Hot gas in clusters of galaxies: the punctuated equilibria model

We develop our model of 'punctuated equilibria' for the hot intracluster gas emitting powerful X-rays. The model considers the gravitational potential wells set by the dark matter as they evolve by hierarchical clustering and engulf outer gas; it assumes that the gas readjusts to a new hydrostatic equilibrium after each merging event. Before merging the gas is heated at the virial temperature when bound in subclusters; at early z it is pre-heated by supernova activity following star formation. In detail, we compute analytically the following steps: the dynamic histories of dark matter haloes with their merging events; the associated infall of gas into a halo, with compressions and shocks establishing the conditions at the cluster boundary; the updated disposition of the gas in the potential well, matching such conditions; and the statistical convolution of observable quantities over the merging histories. For individual objects from groups to clusters, the model yields profiles of density and surface brightness with no free parameters; in particular, the so-called beta parameter is itself an outcome of the model, and the polytropic index gamma is internally constrained to a narrow range. We obtain mildly declining temperature profiles, and profiles for the density and for the surface brightness shallower in groups compared with clusters; our model groups also contain a lower baryonic fraction on average, but with a scatter considerably larger. We present various key quantities over the whole range from groups to clusters. In particular, we predict in different cosmologies the statistical correlation L-T of X-ray luminosity with temperature; similarly, we derive the correlation R-X-T for the size of the X-ray emitting region. The intrinsic scatter in both correlations is also predicted.