The observational distribution of internal velocity dispersions in nearby galaxy clusters

We analyze the internal velocity dispersion a of a sample of 172 nearby galaxy clusters (z less than or equal to 0.15), each of which has at least 30 available galaxy redshifts and spans a large richness range. Cluster membership selection is based on nonparametric methods. In the estimate of galaxy velocity dispersion, we consider the effects of possible velocity anisotropies in galaxy orbits, the infall of late-type galaxies, and velocity gradients. The dynamical uncertainties due to the presence of substructures are also taken into account. Previous a-distributions, based on smaller cluster samples, are complete for the Abell richness class R greater than or equal to 1. In order to improve sigma completeness, we enlarge our sample by also including poorer clusters. By resampling 153 Abell-Abell-Corwin-Olowin clusters, according to the richness class frequencies of the Edinburgh-Durham Cluster Catalog, we obtain a cluster sample which can be taken as representative of the nearby universe. Our cumulative sigma-distribution agrees with previous distributions within their sigma completeness limit (sigma greater than or similar to 800 km s(-1)). We estimate that our distribution is complete for at least sigma greater than or equal to 650 km s(-1). In this completeness range, a fit of the form dN proportional to sigma(alpha) d sigma gives alpha = -(7.4(-0.8)(+0.7)), in fair agreement with results coming from the X-ray temperature distributions of nearby clusters. We briefly discuss our results with respect to sigma-distributions for galaxy groups and to theories of large-scale structure formation.