Proc. Natl. Acad. Sci. USAVol. 90, pp. 4840-4847, June 1993Colloquium Paper

This paper was presented at a coUoquium entitled "Physical Cosmology, " organized by a committee chaired by DavidN. Schramm, held March 27 and 28, 1992, at the National Academy of Sciences, Irvine, CA.

Causes and effects of the first quasarsMARTIN J. REESInstitute of Astronomy, Madingley Road, Cambridge CB3 OHA, United Kingdom

ABSTRACT The light we observe from the most distantknown quasars set out when the Universe was about 200 timesdenser than it is now and less than one-tenth of its present age.The existence ofthese objects implies that galaxy formation hadalready, at that early epoch, proceeded to the stage whenmassive (>108MW) objects had accumulated in the centers of atleast some young galaxies. A specific model is presented to showthat the evolution and luminosity function of quasars arecompatible with the cold dark matter cosmogony. Most biggalaxies probably passed through a quasar phase; the remnantblack holes in nearby galaxies may reveal themselves via theflares that occur whenever a star passes too close to them andgets tidally disrupted. The rich absorption spectra of quasarsserve as a probe of the intervening medium. The gas respon-sible for the Lyman alpha absorption lines may be due toprimordial gas gravitationally confined in minihalos of darkmatter-shallow potential weUls whose evolution and relation todwarf galaxies are briefly discussed. The patchy heat input intothe intergalactic medium from early quasars could modulatethe environment in which galaxies form, leading to large-scalespatial correlations in the galaxy distribution. This reviewconcludes with general comments on the prospects for a fullyquantitative understanding of galaxy formation.

Quasars are important for cosmology for two reasons. First,they tell us that, even at high redshifts, galaxy formation hadproceeded far enough to allow such objects to form. Second,they serve as probes for the intervening medium along theline of sight. In this paper, I shall address both of theseaspects; I shall also discuss, more speculatively, the envi-ronmental effects of quasars on galaxy formation and itspossible implications for large-scale structure. Only in thepast few years have quasar samples become available thathave well-defined selection criteria, which reveal the shape ofthe luminosity function and show how it has evolved withcosmic time. And there are now much more extensive data onthe spectra, structure, and time variation of individual qua-sars.The most remarkable feature of the quasar population is

that it declines sharply between z = 2 and the present epoch(z = 0). This has been known for 20 years and was prefiguredeven earlier by the (then-controversial) radio source counts.The extension to still higher redshifts has been more re-cent-5 years ago, no quasars were known with redshiftsexceeding 4, whereas there are now about 40 in this category.There is some evidence that the comoving density declines atz > 3.5, but the steepness (and even the reality) of this trendis still controversial.

I shall touch on several interlinked issues: (i) the implica-tions for galaxy formation theories of the highest-z quasars,which are now being found in increasing numbers; (ii) pos-

The publication costs of this article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertisement"in accordance with 18 U.S.C. §1734 solely to indicate this fact.

sible explanations for the redshift dependence of the comov-ing density of bright quasars; (iii) the massive black holes-remnants ofdead quasars-that may lie in the centers ofmostgalaxies; (iv) the interpretation of quasar absorption lines,especially the possibility that these are due to low-massprotogalaxies or gravitationally bound gas clouds; and (iv)processes whereby quasars may modulate the efficiency ofgalaxy formation and thereby confuse attempts to discoverand interpret large-scale structure in the cosmic mass distri-bution.

The Formation Epoch of the Earliest Quasars

To put the high-redshift objects into a cosmological context,it is useful to recall the relation between time and redshift inthe standard models. For an Einstein-de Sitter model

t(z) = 13.1h-'(1 + z)3/2 yr. [1]

The highest-z known quasars formed when the Universe wasonly -109 years old, and t was as little as 0.07 t(0).The bigger redshifts now being discovered enable us to

probe earlier epochs than could have been done in the earlydays of quasar research. The observed record redshift has,year by year, gone up. But at the same time, the realizationthat galaxies (with their dark halos) are more extended anddiffuse than was previously suspected has lowered theoret-ical estimates of the redshift of galaxy formation. In the1970s, it was widely believed that galaxy formation happenedat earlier epochs than were directly observable. But sincethat time, not only have quasars been detected at largerredshifts but, for compelling reasons, theorists' estimates ofthe redshift of galaxy formation have come down. Currentideas on extended halos, and on the origin of galactic rota-tion, suggest-almost irrespective of the cosmogonic mod-el-that galaxy formation must still have been going on ateras that we can directly observe (corresponding to redshiftsz > 4).At the epoch corresponding to z = 5, the cosmic expansion

time scale (Eq. 1) is long compared with the dynamical timescale within the luminous part ofa typical galaxy. But it is notlong compared to the time scales for extended halos: thefree-fall time from a radius r in a galactic halo like our ownis -109 [r/l00 kiloparsec (kpc); 1 pc = 3.09 x 1016 m] years,and the Universe must be at least twice as old as this beforematerial at radius r can virialize.The angular momentum ofgalaxies is believed to have been

acquired by tidal interactions with their neighbors at theepoch of turnaround. This process can only, however, imparta transverse velocity that is 5-10% of what is needed forrotational support. If the disks acquired their angular mo-mentum from tidal torques, this implies (see, for instance, ref.1) that the material now residing at -10 kpc in a disk must

Abbreviations: CDM, cold dark matter; AGN, active galactic nu-cleus; IGM, intergalactic medium.

