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Home , Elliptical galaxy, Galaxy cluster, Protogalaxy

Proc. Natl. Acad. Sci. USA Vol. 90, pp. 4835-4839, June 1993 Colloquium Paper

This paper was presented at a colloquium entitled "," organized by a committee chaired by David N. Schramm, held March 27 and 28, 1992, at the National Academy of Sciences, Irvine, CA. Dissipative processes in formation JOSEPH SILK Departments of and Physics, and Center for Particle Astrophysics, University of California, Berkeley, CA 94720

ABSTRACT A galaxy commences its life in a diffuse gas vide significant barriers in regions of galactic formation cloud that evolves into a predominantly stellar aggregation. that are overcome by magnetic and gravitational torquing as Considerable dissipation ofgravitational binding energy occurs well as by magnetic field diffusion. The fundamental physics during this transition. I review here the dissipative processes is poorly understood in galactic , and success- that determine the critical scales of luminous and the ful theories are semiphenomenological. I shall adopt a similar generation oftheir morphology. The universal scaling relations viewpoint with regard to protogalactic star formation: for spirals and ellipticals are shown to be sensitive to the history did form, and simple physical arguments provide a crude ofstar formation. Semiphenomenological expressions are given framework for understanding galaxy formation. Once stars for star-formation rates in and in starbursts. have formed out of the protogalactic cloud, they should Implications are described for formation and subsequently conserve orbital energy and angular momen- for the evolution of disk galaxies. tum. The oldest stars in a galaxy therefore define the proto- galactic potential well. If appreciable protogalactic binding energy was dissipated before formation ofthe first stars, this Critical Scales of Protogalaxies only hampers our ability to discern the relation between parameters and those of the primordial density Dissipation of gravitational binding energy is the key to fluctuations. If dark halos consist of cold parti- forming cosmic structure. This process is poorly understood, cles, no dissipation occurred during their formation, and the insofar as issues of fragmentation and coalescence arise parameters ofdark halo potential wells can therefore be used during the collapse of a self-gravitating primordial gas cloud. to reconstruct, or at least constrain, the primordial fluctua- Does a protogalactic cloud form stars during its initial col- tion power spectrum. lapse, or did its inner regions collapse to form a central It is a satisfying coincidence that the parameters of an L* massive ? The nonspherical and nonlinear collapse galaxy are indeed on the critical locus that in effect defines physics defies any simple prediction. This talk will focus on the most massive systems capable ofundergoing efficient star the role of dissipative processes in galaxy formation, with formation. The identical argument also yields a scale length emphasis on early star formation. For a more detailed review of about 50 kiloparsecs (kpc; 1 pc = 3.09 x 1016 m) that ofgalaxy formation, the reader is referred to an article by Silk corresponds to the region within which efficient star forma- and Wyse (1). tion occurs. One problem that arises is that excessive bary- One can at least state objectively that in order for any rapid onic matter can cool within a Hubble time and further dissipative collapse to be initiated, either locally or globally, augment the derived maximum mass. This cooling catastro- the cloud must satisfy the requirement that the cooling time phe would destroy the coincidence between cooling effi- scale locally be less than the free-fall collapse time. This ciency and L*. condition is quantified by setting the cooling time scale Possible solutions are either that the cooling gas forms (3/2)kT[1AHA(T)n]1-, where A is the cooling rate per hydro- baryonic dark matter or that it is heated to -106 K and gen nucleus in a cosmic plasma of mean molecular weight u thereby mostly remains in the intergalactic medium. The and unit density, n is the density, and T is the