The effects of photoionization on galaxy formation - III. Environmental dependence in the luminosity function

Using semi-analytic modelling techniques, we calculate the luminosity function of galaxy populations residing in cold dark matter haloes of different masses. We pay particular attention to the influence of the re-ionization of the Universe on the number of faint galaxies, and to the effects of dynamical friction and tidal limitation of satellites on the number of bright galaxies. We find substantial differences in the shapes of the galaxy luminosity functions in haloes of different mass, which reflect generic features of the cold dark matter model of galaxy formation, and thus offer the opportunity to test it. We then consider how the individual halo luminosity functions combine to produce the global luminosity function. Surprisingly, the global function ends up having a shallower faint-end slope than those of the constituent halo luminosity functions. We compare our model predictions with the limited observational data sets compiled by Trentham & Hodgkin. We find good agreement with the luminosity functions measured in the Virgo and Coma clusters, but find significant disagreement with the luminosity functions measured in the Local Group and Ursa Minor cluster. We speculate on possible inadequacies in our modelling and in the existing observational samples. The luminosity functions of galaxies in groups and clusters that have been identified in the Two Degree Field (2dF) and Sloan Digital Sky Survey (SDSS) galaxy redshift surveys offer the prospect of testing galaxy formation models in detail.