Velocity dispersions of CNOC clusters and the evolution of the cluster abundance

We present the results of the analysis of the internal velocity dispersions , sigma(upsilon), for the sample of 16 distant galaxy clusters (0.17 less t han or similar to z less than or similar to 0.55) provided by the Canadian Network for Observational Cosmology (CNOC). Different sigma(upsilon) estima tes are provided, all based on an interloper-removal algorithm that is diff erent from that originally applied by Carlberg et al. We find that all such methods provide sigma(upsilon) estimates that are consistent within less t han 10% among themselves and with the original estimates provided by the CN OC collaboration. This result points in favor of a substantial robustness o f currently applied methods for optical studies of the internal cluster dyn amics. The resulting distribution of velocity dispersions is used to trace the redshift evolution of the cluster abundance with the aim of constrainin g the matter density parameter, Omega(m). We find that constrains on Omega( m) are very sensitive to the adopted value of <(sigma)over tilde>(8) = sigm a(8)Omega(m)(alpha) (alpha similar or equal to 0.4-0.5), as constrained by the local cluster abundance. We find that, as <(sigma)over tilde>(8) varies from 0.5 to 0.6, the best fitting density parameter varies in the range 0. 3 less than or similar to Omega(m) less than or similar to 1.0. A further s ource of uncertainty in constraining Omega(m) is the uncertainties in the c orrection for the sigma(upsilon)-incompleteness of the CNOC sample. This ca lls attention to the need to better understand the constraints of local clu ster abundance and to increase the statistics of distant clusters in order to suppress the systematics related to the sample completeness criteria.