4840

Dow

nloa

ded

by g

uest

on

Nov

embe

r 12

, 202

0

Proc. Natl. Acad. Sci. USA 90 (1993) 4841

have fallen in from -100 kpc and then cooled down. Atredshifts of4 or 5, galaxies would not have acquired extendedvirialized halos-indeed, they would not yet have developeddisks.The fact that quasars formed so early in cosmic history is

an important constraint on models for galaxy formation,particularly on "top down" models in which large-scalestructures develop before individual galaxies; for instance,the simple adiabatic (pancake) model dominated by neutrinoscannot, when the amplitude is normalized to fit clusteringdata or the microwave background anisotropies revealed byCOBE (Cosmic Background Explorer satellite), account forcollapsing systems at such high redshifts (2).Much of what I have to say is insensitive to the details of

the cosmogonic model. However, I shall focus my discussionon the incorporation of quasars into the standard cold darkmatter (CDM) model for galaxy formation. This is just one ofa number of alternative models currently in play-it hassuffered several alleged deaths but had as many resurrec-tions, and its implications have been explored in substantialdetail. CDM makes definite predictions about the fluctuationspectrum; it cannot, without some modification or supple-mentation, account for the observed large-scale structure,but it can account for the properties of galactic halos, groups,and clusters.A feature of the CDM model is that structures build up

hierarchically-from small scales to large-but that boundsystems develop rather late; mergers are important even atredshifts of 1 or 2, and large galactic halos would generallyhave assembled rather recently.The earliest quasars would be expected to develop in the

first sufficiently massive and deep potential wells that viri-alize. These would arise from high-amplitude peaks in theinitial dark matter distribution.

Fig. 1 (from ref. 3) shows, as a function of z, the comovingdensity of collapsed halos with various masses. At high z, thenumber of large masses (and deep potential wells) dropsprecipitously, reflecting the shape of the CDM fluctuationspectrum and the extreme rareness of very high-amplitudepeaks in a gaussian distribution.

,-0 8

-281

o02 4 6 8 100.~~~~~~~

z

FIG. 1. Diagram, adapted from Efstathiou and Rees (3), shows asa function of epoch the comoving number-density of virialized halosof different masses that is expected on the basis of a CDM cosmog-ony. The buildup of structure is hierarchical, so the larger-masssystems form more recently, and their density thins out towardhigher redshifts because only exceptionally high peaks of an initiallygaussian distribution would already have collapsed at high redshifts.

The high-amplitude peaks that collapse at z = 5 havemasses 1012MO and develop velocity dispersions V, = 400km s-1. The material most likely to collapse into a quasar is,of course, that which starts off nearest the center. As a roughguess, we suppose that a quasar must involve 109M,, ofbaryonic matter; this would be associated with about 1010M0Dofdark matter [the exact number depending, ofcourse, on theassumed (ib/Q)]. The radius ofthe sphere that would containthe inner 101OME, of dark matter, when the system hasvirialized, would be 5 kpc (the precise value of this radiusdepends on the core radius of the system). What happens tothe -10% of this mass that is in the form of baryons? Unlessit turned immediately into stars, this gas would condensetoward the center until angular momentum became impor-tant. The angular momentum acquired via tidal torques has awide spread from system to system but is in the range A =0.03-0.10 of that needed for rotational support at the turn-around radius. This means that 109M0 of gas can fall to150(A/0.05)2 pc even without getting rid of any angularmomentum. Its self-gravitation becomes important after fall-ing in by a factor between (fQb/fl) and (fib/f)1/3, dependingon whether the dark matter has a density profile resemblinga singular isothermal sphere or has an initial core mass of>1010ME0; thereafter, the gravity of the baryons reacts backon the dark matter.The free-fall time scale from 5 kpc is <108 years. Star

formation could occur during this infall-indeed, this is theway the inner bulge ofa large galaxy might form. Fig. 2 showsschematically some of the processes involved. Production ofheavy elements via high-mass stars can occur during thistime. The branching ratio between star formation and directinfall cannot be predicted.Removal of Angular Momentum. The tidally induced an-

gular momentum of the material that is likely to form thequasar would be enough to provide centrifugal support at adistance -150 pc from the center. The dynamical time scale

TURNS AROUND ATzz.ad AT r5Skpc

tfrefalt S 10 yr

torb ' 3x10 yrOF ANG. MOM.

I /~~~~

REGION S 1 Pc ACROSS-|

= BLACK HOLE

5~11111111 IImv\m/

FIG. 2. Schematic ofwhat happens in the central 1010M0) (109ME,of baryons) within a bound halo of 1011-1012ME0 condensing aroundan exceptionally high-amplitude peak in the initial density distribu-tion (cf. Fig. 1 and legend) that turns around at z t 5. The outcomewould be a stellar bulge surrounding a massive black hole. Thefraction of the mass going into the hole depends on the rapidity withwhich angular momentum can be lost, on the efficiency of starformation, and on feedback effects from high-mass stars. Note thatheavy elements can be synthesized within the period over which theblack hole grows.

Colloquium Paper: Rees

Dow

nloa

ded

by g

uest

on

Nov

embe

r 12

, 202

0

Proc. Natl. Acad. Sci. USA 90 (1993)

at this radius is -3 x 106 years. The next question is thereforehow quickly this material-unprocessed gas, together withmaterial that has been processed through stars-can shed itsangular momentum and accumulate in the center. Specifi-cally, it is important to know whether this gas can lose itsangular momentum in <100 orbital periods (i.e., 3 x 108years). If it cannot, then it will not trigger a quasar as earlyas the epoch z = 5.One certainly cannot give a rigorous answer to this ques-

tion. However, it may be worth listing the types of viscositythat are expected to operate.

Gravitational Instabilities. Provided that star formationdoes not irreversibly consume too much material during theinfall from 5 kpc (see Fig. 2), the gas would be self-gravitatingby a large margin by the time it collapsed into a rotationallysupported configuration. The nonaxisymmetric instabilitiesto which it would then be vulnerable would redistributeangular momentum on a time scale of only a few torb, asdescribed, for instance, by Hemquist (4) or Navarro andWhite (5). This is likely to be the most effective process forremoving angular momentum.

