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

Abstract

In the hot intracluster medium (ICM) in galaxy clusters, plasma microinstabilities may play an important role in the transport of heat and momentum on the large scales. 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 contribute to the observed turbulence. We use a closure for the heat flux inspired by kinetic simulations and show that MTI turbulence with whistler suppression exhibits a critical transition: for modest suppression of the conductivity, the MTI turbulent velocities decrease in agreement with previous MTI scaling laws. However, for suppression above a critical threshold, the MTI loses its ability to maintain equipartition-level magnetic fields through a small-scale dynamo, and the system enters a ``death-spiral''. We propose a model to explain this critical transition, and speculate that conditions in the hot ICM are favourable to the upkeep of the dynamo. Additionaly, with whistler suppression high-$\beta$ regions are brought out of thermal equilibrium while the efficiency of MTI turbulent driving is reduced. Finally, we show that external turbulence interferes with the MTI and leads to lower levels of turbulence. While individually both external turbulence and whistler suppression weaken the MTI, 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.