A brighter past: galaxy luminosity function at high redshifts

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 similar to 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 similar to 2 is not important as the central galaxy luminosity flattens at halo masses around 10(13) M-circle dot. At redshifts similar to 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 10(13) M-circle dot. Based on a comparison of our predictions to the measured ultraviolet (UV) LF of galaxies at redshifts similar to 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 similar to 5 x 10(-3) h(3) Mpc(-3), peaks at a halo mass of similar to 7 x 10(11) h(-1) M-circle dot with a 68 per cent confidence level of (4-21) x 10(11) h(-1) M-circle dot. 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 similar to 6, the halo mass scale is a factor of similar to 2 smaller; the LF predictions at z similar to 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 10(12) M-circle dot must increase in luminosity by a factor of similar to 4-6 between today and redshift of 6.