groups of galaxies which are not dynamically bound to the cluster, but rather are expanding with the general Hubble flow and appear as substructure simply because of projection along the line of

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sight (e.g., the Cancer cluster, see Bothun et al. 1983). While all four types of apparent substructure are important, they have quite different implications for theories of cluster formation and the present dynamical state of clusters. Even with complete radial velocity information, it is still a very difficult task to unambiguously determine whether some apparent clump of galaxies represents a genuine statistically significant region of substructure (rather than simply Poisson noise) and whether the apparent subcluster is actually physically associated with the rich cluster itself. For instance, given a typical cluster line-of-sight velocity dispersion of ~ 1000 kms , galaxies in some group lying as much as 10 h~^ Mpc in front of or behind a rich cluster could easily be erroneously classified as cluster members even with complete redshift information. X-ray observations of clusters also suffer from these same ambiguities. Perhaps the only way to truly distinguish between these possibilities is with independent distance information with which one could, in principle, obtain the peculiar velocity field around clusters. Without precise distance and peculiar velocity information, it is difficult, if not impossible, to distinguish between the different forms which subclustering may take. Thus, it seems worth stressing that it may be premature to assume that the prevalence of observed substructure necessarily implies that many rich clusters are in an unrelaxed state at the present epoch. Another point that has been emphasized by both Geller and Beers (1982) and West and Bothun (1989) is that it is dangerous to make sweeping statements about the frequency with which substructure occurs in rich clusters based on the very inhomogeneous observational samples that are available at present. For instance, Dressier (1980) surveyed regions extending anywhere from ~ 0.5 — 5 h~l Mpc from the centers of 55 clusters, whereas Colless and Hewett (1988) surveyed only the innermost regions (out to radii of ~ 0.5 — 1 h~l Mpc) of a sample of 14 clusters. Consequently, there is a clear bias for substructure to be found more often in those clusters which have been observed over a greater area. Lastly, Alfonso Cavaliere and I have been asked by the organizers of this meeting to address possible reasons why our simulations seem to predict quite different dynamical states for clusters of galaxies today. My answer is that I think that our numerical results do not really differ at all, rather, it is our interpretations of the results that differ. Consider Figure 7, which shows a typical simulation of hierarchical clustering by West, Dekel, and Oemler (1987). This simulation shows the same clumpy appearance seen in many of the simulations of Cavaliere et al. (1986) and others. However, when we assign a physical scale to these simulations, which, as discussed earlier, we can do in an unambiguous manner using the two-point correlation function, then the simulation shown in Figure 7 extends over 20 h Mpc on a side and the individual clumps are separated by distances of ~ 5 — 10 h Mpc. In such a case we would call these clumps three distinct clusters, whereas Cavaliere et al. (1986) would label this a cluster with strong subclustering. Perhaps these clumps will merge someday, perhaps not. Thus, it seems to me that in essence the question of substructure boils down to a semantic point - just how does one choose to define substructure, and how does one assign some statistical significance to the observations? Further thoughts on substructure can be found in the articles by Cavaliere, Fitchett, Forman, and Geller in this volume.

2.6 Cluster Alignments The possibility that clusters of galaxies may show some tendency to be aligned with one another and/or with the surrounding galaxy distribution has profound implications

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for cosmogonic scenarios. Observations indicate that: • the major axes of rich clusters tend to point toward neighboring clusters over scales of ~ 15 - 30 h'1 Mpc, perhaps more (Binggeli 1982; Flin 1987; Rhee and Katgert 1987; West 1989), and • in the regions surrounding clusters, galaxy counts are preferentially higher along the direction defined by cluster major axes, with this effect also extending to ~ 15 - 30 h'1 Mpc (Argyres, Groth, Peebles, and Struble 1987; Lambas, Groth, and Peebles 1988). Such observations provide strong evidence that the galaxy distribution is characterized by a filamentary topology, and suggest a connection between the formation of clusters and the large-scale structure. It should be emphasized here that the two types of observed alignments are not simply redundant measures of the same effect; one could, for instance, have neighboring clusters being aligned with one another due to their mutual tidal forces without necessarily finding a corresponding excess number of galaxies in filaments between clusters. Binggeli (1982) was the first to show the tendency for neighboring rich clusters to point towards one another. While other studies by Struble and Peebles (1985) and Ulmer, McMillan, and Kowalski (1989) were unable to find any significant alignment tendency, I think that it is fairly safe to consider this effect established. As discussed by West (1989), a likely cause of the discrepant results from different studies is the large uncertainties in position angle determinations of cluster major axes. Binggeli's (1982) original results are illustrated in Figure 8, where 9 is the angle between the major axis of an Abell cluster and the line connecting its center to that of its nearest neighboring cluster and D is the spatial separation between the clusters. In the absence of any alignments, the distribution of 9 should be uniform with a mean (9) = 45°. There is a clear tendency for small values of 9 when neighboring clusters are separated by distances D < 15 — 30 h Mpc which indicates a general propensity for neighboring clusters to be aligned with one another. For D < 30 h Mpc, (9) w 30° ± 4 when only nearest neighbor clusters are considered, and (9) R* 36° ± 5 when all neighbors are included. Dekel, West, and Aarseth (1984) searched for similar cluster alignments in different gravitational instability scenarios. Their results are shown in Figure 9 for pancake, hierarchical clustering (n = 0), and hybrid simulations. A strong tendency for alignments can be seen for the pancake scenario for cluster separations less than ~ 30 ft Mpc ((#) w 25° ± 3). A weaker, though still significant, tendency can be seen for the hybrid model ({9) fa 36° ±2). No alignments are found for clusters formed in the n = 0 hierarchical clustering simulations ((9) « 44° ± 2 ) . It is reassuring to note that these results appear to be quite robust; Figure 10 shows the alignment tendency for clusters in pancake and n = 0 hierarchical clustering simulations taken from Frenk, White, and Davis (1983) (in this case (9) ta 30° ± 2 for the pancake scenario, and (9) « 44° ± 1 for hierarchical clustering). The fact that quite different alignment tendencies are found for different cosmogonic scenarios is encouraging, as it means that this simple test may provide a very powerful means of distinguishing between different models. A complementary test for filamentary structure is that of Argyres et al. (1986), who looked for correlations between the orientations of rich clusters and the distribution of galaxies in the regions surrounding them. Given the direction defined by the major axis of a cluster, one can ask whether galaxies in the cluster environs are uniformly distributed with respect to this axis or whether they show some sort of non-uniform distribution. If clusters reside within filaments, for example, the density of galaxies

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Figure 7. Projected galaxy distribution in typical n = 0 hierarchical clustering simulation. The box is ~ 20 h Mpc on a side. in the cluster surroundings should show a systematic tendency to be higher in some preferred direction relative to the cluster major axis. Plotted in Figure 11 are the results obtained by Argyres et al. (1986) when they compared the orientations of a large number of rich clusters with the Shane-Wirtanen galaxy counts. Shown is the surface density of galaxies in excess of the expected mean density if the galaxies were uniformly distributed, for bins of different angular separation from the cluster center. At the typical redshifts in this sample, the bins 0.25 < 6 < 0.5, 0.5 < 6 < 1.0, 1.0 < 0 < 2.0, and 2.0 < 0 < 4.0 should correspond to distances of roughly 2, 4, 8, and 16 A" 1 Mpc from the cluster center. If galaxies are uniformly distributed around clusters, there should be no density excess seen in Figure 11. Instead, there is a clear tendency to find more galaxies in the direction defined by the major axes of the clusters. Similar results have been obtained by Lambas, Groth, and Peebles (1988). Thus, this test provides strong evidence of a filamentary pattern for the large-scale galaxy distribution, with rich clusters residing within these filaments and tending to be oriented such that their major axes are parallel to the filaments. This same analysis was applied by West, Dekel, and Oemler (1989) to the various gravitational instability simulations. These results are shown in Figures 12a-d. A strong signal of alignments is clearly seen in the pancake and the n = —2 hierarchical clustering simulations and at a weaker level in the hybrid model. No evidence of signif-

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0(MAJOR) Figure 8. The so-called "Binggeli effect". Here 0 is the angle between the projected major axis of an Abell cluster and the line connecting its center to that of its nearest neighboring cluster, and D is the spatial distance between the two clusters (from Binggeli 1982). icant alignments is found for either the n = 0 or n = - 1 hierarchical clustering cases. Recalling that the CDM fluctuation spectrum has an effective slope of n « 0 or — 1 on the scale of rich clusters, these results suggest that the CDM scenario may not produce sufficient large-scale filamentary structure to be consistent with the observations. The observations would therefore seem to favor an initial fluctuation spectrum which possessed either a coherence length or good deal of power on large scales. Let me conclude this section by saying that I believe that studies of the large-scale alignment properties of rich clusters (as well as groups and individual galaxies) offer one of the best means available at present for discriminating among the various formation scenarios. Alignment tests are an interesting way of simultaneously probing the initial fluctuation spectrum on more than one scale, since one is looking at the formation and orientations of clusters in relation to the formation of larger scale structures such as superclusters. If clusters are indeed aligned within superclusters and filaments, they cannot have formed long before the large-scale structure. Thus, these observations strongly constrain the sequence of formation of structure. Furthermore, it seems to me that alignment tests should be fairly unaffected by any possible biasing of galaxy formation, since it is difficult to see how such biasing could produce observed alignments

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Cosmogony and the Structure of Rich Clusters of Galaxies

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in the luminous matter that were not also present in the underlying mass distribution. I would especially encourage a detailed study of alignment tendencies in CDM, as it still remains to be seen whether CDM can reproduce the large-scale filaments and alignments of neighboring clusters that are observed. Results presented by Dekel (1984), as well as those discussed here, suggest that CDM may have problems in this area.

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2.7 Radius-Mass Relation Simple analytic arguments suggest that, if structure in the universe has formed by dissipationless gravitational clustering, a relationship should exist between the characteristic radii and masses (or densities) of bound systems such as clusters. Furthermore, the form of this radius-mass relation may depend on the initial fluctuation spectrum. Consider a cluster whose density profile, S(r), can be approximated by something like a de Vaucouleur's profile (such as those shown in Figure 5), S(r) = S e exp[-7.67(r/i? e ) 1 /4 _ 1]

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Cosmogony and the Structure of Rich Clusters of Galaxies

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Note that even though the density profile of equation (3) does not vanish at any finite radius, the total mass, Mtot, and therefore half-mass radius, Re, are well-defined, finite quantities. Given equation (4), the interesting question is how might Se vary from one cosmological scenario to another? Linear theory predicts that the mean internal density of bound lumps in an Einstein-de Sitter universe should scale as pe oc M~^* + n " . Assuming pe oc Se/Re, equation (4) then yields the expected radius-mass relation, (5) Equation (5) predicts /? = 0.56, 0.50, 0.43, and 0.33 for n = 0, - 1 , - 2 , and - 3 , respectively. Given this fairly wide range of values, there is reason to hope that by examining the radius-mass relation for rich clusters one can constrain the slope of the primordial fluctuation spectrum. Similarly, a correlation between radius and mass would seem likely for clusters formed in the pancake scenario, depending on the geometry of the superclusters in which they were born (e.g., two-dimensional sheets or one-dimensional filaments). For example, if clusters fragmented from pancakes of roughly the same mean density, one would expect a relation of the sort Re oc Mt^t . While the above arguments are undoubtedly oversimplified, they nevertheless suggest that a well-defined radius-mass relation should exist for clusters of galaxies and that it could be related to the form of the initial density fluctuation spectrum, even if the density profile is universal. Figure 13 shows the radius-mass relation for the simulated clusters in different cosmogonic scenarios. A well-defined relation is observed in all cases, with the pancake scenario showing the shallowest slope and the n = 0 and hybrid scenarios showing the steepest. A couple of points are interesting to note. First, the actual slopes of the radius-mass relation found for the hierarchical clustering simulations agree rather well with the theoretical predictions of equation (5). Second, the radius-mass relation for the n = 0 hierarchical simulations appears to show no dependence on ft, having roughly the same slope for fl = 1 and il0 = 0.15. Comparing the above results with observations is not straightforward since it is the correlation between cluster radius and mass that is obtained from the simulations, yet it is the relationship between radius and luminosity that is actually observed for clusters. To compare the numerical results with observations, we determined the half-light radii and total luminosities for a sample of 29 clusters. These results are shown in Figure 14. If one adopts the simplest assumptions, namely that the light and mass are distributed in the same way within clusters and that clusters all have similar mass-to-light ratios, then a direct comparison between the numerical and observational data is possible. In that case it is clear from Figure 13 that the scenarios which agree best with the observed radius-luminosity relation are the n = 0 hierarchical clustering (again for both fi = 1 and Cl0 = 0.15) and hybrid models. The pancake simulations and the n = — 2 hierarchical clustering simulations, on the other hand, appear to be quite inconsistent with the observations. Furthermore, the only way to reconcile the radius-mass relation of the pancake clusters with the observed radius-luminosity relation would be if either a) the distributions of mass and light were very dissimilar within clusters or b) global mass-to-light ratios were a decreasing function of increasing system size. Neither of these possibilities has much observational support at present (although they cannot be ruled out either). Thus, the observed cluster radius-luminosity relation may prove to be a serious problem for pancake scenarios as well as for hierarchical clustering scenarios with rather flat initial fluctuation spectra such as the n = — 2 case.

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2.8 Conclusions from Gravitational Instability Models 1) The internal cosmological and velocity have argued

structure of rich clusters appears to yield little information about the initial conditions. This is evidenced by the similarity of the density dispersion profiles of clusters formed in quite different scenarios. We that this is a consequence of the efficiency of violent relaxation at

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Figure 14. Observed radius-luminosity relation for a sample of 29 Abell clusters. Here Ltot l s the total cluster luminosity in units of L*, and Re is the projected half-light radius. rapidly erasing traces of the initial conditions from the final cluster. The similarity of the mass profiles of the simulated clusters and the observed luminosity profiles of real clusters suggests that light traces mass on these scales (although see Section 4.0). 2) Clusters formed in an open universe may exhibit some differences from those formed in a flat universe. For instance, their density and velocity dispersion profiles appear to be somewhat steeper in the inner regions than is observed. Thus, it might be possible to use the observed properties of clusters to constrain the present value of

n. 3) We have argued that little significant substructure is found in the inner regions of most clusters. This is true for both the simulated clusters and observed clusters. This would seem to suggest that the inner regions of most Abell clusters are probably relaxed systems at present. 4) Useful tests of cosmogony are provided by:

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M.J. West • Alignments of clusters with each other and with the surrounding galaxy distribution. The observations seem to require a truncated or flat initial fluctuation spectrum. Such observations may prove to be a problem for CDM, although more work is needed to determine just what sort of coherent structures are produced in that model, and over what scales. • The amount of small-scale clustering present in the regions surrounding rich clusters.This can provide a sensitive test of the form of the initial fluctuation spectrum, specifically, the amount of small-scale power. • The radius-mass relation for clusters. If clusters have formed from gravitational instability, then the observations seem to require a rather steep initial fluctuation spectrum with a slope of n m 0. However, one must again bear in mind that it is the radius-luminosity, rather than radius-mass, relation that is actually observed. Still, as discussed earlier, even with this caveat it would seem rather difficult to reproduce the observed radius-luminosity relation in pancake scenarios or hierarchical scenarios with lots of large-scale power.

Unfortunately, the above list seems to present us with an unhappy dilemma. To reproduce the observed alignment tendencies of rich clusters seems to require a truncated or flat initial fluctuation spectrum, yet it is those very scenarios which appear unable to reproduce the observed radius-luminosity relation. The only model which seems to successfully reproduce most of the observed properties of rich clusters is the hybrid scenario, but in the absence of any compelling a priori motivation such a model seems rather ad hoc at present. There may, of course, be ways around the problems faced by other scenarios, however more contrived models quickly lose the elegance and simplicity of the original theories. Given the seemingly paradoxical situation which seems to arise when the properties of clusters formed in simple gravitational instability scenarios are compared with the observed properties of real clusters, it would seem worthwhile to also consider the possibility of cluster formation by means other than gravitational instability. Cluster formation in the explosion scenario is explored in the next section.

3. CLUSTER FORMATION IN THE EXPLOSION SCENARIO In the explosion scenario, cluster formation is likely to occur in a manner which is quite different from that in gravitational instability models. This is because gravitational instabilities are expected to grow very slowly on isolated expanding shells (e.g., White and Ostriker 1988), so some sort of interaction between shells seems essential for the formation of rich clusters. For this reason, it has been argued that the most likely sites for the formation of rich clusters in the explosion scenario are at the points where neighboring shells intersect, since the deep potential wells at these locations will naturally induce the collapse of structure in three dimensions. Using N-body simulations, Weinberg, Dekel, and Ostriker (1989) have shown that the richest clusters form Figure 15. (opposite page) Temporal evolution of a typical three-shell explosion simulation. Each row shows three orthogonal views of the projected galaxy distribution plotted in comoving coordinates. All galaxy particles are plotted at the beginning of the simulations (a = 1), while subsequent stages show thin slices through the center of the simulated volume. Here a denotes the factor by which the radius of the simulated volume has expanded over its original size.

Cosmogony and the Structure of Rich Clusters of Galaxies

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at the two points of intersection between three shells, with smaller clusters and groups forming in the "rings" where pairs of shells intersect. Clusters formed in this way might be influenced by the geometry of the matter distribution and/or the dynamics of the shell interactions, and therefore it is possible that the properties of clusters formed in the explosion scenario might differ from those of clusters formed in gravitational instability models. If, on the other hand, violent relaxation is still the dominant dynamical process during cluster formation, then most traces of the initial conditions may have been erased, resulting in the formation of clusters in the explosion scenario whose final properties do not differ much from those of clusters formed in other models. David Weinberg, Avishai Dekel, and I have recently looked at the properties of clusters of galaxies formed in N-body simulations of the explosion scenario (West, Weinberg, and Dekel 1989). A simple history of shell evolution was invoked whereby explosions at some early epoch were assumed to have swept up gaseous material into thin shells which subsequently cooled and fragmented to form galaxies prior to the time when neighboring shells begin to overlap. To simulate such a scenario, we performed numerical experiments beginning with three equal-sized expanding shells of material. The shells were given initial expansion velocities of 1.4 times the Hubble velocity. These simulations assumed an Cl = 1 universe of baryons only. A few additional simulations were also performed of open universes and cases in which a dominant non-baryonic dark matter component was included. The reader is referred to the papers by West, Weinberg, and Dekel (1989) and Weinberg, Dekel, and Ostriker (1989) for further details regarding these simulations. The evolution of a typical explosion simulation is shown in Figure 15. Some representative clusters formed in this manner are presented in Figure 16. Projected density profiles of these simulated clusters are plotted in Figure 17. Comparison of this figure with Figure 5 shows that the shapes of the density profiles in the explosion scenario are quite similar to those of the gravitational instability scenarios and the observations. In Figure 18, the mean velocity dispersion profile obtained from the explosion clusters is compared with those of gravitational instability models. Again, the profiles of these clusters all appear to be quite similar. As before, we would argue that violent relaxation during cluster collapse is most likely responsible for the similarity between the internal structures of the explosion and gravitational instability clusters. To examine the alignment tendency of clusters in this model, we applied the test of Argyres et al. (1986) described earlier. The results are shown in Figure 19. A clear signal of alignments is found for the explosion simulations, and quantitatively the strength of these alignments is comparable to that found for observed clusters by Argyres et al. (1986). We have also examined other properties of these clusters, such as substructure, ellipticities, etc. The bottom line is that clusters of galaxies formed in the explosion scenario appear to be quite similar to clusters formed in gravitational instability models and seem to successfully reproduce many of the observed properties of rich clusters. In many ways, the explosion clusters bear a strong resemblance to clusters formed in the pancake scenario, exhibiting quantitatively similar density profiles, ellipticities, and alignment tendencies. However, it should be stressed here that these simulations are only a first, simple attempt to study cluster formation in the explosion scenario and, thus, more sophisticated simulations are required to strengthen conclusions about the properties of clusters in this model. In particular, a wider range of initial conditions needs to be explored to examine the effects of unequal shell sizes, different initial shell expansion velocities, and different redshifts when shell interactions begin (see Weinberg,

Cosmogony and the Structure of Rich Clusters of Galaxies

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LOG r / R 5 0 Figure 17. Density profiles of clusters formed in the explosion scenario. Profiles have been normalized in the same way as those in Figure 5. Dekel, and Ostriker 1989). Such simulations are required before one can obtain meaningful results regarding the cluster radius-mass relation and cluster-cluster alignments, where, for example, unequal shell sizes are likely to play an important role in determining these properties. Furthermore, it would be interesting to consider the possibility that the shells are still largely gaseous at the time they overlap, in which case such a study would also have to incorporate treatment of hydrodynamical processes.

3.1 Conclusions from Explosion Models 1) Properties of clusters formed in the explosion scenario are found to be quite similar to those of gravitational instability scenarios. In particular, these clusters bear a strong resemblance to clusters formed in the pancake scenario. 2) The explosion scenario seems at present to be able to successfully reproduce many of the observed properties of rich clusters. 3) More work is needed to strengthen the above conclusions.

Cosmogony and the Structure of Rich Clusters of Galaxies

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LOG r / R 50 Figure 18. Mean line-of-sight velocity dispersion profile of explosion clusters, compared with those of different gravitational instability models.

4. CLUSTER FORMATION WITH DARK MATTER Although it is widely believed that rich clusters of galaxies are dominated by an unseen mass component, very few simulations of clusters have been performed in which distinct luminous and dark matter components have been followed. Rather, what is usually done (such as in most of the simulations discussed earlier) is to simulate only a single mass component, with the implicit assumption that the dark matter and galaxies are distributed in a similar fashion. However, there is little justification for assuming that the galaxies are in fact fair tracers of the overall mass distribution, since there are numerous physical processes which operate in clusters on timescales less than a Hubble time (e.g., stripping, dynamical friction, mergers) that could quite easily lead to a rather different distribution of the luminous mass relative to the dark matter. To examine this question in more detail, Doug Richstone and I performed simulations of the formation of clusters of galaxies in which we incorporated an explicit treatment of separate dark and luminous matter populations (West and Richstone 1988). The initial conditions for these simulations were very simple. We assumed that 10% of the total cluster mass resides within a few heavy "galaxy" particles, while 90% of the cluster mass is contained in many lighter "dark" particles. In these simulations the ratio of galaxy particle mass to dark particle mass is Tngai/mc[m = 10. Both the galaxies and dark particles were initially distributed at random (hence we assume no biased galaxy formation) and given expansion velocities such that the system should

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Figure 19. Alignments of clusters and their surroundings in the explosion scenario, using the test of Argyres et al. (1986). expand by a factor of ~ 6 before turn around and collapse. Simulations with 1,000 to 10,000 particles were performed. Figure 20 shows the time evolution of a typical simulation with 3,000 particles. In this figure, the galaxies are denoted by the symbol 'X' and the dark matter particles are points. As the system expands, turns around and collapses, the galaxies quickly become more strongly clustered than the dark matter particles. The speed with which this segregation occurs can be seen in Figure 21, which plots the harmonic mean separation of the galaxy particles as a function of time, and the same for the dark matter particles. Again it is evident that the galaxies very quickly become more strongly clustered than the dark matter. Results similar to those found here have been obtained by Barnes (1984) and Evrard (1987) and can, in fact, also be seen in the earlier simulations of White (1976) and Roos and Aarseth (1982; I thank Alain Mazure for pointing out this last reference to me). What is the mechanism responsible for this segregation? The answer seems to be dynamical friction operating within the small subclusters that develop prior to the final cluster collapse which allows energy to be exchanged rapidly between the heavy galaxy and lighter dark particles, causing the galaxies to sink to the bottom of the

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dark matter

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Figure 21. Harmonic mean separation (in model units) of the galaxy particles and of the dark particles as a function of time for a typical simulation. Note how quickly the galaxies become more strongly clustered than the dark matter. virial mass to true mass when all simulation particles are used, and the same when only the galaxy particles are used. Virial mass estimates based on galaxy data alone invariably underestimate the true cluster mass by as much as a factor of ~ 5 to 10. Thus, it would seem that, if clusters have formed in the simple hierarchical manner pictured here, the virial masses of Abell clusters derived from observations of galaxies within them may be grossly underestimating the true cluster masses. If so, then the typical values of Cl0 « 0.1 — 0.2 obtained from rich clusters may really be a factor of 5 to 10 too small, implying that we may, in fact, be living in a flat, fi = 1 universe. Do these simulations produce clusters which look like real ones? This is a difficult question to answer because the number of galaxies in each simulation was usually quite small. Larger simulations with a greater dynamical range are required to fully address this question. As a first essay, Figure 23 shows the mean density profile of the galaxy distribution obtained by superimposing the final stages of all the simulated clusters that we have run to date on top of one another. As can be seen, the distribution of galaxies in these simulated clusters shows a density fall-off that goes as ~ r , which is quite consistent with the observed profiles of real clusters seen in Figure 5. Thus, these preliminary results appear to rule out any gross inconsistencies between the simulated and real clusters. Figure 24 plots the ratio of luminous to non-luminous mass within various distances of the cluster center. It is interesting to note that the dark matter dominates all the way to the center of these clusters.

Cosmogony and the Structure of Rich Clusters of Galaxies

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Figure 22. Distribution of the ratio of computed virial mass to true cluster mass found in different simulations using (a) galaxy particles only and (b) all particles. 4.1 Conclusions from Dark Matter Simulations 1) In simulations of cluster formation with both dark and luminous matter components, spatial segregation between the galaxies and dark matter develops very rapidly, on a timescale much shorter than the cluster collapse time. 2) This segregation seems inevitable in any hierarchical clustering scenario. 3) As a consequence of the segregation, virial mass estimates based on galaxy data alone systematically underestimate the true cluster mass by a factor of 5 to 10. Thus, if clusters have indeed formed by clustering hierarchically, then the derived virial masses of Abell clusters may be greatly in error. Consequently, the values of fl w 0.1 — 0.2 usually obtained from analysis of cluster dynamics may in fact be consistent with a true value of Cl = 1. Hence, there may at long last be a reasonable compromise between theoretical prejudice and observational reality! 4) Although larger simulations spanning a wider range of initial conditions need to be done, it appears that the segregation process does produce "reasonable" looking clusters which have density profiles that are similar to (or at least not inconsistent with) those observed. 5) This segregation process offers a natural dynamical alternative to ad hoc theories

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LOG r / R 50 Figure 23. Projected surface density profile of the galaxy distribution in simulated clusters. This was obtained by superimposing all simulated clusters on top of one another in order to reduce statistical noise. The profile has been normalized as in Figure 5. of biased galaxy formation. Segregation is expected to occur in all relaxed systems up to the scales of rich clusters. On larger scales, such as that of superclusters, the galaxy distribution should reflect the true mass distribution, since segregation has not yet had sufficient time to develop. 6) It seems to me that the segregation mechanism which appears in these simulations is rather robust and, therefore, should be a general phenomenon in any hierarchical clustering scenario. If future observations are (somehow) able to show convincingly that such segregation has not occurred in real clusters, then I think that this would raise serious doubts about whether the formation of structure (or at least clusters) has proceeded by dissipationless clustering from small to large scales. See the article by Richstone in this volume for a further discussion of these results.

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5. SUMMARY The goal here has not been to argue for or against the merits of any particular theoretical scenario. Rather, what has hopefully been accomplished is simply to convince the reader of just how powerful this approach of using N-body simulations of cluster formation in comparison with observations can be in attempting to better understand the origin of rich clusters and the large-scale structure of the universe. Numerical simulations allow one to make a more detailed, quantitative comparison of theory with observations than would otherwise be possible with purely analytic methods. With the new generation of N-body codes that are being developed, such as tree codes (e.g., Barnes and Hut 1986; Hernquist 1987; Bouchet and Hernquist 1988), very high-resolution particle-mesh codes (e.^., Villumsen 1989; Melott and Shandarin 1989), and codes incorporating gas dynamics (see the article by Evrard in this volume), it will be possible to perform better and more sophisticated simulations than those described here. Similarly, with the launch of the Hubble Space Telescope, the amount and quality of observational data for clusters will increase tremendously in the near future. The next few years will no doubt prove to be a very exciting time for both theorists and observers interested in the origin of clusters of galaxies. It's a pleasure to thank Avishai Dekel, Gus Oemler, Doug Richstone, and David

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Weinberg for making our collaborations together very enjoyable and rewarding. In addition to those already mentioned, I would also like to thank Greg Bothun, Mike Fitchett, and Jim Schombert for many stimulating conversations on clusters and cluster formation. All the simulations discussed here were performed using the N-body codes developed by Sverre Aarseth, to whom I am grateful for sharing them with me as well as for providing helpful advice. I thank Cheryl Samsel for a careful reading of this manuscript and for helpful suggestions. Finally, I would like to thank the organizers of this meeting, Bill Oegerle and Mike Fitchett, for having invited me to give a talk on this subject.

REFERENCES Aarseth, S.J. 1963, M.N.R.A.S., 126, 223. Aarseth, S.J. 1966, M.N.R.A.S., 132, 35. Aarseth, S.J. 1969, M.N.R.A.S., 144, 537. Aarseth, S.J., Gott, J.R., and Turner, E.L. 1979, Ap. J., 236, 43. Albrecht, A., and Turok, N. 1985, Phys. Rev. Lett, 54, 1868. Argyres, P.C., Groth, E.J., Peebles, P.J.E., and Struble, M.F. 1986, A. J., 91, 471. Barnes, J. 1984, M.N.R.A.S., 208, 873. Barnes, J., and Hut, P. 1986, Nature, 324, 446. Barnes, J., Dekel, A., Efstathiou, G., and Frenk, C.S. 1985, Ap. J., 295, 368. Batuski, D.J., Melott, A.L., and Burns, J.O. 1987, Ap. J., 322, 48. Bennet, D., and Bouchet, F. 1988, Phys. Rev. Lett, 60, 257. Binggeli, B. 1982, Astron. Astrophys., 107, 338. Bothun, G.D., Geller, M.J., Beers, T.C., and Huchra, J.P. 1983, Ap. J., 268, 47. Bouchet, F.R., and Hernquist, L. 1988, Ap. J. Suppl, 68, 521. Cavaliere, A., Santangelo, P., Tarquini, G., and Vittorio, N. 1986, Ap. J., 305, 651. Centrella, J., and Melott, A.L. 1983, Nature, 305, 196. Colless, M., and Hewett, P. 1987, M.N.R.A.S., 224, 453. Davis, M., Efstathiou, G., Frenk, C.S., and White, S.D.M. 1985, Ap. J., 292, 371. Dekel, A. 1983, Ap. J., 264, 373. Dekel, A. 1984, in the Eighth Johns Hopkins Workshop on Current Problems in Particle Theory, eds. G. Domokos and S. Koveski-Domokos, (Singapore: World Scientific), p. 191. Dekel, A., and Aarseth, S.J. 1984, Ap. J., 283, 1. Dekel, A., West, M.J., and Aarseth, S.J. 1984, Ap. J., 279, 1. Dressier, A. 1980, Ap. J. Suppl., 42, 565. Dressier, A., and Shectman, S. 1988, A. J., 95, 985. de Lapparent, V., Geller, M.J., and Huchra, J.P. 1986, Ap. J. (Letters), 302, LI. Efstathiou, G., and Eastwood, J.W. 1981, M.N.R.A.S., 194, 503. Efstathiou, G., Frenk, C.S., White, S.D.M., and Davis, M. 1988, M.N.R.A.S., 235, 715. Evrard, A.E. 1987, Ap. J., 316, 36. Fillmore, J.A., and Goldreich, P., 1984, Ap. J., 281, 1. Fitchett, M., and Merritt, D. 1988. Ap. J., 335, 18. Fitchett, M.J., and Webster, R.L. 1987, Ap. J., 317, 653. Flin, P., 1987, M.N.R.A.S., 228, 941. Frenk, C.S., White, S.D.M., and Davis, M. 1983, Ap. J., 271, 417.

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Geller, M.J., and Beers, T.C. 1982, Pub.A.S.P., 94, 421. Hernquist, L. 1987, Ap. J. Suppl., 64, 715. Hoffman, Y., and Shaham, J. 1985, Ap. J., 297, 16. Ikeuchi, S. 1981, Pub. Astr. Soc. Japan, 33, 211. Klypin, A.A., and Shandarin, S.F. 1983, M.N.R.A.S., 204, 891. Lambas, D.G., Groth, E.J., and Peebles, P.J.E. 1988, A. J., 95, 996. Mellier, Y., Mathez, G., Mazure, A., Chavineau, B., and Proust, D. 1988, Astron. Astrophys., 199, 67. Melott, A.L., and Shandarin, S.F. 1989, Ap. J., 343, 26. Ostriker, J.P., and Cowie, L.L. 1981, Ap. J. (Letters), 243, L127. Peebles, P.J.E. 1970, Astron. Astrophys., 75, 13. Peebles, P.J.E. 1980, The Large-Scale Structure of the Universe, (Princeton: Princeton University Press). Quinn, P.J., Salmon, J.K., and Zurek, W.H. 1986, Nature, 322, 392. Rhee, G.F.R.N., and Katgert, P. 1987, Astron. Astrophys., 183, 217. Roos, N., and Aarseth, S.J. 1982, Astron. Astrophys., 114, 41. Saarinen, S., Dekel, A., and Carr, B. 1987, Nature, 325, 598. Struble, M.F., and Peebles, P.J.E. 1985, A. J., 90, 582. Ulmer, M.P., McMillan, S.L.W., and Kowalski, M.P. 1989, Ap. J., 338, 711. van Albada, T.S. 1982, M.N.R.A.S., 201, 939. Vilenkin, A. 1985, Phys. Rep., 121, 264. Villumsen, J.V. 1984, Ap. J., 284, 75. Villumsen, J.V. 1989, Ap. J. Suppl., in press. Weinberg, D.H., Dekel, A., and Ostriker, J.P., 1989, in preparation. Weinberg, D.H., Ostriker, J.P., and Dekel, A. 1989, Ap. J., 336, 9. West, M.J. 1989, Ap. J., in press. West, M.J., and Bothun, G.D. 1989, Ap.J., submitted. West, M.J., Dekel, A., and Oemler, A. 1987, Ap. J., 316, 1. West, M.J., Dekel, A., and Oemler, A. 1989, Ap. J., 336, 46. West, M.J., Oemler, A., and Dekel, A. 1988, Ap. J., 327, 1. West, M.J., Oemler, A., and Dekel, A. 1989, Ap. J., in press. West, M.J., and Richstone, D.O. 1988, Ap. J., 335, 532. West, M.J., Weinberg, D.H., and Dekel, A. 1989, Ap.J., submitted. White, S.D.M. 1976, M.N.R.A.S., 177, 717. White, S.D.M., Davis, M., and Frenk, C.S. 1984, M.N.R.A.S., 209, 27P. White, S.D.M., Frenk, C.S., Davis, M., and Efstathiou, G. 1987, Ap. J., 313, 505. White, S.D.M., and Ostriker, J.P. 1988, preprint. Zel'dovich, Ya. B. 1970, Astron. Astrophys., 5, 84. Zel'dovich, Ya. B. 1980, M.N.R.A.S., 192, 663. Zel'dovich, Ya. B., Einasto, J., and Shandarin, S.F. 1982, Nature, 300, 407.

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DISCUSSION Peebles: Isn't one of the problems that there really aren't very many galaxies here and that the segregation effects that you get are typically two small body processes? West: Yes, I think that's true. But the important point is that within the subclumps that's always going to be the case to some extent. We've run simulations with a thousand particles where we had only ten galaxies and simulations where we had ten thousand particles and a hundred galaxies, and we get indistinguishable results. The same rapid segregation effect occurs in all cases. The important point is that in any hierarchical clustering scenario there will always be the formation of these small dense clumps, and thus it will always be possible to develop some segregation within them. I think this is a very general effect which should happen in any hierarchical clustering case. Neta Bahcall: Mike, back to the mass-radius relation. Another thing you can do is rather than comparing with the light-radius relation, is to use velocity dispersions to get the dynamical mass directly. West: That's right, Kashlinsky did that. He examined the relationship between the observed radius and velocity dispersion for a number of rich clusters and found a result which was consistent with constant density systems, although there was a lot of uncertainty. We could do the same thing with the simulations, but we haven't done that. Djorgovski:

But would you get the same answer?

West: Yes, given the correlation between cluster velocity dispersion and luminosity, we should get the same answer. Weinberg: I was quite struck that in your first set of simulations you are assuming that H = 1, light traces mass, you scale with the correlation function and you get velocity dispersions that are consistent with the observed clusters, whereas Jim Peebles told us this morning that when you look at observed clusters, you get il = 0.4. What is the resolution of this puzzle? Huchra: That one's easy. His clusters have dispersions of about 1000 kilometers per second instead of 750. The mass goes as the square. Peebles: Could I ask you about the density profile? In many cases, you assumed density profiles such that the log density is a function of log radius is convex away from the axis, which allows you to define a half-mass or half-count radius. The statistical analog of the density run is the cluster galaxy cross correlation function? That average density run is convex toward the axis if it is convex at all, which means that a half count radius is ill-defined. Can you reconcile these two, results? West: The half-mass radius is well defined when you consider something like a de Vaucouleurs. law.

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Peebles: I agree but then for a de Vaucouleurs law it is well defined because you have convexity in the right direction. West: That's right, and that is true of any density profile provided it is falling rapidly. Peebles: So long as it is falling rapidly enough. How about the observations? West: That's what the observed profiles showed. The cluster luminosity profile showed a steep fall-off at large radii. Peebles: I wonder if that is not a result of problems with the mean. You always have to subtract the background. Oemler: We worried very hard about that. That's an obvious problem, but I don't think that's true. It might be that if you at least operationally define where you go out to, several Abell radii, and normalize things there you would consistently treat the models and the observations. Peebles: If you consistently normalize at several Abell radii, you are subtracting the cluster. Right? The cluster galaxy cross-correlation function is appreciably large at several Abell radii. Oemler: No, I don't think so. That doesn't matter for comparing theory with observations. Petrosian: I just want to make a comment about mass-to-light ratio and its dependance on environment. You showed a lot of results. I don't know which side of the coin you're arguing for—you showed that light traces mass and also that it doesn't. West: I have no bias! (laughter) Petrosian: There is some evidence that I must point out, on luminous arcs. There is A 370, where we can definitely show by modeling of the arc with a gravitational lens model that light does not trace mass. The dark matter which we need for producing the gravitational lens effect is quite differently distributed to the light. Fitchett: My reading of the literature suggested that you have the same M/L within the arc as exterior to it. (laughter) Sellwood: Your amazing conclusion that no matter what initial spectrum you start with, you end up with the same cluster, why should we believe that? Why is that not an artifact of your N-body code? West: I can give you a number of reasons for that. One check is that we compare to other N-body results (laughter). While that's certainly no guarantee, at least it says that there is nothing peculiar about the code that we are using as compared to other N-body codes. Also in simulations of the dissipationless collapse of stellar systems, van Albada and Villumsen have found very similar results where, beginning from a wide range of initial conditions, they get a final universal density profile which looks like a de Vaucouleurs law. In terms of two-body relaxation effects within our simulations, some

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hand-waving calculations suggest that we've used a sufficiently large softening length that we should have been able to survive several tens of crossing times of these clusters before two-body relaxation effects become important. Another interesting thing to note is that in the pancake model, cluster formation cannot have occurred before the pancakes collapse, which occurs at an expansion factor of 4. We examined the clusters at an expansion factor of 6, so this universal density profile that we get must have developed very rapidly, before two-body effects within the clusters could have become significant. Yet we also find the same profile when we look at the hierarchical clustering simulations at much later times. So I think that is consistent with two-body relaxation not having become a big concern in these simulations. In terms of the explosion scenario simulations we've done with David Weinberg, we actually have in some simulations heavy "dark matter" particles, "gas" particles, and lighter "galaxy" particles, so we can look directly for two-body relaxation effects in the form of segregation between these different mass particles, and we don't find any. And these simulations also produce the same final density profile. Sellwood: Softening is a two-edged sword, it can help stop two-body relaxation but it also stops very dense concentration from building up. You loose your substructure that way. West: Yes, that's true. But for the density profiles I showed, the softening length is always much smaller than the scales we measured the density profile on. So I don't think we have poor resolution in the core of clusters, for example. Our softening length was chosen to be comparable to the size of a large galaxy, and thus is also smaller than the size of any interesting substructure which might develop. Tremaine: In your simulations that showed equipartition, of course the particles don't have the appropriate masses for galaxies in clusters, but you've argued that the same process should happen anyway. Of course, you can carry that to an extreme. For example, you could say that if you had an initial soup made out of oranges and grapefruits, now if you made a cluster out of them, the grapefruits would all be in the center and the oranges would all be on the outside. So, what's the dimensionless parameter, the difference between the two cases? What guarantees that the galaxies are going to come to the middle whereas, for example, grapefruits won't? West: This has mostly to do with the ratio of the mass of the galaxies to the dark particles. Provided that ratio is very large, we should expect to always get the same relaxation effect. Tremaine: So if it was grapefruits and neutrinos, the grapefruits would all still be in the center? West: Yes, that's my impression. Jaffe: I think there's two numbers. One you have to have not too many grapefruits. And the difference between the mass has to be large. I think that if you had in these simulations a million grapefruits and one bunch of raisins, we would not see this. West: I agree, for this mechanism to operate requires both that the individual galaxies

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be much more massive than the individual dark particles and that the total dark mass exceed the total luminous mass. Sandage: I have a similar question. We know for sure observationally that there is a factor of ten to the fourth in the mass of galaxies we can see in the Virgo cluster. What would be your prediction if you say that all Abell clusters are virialized for the distribution of the faint dwarfs compared to the giants? West: That's a question that Jim Peebles had asked Doug Richstone and I in an earlier discussion. The answer isn't clear. Again, these are very simple simulations with a limited dynamical range, but I think, as Doug is going to talk about tomorrow, it is possible to make some arguments which suggest that there is an energy transfer or heat transfer between different mass particles species, which in the extreme case where the galaxies are much larger than the dark particles leads to segregation, but may not necessarily do the same for different mass galaxies. Although dwarf galaxies are much smaller than the giant galaxies, it's not obvious that significant mass segregation should occur between them if, for instance, there is a large population of even smaller (dark) objects which could act as a sort of heat sink. But that is a possibility which still needs to be explored further. We tried looking at mass segregation among galaxies in some of our simulations by running a few cases where we had different mass galaxies. We didn't find any mass segregation as a general rule of thumb, but the galaxies only spanned a factor of two in mass, and we are also clobbered by small number statistics in these cases. So, I think it is still an open question both observationally and theoretically. Sandage: It is not an open question observationally because we know what the answer from observations is, and it is that the faint dwarf elliptical galaxies are distributed like the massive ones with a mass ratio of practically a thousand. So, you've got to produce that somehow. I'll show the evidence tomorrow. West: That may or may not be a problem for this mechanism. More work is needed. Kaiser: I would like to follow that line of questioning of the last two speakers. What worries me about what you have done is that you've put 10% of the mass into the galaxies which seems reasonable to me if we want to believe an 17 = 1 universe for this reason, fi = 1 means a total mass to light ratio of a couple of thousand. You are giving galaxies mass-to-light ratios of a couple of hundreds. It certainly implies very extended halos, and I'm not sure if that really renders your results unrealistic. The question seems to be would galaxies retain those halos? Even if the galaxies have such mass associated with them in the process of merging to form groups, would they retain their individual halos out to such large radii. The reason you are getting your effect is that on the group scale you've got about 50% or more of the mass in a couple of galaxies. West: I don't think that this segregation mechanism is terribly sensitive to the specific fraction of mass we actually attribute to each individual galaxy, provided again that this mass is much larger than the dark particle mass. Whether or not galaxies possess large extended halos, at early stages in the clustering hierarchy each galaxy will contribute a significant fraction of the total mass within the subcluster in which it resides, and consequently will rapidly settle to the bottom of the subcluster potential well. So in a sense, the galaxy will still be surrounded by an even larger dark halo. As subclusters merge, the galaxies will end up at the bottom of the potential well of the resulting

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larger subclusters. This has been demonstrated numerically in several studies in which people have done mergers of galaxies, etc., and found that in subsequent mergers on progressively larger scales the most tightly bound particles still end up at the center of the merger remnant. So I think that because we always reach the condition in the early stages of the simulations where the segregation can develop, and because this segregation is likely to be preserved through later stages as subclusters merge, the segregation of luminous and dark matter should exist at present, regardless of whether or not individual galaxies can be considered to retain whatever dark halos they may have had initially. Kaiser: But the baryons will always be a much smaller fraction if the mass-to-light ratio of the baryonic material is a few or ten. Could you do the same kind of experiment but reducing the mass of the galaxy by an order of magnitude or more? West: We didn't change the ratio of the galaxy to dark matter mass. We changed the faction of galaxies we put in, and found that provided you had more than 50% of the mass in dark matter, you always got the same segregation effect, so it seemed to be insensitive to our assumptions of 10% vs. 90% of the matter in the form of galaxies and dark matter. It seems to be a pretty general phenomenon. Djorgovski: It seems to me that you start with unrealistic conditions in that the dark matter is perfectly smoothly distributed, in which you embed these little raisins. Suppose you took seriously a picture in which most of the mass was, say, within a very bounded heavy halo say, 100 kpc? Would you get anything like this? West: Well, Gus Evrard has already explored that case. He started his simulations with dark halos around the galaxies, and found . . . Evrard: Can I speak for my simulations? There is significant agreement with what you have done in the sense of mass-light ratio being low relative to the global value, but there are some subtle discrepancies. One is that the density profile I found is steeper for the galaxies than for the total mass. The mass-light ratio should rise roughly as R^- in clusters of galaxies. Another thing I found in doing the cosmological simulations is that the two-point correlation function had a cusp at small separations because of this effect. This could probably be ruled out by the Turner-Gott evaluation of the correlation function at small scales. West: But how reliable are the density profiles for your small groups, don't you suffer from small numbers and two-body effects? How many galaxies...? Evrard: Yes. They were not rich clusters at all. We are talking about groups of 20 or 30 galaxies. And finally, the last point I would like to make is that I did the same simulations using test particles instead of galaxies, that is zero mass particles, and found no segregation in those particles, as you would probably expect. So, it is a mass dependant effect. So, it is sensitive to the amount of mass that you assume is embedded firmly in galaxies. West: Yes, but again, provided that the galaxy mass is appreciably greater than the mass of the individual dark particles, I would argue that the same effect should always occur in any hierarchical dark matter dominated cosmogony.

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One other point, I think it's fair to say that our simulations, at some early stage after the beginning, are probably somewhat similar to your simulations, Gus, in that each galaxy particle in our simulations has by then effectively accreted its surrounding dark matter to form a halo, so I think our simulations end up being similar to yours. Struble: With regard to the Argyres et al. alignments, could you comment on the strength of the alignments you find? West: Yes, in the pancake models, we find very strong alignments - stronger than you find from the observations Mitch. But observationally it is a difficult problem to determine the major axis of clusters, what with contamination problems, projection effects, and things like that. So because of that, Argyres et al. may be detecting a reduced signal from what is really an intrinsically stronger effect. In a perfect world, free of contamination and projection effects, you might have observed an even stronger signal of alignments. So I think it might be partly that. But, also, these pancake simulations are a pretty gross oversimplification of what is really expected. So I'd take the actual numbers with a grain of salt, take the effect qualitatively. Felten: From your answer to Nick Kaiser's question, I infer that you may not know the answer to my question, but let me ask it anyway. That the factor 5 to 10 mass discrepancy which was on your last view-graph, do you have any idea whether that will just scale inversely proportional to the 10% you started out with. In other words, if you take the fraction 10% up to 50% or down to 1%, do you have any idea whether that factor 5 to 10 just goes inversely? West: No, we did that and we got the same basic results. Felten: Same meaning what? West: That it was a factor 5 to 10 different. Richstone: Isn't it fair to say that we did that going up to 50% but not going down, that's harder. Felten: You might want to go down to 1% . Richstone: Exactly, but that's harder because of the number of particles. Felten: When you went up to 50% what happened ? Richstone: It stayed the same. Felten: You underestimated the mass by a factor of 5? West: Yes, it was consistent with our other results.

THE DARK MATTER DISTRIBUTION IN CLUSTERS

M. J. Fitchett Space Telescope Science Institute 3700 San Martin Drive Baltimore, MD 21218

Abstract. This article describes the current status of various methods for determining the dark matter distribution in clusters. Despite a great deal of progress recently we still do not have good mass constraints for even one cluster. The reasons for this are discussed. New observational tools and methods of analysis should however lead to some results in the near future.

1. INTRODUCTION One of the many interesting aspects of clusters of galaxies is that they appear to contain large amounts of missing mass. The evidence for this has largely been based on the application of the standard virial theorem. More sophisticated approaches which utilize cluster velocity dispersion profiles came to similar conclusions but assumed that the mass distribution in clusters was the same as that of the light (galaxy) distribution. While this may be true it is definitely at present an assumption. Much recent theoretical work has argued for different distributions for the dark and luminous components of the universe. One of the consequences of this is that we should not assume that the mass distribution in clusters parallels the light distribution. Without this assumption it is very difficult to constrain the mass distribution in clusters, and consequently total cluster masses are not as yet well determined (Bailey 1982, The & White 1986, Merritt 1987). The cluster mass distribution is an important 'parameter' in that it directly influences many of the physical processes that occur in clusters. It is therefore essential that one tries to determine the cluster mass distribution in an as assumption free way as possible. This review will concentrate on ways to do this. A definite problem is that many Abell clusters have probably not yet virialized (see reviews by Geller in this volume and Fitchett 1988). The methods discussed here are mainly only applicable to virialized systems and so the subset of clusters to which they can be applied is small. Even for the simplest spherical clusters, with lots of data, it is still currently extremely difficult to derive reliable mass estimates and constraints on the mass distribution. I hope that this review, despite its pessimism, will stimulate new ideas and at least make us all wary of simple assumptions concerning clusters, since even the simplest question

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(what is the mass distribution in clusters?) is still far from answered. This article will be split into several sections. The first will be motivational and will briefly discuss problems associated with the virial theorem, what cosmological theories predict for the dark matter distribution in clusters, and describe how physical processes in clusters depend on the dark matter distribution. The following sections will describe the current status of the methods for determining the dark matter distribution in clusters observationally. There are various options; we can use the dynamics of tracer particles (galaxies), moving in the cluster potential; we can use the observed properties of the X-ray emitting gas which sits in the cluster potential; we might even use substructure as a probe of the matter distribution (related to this I will discuss the mass distribution in clusters with small scale substructure); finally gravitational lensing by clusters may provide new limits on the dark matter distribution and its morphology at small scales in clusters. Another potential method for determining cluster mass distributions is the use of Infall patterns around rich clusters. I will not discuss that method here as Geller will review it in her article. The Coma cluster will be used to illustrate some of these methods, not because it is typical of clusters, but because it is well studied. There is a large amount of redshift and X-ray data on this cluster, and using one cluster allows comparisons to be made between the various methods. For similar review articles see Mushotzky (1987) and Merritt (1988).

2. MOTIVATION So far every rich cluster analyzed appears to have a high mass to light ratio. Clusters therefore present strong evidence for the presence of large amounts of dark matter in the universe. In this article I will try to be consistent and quote mass to light ratios using blue luminosities, Lg, and scale to a Hubble constant of 50 km s Mpc . In these units the M/Lg required to close the universe is ~ 12OO/i5o. Additionally I will try to state the scale on which various M/Lg were determined since this might in general vary throughout the cluster. Average cluster M/Lg ratios scatter around ~ 3OO/15O (e.g., The & White 1986, Merritt 1987, Colless 1987, Sharpies et al. 1988). It is important to note that many of these papers quote large ranges of allowed M/Lg. These ranges do not reflect cases of statistically poorly determined M/Lg . Rather they are cases where the authors have relaxed some of the standard assumptions. I will return to this point later. Notice that if cluster mass to light ratios are typical of the M/Lg for the luminous components of the universe then fi ~ 0.2 — 0.3 (we do not know that this is the case however). Early estimates of cluster masses were based on the standard virial theorem or one of its variants (see Heisler et al. 1985). Bailey (1982), The & White (1986) and Merritt (1987) have shown that these estimates can be grossly wrong once one drops the assumption that mass traces light. Following Merritt (1987) the virial theorem for a spherical system can be written in the form

where the brackets indicate spatial averages and F(r) is the fraction of the total mass of the system within radius r (this function is unknown). Under the assumption that mass traces light one can fit a function (e.g., a deVaucouleurs profile) to the luminosity

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profile and from that evaluate the denominator. With an estimate of (v) 2 one can derive the standard virial mass estimate which I shall denote Mgfj. Once one allows for physically reasonable, but arbitrary, F(r) there is a great deal of leeway in the allowed values of M y j - For instance Myj will be minimized if F(r) = 1 at all r, corresponding to a point mass at the cluster centre. The ratio of Mmin/M8t(j depends on the assumed F(r). For a deVaucouleur profile fitted to the Coma data it is ~ 0.2 (Merritt 1987). Merritt also showed that the virial theorem constrains the minimum density of the system to be />min = 3C?~1(t;2)/47r(r2), and that cluster masses might be very high if the dark matter is fairly uniformly distributed. For Coma Merritt showed that Mmax ~ 80A/ g ^. Once one allows for different distributions of dark and luminous matter virial mass estimates may be incorrect. One should therefore be wary of using the standard virial mass estimator unless one has other reasons to suppose that mass traces light for the system. Better methods which take into account the detailed spatial-dynamical structure of the cluster are described later. What do cosmological theories predict for the dark matter distribution in clusters? West and collaborators (see article by West in this volume) have concluded that most initial fluctuation spectra form clusters with very similar mass profiles. West and Richstone (see articles in this volume by each author) have also recently described a mechanism whereby the galaxies in rich clusters may become more centrally concentrated than the cluster dark matter. This mechanism has important consequences for our determinations of il from clusters, since the additional cluster dark matter "halo" might contribute significantly to the mass density of the universe. Additionally X-ray data has important consequences for theories which postulate that the dark matter is baryonic. Hughes (1989) has shown that the X-ray emission in the Coma cluster is not consistent with a dark matter distribution which parallels the distribution of the hot X-ray emitting gas. Aside from the global cosmological importance of the cluster mass distribution the interior properties of clusters and their constituent galaxies depend on the dark matter distribution in various ways: • Dynamical friction: all galaxies in clusters experience a drag force. This is due to the overdensity generated by the gravitational focussing of the less massive material behind galaxies moving in the cluster. Chandrasekhar (1942) derived the drag force for a point mass in a constant density sea of less massive particles which have an isotropic Maxwellian velocity distribution. He found that the drag force is linear in the background particle density or, in other words, the dark matter density. • Tidal stripping of cluster galaxies by the cluster depends on the dark matter distribution through its second derivative, ie the tidal field. • Ram pressure stripping of gas from galaxies (see the article by Haynes in this volume) depends on the orbits of the galaxies and their velocities - both of these quantities are intimately related to the cluster mass distribution. • Substructure: the interaction between galaxies within clusters depends on the amount of substructure present in the cluster. cD galaxies for example are believed to form through galaxy mergers. This process should be more efficient in subclusters before the final relaxation of the cluster.

3. CLUSTER DYNAMICS As discussed in Section 2, simple mass estimates of clusters based on the mass traces light assumption might be in error. This section describes recent work which attempts

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to assess the importance of deviations from the mass traces light hypothesis. The first papers on this topic were due to The k White (1987) and Merritt (1987). Each derived constraints on the mass distribution in the Coma cluster without making assumptions about the dark matter distribution. Bailey (1982) had previously suggested that the Coma data was consistent with a small dark mass located at the cluster center. These more recent analyses explored a larger range of mass distributions. Analyses of the type presented in these papers were probably motivated by similar work on the dynamics of individual galaxies (e.g., Binney & Mamon 1982). For some galaxies one has radial luminosity and velocity dispersion profiles. Binney and Mamon described a scheme for analyzing data of this form to yield measurements of the galactic mass to light ratio. With the advent of automated fiber systems and the consequent ability to obtain large numbers of redshifts in clusters (Colless and Hewett, 1987, Dressier and Shectman, 1988) it became possible to apply the same techniques to clusters. The projected velocity dispersion profile, <rp(R), where R is the projected distance of a point form the cluster center, is calculated for the cluster by breaking the cluster into disjoint annuli and for each evaluating the dispersion in the line of sight galaxy velocities

where Nann is the number of galaxies in the chosen annulus. This function is plotted for the Coma data in Figure 1. In order to determine (rp(R) at as many projected radii R as possible Nann is chosen to be small, typically 10. This leads to relatively large error bars on this profile. Also such estimates can be strongly affected by a few "outliers", galaxies which are not cluster members but are hard to exclude on the basis of their velocities. Beers et al. (1989) have emphasized the need for, and described several, statistical measures of dispersion (or, technically 'scale') which have small errors even for small samples with outliers. They also made the interesting point that no matter how much data is acquired on clusters, the methodology at present is to break it down into as many subsamples as possible, and so the need for these more resistant scale estimators will continue. One typically needs ~ 100 measured galaxy redshifts in a cluster in order to construct a reasonable velocity dispersion profile. As a simple illustration of the power of the velocity dispersion profile consider the case of a centrally concentrated dark matter distribution (consistent with the virial theorem). Such a mass concentration would cause the velocity dispersion profile to fall as R I at large radii. This is inconsistent with the observed velocity dispersion profile and so the extremely centrally concentrated model can be ruled out. I will now describe the method used by Merritt and The & White. The projected velocity dispersion profile, crp(R), and galaxy surface density Sfla/(i?) are derived observationally. These are related to the actual 3-dimensional properties of the cluster via the usual Abell integral

and by the following equation

crP(R)%al(R) = 2J™ nj$_ ^?r(r? - ^ M r ) 2 - ot(r)2)]

(4)

where r is the three dimensional distance from the cluster center, R is the projected (observed) distance from the cluster center, and 0>(r) and <7<(r) are respectively the

The Dark Matter Distribution in Clusters

1

115

2

Log (Projected Radius (arcain))

Figure 1. The projected velocity dispersion profile for the Coma cluster derived using data from Kent & Gunn (1982). The error bars are la errors, (taken from The & White 1986). galaxy velocity dispersions in the radial and tangential directions. If the system is in equilibrium then we also have the equation of stellar hydrodynamics (obtained by taking the second moment of the Jean's equation) GnQal(r)M(<

W) 2 -*t(O 2 ) = -

r) (5)

For isotropic orbits oy(r) = <7/(r) and there would be a unique solution to these equations. However we do not know that this is the case, and we 'observe' a combination of the quantities o~r(r) and <7<(r). We know T,gai(R), and hence n(r) via the Abell integral inversion. Unfortunately there are therefore three unknowns {cr r (r),a<(r), M(r)} and only two equations. The variables 0>(r)>a<(r) a Q d M(r) can be replaced by the set of variables { 0, ff r t{ ) — 0 a n d dM/dr > 0. The approach taken by Merritt was to step through many assumptions about either /?(r) or M(r) and decide whether the solutions were acceptable or not. In this way the available region of parameter space is reduced, and the bounds on the mass distribution made tighter. Merritt chose various functional forms for M(r); a) King profiles with various r o and Wo, (where r o and Wo are respectively the scale length and central potential of the King model), b) Power law distributions of the form p(r) = po{\ + (r/rc)2)~N/2 with N = 3,4,5 and varying r c . For Coma, Merritt showed that the velocity dispersion profile is consistent with several mass distributions; a fairly point like dark matter distribution with predominantlyy circular galaxy orbits near the cluster center (N = 4,/>o = 4.2 x 10 j gy jg pc and rc = 340/I^Q kpc); a more diffuse dark matter distribution with predominantly radial orbits throughout the cluster (N = 4, p0 = 2.5 x 10 /I^QM© pc and

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rc = 3Ah§Q Mpc); or the usual mass traces light model with isotropic orbits. The constraints on the total cluster mass are better than those from the virial theorem, ranging from 0AMst({ — 3M g l j. Here Mst^ = 3.7 x lO^A^M© is the total cluster mass (i.e., the integral over the King model). Merritt presents a table which allows one to use this total mass to infer the mass within different radii. At radii < 7/I^Q Mpc" 1 the M/Lg for Coma lies in the range 70 — 525/&50, with the mass traces light value being 175/i5o. This large range represents the extent to which the optical study can constrain the mass of the Coma cluster. The mass distribution is plotted in Figure 2 for the two extreme models described above. The mass traces light mass distribution is not shown but will lie between these two curves. Interestingly within 3/I^Q Mpc (~ R^) the various mass models all give similar results. This result is not very satisfying. Coma, after all, is one of the best studied clusters, yet the dynamical method allows close to an order of magnitude range in the total cluster mass. Can this be improved? Following the spirit that led from the simple application of the virial theorem to the more complex equation of stellar hydrodynamics, Merritt attempted to use the fourth moment of the Jean's equation or, in other words, the shape of the velocity distribution. Dejonghe had shown (1987) that in the context of galaxy dynamics different forms of /3(r) lead to quite different shapes for the velocity distribution (or equivalently the velocity histogram, since clusters are discrete systems) at different radii. For very radial orbits galaxies near the cluster center would have a flat velocity histogram, and for the outer regions one would expect to see a peaky velocity histogram centered on the mean cluster velocity. The converse is the case for circular orbits. The shape of the velocity histogram therefore contains information that might allow stronger constraints to be placed on the cluster mass distribution. It is not as yet clear how many redshifts are needed in order to apply this method. Based on our experience with the Hydra cluster (Fitchett & Merritt 1988) I would think one would need ~ 400 redshifts. This is not a firm number as it depends on how well the galaxy sample is selected (some regions of the cluster might allow for a more sensitive shape test than others, see later) and the statistical methods used. Merritt (1987) calculated the theoretical distributions dN/dv{0S (essentially the velocity histogram) for galaxies at R > 680/i^"0 kpc in the Coma cluster for each of the three models described above. Each of these models is consistent with the velocity dispersion data. Figure 3 shows these results and the actual data. Clearly none of the theoretical curves is a particularly good fit to the observations because the velocity histogram is skew ( at a significance level ~ 3 % ). This may indicate that either Coma has not yet equilibrated or that there are galaxies projected onto the cluster that are not members. Merritt was not able to strongly select one model in preference to the other two based on this test. See Merritt (1988) for further discussion. Although the shape test was not useful for galaxies at large radii in Coma one might wonder if it might discriminate between different models for galaxies at small radii. Unfortunately the Coma cluster appears to have substructure on small scales (Fitchett & Webster 1987, Mellier et al. 1988). One would be hard pressed to argue that the galaxy velocities in the core are representative of those expected in a smooth potential well. Therefore it is very difficult to reduce the range inherent in Merritt's extreme models. Of course one could for this, or any other cluster with sufficient data, determine the optimal place at which to apply this test (i.e., the radius /?* beyond which the theoretical curves shown in Figure 3 would be most different from each other). Given the skewness of the Coma data it is unlikely that this approach will help in this case. However for an isolated spherical cluster with a large number of measured redshifts (probably

The Dark Matter Distribution in Clusters

117

. ID

V

O r

O r

0.1

1

10

Rodius (h 5 0 ~ 1 Mpc) Figure 2. The most extreme dynamically allowed dark matter distributions in the Coma cluster. The two curves correspond to the models discussed in the text. The curve which attains the highest mass corresponds to the most diffuse dark matter distribution compatible with the observations. > 400) this approach might be viable and yield the first optically well constrained mass distribution for a cluster. For more typical clumpy clusters, or spherical clusters with fewer measured redshifts, cluster mass estimates based on optical data should be viewed with caution.

4. X-RAY CONSTRAINTS Mass distributions derived from observations of the hot X-ray emitting gas in clusters will undoubtedly, in the future, prove far superior to those derived optically. Cur-

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M. J. Fitchett

— Isolropic — Radial Circular

0.15

0.1 CIN

0.05 -

-2000

-1500

-1000

-500

0

+500

+1000

+1500

+2000

1

Vp (km s' )

Figure 3. The velocity histogram for galaxies in Coma with R > 680h7n kpc. The three curves correspond to dynamical models in which the galaxies have radial, circular and isotropic orbits; the dark matter distribution has been adjusted in each case to give the same projected velocity dispersion profile (taken from Merritt 1988). rently, however, the X-ray approach also has problems. This section will review the methodology behind this approach, describe the present difficulties, and the various methods that have been used to circumvent these difficulties. There are several excellent articles on the general X-ray properties of clusters (Mushotzky 1984, Sarazin 1986, Ulmer 1988). The hot gas in clusters has a typical temperature in the range Tgas = 10 — 10 K, and a cluster crossing time given by

R

(6)

where R is the radius of the cluster (i.e., the hydrostatic assumption is probably valid out to a radius of ~ 10 Mpc). Also the mean-free path of protons in the intracluster plasma (ICP) is \

oor^Wh2r

A= 23[

"e

TbTH 1 0 -3 c m -3]

i-l u kpc

/7\

7

<)

(Sarazin 1986). The small mean-free path compared to the size of clusters ensures that the X-ray emitting plasma can be treated as an isotropic fluid and, so long as tx is less than the timescale on which the cluster potential is changing, the plasma can be assumed to be in hydrostatic equilibrium with the cluster potential (see also the article by Evrard in this volume). For a spherical cluster the equation of hydrostatic equilibrium (Vp ffas = —pgas^ matter) can be solved for the mass interior to r, M(r): Mir\

_

Gum

ff

d log r

d log r

(8)

The Dark Matter Distribution in Clusters

119

Notice the linear dependence of M(r) on T(r). In principle therefore, measurements of Pgas{f) and Tgas(r) directly yield the actual mass distribution M(r). In principle the X-ray method of determining mass distributions in clusters has several advantages over the optical approach described in Section 3 (in practice these advantages will not be realized until the appropriate instrumentation is available - see later discussion). Perhaps most importantly the fact that the gas is isotropic ensures that the X-ray determined mass can be determined unambiguously (in contrast to the optical approach where it is very difficult to disentangle the effect of a radially changing mass to light ratio and the anisotropy of the galaxy orbits); the statistical errors associated with X-ray mass estimates can be reduced by collecting more X-ray photons whereas the number of observable galaxies in a cluster is limited; the mass is derived as a function of radius directly whereas one has to input models for PDM(r) m *° the optical analyses; X-ray mass determinations are not very sensitive to asymmetries in the mass distribution (see for example Fabricant et al. 1986); finally X-ray data is less likely to be affected by contamination effects and subclustering than optical data. Cluster velocity dispersions are notoriously difficult to obtain accurately because of interloping galaxies or groups. In X-rays, even if a group were superposed on the cluster, it would be noticed by its different local temperature, and so it could in principle be removed. The sad fact however is that, at present, there is no instrument capable of deriving the temperature profile Tgas(r) for many clusters. Such an instrument would need to be responsive to a wide range of energies (typical cluster temperatures are ~ 7 keV. and the "break" in the thermal Bremsstrahlung spectrum occurs at E = kTgas, so data is required beyond the break in order to detect it). It would also need fairly high resolution in order to determine the temperature at a point in the cluster (albeit still averaged along the line of sight through the cluster). Finally the instrument needs to be sensitive enough to be able to detect and measure the spectrum of the gas in the outskirts of clusters where the emissivity is low. The Einstein IPC is sensitive to photons in the 0.4-4.5 keV energy range, meaning it can only yield useful temperature information for cool clusters (e.g., Virgo - Stewart et al. 1894). The HEAO-1 A2 experiment is sensitive to photons in the 0.2-30 keV energy range but yields only an integrated spectrum over the field of view (~ 3°). The EXOSAT ME is sensitive to 2-10 keV photons and has a spatial resolution of 45'. A potentially very useful experiment was the Spacelab 2 X-ray telescope which is sensitive to photons in the 2.5-25 keV energy range and consists of two telescopes - a "coarse" resolution instrument with a spatial resolution of 12', and a "fine " resolution instrument with 3' resolution. The coarse mode is particularly useful for mapping extended low surface brightness objects, and has been used to probe the temperature distribution in the Perseus cluster (private communication, Martin Watt). For good cluster temperature measurements we must look forward to the Advanced X-ray Astrophysics Facility AXAF. Mushotzky (1987) has written an excellent review of AXAF, and described how it will be able to obtain mass distributions in clusters at z ~ 0.05 with reasonable integration times (< 25 000 sec). For those people who are impatient for the launch of AXAF the imminent launch of ROSAT will allow mass determinations for cooler clusters. It is worth pointing out that even with AXAF galaxy redshift information in clusters is still very useful. One could in principle use the AXAF derived mass profile, with the equation of stellar hydrodynamics, and the observed line of sight velocity dispersion profile to determine the orbital distribution of the galaxies. This is an important quantity as it determines the way in which galaxies interact with the ICP. Given the lack of spatially resolved X-ray spectra in clusters progress has usually

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M. J. Fitchett

been made by making assumptions. A natural (but not necessarily correct) assumption is that the gas pressure and density are related polytropically (p oc p*). A simple case of this is to assume that T — const (the gas is isothermal). If the galaxy orbits are also assumed isotropic and (Tr(r) is independent of r, then one can use the equation (5), and the equation of hydrostatic equilibrium to show that J k a iirnH^gal ,nx where Pgal P = UT (9) * Klgas see for example Cavaliere and Fusco-Femiano (1976). Galaxy distributions in clusters have often been approximated by pgai oc (1 + (r/r c ) ) ' (corresponding to Ej a /(i2) oc (1 + (R/rc) ) in projected space) and consequently that the X-ray surface brightness profile (ot Jp%asdl along the line of sight through the cluster) is %x(R) <x ((1 + (.R/r c ) 2 )"" 3 ^ +1 A Fits of this functional form to the data (Jones and Forman 1984) yield a range of /? values with (/?) ~ 2/3. However the distribution of /? as derived form observed cluster velocity dispersions and measured temperatures (which I shall term (3spec, a notation taken from Edge 1989) was believed to have a different mean of (Pspec) — 1-2 (Mushotzky 1984). This difference has been termed the "/? discrepancy". Recently however Edge (1989) has derived more accurate cluster temperatures based on EXOSAT ME data, and finds {PSpec) ^ 0.86 (where the Perseus and A2147 clusters have been excluded). He claims that values of (iSpec > 1 a re probably due to clusters where the velocity dispersion has been overestimated due to subclustering. Interestingly Perseus, which has the largest /? discrepancy appears to have spatial-velocity substructure at the ~ 2% level (Fitchett and Smail 1989) which cannot be seen in the velocity data alone (a very similar situation to the Cancer cluster - see Bothun et al. 1983). Thus it is likely that the /? discepancy can be reduced in this cluster. In any case it is still not clear from these analyses that the cluster gas is isothermal. Indeed Henriksen and Mushotzky (1986) presented evidence that the spectrum of the Coma cluster is not consistent with Thermal Bremsstrahlung radiation from an isothermal plasma. In addition spatially resolved spectral data in Coma shows different temperatures at different distances from the cluster centre (see later). The most recent approach is due to Hughes (1989). He argues that since, for the Coma cluster, the IPC data yield an accurate determination of pgas(r), this quantity should be assumed well known and parametrized. Assuming functional forms for the dark matter distribution like those used by Merritt in the optical study (see Section 3) and the equation of Hydrostatic equilibrium one can then derive a temperature profile for each mass profile which can be compared to all available data. Figure 4 (taken from Hughes 1989) shows the results of Hughes' calculation for a model in which the dark matter distribution is given by PDM(r) = P°(^ + ( r / r c) ) > corresponding to Merritt's N = 4 model (see Section 3). Each box corresponds to a different value of rc (given in arcmins, recall l' corresponds to 40/I^Q kpc at Coma) and the different curves represent different po. Lower curves have higher p0. The simplest constraint from the Coma X-ray data is that the X-ray emission must extend to at least 40' we see X-ray emission at this radius. Thus solutions which have T(r) —> 0 at r < 40' can be excluded, in fact they are not plotted in this Figure. These correspond to high central density models and so even this simple constraint can set an interesting upper limit on the central dark matter density in Coma (for this mass distribution). Secondly one knows that the central temperature of Coma is > 4 keV, while the average temperature over a 3° field is 7.5 ± 0.2 keV. This eliminates solutions which have too rapid a rise in temperature - these would yield low central temperatures for a given

The Dark Matter Distribution in Clusters

121

average temperature. Such models have also been excluded from this figure. There are additional constraints which can be applied. Hughes used the following; the Tenma spectrum of a 3° region of the cluster; EXOSAT temperature and flux information at the cluster center and 45' off-center (EXOSAT has a field of view of 45'). These measurements gave JCTQ = 8.5 ±0.3 keV and a ratio of center to off-center temperatures of 1.15^QQy (Hughes et al. 1988). These constraints rule out the solutions shown as dotted lines. Clearly dark matter distributions of the form PDM{r) — Po(l + ( r / r c ) )~ 2 with rc > 25.5' are ruled out by the X-ray data. This represents a significant improvement over the optical constraint where for the same mass distribution one could only rule out r c > 80'. This is an important improvement because the large core radius models give large total masses. The smaller allowed rc reduces the allowed upper limit on Mcoma, and hence the range in M/Lg. In fact the X-ray analysis of Hughes allows M/LQ to lie in the range 90 — 25O/i5o as opposed to a range of 70 — 525/i5o from the optical data. Despite these improvements there is still a considerable amount of uncertainty - and this is a well studied cluster!! To conclude, the X-ray approach certainly will prove to be the most useful method for determining the mass distribution in clusters in the future. For the Coma cluster the X-ray data has improved the limits on M{r) and M/Lg. One should perhaps be a little cautious too in that the X-ray observations do not extend as far as the optical data in Coma (40' versus 3°) - see Merritt (1988) for more discussion. For more distant clusters it is unlikely that the current X-ray data will be a strong contender with the optical methods. In the near future the X-ray constraints on the mass distribution in Coma should be improved by a measurement of the central temperature from the coded mask experiment flown on Spacelab 2 (Skinner et al. 1987). The detection of X-ray emitting gas beyond 40' in this cluster would further constrain the mass distribution.

5. SUBSTRUCTURE AND THE MASS DISTRIBUTION Many Abell clusters exhibit a clumpy galaxy distribution, consistent with the early phase of hierarchical clustering seen in N-body experiments (e.g., Cavaliere et al. 1986). For some of these clusters, for example the bimodal ones such as A98 (Beers et al. 1982), there is good correspondence between the morphology of the X-ray emission in the cluster and the optical galaxy distribution. Recently however several fairly smooth, apparently relaxed, clusters have been found to contain subclumps of galaxies (Coma - Fitchett and Webster 1987, Mellier et al. 1988; Virgo - Binggeli et al. 1987; Hydra I - Fitchett and Merritt 1988). For these clusters the correspondence between the optical and X-ray morphologies is less clear. This is perhaps most striking in the case of the Coma cluster where the central substructure in the galaxy distribution is not reflected in the X-ray emission from this region (see the map in Helfand et al. 1980). This has often been used as an argument against the existence of substructure in this cluster. Another interesting related observation is that X-ray determined cluster centroids differ in the mean by ~ 240/i^g1 kpc from galaxy determined cluster centroids (Beers and Tonry 1986). These observations lead one to question how the mass is distributed in these clusters - is it traced by the galaxies, and therefore clumpy, or is it more smoothly distributed? For a similar discussion of these questions see Ulmer (1988). This section describes a simple model which attempts to explain the substructure observed in the Coma cluster core as the consequence of the accretion of a poor cluster

122

M. J. Fitchett 1

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Figure 4. Model temperature distributions for the N = 4 mass model discussed in the text. The dashed curves satisfy the simple X-ray constraints, while the solid curves satsify all X-ray spectral data on Coma (taken from Hughes 1989). or group. Observationally this is a reasonable hypothesis as clusters do live in the presence of large scale structure (I thank John Huchra for pointing this out to me) and sometimes have neighbouring groups of galaxies (for example Virgo - Binggeli et al.