Gaseous Viscosity. The usual types of viscosity that operatein accretion disks, characterized by an a-parameter, wouldoperate in this context too. The stars themselves wouldcreate extra modes of viscosity. Supernovae would stir up theremaining gas so that it would have high-bulk random mo-tions [cf. Charlton and Salpeter (6)]. The viscous diffusiontime is torb a-1(h/r)2, where h is the disk thickness. Clearlyif a s 1, these viscous processes (which do not require thedisk to be self-gravitating) can operate on a time scale <lOOtorb only if(h/r) - 0.1. A fraction of the gas, however, maybe maintained in a hot corona with (h/r) = 1 (by analogy withthe gaseous halo of our own Galaxy). The coronal materialcould spiral in very quickly-in only -1 orbit if a - 1.Therefore, if dissipation can maintain even 1% of the mass ina hot corona (and assuming that coronal material is replacedfrom the disk as fast as it drains away inward) the entireangular momentum could be lost within 3 x 108 years.The efficiency of angular-momentum transfer is hard to

quantify in all astronomical contexts. However, the onlyoption that would preclude the accumulation of a centralmass concentration would be the efficient conversion ofinfalling gas (see Fig. 2) into stars that are all of such low massthat they neither expel nor recycle any of their material within3 x 108 years. This possibility aside, there is no impedimentto the accumulation of 108-109 solar masses of baryons(already enriched with heavy elements) in a central regionless than a few parsecs in size within a few times 108 years ofthe initial collapse-indeed, such an occurrence seems al-most inescapable, because in a self-gravitating system sim-ulations suggest that it takes only a few dynamical time scalesto transport angular momentum outward.Even in the CDM cosmogony, self-gravitating aggregates

containing at least 109M,, of baryons can form by z = 5, whenthe age of the universe (from Eq. 1) is only 109 years. Theformation of such systems could be even earlier in othercosmogonies-indeed, even if the dark matter is CDM, thereis the possibility of a nongaussian distribution of fluctuationamplitudes, triggered by textures, strings, fluctuations in thebaryon/photon ratio, etc.There are therefore many models in which gravitational

potential wells of sufficient mass to create a quasar and ofsufficient depth to retain baryons efficiently would haveformed by z = 5. The main uncertainty is whether gas startingoff at a distance of a few hundred parsecs from the center canlose angular momentum fast enough. The associated timescales shrink further as the baryons undergo further dissipa-tion. Provided that the material does not take longer than-108 years to shrink from (say) 200 to 100 pc, there seems no

impediment to the accumulation of 108-109Mo of baryons ina central region less than a few parsecs in size.How Long Does It Take a Black Hole to Grow? One has still

to ask whether it is sufficient that the baryons have concen-trated themselves within a few parsecs. A quasar cannotswitch on until this material has condensed into a relativistic(probably fully collapsed) object. Maybe there is a muchlonger time lag before a black hole or relativistic object canform.

In other astronomical contexts where accretion occurs,radiation pressure exerts a negative feedback, which limitsM Ifthe radiative efficiency e were 10% the growth time scaleM/Mcould not be shorter than about 4 x 107 years. (This timewould be even longer if there were other opacity apart fromelectron scattering.) But because a black hole does not havea hard surface, the efficiency is less well defined than it iswhen (for instance) matter accretes onto a neutron star, and1020 ergs has to be disposed offor each gram that lands on thestellar surface. For black hole accretion, e is a function ofMas well as of other parameters (angular momentum, radiativeefficiency, etc.).

In the case of spherically symmetric accretion, one canshow explicitly how, if Mis high, radiation emitted near thehole will be trapped and itself swallowed (see? for instance,ref. 7). The trapping radius moves out as M increases; Eautomatically drops as M increases, so that the hole canaccept an arbitrarily large amount of mass without theemergent luminosity exceeding LEd (Eddington luminosity).(An extreme instance is the collapse of a supermassive starwhen it becomes subject to the well-known postNewtonianinstability. It collapses almost in free-fall. The radiationwithin it, which supplies almost all the internal pressure, iscarried down the hole, because its outward diffusion relativeto the flow is negligibly slow compared to the speed withwhich the bulk flow advects the radiation inward.)

It is not so clear what happens when there is angularmomentum. There are explicit solutions for thick disks, withnarrow funnels along the axis, in which the binding energy ofthe orbit from which material is swallowed tends to zero,again allowing E to become very small, and M to be verylarge, without the luminosity much exceeding LEd. It is,admittedly, possible that the excess mass inflow can bestemmed and the efficiency-the amount of radiation escap-ing per unit mass swallowed-cannot become very low.However, this argument should at least suffice to show thatthere is no obvious limit on the rate at which a black hole cangrow; there are certainly specific models where there is nolimit other than the rate at which material falls toward it.An optimum model requires low efficiency in the early

stages of the hole's growth-otherwise, it would take longerthan the (then) Hubble time for a hole that started off withonly a stellar mass to grow by the requisite 20-odd powers ofe. On the other hand, E must be high during the quasar phaseitself-otherwise, the active lifetime will be <<4 x 107 years(cf. ref. 8). The number of quasar generations would thenneed to be correspondingly larger, and the mean remnantmass per galaxy would become too high to be consistent withthe recent evidence on black holes in galactic nuclei (even ifthese are interpreted as upper limits).A natural assumption is thatM should be roughly constant,

at least until infall and star formation are nearly complete.When the hole mass is still small, it can accept the inflowingmaterial because E adjusts to a sufficiently low value; butwhen M has grown to 108M,D, the efficiency would increase,and the quasar phase would begin. At some stage, moreover,Mwill decrease because the infall stops or because the gasgets used up by star formation (although it may be reactivatedby, for instance, a merger).

Cosmological N-body simulations show that large halos atthe present epoch have a variety of histories-some would

4842 Colloquium Paper: Rees

Dow

nloa

ded

by g

uest

on

Nov

embe

r 12

, 202

0

Proc. Natl. Acad. Sci. USA 90 (1993) 4843

have nucleated around a single peak; others may result froma relatively recent merger of systems that coagulated aroundseparate high peaks in the initial density distribution (see ref.9 and references cited therein). But in general they form fromthe inside outward; the inner 1010M,D may virialize at z - 8even though the halo is not fully assembled until z S 2. Thebaryons most likely to aggregate into a central compactobject are precisely those associated with this inner material:it is by no means improbable that a large fraction of thesebaryons (109M®D) would participate in the central activity.Thus, the quasar could switch on before the halo wasassembled. The host systems would by now have accumu-lated '1012M®D halos. The most promising nearby sites fordead quasars are therefore the centers of very big galaxies(see Dead Remnants in Nearby Galaxies), but this does notmean that the onset of quasar activity had to await theassembly of the entire halo.

