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 towards the center, while X-ray observations imply that the gas is more extended. The additional fact that the gas is cooling in the center 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 such expectation is not correct, and that the gas temperature must remain approximately constant within the cooling region in order to have consistency with the observed X-ray profiles and lenses. 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 inwards and can keep the average temperature constant. Thus, cooling flows result in an {\it increase} of the central temperature, relative to a case where there is no cooling and the gas follows the mass distribution. 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 brings into better agreement with observations the rate of cluster evolution expected in self-similar hierarchical models. We propose that clusters having core radii much larger than their cooling radii are in the process of merging and are not in dynamical equilibrium.