2007ApJ...671.1413C

A number of studies have shown that the convective stability criterion for the intracluster medium (ICM) is very different from the Schwarzchild criterion, due to the effects of anisotropic thermal conduction and cosmic rays. Building on these studies, we develop a model of the ICM in which a central active galactic nucleus (AGN) accretes hot intracluster plasma at the Bondi rate and produces cosmic rays that cause the ICM to become convectively unstable. The resulting convection heats the intracluster plasma and regulates its temperature and density profiles. By adjusting a single parameter in the model (the size of the cosmic-ray acceleration region), we are able to achieve a good match to the observed density and temperature profiles in a sample of eight clusters. Our results suggest that convection is an important process in cluster cores. An interesting feature of our solutions is that the cooling rate is more sharply peaked about the cluster center than is the convective heating rate. As a result, in several of the clusters in our sample, a compact cooling flow arises in the central region with a size r_cf that is typically a few kpc. The cooling flow matches onto a Bondi flow at smaller radii. The mass accretion rate in the Bondi flow is equal to, and controlled by, the rate at which mass flows in through the cooling flow. Our solutions suggest that the AGN regulates the mass accretion rate in these clusters by controlling r_cf: if the AGN power rises above the equilibrium level, r_cfdecreases, the mass accretion rate drops, and the AGN power drops back down to the equilibrium level.