The Dependence of the Galaxy Luminosity Function on Large-Scale Environment

A basic assumption in current halo occupation model is that the properties of a galaxy depend only on the mass of its dark matter halo. An important consequence of this is that the segregation of the galaxy population by large-scale environment is entirely due to the environmental dependence of the halo population. In this paper we use such a model to predict how the galaxy luminosity function depends on large-scale environment. The latter is represented by the density contrast (delta) averaged over a spherical volume of radius R=8Mpc/h. The model predicts that the Schechter function is a good approximation to the luminosity functions of galaxies brighter than ~10^9 h^{-2}L_sun (b_j-band) in virtually all environments. The characteristic luminosity, L^{\star}, increases moderately with \delta. The faint-end slope, \alpha, on the other hand, is quite independent of $\delta$. However, when splitting the galaxy population into early and late types, it is found that for late-types \alpha is virtually constant, whereas for early-types \alpha increases from ~-0.3 in underdense regions (\delta~-0.5) to ~-0.8 in highly overdense regions with \delta ~ 10. The luminosity function at L_{b_j}<10^9 h^{-2} L_sun is significantly steeper than the extrapolation of the Schechter function that fits the brighter galaxies. This steepening is more significant for early-types and in low-density environments. The model also predicts that the luminosity density and mass density are closely correlated. The relation between the two is monotonic but highly non-linear. This suggests that one can use the luminosity density, averaged over a large volume, to rank the mass density. This, in turn, allows the environmental effects predicted here to be tested by observations.