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 ~10⁹ h^-2Lₛun (bⱼ-band) in virtually all environments. The characteristic luminosity, L^\, increases moderately with \. The faint-end slope, \, on the other hand, is quite independent of \. However, when splitting the galaxy population into early and late types, it is found that for late-types \ is virtually constant, whereas for early-types \ increases from ~0 in underdense regions (\~-0. 5) to ~-1 in highly overdense regions with \ ~ 10. The luminosity function at L₁䲛<10⁹ h^-2 Lₛun 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.