The Dark Matter Distribution in Clusters

123

1987). Also the densest rich clusters forming in N-body simulations appear to grow at late stages by the accretion of groups (coincidentally the model of the Coma cluster presented by Evrard in his chapter ingested a group very recently in its history). This simple model lends some insight into the issues discussed above, especially the question of whether the dark matter is clumpy or not. Substructure in fairly relaxed clusters might also help constrain the dark matter distribution - I will discuss that idea briefly. This work was carried out in collaboration with Steve Zepf (ST Scl), Tom McGlynn (ST Scl), and Peter Quinn (Stromlo). We have run several N-body simulations of a group infalling into a cluster using a hierarchical N-body code (Barnes and Hut 1986, Hernquist 1988). We have varied both the group and cluster parameters. Cluster parameters were chosen to reflect the three models for the Coma cluster described in Section 3. The results shown in this section are for a dense group (/>Jw*P ~ 35/>£^™a) of mass Mgroup = 1.5 X l O 1 4 / ^ M© falling radially from rest at 4A^g Mpc into the "mass traces light" Coma potential. Less dense groups exhibit qualitatively similar behaviour (see later). Under the mass traces light assumption the total mass of Coma is 3.7/»^Q x 10 MQ. Thus the ratio Mgroup/Mcoma ~ 0.04 and the group is only a small fraction of the mass of the whole system. The initial mass distribution of the infalling group and the Coma cluster were modelled by King models in the results shown here. For all simulations we find basically the same behaviour. The group falls through the cluster center, and for a period of time gives rise to a bimodal structure consisting of the cluster center and the core of the group. The group leaves the cluster center and is either disrupted or returns to reproduce the bimodal structure on subsequent passages. The principal differences between the simulations are the timescales, tf,, over which bimodality is apparent, and the number of passages the group survives through the cluster center Np. For the high density case we estimate that for the first encounter the double structure appears to be detectable for a total period of t^ ~ 3 — 6/i£~g x 10 years, where the uncertainty reflects the viewing angle and precisely where the line is drawn between a double structure in the core, and a group outside the cluster core. This group has Np = 3. For a low density group (with / C ~ p^™) NP = l but a bimodal structure is still formed in the cluster center on this single passage. This structure persists for approximately half of the time for the densest groups. The timescale estimates are based on inspection of the spatial distribution of our simulations. Since one would also expect a signature of the substructure in velocity space these timescales are underestimates of the true timescales. To compare this model with the Coma cluster it is necessary to assume a viewing angle for the simulation. Since the relative velocity of the subclumps in the center of the Coma cluster is small (~ 600 km s —see Fitchett and Webster 1987) compared to the velocity of the infalling group as it passes through the cluster center (typically ~ 3000 km s ), we assume that Coma corresponds to our looking at a group falling in perpendicular to the line of sight. Figure 5 compares the matter distribution as observed from this angle in the central region of the simulation with the galaxy distribution in the center of Coma (the scale is in arcminutes—recall l' corresponds to ~ 40A^Q kpc at Coma). The group fell in from the right and we show the simulation just after the group has passed through the cluster center. The group itself gives one density maximum (the left density peak) and the cluster center forms the second density peak. Although the group was started with a much greater central density than the cluster, the two density maxima observed appear to be roughly equal. Clearly the spatial distributions agree fairly well. We have also analyzed the velocity histograms of the central region of the

124

M. J. Fitchett

-10

-10

20

Figure 5. Density contours of the central region of the Coma cluster (upper plot) and the corresponding region for the simulation. The data for the Coma cluster is taken from Godwin and Peach (1977) and galaxies down to V25 = 15.5 are plotted. The contours used in the cluster and simulation represent the same density contrasts.

The Dark Matter Distribution in Clusters

125

simulation and the 'core' of the Coma cluster, and find consistency. Figure 6 shows an X-ray map generated under the assumption of hydrostatic equilibrium from the simulation as observed in Figure 5, and viewed from the same direction (for method see Cavaliere et al. 1986). The contours are smooth and and reasonably fit with ellipses. The center of the X-ray distribution is not coincident with either of the density maxima of the simulation but appears to lie between them. The contours become rounder as one gets further from the center of the cluster. This can be compared to the X-ray map shown in Helfand et al. (1980). There is good qualitative agreement with the simulated X-ray map. The observed X-ray center of Coma lies between the two concentrations of galaxies in the cluster shown in Figure 5.

L-20

-10

x (arcmins)

Figure 6. X-ray emission for the simulation shown in Figure 5. This was calculated using the Hydrostatic assumption with 7 = 5/3. The contours are logarithmically spaced and are in arbitrary units. If the galaxies trace the mass distribution then this simple model is consistent with both the observed spatial subclustering in the Coma core and the almost elliptical X-ray emission from this region. Many authors have argued in the past that substructure in the mass distribution should cause substructure in X-ray maps. Indeed since the X-ray emissivity scales as pjias it has also been argued that subclumps should be even more obvious in X-rays. However pgas{r) is determined by the cluster potential <}>DM{T) which, even for a clumpy mass distribution, might have only one minima (being an integral over the mass distribution this is not too surprising). Clearly the number of minima in the potential depends on the details of the mass distribution - subclumps

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within smooth clusters probably perturb the potential little and it remains close to elliptical or circular, whereas large scale substructure (in the form of well separated subclumps, such as A98) will give rise to a potential which has more than one local minima. The main point though is that one should be wary of assuming that smooth X-ray emission automatically guarantees a smooth matter distribution. All that can be safely said is that the potential is smooth. Very high signal to noise ratio X-ray observations would be needed to find the actual mass distribution for clusters with substructure (i.e., to solve PQM = -V2<J>DM/4ITG). I wish to stress that this is not to say that X-ray determined masses will be in large error in these cases. Indeed since the mass of the group remnant is small the X-ray determined mass will be very close to correct. Rather the point is that the X-ray maps might not show the detailed matter distribution in these systems. It is important to stress that by varying the cluster and group parameters, as well as the viewing angle, our scenario might be able to explain substructure seen in other clusters. For example the velocity substructure observed in the Hydra I cluster (Fitchett & Merritt 1988) is probably due to our observing a group infalling along the line of sight to the cluster. Spatially resolved subclumps with large relative velocities most likely correspond to the viewing angle being somewhat intermediate between the Coma and Hydra I cases. The substructure seen in the simulations is most pronounced for the more massive, centrally concentrated groups. Less massive and less dense groups do give rise to similar observable consequences, but their easier disruption leads to a shorter time over which their effects are observable. Observationally the effect of the infall of a larger number of these smaller groups is similar to that of one very massive and dense group. It would be useful to know the frequency of this effect. Large scale cosmological simulations could in principle determine this. Here a simple estimate of the frequency of central substructure will be made. For the high density group simulations spatial bimodality on cluster 'core' scales is observed approximately 10 per cent of the time (assuming an angle between the line-of-sight and the axis of infall of 60 degrees). Most of the remainder of the time, the group is too far from the core to be detected as central substructure, and a small percentage of the time is spent in a configuration in which the cluster and the groups cannot be separated spatially. Encounters with dense groups may be unlikely but our simulations have shown that the less dense groups can give rise to the same feature. This appears to last ~ 1.5 — 3/I^Q X 10 years, and the group disrupts after first passage. It seems likely that clusters will typically accrete at least a few low density groups during the age of the universe. If only three low density groups or one high density group is accreted in a Hubble time then there is a ~ 10 per cent chance of seeing a cluster with central substructure. Indeed this estimate should be viewed as a lower limit since it may be that we are actually living in the epoch of cluster formation. Also it is likely that the densest clusters may accrete at the largest rate. There is also some evidence that the high density groups we used might not be so unusual; some of Hickson's compact groups are found to have spatial densities approximately an order of magnitude larger than that of Coma (Hickson et al. 1988) and some poor clusters containing cDs have central densities at least as high as that in Coma (inferred from the data of Beers et al. 1984). Alternatively we might argue that this phenomenon must be very common as the infall of groups of galaxies into clusters is both observed (e.g., Mellier et al. 1988, Bingelli et al. 1987) and seen in simulations (e.g., Evrard 1989). Furthermore some well-studied clusters do show evidence for central substructure. Careful analysis of a large cluster sample is necessary in order to quantify

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the frequency of this. To summarize, this very simple model gives rise to substructure which appears to be very similar to that observed in the Coma cluster, while producing an almost elliptical distribution of X-ray emission. Clearly in our model, the X-ray centroid will not always coincide with the (ill-determined) galaxy centroid. This reminds us that the X-ray emission from clusters reflects the gravitational potential of the cluster, which is invariably much smoother than the cluster mass distribution. Current X-ray images may give reasonable mass estimates for regions of clusters, but do not have sufficient signal to noise to describe the detailed cluster mass distribution - ironically the galaxies may do a better job. If the accreted group is a poor cD cluster, this scenario gives a natural explanation of the phenomena of 'speeding' cDs (Hill et al. 1988, Sharpies et al. 1988). The cD galaxy belongs not to the cluster but to the group being accreted. This might also be the appropriate mechanism in Coma itself, since the central D galaxies in Coma resemble the central galaxies of poor cD clusters which often lack the extended envelopes of cDs in larger clusters. It was our hope at the start of this project that the observed substructure in the Coma cluster could be used to set limits on the cluster mass distribution. For example if the dark matter were very centrally concentrated infalling groups would be tidally disrupted as they fell into the cluster and not reach the core intact. Simulations of a high density group falling into a centrally concentrated model (corresponding to Merritt's most extreme, but allowed, centrally concentrated model) do show that the group is disrupted after first passage through the cluster center. However there is a time at which the model looks similar to the observations and so this cannot strictly rule out the centrally concentrated model. Allowing the infalling groups to have some angular momentum might lead to more optimistic results in that then the group would explore a larger region of the cluster tidal field and be disrupted before reaching the cluster center. The probability of observing subclumps close to the cluster center might also be higher in this case than in the simple case of radial infall. Constraining the cluster mass distribution by this method is unfortunately further complicated by the need to make some assumptions about the properties of the infalling groups. At this stage it is safest to conclude that this model shows that the dark matter in Coma could be distributed just like the galaxies (i.e., clumpy in the center of the cluster) and yet still give rise to X-ray emission which is close to elliptical in shape.

6. GRAVITATIONAL LENSING Recently giant luminous arcs have been discovered in some high redshift clusters (CL2244-02 Lynds & Petrosian 1986, A370 Soucail et al. 1987). These arcs are typically ~ 20" in length (corresponding to ~ 150/I^Q kpc for A370), and lie ~ 25" from the cluster center with their centers of curvature close to the cluster center. Several mechanisms have been proposed to explain how the arcs were formed - star formation in cooling flows, galaxy-galaxy collisions, explosions and gravitational lensing. The lensing hypothesis is that the arcs are the highly distorted images of background galaxies (Paczynski 1987). This hypothesis can be tested by measuring the redshift of the arc. Since the arcs are intrinsically faint this is a difficult procedure but Soucail et al. (1988), using a curved slit and 6 hours of integration on the ESO 3.6m telescope, found the arc in A370 to be at a redshift zarc — 0.724. The cluster has zc\ = 0.37, suggesting that the arc is not physically associated with the cluster. Coupling this observation with the beautiful symmetry of these arcs, and their location and orientation strongly

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suggests that they arise as a result of gravitational lensing. Under this hypothesis the giant luminous arcs provide a new and independent method for determining cluster masses interior to the arc, and so probe the cluster mass distribution on fairly small scales. As will be discussed later the numerous smaller arcs (arclets) which should accompany their more spectacular cousins provide additional probes of the cluster mass distribution and its morphology. With the launch of The Hubble Space Telescope and its ability to image high redshift clusters at high resolution, especially in the UV (where arcs are most visible) this method will become even more useful. Several detailed calculations have been carried out to determine the mass distribution in clusters using the giant luminous arcs (e.g., Grossman & Narayan 1989, Hammer & Rigaut 1989, Bergmann et al. 1989). These approaches are quite complex and so to get the idea of the basic physics across I will examine an idealized case. Suppose an observed luminous arc is large in angular extent, and can be assumed to represent one of the images which arises if the perfect Einstein ring configuration (source, center of lens and observer all aligned) is perturbed slightly. Assume also that the cluster mass distribution is axially symmetric about the line joining its center to the observer. Then the geometry of the situation and the bending angle formula for the cluster show that for the Einstein ring (and thereby for a small perturbation to it)

M(
c2

Dps

where M(< b) is the total mass interior to 6, the arc's impact parameter at the cluster. The D{j are angular diameter distances between the observer, lens and source. The D(j depend strongly on the source and lens redshifts zSOurce, ziens, a n ^ only weakly on the assumed il of the universe and the quantity of matter in the light beams between these various objects (see Turner et al. 1984). The quantity E cr ,( therefore essentially depends on the source and lens redshifts zSource, and z\ens. For a cluster to have any chance of producing a giant luminous arc it must have a central surface mass density ^cent > ^crit- For the case of perfect alignment an Einstein ring will be formed at the impact parameter b where the average surface mass density interior to the impact parameter b is given by S(< b) = £ cr ,$. For an isothermal sphere model of a cluster mass distribution

How large is Scr,
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this for the main axe in A370 and found M(< 150h^kpc) ~ 1.5 - 2.3 x 10u h^MQ. This corresponds to an M/Lft ~ 100/»50 on this scale. Note that this estimate is independent of the problems we encountered with the dynamical and X-ray approaches. Naturally this is rather an idealized calculation. Even if the giant arcs in A370 and CL2244-02 were caused by slight perturbations to the Einstein ring geometry one would, given the length of the observed arc, expect to see a counter-arc of substantial length on the opposite side of the cluster center. This is not seen in either of these clusters, suggesting the situation is more complex. It is worth pointing out that A963 does appear to have two similar arcs situated opposite each other (Lavery & Henry 1988). This cluster with its single cD galaxy might well approximate the axially symmetric case discussed above. Motivated by the general lack of opposing arcs and the need to calculate the expected frequency of luminous arcs Grossman & Narayan (1988) made more realistic models of gravitational lensing of extended background objects by clusters. They modelled clusters as smooth potential wells with non-zero monopole, quadrupole and octupole moments of the mass distribution. They also included the bumps in the potential generated by individual massive galaxies in the cluster with L > 0.1L*. Their clusters had a high velocity dispersion (1250 km s" 1 ) and core radii drawn from an X-ray determined core radius distribution (Jones & Forman 1984). Grossman and Narayan found that these type of clusters would most often form single extended arcs without counter-arcs. They found that for a background galaxy (source) density of 18 galaxies arcmin" 2 approximately 12% of their simulated clusters generated arcs of length > 10". They also predicted the existence of ~ 5 times as many small arcs in clusters (of lengths ~ 10 - 20") as large arcs (> 20"). Nemiroff and Dekel (1989) also calculated the probability of generating luminous arcs. They used a simpler model for their clusters—an isothermal sphere—and found the fraction of clusters (of given velocity dispersion) which would show an arc as a function of the axial ratio A of the arc, its angular extent, and the limiting surface magnitude to which the cluster is examined. Their model predicts many more arcs at fainter limiting magnitudes, and also that the number of background sources which can have small distortions can be large (it scales approximately as (A — 1) in this model). These predictions have been borne out observationally (A370 - Fort et al. 1988, A2218 - Pello-Descayre et al. 1988). Fort et al. obtained deep high resolution CCD images of A370 and found, in addition to the primary arc, 6 faint blue elongated objects ranging in length from 3 — 9" and lying within ~ l' of the cluster center. Grossman and Narayan (1989) have modelled this system of small arcs with an elliptical mass distribution for the cluster (since the new small arcs appear to lie preferentially to the North and South of the cluster center) with the potential perturbed by the brighter cluster galaxies. Not only do they find the MJLQ within this l' region (corresponding to M/Lg ~ 14O/i5o within ~ 400/I^Q kpc), but they were also able to show that the dark matter distribution had to be significantly elongated (with an axis ratio of at least 4:3) in the North-South direction. Thus even with a few arcs the dark matter morphology in these high redshift clusters can be probed. The really exciting advances now being made in this area are primarily due to attempts to image clusters to even fainter limiting magnitudes. In their paper Grossman & Narayan (1989) showed a simulation of the effect of their best fit model to A370 on a distribution of background sources with a surface density corresponding to that observed by Tyson (i.e., 108 galaxies arcmin ). They showed that many distorted images would be seen, tangentially aligned with respect to the cluster center. I estimate from their

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figure of order 60 obviously aligned arclets, though I suspect that this number (and the 108 galaxies arcmin" 2 ) should both be reduced by a factor of ~ 3 since Tyson actually claims that the high redshift galaxy population (selected by its extremely blue B — R color) has a surface density at 29 B mags arcsec" 2 of 30 galaxies arcmin" 2 . Even a reduction by this factor would still give rise to a large sample of arclets from which the cluster mass and morphology constraints could be improved even more. On the observational side Tyson et al. (1989) have imaged A1689 and CL1409+52 to a limiting surface brightness of 29 B mags arcsec" 2 and do indeed find significant numbers of tangentially aligned images. Analysis of these arc systems by the methods described by Grossman & Narayan (1989) and Grossman et al. (1989) should shed new light on the dark matter and its distribution in clusters.

7. CONCLUSIONS The main points I hope to have made in this article are the following: • Standard virial theorem mass estimates can severely over or under-estimate cluster masses if the cluster dark matter is not distributed like the galaxies in the cluster. • Many redshifts (probably > 400) are required to determine the actual mass distribution even in a simple spherical cluster. Future studies might be able to constrain cluster mass distributions by determining the shape of the cluster velocity histogram as a function of radius. • X-ray determined mass distributions will be extremely reliable in the future. At present the lack of spatially resolved gas temperature measurements means that the X-ray method still allows for a large range of mass distributions. • Although the X-ray approach will one day supersede optical methods, redshift information for galaxies in clusters is still very important. Coupling an X-ray determined M(r) with the observed cluster projected velocity dispersion profile <rp(R) will yield /?(r), the anisotropy of the galaxy orbits. This is an important function for determining how the galaxies interact with the ICP. • The substructure seen in the center of the Coma cluster is consistent with the almost elliptical X-ray emission from this region. One should therefore be wary of assuming that a single maxima in the X-ray emission implies a single dark matter density maxima. The situation can be more complex, and in fact the galaxy distribution might trace the dark matter distribution more precisely than the X-rays (X-ray data would need very high signal to noise to determine the detailed dark matter distribution in these cases). Clusters where the X-ray and galaxy determined centroids differ substantially could also be cases of such an effect. • Giant luminous arcs in clusters can yield measurements of the mass interior to the arc (under certain reasonable assumptions). These mass determinations (on small scales, typically within ~ 150/I^"Q kpc) are not subject to the problems presently associated with the optical and X-ray approaches. • The large number of distorted background galaxies observed behind some rich clusters can probe both the amount of dark matter and its morphology in clusters. Faint distorted galaxies are also observed at greater distances from cluster centers (up to ~ 400h§Q kpc) and so can set limits on the mass distribution at larger radii than the more spectacular giant luminous arcs. Observations made with the Hubble Space Telescope should allow interesting limits to be placed on the mass distribution in clusters by this method.

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There is still a fair way to go before we will have a good constraint on the mass distribution in even one cluster. However the considerable progress over the last few years both observationally and theoretically, coupled with new observational facilities (fiber systems, ROSAT, HST, AXAF), suggest that one should be optimistic - the apparently simple problem of determining the mass distribution in clusters should soon be solved. I am very grateful to my numerous colleagues and friends who have always been very stimulating and willing to share their ideas with me, in particular Tim Beers, Laura Danly, Alistair Edge, Richard Ellis, Bernard Fort, Carlos Frenk, John Huchra, John Lucey, Alain Mazure, Yannick Mellier, Tom McGlynn, Dave Merritt, Richard Mushotzky, Bill Oegerle, Otto Richter, Ian Smail, Tony Tyson, Meg Urry, Martin Watt, Mike West, and Steve Zepf. Thanks too to all of the people who allowed me to use Figures from their papers. Finally a very special thanks to Mary Dagold, Laura Danly, Barb Eller and Meg Urry for being there with cups of tea, and the right comments, just when I needed them.

REFERENCES Bailey, M.E., 1982, M.N.R.A.S 201, 271. Barnes, J. and Hut, P., 1986, Nature 324, 349. Beers, T.C., Flynn, K., and Gebhardt, K., 1989, preprint. Beers, T.C., Geller, M.J., and Huchra, 1982, Ap.J. 257, 23. Beers, T.C., Geller, M.J., Huchra, J.P., Latham, D.W., and Davis R.J. 1984, Ap.J. 283, 33. Beers, T.C. and Tonry, J.L. 1986, Ap.J. 300, 557. Bergmann, A.G., Petrosian, V., and Lynds, R., 1989, preprint. Binggeli, B., Tammann, G.A., and Sandage, A. 1987, A.J. 94, 251. Binney, J. and Mamon, G.A., 1982, M.N.R.A.S 200, 361. Bothun, G.D., Geller, M.J., Beers, T . C , and Huchra, J.P. 1983, Ap.J. 268, 47. Cavaliere, A. and Fusco-Femiano, 1976, Astron. Astrophys. 49, 137. Cavaliere, A., Santangelo, P., Tarquini, G., and Vittorio, N. 1986, Ap. J. 305, 651. Chandrasekhar, S., 1942, Principles of Stellar Dynamics, University of Chicago. Colless, M., 1987, PhD Thesis, University of Cambridge. Colless, M., and Hewett, P. 1987, M.N.R.A.S. 224, 453. Dejonghe, H., 1987, M.N.R.A.S. 224, 13. Dressier, A., and Shectman, S. 1988, A.J. 95, 985. Edge, A.C., 1989, PhD Thesis, University of Leicester. Evrard, A, 1989, preprint. Fabricant, D., Beers, T . C , Geller, M.J., Gorenstein, P., Huchra, J.P., and Kurtz, M.J., 1986, Ap. J. 308, 530 Fitchett, M.J., 1988, Minnesota Lecture Series on Astrophysics: Clusters of Galaxies and Large-scale structure, edited by J. Dickey, A.S.P. Conference Series Volume 5. Fitchett, M.J., and Merritt, D. 1988. Ap.J. 335, 18. Fitchett, M.J., and Webster, R.L. 1987, Ap.J. 317, 653. Fitchett, M.J., and Smail, I. 1989, in preparation.

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Fort, B., Prieur, J.L., Mathez, G., Mellier, Y. and Soucail, G., 1988, Astron. Astrophys. 200, L17 Grossman, S. A. and Narayan, R. 1988, Ap. J. Lett. 324, L37. Grossman, S. A. and Narayan, R. 1989, preprint. Grossman, S. A., Zaritsky, D. and Elston, R., 1989, preprint. Hammer, F. and Rigaut, F. 1989, Astron and Astrophys., in press. Heisler, J., Tremaine, S., Bahcall, J.N., 1985, Ap. J. 298, 8. Helfand, D.J., Ku, W.H.-M., and Abramopoulos, F., 1980, Higlights of Astronomy 5, 747. Henriksen, M.J. and Mushotzky, R.F., 1986, Ap. J. 302, 287. Hernquist, 1988, Comput. Phys. Commun. 48, 107. Hickson, P., Kindl, E., and Huchra J.P 1988, Ap.J. 331, 64. Hill, J.M., Hintzen, P., Oegerle, W.R., Romanishin, W., Lesser, M.P., Eisenhamer, J.D., and Batuski, D.J. 1988, Ap.J. Lett. 332, 23. Hughes, J. P. 1989, Ap. J. 337, 21. Hughes, J. P., Gorenstein, P., and Fabricant, D., 1988, Ap. J. bf 329, 82. Jones, C. and Forman, W. 1984, Ap. J. 276, 38. Kent, S. M. and Gunn, J. E., 1982, A. J. 87, 945. Lavery, R.J., and Henry, J.P., 1988, Ap. J. Lett 329, L21. Lynds, R., and Petrosian, V., 1986, Bull. Am. Astr. Soc. 18, 1014. Mellier, Y., Mathez, G., Mazure, A., Chavineau, B., and Proust, D. 1988, Astron. Astrophys. 199, 67. Merritt, D. 1987, Ap. J. 313, 121. Merritt, D., 1988, Minnesota Lecture Series on Astrophysics: Clusters of Galaxies and Large-scale structure, edited by J. Dickey, A.S.P. Conference Series Volume 5. Mushotzky, R. F. 1984, Physica Scripta T7, 157. Mushotzky, R. F. 1987, Astro. Lett, and Comm. 26, 43. Nemiroff, R.J. and Dekel, A., 1989, Ap. J. 344, 51. Paczynski, P., 1987, Nature 325, 572. Pello-Descayre, R., Soucail, G., Sanahuja, B, Mathez, G. and Ojero, E., 1988, Astron. Astrophys. 190, L l l . Sarazin, C. L. 1986, Rev. Mod. Phys. 58, 1. Sharpies, R. M., Ellis, R. S. and Gray, P. M. 1988, M.N.R.A.S. 231, 479. Skinner, G. K., Eyles,C. J., Willmore, A. P., Bertram, D., Church, M. J., Harper, P. K. S., Herring, J. R. H., Peden, J. C. M., Pollock, A. M. T., Ponman, T. J. and Watt, M. P., 1987. Adv. Space Res. 7, (5)223. Soucail, G., Fort, B., Mellier, Y., Picat, J.P., 1987, Astron. Astrophys. 172, L14. Soucail, G., Mellier, Y., Fort, B., Mathez, G., Cailloux, M., 1988, Astron. Astrophys. 191, L19. Stewart, G.C., Canizares, C.R., Fabian, A.C., and Nulsen, P.E.J., 1984, Ap. J. 278, 536. The, L.S. and White, S.D.M., 1986, A.J. 92, 1248. Turner, E.L., Ostriker, J.P., and Gott, J.R., 1984, Ap. J. 284, 1. Tyson, J.A., Valdes, F. and Wenk, R.A., 1989, preprint. Ulmer, M.P., 1988, Minnesota Lecture Series on Astrophysics: Clusters of Galaxies and Large-scale structure, edited by J. Dickey, A.S.P. Conference Series Volume 5.

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DISCUSSION Felten: You could enhance the incidence of these subclumps if you had large projection angles, if say you were more or less looking along the line of sight. Fitchett: Yes that's true. If you do look directly along the line of sight, you wouldn't see the clump in physical space, but you would see it in velocity space. This could explain the data on Hydra I where when you look in the center you see a bimodal velocity histogram. Kaiser: How do you calculate the gas in this simulation? Fitchett: There's no gas. This is a pure N-body simulation. We don't do any calculations of what happens to the gas. That's what I would really like to do. In looking at Gus, I think he could do it. The plots show the X-ray emission expected from gas in Hydrostatic equilibrium with the matter in our simulation. Kaiser: What about the potential changing? Fitchett: Yes, it will be changing, slightly. The core is probably dynamic. Peebles: What about the spirals? Fitchett: I'm sorry—I thought you were teasing me about the spirals! We haven't got the resolution. You could probably simulate dropping in a group of spirals and see what happens to them. It's beyond our capabilities here anyway at the moment. Unknown: through?

Are you expecting the group gas to retain its coherence as it passes

Fitchett: The group gas is probably stripped even before it gets to the center I would guess - because it is stripped from spirals. Unknown: So, if the X-ray center is not aligning with the galaxy center it is not that the X-ray center is new, it's that the galaxy counts are so dominated by the group passing through the gas. Fitchett: That's what I would guess. It certainly looks like it from the plot. If we said they were all galaxies, then you really would have trouble with finding the centroid anyway. It wouldn't be very meaningful. Rubin: Are there any velocity differences? Could such a model explain Centaurus? Fitchett: Between the clumps, yes, about 3000 km s . But Centaurus is two big clusters, I think. So unless you postulated it was two big clumps falling toward each other it wouldn't work. However, this model may explain Hydra I because in Hydra I the galaxy velocities in the outside region of the cluster look gaussian, whereas the inner region looks bimodal. This is like our model viewed falling towards you. The velocity difference depends on the mass of the cluster, of course. The actual velocity is

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just the infall velocity in the center. Unknown: Don't you think radial orbits axe unrealistic? Fitchett: Yes but it might not matter too much. In fact, the groups in cosmological simulations appear to go straight in anyway. It may also not matter because the groups have got to end up in the center, somehow, as they are unlikely to be projection effects. So the fact that the group explores the whole tidal field probably means that it's going to get disrupted unless it sticks around the outside and you are just seeing a projection. It somehow has got to go through the rough patch and be blown apart. Felten: You have to expect projection effects. You can have high angular momentum and still have projections. Fitchett: Yes the subclumps could be projection effects, but I think the probability is very small. The subclumps cover a very small area, so that would give you some sense of the probability. Also substructure is not just seen in Coma - substructure like this is seen in several clusters. When people are really careful, they find it. So it is unlikely to be projection effects like this in every case. Mushotzky: First a comment then a question. We don't have to wait for an AXAF to find the temperature profile for some clusters. There exists a class of very low X-ray luminosity clusters that also have measured optical dispersions. The temperatures are low enough that it is likely that ROSAT will be likely to derive sensible bounds on the temperature versus radius profile. So those of us who will still be alive next year, rather than ten years from now have a hope. The other thing that you didn't mention from the Jack Hughes's paper, which I thought would be interesting to the audience here, is that the X-ray emitting gas is an ever larger fraction of the total mass of the system and to very large scale lengths. Extrapolating a little bit beyond the well observed surface brightness profile we find the mass of baryons which are contained mostly in the gas is on the order of 20% to 30% of the dynamical total mass of the system, which means that one of the models that we use to arrive at that are incorrect-they are not self consistent. I think a lot of us are going to be upset when we realize that a fair fraction of the mass in these systems is baryons. Fitchett: That's true, any self consistent model should put that in. Struble: Is it true that most of the arc clusters contain double galaxies such as A370? Is it easier for two static centers to produce a single arc? Fitchett: Well for a perfectly spherical cluster, if you get one reasonably long arc then you must form a secondary arc on the opposite side. Grossman and Narayan showed that you need an elliptical potential to generate single arcs and obviously two mass centers would do that. Lavery: arcs

There is a cluster A963 that has a single dominant galaxy and shows two

Fitchett: Yes that is consistent with it having a larger degree of symmetry.

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Petrosian: The two clusters that we have observed with Roger Lynds do have two centers of concentration of mass - both of them you showed - A370 and 2244-02. You see one well defined arc. But in the case of A2218 you see pieces of arc, there is one dominant cD galaxy and also in A963 as was just mentioned. The other thing I wanted to mention is that maybe there is some confusion about what I said about light tracing mass versus the dark matter having a different distribution to the light. This is a little bit a matter of scale. If you think on the scale of the graininess of the distribution of the galaxies, the dark matter cannot have the same graininess. On a scale of 50 to 100 kpc the dark matter should have a different distribution to the galaxies, especially for A370. There's a poster that explains this. On larger scales the galaxies may have the same distribution. I think we can also can use the lens to say something about how concentrated the dark matter is. In fact, in both these clusters, the dark matter has to be very highly concentrated toward the center. It cannot be very spread, because if you spread it too far out, you have a lower surface density and you cannot, as you mentioned, go to a central surface density below the critical value, otherwise you won't have lensing. Otherwise if you don't lower the density and make the mass distribution large, you're going to get masses much bigger than 10 15 solar masses, so Q, would be more than one. You don't want that. (Laughter) Felten: What about the M/L1 What about the total mass? Petrosian: Well, our models give M/L between 200 to 1000. This is M/Lg and that's for a Hubble constant of 50. Bower: In order to get the distorted cores in clusters, you were dropping in fairly massive groups. Do you then have a problem that we must live in a very special epoch in that you are going to have clusters growing at a rapid rate in order to get so many distorted cores. Fitchett: Well, it depends on how many we see anyway. Nobody has actually done a real survey and tried to estimate the frequency of core substructure so I can't say if this is a problem. Jaffe: Wouldn't you expect to see more subclumps at large radii—they move more slowly there. Fitchett: Exactly, and we do. Remember the plot by Mellier - it had many groups at larger radii. You could test that, too, by the time dependence of the position of the groups in the simulation. Jaffe: They should be mostly on the outside too unless we're in a very special epoch. Fitchett: Yes, that's right. Jaffe: You can always find the angular momentum of the observed groups by looking at the velocity of the groups. Fitchett: That's a good idea, the bright velocities especially because they are supposed to be at the centers of the groups. That's a good idea.

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Huchra: I should warn you a little bit that all of those groups might not be at the distance of Coma. West: For this idea don't you basically require il = 1? You want groups to fall in often enough to produce the frequency of substructure that we find in central regions of clusters, then you must have groups infalling fairly frequently even today and that would be more difficult in an open universe. Fitchett: I actually don't know because I don't think we know the observed frequency of core substructure for one thing. If you just drop a dense group in at a random time sometime during the Hubble time, you get 10% of clusters affected now. West: today.

If we live in an open universe, I would expect that happens very infrequently

Fitchett: I guess it all depends on the model. Couldn't there be models with a lot of small scale power, even with low fl, that produce groups on the outskirts of clusters which would then fall in. It's hard to know until you do the calculation. Giacconi: Shouldn't there be a relationship as far as statistics go, between this idea and the idea that Cavaliere proposed this morning that if the binding energy for the subgroups is high enough then this would delay the cluster formation. Couldn't you somehow combine this interaction with his? Fitchett: Ideally, yes, but we specifically modeled a spherically symmetrical system. I don't think he has the resolution. Ideally, you would want to combine both approaches. It's not fair just to assume we have a relaxed cluster and we drop something in, but it is a first approach. Cavaliere: His observation is in some sense saying that dense groups fall at late times into already formed clusters. Fitchett: That's the whole idea, yes. In fact I had a conversation with Gus once where he told me that the highest a peaks form relaxed systems into which small things range. Evrard: You'll see on Wednesday my version of the Coma cluster which looks very similar to this. Unknown: Isn't it true that the substructure in the middle of Coma is really due to the clumping around 4874 and 4889? Neither of these are plausible little groups. Fitchett: These aren't little groups, about 5 x 1O13M0. Presumably a group might evolve, forming say CD and D galaxies within the group. So I wouldn't be surprised if you have a group in which you formed a cD as it fell in or before it fell in. So this is of no surprise to me. Huchra: I just want to make a plea which may or may not help you and that is don't forget that clusters live in the presence of large scale structure or in particular, clusters live in superclusters, so it may well be the case that being carried along with the clusters is other stuff in the form of groups and individual galaxies, and this process

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may happen quite frequently even in a low Q universe. I don't know how to make a good estimate of that, but it might be something to look at. West: I think the perfect way to test it is to look at cosmological simulations with open and closed universes. You can see how frequently you expect it to fall in. Peebles: Or you can look at the observations, the galaxy-cluster cross-correlation function. You know that the density of galaxies is high in the environment of clusters.

THE EFFECT OF THE CLUSTER ENVIRONMENT ON GALAXIES

Bradley C. Whitmore Space Telescope Science Institute 3700 San Martin Drive Baltimore, MD 21218

Abstract. Various observations indicate that the cluster environment can affect the structure and dynamics of galaxies. This review concentrates on the effect the environment can have on three of the most basic properties of a galaxy; the morphological type, the size, and the distribution of mass. A reexamination of the morphology - density relation suggests that the fundamental driver may be related to some global property of the cluster, such as the distance from the cluster center, rather than some local property, such as membership in a local subclump within the cluster. While there is good evidence that the size of a galaxy can be increased (i.e., cD galaxies) or decreased (i.e., early type galaxies near the centers of clusters) by the cluster environment, it is not clear what physical mechanism is responsible. There is tentative evidence that rotation curves of spiral galaxies near the centers of clusters are falling, perhaps indicating that the dark halo has been stripped off. Rotation curves for spiral galaxies in compact groups are even more bizarre, providing strong evidence that the group environment has affected the kinematics of these galaxies.

1. INTRODUCTION Perhaps the three most basic questions an extragalactic astronomer might be asked are: 1. Why are some galaxies flattened into disks while others are elliptical in shape ? 2. How big are galaxies ? 3. How massive are galaxies ? Although we can fill journals with details about galaxies, an astronomer cannot really answer these three basic questions with any confidence. The first question raises the "nature vs. nurture" problem. Is the morphological type of a galaxy determined at birth by its initial conditions, or does the environment of the galaxy control its destiny? While the standard picture that different initial conditions cause the difference in morphology still seems plausible {e.g., Sandage, Freeman, and Stokes 1970, Gott and Thuan 1976), recent interest has centered on Toomre's (1977) suggestion that all galaxies begin as disks and then merge to form elliptical galaxies. The problem with the second question is that a galaxy does not really have an "edge", so the definition of

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size is somewhat arbitrary. What makes things worse is that rotation curves in spiral galaxies stay flat as far out as we can observe them, so the mass is still increasing linearly with radius with no sign of the edge of the dark matter in sight. The third question is also impossible to answer very precisely since we don't know what or where the dark matter is in a galaxy. The fact that only about 10% of a galaxy is luminous means that we are studying only the tip of the iceberg, and shows just how little we really know about galaxies. One of the principle reasons many of us are interested in the study of clusters is that these three basic properties of a galaxy, the morphological type, the size, and the distribution of mass, all appear to be affected by the cluster environment. As early as 1931 (Hubble and Humason 1931) it was known that elliptical galaxies were preferentially found in clusters, providing evidence that the morphological types were closely linked with the environment. The cluster environment also appears to be able to modify the size of a galaxy. cD galaxies can grow to prodigious size, possibly at the expense of the nearby galaxies which become shrunken via tidal stripping. Recent measurements of emission-line rotation curves also suggest that the massive halos of spiral galaxies near the centers of clusters may be stripped, or perhaps were never allowed to form in the first place. The fact that these three basic galactic properties all vary as a function of position within a cluster should provide a fundamental clue about the formation of galaxies. If we are going to answer the three questions posed above in the near future it is likely to be from studies of galaxies within clusters. This article will not be a comprehensive review of the subject, but instead will focus on some of the key studies which are relevant to the three questions posed above. The reader is referred to recent review articles by Haynes, Giovanelli, and Chincarini (1984) and Haynes (1990; radio observations), Richstone (1990; cluster simulations), Binggeli, Sandage, and Tammann (1988; luminosity functions), White (1982; theoretical mechanisms) and Dressier (1984a; general review), for more comprehensive reviews. Our approach will be to examine the evidence for variations in the morphological type, size, and mass as a function of environment; from the dense inner regions of rich clusters and compact groups, to the sparser regions in the outer parts of clusters, the loose groups, and the field. The emphasis will be on methods to distinguish which of the proposed mechanisms are responsible for the various effects. This review will concern itself primarily with optical observations. However, various theoretical mechanisms which may be responsible for modifying the properties of galaxies will be briefly discussed in Section 2, in order to develop a framework from which to examine the observations. Sections 3, 4, and 5 will then examine how the morphological type, size, and distribution of mass within a galaxy are affected by its environment. A short summary is provided in Section 6. 2. POSSIBLE MECHANISMS A wide variety of theoretical mechanisms have been proposed for affecting the structure and dynamics of galaxies in clusters. It is uncertain which of these are actually operating, and to what degree they are important. For example, even after more than a decade of concerted effort we are not certain that ram-pressure sweeping, one of the most "accepted" mechanisms, is the cause of HI deficiencies in cluster galaxies. The main difficulty in distinguishing which of the different mechanisms are occuring is that quite often the resulting observational signatures are nearly identical. In this case, gas evaporation may also be responsible for the HI deficiencies.

Effect of the Cluster Environment on Galaxies This review will often focus on one specific test. Is the effect caused by a local mechanism, such as the tidal interactions between a few nearby galaxies, or a global mechanism, such as the mean tidal shear from the potential well of the cluster? More specifically, we will examine whether correlations are better versus the local projected galaxy density, or a global property such as the distance from the center of the cluster, ^•cluster- This rough breakdown is only a first step in unravelling the puzzle. Several other tests and observations will be required to be certain of specific mechanisms. For example, HI deficiencies appear to correlate quite well with Cluster (although it is not clear whether they have been tested versus local galaxy density). This would suggest that something about the global condition of the cluster, such as the presence of intergalactic gas near the center, is responsible for the effect. In order to pin it down further we need to test whether HI deficient galaxies have a larger velocity dispersion than normal galaxies, since the effectiveness of ram-pressure sweeping should vary as the square of the velocity with respect to the cluster (see Haynes 1990). 2.1 Local Mechanisms The strong correlation between morphology and local projected galaxy density (Dressier 1980), and the recent surge in interest concerning the possibility that subclustering exists (Geller and Beers 1982, Dressier and Shectman 1988, Fitchett 1988) has led to the general opinion that the subclusters are physical entities and play a dominant role in determining several galactic properties (see West, Oemler, and Dekel 1988, for a dissenting opinion). These subclusters have smaller internal velocity dispersions than the cluster as a whole, making galaxy-galaxy encounters stronger, and removing one of the early criticisms that interactions between galaxies traveling at large relative velocities (w 1000 km s ) would have little effect on the galaxies. It is important to carefully define what we mean by a subcluster. In some studies it has been used to mean a small density enhancement with only a few members. In other studies it may contain nearly as many members as the main cluster. Our goal is to test whether the galaxies in an isolated subcluster have the same properties as the galaxies in an equally dense region in the cluster core, so we will assume a subcluster contains relatively few galaxies. The difference between clusters and subclusters becomes semantic if a subcluster is nearly as rich as the main cluster. Some of the major local mechanisms are outlined below. • Initial Conditions (isolated protocloud) - A decade ago, the standard picture for galaxy formation was that initial conditions in an isolated protogalactic cloud determined the final morphology of a galaxy. For example, Sandage, Freeman, and Stokes (1970) suggested that the fundamental parameter was the amount of angular momentum in the protocloud, with the higher momentum material having a slower rate of star formation and therefore settling into a disk after the initial collapse that formed the spheroidal component. Gott and Thuan (1976) suggested that the the strength of the original density enhancement was the prime determinant. The ratio of the rate of star formation (faster in dense protoclouds) to the collapse time determined whether the galaxy would be an elliptical or spiral galaxy. • Tidal Shaking (galaxy-galaxy) - Miller (1988) has argued that a severe "shaking" of a galaxy as it passes by galaxies in the high density core of a cluster may rearrange the distribution of mass into a more elliptical-like distribution without actually adding or removing mass.

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• Tidal stripping (galaxy-galaxy) - Gallagher and Ostriker (1972) originally suggested that interpenetrating collisions between galaxies in clusters may liberate material from the interstellar medium and deposit it on the cD galaxies found near the centers of most dense clusters. This material would have the velocity dispersion of the cluster ( « 1000 km s" 1 ), rather than the velocity dispersion of the galaxy ( « 300 km s ). It now appears that direct collisions are relatively rare, but lower speed encounters between galaxies that pass near each other may cause even more damage (Toomre and Toomre 1972), especially before the cluster has collapsed and the relative velocities between galaxies have increased. One of the reassuring aspects of galaxy-galaxy collisions is that we know they are happening at some level, unlike many of the theoretical mechanisms we are discussing in this section, as becomes evident by a quick look through the Arp Atlas (1966) or Arp-Madore Atlas (1987). The main questions are how frequently do these interactions occur, how much mass is really lost (especially how much dark mass), and will the remnant be distinguishable from the progenitor. Reviews by White (1982), Dressier (1984a), and Kormendy and Djorgovski (1989) discuss tidal interactions in more detail, but answers to these three questions are largely unknown. • Merging - In its simplest form, this theory begins with an initial population of disk galaxies which subsequently merge to form ellipticals. Toomre (1977) noted that based on the frequency of severely interacting galaxies (e.g., the "Antennae galaxy"), and ages estimated from simulations, the number of elliptical galaxies was approximately equal to the number of remnants from these violent interactions. Roos (1981) has extended the merger hypothesis by suggesting that merging can also explain the presence of spheroidal bulges in disk galaxies. Several elliptical and SO galaxies have now been observed with gas that counterrotates with respect to the stars (Galletta 1987, Bertola and Bettoni 1989, Rubin, Ford, and Hunter 1988), providing some support for this idea. However, no counterrotating bulges have been found in spirals (Kormendy and Illingworth 1982, Whitmore, Rubin, and Ford 1984, Fillmore, Boroson, and Dressier 1986). Peanut shaped bulges may also result from the recent accretion of material into a disk galaxy (Binney and Petrou 1985, Whitmore and Bell 1988). Several cosmological N-body simulations (Aarseth and Fall 1980, Roos 1981, Frenk et al. 1985, Zurek, Quinn, and Salmon 1988, and Carlberg and Couchman 1989) provide more support for the potential importance of merging. • Galactic Cannibalism - Ostriker and Tremaine (1975) suggested that the central galaxy in a cluster may grow into a cD galaxy by the accretion of several nearby galaxies. As dynamical friction slows the victims they slowly spiral in and are devoured. This is the merger theory at its extreme, but is defined as a separate item since the remnant in the two cases is different (i.e., a cD galaxy for galactic cannibalism and a normal elliptical for the merger theory), and the existence of one mechanism does not necessarily indicate that both mechanisms are operating.

2.2 Global Mechanisms The difference between local and global mechanisms is not always clearcut, as demonstrated by the fact that several mechanisms are included in both our global and local lists. In this review we shall use the following criteria for differentiating between local and global mechanisms. If it is necessary to know only the conditions in the immediate vicinity of a galaxy (e.g., the number density encompassing the ten nearest

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galaxies) the mechanism will be called local. If it is necessary to know the properties of the cluster as a whole (e.g., the position relative to the dynamical center of the cluster) the mechanism will be called global. We should also note that the term global does not imply that the mechanism is operating thoughout the cluster. • Initial Conditions (hybrid models) - In a hierarchical picture of galaxy formation (e.g., Peebles 1980), with initial conditions in an isolated protogalaxy determining the morphological type, it is difficult to understand how elliptical galaxies preferentially make their way into the higher density regions of the clusters. This led to the expectation that "late" evolution by the cluster environment might play the major role in determining the properties in a cluster (Dressier 1984a). Several mechanisms have recently been suggested for providing this connection, including biased galaxy formation (e.g., Davis et al. 1985, Frenk et al. 1985, Zurek, Quinn, and Salmon 1988, Carlberg and Couchman 1989), adiabatic perturbation models (e.g., Doroshkevich et al. 1980), and tidal torque models (Shaya and Tully 1984). This review will focus on the possible role of late evolution. However, we should keep in mind that initial conditions remain a viable explanation for most of the phenomena we will discuss. • Tidal Shaking (from mean cluster field) - Miller (1988) has argued that a severe "shaking" of a galaxy as it passes by the high density core of a cluster may rearrange the distribution of mass into a more elliptical-like distribution. • Tidal Stripping (shear from mean cluster field) - White (1982) and Merritt (1984) have stressed that the mean tidal field of the cluster may be more effective in stripping stars from the outer regions of galaxies than galaxy-galaxy interactions. The stripped material would probably end up in the extended halo of the central cD galaxies. Merritt argues that the effect may be so strong during the initial cluster collapse that subsequent evolution of the galaxies would be negligible, since the cross sections for dynamical friction and galaxy-galaxy interactions would be much smaller for the haloless galaxies. • Ram Pressure Stripping and Gas Evaporation - The existence of diffuse hot (w 108 K) intracluster gas near the centers of clusters, as evidenced by X-ray observations, makes it very likely that any galaxy that passes near the center of a cluster will lose some or all of its interstellar gas by ram-pressure stripping (Gunn and Gott 1972) or gas evaporation (Cowie and Songaila 1977). The evidence for HI deficiencies (see reviews by Haynes, Giovanelli, and Chincarini 1984, or Haynes 1990) suggest that one or both of these mechanisms is probably occuring. The big question is whether one of these mechanisms can also explain the high fraction of SO galaxies in clusters by shutting off the star formation in spiral galaxies. The fact that the fraction of spirals decreases at roughly the same rate as the fraction of SOs increases (as a function of local projected galaxy density; see Dressier 1980) makes this an attractive hypothesis. However, Dressier points out that most SO galaxies are actually found in the field where ram-pressure stripping is not effective. This makes it very unlikely that spirals are being converted to SO galaxies via this mechanism. • Truncated Star Formation - Several authors advocate the slow buildup of disks from an extended gaseous halo, rather than a rapid formation concurrent with the collapse of the spheroid (e.g., Gunn 1982). Larson, Tinsley, and Caldwell (1980) have suggested that the lack of spiral galaxies near the centers of clusters might be caused by the removal of these gaseous halo during cluster collapse. However, Fall (1983) has pointed out problems with this hypothesis based on angular momentum considerations. In short, the slow rotation of the ellipticals implies the removal of

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so much material that it becomes difficult to understand why ellipticals are more massive than spirals. • Cooling Flows - Fabian and Nulsen (1977), and Cowie and Binney (1977) have suggested the possibility that radiative cooling in the densest parts of the hot intracluster gas may result in significant cooling flows. Observational evidence that this process may be occuring comes from strong Balmer lines (Romanishin 1987), optical filaments (Heckman 1981), and X-ray temperature inversions (Fabian et al. 1981). Accretion rates of up to a few hundred MQ yr" 1 have been computed by Fabian, Nulsen, and Canizares (1982). If these rates are sustained for an appreciable fraction of a Hubble time they may explain the extended envelopes seen around cD galaxies. However, there is no evidence for abnormal color gradients in cD galaxies (Schombert 1988) indicative of continuing star formation. Fabian, Nulsen, and Canizares (1982) have suggested that the accretion may be in the form of very low mass star formation (i.e., dark matter), presumably near the center of the cD galaxies where the density is highest. Measurements of velocity dispersions in cD galaxies (Malumuth and Kirshner 1981, Mathews 1988) indicate that the central values of M/L are normal for elliptical galaxies, so this mechanism is not likely to be relevant for many clusters.

3. THE MORPHOLOGY-DENSITY RELATION 3.1 T h e Morphology of Galaxies in Clusters The fact that nebulae in clusters were different than nebulae in the field was known even before it was understood that these nebulae were galaxies like our own Milky Way. For example, Curtis (1918) observed 304 small diffuse nebulae in the Coma cluster, but his belief that "all the many thousands of nebulae not definitely to be classed as diffuse or planetary are true spirals, and that the very minute spiral nebulae appear as textureless disks or ovals solely because of their small size", kept him from realizing the importance of his observations. By the early 1930's the difference between field and cluster galaxies was clearly understood (Hubble and Humason 1931). Oemler (1974) quantified this trend by defining three types of clusters with various ratios of elliptical, SO, and spiral galaxies. These are "spiral rich" (E/SO/S = 1/2/3; 17/33/50%), "spiral poor" (E/SO/S = 1/2/1; 25/50/25%), and "cD" clusters (E/SO/S = 3/4/2; 33/44/22%). For comparison, the percentages in the field are E/S0/(S+I) = 10/10/80% (Sandage and Tammann 1981). While these figures provide a basic framework for categorizing different types of clusters, the luminosity functions for different morphological types are not the same (Binggeli, Sandage, and Tammann 1988), so the actual percentages will change as a function of limiting magnitude. For example, Tully (1988b) finds percentages of E/S0/(Sp+I) = 3/7/90% in the lowest density regions from the Nearby Galaxies Catalog (Tully 1988a). This sample contains a large number of faint Sd and Im galaxies that would be completely missed in the more distant cluster samples. Melnick and Sargent (1977) demonstrated the existence of population gradients as a function of distance from the center of the cluster, with elliptical galaxies occuring mainly near the centers and spirals predominating in the outer regions. These gradients make the determination of global population fractions dependent on how large a region is included in the calculation. The outer edge of a cluster is difficult to define and often merges into the field or the outer part of another cluster, so the global population is of

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limited usefulness. The classic work in this field is unquestionably that of Dressier (1980). He determined positions, morphological types, magnitudes, and ellipticities for over 6000 galaxies in 55 clusters using excellent plate material. He concluded that the fundamental correlation was between morphological type and local projected galaxy density. Figure 1 shows Dressler's basic result, that the fractions of elliptical and SO galaxies increase as a function of local galaxy density, while the fraction of spirals decrease. As Dressier states "The gradients are much more striking when the density is employed as the independent parameter, which indicates that the local projected density enhancements represent real physical associations and that populations are largely a function of local rather than global conditions". Dressier also examines the morphology-density relation for samples of low-concentration, high-concentration, and X-ray emitting clusters, and concludes that the relations for the three samples are very similar. Although the elliptical fractions look the same in all three samples, there is actually a fairly clear trend for the fractions of spirals to be lower (at the same local galaxy density) in high-concentration and x-ray emitting clusters than in low-concentration clusters. This suggests that the global properties of a cluster may also be important in determining the morphology of galaxies in clusters. We shall return to this point later, since Salvadore-Sole, Sanroma, and Jordana (1989), Sonroma and Salvadore-Sole (1990), and Whitmore and Gilmore (1990) have all suggested that correlations with global properties may actually be the fundamental correlation. Postman and Geller (1984) extended Dressler's morphology-density relation to less dense environments by analyzing the CfA Redshift Survey. They find that the fractions of elliptical, SO, and spiral galaxies within lower density regions in the field join smoothly onto the low density regions in the outer parts of Dressler's clusters. Sodre et al. (1989) have recently shown that the velocity dispersions for the system of spirals in clusters are generally larger than the velocity dispersions for the system of ellipticals. They interpret this as evidence that late-type galaxies are still in the process of falling into the virialized core of the clusters. This would explain the continuity of the population fractions from the field to the outer regions of clusters. Giovanelli, Haynes, and Chincarini (1986) and Tully (1988b) both find that early and late spiral galaxies show different trends in the morphology-density diagram. The fraction of Sa's is approximately constant as a function of local galaxy density, while the Sc, Sd, and Im galaxies show a strong preference for the low density regions of the clusters. Binggeli (1987) has provided tentative evidence that the shape of the luminosity function for each Hubble type is independent of the environment. Only the relative frequency of the Hubble types appear to change. If confirmed, this would rule out various scenarios for explaining the morphology-density relation by changing one type of galaxy into another (e.g., spirals into SOs via ram-pressure stripping). Several mechanisms have been suggested as the cause of the morphology-density relationship, including both local and global mechanisms (i.e., initial conditions, tidal stripping, merging, tidal shear, ram-pressure stripping, gas evaporation, and truncated star formation). At present, none of these explanations are compelling. However, recent cosmological simulations (e.g., Frenk et al. 1985; Zurek, Quinn, and Salmon 1988; and Carlberg and Couchman 1988) offer hope that we may soon be able to pin down the relevant mechanisms, especially when it becomes possible to add dissipation in a physically meaningful way.

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POPULATION VS. PROJECTEO OENSITY (ALL CLUSTERS)

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Figure 1. The fraction of E, SO, and S+I galaxies as a function of the log of the local projected galaxy density, in galaxies Mpc~2 for 55 clusters. An estimated scale of true space density in galaxies Mpc'3 is also included. The upper histogram shows the number distribution, (from Dressier 1980)

3.2 The Morphology of Galaxies in Compact Groups The situation for compact groups of galaxies is not as clear. The space densities are as high or higher in compact groups than even the densest regions in clusters so we might expect the compact groups to consist of essentially all elliptical galaxies, based on the morphology-density relation. This is not the case, however (see Mamon 1986, Figure 2, and Hickson, Kindl, and Huchra 1988; hereafter HKH). The fraction of ellipticals is only about 20% in the Hickson (1982) compact groups (HKH; Rood and Williams 1989), only slightly above the fraction found in the outer regions of a cluster ( « 12%; Dressier 1980), or the loose groups surrounding the compact groups ( « 7%; Rood and Williams 1989). Perhaps the lack of a large percentage of ellipticals is caused by the small number of galaxies in the compact groups, generally only four or five. Although the space density is similar to the densest regions in clusters, the small number of galaxies cannot produce the deep potential well found in clusters. This suggests that the global conditions may be more fundamental than the local conditions

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for the production of elliptical galaxies. Although the fraction of elliptical galaxies in compact groups is much lower than at comparable densities in clusters, the morphology-density relation still appears to hold, but offset to higher densities. HKH find a 97.5% chance that the two parameters are correlated. Much of the reason the correlation is not better is due to the four highest density groups which are all very nearby and tend to be dominated by spirals. If we trim the sample to include only groups in the range 0.015 < z < 0.05, in an attempt to minimize selection effects, the probability that they are correlated increases to 99.99% (using the unbinned data rather than the binned data in HKH). The strongest correlation HKH find is between spiral fraction and velocity dispersion of the group, with the higher dispersion groups containing more elliptical galaxies. This is contrary to what we might expect if mergers are the dominant mechanism since lowvelocity interactions should be most effective. However, if the higher velocity dispersion is indicative of a deeper potential well, then this correlation may again suggest that global conditions are more important than local conditions. One concern is that higher dispersion clusters are also the most distant, introducing the possibility of a systematic bias. At higher redshifts the brighter, more massive galaxies would be easier to detect, implying a higher velocity dispersion. If there is also a systematic tendency to misclassify the more distant galaxies toward earlier type galaxies because of the poorer spatial resolution, the trend between morphology and velocity dispersion could be an artifact. HKH address a similar point and conclude that the relationship between morphology and velocity dispersion is the fundamental correlation, since the statistical significance is much higher than for the morphologyluminosity relationship. We can make an independent check of potential biases caused by the wide range in distance by trimming the sample to only include galaxies in the range 0.02 < z < 0.04. In this range, the average velocity dispersion for 11 elliptical-rich groups (i.e., more than 50% early type galaxies) is 229 ± 43 km s" 1 . The average velocity dispersion for 19 spiral-rich groups (i.e., more than 50% spirals) is 145 ± 40 km s . The corresponding numbers when the whole sample is used are 240 db 19 km s" 1 for the elliptical-rich groups and 105 ± 20 km s" 1 for the spiral-rich groups. So it appears that although a systematic bias related to the distance may affect the results, the morphology-velocity dispersion relation is not dominated by this effect. Higher dispersion groups do tend to be dominated by ellipticals. Recently, Barnes (1989) constructed self-consistent N-body simulations of galaxies within compact groups which indicated that they should merge into a single elliptical galaxy within a few billion years. At intermediate stages the merged galaxies would also appear to be ellipticals, so we might expect the first-ranked galaxy in these compact groups to tend to be ellipticals. HKH find that the morphology of the first-ranked galaxy does not differ significantly from that of the general population found in the groups. A Kolmogorov-Smirnov test, with the galaxies arranged in the normal E-SO-Sa-Sb-ScSd-Im sequence, indicates that the distribution of first-ranked galaxies could arise from the total distribution 15% of the time. This might indicate that rapid merging is not occuring, as also suggested by the fact that the morphology-velocity dispersion relation goes in a sense which is opposite to what would be predicted by simple merger models. Before we write off the merger hypothesis in compact groups completely we should note that the fraction of first-ranked galaxies which are ellipticals actually does rise, from 22% of the total population in compact groups to 35% of the first-ranked galaxies in the groups. What keeps the significance of the K-S test low is that in the next bin,

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the SO galaxies fall from 26% of the total population to 11% of the first-ranked galaxies. If the types of galaxies were placed in order of how likely a merger is to produce a firstranked galaxy of that type, SO galaxies might be placed at the end of the distribution. We might expect merging galaxies to form ellipticals, and in some cases perhaps spirals if interactions spark large global spiral structures that brighten the galaxy. However, we would not expect brighter SO galaxies to be produced by mergers, since the strong interactions would probably disrupt the fragile SO disk, and a new purely stellar disk would take longer than the collapse time of the group to form. This might explain the dramatic decrease in the number of SO galaxies. With the SO galaxies arranged at the end of the distribution (and the few Im and cl galaxies removed) the chance that the first-ranked galaxies come from the same distribution as the total sample drops to 0.02%. The tentative finding of an anomalous population of bluish ellipticals in the Hickson groups by Zepf and Whitmore (1990a) also suggest the presence of merging activity at some level. Another potential tool for determining whether initial conditions or late evolution is responsible for determining morphological types is the possible existence of morphological concordance between galaxies in groups. HKH find that in 20 of the 58 quartets, all four of the galaxies are of the same type (early or late). They calculate the probability of this occurring by chance is 10~*\ Yamagata, Nouguchi, and lye (1989) have examined the CfA redshift survey and also conclude that nearest neighbor galaxy pairs tend to have the same morphological type. Similar studies of morphological concordance in pairs have been made by several other groups (e.g., Noerdlinger 1979) with similar results. This morphology concordance is often taken as evidence that initial conditions are responsible for determining the morphology of the galaxies. Galaxies formed near each other would probably have similar initial conditions, and would therefore evolve in similar manners. However, White (1990) has recently shown that this effect may simply be the result of the morphology-density relation (or more generally, a morphology"anything" relation). Most studies have calculated the probability by assuming the different types of galaxies are evenly mixed. But if certain groups contain higher fractions of one type of galaxies than another due to an effect such as the morphology-density relation, we would automatically expect more cases of morphology concordance. The morphology-density relation might be caused by either initial conditions or late evolution, so the observed morphology concordance cannot tell us anything about the origins of galaxies until this effect is sorted out.

3.3 Is the Fundamental Correlation with Local or Global Conditions ? The determination of the "dynamical center" of a cluster is problematic, especially for very irregular clusters. Because of this, Dressier used the local projected galaxy density (area encompassing the nearest ten galaxies) rather than the distance from the center of the cluster as his independent parameter when examining how the morphology of galaxies varied within a cluster. The use of local density resulted in excellent correlations, and led to the general interpretation that the subclusters are real physical associations and not chance projections, and some local mechanism determined the morphology of galaxies in clusters. In this section we shall reexamine this question by determining whether the morphology correlates better versus local galaxy density or RclU8ter, the distance from the center of the cluster. One difficulty is that the local galaxy density is a rather smooth function of the

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radius in regular clusters, making it difficult to determine which is the fundamental correlation. As a test, Dressier therefore uses both Rcluster a Q d local galaxy density as the independent variable for six moderately irregular clusters. The correlation with local galaxy density appears to be better (see Dressier's Figure 5), leading him to conclude that populations are largely a function of local rather than global conditions. Whitmore and Gilmore (1990; hereafter WG) have reexamlned Dressler's data in order to address this question. Figure 2a shows a comparison using first R c / Ug ( er as the independent parameter. It differs from Dressler's comparison in three respects: 1) it includes all 55 clusters, 2) the center is taken to be the galaxy with the highest local galaxy density rather than the centroid (which can often be in a relatively low density location), 3) the inner bin has been broken into six separate bins. We find that unlike Dressler's earlier results, the total range in the various populations is about the same when Rc/uster i s used as when local density is used, so it is not possible to determine which is the more fundamental parameter from Figure 2a. For example, the elliptical fraction ranges from about 10% in the outer low density regions to about 40% in both the inner regions and the highest density regions. One interesting new result is how sharply peaked the distribution of ellipticals is. Only within 0.5 Mpc of the center does the fraction rise dramatically. Using the local density as the independent parameter tends to obscure this point since the centers of open clusters may have relatively low local densities, and thus appear in the middle of the diagram in Figure 1. If the sample is restricted to the six moderately irregular clusters Dressier used in his Figure 5, the results are essentially the same, with the elliptical fraction going up to about 50% when either ^-cluster o r local density are used. Beers and Tonry (1986) have shown that the true dynamical center of a cluster is better defined by the location of a D or cD galaxy in the cluster, or the location of the peak of the X-ray emission, rather than on the basis of galaxy positions alone. If we restrict ourselves to the 33 clusters in Dressler's sample with D galaxies, the fraction of ellipticals goes up to 61% in the central bin (Figure 2b). This suggests that the elliptical fraction may be controlled by global properties, since D and cD galaxies tend to be found in the richer, more centrally-concentrated, X-ray emitting clusters. The fact that the binning can have such an important role in determining the range in the morphological fractions led WG to divide the sample into 10 equal bins, arranged first by Rciuster and then local density. In both cases the maximum elliptical fraction reaches about 35%, making it impossible from this test to determine which parameter is more fundamental. The success of the morphology-density relation may simply reflect the fact that the local galaxy density is generally very well correlated with the position in the cluster. Another interesting result is the apparent decrease in the fraction of SO galaxies very near the centers of clusters. If this is not the result of some systematic classification problem it may indicate that the strong tidal shear has been able to destroy the disks of the SO galaxies very near the cluster centers. ^•cluster m a y n ° t be the optimal choice as the independent parameter. For example, the center of the Coma cluster is treated the same as the center of a very poor cluster when using R c / us < er , even though the environmental affects are likely to be very different. WG have examined several other global parameters (e.g., local projected binding energy at each point in the cluster), and find that while several parameters result in as wide a range in the percentage of the ellipticals as when using local galaxy density is used, none are clearly better. WG then break the sample into two groups, an inner sample including all galaxies

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within 1 Mpc of the cluster center, and an outer sample for galaxies beyond this radius. Figures 3a and 3b show the normal morphology-density relation for these two regions. The elliptical fraction shows almost no tendency to increase as a function of local density for the outer sample, while the elliptical fraction for the inner sample increases in a smooth progression. An estimate of the space density is also included, showing that this difference occurs for galaxies at similar space densities as well as similar projected galaxy densities. This figure suggests that the environment near the center of a cluster is needed to produce a high percentage of ellipticals. The clearest difference is seen in the elliptical galaxies, although the spiral fraction may also be slightly steeper for the inner sample. The SO fraction looks about the same in both samples. Sanroma and Salvador-Sole (1990) have performed a very clever test that implies that the morphology-density relation is driven by global eflFects for all three galaxy types, not just the ellipticals. Using Dressler's data, they produced artificial clusters by taking each galaxy and randomly repositioning them in angular coordinates around the center of the cluster. In this way they destroy any subclusters that might be present, but keep the global properties (such as richness, central concentration, ^•cluster) the same. They then construct the normal morphology-density relation for the scrambled clusters and compare it to the relation for the real clusters. The two diagrams are essentially identical, indicating that the morphology-density relation is controlled by global conditions rather than subclustering. Sanroma and Salvador-Sole are careful to point out that this does not imply that there are not subclusters, but only that they do not appear to play an important role in determing the morphological type of the galaxies. One useful extension of the Sanroma and Salvador-Sole study would be to repeat the test using only the clusters which show the strongest subclustering. In the regular clusters, no difference would be expected between the morphology-density relation for the randomly scrambled clusters as compared to the observed clusters. The inclusion of these regular clusters may therefore dilute any difference that may actually exist if only the clusters with strong subclustering were included. In summary, the range in the percentages of elliptical, SO, and spiral galaxies is as great, or slightly greater when various global parameters (e.g., clustercentric position or local binding energy) are used as the independent parameter as when local galaxy density is used. It is therefore impossible to clearly determine which is the fundamental correlation, or whether some combination of global and local mechanisms are responsible for determining the morphology of galaxies in clusters.

4. THE SIZE OF GALAXIES IN CLUSTERS 4.1 T h e Size of D and cD Galaxies One of the best indications that the cluster environment can affect the structure of galaxies is the existence of D and cD galaxies near the centers of many clusters. Morgan (1958) and Matthews, Morgan, and Schmidt (1964) originally identified these galaxies as a special class. The "c" stands for supergiant and the "D" means the galaxy is dustless with a large diffuse envelope around it. Kormendy and Djorgovski (1989) have argued that only the cD designation is meaningful, and the defining characteristic is an inflection in the outer brightness profile. The D galaxies do not have this added envelope, but instead have profiles similar to normal elliptical galaxies. However, the D galaxies are too bright to be a statistical fluctuation of the elliptical population (Bhavsar 1989), and hence will be retained in this review.

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A typical giant elliptical galaxy may have a luminosity of about 1.5 L*, where L* is the characteristic luminosity from the Schechter luminosity function. An average D galaxy is 9 L* (Tonry 1987), and a cD galaxy is 12 L* (Kormendy and Djorgovski 1989). Similarly, the effective radius of a typical giant elliptical is 10 kpc, while for a D galaxy it is 40 kpc. The outer halo may extend to several hundred kpc. The large size is caused by a very flat luminosity gradient rather than a difference in the surface brightness of D and cD galaxies with respect to giant ellipticals. An important clue to the origin of D and cD galaxies is that they are almost always found at the dynanucal center of the cluster, and their velocity is very near the systemic velocity of the cluster (Quintana and Lawrie 1982). However, Quintana and Lawrie only had nine cD galaxies in their sample, two of which had residual velocities of more than 300 km s . Recent observations by Hill et al. (1988) and Sharpies, Ellis, and Gray (1988) confirm that the velocities of these two cD galaxies are anomalous. The velocities of D galaxies also tend to be the same as the systemic velocity of the cluster, although there are six of 11 cases with residuals greater than 300 km s" 1 in this case. This fundamental point needs to be checked using a much larger sample. D and cD galaxies are never found in the field (Schombert 1988). D galaxies are found in both rich and poor clusters, but cD galaxies are only found in rich clusters (Thuan and Romanishin 1981, Schombert 1988). Thuan and Romanishin suggests that D galaxies may form from local density enhancements {e.g., by cannibalism) while cD galaxies form by the accumulation of tidal debris. This hypothesis would also explain why only cD galaxies have extended outer halos. The identification of D and cD galaxies as the dynamical center is strengthened by the fact that their positions generally coincide with the X-ray centers of the clusters. In addition, the projected cluster profile shows a clear peak which follows a r" 1 power law when the D galaxy is used as the center (Beers and Tonry 1986). D and cD galaxies often have multiple nuclei (Hoessel and Schneider 1985). This has usually been taken as direct evidence that these galaxies have grown to their prodigious size by cannibalizing nearby companion galaxies. Merrifield and Kent (1989) have obtained CCD images for the inner 250 kpc of 29 clusters. They find that the distribution of galaxies is characteristic of the effects of dynamical friction. However, recent observations by Tonry (1986) have shown that most of the "nuclei" have velocities with respect to the cluster that are much larger (sa 800 km s ) than the internal velocity dispersion of the D and cD galaxies (w 300 km s" 1 ). Tonry interprets this as evidence that only about 25% of the multiple nuclei are bound. Most of the nuclei are simply sharing the bottom of the cluster potential well with the D and cD galaxies, and are not actually multiple nuclei. Cowie and Hu (1986), using a larger sample, argue for a bimodal distribution with a's of 250 km s and 1400 km s . They argue that about 60% of the multiple nuclei are bound. However, they did not normalize by the velocity dispersion of each cluster before adding the data together so this might simply reflect the spread in the types of clusters they studied (Lauer, private communication). Bothun and Schombert (1988) suggest an intermediate value for the fraction of bound companions, since only one of the three clusters they studied (A 2589, the cluster with the most dominant cD galaxy) has a large population of bound nuclei. Lauer (1988) has examined the shape of the multiple nuclei and finds that about 50% show evidence of an interaction with the central galaxy. Curiously, the distorted nuclei do not tend to have lower velocities with respect to the central galaxy as would be expected if this 50% represented the bound nuclei. This may indicate that essentially all nuclei passing near the central galaxy are affected, and the half not showing distortion yet are still on

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their way in toward the central galaxy. However, Bothun and Schombert find the most obvious signatures of tidal stripping occur in the low-velocity nuclei of A 2589. Lauer (1988) estimates from the fraction of distorted galaxies that about 4 L* of material would be accreted by a central galaxy in 10 Gyr. This implies that either the accretion rate was slightly higher in the past, since a typical cD galaxy has 12 L*, or that another mechanism, such as the accumulation of tidal debris, may be needed to augment the process. In any case, this provides clear evidence for fairly substantial amounts of accretion through galactic cannibalism. Several explanations have been proposed for the existence of D and cD galaxies, including: statistical fluctuation in the population of elliptical galaxies (very unlikely, see Bhavsar 1989), preferred location in regions without tidal shear (Merritt 1984, unlikely since field ellipticals with little tidal shear are never D or cD galaxies), cooling flows (Fabian, Nulsen, and Canizares 1984; unlikely, see section 2), galactic cannibalism of nearby companion galaxies (Ostriker and Tremaine 1975, Hausman and Ostriker 1978), and accumulation of tidal debris (Richstone 1976, Malumuth and Richstone 1984). We have already listed several supporting observations for the cannibalism and tidal debris hypotheses. Other evidence includes the fact that D and cD galaxies tend to be flatter than normal ellipticals, tend to be aligned with the axis of the cluster (Binggeli 1982), never show much rotation, and have velocity dispersion profiles that rise rapidly in their outer regions (Dressier 1979, and Carter et al. 1985). Observations of intracluster light in some clusters provide more support (Thuan and Kormendy 1977, Malumuth and Richstone 1984, and Struble 1988; see Gudehus 1989 for a dissenting opinion). Schombert (1986, 1987, 1988) has recently completed an extensive photographic study of a large sample of D and cD galaxies which also supports the dynamical formation of envelopes. More specifically, he finds the luminosity gradient in the outer envelope of a cD is about the same as the gradient of the galaxies in the cluster. He also finds correlations between the envelope luminosity and various cluster properties, including richness, X-ray luminosity, Bautz-Morgan type, and Rood-Sastry type.

4.2 Evidence for Tidal Stripping in Clusters Given the existence of cD galaxies which have grown in size as a result of the cluster environment, we might expect other galaxies in the cluster to have lost material in order to feed the cDs. Unlike many of the mechanisms discussed in Section 2, it is clear that strong tidal effects are present in at least some galaxies. For example, Borne (1988a, 1988b, 1988c) finds that he can nicely model both the azimuthal distortions in the luminosity distribution, and the kinematic data, for several interacting pairs of elliptical galaxies in terms of simple tidal encounters. The question is how often and how much material is lost in these interactions, not whether they occur. Tidal stripping by galaxy-galaxy collisions (Gallagher and Ostriker 1972, Richstone 1976), or the mean tidal field of the cluster (Merritt 1984), have both been suggested on theoretical grounds. Observational support comes from the extensive study by Strom and Strom (1978a, 1978b, 1978c). They studied 600 elliptical and SO galaxies in six clusters using photographic plates. They find that the radii of the elliptical galaxies (measured at the 26th mag arcsec" 2 isophote in the R band) in the dense spiral-poor clusters are about 30% smaller at a given My than in the spiral-rich clusters. In addition, galaxies within 0.5 Mpc (1.0 Mpc in the case of A 2199) of the core appear to be 15% smaller than outer galaxies in the same cluster. Even more striking is that for the cluster with the largest cD, Abell 2199, the difference between the inner and outer

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galaxies is nearly 60% when Re is used for the size measurements. Lugger (1989) also finds evidence that the luminosity functions within 0.5 Mpc of three dense clusters are deficient in bright galaxies. One concern with the Strom's study has always been the use of photographic photometry for the measurements. However, Schombert (1986) recently showed his photometry was in good agreement with the Strom's results. He also found that faint ellipticals in his sample had outer cutoffs in their profiles. Since most of these faint ellipticals were near the centers of clusters this may indicate that they have been tidally truncated. Several other studies including Bothun and Schombert (1988), and Lauer (1988), have also found evidence for tidal truncations. More recent studies that supported the Strom's results have been Peterson et al. (1979), and Giuricin et al. (1985 and 1988). However, Vader (1986) found that Virgo ellipticals were smaller than Coma ellipticals (using the RC2 which may contain systematic biases), and Giuricin et al. (1989) found no effect using the new CCD photometry from Burstein et al. (1987). Kormendy and Djorgovski (1989) have argued that while strong tidal interactions can shrink a galaxy, weak encounters may heat galaxies up and cause a more distended outer envelope. This is based on both photometric observations of ellipticals with companions (Kormendy 1977), and N-body experiments by Aguilar and White (1986). Schombert (1988) and deCarvalho and daCosta (1988) were not able to confirm Kormendy's result.

4.3 Evidence for Tidal Stripping in Compact Groups Hickson, Richstone, and Turner (1977) found a good correlation between the size of the largest galaxy and the intergroup separation for 18 compact groups, using visual estimates of the size from the Palomar Sky Survey plates. Zepf and Whitmore (1990b) have examined new CCD photometry published by Hickson, Kindl, and Auman (1989) to check this effect. Figure 4 shows a plot of the log of the diameter of the largest group member vs. the log of the density of the group. A weak trend is apparent, with a 99.9% confidence of being real, but the correlation is not nearly as obvious as the earlier results from Hickson, Richstone, and Turner. Most of the correlation is in the spirals (correlation coefficient = 0.45) rather than the elliptical and SO galaxies (correlation coefficient = 0.24). A similar result is found when all the galaxies in the compact groups are included, rather than just the largest group members. It would be reassuring to find evidence of a diffuse background of tidal debris in compact groups, as appears to be the case in clusters. Rose (1979) made such a search in two groups with negative results. This lead him to conclude that compact groups are only a transient unbound configuration that occasionally forms from the looser groups which surround the compact groups. However, Hickson and Rood (1988) has convincingly argued that the galaxies in compact groups are physically related based on a growing number of observational studies. In addition, Williams and van Gorkom (1988), and Williams, McMahon, and van Gorkom (1989) find that in three of the four groups they studied the HI contours clearly follow a roughly spherical contour encompassing the whole group. New CCD photometry by Rubin, Ford, and Hunter (1989) also indicates that some groups contain a common envelope.

