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

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 most likely aligned with the gravity. This instability occurs because of the fast anisotropic conduction of heat along magnetic field lines. However, the extent to which it impacts the ICM dynamics, energetics, and overall equilibrium is still a matter of debate. Aims. This work aims to understand MTI turbulence in an astrophysically stratified ICM atmosphere, its underlying saturation mechanism, and its ability to carry energy and to provide non-thermal pressure support. Methods. We performed a series of 2D and 3D numerical simulations of the MTI in global spherical models of a stratified ICM thanks to the finite-volume Godunov-type code IDEFIX and using Braginskii magnetohydrodynamics. We used well-controlled volume-averaged, 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. With realistic Spitzer conductivity, the MTI drives cluster-size motions with Mach numbers up to ℳ ∼ 0.3, even in the presence of strong stable entropy stratification. We show that such mildly compressible flows can provide about ∼15% of the non-thermal pressure support in the outermost ICM regions close to the cluster accretion shock and that the convective transport itself is much less efficient (a few percent only) 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, rather than the adiabatic convective nature, of the instability. Conclusions. The MTI seems relevant to both the dynamics and energetics of the ICM through radially biased magnetic fields that enhance the background Braginskii heat flux. Further work including externally forced turbulence, for instance, mimicking accretion-induced turbulence, is needed to assess its overall relative importance in comparison to other drivers of ICM turbulence.