GALAXIES, FORMATION

George Lake

There are several different ways to define galaxy formation. We leave the problem of generating small fluctuations at a very early epoch or "seeding" at later times to the entries on cosmology. Here we will be concerned with the collapse of a gas cloud and the initial burst of star formation. This definition leads to some ambiguity. Galaxy formation can be the final assembly of the objects that we see today, or it can refer to the formation of the first stars or the formation of a fiducial fraction of the stars. It was once assumed that a large fraction of the stars formed in an initially rapid collapse. In this case, galaxy formation is defined by all of the above happening synchronously. This would produce extremely bright events at high redshift which would be unmistakable. By this criterion, we have not clearly seen any galaxies forming. However, if we adopt either half of the above definitions, we find that galaxy formation is an ongoing process and that it is relatively easy to find nearby examples of galaxies in formation.

THE REDSHIFT OF FORMATION

From direct observations, it is not clear when galaxies formed. The local disk of the Milky Way is an example of continuous galaxy formation. We find that the present rate of star formation is not much smaller than the lifetime average. Generally, the current star formation rate in late-type spiral galaxies multiplied by a Hubble time is approximately the observed disk mass. Similarly, in giant elliptical galaxies with cooling flows, the cooling flow rate multiplied by the Hubble time is roughly the mass of the galaxy. Some nearby objects with high ratios of gas mass to stellar luminosity ( 5 in solar units) have been labeled protogalaxies. Extreme examples are Malin-1 and the Giovanelli-Haynes object, but there are several others (for example, DDO 170 and DDO 154). These objects are fully assembled but have had little star formation.

On the other hand, we find elliptical galaxies at relatively high redshifts (z 0.8) where the 4000-Å break in the spectrum shows that the bulk of the stars in these systems were formed much earlier. These galaxies must have formed before z ~ 2. There are objects with z 3.5 seen around radio sources. One of these, at z = 3.4, is observed to have a high ratio of 2 µM to optical flux, which is interpreted as indicating an old stellar population. These unusual objects, which are found in surveys of radio galaxies or in searches for very red objects, may not be representative of the formation of an average galaxy. Nonetheless, it is striking that old stellar populations exist at high redshift.

The epoch of galaxy "assembly" can be calculated if we assume that the event was isolated in both space and time. Consider the evolution of a "top hat" fluctuation, a spherical region of space with an excess density embedded in a flat Universe (one with exactly the critical density). Such a system behaves like a miniature closed Universe and turns around when its density is 9² / 16 times the critical density, _crit = 3 H² / (8G), where H is the expansion rate or Hubble constant. If pressure is unimportant, it will collapse by a factor of 2 to virialize. Thus its final density is 4.5² _crit@turnaround. Hence, the density of an object that formed without dissipation uniquely specifies its redshift of formation. For a typical disk galaxy, the redshift of turnaround for dissipationless formation is (1 + z_turn)_{no dissipation} ~ 40. Once we know the additional collapse factor owing to dissipation, C, we can correct this number to find the true epoch of formation: (1 + z_turn) = C^-1(1 + z_turn)_{no dissipation}. There are two ways to find C. If galaxies formed as part of a dissipationless clustering hierarchy, then their surface brightnesses would match a smooth extrapolation of the properties of groups and clusters. In reality, their surface brightnesses are roughly 100 times the extrapolated value, which implies that C ~ 10. (A more rigorous determination matches the luminosity density within galaxies to that derived from the two-point correlation function of galaxies.)

The second method of finding C uses the angular momentum of galaxies. The dissipational collapse factor needed for a tidally torqued protogalaxy to produce a centrifugally supported disk again tells us that C ~ 10. Therefore, we find z_turn ~ 3. The maximum half-mass radius of an average disk galaxy was ~ 100 kpc and was achieved at z ~ 4.

The preceding arguments assumed that the dimensionless cosmological density parameter = 1 where = / _crit. If = 0.1, this does not change the evaluation of the collapse factor owing to dissipation, but it does change the formation redshifts. In such a model, galaxy formation occurred at a redshift of ~ 6. For the sake of simplicity, we will continue to assume that the Universe is flat.

