The Virial Mass Function of Nearby SDSS Galaxy Clusters

We present a new determination of the cluster mass function and velocity dispersion function in a volume $\sim10^7 h^3$Mpc$^{-3}$ using the Fourth Data Release of the Sloan Digital Sky Survey (SDSS). 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. The mass function lies between those predicted by the First-Year and Three-Year WMAP data. We constrain the cosmological parameters $\Omega_m$ and $\sigma_8$ and find good agreement with WMAP and constraints from other techniques. With the CIRS mass function alone, we estimate $\Omega_m=0.24^{+0.14}_{-0.09}$ and $\sigma_8=0.92^{+0.24}_{-0.19}$, or $\sigma_8=0.84\pm$0.03 when holding $\Omega_m=0.3$ fixed. We also use the WMAP parameters as priors and constrain velocity segregation in clusters. Using the First and Third-Year results, we infer velocity segregation of $\sigma_{gxy}/\sigma_{DM}\approx0.94\pm$0.05 or 1.28$\pm$0.06 respectively. 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 haloes. The evolution of cluster abundances provides constraints on dark energy models; the mass function presented here offers an important low redshift calibration benchmark.