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 ( 77 ) 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 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 subhalo mass function .
For these high mass , cluster sized haloes we find that total luminosity scales as L _ { tot } \sim M ^ { 0.88 } , while the luminosity of the first brightest galaxy has a much weaker dependence on halo mass , L _ { 1 } \sim 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 \sim M ^ { 4.5 } for M \sim 10 ^ { 10 } h ^ { -1 } M _ { \odot } in the K-band .
The average number of galaxies per halo/cluster is also in very good agreement with observations , scaling as \sim 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 WMAP+SDSS concordance plane of Tegmark et al .
( 73 ) , 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 CMB+2dF study of Sanchez et al .
( 63 ) .
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 .