Annu. Rev. Astron. Astrophys. 1992. 30: 499-542
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4.3 Galaxy Counts as a Function of Redshift or Apparent Magnitude

As discussed in Section 3.4 and illustrated in Figure 6, the variation of dV / dz with cosmological parameters is substantial and offers a promising effect on which OmegaLambda determinations might be based. This has been pursued primarily in terms of counting galaxies, either as a function of their estimated redshifts or their apparent magnitudes in some band. Neither technique has yet given a decisive result despite significant efforts reviewed below.

There are two major difficulties which make galaxy number-redshift counts problematic. First, redshifts for a very large unbiased sample of faint galaxies are required as input data. The sample must be unbiased with respect to redshift, despite the expected strong anti-correlation between redshift and surface brightness. Second, one must take careful account of any galaxy evolution with redshift to make sure the low-z counts refer to the same population of objects as the high-z counts.

The most notable and fearless use of this technique was reported by Loh & Spillar (1986, see also Loh 1986) who used broadband photometry in six optical-near IR bands to estimate redshifts for 1000 galaxies down to a brightness level of approximately 22 in I. They used a very simple model for galaxy evolution (essentially assuming that the luminosities of all galaxies at any past epoch to be a constant factor times their present luminosities) described by a single parameter which they simultaneously fit to the data. Their results were very well fit by a k = 0, OmegaM = 1, OmegaLambda = 0 model and were seen as strong support for that popular cosmological scenario; however, they were in fact consistent with a significant range of other possibilities, including non-zero OmegaLambda cases (Peebles 1988).

More seriously, consideration of even slightly more realistic models of galactic evolution (e.g. allowing for the possibly separate evolution of early and late type galaxy populations) greatly increases the error ranges for the cosmological parameters derived by Loh & Spillar (Bahcall & Tremaine 1988, Yoshii & Takahara 1989). Worse still, the peculiar behavior of faint galaxy counts and color-magnitude diagrams (see below), the surprisingly rapid evolution of the spectroscopic populations of rich galaxy clusters (Dressler 1984), and the redshifts distributions for small samples of faint galaxies studied with slit spectroscopy (Broadhurst et al 1988, Cowie 1991) all make it abundantly clear that low-redshift galaxy evolution is a complex process which probably cannot be described by any simple model with a small number of parameters. These same complications call into doubt the accuracy of photometric redshifts which must rely on the overall spectral shape of galaxy optical-IR emission changing in a predictable and simple way.

It thus appears unlikely that any compelling constraints on cosmological parameters can be derived from galaxy number-redshift counts until there are great improvements in both empirical information on faint galaxies and our theoretical understanding of their evolution.

An observationally less challenging approach to dV / dz tests is to abandon redshift determinations altogether and simply count galaxies as a function of flux (apparent magnitude). In fact, galaxy number-magnitude counts in the B (blue) band (Tyson 1988, Maddox et al 1990b) are substantially better fit by OmegaLambda-dominated cosmologies than by OmegaLambda = 0 ones, even taking into account the uncertainties in relatively sophisticated modern galaxy evolution models (Fukugita et al 1990b). This realization also prompted a flurry of interest in the cosmological constant, but was soon undermined by the discovery that near-IR K band counts do not require (and, in fact, are poorly fit by) OmegaLambda-dominated models (Cowie 1991) and that selection effects, including seeing-dependent ones, must be carefully accounted for in the interpretation of such number-magnitude counts (Fukugita 1991).

Once again, it seems difficult not only to draw any firm conclusions but even to discern which cosmological models are marginally favored by the available data.

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