Optical Radii of Galaxy Clusters

We analyze the density profiles and virial radii for a sample of 90 nearby clusters, using galaxies with available redshifts and positions. Each cluster has at least 20 redshifts measured within an Abell radius, and all the results come from galaxy sets of at least 20 members. Most of the density profiles of our clusters are well fitted by hydrostatic isothermal-like profiles. The slopes we find for many cluster density profiles are consistent with the hypothesis that the galaxies are in equilibrium with the binding cluster potential. The virial radii correlate with the core radii at a very high significance level. The observed relationship between the two sizes estimates is in agreement with the theoretical one computed by using the median values of the density profile parameters fitted on our clusters. After correcting for incompleteness in our cluster sample, we provide the universal distribution functions of core and virial radii (obtained within half an Abell radius).