Non-linear saturation and energy transport in global simulations of magneto-thermal turbulence in the stratified intracluster medium

Abstract

Context. The magneto-thermal instability (MTI) is one of many possible drivers of stratified turbulence in the intracluster medium (ICM) outskirts of galaxy clusters, where the background temperature gradient is aligned with the gravity. This instability occurs because of the fast anisotropic conduction of heat along magnetic field lines; but to what extent it impacts the ICM dynamics, energetics and overall equilibrium is still a matter of debate. Aims. This work aims at understanding MTI turbulence in an astrophysically stratified ICM atmosphere, its saturation mechanism, and its ability to carry energy and to provide non-thermal pressure support. Methods. We perform a series of 2D and 3D numerical simulations of the MTI in global spherical models of stratified ICM, thanks to the finite-volume code IDEFIX, using Braginskii-magnetohydrodynamics. We use volume-, shell-averaged and spectral diagnostics to study the saturation mechanism of the MTI, and its radial transport energy budget. Results. The MTI is found to saturate through a dominant balance between injection and dissipation of available potential energy, which amounts to marginalising the Braginskii heat flux but not the background temperature gradient itself. Accordingly, the strength and injection length of MTI-driven turbulence exhibit clear dependencies on the thermal diffusivity. The MTI drives cluster-size motions with Mach numbers up to $\mathcal{M} \sim 0.3$, even in presence of strong stable entropy stratification. We show that such mildly compressible flows can provide about $\sim 15\%$ of non-thermal pressure support in the outermost ICM regions, and that the convective transport itself is much less efficient than conduction at radially transporting energy. Finally, we show that the MTI saturation can be described by a diffusive mixing-length theory, shedding light on the diffusive buoyant nature of the instability.