2005MNRAS.364..303C

Using the conditional luminosity function - the luminosity distribution of galaxies in a dark matter halo as a function of the halo mass - we present an empirical model to describe the redshift evolution of the rest B-band galaxy luminosity function (LF). The model is compared to various estimates of the LF, in rest UV and B bands, out to a redshift of 6, including estimates of LFs of galaxy types separated to red and blue galaxies. Using the observed LFs out to z∼ 5, we present a general constraint on the redshift evolution of the central galaxy-halo mass relation. The increase in the number density of luminous galaxies, at the bright end of the LF, can be explained as due to a brightening of the luminosity of galaxies present in dark matter halo centres, relative to the luminosity of central galaxies in similar mass haloes today. The lack of strong evolution in the faint end of the LF, however, argues against a model involving pure-luminosity evolution at all halo mass scales. The increase in luminosity at the bright end compensates the rapid decline in the number density of massive haloes as the redshift is increased. The decline in group to cluster-mass dark matter haloes out to a redshift of ∼2 is not important as the central galaxy luminosity flattens at halo masses around 10¹³M_☉. At redshifts ∼2-3, however, the density of bright galaxies begins to decrease due to the rapid decline in the number density of dark matter haloes at mass scales around and below 10¹³M_☉.

Based on a comparison of our predictions to the measured ultraviolet (UV) LF of galaxies at redshifts ∼3, we estimate the probability distribution of halo masses to host Lyman break galaxies (LBGs). This probability for galaxies brighter than AB-absolute magnitudes of -21, with a number density of ∼5x10^–3h³Mpc^–3, peaks at a halo mass of ∼7x10¹¹h^–1M_☉with a 68 per cent confidence level of (4-21)x10¹¹h^–1M_☉. These estimates are consistent with the mass estimates for LBGs using two-point clustering statistics and recent estimates of halo masses based on spectroscopic observations. For galaxies brighter than AB-absolute magnitudes of -21 at z∼ 6, the halo mass scale is a factor of ∼2 smaller; the LF predictions at z∼ 6 are consistent with measured estimates in the literature. Based on the models, we also predict the LF of galaxies at redshifts greater than 6 and also the bias factor of galaxies at redshifts greater than 3; these predictions will soon be tested with observational data. In general, to explain high-redshift LFs, galaxies in dark matter haloes around 10¹²M_☉must increase in luminosity by a factor of ∼4-6 between today and redshift of 6.