Annu. Rev. Astron. Astrophys. 1988. 26: 509-560 Copyright © 1988 by Annual Reviews. All rights reserved

1. THE RELEVANCE OF THE OPTICAL LUMINOSITY FUNCTION

1.1. The General vs. Specific Functions

The optical luminosity function (LF) of galaxies is a probability distribution _T(M) over absolute magnitude M for galaxies of any specified Hubble type T. Summed over all types, it is usually called the general LF (M) (sometimes also labeled the universal function). A distinction is often further made between the general function for field galaxies and for cluster galaxies because of the differing morphological mixes of these two environments (Hubble & Humason 1931, Morgan 1961, Abell 1965, Oemler 1974). We emphasize throughout this review that the concept of the general LF can no longer be maintained with sufficient precision for many cosmological calculations because the relative frequencies of the Hubble types depend so strongly on the environmental density. Dressler's (1980) density-morphology relation for clusters has been shown to apply to sparse groups (Bhavsar 1981, de Souza et al. 1982) and to the general field (Postman & Geller 1984), embracing density ratios of cluster to field as high as 10⁶. Since the specific functions _T(M) differ in shape for different T, their sum over T - the general function - cannot have a universal shape for all environmental densities. At best, such a general function can refer only to an average morphological mix at some average density that applies to galaxies in a particular sample. This theme of increasing detail, going from an average general function to particular sums of specific functions _T(M) in different environments is the principal one of this review.

The fact that the concept of a general function is now inadequate is not trivial in its consequences. Accurate knowledge of the LF is required for many calculations in cosmology. Integrations over space and time must be made to predict various observable distributions. These functions, often at the core of observational cosmology, either test world models or are important in the search for secular evolution in the look-back time. It is here that the LF forms a basic ingredient in practical cosmology, in addition, of course, to its deeper significance concerning the physical characteristics of galaxies. In this latter role, the LF holds clues to the formation and evolution of galaxies and of clusters, especially evident from the consequences of the type-density relation [see Dressler (1984) for a review].