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5. THE DISTRIBUTION OF MASS FOR GALAXIES IN CLUSTERS 5.1 Velocity Dispersions for Elliptical Galaxies in Clusters The velocity dispersion profiles for most elliptical galaxies are flat or falling. However, Dressier (1979) and Carter et al. (1985) have observed rising rotation curves in the outer regions of several cD galaxies. This provides evidence that the cluster environment can affect the distribution of mass for galaxies in the centers of clusters, and more specifically, provides support for the cannibalism or tidal accretion theory for cD formation. Dressier (1979) argues that three components are required to fit his data; an inner region similar to normal elliptical galaxies (M/L « 10), an intermediate region that might represent accreted cluster members (M/L « 35), and an extended cluster-filling halo (M/L w 500). Although this would agree with several of the argu-

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merits presented in Section 4.1, more extensive observational data is clearly needed to make the case based on velocity dispersion gradients alone. Observations of the globular cluster system (Mould, Oke, and Nemec 1987) and the X-ray halo around M87 (Fabricant and Gorenstein 1983) also provide evidence that the mass around central cluster galaxies can grow to prodigious amounts. On a smaller scale, Dressier (1984b, 1987) and Dressier et al. (1987) found that the Faber-Jackson and the Dn-cr relations for both ellipticals and spiral bulges in clusters are similar to their counterpart relations in the field. There is no apparent difference in the Faber-Jackson relation for cD galaxies once light from the outer envelope is removed from the comparison (Malumuth and Kirshner 1981). Even severly interacting galaxies have a similar Faber-Jackson relation (Lake and Dressier 1986). It appears that the strongly bound stars near the centers of galaxies are not unduly affected by the environment. However, Djorgovski, de Carvalho, and Han (1989) find tentative evidence that both the Dn-
5.2 Rotation Curves for Spiral Galaxies in Clusters Without detailed information about the orbits of stars in elliptical galaxies, it is not possible to determine the distribution of mass in these types of galaxies (Tremaine and Ostriker 1982). The measurement of circular velocities in the disks of spiral galaxies provides a much better tool for determining the distribution of mass. It is also easier to measure the position of strong emission lines rather than the shape of weak absorption lines. While velocity dispersion curves generally only extend to a few tenths of the radius at the 25th mag arcsec B isophote, R25, optical emission-line rotation curves typically reach to 1.0 R25, and 21 cm rotation curves often extend two or three times as far. With all the interest in the possibility that the cluster environment may affect the structure and dynamics of galaxies, it is surprising that it has only been during the last few years that a sample of extended emission-line rotation curves has become available for galaxies in these dense environments. Based on limited optical material, Chincarini and de Souza (1985) concluded that there was no qualitative difference between the rotation curves of 10 spiral galaxies in clusters and the rotation curves of field spirals. However, their rotation curves generally only extended to a few tenths of R25, and were generally for galaxies far from the core of the clusters. Burstein et al. (1986) used observations of 20 spirals in four clusters from Rubin, Whitmore, and Ford (1988) to show that there was a difference in the distribution of mass curves (i.e., the integral mass derived from the rotation curve) between cluster and field galaxies. They found that one-third of the galaxies in the field are mass type I (i.e., the inner and outer gradients of the mass curve are most similar), but none of the 20 spirals in the cluster sample are mass type I. Forbes and Whitmore (1989) have confirmed this effect using a more objective chi-squared method to determine the mass types. Rubin, Whitmore, and Ford (1988) recently presented extended emission-line ro-

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tation curves for 21 galaxies in four large spiral-rich clusters; Cancer, Hercules, Peg I, and DC 1842-63. They examined the correlations between the four global properties: luminosity, radius, maximum rotational velocity, and mass. Perhaps the most interesting result was the finding that the Tully-Fisher relationship (Tully and Fisher 1977) between maximum rotational velocity and luminosity may be different for cluster galaxies than for field galaxies. Cluster galaxies tend to have lower rotational velocities than their counterparts in the field with the same luminosity and type. This is only a 2 a result, and since a variety of systematic effects are possible (e.g., internal extinction may be less in cluster galaxies, cluster galaxies may be typed too early with respect to field galaxies, large scale motions of the cluster relative to the smooth Hubble flow may be present) the result must be considered tentative. Djorgovski, de Carvalho, and Han (1989) also find evidence that the slope of the Tully-Fisher relation may depend on various cluster properties such as the velocity dispersion and richness class. The measurement of the shape of the rotation curve, and hence, the distribution of mass in the galaxies, is much less problematic than the determination of the global properties. Uncertainties such as corrections for extinction, inclination, or the motion of the cluster, are not relevant. In Whitmore, Forbes, and Rubin (1988; hereafter WFR) the shape of the cluster rotation curves are parameterized using various gradients. The most dramatic correlation is found using the outer gradient (OG), which is the percentage increase of the rotation curve between 0.4 R25 and 0.8 R25, normalized to the maximum rotational velocity. Figure 5a shows the correlation between OG and Kciusfer. A clear trend exist between these two properties, with a probability of 99.9% that OG and Rc/U«<er a r e correlated. The average value of OG for the field sample is also indicated with error bars showing the 1 a scatter of the distribution. The rotation curves for galaxies near the centers of clusters tend to have falling rotation curves in their outer regions. Galaxies farther from the cluster center, or in the field, tend to have flat or rising rotation curves. Figure 5b shows the correlation of OG with the local projected galaxy density in an attempt to determine whether the fundamental parameter is a global or local property. It is currently impossible to determine which correlation is better with the small number of galaxies in the sample. Has the dark halo been stripped, either by tidal interactions with other galaxies or with the mean gravitational field of the cluster? Perhaps the inner cluster environment never allowed the galaxy to form a halo, or modified the halo properties as the protogalaxy was forming (e.g., Zurek, Quinn, and Salmon 1988). Miller (1988) has argued that a severe "shaking" of a galaxy as it passes through the high density core of a cluster may be sufficient to rearrange the distribution of mass into a more elliptical-like distribution without actually adding or removing much mass. To address these questions, WFR calculated integral mass-to-light gradients (M/L = V 2 R/L). Figure 6 shows the M/L gradients from 0.1 R25 to 0.8 R25 versus the clustercentric position. WFR find that the inner cluster galaxies have flatter M/L gradients than the galaxies in the outer regions of the cluster. If a strong gradient in M/L is indicative of a large fraction of dark matter in the outer regions of a galaxy, then the present sample provides evidence that the galaxies near the centers of clusters have a lower fraction of their mass in the form of dark matter than the galaxies in the outer regions. This is consistent with the finding of falling rotation curves for inner cluster galaxies, again suggesting that a sizeable halo does not exist for them. More realistic mass models which use the observed distribution of light to predict the detailed rotation curve (e.g., Kalnajs 1983, Kent 1986, 1987, 1988) have shown that the amount of dark matter required to explain the observed rotation curve of field

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optical emission-line data, although the lack of many galaxies near the center of the cluster makes the relationship much less compelling. Although the presence of falling rotation curves for central cluster galaxies appears to be significant at about the 4 a level, we should keep in mind that it is based on only a half dozen galaxies near the centers of clusters. A larger sample is needed before we should consider this a firm result.

5.3 Rotation Curves for Spiral Galaxies in Compact Groups The effects of the cluster environment on emission-line rotation curves is subtle, with the outer galaxies showing essentially no effect, and the inner galaxies having outer gradients which are typically 10-30% lower than field galaxies. The two sides of the rotation curves generally match relatively well, indicating the gas is in circular motion. Most of the rotation curves for cluster galaxies would be described as "normal". In compact groups, where the density is generally as high or higher than in the cores of clusters, and the relative velocities are lower, the effect of the environment on rotation curves is often much stronger. Rubin, Ford, and Hunter (1989) have obtained spectra of 45 galaxies in 16 groups. Of the 33 spirals in the sample, nine are too abnormal to classify, 13 are peculiar or irregular, and only 11 are normal. The rotation curves which are defined as peculiar generally fall into two categories: asymmetric, with the two sides of the rotation curve having very different outer gradients; and sinusoidal, with velocities reversing at large radii and actually going to zero in some cases. Figure 7 shows an image of Hickson 16, along with four of the rotation curves. Hickson 16A is a good example of a galaxy with an asymmetric rotation curve, with one side rising and the other falling. Hickson 16C has a sinusoidal rotation curve. Both 16B and 16D would be in the abnormal category. Rubin, Ford, and Hunter also find that the brightest group member is more likely to have a peculiar or abnormal rotation curve than the dimmer galaxies in the group. Rotation curves which are similar to the sinusoidal curves have been observed in the case of the famous merger candidate NGC 7252 by Schweizer (1982), and the interacting pair NGC 450/UGC 807 by Rubin and Ford (1983). This provides support for the idea that these unusual rotation curves are the result of recent interactions. The large deformities in these rotation curves indicate that the galaxies are not in an equilibrium state, and developing a reasonable mass model is not straightforward. It is therefore not possible to determine whether a dark massive halo is being removed from these galaxies and deposited into the intergroup potential, or whether the galaxy is simply rearranging itself after a severe jolt. Rubin, Ford, and Hunter have also obtained spectra of 12 elliptical and SO galaxies in the Hickson groups. They find a very high incidence of extended emission in these galaxies, and in one case (Hickson 23c = NGC 1216), the gas is actually counterrotating with respect to the stellar component. The presence of this gas in generally gas-free system is more evidence for the recent accretion of material from another galaxy during an interaction or merger event.

6. SUMMARY A wide variety of physical mechanisms may be affecting the structure and dynamics of galaxies in clusters. Which of these mechanisms are we certain are operating and

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which are still just possibilities? The cause of the morphology-density relation is still unknown. Nearly all the mechanisms listed in Section 2 are still candidates. It is generally believed that a local mechanism is responsible for the effect, but this review argues that global conditions may be more important than local conditions in determining the morphological type of a galaxy. This is based on the fact that the correlation of the morphology with clustercentric distance is as good as with local galaxy density. The low fraction of ellipticals in compact groups, which have very high local galaxy densities but low binding energy, also suggest that global conditions may be the more fundamental parameter. There is good evidence that galactic cannibalism is occuring in D and cD galaxies, as well as tentative evidence that the extended envelopes of cD galaxies arise from the accumulated tidal debris of the cluster (whether from galaxy-galaxy interactions or the tidal shear from the mean cluster potential is unknown). HI deficiencies for central cluster galaxies, and smaller HI radii, are clearly established, but whether ram-pressure stripping or gas evaporation is responsible is unknown. The central stellar velocity dispersions of galaxies do not appear to be greatly affected by the cluster environment, although caution is advised if differences of only a few percent are important (e.g., determination of peculiar motions). Velocity dispersion profiles in cD galaxies appear to rise in their outer regions, suggesting the accretion of material from galactic cannibalism or tidal stripping. There is tentative evidence that rotation curves for spiral galaxies near the centers of clusters are falling, but no clear indication of what mechanism is responsible. While the removal of the dark matter halo by tidal stripping seems like the simplest explanation several other possibilities exist. As cosmological simulations become more sophisticated they offer the possibility of answering some of the questions posed in this review. In the past, the emphasis has been on cD formation. Several recent simulations are now examining the role of merging halos, and beginning to add dissipational processes to the calculations. These simulations offer the hope that we can begin to address details such as the evolution of morphology, size, and distribution of mass in the not too distant future. There is no conclusive evidence that any of the forms of late evolution we have discussed is a dominant mechanism for most of the galaxies in the cluster. Many people advocate the idea that most of the interactions happened early in the evolution of the cluster, and the recent interactions have only introduced relatively minor changes since that time. Some of the key observations that need to be made are: determination of positions and relative velocities for a large sample of both D and cD galaxies (i.e., are they in local enhancements or the dynamical center of the cluster), measurements of intracluster light in a large sample of groups and clusters with different morphologies, velocity dispersion profiles in the outer regions of elliptical galaxies (both stripped galaxies and cD galaxies), and rotation curves for spiral galaxies in groups and clusters. Of particular interest for the sponsor of this workshop is the potential for using the Hubble Space Telescope to see deeper, and hence farther back in time, to an epoch when many of these processes are occuring. As Dressier (1984a) states, we are all "looking forward to looking back". I would like to thank Vera Rubin, Duncan Forbes, Steve Zepf, Diane Gilmore, Marylin Bell, and Kent Ford who collaborated on several projects reported in this paper. I would especially like to thank Alan Dressier for sending me his computer files containing his measurements for over 6000 galaxies in the 55 clusters he studied and to

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thank Vera Rubin for permitting me to present Figure 7 prior to publication. Finally, I would like to thank Alan Dressier, Mike Fall, Mike Fitchett, Paul Hickson, Bill Oegerle, and Steve Zepf for commenting on early versions of this paper, and the Astrophysical Journal for allowing the use of the figures which originally appeared in their publication.

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DISCUSSION Bothun: I have a fair number of comments I could say in rapid fire succession. Hopefully, I won't start a riot here, (laughter) Of the galaxies you showed, NGC 6045 is an edge-on galaxy with a warp and a companion stuck on the end of it—very disturbed. NGC 6054 is in the center of the Hercules cluster and has a ring around it—also very

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disturbed. Neither of these two galaxies are used in the Tully-Fisher relation for that reason. NGC 7591 is a background galaxy projected onto the center of the Pegasus cluster. Now, what I really want to say is that I think all this is irrelevant with respect to the Aaronson et al. infrared Tully-Fisher relationship for the following two reasons: because the centers of the clusters are nasty places, they don't yield us a sample of nice spirals with high S/N HI. So, our sample consists entirely of galaxies between half a megaparsec and three megaparsecs from the cluster center. Number two, apertures that we use essentially measures the light inside one scale length and that's it. So, for this to be an effect, you have to appeal to the differences in mass-to-light ratio in the inner scale length of the galaxies as a function of environment, and I think that's implausible. So, I think that the falling rotation curves are irrelevant with respect to the infrared Tully-Fisher relationship. That's the major point I want to make. Whitmore: I agree that the effect of the falling rotation curves on most studies using the Tully-Fisher relation are probably negligible. They tend to use the outer galaxies in the clusters where this effect doesn't seem to be happening, probably because that's where they have good HI measurements. So, I am mainly advising caution to make sure that you don't use central cluster galaxies. On your second point, the main point is that if you compute the M/L gradient over the galaxy, from 0.1 to O.8R25, the M/L gradients do seem to be different. A few more notes on the galaxies you mentioned: I agree that inclusion of NGC 6045 is a little questionable, although the rotation curve looks relatively normal, unlike many cases where tidal companions have caused severe effects to the rotation curves. NGC 6054 looks quite regular, and only its barred nature with two tightly wound spiral arms give it a slightly ring-like nature, similar to many other bars. Again its rotation curve looks quite normal, The velocity of NGC 7591 is only about 1000 km s higher that the mean velocity of the cluster so it is probably a cluster member. In any case, NGC 7591 is an outer galaxy, so it is less critical to the analysis (removing it would improve the correlation slightly). Bothun: Well, I think that the actual gradient may be small—any gradient in M/L over the inner scale length, the inner one-third of the galaxy, is pretty small, and that at most it contributes a little bit of scatter to the relation but nothing more. Beers: I think perhaps you're taking a giant step backwards in considering this distance from the center as the fundamental parameter, and if you pause and think about it, I think you convince yourself that that's the case. First off, when you define a center, what you're doing, I think, if I understood you correctly, is sitting on the densest region anyway. So, you have to realize that when you sit on the densest region to begin with, it's no surprise that by the time you get out to other lumps or bumps or whatever's out there, many of which are factors of 5 or 10 lower in density, that you see less action going on anyway. Initially, what I think you're doing is reproducing the same kind of effect that Dressier had all along. I don't see when you define the center as the densest reason anyway, this much of a difference. Whitmore: We actually defined the center using several different methods. They all give pretty much the same results (i.e., highest density region, location of D galaxy, visual estimate.) Beers: How about for Abell 548?

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Whitmore: I haven't broken it down to particular clusters yet. In fact, A 548 is a double cluster, we probably ought to throw it out. So, actually I . . . Beers: If you throw out all the ones with lumps and bumps, I would say what you're left with is the clusters which happen to only have one . . . Whitmore: Well, I would only say about half a dozen of Dressler's 55 clusters show real severe lumps and bumps. Abell 548 should probably be considered two clusters rather than lumps and bumps. I think the local environment parameter is very useful in many ways. One of the nice thing it does is it allows us to bin all the different clusters in something that is meaningful. In some cases, if you've got a very low density cluster and use Rc/U8<er and you've got a high density cluster and use R c / U ^ er , you really don't physically expect those to be quite the same thing. So, I agree from that standpoint. I'm probably pushing the potential use of R c / us < cr too hard, but the main point is that we've been led to think that the local environment is the whole story; that correlations versus ^cluster a r e v e r v poor. What I'm saying is that using local environment or Rciuster &ve about the same correlations and we need to look a little bit more closely to see whether it really is the global cluster potential driving things or the local environment. A point on the poster by Sanroma and Salvador-Sole; they did something completely different but also seem to find that the local environment may not be the fundamental parameter. Beers: How is the center defined? Whitmore: Maybe they can answer themselves but I think that they use the median position. Sanroma: We take the baricenter but it doesn't matter what center we take. I mean, the cD or the mean or whatever, the result is much the same. Whitmore: One of the things we did is versus the distance from the cD. This actually gave even stronger correlations. (Figure 26) Sanroma: We did it with 55 clusters. There are clusters which are lumpy, irregular, with two subclumps, whatever. It doesn't matter, the result is exactly the same. Beers: The other thing you have to consider when you're doing this is that you're averaging as you go further out, of course, over a much, much larger regions, so that the tendency, I would think, is to smooth out much of the signal so I'm not surprised actually that that at least in the outer regions, you see very similiar results to Dressler's. Beers: The other question I had is how you measure the density of the Hickson compact group? Whitmore: John, [Huchra] do you want to answer that one. Huchra: It was very difficult. Beers: Could you put up that original figure where you showed that there is a different density-morphology relationship? While you're looking for that, I should remind the

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people that perhaps might not recall the original Dressier paper, that you're measuring these local densities by a nearest neighbor technique, which means we can take N = 10 as a representative nearest neighbor scale length. What you're doing is marching out away from a given galaxy until you run into the tenth nearest neighbor and you're calling that the scale, which is your area that you're dividing by. So, I would argue that you could explain the difference between the morphology-density relationship for underpopulated groups, like the Hickson groups of 4 or 5, by the fact that those were selected by an isolation criteria to begin with. In other words, if you were to take Dressler's original 55 clusters and use an N = 3 nearest neighbor, I would say you would get density readings which are just as high as some of the Hickson compact groups. Huchra: Well, let me answer Tim [Beers] very quickly. First of all, if you use an N = 10 nearest neighbor technique on a Hickson compact group, the densities are going to be microscopically small. You can put it the other way, Tim, you're wrong. Right, so the 10th nearest neighbor is so far away, the density can be very small, not very high. Postman: The densities used in the Postman and Geller study were essentially done by Dressler's technique, just generating catalogs of different densities and looking at the difference in the morphological mix between groups found in one density versus groups found at the next lowest density. That's why the dashed histograms are a re-analysis of the Dressier data, essentially consistent with the tenth nearest neighbor but slight differences. Beers: Well, aren't you concerned at all when you pick out an isolated group which has the isolation criteria of a Hickson compact group? I would say you can find one or two galaxies, three or four galaxies sitting very close to one another in any number of clusters, and the only difference between a few overlapping galaxies in a Dressier cluster and at least some examples of Hickson groups is the fact that the Dressier clusters don't satisfy an isolation criteria. Moderator: Well, let's move on to some other questions. van Gorkom: I have a question about the shape of your rotation curves. How much does it actually say about M/L ratio and how much does it say about mass distribution? The reason I ask is because if you look at field spirals, for example, if they have strong bulges, you see that in the inner part, the rotation curve rises steeply then goes down slightly. Now, you expect with this morphological segregation that in the center, the bulges are stronger, so you actually expect a slightly falling, optical rotation curve. Whitmore: The first point is that we use the outer part of the rotation curve, (the last data point for a typical galaxy is about O.8R25 and so we use the gradient from O.4R25 to O.8R25) to keep away from the central regions where the bulge has the greatest effect. We're really just trying to say something about the outer part of the galaxy. As far as the inner part, it's a real question right now of what's happening in the Sa galaxies. For example, the emission line rotation curves really aren't doing what we expected from the luminosity distribution (i.e., they don't always rise rapidly; see Kent 1988 A.J., 96, 514). I should also point out that just by coincidence, most of our central galaxies turn out to be Sc galaxies which tend to have rising rotation curves in the field. This makes falling rotation curves even more convincing for the central cluster galaxies.

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VanGorkom: Did you do any modelling? Whitmore; We did some preliminary modelling. We stopped for two reasons: partly, we lost confidence in the modelling techniques themselves. It looked like there was too much freedom. Generally what you do is determine the bulge component from the luminosity profile, the disk component from the luminosity profile and then adjust the mass-to-light ratios of the two until you get a good fit. I'm worried that by having the mass-to-light ratio of the bulge and the disk able to float in these models, that you may be putting in the answer. I mean by having two parameters you can always fit a rotation curve at least relatively well, even if unreasonable M/L ratios result. For example, Kent found that you needed M/L(bulge) = 0 for about 1/2 of his models in the reference given above. In addition, our data isn't quite as good for the clusters as it is for the field, so you don't have as good a range, to fit, so I don't think it really justified a detailed model. Jaffe: I showed that the spirals in cluster environments, both Coma and Virgo, tend to have more emission lines due to their interaction with the environment. So, any test that you run that has some dependence on the morphological type, the Hubble type, if that's been determined let's say by emission lines, or blue light or something, is dangerous because what you thought might be an Sb galaxy is really an Sa which has been given more blue light or more emission lines because of its interaction with the cluster gas, but both the Tully-Fisher relation and now, you say the interpretation of the shapes of the rotation curves also depends a little bit on your assumption on the morphological type of the galaxy. That can be very dangerous. Whitmore: Actually the results do not appear to depend on morphological type, although there are not really enough in the sample to check this in much detail. Richter: Let me say something contrary to what Rob Kennicut found, namely that the star formation rates of Sc galaxies in the Virgo cluster look more like star formation rates of Sb galaxies in the field. Jaffe: It depends on which part of the galaxy you looked at. I believe if you looked just at the nuclear regions of the galaxies which was, I think, what Kennicut did. Richter: No, it was Ha imaging. Jaffe: Well, we found very clearly that the spirals which are close to the Coma cluster, in the Coma and 1367 supercluster, which were close to the cluster itself, had much higher continuum radio emission, blue light and Ha equivalent widths than the same mass spirals in the field. Whitmore: I would like to comment on that. As I mentioned in the talk, I'm also worried about various systematic effects affecting the comparison of the global properties of cluster galaxies with field galaxies. For example, Sb galaxies may not be classed the same for the field and cluster samples, so I really agree with you there. However, for the shape of the rotation curves, it really doesn't come in to play. Essentially the Sa's and Sb's and Sc's are all doing exactly the same thing as I mentioned a minute ago.

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Jaffe: And my point is that what you think are Sc's may be Sa's. Whitmore: Take a look at these things. They clearly don't look like Sa galaxies. Schommer: I certainly think that some interesting things happen in the very cores of some of these clusters. We are in agreement on that. However, the strongest effect you see is on a small number of galaxies, right in the cores, and I think you said in your paper that they're peculiar galaxies in that they seem to have peculiar velocity fields. I worry a little bit that some of these observations are for galaxies that might be peculiar and then concluding that those rotation curves fall is a little bit of a dangerous procedure. The second point is reiterating Jacqueline's point that it's very dangerous to conclude anything about dark matter from optical rotation curves alone. Some of us remember Kalnaj's demonstration. The optical rotation curves simply don't go far enough to have much leverage on the dark halos. So, it seems to me while something may be happening, it is hard to say what happened to those dark matter halos just from these data. Whitmore: Okay, let me try the first point first. There were roughly three or four fairly peculiar rotation curves in the cluster sample. We threw them out of the sample before looking for various correlations. There was really no tendency for the central galaxies in those clusters to either optically look different or for the rotation curves to be more asymmetric: the two sides seem to be doing about the same thing. So I'm not too worried about your first point—we threw out the bad galaxies. Let me mention that your Fabry-Perot work looks real interesting. I was worried about the statement in your poster abstract that there are no falling rotation curves in your sample yet, but it sounds like in your abstract you don't have any galaxies in the central part of the cluster. You're mainly interested in the infrared Tully-Fisher, so you're staying away from centers of the clusters. Getting back to van Gorkom's point, while it would certainly be nice to have more extended rotation curves, the optical curves seem to show some effect. The simplest explanation, at least to me, would be that the dark matter may have been affected, but I agree that we can not be certain this is the cause based on the optical rotation curves alone. Moderator: Any further questions? Djorgovski: You touched upon something which I think is really promising, a new way to go about things. It's somewhat dangerous to compare properties of individual objects or files of individual objects as Greg [Bothun] said. For instance, this one's interacting and this one's peculiar and so forth. It's much more interesting, I think, to look at how different scaling laws and known empirical correlations between galaxy properties change in different environments because that way you are not sensitive to selection effects. I think the jury is still out whether it really matters or not for the Tully-Fisher relation. I know that in the elliptical galaxies there is a good hint that the Dn — a relation varies with cluster properties. But it's the correlations, not properties of individual objects, but the correlations of galaxy samples and families which one should measure. Edge: I've got a few viewgraphs to show, (laughter) This one is Figure 8 from my abstract taking the X-ray luminosity and correlating it with the fraction of spirals— and I think this is within a megaparsec, no radial information at all—take the X-ray

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luminosity which is proportional to the gas mass which is proportional to the gas density in the cluster. You take the temperature which is related to the depth of the potential, the correlation is still there but it's no where near as tight as this. So, that would indicate to me that it's not the depth of the potential but it's an environmental effect to do with the density of the intracluster gas. Whitmore: But that is a global property of the cluster. I mean the gas is in the center of the cluster, so I would argue from the same data exactly that the fundamental correlation is at least with some global property rather than local density. Mushotzky: But the density of the gas is not its mass. So, while they're both global properties, he's been able to split what you've been calling global properties into two variables and test those independently. Edge: There are some clusters that are denser than others but with the same potential depth, but the amount of gas is different and they produce different fractions of spirals. It's the same cluster potential, but it's a different amount of gas in it, so you get different proportions of spirals. Name Unknown: Apart from Perseus, isn't most of the difference between the higher uncertainty in the temperature and the luminosity? Edge: Possibly but the stronger signal always pulls you off. Moderator: Further questions? Sandage: Why do you think that this dispersion in your optical Tully-Fisher relation is so great, like 0.7 or 1 magnitude, compared with what other people believe from the infrared? Whitmore: Well, I think it could be the various systematic effects that we're worried about. For example part of it may just be the spatial resolution of the more distant cluster galaxies may result in a wider spread in determining the Hubble types. Sandage: Oh, they're not in the field in that diagram. Could we see the field diagram? There are no environmental effects in the field, so that's a very large dispersion for a field sample. Whitmore: This is a long standing question. Most of the radio samples have been treating the Tully-Fisher relationship as though it is just one correlation. It doesn't separate for the Sa's, Sb's and Sc's. I think part of it tends to be that we use blue luminosities rather than infrared, but that's a long subject. I don't know if Vera [Rubin] wants to comment or any of the radio people, but there's a lot of history on this. I think the main advantage for the infrared Tully-Fisher is their use of the infrared. Bothun: Well, it's a question of aperture, where you put it on the bloody galaxy. Infrared is nice but it's got a lot of problems. It homogenizes things by using dinky apertures and the center parts of all galaxies seem to be similar independent of their Hubble type in the inner scale length or at least the dispersion is smaller. But if you use bigger apertures, you might get larger scatter.

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Whitmore: Okay, so that might be part of it too. Sandage: Your ordinate values are what? Blue magnitudes? Whitmore: Total blue luminosity. Richter: I would like to know how significant is your effect about type segregation because consistently when you look at HI you continue to fail to see a very significant effect. Usually the HI data, of course, they give you an integrated profile so they look at the rotation curves at large radii. Whitmore: Well, statistically, there's a very clear difference. I don't know, if it's 3CT, 4er, 5
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ever been published or who to properly attribute it to, the first person who I talked to about this was Ed Turner. So, it probably goes back to Ed. He looked very carefully at the luminosity functions that were derived for Hickson compact groups in different places in the integral luminosity function and in fact, there's an interesting difficulty because Hickson compact groups consist of galaxies that are primarily about the same luminosity in each group. So, you tend to have something very funny which is groups of very low luminosity galaxies and groups of very high luminosity galaxies and it's rarely the case that you have enough of a range in any individual group to really think you have a normal luminosity function. That's a real interesting difficulty, and I don't really understand how that comes about, other than possibly by selection. However, if you take everything and lump it all together—you take all the galaxies and all the groups and lump them all together to try to come up with say a combined luminosity function for the galaxies in the groups or even split them between early type and late type galaxies, the luminosity functions for the combined sample are almost exactly normal or are normal to within the errors. You couldn't tell the differences, and one of the things that that tells me is that there is not at least a huge amount of increase in brightness in this environment caused by the interactions. I mean there might be some, just the errors in the magnitudes are fairly large and the systematics could be fairly large when you consider these things compared to say, Zwicky. But we know that things aren't quite as perverse as they could be. It's not a magnitude off. It could be three-tenths of a magnitude off. The spirals could be that much brighter but they're not a magnitude brighter. So, there are some problems with this but I don't think they're as bad as they could be and some things you're telling me suggest that this is probably right. Sandage: John, are there dwarfs in Hickson groups? Huchra: Yes. Sandage: dE's? Huchra: Interesting question. I don't really know. Sandage: How far down does the luminosity . . . Huchra: I haven't measured redshifts for any, so I . . . Sandage: Well, you don't need redshifts to say . . . Huchra: No, but you need a redshift to say if they're in a group, which is part of the problem. There are dwarfs irregulars. I don't believe I've ever seen a dwarf elliptical. The average redshift in these things is sort of 10,000 to 15,000 . . . Sandage: Oh, okay. Huchra:

...so, it's a real pain in the yo-yo.

Felten: You made a big deal of whether the morphology depends on a local or a global properties of clusters, but the projected surface density is itself a global property. I think in the same sense, say that the projected radius is a global property. You were looking

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also at projected surface densities, however, you did show at least one view graph in which someone, maybe Dressier, had attempted to de-project and had attempted to express a morphology in terms of the local density of galaxies per cubic megaparsec. Now, there might be problems in doing that, but supposing we knew how to do that and suppose we in fact found that the morphology was a function of the local surface density. I'd like you to get into this area a little. What would this possibly mean? Could this mean, for example, that most of the galaxies in the little local region have interacted recently in this little local region so they don't remember what things were like earlier, when they were in other parts of the cluster? Or could it mean perhaps that the cluster is spherically symmetric and most of the galaxies are on tangential orbits so that they were always at more or less the same density and never passed through the center of the cluster? Let me say, neither of those two scenarios seems to me to make an awful lot of sense but physically I find it hard to see what kind of interpretation you would give this kind of strong correlation with the local galaxy density. Am I the only one who doesn't understand this? What could the physical basis of all this mean? Can you comment on that? Whitmore: It was these kinds of cenerns that led me to take another look at Dressler's data. If the fundamental correlation is with local density rather than say, R c / us < er , the implication is that there are local, physically bound subclumps in clusters that drive the determination of the Hubble type. But how would these survive the original cluster collapse in dense clusters like Coma? Also, while there is certainly some evidence for subclumps in clusters, they do not seem to be so obvious that they could be driving such clear correlations with the morphology. Salvadore-Sole: I just wanted to say that in Ap. J., February, there was a paper of ours analyzing the correlation of morphological type and surface density. First assuming a Hubble model for the density profile of clusters, then one can de-project the relation and find that there is a dependence of the concentration of the cluster which is much more apparent than the one you see in two dimensions. Second, that this kind of dependence on central concentration of the cluster is at least consistent with what one would expect from correlations between the radius and environmental evolution of galaxies. So, I don't know if I answered your question but at least there has been an attempt to do it. Whitmore: The way I understood his paper was that, if you just assume there's a real simple correlation in the space density and then you go ahead and ask, well, how is that going to look in two dimensions on the sky versus three dimensions, you can pretty much explain why the two-dimensional correlations are happening that way. The main thing I tried to emphasize was that I think the way to interpret the morphology-density relationship is that the local density is giving you a pretty nice way of measuring a global property of the cluster. Fruchter: Is there any correlation in your sample between luminosity and distance from the center of a cluster? Whitmore: Nothing real apparent, although we haven't looked specifically at that. We only have 20 galaxies to start with, but it's probably worth at least taking a closer look.

EVIDENCE FOR GAS DEFICIENCY IN CLUSTER GALAXIES

Martha P. Haynes National Astronomy and Ionosphere Center1 Space Sciences Building Cornell University Ithaca, NY 14853

Abstract. On-going removal of the low density outer interstellar HI gas occurs in galaxies passing through the central regions of clusters with moderately high X-ray luminosity. Although the galaxies currently maintain their spiral morphology, they are HI deficient by as much as a factor of ten relative to their counterparts at larger cluster radii or in the field. The HI distribution in deficient galaxies is truncated well interior to the optical radius as the gas is removed preferentially from the outer portions. In contrast, the molecular hydrogen component, derived from observations of CO, seems undisturbed. Galaxies that are Hi poor by a factor of ten may be gas poor by only a factor of three. At the same time, other indicators suggest a reduction in the star formation rate in most H I deficient galaxies, but some objects may suffer an enhanced gas depletion if star formation is actually induced by the interaction. While the intracluster medium is the likely catalyst for gas removal, the exact sweeping mechanism is unclear. Early-type objects seem to be even more HI poor than latetype ones, perhaps supporting the suggestion of a fundamental difference in the orbital anisotropy of early and late type spirals. While it seems possible that after disk fading, stripped spirals would ultimately resemble SO's, it is unlikely that all SO's result from such gas sweeping events since the process seems viable only in the cores of rich clusters.

1. INTRODUCTION The study of the gas content of galaxies in clusters affords us the opportunity to search for environmental effects on the star formation process in cluster members and by implication may lead to an estimate of the effectiveness of morphological alteration at the current epoch. Currently, HI observations exist for significant numbers of galaxies in about a dozen clusters. While the link between the HI content of a galaxy and its current evolutionary state can only be surmised in a statistical sense, the availability of HI observations for increasing numbers of galaxies in clusters of differing properties The National Astronomy and Ionosphere Center is operated by Cornell University under a management agreement with the National Science Foundation and Center for Radiophysics and Space Research, Cornell University.

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makes the comparative studies performed using the HI line a sensitive, though indirect, probe of the effect of environment on the evolution of spiral disks. It has been over 15 years since the study of the HI content of galaxies in different environments was first addressed. Davies and Lewis (1973) conducted a survey of about 25 galaxies in the Virgo cluster and compared those observations with a similar sample of nearby galaxies. Davies and Lewis used both the hydrogen mass to luminosity ratio M|j j /L and the HI surface density <7H i to conclude that the Virgo cluster spirals were Hi poor with respect to their field sample. This result was quickly questioned by Bottinelli and Gouguenheim (1974) who pointed out that the Virgo spirals were typically more luminous than the field objects and hence the comparison was effected by bias. As the Virgo cluster HI sample has grown and extended to fainter objects, the initial conclusion of Davies and Lewis seems to have been established (Huchtmeier et al. 1976; Chamaraux et al. 1980; Giovanardi et al. 1983a; Haynes and Giovanelli 1986; Hoffman et al. 1988), although some doubts have been raised even fairly recently (Tully and Shaya 1985). One of the difficulties over the years has been in the definition of a comparative HI content parameter and its possible dependence on intrinsic properties like luminosity and morphological type, both of which are likely to be represented differently in typical cluster and field samples. The definition and choice of the Hi deficiency parameter (DEF) is discussed in Haynes et al. (1984) and Giovanelli and Haynes (1988). For spirals, the disk size, not the luminosity, seems to provide the best normalization: the Hi, as a disk constituent, is marked by a nearly constant globally averaged surface density crH j . In contrast, the HI mass to luminosity ratio Mg j /L is not purely a disk property, particularly for early type systems for which the gas-free bulge contributes significantly to the light. Thus Mg j /L is suspected to be more type-dependent and susceptible to differences in the luminosity distribution of the cluster and comparison samples. In keeping with the general discussions given in the preceding references, I will hereafter use our standard definition of the comparative HI content of galaxies in terms of the H I deficiency parameter (DEF) = (logM H i(D,T)) - logM H i(D,T) o 6 s defined as the difference, on a logarithmic scale, between the observed HI mass and that expected for a "normal" galaxy of similar linear size and optical morphology. A galaxy that is Hi poor by a factor of ten thus has (DEF) = -f 1.0. In order to set a standard of normalcy, Haynes and Giovanelli (1984) observed a subset of galaxies listed in the Catalog of Isolated Galaxies (Karachentseva 1973; CIG), allowing them to establish the relationships between HI mass and linear diameter for galaxies of morphological type Sab to Irr. Normal galaxies show a range in (DEF) that is approximately gaussian with a dispersion of about 0.25. In this definition, galaxies are not considered "deficient" unless (DEF) > +0.3 (deficient by a factor of two), or preferably, +0.48 (factor of three). It should be kept in mind that the establishment of a normal HI content for galaxies earlier than Sab is still in doubt, and indeed even new high sensitivity Hi observations of nearby Sa's show that class to be much more heterogeneous in its properties than later type spirals (Magri and Haynes, in preparation). In the years since the publication of the Virgo results, numerous studies have presented conclusions, some in agreement and some in disagreement, with the picture of HI depletion of cluster spirals. The accumulation of observations of galaxies in a variety of clusters themselves characterized by different morphologies, densities and X-ray luminosities has permitted an examination of the circumstances in which HI deficiency is observed. Furthermore, more recent work on the Virgo cluster has probed the molecular

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constituent as well as the atomic and has attempted to investigate the star formation rate at the current epoch. In the remainder of this paper, I will review the status of today's results concerning the observed gas deficiency in cluster spirals with particular regard to their implications for star formation and galaxy evolution.

2. HI DEFICIENCY IN CLUSTERS Over the past fifteen years, observations of cluster spirals have been accumulated by a number of groups. In this presentation, I am not attempting a review of all findings, but rather an assimilation of the results, and hence apologize in advance to those whose work is not mentioned here explicitly. Tremendous improvements in radio receiver and spectrometer technology have allowed the acquisition of HI spectra from a galaxy in a cluster like Hercules to require a factor of ten less time than such observations typically needed in the early 1970's. In 1973, the Arecibo antenna was in the midst of its resurfacing and the first real observations of extragalactic HI were made with it in 1975. Because of its great collecting area, Arecibo has been the instrument of choice for studies of HI in distant objects. In nearer clusters, improvements have increased the potential of studying clusters with smaller filled aperture telescopes so that several clusters outside of Arecibo's declination window have also been studied. In addition, aperture synthesis studies have allowed the detailed mapping of the HI distribution and velocity field in galaxies in the nearest clusters. The design of experiments to look for HI deficiency in clusters has been dominated by technical constraints placed on scheduling, integration time and interference potential. Studies of redshifted HI are subject to man-made radio interference that can not only saturate receivers but also mimic weak HI emission. In the United States, the band from 1400 to 1427 MHz is protected for passive use with an extension to 1360 MHz in the form of a footnote to the regulations that urges non-interference. No protection is set below 1360 MHz, which corresponds to a redshift z > 0.04. Other countries have similar regulations. The interference situation in reality varies widely and can be devastating at certain times and frequencies. Most of the clusters with z < 0.03 that are accessible to Arecibo have been studied, as well as several others that are of particular interest. The clusters for which HI content observations have been compiled are listed in Table 1. These clusters cover a range in redshift, in morphology, in galaxy density and in X-ray luminosity. Note that, because of the nature of a study of HI in galaxies, all of these clusters contain a significant population of spirals. The need for a sample with which to compare the cluster galaxies has been fulfilled in two different ways. It is possible to compare the HI content of a core sample with a sample at larger distance from the cluster center in order to look for radius-dependent differences within a given cluster: the "IN versus OUT" approach. Because of the controversy over possible differences between the cluster and comparison samples, Haynes and Giovanelli (1984) established their definition of Hi content with respect to a sample of isolated objects that are outlying members of the nearby superclusters (Haynes and Giovanelli 1983). The isolated galaxies have similar distributions of magnitudes, sizes and redshifts as the galaxies in most nearby clusters, so that selection biases based on sensitivity and resolution are likely to be minimized. As expected from morphological segregation, the isolated galaxy sample is heavily represented by late type spirals and irregulars.

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Martha P. Haynes TABLE 1 Observations of HI Deficiency in Clusters Cluster Virgo A1060 Pegasus A262 Cancer A426 Z1400+09 A1367 A1656 A2147 A2151

Redshift"

a

S:S0:E

Lxi

d.f.c

ref.d

.0035 .0114 .0115 .0161 .0167 .0183 .0205 .0215 .0232 .0356 .0371

721e 676 616 540 300* 1050 400* 760 920 810 890

(46:39:15) (39:48:13) 59:29:12 (47:32:21) 71:18:11 (35:40:25) 62:28:10 43:40:17 18:47:35 42:31:27 51:35:14

4.5 1.5: <0.6 3.1 <0.2 46.1 <1.0 4.5 40.5 6.1 0.9

0.56 ... 0.18 0.48 0.21 >• • 0.00 0.42 0.77 0.50 0.21

f g GH85 GH85 GH85 i GH85 GH85 GH85 GH85 GH85

"Redshifts and velocity dispersions are taken from Struble and Rood (1987) where available and are corrected with respect to the barycenter of the Local Group. The X-ray luminosity is given in units of 10~ ergs s and is derived within the 0.5 - 3.0 keV range over the inner 0.5 Mpc of the cluster. c The deficient fraction d.f. is the fraction of observed cluster galaxies that are HI deficient by more than a factor of two. The listed reference presents a recent comprehensive summary of observations of this cluster. See references therein for details of other results. e Mean dispersion for the cluster. The relaxed elliptical population shows a lower characteristic dispersion and the spirals a higher one. 'Hoffman et al. 1988. ff Richter and Huchtmeier 1983. Cancer is not a single cluster, but a collection of bound groups, each with a velocity dispersion of about 300 km s'^Bothun et al. 1983). Z1400+0949 may be similar. (Thompson et al. 1979) 'Magri et al. 1988. The first studies of clusters more distant than Virgo produced some contradictory results in which some clusters appeared to show marked HI deficiency and others none at all (Giovanelli et al. 1981; Sullivan et al. 1981; Schommer et al. 1981; Chincarini et al. 1983). It took the accumulation of of amounts of data by several groups to permit the understanding of the discrepancies. Indeed, not all clusters contain HI poor galaxies, but in some, almost all of the core spirals are severely deficient in their interstellar HI gas. An examination of the results for nine clusters has been presented in Giovanelli and Haynes (1985; hereafter GH85). That analysis made use of most of the Arecibo observations made at that time, including those made by other groups, and included about 300 objects. The clusters themselves cover a range in distance, in degree of central concentration and morphological mix, and in X-ray luminosity. Of the nine clusters, six show significant HI deficiency, but to varying degrees, and three contain galaxies with "normal" HI content. The latter three clusters are all characterized by a loose, irregular structure, a low X-ray luminosity and a high spiral fraction, while the others are richer, more evolved objects. The zone of HI depletion within each deficient

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cluster is restricted to the inner Abell radius or less, except in the Coma cluster where Hi poor spirals are observed out to 1.5 R4. Because a certain fraction of the galaxies at small radii are expected to be objects at large radii seen in projection, the results are consistent with gas removal in all spirals passing through the core. With the accumulation of sufficient data, the case for gas sweeping in cluster core galaxies seems firmly established where the gas and galaxy density are high enough. Efforts to examine which of the possible gas removal mechanisms might be most effective in these rare environments require an examination of data at a variety of wavelengths and have been helped enormously by studies of the nearest cluster, Virgo. A review of the current state of relevant observations of galaxies in and around Virgo is thus presented in the next section.

3. OBSERVATIONS OF THE VIRGO CLUSTER Because of its proximity, the Virgo cluster serves as a prime laboratory for the study of environmental influences because of the large number of observational tools that can be used to study its member galaxies. Although not a terribly rich cluster, the Virgo environment is nonetheless condusive to the conditions in which we expect to find morphological alteration and gas sweeping. Therefore, it is important to review the evidence for gas deficiency in Virgo at this point. To date, HI observations have been made of several hundred galaxies in and around the Virgo cluster covering a wide variety of morphologies, types, luminosities, masses and star formation histories. Several authors have examined the occurence of H I deficiency within the cluster {e.g., Haynes and Giovanelli 1986; Hoffman et al. 1988). A substantial number of galaxies covering a wide range of luminosity and morphological type are HI deficient by more than a factor of ten. Haynes and Giovanelli noted that the zone of HI deficiency extends through the region within about three degrees of M87. Within that zone, nearly all galaxies not seen in projection seem to be effected. Several studies have used single dish observations to investigate the relative extent of the Hi and stellar distributions of Virgo galaxies {e.g., Helou et al. 1981). Hewitt et al. (1983) matched a model Hi distribution with Arecibo flat feed major axis mapping observations to derive the characteristic Hi sizes of large angular diameter galaxies from the CIG. Haynes and Giovanelli (1983) then compared the Hi radii measured similarly for Virgo spirals with those derived by Hewitt et al. They found that galaxies within the five degree Virgo core have H I-to-optical sizes a factor of two smaller on average than galaxies further from the cluster center. At the same time, the HI sizes are reduced along with the HI masses so that the globally averaged HI surface density scaled with the Hi (not optical) radius (logMg j / D ^ j) remains constant. In all respects the peripheral galaxies resembled the general isolated galaxy sample. Furthermore, Haynes and Giovanelli (1986) emphasized the one-to-one correspondence between large HI deficiency and small H I-to-optical disk size. Aperture synthesis studies of the HI emission in galaxies in the Virgo cluster have been undertaken both with the Westerbork Synthesis Radio Telescope by Warmels (1988a,b) and with the Very Large Array (VLA) (van Gorkom and Kotanyi 1985; Cayatte et al. 1989). Both studies confirm the earlier single dish findings that the H I is preferentially removed from the outer parts of the galaxy and that the zone of stripped galaxies extends to about three degrees from M87. Warmels (1986) has found not only a systematic shrinking in the HI diameter relative to the optical for the subset within the core, but also concluded that the ratio DJJ / /Dop< decreases fairly smoothly with

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distance from M87. He identified the region within three to five degrees as a transition region where only moderate reduction of DJJ / /Doptia evident. This scale is comparable to the zone of HI deficiency noticed by Haynes and Giovanelli (1986). The VLA surveys add more information about the structure within the HI distribution and its velocity field. For more discussion of the rotation curve issue, the reader is referred to Whitmore's chapter in this volume and to Guhathakurta et al. (1988). It is clearly evident from the global display of the Hi distribution in Virgo spirals shown by Jaqueline van Gorkom (van Gorkom and Kotanyi 1985), that the inner spirals have shrunken HI disks. Furthermore, the higher resolution maps presented by Cayatte et al. (1989) show peculiar details of the Hi distribution. Galaxies in the western half of the cluster are typical larger in HI than objects in the eastern part, and several galaxies show HI asymmetry with a sharp edge on the side of the galaxy oriented toward M87 and a more extended distribution on the opposite side. In Virgo, we have the opportunity to identify and study galaxies in a current stripping stage. The proximity of the Virgo cluster makes it possible to examine the molecular content, as derived from the millimeter transitions of CO, in galaxies at different distances from M87. Two major surveys of CO in Virgo spirals have been contributed by Kenney and Young (1986) and by Stark et al. (1986). Galaxies that are Hi deficient have systematically larger ratios of CO flux to HI flux. If the normal conversion from CO flux to H2 mass is applied, the core spirals that are deficient by a factor of ten or more in HI may be gas-poor (HI + H2) by only a factor of two to three. Some spatial mapping has been performed so that an estimate of size of the molecular cloud distribution relative to the HI and optical disks can also be made. The spatial distributions of CO in HI poor galaxies are not smaller than those of similar objects seen in the field. It appears that the peripheral diffuse H I clouds are swept away, but the high density molecular clouds remain relatively undisturbed throughout the process. Another estimate of the dust content within galaxies is provided by the far infrared emission detected by the Infrared Astronomical Satellite (IRAS), although the precise derivation of dust mass is complicated by the mixture of dust components at different temperatures and the unknown size distribution of the grains. In order to relate the dust and gas properties, Doyon and Joseph (1989) have found that the Hi deficient galaxies in Virgo have lower 60 and 100 micron fluxes and inferred temperatures that are cooler than those with normal HI content. With the caution that several factors could play critical roles in the observed emission at the IRAS wavelength bands, those authors conclude that at least half of the cool diffuse dust has been removed from typical Virgo core spirals. This cool dust, of course is the "cirrus" identified with the atomic hydrogen component of the interstellar medium. Indirectly, van den Bergh (1984) has explained the inclination dependence of deviations of individual galaxies from the mean blue Tully-Fisher relation in terms of a lowered dust content among Virgo spirals. Numerous authors have pointed out peculiarities in the properties of Virgo galaxies that can be explained by morphological alteration. Peterson et al. (1979) have claimed that the optical disks of early type galaxies in Virgo are smaller than those in the field. Bosma (1985) has examined the disk diameters of Virgo members at the same surface brightness limits and finds that although some field spirals have low surface brightness extensions, no Virgo galaxies have large outer disks. Forman et al. (1979) interpret individual galaxy X-ray sources (e.g., M84, M86, NGC 4388) as ram pressure sweeping events. There are numerous other clues as to the star formation rate and history in Virgo cluster objects that are likely to be of relevance. Stauffer (1983) has found a much

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higher occurrence of the anemic phenomenon among Virgo spirals than his field sample. Kennicutt (1983) notes that the average Virgo spiral of a given morphological type is redder by about 0.07 in (B-V) than a field object of the same class. Taken alternatively, for the same color, a Virgo spiral appears morphologically about half a Hubble class later than a field spiral. Kennicutt points out that, in order to account for anemia and the color shift, one must both get rid of the blue galaxies and make all the galaxies redder. Kennicutt and Kent (1983) derive a significantly reduced high mass star formation rate for Virgo core galaxies from integrated Ha measurements. Indeed, the HI deficiency in Virgo is seen to correlate with the (B-V) colors, the disk line emission and the (U(242lA)-V) colors in the sense that the Hi poor galaxies are always redder (Guiderdoni and Rocca-Volmerange 1985). Even the dwarf distribution appears to have been reddened by a reduction of star formation (Gallagher and Hunter 1986). Kennicutt(1983) suggests that the reddening can be explained as a reduction in the star formation rate by a factor of two about 10 years ago. The combination of all of this evidence leads us to believe that spirals that pass through the center of the Virgo cluster can lose as much as ninety percent of their HI mass and suffer a reduction of their star formation rate by about a factor of two. At the same time, the molecular constituent remains relatively intact. At larger distances, we are not able to study the stripping event in as much detail as in Virgo, but can use our knowledge of the Virgo cluster to ask the appropriate questions.

4. CONSTRAINTS ON THE SWEEPING MECHANISM With the occurrence of HI deficiency well established in some clusters and not in others, it is possible to examine the evidence for on-going sweeping in an attempt to identify the mechanism(s) that are responsible for the gas depletion. It is likely that several processes play a role, some more likely than others but all may occur in individual situations. Gas removal mechanisms need not necessarily arise from external causes, driven by the environment. However, since the HI deficient spirals at least to a visual inspection show similar optical morphology to their HI rich counterparts outside clusters, it seems most likely that the cause of the deficiency is indeed governed by the peculiar circumstance of the galaxy's location within a cluster core. Thus we are led to examine the occurrence of HI deficiency in terms of the likely environment-dependent gas removal mechanisms generally divided into two categories: interactions among neighboring galaxies in the cluster and interactions between a galaxy and the intracluster medium (ICM) in which it is immersed. In the environments of loose groups, tidal encounters are likely to remove gas from galaxies that come closer than a galaxy diameter (Toomre and Toomre 1972). There are many examples of such HI appendages and their explanations are, with few exceptions, quite straightfoward in terms of tidal disruption (Haynes et al. 1984). In several cases, large fractions of the disk H I have been removed to larger radii. The ultimate fate of the disturbed HI is unclear. Cottrell (1978) would like to explain the occurrence of Irrll galaxies in terms of tidal distruption with subsequent gas infall and enhanced star formation. The likelihood that a galaxy will suffer a tidal collision depends on its cross section, the mean separation and the local velocity dispersion. The actual damage a galaxy suffers depends critically on parameters like the relative orientations of spin and orbital angular momentum, but can be examined, to first order, in terms of the separation and relative radial velocity of likely participants. In the impulse

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approximation, the "disruption damage" is just proportional to l/a 2 u, where a is the separation and v is the relative velocity of the interacting galaxies. Hence, for the same perigalactic distance, a tidal encounter in a loose group will inflict more damage than will one in a cluster because the duration of the tidal pull will be longer where the velocity disperion is lower. On the other hand, tidal encounters are more likely to occur in clusters where the cross section for an interaction is much larger. Because of the high density of galaxies, it is also possible that direct collisions among galaxies might lead to the gas removal in clusters. Spitzer and Baade (1951) proposed that collisions could remove most of the interstellar medium from galaxies which suffer a head-on collision although the two stellar components would remain relatively intact albeit without their dust and gas. The stellar remnants would resemble SO galaxies and the interstellar material, having been heated by the collisional shock to high temperatures, could expand and dissipate into the ICM. Direct collisions undoubtedly lead to dramatic events, and interpenetrating encounters are the likely cause of ring galaxies (Lynds and Toomre 1976). In clusters, the collisional cross section is higher, but it is not likely that it is high enough to lead to the observed deficiency seen in cluster spirals today, especially if orbits are preferentially radial. Sarazin (1979) has estimated a collision rate about 1000 times lower than that calculated by Spitzer and Baade. Galaxy-ICM interactions have been the subject of a large number of papers many of which are referenced in Sarazin (1986). One of the most popular and simple treatments considers the ram pressure induced by the motion of a galaxy with a uniform velocity through a uniform ICM (Gunn and Gott 1972). In this picture, the pressure of the ICM felt by the cold interstellar gas competes with the gravitational force (per unit area) within the galaxy so that ram pressure sweeping is effective in the circumstance that

A typical spiral galaxy of total mass of IO^MQ, radius of 10 kpc, gas density njj of 1 cm" , and Hi scale height of 100 pc has a surface mass density of stars a* of about 0.06 g cm" 2 and of gas crg about 10 g cm" , so that the restoring force created by its gravitational potential is 2 x 10 dyn cm" . In rich clusters, the velocity dispersion yields an estimate of the three-dimension velocity of order 1700 kms (although note that we actually need the component of the galaxy's orbital velocity normal to its disk). Therefore the ram pressure in a typical cluster can be written in terms of the local ICM density njcMi itself a function of the distance to the cluster center: > 5 x 10" 8 nICM dyn cm" 2 . For the typical spiral then, stripping will occur when the ram pressure exceeds the restoring force, that is, when n/cA/ > 5 x 10~4 cm" 3 . Other mechanisms also arise from galaxy-ICM interactions. Cowie and Songaila (1977) have investigated the case of thermal evaporation. Examining the simple stationary case, they find that heat conduction leads to subsequent evaporation of the interstellar H I gas. The evaporative mass loss rate is a sensitive function of the ICM temperature (largely uncertain) and less sensitively of the ICM density. In fact, if radiation from the interface between the hot and cold gas becomes important, material may actually condense onto the galaxy, causing an increase in the mass density and perhaps an enhancement of the star formation rate. In several papers, Nulsen and coworkers (Nulsen 1982; Takeda et al. 1984) have considered the more realistic case of a galaxy moving through the cluster on a radial orbit so that the ram pressure encountered varies greatly along its path. While in the outer regions of the cluster, the galaxy accumulates

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gas subsequently lost during its passage through the core. This treatment of turbulent viscosity predicts that some galaxies in low density, low dispersion clusters should retain their stripped interstellar gas as a hot X-ray halo. X-ray sources seen to be associated with individual galaxies in Virgo (Forman et al. 1979) and A1367 (Bechtold et al. 1983) might be identified as such objects. Rather more complicated two-dimensional codes which include hyrodynamical calculations have been examined by Gaetz et al. (1987) to study the effect of cluster passage on spherical galaxies. A real treatment of the problem for a disk of gas and stars requires added complexity and has yet to be fully solved. Sarazin (1986) discusses in more detail the various calculations that have been performed to investigate the stripping process. Of the various mechanisms, several predict correlations that may lead to a variation in the observed degree of deficiency among clusters of different morphologies and properties. Based on the simple ram pressure sweeping model, we expect that galaxies travelling at high velocities through clusters with a dense ICM would be expected to be stripped. Thus the ram pressure scenario predicts greater stripping in clusters characterized by high velocity dispersion and higher ICM density. The efficiency of evaporative stripping is only weakly dependent on ICM density, but is strongly dependent on,the ICM temperature. Therefore, it would be valuable for the comparison between ram pressure and evaporative stripping to discern any difference in the temperatures of the clusters with different degrees of deficiency. Note, however, that it is likely that high temperature clusters may also have a high velocity dispersion. A correlation is already noted between high X-ray luminosity and high velocity dispersion. As part of their analysis, GH85 looked for correlations between the degree of HI deficiency and the X-ray properties of the cluster. A useful parameter derived by GH85 and presented in Table 1 is the "deficient fraction," d.f., the fraction of cluster galaxies in the observational sample that are HI deficient. Use of this fraction requires the assumption that there has been no particular bias introduced in choosing the observational sample, that is, that all candidate spirals have been observed. For the GH85 sample, Dressier (1986) has suggested that such is the case. GH85 find that d.f. correlates with the X-ray luminosity of the cluster: the clusters with the highest Lx contain the greatest proportion of highly HI deficient objects. There are two clusters that have been used in the direct comparison of the efficiency of galaxy-galaxy and galaxy-ICM interactions because they lie at the same distance and are close together on the sky: A2147 and A2151 (Giovanelli et al. 1981). In contrast to A2151 (the Hercules cluster), A2147 is more centrally concentrated, contains a greater elliptical fraction and has a stronger cluster X-ray source. A2151, however, contains a higher density of galaxies, so that the cross section for galaxy-galaxy interactions is expected to be higher in its core. While A2151 does contain some Hi poor objects, the overall HI deficiency is significantly higher in A2147, thus supporting the relative importance of galaxy-ICM interactions. Furthermore, A2147 is characterized by a relatively low ICM temperature (Mushotsky 1984) so that ram pressure is more likely to be effective than evaporation. It should be noted, however, that this result depends on the comparison of only these two clusters which themselves are the most distant in the current sample, and hence should be considered supportive though not conclusive. In an attempt to pin down which one of the likely mechanisms was in fact responsible for the observed gas deficiency, Magri et al. (1988) have undertaken a detailed statistical analysis of the H I, optical and X-ray data available for galaxies in six clusters. They used maximum likelihood and non-parametric techniques to search for correlations between the observed HI deficiency in the galaxies and tracers of the likely

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stripping processes: (a) r, the distance to the cluster center, (b) r/r c , the same distance scaled to the cluster core radius, (c) rip^y, the number density of galaxies projected locally, (d) V, the galaxy velocity relative to the cluster mean, (e) V 2 , the square of the velocity, (f) piCMi the local ICM density derived from fitting the X-ray surface brightness distribution, and (e) PiCM^i the intracluster ram pressure. Magri et al. find that HI deficiency is a monotonically decreasing function of distance from the cluster center. It is unclear whether the dependence is on the radius itself or on n or p, since a linear dependence on density is almost equivalent to a dependence on r~ 3 ^, with /? obtained from the fit to the surface brightness. As a mechanism, ram pressure should predict a correlation with p, V 2 , or their product />V2, but no such dependence was observed. GH85 have employed Monte Carlo simulations to illustrate that the signature of the velocity dependence of ram pressure stripping would likely be masked by randomizing projection effects which reduce the sensitivity of the observational variable. For one problem, galaxies with normal HI contents but actually at large radii may be only projected on the core. In addition, the important vector in ram pressure is the component of the galaxy's orbital motion in the direction normal to the disk. Galaxies passing through the cluster edge-on will emerge relatively unscathed. In many galaxies, the surface mass density <7+ at the Holmberg radius is significantly lower than in the Milky Way (Bosma 1981) by as much as an order of magnitude. Since the simple ram pressure criterion described by Gunn and Gott (1972) balances the ram pressure force with the restoring force within the galaxy's disk, it is to be expected that dwarf galaxies, possessing smaller potential wells, should be preferentially stripped of the HI gas. However, such a dependence of HI deficiency on mass surface density has not been observed even among the Virgo dwarfs (Hoffman et al. 1985). Thus, while ram pressure sweeping is an often-invoked explanation for the gas removal, its direct predictions of velocity and mass dependence are not evident in the observational data. While the effectiveness of ram pressure is highly dependent on galaxy orientation, the amount of gas lost through turbulent viscous stripping is comparable to the mass of hot ICM material encountered by the galaxy disk as it travels through the cluster and depends on the amount of time spent in the high density ICM core. As noted by Pryor and Geller (1984), a galaxy seen at a large projected distance must have a long period even if its orbit is highly radial. When in the outer portions of the cluster, such a galaxy has the opportunity to accumulate material lost by evolving stars. Several objects that are extremely HI deficient lie on the outskirts of the Virgo cluster and may be in the gas accumulation phase (Giovanelli and Haynes 1983). Based on the occurrence of HI deficiency relative to the X-ray emission seen in the center of Virgo, Haynes and Giovanelli (1986) argue that turbulent viscous stripping can account for the observed HI deficiency of galaxies within three degrees of M87. The fact that the H2 component, as derived from the CO observations, remains intact argues again for an external gas sweeping mechanism, but may be easy to explain. Since the filling factor of molecular clouds in the ISM is much lower than that of HI clouds, collisions among the densest clouds during galaxy collisions will be unlikely, whereas the lower density clouds may be more susceptible. Numerical calculations by Kritsuk (1983) show that the molecular component will survive a sweeping event. What remains is our lack of understanding of the long-term effect of the removal of over ninety percent of a galaxy's HI mass. Surely its disk will fade. As noted by Dressier (1986), the HI deficiency observed for spirals of types Sb and earlier is marked more severe than that observed for later types. He has examined the velocity distribution of deficient and H I-normal galaxies and concludes that this

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variation in the typical degree of HI depletion can be explained in terms of differences in the characteristic anisotropy of the orbits of different types. He suggests that early type spirals travel through the cluster on orbits that are preferentially more radial than the later spirals. A similar conclusion was reached for the H I-deficient galaxies in Virgo by Giraud (1986). Thus some fundamental fine-tuning of the orbital characteristics of the galaxies plays an important role in their likelihood of gas depletion and perhaps of the overall morphology as well. However, such kinematic differences are quite uncertain, and indeed, Pryor and Geller (1984) conclude that, based on current data, the most likely models are isotropic. At the present time, the available data allow limited analysis of the three dimensional distribution of gas and galaxies in clusters. In several of the six clusters studied by Magri et al. , both the galaxy and X-ray surface densities show strong asymmetries in their azimuthal distributions and exhibit significant subclumping. Spatially resolved X-ray spectroscopy and imaging are needed in order to determine structure in both the temperature and density distributions of the intracluster gas.

5. INDUCED STAR FORMATION From simple arguments, the interaction with the ICM may also be expected to increase temporarily the star formation rate, particularly on the forward side of the galaxy where intracluster material may be accreted by the galaxy and where the ram pressure will compress the interstellar clouds. Evidence that such is the case comes from studies both of the gas distributions and star formation indicators. Indeed, Cayatte et al. (1989) find that the distribution of Hi is generally asymmetric with the side away from M87 being the more extensive. Kenney et al. (1989) have mapped the CO emission in the HI poor Sa NGC 4419 and find the molecular distribution itself to be significantly asymmetric, suggesting that the molecular as well as the atomic gas in this central located, high velocity galaxy is currently undergoing a strong interaction with the ICM in Virgo. Gavazzi and Jaffe (1986) have conducted a radio continuum survey of galaxies in the Coma/A1367 supercluster with the VLA and find that the cluster spirals, although HI deficient, have actually stronger radio continuum emissivity. In particular, they find a number of HI poor, radio loud, rather blue objects just at the edge of the the X-ray distribution around A1367, and suggest that the interaction of the hot X-ray gas with the cool interstellar clouds in the galaxy leads to a collapse of the molecular clouds and an enhancement of the star formation rate. It is generally assumed that the molecular clouds are the precursors of the massive star formation regions. Interestingly, Kennicutt (1989) has concluded from a comparison of the distributions of Ha emission, HI and CO in 15 nearby galaxies that the disk averaged Ha surface brightness is well correlated with the mean atomic and total gas surface densities and only weakly so with the mean molecular surface density derived from the CO observations. This finding implies that the coupling between the active star formation and the molecular clouds is not as strong as one might have expected. Rubin at this meeting has presented preliminary results on rotation curves derived for Virgo cluster spirals in which the Ha emission cuts off inside the optical disk, at the same radius where the HI disk truncates. Hence we see that the massive star formation and the HI are both seemingly affected whereas the dense molecular component remains intact. The rates of massive star formation derived from the Ha, radio continuum and FIR emission are a factor of two or three lower in the HI deficient objects.

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Thus as discussed by Kenney and Young (1989), the retention of the molecular component maintains at least a moderate rate of massive star formation. An interesting point presented by Kenney and Young is that, while the outer disks are very HI deficient, the inner ones are at least moderately so, and it is actually possible that some of the inner HI has been compressed into the molecular stage. The increased mass surface density of the molecular clouds and their central location are able to defend them from the effects of ram pressure. Several of the most severely stripped galaxies in Virgo show signs of peculiar nuclear activity or strong gas asymmetries that are consistent with a picture of gas infall or induced star formation (Cayatte et al. 1989). In the past, it is likely that such gas sweeping events were even more prevalent. Thus, it is of interest to study current epoch stripping with an eye on the expectations for observations of clusters at higher redshifts. As discussed by Bothun and Dressier (1986), star formation induced by galaxy-galaxy or galaxy ICM interactions could be important at earlie: epochs and the present existence of some blue disk galaxies in the Coma cluster is consistent with a ram pressure induced process of star formation. While the picture of sweeping is attractive, one should keep in mind the numerous enigmas that have been long known and remain unexplained. NGC 1961 mapped at Westerbork by Shostak et al. (1982) seems to have suffered a gas removal event, yet it is not located in a particularly dense environment.

6. RECENT RESULTS FOR EARLY TYPE GALAXIES The much greater spread in the distribution of Hi surface densities among the early type galaxies remains a puzzle. While some E and SO galaxies are undetectable in the HI line at a sensitivity level corresponding to as little as 10 M Q , others contain a relatively large amount of neutral gas (Wardle and Knapp 1986). The case of the SO galaxies is particularly relevant since we have seen that the HI deficient galaxies could evolve into SO-like objects in X-ray clusters. In the context of identifying the high redshift blue cluster galaxies as the stripped progenitors of today's cluster SO's, Larson et al. (1980) have proposed that SO's in the cluster environment were stripped of their outer gas reservoirs at an early epoch so that star formation and continued disk growth were arrested early on. This process would continue to strip any disk object that passed through the core of a rich cluster. Under this scenario, SO galaxies in low density regions might still possess some gas, and thus a segregation into H I-normal and H I-poor objects would be expected. In other cases, most notably those of the polar ring or spindle SO's, authors have invoked an external origin for the gas, probably through the accretion of a low-mass gas-rich neighbor (van Driel 1987). The recent acquisition of gas is particularly appealing to explain not only the polar rings but also the annular distribution of HI seen exterior to the optical disk in some SO's. In an early study of the HI in SO galaxies in the Virgo cluster, Giovanardi et al. (1983b) applied the "IN versus OUT" technique to show that early type spirals - SO, SO/a and Sa's - outside the Virgo core were more likely to be detected in Hi than were similar objects within the core. This finding was more quantitatively confirmed by Chamaraux et al. (1986). Thus, it seems that the SO galaxies follow the trend noted by Dressier (1986) that early-type objects are even more Hi poor than later spirals. In an attempt to examine the cause of the greater gas depletion among early type spirals, Haynes et al. (1989) have examined the HI and far infrared emission in samples of relatively bright SO, Sa and Sc galaxies in the Local Supercluster. For the early

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type objects, new high sensitivity HI observations were conducted of previously undetected or unobserved objects using either the Arecibo 305m or the late N.R.A.O. 91m telescope whichever was appropriate. Coaddition of the Infrared Astronomical Satellite IRAS far infrared observations were made using the Infrared Processing and Data Analysis Center . This effort has concentrated on an examination of the occurrence of HI deficiency in terms of local environment. In order to test for possible differences in the HI content that are dependent on local parameters, Haynes et al. have calculated two measures of local environment using a complete redshift catalog of the Local Supercluster. The first parameter is a local "density" counted as the number of companions within a sphere of 1 Mpc centered on each sample object. The second attempts to measure the sum of tidal forces caused by objects within the same 1 Mpc sphere and incorporates both the projected separation and relative radial velocity. Within the Local Supercluster, the environments as characterized by these two parameters, vary by a factor of 200 according to this density measure. Segregation is only seen in the highest density bins (the center of the Virgo cluster) where few Sc's reside. The environmental influences have been tested by the comparison of the distribution functions of HI content for populations representing the high density and low density regions. Non-parametric statistical techniques that make use of non-detections have been employed, since despite the increased sensitivity of the new observations, many SO galaxies still remain undetected. Haynes et al. quantitatively confirm the results of previous authors that the SO galaxies in the highest density regions of the Local Supercluster, namely the Virgo core, are characterized by an average HI surface density a factor of four lower than those in the lowest density regions. At the same time, they find no significant difference in the far infrared properties of galaxies in high and low density regions. By extending the analysis to similar samples of Sa and Sc galaxies which represent subsets of the survey of Magri and Haynes (in preparation), they conclude that the depletion of HI in galaxies in high density regions is more severe among both SO's and Sa's than among Sc galaxies. A similar analysis was conducted using the tidal disruption parameter but, unlike in the density case, no statistically significant difference in the HI content was seen in high damage cases versus low damage ones. The distribution of the tidal parameter for a given value of the density parameter is quite large and we believe this result occurs because of the uncertainty of projected separations, radial velocities, orbits and angular momentum vectors and the higher velocity dispersion in clusters, for which the disruption parameter as defined will be reduced for collisions of the same projected impact parameter. Interestingly, the most gas-rich SO's can all be explained in terms of recent accretion events. It should be kept in mind that there is a wide range in the HI and FIR surface densities seen among the SO's. While some seem to possess interstellar properties typically associated with mid spirals (the "closet" Sb's), others are extremely gas and dust poor. While the mechanism for gas removal is yet unclear, it seems likely that the processes that affect spiral galaxies passing through the cores of rich clusters will also affect the SO's that reside there. With a reduction of the gas content and subsequent disk fading, spiral structure must fade. While it is is difficult to take a highly flattened Sc disk and turn it into a bulge-dominated SO (although see Farouki and Shapiro 1980), it may be possible to turn early spirals (Sa's) into SO's. 2

The National Radio Astronomy Observatory is operated by Associated Universities Inc. under contract from the National Science Foundation 3 The Infrared Processing and Analysis Center is operated by the California Institute of Technology for the National Aeronautics and Space Administration.

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7. SUMMARY AND CONCLUSIONS The basic results of the recent efforts concerning observations of gas deficiency in cluster spirals can be summarized as follows: 1) Spiral galaxies that pass within the central regions of rich clusters with moderate X-ray luminosities may lose as much as ninety percent of their interstellar HI gas. 2) The HI is preferentially removed from the outer portions of the disk so that the deficient galaxies have shrunken HI disks. The inner disks are only moderately HI deficient. The stripping mechanism displaces the affected galaxies along tracks of nearly constant MJJ j /DJJ j . 3) The molecular component of the ISM is relatively unaffected both in terms of its content and its distribution. Galaxies that are Hi-poor by a factor of ten may be gas poor by only a factor of two or three. 4) The presence of spiral structure and normal CO content argue for a recent timescale, but most highly HI deficient galaxies show reddened colors indicating that disk fading has already set it. The shift in colors can be explained by a reduction in the star formation rate by a factor of two about 10 years ago. 5) The star formation rate can also be enhanced by the stripping process. Individual objects may show signs of starburst or Seyfert activity over short time scales. Star formation without replenishment is a further cause of eventual gas depletion. 6) Galaxy-ICM interactions are the most likely cause of gas removal although the efficiency of competing mechanisms - ram pressure sweeping, evaporation or turbulent viscosity - is not yet well evaluated. Among clusters, the fraction of galaxies observed to be deficient is greatest where the X-ray luminosity is highest, but there is no evident dependence on p, pV or galaxy mass. 7) Early-type spirals are more HI poor relative to their counterparts in lower density regions than are late-type spirals. There are suggestions that this dichotomy may result from fundamental differences in the orbital characteristics of galaxies along the spiral sequence. 8) The stripping mechanism is effective only within the small volume occupied by the cluster core and is unlikely to be responsible for the morphological segregation seen on supercluster scales. After 15 years of effort, the cluster samples are significant but not terribly large, and statistical studies are still plagued by small numbers, especially when one is trying to investigate individual variables for which subsamples must be compared. It is also important to keep in mind that specific objects - whether single galaxies within a cluster or individual clusters - may not be representative of the universe at large. There are several additional points that best illustrate our uncertainties: 9) No single physical gas sweeping process can easily reproduce all of the observations. 10) In fact, all responsible processes (e.g., those under the broad category of galaxy-ICM interactions) might show the observed dependence of the degree of HI deficiency on distance from the cluster center. 11) Many galaxies remain unaltered over their lifetime, although morphological segregation is observed over supercluster scales. 12) The direct relationship between atomic hydrogen, molecular hydrogen and star formation is unclear. It is not clear how the removal of over ninety percent of a galaxy's atomic gas, the long term potential for future star formation, may effect the inner molecular component, and whether the general heating of the interstellar medium during the sweeping process may alter the mass spectrum of molecular

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clouds. In interpreting the CO data for Virgo objects, one must recognize the uncertainty in applying a universal conversion from CO to H2. 13) It appears that early-type galaxies are even more depleted that later-type spirals so that the evolution even within a class is dependent to some extent on the local environment. The future offers us a number of opportunities to follow the study of gas deficiency. The study of the HI content of cluster spirals and especially of early type objects will be greatly enhanced by the increases in sensitivity gained by the Arecibo gregorian feed upgrade and by the construction of the new Green Bank telescope. Aperture synthesis observations of both HI and CO in additional galaxies in Virgo, in Hydra and in other nearby clusters are vital to our understanding both of the sweeping mechanism and its effect on the conversion of gas to stars in galaxies. Further clues to the star formation process will be sought through careful studies of indicators such as Ha emission with the spatial dimension included. Possible environmental influences on the dark matter distribution are critical both to our understanding of galaxy formation and to application of the Tully-Fisher relation to obtain the distance scale. The Hubble Space Telescope will contribute enormously to our ability to study galaxies in clusters at higher redshifts when we know galaxies were not all like the objects we see in clusters today. Of particular relevance will be the continued study of the blue cluster objects seen at z > 0.3. Are they spirals falling into the core and suffering HI depletion both by induced star formation and sweeping? Based on the indirect evidence of the observed HI deficiency in cluster spirals, it now seems well established that selected spirals that pass through the cores of rich clusters lose significant portions of their cool interstellar gas. We are led to return to the longstanding debate over whether stripped spirals are responsible for the SO class. Based on the usual arguments about the occurrence of SO's in the field and the fundamental differences in the dominance of disk and bulge components (Dressier 1980), it does not seem likely that all SO's are stripped spirals. The loss of nearly all of the HI gas, despite the retention of the molecular component, must affect the galaxy's future evolutionary path. It still remains difficult to see how one could turn an Sc into an SO, but the possibility that the early type spirals may preferentially evolve towards the SO class because they follow radial orbits (Dressier 1986) is intriguing, de Freitas et al. (1985) have noted already the tendency for cluster SO's to have flatter axial ratios than field ones, implying a contribution to the SO population of stripped spirals. In comparing the morphology-density relation in clusters with high and low X-ray luminosity separately, GH85 have noted a decrease in the population of spirals and a corresponding increase in the population of SO's, for the same galaxy density, in the clusters with high X-ray luminosity. While we can recognize candidates for stripping and plausible galaxy-ICM interactions that could result in adequate gas removal, the same stripping mechanism(s) cannot be responsible for the SO's seen in less dense regions. Hence, we conclude that there are effective mechanisms for environmentally-driven galaxy evolution in operation in cluster cores containing a hot, healthy ICM, but the regimes of density within which such mechanisms could be of significance in enhancing the morphological segregation represent only a small fraction of the volume of the universe. I thank R. Giovanelli, T.L. Herter and M.S. Roberts for many discussions on the continuing questions about stripping. My talk was greatly aided by the contribution of unpublished data by L. Cayatte, C. Balkowski and J. van Gorkom and V. Rubin. This work has been supported in part by NASA-JPL contract no. 957289. The study

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of Sa and Sc galaxies has been conducted in collaboration with C. Magri as part of his dissertation research at Cornell University.