Luminosity Function of Active Galactic Nuclei (AGNs) andIts Evolution

The luminosity function of AGNs seems to have a break orbend that occurs at a higher L at high z (10, 11). There arecompelling reasons for believing that the lifetime of anindividual source (at least for those with high L) is <<109years. The luminosity function must therefore involve anintegral over the life cycle of each source, as well as being afunction of other parameters, such as orientation relative toour line of sight. It is therefore surprising that any reasonablysharp feature survives in the integrated luminosity function.How might we account for this?For black hole processes, the key parameter is L/LEd.

(This ratio obviously controls the importance of radiationpressure relative to gravity. It also controls another keyparameter-the ratio of the cooling and inflow time scale-which may determine the efficiency and the ratio of thermaland nonthermal radiation, etc.) It is therefore natural toidentify the break in the luminosity function with a specificvalue of L/LEd-But if this is so, we must conclude that higher-z quasars

typically involve bigger black holes. This would be impos-sible if the z-dependence resulted from the evolution of asingle generation of objects, which live >109 years. But itwould be possible if there were many generations of short-lived AGNs, whose luminosity peaked soon after a black holeformed, and if conditions were more propitious for formingreally big holes at high z.At first sight, one might think that a hierarchical cosmog-

ony, where the potential wells get progressively deeper andmore massive, would predict even bigger black holes, andhence even more powerful AGNs, at recent epochs, contraryto what is observed. But the fraction of the mass going intoa black hole may depend notjust on the depth of the potentialwell, but also on the density. The latter is expected to be aparameter because, for a potential well of given depth, theretention of gas will be more efficient at high densities, sincedissipative processes are then more efficient; also the angularmomentum of a system of given mass would be less if itcollapsed at higher density. As an illustrative example, let ussuppose that the hole mass is related to that of the virializedhalo around it by a formula of the form

MHole x MHalo(l + z) exp - ( [2]

In this formula, z is the collapse redshift of a halo with velocitydispersion Vc. This is related to mass by Vc c (1 + z)1/2Ml/3(cf. Fig. 1). The first term in relation 2 incorporates the densitydependence, the characteristic density scaling as (1 + Z)3; the

second term describes how the retention is more efficient indeeper potential wells. The standardCDM model predicts howmany halos of mass MHa1o collapse at redshift z.Combining this with relation 2, one derives the number of

black holes of mass MHole that form at each cosmic epoch.Fig. 3 shows, for a particular choice of parameters, how thiscan reproduce a rise and a fall in the black hole formationrate. Moreover, the rate peaks at an earlier epoch for the mostmassive holes.

If each newly formed black hole were to radiate at aroundits Eddington limit for a few times 107 years (the naturalgrowth time scale for high efficiency) and then fade, thenumber of quasars, as well as their luminosity function,would be roughly reproduced (see Fig. 3 for an illustrativeexample). It is not realistic to push this model too far, becausethe luminosity function is influenced by several furtherfactors-certainly by beaming effects and perhaps also (at thebright end) by gravitational lensing.The brightest quasars would be associated with -3r peaks

collapsing at redshifts z = 3-4 to form halos with V, 400km-s (cf. Fig. 1). At higher redshifts, no sufficiently largemasses (with deep potential wells) would have formed;systems turning around later would have lower densities, andthis would militate against black hole accumulation if there isindeed a strong dependence on density in relation 2. Specificmodels of this kind are explored and discussed more fully byHaehnelt and Rees (13).

Dead Remnants in Nearby Galaxies

One very important development in the past few years hasbeen the strengthening evidence for massive black holes innearby galaxies [see Kormendy (14) for a review, and as-sessment of this evidence]. Indeed, the evidence is consistentwith the view that all large galaxies have central dark mass

1o4

10-r-7

r-

0)

0cl

0-.2

0

-

E0

10-

10

1o-I

o-1

lo-,0 2 4 6 8

FIG. 3. Diagram, from ref. 12, shows as a function of z the ratesat which black holes of various masses might form. Calculation isdone for a specific CDM model, with biasing factor b = 2.5. Fractionof virialized mass that goes into the hole is assumed to be governedby Eq. 2; the particular parameters chosen are a = 5.5, V* = 400km s-1, and,8 = 2. Note that the production rate of the most massiveholes peaks at z = 3, even though halos build up to larger masses atlower redshifts. The actual masses depend, of course, on a particularchoice of the constant of proportionality in Eq. 2. If it is supposedthat each forming black hole radiates at its Eddington luminosity fora few times 107 years (while the processes depicted in Fig. 2 are goingon), the quasar luminosity function, and its dependence on z, can bebroadly reproduced.

