  We introduce an analytic model of the diffuse intergalactic medium in galaxy
clusters based on a polytropic equation of state for the gas in hydrostatic
equilibrium with the cluster gravitational potential. This model is directly
applicable to the analysis of X-ray and Sunyaev-Zeldovich Effect observations
from the cluster core to the virial radius, with 5 global parameters and 3
parameters describing the cluster core. We validate the model using Chandra
X-ray observations of two polytropic clusters, MS 1137.5+6625 and CL
J1226.9+3332, and two cool core clusters, Abell 1835 and Abell 2204. We show
that the model accurately describes the spatially resolved spectroscopic and
imaging data, including the cluster core region where significant cooling of
the plasma is observed.
