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 the two processes that compete for governing the density and the thermodynamic state of the hot intra-cluster medium pervading clusters and groups of galaxies: the hierarchical clustering of the DM; the non-gravitational energy and momentum fed back into the ICM by the condensing baryons. We base on a SAM of galaxy formation and clustering to describe how the baryons are partitioned among the hot, the cool and the stellar phase; the partition shifts as the galaxies cluster hierarchically, and as the feedback by stellar winds and SN explosions follows the star formation. Their impact is amplified by the same large scale accretion shocks that thermalize the gravitational energy of gas falling into the growing potential wells. We compute the Compton parameter $y$, and find a relation of $y$ with the ICM temperature, the $y-T$ relation, which departs from the self-similar scaling and bends down at temperatures typical of galaxy groups. We model-independently relate this with the analogous behaviour of the L_x - T relation, and discuss to what extent our results are generic of the hierarchical models of galaxy formation and clustering.