Equilibrium Models of Galaxy Clusters with Cooling, Heating and Conduction

It is generally argued that most clusters of galaxies host cooling flows in which radiative cooling in the centre causes a slow inflow. However, recent observations by Chandra and XMM conflict with the predicted cooling flow rates. Amongst other mechanisms, heating by a central active galactic nucleus and thermal conduction have been invoked in order to account for the small mass deposition rates. Here, we present a family of hydrostatic models for the intra-cluster medium where radiative losses are exactly balanced by thermal conduction and heating by a central source. We describe the features of this simple model and fit its parameters to the density and temperature profiles of Hydra A.