Magneto-Thermal Instability in Galaxy Clusters -- III. The Limit of Adiabatic Stratification
In the hot and dilute intracluster medium of galaxy clusters, large-scale buoyancy instabilities can develop due to the transport of heat along magnetic field lines. In particular, the peripheries of galaxy clusters are unstable to the magneto-thermal instability (MTI), which may contribute to the observed levels of turbulence. Recent theoretical and numerical work has revealed that the stable background entropy stratification controls the nonlinear saturation of the instability, by setting the strength and the integral scale of the resulting turbulent state. However, observations of the periphery of galaxy clusters show that the radial entropy profiles near the virial radii $R_{500}$ may be flatter than predicted by models of smooth gravitational accretion. This motivates us to investigate the saturation of the MTI in adiabatic (buoyantly neutral) atmospheres, using both phenomenological approaches and Boussinesq numerical simulations, carried out with the pseudospectral code SNOOPY. We find that the adiabatic MTI saturates in a state characterised by the formation of large-scale plumes and their destruction by shear instability, yielding a new scaling law for the saturated turbulent kinetic energy, $\sim$$\chi \omega_T$, as the adiabatic limit is approached, where $\chi$ is the effective thermal diffusivity and $\omega_T$ is the MTI frequency. This predicts that the MTI plumes may achieve near sonic speeds in cluster outskirts, thus providing significant turbulent pressure support, even in the face of suppressed thermal conduction.