The baseline intracluster entropy profile from gravitational structure   formation
  The radial entropy profile of the hot gas in clusters of galaxies tends to follow a power law in radius outside of the cluster core. Here we present a simple formula giving both the normalization and slope for the power-law entropy profiles of clusters that form in the absence of non-gravitational processes such as radiative cooling and subsequent feedback. It is based on seventy-one clusters drawn from four separate cosmological simulations, two using smoothed-particle hydrodynamics (SPH) and two using adaptive-mesh refinement (AMR), and can be used as a baseline for assessing the impact of non-gravitational processes on the intracluster medium outside of cluster cores. All the simulations produce clusters with self-similar structure in which the normalization of the entropy profile scales linearly with cluster temperature, and these profiles are in excellent agreement outside of 0.2 r_200. Because the observed entropy profiles of clusters do not scale linearly with temperature, our models confirm that non-gravitational processes are necessary to break the self-similarity seen in the simulations. However, the core entropy levels found by the two codes used here significantly differ, with the AMR code producing nearly twice as much entropy at the centre of a cluster. 
G. Mark Voit, Scott T. Kay, and Greg L. Bryan