Using a linear stability analysis and two and three-dimensional nonlinear simulations , we study the physics of buoyancy instabilities in a combined thermal and relativistic ( cosmic ray ) plasma , motivated by the application to clusters of galaxies .
We argue that cosmic ray diffusion is likely to be slow compared to the buoyancy time on large length scales , so that cosmic rays are effectively adiabatic .
If the cosmic ray pressure p _ { cr } is \gtrsim 25 \% of the thermal pressure , and the cosmic ray entropy ( p _ { cr } / \rho ^ { 4 / 3 } ; \rho is the thermal plasma density ) decreases outwards , cosmic rays drive an adiabatic convective instability analogous to Schwarzschild convection in stars .
Global simulations of galaxy cluster cores show that this instability saturates by reducing the cosmic ray entropy gradient and driving efficient convection and turbulent mixing .
At larger radii in cluster cores , the thermal plasma is unstable to the heat flux-driven buoyancy instability ( HBI ) , a convective instability generated by anisotropic thermal conduction and a background conductive heat flux .
The HBI saturates by rearranging the magnetic field lines to become largely perpendicular to the local gravitational field ; the resulting turbulence also primarily mixes plasma in the perpendicular plane .
Cosmic-ray driven convection and the HBI may contribute to redistributing metals produced by Type 1a supernovae in clusters .
Our calculations demonstrate that adiabatic simulations of galaxy clusters can artificially suppress the mixing of thermal and relativistic plasma ; anisotropic thermal conduction allows more efficient mixing , which may contribute to cosmic rays being distributed throughout the cluster volume .