The Velocity Dispersion--Temperature Correlation from a Limited Cluster Sample

Most studies of correlations between X-ray and optical properties of galaxy clusters have used the largest samples of data available, regardless of the morphological types of clusters included. Given the increasing evidence that morphology is related to a cluster's degree of dynamical evolution, we approach the study of X-ray and optical correlations differently. We evaluate the relationship between velocity dispersion and temperature for a limited set of galaxy clusters taken from Bird (1994) which all possess dominant central galaxies and which have been explicitly corrected for the presence of substructure. We find that σr ∝ T0.61±0.13 We use a Monte Carlo computer routine to estimate the significance of this deviation from the σr ∝ T0.5 relationship predicted by the virial theorem. We find that the simulated correlation is steeper than the observed value only 4% of the time, which suggests that the deviation is significant. The combination of protogalactic winds and dynamical friction reproduces nearly exactly the observed relationship between σr and T.