Thermal conductivity with bells and whistlers: Suppression of the magnetothermal instability in galaxy clusters

Abstract

In the hot and dilute intracluster medium (ICM) in galaxy clusters, kinetic plasma instabilities that are excited at the particle gyroradius may play an important role in the transport of heat and momentum, thus affecting the large-scale evolution of these systems. In this paper, we continue our investigation of the effect of whistler suppression of thermal conductivity on the magneto-thermal instability (MTI), which may be active in the periphery of galaxy clusters and may contribute to the observed levels of turbulence. We use a subgrid closure for the heat flux inspired from kinetic simulations and show that MTI turbulence with whistler suppression exhibits a critical transition as the suppression parameter is increased: for modest suppression of the conductivity, the turbulent velocities generated by the MTI decrease accordingly, in agreement with scaling laws found in previous studies of the MTI. However, for suppression above a critical threshold, the MTI loses its ability to maintain equipartition-level magnetic fields through a small-scale dynamo (SSD), and the system enters a ``death-spiral.'' We show that analogous levels of suppression of thermal conductivity with a simple model of flat uniform suppression would not inhibit the dynamo. We propose a model to explain this critical transition, and speculate that conditions in the hot ICM are such that in substantial portions of the galaxy cluster periphery the MTI might struggle to sustain its own dynamo. We then look at spatial correlations and energy transfers in spectral space and find that, with whistler suppression, most of the heat is transported along thin bundles of strong magnetic fields (the Autobahns of electrons), while high-beta regions are brought out of thermal equilibrium. We link this behavior to the intermittent nature of magnetic fields, and we observe an overall reduction of the efficiency of MTI turbulent driving at the largest turbulent scales. Finally, we show that external turbulence interferes with the MTI and leads to reduced levels of MTI turbulence. While individually both external turbulence and whistler suppression reduce MTI turbulence, we find that they can exhibit a complex interplay when acting in conjunction, with external turbulence boosting the whistler-suppressed thermal conductivity and even reviving a ``dead'' MTI. Our study illustrates how extending magnetohydrodynamics with a simple prescription for microscale plasma physics can lead to the formation of a complicated dynamical system and demonstrates that further work is needed in order to bridge the gap between micro- and macro scales in galaxy clusters.