A Faber-Jackson relation for clusters of galaxies: Implications for modified dynamics

In a sample of 20 rich clusters of galaxies, the mass of the hot X-ray emitting gas is correlated with the square of the gas temperature. Because the hot intra-cluster gas comprises most of the baryonic mass in rich clusters, this correlation implies a mass-velocity dispersion relation of the form seen in elliptical galaxies- the Faber-Jackson relation. Indeed, within the errors and uncertainty in the Hubble parameter, clusters appear to lie on the high mass extention of the Faber-Jackson relation for ellipticals. Although this result is difficult to understand in terms of conventional scenarios for structure formation, it is a direct consequence of Milgrom's modified dynamics (MOND). Applying Milgrom's mass temperature relation for isothermal spheres to this sample of clusters, one finds agreement between the predicted and observed gas masses to within a factor of two.