1.1. Initial Conditions: CDM Cosmology
The initial conditions for the formation of galaxies are provided by the now-standard CDM cosmological model. The combined results of the WMAP satellite study of Cosmic Microwave Background anisotropies, large-scale structure, and Type Ia supernovae observations yield best-fit values for the cosmological parameters of roughly = 0.7, m = 0.3, b = 0.04, and H0 = 70h70 km s-1 Mpc-1 (Bennett et al. 2003). 1 The original model of galaxy formation was Monolithic Collapse (Eggen et al. 1962), where gravitational collapse of a cloud of primordial gas very early in the lifetime of the Universe formed all parts of each galaxy at the same time. Modern evidence rules out this model on two fronts; the widely varying ages of different components of the Galaxy provide a counter-example, and the CDM cosmology predicts "bottom-up" i.e. hierarchical rather than "top-down" structure formation.
Hierarchical structure formation is a generic feature of Cold Dark Matter (CDM) models. Small overdensities are able to overcome the cosmological expansion and collapse first, and the resulting dark matter "halos" merge together to form larger halos which serve as sites of galaxy formation. This process continues until the present day, making galaxy formation an ongoing process. The nearly-scale-invariant primordial power spectrum inferred from combining WMAP with large-scale structure observations provides power on all scales in the distribution of CDM. The baryons fall into the CDM potential wells after decoupling, leaving only trace evidence of their previous acoustic oscillations as a series of low-amplitude peaks in the matter power spectrum. The non-linear collapse of dark matter overdensities occurs on larger and larger scales, so the typical collapsed halo mass grows with time, but no preferred scale is introduced. CDM therefore provides a distribution of halos where galaxies can form, with the details of the process up to baryonic physics.
Despite the lack of preferred galaxy scales in the distribution of dark matter halos, baryonic physics causes galaxies to have minimum and maximum masses. The maximum mass is that of CD galaxies in cluster centers with baryonic masses ~ 1012 M and virial masses ~ 1013 M; there are ~ 1014 M of baryons available in a rich cluster but virialization of galaxies and heating of gas to the high virial temperature prevent most of this mass from finding its way to the central galaxy. The minimum mass observed today is that of dwarf galaxies, ~ 108 M, but galaxies may initially have formed as small as 106 M (the baryonic Jean's mass after recombination i.e. the minimum mass for which gravity overwhelmed pressure support). Explaining the lack of observed galaxies with circular velocities below 30 km/s is a major goal; it is suspected that feedback from supernovae explosions may have quenched star formation in such low-mass objects immediately after a single burst of star formation (Dekel & Silk 1986).
The growth of cosmological structure and collapse of dark matter halos is a feature of the matter-dominated epoch. During radiation-domination, perturbations on scales smaller than the sound horizon were unable to grow due to acoustic oscillations in the photon-baryon fluid that gave rise to the famous peaks in the CMB angular power spectrum and the lower-amplitude peaks in the matter power spectrum. Now that we have entered a phase of dark energy domination, structure growth is slowing and will cease entirely as the universe enters a new phase of inflation. This cosmological "freeze-out" in structure formation is recent, since equality between the dark energy and matter densities occurred at zeq = 0.4. The slowing of structure formation occurs gradually, so the growth of cosmological structure continued nearly unabated until zeq, even though we see strong observational evidence for "downsizing" at z < 1 where high-mass galaxies grow far more slowly than lower-mass galaxies (e.g. Treu et al. 2005, Smith 2005). Another term being used by some is "anti-hierarchical", which is basically a synonym for "downsizing" but seems to imply inconsistency with hierarchical cosmology. However, the observed freeze-out in galaxy (and possibly supermassive black hole) formation in massive galaxies is not inconsistent with CDM models; rather, it appears to be caused by baryonic feedback which is not well understood at present (see Section 6.). The slowing of cosmological structure growth since z 0.4 may, however, play a role in the recent decline of the cosmic star formation rate density discussed by Bell et al. (2005).
1.2. Final Conditions: Low-redshift Galaxies
The study of galaxy formation is made easier by having full boundary conditions. The final conditions are the Hubble sequence of mature galaxies we see in the nearby universe at redshift zero. Indeed, much has been learned about galaxy formation from "archaeological" evidence in the ages and chemical abundances of various Galactic stellar populations, and expanding these studies to the rest of the Local Group and beyond is quite useful. Nonetheless, there are great advantages to observing galaxies in the act of formation, which motivates the study of high-redshift galaxies. At z > 2, galaxy-mass halos are rare so the majority of galaxies we observe reside in dark matter halos that have only recently collapsed i.e. at high-redshift most galaxies are young. In this sense, z > 2 can be considered the epoch of galaxy formation.
1 We include h70, analogous to the traditional parameter h h100, even though its value appears quite close to 1. Back.