temperature, former possibility seems hard to justify given our knowledge equal to the collapse time, proportional to (Gn)-1/2. The of the inefficiency ofgalactic star formation, although cluster resulting locus in the density-temperature plane (Fig. 1) may cooling flows have been argued to provide a suitable envi- be interpreted as a restriction on the minimum mean density ronment for almost exclusively very low mass (0.2Mo) star at the appropriate value of the virial temperature for a cloud formation. Heating of the intergalactic medium is a process of arbitrary mass. This condition also applies to a highly that certainly occurred in galaxy clusters and may well have nonuniform self-gravitating cloud, since fragments will ac- been prevalent at early epochs. quire the virial velocity if their density contrast is high. Note that lines of constant mass intersect the cooling locus in the and Morphology vicinity of the galactic virial temperature (105-107 K for normal galaxies) at a total (including dark) mass of about Numerical simulations of tidal torques between neighboring 1012M®. protogalaxies result in acquisition of angular momentum at a The significance of this result is the following. Once a level (2, 3) (A) 0.06, where the dimensionless angular protogalaxy is capable of local cooling, fragmentation and momentum parameter A has a broad dispersion, AA -A, and star formation may rapidly ensue. The cooling condition is is defined as necessary for star formation but is not sufficient to guarantee that it occurs. Angular momentum and magnetic fields pro- A - JE112G-1M - 5/2 0.3vl/o The publication costs of this article were defrayed in part by page charge for a de Vaucouleurs density profile, in a system of mass M, payment. This article must therefore be hereby marked "advertisement" angular momentum J, potential energy E, rotational velocity in accordance with 18 U.S.C. §1734 solely to indicate this fact. v, and virial oa. 4835 Downloaded by guest on October 1, 2021 4836 Colloquium Paper: Silk Proc. Natl. Acad. Sci. USA 90 (1993) For ellipticals, the low observed (A) of 0.07 requires that efficient angular momentum transfer must have occurred to avoid spin-up as the gas contracted toward the final high- density state of the stellar component. The angular momen- tum transfer occurs via dynamical friction provided that stars formed sufficiently early and in massive dense clusters. -22 Bulges should have formed in a similar although less efficient manner, but most of the star formation in protodisks must 4) have been very inefficient to avoid a similar fate. There indeed is evidence for widely differing rates of past star formation in elliptical and disk galaxies, obtained from -23 population synthesis and chemical evolution modeling, re- spectively. Star-formation rates would have differed because ofinefficiency ifthe star-forming protogalactic clouds were of widely differing mass. Low mass clouds disrupt easily once 16 a few massive stars have evolved into supernovae, whereas massive clouds tend to retain the stellar ejecta, recycling it into successive generations of stars. Perhaps ellipticals formed via disk mergers. Enrichment results in efficient cooling, which in turn should lead to effective cloud coagulation and massive cloud formation. 14 Simulations of mergers indeed indicate that the gas rapidly develops into a central (s1-kpc scale) dense concentration (4). The central stellar cores of ellipticals are a plausible outcome of the massive central clouds. This hypothesis would naturally be consistent with the predominance of 12 ellipticals in dense environments, where a past high rate of galaxy mergers presumably occurred. The building blocks for galaxies in such a picture would be gas-rich irregular galaxies that, in isolated regions, have inefficiently undergone minor mergers to form spiral disks. Recent major mergers in denser 2 regions triggered massive cloud formation that in turn led to efficient star formation and development of elliptical mor- phologies. Scaling Relations

