2011ApJ...740...28V

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 active galactic nucleus (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.