We calculated the above numbers for disk galaxies. We run into difficulties if we instead consider elliptical galaxies. Using the density argument, one concludes that elliptical galaxies have dissipated by a factor of 20. However, the angular momentum of ellipticals is exactly what is expected from tidal torques without any subsequent dissipation. For this reason, understanding the origin of the Hubble sequence of galaxy shapes has been a stumbling block for theories of galaxy formation.

THE FORMATION OF THE HUBBLE SEQUENCE

Ten years ago, one popular picture was that ellipticals were products of dissipationless collapse at high redshift, whereas spirals formed later with considerable dissipation. Here, ellipticals and bulges are formed in an early epoch of Compton cooling, whereas disks result from radiative cooling at a later time. For some time, this was the standard model of dissipational galaxy formation. In this picture, the problem was split into two halves, where the morphological types are cooled by different physical processes from perturbations of vastly different amplitudes and owe their luminosity functions to two independent processes.

It would be preferable to discover a control parameter that causes a bifurcation leading to disks and spheroids. Over 50 years ago, Sir James Jeans noted that the flattest spheroids had the maximum flattening of the Maclaurin sequence. He proposed that angular momentum was the control parameter and the dynamical instability of rapidly rotating systems was the physical mechanism that separated disk galaxies and spheroids. A variant of this scheme links initial angular momentum to "overdensity," and hence the clustering environment. Unfortunately, the range of spins measured in N-body experiments is not sufficiently broad to explain the full Hubble sequence. These simulations and other calculations also show that the spin has a relatively weak overdensity dependence. Nevertheless, the Hubble sequence is a sequence of angular momentum and, until recently, most schemes focused on stretching the range of initial angular momentum to produce the final range.

The key to the shift away from this picture has been the realization that, to first order, the Hubble sequence is a velocity or mass sequence. The characteristic velocity dispersion of an elliptical galaxy is ~ 250 km s^-1, which implies a circular velocity of ~ 425 km s^-1, whereas a typical spiral galaxy has a rotation velocity of only ~ 180 km s^-1. Recent N-body simulations have shown how the final virial velocity of a system determines its morphology. If the dark matter has a characteristic velocity dispersion at the epoch of galaxy formation, then more-massive objects underwent "cold collapses," and the less-massive collapses were "warm." Gas settles gently into circular orbits in warm collapses, leading to a disk galaxy. In cold collapses, the gas undergoes violent relaxation leading to strong density gradients and the outward transport of angular momentum. The dense inner region quickly makes stars, whereas the gas in the outer parts takes a long time to cool. After 10 dynamical times, roughly half of the gas (with approximately a third of the specific angular momentum) forms a dense slowly rotating bulge.

The final outcome of these simulations is that the more-massive elliptical galaxies have a half-light radius that is half that of a spiral galaxy and a specific angular momentum that is down by a factor of 3 from that of a spiral. This is an excellent match to the observations and shows that it is possible for disks and ellipticals to form from a continuous fluctuation spectrum.

Disks form in these experiments with an angular momentum distribution similar to that in the initial state. This validates our early calculation for the redshift of formation, z_turn. The observed differences between spirals and ellipticals also fix the velocity dispersion of the dark matter at turnaround, _turn. Numerous simulations have shown that z_turn, _turn, and the mass of the protogalaxy uniquely determine the density profile and core radius of the dark matter. This prediction of the density distributions is qualitatively borne out by current observations and may prove to be a stringent test of the theory.

The characteristic velocity dispersion needed to separate disks from spheroids results in a pressure that is more important for the perturbations that become disks. As a result, we expect that disk formation will be delayed by comparison to that of the spheroids. Indeed, the simulations show a rapid early formation of spheroids (during the violent relaxation phase which occurs on a collapse time scale), whereas disks are formed more slowly by continual infall.