REFERENCES Bechtold, J., Forman, W., Giacconi, R., Jones, C , Schwarz, J., Tucker, W., and van Speybroek, L. 1983, Astron. J., 265, 26. Bosma, A. 1981, Astron. J., 86, 825. Bosma, A. 1985, Astr. Ap., 149, 482. Bothun, G.D. and Dressier, A. 1986, Ap. J., 301, 57. Bothun, G.D., Geller, M.J., Beers, T.C. and Huchra, J.P. 1983, Ap. J., 268, 47. Bottinelli, L. and Gouguenheim, L. 1974, Astr. Ap., 36, 461. Cayatte, V., van Gorkom, J.H., Balkowski, C. and Kotanyi, C. 1989, preprint. Chamaraux, P., Balkowski, C. and Gerard, E. 1980, Astr. Ap., 83, 38. Chamaraux, P., Balkowski, C. and Fontanelli, P. 1986, Astr. Ap., 165, 15. Chincarini, G.L., Giovanelli, R. and Haynes, M.P. 1983 Ap. J., 269, 13. Cottrell, G.A. 1978, M.N.R.A.S., 184, 259. Cowie, L.L. and Songaila, A., 1977, Nature, bf 266, 501 Davies, R.D. and Lewis, B.M. 1973, M.N.R.A.S., 165, 231. deFreitas, J.A., deSouza, R.E. and Arakaki, L.E. 1983, Astron. J., 88, 1435. Doyon, R. and Joseph, R.D. 1989, preprint. Dressier, A. 1980, Ap. J., 236, 351. Dressier, A. 1984, Ann. Rev. Astr. Ap., 22, 185. Dressier, A. 1986, Ap. J., 301, 55. Farouki, R. and Shapiro, S.L. 1980, Ap. J., 241, 928. Forman, W, Schwarz, J., Jones, C , Liller, W. and Fabian, A.C. 1979, Ap. J. (Letters), 234, L27. Gaetz, T., Salpeter, E.E. and Shaviv, G. 1987, Ap. J., 316, 530. Gallagher, J.S. and Hunter , D.A. 1986, Astron. J., 92, 557. Gavazzi, G. and Jaffe, W. 1986, Ap. J., 310, 53. Giovanardi, C , Helou, G., Krumm, N., and Salpeter, E.E. 1983a, Ap. J., 267, 35. Giovanardi, C , Krumm, N., and Salpeter, E.E. 1983b, Astron. J., 88, 1719. Giovanelli, R., Chincarini, G.L. and Haynes, M.P. 1981, Ap. J., 247, 383. Giovanelli, R. and Haynes, M.P. 1983, Astron. J., 88, 881. Giovanelli, R. and Haynes, M.P. 1985, Ap. J., 292, 404 (GH85). Giovanelli, R. and Haynes, M.P. 1988, in Galactic and Extragalactic Radio Astronomy, ed. by G.L. Verschuur and K.I. Kellermann, (New York: Springer-Verlag), pp. 522. Giraud, E. 1986, Astr. Ap., 167, 25. Guhathakurta, P. , van Gorkom, J., Kotanyi, C.G. and Balkowski, C. 1988, Astron. J., 96, 851. Guiderdoni, B. and Rocca-Volmerange, R. 1985, Astr. Ap., 151, 108. Gunn, J.E. and Gott, J.R. 1972, Ap. J., 176, 1. Haynes, M.P. and Giovanelli, R. 1983, Ap. J., 275, 472. Haynes, M.P. and Giovanelli, R. 1984, Astron. J., 89, 758. Haynes, M.P. and Giovanelli, R. 1986, Ap. J., 333, 136. Haynes, M.P., Giovanelli, R. and Chincarini, G.L. 1984, Ann. Rev. Astr. Ap., 22, 445.

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Haynes, M.P., Herter, T.L., Barton, A.S. and Benensohn, J.S. 1989, preprint. Helou, G., Giovanardi, C , Salpeter, E.E. and Krumm, N. 1981, Ap. J. Suppi, 46, 267. Hewitt, J.N., Haynes, M.P. and Giovanelli, R. 1983, Astron. J., 88, 272. Hoffman, G., Helou, G., Salpeter, E. and Sandage, A. 1985, Ap. J. (Letters), 289, L15. Hoffman, G.L., Helou, G. and Salpeter, E.E. 1988 Ap. J., 324, 75. Huchtmeier, W.K., Tammann, G.A. and Wendker, H.J. 1976, Astr. Ap., 46, 381. Karachentseva, V.E. 1973, Soobs. Spets. Astrofiz. Obs. 8, 1 (CIG). Kenney, J.D.P. and Young, J.S. 1986, Ap. J. (Letters), 301, L13. Kenney, J.D.P. and Young, J.S. 1989, preprint. Kenney, J.D.P., Young, J.S., Hasegawa, T. and Nakai, N. 1989, preprint. Kennicutt, R.B. 1983, Astron. J., 88, 483. Kennicutt, R.B. 1989, preprint. Kennicutt, R.B. and Kent, S.M. 1983, Astron. J., 88, 1094. Kritsuk, A.G. 1983, Astrofizika, 19, 263. Larson, R.B., Tinsley, B.M., and Caldwell, C.N. 1980, Ap. J., 237, 692. Lynds, R., and Toomre, A. 1976, Ap. J., 209, 382. Magri, C , Haynes, M.P., Forman, W. Jones, C. and Giovanelli, R. 1988, Ap. J., 333, 136. Mushotsky, R.F. 1984, Phys. Scripts, T7, 157. Nulsen, P.E.J. 1982, M.N.R.A.S., 198, 1007. Peterson, B.M., Strom, S.E. and Strom, K.M. 1979, Astron. J., 84, 735. Pryor, C. and Geller, M.J. 1984, Ap. J., 278, 457. Richter, O.G., and Huchtmeier, W.K., 1983, Astr. Ap., 125, 187 Sarazin, C. 1979, Astrophysics! Letters, 20, 93. Sarazin, C. 1986, in Rev. Mod. Phys., 58, 1. Schommer, R.A., Sullivan, W.T. and Bothun, G.D. 1981, Astron. J., 86, 943. Shostak, G.S., Hummel, E., Shaver, P.A., van der Hulst, J.M., van der Kruit, P.C. 1982, Astr. Ap., 115, 293. Spitzer, L., and Baade, W. 1951, Ap. J., 113, 413. Stark, A.A., Knapp, G.L., Bally, J., Wilson, R.W., Penzias, A.A., and Rowe, H.E. 1986, Ap. J., 310, 660. Stauffer, J. 1983, Ap. J., 264, 14. Sullivan, W.T., Bothun, G.D., Bates, B. and Schommer, R.A. 1981, Astron. J., 86, 919. Takeda, J., Nulsen, P.E.J., and Fabian, A.C. 1984, M.N.R.A.S., 208, 261. Thompson, L.A., Welker, J. and Gregory, S.A. 1979, Pub. Astron. Soc. Pacific, 90, 644. Toomre, A. and Toomre, J. 1972, Ap. J., 178, 623. Tully, R.B. and Shaya, E.J. 1984, Ap. J., 281, 31. van den Bergh, S. 1984, Astron. J., 89, 608. van Driel, W. 1987, Ph.D. thesis, Univ. Groningen. van Gorkom, J. and Kotanyi, C. 1985, in £ 5 0 Workshop on the Virgo Cluster, ed. by O.-G. Richter and B. Binggeli (Munchen: European Southern Observatory), p. 61. Wardle, M. and Knapp, G.R. 1986, Astron. J., 91, 23. Warmels, R.H. 1988a, Astr. Ap. Suppi, 72, 19. Warmels, R.H. 1988b, Astr. Ap. Suppi, 72, 57. Warmels, R.H. 1986, Ph.D. thesis, Univ. Groningen.

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DISCUSSION Whitmore: As you know, one of the criticisms early on as to why you couldn't have stripped spirals forming SO's was that the bulges from SO's tend to be larger. Now, is it the feeling that maybe if the Sa's tend to get stripped more easily, the numbers are going to work out right so that maybe that explains why we do get bigger bulge SO's? Haynes: I don't think we can be very quantitative yet. The only cluster where we can really study well the the SO's and Sa's is Virgo. And, the SO's and the Sa's look similarly deficient, but this is just based on the one cluster and many of the galaxies are still undetected in HI. Bothun: I have a comment that might help reconcile this business about the CO and H I, because I think a very consistent picture has formed now. If you compare the properties of most HI deficient galaxies in Virgo to the most HI deficient galaxies in Coma, where you have probably an order of magnitude more in the intracluster medium densities, and higher ram pressure, what you find in Coma are certainly some examples of very red galaxies which are very HI deficient, but there are about eight galaxies in the Abell radius that are very, very blue, and very HI deficient. Their optical spectra look for all the world like the spectra of blue galaxies of z = 0.5 clusters and the only difference between Virgo and Coma is that it's possible that the ram pressure is sufficient to squeeze the molecular clouds and cause a very large rate of star formation. Haynes: Well, this comes back to what Walter Jaffe brought up before. Gavazzi and Jaffe's work on Abell 1367 and on Coma actually showed blue galaxies that are HI deficient but have their radio continuum emission looking tail-like or ofFset from the optical image. These objects tend to lie right on the outside of the X-ray contours. We might expect that star formation might be induced by the compression of gas within the forward portion of the galaxy. It's also possible in some of the models that you get condensation of gas onto the front of the galaxy. You, of course, use up the HI that way also. We have to worry about enhancing the star formation for a short period of time, we don't exactly know what the IMF would be if we can change the fragmentation structure of the clouds. So, there are lots of questions that come up. Gunn: That's a question which comes up really quite strongly in Dressier and my observations of the very distant clusters and I think this is a fairly important dimensionless ratio (i.e., ram pressure/ISM pressure) that one should look at. I think it goes through one just about the place that you start seeing severe anemia. At the same time that you have ram pressure since the galaxies are just moving transonically into gas, you have to worry about the static pressure. The static pressure, or the ram pressure because they're the same order of magnitude, become significantly larger than typical interstellar medium pressures at about the same time that you start seeing these things. So, I think it would be very peculiar if one did not see funny differences perhaps in the stellar populations in these galaxies at about this force. Burns: Martha, what do you know about the HI deficiency in the poor groups? In particular, if you look at a sample of fairly compact poor groups, can you tell if their deficiency is a function more of local density or of the global cluster properties?

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Haynes: The best place to study larger scale than Abell clusters is probably PiscesPerseus since there have been lots of galaxies looked for there. The only places where you really see the strong deficiency that's statistically significant is in the richest of the Abell clusters with high X-ray luminosities. In some cases you'll see things such as we see in Hercules where there are a few HI deficient galaxies, but globally you can't really say anything that's at the same level that you see here. It's a threshhold effect, I think. Of course there are examples of strange HI distributions probably due to tides or collisions in some of the compact groups like Stephan's Quintet. Canizares: I just wanted to mention a related study of gas in ellipticals in Coma where we were able to set only an upper limit on the X-ray luminosity of individual ellipticals in Coma which were a factor of several below the mean for, say the ellipticals in the outer region in Virgo, indicating ellipticals are also deficient in their higher temperature gas. Tammann: I'm quite impressed by the segregation between the hydrogen deficient galaxies and the normal galaxies within classes. You see only the hydrogen deficient fellows in the very center, which means they have not moved out since they are hydrogen deficient, which means they have become very recently hydrogen deficient. Otherwise, the whole thing would be mixed. So, I get the impression that this momentary picture you see is a very recent thing. If we wait another billion years, the hydrogen deficient fellows will have moved out. You'll find them anywhere in the cluster, and equally hydrogen normal galaxies will have moved into the center and more and more spirals will become hydrogen deficient. So, I cannot help to see the only possibility to understand this present picture that all spirals had fallen into the clusters very recently and the ones which accidentally go through the center now are presently becoming hydrogen deficient. Haynes: One of the points that I tried to make is that this deficiency seems to be a recent event. The galaxies that are Hi poor are right now in the core, and you don't see deficiency once you get outside. But there are a couple of possibilities. One is that they've fallen in for the first time. Another one is that the disks fade and they no longer look like spirals or they no longer look like Sc's anyway. A third idea is that they build back their interstellar media over the course of time. I don't think we know which of those is the best possibility. Ferguson: Doesn't the fact that most of your trails in Virgo point outwards indicate that they can't come back out again and look like spirals again? Haynes: But if they spend most of their lifetimes on the outer parts, they could build back up their interstellar media and we wouldn't recognize them as ever having been stripped. Ferguson: Is there any estimate for the time scale that it takes to replenish the interstellar media? Balbus: It may be rapid if they preserve their CO disks ... the clouds go through spiral arms and are rapidly converted to HI. Ferguson:

Okay, but then I would argue we'd see things with H I trails pointing

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towards the center of Virgo, if they could reform a gas disk . . . Felten: The tails of comets always pointed outward. (Laughter) Djorgovski: Disney had a paper where he claimed there was a correlation between central disk surface brightness and HI deficiency in Virgo and then he went on to argue with colors and whatnot, it has to be an old effect. Do you have any comments? Haynes: The only comment I can say is that all the other evidence, the CO in particular, I think, argues that it has to be a recent effect. Otherwise, the star formation rate has only gone down by a small factor. That may be because at some point you may also get an enhanced star formation rate, but this phase would last only for a short time. But the fact that you only see these galaxies deficient right in the very center, I think, argues that those galaxies are right there right now and because they still look like Sc's, the stripping must be recent. Van Gorkom: Okay, I have two comments. One is related to Jim Gunn's remark. We have three observations in the Virgo Cluster and one in Hydra, where the HI is on one side very, very sharp edged and you see there signs of enhanced star formation while on the other side it's much more round, so I really think that ram pressure sweeping is causing that, and also enhancing star formation. Secondly, that it isn't fair to say that the galaxies that have been stripped or that have HI deficiency are being replinished. The reason, I think it is clear, is that you can't possibly get these sharp edges. Haynes: medium.

I am not sure it is ram pressure but it is associated with the intracluster

Van Gorkom: Well, but that could be a consequence too, right? You fill up the intracluster medium with swept gas? Haynes: Okay but you're also seeing systematic eating from the outside and you do get the sharp edges. What I'm just saying is there are two things that ram pressure predicts. One is that the lower luminosity, lower mass object should be more stripped and the other one is that you should see a correlation with the relative velocity, and we see neither of those, and that bothers me. We have one paper, Riccardo [Giovanelli] and I, in which we published the correlation with relative velocity and then it went away when we got more data. Schommer: Two comments. One way to characterize it is the question of what the mechanism is, that's a little bit up in the air, where it's occuring and I think we have strong evidence of where its occuring and when its happening and some of these comments I think really do lead to the conclusion that in some cases in the course of these clusters, it is happening today. There's a paper by Kennicutt, Bothun & Schommer a few years ago that looked at the Ha fluxes and equivalent widths of those blue Hi deficient galaxies in the core of Coma and said that the gas depletion time scales were very short, less than 10 years, which certainly seem to be arguing that it was happening now. The second comment was that if you really want to identify this sweeping and stripping mechanism with the morphology-density relation, I think you have a little bit of a problem from the Postman and Geller results on the loose groups or the poor groups and the things that don't seem to show intracluster media.

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Haynes: That's the point that I'm trying to make; that this mechanism—these mechanisms, if it is ram pressure or whatever, only occur in a very small volume and there's no way to get the morphology density relation extending outside of those volumes. So, maybe there's a further enhancement of the morphology-density relation in the centers of clusters due to this kind of a mechanism but it's not going to solve the problem globally. Gunn: Martha, from the point of the low luminosity Sc's and irregulars, it seems to me that one possibility, and you've doubtless thought about this, is that for normal systems of that type, most of the light we see comes from a very young stellar population which is extinguished almost immediately when they're stripped. Whereas, for bigger galaxies, a much larger proportion comes from the old stellar population, it is entirely possible that those galaxies simply disappear when they're stripped. Haynes: Well, we see some that are stripped now. It could be that that happens, that they all disappear but we see some that are being stripped, that are HI deficient by a large factor and that haven't changed yet, so, it's a balancing of time scales. Gunn: But if you have a population which say disappears once it gets into the central parts of the cluster and you see a few in transition, then the proportion of those which get stripped to the projected ones is very large, and so, of the ones you see, you would see very little stripping because they're all simply projected on the cluster center. Haynes: Then you would expect that proportionately we might see them to be characteristically less stripped then the others. Gunn: Yes, and that's what you find . . . Haynes: It's marginally less. It's certainly not more than you would expect. If anything, it's a little bit less but I wouldn't say that it's a lot less. Sandage: To your point, I'll show this afternoon the distribution of Im's as a function of position in the cluster and in the region near M87 but not right on M87, there are no Im's, so that's exactly your point. So, we find no galaxies and therefore, if you're looking for galaxies that are stripped, they're just not there. That region is about one degree in diameter and there are simply no Im's in that region. Haynes: In the Virgo cluster, there are no galaxies that have been studied within about 3/4 of a megaparsec to M87 because there aren't any galaxies there. Sandage: Because there are no galaxies there. W h i t m o r e : On this point from Bob Schommer about the morphology-density relation and the idea that sweeping is causing that, I don't really see that that's a problem. In the outer parts, at least Geller and Postman think, in the outer parts there are really low density groups, there's really no trend to the local morphology density relationship. It only starts in a little bit farther, and there we'd argue that it's this kind of confusion that what looks like a local density is going up, in many cases it's just that that's the center of a low density group, and so, it's not as simple. Once you actually do it versus ^cluster) v o u fi11^ that * n e trends are very weak until you get right into the center of

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the clusters and then it just falls right off the table, and so I think that's more or less what we would expect from the sweeping. Huchra: In your 1985 paper you did a Monte Carlo simulation with the dependence going like pv and by including contamination and such, you were able to wash out the effect. Do you not have confidence in the results ? Haynes: Yes, I'm basically saying that it really doesn't surprise me that we don't see stronger correlations because any correlation that you can think of will go away or at least be greatly washed out by projection effects. That's why if you want to show me a particular galaxy in a particular cluster and try to correlate it properties with some kind of substructure, I'd be very hesitant to do it because you have to look for large scale statistical effects. Name Unknown: Do you have an explanation for why the dwarfs seem to still have their gas? Haynes: The mechanism could not be ram pressure. It could be that the dwarfs have a stronger restoring force than we think they do, particularly, in the outer portions. It could be that they're not really in the center of the cluster or have circular orbits. Sandage: But couldn't it be your threshold effect, that after you get outside this one degree of radius? Haynes: The spirals do show HI deficiency outside that one degree portion. It goes out to about three to four degrees in Virgo. Richter: I'd like to point out that the restoring force might not be enough to hold any of the H I. They're so quickly transformed into something else, we may no longer classify them as Im's and therefore, the ones that you do see as Im's, simply haven't gone through the process yet, or never will. Name Unknown: Well, the Im's don't show any degree of concentration toward the center of the cluster. The ones that you see as being three or four degrees from the center, maybe they will be forground and really be several megaparsecs away from the center. Richter: Also, their velocity dispersions would be much higher than that of the rest of the cluster, which indicates they're preferentially foreground. Haynes: There's another point that I didn't really get into that I think is important, and that is that in trying to understand the CO, we're assuming that the conversion from CO to H2, of course, is the same in the Milky Way as it is in these Virgo cluster galaxies, and we don't really know that that's true. We also really don't know about how you actually form stars from giant molecular clouds, and so, in trying to understand the CO observations, we could sort of brush it over and say just about anything we want. Chantal, did you have a comment? Balkowski: Yes, we have two dwarf galaxies in our sample and one is about one degree from M87. It is apparently not stripped at all and its velocity is about 100

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km/s. So, it could be right in the cluster. It has the same velocity as the other one. Haynes: You just have no idea. That's why in any one galaxy, you can argue in more than one way.

PROPERTIES OF GALAXIES IN GROUPS AND CLUSTERS

Allan Sandage The Observatories of the Carnegie Institution of Washington 813 Santa Barbara St. Pasadena, CA 91101

Abstract. Data on kinematics, spatial distributions, and galaxy morphology in different density regimes within individual galaxy clusters show that many clusters are not in a stationary state but are still in the process of forming.

1. INTRODUCTION Paradigms for galaxy clusters are changing. As in all tearing away from secure positions (Kuhn 1970) the process is controversial, yet continuing. Most papers in this volume suggest directions that will probably lead to even stronger new ideas about cluster cosmogony. We are concerned in this review with physical properties that have relevance for the question of whether clusters of galaxies are generally stationary, changing only slowly in a crossing time or if they are dynamically young. We examine if parts of a cluster may still be forming, falling onto an old dense core that would have been the first part of a density fluctuation to collapse even if all galaxies in a cluster are the same age, having formed before the cluster. During the 1930's the stationary nature of clusters seemed beyond doubt. A suggestion that they are dynamically young would have been too radical even for Zwicky who was the model of prophetic radicals. Rather, Zwicky (1937) took the stationary state to be given in making his calculation of a total mass, following an earlier calculation by Sinclair Smith (1936). The justification was that rich clusters such as Coma (1257 +2812; or Abell A1656), Cor Bor (1520 +2754; A2065), Bootis (1431 +3146; A1930), and Ursa Major No.2 (1055 +5702; A1132), known already to Hubble (1936) and to Humason (1936), appear so regular. The projected density distributions of clusters imitate that of an Emden truncated isothermal sphere (Hubble 1930), leading Zwicky (1937, 1957 p. 138 ff) to the large mass found by Smith for Virgo and even earlier to the clear statement that the total mass of the Coma cluster is 400 times its visible mass (Zwicky 1933). However, signs that clusters may not be stationary were already known 30 years ago. Zwicky (1957, his pp. 78-79) was aware of the different areal distributions of ellipticals and spirals in the Virgo cluster. Later, the increased velocity dispersion of spirals relative to ellipticals was demonstrated (de Vaucouleurs 1961, Sandage and Tammann 1976), violating the known decrease in velocity dispersion with radius for

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stationary structures if spirals and E galaxies were well mixed. It is also known that the mean velocity dispersion varies by more than a factor of 3 between the north and south parts of Virgo (Figure 26 of Binggeli, Tammann, and Sandage 1987, hereafter BTS 87). The most telling new datum is Dressier's (1980) demonstration that the morphological-density (hereafter M-D) relation (Hubble and Humason 1931) is satisfied in detail in regions of any given cluster, showing that kinematical mixing of cluster members cannot have occurred in a cluster's lifetime. Otherwise the different Hubble galaxy types would be well mixed in only several cluster crossings. The conclusion of little mixing is firm provided that there are no transformations of one galaxy type into another by mergers for example, or by sweeping in the harsh cluster environment. Because Dressier's M-D relation is so central to ideas of cluster cosmogony, its explanation is required if cluster formation and evolution are to be understood. We set out evidence concerning these problems in this review. New data obtained in recent surveys of the Virgo cluster (Binggeli, Sandage, and Tammann 1985, hereafter BST 85), the Fornax cluster (Ferguson and Sandage 1988, hereafter FS 88; Ferguson 1989), and of several other groups and in the general field are described in sections 2, 3, and 4 from which we determine how luminosity functions vary with richness. Correlations of diameters and surface brightness with absolute magnitudes are shown in Section 5 for E galaxies in the Virgo, Fornax, and Coma clusters and in the nearby general field. The significance of the new data are discussed in the final Sections for the problems of (a) the dynamical youth of clusters, (b) the origin of the morphologydensity relation, and (c) possible transformations of one galaxy morphological type into another in cluster centers.

2. THE VIRGO CLUSTER SURVEY 2.1 Areal and Kinematic Distribution on the sky Figure 1 shows the distribution of the 2096 galaxies contained in the Virgo Cluster Catalog (VVC) in BST 85. Figure 2 shows the subset of the catalog entries which we considered to be cluster members on the basis of galaxy morphology (cf. Sandage and Binggeli 1984 for a justification). The important feature of this distribution is its evident double structure, denoted as subcluster A and subcluster B. Known already by de Vaucouleurs (1961) and discussed in detail by BTS 87, subcluster A near M87 is E rich and spiral poor relative to subcluster B. There also is a kinematic difference in the mean velocities and their dispersions. Subcluster A has (v) = 1061 ± 83 km s with a dispersion of a = 760 km s" 1 . Subcluster B has (v) = 963 ± 81 km s" 1 with a significantly smaller dispersion of 390 km s" 1 (Table 4 and Figure 23 of BTS 87). Of most significance, the dE and Im dwarfs show different distributions over the face of the cluster. Dwarf ellipticals are peaked at subcluster A, defining its geometrical center. Im types avoid the center of subcluster A, being absent within a radius of 0.7° of it (BTS 87, Figure lOd). There is a similar central hole in the distribution of Im galaxies in Fornax (Ferguson 1989) where the dE dwarfs have their peak concentration. Two principal conclusions from the surveys are (1) in both Virgo and Fornax the Im's are absent where the dE's concentrate, and (2) the morphological mix differs fundamentally between Virgo subclusters A and B: E, SO, and dE dwarfs dominate subcluster A, while spirals are frequent in subcluster B (compare Figures 7 to 10 of BTS 87 where the difference in the morphological mix is striking).

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(3) A third conclusion related to (2) concerns the difference in the distribution of spirals and E, SO, and dE galaxies over the 40 square degree Virgo area that was surveyed. Spirals and Im dwarfs are more widely spread than the early type members (BTS 87, Figures 9 and 10 compared with Figures 7 and 8 of the same reference). The result, already known by Zwicky (1957, pp. 78-79) from the brightest galaxies, is striking in the data from the complete catalog. Figure 3 summarizes this fact, shown by fitting assumed exponential decays to the projected density distribution of the early and late type Virgo members separately. The lengths are 1.7 degrees (0.66 Mpc) for the combined E + SO + dE sample, and 3.3 degrees (1.26 Mpc) for the S + Im sample. The difference is highly significant statistically. These linear scale lengths assume the Virgo distance to be 21.9 Mpc (i.e., m — M = 31.7). The three conclusions can be summarized as "late type galaxies are more dispersed than early type galaxies: subcluster A is dominated by early types, subcluster B by late types."

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Five additional conclusions reached by BTS 87 are (4) M87 is not at the center of the swarm of dE members that define the center of subcluster A but lies 40 arc minutes southeast of that center (Figure 8 of BTS 87), (5) the velocity of M87 is 197 km s" 1 higher than the mean velocity of subcluster A ,(6) there is no significant difference in the mean velocities of the spirals and the early type galaxies averaged over the 6 degree (radius) field (BTS 87, Table IV), putting to rest an earlier futile debate, (7) the velocity dispersion of early type (E, SO, dE, and dSO) galaxies is significantly smaller (573 km s~*) than for the spiral plus Im types (888 km s" 1 ) (details are in Table IV of BTS 87), (8) the mean "local" velocities of various sub regions over the face of the cluster differ widely (BTS 87, Figure 24), as do the "local" velocity dispersions mentioned earlier (BTS 87, Figure 26). The last four points show that the velocity structure of the Virgo "cluster" is highly complex (c/. also Huchra 1985), differing from that of a regular "isothermal gravitating sphere." Tully and Shaya (1984), and Tammann and Binggeli (1988) argue that most of these eight points would be untrue for a stationary aggregate that is in virial equilibrium. Tammann and Binggeli show that many of these features are also present in other well studied clusters. Sodre et al. (1989), using kinematic data by Dressier and Shectman (1988), showed that spirals and Im galaxies invariably have a significa'ntly higher velocity dispersion than E and SO types in a 15 cluster sample studied by them, adding weight to a similar earlier conclusion by Moss and Dickens (1977). Temporarily leaving this topic of spatial and kinematic distributions, we discuss in the next section a new determination of the luminosity function of Virgo cluster members as a preliminary to comments on the problem of biased galaxy formation in Sections 3 and 4, and the possible transformation of one type of dwarf galaxy into another in Section 6.

2.2 The Virgo Cluster Luminosity Function Hubble (1936) wrote (and undoubtedly believed) that the luminosity function of galaxies was approximately Gaussian with a small dispersion of ~ 0.8 mag. Zwicky (1942, 1957, 1964) wrote (and undoubtedly hoped) that the function was exponentially increasing toward the faint end, merging smoothly from clusters of galaxies into galaxies, thence to stars, to pebbles, to grains, and then to atoms, nuclei, etc. Both Hubble and Zwicky were right and both were wrong; each had used the same words with different meanings. Hubble's function referred to regular spirals and brightest ellipticals, all contained as the subset of a list that eventually became the ShapleyAmes catalog. We now know that the luminosity function for spiral and E galaxies is bounded bright and faint because (1) there are no dwarf spirals, and (2) dwarf ellipticals are of a different morphological type than E galaxies. Hence, if the luminosity function is defined by a magnitude limited sample whose limit is bright, as Hubble's sample was, an upper and lower bound luminosity function is inevitable. This is due to the selection effect that causes such a sample to be giant dominated. On the other hand, having begun to discover faint Sm and Im dwarfs (e.g., Leo A, Pegasus, Sextans A, Sextans B) - a class that was hardly known before - Zwicky made a leap of generalization which proved to be correct when the faint systems were added to the morphological mix in a volume limited sample. The shape of the luminosity function depends on the details of the mix of morphological types that are included. It is clear that differences are expected in luminosity functions of aggregates in differ-

Properties of Galaxies in Groups and Clusters

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ent environments because of Dressler's morphology-density relation. This new way of looking at the luminosity function was first suggested by Tammann and Kraan (1978), discussed by Binggeli (1987), reviewed in its consequences by Binggeli, Sandage, and Tammann (1988, hereafter BST 88), and is emphasized in the remainder of this section. log N(Am) +1

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The Abell and/or Schechter function takes no cognizance of morphological types, hence suppressing information about the change of type as the absolute magnitude varies. The fascinating discussion by Binggeli (1987) emphasizes the consequences of hiding this information in any determination of the function that is not type-specific. Figure 5 (taken from Binggeli (1987)) shows how the important type-specific details are buried under foot if only the "universal" function has been measured. Type-specific luminosity functions were found (Sandage, Binggeli, and Tammann 1985, hereafter SBT 85) from the Virgo cluster catalog (BST 85) for each of the major Hubble types. The "general" function shown in Figure 6 was obtained from the sum over the total cluster membership in the Virgo cluster catalog. The type-specific individual functions in Virgo that make up Figure 6 are shown in Figure 7, taken from Binggeli's (1987) summary. The morphological mix in the Virgo cluster is in Figure 8. It is obvious from the variation of the Hubble type with magnitude in Figure 8 why Hubble's and Zwicky's conception of the shape of the luminosity function were so different. The conclusions depend on the mix of galaxy types in the particular sample being discussed. Furthermore, because the percentage of the various types differ between high and low density regions due to the morphological-density relation, it is clear that the shape of the total luminosity function must also differ between such regions. Hence, there cannot be such a thing as the universal luminosity function."

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Properties of Galaxies in Groups and Clusters

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galaxy formation, is treated in Section 4 where conclusions from new field surveys by Eder et al. (1989), by Schombert and Bothun (1988), and by Binggeli, Tarenghi, and Sandage (1990) are discussed.

3. SURVEY OF THE FORNAX CLUSTER AND LOOSE GROUPS To test further if the faint-end slope of the luminosity function depends on environmental richness, we began surveys in 1980 of the Fornax cluster and of low density groups. In the strong version of the biased galaxy formation model the dwarf to giant ratio should be a function of density (Kaiser 1986, Bardeen 1986, Dekel and Silk 1986). The prediction from the model is that the dwarf/giant ratio should be larger in low density regions than in clusters, opposite to the result in Figure 10 which shows the faint-end slope to be steeper in the cluster than in the field. In this and in the following section we generalize the result by adding data for sparse clusters and loose groups and for the "general field" from several new surveys. Ferguson (1989) has analyzed the du Pont plate material for the Fornax cluster and has combined it with similar data for the loose groups of Leo, Dorado, NGC 1400, NGC 5044, and Antlia. He has constructed maps of the surface distributions of the various types of galaxies in each of these aggregates, and has made catalogs of the groups similar to the Virgo cluster catalog. The Fornax cluster catalog (Ferguson 1989) and the luminosity function (Ferguson and Sandage 1988) based on it have been published. Our principal conclusion is that the luminosity functions of Fornax and Virgo are indistinguishable. A large population of dE early type dwarfs is present in Fornax, as was known to Hodge (1959, 1960), Reaves (1964), and to Hodge, Pyper, and Webb (1965) who began a catalog. Our result that the dwarf to giant ratio in Fornax is statistically the same as in Virgo is contrary to the conclusion of Caldwell (1987) who wrote that a significant difference exists between the clusters, Fornax having fewer dwarfs per giant. However, Ferguson (1989) shows that Caldwell's catalog is incomplete in its faint dwarf listings due to the nature of his plate material found by comparing his data with those obtained with the large scale du Pont reflector plates. However, the situation is different in the looser groups where a significant difference does exist in the faint-end slopes compared with Virgo -f- Fornax + Antlia, in agreement with the result in Figure 10. The dwarf to giant ratio is larger in rich regions than in sparse environments as shown in Figure 11. Here, the type - specific luminosity function of giant E + SO galaxies is added to that for the dwarf dE + dSO types for the Virgo cluster alone, and the sum is compared with similar data for poorer groups (Leo + Dorado + NGC 1400 + NGC 5044). The heavy solid line for the Virgo cluster has a steeper faint - end slope than the heavy dashed line for the poor groups, both being normalized to the same total number of E and SO galaxies. The sense of the difference in Figure 11 is that the number of dwarfs per giant is smaller in the poor groups, which, as in Figure 10, is again opposite to the predicted effect for biased galaxy formation.

4. FIELD SURVEY FOR THE RATIO OF DWARFS TO GIANTS We next generalized the problem by a new study of the general field. Many recent searches have been made for dwarfs in voids but mostly for Im types using either radio or objective prism techniques. In our survey (Binggeli, Tarenghi, and Sandage 1990, hereafter BTS 90) we were searching for dE type dwarfs as well as Im's by inspecting

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Properties of Galaxies in Groups and Clusters

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results (BTS 1990), and those of Schombert and Bothun (1988), and of Eder et al. (1989) show, contrary to the "biased formation" model that (1) dwarfs have the same general spatial distribution as the giants, and (2) the dwarf to giant ratio decreases rather than increases in low richness regions compared to clusters.

5. VARIATION OF EFFECTIVE SIZE AND SURFACE BRIGHTNESS WITH ABSOLUTE MAGNITUDE FOR E AND dE GALAXIES Before discussing possible transformations of one Hubble type into another for any reason in a harsh cluster environment, we need data on the surface brightness (hereafter SB) properties of galaxies of different Hubble types and absolute magnitudes. It is well known that the average surface brightness of galaxies decreases along the Hubble sequence from E galaxies through SO's to Sm and Im types (Sandage 1983). Furthermore, within a given Hubble type the average SB varies with absolute magnitude. Within the E and dE types alone the trend with absolute magnitude is most easily revealed in samples taken within particular clusters where all galaxies are at the same distance and where the sampling can be complete. In the Virgo cluster, Binggeli, Sandage, and Tarenghi (1984, hereafter BST 84, their Figure 8) found that the surface brightness of giant E galaxies is faintest for the brightest galaxies, confirming previous results by Kormendy, Oemler, and others. The brightest SB occurs near absolute magnitude Mg = —20, decreasing monotonically for the dE types from Mg = —19 to the limit of the survey at about Mg = —12, and, as mentioned, decreasing also for E galaxies brighter than —20 i.e., there is a maximum SB at the intermediate absolute magnitude of MQ = —20 (see Figure 14). In a more recent review Sandage and Perelmuter (1990, hereafter SP 90) used five independent data sets for E galaxies to obtain the following results. (1) Combining data from the literature for galaxies in the Virgo, Fornax, and Coma clusters with data from field E galaxies from the Revised Shapley-Ames catalog and Sadler's (1984) sample gave the correlation in Figure 13 for E and dE galaxies. Plotted is the half light radius in parsecs (based on m—M = 31.7 for Virgo, 31.9 for Fornax, 35.5 for Coma, and Ho = 50 for the field galaxies) as ordinate vs. absolute blue magnitude. The constant surface brightness m ~ blogr scaling law of Hubble (1926) is shown as the straight line. It fails to describe the correlation except over the narrow luminosity range from Mg = —18 to —21. Galaxies both brighter and fainter than Mg = —20 have lower surface brightness than those at —20. (2) Figure 14 is the equivalent diagram showing the variation of surface brightness. The many dE dwarfs discussed by Ferguson (1989) in Fornax are added as closed circles. The trends in this diagram are the same as found by BST 84 (their Figure 8) from a different data sample using different photometry. Disney and collaborators (cf. Ferguson 1989 for a review) claim that the correlations in Figures 13 and 14 do not exist but are a result of a selection effect. They state (cf. Davies et al. 1988) that our surveys have been biased so that our catalogs have missed low surface brightness cluster members, which, according to them, exist between Mg/ T \ = —20 and —18 in their survey of the Fornax region. Such galaxies would fill in the SB distribution of Figure 14 to form a scatter diagram showing no correlation of SB with absolute magnitude. Ferguson and Sandage (1988, hereafter FS 88) answered by showing that the Fornax sample used by Davies et al. contains a large number of galaxies which FS had assigned to the background by inspection of the large scale Las Campanas du Pont plates. The

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6. ARE THERE TRANSFIGURATIONS ALONG THE HUBBLE SEQUENCE? Speculation exists that galaxies can change their Hubble types in the harsh environment of clusters. The most persistent of such notions is that SO's are stripped spirals. However, the variation of surface brightness along the Hubble sequence belie all simple stripping arguments; SO galaxies have as high a mean SB as do the brightest E galaxies, and this level of surface brightness is much higher than any present-day spiral disk, showing clearly that SO's are generic to the Hubble sequence, not formed either by mergers or by the stripping of later type spirals (Sandage 1983). However, various types of data do suggest that some types of dwarf galaxies may have been transformed from other types. Clear evidence is the following:

Properties of Galaxies in Groups and Clusters

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(1) No Im dwarfs exist within 2° (radius) of M87, near the center of the dE swarm that defines the center of Virgo subcluster A. Figure 15 shows the hole in the Im distribution (panel d). The Virgo cluster environment is harshest in this region because of the strong X - ray flux from M87. The absence of the fragile Im types in this region suggests sweeping. (2) Im dwarfs also avoid the center of the Fornax cluster. Ferguson's morphological maps show that the region near NGC 1399 is devoid of Im and late type spirals over an area of 2° in diameter. As in Virgo, this region has the highest concentration of dE types which themselves define the center of the Fornax cluster. NGC 1399 is an X-ray source. The statistical significance of the holes in the Im distribution in both Virgo and Fornax is questioned by Ferguson, but there can be no doubt that the ratio of dE to Im types in each cluster is a strong function of position. The ratio peaks at each cluster's center. The variation of this ratio with position is striking and beypnd doubt. It can be seen by comparing Figures 15a, c, and d with Figure 16a and b, taken from Figures 9 and 10 of BTS 87. (3) Figures 16a and b show the significant difference in the distribution of Virgo cluster dE galaxies depending whether they have nuclei (dE,N type) or not. Based on these data BTS 87 concluded that "non-nucleated dwarfs are more dispersed than nucleated ones." The same effect has been found in Fornax. By fitting density profiles to the projected number distributions in Virgo and in Fornax we could show (Ferguson and Sandage 1989, hereafter FS 89) that the bright dE,N galaxies have an exponential scale length in their distribution like that of E, SO giants and faint dE's. In contrast, the bright dE's with no nuclei have the same distribution as the spirals and the Im types. The result is definite in both clusters, suggesting that the subset of bright dE (no N) dwarfs has had a different formation history than the dE,N dwarfs with nuclei and that they may therefore be related to Im's. However, belying this it has been clear for some time that present day dE (no N) galaxies cannot simply be stripped Im's because the SBs of the dE's are higher than would be the end product of such a stripping of present day Im types (Hunter and Gallagher 1985, Binggeli 1986, Bothun et al. 1986). Because of this strong counter argument no definite conclusion is possible at the moment. (4) The two most potent arguments that dE's are not stripped Im's (Sandage, Binggeli, and Tammann 1985) were always: (a) Im's do not have sharp nuclei like the very bright (reaching as bright as absolute magnitude Mg = —13) unresolved nuclei of dE,N's, and (b) the flattening distribution of dE's as a whole is different from Im's. But with the distinction now made between dE's and dE,N's in point (3) above, these arguments have lost their strength. FS 89 show that the flattening distribution differs between dE and dE,N, and that the bright dE (no N) have the same flattening distribution as the Im's! It would seem that an obvious evolutionary conclusion concerning stripping might follow from these data. A summary of environmental processes in clusters is given by Gallagher and Hunter (1989) where various transformation possibilities are discussed.

7. GALAXY CLUSTERS ARE STILL YOUNG A common feature in most galaxy clusters is subclustering (many papers in this volume). This fact together with the morphological and kinematical differences between

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Figure 16. Distribution of dE types (with and without bright unresolved nuclei) in Virgo. Contrast with Figure 15 for the late type dwarfs and note the difference in the concentrations toward the center of cluster A of dE,N and dE (no N) in panels (a) and (b). Diagram is from Figure 9 of BTS 87.

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parts of clusters (such as in Virgo as in section 2.1) makes it clear that many clusters are not in a stationary state. The strongest evidence comes from the morphological-density relation (Dressier 1980) for the reasons discussed in the first section. The ideas by Tully and Shaya (1984), Shaya and Tully (1984), and by Tammann and Binggeli (1987) for an explanation appear highly satisfactory. We suppose that E and SO galaxies form in the densest perturbations of the initial fluctuation spectrum (Sandage, Freedman, and Stokes 1970). Hence, in the shells of the small Friedmann universes that have the highest over-critical density, and therefore are the first to begin collapse (after the initial expansion as part of the general expanding manifold of the large scale universe), E galaxies predominate. Because these densest shells collapse first, they will form the oldest core of the developing cluster composed at first entirely of E and SO galaxies. Less dense parts of the fluctuation expand further before turn around and take longer to collapse onto the already formed core. Galaxies formed in these intermediate density shells are not mainly E and SO types but are spirals of Hubble class Sa and early Sb. Such galaxies will, then, arrive onto the core after the E types but before the late type Sc, Sd, Sm, and Im types that form in the smallest density regions of the perturbation that will arrive to the core even later. Tully and Shaya's picture is, then, that late type spirals in the Virgo region are only now arriving near the cluster proper, having been in the outer shells of the hierarchy of Friedmann low density shells. Nevertheless, these shells have densities that are still above the critical value so that collapse toward the core will occur eventually. Because of their low Q (effective) values, which, however are still slightly greater than 1, these outer shells take, of course, a very long time to turnaround. In this picture, the Virgo cluster is still in the process of buildup; successive layers still being placed upon the old E and SO rich core, and each layer with a different morphological mix from those that have gone before. Said differently, the morphological mix of a cluster depends on time. The newly arriving shells are composed of successively later Hubble galaxy types because the type of galaxy that is made from the density fluctuations depends on the density out of which it is formed (Sandage, Freeman, and Stokes 1970). This model, explains naturally the Dressier M-D details. It requires the clusters that show the morphology-density relation to still be in the process of formation. At earlier times the percentage of E to spiral members near the core should be larger than at later times (at the earliest times all galaxies in the cluster proper were E and SO types), because the outer shells of mainly spirals had not yet arrived. Hence the form of the M-D relation should be time dependent. This prediction provides a test. The amplitude of the morphological- density relation should depend on redshift. Clusters at large redshift should be spiral-deficient compared with nearby clusters. The paradigm change concerning cluster youth therefore seems necessary. The many new data now available on cluster properties set out in previous sections can apparently be understood only if clusters are not stationary, but are still in the process of forming. Much of this review has centered about data obtained in the Las Campanas surveys of the Virgo and Fornax clusters and selected loose groups. The Virgo survey was made in a team effort by Binggeli, Tammann, Tarenghi, and the author. The Fornax cluster plus loose groups survey was completed by Ferguson as part of his PhD thesis research. The field survey was a joint effort with Binggeli and Tarenghi, as was the work with graduate student J.-M. Perelmuter of Johns Hopkins on the surface brightness problems. I am grateful to these astronomers for the enjoyable times we have had in

Properties of Galaxies in Groups and Clusters

22S

these collaborations. It is a special pleasure to acknowledge the conversations with Gustav Tammann on the problem of the youth of clusters and on his model discussed in the text for the explanation of the Dressier morphological-density relation that is time dependent. His insight was crucial to the completion of this review. It is also a pleasure to thank the staffs at Space Telescope Science Institute and at the Physics and Astronomy Department of The Johns Hopkins University for their hospitality during the organization of this review in March and April 1989.

REFERENCES Abell, G.O. 1962, in Problems of Extragalactic research, ed. G.C. McVittie (New York: Macmillan), p 232. Abell, G.O. 1975, in Galaxies and the Universe (Stars and Stellar Systems, Vol. 9), ed. A. Sandage, M. Sandage, and J. Kristian, (Chicago: Univ. Chicago Press), p 601. Baade, W. 1944, Ap. J., 100, 147. Baade, W. 1950, Pub. Michigan Obs., 10, 7. Bardeen, J. M. 1986, in Inner Space/Outer Space, ed. E.W Kolb et al. (Chicago: Univ. Chicago Press), p 212. Binggeli, B. 1986, in Star - Forming Dwarf Galaxies and Related Objects, ed. D. Kunth, T.X. Thuan, and J. Tran Thanh Van, (Editions Frontieres, Tvette), p 53. Binggeli, B. 1987, in Nearly Normal Galaxies, ed. S. Faber, (New York: Springer Verlag), p 195. Binggeli, B., Sandage, A., and Tammann, G.A. 1985, A. J., 90, 1681. Binggeli, B., Sandage, A., and Tammann, G.A. 1988, Ann. Rev. Astr. Ap., 26, 509. Binggeli, B., Sandage, A., and Tarenghi, M. 1984, A. J., 89, 64. Binggeli, B., Tammann, G.A., and Sandage, A., 1987, A. J., 94, 251. Binggeli, B., Tarenghi, M., and Sandage, A., 1990, Astron. Astrophys., in press. Bothun, G.D., Mould, J.R., Caldwell, N., and MacGillivray, H.T. 1986, A. J., 92, 1007. Caldwell, N. 1987, A. J., 94, 1116. Davies, J.I., Phillipps, S., and Disney, M.J. 1989, M.N.R.A.S., 238, 703. Davies, J.I., Phillipps, S., Cawson, M.G.M., Disney, M.J., and Kibblewhite, E.J. 1988,

M.N.R.A.S., 232, 239. Dekel, A., and Silk, J. 1986, Ap. J., 303, 39. de Vaucouleurs, G. 1961, Ap. J. Suppl., 6, 213. Dressier, A. 1980, Ap. J., 236, 351. Dressier, A., and Shectman, S.A. 1988, A. J., 95, 284. Eder, J., Schombert, J.M., Dekel, A., and Oemler, A. 1989, Ap. J., 340, 29. Ferguson, H. 1989, A. J., 98, 367. Ferguson, H., and Sandage, A. 1988, A. J., 96, 1520. Ferguson, H., and Sandage, A. 1989, Ap. J. (Letters), 346, L53. Gallagher, J.S., and Hunter, D.A. 1989, A. J., 98, 806. Hodge, P.W., Pyper, D.M., and Webb, C.J. 1965, A. J., 70, 559. Hodge, P.W. 1959, Pub. A.S.P., 71, 28. Hodge, P.W. 1960, Pub. A.S.P., 72, 188. Holmberg, E. 1969, Ark. Astron., 5, 305. Hubble, E. 1926, Ap. J., 64, 321.

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Hubble, E. 1930, Ap. J., 71, 231. Hubble, E. 1936, Ap. J., 84, 270. Hubble, E., and Humason, M.L. 1931, Ap. J., 74, 43. Huchra, J. 1985, in The Virgo Cluster of Galaxies, ESO Workshop, ed. O.-G. Richter and B. Binggeli (ESO, Garching), p 181. Humason, M.L. 1936, Ap. J., 83, 10. Hunter, D.A. and Gallagher, J.S. 1985, Ap. J. Suppl, 58, 533. Kaiser, N. 1986, in Inner Space/Outer Space, ed. E.W. Kolb et al. (Chicago: Univ. Chicago Press), p 258. Kraan-Korteweg, R.C., and Tammann, G.A. 1979, Astron. Nach., 300, 181. Kuhn, T. 1970, The Structure of Scientific Revolutions (Chicago: Univ. Chicago Press), second edition. Moss, C. and Dickens, R.J. 1977, M.N.R.A.S., 178, 701. Reaves, G. 1956, A. J., 61, 69. Reaves, G. 1964, Ap. J., 69, 556. Rood, H.J. 1969, Ap. J., 158, 657. Sadler, E. 1984, A. J., 89, 34. Sandage, A. 1983, in Internal Kinematics and Dynamics of Galaxies, IAU Symp. 100, ed. E. Athanassoula (Reidel: Dordrecht) p 367. Sandage, A. and Binggeli, B. 1984, A. J., 89, 919. Sandage, A., Binggeli, B., and Tammann, G.A. 1985, in The Virgo Cluster of Galaxies, ESO Workshop, ed. O.-G. Richter and B. Binggeli (ESO, Garching), p 239. Sandage, A., Binggeli, B., and Tammann, G.A. 1985, A. J., 90, 1759. Sandage, A., Freeman, K.C., and Stokes, N. R. 1970, Ap. J., 160, 831. Sandage, A., and Perelmuter, J. M. 1990, Ap. J., in press (20 February issue). Sandage, A., and Tammann, G.A. 1976, Ap. J., 207, LI. Schechter, P. 1976, Ap. J., 203, 297. Schombert, J.M., and Bothun, G.D. 1988, A. J., 95, 1389. Shaya, E. J., and Tully, R. B. 1984, Ap. J., 281, 56. Smith, S. 1936, Ap. J., 83, 23. Sodre, L., Capelato, H.V., Steiner, J.E., and Mazure, A. 1989, A. J., 97, 1279. Tammann, G.A., and Binggeli, B. 1988, in an I.A.U. Sypmosium procedings. Tammann, G.A., and Kraan, R. 1978, in The Large Scale Structure of the Universe, IAU Symp. (Reidel: Dordrecht), p 71. Thompson, L.A., and Gregory, S.A. 1980, Ap. J., 242, 1. Tully, R.B., and Shaya, J. 1984, Ap. J., 281, 31. Zwicky, F. 1933, Hel. Phys. Acta, 6, No. 2. 110. Zwicky, F. 1937, Ap. J., 86, 217. Zwicky, F. 1942, Phys. Rev., 61, 489. Zwicky, F. 1957, Morphological Astronomy (SpringenBerlin). Zwicky, F. 1964, Ap. J., 140, 1624.

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DISCUSSION Djorgovski: You repeatedly made the point how nucleated dwarfs are distributed in different ways showing different correlations than non-nucleated ones. Could that be really a luminosity effect? Sandage: You can divide the sample also into a bright and faint sample, and since the nucleated ones are in the bright sample, they themselves form the population that you look at. If you look at the faint dE's, they are distributed differently. That was a detail which I didn't go into. Harry? Ferguson: The faint non-nucleated dE's are distributed in the same way as the bright nucleated dE's and the bright E's and SO's. It's only the bright non-nucleated dE's that show the more extended distribution. Sandage: The bright non-nucleated ones are distributed like the spirals and the Im's. All the others are distributed like the E's. Bothun: Okay, I've got a couple points I'd like to badger you on. The first is, I have no problem with some of these dE's being stripped, but I think you cannot identify the present day population of Im's as the progenitor population of these dE's for the following rather simple reason. The surface brightnesses of the Im's if anything are slightly below the dE's. They are about 0.4 magnitudes bluer. Presumably stripping causes things to fade and redden and they will fall below your detection threshold limit but not below Malin's detection threshold limit. We have uncovered a population of objects below your detection threshold and there is unfortunately, no color-surface brightness relation as you would expect in this simple fading argument. So, I think the present day population of Im's is not the progenitor. But the blue compact dwarfs, maybe those, if faded, will fall right into the dE range. Sandage: That, in fact, was one of the fading vectors that Bruno [Binggeli] shows that the BCD's will fall right where you see them. Bothun: The other point I think is kind of critical here. One's never magnitude limited when one makes a luminosity function. One is always surface brightness limited. If there, for instance, exists a population of extremely low surface brightness objects, with large core radii that are below your detection threshold, you would have missed them. But those objects could have been relatively bright: instead of V = —12 maybe V = —15. Such a population exists and we've found some of them, so I think that we really don't know what the faint end of the luminosity function is at all, and I agree completely with Peebles that we don't know what the luminosity function is precisely because of the surface brightness problem. Sandage: There was a claim in the literature that huge galaxies cover the face of Fornax: if we went just a magnitude fainter, we'd see these throughout the Fornax cluster. I forget who made that claim. So, we Malinized the plates we had and looked for them and we couldn't find them. Bothun: Well, they're hard to find.

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Sandage: Right, yes. (Laughter) Bothun: No, seriously... Sandage: But a difference to be a difference must make a difference. Bothun: Well, we find things as low as 28 mag per arcsec2. I mean that's invisible, but they're big. Sandage: Sure, they're big, yes. Rubin: Can you tell us what the nuclei are in these dwarf ellipticals? Sandage: Ruth Peterson and Nelson Caldwell have now gotten good spectra. Some spectra had been attempted over the years. Ruth says that of the ones she's observed, they look just like globular cluster spectra and the velocity dispersion of the brightest ones, and these are —13 absolute magnitude, is 40 kilometers a second. So, that gives an M/L, she says, of normal proportions like two. Haynes: Is there any evidence for young stars? Sandage: They only have about five and she says, all five that they have looked like M5—old. But if you now look in the center of NGC 205, there certainly is evidence, both direct and spectroscopic, for a young population. So, certainly star formation is going on in NGC 205 and it's certainly going on in the SO NGC 5102. In a related idea, Michael Greg's thesis is very suggestive where he blocks out the bulge of SO's and just looks at the light of the disk and he believes that there's evidence for a younger population in the disk of SO's. So the SO's could be the next stage beyond the Sa's where the gas has just been used up and you don't need sweeping to make most of the field SO's. Struble: Do you have any feeling for the velocity difference between your dE/N's and the central galaxy which you supposed may be gobbling them? Sandage: That's a mystery. M87 does not sit at the mean velocity of the Virgo by 200 km/s and we don't know the answer to that but now, two or three other clusters have the same thing and one speculates that M87 is not the mass center because of a massive amount of dark matter. I've heard that speculation. I don't believe it, but anyway that's the observation, 200 km/s motion of M87. Felten: You were protesting loudly against the idea of a universal luminosity function but in fact, when you showed the total luminosity function of the Virgo cluster compared with the total luminosity function in the field, they looked pretty similar. I wonder what principal effects do you think there are that make the luminosity function non-universal? Is it mainly that at the very faint end that in rich clusters there are extra dwarfs? Is that your main point or are there other significant differences besides? What are the significant failings that you see in the concept of a universal luminosity function? Sandage: If you just look at the early type galaxies, the ellipticals and the dwarf ellipticals, and if you change the ratio of E's to dE's, as a function of whatever environ-

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ment you want to put, then you're going to change the effective slope a in the bright end. And Harry Ferguson has shown that if he divides his sample into poor groups and rich groups, then the number of dwarfs per giant is a strong function of the number in the cluster or in the group. So, there is a difference in the slope of the total luminosity function between his groups depending upon the total number in the group. Is that a fair statement, Harry? Ferguson: It's a fair statement. It doesn't show up if you just try to parameterize it by a difference in a and/or M* because the Schecter function isn't a good fit for that combined distribution. So, a may get a little bit flatter as we go to poorer groups but we wouldn't look at that and say that's different. We'd just look at the dwarf to giant ratio classified on morphology, and the factor of five more dwarfs per giant in the Virgo cluster than the poorest groups is significant. Felten: May I just comment? My impression is that many of the theorist or cosmologists to whom you refer who use the universal luminosity function— I think this might not affect them much because as long as that faint end slope is considerably flatter than that divergent slope which you showed on one of your slides, I suspect it might not affect many of those calculations much if it rises or falls with it. Sandage: I agree. Huchra: Two things. One, I wanted to argue with Ken Freeman if he really wants to make the argument about the creation of the globular cluster systems from the nuclei of the nucleated dwarfs. The nuclei and the nucleated dwarfs, I have a lot of spectra on them, are very metal poor; whereas, your average M87 globular cluster is fairly metal rich. I might argue against that, number one. Number two, they also were faint. The nuclei are too bright by about three magnitudes relative to your average globular cluster Sandage: Oh, he has an answer to that one. Huchra: Well, let him give it to me. (Laughter) Freeman: Do you really want that answer? (Laughter) Huchra: Sure. But one question I wanted to ask before he can give me an answer. There was a graph that you presented that had a couple of interesting numbers for M* in the Virgo cluster. They were very small, —17.5 or something like that. Was that the M* for the dwarf population or for the population as a whole? Sandage: M* for the total luminosity function for Virgo is —21.1 (Figure 6 of the text), based on m - M = 31.7. Ken? Freeman: Okay, well, the first of John's points was that the spectra are metal weak. I don't believe that's correct. I have numerous spectra of these too and so have Mould and Bothun and I think the experience of both of these groups is that you get them as metal rich apparently as 47 Tuc. The other point about the nuclei being significantly brighter than globular clusters are now, well, you'd certainly want that because when you drop a nucleus into a severe tidal field, we're going to truncate it quite a lot. You

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might, in fact, truncate it back to just a percent of its original mass. So, you'd certainly want to have a few units of absolute magnitude under your sleeve before you do this. Huchra: I disagree very much with your first statement, Ken, which is that—it is indeed true that the most metal rich ones are metal rich but on the average, they're a lot less metal rich than the M87 globulars and Mould and I and between us—and Jean Brodie and Nemec and company—now have about 40 clusters and the average metalicity is very high. Freeman: What is it? Huchra: Oh, it's about—a little less than a half solar for the globulars. Whereas, the dwarfs are maybe —1.5 dex or about 20 times or 30 times less than solar. Bothun: I think that's crazy. (Laughter) If you make a plot in Ca II K line strength versus... Huchra: A Call line strength is an extremely dangerous thing to use. I would suggest you use Mg II. When you do that, you get low metalicities. Bothun: You can make that plot in comparison with galactic globular clusters and it would brush up against 47 Tuc. Huchra: Okay, I won't disagree with that. Bothun: I don't think your —1.5 does it by any means. There a substantial number that are like 47 Tuc. Whitmore: How clear is it that the dwarf ellipticals versus the ellipticals represent a bimodal distribution rather than a continuum from ellipticals to dwarf ellipticals, just in morphologically trying to type them. Sandage: You mean how well can the morphologist . . . Whitmore: Right, tell them apart and whether there's a continuum or they're really definitely bimodal. Sandage: OK. In that transition of the two branches of the surface brightness-absolute magnitude diagram (Figure 14 of the text), if you're up near —19, of course, it is very hard to decide what's happening but most of these correlations are for much fainter dE's, where there's no question whatsoever that you're low surface brightness. So, these are real low surface brightness dE's where there is no ambiguity about the morphology. Now, one might ask the following. In those diagrams [see Figure 14] you saw M32 sitting up there which might be an extension of the elliptical branch and there'd be no separation. Well, M32, if it's stripped, is an environmental situation. There were some 15 possible candidates in the Virgo cluster of M32-like objects that were in the final table in the catalogue. Now Kimball and Davidson have gotten redshifts of those in the Virgo cluster and most of those, some 90%, have proved to be Virgo cluster members but almost every one of those are in the neighborhood of a giant galaxy. So, the comment that Wirth and Gallagher have made that the branch continues way far

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up into a whole bunch of M32 like galaxies it would seem is due to an environmental effect. Djorgovski: Well, I have to disagree with that because that branch does continue when you look across the local supercluster and you look at multi-parameter correlations, there is simply no separation. Those are genuine low luminosity ellipticals. Oegerle: Yesterday, we had a long discussion about the reality of subclustering and this seems to be at least one cluster where we can say that there is. That must be a fairly young cluster. So, does this suggest then that the galaxies formed before the cluster and that cold dark matter is preferred in this situation? (Laughter) Sandage: Well, I don't know about the last phrase but Shaya and Tully did postulate that the spirals are just now arriving near the core that's been around for quite some time, and that's the picture that Tammann mentioned in the discussion at the morning session, and that's the one that, of and by itself, probably can give an explanation of the Dressier morphological-density relation. At the beginning, the Dressier density morphology relation was all ellipticals and no spirals, and then as a function of time, as the spirals come in, the number of spirals keeps going up and the elliptical number is the same. So, the Dressier relation would be time dependent and what we see now is what it is at the moment. Yes, the spirals would then just be arriving at the position in the core. Bothun: I realize it's dangerous to ask you a question regarding distances but do you think M87 and 4472 are the same distance or is one behind the other? Sandage: I don't know. Bothun: We have some evidence that there is a slight depth effect and Bill Harris has some evidence that there's a slight depth effect as well. Harris: No, no ... Bothun: No, you don't have it anymore? (Laughter) Harris: If you look at the luminosity distribution of globular clusters around both of those Virgo ellipticals, you can't tell the difference except just by shear numbers. The bright part of the luminosity distribution where the turnover is similiar, they're identical within two-tenths of a magnitude in both of those big ellipticals, and also two of the other Virgo ellipticals, but from that you'd have to say that they're within ten percent of the same place. Sandage: I might say that I'm so glad to see Harris here because he's the one that has pointed out the peculiarity of these four elliptical galaxies with a very high specific number of globular clusters sitting at the center of dense clusters, and that's your statement and I'm very glad to see you here. Richter: I was struck by the evidence that you've presented so far about this stripping of the Im's and making them into dE's. I think there was an additional test you could make in order to tighten that up further. As I understand it, it's only the bright and

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non-nucleated dE's that are basically the candidates. Now, their luminosity function in that case should be bound the same way as the Im luminosity function if you want to make them out of the Im's. Now, presently, you can't distinguish the bright nonnucleated dE's from the faint non-nucleated dE's but is there a possibility that you could look at the bright nucleated dE's and look at their progression of the relative luminosity of the nucleus to the total luminosity of those ellipticals, and see if that goes down, so that the very faint non-nucleated dE's could be in a continuum with a bright nucleated ones. Sandage: Be interesting to look.

DYNAMICAL EVOLUTION OF CLUSTERS OF GALAXIES

Douglas Richstone Department of Astronomy University of Michigan Ann Arbor, MI 48109

Abstract. Recent progress in understanding four processes that play a large role in the evolution of clusters of galaxies is reviewed. These are dynamical friction, mergers, collisional tidal stripping and the cluster mean field tide. Recent estimates for the growth rate of the cD galaxy and its frequency of appearance are discussed. In spherical relaxed clusters the theoretical and observational results for the accretion rate of a central massive galaxy seem to be quite consistent. It appears that a major part of the cD formation must occur in subclusters. Recent work on the formation of clusters containing galaxies and dark matter suggests that considerable mass segregation occurs in small subclusters (provided clusters form in a bottom up manner). This appears to be a result of dynamical friction. It may imply that visible clusters are embedded in large dark matter halos and that cluster M/L's have been underestimated.

1. INTRODUCTION Clusters of galaxies represent a fascinating, if formidable, challenge for the theorist. Although relatively young in terms of their crossing times (T cr = R/v), the galaxies are sufficiently large and massive that they interact with each other and the intracluster medium on a timescale comparable to their ages. A sensible way to organize a report on this complicated subject is, by analogy with stellar structure, to report first on the detailed processes which may occur (the 'hydrodyamics' and atomic 'physics' of the problem) and then to examine the effects of these processes (the analog of 'evolution') on the galaxies and the cluster. I will attempt to follow that plan. Accordingly, in Section 2 we describe the 'atomic physics' of interactions between cluster galaxies and each other and the intracluster medium. In Section 3 we discuss the new results on the evolution of virialized clusters with spherical symmetry, and a few relevant observational results, especially those which bear on the 'cannibalism' hypothesis for brightest cluster galaxies. Finally, in Section 4 I report on the somewhat surprising results West and I have recently obtained by simulating formation of clusters of galaxies containing both dark matter and galaxies. These simulations raise questions about the standard model in

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which the evolution of galaxy clusters is studied, in which we assume that they are quasi-static, and well-mixed, and that the galaxies carry ~ 10% of the mass. They also suggest that estimates of the mass density of the Universe obtained by combining cluster M/Z's with galaxy surveys may in fact be consistent with Qo — 1 cosmologies. An important component of the physics of clusters of galaxies is the behavior of the hot X-ray emitting gas in the cluster, and the interaction of that gas with the interstellar media of the galaxies. There is, in addition, a rat's nest of frustrating issues which arise in the interpretation of cluster structure and dynamics, including the significance or importance of observed subclustering, the shape of the velocity distribution profile in projection and putative structure in that profile, the role of velocity anisotropy in confounding mass estimates, and the problem of identifying true members. Those topics are not addresssed in this review. I have been significantly influenced in preparing this report by the recent reviews by Dressier (1984), Merritt (1988), Geller (1987) and White (1982).

2. PHYSICAL PROCESSES 2.1 Dynamical Friction Dynamical Friction is the loss of energy of a massive object by gravitational scattering of less massive objects. Most work on the application of this process to clusters uses the formula derived by Chandrasekhar (1943) for drag on a massive particle traveling with velocity v through an infinite fluid of less massive objects whose velocity distribution is Maxwellian. That formula may be written as dv

~dt

— =

tf

'

where m is the mass of the heavy object, />& is the mass density of the lighter objects, f(v) = erf(X) — X erf(X)1 is the 'active' mass fraction (see Binney and Tremaine 1987), X = t>/(v2<7) , and A is the usual ratio of most distant to closest encounters. As written above the formula is correct only in the limit that the background particles are much heavier than the test particle. If that is not the case it should be multiplied by the factor (1 + mb/m). Considerable effort during the past decade has been spent on investigating the applicability of the dynamical friction formula to binary stellar systems and heavy point masses embedded in spherical systems (Lin and Tremaine 1983, White 1983, Weinberg 1986). A fair summary of those studies could fill a review paper, but it seems reasonably clear that the Chandrasekhar formula, at least to a factor of two, provides a reasonable description of the angular momentum loss of a heavy object on a nearly circular orbit, embedded in a cluster of less massive points. It is not altogether clear to this reviewer what these studies suggest about its reliability for elongated orbits or background distributions with non Maxwellian or anisotropic distribution functions. A massive object moving through a sea of particles loses energy on a timescale r = (1/u dv/dt)i . If this formula is applicable to the orbiting galaxies in clusters, then the timescale for velocity loss (or for orbital decay in a singular isothermal potential well, is

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283

So if no other process intervenes, the dynamical friction formula indicates that the heaviest galaxies near the cluster center should spiral to the center in a time of order 10 yr. In the estimate above we have evaluated f(v) at X = 1 and taken inA = 3. Note however, that when the erf and erf' are evaluated at small v, the frictional drag is proportional to v. Thus the galaxy does not sink like a stone in honey. In a homogeneous cluster core, the galaxy's equation of motion is that of a damped 3-dimensional simple harmonic oscillator, and for any reasonable cluster and galaxy parameters it is an underdamped oscillator.

2.2 Mergers Two galaxies which pass each other slowly and closely gravitationally deflect the stars in each other, increasing the internal energy of each. The source of this energy is the relative orbital energy of the galaxies. If the passage is sufficiently slow and close, an unbound orbit will become a bound orbit and the galaxies will merge. This process has been discussed extensively in the literature. A particularly useful set of approximate merger criteria is provided by Tremaine (1981). These formulae are descended from earlier work by Spitzer (1958) and are based on the impulsive approximation, which appears to provide rather good estimates for the energy transfer to stellar orbits even in fairly slow encounters. Since grazing encounters are much more common than head-on ones, we show below the formula for the energy transfered to the individual stellar orbits in a galaxy of mass mg and mean square radius (r?) by a perturber of mass m p passing at velocity v and impact parameter p:

This formula can be easily modified to include the energy dissipated in galaxy p by galaxy g, to obtain

The total can be divided by the kinetic energy of the galaxies in the center of mass frame fiv /2 where \i = (trig mp)/(mg + m p ), to obtain a criterion for mergers:

where AE ~E~ This criterion can be used to obtain a merger cross section by solving AE/E p . This gives 2

\8G2(mp + m) L

P =[

^

2

21

= 1 for

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Since collisions at this velocity with impact parameter less than the indicated value of p will lead to mergers, irp is the cross section for merger. This criterion reduces to Tremaine's for equal mass galaxies. Since one galaxy may grow considerably as a result of mergers, it is of some interest to look at the merger rate in the limit mg » m«. We use r oc m ' to evaluate the above expression, which reduces to p oc mgy/mpv. Then the merger rate, per galaxy, which varies as ripCc\%p^, is proportional to mg, while the material accreted at each step varies as mp. In this model, the merger product grows exponentially. There have been numerous numerical simulations of mergers during the last decade, especially by White (1978, 1979, 1980), van Albada (1982), Villumsen (1982 a, b and 1983), Duncan, Farouki and Shapiro (1983) and May and van Albada (1984). These experiments show that formulae derived from the impulsive approximation provide a reasonable merger criterion, that gradients in population, metallicity or M/L are washed out, but only slowly, and that merger remnants tend to exhibit deVaucouleurs' law surface density profiles. Two results seem particularly interesting. First, White has noted that head-on mergers tend to produce prolate elliptical galaxies, while grazing mergers send to produce oblate ones, which however have rather large spin parameters (that is, unlike giant elliptical galaxies, they seem to be flattened by rotation rather than velocity anisotropy). These results are substantiated by Villumsen, who sees little velocity anisotropy in his merger products. Since, barring special tuning, a random distribution of collisions will favor grazing encounters over head-on ones, ellipticals resulting from few mergers should spin rapidly. Hence, it's hard to see how giant ellipticals could result from hierarchical mergers of comparable mass partners at each step. Second, Quinn and Goodman (1986) have shown that the stellar disks are easily thickened by accretion of companions totaling as little as 10% of the disk mass. So if there is significant merging in the cluster or in subclusters, spirals and SO's must avoid those regions.

2.3 Collisional Tidal Stripping During galaxy encounters (which may or may not) lead to mergers, some of the stars which acquire energy may become unbound. From the standpoint of cluster evolution, the most interesting single parameter is the fractional rate at which galaxies lose mass. Aguilar and White (1985) have performed a thorough set of numerical experiments which now constitute the best estimate of mass loss rates due to tidal stripping in clusters. Since the rate at which an individual galaxy encounters others must be proportional to n
1 dmg mff di

=

-1 f n \ f od \ / rg V 10 3 3 1 10 yr V l O - M 0 p c - ; VlOSkmsec- / \10kpcy

where 7 is between 2 and 3. For the important parameter range ITC//(4
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ancient work by this author (Richstone 1974, 1976 see also Dekel et. al 1980 and Gerhard 1981). However, they clearly also demonstrate that certain scaling rules adopted in that work are incorrect, and they find a much steeper dependence on o~c\lo~g. Tidal stripping may play a role in limiting the size of galaxy halos or in limiting the size of merger products. It may also have contributed to the halos of cD galaxies if ordinary galaxies had more extended luminosity profiles in the past. Unlike the mean field tide discussed below, collisional stripping is likely to continue to play a role in the future, although at a slow rate.

2.4 Mean Field Tide The mean gravitational field of the cluster limits the size of galaxies. For circular orbits, this phenomenon is similar to the Roche limit. Although well known in the solar system, the importance of this process in the evolution of clusters has only recently been emphasized. Much of the work is due to Merritt(1984, 1985, 1988) who shows that, on circular orbits near the cluster center, a galaxy is limited to a size rq < <7cl

where the subscript g refers to the galaxy and cl refers to the cluster, and Ro is the cluster core radius. In reasonable cluster mass distributions, galaxies experience the greatest tidal stress near Ro. For galaxies with isothermal mass distributions, this implies a mass limit of the form Mg < 1 This translates to size and mass limits of ~ 50 kpc and ~ 8 x l O n M 0 near the center of a rich cluster. The numerical coefficients in the two above equations were derived from Merritt (1988). Merritt's work recalls work by Gunn (1977) which argued that the mean field tide of a protocluster limits the size and mass of galaxies at formation. Merritt has also recently drawn attention to the work of Noonan (1970) who had also discussed mean field tides in clusters some time ago. A set of numerical experiments (Allen and Richstone 1988) suggest that the results of circular orbit theory applied at the pericenter of an elongated orbit may not provide a good estimate of the tidal limitation of galaxies on elongated orbits. These galaxies, because of the short time spent near pericenter, lose only some subset of their stars orbiting outside the tidal radius. These simulations also exhibit some heating of the loosely bound stars in a manner reminiscent of tidal shocking (see Spitzer and Chevalier 1973). On the other hand, Merritt and White (1987) find that repeated pericenter passes of galaxies on elongated orbits reduce their mass below the limit expected for circular orbits.

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3. EVOLUTION OF SPHERICAL VIRIALIZED CLUSTERS Although somewhat limited, the dynamical evolution of galaxies in spherical, virialized clusters is a useful idealized problem. It should be reproducibly solvable and ought to illuminate various suggestions about galaxy evolution.

3.1 Dynamical Friction in Cluster Cores An important recent development in this area has been the application of a simple theory of mean field tides to the problem of accretion of galaxies by the cluster center. Earlier work (Ostriker and Tremaine 1975, White 1976, Hausmann and Ostriker 1978 and references cited therein) had shown that massive galaxies would be accreted by the cluster center at a sufficiently rapid rate to account for the presence of a massive centrally located 'cD' galaxy in some clusters. Merritt (1984, 1985) has shown that tides limit the size of galaxies in cluster cores to ~ Ro/l0, that, once inside the core radius, the galaxy orbits do not circularize faster than they decay (so isotropic distribution functions are preserved), and that the mass (or luminosity) accreted by the central region of the cluster increases exponentially with time. Merritt finds that the accreted luminosity is ~ (2 — 4)L* in 10 yr. Merritt's work addresses an average cluster; this may be an important limitation. Merritt's original calculation used a cluster core radius of about 125 kpc. Since enlarging the core radius reduces the effect of tidal limitation, one might suppose that a larger core radius could accrete more luminosity. In fact, the opposite is true. The galaxy mass permitted by the tide varies linearly with the core radius (for truncated isothermal spheres; more slowly for other models). The central density of dark matter in the cluster varies inversely as the square of the core radius for fixed velocity dispersion. Since the sinking rate is proportional to the product of these two terms, it varies inversely with the core radius. So enlarging the core radius decreases the accretion rate.