-2 The fossilized characteristic properties of galaxies contain bo important information about their formation. Notable among c) these properties are the remarkably low dispersion scaling aE relations: Tully-Fisher for spirals, L a v4, and the fundamen- tal plane for ellipticals and bulges, L acr3Aj3/4, where ois the virial velocity dispersion and AtL iS the surface brightness within the half-light radius. Combination of these observed relations with the , expressible as L LALoc o,4 UL(MIL)-' 6 leads to MIL oc pUZY1/2 and M/L x L1/6, respectively, for the Log(T), K spiral and elliptical correlations. These are relations between intrinsic properties that pri- FIG. 1. (Top) Cooling rate for an of unit marily involve star formation rather than structure. How- density, for various abundances that range from solar to depleted by ever, star formation and morphology are inseparable. The up to a factor of 1000. In the depleted cases, ratios of heavy element degree of rotational support and bulge/disk ratio varies abundances are used that correspond to the ratios measured for smoothly within the fundamental plane for the dynamically extremely metal-poor halo stars. New cooling cross-sections have hot components, suggesting that gas dissipation is important been incorporated by Sutherland (18) to give plotted curves. (Middle) Same as Top, but cooling time scale is plotted versus electron and systematically played a larger role for the smaller sys- temperature. (Bottom) Loci of cooling conditions, cooling time scale tems where gas cooling was most efficient (5). = free-fall time (solid lines) and cooling time scale = Hubble time One can attempt to distinguish purely intrinsic star- (dashed lines) for various abundances as in Top. Loci of constant formation-related aspects from initial conditions as follows. virial mass (in ME)) and the condition that dynamical time equals a The initial stellar mass function determines the mass/ Hubble time are also shown. ratio. The mean surface density ofa newly formed virialized system, in the absence of any dissipation, scales The observed (A) 0.7 in disks is simply explained by with formation as (1 + z)2(n+2)/(n+3) or roughly as 1 + dissipative collapse, conserving specific angular momentum z for the spectral index n -1 that is appropriate on galaxy of the gas. The dark halo acquires a rotational torque as the scales 1010-1012M®. Here the power spectrum of primordial gas contracts in radius by about a factor of 10. The final radius density fluctuations is taken to be I8kI2 X kn, equivalent to a of the disk, identified with the disk scale length, is in mass fluctuation spectrum AM/M oc M-(n+3)16. reasonable accord with R* (as inferred from the cooling This immediately suggests that the zero point of the diagram). Tully-Fisher relation should depend on the redshift ofgalaxy Downloaded by guest on October 1, 2021 Colloquium Paper: Silk Proc. Natl. Acad. Sci. USA 90 (1993) 4837

formation, albeit with large dispersion, whereas that of the SFR*pSN = ILgasOga [21 fundamental plane should not, if we can assume that the initial stellar mass function, and hence MIL, is independent Here PSN = 2ESN(VCMSN)-1 is the final specific momentum of the formation epoch and environment. Indeed, there is a deposited into the by a supernova rem- well-known variation of zero point with Hubble type for the nant of initial kinetic energy 1051E51 ergs, and spiral sequence that is generally attributed to the increase in MIL for the associated with increasingly VC = 208E1114Z-3114n1/7 km s-1 bulge-dominated galaxies. One expects the large dispersion in formation redshift to lead to a large dispersion in galaxy is the cooling velocity at which a supernova remnant expand- surface brightness UL (or at least surface density y). The low ing into a uniform medium of density n and Z dispersion observed for the Tully-Fisher relation can only (relative to solar) first enters the approximately momentum- arise if the residuals in ,L and MIL are anticorrelated. Large conserving phase (10). The mean mass in stars that form for ,u, early-forming galaxies (this being the sense of the corre- each supernova is mSN, with a typical numerical value being lation expected in any hierarchical scheme), should system- mSN 300m 300M®E with m300 1 for a present-day star atically have lower MIL. Ifone considers a mass sequence of formation rate of -6M®D