Convective Stability of Galaxy‐Cluster Plasmas

Abstract

Recent studies suggest that active galactic nuclei and cosmic rays drive convection in galaxy-cluster plasmas and that convection heats cluster cores and regulates the plasma temperature profile. In this paper, we investigate the convective stability of the intracluster medium. Previous work has described how magnetic fields modify the con-vective stability criterion by causing heat to diffuse primarily along magnetic field lines. We extend earlier analyses by including cosmic rays and cosmic-ray diffusion. We consider an equilibrium in which the gravitational acceleration is in the À-direction, the magnetic field is perpendicular tô z, and the magnetic pressure is much less than the thermal pres-sure. We use a local linear stability analysis to show that the convective stability criterion is nk B dT/dz þ dp cr /dz > 0, where n, T, and p cr are the plasma particle density, temperature, and cosmic-ray pressure, respectively. We also present approximate solutions to the dispersion relation and describe the different waves and instabilities present in the plasma. Because the stability criterion differs markedly from the Schwarzschild criterion, galaxy-cluster plasmas can be con-vective even though the specific entropy increases outward.