Hot gas in clusters of galaxies: the punctuated equilibria model

We develop our model of 'punctuated equilibria' for the hot intracluster ga s 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 e quilibrium after each merging event. Before merging the gas is heated at th e 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 histori es of dark matter haloes with their merging events; the associated infall o f gas into a halo, with compressions and shocks establishing the conditions at the cluster boundary; the updated disposition of the gas in the potenti al well, matching such conditions; and the statistical convolution of obser vable quantities over the merging histories. For individual objects from groups to clusters, the model yields profiles o f density and surface brightness with no free parameters; in particular, th e so-called beta parameter is itself an outcome of the model, and the polyt ropic index gamma is internally constrained to a narrow range. We obtain mi ldly declining temperature profiles, and profiles for the density and for t he surface brightness shallower in groups compared with clusters; our model groups also contain a lower baryonic fraction on average, but with a scatt er considerably larger. We present various key quantities over the whole range from groups to clust ers. In particular, we predict in different cosmologies the statistical cor relation 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.