yr-1 and disk supernova rate of disks, the late-forming, more massive disks have undergone -"0.02 yr-1. One obtains PSN = 600ES3/14n-'/7mjOkm3s01. more dissipation and should have progressively higher AL Eq. 2 suggests that the star-formation rate initially decreases and lower MIL. in proportion to ggas: the e-folding time scale for gas depletion This appears to be consistent with the expectation of iS -(PSN1/ag)D1 100alofl , where o-g -lOalo kmss. merger-dominated formation, whereas the early-type galax- The initial value of Agas is likely to be determined by ies have undergone mergers and actually "form" later than cloud-cloud collisions. Consider the following simple model most of the gas-rich isolated systems. The age of the Milky of identical protogalactic clouds in the protodisk. Gas dissi- Way suggests a relatively high epoch of formation (z - 1) pation is primarily due to energy loss in cloud-cloud colli- compared to the median redshift measured for samples of sions, which occur at a rate toi (pgasco)(g/H) where /l faint blue-field galaxies (z - 0.4), many of which seem to be is the mean cloud surface density and the disk scale height vigorous star-forming systems. Clearly, we need insight into how arises before hoping to understand the observed / ~~-1 MIL a* galaxy parameter correlations. H= I) gfas+ Qag/Q . r7rG g' Q0g/?l Star-Formation Rates in Protogalaxies Clouds form at a rate - fl, as expected if cloud growth is The star-formation rate in a is approximately driven by coagulation of smaller gas clouds in a gravitation- proportional to its gas content. An adopted star-formation ally unstable disk. It seems reasonable to expect that a pure rate of the form gas disk will be sufficiently unstable that clouds are contin- uously regenerated by nonaxisymmetric gravitational insta- bilities in the disk over a rotation period until viscous effects SFR Agast (1 -/cr/gas) play any role in redistributing the gas. In a steady state, with cloud motions being maintained by disk gravitational insta- enshrines the semiphenomenological physics of spiral disks. bilities, t 1 - Q or Q -Igas/ll. If self-regulation maintains Here Trj is the disk linear instability growth rate, equal to Q - 1, one can thereby infer g(iaL - -pl - ,d as observed. In -IrG/lgasoa1a'S, Agas is the gas (HI + H2 + HII) surface density, the interstellar medium of our Galaxy, molecular clouds 0'gas is the gas velocity dispersion, and Pcr is the critical satisfy (11) al 160M®D pc-2, and this bounds Uggas early in surface density above which gravitational instabilities are the evolution of the galactic disk. operative. Analyses of both axisymmetric and nonaxisym- metric instabilities of thin self-gravitating gaseous (6) and Implications for Scaling Relations stellar (7) disks suggest that the disk is gravitationally unsta- ble when the mean surface density exceeds a critical value There is an important consequence of describing present IA,r. For a gas disk, Icr KOgas(IG)-1, where K iS the inner disk star-formation by a more or less quadratic law, epicyclic frequency. I define Q 8 Lcr/A; in the solar neigh- borhood, Lcr 8M® pc-2, and ugas 13M(D pc-2, indicating SFR oc g,a with a 2; that Qgas : 1 near the sun. This effectively describes the ability of the gas-rich inner disk to form both note that a 1.5 may be slightly favored by the data. The molecular cloud complexes and stars. Indeed, the rate in Eq. present star-formation rate is proportional to the current gas 1 provides an acceptable description ofdisk star formation at content. However, this in turn depends on the disk age. For late times, resembling a Schmidt law SFR a 1.gas in the inner example, with a = 2, we may use Eq. 1 in particular as disk where /gas >> cr. Nearby star-forming galaxies display appropriate for self-regulation by gravitational instabilities both a nearly quadratic star-formation law as well as a heating the disk and gas cooling providing the destabilizing star-formation threshold when ggas drops below the critical mechanism. We find that in this case Ugas = 0-gas(1rGTd)-1, value (8). and the star-formation rate ,u* = crg(EirGTd2)-. At early times, however, one must restrict the gas con- The feedback via