Stability Analysis of Convection in the Intracluster Medium

TL;DR

This paper analyzes the stability of convection in the intracluster medium's magnetized plasma, applying Rayleigh--Bénard convection theory to understand the onset of magnetothermal and heat-flux-buoyancy instabilities.

Contribution

It develops a framework connecting analytical and numerical studies of plasma instabilities, incorporating magnetic tension effects and deriving conditions for instability onset.

Findings

Derived expressions for the Rayleigh number related to instability modes.

Identified conditions under which oscillatory marginal states occur.

Provided criteria for the first unstable modes in plasma convection.

Abstract

We use the machinery usually employed for studying the onset of Rayleigh--B\'enard 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.