3.2 Observational Estimates of the Accretion Rate Although Merritt's work has the important limitation that it does not include the graininess of the galaxy distribution and the stochasticity of galaxy encounters, it is the most appropriate estimate of mean accretion rates to compare with Lauer's (1989; see also Tonry 1975 and Merrifield and Kent 1989) estimates of accretion rates based on multiple nuclei of brightest cluster galaxies. Some of Lauer's (1989) work is particularly interesting as it attempts to distinguish galaxies actually at the cluster center from those projected against the cluster center via the identification of indicators of tidal damage. The features Lauer feels are indicative include nonconcentric isophotes, tidal limitation, excess light and dynamical friction wakes. This list could be sharpened through comparison with simulations of galactic encounters, as have been conducted by Borne and co-workers (Borne 1988a and b, Borne and Hoessel 1988 and Balcells, Borne and Hoessel 1989). Lauer's work represents a most interesting avenue, but three reservations may be noted. First, the retrieval of subtle features in the light distribution by elliptical isophote fitting and subtraction always raises questions about the significance of the result. One would like to see the features

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indicated in the data before manipulation. Second, the identification of a list of features attributable to interactions places considerable confidence in our ability to characterize a 'normal' galaxy either in theory or by observation. Finally, Lauer interpreted his data in terms of the old circular orbit formulae for the time dependence of accreted luminosity. It would be useful to also compare to Merritt's recent work for isotropic distribution functions for accreted objects. Lauer estimates that his clusters have accreted 2 to 4 L* in the last 10 years, in good agreement with Merritt's theoretical estimates.

o

140

Figure 1. Random realization of exponential growth as a function of time (see text). The top line is the average of 100 simulations. The other four lines are individual runs. Three e-folding times are illustrated.

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Bothun and Schombert (at this meeting and in preparation) have taken an alternate approach to this problem. They identify a slow moving population in the projected velocity distribution of the galaxies in the inner 0.2 Mpc of the cluster. They then find that these objects appear to be tidally truncated. Although their estimates of accretion rates are somewhat sensitive to their interpretation of the observed tidal truncation, they obtain estimates of about 5L* per 10 years.

3.3 Stochasticity and Mergers An important limitation of Merritt's calculations is that they focus on the mean rate of galaxy growth in a situation where luck may play a significant role. The importance of stochasticity can be seen in Figure 1, which illustrates this effect on growth by mergers. Based on the merger rates obtained in Section 2.2, we have used a random number generator to sample growth by a constant increment AM, but with a probability of gaining that increment that is proportional to M. This simulates different random realizations of a process which, if continuous, would be described by an equation of the form dM/dt = M/T, which leads to exponential growth on timescale r. The results of 100 simulations averaged together are shown with a few individual cases in Figure 1. It is clear that between t/r = 1 and t/r = 2 there is enormous variance from case to case. A few years ago Malumuth and I (1983, 1984) simulated the evolution of clusters of galaxies in fixed, spherically symmetric gravitational fields, tracking the orbits of the galaxies and applying a set of collision rules when they encountered each other. These rules attempted to represent the effects of stripping, mergers and dynamical friction, but they predated most of Merritt's work on mean field tides. Although the average brightest cluster member produced by these simulations was only around 3L*, there was one galaxy more luminous than 5L* in ~ 30 % of the simulations of rich clusters. Although Merritt suspects this large a result is an artifact of unusual initial conditions or of failure to include mean field tides, nearly all the galaxies in these simulations are smaller than his tidal limit, expressed in terms of the simulations' cluster core radii, and the average growth rates are not much larger than his results. Two differences, which are surely appropriate to this kind of problem, are the inclusion of mergers of non-central galaxies, and the noise produced by the random realization of the galaxy distribution in space and velocity. That work identified a number of observational properties of clusters also seen in the simulations. The combination of merging, friction and stripping in a static potential seemed to account for the observed lack of a relationship between the frequency of a cD galaxy and the cluster richness (Leir and van den Bergh 1977), the mild anti-correlation of the luminosity of the brightest galaxy with the ratio of the first and second brightest galaxies (the Bautz-Morgan 1970 effect), and the relationship of the fraction of galaxies that are elliptical to the presence of a cD galaxy (Oemler 1976). A relatively neglected, but important, issue, is the quantification of the centrality of the brightest cluster galaxy, and the possible relationship of centrality to the morphology of the galaxy. This issue was studied by Quintana and Lawrie (1982), and Malumuth and I felt that their results were rather consistent with cannibalism. But the recent work by Hill et. al. (1988) that shows that the cD in Abell 1795 has a peculiar velocity relative to the cluster center of 365 km see" seems a little surprising. Systematic velocity studies are certainly valuable.

Dynamical Evolution of Clusters of Galaxies

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3.4 Strong versus Weak Cannibalism Although our results seemed rather encouraging at the time, Dressier (1984) has emphasized that the 'success' rate of production of very massive galaxies obtained in those simulations is insufficient to account for the fractional abundance of cD clusters among rich clusters, since he believes that a fair fraction of clusters are fairly young. Dressler's argument, together with the estimates of accretion rates from multiple nuclei and the theoretical studies described above, make a compelling case that in spherical, relaxed clusters, there is insufficient merging or dynamical friction to account for the formation of very luminous galaxies. Merritt (1988) has sharpened this view by dividing the 'cannibalism' hypothesis into strong and weak versions. He defines strong cannibalism as the formation of a galaxy of luminosity > 5L* at the cluster center by dynamical friction. He defines weak cannibalism as the accretion of significant luminosity by an extant massive galaxy at the cluster center. Merritt feels that the strong cannibalism hypothesis, most clearly articulated by Hausmann and Ostriker (1978), is in some jeopardy on the theoretical side due to his work on mean field tides, and on the observational side due to the low rates of accretion estimated by Lauer and Tonry. To adopt Merritt's terminology, even considering both galaxy mergers and dynamical friction, the growth rate of large galaxies in virialized clusters appears to be too low to support the strong cannibalism hypothesis, although the weak cannibalism hypothesis seems well founded in theory and supported (or at least unrejected) by the observations. However, as Dressier (1984) has noted, "the high frequency of cD occurrence must be telling us that the primary evolution of such systems occurs in subcondensations before mergers."

4. FORMATION AND EVOLUTION OF SUBCLUSTERS There are at least three reasons, then, to consider the early dynamical evolution of clusters of galaxies in terms of the mergers of subclusters. First, if the discussion above is largely correct, then while mergers, friction and tides may well play a role in shaping the galaxy content that we see today, they probably do not operate rapidly enough in current clusters. Numerous authors have suggested that mergers in particular will be more effective in subclusters, so it is worth investigating that. Second, cold or baryonic dark matter is argued to exhibit structure after recombination in which the fluctuations on the scale of clusters of galaxies will be approximated by an n = 0 to —1 power spectrum. The small fluctuations in this spectrum are denser than the large ones, and will therefore collapse first. Finally since clusters are now observed to exhibit substructure which must be washed out on a timescale on the order of Tcr, that substructure must represent the merger of subclusters. This last point is controversial. West (in this volume) does not believe that substructure in the inner megaparsec of rich clusters is statistically or dynamically significant. On the other hand Geller (see her review in this volume) and her co-workers have argued that the substructure is significant. If this is the case, it calls into question the astrophysical relevance of some of the results of Section 3. To attempt to clarify the issue a bit, there seem to really be at least two questions. The first is whether the claimed substructure is a random realization of a smooth distribution (or whether it

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is statistically significant). The second is how the observed distribution constrains the dynamical history of the cluster. Hopefully these issues will be clarified.

4.1 A Model for Settling in Subclusters Stimulated by the above arguments, and by a desire to extend the simulations of quasi-static clusters to the cluster formation epoch, West and I (West and Richstone 1988) have conducted a number of simulations of clusters of galaxies in formation with heavy points representing galaxies and light points representing dark matter particles. Peebles (this volume) and West (this volume) have described some of the features of this work. Nonetheless, the results are sufficiently suprising and controversial that it seems worthwhile to review them here, to attempt to demonstrate that they could, in fact, have been derived by 'pure thought' rather than numerical experiment. The logic of our approach is straightforward. The current cluster 'standard model' is a spherical, well mixed cloud containing 10% galaxy mass and 90% dark matter (we have idealized away the gas content). Since both the currently fashionable theories of dark matter and the observations of subclustering indicate that small structures form first, we start the simulations with galaxies extant and with galaxies and dark matter randomly sampling the same power spectrum, but thrown down independently of each other. The mass of the dark matter particles is remarkably poorly determined ranging from 10 ev axions to 10 M© black holes (see Turner 1987), so the mass ratio of dark matter particles mj/mg is only constrained to about < 10- 6 .

10-82 < ^ TTlg

Fortunately, tidal effects due to individual dark matter particles seem unimportant even at the high mass limit, and mj enters as (l + mj/mg) in dynamical friction, so for these effects the uncertainty in the mass of dark matter particles need not concern us. In virial equilibrium, we may combine the virial theorem [V

'

R

(a ~ 0.4 for reasonable mass distributions) with the definition of the crossing time,

Tcr = R/v, and with the definition of the galaxy mass fraction / f J

-

N m

9 9

~ Mtot '

to show that the dynamical friction time varies as QlNgTcr f

A similar argument can be applied to the standard formula for the relaxation time, yielding

Dynamical Evolution of Clusters of Galaxies

241

O.lNgTgr If we now adopt numbers appropriate to rich clusters of galaxies to evaluate these two expressions, / = 0.1, Ng = 10 , lnA = 3, and T cr = 109yr, then we obtain il. Tf -=m10"yr, and

Tr = 1012yr.

This result, together with the fact that violent relaxation scatters particles off large scale gravitational potential fluctuations rather than each other, and thus randomizes energy per unit mass rather than energy, is the basis of the commonly held belief that in clusters of galaxies only the very heaviest galaxies, if any, have lost energy to the dark matter in the clusters, and therefore that the clusters are well mixed and the galaxies trace the mass.

Figure 2. Orbital plane projection of an N-body simulation of the merger of two subclusters. One particle (drawn as a large knot) is 10 times more massive than each of the others. If we repeat the same estimate for Ng = 1 and Tcr = 10 yr, suitable for a very small protocluster, Tt = 3 x 10 yr. So, in the early stages of protocluster formation, the

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D. Richstone

Figure 3. N(E) vs. E histogram as a function of time for the simulation shown in Figure 2. Each frame corresponds to the same epoch as the frames in Figure 2. The vertical line indicates the energy of the massive object. The first two frames have vertical scales expanded by a factor of 2 relative to the others. friction time is very short, and galaxies sink to the bottom of lumps of dark matter on a very few crossing times. Since the timescale between subcluster mergers is greater than their crossing time (it must be so, since, by definition the subclusters are denser than averages over larger regions), the galaxies do have sufficient time to settle in the lumps prior to the next merger. During the subcluster mergers, the galaxies are scattered in energy, but (as in the case of color gradients in galaxies) only a large number of mergers will wash out the segregation in energy. We (Ashe, West and Richstone, 1990) have investigated a number of properties of this process. In particular, in Figure 2 and Figure 3 we show a simulation of a merger and the energy spectrum N(E) of 200 low mass particles before and after a merger. The position of the one massive particle is marked. It is clearly not scattered to higher energies. There are two possible explanations for this. First, it may be that the merger introduces energy changes that are small compared to the binding energy of the particles. Alternatively, it may be that the centers of the merging objects, which contain the heavy particles, retain their structure long enough to spiral to the center of the merger product (I am indebted to Scott Tremaine for suggesting this possibility).

Dynamical Evolution of Clusters of Galaxies

0.5

243

1.5 t / T collapse

Figure 4. Mean harmonic separation of the 'galaxies' and dark matter particles in a simulation with white noise initial conditions. Note that the galaxies become significantly more clustered long before the 'top hat' model collapse time. In fact, it seems likely that both effects matter; the dominant one may well depend on the central concentration of the proto-clusters and their orbital angular momenta. So it's clear that in a system with few heavy and many light particles, which forms via a bottom-up merger of gravitationally bound subunits, that the heavy particles may lose most of their energy to the light ones very rapidly in the early stages of the process, and never regain it by scattering during mergers of the subunits. Although this environment is clearly much more favorable for mergers and possibly building cD galaxies than the eventual product of all these subunits, we have not yet followed through on this aspect of the problem. West's report in this volume includes a representative simulation and the mean harmonic radius of the dark matter particles and galaxies as a function of time. If the graphics of the simulations were not sufficiently convincing in themselves, the fact that the galaxies become markedly more centrally concentrated than the dark matter well before the collapse time for the entire protocluster (based on the top hat model) indicates that the segregation process is occuring in the subclusters. In Figure 4 we show the time dependence of the mean harmonic separation of the dark matter particles

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and the galaxy particles as a function of time in a selected simulation. It is very clear that the galaxies are settling in the subclusters long before the "top hat" collapses on the scale of the cluster. In Figure 5, we show (with finer time steps) the evolution of an expansion and collapse. It is also quite clear in these figures that the galaxies settle in the dark matter very early, and that the lumps then merge.

4.2 Is fto = 1? In a variety of simulations with / varying from 0.1 to 0.5 we find that the ratio of the mean harmonic radius of the dark matter to the galaxies is about a factor of 5. The velocity dispersion of the dark matter is not appreciably different than the galaxies, and the mass and galaxy distributions (based on superimposing many simulations) fall in density as R~2 to R~^. If real clusters of galaxies are so segregated, then the application of the virial theorem to determine masses, which is based on the assumption that galaxies trace the mass distribution, is flawed. Applying the virial theorem to our simulations as though they were real clusters underestimates their mass by a factor of 2 to 10. Note that there is a certain reductio-ad-absurdum flavor to this argument. We assume that / = 0.1 based on the application of the virial theorem to clusters and use it to show that in fact / ~ 0.02. Limitations in the number of particles we can simulate have made it difficult for us to close the loop by simulating clusters with / = 0.02 to see if they are consistent with the data. This clearly has serious implications for cosmology. One of the simplest arguments in favor of a low density Universe is the comparison of the mean density to the critical density necessary to bind the Universe (see Oemler 1988 for an excellent review). The mean density is obtained from the product of the luminosity density of galaxies and the mean M/L of the matter associated with galaxies. By assumption, clusters of galaxies are thought to be well-mixed representative samples of the Universe. If the regions which form clusters are indeed representative, but segregate during formation in the manner of our simulations, then the M/L of matter associated with galaxies is underestimated by a factor of 2 to 10 by the present application of this test. In the extreme case of a factor of 10 error, the result would indicate £2O = 1. Since both the luminosity density of galaxies and the estimates of cluster virial masses are uncertain by a factor of two in any case, the best we can say is that our work indicates that the direct estimate of the mass density of the universe, using cluster M/L's, now appears to be consistent with a critical cosmological model.

4.3 Possible Problems This result is sufficiently important and controversial that it appears to be appropriate to survey the list of possible errors we may have made (most of which have already been voiced during the discussions after earlier reviews). Figure 5a. (opposite page) Planar projection of a white noise simulation. Dots are dark matter, crosses are galaxies. The contours are the distribution of the dark matter. These frames are equally spaced in time and run to 0.83 in units of the 'top hat' collapse time.

f

Mm :

II

-3

u

CO

II o

p

t":^i;:^-;

.•.r-"-'--.f?S'?:/;AJ;i; .-:-i.-v->4. --i.: • ':**•> r.>- :.i.'': : «r.\-^ ; .' : " •>-.'••"- v-:.'

.:X';

.^.•xr-vyv V* .>Fi:?-:,:.

p

J."

-


II

p in o

i

245 Dynamical Evolution of Clusters of Galaxies

246

D. Richstone

S i I

p oi

Dynamical Evolution of Clusters of Galaxies

247

First, we may have just blundered in the N-body experiments. This seems unlikely as (i) the code is Aarseth's reliable and extensively used program; (ii) similar results have been obtained by other investigators in similar situations, although they did not interpret their results as we have (Roos and Aarseth 1982, Farouki, Hoffman and Salpeter 1983, Barnes 1983, 1984 and Evrard 1987); and (iii) there is a plausible, if not compelling theoretical argument which is consistent with our results. There is, however a particular problem which we wish to expose. Given a fluctuation spectrum, the simulations are characterized by 3 parameters. We can define any two of the following 3: Ng, f and mg/Mtot. They are related through the definition of / = Ngmg/MtotThe one remaining parameter is mj/rrig. The simulations described here have Ng as large as 100 and / as small as 0.1. Although further exploration of these parameters is in order, the real problem may arise with the parameter mj/mg, which we have so far taken as 0.1. This should certainly be reduced further, but our ability to do so is limited by the practical limitations of N-body programs. The number of dark matter particles is set by this ratio via

Nd = —f-

—

We need to do simulations with N > 10 to drive / below 0.1 or m^jmg below 0.1. Although we are now doing so, this will be slow going. Second, the absence of luminosity segregation in clusters of galaxies implies that energy equipartition has not occured during the evolution of the cluster. This objection has its own difficulties on 4 counts. First, claims about luminosity segregation (for and against) are controversial in themselves and there are many experts on both sides of this issue (see West and Richstone 1988 for references). Second, equipartition predicts mass segregation while observers detect the presence or absence of luminosity segregation (although it is distressing to retreat to an unverifiable argument). Third, while intermediate mass objects lose energy to the background at a rate proportional to m,7)(l — / ) , they also gain energy, from the heavy galaxies, according to the FokkerPlanck equation at a rate proportional to m/,/)/,/. One can find a mass spectrum where the intermediate objects gain energy from heavier ones at the same rate they lose it to the dark matter. Finally, and most plausibly, it may well be that some fraction of the low mass galaxies in the proto-cluster form bound to high mass galaxies and are dragged to lower energy by their high mass companions, before being liberated there by either the cluster (or subcluster) mean field tide or by a collision with another massive galaxy. This mechanism is akin to gluing some wood to a brick to sink it to the bottom of a pond. Third, if clusters carry much more mass might there be an abundance of gravitationally lensed distant objects that are not observed? Or, less negatively, can gravitational lensing constrain the mass of clusters of galaxies at large radii? Unfortunately, the answer appears to be no. For small deflections the deflection of a ray passing through a singular isothermal mass distribution of size rmax [therefore with the density distribution p = 2
Figure 5b. (opposite page) Same as Figure 5a for later times. In the later stages there are nearly twenty galaxies in the dense lump near the center.

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by

where c is the speed of light and b is the impact parameter of the ray. As x varies from 10 to 100 (a reasonable alteration if our simulations are appropriate), A 6 changes by only 6%. The added effect is so small because most of the deflection, even in this logarithmic potential, occurs when the light ray passes near the cluster center. Adding mass at large radii affects gravitational lensing very inefficiently. Fourth, some have argued that the analysis of large scale flows yield fio < < 1, inconsistent with our result. In fact, our results are consistent with 0.3 < fl o < 1, and in a review of the best studied flow, the flow around the Virgo Cluster, Kaiser (this volume) reports ft0 = 0.35. In principle, understanding large scale flows offers a very potent tool to measure fto- Nonetheless, it seems only fair to say that the analysis of large scale flows has its own set of difficulties and uncertainties. Given that, at this time it seems a subjective question of how to weigh marginally conflicting results from different methods. A final way out is to argue that the protocluster mass distribution is quite smooth and that cluster struture forms after collapse. In our simulations with extremely smooth galaxy and dark matter distributions mass segregation does not occur. This sort of choice of protocluster conditions is, of course, inconsistent with cold or baryonic dark matter but not with other possibilities. I suspect it is also inconsistent with the work of Geller and her collaborators (see her review in this volume) and Dressier and Shectman (1988) on the incidence of subclustering in galaxy clusters.

5. S U M M A R Y Over the past decade some progress has been made in improving our understanding of dynamical friction, mergers, collisional tidal stripping and mean field tidal stripping. All of these processes are probably important in cluster evolution. In particular, the mean field tide may limit the size of galaxies in clusters. Depending on the size of the cluster core radius (a quantity in some dispute), the effect may be so severe that even massive galaxies near the cluster center will not be drawn all the way to the center by dynamical friction. Most calculations of cD galaxy growth by accretion of other galaxies in the past decade have produced fairly modest yields either in the fraction of clusters that will carry cDs or in the average growth rate of the central galaxy in a putative average cluster. The distinction between strong cannibalism, in which a galaxy of luminosity > 10L* grows during a Hubble time, and weak cannibalism in which a pre-existing central galaxy may grow by up to 5L* in a Hubble time, may be a useful way to discuss this issue. Most recent observational work favors the weak cannibalism hypothesis. A number of recent simulations show that if clusters form by the merger of subclusters the galaxies have settled relative to the lighter particles of dark matter in these subclusters. This effect appears to be due to energy equilibration, which may procede very rapidly early in the clustering process when each galaxy carries a significant fraction of the mass in its subcluster. These results suggest that clusters of galaxies are embedded in still larger clusters of dark matter and that the estimate of the en-

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tire system's mass by the virial theorem or its kin underestimates the M/L of matter associated with galaxies in the universe. This work was supported by the National Science Foundation through grant AST 87-20028 to the University of Michigan.

REFERENCES Aguilar, L. A. and White, S. D. M. 1985 Ap. J., 295, 374. Allen, A. J. and Richstone, D. 0. 1988 Ap. J., 325, 583. Ashe, G., Richstone, D. and West, M. 1990 in preparation. Beers, T. C. and Tonry, J. L. 1986 Ap. J., 300, 557. Binney, J. and Tremaine, S. 1987 Galactic Dynamics (Princeton: Princeton University Press). Balcells, M., Borne, K. D. and Hoessel, J. G. 1988 Ap. J., 336, 665. Barnes, J. 1983 M.N.R.A.S., 203, 223. —, 1984 ibid. 204, 873. Bautz, L. P. and Morgan, W. W. 1970 Ap. J. (Letters), 162, L149. Borne, K. D. 1988 Ap. J., 330, 38. Borne, K. D. and Hoessel, J. G. 1988 Ap. J., 330, 51. Chandrasekhar, S. 1943 Ap. J., 97, 255. Dekel, A., Lecar, M. and Shaham, J. 1980 Ap. J., 241, 946. Dressier, A. 1984 Ann. Rev. Astron. Astroph. 22, 185. Dressier, A. and Shectman, S. A. 1988 A. J., 95, 985. Duncan, M. J., Farouki, R. T. and Shapiro, S. L. 1983 Ap. J., 271, 22. Evrard, A. E. 1987 Ap. J., 316, 36. Farouki, R. T., Hoffman, G. L. and Salpeter, E. E. 1983 Ap. J., 271, 11. Geller, M. 1987 in Large Scale Structures in the Universe, ed. L. Martinet and M. Mayor (Sauverny: Geneva Obs). Gerhard, 0 . E. 1981, M.N.R.A.S., 197, 179. Hausmann, M. A. and Ostriker, J. P. 1978 Ap. J., 224, 320. Hill, J. M. Hintzen, P., Oegerle, W. R., Romanishin, W., Lesser, M. P., Eisenhamer, J. D. and Batuski, D. J. 1988 Ap. J. (Letters), 332, L23. Lauer, T. R. 1989 Ap. J. submitted. Leir, A. A. and van den Bergh, S. 1977 Ap. J. Suppl., 34, 381. Lin, D. N. C. and Tremaine, S. 1983 Ap. J., 264, 364. Malumuth, E. M. and Richstone, D. O. 1984 Ap. J., 276, 413. May, A. and van Albada, T. S. 1984, M.N.R.A.S., 209, 15. Merrifield, M. R. and Kent, S. M. 1989 A. J., 98, 351. Merritt, D. 1984 Ap. J., 276, 26. —, 1985 Ap. J., 289, 18. Merritt, D. 1988 A. S. P. Conference Series Volume 5, Minnesota Lectures on Clusters of Galaxies and Large Scale Structure ed. J. J. Dickey (Provo: BYU Print Services) Merritt, D. and White, S. D. M. 1987 in Dark Matter in the Universe ed. J. Kormendy and G. R. Knapp (Dordrecht: Reidel). Noonan, T. W. 1970 Pub. A.S.P., 82, 821. Oemler, A. 1976 Ap. J., 209, 693.

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Oemler, A. 1988 A. S. P. Conference Series Volume 5, Minnesota Lectures on Clusters of Galaxies and Large Scale Structure ed. J. J. Dickey (Provo: BYU Print Services). Ostriker, J. P. and Tremaine, S. D. 1975 Ap. J. (Letters), 202, LI 13. Quinn, P. J. and Goodman, J. 1986 Ap. J., 309, 472. Quintana, H. and Lawrie, D. G. 1982 A. J., 81, 1. Richstone, D. 1975 Ap. J., 200, 535. — 1976 ibid 204, 642. Richstone, D. O. and Malumuth, E. M. 1983 Ap. J., 268, 30. Roos, N. and Aarseth, S. J. 1982 Astron. Astrophys., 115, 41. Spitzer, L. 1958 Ap. J., 127, 17. Spitzer, L. and Chevalier, R. A. 1973 Ap. J., 183, 565. Tonry, J. L. 1985 A. J., 90, 2431. Tremaine, S. 1981 in The Structure and Evolution of Normal Galaxies, ed. S. M. Fall and D. Lynden-Bell (Cambridge: Cambridge University Press). Turner, M. S. 1987 in Dark Matter in the Universe, ed. J. Kormendy and G. R. Knapp (Dordrecht: Reidel). van Albada, T. S. 1982 M.N.R.A.S., 201, 939. Villumsen, J. 1982a Ph.D. Thesis, Yale University. —, 1982b M.N.R.A.S., 199, 493. —, 1983 ibid. 204, 219. Weinberg, M. D. 1986 Ap. J., 300, 93. West, M. J. and Richstone, D. O. 1988 Ap. J., 335, 532. White, S. 1976 M.N.R.A.S., 174, 19. White, S. D. M. 1978 M.N.R.A.S., 184, 185. —, 1978 ibid 189, 831. —, 1980 ibid 191, IP. —, 1983 Ap. J., 274, 53. —, 1982 in Morphology and Dynamics of Galaxies, ed. L. Martinet and M. Mayor (Sauverny: Genera Obs).

DISCUSSION Richstone: I do hope that during this session there will be more discussion about the importance of subclustering, because I think it has tremendous impact on how to compute the dynamical evolution of clusters. Oegerle (moderator): Would anyone care to comment? Fitchett:

I think subclustering is incredibly important (laughter).

Giacconi: There is some data that I didn't hear you mention in this respect, that's from Forman and Jones, and I think Bill is here so . . .

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Forman: Yes, as fax as subclustering goes, I was going to wait until I got my chance to talk. I think there is lots of subclustering seen in the X-rays and I'll show you some pictures of it, and then also give you the statistics of it for a sample of 225 images. Giacconi: So, the presence of subclustering is independent of the state of dynamical evolution? Richstone: Yes, it is, at least, judging from the observational data. Owen: Sort of along that same line, based on your arguments about tidal radii, are you bothered by the existence of multiple D galaxies in the same cluster which violates tidal limitation? Is that the same as subclustering from this point of view? Richstone: No, I don't think so. Do they really violate it? Owen: Well, I'm asking it as a hypothetical question. I'm not arguing about whether it is true or not, but there certainly are people who report more than one D galaxy in a cluster. Richstone: Yes. Beers: The majority of those are resolvable, as they have other things around them. So, I mean the simple interpretation is that those D galaxies develop within their own lumps, and the lumps are merging. Now, I suppose if you had a single lump, right, which had three or four big halo galaxies, all of which were displaced from the velocity center, one might imagine a problem but I don't think that's happened. Richstone: Let's see. I still don't entirely understand the question. Which tidal limit were you referring to? Owen: Well, you keep referring to the core radius, finding an object which has more than a tenth of the tidal radius. Richstone: Right. Well, of course, now if the core radius is around 200 kiloparsecs, that means you could have an object as large as 40 kiloparsecs in diameter. That's a pretty impressive D galaxy. Burns: So, the answer is that will be a problem, you are saying. Richstone: It would be a problem getting it there. Once it's in the core, it's safe. Evrard: But aren't the effective masses of your luminous particles much larger than you would expect? Richstone: Sorry, which of the calculations which I've done are you referring to? Evrard: The N-body simulations in which the luminous material exhibits significant segregation . . . Richstone: You mean the work with West?

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Evrard: That's right. The masses are much larger and would be consistent with the tidal limitation. Richstone: Yes, indeed they are. On the other hand, what's going on in that case is at a very early stage and all the action is prior to the cluster collapse. It's all in the small sub-groups. So, I don't think we've done it wrong, due to that reason. Burns: Doug, I wanted to follow up on this observation you mentioned of Abell 1795, this apparently large velocity of three or four hundred kilometers per second for the cD galaxy. There you have an interesting case. With that large a velocity, if it were moving through the tidal field as you mentioned, the halo would be stripped pretty quickly, and the usual argument out of that may be subgrouping but I don't think there's any good evidence of subclustering in that particular case. The X-ray contours are very smooth; the cD lies right in the center. Beers: You're starting to tick off evidence which I think we've already presented; presumably Forman will give us more evidence that this isn't always the case. Burns: Bill Oegerle has a paper recently in which he showed that there is little, if any, evidence in the optical for subclustering. So, you have optical and X-ray. It seems to me that's a very confusing situation. Fitchett: It's very difficult in the case of A1795. It's very difficult to find the subclustering statistically because there are so few galaxies. We need a deeper survey in the cluster core—there are only a few dozen bright galaxies in the center, and that's just not enough to be statistically significant. So, just because you can't find it, it doesn't mean it's not there. We just need more data. Burns: Well, how about the X-rays? I mean the X-ray contour is smooth and centered on the cooling flow. Fitchett: Coma's got smooth X-rays and yet, the X-rays don't necessarily follow the galaxy distribution . Richstone: Well, I think the crucial thing is, what's the mass distribution doing. Weinberg: If there aren't enough galaxies to provide a statistic that shows convincingly that it's not there, I certainly don't think there's enough to argue convincingly that it is. So, we may conclude that we just don't know, but as I understand what I've read of the debate, West, Dekel and Oemler claim that much of the signal of subclustering is consistent with Poisson fluctuations in the number of galaxies, as far as the angular positions on the sky, and I guess I'd like to know if people who think there is subclustering think that the problem is with the statistics that they have chosen or if it's because they're either using different angular data, or it's also taking into account the redshift and X-ray data. Huchra: Okay, I can give you a not very clean answer because it doesn't have a very clean answer. If you actually try to go through the literature and collect up the clusters that have, say, 100 plus redshifts plus good positional data on what's likely to be several hundred cluster members to do adequate maps plus X-rays maps, you'll find you can

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25S

tick off the number of those clusters on the fingers of one's foot, almost (Laughter). They're really only three or four clusters that really have been beaten down on hard enough that we could present convincing cases one way or the other. There are a lot where there are a lot of suggestions but, you know, small number statistics rule. You can't really say anything adequately. Weinberg: So, would you say the answer is that we don't know whether there is substructure in clusters? Huchra: For several clusters, we know for sure. Virgo is a good example, which has several hundred velocities and lots of data from the maps of Sandage, Tammann, Binggeli and company. That we have a pretty good idea. We have some idea of what's going on in Coma. We have some idea of what's going on in Perseus, but then it goes to hell in a handbasket the minute we start going much further away than 10,000 kilometers per second where most of the clusters are. We have some idea that there's something funny going on in Centaurus. If you look at the clusters where we do have a lot of data, which is a small number, ten or less, a very large fraction of those show something going on. Okay, then there's also a question of degree. What do you mean by subclustering? If you look at Virgo and just look within two degrees around M87, you'd be hard-pressed to argue for the existence of subclustering, but if you go out just a little bit further, there's N4472 and all its friends which you can say is another lump. So, the definitions are sometimes soft too. The data is poor. The definitions are weak. Weinberg: But the data on angular positions on the sky are presumably not so poor. Huchra: As soon as you get distant, you start running into background problems. They are very poor. Beers: Yes, the thing to remember is that—on all these maps—you only go maybe one magnitude beyond the knee of the luminosity function. On Dressler's maps you're lucky if you get two magnitudes below the knee. So, what we'd really like to do is go another two magnitudes or so deeper. Forman: From the X-rays, it's pretty easy to see the substructure. 80% of the clusters we looked at have been detected; about 30% of those have multiple substructure. You can really see it though it's not on scales of 5 megaparsecs. It's on scales of either one or two. I think it's pretty clear. Sometimes it correlates very well with the optical galaxy count; sometimes not so well, but I think it's pretty clear that it's there. Gunn: Doug, in your simulations—I unfortunately was not here yesterday—but did you distribute the galaxies in a Poisson fashion? Richstone: Also, the dark matter points. So, they're strewn . . . Gunn: My question is, in the real world, presumably if galaxies were formed from some smoother thing, there is some amount of substructure present due to the spectrum of whatever fluctuations are present, and putting down galaxies at random is a good way to seriously overestimate the small scale noise because a galaxy carves out a chunk of the universe that's proportional to its mass. I think there were a lot of early simulations when people started talking about mergers in which this happened

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because galaxies can't really be Poisson distributed if they're all the same mass in the universe because you can't make two things that are very close together. There just isn't enough mass there. So, what you have to do, it seems to me, is to decide that this is a la peak—this tophat—and put in small scale structure that is consistent with that and whatever spectrum you believe, before you can say anything about the interaction of this primordial substructure with what goes on afterwards. Richstone: Is another way of putting this, that you fear that we have put too much mass in small volumes when there are two galaxies close together . . . Gunn: Yes. Because in the initial conditions, you don't expect the galaxies to come from a Poisson net. Richstone: I suspect then—although obviously what we will do is go home and redo things—but I suspect that that will not change the story too much, because in the development of these simulations, normally the first thing that happens is the galaxy finds the nearest lump in dark matter and goes right to the bottom. Gunn: If you have too much power in the lumps and dark matter, then that's something that won't happen in the real simulations and it makes a great deal of difference. Neal Katz is here, I think, and he looked at this question with regard to galaxy morphology. It makes an enormous amount of difference . . . Felten: You just slow down the time scale? Gunn: No, no, because you're competing—the thing that's competing is the growth of the lumps versus the overall collapse. In order for that to happen, the lumps have to collapse on a significantly shorter time scale. If you have less power in the lumps, that won't happen and the whole thing will collapse as a unit more or less, which is sort of what you expect if the cluster really grows from a three or four sigma perturbation. You expect the overall sort of spherical thing to be dominant. It doesn't say there won't be substructure, but it may well not be dynamically nearly so dominant as these simulations suggest. Peebles: Could you be persuaded also to lower the masses of the galaxies by adding an analytic time variable potential? Richstone: (long pause). Yes, if I can figure out how to do it. (laughter) Evrard: There may be a possible way to rescue your problem with mass segregation, right? When you think of the fact that this segregation mechanism that you're seeing really might come from two effects. One of which is dynamical friction but another of which doesn't have a name yet but it's the hysteresis of things which start out at high binding energy in sublumps which go through, not really violent relaxation but some moderately less violent relaxation and end up in the next level of the hierarchy. That process is dominant, although violent relaxation is not unimportant, but the other process is a dominant mechanism, and if that process is roughly independent of mass, then you might be able to get a sufficient segregation for a wide range of masses just through that mechanism alone. You'd expect that because galaxies form—I mean if you believe galaxies form dissipationally—from lots of gas into local potential wells,

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and they're born at the bottom of potential wells. Struble: Having done a survey of all Abell clusters, it would seem very obvious that probably about 50 percent of the clusters have substructure—but not the kind of substructure that Fitchett is pushing for—you don't see that. Fitchett: I don't want to say I'm wishing for any particular kind of subcluster but I believe that it exists on large scales. It may also appear on small scales too, and that's what's hardest to prove because you've got small number statistics. Oemler: Yes, I just want to say that we never claimed there was no substructure in clusters. Just that it was not as strong as had been claimed before. West: I'd also just like to remind people that just because you see substructure in the distribution of the galaxies, usually people are interested because that seems to imply clusters are dynamically young or just forming, and I don't think that's the case at all. Mike's work yesterday shows that you can have a relaxed cluster which shows clumps in it and so it's still an old system. Similarly, we see galaxies in projection, so I think just because we see substructure, it doesn't mean that clusters have only recently formed.

HOT GAS IN CLUSTERS OF GALAXIES

W. Forman and C. Jones Smithsonian Astrophysical Observatory Harvard-Smithsonian Center for Astrophysics 60 Garden St. Cambridge, MA 02138

Abstract. This contribution reviews the X-ray properties of clusters of galaxies and includes a brief summary of the X-ray characteristics of early-type galaxies and compact, dense groups. The discussion of clusters of galaxies emphasizes the importance of X-ray observations for determining cluster substructure and the role of central, dominant galaxies. The X-ray images show that substructure is present in at least 30% of rich (Abell) clusters and, hence that many rich clusters whose other properties are those of dynamically young systems, suggests that most cluster classification systems which utilize a property related to dynamical evolution, require a second dimension related to the dominance of the central galaxy. X-ray surveys of rich clusters show that central, dominant galaxies are twice as common as optical classifications suggest. The evidence for mass deposition ("cooling flows") around central, dominant galaxies is reviewed. Finally, the implications of X-ray gas mass and iron abundance measurements for understanding the origin of the intracluster medium are discussed.

1. HOT GAS IN GALAXIES, GROUPS, AND CLUSTERS Hot gas has been been found to be commonly associated with both individual early-type galaxies and with the poor and rich clusters in which they lie. Although this presentation will concentrate on the hot gas in rich clusters, we briefly describe the characteristics of individual galaxies and groups, as well as clusters since their evolution and present epoch properties are interrelated. Recent reviews of X-ray properties of clusters of galaxies include Forman and Jones (1982) and Sarazin (1986). Optically bright early-type (E and SO) galaxies, outside the cores of rich clusters, have X-ray luminosities from 10—10 ergs see" (in the 0.5-4.5 keV band) which arise from thermal radiation from hot gas at temperatures around 10 K. The gas masses of the individual galaxies lie in the range ~ 10—10 M© (see Forman et al. 1979; Nulsen, Stewart, and Fabian 1984; Forman, Jones, and Tucker 1985; and Canizares, Fabbiano, and Trinchieri 1987 for details). An example of the X-ray observations of two early-type galaxies is shown in Figure 1. The presence of relatively large amounts of hot gas in these galaxies has demonstrated the existence of massive dark halos to gravitationally

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confine the hot gas (Forman, Jones, and Tucker 1985; Fabian et al. 1986; Mathews and Loewenstein 1986; Sarazin and White 1988). Estimates of the mass-to-light ratio for some galaxies exceed 100 (in solar units).

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•; t • .

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Figure 1. X-ray contours are shown superposed on the optical photographs of N499 and N507. The X-ray emission around these two galaxies is typical of optically bright E and SO galaxies. The large gas masses imply that the gas must be in quasi-hydrostatic equilibrium since if the gas were being expelled in a wind the sweeping time is so short that the mass replenishment rates needed to maintain the present X-ray luminosity would be 10-100 times the rates predicted. The contribution to the X-ray luminosity of early-type galaxies from discrete sources, like those seen in our own galaxy (e.g., neutron star binaries, supernova remnants), is uncertain. Estimates have been derived using observations of Cen A and the bulge of M31 (Forman, Jones, and Tucker 1985; Trinchieri and Fabbiano 1985). In optically faint early-type galaxies (below M# = —19), discrete sources may be the dominant source of X-ray emission since these galaxies may have sufficiently small masses that they cannot gravitationally bind the hot gas. However, no discrete sources have been resolved in any early-type galaxy. Compact (dense) groups of galaxies (notably those selected by Morgan, Kayser, and White 1975 and Albert, White, and Morgan 1977), have predominantly early-type galaxy populations and are bright in X-rays (Schwartz, Schwarz, and Tucker 1980; Kriss, Cioffi, and Canizares 1983). These groups have gas masses of ~ 10 — 10 M© (within ~ 0.5 Mpc) and gas temperatures up to a few 10 K. Luminosities range up to 1044 ergs sec" 1 , well into the region populated by rich clusters. An example of the

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X-ray emission from a compact group is shown in Figure 2. In general, and as the image illustrates for MKW4, the X-ray emission from compact groups is azimuthally symmetric and is centered on the bright D galaxy which dominates the group.

V

Q .. *.

Figure 2. X-ray contours are shown superposed on the optical photograph of the MKW4 group of galaxies (North is up, East to the left). The group has a redshift of 0.0196 and has an X-ray luminosity of 2 X 10 ergs sec . An unresolved source (unrelated to the group) lies to the northwest of the extended emission. Rich (Abell-like) clusters have X-ray luminosities ranging from as low as those of individual bright galaxies up to 1000 times higher: 104^ - 10 45 ergs sec" 1 (Jones et al. 1979; Abramopoulos and Ku 1983; Jones and Forman 1984). Gas temperatures range from a few 10 to 10 K (Mushotzky et al. 1978) and gas masses can exceed 10 M© within the central few Mpc. The gas densities in the cores of rich clusters lie in the range 10 - 10 cm"^ and the inferred cooling times of the gas can be as small as 10^ years (Fabian, Nulsen and Canizares 1982). The optical and X-ray images of A1367 (see Figure 3), a richness 2 cluster, emphasize the differences between the two wavelengths. Optically, A1367 appears as an irregularly shaped cluster whose center is difficult to define. There is a noticeable concentration of galaxies to the northwest and a bright galaxy, NGC3862, which is radio and X-ray luminous, is located to the southeast. In X-rays, the cluster structure is clearly seen as an elongated structure with a broad distribution (large core radius).

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Figure 3. X-ray contours for A1367 are shown superposed on the optical photograph (see Bechtold et al. 1983 for a detailed discussion of the X-ray properties of A1367). The cluster has an X-ray luminosity of 4 X 10 ergs sec within a 0.5 Mpc radius (assuming a distance corresponding to z=0.0213 for HQ = 50 km sec Mpc . The galaxy N3862, in the southeast, is bright in X-rays (Elvis et al. 1981). The source in the northwest (near the bright galaxy N3842) is resolved into two sources by the HRI and each is associated with a quasar (Bechtold et al. 1983 and Arp 1984).

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2. IMPORTANCE OF STUDIES OF THE HOT INTRACLUSTER MEDIUM In rich clusters the hot intracluster medium (ICM) is the dominant, luminous component of the mass, i.e. the gas mass exceeds that in the stellar component of the galaxies in the cluster. Therefore, to understand clusters (and the galaxies in them), we must understand the origin and evolution of the gaseous component. More specifically, studies of the ICM yield information on a rich variety of phenomena including: • Mapping the structure and mass distribution of clusters— Since the X-ray emission emphasizes the potential wells, the X-ray images are relatively insensitive to superpositions of low mass systems. X- ray cluster surveys show that substructure in optically selected clusters is very common and, therefore, that many clusters are dynamically young. • Role of the central galaxy—The X-ray observations of clusters have emphasized the special nature of bright centrally located galaxies (like M87 in Virgo, N4696 in Centaurus) and have suggested the presence of "cooling flows" around central galaxies. • Interactions of gas with radio emitting plasmas—The detection of the ICM and detailed maps have permitted studies related to confinement and morphology of radio emitting plasmas {e.g., WAT and head-tail sources). • Measurement of H o through the Sunyaev-Zel'dovich Effect— Combination of imaging and spectroscopy of the X-ray emitting plasma with radio measurements of the microwave decrement have provided estimates of H o and suggest that the next generation of X-ray observatories {e.g., ASTRO-D, BBXRT, and AXAF) will have adequate sensitivity to yield precise (10-20%) estimates of the value of the Hubble constant for clusters with redshifts up to z ~ 0.5. • Trace large scale structure—Clusters are luminous X-ray sources and are readily identifiable to large redshift (with moderate angular resolution) because of their large physical sizes. Therefore, they can be used to trace the large scale distribution of matter. • Study evolution of clusters with redshift—One of the dominant-factors controlling the X-ray properties of clusters {e.g., substructure and X-ray luminosity) is the gravitational collapse of the cluster system. Therefore, X-ray cluster studies at different epochs can provide information on the initial perturbations from which large scale structures form. • Determine the properties of the X-ray emitting gas at various epochs. The X-ray emitting gas in clusters has been found to contain heavy elements which can only be produced through nucleosynthesis in stellar systems. Thus, studies of the ICM can tell us about galaxy evolution, the IMF of galaxies, the formation efficiency of galaxies in clusters (and groups), and the mass loss history of galaxies. The above list of topics shows the rich variety of problems which can be addressed through studies of the ICM. The X-ray study of clusters has become sufficiently vast that it is no longer possible to review all of the material in a single presentation and, hence, this contribution emphasizes four topics—the dynamical evolution of clusters (and the role of the central galaxy), substructure in clusters, the origin of the ICM, and concludes with a brief review of what we can expect to learn from future X-ray astronomy missions.

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3. DYNAMICAL CLASSIFICATION OF CLUSTERS OF GALAXIES AND THE ROLE OF THE CENTRAL GALAXY The parameters in most cluster classification systems can be related to dynamical indicators of cluster evolution. This provides a unification of a variety of properties in a simple framework. In such a scheme, long dynamical times are associated with clusters having low mass densities, low velocity dispersions, a cool (few times 10 K) intracluster medium, irregular galaxy and gas distributions, and usually large populations of spiral galaxies. More dynamically evolved systems (those with shorter dynamical timescales) have higher mass densities, higher velocity dispersions, hot intracluster gas temperatures, regular galaxy and gas distributions, and small populations of spiral galaxies. Some of the classification parameters are tied closely to dynamical indicators. For example, increases in central galaxy density and X-ray luminosity are related to the deepening of the gravitational potential during cluster collapse and relaxation. Other properties such as spiral fraction are related less directly through correlations such as those of Dressier (1980) who showed that galactic populations are related to the local density which in turn is related to dynamical evolution. Classification systems based on cluster morphology (Zwicky et al. 1961-1968; Rood and Sastry 1971), the dominance of the central galaxy (Bautz and Morgan 1970 and Hausman and Ostriker 1978), the galaxy population (Oemler 1974), and others (see Bahcall 1977a for an excellent summary) can all be interpreted in terms of a dynamical indicator. The X-ray observations of rich clusters have demonstrated the need for additional complexity in this otherwise simple, linear classification scheme. The added complication arises from the presence of massive dominant galaxies in clusters whose other properties—low X-ray luminosities, cool gas temperatures, high spiral fractions, low velocity dispersion, irregular galaxy distributions—are indicative of dynamical youth. Examples are Virgo, Centaurus, A262, and A1060 whose dominant galaxies are M87, N4696, N708, and N3311. These clusters are often of late Bautz-Morgan type with two or more bright galaxies of comparable optical luminosity (e.g., M87 and N4472 in Virgo), but X-ray observations suggest one of the galaxies is a unique object and is centrally located in the cluster potential. The best studied examples of massive galaxies in otherwise dynamically young clusters are M87 and N4696 which were studied in detail by Fabricant and Gorenstein (1983) and Matilsky, Jones, and Forman (1985). Table 1 lists the properties of the galaxies and their respective clusters. Very large masses are found within even a few hundred kpc of these galaxies. The presence of massive central galaxies in clusters whose other properties are those of dynamically young systems suggests the addition of a second dimension to the cluster classification system, related to the dominance of a central galaxy (Jones and Forman 1984). Figure 4 and Table 2 illustrate the two-dimensional classification system. 3.1 Substructure in Clusters One of the indicators of the dynamical state of a cluster is the degree of substructure as demonstrated by either the galaxy or the gas distribution. The X-ray observations have been found to be particularly suited to studies of the structure of the cluster potential. Figure 5 shows X-ray isointensity contours of four clusters— SC0627-54, A98, A1750, and A115—each of which had been selected optically as a single system. The figure shows that each cluster consists of two separate structures. Subsequent detailed optical observations of the galaxy distributions confirm the bimodal nature

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Table 1. Properties of M87/Virgo and N4696/Centaurus

X-ray Luminosity ° ( ergs sec ) Gas Temperature (keV) Mass Deposition Ratec(Af© yr~l) Gas Mass d (M 0 )within 200 kpc Spiral Fraction6 Velocity Dispersion-^ (1-o-s; km sec" 1 ) Total Mass " (M 0 )within 200 kpc

M87/Virgo

N4696/Centaurus

3 x 1043 2.4 1-10 1 x 1012 55% 673 3 x 1013

7 x 1043 2.1 ~50 2 x 10 12 45% 507 2 x 1013

"Jones and Forman 1978 scaled to 2-6 keV; Lea et al. 1982. Matilsky Matilsky, Jones, and Forman 1985 and Fabricant and Gorenstein 1983. c Matilsky Matilsky, Jones, and Forman 1985 and Stewart et al. 1984. Matilsky Matilsky, Jones, and Forman 1985 and Fabricant and Gorenstein 1983. e Bahcall 1977b. •^Lucey, Dickens, and Dawe, 1980 and Danese, DeZotti, and di Tullio 1980.

Table 2. Two-Dimensional Cluster Classification No X-ray Dominant Galaxy (nXD)

A1367

A2256

Large core radii

X-ray Dominant Galaxy (XD) Low X-Ray Luminosity (< 10 ergs sec High Spiral Fraction (> 40%) Low Central Density Cool Gas (~few keV) Irregular Gas and Galaxy

)

High X-ray Luminosity (> 10 ergs sec ) Low Spiral Fraction (< 40%) High Central Density Hot Gas (> 6 keV) Regular Gas and Galaxy Distributions

A262 Distributions

A85

Small core radii

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Figure 4. The X-ray contours of four clusters (A1367, A262, A2256, and A85) are shown superposed on optical photographs. These illustrate the cluster classification described in Table 2. The top and bottom pairs of clusters are at comparable distances. The pair of clusters on the right have bright central galaxy (XD). The X-ray emission is centrally concentrated with a small core radius for the clusters on the right compared to the nXD systems on the left. of these clusters and for A115 suggest a third component (Beers, Huchra, and Geller 1983). Furthermore, each of the pair of subclusters have redshifts consistent with being members of a single collapsing system (see Forman et al. 1981 and Henry et al. 1981). Beers, Geller, and Huchra (1982) have analyzed A98 in detail using extensive spectroscopic observations and argued that the two subclusters are presently falling toward each other and will merge on a time scale of roughly 10 years. Other X-ray cluster images show still richer substructure. For example, A514, shown in Figure 6, has at least three mass condensations.

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3.2 Frequencies of Cluster Types We have surveyed a sample of ~ 250 clusters with redshifts less than about 0.15 which were observed by the Einstein Observatory (Jones and Forman 1989a). Of these clusters about 185 are detected and 149 are bright enough to "classify". Of the sample which can be classified, 70% have single peaks and 30% have more than one peak (i.e. multiple substructures). Of this 30%, two-thirds are primarily bimodal (show double structures as in Figure 5, although some may have a considerably weaker third peak). One-third of the multiple-peaked systems are complex with more than two structures (as in Figure 6 and 7). We also can estimate the fraction of clusters that have central dominant galaxies (XD systems) since Jones and Forman (1984) showed that small core radius clusters have central dominant galaxies. From a sample of about 100 clusters which are sufficiently bright to allow the determination of surface brightness profiles, 40% have small core radii with bright galaxies at their centers. However, only 20% are optically classified as

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Figure 7. /in X-ray isointensity contour map of the Einstein IPC image around A3562 is superposed on an optical photograph. This 6500 second observation shows three extended regions of cluster-like X-ray emission. The eastern most region is coincident with A3562. Note that it appears as two separate sections because of the obscuration of the IPC window support structure (dashed line). The remaining two cluster-like structures were not distinguished optically although they clearly represent major concentrations of matter. The cluster to the west lies on the edge of the IPC field of view. The X-ray observations can provide a complementary view of large scale structures and more readily distinguish substructure in the gravitational potential than do the optical observations. Bautz-Morgan types I and I-II. Thus, only a relatively small percentage have a dominant galaxy based on optical observations, while the X-ray observations suggest that twice as many clusters have central dominant galaxies. This difference in the number of clusters with dominant central galaxies arises since the two brightest galaxies in a considerable number of clusters have comparable optical luminosities and, hence, are of late BautzMorgan type. However, only one of the galaxies is centrally located in the cluster (e.g., M87 in Virgo and N708 in A262).

3.3 XD Clusters and Mass Deposition As described above, clusters with massive dominant, central galaxies (XD clusters) are common and are easily seen in X-rays because of their high central surface bright-

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ness. Considerable evidence has accumulated that the hot X-ray emitting gas in the cores of these clusters is cooling around these central galaxies (see "Cooling Flows in Clusters and Galaxies" ed. A. Fabian for an extensive collection of reviews and papers on all aspects of cooling gas in galaxies and clusters). The evidence for cooling gas is threefold: • observed X-ray surface brightness profiles imply high central gas densities and therefore short cooling times, • X-ray spectroscopic observations show the presence of gas in the cores of these clusters with temperatures up to 10 times lower than the cluster mean, • optical observations show the presence of emission line filaments in clusters where there is evidence for cooling gas. The surface brightness profiles of clusters have been analyzed in two ways. First, comparison of cluster models to the profiles (Jones and Forman 1984) show that some clusters exhibit an excess of X-ray emission in their cores over a simple function which adequately describes the profiles at large radii. The excesses originate within a radius where the gas cooling time is comparable to a Hubble time. These excesses are not found in symmetrical clusters where the central gas density is low (and hence the cooling time of the gas is long). Also, the excesses occur in clusters which have a central dominant galaxy. A second method of analysis uses a deprojection method to determine the gas temperature and density profile, by assuming a gravitational potential (Fabian et al. 1981; Stewart et al. 1984; Arnaud 1988). The most complete study of mass deposition in clusters is that of Arnaud (1988) who analyzed 103 single-peaked clusters from the Einstein survey. He found that 40% of these single-peaked clusters have central cooling times less than 2 X 10 years and that of these cooling clusters, 20% have inferred mass deposition rates exceeding 100 M©yr . The mass deposition rates derived from this method correlate well with the excesses measured from the first technique (Stewart et al. 1984). These surveys show that this phenomenon is widespread and can potentially deposit enormous amounts of material. The strongest evidence for cooling gas, although from a smaller number of clusters, comes from the X-ray spectroscopic observations. Different instruments have been used to sample emission from different temperature regimes. Detailed analyses yield mass deposition rates which are in agreement over a wide range of temperatures. The best studied example is Perseus (NGC1275) where emission from gas at T ~ 5 x 106K implies mass deposition at a rate of 200 MQ yr~ *. The analysis of emission from gas at ten times higher temperatures yields comparable mass deposition rates (120 MQ yr~ ; Mushotzky and Szymkowiak 1988 and Canizares, Markert, and Donahue 1988). Both estimates agree with that derived by Arnaud (1988) from the image deprojection technique. In addition to the evidence from the X-ray observations for cooling gas, extensive optical emission line observations have been made which show gaseous filaments in and near the central dominant galaxy at temperatures around 10,000K (e.g., Cowie et al. 1983; Hu, Cowie, and Wang 1985; Heckman et al. 1989). In general, extensive emission lines are found in clusters with large inferred mass deposition rates (see e.g., Heckman et al. 1989). Objections to the existence and magnitude of the rates of mass deposition around central galaxies in clusters arise from three major considerations: • the inferred mass deposition rates are large and can exceed 100 MQ yr~* (PKS0745, A1795, A2597, Hydra A), • the final repository of the cooling mass, assumed to be low mass stars, is unobserved,

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• the X-ray and optical emission-line estimates of the amount of cooling gas are inconsistent since the X-ray observations require the matter to be deposited over a wide range of radii (roughly m a r ) while the emission lines are concentrated to the cluster center and the emission lines require 100-1000 recombinations per cooling atom. Various heating mechanisms, such as thermal conduction and supernova explosions, could reduce the mass deposition rate. However, detailed calculations have not been successful in modelling the observed temperature distributions and reducing the mass deposition rate. For example, Bregman and David (1988) showed that the mass deposition rate could be reduced by factors of about 3 if the conduction efficiency factor is fine-tuned from cluster to cluster which they found to be implausible. Supernovae also could reduce the mass deposition rate but would require 3-5 supernovae yr , which are not observed, to produce reductions by a factor of 10. The evidence for large mass deposition rates is considerable. As Fabian (1987) has emphasized, either extensive mass deposition occurs around central cluster galaxies and produces low mass stars (considerably less than 1 M Q ) or there is a heating mechanism operating in these clusters which is poorly understood and can provide 10 —10 ergs over the lifetimes of these systems. While gaps remain in our understanding of large mass deposition rates in clusters, the alternatives remain poorly developed and unattractive. 4. T H E O R I G I N O F T H E I N T R A C L U S T E R M E D I U M The discussion above has illustrated the importance of X-ray observations of the intracluster medium for understanding the overall properties of clusters. In addition to providing information on the structure and morphology of clusters, the amounts of accreting material, and the total mass distribution, the intracluster medium is important in its own right. The ICM is a major baryonic component of the cluster being equal or greater in mass than the stellar matter. It is, thus, of particular importance to determine the origin of such a large fraction of the known baryonic mass of the cluster. Two opposing models for the origin of the ICM are those that suggest the gas is either primordial or that it has been ejected from galaxies. The primordial origin of the ICM assumes that the gas has not undergone nucleosynthesis in stellar systems but has fallen into the gravitational potential of the cluster (e.g., Gunn and Gott 1972). Alternatively, galaxy formation could have been 100% efficient and the observed ICM would then have been ejected or stripped from galaxies comprising the cluster. As discussed below, a combination of the two processes is most likely. The large fraction of the luminous baryonic matter in the ICM implies a primordial component of the ICM (in most standard scenarios) and the abundances of heavy elements (25% to 50% of the solar value) in the ICM require injection of enriched material that has undergone nucleosynthesis in stellar systems. To begin to address the questions of the origin of the ICM and the efficiency of galaxy formation in different environments, it is useful to compare the ratio of gas mass to stellar mass in a variety of systems ranging from groups of galaxies to rich clusters. It is well known that the mass-to-light ratio increases with the size of the system (e.g., Blumenthal et al. 1984). However, from poor to rich clusters the fraction of X-ray emitting gas to virial mass remains relatively constant (~ 10% within the central five core radii; Abramopoulos and Ku 1983). Therefore, the ratio of gas mass to stellar mass should increase from the poor to rich clusters. As shown in Figure 8,

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in groups of galaxies the gas mass is approximately equal to the stellar mass, while in very rich clusters, the gas mass exceeds the stellar mass by as much as a factor of six.

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Figure 8. The ratio of the gas mass as measured by the X-ray observations to the stellar mass is plotted against the temperature of the gas. The gas and stellar masses are evaluated within five core radii. The temperature of the gas reflects the gravitational potential of the system. The increasing ratio of gas mass to stellar mass with increasing gas temperature suggests a decreasing efficiency of galaxy formation (conversion of gas to luminous stellar matter) between groups and rich clusters (see David et al. 1989a for details). The observational material needed to add additional data points to Figure 8 is only just becoming available and more data are needed to confirm the relation. Oemler (private communication) has obtained a similar result for a different set of clusters by comparing optical luminosity and X-ray gas mass. He found that the dependence of gas mass on optical luminosity could be described by a power law with an exponent considerably in excess of unity. The discovery of heavy elements in the ICM (Mitchell et al. 1976 and Serlemitsos et al. 1977) revealed an entirely new aspect to the study of the ICM—one which is crucial in determining its origin. Since heavy elements can be produced only through thermonuclear reactions in stars or by supernovae, the discovery that the intracluster medium was enriched in iron required that material processed through stars be ejected into the ICM. The near solar abundance of the ICM measured by early X-ray experiments (see Mushotzky 1984 for an early summary and Edge 1989 for a recent compilation) led to the suggestion that a large fraction of the material in the ICM was

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ejected from galaxies (e.g., DeYoung 1978). While the enriched material must come from the galaxies (in the absence of a Population III stellar component), more recent studies suggest that the bulk of the ICM of a rich cluster could not have originated within the galaxies because its mass is several times larger than the mass of the galactic stellar component. Thus, the bulk of the ICM in rich clusters must be "left over" from the formation of the galaxies. In particular, numerical modelling of the hot gaseous coronae around elliptical galaxies shows that over a Hubble time these galaxies can contribute only a fraction of their stellar mass to the IGM (David, Forman, and Jones, 1989b). While such an analysis constrains the contribution from present epoch galaxies to the ICM, we can use the ratios of the stellar mass to gas mass in groups and clusters to limit both the mass lost to the ICM from present epoch galaxies as well as any contribution from early, Population III stars. Specifically, so long as the IMF's and the Population III component of groups and clusters are similar and no gas is lost from the system, then we would expect the stellar contribution to the ICM per unit stellar mass to be the same in all groups and clusters. The approximate equality of gas mass and stellar mass in the low X-ray luminosity Morgan groups (MKW4, MKW9, and AWM4) limits the contribution to the ICM by all stars to no more than the present stellar mass. Thus, in the richest clusters where the gas mass is three to six times the stellar mass, only a small fraction of the ICM could have been produced in stars. In the rich clusters, most of the gas in the intracluster medium must be primordial. 4.1 Implications of the Correlation of Mga8/M8teuar

with Tga8

Although the correlation between Mgas/Mgteiiar a n ( l Tgas is based on only a few systems and requires further confirmation, we briefly explore the possible implications of the correlation.

4.1.1 Efficiency of Galaxy Formation The ratio of the gas mass to the stellar mass, Mgas/MSfenar, shown in Figure 8, can be related to the efficiency of star formation. We assume a scenario in which the luminous matter (stars and the ICM) form the bulk of the baryonic material and the remainder of the virial mass is in the form of hot or cold dark matter. Then, as long as groups and clusters are closed systems which do not lose their intracluster material, the efficiency of galaxy formation, the conversion of baryons from gas to stars in galaxies, can be written as c = MsteUar/Mlum (2) where M\um = Msteuar + Mgas, or equivalently as ^ ( l + AW^e/Zar)-1

(3)

(assuming the expelled gas from galaxies is small and can be neglected). Thus by measuring Mga8/Mstenar, we can study the efficiency of star formation in systems ranging from groups to rich clusters. Our analysis shows that the star (and galaxy) formation efficiency ranges from 50% for groups to as little as «15% for rich clusters. If all the ICM in groups is gas ejected from galaxies, and we use this injection rate for all clusters, then the galaxy formation efficiency would be 100% for groups but lower for rich clusters (as low as «17% for Mgas/^stellar = 6 to as high as «50% for

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j = 3). Although the amount of luminous material (gas+stars) remains relatively constant for all clusters (Blumenthal et al. 1984), the efficiency of galaxy formation decreases as one moves to richer systems. In other words although the richest systems obviously produced more galaxies, their efficiency of galaxy formation was lower. Interpreting the ratio of gas mass to stellar mass as a measure of galaxy formation efficiency requires that clusters be "closed" systems, that is, no material may be added or lost. The gas in the ICM is enriched both during an early phase of massive star supernovae (Type II) and continuing through the present with primarily Type I supernovae and mass loss from older stars. Since the gravitational potential of poor clusters is sufficient to bind the enriched material ejected in supernova winds driven from the galaxies, none of the material in the ICM should be lost from these systems. Furthermore, based on the computed enrichment rates, extensive amounts of matter could not have been expelled by the galaxies and entirely lost from poor and rich clusters if their ICM's are to have significant heavy-element abundances. Therefore the change in the ratio of gas mass to stellar mass with cluster richness cannot be explained by a loss of hot intracluster material from the groups and poor clusters. The relative constancy over rich and poor clusters of the fraction of the cluster virial mass made up by luminous material (stars and gas) also supports the notion of a "closed" system.

4.1.2 Correlation of Iron Abundance with Tgas As described above (see also Jones and Forman 1989b and David et al. 1989a) the increases from unity in groups and ratio of the gas to stellar mass, Mgas/M^enar, poor clusters with low temperatures (~ 2 keV) to values of 3-6 in systems with high gas temperatures (6-10 keV). This correlation, combined with an understanding of the production of heavy elements, predicts a correlation of heavy element abundance with gas temperature. The groups which are luminous X-ray sources are dense systems and have stellar populations comparable to rich clusters (Morgan Kayser, and White 1975). Also, the correlation of galaxy population with local density (Dressier 1980, and Postman and Geller 1984) supports the similarity of the galaxy populations in the groups and clusters. Therefore, the production of heavy elements should be directly proportional to the stellar light, or equivalently stellar mass, since comparable populations will have similar mass-to-light ratios. Thus, the larger the ratio of gas mass to stellar mass, the more dilute the stellar products like iron. Since Mgas/Msie[iar increases with increasing Tgas, we predict that hotter clusters (those with larger Mffa«/Afs<e//ar) will have lower iron abundances than cooler clusters. This prediction assumes that the clusters and groups are closed systems, i.e. no gas is expelled or accreted. Figure 9 shows quantitative predictions for the correlation of iron abundance with gas temperature. The two solid curves are derived by taking a simple parameterization for the dependence of Mgas/Msteuar on Tga8 and assuming that enriched material is expelled from galaxies only during an early wind phase during which Type II supernovae can readily drive a galactic wind (see David, Forman, and Jones, 1989b). The two curves assume different initial mass functions (the upper curve has a power law exponent a = 2 and the lower curve has a = 2.5). Note that an amount of enriched material equal to that expelled in the wind is produced by stellar evolution and could be liberated by ram pressure stripping. The present estimates of supernova yields can explain the observed heavy element abundances in the intracluster gas as Figure 9 shows. The ejected gas is extremely enriched and is diluted to the observed values by mixing with

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MTRACUJSTER GAS TEMPERATURE (X»V)

Figure 9. The iron abundance (as a fraction of the solar value) is plotted against gas temperature. The data are taken from Henriksen (1985), Hughes et al. (1988) and Arnaud et al. (1987). The smooth curves are predictions based on a parameterization of the relation between Mgas/Mstenar and Tgas as well as a model for the evolution of stars with two different initial mass functions. the predominantly primordial component of the intracluster medium. The assumption that groups and clusters are closed systems (i.e. gas is not expelled or accreted in significant quantities) can be tested by observing clusters with progressively lower temperatures. If ejection becomes important below some temperature, Tcrn, then one would observe an increasing heavy element abundance from the hottest clusters down to those with temperatures equal to Tcru. Below Tcrn, the winds would serve to expel enriched material and the abundance would decline (or remain constant) as the gas temperature decreases further. The present measurements of iron abundances are too inaccurate to verify the above model or test possibilities for the origin of the ICM. Mushotzky (1984) and Henriksen (1985) summarize present results. For rich clusters, Henriksen reports a possible correlation of decreasing iron abundance with increasing gas temperature, as predicted, but the data are not sufficiently precise to yield quantitative results. Those observations were for only quite luminous clusters (Lx > 2 x 1044 ergs sec" 1 ) while in general we expect the abundances to be highest in the low luminosity clusters. Hughes et al. (1988) have measured a precise iron abundance of 22% of the solar value for the rich Coma cluster. To adequately test for differences in abundances, it is particularly important to obtain comparable measurements for low temperature (high galaxy formation efficiency) systems. By determining accurate values of the heavy-element abundances of the ICM in both poor and rich clusters, one could better investigate the properties of the IMF (e.g., exponent), the efficiency of galaxy formation, and the origin and enrichment of the ICM. A precise determination of the heavy element abundance of the intracluster medium for a sample of clusters ranging from groups to rich clusters has implications for the amount of material in the ICM that must be primordial. In particular, determining a high solar abundance for the ICM in Morgan groups, as suggested

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by the arguments above, would confirm that the origin of most of the hot gas in rich clusters must be primordial.

4.1.3 The Energy Content of the ICM The changing ratio of gas mass to stellar mass also will affect the energy (or temperature) of the ICM. By measuring the surface brightness profiles and independently by measuring the ratio of the velocity dispersion to the gas temperature, one can estimate the energy per unit mass of the galaxies compared to that of the gas. From the surface brightness profiles, this value for rich clusters is generally ~ 2/3. The values calculated from the measured velocity dispersions and gas temperatures have a wider range (but see Flanagan (1988) who suggests a resolution for the Perseus discrepancy). By comparison to rich clusters, the surface brightness profiles for hot gas around single dominant cluster galaxies such as M87 and the cD groups such as AWM7 yield a value ~ 1/2 (Kriss, Cioffi, and Canizares 1983; their parameter a = —3/8). This implies that the groups and individual central galaxies have more energy per unit mass in gas compared to the constituent galaxies than do rich clusters. For the groups and poor clusters where the stellar mass is comparable to the gas mass, there may be significant heating of the ICM by the ejected material which may account for the observed difference between the groups and the clusters.

5. FUTURE PROGRESS Present observations do provide some precise quantitative information. For example, we have good estimates of the gas mass as a function of radius. We have a good estimates for the mean iron abundance in clusters with the best value around 20% for Coma. We have high quality images of a large sample of clusters and good integrated temperatures for the brighter clusters. The most poorly known cluster properties are those which require spatially resolved spectroscopic information. For example, the radial distribution of the heavy elements is very poorly known and better observations could provide information relating to the enrichment mechanism and the epoch of enrichment. Similarly, temperature profiles are not known for many systems and hence virial mass determinations (based on gas density and gas temperature profiles) still have large uncertainties. Optical estimates are subject to contamination and sub-structure and X-ray observations seem to provide the most direct method for obtaining detailed mass distributions. Future missions will provide the missing information to expand our understanding of clusters. Questions we can address with future missions like ASTRO-D, AXAF, XSPECT, and XMM, include: • measurements of T(r)—combined with surface brightness profiles (which can be used to determine the gas density profile), the temperature profiles will give precise estimates for the gravitating mass as a function of radius. Assuming hydrostatic equilibrium and spherical symmetry, the gravitating mass is given by

v

fdlnp

dlnTg

where p is the gas density and r is the radial distance from the cluster center. Only M87 and Centaurus (NGC4696) have measured density and temperature gradients (Fabricant and Gorenstein 1983, Matilsky et al. 1985). For most clusters Tgas{r)

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remains unknown (or very uncertain). Thus, ASTRO-D, AXAF, and XMM can add immeasurably to our present knowledge of the gravitating mass distributions which can be directly compared to formation models of clusters. • heavy element abundance determinations - these should provide constraints on some cosmological models, e.g., cold dark matter. • radial distribution of iron—since the stellar light (and therefore mass) declines more rapidly than the gas mass as a function of radius, we might expect to find a radial decline in the iron abundance if the iron originated from now dead stellar systems in the galaxies we see today. Other enrichment scenarios could produce differing radial dependences. • Determine abundances in clusters at a wide range of redshifts —if infall is important, then we might expect abundances to increase with redshift. The dependence of abundance with redshift will provide important information on the epoch of enrichment of the ICM and on the evolution of galaxies which are the most likely source of the enriched material. In conclusion, while considerable advances have been made in understanding clusters through their X-ray emission, the potential of X-ray observations has yet to be fully achieved and awaits the application of spatially resolved spectroscopic observations and studies of clusters at high redshifts.

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Dressier, A. 1980, Ap. J., 236, 351. Edge, A. 1989, Ph. D. thesis, Leicester University. Elvis, M., Schreier, E., Tonry, J., Davis, M., and Huchra, J. 1981, Ap. J., 246, 20. Fabian, A., Hu, E., Cowie, L., and Grindlay, J. 1981, Ap. J., 248, 47. Fabian, A., Nulsen, P., and Canizares, C. 1982, M.N.R.A.S., 210, 933. Fabian A.C., Thomas, P.A., Fall, S. M., and White, R. E. 1986, M.N.R.A.S., 221,1049. Fabian, A. 1988, in Cooling Flows in Clusters and Galaxies, ed. A. Fabian (Kluwer Academic Publishers, Dordrecht), p.315. Fabian, A. 1987, Astrophys. Letters and Comm.,26, 147. Fabricant, D. and Gorenstein, P. 1983, Ap. J., 267, 535. Flanagan, J. 1988, senior thesis, Harvard University. Forman, W., Schwarz, J., Jones, C , Liller, W., and Fabian, A. 1979, Ap. J. (Letters), 234, L27. Forman, W. Bechtold, J., Blair, W., Giacconi, R., Van Speybroeck, L., and Jones, C. 1981, Ap. J. (Letters), 243, L133. Forman, W. and Jones, C. 1982, Ann. Rev. Astr. Ap., 20, 547. Forman, W., Jones, C. and Tucker, W. 1985, Ap. J., 293, 102. Gunn, J.E. and Gott, J.R. 1972, Ap. J., 176, 1. Hausman, M.A. and Ostriker, J.P. 1978, Ap. J., 224, 320. Heckman, T., Baum, S., van Breugel, W., and McCarthy, P. 1989, Ap. J., 338, 48. Henriksen, M. 1985 Ph. D. thesis, University of Maryland. Henry, J.P., Henriksen, M., Charles, P., Thorstensen, J. 1981, Ap. J. (Letters), 243, L137. Hu, E., Cowie, L., and Wang, 1985, Ap. J. Suppl, 59, 447. Hughes, J., Yamashita, K., Okumura, Y., Tsunemi, H., and Matsuoka, M. 1988, Ap. J., 327, 615. Jones, C , Mandel, E., Schwarz, J., Forman, W., Murray, S., and Harnden, F. R. 1979, Ap. J. (Letters), 234, L21. Jones, C. and Forman, W. 1978, Ap. J., 224, 1. Jones, C. and Forman, W. 1984, Ap. J., 276, 38. Jones, C. and Forman, W. 1989a, in preparation. Jones, C. and Forman, W. 1989b, Adv. in Space Research, 10, 209. Kriss, G., Cioffi, D., and Canizares, C. 1983, Ap. J., 272, 439. Lucey, J. R., Dickens, R. J., and Dawe, J. A. 1980 Nature, 285, 303. Mathews, W. and Loewenstein, M. 1986, Ap. J. (Letters), 306, L7. Matilsky, T., Jones, C , and Forman, W. 1985, Ap. J., 291, 621. Mitchell, R., Culhane, J.L., Davison, P.J., and Ives, J.C. 1976, M.N.R.A.S., 176, 29p. Morgan, W.W., Kayser, S., and White, R.A. 1975, Ap. J., 199, 545. Mushotzky, R., Serlemitsos, P., Smith, B., Boldt, E., and Holt, S. 1978, Ap. J., 225, 21. Mushotzky, R. 1984, Phys. Scripta., T7, 157. Mushotzky, R. and Szymkowiak, A. 1988, in Cooling Flows in Clusters and Galaxies, ed. A. Fabian (Kluwer Academic Publishers, Dordrecht), 53. Nulsen, P.E.J., Stewart, G., and Fabian, A.C. 1984, M.N.R.A.S., 208, 185. Oemler, A. 1974, Ap. J., 194, 1. Postman, M. and Geller, M. 1984, Ap. J., 281, 95. Rood, H. and Sastry, G. 1971, Pub. A.S.P., 83, 313.

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Sarazin, C. 1986, Rev. of Modern Phys., 58, 1. Sarazin, C. and White, R. 1988, Ap. J., 331, 102. Scaramella, R., Baiesi-Pillastrini, G., Chincarini, G., Vettolani, G., and Zamorani, G. 1989, Nature, 338, 562. Schwartz, D., Schwarz, J., Tucker, W. 1980, Ap. J. (Letters), 238, L59. Serlemitsos, P.J., Smith, B.W., Boldt, E.A., Holt, S.S., and Swank, J.H. 1977, Ap. J., 211, L63. Stewart, G., Fabian, A., Jones, C , and Forman, W. 1984, Ap. J., 285, 1. Trinchieri, G. and Fabbiano, G. 1985, Ap. J., 296, 447. Zwicky, F., Herzog, E., Wild, P., Karpowicz, M., and Kowal, C. 1961-1968, Catalogue of Galaxies and Clusters of Galaxies (Pasadena: Calif. Inst. Tech. Press).