supernova-driven winds specifies the sumption rate in order to reproduce the observed slow normalization parameter, in effect the star-formation effi- variation of star-formation rate with epoch in spiral disks that ciency, and prescribes the gas surface density that can be results in gas-rich disks at late times. The obvious physical regulated by a given star-formation rate: mechanism is via feedback from massive star formation. The following argument is adapted from Silk (9) and B. Wang and J.S. (unpublished data). M* PSN Once massive stars form and die, the energy input from HII ..s M G regions, OB star winds, and, especially, supernova remnants provides a source of momentum to the interstellar gas. I This yields an efficiency e = (0gasPsN)G.*/Agas), and com- incorporate the supernova feedback by writing bination with the late time limit for lgas -yields y*= Downloaded by guest on October 1, 2021 4838 Colloquium Paper: Silk Proc. Natl. Acad. Sci. USA 90 (1993) PSN(GTd)-1. Hence, the mass/luminosity ratio of the star- longer given by a Schmidt-type law appropriate to disks. forming disk is proportional to pL*/pi* S8PSNTd1/Yg Feedback effects from massive star formation, and in par- Note that the disk (M/L)d increases with disk age, and ticular supernova energy input, must inevitably limit the decreases for older disks. Remarkably, the product Aj2. star-formation rate. (M/L)d is independent of disk age. The zero point of the I estimate the limiting star-formation rate as follows (13). Tully-Fisher relation is affected insofar as the current star- Let supernova remnants overlap and produce a hot coronal formation rate is not an accurate measure of current disk medium that pressurizes interstellar clouds. When the hot luminosity in the appropriate wavelength band. This should medium becomes sufficiently porous and dominates the be more of a problem for bulge-dominated galaxies. In this volume, the cold gas fraction will diminish. Define the case, L/V4 °c (L/M)d1 a LdT2 increases as a function of porosity of the hot interstellar medium by disk age, the rate of increase of Ld depending on the initial mass function dN/dm ofstars near the main sequence turn off P = P*VSN/(MSN), if Ld is predominantly due to old stars: Lold - t-(2+x)/3 for dN/dm - m-1-x with x 2-3. There is an additional factor where VSN is the 4 volumes occupied by an old supernova from the star-formation threshold: since vr/I.L oc fl/t o v-1 remnant halted by the pressure of the ambient medium. A this can result in a steepening of the L oc v 4 relation at low Vr, spherically symmetric remnant expanding into a uniform since ,u* c 1 - /r/u. More important, however, is the medium of pressure p 104p4k cm-3 K and density n fills a inference of an age-dependent offset of the zero point in the 4-volume Tully-Fisher relation, especially for the near infrared I and K bands, where the young stars contribute a significant fraction VSN = 7.82 x 10'2p-1l36n-0-11Elj26Z-0.204 pC3 yr, of the light. The observed dispersion in iLL is known to be <10%, where Z (in units of Z0) is the metallicity. suggesting a similar limit on the dispersion in disk ages for The volume-filling factor of the cold medium is fv = e-P. nearby luminous spirals. Tully-Fisher offsets could therefore and the mass fraction is be as large as 5% if half the light comes from the old stellar population. Residuals in ,* and in the peculiar velocities deduced from Tully-Fisher should be anticorrelated: 6IL* cc fm=min[ \Pgas/e -5Td, 8Vpec a-,r oc -8(L/v4)1/2 cc 1/28Td-that is, 8vpec - where (Pci/Pgas) is the ratio of characteristic cloud density to average density of the cold gas. The triggering of star Starbursts and Ellipticals formation drives high porosity and ensuing gas outflows via a supernova-driven wind iffm < 1; that is, if There are analogous implications for the fundamental plane of ellipticals equivalent to a weak dependence of MIL on L. P z However, the MIL for ellipticals is determined by their ln((pcj/ppa)), star-formation histories, known to resemble those of star- one can self-regulate star formation by disrupting the gas bursts. Most likely, protoelliptical starbursts are merger supply. On the other hand, the porosity cannot be too