Next Contents Previous

5. Luminosity Functions

The luminosity function (LF) of galaxies reflects both the initial conditions (e.g. the power spectrum of density fluctuations in the gravitational instability scenario) and the complicated physics of collapse, cooling, star formation, and feedback that govern how mass is converted into light. Based on arguments for hierarchical structure formation (Press and Schechter 1974), Schechter (1976) proposed the following functional form for the luminosity function:

Equation 6 (6)

where is phi (L) is the number of galaxies per unit volume per unit luminosity, L* is a ``characteristic'' luminosity, and alpha is a ``characteristic'' faint-end slope. The arguments behind the Press and Schechter (1974) formalism have recently been made more rigorous (Bond et al. 1991; Bower 1991), but these apply to the collapse of galaxy halos, and do not directly translate into a luminosity function. The various attempts to incorporate star-formation physics into hierarchical models (Sect. 7) produce a break at L*, due to the requirement that galaxies radiatively cool while they are collapsing. The power-law form at faint magnitudes is imposed by the initial power spectrum but modified by a mass-dependent star-formation efficiency due to galactic winds and by galaxy mergers.

While the Schechter function is a good first-order approximation to the overall LF, there is information as well in the type specific luminosity functions, which are typically not well-fit by Schechter functions. Binggeli et al. (1988) reviewed the type-specific LF in clusters and the field and hypothesized that the LF's of the individual morphological types are constant, independent of environment. The observed environmental variation in the total LF (summed over all types) could then be explained as a simple change in the morphological mix with environment, via the morphology-density relation (see also Thompson and Gregory 1980; Jerjen et al. 1992). The theoretical implication is that the physics that governs the LF within a given Hubble class is (to first order at least) independent of environment, while the creation/destruction processes that govern the mix of types are not.

The faint end of the LF is dominated by dE galaxies in clusters, while Sd and Im galaxies dominate in lower-density environments. A working hypothesis (Binggeli et al. 1988) is that variations in the faint end slope of the LF can be explained entirely by variations in the relative proportions of dE and Sd-Im galaxies. However, before assessing this hypothesis, we must highlight the uncertainties in current LF estimates and the selection effects that could bias the faint-end slope.

Next Contents Previous