DISCUSSION Carter: Could I just ask you something about substructure? It seems I'm probably the only person who hasn't asked anything about substructure. You show quite convincingly there's all this structure in the X-ray isophotes, which is fine and I think everyone believes that. But does this necessarily mean there has to be structure in the potential? Clearly there is some structure in the clusters as seen in the galaxies. The galaxies must affect the gas. We know they affect the gas because they're in places where gas focuses on them in cores. So, is that in many instances what's happening in your maps? It's the galaxies actually causing the substructure in the X-ray distribution, more than the X-ray distribution reflecting the potential? Forman: I think there are two things. The X-ray emission behaves a bit differently than the galaxies in the sense that the X-ray emission depends on the square of the density. So it's a little bit easier perhaps to see the small dips in the potential. That was one of the things that Alphonso Cavaliere had emphasized yesterday. It certainly seems to me that the gas should respond fairly quickly to the potential on a sound crossing time, and it seems to me that what you see at some level must be real structure. Carter: Is it anymore than just having a big galaxy there which has got a lot of mass attached to it? Forman: Well, certainly for some of them, there'll be an M87 sitting over here and then many other galaxies over here — that certainly must happen. Other times, you don't see just a single galaxy with nice concentric [isophotes] . . . Giacconi: But there are hundreds of galaxy masses in gas in the blobs. Forman: Yes, you're seeing lots and lots of gas mass. So, it's not as though these are just little. Carter:

How firm are those gas masses? You don't, for instance, know the temper-

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atures — you're assuming a constant temperature for the whole thing, right? Would you reduce that number by having the temperature . . . Forman: You can change it by factors of a few. Carter: But not a hundred? Forman: But not a hundred because otherwise if you crank the temperature down enough, one won't see it. Unknown: It's hard for the tail to wag the dog. Meiksin: I have a related question. Is there any prospect of getting an estimate of the potential well in some of the subclustered regions that may not even have a galaxy near the center? Forman: The only difficulty is that - as was emphasized with Coma - what you really need is the temperature, and so, one can assume average temperatures and get rough ideas. But if you said you wanted to really know, with some precision, how much mass was in this particular clump, you would really want to know at least its mean temperature, and if it's only contributing a tenth of the total luminosity, then you're more uncertain by larger factors because you just don't know what its temperature is over a range of a factor of five to seven. Daly: You initially said that most clusters have a gas mass of a few times 1014M©. Is that observed regularly or are you extrapolating the surface brightness profile to some radius? Forman: If said most, that's probably a bit of an exaggeration. For the ones that are bright, they can be traced out a fair way, which is a fair number. Those are real observed numbers, 1014 or a few times IO^MQ. Daly: What would be more typical numbers? Forman: I would guess they must range down by factors of certainly 10 for the lower luminosity systems. Daly: Okay. Also, how were the 250 clusters selected? Forman: I would say in a reasonably random way (laughter). It's sort of a collection of various people's observing proposals, what they were interested in, people interested in radio objects, more complete surveys of the near Abell clusters but again, I don't think there's any particular biases either in richness or anything strange that you would think of to make lots of substructure certainly. Felten: Are they all Abell clusters? Forman: No. Djorgovski:

Well, in terms of where gas comes from, there is a little noticed but I

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think interesting result by Jim Schombert who may want to say more about it. Optical luminosities of cD envelopes, not the whole thing but just the envelope, seem to be well correlated with external luminosities with their parent clusters and to me that suggests that the same process may be responsible for both, possibly the integral over all dynamical interactions in a cluster. Forman: I think A last air Edge wants to show us something. Edge: The general conclusion of results [from my poster paper upstairs] would be that there isn't a strong correlation but there is a definite variation in the amount of gas to the amount of galaxies between clusters. Giacconi: Let me turn [our earlier discussion] around. What evidence exists that there is a smooth potential for the clusters from any measurement by anybody? In particular, to the speaker, I want to ask the following: is there any cluster for which we have lots of statistics which is consistent with a completely radial and spherically symmetric distribution of gas? Is there any in your data? Have you ever tried to fit and see whether you have any evidence for this? What do you find? Forman: Over the whole cluster, there's probably no cluster that's perfectly symmetrical over its whole face. The one I showed a minute ago . . . Giacconi: Well, some of it might be due to background sources or whatever. Forman: Here's Abell 85 which one would have described as a reasonably round, relaxed system but it's got a little bit of something down there [pointing at slide]. Jaffe: Do you have the temperature of A85? Forman: Abell 85 is like six or seven kilovolts, a fairly hot system. Jaffe: Then just as a very simple question, if that's the temperature, what mass do you need to . . . Forman: I don't know the answer to that, but that's just the mean temperature of the whole thing. Then, there's Abell 2256, which also you can see is reasonably symmetrical but not perfectly nice — and then there are the double [clusters]. Giacconi: But I mean it's also true that the scale height of the gas is larger than the scale height of the galaxies, so eventually the distribution of the potential would be even worse for the galaxies. Burns: This might be a good time to just say a couple words about an unappreciated component of clusters, namely, radio emission coming from individual galaxies because recent evidence suggests there are certain aspects of the gas distribution in clusters that really aren't sampled either in the X-ray or in the optical. One finds a rather nice correlation, particularly for dominant galaxies between X-ray properties and some radio properties. For example, in a poster upstairs, there's some discussion that in cooling flow clusters, one finds that nearly 75% of those cooling flow clusters from a subsample from Keith Arnaud, one finds radio emission. In many instances, that radio

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emission is very compact. It's very steep spectrum, and it has very little or in many cases, no radio jets associated with them whatsoever. On the other hand, if you look at clusters without cooling flows, you find a totally different type of radio morphology: much larger, often with twin jets that extend out 10 to 50 kiloparsecs or so in radius and disrupt very, very suddenly at those types of distances. The whole source goes out to maybe a couple of hundred kiloparsecs. The point there being that it appears there's something very dramatic that is happening at these distances of 10 to 50 kiloparsecs that causes the jets to suddenly disrupt, possibly a shock, possibly going through a sonic point and a cooling flow, but currently with the resolution that exists, one can't see that in the X-ray. Radio is really the only way to currently probe that. So in some sense, the gas mass or the gas distribution, have kind of a hard edge surrounding these dominant galaxies in clusters. Owen: Well, the other thing along that line that may be important to point out is that we are now, in cooling flow clusters, seeing large, Faraday rotations which seem to be most consistent with an important component of this medium being a magnetic field. This is just starting out, but right now that's the simplest explanation for the new observations. I think I'd suggest staying tuned and also people working in the theory of these, be careful about discounting the importance of magnetic fields in this problem. Mushotzky: I'd just like to give a small pitch for the future again - about the problems of clumping. When we have X-ray imaging spectroscopy, we could assume that the clumps are not equal mass, in other words, the depths of the potentials are different. So when we have a picture that has spectroscopy we will be able to see whether there are temperature fluctuations. We'll actually visualize—in addition to the isophotes which may suffer from projection effects—we'll be able to visualize the depth of the potential along the line of sight and we'll actually measure if the clumps are virialized or unreal, that is, if they're just projections like Mike Fitchett was talking about yesterday. So this is a pitch for the future. I hope we'll all be alive. (Laughter) Forman: But just before everybody goes away with a misconception — the clumps, regardless of what the mass might be, whether the temperatures are two kilovolts or five or seven, the clumps there are real clumps of gas. Mushotzky: All I wanted to say is that we can measure . . . Forman: The actual potential. Mushotzky: Yes. We can de-project them and see if they are different colors. Giacconi: Richard, the point that I think has to be made is that it is difficult for people to believe that there's a lot of mass not in those little balls that look black on the Palomar plates. Mushotzky: Oh, absolutely. I think that the X-ray guys should make the strong case that the mass in clusters are in X-ray objects, and the galaxies are little random things (Laughter). West: You said that many of these bi-modal clumps are at the same redshift. Do you

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know how precise that can be? Because if they are separated by say a 1,000 kilometers per second, that's still 10 megaparsecs along the line of sight. So, again, talking about projection effects, just because you see two clumps in X-rays with a relatively small velocity difference, doesn't say that the two can be associated with one another. For man: Is Tim here? Do you want to make a comment about this? Beers: Yes, that's a valid criticism. One has to always be careful when we see that. You want to go and get the redshifts but you have to understand that for most of these systems, if you were to follow the evolution of this two-body system, that's the re-collapse velocity as well. I mean just to say that you measure a difference of a 1,000 kilometers per second, doesn't mean that it's necessarily a projection. There are other factors. West: It doesn't mean that they're bound either because if they're expanding with the Hubble flow . . . Forman: For this particular sample, what we did was we actually took what we thought then was the cluster luminosity function and looked to see whether we could get these as random occurences, if they weren't members of one cluster. This was eight years ago—I don't remember what the number is exactly. But, in the small sample of clusters we looked at, you could only get a very, very small number of objects with small relative velocity separation just at random. It was very, very unlikely. West: But I guess I'm saying that you're estimating 30 percent of the clusters show substructure. It's probably going to be an upper limit because you must have some contamination effect. The real number is probably quite significantly smaller. In fact, I would argue it just the opposite way, and the reason it's a lower limit is because when you look at an IPC image you aim where someone told you there was a cluster. Okay, so, we're already going through a filter, at least with the Einstein survey. You're going through the filter where Abell said "point your X-ray telescope". For example, Abell picked out Abell 98-South. What you're looking at here [pointing to slide] is a very small region of redshift space where you can fit 2 lumps inside the IPC detector, and as an example of just how bad things can get, as you get closer than this redshift range, the poor clusters MKW7 and MKW8, which because M, K, and W gave them two different names, have always been thought of as two different objects. But these can also be thought of as two pieces of a bound entity. If you take the mass that's estimated from the velocity of MKW7 and the mass of MKW8, then you ask the relative velocity of the pieces, they're bound—at least in a two body model. So I would argue that that sort of thing is more how we label what we point a telescope at and we're looking at very low number. Forman: Also, the number of objects where we can actually see the substructure is very dependent on variable exposure times and sensitivies. Okay, this is again another example, as Tim Beers says. We almost didn't see this other piece. Balbus: I'd like to get back to the cooling flows for just a second—just a quick comment. This rather extraordinary result that several hundred solar masses per year are disappearing into low mass stars without a trace, that conclusion is based crucially

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on the assumption that the region of cooling flow under consideration is in a steady state. That, in turn, is based on an argument that the calculated flow time is shorter than a Hubble time and my comment is that one can think of numerous processes that might give you a time scale associated with the cooling flow considerably shorter than a Hubble time, in which case, one has to be very careful about drawing conclusions about mass dropping out of the cooling flows. Unknown: That's not true though because you see cooling flows from such a large number of clusters, that if the time scale is a lot shorter than the Hubble time, it's just extremely unlikely that you would see [this many]. Balbus: You could have some sporadic process going on. Burg: What's the fraction of clusters with cooling flows? Forman: It's a large fraction. Unknown: And those are just the ones we resolved . . . Balbus: Yes, but then you have to worry about—those are obviously selected because they're going to be the brightest as well. The point is that any process that gives you any kind of a sporadic or a non-steady time scale associated with the flow, is going to give you a non-zero dp/dt and the conclusion that mass is disappearing out of the flow, particularly, when I don't believe there's any hydrodynamic basis for such a process, one has to be extremely careful about whether one is observing or one is concluding that mass is disappearing or whether density is just temporarily piling up somewhere. Meiksin: I'd like to interject some comments. I have a poster upstairs. I have performed hydrodynamic computations of flow onto a cD inside a cluster and one question I wanted to address is — I wanted to follow how this flow would reach a steady state and what I found, in fact, is that it doesn't. Instead the gas is still continuing to settle within the cluster potential, and that the argument for the steady state—well, the argument that Steve [Balbus] gave, is maybe correct which is that you want the flow time to be short compared to the age, and in fact, we can't measure the flow time directly. We can measure the cooling time and that's found to be small compared to the age, but on the other hand, that doesn't require you to have a steady state. It only requires you to have some sort of energy source that is comparable to the cooling time and compression within the gravitational well can do that. It doesn't have to be in a steady state to keep the gas hot. Moderator: Claude [Canizares], do you want to make a comment? Canizares: I think Bill said in the case of at least a few of these, one sees gas at temperatures differing by factors of ten, the cooling time of the cool gas in Perseus is probably a factor of 20 or 30 shorter than that of the hot gas because not only is it cooler but the cooling function is more efficient there and your heating mechanisms have to be extremely well-tuned and contrived to be able to counteract that and keep that from getting down to very cool temperatures. Meiksin: Well, in the case of Perseus, where the temperatures may be low, the cooling

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rate is also low and so there it may start approaching a steady state, but 20 or 30 solar masses per year in a steady state in the cluster center is fine. It doesn't contradict any optical or radio observations. Balbus: Well, even in the absence of heating, it's not at all clear that one reaches a steady state solution just when the flow time is shorter than the Hubble time. I think it's a much more complicated system than is appreciated. For man: I don't want to minimize the complications and that's why I emphasized what some of the problems had been but I think to be fair, I think people have worked reasonably hard . . . Balbus: I disagree. (Laughter) Forman: My impression is that people had worked reasonably hard to try to make models to provide the heat. Balbus: I think even if you had, it wouldn't help because if you could balance it, it would still be thermally unstable. I think there's no question but that there's gas cooling in cooling flows. The only question is whether these mass drop-outs that people infer on the basis of radially symmetric steady state flow really describes the situation. I think it's more complicated. Felten: I'd like to ask explicity a question that several early questioners alluded to. Of that 30 percent, with double or multiple peaks, can you account for any significant fraction of them as chance superpositions based, for example, on the cluster-cluster correlation function? This surely is a fairly well posed statistical problem. You must have an idea of whether that's a negligible fraction or not. Forman: Yes, actually, we've just sort of accumulated the sample. I don't actually know what the contamination would be. Giacconi: I actually know this. At the ROSAT level, which is much deeper than this, the chance coincidence is something like 10%. Felten: That's probably on a Poisson basis. But in fact, clusters are correlated. Fitchett: This was calculated because people were interested in explaining the very large separation double quasar lens system. Recently Crawford et al. calculated the chance of superposing two rich clusters because you need two rich clusters to produce this lens. And it turned out you probably have four such systems in the entire sky out to a redshift of 0.5 or so. It's a very small effect. There must be less than four of them in the sample. So, that gives you an answer I think. Moderator: Nick, do you have anything to add? Kaiser: I was just going to say there's another way to do the calculation - just to integrate up the spatial correlation function which Neta [Bahcall] gives and you end up with an excess — neighbors in excess of Poisson of 2 or 3 but that's out at 30 megaparsecs and it grows linearly with radius, so I'd go along with Mike that it's

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probably pretty small. It is the case nonetheless that people have claimed to measure clustering of X-ray clusters, is it not? Forman: Yes, somewhat - but again, at least in the plane of the sky, these guys are pretty close. N. Bahcall: The work that Ofer Lahav did answers that question directly. Maybe he would like to speak? Lahav: Just a comment. In the sample we've used of 53 clusters, we had five pairs with separations smaller than ten megaparsecs, right, and then that gives a correlation function with a correlation length of 20 or so megaparsecs for Ho = 100. And then if one just extrapolates those pairs by saying the ten percent are in pairs of that separation, about one megaparsec just falls on the same curve, but it would be interesting in the future really to extend it with a better statistic. Actually, I'd like to ask a question to the N-body people. Is the separation between pairs—double clusters—is the separation in redshift space smaller or larger than the separation in real space because obvidusly what we measure are redshifts to those objects and one can imagine clusters which are at the same distance but at different redshifts, and vice versa. Is there any clear . . . West: I mean we haven't looked at it directly but I would guess that it's probably smaller because the systems are probably turning around and collapsing. Lahav: What is smaller? West: I would assume that the velocity difference between them would indicate a smaller difference than their actual physical separation because they probably are turning around and collapsing at some point but we really haven't looked at it. Romanishin: I just want to say something about cooling flows—people talk about these hundreds of solar masses which they can't see which bothers a lot of people but there are now at least 15 or so clusters that do show evidence of star formation in the central galaxies, and even if you assume a normal IMF, you get star formation rates of tens of solar masses. So, there's definitely some gas turning into stars in at least some of these clusters. Djorgovski: Well, I thought that is really one of the major objections to this whole scheme is that you see tens but not hundreds of solar masses forming a normal IMF, but there are a couple more difficult things to answer there. One is even if you modified the IMF, you make brown dwarfs or Jupiters or snowballs or anything, you have to dissipate the binding energy — lots of it — and somehow it has to get out somewhere, in some wavelength range, and it's not seen. The second thing is if you coagulate this into anything, you change M/L of these galaxies and they are perfectly normal in M/L. Is there any way to duck out of that? White: Yes, you change the M/L in the center part and the stuff is deposited in a distributed fashion where you don't have velocity dispersion assessing the M/L ratio. Forman: The attraction for some people is that in fact it is not deposited in the center, it's deposited in what looks like the profile of dark halos that people like to put

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around the galaxies. Djorgovski: Then you can't see it form. That's wonderful right? Balbus: Can someone suggest a mechanism for this mass subdivision? Meiksin: I have a question - I don't think you should ignore the simulations that we did of metal enrichment of clusters which has been a puzzle for a long time and the question I have is, did you consider the metals deposited uniformly throughout the cluster, and if you allowed it to be concentrated, would that help you to meet the iron abundance. For man: Yes, those were uniformly mixed with the gas. Unknown: Please speak up! For man: The question was whether or not there is any need to concentrate the heavy elements at the centers. One certainly could do that. It's not obvious until one actually gets better observations and certainly better estimates of what the yields from supernovae are, whether you actually need to do that. And it certainly looks like — there's within factors of a few, certainly enough heavy elements produced from what one would guess happened early on to make what one sees now. White: More about the galactic wind versus stripping and what-not, I was doing more qualitative work than you guys were doing and concluded that protogalactic winds must have occured because of the specific energy that would have been dumped into the intracluster gas. Because the velocity dispersions of cool clusters is on the order of those of individual bright galaxies, you would expect that the energy deposition would be significant in the gas in cool clusters but completely insignificant in the gas in hot clusters. A prediction, if protogalactic winds occurred as opposed to your having the supernovae energy radiated before it got thermalized, would be that you'd expect to see the temperatures of cool clusters higher than you would guess from their velocity dispersions and by the time you got to hot clusters, the temperatures would be what you expect from their velocity dispersions. Also, for cool clusters because the temperature is higher, you'd expect to see the surface brightness profile to be shallower than those in hot clusters if the binding mass is distributed similarly, and that is also observed for the few surface brightness profiles that are published for the cool versus hot clusters. So, that suggests that protogalactic winds do occur which would cause the metals to be distributed homogeneously. Forman: The only comment I would like to make is that, while there are tendencies for the energy deposition to be more significant in the cool clusters rather than the hot ones, it's not obvious whether or not there's enough energy deposit to actually blow significant stuff out of the whole system... White: No, it's not out of the whole system.... Forman: Just out of the galaxies, okay. Moderator: Let's thank our speaker.

HYDRODYNAMIC SIMULATIONS OF THE INTRACLUSTER MEDIUM

August E. Evrard Astronomy Department University of California Berkeley, CA 94720

Abstract. A new, combined N-body and 3D hydrodynamic simulation algorithm is used to study the dynamics of the intracluster medium (ICM) in rich clusters of galaxies. Results of a program to study an ensemble of clusters covering a range of cluster richness within the framework of a cold dark matter (CDM) dominated universe are presented. Comparison with observations for both individual cluster characteristics and properties of the ensemble is emphasized. Predictions arising from the numerical models will be discussed and directions for future work in this area outlined.

1. INTRODUCTION The intergalactic space in rich clusters of galaxies is permeated by a hot, ionized plasma which emits a continuum of X-rays generated by the scattering of energetic electrons off protons and ions. This thermal bremsstrahlung emission is observed to distances / 2 ~ 1 Mpc and spectral fits indicate temperatures T ~ 10 K, so if the gas is confined by the gravitational potential of the cluster the binding mass must be of order M~G~l(kT/fimp)R ~ 3 x 1014 M Q . The X-rays from the extended intracluster medium thus reflect emission from the largest relaxed, self-gravitating entities known in the universe. The issues one would like to understand both observationally and theoretically range from the internal and structural—What are the spatial gas density and temperature profiles? Intrinsic shapes? How do these relate to optical properties? How do they evolve with redshift? —to the global and statistical—What is the expected abundance of clusters as a function of luminosity, temperature or any other observable? How do internal properties correlate for an ensemble? What constraints can be placed on cosmological models using X-ray data? After the discovery of X-ray emission from the Coma cluster (Meekins et al. 1971; Gursky et al. 1971), Gunn and Gott (1972) proposed a spherical infall model which laid much of the groundwork upon which subsequent dynamical models have been based. They suggested the ICM originates in part from gas leftover from the galaxy formation era which collapses and is heated to higher temperatures as hierarchical clustering proceeds from galactic to cluster scales. Along the way, this primordial gas is mixed

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with enriched material ram pressure stripped or perhaps tidally disrupted from galaxies infalling into the deepening potential. In this picture, the distinction between open, irregular clusters which are spiral-rich and compact, regular ones which are spiral-poor is essentially one of age — their collapse times are longer and shorter than a Hubble time, respectively. It was not soon after that numerical calculations were performed to investigate some details of this model. Gull and Northover (1975), Lea (1976), Takahara et al. (1976) and Cowie and Perrenod (1978) performed one-dimensional hydrodynamic simulations in which gas collapsed into a static, spherical potential well representing, perhaps paradoxically, a cluster already in place. The dynamical evolution for most of these calculations is characterized by a shock front forming in the cluster center which propagates outward at nearly the cluster free-fall speed, leaving behind a quasi-static distribution of gas whose total X-ray luminosity varies little after passage of the shock front. (An exception was the work of Lea (1976) whose models showed cyclic oscillations during which the X-ray luminosity varied between 1041 and 10 48 erg s . This behavior has not been reproduced in any other numerical work and has, at any rate, been ruled out observationally (Schwartz 1978).) Cowie and Perrenod (1978) also considered injection models put forward by Yahil and Ostriker (1973) in which it is assumed that galaxies during their formation era swallow 100% of their surrounding gas and later lose a significant portion of it through stellar winds and supernova ejecta. Such models have extra input parameters, the gas injection rate and temperature, which control the overall evolution of the X-ray emitting gas. Perrenod (1978) showed that plausible values for these parameters could produce satisfactory results. In the same paper, Perrenod introduced into the infall picture a time-varying ID potential extracted from White's (1976) N-body model of Coma. The secular deepening of the potential after gas infall into the cluster center caused the total luminosity of this model to increase by a factor of 10 from z = 1 to the present. However, this large increase may be an overestimate because White's model assumed all mass resided in galaxies, hence two-body relaxation drove the central density to values higher than would have been achieved if smooth dark matter were assumed to dominate the cluster mass distribution (Sarazin 1986). The one-dimensional simulations provided useful insight into the collapse and relaxation process. However, the imposed symmetry clearly constrains their range of applicability. In particular, they provide no detailed morphological information. The imaging data gathered by the HEAO-2 (Einstein) satellite showed that clusters come in a variety of shapes which have been broadly categorized by Forrnan and Jones (1982, see also Forman's contribution to this volume). The first attempt at simulating Xray morphologies in the hierarchical clustering scenario was made by Cavaliere et al. (1986). They used collisionless N-body simulations combined with the assumption of hydrostatic equilibrium of an assumed polytropic gas to produce "snapshots" of the cluster X-ray emission. Their maps with nearly isothermal gas (7 = 1.1) resembled the Einstein images of real clusters. In particular, they were able to clearly demonstrate the link between morphology and dynamical state as suggested by Gunn and Gott (1972). This paper will review results from a new set of simulations performed using a combined N-body and 3D hydrodynamics algorithm (Evrard 1988) which selfconsistently computes the dynamical evolution of a coupled system of baryonic gas and collisionless matter. The aim of the project is two-fold. The first is to investigate the dynamical evolution of clusters treating the gas and collisionless material selfconsistently in three dimensions. The second is to produce a simulated catalogue of

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such clusters in a prescribed cosmological setting, the intent being to use statistical properties of the ensemble as constraints on the theoretical model.

2. THEORETICAL OVERVIEW The picture for large-scale structure formation assumed in this work is a more-orless "standard" cold dark matter model in which the bulk of the matter in the universe is in some weakly interacting, presently unidentified form (Peebles 1982; Blumenthal et al. 1984; Davis et al. 1985; Kolb and Turner 1990). The principal cosmological parameters are taken to be 0 = 1, 06 = 0-1, Ho = 50 km s" 1 Mpc" 1 , A = 0

(1)

reflecting an older, closed universe with small baryonic fraction and zero cosmological constant. The N-body studies of Davis, Efstathiou, Frenk and White (1985, see also reviews by Frenk 1987 and Davis and Efstathiou 1988) coupled with the idea of "biased" galaxy formation (Kaiser 1984) appear capable of reproducing a wide range of observational data. Although not perfect, the model has received extensive attention in recent years primarily because of its predictive power. Although the statement that there are "no free parameters" in the theory is not entirely true, most of the controlling parameters are known to within a factor of two. A major source of uncertainty is the normalization of the spectrum, typically expressed as the present rms linearly extrapolated level of fluctuations in a sphere of radius 16 h^Q Mpc. ' In this work, I will assume
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A fair amount of star formation could have commenced in dwarf galaxy scale halos collapsed at redshifts z Z 5 (White 1989; Evrard 1989a; Carlberg and Couchman 1989), almost ~ 10 10 yr before cluster formation and need not have been concentrated solely in bright galaxies. Hence, the "proto-ICM" could have been enriched to a level perhaps comparable to roughly half-solar observed levels. Ram pressure stripping of enriched gas from infalling galaxies will also contribute, but this mechanism is passive, in the sense that no energy in excess of that generated by the potential well of the cluster is added to the gas upon injection. The simple picture of a cluster which will be adopted here is one of a gravitationally coupled system of coUisionless dark matter and an ideal gas of baryons. If galaxies act essentially as coUisionless objects in a cluster, then the dark matter particle orbits can be used as tracers for galaxy trajectories. In this way, "optical" characteristics of the cluster can be studied by sampling the kinematics of the dark particles. This procedure assumes that secondary dynamical effects such as dynamical friction (Hoffman, Shaham and Shaviv 1982; Barnes 1984; Evrard 1987 and articles by Richstone and West in this volume) are unimportant for rich clusters. A simulated catalogue of clusters is useful to explore cluster properties over a range of richness. For a coeval population at some viewing redshift z arising from peak perturbations with a constant linear overdensity 6coc(l + z), a range in cluster richness is spanned by covering a range in cluster mass (see Kaiser (1986) and his article in this volume for a description of self-similar cluster models). Here the cluster mass is defined as the mass within a radius R$ at which the mean density is a fixed contrast P/Pb(z) — l^O above the background at redshift z. In the mass range resolved by the simulations, the CDM spectrum can be approximated as a power law a{M) = <7i5 M~a

(3)

with a = 1/3 and <7\^ = 0.62 and mass M in units of 10 M Q . This implies that the normalized peak heights fp^ are an increasing function of mass

The 22 numerical simulations performed span filter masses ranging between 10 and lO1^ M0 and use £c = 3.4 leading to peaks in the range of 2.5 < v^y. < 5.5. Note that the actual cluster mass (defined within R$) grows as a function of time and should roughly equal the filtering mass at the characteristic collapse redshift 1 + zc ~ 6C/1.68 ~ 1. The cluster mass at z = 0 is typically a factor ~ 3 larger than the filtering mass due to accretion from z ~ 1 to z ~ 0 . Figure 1 shows the final cluster mass plotted against peak height for the ensemble of simulations. Also shown is the expected abundance of clusters as a function of mass based on the Press-Schechter formalism (see §7). The number density ranges from n ~ 1 0 ~ 5 h50s Mpc~ 3 at 4 x 1014 M 0 to n ~ 1 0 ~ 1 0 /t 50 3 Mpc~ 3 at 4 x 10 15 M o .

3. NUMERICAL DETAILS 3.1 Generating Constrained Linear-era Realizations As seen in Figure 1, the abundances of clusters in the mass range covered by the numerical experiments encompasses a wide (factor ~ 10 ) dynamic range. It is

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Log Cluster Mass (Mo) Figure 1. Peak heights of initial, linear perturbations versus measured cluster mass within Rfi at z = 0 for the ensemble of 22 simulations. Filter mass scale ranges from 10 MQ for the lowest peaks to 10 MQ for the highest. Solid line shows expected abundance of clusters at z = 0 using the Press-Schechter formula. currently not technically feasible to perform simulations capable of resolving this range of structure. For example, simulating a total volume of 109 Mpc 3 to sample the richest, rare clusters using 128 particles will mean that a 10 M0 cluster will contain only 30 particles. Thus, generating an ensemble of clusters by simulating a large region of space and extracting some kind of "complete" catalogue is impractical. The alternative approach taken here is to grow clusters individually. This is achieved by simulating smaller regions of space (~ 10 Mpc total volume) with density fields constrained to possess rare, high peak fluctuations on mass scales appropriate for rich clusters. The machinery to construct such constrained, random realizations from Gaussian spectra has been developed by Bertschinger (1987). The procedure is designed to generate a random realization of the density field at N spatial grid points in a periodic volume subject to a specified linear input constraint. The method first solves for a mean field satisfying the constraint and then adds a random field drawn from N — 1 wave modes. Power in a final constrained wavevector is added such that the total random field is guaranteed orthogonal to the input constraint. The random field sampling is done iteratively to ensure that the power in the constrained mode is not excessive. For the purpose of generating high a perturbations, we employ the constraint that the density field convolved with a Gaussian window of scale Rj equal an imposed value 6C at the center of a cube of length L. That is = Sc

(5)

where r c = (L/2, L/2, L/2) and the sum in k is over all points in the lattice. To span

292

A. E. Evrard

the desired range of masses, the filter length scale Rt is varied between 5 h^ Mpc and 12 h^Q Mpc. The mass scale with Gaussian filtering is related to the filter length by Mf = (2n)V2pbRJ = 1.1 x 10 15 (i?//10 Mpc) 3 M 0 (Bardeen et al. 1986). In order to span the same dynamic range in density within each cluster, the length of the simulated region L is scaled with the filter length as L = 5Rf. Cubes ranging from 25h§Q Mpc to 60 h^Q Mpc on a side will thus be modelled. Note that there is no direct constraint on the location of the peak of the smoothed density distribution. However, since 6C is 2.5 to 5.5 times the variance on the mass scales considered, it is likely that a peak will arise near the constrained location. Given the sampled density fluctuation amplitudes in Ar-space, 6(k), the solution to Poisson's equation combined with the linear growth rate of fluctuations in an il = 1 universe give the spatial displacement field *P(z) at some initial epoch z,- (Peebles 1980; Efstathiou et al. 1985)

tf (z) = (1 + z,)" 1 Jd3k eikx k lm(6(k))/Jfc2

(6)

where the (1 + Zj) - 1 factor arises because the power spectrum is normalized to the present epoch. For the finite, periodic box used in the simulations, the integral above is replaced by its discrete Fourier equivalent.

3.2 The Simulation Algorithm P3MSPH The numerical algorithm used to propagate the initial, linear field forward into the non-linear regime is a combination of the particle-particle particle-mesh (P3M) N-body code developed by Efstathiou and Eastwood (1981) and the Smoothed Particle Hydrodynamics (SPH) method of Gingold and Monaghan (1977). A detailed explanation of P3M is given in the book by Hockney and Eastwood (1981), a more cosmologically oriented description along with comparison to other methods is given by Efstathiou et al. (1985). A review of SPH is given by Monaghan (1985) and the combined algorithm used here is described in Evrard (1988). A similar approach combining SPH with a tree N-body algorithm has recently been developed by Hernquist and Katz (1989). An initial application of P3MSPH to study the formation of X-ray clusters in a neutrino dominated cosmology can be found in Evrard and Davis (1988). The basic approach of simulation methods is to discretize the universe in mass and time (and space for grid based schemes) and integrate the difference approximations to the equations of motion for mass elements including as much of the relevant physics as possible. Dynamically distinct types of matter (e.g. dark matter, gas, clouds, stars) can be accommodated by using different sets of mass elements with appropriate equations of motion for each set. For the cluster simulations, we simplify the universe into two types of matter — collisionless dark matter and collisional baryonic gas — represented by two sets of particles. The dark matter and gas particles are labelled with kinematic variables z, v and masses m,f and mg, respectively. In addition, the gas particles carry thermodynamic variables describing local gas density p and internal energy e = (7 — l)~*kT/p.rrip. For the cluster problem, the ICM is treated as a fully ionized, primordial plasma with constant molecular weight p. = 0.6 and an ideal gas (7 = 5/3) equation of state

P(x) = I e(z) p(x).

(7)

Hydrodynamic Simulations of the ICM

298

Working in the comoving frame, x = r/a, where a is the cosmic scale factor, the gas elements follow the equations of motion

it ~ p> dt

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Here v is the peculiar velocity, H = a/a is the Hubble parameter, $(x) is the peculiar gravitational potential arising from both the dark matter and gas, and A(e) is a radiative cooling function. The models presented here ignore cooling A = 0 and neglect any other source or transport terms in the energy equation. The equations of motion for the dark matter are given by the above equations with P = e = 0. Energy conservation for a comoving volume, given by the cosmic energy equation (Peebles 1980) modified to take into account PdV work and radiative losses, provides an integration diagnostic. In the cluster simulations, energy is typically conserved to better than 1% in the sense described by Efstathiou et al. (1985). Local densities pi at the location of particle i are calculated by smoothing the nearby mass distribution Pi = mg^Wir^hi) (11) i where ,

is a Gaussian kernel which interpolates on a local smoothing scale A,-. The smoothing scale is allowed to vary both spatially and temporally to increase the dynamic range accessible to a given experiment. The scaling is such that a roughly constant number (~ 20 — 30) of neighboring particles is contained within a distance A,- of particle i. In similar fashion, the local pressure gradient is written as an anti-symmetric pairwise sum over neighboring particles " ~7W(rijihij)

(13)

where h{j = ^(h( + hj). This guarantees momentum and angular momentum conservation to machine accuracy. Regions of velocity discontinuity will arise naturally during approach to equilibrium in gravitational systems through, for example, accretion of infalling gas or merging of sub-units. If the infalling gas or colliding sub-systems are supersonic, then shocks will develop. To incorporate shock heating within the code, an artificial viscosity (Von Neumann and Richtmyer 1950; Richtmyer and Morton 1967) is introduced. The artificial viscosity essentially mimics the true molecular viscosity of a gas in such a way that the jump conditions are satisfied across a shock front. The front is typically smeared out over several grid cells which for SPH means over the neighboring ~ 20 — 30 particles. The terms describing the artificial viscosity can be found in Evrard (1988), the

294

A. E. Evrard

general effect is one of increasing the pressure in strongly convergent flows from Pcxcr to Pocv . Spherical cluster evolution and planar shock tube experiments show that the form of the viscosity employed is effective in preventing interparticle penetration and satisfying shock jump conditions even in very strong shocks (Monaghan and Gingold 1983; Lattanzio et al. 1986; Evrard 1988; Hernquist and Katz 1989).

3.3 Cluster Model Parameters Each of the 22 simulations contains a total of 8192 particles representing the gas and dark matter. The spatial resolution of the simulations is determined by the gravitational softening e and the hydrodynamic smoothing length h. Plummer model softening is used with e = 150(L/50 Mpc) kpc kept fixed in the physical frame. The local value of h is controlled by discreteness and by the Courant condition. Careful choice of timestep 6t allows the minimum value of h to be comparable to e. A total of 700 timesteps cover the 12.7 x 109 yr from z; = 7 to the present. The initial condition generator allows for a DC component of the power within the volume to represent the power at wavelengths larger than the box size. The simulated volumes typically have net positive overdensities 6{ ~ 0.1. The mean recession velocities are reduced by an amount 1 — 26,-/3 in agreement with linear theory and the models are evolved using scale factors R(t) consistent with background metrics of positive curvature.

4. NOT ANOTHER COMA CLUSTER To illustrate in some detail the dynamics occurring during cluster formation, a single cluster's evolution is examined in this section. Departing from the tradition established by Peebles (1970) and White (1976), the model is compared not to the Coma cluster but to a close relative, the Abell cluster A2256 recently studied in both X-ray and optical characteristics by Fabricant, Kent and Kurtz (1989).

4.1 Dynamical History The spatial and thermodynamic phase space evolution of the gas within a comoving 20 Mpc cube centered on the present cluster position is shown in Figure 2. In Figure 2a, gas particles are binned in density with divisions occurring at n = 10~ 3 , 10 , Figure 2. (opposite page—2a at top, 2b at bottom) "Phase space" scatter plots showing the gas particles in a comoving 20 /igg Mpc cube centered on the present cluster position. Particles are binned in density and temperature ranges: (a) bins in density — row I, (n/ cm~z) > 10~ 3 ; row II, 10~ 3 > (n/ cm~3) > 10~*; row III, 10~4 > (n/ cm~*) > 10~ 5 ; row IV, (n/ cm~*) < 10"**; (b) bins in temperature — row I, (T/ keV)> 6; row II, 6 > (T/ keV) > 0.6; row III, 0.6 > (T/ keV) > 0.06; row IV, (T/ keV) < 0.06. Evolution proceeds from left to right with redshifts indicated at the top of each column. The number of particles falling within each frame is indicated; each particle represents 2.1 x 10 MQ of ICM gas.

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and 10~"5 cm" 3 (row I to row IV). Similarly, Figure 2b bins particles in temperature with cuts at 6, 0.6 and 0.06 keV '. A small cluster containing ~ 3 x 1013 M0 of gas has collapsed at 2 = 1.62 at the intersection of mildly non-linear filaments and sheets. The virial temperature is T ~ 3 keV and density n ~ 10 cm which at this epoch is about 100 times the background. Within the filament to the southeast, a smaller knot condenses (most evident in Figure 2a at z = 0.54) which eventually merges with the parent at 2 ~ 0.1. In the 2 x 109 yr interval from 2 = 0.1 to the present, the gas distribution relaxes since the sound crossing time r_ 3Mpc ^ 2xlQ9 ( u ) V ; c8 1400 km s" 1 is this time scale. The relaxation is evident in the rounder gas particle distributions seen in row III of Figure 2a and row II of Figure 2b at z = 0 compared to those at z = 0.15. A more detailed look at the gas merger is shown in Figure 3. Here color is used to demarcate temperature regimes and projected velocity vectors are included to describe the flow field. Temperature levels are color encoded as : (T/10 K) < 0.4, grey; 0.4 < (T/10 8 K) < 0.8, blue; 0.8 < (T/10 8 K) < 1.2, yellow; (T/10 8 K) > 1.2, red. The velocity scaling is such that 2500 km s~* ~ 1 Mpc. At a redshift z = 0.21 (Figure 3a), the satellite contains ~ 10 M© of gas within the inner 0.6 Mpc at a relative overdensity greater than 1000 and a temperature T = 3 X 10 K. The parent cluster within the same overdensity is roughly 5 times as massive, almost twice as big spatially and twice as hot at T = 6 X 107 K. The flow field is fairly regular at this time except at the interface between the parent and satellite, where a small amount of hot gas is seen being squeezed off the collision axis by the compressive action of the collision. The relative velocity of the parent and satellite is u~1500 km s and the gas sound speed is c s = 1500 (T/10 8 K) 1 / 2 so the Mach number of the collision M = i>/c s ~l indicating a roughly sonic encounter. After 7 X 10 yr at 0 = 0.15 (Figure 3b), the centers of the two merging units are separated by 1 Mpc and the intervening compressed region is forcing hot (T > 10 K) gas off the collision axis at subsonic velocities ~ 600 km s . Cooler (T < 4 X 107 K) gas from the large-scale filament is streaming inward from the southeast behind the impinging knot. The ram pressure of the central 10 MQ in the satellite ^

= ni) 2 ~ (6x 10" 4 cm" 3 ) (1500 km s" 1 ) 2 = 1.0 x 105 K cm" 3

(15)

is only a factor ~ 3 smaller than the central thermal pressure of the parent. At 2 = 0.11 (Figure 3c), this core of the satellite has penetrated to nearly the center of the parent cluster. Momentum transferred to the parent from the collision causes compressive heating of the now infalling warm gas to the northwest. Cooler gas infalling from distances r ^ 1.5 Mpc is being moderately shock heated. The kinetic energy of Figure 3. (opposite and following page) Evolution of the gas during the merger event viewed at (a) 2 = 0.21, (b) 2 = 0.15, (c) 2 = 0.11, (d) 2 = 0.08 and (e) 2 = 0. The region shown at z — 0 is slightly larger than that shown at earlier epochs. Particles are colored according to the local temperature : (T/10 8 K) < 0.4, grey; 0.4 < (T/10 8 K) < 0.8, blue; 0.8 < (T/10 8 K) < 1.2, yellow; (T/10 8 K) > 1.2, red. Vectors show particles' velocities projected onto the viewing plane. The scaling is such that 2500 km s~\^ 1 Mpc. t Recall that 108 K = 8.6 keV.

Hydrodynamic Simulations of the ICM

297

the collision is being thermalized—the amount of gas above 1.2 x 10 K increases from 2.6 x 10 13 M© at z = 0.15 to 6.1 x 10 13 M 0 at z = 0.11. The collisionless dark matter associated with the satellite core is streaming through the parent center at this time (see Figure 4 below), the gas from the satellite is stripped and remains trapped near the center of the merged cluster. The relaxation of the central potential after the impulse generated by the infalling dark matter in the satellite causes the "splashy" appearance of the gas at z = 0.08 shown in Figure 3d. The cluster is expanding adiabatically throughout most of the plotted region; again, with the exception of some residual infalling gas from the southeast and northwest. A somewhat larger view of the cluster at the present epoch (Figure 3e) shows a much quieter velocity field within an Abell radius R& = 3 Mpc. The ID velocity dispersion of the gas particles within Rj± is Oga8 = 390 km s , roughly one-third of the collisionless dispersion o~ = 1150 km s . There is thus ~ 15% residual kinetic energy in the final gas distribution — the gas is not completely thermalized. This should not be too surprising given that (1) only ~ 1 dynamical time has passed since the merger occurred and (2) the system is not isolated. Figures 4 and 5 exhibit the different dynamical behavior of the gas and dark matter during the encounter. In Figure 4, all particles within a 3 Mpc window centered on the present cluster position are shown with the core particles of the satellite highlighted as circles with projected velocity vectors scaled to 1500 km s" 1 = 1 Mpc. Here members of the core are defined as the mass within the inner 6p/p > 1000 at a pre-collision redshift of z = 0.25. In Figure 5, the relative center-of-mass motion based on the tracing the original members the cores of the satellite and parent are presented for both the gas and dark matter. Also shown are mean densities and temperatures for the gas particles originally in each core. The dots in these curves represent intervals of 1.8 x 108 yr. The dark matter core of the satellite streams freely through the parent with a maximum velocity ~ 2000 km s" 1 . The gas is stripped out of its embedding halo when the collision occurs and remains in the inner 800 kpc of the parent cluster. The parent core behaves essentially adiabatically during the compression caused by the satellite infall. Figure 5b shows that the density scales with temperature as n<xT*'1~^ = T 3 ' . The satellite also behaves nearly adiabatically, being mildly shock heated at closest passage. Before the collision, the temperature of the satellite is nearly a factor 2 smaller than that of the parent whereas at z = 0, the material originally in the satellite core is ~ 20% hotter than the gas in the core of the parent. The bulk of this increase is due to PdV work rather than shock heating. Note that at z = 0 the dark matter from the satellite is just making its first return back toward the cluster center. The elongated shape of the dark matter supported by its anisotropic velocity field should be contrasted with the nearly isotropic gas particle distribution at z = 0. Radial profiles of the gas density and temperature as well as dark matter velocity dispersion and velocity anisotropy parameter A(r) = 1 — v^/v^ are shown in Figure 6. The most bound collisionless particle is used to define the center of the cluster at any epoch. Profiles are plotted versus proper radius at redshifts z = l, 0.25 and 0 and are truncated at an interior radius of 200 kpc, roughly the resolution limit of the numerical experiment. The central density and temperature vary little from a redshift of 1 to the present. Thinking of the evolution in purely spherical terms, a shock front moving outward at roughly 400 km s heats the gas infalling at progressively larger radii. The temperature profile at z = 0 is close to isothermal within an Abell radius—radial variations about the mean, mass weighted temperature T ~ 7.2 keV are ^ 30%. The emission weighted temperature is ~ 10% lower than the mass weighted temperature

298

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Figure 4. Comparison of the dynamics of the ICM gas (top row) and dark matter (bottom row) during the merger. A 3 h§Q Mpc window is shown at the redshifts indicated. All particles within the viewing window are plotted with those originally in the core (6p/p > 1000 at z = 0.25,) of the satellite system are highlighted by open circles and velocity vectors scaled to 1500 km s~^=l Mpc. The collisionless dark matter freely streams through the parent cluster while the gas is stripped and thermalized on a timescale~ 10 yr. due to the modest temperature inversion in the core. The temperature drops rapidly beyond ~ 4 Mpc where cooler, infalling material dominates. Note that the profile is not well described by a polytropic model with a fixed polytropic index. The shock heating history for gas parcels varies with position and time due to the Gaussian random nature of the initial conditions. A range of final adiabats results and a simple polytropic description P = const X p"" no longer holds globally. The dark matter velocity dispersion is also very nearly isothermal at a = 1150 km s . The mean orbital anisotropy shows the typical trend of preferring more radial orbits at larger radii (Merritt 1987). Within 1 Mpc at 2 = 0, the orbits are only mildly anisotropic A~0.2. The anisotropy rises to /4~0.75 at r = 4 Mpc, the "edge" of the cluster beyond which infall dominates. There is no clearly resolved core radius in either the gas or dark matter density distributions. The profiles do tend to flatten in the inner regions, but only to the level p<xr~ • . The size and sometimes the very existence of core radii in real clusters is often uncertain. The X-ray emission in a few of the clusters fit by Jones and Forman (1984) show clear evidence for a constant central density with core radius r x ~ 0 . 5 Mpc (A2255, A2256 and A2319, as well as Coma). However, the majority of clusters in that sample have much smaller and more poorly resolved core radii. This is true even after subtracting out central excess emission arising from possible cooling flows. In the optical, the galaxy density profile is sensitive to the choice of cluster center (Beers and Tonry 1986; Merrifield and Kent 1989). Often, no core radius is found when counts

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4.2 Simulated Observations The X-ray emission from this simulated cluster as it might have been mapped by the Einstein satellite is shown in Figure 7. Two viewing redshifts are shown; z = 0.11 at the height of the merger event in Figure 7a and z = 0.023, the distance to Coma, in Figure 7b. The pictures have a resolution of 1 arcmin and the flux is scaled to an IPC count rate by a simple conversion factor (Giacconi et al. 1979) 1 IPC cts s" 1 arcmin" 2 = 2.5 x 10" 1 1 erg s~ 1 cm~ 2 . No background has been added to the images (true theorist's observations!), a typical background rate for the IPC instrument was ~ 3 x 10~4 cts s" 1 (Forman, private communication). Note the enlarged field of view at the lower redshift, roughly twice the size of the Einstein field. At z = 0.11, a sharp edge in the surface brightness at a level ~ 10~ 3 cts s" 1 to the southeast provides a clear signature of the merger event. This feature is transient, relaxing on a timescale ~ 109 yr. A similar sharp edge has been seen observationally in the Einstein image of the cluster A754 (Fabricant et al. 1986). This cluster also shows bimodal structure in its galaxy distribution, making it a strong candidate for recent

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Figure 6. Radial profiles for the ICM gas and dark matter at different epochs showing (a) density for both DM (upper curves) and gas (lower), (b) gas temperature, (c) DM velocity dispersion and (d) DM velocity anisotropy. Different line styles correspond to different redshifts : dotted, z = 1.09; dashed, z = 0.25; and solid, 2 = 0. merger activity. 1 s" 1 in the The cluster luminosity at 0 = 0.11 is at its peak of La: = 1.35 x 10 45 erg s" 2 — 10 keV band. At z = 0.02, the system has relaxed considerably — inner isophotes are fairly round, becoming modestly elliptical at angular scales J£ 10 arcmin. The hard X-ray luminosity has dropped by almost a factor two to Lx = 7.4 x 10 erg s~ . The projected, mass weighted temperature maps shown in Figures 7c and 7d indicate that hot, nearly isothermal gas extends over almost the entire emitting regions of Figures 7a and 7b. Again, the edge marking the collision interface is clearly evident at Figure 7. (a-c on opposite page, d-f on following page), (a) Cluster X-ray emission at z = 0.11 as it would have been imaged by the Einstein satellite. The flat edge in emission is a signature of the occurring merger, (b) Image at the distance of Coma z = 0.023 in an expanded field of view. Elliptical isophotes retain the memory of the recent merger, (c) Projected, mass weighted mean temperature seen at z — 0.15. (d) temperature field for the same field as in (b). The cluster gas is close to isothermal at ~ 7.2 keV. (e) Image showing the expected magnitude of the Sunyaev-Zel'dovich effect for the same field as in (a), (f) same for the field shown in (b).

Hydrodynamic Simulations of the ICM

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the higher redshift. At 2 = 0.02, the entire Einstein field of view would be seeing nearly isothermal gas at T=7.2 keV. At ~ 45 arcmin off the cluster center, the temperature begins to decline. A study of the temperature distribution for gas in the Coma cluster using EXOSAT data by Hughes, Fabricant and Gorenstein (1989) showed that the mean temperature in regions 45 arcmin off cluster center was ~ 15% lower than the central temperature. The model cluster may be consistent with this finding, but it is difficult to know with any precision just from the appearance of Figure 7d. A proper analysis using Monte Carlo spectra taking into account the appropriate instrument response functions and reducing the data in like manner to the observations still remains to be done. Other spectral evidence for non-isothermality in the Coma cluster exists (Henriksen and Mushotzky 1986; Hughes et al. 1988), but the inferred temperature variations are not large and may very well be compatible with the variation seen in Figure 6 above. The expected Sunyaev-Zeldovich decrement (Zel'dovich and Sunyaev 1969) from the simulated cluster viewed with l' resolution is displayed in Figures 7e and 7f. The diminution in microwave background temperature in the Rayleigh-Jeans portion of the spectrum caused by inverse-Compton scattering is given by the line-of-sight integral of the electron pressure

f-

where ne, Te and me are the electron number density, temperature and mass, and O~T is the Compton scattering cross-section. Observations of this effect are difficult and to date, only a few robust detections presently exist at measured amplitudes of around ATr ~ -0.5 mK (Birkinshaw 1989; Uson and Wilkinson 1988). At z = 0.11, a peak central decrement comparable to those observed AT r = —0.5 mK would be observed in the inner few arcminutes of the simulated cluster. Beyond 10 arcmin, the signal has dropped by more than a factor 10. At the distance of Coma, a central 0.5 mK decrement is evident within ~ 15 arcmin from the cluster center. However, obtaining a relatively clean reference beam to identify the central signal would require a beam throw J> 40 arcmin.

4.3 Combined X-ray/Optical Comparison with A2256 The simulated cluster has several gross observational attributes (luminosity, temperature, velocity dispersion) similar to those of the rich cluster Abell 2256 recently studied by Fabricant, Kent and Kurtz (1989). There are also a few more subtle similarities which may provide some insight into the recent dynamical history of A2256. Figure 8a shows a comparison of the 0.5 — 3 keV X-ray emission for A2256 and the model viewed at the same distance z = 0.06. Both maps have ~ 3' resolution and the same isophote levels separated by a factor of 1.5 in flux. Note that the map of the numerical model in Figure 8a is rotated counter-clockwise by 90° with respect to the plots above. Figure 8b shows fits of radially averaged profiles to the fiducial form = E o (1 + ( 0 / 0 x ) 2 ) - 3 / ? / t < + 1 / 2 -

(17)

Best fit values for the core radii and outer slope measure are 0x = 5'.6^/Lg and /fya =O.83io;o7 f o r A2256 and 0x = 4'.3 ± 0'.4 and Pfit = 0M ± 0.02 for the numerical simulation. Both surface brightness maps have elliptical contours with the centers of the outer contours offset with respect to the emission peak. The elliptical contours and isophote

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(b) Figure 8. (a) Simulated IPC Image of the numerical model (left) compared to the real image for the cluster A2256 from Fabricant et al. (1989). (b) Comparison of spherically averaged surface brightness profiles and fits to the form of equation (17). offsets in the model result from the momentum recently transferred into the parent halo by the merger with the subsumed satellite. This implies that A2256 has itself undergone a similar type of merger in the ~ 10 yr prior to viewing. Indeed, a successful kinematic model put forth by Fabricant et al. for this cluster consisted of a superposition of two unequal, spherical lumps displaced by ~ 500 kpc. This is qualitatively similar to the parent-satellite system seen in the numerical experiment. The optimistic cosmologist would think that gathering a sufficiently large number of redshifts for cluster galaxies would provide conclusive evidence for such a "two lump" model. Unfortunately, Figure 9 shows that the velocity histogram for A2256 obtained from 87 galaxy redshifts provides no clear evidence for substructure. However, the flat shape and skewed nature relative to the peak at 17900 km s - 1 may provide some subtle

Hydrodynamic Simulations of the ICM

SOS

clues. For comparison, Figure 9 shows a histogram for the simulated cluster using 90 randomly chosen dark matter particle orbits within a projected separation of 2 Mpc from the cluster center. The model velocities are offset to the redshift of A2256. The histogram from the simulation is very similar in shape to that of A2256; a K-S test fails to distinguish the two histograms.

10 A2256

5 | z

rr

o 10 Model

14

15

16

17

18

19

1

20

21

22

v (1000 km s" ) Figure 9. Comparison of velocity histograms for A2256 and the numerical model scaled to the distance of A2256. Ninety "redshifts" for the simulation were measured by randomly sampling collisionless particle orbits within a projected 2 Mpc region around the cluster center. Closer examination of the model histogram shows that the asymmetry about the peak at 17,900 km s -1 arises from velocities of 9 particles originally in the swallowed satellite which are now spread out in velocity between 16,000 and 18,000 km s . Recall from Figure 4 that the satellite dark matter has not yet reached its turnaround radius at z = 0.08. However, because the dark matter in the satellite was already "warm" (velocity dispersion only ~ 40% lower than that of the parent) before the merger, the orbits are sufficiently mixed in phase space to avoid obvious detection. Although the similarities in both X-ray and "optical" characteristics between the model and A2256 could be simply blind luck, the more sensible conclusion is that we have modelled a cluster whose evolutionary history represents closely that followed by A2256. It then appears likely that A2256 swallowed a modest companion cluster at a redshift z~0.2.

304

A. E. Evrard

5. THE HYDROSTATIC ISOTHERMAL MODEL AND BINDING MASS ESTIMATES A simple model for the structure of mass in clusters assumes that both the gas and collisionless matter (galaxies or dark matter) are isothermal and in hydrostatic equilibrium with the binding cluster potential. Historically, this model has been plagued with inconsistencies regarding the question of whether or not the gas distribution is hotter and more extended than that of the galaxies in the cluster (Sarazin 1986; Mushotzky 1984; 1988). The answer to this question clearly has implications concerning the past thermal history of the ICM. With the full three-dimensional history of the gas available in the numerical simulations, we can address this issue in some detail. The hydrostatic isothermal /?-model model assumes the gas and collisionless matter obey d\npga8{r)

kT (imp 2

GMb(r) =

j

9

rL

ar

dlnpcoU(r)

2A(r)4

GMb(r)

where A(r) is the orbital anisotropy and Mi,(r) is the binding mass of the cluster. The density profiles are parameterized with the following form P.(r) = *>,*(!+ ( r / r c , s ) 2 ) - 3 a ' / 2

(20)

where the subscript s can denote either gas or collisionless matter. Since the gas is assumed isothermal, the gas density profile can be derived directly from the X-ray surface brightness profile equation (17), so that agas = P{itDefine /? to be the ratio of specific kinetic energy in the galaxies to specific thermal energy in the gas

then, outside of the core, the ratio of equations (18) and (19) gives

"

=

acoll-2/3A(ry

(22)

The usual way to proceed (Cavaliere and Fusco-Femiano 1976; Sarazin and Bahcall 1977) is to assume that the collisionless density profile follows a King (1962) approximation to an isothermal sphere and that the orbits are isotropic. This leads to the result that the ratio of specific energies j3 can be found by simply measuring the slope of the outer parts of the X-ray surface brightness profile acoU = 1, A(r) = 0

=4> /? = /? / f t .

(23)

Of course, the other way to determine /? is by obtaining galaxy redshifts and an Xray spectrum to estimate both the collisionless velocity dispersion a\os and the gas temperature T8pec

ol

(24)

The problem that has developed, the so-called ^-discrepancy, is that imaging estimates are typically less than unity — (/?/,<) — 0.7 — while spectroscopic estimates

Hydrodynamic Simulations of the ICM

305

are typically greater than unity — (Pspec) — 1.2. A good example is the cluster A2256 examined above. Fabricant et al. (1989) find f)fn = 0.83 ± 0.06 while the velocity dispersion o\08 = 1300 ± 100 km s -1 and gas temperature Tspec = 7.4 ± 1.0 K combine to givefigpec= 1.4 ± 0.3. The simulated cluster has fy« = 0.84 ± 0.02 while the true ratio of specific energies is /?= 1.2. The simulation exhibits the same ^-discrepancy as observed. Analysis of the numerical model reveals that the cause is due to three small effects which all push in the same direction to make fi8pec larger than /?/#. The first is that the gas is not completely thermalized, the ratio of gas kinetic to thermal energy at z = 0 is small, but non-zero o-gas/(kT/(imp)~ 0.15. Including the support of kinetic pressure changes equation (22) to fi

~

« c o W -2/3A(r)

•

The other two effects are the anisotropy of the cluster orbits and the deviation of the outer dark matter density profile from the King approximation. Figure 6 shows A(r) ~ 0.2 at r ^ 2 Mpc and a fit to the density dark matter density profile yields a DM = 0-85 i 0-04 at z = 0. Note that the outer galaxy density profile in A2256 also appears to be shallower than the King model — the density falls as r at radii r ~ 1 — 3 Mpc (Fabricant et al. 1989). Plugging in these characteristic values into equation (25) exhibits consistency between /fyf<~0.8 and /?~1.2. 5.1 Results for the Ensemble Values of /?/# and f3Spec for the ensemble of models are compared to data from the sample of Jones and Forman (1984) in Figure 10. The brightest 24 of the 46 clusters in that sample are shown, the rest have luminosities lower than those seen in the numerical experiments. Values of fiSpec were known for 11 of these 24. Error bars in /38pec for the data are omitted for clarity but it should be kept in mind that uncertainties are typically £ 40%. The /3 values are plotted against the 0.5 — 3 keV luminosity from the inner 0.5 Mpc of the cluster. An attempt to mimic the selection effects of the observational sample has been made by viewing the set of simulated clusters with a similar luminosity-redshift distribution as the data. Simulated 5000 second Einstein exposures with a Poisson background added and then mean subtracted are used to determine /}*# for the models. Values of /3Spec are calculated directly from the full three-dimensional data using the mean, mass weighted temperature and velocity dispersion within Rg, the radius of mean overdensity £ = 170. On average, a similar discrepancy between 0fn and 0Spec is found in the models and in the observational data. A median value offlspec= 1.2 is found for both sets while medians of firft= 0.7 and /if ft = 0.8 are seen in the observed and experimental samples, respectively. At high luminosity, the surface brightness profiles usually show Pfft ~ 0.7 — 0.8 while at lower luminosity, the smaller dynamic range in surface brightness leads to poorer fits and a wider range in values of Pfft. In the simulations, the largest values of the true specific energy ratio /? £ 1.5 arise from systems which have had very recent (within the last ~ 10 yr) merger activity. The gas in these clusters is farther out of thermal equilibrium than the gas in clusters with /?~ 1.2.

306

A. E. Evrard

Experiments 1

1 Mil

l

Observations

l

l

l

l l l

1.5 —

*** ^ f

-

* ,

1 1 1 1 1 1 1 1 1

.5

IH

-

-

1 Mil

1

1

1

1 1 1 1

Luminosity within 0.5 Mpc / 10

erg s- l

Figure 10. Values of'fifH and Pspec are plotted against 0.5 — 3 keV luminosity within 0.5 Mpc for both the numerical sample and data from the sample of Jones and Forman (1984)- The simulated and real data sets exhibit the same ^-discrepancy.

5.2 Binding Mass Estimates Given an X-ray image and a gas temperature estimate, the hydrostatic, isothermal/? model produces a straightforward binding mass estimate

(26) in

14

Plugging in the measured values for /?«$, T and r^ from the simulation examined above yields a binding mass estimate that underestimates the actual total mass within an Abell radius by ~ 30%. At large radii, the actual mass is smaller than the estimate of equation (26) because the true density profile is steeper than r . Equality between the estimated and true values occurs at a radius r = 5 Mpc. However, the model is inapplicable once the non-equilibrium infall regime is reached at r J£ 4 Mpc. Figure 11 shows how the mass estimate fares for the ensemble of clusters. It is apparent that the accuracy depends on the value of ft fa- When fifn < 0.8, the mass is typically underestimated by ~ 30% whereas no bias or a slight overestimate is likely when fifn > 0.8. However, few of the clusters in the Jones and Forman sample have Pfit > 0-8. It is likely then that, in general, X-ray based masses and hence mass-to-light ratios currently fall short of the actual value by ~ 30%.

Hydrodynamic Simulations of the ICM

1

V) V)

15.5

cO

~

Mass within Abell Radius 1 i i i i i 1 1 1 1

-x- /3m < o Au >

•d

15 CD

0.8

V y#

-

cd

: 8/

A M*

-

•X-

-

'

o

V

0.8

-

6

307

-X•X-

A ,

1

14.5

1

I

i

i

i

i

15

1

1

15.5

Log actual mass (Mo) Figure 11. Predictions for the binding mass within an Abell radius Rj^ = 3h^Q Mpc based on the hydrostatic, isothermal {3-model compared to the actual mass for the ensemble of simulations at z = 0. Clusters with /?/,$ < 0.8 (asterisks) are likely to have their binding masses underestimated by ~ 30% on average.

6. CHARACTERISTICS OF THE ENSEMBLE 6.1 Range of Cluster Morphology The images of clusters observed by Einstein (Jones et al. 1979; Forman and Jones 1982) display a variety of morphologies from smooth, nearly spherical (e.g., A576, White and Silk 1980) to binary {e.g., A98, Henry et al. 1981; Forman et al. 1981) to highly irregular systems (e.$>., A1367, Jones et al. 1979; Bechtold et al. 1983). Much of the lumpy emission seen in the prototype of the irregulars, A1367, is associated with emission from galaxies within the cluster (Bechtold et al. 1983). Since the numerical models cannot resolve galaxies or galactic-scale halos, they cannot be expected to have morphologies as lumpy as that of Al367. Also, most irregular clusters have luminosities lower than any of the simulated clusters. Still, there is a considerable variety of morphology seen in the simulations. Figure 12 shows six examples covering a range in cluster richness. The upper three are placed at a redshift z = 0.04 while the lower are at z = 0.07. All are viewed with ~ l' resolution with emission contours starting at 10~ 4 IPC cts s" 1 and spaced logarithmically in factors of 2. The luminosities of the clusters shown span a factor of 30, increasing clockwise from the upper left as one goes to higher peak heights vpf. at larger mass scales. The cluster morphology also appears connected to the initial conditions. The highest peaks are smooth and regular while the lower peaks show more diversity of structure. In the context of Gaussian random fields, the trend of smoother, more relaxed morphologies

308

A. E. Evrard

L,=0.22 a =0.41

L,=0.29

1^=0.47

i/pk =2.6

i/pk =3.3

M,=0.51

Ma=0.71

1^=3.0

L»=1.8

v pk =4.3

u pk =4.0

Md=2.0

M,=2.1

5 a r c m i n I—I

Figure 12. Simulated IPC images displaying the range of morphology seen in the numerical catalogue. X44 is the 0.5 — 3 keV luminosity in units of 1044 erg s~l, vp). the height of the initial peak perturbation and M$ the cluster mass measured within a radius of mean overdensity Sp/p = 170. Clusters in the upper row are viewed at a redshift z = 0.04 while those in the bottom row are at z = 0.07. Contours start at 10~ 4 IPC cts s - 1 and are spaced logarithmically by factors of 2. being more frequent in the highest peaks can be understood as being due to the larger degree of coherence necessary to build the highest peaks. Higher peaks tend to be more spherical (Bardeen et al. 1986). Profiles of the X-ray surface brightness measured in spherical annuli from the peak of the emission are shown for these six clusters in Figure 13. Also shown are residuals from fits to the fiducial profile equation (17). The fits were performed on simulated 5000 sec IPC exposures with a Poisson background added with mean rate Efcff = 3.4 x 10~4 cts s" 1 arcmin" 2 . A flat background subtraction at the known mean rate is done before fitting. Core radii fall in the range rx ~ 100 — 430 kpc, roughly the same as that spanned by the clusters in the sample of Jones and Forman (1984). The steepest models with /?™ ~ 1 are somewhat steeper than those listed in the Jones and Forman sample. However, values of /3JH are sensitive to both the assumed background subtraction and the presence of excess central emission. A ~ 50% underestimate of the mean background rate flattens the fits in the simulations, bringing them into line with the range of /?*# observed. Another, perhaps more likely, cause for a discrepancy is that the majority of the Jones and Forman cluster sample are XD systems—those with emission profiles concentrated around bright, central galaxies. These systems typically have small core radii ~ 200 kpc which tends to imply a shallower fit to the outer surface brightness profile (Mushotzky 1988).

1 309

Hydrodynamic Simulations of the ICM I II

-2

I III

I

I

1

I I I

— -—

|

.2

=-•

0

|I Ii

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<2=o 44

-.2 -4

hill MI n '

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ll'lllllll r

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i. 1 1 1 1 .

t I nij j -.2 -4

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1 1

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-.2

/3fil=0.59

Ii

= Ift " -

1

llPlIr 1

TJ1-TT

r x =0.2?

—

.76 11 l 11 1

n

!

-.2

i^ 1 1 1 1 1 I I

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-*

.70 =

-4

0

•*-

.2

-2

:

-.2 -4

.is :

1

6 (arcmin)

10

i , i

-:

i

1

10

(arcmin)

Figure 13. Surface brightness profiles and fits to the fiducial form, equation (17), for the clusters shown in Figure 12. Cluster luminosity increases from top to bottom.

310

A. E. Evrard **o

em u

1

i

•

1

M

44

i

\

1

y

°§J& -

1

1

1

1

1

1

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43

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i

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o

1/

7/3=1.5

2.8

1

1

t

i

i

> •

3

3.2

Log a (km s )

Log T (keV)

Figure 14. Correlations of cluster observables drawn from the numerical simulations and observations : (a) luminosity-temperature, (b) luminosity-velocity dispersion, (c) temperature-velocity dispersion, and (d) central SZ decrement-temperature. Observational data from HEAO-1 (Mushotzky 1988) and EXOSAT (Edge 1989) art shown. Solid lines are best fit relations from the numerical models, dashed lines are fits to the EXOSAT data.

6.2 Correlations Correlations between cluster observables provide clues to their formation mechanisms. Figure 14 shows correlations from the set of simulated clusters for (a) Lx — T, (b) Lx — o~, (c) T — a and (d) |AT r | — T. Table 1 summarizes power law fits of the form Y =

(27)

The existence of a luminosity-temperature relation was observationally established by Mitchell et al. (1977; 1979) and Mushotzky et al. (1978). Data from Mushotzky (1988) as well as EXOSAT data from Edge (1989) are shown in Figure 14a. The models closely follow the observed clusters, having a slope p — 2A6 ± 0.14 which is shallower than that obtained from the EXOSAT data p ~ 3 . 3 . The dispersion is much narrower in the simulations. Note that the dispersion in the EXOSAT data is larger than that

Hydrodynamic Simulations of the ICM

311

expected from measurement errors alone, the scatter is probably intrinsic. The likely inference is that physics missing in the numerical simulations (due to dynamic range constraints or lack of gas cooling, for example) is the source of this observational scatter. The relation between luminosity and velocity dispersion in the models is similar in level of agreement with observations. However, in this case, the simulations show a slightly steeper relation than the observations.

Table 1 : Parameter Correlations Y

X

L44 I44

T»

T* |AT r | |A7V|

IAJVI Z44 = 78 = 03 = |AT r | = Rg = Ay =

^3 <73

T* L44

Xo

P 2.46 ± 0.14 5.19 ± 0.30 2.09 ± 0.07 1.78 ± 0.05 0.69 ± 0.03 3.51 ± 0.15

0.38 ± 0.03 0.81 ± 0.02 1.28 ±0.02 1.39 ±0.04 21.9 ±3.2 1.50 ± 0.03

Ay 0.14 0.14 0.04 0.06 0.08 0.09

total luminosity in 2 — 10 keV band / 10 erg s 1 mass weighted temperature within R(j / 10 K collisionless ID velocity dispersion within R$ / 10 kms central SZ decrement in mK on l' scale at z = 0.11 radius within which total mean overdensity Sp/p = 170 rms of residuals to log — log fit

The correlation between temperature and velocity dispersion is more complex. The simulations favor the slope preferred on dimensional grounds T oc a , i.e., a line of constant /?. All the 22 models lie in the range 1 < /? < 1.5. The HEAO-1 compilation from Mushotzky (1988) has a slope similar to the numerical results but much larger scatter. However, the new data from Edge (1989) show a much shallower relation T <x a . Values of f3Spec < 1 are preferred for systems with T < 5 keV while hotter clusters tend to have (3Spec > 1. From Edge's point of view, the rich clusters with fiSpec > 1 are probably those with overestimated values of a. However, Henry (1989, private communication) has compiled a literature sample of 14 clusters with X-ray temperatures and velocity dispersion estimates based on more than 70 redshifts per cluster. For these optically well-sampled clusters, he finds a mean value = 1.3±0.1. Thus, unless systematic effects contaminate nearly all high velocity dispersion clusters, there appears little hope of reconciling fir# = fispec for oil clusters. An alternative point of view in interpreting Edge's data is that the gas in low velocity dispersion systems is heated by non-gravitational sources, such as winds from galaxies (Mathews and Baker 1971; Yahil and Ostriker 1973; David, Forman and Jones 1989) making their X-ray temperatures larger than the simple gravitational models would indicate. A simple argument in favor of a feedback interpretation over Edge's point of view can be made on dimensional grounds. The bolometric X-ray luminosity scales as Lbol

oc pMT1'2.

(28)

For a self-similar, coeval (p ~ const) population of clusters with no non-gravitational

312

A. E. Evrard

heat sources for the gas, we expect MocT3'2 LM

and Toco2 leading to

oc T2 and LM

oc
(29)

The numerical models are consistent with these expectations. The EXOSAT data from Edge (1989) have Lhol oc T2S±0A and Lhol oc a 4 0±0- 2 , i.e., the scaling with velocity agrees with the dimensional analysis while the scaling with temperature is steeper. This is consistent with a picture in which the gas in lower luminosity systems is heated above the characteristic gravitational temperature. On the other hand, if observed gas temperatures were purely due to gravitational infall and there were a systematic trend for overestimating velocity dispersions in richer systems, then we'd expect the opposite disagreement to that observed — the L — a correlation should be shallower while the L — T relation should agree with the dimensional model. Unfortunately, this argument is not ironclad because the scalings in equation (29) are sensitive to other possible systematic effects, such as departure of the density profile from self-similarity. The correlation of the central Sunyaev-Zel'dovich decrement with X-ray temperature indicates that signals approaching 1 mK can be expected from the hottest ( r ~ 1 0 keV), most luminous ( L ~ 2 x 1045 erg s" 1 ) clusters. The Abell cluster A665 has a temperature and luminosity near these values and shows a central decrement of about —0.8 mK (Birkinshaw 1989), consistent with this expectation. The models and predict the decrement to scale with temperature and luminosity as AT r oc T ATrOcZ,07 with L measured in the 2 - 1 0 keV band. One of the assumptions of this work which strongly affects the above correlations is that of a constant ICM mass fraction in clusters fiCM =0.1. It is possible that the ICM fraction may vary as a function of cluster mass due to a variation in the efficiency of galaxy formation. Some observational evidence for this trend has recently been reported by David et al. (1989). Moreover, there is no reason why there can't be considerable scatter in the ICM fraction even at a fixed mass scale. If the ICM fraction is expressed as a power law function of binding mass fiCM

« M<

(30)

then, since Lxocf2QM and TocAf 2 ' 3, the slope in the Lx — T relation will be increased by an amount 3e. Forcing agreement between the slopes of the simulated and EXOSAT data would require e ~ 0.3, implying 101{* MQ clusters have roughly twice the ICM fraction as their 1014 M© cousins. This is the same direction implied observationally (David et al. 1989). However, the situation is complicated by the Lx — cr relation, the slope of which would be changed by an amount 6c. Since the simulations are already steeper than the observations, agreement for this correlation would require e ~ —0.1. Poor clusters would have a higher ICM fraction than rich clusters. Perhaps a hidden systematic bias in velocity dispersion estimates will eventually be found to blame for this disagreement. More observational data with velocity dispersions based on £ 100 redshifts per cluster will help clarify the situation.

7. ESTIMATED ABUNDANCE FUNCTIONS 7.1 Technique The abundance of objects as a function of some observable Y is a useful cosmological diagnostic. In Gaussian, hierarchical models, the comoving abundance at a given

Hydrodynamic Simulations of the ICM redshift and mass n(M,z) and Schechter (1974)

313

can be calculated using the theory put forward by Press

n(M,z) din M = - ^ ^ ^ " J i l T "'(M) «cp(-i£(M)/2) din M

(31)

where vz(M) = 1.68(1 + z)/o~(M) and p0 is the present background density. The predictions of equation (31) have been shown to agree well with the multiplicity functions determined by N-body experiments over a fairly wide range of self-similar initial conditions (Efstathiou et al. 1988; Cole 1989). Let us locally characterize the power spectrum by the scale invariant form o~(M) = ai^M~a where the mass M in units of 1015 M©. Suppose we have an observable Y scaling as a power law in mass at z = 0 Y = Y15 MP.

(32)

Then equation (31) can be transformed to give the abundance per logarithmic interval of that observable in the form n(Y) din Y = n , (Y/Y*)-V e x p ( - ( r / n ) A ) din Y

(33)

where A = 2 p - 1 a,

r, =

p-1(l-a),

n = (1.41
(M)

n«, = 9.3 x Nr 5 <7f 5 1 ap- 1 (1.41<7i 5 - 2 ) r '/ A Mpc" 3 . This approach was originally applied to cluster abundances by Perrenod (1980). Note the exponential sensitivity of the abundance to the square of the spectrum normalization CT15. This makes it look like it should be easy to determine the normalization by comparing theoretical predictions with observed number densities. In practice, it is a complicated business, because the discriminating power is on the tail of a sharply falling distribution. This makes the procedure highly sensitive to both observational noise and theoretical uncertainty (Cole and Kaiser 1989; Evrard 1989b; Frenk 1989). The predicted observed abundance must take into account any intrinsic scatter in the Y — M correlation as well as dispersion due to measurement errors. For log-normal scatter, this can be modelled as a convolution of the raw abundance

= I

d6Y

PW) n(Y •io6y)

(35)

with a probability distribution P(SY) taken to be Gaussian distributed about zero with variance Ay.

7.2 Model Predictions The correlations with mass of the 2 — 10 keV X-ray luminosity, gas temperature and dark matter velocity dispersion are summarized in Table 2. The parameters in the n(Y) equation are also listed in Table 2 assuming a\§ = 0.62 and a = 1/3. Note that \ — t) for the value a = 1/3. The number densities n(Y) calculated by the method outlined above are shown in Figure 15. The actual CDM spectrum has been used in

314

A. E. Evrard

o a O

a

c 00

o

-9 43

45

44

Log L2_10

keV

(erg s

46

)

.5

1

Log T (keV)

Log o" (km s )

Figure 15. Number density of clusters per logarithmic interval of luminosity, temperature and velocity dispersion. Dashed lines show model predictions with no scatter in the observable-mass relations, solid lines show the prediction for log-normal scatter with variance 0.3, 0.1 and 0.1 for L, T, and a, respectively. Observational estimates of n(L) are shown — the solid circles from Johnson et al. (1983) and the dot-dashed line from Piccinotti et al. (1982). The dot-dashed line in the n(T) plot is derived from the Piccinotti n(L) by using the observed mean L — T relation. Solid circles in the n(cr) figure are estimates by Cole and Kaiser (1989).

