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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 1014 M⊙, estimates of the total feedback energy, (1-3) x 1063 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 involving 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. [ABSTRACT FROM AUTHOR]

The origin of the bimodality in cluster core entropy is still unknown. At the same time, recent work has shown that thermal conduction in clusters is likely a time-variable phenomenon. We consider if time-variable conduction and active galactic nuclei (AGN) outbursts could be responsible for the cool-core (CC), non-cool-core (NCC) dichotomy. We show that strong AGN heating can bring a CC cluster to an NCC state, which can be stably maintained by conductive heating from the cluster outskirts. On the other hand, if conduction is shut off by the heat-flux-driven buoyancy instability, then the cluster will cool to the CC state again, where it is stabilized by low-level AGN heating. Thus, the cluster cycles between CC and NCC states. In contrast with massive clusters, we predict the CC/NCC bimodality should vanish in groups, due to the lesser role of conductive heating there. We find tentative support from the distribution of central entropy in groups, though firm conclusions require a larger sample carefully controlled for selection effects. [ABSTRACT FROM AUTHOR]