Gas density and X-ray surface brightness profiles of clusters of galaxies from dark matter halo potentials: beyond the isothermal beta 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 $beta$-model, the present method provides a physical basis to directly probe the shape of dark matter halo from the observed X-ray surface brightness and temperature profiles of clusters of galaxies. Specifically, we examine the extent to which the resulting gas density and X-ray surface brightness profiles are sensitive to the inner slope of the dark matter halo density and other more realistic effects 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 profiles from future X-ray observations.