5

6.

~~~ ~~~~~~.................... ...

. / . .. I~~~~~ogM "- 8,.0lo -----.-.. logM = 8.5

,ogM = 9.0...... IogM = 9.5

12 ...,

C . I I I l wlw

Colloquium Paper: Rees

I0-

Dow

nloa

ded

by g

uest

on

Nov

embe

r 12

, 202

0

Proc. Natl. Acad. Sci. USA 90 (1993)

concentrations. Moreover, the mass of the hole seems toscale with that of the stellar bulge (15)-a natural conse-quence of the picture outlined above.Such holes could reveal their presence by the flares that

occur whenever stars pass sufficiently close to the centralhole that they get disrupted (16, 17). The flare is energized byaccretion onto the hole of some of the debris from thedisrupted star; the remainder of the debris is ejected. Theaccretion process is very complicated-it is unsteady, theorbits are highly elliptical, and relativistic effects are impor-tant. Moreover, because the orbital angular momentum ofthedisrupted star will generally be misaligned with the hole'sspin, Lense-Thirring precession would destroy axisymmetryeven if the debris had acquired circular orbits as a result ofviscous effects.Because of these difficulties, the time scale for the flare is

uncertain; so also is its spectrum, and the consequent bolo-metric correction. Further work on this problem is certainlyneeded. All that can be said at the moment is that, for acharacteristic time scale of a few months, the bolometricluminosity could approach the Eddington luminosity corre-sponding to the hole's mass-much brighter, therefore, thana supernova. The time dependence is uncertain, but there isno reason why it should mimic the light curve ofa supernova.Any such event should therefore be recognizable and de-tected by supernova searches, especially those using non-photographic techniques that do not discriminate againstevents in the high-surface-brightness central parts of galax-ies.The event rate in a galaxy harboring a 108M®D hole depends,

of course, on the properties of the compact system surround-ing it; typical estimates are that there should be one disrup-tion every 103-104 years. Supernova searches with an expo-sure of several thousand galaxy years have not yet found anyevent of this kind. The flare spectrum may extend into thex-ray band; if so, interesting evidence may come from theROSAT survey (18). The significance of any observations orupper limits cannot be fully quantified until the bolometriccorrection is better known. But monitoring programs andsurveys should either soon reveal instances of this phenom-enon or else start to put significant limits on central blackholes and/or the stellar distributions around them.

Quasars as Probes: Lyman a Clouds and Low-Mass Halos

Quasars are tracers of the highest-amplitude fluctuations-the deepest potential wells and the earliest-forming boundsystems of galactic scale. Smaller-amplitude perturbations,collapsing later to form halos of lowerM and much shallower(lower Vc) potential wells, are relevant to the lower-massgalaxies. Indeed, quasar spectra may offer the best probe ofhow these small systems evolve, because the gas gravita-tionally confined within them may be responsible for theLyman a forest (19-22).

Minihalos with Vc in the range 20-50 km s-1 have thefeature that photoionized gas can be stably confined withinthem. An absorption line would result whenever a minihalointercepted the line of sight from a quasar. The columndensity depends on the impact parameter, and an attractivefeature of this model is that the very simplest assumption-that the gas has an isothermal distribution with total densitya: r-2 (and therefore neutral density a r-4) predicts a number-versus-column density relation going as N 5/3 (see ref. 20),comparable to what is observed. In reality, the minihaloswould have a range of VY; even if the halo were an exactisothermal sphere, the gas temperature would differ from thevirial temperature, and the density profile would obey apower law with a different slope. Moreover, the assumptionsof spherical symmetry and stationary virial equilibrium havelimited validity.

The only part of such a system that is virialized will be thepart that has an overdensity of more than 200; a simplespherical infall model yields a radius of

12.2h-1 ( VCk )( +z -3/23) kpc [3]

for this part. Outside this region, the overdensity would dropgradually toward unity-moreover, the lines of column den-sity below 1015 cm-2 would all come from these outer parts.A proper interpretation of the (much more numerous) sys-tems with lower column density therefore requires us toconsider the nonequilibrium dynamics of the outer regions,on scales of 10-50 kpc. The spherical assumption, likely to bea good one for the virialized region, will be inadequate atlarger radii-indeed, simulations suggest that the protostruc-tures are likely to be sheetlike, so a one-dimensional modelof infall toward a plane may be no worse than an assumptionof spherical symmetry. The line profiles here would beaffected by bulk Doppler broadening. A further complicationis that the gas temperature depends on the prior history oftheintergalactic medium; this is because at these low densitiesthe thermal equilibration time scale is slower than the dy-namical time scale.The high-column-density lines come from gas in the viri-

alized inner parts of the minihalos, where the density issufficiently high to guarantee thermal equilibrium at thetemperature for which heating from photoionization balancescooling. The more rarefied outer parts, however, need not bein thermal equilibrium. At the time of turnaround, the tem-perature could be quite low owing to adiabatic coolingbetween the original epoch of photoionization and the epochof turnaround. Moreover, adiabatic heating may dominateradiative cooling during much of the infall. Radiative coolingvia recombinations (and via collisional excitation of lines) issuppressed as compared with a gas at the same temperaturethat is ionized only by collisions; as a result, the cooling maynot be competitive with adiabatic heating until the overden-sity exceeds 100, even if the UV background is very intense(Fig. 4). The infall may therefore be almost adiabatic until theoverdensity becomes >100. This implies that, even in po-tential wells with V, as large as 100 km s-1, the gas mayexperience a quasi-static pressure-supported phase with T>105 K. Such systems may contribute lines that are broad buthave a low column density.

Proper modeling of the Lyman forest must await numericalsimulations, incorporating gas dynamics and cooling, withenough resolution and dynamic range to handle these small-scale systems. A preliminary discussion is given by Miralda-Escude and Rees (22). The aim should be to account for thenumber-versus-column density relation for the clouds as wellas any correlation between line width and column density.Something else that must be explained is the way the

