Empirical Properties of the Mass Discrepancy in Groups and Clusters of Galaxies

Abstract

Data compiled by de Vaucouleurs are used to derive dynamical parameters of nearby groups and clusters of galaxies. It is found that the mass ratio MvT/M (ratio of virial-theorem mass to that derived by summing the masses of individual galaxies) is significantly correlated with both radius and velocity dispersion. Radius versus velocity dispersion gives only a marginal correlation. Analysis of supplementary data by Karachentsev corroborates these results. The ratio of the largest to smallest line-of-sight velocity of galaxies assigned to a group is nearly independent of their difference in apparent magnitudes. This and other tests suggest that contamination of groups by nonmembers is insignificant. If the groups are unstable, then the velocity-radius diagram suggests that the groups commenced hyperbolic expansion at a variety of epochs. If the groups are stabilized by hidden mass, then the empirical results imply that the fraction of hidden material increases with increasing radius (decreasing density) and increasing velocity dispersion.