Radial density and temperature profiles of the intracluster gas   constructed jointly from the X-ray surface brightness measurement and the   universal density profile
  In this paper we have made an attempt to derive the radial profiles of density and temperature of intracluster gas based on the two well-established facts at present: the X-ray observed surface brightness of clusters described by the standard beta model and the (NFW) universal density profile as the underlying dark matter distribution. We have numerically solved the hydrostatic equation by demanding that the volumed-averaged baryon fraction of a cluster should asymptotically approach the universal value at its viral radius. We have shown that the radial temperature variation derived from these constraints differs significantly from the conventional polytropic equation of state: The gas temperature profile may show a dramatic increase or decrease with outward radius, depending sensitively on the beta parameter. A large beta value (typically greater than 0.8) is required in order to ensure that the X-ray temperature makes a drop at the virial radius. This indicates that either the NFW profile is inappropriate to apply for the overall dark matter distribution of clusters or other non-gravitational heating processes may play an important role in the dynamical evolution of clusters. 
Xiang-Ping Wu and Tzihong Chiueh