large, induced, as is known to be the case for extreme infrared or there will be no cold gas. astronomical satellite (IRAS) starbursts. A typical value for (pjl/pga) is 10, and (Q.) is =0.5. I Somewhat different theoretical considerations certainly conclude that self-regulation during a starburst restricts the apply to protogalaxies. The specific star-formation rate is porosity toP PO 2-3. similar for protoellipticals and for starbursts. This had led to I can now deduce the self-limiting star-formation rate the suggestion that in extreme starbursts we are seeing during a starburst with P - 1, ellipticals in the process offormation. The measurement ofde Vaucouleurs profiles in light both of starburst and of merging c*c p1.4no.0r3 xcV5c8(mgaSm*)312 galaxies (not inevitably coincident) supports this contention. Mergers are relatively rare today, however, although all The star-formation time scale is t* = M* 0 9Piajs(P*/pgas)1/2, ultraluminous IRAS galaxies show signs of recent or ongoing suggesting that low-mass systems may remain gas-rich until mergers. In the past, however, hierarchical structure- a late epoch. A porosity larger than unity results in a wind if formation models predict a rate that increased sharply with the star-formation rate is larger than this value. However, the increasing redshift. The fragility of disks is interpreted to star-formation rate cannot exceed the available gas supply show that <4% of the disk mass may have been accreted that can be supplied in spherically symmetric free-fall- discontinuously in the past 5 Gyr (12). This suggests that namely, v3/G-as inferred from the collapse rate of an environments of present-day disks and ellipticals are suffi- isothermal sphere, where v is the free-fall velocity. It follows ciently different to have had distinctly different histories of that v S 50 (M*/Mgas)1/2 kmi s1, a condition that is necessary merging activity. for a wind-driven outflow to occur and restricts such a One can construct a reasonably self-consistent description phenomenon to gas-rich dwarf galaxies undergoing a star- that appeals to major mergers ofmassive clouds or protodisks burst. For a wind to actually be generated, one also requires in dense environments as the precursors of ellipticals, with tcool > tdyn, generally satisfied for dwarfs. present-day disks having formed via protodisks undergoing Efficient star formation as required in a starburst results if minor mergers including relatively low-mass clouds charac- t* «< td. The efficiency increases because of the deepening teristic of present-day gas-rich dwarf galaxies. J.S. and potential well. Relative to the dynamical time, one has for R. F. G. Wyse (unpublished data) develop a star-formation fixed gas fraction efficiency argument that can account in this manner for many present-day characteristics of galaxies. t*ctdcx M-0.9p-1/2 In a starburst situation, gas inflows to the central region of the dominant galaxy are greatly enhanced by tidal interac- For hierarchical clustering with Ap/p M-2/(n+3)(1A + z,)-l tions between the nonaxisymmetric distribution of the stellar one obtains for recently virialized potential wells, component in a merger and the gas. A dense central complex of gas rapidly develops. Clearly, the star-formation rate is no M c (1 + Z)-6/(n+3) Downloaded by guest on October 1, 2021 Colloquium Paper: Silk Proc. Natl. Acad. Sci. USA 90 (1993) 4839

and cm-3 K) if Ap l00pb -- 10-5 cm-3 at 5h-1 Mpc or further from the cluster center. (p) (1 + Z)3, Several observations lend support to the idea that disk may be enhanced on scales. These where t*/td a (1 + z )-3/2+554(n+3)X (1 + Z)2 for n -1.4, or include the enhanced correlations for luminous spirals found (1 + Z)1'2 to (1 + Z)3 9 for -1 S n c-2. Hence, star formation is less efficient on small-mass scales by Hamilton (14), the occurrence in distant clusters of and at early epochs in a bottom-up formation model for dark poststarburst galaxies with E + A spectra (15) with enhanced matter potential wells. This is precisely what one needs to vpec relative to the cluster velocity dispersion, and the ap- keep the gas-rich: one must preserve most ofthe gas parent dominance of in pencil-beam surveys to a