W. Ho about "the relation between galaxy propteries and the dark matter halo"
Galaxies residein halos of dark matter (DM) which form from initial density fluctuations. They are believed to well understood since they only interact gravitationally and can be simulated. But how do galaxies form in DM halos? Does every DM halo have a galaxy? How many galaxies are there in large halos as in galaxy clusters?
How does the mass function of MD halos translate into the luminosity function of galaxies? They do not really match well, but the "conversion", i.e. the conditional luminosity function (CLF) can be well constrained by theory and observations. Clustering in dependance of mass also comes in here. He assumes this CLF to have a Schechter-form and one outcome is that the luminosity per halo mass is not linear at all.
Once having the CLF you can use it to derive other properties. For example that the most light comes from halos of round 10^12 solar masses, or that the halo-distribution of L-star galaxies can have a quite wide distribution in halo mass.