Stability analysis of convection in the intracluster medium

• Stability analysis of the HBI and the MTI are presented taking into account the boundary conditions employed in the simulations.
• It has been shown that the HBI doesn't set in as an oscillatory marginal state whereas the MTI can do so.
• The HBI and the MTI criteria have been modified to include the affects of the magnetic tension.

We use the machinery usually employed for studying the onset of Rayleigh–Bénard convection in hydro- and magnetohydro-dynamic settings to address the onset of convection induced by the magnetothermal instability and the heat-flux-buoyancy-driven-instability in the weakly-collisional magnetized plasma permeating the intracluster medium. Since most of the related numerical simulations consider the plasma being bounded between two ‘plates’ on which boundary conditions are specified, our strategy provides a framework that could enable a more direct connection between analytical and numerical studies. We derive the conditions for the onset of these instabilities considering the effects of induced magnetic tension resulting from a finite plasma beta. We provide expressions for the Rayleigh number in terms of the wave vector associated with a given mode, which allow us to characterize the modes that are first to become unstable. For both the heat-flux-buoyancy-driven-instability and the magnetothermal instability, oscillatory marginal stable states are possible.