The total feedback energy injected into hot gas in galaxy clusters by central black holes can be estimated by comparing the potential energy of observed cluster gas profiles with the potential energy of non-radiating, feedback-free hot gas atmospheres resulting from gravitational collapse in clusters of the same total mass. Feedback energy from cluster-centered black holes expands the cluster gas, lowering the gas-to-dark-matter mass ratio below the cosmic value. Feedback energy is unnecessarily delivered by radio-emitting jets to distant gas far beyond the cooling radius where the cooling time equals the cluster lifetime. For clusters of mass (4-11) x 10{sup 14} M{sub sun}, estimates of the total feedback energy, (1-3) x 10{sup 63} erg, far exceed feedback energies estimated from observations of X-ray cavities and shocks in the cluster gas, energies gained from supernovae, and energies lost from cluster gas by radiation. The time-averaged mean feedback luminosity is comparable to those of powerful quasars, implying that some significant fraction of this energy may arise from the spin of the black hole. The universal entropy profile in feedback-free gaseous atmospheres in Navarro-Frenk-White cluster halos can be recovered by multiplying the observed gas entropy profile of any relaxed cluster by a factor involvingmore » the gas fraction profile. While the feedback energy and associated mass outflow in the clusters we consider far exceed that necessary to stop cooling inflow, the time-averaged mass outflow at the cooling radius almost exactly balances the mass that cools within this radius, an essential condition to shut down cluster cooling flows.« less

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