Dynamical stability of a thermally stratified intracluster medium with anisotropic momentum and heat transport

In weakly collisional plasmas such as the intracluster medium (ICM), heat and momentum transport become anisotropic with respect to the local magnetic field direction. Anisotropic heat conduction causes the slow magnetosonic wave to become buoyantly unstable to the magnetothermal instability (MTI) when the temperature increases in the direction of gravity and to the heat-flux-driven buoyancy instability (HBI) when the temperature decreases in the direction of gravity. The local changes in magnetic field strength that attend these instabilities cause pressure anisotropies that viscously damp motions parallel to the magnetic field. In this paper we employ a linear stability analysis to elucidate the effects of anisotropic viscosity (i.e. Braginskii pressure anisotropy) on the MTI and HBI. By stifling the convergence/divergence of magnetic field lines, pressure anisotropy significantly affects how the ICM interacts with the temperature gradient. Instabilities which depend upon the convergence/divergence of magnetic field lines to generate unstable buoyant motions (the HBI) are suppressed over much of the wavenumber space, whereas those which are otherwise impeded by field-line convergence/divergence (the MTI) are strengthened. As a result, the wavenumbers at which the HBI survives largely unsuppressed in the ICM have parallel components too small to rigorously be considered local. This is particularly true as the magnetic field becomes more and more orthogonal to the temperature gradient. The field-line insulation found by recent numerical simulations to be a non-linear consequence of the standard HBI might therefore be attenuated. In contrast, the fastest growing MTI modes are unaffected by anisotropic viscosity. However, we find that anisotropic viscosity couples slow and Alfvén waves in such a way as to buoyantly destabilize Alfvénic fluctuations when the temperature increases in the direction of gravity. Consequently, many wavenumbers previously considered MTI stable or slow growing are in fact maximally unstable. We discuss the physical interpretation of these instabilities in detail.