THE INTRINSIC SHAPE OF CLUSTERS OF GALAXIES - CORRELATIONS AMONG FLATTENING, RICHNESS, AND VELOCITY DISPERSION

We examine relations between shape, richness, and velocity dispersion for a sample of 350 clusters of galaxies of all morphologies, including those with visible substructure. For our sample the apparent shape of clusters is correlated with velocity dispersion and Abell [ApJS, 3, 211. (1958)] richness in the sense that poor, low dispersion clusters are flatter in the mean than their richer, Higher dispersion counterparts. These characteristics are also exhibited by the x-ray emitting gas. There are virtually no highly flattened clusters having high richness or high velocity dispersions in the sample. We find that the variation of richness and velocity dispersion with apparent shape is too steep to be assigned to projection effects, and conclude rich, high dispersion clusters are intrinsically more nearly spherical than poorer clusters and that two-body relaxation is probably not an effective anisotropy damping mechanism in Abell clusters.