density of the Lyman absorption lines depends on redshift.Such an explanation should eventually emerge as a by-product of a general theory for the emergence and buildup ofstructure. However, one can already envisage several effectsthat would cause a z dependence of the cloud population.

(i) First, there will be a z dependence in the number ofpotential wells whose depth lies in the range that allows stableconfinement. Minihalos form whenever a low-mass systemturns around and virializes, but they are eliminated whenthey merge to form larger halos with deeper potential wells.The relevant masses are in the part of the fluctuation spec-trum where, for standard CDM, dlog[P(k)]/dlogk is close to-3. For this slope, the rms amplitude depends only logarith-mically on M, so objects with a wide range ofmasses collapsealmost simultaneously. Numerical simulations do not yethave enough dynamic range to yield reliable numbers. How-

4844 Colloquium Paper: Rees

Dow

nloa

ded

by g

uest

on

Nov

embe

r 12

, 202

0

Proc. Natl. Acad. Sci. USA 90 (1993) 4845

106

104

tcool >tHubb> e

NOTPHOTOIONIZED .*

-~~~~~~~~~~~~4105 - .* I ZtcnoI tHubble<

-~~~~~ a

I 1_

____-__l,_ PHOTOIONIZED

I I1 10 laD0

FIG. 4. Diagram shows the regions in the temperature-density plane where primordial gas in a bound system cools in less than the Hubbletime (cf. ref. 23). Curves correspond to the epoch z = 5 in a cosmological model with fib = 0.1 and fQ = 1. Solid line delineates this region onthe standard assumption that the ionization state of the gas is determined just by collisions; dashed line (delineating a much reduced domainwithin which cooling is faster than tHubble) corresponds to the case when the gas is completely ionized by an intense UV background. Cloudsthat collapse when the gas is already photoionized would be heated adiabatically and would undergo a quasi-static phase unless they were ina deep enough potential well to allow adiabatic heating to several times 105 K. (Dotted lines show trajectory for different choices of turnaroundtemperature.)

ever, White and Frenk (figure 1 in ref. 24) present curves forthe comoving density of shallow potential wells (down to V;= 50 km-s-1), which indicate that the minihalos should bethinning out, owing to mergers into larger systems with biggerV, at redshifts < 3. The exact dependence is a function of theuncertain amplitude of the CDM spectrum, related to thebiasing factor, but analytic models suggest that the depen-dence might be as steep as (1 + Z)2.5 (see ref. 25).Two other interesting effects are both consequences of the

change with redshift in the intensity and spectrum of the UVbackground.

(ii) For a cloud in ionization equilibrium with externalbackground radiation, the column density for a given impactparameter is proportional to J-1. This then translates into aline density above a given column density depending onJ-(0-1), where 8 is the power-law index of the column densitydistribution. For z - 2, we expect J to change rather slowlywith redshift, since the abundance of quasars does not seemto increase at z > 2, and the attenuation produced by Lymanlimit systems increases with redshift (26, 27). At z < 2,however, the quasar population thins out sharply; therefore,even though the attenuation is small, J is expected to dropsteeply with cosmic time. This can increase the number ofabsorption lines at z < 1 (see refs. 28 and 29), as is indicatedby recent Hubble space telescope observations.

(iii) Another consequence of J decreasing toward thepresent epoch is that the UV background may no longer beable to keep some of the clouds completely ionized. When theHI column density through the center (proportional to J-1)exceeds a few times 1017 cm-2, self-shielding becomes sig-nificant; the neutral fraction then rises, and a Stromgrensurface forms and starts to propagate outward. Pressuresupport is then lost, and a burst of star formation would betriggered. The outcome is then unclear, but it seems that thegas in the halo should either turn into stars or be expelled by

supernova explosions or stellar winds. This reduces thenumber of lines.

Possibility iii, that gravitationally bound clouds may re-main gaseous and quiescent for a long interval (e.g., from z= 5 to z < 1), manifesting themselves only as Lymanabsorbers, may have an interesting bearing on dwarf galaxies(cf. ref. 30). The resultant starbursts at relatively low red-shifts (z < 1) could give rise to a population of faint bluegalaxies, which quickly fade (perhaps expelling whatevermass remains gaseous) after the starburst phase is over.

Environmental Impact of Quasars: Implications for GalaxyFormation and Large-Scale Structure

The question of what heats up the intergalactic medium, andwhen it becomes (re)ionized, has been widely discussed. InCDM models (indeed, in most hierarchical models), the veryfirst bound systems would have formed by redshifts 10-20.Their masses would only be 105MO (see ref. 31), and if theseturn into high-mass stars they may be the earliest UVsources. These first-generation objects may generate enoughUV to raise the intergalactic medium (IGM) from the tem-perature S100 K to which it would have cooled by pos-trecombination adiabatic expansion onto a higher (-104 K)adiabat, and thereby boost the baryonic Jeans mass to108M®; such objects are therefore important for the cosmog-onic sequence.The IGM is certainly highly ionized at the epochs probed

by high-z quasar observations. If this results from photoion-izations, a strong UV background is required. This back-ground cannot be a relic of sources at z > 10-quasarobservations tell us that, along a typical line of sight, there areenough absorbers opaque to the Lyman continuum to havesoaked up any such photons. There has been debate about theUV contribution from quasars themselves. As more z > 4quasars are discovered, it becomes less problematic to main-

s - w

%.%~% I V%gwwww. -ole_.- I -..w iI 't.,or 0

4r1. - II r

-. w

. or &=::0

Colloquium Paper: Rees

-

IIIIIIIIIIIIIII-10.

Dow

nloa

ded

by g

uest

on

Nov

embe

r 12

, 202

0

Proc. Natl. Acad. Sci. USA 90 (1993)

tain the view that UV from quasars is the primary ionizationagent for the IGM and accounts for the smallness of theGunn-Peterson effect. [However, there is still no particularreason why quasars should be more important than brightstellar populations in young low-mass galaxies as sources ofthe overall UV background (26).]One potentially important difference between quasars and

