What Is L⋆?: Anatomy of the Galaxy Luminosity Function

Using the empirical relations between the central galaxy luminosity and the halo mass, and between the total luminosity of galaxies in a halo and the halo mass, we construct the galaxy luminosity function (LF). To the luminosity of the central galaxy in a halo of a given mass we assign log-normal scatter with the mean and the dispersion of the luminosity directly calibrated against the observations. In halos where the total galaxy luminosity exceeds that of the central galaxy, satellite galaxies are assumed to be distributed as a power-law in luminosity. Combined with the halo mass function, this description reproduces the observed characteristics of the galaxy LF, including a shape consistent with the Schechter function. When all galaxies are included, regardless of the environment or the Hubble type, the Schechter L⋆ is the luminosity scale at which the central galaxy luminosity-halo mass relation flattens; the flattening occurs on halo mass scales above a few times 10M⊙. If a selection criterion is imposed on the mass of the systems for which the LF is computed, L⋆ is simply the mean luminosity of central galaxies in halos at the upper end of the selected mass range, and thus has no physical significance. The smooth, exponential decay of the Schechter function toward high luminosities reflects the intrinsic scatter in the central galaxy luminosity-halo mass relation. In addition to the LF, the model successfully reproduces the observed dependence of galaxy clustering bias on luminosity. Subject headings: cosmology: observations — cosmology: theory — galaxies: clusters: general — galaxies: formation — galaxies: fundamental parameters