The Cluster Gas Mass - Temperature Relation: Evidence for a High Level   of Preheating
  Recent X-ray observations have been used to demonstrate that the cluster gas mass-temperature relation is steeper than theoretical self-similar predictions drawn from numerical simulations that consider the evolution of the cluster gas through the effects of gravity and shock heating alone. One possible explanation for this is that the gas mass fraction is not constant across clusters of different temperature, as is usually assumed. Observationally, however, there is no compelling evidence for gas mass fraction variation, especially in the case of hot clusters. Seeking an alternative physical explanation for the observed trends, we investigate the role in the cluster gas mass - temperature relation of the preheating of the intracluster medium by some arbitrary source for clusters with emission-weighted mean temperatures of greater than about 3 keV. Making use of the physically-motivated, analytic models developed in 2002 by Babul and coworkers, we find that preheating does, indeed, lead to a steeper relation. This is in agreement with previous theoretical studies on the relation. However, in apparent conflict with these studies, we argue that a ``high'' level of entropy injection is required to match observations. In particular, an entropy floor of greater than about 300 keV cm^2 is required. We also present a new test, namely, the study of the relation within different fixed radii. This allows one to indirectly probe the density profiles of clusters, since it samples different fractions of the virial radius for clusters of different temperature. This test also confirms that a high level of preheating is required to match observations. 
Ian G. McCarthy (1), Arif Babul (1), Michael L. Balogh (2) ((1)   University of Victoria, (2) University of Durham)