Turbulence and Mixing in the Intracluster Medium

TL;DR

This paper investigates how magnetic field reorientation due to temperature-gradient-driven instabilities stabilizes the intracluster medium and sets a threshold for turbulence generation, impacting heat and metal mixing.

Contribution

It demonstrates that magnetic reorientation stabilizes the ICM against turbulence and establishes a velocity threshold for turbulence onset, which was not previously understood.

Findings

Magnetic field reorientation stabilizes the ICM against sustained convection.

Turbulence in the ICM requires driving velocities exceeding 10-100 km/s.

Stable magnetic configurations suppress turbulent mixing at lower driving strengths.

Abstract

The intracluster medium (ICM) is stably stratified in the hydrodynamic sense with the entropy $s$ increasing outwards. However, thermal conduction along magnetic field lines fundamentally changes the stability of the ICM, leading to the "heat-flux buoyancy instability" when $dT/dr>0$ and the "magnetothermal instability" when $dT/dr<0$. The ICM is thus buoyantly unstable regardless of the signs of $dT/dr$ and $ds/dr$. On the other hand, these temperature-gradient-driven instabilities saturate by reorienting the magnetic field (perpendicular to $\hat{\bf r}$ when $dT/dr>0$ and parallel to $\hat{\bf r}$ when $dT/dr<0$), without generating sustained convection. We show that after an anisotropically conducting plasma reaches this nonlinearly stable magnetic configuration, it experiences a buoyant restoring force that resists further distortions of the magnetic field. This restoring force is analogous to the buoyant restoring force experienced by a stably stratified adiabatic plasma. We argue that in order for a driving mechanism (e.g, galaxy motions or cosmic-ray buoyancy) to overcome this restoring force and generate turbulence in the ICM, the strength of the driving must exceed a threshold, corresponding to turbulent velocities $\gtrsim 10 -100 {km/s}$. For weaker driving, the ICM remains in its nonlinearly stable magnetic configuration, and turbulent mixing is effectively absent. We discuss the implications of these findings for the turbulent diffusion of metals and heat in the ICM.