Alternative approaches to galaxy formation emphasize environmental factors. These are the ongoing addition and removal of mass: accretion, cannibalism, merging, and stripping. The merger hypothesis proposes to make disks and collide them to make ellipticals. Accretion advocates envision forming spheroids early and slowly depositing disk material around them. There are composite schemes where systems that undergo a lot of merging become ellipticals, and relatively undisturbed coherent collapses turn into disks. These schemes require that star formation is carefully timed to take advantage of the merger dynamics. There is no doubt that all of these effects have varying degrees of importance.

OBSERVING THE EPOCH OF FORMATION

Evidence is rapidly emerging that supports the notion that galaxies formed at a z ~ 3. In deep surveys, a population of blue galaxies emerges at B-magnitudes greater than 22. These objects are so numerous that it is difficult to explain them as anything other than a cosmologically distant population of star-forming galaxies. They must have a redshift z > 0.8, as an irregular galaxy at lower redshift would be too red. They cannot have z > 3.5, as this would place the Lyman continuum break in the B-band and they would again become too red. More recently, a large population of spatially extended objects with "flat red" spectra have been discovered. If we attribute the red population to the Lyman break and note that no "ultrared" objects have been found, we conclude that the process of galaxy formation started at z ~ 4.

A recent study of z > 4 quasars indicates that the illusive Gunn-Peterson trough has been found. (The trough is caused by the Lyman absorption of intervening hydrogen, which lies at all redshifts up to that of the quasar.) At lower redshifts, absorption-line systems with low neutral fractions are seen. Since it is now believed that significant ionization sources other than quasars are needed to ionize these clouds, the output from young galaxies staring at z 4 is an appealing option.

The absorption-line systems at lower redshifts may also probe galaxy formation. If the clouds with high optical depths (neutral column densities 10¹⁸ cm^-2) are normally associated with galaxies, it would imply a covering fraction of order unity to a radius of 50 kpc. This is in good agreement with our estimated size of protogalaxies.

Also seen are Lyman- clouds, which have lower column densities. These clouds may be a part of the galaxy-formation process, either small-scale gravitational collapse in the hierarchical growth of galaxies or condensations from thermal instabilities in the protogalaxy. An alternative proposal is that they are intergalactic, confined by an explosively heated medium. Searches for He⁺(304) and He I(584) absorption features are the key to determining where these clouds fit in the formation process.

SUMMARY

The formation of galaxies was a gradual process beginning at a redshift of ~ 4 and continuing today. There are numerous observations of galaxies forming. Current and average rates of star formation are known in disk galaxies. Extended emission around radio galaxies has been seen to a redshift of 3.4. Protogalaxies have been "discovered" in the form of large numbers of blue objects in deep surveys, flat-red extended sources, fuzz around high-redshift radio galaxies and nearby gas-rich, low-surface-brightness objects. Relating all these observations to systematic properties of the distribution of dark and luminous matter as well as the cosmological conditions proposed for galaxy formation is the hard work for the coming decade.

Additional Reading

Berry, M.(1978). Principles of Cosmology and Gravitation. Cambridge University Press, Cambridge.

Binney, J. and Tremaine, S.(1988). Galactic Dynamics. Princeton University Press, Princeton.

Faber, S.(1982). Galaxy formation via hierarchical clustering and dissipation: the structure of disk systems and Galaxy formation via hierarchical clustering and dissipation: the structure of spheroids. In Astrophysical Cosmology, H.A. Bruck, G.V. Coyne, and M.S. Longair, eds. Pontificia Academia Scientarum, Vatican City, 191 and 219.

Gunn, J.E.(1982). The evolution of galaxies. In Astrophysical Cosmology, H.A. Bruck, G.V. Coyne, and M.S. Longair, eds. Pontificia Academia Scientarum, Vatican City, p. 233.

Hodge, P.(1986). Galaxies. Harvard University Press, Cambridge.

Kaiser, N. and Lasenby, A.N., eds.(1988). The Post-Recombination Universe. Kluwer, Dordrecht.

Sandage, A.(1961). The Hubble Atlas of Galaxies. Carnegie Institute of Washington, Washington, DC.

Adapted from The Astronomy and Astophysics Encyclopedia, ed. Stephen P. Maran