Galaxy Clusters: New Insights into the beta Problem

Previous comparisons between optical and X-ray observations of galaxy clusters have led to the Beta problem. This problem results from the non-observed equality between two different measures of the ratio between galaxy and gas specific energies (here Beta(spec)and Beta(fit)), as expected on the assumption that galaxies and gas are in dynamical equilibrium within the cluster potential. The value of Beta(spec) is determined directly from observations of cluster-galaxy velocity dispersion and intracluster gas temperature. The value of Beta(fit) is expressed as a function of geometrical quantities which are obtained by fitting galaxy and gas distributions and its precise formulation depends on some additional hypotheses. The discrepancy between Beta(spec) and Beta(fit) was recently claimed to disappear when less restrictive hypotheses are considered. However, the question is not completely clarified for some individual clusters (e.g. Perseus). Here, we propose a re-formulation of the value of Beta(fit) relaxing two of the usual hypotheses: the isothermal behaviour of the galaxy distribution and the negligibility of galaxy velocity anisotropy. The advantage of our formulation is to be totally independent of the value of velocity anisotropy. In the case of Perseus cluster we solve the beta problem. Moreover, by assuming average parameters for galaxy clusters, we obtain Beta(fit) about 1 as expected in the theory of cluster violent relaxation.