Cluster Richness as a measure of cluster mass

Because of sensitivity and wide sky coverage (e.g., SDSS) galaxy clusters are most easily detected optically as an overdensity in galaxies on the scale of ~ Mpc. Here (http://arxiv.org/abs/0709.1159) is a good paper that goes through the details of calibrating richness (N_200, number of early type galaxies larger than a threshold luminosity) with mass measured from weak lensing shear profiles. They bin their ~ 13,000 clusters using 12 bins in N_200 (total luminosity of elliptical galaxies can also be used) and for each bin they obtain average weak lensing shear profiles which they convert into matter density profile and enclosed mass profile and obtain R_200. They find a rather tight correlation between N_200 and M_200, and argue that richness can be used as a good mass proxy (Fig. 11). They have to account for several mass contributions, e.g., the mass profile of the central bright galaxy, miscentered halo component (if cluster DM is not centered on the central bright galaxy) , neighboring halos, etc. They find that NFW is a good fit to the DM density profile. The concentration-mass relation they obtain is also consistent with simulations. They find that their best fit BCG mass is correlated with M_200 (Fig. 14). Its still a puzzle then why the SZ signal predicted by M_200-N_200 relation is larger than what is observed!