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

Non-parametric, empirically based, models for associating galaxy luminosities with halo/ subhalo masses are being developed by several groups and we present here an updated version of the Vale & Ostriker version of this model. This is based on a more accurate, self-consistent treatment of subhalo mass loss and revised results for the subhalo mass function (SHMF) to address this question anew. We find that the mass-luminosity relation, at high mass, particularly for first brightest galaxies and less so for group total, is almost independent of the actual luminosity function considered, when luminosity is scaled by the characteristic luminosity L-*. Additionally, the shape of the total luminosity depends on the slope of the SHMF. For these high mass, cluster-sized haloes, we find that total luminosity scales as L-tot similar to M-0.88, while the luminosity of the first brightest galaxy has a much weaker dependence on halo mass, L-1 similar to M-0.28, 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 similar to M-4.5 for M similar to 10(10) h(-1) in the K band. The average number of galaxies per halo/ cluster is also in very good agreement with observations, scaling as similar to M-0.9. In general, we obtain a good agreement with several independent sets of observational data. Taking the model as essentially correct, we consider two additional possible sources for remaining discrepancies: problems with the underlying cosmology and with the observational mass determination. We find that, when comparing with observations and for a flat cosmology, the model tends to prefer lower values for Omega m and sigma(8). Within the Wilkinson Microwave Anisotropy Probe (WMAP)+Sloan Digital Sky Survey (SDSS) concordance plane of Tegmark et al., we find best agreement around Omega m=0.25 and sigma(8)=0.8; this is also in very good agreement with the results of the cosmic microwave background (CMB)+2dF study of Sanchez et al. 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.