5. Galaxy counts

Counts of galaxies - or of other objects whose number density as a function of redshift may be modeled - probe the volume element (dV / dz)dz defined by a solid angle in the sky and a redshift interval dz. The volume is fixed by the angular size distance (Eq. [69]), which determines the area subtended by the solid angle, in combination with the redshift-time relation (Eq. [64]), which fixes the radial distance belonging to the redshift interval.

Sandage (1961a) and Brown and Tinsley (1974) showed that with the technology then available galaxy counts are not a very sensitive probe of the cosmological parameters. Loh and Spillar (1986) opened the modern exploration of the galaxy count-redshift relation at redshifts near unity, where the predicted counts are quite different in models with and without a cosmological constant (as illustrated in Figure 13.8 in Peebles, 1993).

The interpretation of galaxy counts requires an understanding of the evolution of galaxy luminosities and the gain and loss of galaxies by merging. Here is an example of the former in a spatially-flat cosmological model with _M0 = 0.25. The expansion time from high redshift is t₃ = 2.4 Gyr at redshift z = 3 and t₀ = 15 Gyr now. Consider a galaxy observed at z = 3. Suppose the bulk of the stars in this galaxy formed at time t_f, and the population then aged and faded without significant later star formation. Then if t_f << t₃ the ratio of the observed luminosity at z = 3 to its present luminosity would be (Tinsley, 1972; Worthey, 1994)

(75)

If t_f were larger, but still less than t₃, this ratio would be larger. If t_f were greater than t₃ the galaxy would not be seen, absent earlier generations of stars. In a more realistic picture significant star formation may be distributed over a considerable range of redshifts, and the effect on the typical galaxy luminosity at a given redshift accordingly more complicated. Since there are many more galaxies with low luminosities than galaxies with high luminosities, one has to know the luminosity evolution quite well for a meaningful comparison of galaxy counts at high and low redshifts. The present situation is illustrated by the rather different indications from studies by Phillipps et al. (2000) and Totani et al. (2001).

The understanding of galaxy evolution and the interpretation of galaxy counts will be improved by large samples of counts of galaxies as a function of color, apparent magnitude, and redshift. Newman and Davis (2000) point to a promising alternative: count galaxies as a function of the internal velocity dispersion that in spirals correlates with the dispersion in the dark matter halo. That could eliminate the need to understand the evolution of star populations. There is still the issue of evolution of the dark halos by merging and accretion, but that might be reliably modeled by numerical simulations within the CDM picture. Either way, with further work galaxy counts may provide an important test for dark energy and its evolution (Newman and Davis, 2000; Huterer and Turner, 2001; Podariu and Ratra, 2001).