young galaxies as UV sources is that the former, beingindividually so much more luminous, would be more sparselydistributed, so that the ionization would occur inhomoge-neously. Moreover, unless all quasars had identical UVspectra, the IGM, after it had all been ionized, would have atemperature that might depend on the hardness of the spec-trum of the quasar that happened to ionize it. Patchy ornonsimultaneous ionization by the first quasars, separated by-50 Mpc, could create a large-scale environmental inhomo-geneity (of nongravitational origin) that modulates the effi-ciency of galaxy formation. This could be relevant to thesurprisingly prominent large-scale features observed in thedistribution of galaxies if, for some reason, propinquity to aquasar affected the way galaxies formed (23, 32-34).There may be a spread in the times at which the IGM was

first ionized and in the temperature (which, being determinedby the mean energy per photoelectron, depends on thehardness of the quasar UV spectrum, and especially onwhether He is doubly ionized). The spatial variations in theIGM temperature may amount to a factor of 2. The low-masspotential wells, which are relevant to small galaxies (and tothe gas clouds discussed above) are shallow, so the infall ofgas into them is resisted by pressure. It would make adifference if the gas had a temperature of (say) 20,000 ratherthan 40,000 K. This would then change the efficiency ofcooling and star formation during the early stages of hierar-chical galaxy formation. Furthermore, the cooling efficiencyof gas in the temperature range 104-105 K depends on its stateof ionization. If photoionization is complete, the recombina-tion and line cooling, which contribute the peaks in thecooling curve in this temperature range, are suppressedand/or compensated by the heat input from photoionization(23). This makes a big difference to the formation of smallgalaxies. If not already photoionized, gas falls isothermallywith T = 104 K into potential wells with V1 > 20. However,if it is already photoionized the cooling efficiency is so muchreduced that the gas will be heated adiabatically as it iscompressed during the infall and may not enter the tcool < tdyndomain unless and until it reaches 3 x 105 K (see Fig. 4 andlegend).There are, in principle, other ways in which quasars could

have a long-range influence (32, 34). And there are othernongravitational effects with a possible large-scale spatialdependence (e.g., primordial magnetic fields), which are lessquantifiable, although they cannot be ruled out. The potentialimportance of any such effect is that it could lead to large-scale correlations or structures in the distribution of galaxies(or of Lyman clouds), which are not directly induced bygravitational perturbations on the corresponding scales.One further (rather pessimistic) remark before leaving this

topic. Any process that modulates the efficiency with whichgas settles into a given potential well, or which affects theinitial mass function of the stars that the gas turns into, wouldbe likely to affect the zero point on the standard distancecalibrators. It would therefore produce systematic errors,correlated over large spatial domains, in the distance esti-mates. Any process that modulates galaxy formation on alarge spatial scale will therefore affect the properties ofgalaxies in such a way that the application of standardtechniques would lead to the erroneous impression of large-scale streaming motions. This is very bad news indeed,because such motions (if real) potentially offer a direct probeof the gravitational field (and hence the overall dark matter

distribution) on large scales. This possibility highlights theimportance of trying to use several independent distanceindicators in this type of work in the hope that these envi-ronmental effects would not be so perverse as to modulate allthe different indicators in the same way.

Concluding Homily

Cosmology is a subject that straddles the boundary betweenfundamental physics and what might be called environmentalscience. It consequently confronts us with two contrastingstyles of problems.Some aspects ofcosmology resemble particle physics-we

can aspire to a model with only a few parameters, which canbe accurately compared with the data. Indeed, there areessentially just four basic cosmic numbers: the overall den-sity (or curvature) parameter; the baryonic density parameter(or, almost equivalently, the present photon/baryon ratio);the Harrison-Zeldovich fluctuation amplitude 4 (ifindeed theinitial fluctuations have this natural scale-independent form);and the cosmological constant A (if this is not zero). Inaddition, cosmic evolution obviously depends on the funda-mental constants of microphysics, and especially on the largenumbers that relate these to the gravitational constant G. Itis a measure of the progress already made that there is a realhope of deducing these cosmic numbers from fundamentalphysics. Moreover, these numbers, supplemented by knowl-edge of what the dark matter is (which may itself soon comefrom basic physics), determine (in principle) the main fea-tures of our present universe-the clustering, the epoch ofgalaxy formation, the large-scale structure, the light ele-ments, etc.Some cosmological observations are what I would term

type 1: these relate rather directly, and even unambiguously,to the basic cosmic numbers. One good example is the Heabundance predicted by standard big bang nucleosynthesis.Another is the microwave background anisotropy on largeangular scales, which is a direct measure of 4. A furtherexample (though admittedly a less clean one) is gravitationalclustering of nondissipative dark matter, which can be com-puted via numerical simulations.But other cosmological data (type 2 data) are harder to

interpret. Only via a long and uncertain chain ofargument canthese latter types of observation be related to some funda-mental aspect of physics or the early universe. Unfortu-nately, most of the things astronomers can tell us aboutgalaxies-how bright they are, how they are clustered, etc.-are of this second type. The efficiency with which baryonscondense into a potential well, the processes of star forma-tion, the feedbacks from early generations of stars, and theform of the resultant galaxy are clearly crucial determinantsof the final morphology and luminosity. Most astronomicalmeasurements tell us about the outcome of such immenselycomplex and messy processes, which we shall never be ableto simulate or model adequately.When we do not have an adequate detailed model, it makes

