Convection in galaxy cluster plasmas driven by active galactic nuclei and cosmic ray buoyancy

Turbulent heating may play an important role in galaxy-cluster plasmas, but if turbulent heating is to balance radiative cooling in a quasi-steady state, some mechanism must regulate the turbulent velocity so that it is neither too large nor too small. This paper explores one possible regulating mechanism associated with an active galactic nucleus at cluster center. A steady-state model for the intracluster medium is presented in which radiative cooling is balanced by a combination of turbulent heating and thermal conduction. The turbulence is generated by convection driven by the buoyancy of cosmic rays produced by a central radio source. The cosmic-ray luminosity is powered by the accretion of intracluster plasma onto a central black hole. The model makes the rather extreme assumption that the cosmic rays and thermal plasma are completely mixed. Although the intracluster medium is convectively unstable near cluster center in the model solutions, the specific entropy of the thermal plasma still increases outwards because of the cosmic-ray modification to the stability criterion. The model provides a self-consistent calculation of the turbulent velocity as a function of position, but fails to reproduce the steep central density profiles observed in clusters. The principal difficulty is that in order for the fully mixed intracluster medium to become convectively unstable, the cosmic-ray pressure must become comparable to or greater than the thermal pressure within the convective region. The large cosmic-ray pressure gradient then provides much of the support against gravity, reducing the thermal pressure gradient near cluster center and decreasing the central plasma density gradient. A more realistic AGN-feedback model of intracluster turbulence in which relativistic and thermal plasmas are only partially mixed may have greater success.