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

6. THE LUMINOSITY FUNCTION FOR DIFFERENT ENVIRONMENTS

In Section 5 it became evident that different LFs apply to different morphological types T. Hence, we have = _T(M). Throughout this review we have also emphasized that the general (M), summed over all types, depends on the environmental density. This is especially true for the faint-end slope, which is found to be notably different for field and clusters, varying among the clusters (cf. Section 4) as well as between clusters and the field.

It is clear that we must distinguish between an environmental dependence of the general (M), which is merely due to the type mixture differences, and a dependence of the type-specific _T(M)'s on the environment. As previously mentioned, we hypothesize that there is only a negligible environmental variance of the type-specific _T(M)'s, and therefore that the variation of the type mix is the major parameter responsible for the variance of the total (M) from sample to sample.

But before we come to this simple scheme in Section 6.3, it is desirable to approach the problem in a more systematic and general way. We consider first giving up the artificial dichotomy of "clusters" and "field" and substituting for it the notion of a continuous variation of density D. The distribution of galaxies is known to be inhomogeneous on all scales up to at least 100(50/H₀) Mpc. A rich cluster of galaxies is like a Matterhorn in a grand Alpine landscape of mountain ridges and valleys of lengths up to 100 km. Correspondingly, the galaxy density d (x, y, z) is a continuous parameter, and the most general approach is therefore to great the specific _T(M) as a continuous function of this density, _T(M, D). The consequence is that the universally adopted assumption of separability of and D, as expressed in Equation 8, should now be abandoned, giving way to a general LF-density relation through the Dressler (1980) density-type relation.