On the prevalence of R exp -3 density profiles in extragalactic systems

Abstract

If the galaxy velocity dispersion in a cluster of galaxies is constant, the cluster is in hydrostatic equilibrium, and it has a dark-matter component, then virial considerations reveal the average logarithmic slope of the galaxy distribution profile to be -3. This applies both to isotropic and (constant) anisotropic galaxy velocity distributions. Maximum-entropy considerations indicate that hydrostatic equilibrium is most likely to be manifested in connection with a flat dispersion curve. Combined with logarithmic potential, whose preferred status has theoretical and observational support, an r exp (-2.9 + or - 0.1) profile is enforced for the galaxy spatial distribution. Since constant velocity dispersion and the logarithmic potential are a likely combination in stationary systems, approximately r exp -3 galaxy density profiles should be prevalent in clusters, as is indeed observed. 35 refs.