2005ApJ...632..809C

This paper describes how active galactic nuclei can heat galaxy-cluster plasmas by driving convection in the intracluster medium. A model is proposed in which a central supermassive black hole accretes intracluster plasma at the Bondi rate M{dot}_Bondiand powers a radio source. The central radio source produces cosmic rays, which mix into the thermal plasma. The cosmic-ray luminosity L_cris ∝M{dot}_Bondic². The cosmic-ray pressure gradient drives convection, which causes plasma heating. It is assumed that plasma heating balances radiative cooling. The plasma heating rate is self-regulating because M{dot}_Bondiis a decreasing function of the specific entropy near the cluster center s₀; if heating exceeds cooling, then s₀ increases, M{dot}_Bondiand L_crdecrease, and the convective heating rate is reduced. This paper focuses on the role of intracluster magnetic fields, which affect convection by causing heat and cosmic rays to diffuse primarily along magnetic field lines. A new stability criterion is derived for convection in a thermal-plasma/cosmic-ray fluid, and equations for the average fluid properties in a convective cluster are obtained with the use of a nonlocal two-fluid mixing-length theory. Numerical solutions of the model equations compare reasonably well with observations without requiring fine-tuning of the model parameters.