What is L ⋆ ? Anatomy of the Galaxy Luminosity Function

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Abstract
Using the empirical relations between the central galaxy luminosity and the halo mass, and between the total galaxy luminosity 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 lognormal scatter with a mean calibrated against the observations. In halos where the total galaxy luminosity exceeds that of the central galaxy, satellite galaxies are 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. The L in the LF is the luminosity above which the central galaxy luminosity-halo mass relation begins to flatten in halos above ~1013 M☉. In surveys in which central galaxies in massive clusters are neglected, either by design or because of the cosmic variance, L is simply the mean luminosity of central galaxies in halos at the upper end of the selected mass range. 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.