The ESO Nearby Abell Cluster Survey. II. The Distribution of Velocity\n Dispersions of Rich Galaxy Clusters

Summary - By combining the 5634 redshifts from the ESO Nearby Abell Cluster\nSurvey (the ENACS) with another 1000 redshifts from the literature we are able\nto study the distribution of velocity dispersions for a volume-limited sample\nof 128 $R_{\\rm ACO} \\geq 1$ clusters, out to a redshift $z=0.1$, in a solid\nangle of 2.55 sr centered on the South Galactic Pole. In deriving velocity\ndispersions we apply a new, physically motivated method for removing fore- and\nbackground galaxies. We discuss in detail the completeness of the cluster\nsample for which we derive the distribution of cluster velocity dispersions.\nThe large apparent spread between velocity dispersion and richness must be\nlargely intrinsic. A consequence of the very broad relation between richness\nand velocity dispersion is that all cluster samples complete in richness are\nbiased against low dispersions. For the richness limit of our sample this bias\noperates below about 800 km/sec. Above 800 km/s, our distribution of global\nvelocity dispersions is free from systematic errors and biases, and agrees very\nwell with the most recent determination of the distribution of cluster X-ray\ntemperatures. Therefore, we conclude that X-ray temperature and velocity\ndispersion distributions statistically measure the same cluster property. We\nstress the need for model predictions that produce exactly the same information\nas provided by the observations, for a sample of model clusters with a richness\nlimit that mimics that of the sample of observed clusters.\n