We present a new determination of the cluster mass function and velocity dispersion function in a volume \sim 10 ^ { 7 } h ^ { 3 } Mpc ^ { -3 } 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 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 } \approx 0.94 \pm 0.05 or 1.28 \pm 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 haloes .
Future studies of galaxy groups are needed to study the transition between dark matter haloes containing individiual 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 .