good sense to start off by parametrizing our ignorance into afew numbers-the star formation efficiency, the biasingparameter, etc. These parameters will have to be fittedempirically for the foreseeable future, and we could justifi-ably feel we were making progress if we had a set ofparameters that could, for instance, fit the present luminosityfunction of galaxies and what we now know about its evo-lution with redshift. But there is no reason to expect thatthese processes will be described by neat mathematics. Thiscontrasts with, for instance, the spectrum of the linearfluctuations, where there are plausible reasons for gaussianfluctuations obeying a scale-free Harrison-Zeldovich law,whose only free parameter is then the amplitude 4. Theradiative and magnetogas dynamical processes involved in

4846 Colloquium Paper: Rees

Dow

nloa

ded

by g

uest

on

Nov

embe

r 12

, 202

0

Proc. Natl. Acad. Sci. USA 90 (1993) 4847

the formation of a single star are too complicated to bereliably simulated, even when the starting conditions (e.g.,those prevailing now in the Orion Nebula) are known. Theformation of an ensemble of stars in the poorly understoodprotogalactic environment (including all the effects of feed-back from the first generation onto later ones) is morecomplicated still. When we approximate the stellar initialmass function, or the galactic luminosity function, by a powerlaw or other simple expression, this is done for mathematicalconvenience-nobody really believes that any simple for-mula will give a precise description here, any more than theyexpect it in meteorology or geophysics.One concept that has featured prominently at this meeting

is the biasing of luminous galaxies relative to the dark matter.The first guess is that this can be described by a singleparameter b. But why should we expect the complicatedprocesses that determine what sort of galaxy forms in a givendark matter halo-involving dissipative gas dynamics, starformation, and the feedback from stars and the intergalacticenvironment-to be describable by a single number indepen-dent of scale? (Indeed, as was suggested in the previoussection, the present distribution of galaxies may have beenpartly molded by environmental and historical factors that donot simply depend on the dark matter density or the gravi-tational field.) When a single b factor does not yield a goodfit, the realistic next step may be to accept that the physicsof biasing may be more complicated, rather than to immedi-ately transfer alliegance to a different model for the darkmatter distribution.A good theory ofgalaxy formation will never be as "clean"

as the theories to which particle physicists aspire. In somerespects, it will more closely resemble a good theory ingeophysics-plate tectonics, for instance. This is a unifyingidea that gives insight into previously unrelated facts, but itis no disparagement of plate tectonics that it cannot predictthe shape of the continents.There are, fortunately, several empirical cosmological

tests that are of type 1. These include probes of the darkmatter distribution via dynamical effects and gravitationallensing, evidence on the fluctuations at high z (when they arestill in the linear regime) from the microwave background,and the light element nucleosynthesis. But we should nothave unrealistic expectations about the neatness and sim-plicity of theories that can adequately explain galaxies andtheir distribution-many key aspects of the low-z Universeare irretrievably of type 2.

I am grateful to Jordi Miralda-Escude and Martin Haehnelt fordiscussion and collaboration on topics included in this paper. Iacknowledge support from the Royal Society and also thank Prof.John Bahcall for hospitality during a visit to the Institute forAdvanced Study (Princeton, NJ), where this paper was prepared.

1. Fall, S. M. & Efstathiou, G. P. (1980) Mon. Not. R. Astron.Soc. 193, 189-206.

2. Blanchard, A., Buchert, T. & Klaffl, R. (1993) Astron. Astro-phys. 267, 1-10.

3. Efstathiou, G. P. & Rees, M. J. (1988) Mon. Not. R. Astron.Soc. 230, 5P-9P.

4. Hernquist, L. (1989) Nature (London) 340, 687-692.5. Navarro, J. & White, S. D. M. (1992) Mon. Not. R. Astron.

Soc., submitted.6. Charlton, J. C. & Salpeter, E. E. (1989) Astrophys. J. 346,

101-107.7. Begelman, M. C. (1978) Mon. Not. R. Astron. Soc. 184, 53-68.8. Turner, E. (1990) Astron. J. 101, 5-17.9. Kaufmann, G. & White, S. D. M. (1992) Mon. Not. R. Astron.

Soc., submitted.10. Boyle, B. J., Fong, R., Shanks, T. & Peterson, B. (1990) Mon.

Not. R. Astron. Soc. 243, 1-56.11. Hewett, P. C., Foltz, C. B. & Chaffee, F. H. (1993) Astrophys.

J. Lett. 406, L43-L46.12. Haehnelt, M. (1992) in First Light in the Universe: Stars or

Quasars, ed. Rocca-Velmerange, B. (Edition Frontieres, Par-is), in press.

13. Haehnelt, M. & Rees, M. J. (1992) Mon. Not. R. Astron. Soc.,in press.

14. Kormendy, J. (1992) in Testing the AGN Paradigm, eds. Holt,S., Neff, S. & Urry, M. (AIP, New York), pp. 23-34.

15. Dressler, A. & Richstone, D. 0. (1988) Astrophys. J. 324,701-713.

16. Rees, M. J. (1988) Nature (London) 333, 523-528.17. Rees, M. J. (1990) Science 247, 817-823.18. Sambay, S. & West, R. G. (1992) Mon. Not. R. Astron. Soc.,

in press.19. Rees, M. J. (1986) Mon. Not. R. Astron. Soc. 218, 25P-28P.20. Rees, M. J. (1988) in QSO Absorption Lines, eds. Blades, J. C.,

Turnshek, D. & Norman, C. (Cambridge Univ. Press, Cam-bridge, U.K.), pp. 107-123.

21. Ikeuchi, S. (1986) Astrophys. Space Sci. 118, 509-515.22. Miralda-Escude, J. & Rees, M. J. (1993) Mon. Not. R. Astron.

Soc. 260, 617-624.23. Efstathiou, G. (1992) Mon. Not. R. Astron. Soc. 256, 43P-47P.24. White, S. D. M. & Frenk, C. S. (1991) Astrophys. J. 379,

52-79.25. Mo, H. Y., Miralda-Escude, J. & Rees, M. J. (1993) Mon. Not.

R. Astron. Soc., in press.26. Bechtold, J., Weymann, R. J., Lin, Z. & Malkan, M. A. (1987)

Astrophys. J. 315, 180-197.27. Miralda-Escude, J. & Ostriker, J. P. (1990) Astrophys. J. 350,

1-22.28. Ikeuchi, S. & Turner, E. (1991) Astrophys. J. Lett. 381, L.1-L4.29. Miralda-Escude, J. & Ostriker, J. P. (1992) Astrophys. J. 392,

15-22.30. Babul, A. & Rees, M. J. (1992) Mon. Not. R. Astron. Soc. 255,

346-350.31. Couchman, H. M. P. & Rees, M. J. (1986) Mon. Not. R.

Astron. Soc. 221, 53-63.32. Dekel, A. & Rees, M. J. (1987) Nature (London) 326, 455-462.33. Babul, A. & White, S. D. M. (1991) Mon. Not. R. Astron. Soc.

253, 31P-36P.34. Rees, M. J. (1987) in Large Scale Structure of the Universe,

eds. Audouze, J., Pelleton, M.-C. & Szalay, A. (Reidel, Dor-drecht, The Netherlands), p. 437.

Colloquium Paper: Rees

Dow

nloa

ded

by g

uest

on

Nov

embe

r 12

, 202

0