late epoch, when the largest systems form. (16) and large-scale cell counts (17). For dwarf galaxies, obvious implications include the survival of low-surface Implications brightness gas-poor dEs in cluster environments and the prevalence of gas-rich dwarfs in low-density regions, the The large (10-30%) gas fraction in galaxy clusters directly latter population perhaps being identifiable with the weakly supports the contention that early star formation was ineffi- clustered Lyman alpha forest clouds. cient. It is tempting to infer that most of the gas in clusters Finally, I note that systematic variations are expected from would form disks in less-extreme environments. For disks cluster to cluster in the star-formation history of both disks that undergo starbursts, the limiting star-formation rate is and ellipticals. The resulting MIL variations may affect the strongly affected, at a given scale length, by external pres- interpretation of offsets in the Tully-Fisher and fundamental sure, with M* a pl-4. First infall to clusters and even to plane zero points as being exclusively due to peculiar veloc- superclusters should be sufficient to give an appreciable ities and large-scale flows. modulation of the disk star-formation rate. To quantify this assertion, I note that tidal stirring of disk I am indebted to Max Tegmark for preparing Fig. 1, and to my gas is important provided Vtidal - 10 km s-1, the characteristic collaborators Rosemary Wyse and Boqi Wang for many discussions dispersion of cold interstellar clouds. Infall of a disk to a of related topics. This research has also been supported in part by a supercluster generates a tidal velocity field of order Vtidal - grant from the National Science Foundation. across a disk of half-mass radius rg at distance r (rg/r)vjaajj, 1. Silk, J. & Wyse, R. F. G. (1992) Phys. Rep., in press. from the supercluster center. One can calculate the typical 2. Barnes, J. & Efstathiou, G. (1987) Astrophys. J. 319, 575-600. infall velocity by assuming that the galaxy-cluster correlation 3. Zurek, W., Quinn, P. J. & Solomon, J. K. (1988) Astrophys. J. function 330, 519-534. 4. Barnes, J. & Hernquist, L. (1992) Annu. Rev. Astron. Astro- 4gc = (r/8.8h-1 Mpc)-2f2; r S 20h-1 Mpc phys. 30, 705-742. 5. Bender, A., Burstein, D. & Faber, S. M. (1992) Astrophys. J. describes the enhancement in mass distribution around a 399, 462-477. cluster, in which case a spherical infall model yields 6. Goldreich, P. & Lynden-Bell, D. (1965) Mon. Not. R. Astron. Soc. 130, 125-158. vz:% 1.5 x 104 Q0.6(hrMpf12kmpsc. 7. Toomre, A. (1964) Astrophys. J. 139, 1217-1238. 8. Kennicutt, R. (1989) Astrophys. J. 344, 685-703. Evidently protodisks (rg - 50 kpc) can undergo considerable 9. Silk, J. (1992) Aust. J. Phys. 45, 437-450. tidal stirring out to a radial distance -5h-1 Mpc from the 10. Cioffi, D., McKee, C. & Bertschinger, E. (1989) Astrophys. J. supercluster. The frequency ofdamped Lyman alpha absorp- 334, 252-265. tion line systems toward at high implies an 11. Solomon, P. M., Rivolo, A. R., Barrett, J. & Yahil, S. (1987) effective cross-section that, if interpreted as due to proto- Astrophys. J. 319, 730-761. disks, yields rg - 100 kpc. 12. Toth, G. & Ostriker, J. P. (1992) Astrophys. J. 389, 5-26. can also be significant out to comparable 13. Silk, J. (1993) Astrophys. J., in press. distances. One can trace hot intracluster gas out to 22h-1 14. Hamilton, A. (1988) Astrophys. J. Lett. 331, L59-L62. Mpc via its x-ray emission. one would that 15. Dressler, A. &Gunn, J. F. (1992) Astrophys. J. Suppl. 78, 1-60. Moreover, expect 16. Broadhurst, T., Ellis, R., Koo, D. & Szalay, A. (1990) Nature peculiar velocities vpec - vinfall arise naturally in clumpy, (London) 343, 726-728. anisotropic collapse that is expected in most clustering mod- 17. Efstathiou, G., Kaiser, N., Sanders, W., Lawrence, A., Row- els and seen directly via deep x-ray imaging of clusters. The an-Robinson, M., Ellis, R. & Frank, C. (1990) Mon. Not. R. associated ram pressure on a disk galaxy amounts to Apvec Astron. Soc. 247, 1OP-14P. and can easily exceed the mean interstellar pressure (-3600k 18. Sutherland, R. (1993) Astrophys. J., in press. Downloaded by guest on October 1, 2021