  X-ray observations of galaxy groups and clusters are inconsistent with the
predictions of the simplest hierarchical clustering models, wherein
non-baryonic and baryonic components are assembled together under the sole
influence of gravity. These departures are in the sense that the intergalactic
medium is hotter and more extended than expected, and become increasingly
strong for less massive systems. I model these effects by constructing baseline
sequences of hydrostatic polytropic models normalized to observations of
high-temperature clusters and numerical simulations, and then transforming them
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
gravitational) mass-temperature and entropy-temperature relations. The required
amount of energy injection is consistent with constraints on the number of
supernovae needed to account for observed intracluster silicon abundances,
provided that energy injection is centrally concentrated. I argue that most of
the heating occurred during or after the assembly of the cluster, and not
exclusively in pre-collapse proto-cluster fragments.