Table 2 : Correlations with Mass and Abundance Parameters Y

Ylb

1.65 ± 0.12 1.60 ±0.18 0.68 ± 0.02 0.46 ±0.01 0.33 ± 0.01 0.88 ±0.01 units of 10~ 4 Mpc"

£44 0

P

Ay

X = r,

n

na

0.18 0.03 0.02

0.40 1.0 2.0

0.064 0.13 0.46

1. 1 2. 7 5. 5

*

these calculations, but the power law approximations do not differ appreciably. Dashed lines show the raw predictions, solid lines show the predictions after convolving with scatter of Ay = 0.3, 0.1 and 0.1 for Lx, T and a respectively. Also shown in the first panel of Figure 15 are data for the local X-ray luminosity function taken from Johnson et al. (1983) and Piccinotti et al. (1982). The X-ray luminosity function determined by Johnson et al. was derived from HEAO-1 detections of 128 known Abell clusters and so is not based on an X-ray selected sample. It's completeness must therefore be called into question, particularly for low luminosity clusters. Johnson et al. point out that up to ~ 50% of the 2393 Abell clusters searched for emission in their catalogue have 2 — 6 keV luminosities Lx & 10 erg s . The Xray selected luminosity function of Piccinotti et al. (1982) based on the HEAO-1 A2 sky survey is consistent with the Johnson et al. determination, but its limiting sensitivity is slightly poorer. Nearly all of the total of 30 detected clusters in that sample have 2 — 10 keV luminosities larger than 10 erg s . The agreement between the theory and data at the bright end of the luminosity function is encouraging, since the observations are likely to be more nearly complete

Hydrodynamic Simulations of the ICM

315

at high luminosities. The models predict a large degree of incompleteness even at 10 erg s . The expected number at 10 e r g s " is a factor J£ 5 larger than observations indicate. The increased sensitivity and lower energy bandpass of the ROSAT satellite should allow a more reliable abundance estimate for low luminosity, low temperature clusters. These data should be able to confirm or deny the model predictions. There have been no systematic surveys to determine either a temperature or velocity dispersion abundance function. The dot-dashed line in the n(T) function of Figure 15 is derived by convolving the Piccinotti et al. luminosity function with the observed Lx — T correlation. The relation between the observational and theoretical estimates is similar to that for the luminosities. The observational estimates for n(a) are taken from Cole and Kaiser (1989) who used the heterogeneous compilation of velocity dispersions for Abell clusters produced by Struble and Rood (1987). The different data points represent characteristic values of 4, 3, 2, and 1. There appears to be rough consistency between the theoretical prediction and Cole and Kaiser's abundance estimate. A more systematic effort to determine n(a) from a homogeneous, complete sample, such as that now being undertaken at CfA (Zabludoff, Huchra and Geller 1989; see also Geller in this volume) would be most useful.

7.3 Constraining the CDM Spectrum Normalization As indicated above, the expected abundance of clusters of a given mass is extremely sensitive to the spectrum normalization o~\§. Out on the tail of the number density distribution, the abundance is controlled by the normalized perturbation height which scales roughly as J / O C C T ^ ^ M 1 ' 3 . The mass scale Mn<. defining at a constant number density nc thus scales as Mn<.<x(j\f?. Given how the 2 — 10 keV luminosity scales with mass, L o c M 1 ^ (Table 2), we find the luminosity at constant abundance scales as Lnc

« *155-

(36)

However, the X-ray luminosities also scale with ICM fraction LOC/JQ^, so a larger ICM fraction can offset a lower value of the normalization. The constraint that the models produce the observed abundance of bright L ~ 10 erg s clusters then provides a constraint on the ICM baryon fraction for different normalizations

Unless large fluctuations in baryon density on scales J> 10 M© are generated in the early universe, the baryonic fraction in the ICM sets a lower bound on the total baryonic mass fraction fij > fjCM- The preferred normalization of Davis et al. (1985) 0.3. This value is at odds with both standard nucleosynthesis constraints Oj ^ 0 . 1 h^Q (Kawano, Schramm and Steigman 1988) and the canonical view that baryons accounts for ~ 10% of the binding mass in rich clusters. However, the possibility of non-standard nucleosynthesis (Applegate, Hogan and Scherrer 1987) and the imprecision of present cluster mass estimates provide some room for maneuvering around this argument.

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There is another way to attempt to constrain a\^ using the luminosity-temperature relation. Although the luminosities for lower normalizations can be beefed up by increasing fij, the cluster temperatures will decline with decreasing 015, unaffected by flj since it is the total mass that sets the virial temperature. For outputs of the numerical models, the viewing redshift scales with normalization as (1 + z)ocai^~i, so this effect can be examined directly by taking early outputs of the canonical
(38)

where Z/44 is the 2 — 10 keV luminosity in units of 10 erg s were performed for each normalization as well as for the data of Mushotzky (1988) and Edge (1989). A comparison of the 90% confidence regions for the characteristic temperature T* and exponent q for these data sets is shown in Figure 16. The observational samples (heavy lines) overlap around q = 0.30 and Log(T*/K) = 7.6. As previously noted, the models show a somewhat different (but just consistent) slope q ~ 0.37. More importantly, the characteristic temperature expected at L = 10 erg s decreases with normalization as expected. The value atCT15= 0.4 is ~ 60% lower than observed. Taking the data in Figure 16 at face value would imply a\§ i£ 0.54 with a rough upper bound of (715 ^ 0.75 inferred from the trend of T* with a\§. Once again, there is some freedom in this argument which renders the above interpretation suggestive rather than conclusive. One source of uncertainty is the amount of convolved scatter in the estimate of the observed abundance, equation (35). One could reconcile both the number density and the Lx — T relation for a\^ = 0.4 by using a scatter of Ay ~ 0.8, or a factor ~ 6 dispersion in luminosity at a given mass. There appears to be no way to rule this out observationally at present. Eventually, improved theoretical modelling of the intracluster gas coupled with observational abundance distributions based on complete, homogeneous data sets will provide robust constraints on the amplitude and, perhaps, shape of the initial fluctuation spectrum. 8. S U M M A R Y A N D DISCUSSION This paper reviewed results from a set of numerical simulations intended to study the dynamics of the ICM in clusters forming within a cold dark matter dominated universe. A combined N-body and 3D hydrodynamic algorithm was used to follow self-consistently the evolution of gas and dark matter in clusters spanning roughly a decade in mass. The principal motivations were (1) to investigate the internal structure and observational expectations of an ICM formed by hierarchical clustering in three dimensions and (2) to extract statistics from the set of simulations as diagnostics for the cosmological model. Some of the lessons learned regarding internal and structural properties include the following : • The fiducial hydrostatic isothermal /3-model model provides a good description of the gas density and temperature profiles but the outer slope measure /fy# is not an accurate indicator of the true value of the specific energy ratio

Hydrodynamic Simulations of the ICM

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exponent q Figure 16. Ninety percent confidence regions for the free parameters q and T* in the relation T = T*L\4 with L 44 the 2 - 1 0 keV luminosity in units of 10 44 erg s~l. Heavy curves labeled E and M are for the observational samples of Edge and Mushotzky. The rest are for the simulated set of clusters measured in CDM models with different normalizations o~i§ for which the ICM fraction is adjusted to produce the correct abundance of bright sources. Lowering the normalization produces cooler clusters at a given luminosity. /3 = o^KkT/firrip). The discrepancy is caused by three small departures from the standard model assumptions which all push in the same direction. Mass estimates based on this model are likely to underestimate the true mass within an Abell radius by ~ 30%. No significant segregation of the gas and dark matter occurs during the dynamical evolution; however, the gas is typically more spherical than the underlying dark matter distribution due to support from its isotropic pressure tensor. Emission morphologies appear related to perturbation peak height. The highest peaks (up/,. £ 3.5) tend to be smooth and centrally concentrated (but not necessarily spherical) while lower peaks display a wider variety of shapes, including multiply peaked and binary structures. Detailed examination of a merger event showed that the ram pressure of the core of an infalling companion was sufficient to allow it to penetrate to the center of the target cluster. Relative velocities between the cores of the parent and satellite systems of order 1000 km s~1existed for 109 yr during the merger. The cores are not strongly shocked during the roughly sonic encounter, but are heated nearly adiabatically by the compressive action of the collision. The cluster X-ray luminosity fluctuates up and down by about a factor 2 over the course of the merger.

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Some observational consequences of this collision deserve mention. If the system is viewed at a fairly large angle with respect to the collision axis, then the X-ray image may likely show a relatively sharp, linear feature at low flux levels perpendicular to the collision axis (see Figure 7a). If viewed nearly along the direction of collision, then the X-ray image may not appear abnormal. However, emission line features in the X-ray spectrum should show two components separated by an amount AE/E ~ .003 (umery/1000 km s" 1 ), the details depending on the properties of the two merging units. As an example, the encounter examined in §4 had Vmerg ~ 1500 km s" 1 , so for this system we might expect the 6.7 keV FeXXV line to be split by an amount AE ~ 33 eV. The microcalorimeter planned for the AXAF mission (Giacconi et al. 1980) is expected to have sufficient energy resolution to detect splitting at this level. This may be a good way to detect "buried" substructure; i.e., remnants of the cores of recently accreted companions. A good candidate list for such observations could be those clusters already showing evidence for substructure in their velocity histograms (see Fitchett's contribution to these proceedings). Some sensitivity of these results to initial conditions and numerical parameters has been tested; results can be found in Evrard (1990). The initial gas temperature is a parameter that has some control on the final gas density and, hence, surface brightness profile. If the cooling time of the gas is long, the entropy of a parcel of gas cannot decrease; so, for a cluster with characteristic virial temperature Tc/, the initial gas temperature and density T,- and p{ constrain the maximum (central) virial density to be

j

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.

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Using the initial epoch of the simulation Z{ — 7, at which time the density field is essentially linear, gives for 7 = 5/3 -4 C*dY" po < 2.4 X lO"' [ ^ j

_-3 cm

For the cluster shown in Figure 6, the density within a few hundred kpc will become affected for initial temperatures T,- £ 107 K. If feedback during galaxy formation or some other heat source can raise the gas temperature to such levels, then a core radius larger than that of the collisionless mass could be generated in the gas distribution. The set of models provided some insight into the ability of CDM model to reproduce statistical aspects of the cluster distribution. • Correlations of cluster luminosity with temperature and velocity dispersion are in generally good agreement with observational correlations. However, there is a discrepancy between the model T—a relation and the new data of Edge (1989) which remains to be resolved. Two possible interpretations are (i) that velocity dispersions in most of the richest clusters are systematically overestimated by J£ 20% or (ii) non-gravitational heat sources are more important in poorer clusters. • The predicted X-ray luminosity function produces the observed abundance of very bright Lx ~ 10 45 erg s - 1 clusters and suggests a large (factor £, 5) degree of incompleteness in the present luminosity function at luminosities Lx £> 1044 e r g s " 1 . Data from the ROSAT mission should prove a useful discriminant. • Simultaneously satisfying the bright end of the cluster luminosity function and the Lx — T correlation requires that the amplitude of the CDM spectrum be

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within ~ 15% of that used in the numerical models. However, the valueCT15= 0.4 inferred from the N-body work of Davis et al. (1985) can be reconciled with observations by having either (i) ft& £ 0.3 and a factor ~ 2 non-gravitational heat input into the gas or (ii) a dispersion of a factor ~ 6 in cluster X-ray luminosity at a given mass. • The models predict scaling relations between the Sunyaev-Zel'dovich microwave decrement and cluster temperature ATr <x T 1 8 and 2 — 10 keV luminosity AT r oc Ir . Signals of 1 mK are expected from clusters with temperature T ~ 1 0 keV and 2 - 1 0 keV luminosities L ~ 2 x 1045 erg s" 1 . These numbers are consistent with the data for A665. More observational data, particularly on abundance distributions, will help tighten the currently, rather loose constraints on the CDM model. The AXAF satellite could be used to deliver a useful n(T) distribution, especially once the ROSAT survey produces an expanded, X-ray selected list of cluster targets. These data could be enhanced with redshift surveys aimed at obtaining velocity dispersions for the same candidate clusters. Combined X-ray and optical analysis can be quite powerful. For example, one of the simulated clusters shows no obvious sign of substructure in its velocity histogram but displays a clear binary X-ray morphology. This situation arises because the relative velocities of the two components of the binary are lower than their internal dispersions. So instead of a two-humped distribution, one finds a rather smooth, blended velocity histogram. In the opposite direction, there is a model which has nearly perfectly spherical X-ray isophotes but whose velocity histogram shows two distinct peaks separated by ~ 1500 km s . This system suffered a recent merger nearly along the viewing axis. These examples demonstrate the value of having several independent dynamical diagnostics. What else can be done with these numerical models? One offshoot of this work was a study of "first infalP interpretation of the enhanced fraction of active galaxies seen in higher redshift clusters (Dressier 1987; Gunn 1989). The model suggests starbursts are triggered in gas-rich galaxies once they pass into a region where the ICM pressure greatly exceeds the internal ISM pressure. By tracing pressure histories of collisionless particles orbits and using a simple pressure-sensitive trigger to define "active" orbits, several observed characteristics of the post-starburst population were reproduced, lending support to the first-infall interpretation (Evrard 1989c). Another project worth investigating is to generate and analyze synthetic spectra based on the temperature and density information in the numerical experiments. In particular, the run compared to A2256 could be analyzed in analogous fashion to studies of Coma (Henriksen and Mushotzky 1986; Hughes, Gorenstein and Fabricant 1988; Hughes et al. 1988). Also, emission line profiles expected from gas in clusters undergoing mergers could be detailed. Finally, given a sufficiently large ensemble of numerical simulations, one might dream of creating an "expert system" (team of graduate students?) capable of taking a variety of observational input and recognizing the dynamical state of a cluster with a degree of accuracy sufficient to allow a map of the binding mass distribution to be made. The simulation algorithm is new and admittedly primitive in some respects. Most of the larger observed dispersion about the mean correlations in Figure 14 is probably due to physics currently ignored in the numerical models such as gas cooling, galactic sources of mass and energy, and variation of ICM mass fraction from cluster to cluster. Efforts to include these effects by extending the dynamic range beyond that of the present calculations are presently under way. Some 2 x 32 versions of the models

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presented here have been performed. In general, features resolved by the 16 runs are robust, but quantities based on information from fewer than ~ 30 particles, such as estimates of central densities and cooling times, can be strongly affected. With increased resolution comes the responsibility of including all the physics which affects the newly resolved scales. Following the formation of galaxies within clusters is an obvious, if ambitious, goal of these methods that has already received some attention (Carlberg and Couchman 1989) and will certainly be attacked with ever increasing numerical firepower in the future. Given that there are a large number of possibly important physical processes at work over a wide range of both spatial and temporal scales, it will likely be some time before the appropriate multi-dimensional parameter space for galaxy formation models is first defined, then explored and finally (?) understood. However, we now have budding numerical tools (Carlberg 1988; Evrard 1988; Hernquist and Katz 1989) which will allow us to at least begin detailed, quantitative studies of galaxy and cluster formation. I am grateful to Ed Bertschinger for the generous use of his initial condition generator and to Alastair Edge for providing me with a copy of his thesis and two cans of Abott. Thanks are due to Christine Jones, Bill Forman, Dan Fabricant, Jack Hughes and many others in the CfA High Energy group for illuminating discussions and kind hospitality while this paper was in its conception stage. I'd also like to thank Mike Fitchett, Bill Oegerle and the rest of the organizing committee for inviting me to make this contribution and for running such a splendid meeting. This work was supported by a NATO Fellowship and an SERC Research Fellowship at the Institute of Astronomy, Cambridge and by the Miller Institute for Basic Research in Science at the University of California, Berkeley.

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DISCUSSION Mushotzky: A quick comment about the data. My data is being partially criticized here. Evrard: No, I like your data. I don't like Alastair's data (laughter). Mushotzky: Alastair and I checked our results last week, and when we have objects in common, our temperatures are in very good agreement or within the error bars. So, there's only two possible causes of the discrepancy. One is in the samples that he and I had, and two, in the epoch of the optical data that we used. The epoch that I used is 1986 and it was based on the compilations of Struble and Rood and—I think Schmidt's compilation. I also see some more recent stuff in the literature where there were larger samples. That's one possible origin of discrepancy. I think Bill Forman pointed out that dcr/dt is negative. The computed velocity dispersions are declining with time. That's point number one. Point number two is the sample selection, and we haven't checked that in detail, but I tend to believe that my sample tends to be biased towards higher luminosity systems than Alastair's sample. But they do overlap. Let me stress that—and so if there is any trend—if data is a function of anything besides epoch, then it's a function of luminosity of the system, and I don't know if epoch doesn't completely dominate the case. The X-ray temperatures are stable with time. Evrard: Yes, one comment to add to that is that I think that the idea that /? should be greater than one just in the gravitational infall picture makes sense because you really have to thermalize very efficiently the gas in order to get /? close to one. You need extra energy input to make it less than one. So, if /? is really around 0.8, it would be saying that my ignoring thermal input from galaxies or any other kind of heat source is a wrong approximation at the 20% level.

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Eilfik: If I understand you, the dark matter is elongated two to one, roughly, but the gas is close to spherical, and yet the gas is in hydrostatic equilibrium. Evrard: Well, the potential is more spherical than the mass distribution. If you look at models of elliptical galaxies, the equi-potentials are always much rounder than the equi-density. Richstone: I was going to ask the same question. I've made quite a number of models of elliptical galaxies, and for mass distributions like this, the potential is about half as flat as the mass distribution. Now, I was tremendously impressed by your slide with the dark matter distribution and the gas distribution, that the gas was rounder than what an observer would call E9 and that the dark matter looked to me to be E5, and that's too much. See, you could also do it with angular variation in the temperature because it's the pressure gradient that has to match up to the gravity field, not the density gradient, and you showed the density not pressure—but I'd wondered if you'd gone back and looked at. Evrard: Well, I think if you remember, that temperature slide that I had shown at about a redshift of 0.15, where you saw hot gas streaming out to the sides, I think that's the situation—that the gas is probably hotter or maybe you've got a temperature gradient in that direction which is giving you a stronger pressure gradient and at the 20% level, you may not be in hydrostatic equilibrium. There could be some residual outflow along those directions. It's only been roughly one dynamical time since that collision occurred, okay. Gunn: It hasn't been long enough to forget that stuff and that's what you're saying I guess . . . Evrard: That's right. Yes, that could be making the gas appear more spherical than it actually should be in equilibrium. Fall: I have some questions concerning the X-ray luminosity function and the relations between X-ray luminosity and temperature and redshift. It seems to me that the general shapes of those relations are fit very beautifully by this model and therefore, show a consistency but it also seems to me that the scaling of luminosity axis is actually a measurement of the amount of gas that went into the thing at the beginning and I don't think you emphasized that enough. That seems to work out very beautifully with the data but you could turn the argument around. Presumably, the luminosity scales as the square of the amount of gas. So, in some sense you actually have an indirect way to measure—well, measurement is probably too strong a word, but you have a way of getting at the sort of primordial gas to dark matter relation. It's very important . . . Evrard: That's right. There's freedom in flj and the normalization of the spectrum, as well as h. Right, so if we fix h, let's say, then I could increase fij and decrease the normalization of the spectrum, or vice versa and still be consistent with the observed abundance of bright sources. The thing is that playing around with fij does nothing to the temperatures. So, what you should be able to do is constrain CDM for a fixed h. You should be able to constrain the CDM parameters within a given range by looking at the Lx — T relation and the agreement with the luminosity function because you

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have two independent constraints there. Eall: I mean once you get the amplitude fixed in some other way, then don't you have this estimate of this ratio of gas to dark matter? Evrard: Well, if you believe you have an amplitude. That's another way just to say that I've fixed o~\§ = 0.6, and then that implies that fi/CM ia 0-1Giacconi: If I take this prediction, then there is a tight correlation between the Xray luminosity and the mass, and unless there is no relationship between the mass in galaxies and the dark mass, then we know for a certain richness class, which presumably defines a mass, we have a spread in luminosity of a factor of 100, which presumably has something to do with initial conditions and the evolution. So, there is a parameter—you can't have it as one variable—it needs a second variable which describes the state of dynamical evolution, and has something to do with the peak over-density or something like that. Evrard: I guess I see the . . . Giacconi: I'm not complaining. I think it's beautiful. I would love to see some more of the slide show. I mean I am willing to give up my cigarette . . . (laughter). I have no higher compliment. Jaffe: You've had a lot of questions of how much kinetic energy is still left in the gas and it's measurable, at least an upper limit can be put on that from the fluctuations in the trailed radio sources—at least for things on a shorter distance scale than a few hundred kiloparsecs. I did that about 15 years ago. I got a rather small value. Evrard: Do you remember what the value was? Jaffe: Yes, essentially the velocity still remaining in the gas was no more than say 200 km/sec. Evrard: Is that a one-dimensional or a three-dimensional velocity? Jaffe: It's a one-dimensional velocity, and so, it's only about four percent in energy. Some of that could be due to intrinsic effects in the galaxy that makes the trail and some of it is due to the galaxies themselves distorting the trail. Owen: The central C-shape, however, which are the wide-angle tails, are thin streams of gas being shot out into this medium. We always had trouble understanding how something attached to a simple galaxy can be bent, and it seems to me that this provides maybe the most promising mechanism for getting the sorts of velocities that we need to be able to explain these sources. That really should get looked at—maybe this is the best test for the sort of velocity that you are looking for. Katz: I'm just wondering if you're worried since you're using periodic boundary conditions, that your clusters are a large percentage of your volume and how that would affect your results.

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Evrard: Yes, I mean that's potentially a worry, but the way that I make an attempt to get around that is by evolving in a box which has a density greater than critical, and that's why I add a DC component. It very well might affect the run of density in the very outer parts but I just don't have the computational power to check that. Unknown: Your total X-ray luminosity is dominated by the core but you don't resolve the cores very well in here. Could it be that that's possibly a second parameter—just what happens to the core in these simulations? I mean your core is always a fixed number of particles, so that limits the variation in the X-ray luminosity which you've predicted . . . Evrard: Yes, you're right in the sense that one can add more luminosity to these clusters by continuing the rising density profile to arbitrarily small radii; but there are a couple of practical limitations. One is that the cooling time for the gas will eventually become so short that it would be invisible around keV energies. Another is that the core radii apparent in the current set of models already lie in the same range as the observed clusters fit by Jones and Forman. There's not much freedom for large variations in the core emission without ruining this argreement.

EVOLUTION OF CLUSTERS IN THE HIERARCHICAL SCENARIO

Nick Kaiser CIAR Cosmology Program CITA, University of Toronto 60 St. George Street Toronto, Ontario, M5S 1A1 Canada

Abstract. If the universe has closure density and the spectrum of primordial density fluctuations is a power law, the lack of any preferred scale means that the clustering should evolve in a scale invariant manner. These self-similar models allow one to approximately predict the evolution of the clustering in e.g., the 'standard' cold dark matter model. I describe how these models yield predictions for the evolution of the cluster populations. Particular attention is given to the range of spectral indices for which the scaling should be valid. I argue than the allowed range is — 3 < n < 1, though quite what happens for spectra near the upper bound is somewhat unclear. The cold dark matter power spectrum has spectral index n ~ — 1 on the mass scale of clusters. For this value of n, I find that the comoving density of clusters classified according to virial temperature Tv or by Abell's richness, should show weak positive density evolution 9log n(Tv, z)/dz ~ +0.3. Clusters classified by total X-ray luminosity should show ~ +3, but the assumptions used to strong positive density evolution dlogn(Lx,z)/dz predict the total X-ray luminosity are somewhat questionable. More robust predictions can be made for the halo emission, and I describe an evolutionary test which should be feasible with ROSAT.

1. INTRODUCTION Rich clusters have had much impact on cosmological theory. They give the strongest indication that the universe contains copious amounts of dark matter and give an empirical estimate of the baryon to dark matter ratio. Correlation analysis of clusters reveals very strong clustering on a large scale, with important implications for the spectrum of primordial fluctuations, though quite how this structure is related to the underlying density fluctuations remains unclear. Clusters are very useful for normalisation — setting the overall amplitude of primordial fluctuations — as it is in these objects that we 'see' the dark matter distribution directly via the velocity dispersion of galaxies or the temperature of the hot gas. The feature I will consider here is the evolution of the cluster population, which provides us with an additional discriminatory test. In a previous paper (Kaiser, 1986) I considered the evolution of clusters in self-

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similar hierarchical clustering models. I argued that these models would give a reasonable approximation to the evolution predicted in more realistic theories such as the 'standard' cold-dark-matter model. These calculations predict that while the high mass end of the distribution function n(M) should show negative density evolution (i.e., fewer massive clusters in the past), what was more relevant to counts of Abell clusters was n(Tv), where Tv is the virial temperature, and that n(Tv) would show little or no evolution. The reason for this somewhat puzzling behaviour is that since the clusters forming at any time have a density which is just some multiple of the background density, a smaller mass cluster in the past is needed to give a given richness or Tv, and these have an abundance which turns out to be very similar to the abundance of clusters of the same Tv today. Using these models to predict the X-ray properties I argued that clusters selected by Lx would be expected to show very strong positive evolution. At that time, the data did not provide very strong constraints. The Abell counts were compatible with no evolution, but only extended to low redshifts. The X-ray constraints were also rather weak and somewhat contradictory. Since then there have been various interesting developments. On the theoretical side, the theory of hierarchical clustering has been extended using the Press-Schechter approximation and the statistics of peaks to incorporate (more realistically one hopes) the effect of curvature in the fluctuation spectrum. More recently we have the advent of highly sophisticated N-body/hydro simulations (see Evrard, these proceedings). On the observational side Gunn and his collaborators (these proceedings) have found several high redshift clusters, indicating an abundance of high velocity dispersion clusters at high z similar to the present abundance, and there has been extension and reassessment of X-ray evolution constraints (Henry et al. poster paper this meeting). The future prospect for testing theory against cluster evolution seems bright, particularly with the upcoming ROSAT mission. It therefore seems timely to review some of the earlier calculations, and I will also critically discuss what seem to me to be the weakest assumptions, particularly with regard to X-ray properties, since these have for the most part also been adopted in the new generation of numerical studies. I will start with a discussion of self-similar models, paying particular attention to the question of what range of initial spectral indices would give rise to self-similar clustering. I will then discuss how these models should approximate the clustering in physically more interesting models such as the cold-dark-matter model, and briefly describe the results from the Press-Schechter approximation. These largely bear out the predictions from scale free models, but also give a useful guide to the evolution expected at higher redshifts. Finally, I will consider some caveats. I will argue that the most robust prediction (whether this be made from self-similar models, Press-Schechter models, peaks or full blown numerical simulation) is for the number of clusters as a function of velocity dispersion or virial temperature. To predict the total X-ray luminosity requires numerous auxiliary assumptions which are somewhat questionable. This is somewhat unfortunate, since it is the n(Lx) predictions which are most dramatic. I will then describe an evolutionary test using cluster halo emission which may be feasible with ROSAT, and which avoids many of the problems associated with predicting the total X-ray luminosity.

2. SELF-SIMILAR CLUSTERING The idea here is that if one has an Einstein-de Sitter universe, so the expansion factors etc. are power laws, and if the initial fluctuation spectrum is also a power law,

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the lack of any preferred scale in the system means that the clustering should evolve in a scale invariant manner - i.e., should look the same at different times aside from some suitable scaling of length/velocities (see e.g., Peebles, 1980; Efstathiou, Fall and Hogan, 1979). To understand how and when this result might arise consider the following set up. Imagine laying down a very large number of collisionless particles on a uniform grid. Perturb these from the grid with sinusoidal displacements with random phases to generate a Gaussian random field with small amplitude density ripples, power law spectrum P(k) oc kn and some small cut-off at a mass scale M\. Now start evolving this. At early times linear theory gives Ap/p oc tf2'3 as usual. Eventually some regions with scale similar to the cut-off reach non-linearity; Ap/p ~ 1, turn around and make virialised* clumps of scale M\ and with density equal to the current background density modulo some factor of order unity (~ 200 if the cold spherical collapse model is anything to go by). At later times larger regions will approach the non-linear regime, turn around and subsume smaller scale clumps. Since, in linear theory, density perturbations grow like a, the mass scale of non-linearity grows as M* oc a"+3, the characteristic density scales as p* oc a" 3 , and the virial temperature scales as T* oc M/R oc Mj

pj

oc a"+5.

Aside from the small mass scale cut-off, the system we have set up is exactly self-similar. The crucial question is whether the system will effectively forget about the cut-off at late times. If so, then the clustering must obey an exact scaling relation. For example, the correlation function must obey

t(r,t) = where, for comoving r coordinate, r*(£) ~ Mj OC a 2 ' n + 3 . Similarly, the mass spectrum of bound clusters catalogued according to some physical variable X (e.g., mass, virial temperature etc.) must satisfy

which follows from the requirement that the mass fraction per log interval of the dimensionless, scaled variable Y = X/X+ be constant in time. Note that these relations say nothing about the form of £ of n(M), though if one makes the additional assumption that the small scale clustering be statistically stable (Davis and Peebles, 1977; Peebles, 1980) this constrains the form of the 2-point function. What these equations do allow us to do though is to retrodict the state of clustering in the past from knowledge of the * That is, having no appreciable expansion or contraction, but not necessarily being particularly relaxed in any other sense.

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present, plus, of course, the assumption of a hierarchical scenario with some effective value of n. The specific thought experiment considered here assumed collisionless particles, and Gaussian fluctuations for concreteness. The results are not restricted to this. One can include gas, with shocks etc., but one cannot allow dissipation or non-gravitationally induced heating, as this would introduce a physical scale in the system. One can also have non-Gaussian fluctuations. For example, a power law distribution of randomly placed seed masses would fulfil the scale-invariance requirement.

3. ALLOWED RANGE OF SPECTRAL INDICES The question of what range of values of n lead to self-similar behaviour is a sticky one. Peebles (1980) argues that the valid range is — 1 < n < 1, from consideration of finiteness of the kinetic and potential energy densities associated with clustering; T = (up/2), where u p is the peculiar velocity, and W = Gp fd r £(r)/r. The same range has been advocated by Efstathiou et al. (1988). Let us consider first the lower limit on n. To be sure, if n < — 1 then T and W are formally divergent at large scales. For example, the contribution to the peculiar velocity variance per log interval of wavelength scales as (v?) a A~( + >' . However, this need not disrupt the development of small scale clustering. One might imagine imposing a very long-wavelength cut-off to render the energy finite. The only effect on small scale clustering is the absence of the tidal field due to the missing long-wave perturbations, but this is just on the order of the rms density fluctuation at the long-wavelength cut-off and is tiny compared to the small scale tides. This is true for any n > —3, so the only real lower bound on n is that clustering should proceed from small to large scales. The problem with the divergence of energy at small scales if n > 1 is more worrying. There is certainly nothing to stop one setting up an initial fluctuation field with n > 1. We do, however have the well known result that one cannot set up a random fluctuation field with n > 4 since large scale growing fluctuations with this spectrum are spontaneously generated by any small scale fluctuations.* For n < 1, the binding energy of the small mass cut-off scale clumps is much smaller than the binding energy of larger scale overdense regions when they eventually turn around. If the clustering energy T + W was conserved then one could confidently argue that in such a case, the system would effectively forget about the small scale cut-off, since varying M\ by a factor 2 say would have a tiny effect on the final total energy. Conversely, one might expect that with n > 1, the system would always remember the cut-off scale. It might be that this binding energy gets tied up in dense knots of matter which then effectively decouple from the growth of larger structures. If so, the scaling solutions would still be expected * This result can be understood physically as follows: What counts for the growing mode amplitude is the perturbation to the Newtonian potential. A Poisson distribution of mass points has rms mass fluctuations growinglike \ / M , and consequently the fluctuation in the Newtonian potential grows like y/M/R oc M1'6. If some local process rearranges matter on small scales, then the monopole and dipole of the mass distribution must vanish by conservation of mass and momentum. Consequently, the dominant long range fluctuations in <j> correspond to a random distribution of quadrupole sources, and the <j>fluctuationsthen fall with scale 2 powers of wavelength faster than with a Poisson distribution of monopoles — consequently the power spectrum is P oc k rather

than Pock0.

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to hold, provided we smooth over the very small scale dumpiness. However, it seems more likely that the substructure will get rapidly erased, and if so, this would mean that the velocity dispersions of late collapsing large mass clumps would reflect the Mi scale binding energy; i.e., much larger than the simple linear theory plus cold spherical collapse expectation. This might sound like an argument for a 'non-linear bootstrap' to accelerate the growth of clustering over that of linear theory as hypothesised by Press and Schechter (1974), but this need not be the case. It seems more likely to me that bound regions would turn around much as predicted by linear theory, but then collapse to much higher density as they soak up the very negative total energy of the subclumps from which they are made. If this picture is correct, then some predictions of self-similar solutions, say for the abundance of regions with moderate overdensity (say a few hundred), might again still be valid for spectra with n > 1. The situation is further complicated by the fact that T + W is not conserved in an expanding universe. The Layzer—Irvine equation is

This equation can be read as dE = —PdV, where E is the internal energy associated with clustering in some region of volume V, and P = p(2T + W)/3 is the pressure. The first contribution to the pressure is the usual kinetic pressure, while the second term is just the gravitational force per unit area across a boundary due to the clustering. As noted by Peebles, if a self-similar scaling solution is to hold, then this requires that T = -AW/(n + 7), or equivalently that P = ~p{\ - n)T/l2. Not surprisingly, for n > 1, this requires a net negative pressure, so the universe can do work on the internal dynamics of the clustering process at just the rate required to unbind the tight small scale clumps. While this might sound a bit fishy, a negative net pressure is not forbidden on energetic grounds, as there are counter examples — decaying linear perturbations, for instance. In Peebles discussion of the Layzer-Irvine equation (Peebles 1980) he argues that —W/2 < T < W, in which case clusters can only lose energy to the expanding universe, but the lower bound comes from the assumption that dW/dt will always negative, so that is not much help here. It may be that the net pressure does always tend to be positive. If so, a n n > l spectrum cannot give rise to an exactly self-similar clustering pattern (though some features may be approximately scale free as discussed above). Moreover, these considerations cast some doubt over the argument that with n < 1 things are alright. Perhaps spectra with n less than but close to unity will on close inspection, be found not to be exactly self-similar. Clearly, some input from numerical experiments is needed to sort out this mess. Some numerical experiments have been made which should have been able to resolve this issue. Both Press and Schechter (1974) and Efstathiou, Fall and Hogan (1979) have looked at a simulation with fluctuations imposed by placing particles at random within cubical cells but requiring that all cells have exactly one particle. They both identified this with a n n = l spectrum, since fluctuations in a top-hat sphere then vary as M i . In fact, this process generates an n = 2 spectrum — the variance for a tophat is a bad guide to the spectral index for any n > 1, since then the fluctuations are dominated by surface effects. A better way to think about this is to think of the source for the long range gravitational fluctuations which are a set of randomly aligned dipoles. This gives a spectrum intermediate between randomly placed monopoles (n = 0) and the limiting n = 4 case mentioned above. This spectrum is then well into the regime where one might expect self-similarity to be disturbed. Press and Schechter found that the characteristic mass of clusters grew faster than or' as they expected from linear

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theory with n = 1 (and therefore much faster than the Af«, oc a 6 ' 5 predicted for n = 2). Efstathiou, Fall and Hogan, on the other hand, found that the mass scale grew more slowly than ar' , but it looks to me that their results would agree very well with the n = 2 predictions. Clearly, better experiments are needed to resolve this interesting problem. The most extensive numerical simulations of scale free models have been made by Efstathiou et al. (1988), but they restricted attention to spectra with n < 1, which, perhaps with the exception of the n = 1 case would not be expected to show any departures from scaling. Strangely, they did find departures with n = —2, though that may just reflect difficulty of evolving such a flat spectrum over sufficient time to establish scaling without exhausting the limited spatial bandwidth available. Let me summarize this rather confusing and inconclusive section: A simple (though questionable) argument suggests that — 3 < n < 1 is the allowed range of initial spectral indices compatible with exact self-similarity — the upper bound being set by the requirement that the binding energies of systems not be dominated by the cut-off scale. For n > 1, some properties of the clustering may still be well approximated by the scaling solution. A more careful consideration of the energy budget opens up the possibilities that even spectra with n > 1 may lead to self-similar clustering, or that some spectra with n < 1 would not. The evidence from numerical simulations is, as yet, inconclusive. These problems notwithstanding, I think one can be reasonably confident in applying self-similar models provided n is substantially less than unity.

4. APPLICATION TO PHYSICALLY PLAUSIBLE SPECTRA The perfect power-law initial spectrum assumed above is physically implausible. We know that the physics of perturbation growth around zeq will impose a feature on relevant scales even if the primordial spectrum is a perfect power-law. In the cold-darkmatter model for instance, there is a transition from an n = —3 spectrum at short wavelengths to the primordial n = 1 slope at large scales. However, the transition between these two asymptotic regimes is very gradual, spanning many orders of magnitude in mass, so a self-similar model with an appropriately chosen spectral index should be a good approximation. For the cold dark matter model the effective slope on the scale of galaxy clusters is around n — — 1.

5. OPTICAL CLUSTERS If the primordial density fluctuations are a Gaussian random field then one expects that the high mass end of the mass distribution function n(M) will fall precipitously, reflecting the sharply falling tail of a Gaussian distribution. In the self-similar approximation, the mass distribution function at an earlier time z looks just like the mass distribution today, only with masses scaled down by a factor M*(z)/Af+(0). This would lead one to think that there should be very strong negative evolution of high mass clusters — if we look at the objects corresponding to say 3
Evolution of Clusters in the Hierarchical Scenario

SSS

What Abell did, in contrast, was to measure the number of galaxies within a certain metric radius of the cluster centre, not at a given density contrast. If mass-to-light ratios for all clusters are similar, then Abell's richness is roughly equivalent to virial temperature Tv ~ M/R. Similarly Gunn's observation was really that the clusters he found had similar velocity dispersions to those of very rich clusters today. What we have to do then is calculate the evolution of n(Tv), the distribution in temperature, and this gives a very different prediction. We can use equation 1 with X = Tv. Now T* oc a( 1 -")/( n + 3 ) and M* oc a 6 /( n + 3 ), so we have _^ .^ n(Tv,z)dTv = (1 + z)"+ 3 n((l + z)»-**Tv,0)dTv. (2) The present rate of change of the comoving number density of clusters is then given by

*)\ dz j

= T v

7-nn^s) n + 3 "'

|

l-nT(dn(Tv,z)\ n + 3 v \ dTv )

^ z=0

To estimate the evolution rate we need an estimate of the logarithmic slope of the distribution function n(Tv). This is somewhat uncertain, but it is encouraging that both the Abell counts and the X-ray luminosity function (combined with the empirical Lx—T relation) give the same answer: N(> Tv) oc T^ 2 - 7 , or for the differential 'temperature function' n(Tv) oc T " 3 7 , so Tv{dn/dTv) ~ -3.7n(T v ). If the clusters we see really do form from an initial spectrum with index close to —1, there is then approximate cancellation between the two terms in equation 3. In fact, the prediction is for mild

positive evolution: d\ogn(Tv,z)/dz

= ((7-n)+(l-n)d\ogn(T v , z)/dlogTv)/(n+3) ~

0.3. If we perform the analogous calculation for the evolution of the number of clusters at a given M& (where the subscript indicates that the mass is to be taken at a fixed density contrast) we get a very different answer. If we use the same estimate of N(> Tv) this implies JV(> M&) oc M 7 1 ' 8 since Tv ~ M&/R oc M^ . Following the same steps = —2.4, i.e., quite strong negative evolution. as above then yields d\ogn{M^,z)/dz The same effect can be seen in calculations using the Press-Schechter approximation (Cole and Kaiser, 1989). If one calculates number density as a function of z and M A then one finds that the surface slopes steeply down with increasing M& and z as expected. However, a line of constant Tv on such a plot traverses the slope. The calculations extend the simple estimate of the present rate of evolution (equation 2), and indicate that at moderately high redshifts we do expect to see the number of clusters at given Tv start to fall — the cancellation is between a power law and the exponential from the Gaussian tail, and eventually the Gaussian has to win. Similarly, the small present rate of evolution derived above is only valid where our estimate of the slope of the temperature function is valid. If the logarithmic slope gets much steeper at larger Tv, as one would expect from Gaussian fluctuations, then these extremely hot clusters would show negative evolution. 6. X-RAY CLUSTERS An analogous calculation can be made for the evolution of clusters selected according to X-ray luminosity. If one assumes that cooling and non-gravitationally induced heating are negligible then the scaling laws derived above should apply equally to the gas as to the collisionless dark matter. The total X-ray luminosity is on the order of Lx ~ MpTv , so the characteristic luminosity is

U oc

M^TV1.

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Now the important thing to notice is that for the spectral index n ~ — 1, as is appropriate for cold dark matter, the product M*p* is independent of redshift, even though individually both JM* and p+ vary as high powers of (1 + z). This means that the characteristic luminosity is essentially constant in time, and so consequently we expect the number of clusters at constant Lx to increase with redshift roughly as M^"1 i.e., as (1 + z) 6 /( n + 3 ). This is very dramatic evolution indeed, and with R.OSAT it should be quite easy to test for this. The fly in the ointment is that there are several dubious features about the assumptions that must be made in order to predict the total X-ray luminosity. The big problem with the total X-ray luminosity is that it is dominated by the core region of the cluster, and it may well be that the simple minded picture of primordial gas falling in, shock heating etc. may not be applicable. One problem is the presence of cooling flows. These have some influence on the total X-ray luminosities today, and matters will only get worse at higher redshift since the ratio of cooling time to dynamical time will decrease. Another unsettling feature is the high metal content of the intra-cluster gas—this may be due to ram stripping of galaxies passing near the centre of the cluster, and which might again disturb the cosy idealised picture used here. Models incorporating gas injection have been widely studied by Cavaliere (these proceedings). Another problem is the question of what determines the X-ray core radii of clusters. It is plausible that this is controlled not by gravity, as the model here assumes, but by thermal history of the gas before it became incorporated in the cluster. Indeed, we know from the Gunn—Peterson test that something pretty dramatic must have happened to the primordial gas at z > 3; one possibility is that the gas was shock heated by explosions to some very high temperature. If this temperature was high enough, the gas would never be able to fall into cluster potential wells, and the scenario envisaged here would be entirely inappropriate. While such a high energy input is somewhat extreme, and is much more than is strictly necessary to avoid the Gunn— Peterson constraint, a more reasonable worry is that the gas was heated to an adiabat similar to that of the gas in cluster cores today. The core gas density contrast is around Agas ~ 10 — 10 , so jf,the gas starts off uniform then the gas need only be heated to a temperature T ~ Ajas Cluster to fall below the entropy of the gas in cluster cores at present. On this view, it seems entirely plausible that the total X-ray luminosity might be strongly affected by early energy input into the gas. A further technical problem is that the dark matter density profiles in cores of clusters may reflect the spectral index on a mass scale much smaller than that of the cluster as a whole. This is no problem if the initial spectrum is exactly scale invariant, but is a worry if one is trying to use these models to infer the behaviour in models like cold dark matter. These are very real worries; not only for the type of calculations shown here, but also for numerical simulations with hydrodynamics which make the same simplifying assumptions about the thermal history of the gas. These problems can be largely avoided if instead of using total X-ray luminosity we use only the low surface brightness emission from regions well outside the core of the cluster. This type of test should be possible with ROSAT with it's high angular resolution. The essential assumptions needed here are that the low density gas at these radii is sitting in hydrostatic equilibrium in the potential well, and that the gas to mass ratios and dark matter profiles of clusters at earlier times are just like those of present day clusters. What would be most desirable from a theoretical point of view is some X-ray surface brightness criterion to pick out the regions of a clusters at a given overdensity — ideally way outside the core, but still at sufficiently high density that one can believe the cluster

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is virialised (say at density contrasts greater than a couple of hundred). This is easily managed: With the above assumptions the X-ray surface brightness at projected radius r (as seen by an observer near the cluster) is

Z(E)dE = Jdl where the quantities under the integral are evaluated at radius v / 2 + r 2 . Now the temperature is given, to order of magnitude, by T ~ M/r ~ pl'2r2, so we have T,{E)dE =

apV2g(E/kT)exp(-E/kT)

where a is a geometrical factor of order unity determined by the shape of the cluster. Now for constant density contrast p oc (1 + z) , and putting in the redshift effect on the surface brightness and temperature gives. XA(Eo)dEo = a (1 + zfl2g{EolkTo)

exp(Eo/kTo)dEo

where To is the observed temperature and some additional constants have now been absorbed into a. Thus, for a low energy detector, were it not for the Gaunt factor, an isophotal radius at surface brightness oc (1 + z) ' gives precisely what is needed — i.e., a radius where the density contrast is constant*. Since the Gaunt factor is a fairly weak function of temperature, a crude estimate of To should suffice to correct for this. Let me re-emphasise that one need not assume that all clusters have the same shape — i.e., the same a parameters — what is assumed is that the distribution of a's, or, more generally the joint distribution in a and T/T* is the same at different epochs. These considerations suggest the following evolutionary test which can be sketched in outline as follows: 1. Identify the extended sources 2. Get redshifts z 3. Get crude temperatures — either from the X-ray colours or from the velocity dispersions — and crudely estimate g(Eo/kTp) for each cluster. 4. Measure the radius r of the S = (1 + z)^' gT,o isophote, where E o is some observationally convenient surface brightness — say equal to that of Coma at 2-3 core radii. If all has gone well these radii are radii of constant density contrast, and therefore the characteristic radius (in comoving coordinates) scales as r* oc Mj OC a2An+•*), and consequently the evolution in the differential 'radius function' evolves as n(r, z) = (1 + z) 8 /( n + 3 )n((l + z)2^n+%

z = 0).

(4)

The evolution rate at the present is d log n(r, z) 8z

1 / (i» + 3) V

n

d log n(r,z) dlogr

If we use the same empirical estimate for the slope of the cumulative distribution function N(> M A ) oc M ^ L 8 -» N(> r) oc r ~ 5 4 -» n(r) oc r ~ 6 4 we find dlogn(r,z) _ -4.8 dz (n + 3)*

K)

* In my paper of 1986 this A = constant surface brightness was erroneously given as being proportional to 1 + z.

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For the spectral index n ~ — 1 as appropriate to the cold dark matter case, this gives the same negative evolution index d log n(r,z)/dz = —2.4 as for clusters selected according to M&. Note that this is not inconsistent with the strong positive evolution predicted for clusters selected according to Lx; the marginal surface brightness (as seen by an observer next to the cluster) is higher in the past by a factor p^<^ ~ (1 + z)^'"*, the physical radius is R = r / ( l + z) 2 , so at constant r we are selecting clusters according to a absolute halo luminosity Z-halo — %$ oc (1 + •?)^'2, which is higher in the past. It is apparent from equation (6) that the evolution rate is quite sensitive to the spectral varies by a factor 3, so index. For n varying from 0 to —2, for example, d\ogn(r,z)/dz this should be quite a sensitive probe of the spectrum of fluctuations.

REFERENCES Cole, S., and Kaiser, N., 1989. Mon. Not. R. Astron. Soc, 237, 1127. Davis, M. and Peebles, P. J. E., 1977. Ap. J. Suppl., 34, 425. Efstathiou, G., Fall, S. and Hogan, C , 1979. Mon. Not. R. Astron. Soc., 189, 203. Efstathiou, G., Frenk, C , White, S. and Davis, M., 1988, Mon. Not. R. Astron. Soc, 235, 715. Kaiser, N., 1986. Mon. Not. R. Astron. Soc, 222, 232. Peebles, P. J. E., 1980. "The Large Scale Structure of The Universe", Princeton: Princeton University Press. Press, W. H. and Schechter, P., 1974. Ap. J., 187, 425.

DISCUSSION Henry: Can I make a comment on the Henry, et al. (Einstein) data? There's a more conservative interpretation of the data which is only that the bandpasses of the two instruments used to measure the low and high redshift fluxes are different, and the differences in the luminosity function could be only due to a color correction—it could also be due to what you're saying. Now, I'm an observer. I'm taking the conservative approach first. Kaiser:

No, no, no, CDM is the most conservative theory (uproar).

Juszkiewicz: I think I should make a comment at this point. Clearly, you know that this kind of normalization ( 6 = 1 ) means disaster for the small scale provisions of CDM. Kaiser: Well, I'm glad you're here to debate that because I have a viewgraph on that—but it's not obvious to me, but I think this is the way to look at it. Burg: How do you get velocity dispersions as a function of richness? Kaiser: We just use the Struble/Rood compilation. What we're assuming is that there's a fair sample of velocity dispersions at any richness. . . .

Evolution of Clusters in the Hierarchical Scenario

SS7

Daly: At a given X-ray luminosity, if you compare a cluster at low redshift with one at higher redshift, would you expect much less gas mass in the higher redshift cluster? Kaiser: Yes, it would be denser by a factor of (1 + z) 3 and that counteracts the fact that the . . . Daly: So, there will be strong evolution in the relationship between the x-ray luminosity and the gas mass? Kaiser: I think that's right. The core radii in this naive sort of picture is smaller in the past. Evrard: You've got to be careful about how you measure the mass, right? The mass has got to be in a fixed overdensity, so . . . Kaiser: Within a core radius or something? Within the X-ray emitting region? That's fine. Henry: A previous speaker said that the luminosity functions have negative evolution with redshift and you are saying they have positive. For us poor observers, who are confused, I don't understand (laughter) . . . Kaiser: Yeah, he's wrong (laughter). Evrard: I knew this was going to come up. In a self-similar hierarchy, Nick, you expect a number density distribution of a generic Schechter-like form with a power law faint end and exponential cutoff at high luminosities. What you're saying is that the faint end abundance grows at higher z but, since V is decreasing with z, the number above the knee must decrease. So the key question is what is L*l I would be very suprised—probably willing to bet a bottle of California wine against it—if there are more clusters above 10 erg s at high z than there are today. There may be more at 10 43 but not at 10 45 . Kaiser: Because you're making additional assumptions that I'm not really making. If your prejudice is correct, that the luminosity function looks like that, then what you say is true. Evrard: You don't have perturbations high enough to generate anything well beyond the knee. They just haven't collapsed yet. Kaiser: Well, but we don't see anything with a bend like that. Evrard: Yes, that's because the data lie in that very narrow mass range, so the knee gets streched out. Kaiser: Say I take the clusters in some logarithmic range of luminosity here. Then they have cousins at high redshift who look just the same in density contrast but are smaller and also denser and they're more numerous inversely as the mass, and the smallness and the denseness counteract each other.

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Evrard: I think that argument is correct below the knee but not above it. That's all. Daly: I think there's an important point here, to define clusters in different ways in a fixed density contrast. If you have a cluster which is not evolving in Gus' model, in yours it's evolving quite strongly when the background is dropping away. Kaiser: Right. Fall: I have a comment to make, and that is we know that at least some and perhaps all of the gas in the clusters has come out of galaxies because it's got metals, and if it did that recently, and in particular, if it did that as part of the formation process, say by stripping, then that would modify these predictions, very dramatically. Kaiser: It certainly would. Then, you'd have to go back . . . l: Whether cold dark matter is right or wrong. So, I mean I'm a little bit nervous about you using this as a strong test of a particular background model. Kaiser: Well, you'd want to do checks to see that you were getting the same gas to mass fraction. Giacconi: Well, that's right. Neither model assumes an evolution of the gas. Eall: That's what I'm saying. Kaiser: It's definitely a weakness. Burg: We see a gas mass to dark mass variation—a strong variation in present day clusters. Kaiser: But that may be okay. Fall: The observations may be a stronger test than they are of, say, the power spectrum slope or something like that. Kaiser: What we'd be led back to is saying what the theory really predicts robustly is the distribution of potential wells and you'd have to say, after doing ROSAT, you would then have to go and do spectroscopy and get temperatures for all the candidate wells. Juszkiewicz: I think I should explain what I alluded to earlier. What I had in mind were all of the incredible problems that CDM would face on small scales if you choose 6 = 1 normalization, and it's not only the pair-wise velocity dispersion which is by a factor of several larger than observed, but one cannot also reproduce the slope of the galaxy/galaxy correlation function. What happens is that when you evolve the N-body simulations between density perturbations on small scales that grow faster than density perturbations on large scales, the slope of the correlation function similarly steepens with time. Davies, Efstathiou, Frenk & White discovered in their simulations—that when they used b = 1, the correlation function was far too steep. So, what all this tells me is that there's something wrong with the slope of the CDM spectrum. If I need

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b = 2.5 to account for small scale structure and I need 6 = 1 , which is a completely different normalization, to account for the long wavelength tails and make it compatible with observations then there's something wrong with the whole spectrum. Okay, and I'm really glad, Nick, that you said that CDM with 6 = 2.5 is ruled out by large-scale velocities. I absolutely agree with you on that. However, I also agree with Simon White who says that CDM with 6 = 1 is ruled out. Kaiser: But they turned the computer ofF at a redshift of one. Juszkiewicz: Well, if they'd waited, the correlation function would get even steeper. Kaiser: How do you know? Weinberg: Well, I think in the very first paper, they did run it all the way up to z = 0 and 6 = 1, and that was where they found problems. Kaiser: Then they started at redshift 0.4 though. Weinberg: I mean it does seem that a place where you have to take refuge is in saying that numerical simulations on the small scales are inadequate and then add— which is possible, given the sorts of effects that West and Richstone talked about, at that point, it may actually be important to really model the galaxies with their halos and relaxation and so on. It seems like the only way it can survive is if effects that are not currently in the numerical simulations do come in and save you. Kaiser: Well, this Carlberg & Couchman thing I find very interesting. I'm not sure if you have to believe how they identified galaxies but it's impressive. It made an enormous difference to the velocity. Weinberg: Well, we've been told and I don't know if it's true but we've been told by Simon White that the normalization that Carlberg & Couchman used was, in fact, 6 = 2.5 and that they misstated . . . Juszkiewicz: They defined it in a different way than the guy before and when one renormalizes, you end up with the same value of 6. Kaiser: I wasn't aware of that (laughter). Oh, well, its dead (more laughter). Juszkiewicz: There's one more thing that I should say—I think it's important. It's about this 6 = 1 , predicted velocity. I don't think it's a prediction, because when you normalize the spectrum to agree with the amount of the clusters, you essentially normalize it to agree with the peculiar velocity because the two things are not independent. Kaiser: Oh, I think you're talking about very different length scales and very different mass scales. Juszkiewicz: Well, I think that I can prove that for a very wide range of logarithmic slopes of the power spectrum normalizing the one thing against the other thing, right, unless I use an extremely steep spectrum. So . . .

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Kaiser: Well, obviously, one would like a bigger lever arm between the scale you normalize on and the scale you test. Juszkiewicz: Okay. One last question? Djorgovski: Well, obviously the large scale motions are important and you alluded that there may be sampling or interpretive problems. I'd like to show just one transparency. It's a very simple exercise that de Carvalho and myself did and each and every one of you can do it. You open up the Ap. J., write up peculiar velocities from Tully-Fisher papers and those from the Faber-Z)n — o relation paper and here is the comparison for the same clusters—notice the scale. I think at this point, you have a choice of either believing Tully-Fisher velocities or Dn — a velocities or the obvious third choice (laughter). Kaiser: Are those very distant clusters? Djorgovski: That's all the clusters in the overlap between Seven Samurai and Aaronson, et al.

DISTANT CLUSTERS AS COSMOLOGICAL LABORATORIES

James E. Gunn Princeton University Observatory Princeton, NJ 08544

Abstract. Distant clusters provide ideal samples of galaxies in more-or-less standard environments in which to study the evolution of the galaxies themselves, bound structures, the larger-scale environment, and perhaps eventually to provide data for the classical cosmological tests. We review some of the the observational and theoretical aspects of these topics.

1. INTRODUCTION Clusters of galaxies at large redshifts provide, in principle, a set of objects whose evolution can be traced directly from epochs as early as z w 1 with present observational capabilities to the present. It seems almost inconceivable that large clusters are destroyed, and although it is quite clear that clusters are still forming, the inner regions of dense clusters must be quite old. Thus if one looks at galaxies in such regions and takes care to sample clusters whose comoving space densities are roughly the same at all epochs, it would seem as if one could define a quite homogeneous sample of galaxies in which the direct forbears of a set of present-day objects could be studied. We are not quite in a position to do that because the cluster catalogs are in such a sad state, but some progress is being made in this direction; we will discuss this at greater length below. If one could choose clusters at epochs from the present back to large redshifts in some objective way, it would also be possible to study the evolution of the cluster population itself. The dynamical times of relatively low-density clusters like Hercules are so long and their structure so chaotic that they cannot be very old, and indeed most theories of the formation of structure predict that structures at cluster scales, of order 10 5 MQ or larger, are typically just forming, with only the high-density tail of the fluctuations at these masses in relaxed, "virialized" structures at the present time. This evolution is very highly diagnostic of the perturbation spectrum at these masses, as has been recently emphasized by Peebles et al. (1989) and Evrard (1989) (but see the paper by Kaiser (1989) in this volume for a somewhat contrary view). We will discuss this question in more detail below as it relates to the present very incomplete observations. In a similar vein, one obtains a rather different kind of dynamical data from clusters

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than one gets from observations of the form of large-scale structure which is almost in the linear regime; since one can obtain the masses of clusters from virial analyses and the formation of clusters is readily investigated by N-body techniques, it should be possible to determine the details of the bias, for example, by insisting that the clusters at each epoch fit smoothly into the spectrum obtained from the large-scale structure. Attempts to do this using the (poor) present-day data have been done by Frenk (1988) and Frenk et al. (1989) and by Kaiser (1989) (with predictably contradictory results), but we are not by any means yet in a position to do it as one would like with cluster catalogs which reach from the present out to large redshifts. Finally, it still seems possible to some of us that we will understand the evolutionary effects well enough that cluster galaxies or perhaps cluster dynamics will be useful for the classical cosmological tests. It is clear at this point that the data are most or perhaps only useful for studying the evolution of the objects themselves, but there are galaxies at large redshifts which appear spectroscopically very dead, and there is still some hope that they can be used for determining the deceleration parameter. It is always worth remembering that however well one determines the density parameter Q, locally, the measurement of the deceleration describes much different global physics, and must be pursued if at all possible.

2. CATALOGS, SURVEYS, AND OUTLOOK FOR THE FUTURE Cluster catalogs to date have all been prepared by visual inspection of plate material, either the original Palomar survey plates (Abell 1958) or their more modern (and better) Southern counterparts (Abell, Corwin, and Olowin 1989). The faint survey by Gunn, Hoessel, and Oke (1986) used similar 'techniques' on deeper plate material, starting, in fact, with fine-grained Schmidt plates no better in principle than the new Southern survey plates, and going on to plate material gathered by a variety of techniques on large reflectors. These catalogs have a number of serious flaws as quantitative tools, all of which have been extensively discussed; suffice it to say that probably nowhere in astrophysics is the connection between the theorists's notion of an object and the observer's notion so tenuous as the question of what a cluster is and what its properties are. Attempts to do better are underway. The Cambridge APM survey, under the direction of George Efstathiou, seeks to produce a catalog of clusters made with objective critera from a catalog of galaxies constructed objectively from automated scans of finegrained UK Schmidt plates, and results are starting to emerge from that effort. On the distant-cluster front, a survey has been underway at Palomar for the last three years by Hoessel, Oke, Postman, Schneider and myself, using the Four-Shooter CCD camera (Gunn et al. 1987) in scanning (TDI) mode with very broad-band HST filters (F555W and F785LP). The Gunn-Hoessel-Oke survey became seriously incomplete at a redshift of about 0.5, or in any case the number of clusters per unit redshift per unit area dropped precipitously there. Since various scenarios for the formation of structure predict vastly different frequencies of rich clusters at early times, the question of what the number-redshift relation really looks like is of very great importance. The new survey is designed to reach with reasonable completeness objects of roughly Abell richness 2 to redshifts near unity with no luminosity evolution, and correspondingly greater distances with moderate evolution. Automatic star/galaxy separation and, to the extent possible, galaxy subclassification based on image form, are being done with a modified version of the Tyson-Jarvis (1979) FOCAS code. The cluster selection is then

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done on that catalog data, using a matched detector which fits the form of the cluster in x-y space with a softened and truncated 1/r profile and in magnitude space with a Schechter function. Figure 1 shows a subfield of our 16-hour survey field (there are 6 one-degree square areas around the sky, all at galactic latitude 30 degrees or greater.) 15701 Galaxies V £ 24

16 hr

(Cluster candidates circled)

1500 o 4) V) 0

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Figure 1. A 0.5 x 1.0 degree subfield of the 16 hour deep cluster field in V, showing all galaxies to V = 24. Cluster candidates chosen with a low density excess threshold are circled; the positions of bright stars are marked with crosses. The centers of cluster candidates from a preliminary pass of the cluster finder with a very low threshold are circled. In the final reductions, coincidences will be counted in the two colors, though strong signals in either one will be investigated. The work of Guhathakurta and Tyson (1989) indicates that the extremely blue objects which are somewhat fainter than our limit are often strongly clustered. The current views on galaxy evolution would support the notion that very high-redshift objects should be blue, the ultraviolet contribution from young stars more than compensating the redshift. This effect will have to be quite strong, however, to overcome the blueness of the field at somewhat lower redshifts. Figure 2 shows the contrast against the field assuming neither color nor luminosity evolution; plotted is the ratio of the mean counts of cluster galaxies to the mean background in a region of radius half an Abell radius for a Coma-like cluster in the V (555W) and / (785LP) bands, and it is seen that for reddish, "passive" galaxies, the V band is not the place to look for clusters at large z. The techniques used for finding clusters in this survey (and similar ones being used in the APM survey for nearer clusters) hold out the hope that quantitative comparisons with theories for the formation of structure can be made, if by no other means by the comparison with simulations. We hope, however, that the selection functions can be kept simple enough that reasonably good calculations can be made directly.

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Figure 2. Plots showing, at the top, the ratio of the counts of cluster galaxies to the background in V (555W) inside half an Abell radius for a Coma-richness cluster at redshifts of 0.1, 0.5, and 1.0, assuming no luminosity or color evolution in the cluster, and using the observed field counts; at the bottom is the same data for counts in I (785LP) This work cannot be interpreted properly, however, without quantitative work on nearer-by objects. This will be provided to some extent by the APM survey, but it is possible that in a few years a survey will be done which will revolutionize the subject; planning for it by a number of individuals at several institutions is well underway, and the funding situation looks at this point far from impossible. The hope is to build a fast 2.5-meter telescope with a 3-degree field; an optical design with 0.5 arcsecond images at the field periphery has been done by the author. It will be equipped with two instruments, a twin R=1000 spectrograph each with 300 fibers, enough to observe all

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galaxies to J = 19 in the field, and a camera with 30 (!) 2048 X 2048 CCDs to operate in transit (TDI) mode, arranged as 6 rows of 5 each. Each transit path will half-cover a 2-degree wide swath in 4 colors (2 of the 5 chips have u filters to get adequate signal-tonoise), so that full coverage of the 2-degree swath is accomplished in two passes. The imaging and spectroscopic survey of the north polar cap (b > 30°) is expected to take about five years and will yield about a million galaxy redshifts, 100,000 quasar redshifts (candidates chosen photometrically from the imaging survey), and photometric coverage to about 23 in J and R, 22 in U and / . A sample essentially equivalent to the Abell survey can be pulled from this sample in redshift space, and the small-redshift end of the cluster distribution pinned down quite unambiguously. Like all proposed projects, this one may not come to be, but those of us involved in it are very enthusiastic, and the scientific case seems quite sound; the cluster catalog is, of course, only a tiny part of the potential output of such a project, which will address questions of large-scale structure, the distribution of quasars in space, the density-morphology relation, the existence of brown dwarfs, and the stellar population of the halo, to mention a few.

3. THE EVOLUTION OF CLUSTER GALAXIES It has been known since the work of Butcher and Oemler in 1978 that clusters at even moderate redshifts have a large population of blue and therefore supposedly actively star-forming galaxies, in marked contrast to the present-day cluster population, which is almost "dead". Spectroscopic follow-up has been carried out by several teams; see, for example, Dressier and Gunn (1982, 1983), Dressier et al. (1985), Gunn and Dressier (1988), Butcher and Oemler (1984), Lavery and Henry (1986), Couch and Sharpies (1987), and Mellier (1988) (see also Soucail et al. 1987). What all have found, as is well know, is an increasing population with redshift of three kinds of objects: first, bona fide AGNs (for which the statistics are still not very good), second, galaxies with strong narrow emission lines and blue colors which would appear to be forming large numbers of massive stars at the epoch of observation, and, third, yellow ("E+A") galaxies with very strong Balmer absorption lines, rarely any measureable emission at all, which are most readily interpreted as objects seen some 10 years after a massive burst of star formation which was quenched on at least as short a timescale as it occurred. This work is all published, and several recent reviews have appeared in conference proceedings (see, for example, Gunn (1988) and Dressier and Gunn (1987)). I will only review the work very briefly here and report on some quite recent results that Dressier and I have obtained at larger redshifts. The "active fraction", defined as the fraction of galaxies falling into one of the above three bins (detectable Seyfert I characteristics, greater than 20 A rest equivalent width of A3727 in emission, or greater than 5 A rest equivalent width of Hfi + H~f in absorption, rises from a few percent (all emission objects) at z = 0.0 — 0.5 to about 30 percent at z = 0.4 — 0.55, based on the analysis of a large number of nearby clusters by Dressier and Shectman (1988) and 7 clusters in the redshift range 0.4 — 0.55 by Dressier and Gunn (1987). For representative spectra, see the review by Gunn (1988). The active galaxies are distinguished from other cluster members by more than their spectra and colors; both their spatial distribution and their kinematics are peculiar. The spatial distribution is much less centrally concentrated than the red galaxies, with a strong hint that they avoid the central regions of the cluster altogether; the difference in the distributions is established at the 99.9 percent confidence level. The velocity

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dispersion is almost 70 percent larger than the that of the passive galaxies. These properties must be telling us something about the mechanism which triggers the activity. There have been several suggestions, including mergers by Lavery and Henry, based upon their investigation of active galaxies in clusters at redshifts around 0.2. Dressier and I find no hint of duplicity or smaller-than-average nearest neighbor distances among the large number of active blue galaxies in our sample, and have suggested (Dressier et al. 1985, Bothun and Dressier (1986)) that the activity is associated with the interaction of galaxies coming into the cluster for the first time from outside with the hot intracluster medium. One in general expects that the hot medium will be separated from the cold, infalling gas by a standing shock. The pressures in the central regions of clusters are hundreds of times larger than the typical interstellar pressures in galaxies, and if the shock transition is not too far out, a galaxy falling across the shock will suddenly find itself in a very high-pressure medium and will in addition (Gunn and Gott 1972) find itself subjected to a strong ram pressure as it moves now transonically through the almost stationary hot medium. It would not seem too far-fetched under the circumstances to believe that the tenuous, thermally fragile intercloud medium would be lost to the ram pressure and that the dense clouds would collapse to form stars, on a timescale which could be very much shorter than the dynamical timescale of the galaxy-just the time required to cross the shock at more than a thousand km s . One would expect if this is correct that the phenomenon would happen only once in the lifetime of a galaxy, and after the burst the galaxy would quickly become passive; this is supported by the statistics, as we shall see, and accords with the lack of emission or evidence of ongoing star formation in the E+As. Whether the scheme will work or not depends critically on where the shock is, and the whole picture has become much more attractive in the past two years with calculations of cluster formation and evolution including hydrodyamical effects by Evrard (1988 and this conference). He finds that the shock originates, as one would expect, with the collapse of the core of the cluster, and moves outward at about a quarter of the velocity dispersion of the cluster as the cluster grows. The velocity dispersion and the temperature of the gas inside the shock hardly change at all during the evolution (a point we will return to shortly). He does not actually see a sharp shock transition in his spherically averaged pressure and density profiles, but a fairly abrupt change in slope in the pressure-radius relation from an isothermal r dependence inside to a roughly r dependence outside. This behavior is partly due to numerical viscosity, partly to lack of spherical symmetry, so the shock front is averaged over different radii in different directions, and partly due to a real phenomenon which can be expected to some extent in hierarchical models, namely preheating by collapse of substructure during the infall phase. It is not clear how much each contributes; it is clear that along any given orbit the transition will be sharper than indicated in the spherically averaged profiles, but the important thing is that even if that were not the case, the transition is sharp enough at moderate redshifts to cause the burst on a satisfactorily short timescale—but not at the present epoch. By now, the shock radii have grown so large that the pressure inside the shock is only a little larger than interstellar pressures, and it takes two billion years or so to climb the pressure gradient to the location of the shock at z = 0.5 This by itself may not be sufficient to explain the drastic increase of activity over relatively recent times, but combined with moderate consumption of the gas in large galaxies by ongoing star formation, it may well be enough. It is striking that if one shocked the Milky Way in the fashion described above, the burst would not be nearly so spectacular as the ones observed in the clusters unless the IMF were very different from the present-day one;

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there simply is not enough gas now. Confirmation of the picture could come nicely from high signal-to-noise ROSAT observations of some of the clusters which have been studied optically. One should be able to see the location of the shock transition, and from typical orbits of infalling galaxies from simulations, match the spatial distribution of the blue and E+A objects predicted with those observed. Qualitatively the situation is as one would expect; the objects are rapidly moving because they are only in this phase during first pericenter passage, and they are not centrally condensed because they typically have enough transverse velocity simply because they have come from far outside and have been acted upon by the gravitational acceleration of substructures that they do not penetrate the core. But the missing ingredient is the shock location, and only X-ray observations will yield that. Dressier and I have been working for some years on a set of galaxies at yet larger redshifts, and have a sample from the Gunn, Hoessel and Oke catalog with clusters at z = 0.70,0.74,0.76, and one at 0.92 which turns out to be two clusters at 0.90 and 0.94. We now have extensive data of reasonable quality for C1132229+30274 at z = 0.76; of 25 cluster members, 13 are active, and the spectra are of insufficient signal to noise to uncover all the E+A galaxies that have been seen at lower redshifts. Of the whole highredshift sample, 26 of the 47 cluster members are active. It seems clear from these data that the activity continues to increase as one goes earlier (it would have been fully as enigmatic as the rapid increase at moderate redshift had it not done so.) We have made the case (see Gunn,1988) on the basis of less secure data (which the new data reinforce), that the statistics are consistent within a factor of about 2, which is the uncertainty of the burst timing, with almost every galaxy having gone through the E+A phase exactly once. Since about half the galaxies in the central region are ellipticals and half SOs, it is also consistent with every SO (or, if you feel perverse, every elliptical) having done it once. HST imaging of the active galaxies will give unambiguous information about where the burst is occurring and the morphology of the underlying galaxy. The next few years should be interesting ones indeed for this subject.

4. THE IMPLICATIONS OF THE DYNAMICS OF DISTANT CLUSTERS As indicated in the introduction, there has been considerable interest in the last year in dynamical data on distant clusters, the notion being that the existence of even a few rich objects at high redshift would sound the death knell once again for the cold-dark-matter scenario (Peebles, Daly, and Juskiewicz (1989), Evrard (1989)). The argument is beautiful in its simplicity. From the Press-Schechter (1974) formalism, which has now been verified by many workers from N-body simulations to work much better than it could reasonably be expected to, one can calculate the number density of collapsed objects of a given mass at any epoch, given a fluctuation spectrum and its normalization. If one could observe the mass directly (and had a cluster catalog one understood even approximately), one could make a comparison with the observations and, in the best of possible worlds, deduce the spectrum. None of these things are true, however, and one needs thus to do the best one can with the data at hand. What can one say about the frequencies? Clearly nothing except about the very richest clusters, and only very carefully, if at all, then. In the GHO catalog, there are five clusters which are probably as rich as Coma in the redshift range above z = 0.7; if we arbitrarily divide the range into 0.7 < z < 0.85 and 0.85 < z < 1 the numbers are

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4 and 1, respectively, and contain almost equal comoving volumes for the areas of the KPNO 4-meter IV-N plates good enough to have allowed us to find them. The volumes are, in each redshift range, about 1.5 x 106/i~^ Mpc 3 (comoving.) Dressier and I have dispersions for two of these clusters, and both are of order 950 km s" 1 , comparable to that of Coma; the indications are that these structures are indeed like the Coma Cluster. The densities imply mean separations of the order of 75 to 100 h~l Mpc, a little larger but not enormously so, than the mean separtion today-and especially in the higher redshift bin, the incompleteness is likely to be severe, so the density estimate here must be a firm lower limit. It thus does not appear that Coma-like objects were much rarer at z m 0.8 than at present- certainly not by so much as an order of magnitude, and probably much less. It would appear that this might give very useful constraints. For the CDM spectrum, for example, the slope is near —1 in the range around cluster masses, and the PressSchechter formalism gives for the comoving number density of collapsed objects of mass M 1 dN « C{M)exp{--[1.66(1 + z)M[l*)2}dlnM (1) (Evrard 1989). M\§ is the mass in units of 10 MQ, b is the bias parameter, and C(M) a slowly varying function of M. Now in the spherical infall model, the velocity dispersion is related to the collapsed mass by a « 650(1 + ^) 1/2 M 1 1 5 /3

(2)

and this result is both robust and almost independent of the details of the collapse. Thus the dependence of the number density on velocity dispersion is approximately dN oc exp(-C(l

+ z)a2)

(3)

Now in order to get the density of Coma-like clusters correct at the present epoch, the exponent in this expression must be about —2.5, and so at z « 0.8, the exponent will be —4.5 for objects of comparable velocity dispersions. Buried in all of this, of course, are the arguments about the value of b and the spectrum. If the slope is roughly —1 (and the mass-velocity dispersion data taken at face value strongly suggest such a value (Gunn 1982)), however, the density of Coma-like clusters demands a value of the exponent of about —2.5 and a dependence on z much like the one we have exhibited. The normalization and bias will come out however they come out, but will not change this result. This suggests that the ratio of the space density at z = 0.8 to that at the present is about e . This seems just possible with the constraints worked out above, but not very likely. The sad thing is that it is in any case not really relevant, and even very much better data would not help. The Press-Schechter arguments are very pretty and very powerful, but they do not correspond well to the observed quantities. In the Evrard simulations, the core velocity dispersion does not change once the core forms; the core of the Coma cluster formed at a redshift considerbly in excess of 1, and it is the core velocity dispersion which one measures for distant clusters, because it is only the core region which one can see above the background. Thus the density of Coma cores is expected to be the same at a redshift of 1 as now (there may be slightly fewer because of mergers, if anything). Equation (2), which doubtless gives the average velocity dispersion over the whole collapsed mass correctly, does not correspond well to the measured quantity, and hence does not relate the measured velocity dispersion to the Press-Schechter mass well. All of this is not to say that cluster dynamics is irrelevant

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to such questions, only that the connection is not so simple as the work to date has assumed.

5. THE EPOCH OF GALAXY FORMATION The ages of the "passive" galaxies and the implications for the epoch of galaxy formation has been widely discussed, but I would like to leave with you a caveat which I discussed much more fully in the Durham review (Gunn 1988). There it was shown that the central galaxy in the z = 0.76 cluster discussed above probably formed at about a redshift of 3; evolution in the spectra of the passive galaxies is strongly detected (Dressier and Gunn 1988, Dressier 1986) in the expected sense that the amplitude of the 4000 A break is seen to decrease with redshift, quite strongly above redshift 0.5.

Figures 3 (left), 4 (right). Deep CCD images in the g and i bands of Cl 132229+30274 at z = 0.76. Note the strong concentration of bright red galaxies in the cluster center, and the much less concentrated cloud of very blue objects filling out the cluster. The galaxy discussed in the Durham paper in this cluster is the bright central cD; it is relatively easy to get high signal-to-noise spectra for such objects, which are needed for this work. The obvious problem is seen in Figures 3 and 4, which are frames of the cluster taken at 5000 A (g), 2840 A rest, and at 8500 (t), 5400 A rest, in which it is seen that the galaxies in the central region are much redder than those farther out. Whether this implies a different time of birth or not is, of course, by no means certain, but it certainly at least implies a very different star formation history. Thus studying the epoch of formation of cluster galaxies in the central regions has relevance to the epoch of formation of cluster galaxies in the central regions, but generalizing to the epoch of formation of galaxies elsewhere is a game one plays at one's considerable peril, and the suggestion is in fact the obvious one, that galaxies in such dense regions form earlier than their cousins elsewhere, or at the very least complete the bulk of their star formation earlier.

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6. PARTING COMMENTS We have considered here only a few aspects of the study of distant clusters, and it is clear that the subject is, despite a very large effort on both the observational and theoretical aspects of the problem, in a very preliminary state. The development in the last few years of CCD imagers, CCD multislit spectrographs, P*M, tree, and SPH N-body and hydro codes, and proliferation of tools and understanding of gaussian processes (brought about largely by the seminal paper of Bardeen et al. (1986)) has transformed the field, but the metamorphosis is not quite complete; the basic question of what a cluster is, for example, is none too well understood-so we have catalogs of things, but are none too sure just what they are. We seem to be just entering a new era in which we may finally understand what Nature presents us with in some quantitative fashion, which is certainly a prerequisite to understanding the underlying phenomena. The next decade should be a very exciting one. This research was supported by the National Science Foundation, the National Aeronautics and Space Administration, and the John D. and Catherine T. MacArthur Foundation.

