Gas Density and X‐Ray Surface Brightness Profiles of Clusters of Galaxies from Dark Matter Halo Potentials: Beyond the Isothermal β‐Model

We describe a theoretical framework to compute the cluster gas distribution in hydrostatic equilibrium embedded in a class of spherical dark matter halo potentials. Unlike the conventional isothermal b-model, the present method provides a physical basis to directly probe the shape of the dark matter halo from the observed X-ray surface brightness and temperature proles of clusters of galaxies. Specically, we examine the extent to which the resulting gas density and X-ray surface brightness proles are sensitive to the inner slope of the dark matter halo density and other more realistic e ects, including the self-gravity of the gas and the polytropic equation of state. We also discuss a practical strategy to apply the present methodology to the actual cluster proles from future X-ray observations.