Entropy generation in merging galaxy clusters

This conference has seen much discussion about non-gravitational heating of the intracluster medium, as required to reduce cooling rates and central densities sufficiently to explain the observed properties of galaxy clusters. The amount of energy input required is often computed by comparing to the entropy profile that would be expected from gravitational processes alone, as determined, for example, from cosmological simulations. Indeed, observations of relaxed clusters show that, except for the innermost regions, their entropy profiles follow a power-law profile that scales self-similarly with the cluster mass (e.g. McCarthy et al., 2004, 2005; Voit et al., 2005). However, the origin of this default entropy profile and apparent selfsimilarity is not really understood in detail. Models of smooth, spherical accretion are able to reproduce the power-law slope of the entropy gradient (e.g. Cavaliere et al., 1998; Abadi et al., 2000; Tozzi & Norman, 2001; Dos Santos & Doré, 2002), but the normalization is very sensitive to the initial gas density distribution. In particular, if accretion is lumpy rather than smooth (as expected in a universe dominated by cold dark matter), insufficient entropy is generated to explain the observations (Voit et al., 2003). If there is such a strong dependence on initial density, it is unclear why (or if) numerical simulations with different resolutions (and hence smoothing scales) and implementations (e.g. Eularian or Lagrangian) are able to produce self-similar clusters. The source of this puzzle is illuminated by writing the equation of hydrostatic equilibrium as 1