The non-parametric model for linking galaxy luminosity with halo/subhalo mass

We present a non-parametric, empirically based, model for associating galaxy luminosities with halo/subhalo masses, based on a self-consistent treatment of subhalo mass loss and the subhalo mass function. We find that, at high mass, the mass-luminosity relation is almost independent of the actual luminosity function considered, when luminosity is scaled by the characteristic luminosity L*. Additionally, the shape of the total halo luminosity depends on the slope of the subhalo mass function. For these high mass, cluster sized haloes, we find that total luminosity scales as Lₜot ~ M⁰. 88, while the luminosity of the first brightest galaxy has a much weaker dependence on halo mass, L₁ ~ M⁰. 28, in good agreement with observations and previous results. At low mass, the resulting slope of the mass-luminosity relation depends strongly of the faint end slope of the luminosity function, and we obtain a steep relation, with approximately L ~ M⁴. 5 in the K-band. The average number of galaxies per halo/cluster is also in very good agreement with observations, scaling as M⁰. 9. In general, we obtain a good agreement with several independent sets of observational data. We find that, when comparing with observations and for a flat cosmology, the model tends to prefer lower values for Omegaₘ and sigma₈. Within the WMAP+SDSS concordance plane of Tegmark et al. (2004), we find best agreement around Omegaₘ=0. 25 and sigma₈=0. 8, also in very good agreement with the results of the CMB+2dF study of Sanchez et al. (2005). We also check on possible corrections for observed mass based on a comparison of the equivalent number of haloes/clusters. Additionally, we include further checks on the model results based on the mass to light ratio, the occupation number, the group luminosity function and the multiplicity function. (abridged)