The Virial Mass Function of Nearby SDSS Galaxy Clusters

We present a new determination of the cluster mass function and velocitydispersion function in a volume $\sim10^7 h^3$Mpc$^{-3}$ using the Fourth DataRelease of the Sloan Digital Sky Survey (SDSS). We use the caustic technique toremove foreground and background galaxies. The cluster virial mass functionagrees well with recent estimates from both X-ray observations and clusterrichnesses. The mass function lies between those predicted by the First-Yearand Three-Year WMAP data. We constrain the cosmological parameters $\Omega_m$and $\sigma_8$ and find good agreement with WMAP and constraints from othertechniques. 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 WMAPparameters as priors and constrain velocity segregation in clusters. Using theFirst 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. Wecompare the velocity dispersion function of clusters to that of early-typegalaxies and conclude that clusters comprise the high-velocity end of thevelocity dispersion function of dark matter haloes. The evolution of clusterabundances provides constraints on dark energy models; the mass functionpresented here offers an important low redshift calibration benchmark.Comment: 22 pages, 11 figures, ApJ in press, revised figure