REFERENCES Abell, G. 0., 1958, Ap. J. Suppl., 3, 211. Abell, G. 0., Corwin, H. G., and Olowin, R. P., 1989, Ap. J. Suppl. 70, 1 Bardeen, J. M., Bond, J. R., Kaiser, N., and Szalay, A. S., 1986, Ap. J. 304, 15. Bothun, Gregory D., Dressier, A., 1986, Ap. J. 301, 57. Butcher, H., and Oemler, A., 1978, Ap. J. 219, 18. Butcher, H., and Oemler, A., 1984, Nature 310, 31. Couch, W. J., and Sharpies R. M., 1987, M. N. R. A. S. 229, 423. Dressier, A., and Gunn, J. E., 1982, Ap. J. 263, 533. Dressier, A., and Gunn, J. E., 1983, Ap. J. 270, 7. Dressier, A., Gunn, J. E., and Schneider, D. P., 1985, Ap. J. 294, 70. Dressier, A., 1987, in Nearly Normal Galaxies from the Planck Time to the Present, S. M. Faber, ed., Springer-Verlag, New York, 265. Dressier, A., and Shectman, S. A., 1988, A. J. 95, 284. Dressier, A., and Gunn, J. E., 1988, in The Large Scale Structure of the Universe, (IAU Symposium 130, Balaton, Hungary), J. Audouze, ed, Reidel, Dordrecht. Evrard, G., 1989, preprint. Frenk, C. S., 1988, in The Epoch of Galaxy Formation, C. S. Frenk et al. , eds., Kluwer, Dordrecht, 257. Frenk, C. S., White, S. D. M., Davis, M., Efstathiou, G., 1989, preprint. Guhathakurta, P., and Tyson, J. A., 1989, in preparation. Gunn, J. E., and Gott, J. R., 1972, Ap. J. 176, 1. Gunn, J. E., in Astrophysical Cosmology, H. A. Brueck, G. V. Coyne, and M. S. Longair, eds., (Vatican: Pontificia Academia Scientarum), 233. Gunn, J. E., Hoessel, J. G., and Oke, J. B., 1986, Ap. J. 306, 30. Gunn, J. E, Carr, M., Danielson, G. E., Lorenz, E., Lucinio, R.,Nenow, V., Schneider, D. P., Smith, J. D., Westphal, J. A., and Zimmerman, B. A., 1987, Optical Engineering 26, 779.

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Gunn, J. E., 1988, in The Epoch of Galaxy Formation, C. S. Frenk et al. , eds., Kluwer, Dordrecht, 167. Lavery, R. J., and Henry, J. P., 1986, Ap. J. (Lett.) 304, L5. Mellier, Y., 1988, in Towards Understanding Galaxies at Large Redshift, R. G. Kron and A. Renzini, eds, Kluwer, Dordrecht, p. 227. Peebles, P. J. E., Daly, R., and Juszkiewicz, R., 1989, preprint. Press, W., and Schechter, P., 1974, Ap. J187, 425. Soucail, G., Mellier, Y., Fort, B., and Cailloux, M., 1988, Ast. and Ap. Suppl. 73 471. Tyson, J. A., and Jarvis, J. F., Ap. J. (Letters) 230, L153.

DISCUSSION Felten: How many cluster members can we see on this plate (a slide of a distant cluster of galaxies, z ~ 0.75)? Gunn: Most of the objects you see on this plate are cluster members. There may be one or two stars and probably 70% of the rest of the black spots are cluster members. Felten: Would they be typically L* galaxies? Gunn: No, you see considerably fainter than L*. You see galaxies that are two or three magnitudes fainter than L*. N . Bahcall: Is there redshift information? Gunn: We have a fair number of redshifts in this cluster but not, of course, of the faintest members—we can only work down to about twenty-third mag . . . Giacconi: What is the angular scale? Gunn: The angular scale is three minutes of arc across here, okay. N. Bahcall: Shouldn't you be using a systematic, computerized way of finding your clusters? Gunn: On, Neta, computers weren't invented when this survey was started (laughter). We're addressing that problem but we're not quite there yet. N. Bahcall: What typically is the overdensity over the mean field, because from one of the first slides that you showed at this redshift you expect really not to even see the cluster. Gunn: If there is no color evolution. This is the V band, so you would not expect to see these clusters at all in the V, I think. But the assumption was wrong, I think,

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about no color evolution. We'll get to that in just a minute. Felten: Jim, would you clarify, this burst is supposed to have occurred 10 years before the present? Gunn: No, 10 years before the time the photons left; that is, we're seeing the burst 10 years after it happened, right, because you have to burn away the B-stars and leave the hydrogen-line objects . . . Felten: And that's true for all these clusters over a wide range of redshifts? Gunn: Oh, yes, you see, but that's okay. I'm glad you asked the question, Jim. Let me go back a little bit. I'm going to talk a little bit about where these active things are. What are they? Well, you notice in the fractions here that there are roughly equal numbers of the emission line objects and the E + A objects, and one would like very much to be able to connect these things evolutionarily and—I've given this talk too many times because I tend to gloss over these important points. The numbers of E + A and the number of emission line things is roughly the same. Now, suppose you wanted to say that they were the same kind of phenomenon. Well, then I think the picture you're driven to, and it's a very natural one, is to say that the emission line objects are galaxies that you sort of catch in the act of doing this burst. Alright, you have lots of young stars present. You have lots of UV. It excites the gas. It makes emission lines. You're seeing a star burst galaxy—what would be called a star burst galaxy today, right? You wait 10 years and the A stars and the B stars are gone. The gas is also gone, and that's an interesting thing that we'll come back to, and what's left is a spectrum that's dominated by the sort of 2 MQ part of the mass function that was made in the burst. Well, you say, no, Gunn, you're crazy. You can't have that because the burst phase is maybe only ~ 10 years old. I should see only a tenth as many emission line objects as I see E + As because they last 10 years, right. After 109 years, there's nothing left that you can tell in the spectrum. So, it's not a question of a unique epoch. These things are happening all the time. You just see the ones that are ~ 2 X 108 to 109 years old, right. Felten: But not 108, you said? Gunn: Well, yes, I think the young galaxies are these emission line things and the reason that I can do this and get away with the numbers is that during the burst, the thing is enormously bright and so, you're reaching way down in the luminosity function to pick up these where the numbers are very much larger, and in fact, when you look at the expected brightenings and colors, it works out at least qualitatively, I think, to satisfactory accuracy with this. So, that's the kind of picture we would like to put forward of what's happening: that there are these very strong bursts. The main thing about them is that indicatively, at least, they're using up an awful lot of mass in the galaxy. Mushotzky: Since you've just shown the velocity distribution of the blue galaxies is much larger than the velocity distribution of the red galaxies, when you calculate the velocity dispersion of the clusters that you've showed, how do you handle that?

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Gunn: I don't calculate dispersions using moments. I use histogram fitting. Mushotzky: And you throw out the blue galaxies? No, no, they were done separately. Mushotzky: I understand, but you've just shown that knowing the central velocity, when you look at the reds averaged over all your clusters and you look at the blues averaged over all your clusters, the blues have larger velocity. So, that means in each individual cluster, the blues are contributing more of the
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you can get the A paxt, that's what we see in the Coma cluster, the A part. But there's no elliptical cause they're already in the cluster—the only thing that can infall now at the present epoch to simulate the same phenomena that you observe in these high redshift clusters are spirals—to make the strong Balmer lines. But it's only the Coma cluster that shows that and no other cluster shows an infalling population with strong Balmer lines. Gunn: Yes, they're blue looking spirals at the present because they don't have the strong, underlying old population. Djorgovski: Jim, maybe the existence of clusters is not a problem for CDM at a redshift of one, but isn't the existence of mature galaxies at that redshift a problem for CDM? Gunn: Oh, I think it is actually. If I hadn't gone over my time so badly, I would talk about it. By a redshift of 0.75, the very red cluster galaxies, including the brightest one for which we have a very good spectrum, one can attempt to date it with a stellar population kind of method. In that case, I think there's, as you know, enormous uncertainties to this game, but through several avenues you reach the conclusion that that galaxy formed at about a redshift of three and as you know, that's an interesting redshift because people are seeing lots of these things. There is almost nothing else in the cluster that red, and it sits right at the bottom of what must have been an enormous density perturbation. A thing on the scale of 10 15 M®, but it was that 10 12 M® which formed almost immediately. So, I'm not sure that there's any problem, especially given the very enormous level of activity that's shown by the other members in the cluster. You certainly can't date them and say that they didn't form at a redshift of 1.2. I don't know. Certainly, the central one did but I think you would expect that. So, I don't think that you're in any trouble. Carter: I'm a bit worried about two things. First, your statement that—well, sort of implication, the active galaxies lie in a shell because obviously, there's a zone of avoidance in the middle, but from your plots, it looked as if the outer boundary of that shell was defined by the boundary of where you looked. Gunn: Well, that is true in most cases, I think. If you plot the mean radial distribution and look at that versus the radial distribution in the galaxies in the frame, it certainly falls off but I cannot swear to you that that's not some selection. We should certainly do spectroscopy over a bigger area in these clusters and we're engaged in that. It may be that there really isn't an outer bound, in which case this explanation is in trouble. Carter: Okay, another point which is related to this, that if you actually measure from your red galaxies the velocity dispersion of the cluster, and then use some conventional membership test based on that velocity dispersion to decide whether the blue galaxies members or not, would you not throw quite a lot of them out? Gunn: No, no, the concentration in velocity space is such that we—that's an obvious thing that we've thought about and it just makes no difference at all. The distribution in velocity space is sufficiently clumpy because of the large scale structure; that there just isn't any ambiguity. Now, we have been accused of taking the blue things out of the supercluster population that belongs to this cluster, and I don't know what that is.

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We certainly do if they're there. Yes, no question about that. Oemler: It certainly is true, I think, that the blue galaxies do tend to be in the shell. A fraction of blue galaxies falls outside of that. Gunn: Say it again, Gus. Oemler: I said, maybe that's the explanation for something that always seemed to us odd; that the fraction of blue galaxies reached a peak and then . . . Gunn: And then fell off again, yes. Felten: Taking your explanation of the origin of this activity in terms of the standing shock and taking that table of percentages that you showed us earlier, I guess implies the following: it implies that if you look at a cluster of redshift 0.8, roughly 50% of the galaxies in that cluster have fallen in through the standing shock during the past billion years . . . Yes. Felten: And had in fact done so for the first time. Gunn: Yes. Felten: Now, taking into account the age of the universe at a redshift of 0.8 and taking into account the size of that standing shock and the law of its growth and so on, it seems to me that might put some significant constraints on dynamical models of the evolution, and on simulations . . . Gunn: You must remember that it takes a finite amount of time for the cluster to form, so you don't have the whole time before you. Before that, we wouldn't have identified this as a cluster because it didn't exist at that point, okay. I think that the statistics are in fact consistent with them only going through one time, if you look at all the numbers. For man: Is there a problem holding up this 20% of the mass just until that time? Gunn: Holding up? For man: Holding up the 20% of the mass that you're going to turn all of a sudden into stars in a fairly short period of time? What happens to the E galaxies that haven't been through such a shock that we see now that haven't been through a shock? Gunn: Well, that's all connected with this notion that galaxies were much more pregnant at a redshift of a half than they are now. We don't see big galaxies with anything like 20% gas fractions now, but we know that they're using up stars with a time constant that is disturbingly short. So, what this suggests is something a little funny: that for galaxies of the order of L* we are now sitting at an epoch, at which they are basically breathing their last gasps. So, I'm asking you to believe the numbers about the star formation and gas depletion rates at some level. It isn't actually quite

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that bad but . . . Lavery: Yes, I don't think the explanation of spiral galaxies falling into Coma explains this phenomenon completely. These post-starburst galaxies are at a redshift of 0.2 and if you explain them as being a 20% mass burst—according to what Bothun is saying, these elliptical galaxies at a redshift of 0.2 have 20% of their mass in gas. I don't think it's quite that simple. The morphology of those infalling galaxies is unknown and so you can't explain it just . . . Gunn: Are any of your bursts that strong, Russ? I thought that they weren't. Lavery: They were, yes. Gunn: Okay, then that's a possible problem. Fall: Jim, isn't the way to test this shock idea, just to look in X-rays? Gunn: Sure. It only takes a few hundred kiloseconds of ROSAT time, (laughter). Henry: Jim, would there be any dependence of the active fraction with X-ray luminosity at a given epoch? Gunn: Well, there certainly should. It depends on what the X-ray luminosity measures. See, it's a kind of threshold phenomenon, I think. The important thing is where the shock is and that the shock be strong enough, and once you're at that point, increasing the gas fraction against the X-ray luminosity by a factor of 10 probably doesn't matter a whole lot. Alright, I'm not really sure—it would obviously depend on the exact interpretation of what goes on, and you would have to know more about star formation than we know to do that in any quantitative way, I think. Maybe a factor of 10 isn't enough over-pressure but I think the observations suggest—some of these clusters are not very rich and you saw the velocity dispersions. They are 500 — 600 km/sec. Was the factor 10 over-pressure in comparison with the typical ISM pressure

Kaiser: So, if you wanted the things to be much more gas rich in the past, that's not necessarily the right . . . Gunn: That's a fair statement. I think, if anything, you might expect the pressure to go down in the gas because it's much more efficient cooling but . . . Kaiser: It's still sitting in the same kind of confining potential. Fall: Let's just have one more question. N. Bahcall: Is it clear observationally that this process of activity one sees only occurs in clusters and you don't see it in the field?

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Oh, no, no. I should mention that again. One sees the same sort of activity in the field. I think that's fairly clear from the surveys. The Durham group in particular, I think, have reached deeper and in a more systematic way. The fraction in the field is smaller and the E + A phenomenon is qualitatively different—you see galaxies with young stars, with A stars, but they're galaxies that have emission lines as well. So, what you're seeing is a thing which is not so quick but protracted over a long period. It's another thing, I think, which says that these galaxies are very much gasier in the past than they are today, and there are a number of things that can kick them over the edge. This is just one of them, okay. There can be mergers. There can be all kinds of things that can make the burst in the past. You have to have enough gas to support it—you don't see this in big galaxies today but I think, once you have a galaxy that's full of gas, there is an enormous range of phenomena that can cause this problem. The thing that we're looking for is to identify exactly what's going on in this particular situation.

FUTURE KEY OPTICAL OBSERVATIONS OF GALAXY CLUSTERS

John P. Huchra Center for Astrophysics 60 Garden Street Cambridge, MA 02138

Abstract. A program is proposed for future optical research on clusters of galaxies. This program includes detailed studies of the internal properties of clusters, the connection between clusters and their environment, and the role of clusters in the study of large-scale structure. It is argued that a digital all-sky survey can be feasibly made with a small telescope and a CCD camera, for studies of nearby and intermediate redshift clusters.

1. INTRODUCTION Well, we have now heard and seen a large variety of papers on the properties of clusters of galaxies covering topics which range from determining some of their simple "internal" properties, such as dynamical age and mass, through their use as probes of the large-scale-structure of the Universe. Hearing these, it is quite obvious to me that our knowledge of clusters and their place in the Universe has increased tremendously in the last decade— including what some may call a few backward steps with the realization that many, if not most, clusters are dynamically quite complex and probably "young." I have been fortunately given the easy task of describing where to go next—always a lot of fun when you have both found out what you don't know and are preparing many new marvelous tools, like the Hubble Space Telescope and suites of new 8-meter class and survey telescopes, with which to attack the problem. In this talk, I will concentrate on optical observations and particularly those in three main areas of cluster research: 1. The Internal Properties of Clusters 2. The Connection Between Clusters and their Environment 3. The Role of Clusters in Large-Scale-Structure Studies The first of these areas is best described as the study of the dynamical state of clusters including their mass (M), mass-to-light ratio (M/L), the mix of morphological types of their constituency, structure and the evolution of these properties with time. By definition, such studies are intimately connected to the "Dark Side" of cosmological research—the hunt for the matter required to bind the Universe and make your local

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theorist happy (unless you are mean, like me, and want to keep them unhappy and productive!). The second relates to the relatively new industry of mapping flow fields, cluster infall patterns and studying cluster-cluster dynamics. The last concerns the study of the clustering of clusters, particularly the evolution of such clustering, and unfortunately will require a thorough understanding of the first area for a proper analysis. I will not spend much time on the important but easy stuff like gravitational lensing and the Sunyaev-Zeldovich effect. And I will not give too many suggestions to theorists; I don't want them to get too far ahead! Before getting into the meat of this talk, I do want to issue a few caveats about some areas where caution is required. One is the bugaboo of EVOLUTION, which haunts all attempts to do cosmology with galaxies and clusters. The second is SEMANTICS, perhaps even more important because it forms a block between observers and theorists (and sometimes even observer and observer!). We observers need to agree on a good objective, uniform (in z and 0) definition of a cluster; theorists and model makers need to properly match this definition in their simulations ("theoretical observations"—AR.RGGH). There are many magic words that get used and abused: bound, virialized,relaxed, density-enhancement, substructure, etc. These require robust definitions before we can proceed to the next phase in the study of clusters.

2. INTERNAL PROPERTIES OF CLUSTERS It was less than a decade ago that the existence and prevalence of structure in clusters and the effect of such structure on the determination of cluster dynamics was all but a forgotten issue (e.g., the review by Bahcall 1977). Only a few years later, with the X-ray maps from Einstein (reviewed by Forman and Jones 1984), optical spatial and velocity maps (e.g., Dressier 1980a; Geller and Beers 1982; Huchra 1985), the "calibration" of a well defined morphology-density (T-p) relation (reviewed by Dressier 1984), and good N-body models of cluster evolution (White 1976), our picture of clusters radically changed. Even some of our old friends like the Coma cluster, long thought to be the exemplary relaxed cluster shows signs of underlying complexity (Fitchett and Webster 1987). We now know that proper determination of cluster masses and ages (their dynamical states) depends critically on investigating and unraveling substructure. In particular, one significantly overestimates a cluster's mass if one mistakes a just bound or, worse, a still infalling system for a virialized system. In one case, the Cancer Cluster, a more detailed study showed that the "cluster" was actually a line-of-sight projection of rich groups (Bothun, et al. 1983) and dropped the M/L of the system by a factor of 3! As in studies of galactic star clusters, it is extremely important to ascertain cluster membership before proceeding with any analysis, including the study of the evolution of galaxies in clusters. The solution to this problem is simple and merely requires hard work. We need a complete study of a large sample of clusters. Such studies must include good surfacedensity maps (p(x,y)), velocities for many more than 100 cluster members (cr(x,y)), accurate determinations of field (background/foreground) contamination, and additional important information such as gas density maps from X-ray observations and Figure 1. (opposite page) (a) Isopleths as a function of redshift for the Virgo cluster. The upper left contours are for all galaxies with v < 3000 km/s. The velocity ranges of the other contours are labeled, (from Huchra 1985) (b) The velocity histograms for galaxies of different morphological types in the Virgo Cluster (from Huchra 1985).

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high quality photometry, optical spectroscopy, and radio observations (both 21-cm and continuum). These last are essential for the study of the internal cluster environment and its evolution. Currently, the "mess-to-light" ratio is too big. The published literature contains fewer than 20 clusters that have more than 100 measured velocities, and only scattered and non-homogeneous surface maps (Zabludoff, Huchra and Geller 1990). There are perhaps 5 clusters with more than 200 velocities (Virgo, Coma, Perseus and Abell 2670 are the only ones that come quickly to mind). The best example of such a study is that of the Virgo cluster, shown in Figure 1, and involving redshifts for over 600 galaxies of which over 350 are members of the cluster. It is now easily possible with multi-fiber spectrographs to obtain hundreds of accurate redshifts for galaxies in nearby (z < 0.1) clusters using 4-meter telescopes, and, with CCDs on small telescopes, to map the galaxy distribution around and in such clusters easily. I think an important goal for the next five years should be to do Neta Bahcall's 104 clusters (Bahcall and Soniera 1983; Hoessel, Gunn and Thuan 1980) up right. This means (A) Maps to 0.1 L* (~ 20th magnitude at 20,000 km/s) to R ~ 1.5-2 Mpc. (and Types to 0.3 L*??) (B) 200+ velocities for a magnitude limited sample (in the same area, fibers) (C) Maps to 0.5 L* out to 10 Mpc (D) 100 — 200 velocities in the same area because we have to see the cluster environment! My additional plea would be to be sure to do all of this in the B band in order to enable easy comparison with high redshift systems in nearly the same rest wavelengths. The establishment of a good, well studied baseline sample of clusters and cluster members is extremely important in any attempt to understand the evolution of clusters and cluster members. I can't stress that enough. A longer term goal, perhaps for 10 years, should be to do the same thing for a similar sample of clusters at redshifts near 1.0 using the new generation of 8-meter class telescopes for the spectroscopy and HST for the photometry and galaxy morphology.

3. CONNECTION TO THE ENVIRONMENT The relation between clusters and their environment—infall into clusters, the formation of clusters as well as supercluster dynamics, is a relatively new field. Although de Vaucouleurs recognized the existence of the Local Supercluster over 30 years ago (de Vaucouleurs 1956, 1958), detailed studies of the dynamics of the Local Supercluster had to await the great renaissance in the measurement of galaxy distances and redshifts that took place in the late 1970's. The combination of three-dimensional galaxy density maps (Sandage and Tammann 1981; Huchra et al. 1983) with accurate determinations of distances and velocities—thus the flow field (Figure 2) —for galaxies in the Local Supercluster (Aaronson et al. 1982 = AHMST) not only improved our understanding of how superclusters form but also provided a new approach to the measurement of masses of systems of galaxies on Megaparsec scales. Despite the promise of infall patterns for determining Q, one of the most fundamental parameters of cosmology (Davis et al. 1980; Davis and Peebles 1983), only one

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Figure 2. A model of the infall into the Local Supercluster fitted to data on galaxy distances and radial velocities (from AHMST 1982). The infall pattern velocity is ~ 260 km/s. supercluster, the LSC, has been well studied and even that one can use more work. With the HST relative distances can be measured via brightest stars to large numbers of galaxies in superclusters out to Coma —Perseus-Pisces, Coma-Al367, HydraCentaurus. The problem can be attacked even without HST using the Tully-Fisher and Faber-Jackson relations, which may work even better than brightest stars. One use of this approach has been to try to understand whether the non-Gaussian velocity histogram of the spiral galaxies in the Virgo core is indicating that these galaxies are still infalling (Huchra 1985; Pierce and Tully 1988). Figure 3 shows the Tully-Fisher distances for the ~ 30 spirals that have been measured so far in the Virgo core. With only 30 galaxy distances, the affect of infall is seen at only the 2.4er level, the galaxies at low redshift with respect to the cluster mean are slightly behind the cluster while those at higher redshifts are slightly in front of the cluster. The fundamental limitation in our ability to map infall patterns is given by the combination of y/N statistics and the accuracy of the relative distance indicator transformed into AV/V. One program for the 1990's should be to map the infall patterns around the five nearest superclusters. It is also possible to study cluster infall just by examining the caustics in redshift space indicative of such infall (Kaiser 1987, Regos and Geller 1989). This type of study does not require distances but rather just hundreds of accurate radial velocities in the cluster outskirts—studying the caustics around perhaps a dozen clusters is another relatively simple goal for cluster studies in the 1990's. This is a program that will fall out naturally from our above mentioned program (D) above to study the velocity fields surrounding clusters. Lastly, we should consider the even newer field of large-scale flows. Largely due to the recent work of the "Seven Samurai" (Burstein et al. 1986; Dressier et al. 1987; Lynden-Bell et al. 1988) on the "Great Attractor" (GA), the interest of a large number of observational cosmologists has been focused on the problem of matching, if possible, the galaxy velocity field with the motion of the Local Group "observed" as a dipole in the /x-wave background. Excellent reviews of the problem can be found in Madore and Tully (1986) and Rubin and Coyne (1988). Because they are, by definition, large

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Figure 4. 7%e predicted flow field from the IRAS galaxy redshift survey density map. The flow in the Supergalactic plane is shown in this plot from Yahil (1988). The first IRAS galaxy redshift survey, described above, is limited to 1.936 Jy at 60^ and contained approximately 2600 galaxies. It only effectively sampled the galaxy density field to 4000 or 5000 km/s. We are presently obtaining redshifts for a much deeper sample of about 7000 galaxies to 1.2 Jy which should go correspondingly deeper. IRAS samples unfortunately are dominated by late-type dusty spiral galaxies, and do not sample clusters and the distribution of early type galaxies very well. This is a significant drawback, since the derivation of Vt from the velocity field/density field match depends critically on the size of the overdensity. The density of dense regions will be underestimated because of the morphology-density relation (Dressier 1980b; Postman and Geller 1984). Ideally, we would wish to produce a sample with the galactic extinction cutting properties and uniformity so useful in the IRAS sample, but at a wavelength that would not bias against the selection of early type galaxies—a wavelength, however, optimized for picking out the luminosity of the cool giant stars and lower mass stars that trace the masses in galaxies. Such a survey, at 2/z, has been proposed by Kleinmann and collaborators (Kleinmann et al. 1989). This survey would be both whole sky and uniform and will be capable, when coupled to existing optical photographic surveys, of identifying galaxies to 13th magnitude in the K band, or equivalently 17th magnitude at B, thus yielding a catalogue of a few hundred thousand galaxies. This survey's production and analysis (including redshift measurments) represents another extremely important key observation of both galaxies and nearby clusters for the 1990's.

866

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4. CLUSTERS AND LARGE-SCALE STRUCTURE Although clusters were always considered an important constituent of the Universe, their importance as tracers of large-scale structure was also first highlighted less than a decade ago (Bahcall and Soniera 1983, hereafter BS). BS analyzed a small sample of 104 cluster redshifts accumulated over a decade by Hoessel, Gunn and Thuan (1980) and others. Analysis of this sample showed that clusters are extremely clustered—the amplitude of the two-point cluster-cluster correlation function was an order of magnitude higher than that for individual galaxies (see Peebles 1980 for a comprehensive discussion of correlation functions). Since then, several other samples of cluster redshifts have been collected—most notably the deep cluster sample of Huchra et al. (1990), and the shallower sample of ~ 350 clusters of Postman, Geller and Huchra (1990). The first of these samples contains 145 clusters to the limit of the Abell catalog but covers only a very small area of the sky. The second is a "magnitude limited" cluster sample and contains redshifts for all clusters with m\Q < 16.5. Currently there are redshifts known for ~1000 of the 4076 clusters in the expanded, whole sky catalog of Abell, Corwin and Olowin (1989), primarily through our surveys and the work of the Soviets with the 6-meter (e.g., Kopylov et al. 1984; Fetisova 1982, see Andernach 1990); in a few years, I expect that redshifts will exist for almost all this catalog, at least at the level of one galaxy per cluster. Spatial maps of the large-scale cluster distribution can already be produced —Figure 5 is a pie plot of the distribution of the 160 clusters with known redshifts less than 0.2 and with 20° < 6 < 40°. Over the next decade, this catalog should actually be completed at the level of several galaxy redshifts per cluster (~20,000 new galaxy redshifts!) probably best done with multi-object (aperture plate) spectrographs. Unfortunately, the connection between galaxy clusters and large-scale structure is one of the places where semantics causes "some antics"— where the definition of a cluster is extremely important and where our catalogs certainly fail us at large redshift and may be failing us even at low redshift. In the deep sample of Huchra et al. (1990), where several redshifts exist for a given cluster, 10-15% of the clusters are multiple along the line of sight, 40% are extended in redshift (suggesting either a situation like Cancer or the presence of an extended supercluster like ours) and a few percent are just not real. These last are either not visible on the combination of the POSS red prints and the sky as seen from the MMT, or consist of several galaxies well spaced in redshift (e.g., z's = 0.1, 0.15, 0.2, 0.25, 0.3 ...). These are not just the suggested problems with projection that have been described by Dekel et al. (1989) and Sutherland (1988). Other examples of this problem are even more famous/insidious. Abell 34, classified by Abell (1958) as richness class 2 and distance class 6 had a "measured" redshift in the literature (source to remain nameless) of only 0.041. At this redshift, it figured prominently in the map of Batuski and Burns (1985). However, its "estimated" redshift is 0.165. A measurement of a second galaxy in the field gives a redshift of 0.131. The cluster as it appears on the POSS prints also does not really qualify as richness = 2. Abell 1318 is another richness = 1 cluster with a very low published redshift, 0.019. Its position places it, if that redshift is correct, on a triangle with Coma and Abell 1367, only ~ 35/i - 1 Mpc away from either, thus a major contributor to the signal in the cluster-cluster correlation function of BS. New redshift measurements by Huchra and Zabludoff (1990) of 14 galaxies show that there is a rich, foreground group at the low redshift, but that the majority of the galaxies in the field, especially those near the Abell center, are at a redshift of 0.058! The estimated redshift, by the way, is 0.034.

Future Key Optical Observations of Clusters

0.0 i 6 <

367

20 0*

Figure 5. The spatial distribution of Abel I clusters with known redshifts in the declination range 20° < 6 < 40° and with z < 0.2. This sample is fairly complete to a redshift of~0.1 (from Huchra, Postman and Geller 1990). Obviously we have a problem here that even manifests itself at very low redshift and in supposedly rich clusters. The difficulty of understanding what the clusters are doing with respect to the galaxy distribution has also been mentioned earlier in this conference by M. Geller. The CfA Redshift Survey extension now is complete over significant fractions of the sky to 15.5 magnitude in the Zwicky catalogue. This provides a reasonable look at the galaxy distribution to redshifts in excess of 10,000 km/s. We can also look at the distribution of Abell clusters in those volumes of space covered by the individual galaxy survey. Figure 6 shows the correspondence between the galaxy and cluster distribution in an 18° degree wedge cutting through the north galactic pole. The one or two richest clusters, like Coma and A2197/99, stand out very well and manifest themselves as well defined "fingers-of-God" in the galaxy distribution. Others, like Abell 1185, 1228, 1257 and 1267 lie in a fairly confused region and do not appear any denser than many of the richest galaxy groups (Ramella, Geller and Huchra 1989) that are not in Abell's catalog.

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J. P. Huchra

16

17

IOOOO

5000 8.9 < m § 26.5 § 6 <

15.5

cz (km/s)

44.r>"

13 14 10

15

16

17

10000 5000

0.0 < m S 26.5 $• 6 <

2.0 44.5

cz (km/s)

Figure 6. ('aj The galaxy distribution in an iS° wedge cutting through the north galactic pole from the CfA Redshift Survey, (b) The corresponding Abell cluster distribution.

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5. A PRESCRIPTION FOR THE ABELL BLUES What can we do about it? Well, I think that an adaptation of a quote from Lewis Carroll is in order. "The time has come," the Walrus said, "to speak of" a Digital Sky Survey. This is the best way of solving our sampling problems for both galaxies and clusters. There are now a number of people thinking about this problem—Jim Gunn, Steve Kent, Tony Tyson, Rich Burg just to name a few. The Palomar Sky Survey is nearly 40 years old and should be replaced by something that is both digital (read: computer accessible) and well calibrated for photometry. More to the point, a digital sky survey is a project that does not require large telescope time but rather is well suited to many of the smaller, but well instrumented, facilities that already exist. The major part of any such effort is actually in the data-reduction and analysis. A simple baseline example is one that I and Steve Kent have been thinking about for the soon-to-be completed SAO 48-inch telescope at Mt. Hopkins. Our survey would essentially be done in the "point-and-shoot" mode with 5 minute exposures and ~ l" pixels. Such a survey is possible to schedule because we can, at the same time as the survey is proceeding, also schedule observations for other projects (e.g., X-ray source identifications, SN searches, etc.). Point-and-shoot is preferable to the scanning (or TDI) mode because you have better control over the uniformity of exposure time (as a function of declination), spatial differential refraction, extinction (it's easier to get standards frequently), and scheduling backup programs. The properties of such a survey can be calculated with some simple calibrations and assumptions. Lets think of a two-color survey. Nearly simultaneous observations in two colors are necessary to properly deal with atmospheric extinction at the few percent level—a goal that I think is necessary and appropriate scientifically for a digital survey. In the table below, "Q.E" is the detector quantum efficiency and "Cal" the number of photons from a Oth magnitude star. We will assume 1 arcsec pixels. Table 1

Sky Survey Assumptions

Band

B (A 4400 A)

R (A 6700A)

Bandwidth (BW) Q. E. Sky Brightness Cal(#/s/cm 2 /A)

1000 A 0.3 22.5 mag 1595

1500 A 0.6 21.9 mag 620

Including reflectivity, filter transmission and obscuration, the telescope effective area, A, is ~ 2000 cm , so for a 5 minute exposure the number of photons collected is: JVA5 = 300s x BW xQEx = 3.0 x 10 u /pixel

AxCal

(B) ; 3.3 x 10 u /pixel

(R)

for a Oth magnitude object in the B and R bands respectively. In both filters there will be about 300 photons per pixel in 5 minutes from the sky, so the sky noise is y/S = 1 7 . Roughly, to get a signal to noise of 10-to-l with respect to the sky we need ^object ject

= in10 X 17i* X

= 10 x 17 x Q—355

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J. P. Huchra

or, we achieve approximately 10% photometry at B = 22.8 magnitude and R = 22.1 magnitude. We can achieve 2% photometry to neary 20th magnitude in B in our 5 minute exposures! How long will it take? With current technology—20482 arrays from Ford Aerospace or Tektronix—l" pixels imply a 34' x 34' field. So with overhead and overlap we can do about 1 square-degree per hour in two colors. If there are 100 useable nights per year (50% photometric and 50% dark) and we want to cover a hemisphere above |fr"| = 30°, which is 10,000 square degrees, it takes about 10 years! We can help this along a little by using marginal nights and calibrating when the moon is up. We can also cover the galactic plane (or work in another filter, perhaps the / band) when the moon is up. This estimate is not encouraging. However, there are two things that can help enormously. We can (1) use dichroics and multiple dewars to observe in two, well separated, filters simultaneously — halving the observing time, and (2) we may be able to closely butt or mosaic arrays of 2x2 chips, covering 4 times more sky area per exposure. If both are done, the time necessary to cover a hemisphere at high latitude drops by a factor of eight to only 1.25 years! Then we can even think of using smaller pixels (< l") to get better spatial resolution, using longer exposures or observing in more colors. Such a digital survey, even if done with l" pixels, solves several problems at once. We can easily assemble uniform, samples of galaxies to 20th magnitude (15 million high latitude galaxies!) which should keep the large-scale structure people happy for years to come. We can also use the source counts to 21st or 22nd magnitude to optically select clusters of galaxies to redshifts near unity (at 2 = 1, mio is about 21st magnitude). This is a good way of getting intermediate redshift cluster samples to compare to both the low redshift sample mentioned above and also the high redshift samples we expect to identify with larger telescopes, with AXAF and with HST. This is also the way to make a first cut at the evolution of large-scale clustering by studying the spatial distribution of clusters at redshifts between 0.5 and 1.0 (more redshifts required!). As one of many side benefits of such a digital survey, we obtain very accurate photometry for brighter galaxies, allowing the construction of shallower, but photometrically uniform samples, and the selection of galaxy samples by color. We also get the accurate photometry needed to apply many of the new redshift-independent galaxy distance indicators—the Tully-Fisher and T)n-o relations. Lastly, we also provide all the necessary material for the casual optical identification of radio, X-ray, gamma-ray, and infrared sources and for selecting faint stellar samples. Lots of merits, if I do say so myself—keep us all busy for many years just as the photographic Palomar Sky Survey has done. 6. S U M M A R Y The program proposed for the next several years can be summarized as: 1. The development of rigorous definitions for clusters and their properties. 2. Spatial and velocity maps for the cores of 100 rich clusters. Baseline spectroscopic surveys of cluster galaxy properties. 3. Velocity maps for the outskirts of clusters. 4. Flow fields (distances for galaxies) in the 5 nearest clusters/superclusters. 5. Large galaxy redshift surveys to study the relationship between clusters and their surroundings.

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6. Distances for large samples of nearby galaxies (z < 0.05) to study large-scale flows. 7. A digital sky survey to select both intermediate and nearby galaxy and cluster samples. One additional program must be added to this list to make it complete: 8. Selection of deep, high redshift cluster samples via HST, AXAF and optical digital surveys done with 4-m and 8-m class telescopes. For the obvious, difficult and often mentioned study of cluster evolution. I think I've outlined enough work to keep all of us observers busy for the next decade. Let's go to it! I would like to thank all my colleagues who have made my work in this field fun for the last decade — Tim Beers, Greg Bothun, Rich Burg, Marc Davis, Margaret Geller, Riccardo Giaconni, Pat Henry, Steve Kent, Mike Kurtz, Jeremy Mould, Marc Postman, Massimo Ramella, Michael Strauss, Amos Yahil and of course the late Marc Aaronson who drove us all to keep better track of distances. This work has been supported by NASA grant NAGW-201.

REFERENCES Aaronson, M., Huchra, J., Mould, J., Schechter, P. and Tully, R. B. 1982, Ap. J. 258, 64. Abell, G. 1958, Ap. J. Suppl. 3, 211. Abell, G., Corwin, H. and Olowin, R. 1989, Ap. J. Suppl. 70, 1. Andernach, H. 1990, in Large Sacle Structure and Peculiar Motions, Latham and da Costa, eds. Bahcall, N. 1977, Ann. Rev. of Astron. and Ap. 15, 505. Bahcall, N. and Soniera, R. 1983, Ap. J. 270, 20. Batuski, D. and Burns, J. 1985, Ap. J. 299, 5. Bothun, G., Geller, M., Beers, T. and Huchra, J. 1983, Ap. J. 268, 47. Davis, M. and Peebles, P. J. E. 1983, Ann. Rev. Astron. and Ap., 21, 109. Davis, M., Tonry, J., Huchra, J. and Latham, D. 1980, Ap. J. Letters 238, LI 13. Dekel, A., Blumenthal, G., Primack, J. and Olivier, S. 1989, Ap.J. 338, 5. de Vaucouleurs, G. 1956, in Vistas in Astronomy, Vol. 2, A. Beer, ed. (New York: Pergammon), p. 1584. de Vaucouleurs, G. 1958, A. J. 63, 253. Dressier, A. 1980a, Ap. J. Suppl. 42, 565. Dressier, A. 1980b, Ap. J. 236, 351. Dressier, A. 1984, Ann. Rev. of Astron. and Ap. 22, 185. Dressier, A., Faber, S., Burstein, D., Davies, R., Lynden-Bell, D., Terlevich, R. and Wegner, G. 1987, Ap. J. Letters 313, L37. Fitchett, M. and Webster, R. 1987, Ap. J. 317, 653. Fetisova, T. 1982, Sov Astron. 25, 647. Forman, W. and Jones, C. 1982, Ann. Rev. of Astron. and Ap. 20, 547. Geller, M. and Beers, T. 1982, P.A.S.P. 94, 421. Hoessel, J., Gunn, J. and Thuan, T. X. 1980, Ap. J. 241, 486.

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Huchra, J. 1985, in The Virgo Cluster, O.-G. Richter and B, Binggeli, eds., (Munich: ESO), p. 181. Huchra, J., Davis, M., Latham, D. and Tonry, J. 1983, Ap. J. Suppl. 52, 89. Huchra, J., Henry, J. P., Postman, M. and Geller, M. 1990, Ap. J. in press. Huchra, J., Postman, M. and Geller, M. 1990, Ap. J. in prep. Huchra, J. and Zabludoff, A. 1990, A. J. in prep. Kaiser, N. 1987, M. N. R. A. S. 227, 1. Kleinmann, S. et al. 1989, private communication. Kopylov, K. et. al. 1984, Astron. Tsirk 1344. Lynden-Bell, D., Faber, S., Burstein, D., Davies, R., Dressier, A., Terlevich, R. and Wegner, G. 1987, Ap. J. Letters 313, L37. Madore, B. and Tully, R. B. 1986, eds Galaxy Distances and Deviations from Universal Expansion, (Dordrecht: Reidel). Peebles, P. J. E. 1980, The Large-Scale Structure of the Universe, (Princeton: Princeton). Pierce, M. and Tully, R. B. 1988, A. J. 330, 579. Postman, M. and Geller, M. 1984, Ap. J. 291, 85. Ramella, M., Geller, M. and Huchra, J. 1989, Ap. J. 344, 57. Regos, E. and Geller, M. 1989, A. J. 98, 755. Rubin V. and Coyne, G. eds. 1988, Large Scale Motions in the Universe, (Princeton: Princeton). Sandage, A. and Tammann, G. 1981, Revised Shapley-Ames Catalog of Bright Galaxies, (Washington: Carnegie Institution). Strauss, M. and Davis, M. 1988, in Large Scale Motions in the Universe, Rubin and Coyne, eds. (Princeton: Princeton), p. 256. Strauss, M., Davis, M., Yahil, A. and Huchra, J. 1990 Ap. J. in press. Sutherland, W. 1988, M.N.R.A.S. 234, 159. White, S. D. M. 1976, M.N.R.A.S. 177, 717. Yahil, A. 1988, in Large Scale Motions in the Universe, Rubin and Coyne, eds. (Princeton: Princeton), p. 219. Zabludoff, A., Huchra, J. and Geller, M. 1990, Ap. J. in press.

DISCUSSION Bothun: This is an alternate advertisement for a cheaper version of a digital sky survey—a practical one where you don't have to change tapes every ten minutes. You build yourself a reducing camera which is about $15,000. We built a 4:1 focal reducer. You get big pixels. Big pixels are good if you have a flat frame. The way to find galaxies is by some kind of isophotal criteria. We built one for our 52 inch at McGraw-Hill and in ten seconds you get down to 25 mag arcsec . So, if I wanted to generate a catalogue of all galaxies with diameters greater than 10 arc-seconds down to 25 mag arcsec , I could do that in 10-second exposures and if anyone is willing to pay the money, they can do it.

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Huchra: Greg, I agree. That's a new thing to do. The only thing is that this is a clusters conference and that won't work if you want to try to fix the Abell catalog to a redshift of 0.2 or 0.3 because the galaxies will be too faint for 10 square arc-seconds or whatever your pixel size is. Bothun: Well, the thing is you put a digital sky survey in this pipe dream fantasy land, and I think that's selling it short. I think it's very easy to do. Huchra: I don't think this is pipe dream and fantasy land. Let's put it this way: if nothing else happens, I'm going to try to do this with that 48 inch (Mt. Hopkins). Burg: And we have plenty of optical disks for the data. Struble: How many of these interesting superposed clusters like A1318 did you come up with? Where you felt that there was a sufficient number of redshifts to say whether it was or wasn't a real Abell cluster. Huchra: That I've come up with? Let's do it this way—the deep cluster sample is probably where I tried the hardest to see if there were problems like that. As I said, the fraction of confused clusters is about 10%. So, there were maybe 12 or 15 clusters where I really had a hard time figuring out which redshift was the primary density enhancement. Rubin: I went to my first galaxy cluster meeting in 1961. I don't think there's anyone here—maybe Allan Sandage was there. I asked a question then that has not yet been answered or really addressed and I'd like to ask it again here. Is there any observational evidence that velocity dispersions do not go up with velocity of the cluster; that is, as you get further and further out into the universe, velocity dispersions do not go up? Huchra: This is something I ought to know the answer to and . . . Rubin: Well, you referred to clusters with very large velocity dispersions . . . Huchra: No, I didn't say that. I said there were several that had large extent with the five or six galaxies that we have in the field—but that's not the same as velocity dispersion. The best sample I can think of is one that's been analyzed and being written up by Anne Zabludoff, a student of Margaret and I, who has been trying to collect up all the redshifts for clusters that have enough redshifts to make this worthwhile, for about 80 clusters over the redshift range of 0.0 to 0.1 or so. I don't believe she's found any significant change in velocity dispersion as a function of redshift and she has looked for it; and if she'd found it, I would have known it but since she didn't tell me, she probably didn't find it. That's the best I can tell you. Gunn: In our immediate cluster survey, the clusters have about the same space density as the Abell, and you saw the numbers—they ranged from 400 to 1,200 or more. Huchra: Yes. Djorgovski: John, your redshift survey has shown this feature that goes across half the sky at 10,000 km per second. Would you care to comment?

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J- P- Huchra

Huchra: Yes, I think it's there. That's what Martha Haynes and Riccardo Giovanelli saw on the other side of the sky. We now have good data for the Northern hemisphere. It's the extension of what was in the old days called the Coma supercluster. It runs between A1367 and Coma and extends on up to A2199-2197. I don't think I see it going down to Hercules but I wouldn't bet that it doesn't. Let's put it that way. Djorgovski: So, let's see, it's 100 Mpc or what? Huchra: Well, let's see, it's at 10,000 km/sec and it covers about 100 degrees on the sky. So, say two radians at 100 Mpc. Djorgovski: What would that do to the microwave background I wonder? Huchra: At the observed redshift the density is low enough that it probably doesn't do very much to it. But what would it do to the microwave background if it was something that's been around since a redshift of three, —the answer is something! Felten: I also wanted to ask about this business of superpositions and multiple redshifts because I know that the other day most people felt quite strongly that the double peaked X-ray sources couldn't be just superpositions. You couldn't account for that statistically. You showed several interesting examples of multiple redshifts but let's concentrate on that deep cluster sample. You said something like 10-15% are multiple, and can you say a little more about this? Huchra: Jim, I'll tell you what the data is. The data on those clusters, is, on the average, only a few redshifts per cluster. The brightest galaxies in the field. In some cases like Gunn's (clusters)—he showed you the pictures of these things—it is clearly a well defined cluster with a central cD or the equivalent looking galaxy. You measure it and you measure a companion and they're at the same redshift and you quit because these are not easy to measure. I don't get that much telescope time on big telescopes. What we've been trying to do is use a multislit spectograph to try to get as many as eight redshifts per cluster all at the same time, although it's not always possible to do that. When you try to do that, you often find that when you take the eight brightest galaxies in the field, that there are two clumps. I have examples where I have five galaxies in the field that are at 40,000, 50,000, 60,000, 70,000 and 80,000 km/sec and I don't know what to call that. Primarily when you find things that are multiple what you find is there'll be a lump of galaxies at 60,000 and another lump at say 75,000. When there's not enough velocity separation that you can say foreground or background, then you ask what did Abell really identify, and you throw your hands up. Felten: The incidence does seem surprising. Huchra: The incidence is 10% at a redshift on the average of 0.15 to 0.2. I'm not surprised by that at all. N. Bahcall: The fraction of such superpositions increases with redshift. So, when you look at a big survey... Felten: Yes, but you have to ask about the depth involved...

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Huchra: You expect a lot of contamination. N . Bahcall: But 10-15% is a reasonably small amount of contamination. Postman: For mjo fainter than 16.5, the number of interloping galaxies becomes comparable or greater than ten, so, the chance of Abell misidentifying the tenth ranked galaxy is fairly high. Huchra: And in this deep cluster sample, most of the clusters have mio fainter than 16.5. In fact, our record is 18.2 for the tenth brightest galaxy. Gunn: There's also a very important fact—a very strong selection effect, that is that these things make it into the Abell catalogue precisely because they are superpositions— because otherwise there wouldn't be enough galaxies to see in that cluster.

CLUSTER RESEARCH WITH X-RAY OBSERVATIONS

Riccardo Giacconi and Richard Burg Space Telescope Science Institute 3700 San Martin Drive Baltimore, MD 21218

Abstract. Past X-ray surveys have shown that clusters of galaxies contain hot gas. Observations of this hot gas yield measurements of the fundamental properties of clusters. Results from a recent study of the X-ray luminosity function of local Abell clusters is described. Future surveys are discussed and the potential for studying the evolution of clusters is analyzed.

1. INTRODUCTION The systematic study of clusters began with the surveys of Abell (1958) and Zwicky et al. (1968) who each created well defined catalogues according to specific definitions of the object class. In particular Abell defined clusters as overdensities of galaxies within a fixed physical radius around a center, classifying such objects as a function of their apparent magnitude (distance) and of their overdensity ("richness"). The first X-ray survey of the sky by the UHURU X-ray satellite showed that "rich" nearby clusters were powerful X-ray sources (Gursky, et al. 1971, Kellogg et al. 1972). Subsequent spectroscopic studies detected X-ray emission lines of highly ionized iron and demonstrated that the X-ray emission was produced by thermal radiation of a hot gas with temperatures in the range of 30 to 100 million degrees (Mitchell et al. 1976, Serlemitsos, et al. 1977). With the launch of the HEAO1 and the Einstein Observatories, surveys of significant samples of nearby clusters demonstrated that as a class, clusters of galaxies are bright X-ray sources with luminosities between 10 and 10 ergs/sec (Johnson, et al. 1983, Abramopoulos and Ku 1983, and Jones and Forman 1984). The increased sensitivity of the Einstein imaging detectors also provided the capability to study clusters at large redshifts (z £ 0.5) (Henry et al. 1979). The general problem one wishes to attack by means of X-ray observations is the study of the formation and dynamic evolution of structures consisting of gravitationally bound galaxies. It has been pointed out by several authors (Kaiser 1986, Shaeffer and Silk 1988) that X-ray observations of such systems may offer important advantages with respect to studies in other wavelength domains, particularly at early epochs of the universe. In Table 1 we list the fundamental properties of clusters that can be measured

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R. Giacconi and R. Burg

in X-ray surveys along with a brief description of the measurement. We also include, for comparison, the analogous measurement in the optical. Table 1 Property

Optical

X-rays

Detection

Ngai(m3 - 1113 + 2) > n

S > Smi

in RA = 1.7/z arcmin

0>

L op t =

L* =

Luminosity Mass

nun

1 1

T/ g a s ••• g a s

M(R) ~ 3(kTR/pm h G)

3a? = Temperature Metallicity

Zgaj

Zgas

Morphology

Morphology with N ga j

Morphology gas(p )

In order to be efficiently detected in X-rays such systems can be empirically defined as having the following properties: 1. They must contain sufficient intergalactic gas (typically 1/10 of the cluster mass). 2. The gas must have been heated to X-ray emitting temperatures typically larger than those corresponding to escape velocity from a single galaxy. It should be noted that the efficiency of X-ray emission depends on metallicity. 3. The gas must be centrally concentrated in the cluster, (L^ ~ p ), although not more so than the galaxies in nearby observed systems. Such properties have been shown to exist in Abell-type clusters, as well as in much poorer systems such as cD groups (Kriss et al. 1980). Thus the class of X-ray luminous clusters of galaxies which may be retrieved in future sensitive X-ray surveys in a sufficiently soft X-ray band (for example 0.1-2 KeV), will include both optically defined classes of rich clusters (such as Abell or Zwicky) as well as poorer clusters or any gravitationally bound system of galaxies containing high temperature gas. The Einstein Observatory Medium Sensitivity Survey which uses the IPC data (0.35 to 3.5 keV) has in fact detected a number of optically poor X-ray emitting clusters (Gioia, et al. 1982).

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2. X-RAY LUMINOSITY FUNCTION We would like to briefly summarize some of the recent work by Forman, Jones and ourselves on the X-ray luminosity function of Abell cluster as an introduction to the subject. The earliest determinations of the X-ray luminosity function for Abell-like clusters of galaxies were based on the UHURU and Ariel surveys. Schwartz used a sample of 6 clusters and McHardy a sample of 20 clusters to derive luminosity functions. Extensions of these first attempts included the analysis of HEAO1-A2 data (Piccinotti, et al. 1982), with samples of 30 clusters. More recent surveys with HEAO1-A2 were based on 128 detected clusters (Johnson et al. 1983). Finally, Abramopoulos and Ku (1983) used Einstein imaging observations of 74 nearby clusters with z < 0.27. It should be noted that while the UHURU, Ariel and HEAOl surveys were X-ray flux limited surveys which, in principle, could have studied the X-ray luminosity of a more general cluster population, they were severely biased by their sensitivity and energy range to the detection of Abell-like rich, high temperature clusters, although some X-ray emitting groups were observed (Schwarz et al. 1980). These determinations of the X-ray luminosity function of Abell-like clusters were based on relatively small samples and had intrinsic limitations or deficiencies. In particular, previous determinations of the Abell-like cluster X-ray luminosity function did not take into account the incompleteness for richness 0 clusters (Abramopolos and Ku 1983), did not include richness 0 clusters (Kowalski et al. 1983), or were not sensitive to low temperatures because of their effective energy band (Piccinotti et al. 1982, Kowalski et al. 1983). The last limitation could be quite important in attempting to understand the low end of the X-ray luminosity function since there appears to be (at least for R > 1) a correlation between X-ray luminosity and temperature (Mushotzky 1988). In our recent work we have investigated the statistical properties of the 226 Abell clusters with z < 0.15 observed by the Einstein Observatory (Burg et al. 1990, hereafter referred to as BFGJ). This sample is taken from the larger compilation of Einstein cluster observations analyzed by Jones and Forman. We show that this set of clusters form, for the purpose of this work, an unbiased sample of Abell clusters that spans richness classes 0 to 2. We use the Einstein sample to derive an X-ray luminosity function which is free of some of the problems which beset previous analyses. The main advantages of this determination are: the ability to detect low temperature clusters because of the energy band (0.5 to 4.5 keV) (in common with the Abramopoulos and Ku survey); the larger sample which allows us to adopt stringent criteria to insure completeness and allows us to determine the X-ray luminosity function for different richness classes; and the higher sensitivity which allows us to explore the low luminosity end of the luminosity function. The redshift limit of 0.15 was chosen for our sample since within this range the Abell richness classification is distance independent. Furthermore we have established that for redshifts < 0.15 there is no correlation between redshift and X-ray luminosity (see Figure 1). Thus this subset of the Abell catalog can indeed be considered a proper sample to derive the shape of the X-ray luminosity function by richness class since the entire range of X-ray luminosity can be observed throughout the chosen volume. The IPC fluxes from the compilation of Jones and Forman (1990) have been obtained by integration over a region of 1 Mpc radius centered on the X-ray determined cluster center. These fluxes are computed in the 0.5-4.5 keV (observed) band, from the observed counting rates, using the hydrogen column density and either the observed

S80

R. Giacconi and R. Burg

R1 BFGJ

^

o

in

o

T

§

in

i-

8 .

o o o

0.01

0.05

0.1

0.5

redshift

Figure 1. Scatter diagram of X-ray luminosity versus redshift for richness 1 clusters. or estimated gas temperature. The estimated gas temperature is computed using the observed luminosity temperature relation, which we have rederived for our sample and is given by L x oc T*/ 2 (Mushotzky 1988). The luminosity at the source is computed utilizing the measured X-ray flux and the measured or estimated redshift. K-corrections have been computed using the RaymondSmith model, assuming 0.5 solar metallicity, and they are of order 20% over the redshift and temperature range of the sample (Burg and Giacconi 1990). The method used for computing the luminosity function is dictated by the criteria used in selectmg the sample. In this work the underlying sample is defined by optical properties (i.e., the number of galaxies in an Abell radius) and not by X-ray properties. Thus the computed luminosity function is a bi-variate function of both Lx and cluster richness R. The sample is volume limited in the sense that the Abell sample (with the same redshift cutoff) is volume limited and with the same incompleteness problems. Therefore each cluster contributes l/V^Wl ^° * n e luminosity function. This is different from the methodology used for an X-ray flux limited survey where each cluster would contribute 1 'iim, Lx) To calculate the cumulative luminosity function, we use the Kaplan-Meier product limit estimate method (Cox and Oakes 1984; Schmitt 1985, Feigelson and Nelson 1985).

Cluster Research with X-ray Observations

S81

This is equivalent to the techniques developed by Avni et al. (1980). Specifically, the following probability is calculated:

This is the unnormalized cumulative luminosity function and is formally the maximum likelihood estimate of the luminosity function. The results are shown in Figure 2a.

Lum Fncfor R=0,1,2

Ro -

Ri

I .a R2

_

#

^

-

W i

50 100

500

i

i

i

5000

ot i

50000

500000

L(1e40 ergs/sec)

Figure 2a. Non-parametric luminosity function by richness class. Since our X-ray sample is not an independent complete sample, we must rely on the understanding of the completeness characteristics of the Abell sample to derive the normalization. The Abell Catalogue is known to be incomplete for richness class 0. Abell recognized this and did not include the richness class 0 objects in his "statistical" sample. Later work by Bahcall (1979) (see also Lucy 1983), based on analysis of the multiplicity function (the number of clusters per unit volume versus richness) has shown that richness 0 clusters are incomplete by a factor of > 3. Quantitatively we fit Schechter functions to the data with the results shown in Figure 2b. It must be stressed that the normalization does not affect the shape of the luminosity function. Some aspects of our results are immediately apparent: a. The shape of the luminosity function is similar for each richness class, although there is a change in scale.

382

R. Giacconi and R. Burg

Fits to BFGJ Luminosity Functions

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£

A

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Figure 2b. Schechter function fits. b. Richer clusters are systematically brighter in X-rays. The value of L*, the characteristic luminosity for each richness class is roughly proportional to (N* j) e , (where N* is the characteristic number of galaxies per richness class, Lucy 1983), Q = 1.6 ± 0.4. (See Figure 3). This is to be compared with Abramopoulos and Ku (1983) who derived L x ~ M a ? c. There is within each richness class a wide range of X-ray luminosities. There is an apparent flattening of the slope of the luminosity function for each richness class. d. Our observed luminosity functions can be described as Schechter functions with approximately the same slope and different L£. A less obvious aspect of our result deserves some note. A priori we would have expected to observe a distribution of X-ray luminosity of clusters bound between two values. A minimum due to the integrated contribution of the individual galaxies (Mushotzky 1988) and a maximum which corresponds to the X-ray emission of clusters whose state of dynamic evolution, central condensation and original conditions lead to the maximum energy dissipation in X-rays at the current epoch. In Figure 4 we present our combined luminosity function for R > 1 and R > 0. We show both cases since for R > 0 we are dominated by the normalization uncertainty. On the same plot we include previously reported luminosity functions. We agree at the high

Cluster Research with X-ray Observations

383

Abell Clusters - L* vs Richness 8 o

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N* Figure 3. Characteristic luminosity versus richness. luminosity end with previous results and we are not inconsistent at the low luminosity end where use of the Bahcall normalization, to take into account R = 0 incompleteness, has the biggest effect. As mentioned above, the X-ray luminosity which we measure must be in all cases the sum of the X-ray luminosity of the individual galaxies plus a component due to intergalactic hot dense gas. For evolved systems we would expect this latter component to dominate. For instance a cluster such as Coma (R = 2) has an Xray luminosity of 3.7 X 1044 ergs s" 1 , while the integrated emission from single galaxies is about 10 43 erg s" 1 . A1367, which was previously studied in some detail (Bechtold et al. 1983) could be an example of a cluster where summed galaxy emission is a large fraction of the total cluster luminosity. A1367 is a loose, seemingly unevolved structure, the relatively low temperature of 4 keV. In their work Bechtold et al. showed that the summed contribution of the 10 brightest galaxies was ~ 3 X 1042 ergs/sec. This is 5% of the total luminosity of the cluster. Roughly 80% of the galaxies (brighter than L*) were not detected as individual sources (the high background due to the intracluster medium causes a high detection threshold) but they may still have contributed significantly to the cluster emission. We note that in our data the minimum observed X-ray luminosities for R = 0,1 and 2 clusters are 3 x 10 42 , and 8 x 1042 and 3 x 10 43 erg sec" 1 respectively. In the three cases the expected summed contribution from individual galaxies (Forman et al. 1983) is roughly 4 x 10 42,6.4 x 1042 and 104"* erg sec" 1 respectively. This is evidence that

384

R- Giacconi and R. Burg

Summed BFGJ Luminosity Functions

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a-

I 3

100

1000

10000

100000

Luminosity (1e40 ergs/sec) Figure 4. Summed non-parametric luminosities for R>0 is HEAO1-A1 R > 1 luminosity function.

and R > 1. Also included

there is a substantial number of clusters in which the X-ray emission from intracluster gas is not dominant.

3. INTERPRETATION OF THE LUMINOSITY FUNCTION Studying the wide range of X-ray luminosity of clusters selected by richness class (presumably therefore of given total mass) we are in a position to emphasize a fundamental property of X-ray emission from clusters. Specifically we can attempt to separate out the factors which determine the X-ray emission and relate them to initial conditions and dynamic evolution of the cluster. Using the thermal bremmstrahlung expression we can write: T

\/l

T>1/2

Ltx ~ /'gas •'"gas-'gas

Using the virial theorem and equipartition we can relate T ga s to the virial gas mass, Mv, and density, pv, _. Mv GMV ,_

Cluster Research with X-ray Observations

j T

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and Lx ~ />gasMgasMv

385

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and

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Tt{t)),

i

This allows us to separate the various contributions to the X-ray luminosity namely: • the initial fraction fp of gas and any injection mechanism of gas after formation • a term which includes the effects of cosmology and dynamical evolution. • the virial mass of the cluster. We are currently working with A. Cavaliere (Cavaliere et al. 1989) on a refinement of this approach, where we directly relate these various quantities to the density fluctuation spectrum, |6| ~ Jfcn. This results in an expression for L x of the form Lx = in which a represents the cosmological term, b the dynamical term, and c the gas injection or stripping mechanisms. In summary: • The X-ray emission of a cluster depends not only on its mass but also on the initial conditions, the subsequent dynamical evolution of the system and the mechanism and history of the gas injection. • Studying the luminosity function at the current epoch is not sufficient to disentangle the various contributions. • On the other hand, coupling the local luminosity function for each range of masses with luminosity functions for the same mass objects at different redshifts will allow us to study in detail the various processes in the evolution of the gas. • Future X-ray surveys will allow us to obtain direct information on the initial density fluctuation spectrum. 4. F U T U R E SURVEYS We focus our attention in this discussion on only two missions: ROSAT as the precursor survey mission to be launched in 1990 and AXAF the follow-on mission which will dominate X-ray astronomy for many years after its planned launch in 1996. In Table 2, we summarize the principal characteristics of the two missions from the point of view of the relevant instrumentation. Figure 5 shows the effective area of ROSAT and AXAF as a function of energy.

386

R. Giacconi and R. Bury

Table 2 Telescope

ROSAT

AXAF

Diameter

84 cm

120 cm diameter

Number of surfaces

4

6

field of view

2 degrees

1 degree

geometric area

1141 cm 2

1700 cm2

Center of field

-3"

-.5"

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-5"

- 3.5"

30' off axis

-60"

-60"

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H R I - 30', none

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CCD - 14' AE - 150 eV (.5 - 8) keV

Angular resolution

Imaging Instruments (field, spectral resolution)

Spectroscopy

Transmission gratings high energy R - 100 at 4.5 keV, R - 700 at .4 keV low energy R - 100 at 1.5 keV, R - 750 at .1 KeV Calorimeter .78 sq. arc min. AE < 12 eV

Cluster Research with X-ray Observations

387

1

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Effective Area vs. Energy

10

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Figure 5. Comparison of ROSAT and AXAF. It is clear that with these capabilities many of the investigations initiated with Einstein can be pursued with greater depth and scope. They can be roughly divided in a few general headings. (See Table 3) A good starting point to understand the impact of the new X-ray missions on the topics of cluster research is the review "The Advanced X-ray Astrophysics Facility", a special volume of Astrophysical Letters and Communications (Vol. 26, 1987), and references herein. We would like to discuss here in some detail only one aspect of the program in which we are personally interested. It deals with the study of cluster formation and evolution by means of surveys with ROSAT and AXAF. The two missions differ in a fundamental way. For each cluster the X-ray observations can yield two basic quantities: 1. The X-ray surface brightness distribution at the source as well as its integral. 2. The spectrum (and/or temperature) at each point or (for weaker sources) the spectrum (or temperature) of the integrated source emission. The detection of redshifted line emission from heavy elements may permit direct determination of the redshift and metallicity. 1 and 2 together yield a direct measure of Mv (the virial mass). As we discussed above, X-ray emission from a cluster will ultimately depend both on the initial conditions at formation and on its state of chemical and dynamic evolution. Thus, at least two observables will be required to characterize each cluster, in order to derive its properties without a very large number of simplifying assumptions. Basically, the ROSAT experiments only yields one quantity (the distribution of L x ). Future missions such as ASTRO-D, Jet X and XMM will yield spectra with some angular

888

R. Giacconi and R. Burg Table 3 Individual galaxies-interaction with the intracluster medium - Galaxy halos - Galaxy stripping (M86) - Cooling flows (M87) The intracluster medium - metallicity (spectra from SSS Einstein ) Cluster emission : Morphology and state of dynamic evolution (double clusters) : S(r) = S(0)(l + r 2 / a 2 ) " 3 ^ + 1 / 2 surface brightness density profiles Correlations : Lx vs N : Lx vs N o : Lx vs Tgas ~ : Lx vs % spiral : p = fi m pp _£ Cluster evolution evolution of intergalactic medium with z (evolution of a single cluster in time) evolution of the luminosity function evolution of metallicity Cluster formation and cosmology dark mass correlation functions protoclusters primordial gas Zeldovich-Sunyaev effect, Krolik-Raymond method: H o , qo

resolution for the nearest systems but only integral luminosity and integral spectra for the more distant ones. Only with AXAF will one have high angular resolution coupled with spectral resolution for the most distant detectable clusters (~ z » 1). The ROSAT all sky survey is an important precursor to AXAF. No cluster for which one plans to do detailed spectral or morphological studies with AXAF can be much fainter than those detected in the ROSAT all sky survey. The detection capabilities of ROSAT are such that we expect to detect a large sample of clusters. Figures 6 and 7 show the Log N-Log S relation derived by Burg and Giacconi (1990) for z < 0.5 and 1.0 respectively. These figures are derived from the luminosity function of Burg et al. 1989 for R>0 Abell clusters at z < 0.15. It is important to note that uncertainties in the normalization parameter (of the Schechter functions fitted to the

Cluster Research with X-ray Observations

389

Number Flux for R=0,1,2 Derived from BFGJ Lum Fnc

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O

d 1 e-15

1 e-14

1

1 1 e-13 e-12 e-11 S (ergs/s/sq. cm) Zcut=.5

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Figure 6. Log N-Log S for clusters using BFGJ luminosity functions (Burg et al. 1989) with no evolution and cut-off redshift of 0.5. Number Flux for R=0,1,2 Derived from BFGJ Lum Fnc g S J

,

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Figure 7. Log N-Log S with redshift cut-off of 1.0.

1 e-10

1 e-9

390

R. Giacconi and R. Burg

RO

R1

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

redshift

redshift

R2

0.0 0.2 0.4 0.6 0.8 1.0 redshift

Figure 8. Redshift distribution of clusters to Smin = 10

l3

ergs s ^cm

2

.

local luminosity functions) result in large uncertainties in Log N - Log S. However, the relative z distribution of clusters by richness class (Figure 8) assuming no evolution is a direct consequence only of the shape of the luminosity function, which is much better established. This means that we expect to detect in the ROSAT surveys a substantial fraction of clusters at 0.5 < z < 1.0. However, the angular resolution of the PSPC, the detector with which the survey will be conducted, is of order ~ 30" and except for nearby clusters (z < 0.2) it will be difficult from X-ray observations alone to classify the objects as clusters rather than stars or AGNs. A collaboration between the Max Planck Institute, STScI and ROE is planning a rapid (quasi real-time) classification of X-ray sources in the all sky ROSAT survey by utilizing existing ground based optical sky surveys. The purpose of this program is to permit the follow up of PSPC detections of particularly interesting clusters with HRI high angular resolution observations capable of resolving the details of the cluster morphology. This classification technique relies on utilizing all available X-ray and optical information and the observational constraints derived from the MSS survey to divide the ROSAT survey sources into appropriate bins. The observational base for discrimination is given by studies such as those of Maccacaro and Gioia on the MSS sources which are shown in Figure 9. In Figure 10 we show a tentative conceptual flow diagram which will be refined and implemented in an automated expert system. We hope by these means to isolate an enriched sample of distant clusters which could then be further studied with later X-ray missions.

Cluster Research with X-ray Observations

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Figure 9. Classification of Einstein Medium Sensitivity Survey. What we hope to achieve from the ROSAT all-sky survey is the following: • X-ray flux measurements (or upper limits) for all classes of optically defined clusters (whether Abell, Zwicky or poor groups). We will be able to derive bivariate luminosity functions with methods similar to those used for the Einstein sources (Burg et al. 1990). • A flux limited X-ray survey for all types of clusters defined as gravitationally bound systems of galaxies containing intracluster gas with a high degree of metallicity and central condensation. Such surveys are naturally biased toward systems which are both chemically and dynamically evolved. • Detailed study of morphology and rough temperature determination (for low temperature systems) for all nearby systems. • Point to point correlations (with a large sample of X-ray defined clusters) to study large scale structure. • Study of prevalence of cooling flows, galactic halos, (both in clusters and in isolated systems), etc. for nearby systems. • Confrontation between model predicted redshift distributions and observed redshift distributions for optically characterized subsamples.

392

R. Giacconi and R. Burg

DECISION TREE FOR CLASSIFICATION OF X-RAY SOURCES

Sx22xi0nergcm2s" 1-2 keV - 100,000 sources

#5100

#94900

Extended in X-ray

Point-like in X-ray

43400

i 51500 Star or Gal. m»< 15.5 (3% false coinc. stars)

Star or Galaxy m v >15.5 N-1

10000 Stellar Object 19<mv<20.5 log fx/tv > 0

Stellar Object i5.5<mv
6000 Galaxies 15.5 <m v < 20.5

N.B.: ID includes - 1300 False Coinc.

\ Proper Motion

No Proper Motion

N- 1

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-1 s log fx/fv < 0

» 0 Red

r

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F

Figure 10. Proposed categorization algorithm for ROSAT.

Includes 3400 LLAGN'S & 1300 Clusters z>.5

N» 1

Cluster Research with X-ray Observations

counts/cm2-scc-keV

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394

R- Giacconi and R. Burg

The tremendous advantage of AXAF with respect to ROS AT is given by two specific technical improvements coupled together: the high quantum efficiency and spectral resolution of the CCD detectors coupled to a high angular resolution telescope. Within the field of view of the CCD, any cluster, at any z, which is detected, can be resolved as an extended structure. For given models of cluster evolution we can estimate the characteristic core radius of clusters at different z's: _5+n

i ? ~ ( l + z ) "+3. For n = — 1 and Friedman cosmology with qo = 1/2 and Ho = 50 kms" 1 Mpc" 1 the linear dimensions of clusters at z = 1 and 2 would correspond to angular diameters of 15 to 7 arc seconds. This angular extent can easily be measured by AXAF within the field of view of the CCD. AXAF therefore possesses the angular resolution and spectroscopic capability to directly determine the angular extent of a cluster as well as the ability to directly measure its redshift (if the X-ray emitting gas is enriched). Figure 11 shows a simulation carried out by G. Garmire and colleagues of the expected surface brightness profile and spectrum which will be obtained with the AXAF CCD X-ray camera for a rich cluster at different redshifts. 5. SUMMARY • With ROSAT observations we will obtain the only all sky X-ray flux limited sample of clusters for years to come. We might be able to show the existence of evolutionary effects by extensive optical follow up (to measure z) and by studying the z distribution of carefully selected subsamples. However, the causes for the apparent evolutionary effects, if any, will be difficult to determine. In particular, given the lack of X-ray spectroscopy we will be unable to measure the evolution of metallicity and gas of temperature and mass (except with very restrictive assumptions). • With the advent of ASTRO-D and Jet X etc. which will combine moderate angular and spectral resolution capabilities with a wide bandwidth, we will be able to directly measure redshift, metallicity and temperature. For low redshift systems (z < 0.25) we will be able to also measure the distribution of surface brightness, temperature and metallicity. This will enable us to determine the state of dynamic and chemical evolution and directly measure the dark mass. • Similar measurements can be extended by AXAF to very large redshifts, from z > 0.25 to z of order of 2. When this program is completed there will emerge a new understanding of the formation and evolution of these objects, among the most massive gravitationally bound structures in the Universe. Furthermore, we hope this will lead to a more complete picture of the structure of the Universe.

REFERENCES Abell, G. 0 . 1958, Astrophys. J. Suppi, 3, 211. Abramopoulos F., and Ku, W. 1983, Astrophys. J., 271, 446. Avni, Y., Soltan, A., Tannenbaum, H., and Zamorani, G. 1980, Ap. J., 238, 800. Bahcall, N. 1979, Ap. J., 232, 689.

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Bechtold, J., Forman, W., Giacconi, R., Jones, C , Schwarz, J., Tucker, W., and VanSpeybroeck, L. 1983, Astrophys. J., 265, 26. Burg, R., and Giacconi, R. 1990, In preparation. Burg, R., Forman, W., Giacconi, R., and Jones, C. 1990, In preparation, (BFGJ). Cavaliere, A., Burg, R., and Giacconi R. 1989, In preparation. Cox, D. R., and Oakes, D. 1984, Analysis of Survival Data, Chapman and Hall, Cambridge. Feigelson, E.D., and Nelson, P.I. 1985, Ap. J., 293, 192. Forman, W., Jones C , and Tucker W., 1983, Astrophys. J., 293, 102. Gioia, I. M., Geller, M.J., Huchra, J.P., Maccacaro, T., Steiner, J.E., and Stocke J. 1982, Ap. J. (Letters), 255, L 17. Gursky, H., Kellog, E.M., Murray, S., Leoug, C , Tananbaum, H., and Giacconi, R. 1971, Ap. J. (Letters), 169, L81. Henry, J. P., Brandvardi, G., Briel, V., Fabricant, D., Feigelson, E., Murray, S., Soltan, A., and Tananbaum, H. 1979, Ap. J. (Letters), 238, L15. Johnson, M. W., Cruddace, R.G., Ulmer, M.P., Kowalski, M.P., and Wood, K.S. 1983, Ap. J., 266, 425. Jones, C , and Forman, W. 1984, Ap. J., 276, 38. Jones, C , and Forman, F. 1990, in preparation. Kaiser, N. 1986, M.N.R.A.S., 222, 323. Kellog, E. M., Gursky, H., Tanabaum, H., Giacconi, R. and Pounds, K. 1972, Ap. J. (Letters), 174, L65. Kowalski, M. P., Ulmer, M.P., Cruddace^l.G. 1983, Ap. J., 268, 540. Kriss, G. A., Canizares, C.E., McClintock, J.E. and Feigelson, E.D. 1980, Ap. J. (Letters), 235, L61. Lucy, J. R., 1983, M.N.R.A.S., 204, 33. Mitchell, R. J., Culhane, J.L., Davison, P.J., and Ives, J.C. 1976, Mon. Not. R. Astron. Soc, 176, 29p. Mushotzky, R. 1988, Proceedings of the NATO summer school on Hot Astrophysical Plasmas, Palluviccini, R., Editor. Piccinotti, G., Mushotzky, R.F., Boldt, E.F., Holt, S.S., Marshall, F.E., Serlenitsos, P.J., and Shafer, R.A. 1982, Ap. J., 253, 485. Schmitt, J.H.M.M., 1985, Ap. J., 293, 198. Serlemitsos P. J., Smith, B.W., Boldt, E.A., Holt, S.S., and Swank, J.A. 1977, Ap. J. (Letters), 211, L63. Shaeffer, R., and Silk, J. 1988, Ap. J., 333, 509. Shwartz, D. A., Davis, M., Doxsey, R. E., Griffiths, R.E., Huchra, J., Johnston, M. D., Mushotzky, R.F., Swank, J., and Tonry J. 1980, Ap. J. (Letters), 238, L53. Stocke, J.T., et al. 1983, Ap. J., 273, 458. Zwicky F., Herzog, E., Wild, P., Karpowicz, M., and Kowal, C.T. 1961-1968, Catalogue of Galaxies and Clusters of Galaxies, Volumes 1-6, Caltech, Pasadena.

3a

3b

3c

{facing p. 296)

7a Log IPC counts s"

i » 0.11 - 0.76

7b -4 -3 -2 Log IPC counts s"'

V = 0.04 Wpc

(facing p. 300)

7d

7e

7f Log SZ Decrement (ml<) 4

-60 -40

-20

0

20

40

60

BBKS-30av0