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

7.2. Theoretical

The role of the LF in practical cosmology is discussed in Section 1 and is not further taken up here.

It has always been clear that the LF of galaxies is fundamental for an understanding of galaxy formation. Many of the processes involved in the formation events undoubtedly have determined the LF of galaxies. However, the problem is so difficult that it is not surprising that, to date, theoretical interest has essentially been with the cosmological applications and not with the physics that determines the LF. Notable exceptions are Zwicky's (1942, 1957) attempt to explain the exponential form of the LF on the grounds of statistical mechanics, and Press & Schechter's (1974) self-similar gravitational condensation model of galaxy and cluster formation, which closely reproduces a Schechter-type LF. An approximately exponential behavior of the LF of galaxy systems (from single galaxies and small groups to rich clusters; Bahcall 1979) is generally in qualitative agreement with a hierarchical clustering scenario of galaxy formation (e.g. Silk & White 1978).

It must be suspected that the type-specific LFs, which now are established (i.e. the differences between the types), carry more stringent clues to the formation and evolution of galaxies than the general (M). However, galaxy formation theories have just barely reached the stage of being able to address the origin of the Hubble sequence.

The most basic morphological detail of the LF may be that all classes of high-surface-brightness (i.e. "normal") galaxies have a bell-shaped LF, whereas low-surface-brightness galaxies (dEs and possibly Im's), and only these, have an exponential or Schechter-type LF. These two basic branches of galaxies also appear distinct in the magnitude-surface brightness diagram (Wirth & Gallagher 1984, Kormendy 1985) that prompted Dekel & Silk (1986) to develop a model in which the low-surface-brightness dwarfs are the residuals of a mass-loss instability that occurs below a certain critical mass. In this case, the present Im's may be dEs repowered by infalling cooling gas (Silk et al. 1987). This mechanism, if restricted to the bigger systems, could possibly account for the bell-shaped LF of Im's, as well as for the exponential LFs of dE's and the transition class "dE or Im." An explanation of the LF dichotomy (bell-shaped vs. exponential) has been attempted by Schaeffer & Silk (1986). A more detailed understanding of the _T(M)'s must await further theoretical progress.

Besides the variety of shapes of the type-specific LFs, the observation that _T(M) is independent of environment, if confirmed, will also put very strong constraints on theories of galaxy formation.

ACKNOWLEDGMENTS

We are grateful to our many colleagues for preprints and reprints of their work. Two of us (BB and GAT) thank the Swiss National Science Foundation for financial support.