Annu. Rev. Astron. Astrophys. 1991. 29: 499-541 Copyright © 1991 by Annual Reviews. All rights reserved

5.3 The Luminosity Function and Field Galaxy Evolution

The galaxy luminosity function at optical wavelengths, (M), is an essential tool in the interpretation of large-scale structure data bases and galaxy number counts, in the derivation of the universe's mean properties such as its luminosity density, and in constraining models of galaxy formation. Binggeli et al (1988) recently reviewed the subject. The two most recent determinations of (M) have been obtained by Efstathiou et al (1988) and de Lapparent et al (1989). The former analyzed the results of the first CfA, DARS, and KOSS surveys, while the latter concentrated on the results of two 6° x 135° slices. Schechter-type fits of the form (L) dL = ^* (L / L^*) exp (-L / L^*) d (L / L^*), where L is the luminosity (so L and L^* are related to magnitudes M and M^* in the usual form), yield relatively consistent results; the shape of (M) appears relatively well defined, with M_B^* -19.2 ± 0.1 and -1.1 ± 0.1 for h = 1. The errors in the CGCG magnitudes, which form the basic photometric system for the CfA as well as for most northern samples, are a serious concern. The magnitudes contained in the first volume of the CGCG (which partly covers the region in the de Lapparent et al (1989) work] are particularly erratic. An additional source of concern in these determinations is of course related to the issue of fair sampling. The amplitude of (M) is particularly affected by these uncertainties: Efstathiou et al. obtain a value of ^* = 0.00156 ± 0.00034 h³ Mpc^-3, while the value given by de Lapparent et al is ^* = 0.0020 ± 0.0005 h³ Mpc^-3. The mean luminosity density associated with a functional description of (L) as given above is _L = ^* ( + 2) L^*, where is the incomplete gamma function. The main uncertainty on _L derives from that on ^*, and its value is _L = 1.5 ± 0.4 x 10⁸ hL Mpc^-3, adopting the luminosity function parameters of de Lapparent et al. With this determination, a universe with critical mass would have a mass-to-light ratio of 1800 ± 500 h M / L, a value significantly larger than the best-determined values for clusters of galaxies (typically < 500 h M /L).

The issue of the local density dependence of (M) has been extensively debated. It has been proved convincingly (Binggeli et al 1988 and refs. therein) in Local Supercluster samples - where morphological types are most reliable - that different morphological types have different (M)s, so that (M) = _{t t} (M) f_t, where f is the population fraction of galaxies of morphological type t. Efstathiou et al indicate a similar phenomenon, in the sense that galaxies later than Sb are significantly fainter than earlier ones. In addition, (M) may depend explicitly on local density (Giovanelli 1990, Haynes & Giovanelli 1988), although disentangling the morphology-density and the luminosity-density dependences from each other is an uncertain, uneasy task. Related to this issue is the topic of the evolution of (M). It has been known for some time (Kron 1982) that the number-magnitude relation N(m) gets steeper than expected with z. It is not known whether this steepening is caused by a largely enhanced star formation rate in galaxies at z > 0.1 or by a population of faint, local dwarfs. Broadhurst et al (1988) have suggested that, out to z ~ 0.5, little evolution of the bright end of (M) has occurred, but the faint-end slope of (M) could get steeper with redshift. The count excess would then result from a luminosity-dependent luminosity evolution. Ellis (1990) and Koo (1990) recently reviewed the status of this issue, contributing further cause for skepticism in believing that the bulk of faint galaxies result from nearby, extremely low luminosity dwarfs. Koo also proposes that unless very significant merging of galaxies occurred at high redshift (enough to over-come the volume factor at high z; i.e. if = 1, the volume increases much more slowly with z than if = 0), observations of high redshift galaxies favor a low universe.