Heating of intergalactic gas and cluster scaling relations

X-ray observations of galaxy groups and clusters are inconsistent with the predictions of the simplest hierarchical clustering models, wherein nonbary onic and baryonic components are assembled together under the sole influenc e of gravity. These departures are in the sense that the intergalactic medi um is hotter and more extended than expected, and become increasingly stron g for less massive systems. I model these effects by constructing baseline sequences of hydrostatic polytropic models normalized to observations of hi gh-temperature clusters and numerical simulations, and then transforming th em by adding proscribed amounts of heat per particle at the cluster center. I present sequences with a universal value of this heating parameter that simultaneously reproduce recently published observed (gas and total gravita tional) mass-temperature and entropy-temperature relations. The required am ount of energy injection is consistent with constraints on the number of su pernovae needed to account for observed intracluster silicon abundances, pr ovided that energy injection is centrally concentrated. I argue that most o f the heating occurred during or after the assembly of the cluster, and not exclusively in precollapse proto-cluster fragments.