The Effects of Anisotropic Viscosity on Turbulence and Heat Transport in the Intracluster Medium

In the intracluster medium (ICM) of galaxy clusters, heat and momentum are transported almost entirely along (but not across) magnetic field lines. We perform the first fully self-consistent Braginskii-MHD simulations of galaxy clusters including both of these effects. Specifically, we perform local and global simulations of the magnetothermal instability (MTI) and the heat-flux-driven buoyancy instability (HBI) and assess the effects of viscosity on their saturation and astrophysical implications. We find that viscosity has only a modest effect on the saturation of the MTI. As in previous calculations, we find that the MTI can generate nearly sonic turbulent velocities in the outer parts of galaxy clusters, although viscosity somewhat suppresses the magnetic field amplification. At smaller radii in cool-core clusters, viscosity can decrease the linear growth rates of the HBI. However, it has less of an effect on the HBI’s nonlinear saturation, in part because three-dimensional interchange motions (magnetic flux tubes slipping past each other) are not damped by anisotropic viscosity. In global simulations of cool core clusters, we show that the HBI robustly inhibits radial thermal conduction and thus precipitates a cooling catastrophe. The effects of viscosity are, however, more important for higher entropy clusters. We argue that viscosity can contribute to the global transition of cluster cores from cool-core to non cool-core states: additional sources of intracluster turbulence, such as can be produced by AGN feedback or galactic wakes, suppress the HBI, heating the cluster core by thermal conduction; this makes the ICM more viscous, which slows the growth of the HBI, allowing further conductive heating of the cluster core and a transition to a non cool-core state.

💡 Research Summary

The paper presents the first fully self‑consistent Braginskii‑MHD simulations of galaxy clusters that incorporate both anisotropic thermal conduction and anisotropic viscosity, the latter being the Braginskii viscosity that acts only along magnetic field lines. The authors focus on two buoyancy‑driven instabilities that dominate the intracluster medium (ICM): the magnetothermal instability (MTI), which operates when the temperature gradient is positive (dT/dr > 0), and the heat‑flux‑driven buoyancy instability (HBI), which occurs for a negative temperature gradient (dT/dr < 0). By running both local (small‑box) and global (cluster‑scale) simulations, they assess how viscosity influences the linear growth, nonlinear saturation, and astrophysical consequences of each instability.
For the MTI, the inclusion of Braginskii viscosity modestly reduces the linear growth rate, but the effect on the saturated state is minor. The MTI still drives vigorous, nearly sonic turbulence in the outer parts of clusters, and the magnetic field is amplified, albeit at a level 10–20 % lower than in inviscid runs. This modest suppression arises because the viscosity tensor damps compressive motions more strongly than shear, and the MTI’s turbulent cascade is dominated by shear that is only weakly affected. Consequently, the MTI remains an efficient mechanism for generating large‑scale turbulent pressure support and for reorienting magnetic fields toward a more vertical configuration, even in a viscous plasma.
In contrast, the HBI is more sensitive to anisotropic viscosity. The linear growth rates are significantly lowered, especially in high‑temperature, low‑density regions where the Braginskii viscosity coefficient is largest. Nevertheless, three‑dimensional interchange motions—where magnetic flux tubes slip past one another—are essentially undamped because the viscosity acts only on motions parallel to the field lines. As a result, the nonlinear saturation of the HBI is only modestly altered: the instability still reorients magnetic fields to lie preferentially in the horizontal plane, thereby suppressing radial conductive heat flux.
Global simulations of cool‑core clusters reveal that, despite the viscous damping of the HBI’s early growth, the instability ultimately dominates the core’s thermal evolution. The HBI efficiently blocks conductive heat inflow, leading to a rapid cooling catastrophe unless an external heating source intervenes. In higher‑entropy (non‑cool‑core) clusters, however, the enhanced viscosity more effectively curtails HBI development, allowing a larger fraction of the Spitzer conductivity to operate and keeping the core temperature stable.
The authors argue that anisotropic viscosity can play a decisive role in the observed bimodality of cluster cores. Turbulence injected by active galactic nucleus (AGN) feedback, galaxy wakes, or mergers can suppress the HBI, permitting conductive heating of the core. The resulting temperature rise increases the Braginskii viscosity, which in turn further slows HBI growth—a positive feedback loop that can drive a transition from a cool‑core to a non‑cool‑core state. This mechanism provides a natural explanation for why some clusters maintain high central entropies while others remain in a radiatively cooling state.
Overall, the study demonstrates that while viscosity has only a modest impact on MTI‑driven turbulence, it substantially modifies the linear phase of the HBI and can influence the long‑term thermal balance of cluster cores. By incorporating both anisotropic conduction and viscosity, the work offers a more realistic theoretical framework for interpreting X‑ray observations of cluster temperature profiles, magnetic field orientations, and the prevalence of cool‑core versus non‑cool‑core systems.