On estimating the kinetic energies of clusters of galaxies

The extent to which a kinetic energy estimate would be affected by a possible mass dependence of the velocity dispersion of galaxies in clusters is considered. It is shown that, while the replacement of the true kinetic energy T by the separately defined T-prime leads to an overestimation of kinetic energy by a factor that is greater than unity for the case of a negative correlation between velocity dispersion and mass, the kinetic energy may in practice be underestimated due to the velocity dispersion obtained from galaxies of the highest mass luminosity. The coefficient corresponding to this latter case is determined for various mass distribution functions and under the assumption of kinetic energy equipartition.