The SZ effect as a probe of non-gravitational entropy in groups and clusters of galaxies

We investigate how strongly and at what scales the Sunyaev-Zel'dovich effect reflects the shifting balance between two processes that compete for governing the density and the thermodynamic state of the hot intracluster medium (ICM) pervading clusters and groups of galaxies. One such process is the hierarchical clustering of the dark matter; this induces gravitational heating of the diffuse baryons, and strives to push not only the galaxy systems but also the ICM they contain toward self-similarity. Away from it drives the other process, constituted by non-gravitational energy fed back into the ICM by the condensing baryons. We base our analysis on a semi-analytic model of galaxy formation and clustering to describe how the baryons are partitioned among the hot, the cool and the stellar phases; the partition shifts as the galaxies cluster hierarchically, and as feedback processes (here we focus on stellar winds and supernova explosions) follow the star formation. Such processes provide a moderate feedback, whose impact is amplified by the same large-scale accretion shocks that thermalize the gravitational energy of gas falling into the growing potential wells. We use the model to compute the Compton parameter y, and to predict how this is affected by the feedback; for individual clusters or groups we find a relation of y with the ICM temperature, the y - T relation. which departs from the form suggested by the self-similar scaling, and bends down at temperatures typical of galaxy groups. We also compute the average (y) and the source counts as a function of y under different assumptions concerning feedback strength and cosmology/cosmogony. We then discuss to what extent our results are generic of the hierarchical models of galaxy formation and clustering; we show how the y - T relation, to be measured at microwave or submillimetre wavelengths, is model-independently related to the shape of the L - T correlation measured in X-rays. We conclude that these observables together - because of their complementarity and their observational independence - can firmly bound the processes responsible for non-gravitational entropy injections into the ICM.