THE KINEMATICS OF DENSE CLUSTERS OF GALAXIES .2. THE DISTRIBUTION OF VELOCITY DISPERSIONS

From the survey of 31 Abell R greater-than-or-equal-to 1 cluster fields within 0.02 less-than-or-equal-to z less-than-or-equal-to 0.05 [Zabludoff et al., AJ, 106, 1273 (1993)] we extract 25 dense clusters with velocity dispersions sigma > 300 km s-1 and with number densities exceeding the mean for the Great Wall of galaxies [Geller & Huchra, Science, 246, 897, (1989)] by one deviation. From the CfA Redshift Survey (Huchra et al. 1993, in preparation), we obtain an approximately volume-limited catalog of 31 groups with velocity dispersions > 100 km s-1 and with the same number density limit. We combine these well-defined samples to obtain the distribution of cluster velocity dispersions. The group sample enables us to correct for incompleteness in the Abell catalog at low velocity dispersions. The clusters from the Abell cluster fields populate the high dispersion tail. For systems with velocity dispersions > 700 km s-1 approximately the median for R = 1 clusters [Zabludoff et al., ApJS, 74, 1 (1990)], the group and cluster abundances are consistent. The cumulative distributions of dispersions for clusters with or > 700 km s-1 and for groups are exponential laws of the form is-proportional-to 10-nsigma, n approximately 0.0015. The combined distribution is consistent with cluster x-ray temperature functions [Edge et al, MNRAS, 245, 559 (1990), and Henry & Arnaud, ApJ, 372, 410 (1991)].