Proc. Natl. Acad. Sci. USA Vol. 90, pp. 4835-4839, June 1993 Colloquium Paper This paper was presented at a colloquium entitled "Physical Cosmology," 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 galaxy formation JOSEPH SILK Departments of Astronomy 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 star 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 star formation, and success- that determine the critical scales of luminous galaxies 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: stars 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 protogalaxies and in starbursts. have formed out of the protogalactic cloud, they should Implications are described for elliptical galaxy 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 protogalaxy parameters and those of the primordial density Dissipation of gravitational binding energy is the key to fluctuations. If dark halos consist of cold dark matter 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 black hole? 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 Angular Momentum 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 velocity dispersion 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 virial theorem, 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 astrophysical plasma 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,