Velocity Dispersions of CNOC Clusters and the Evolution of the Cluster Abundance

We present the results of the analysis of the internal velocity dispersions, σ_v, for the sample of 16 distant galaxy clusters (0.17 ≲ z ≲ 0.55) provided by the Canadian Network for Observational Cosmology (CNOC). Different σ_v estimates are provided, all based on an interloper-removal algorithm that is different from that originally applied by Carlberg et al. We find that all such methods provide σ_v estimates that are consistent within less than 10% among themselves and with the original estimates provided by the CNOC collaboration. This result points in favor of a substantial robustness of currently applied methods for optical studies of the internal cluster dynamics. The resulting distribution of velocity dispersions is used to trace the redshift evolution of the cluster abundance with the aim of constraining the matter density parameter, Ω_m. We find that constrains on Ω_m are very sensitive to the adopted value of ₈ = σ₈Ω (α ≃ 0.4-0.5), as constrained by the local cluster abundance. We find that, as ₈ varies from 0.5 to 0.6, the best fitting density parameter varies in the range 0.3 ≲ Ω_m ≲ 1.0. A further source of uncertainty in constraining Ω_m is the uncertainties in the correction for the σ_v-incompleteness of the CNOC sample. This calls attention to the need to better understand the constraints of local cluster abundance and to increase the statistics of distant clusters in order to suppress the systematics related to the sample completeness criteria.