Estimate of the total mechanical feedback energy from galaxy
  cluster-centered black holes: implications for black hole evolution, cluster
  gas fraction and entropy
  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 10^14 Msun estimates of the total
feedback energy, 1-3 X 10^63 ergs, 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 NFW 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.
