THE DISTRIBUTION OF MASS AND GAS IN THE CENTER OF CLUSTERS OF GALAXIES IMPLIED BY X-RAY AND LENSING OBSERVATIONS

Observations of gravitational lensing indicate that the mass distribution in clusters of galaxies (where most of the mass is dark matter) is highly peaked toward the center, while X-ray observations imply that the gas is more extended near the center. At the same time, the short cooling times for the gas and the observed X-ray spectra have demonstrated that the gas is cooling in these central regions; this fact has often led one to expect that the gas temperature should be lower near the center, and therefore the gas should be more concentrated than the dark matter. We show that, for the mass profiles that are implied by gravitational lensing, the gas temperature must remain approximately constant within the cooling region in order to have consistency with the observed X-ray profiles. The gas temperature must also be similar to the galaxy velocity dispersion, since the profiles of the galaxies and the gas at large radius are similar. This is a consequence of hydrostatic equilibrium and is independent of cooling flow models. We then find that a multiphase cooling flow naturally produces an approximately constant temperature profile and a more extended distribution for the gas compared to the mass. Cool phases are deposited at relatively large radius, while hot phases are adiabatically heated as they flow inward and can keep the average temperature constant. Thus, cooling hows result in an increase of the central temperature, relative to a case where there is no cooling and the gas follows the mass distribution. The total mass deposition rates are determined primarily by the emissivity profile and the temperature at the cooling radius. They are also more sensitive to the assumed cluster age than in previous models, which assumed much more extended mass profiles. The increased central temperatures caused by cooling flows give a characteristic core radius to the gas profiles, which is of order the cooling radius. This provides a natural explanation for the typical cores observed in X-ray clusters. It also changes the rate of cluster evolution expected in self-similar hierarchical models, since cooling occurred over a larger fraction of the gaseous halos in the past. We show that the inclusion of the effects of cooling flows predicts negative evolution for the high-luminosity clusters if n less than or similar to -0.5, as is observed, but positive evolution for clusters of low luminosity. Some clusters are observed to have anomalously large core radii; we propose that these are in the process of merging and are not in dynamical equilibrium.