Annu. Rev. Astron. Astrophys. 1992. 30: 613-52 Copyright © 1992 by Annual Reviews. All rights reserved

3.2. Magnitude and Redshift Distributions

Counts of galaxies as a function of apparent magnitude, A(m), depend on the cosmological model, clustering characteristics, the luminosity function, and the mixture of galaxy types (meaning their intrinsic surface brightness profiles and their spectral energy distributions). The cosmological model enters via the volume element dV / dz and the luminosity distance d_L at each redshift. If the evolution of the stellar population is specified in terms of look-back time, then the cosmological model enters in an additional way because it determines the conversion between look-back time and the measured redshift.

For a given apparent surface brightness, different physical radii are reached for galaxies at different redshifts. At high redshifts especially, the fraction of the light seen above the threshold may be very sensitive to observational details, such as the degree of image blur from seeing and other sources, depending on the shape of the intrinsic profile for each galaxy (Pritchet and Kline 1981). For this reason, it is of critical importance in a galaxy-count model to know the frequency distribution of galaxy intrinsic profile types. Since the visibility of distant galaxies depends on image profile and the spectral energy distribution, ideally a more general statistical distribution function than the luminosity function (M) should be used, say (M, color, surface brightness). Unfortunately, catalogues of nearby galaxies suitable for deriving do not yet exist. The alternative is to adopt different functions for (M) according to galaxy type.

3.2.1 SPECTRAL ENERGY DISTRIBUTIONS Knowledge of galaxy spectral energy distributions allows computation of their K-corrections, and ultimately of their redshifts. The mix of spectral types can be usefully considered a function of a single rest-frame color, since galaxy colors tend to be well correlated with each other. However, most models compute the space density as a function of morphological type instead of color, because of the availability of such data. This practice is unfortunate in a number of regards: the difficulty in assigning a meaningful average color to a morphological type; the imperfect agreement between the distributions of types for independent samples (or even between independent classifications for the same galaxy); and uncertainties inherent in the morphological classification procedure.

Most galaxy count models use only five or six galaxy types. This coarse grid of spectra can be traced back to Wells's (1972) large-aperture spectrophotometry of field galaxies. This set of data allowed K-corrections and colors as a function of redshift to be computed, for similar galaxies, once the spectra were suitably extrapolated to shorter and longer wavelengths (Wells's spectra covered only the range 3500-5500). These spectra were first used by Brown and Tinsley (1974) and Pence (1976), and later by Coleman, Wu, and Weedman (1980) and Tinsley (1980). Subsequent models have followed implicitly the same procedure, for instance King and Ellis (1985), Guiderdoni and Rocca-Volmerange (1990), Yoshii and Peterson (1991), and Cole, Treyer, and Silk (1992).

It is sobering to consider the foundations of this work. Large-aperture spectrophotometry of luminous elliptical galaxies had already been made by Schild and Oke (1971), and it was known that the galaxies contributing to faint counts would be mainly spirals. Wells was able to observe only seven spiral galaxies. These fell naturally into three groups of similar spectra, which were then averaged. These mean spectra could be characterized by the respective mean colors, but have been more commonly labelled by nominal morphological type ``Sdm-Im,'' ``Sbc,'' and ``Sab.'' A class called ``Scd'' was invented by Pence (1976) by interpolation between ``Sdm-Im'' and ``Sbc'' and has been adopted by others (e.g. Coleman et al. 1980).

The bluest categories are of particular interest because of the anticipation that such galaxies may appear in greater proportions at high redshifts, since their K-corrections are smaller. Pence's (1976) bluest class (``Im'') contains NGC 1140 and NGC 145. NGC 1140 is called Sb pec: in the Revised Shapley Ames Catalog (Sandage and Tammann 1981), it appears on the Palomar Sky Survey to have high surface brightness, and on the RSA system has M_B = -20.4. NGC 145 is listed in the Arp (1966) atlas (No. 019) and is a striking, high-surface-brightness spiral; it has M_B = -21.5. Neither galaxy bears any resemblance to Magellanic irregulars. Coleman, Wu, and Weedman (1980) chose not to use NGC 145 in their mean spectra because it was not sufficiently blue for their bluest class. In fact, in their list only NGC 4449 is bluer in (B - V)_T⁰, by only 0.01 mag.) The next-bluest galaxy measured by Wells is NGC 1659, which has M_B = -22.1. Thus the galaxies in Wells's list, and the galaxies observed in the ultraviolet by Coleman, Wu, and Weedman (1980), are for the most part quite luminous systems. NGC 4449 at M_B = -18.8 is the least luminous galaxy in either of these lists. Since there is a trend for lower-luminosity galaxies to be bluer (Huchra 1977), the complete lack of low-luminosity galaxies in the library of galaxy spectral energy distributions is an important limitation.

In summary, the models ultimately based on Wells's spectrophotometry suffer from several shortcomings: the galaxies used to define the classes are few and do not properly span the range of colors or luminosities; the blue galaxies do not represent their designated morphological types (and even if they did, the calculation of the numbers of such galaxies per cubic megaparsec would be problematic); it seems likely that there is a selection bias in the spectrophotometric samples in favor of high-surface-brightness galaxies; and it has not been demonstrated that the galaxies are representative of either magnitude-limited or volume-limited samples.