High resolution X-ray spectroscopy of the hot gas in galaxy clusters has shown that the gas is not cooling to low temperatures at the predicted rates of hundreds to thousands of solar masses per year. X-ray images have revealed giant cavities and shock fronts in the hot gas that provide a direct and relatively reliable means of measuring the energy injected into hot atmospheres by active galactic nuclei (AGN). Average radio jet powers are near those required to offset radiative losses and to suppress cooling in isolated giant elliptical galaxies, and in larger systems up to the richest galaxy clusters. This coincidence suggests that heating and cooling are coupled by feedback, which suppresses star formation and the growth of luminous galaxies. How jet energy is converted to heat and the degree to which other heating mechanisms are contributing, eg. thermal conduction, are not well understood. Outburst energies require substantial late growth of supermassive black holes. Unless all of the approximately 10E62 erg required to suppress star formation is deposited in the cooling regions of clusters, AGN outbursts must alter large-scale properties of the intracluster medium.
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