2007ApJ...657..183R

We present a new determination of the cluster mass function and velocity dispersion function in a volume ∼10⁷ h³/Mpc3 using data from the Fourth Data Release of the Sloan Digital Sky Survey (SDSS) to determine virial masses. We use the caustic technique to remove foreground and background galaxies. The cluster virial mass function agrees well with recent estimates from both X-ray observations and cluster richnesses. Our determination of the mass function lies between those predicted by the 1 and 3 year WMAP data. We constrain the cosmological parameters Ω_mand σ₈ and find good agreement with WMAP and constraints from other techniques. With the CIRS mass function alone, we estimate Ω_m=0.24^+0.14_–0.09 and σ₈=0.92^+0.24_–0.19, or σ₈=0.84±0.03 when holding Ω_m=0.3 fixed. We also use the WMAP parameters as priors and constrain velocity segregation in clusters. Using the 1 and 3 year results, we infer velocity segregation of σ_gxy/σ_DM~0.94±0.05 or 1.28±0.06, respectively. The good agreement of various estimates of the cluster mass function shows that it is a useful independent constraint on estimates of cosmological parameters. We compare the velocity dispersion function of clusters to that of early-type galaxies and conclude that clusters comprise the high-velocity end of the velocity dispersion function of dark matter halos. Future studies of galaxy groups are needed to study the transition between dark matter halos containing individual galaxies and those containing systems of galaxies. The evolution of cluster abundances provides constraints on dark energy models; the mass function presented here offers an important low-redshift calibration benchmark.