  The radial distributions of temperature, density, and gas entropy among
cool-core clusters tend to be quite similar, suggesting that they have entered
a quasi-steady state. If that state is regulated by a combination of thermal
conduction and feedback from a central AGN, then the characteristics of those
radial profiles ought to contain information about the spatial distribution of
AGN heat input and the relative importance of thermal conduction. This paper
addresses those topics by deriving steady-state solutions for clusters in which
radiative cooling, electron thermal conduction, and thermal feedback fueled by
accretion are all present, with the aim of interpreting the configurations of
cool-core clusters in terms of steady-state models. It finds that the core
configurations of many cool-core clusters have entropy levels just below those
of conductively balanced solutions in which magnetic fields have suppressed
electron thermal conduction to ~1/3 of the full Spitzer value, suggesting that
AGN feedback is triggered when conduction can no longer compensate for
radiative cooling. And even when feedback is necessary to heat the central ~30
kpc, conduction may still be the most important heating mechanism within a
cluster's central ~100 kpc.
