  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.
