Effects of Viscosity on Sloshing Cold Fronts in Galaxy Clusters

TL;DR

This study investigates how intracluster medium viscosity and magnetic fields influence sloshing cold fronts via 3D Braginsky-MHD simulations. It compares four viscosity models—no viscosity, isotropic Spitzer viscosity, Braginskii anisotropic viscosity, and Braginskii viscosity limited by microinstabilities—across two plasma $β$ values to assess Kelvin–Helmholtz instability suppression and front morphology. The results show that isotropic Spitzer viscosity strongly damps KHI leading to smooth fronts, Braginskii anisotropic viscosity provides intermediate suppression, and microinstability limits reduce the viscous suppression, with stronger magnetic fields further stabilizing fronts; lower $β$ amplifies magnetic tension effects and widens the permissible anisotropy range under microinstability constraints. These findings help interpret the diversity of observed cold-front morphologies and offer constraints on ICM microphysics from X-ray observations.

Abstract

The viscous properties of the intracluster medium (ICM) remain poorly constrained. Cold fronts-sharp discontinuities formed during cluster mergers-offer a potential avenue to probe the effective viscosity of the ICM. Velocity shear across these fronts should generate Kelvin-Helmholtz instabilities (KHI), unless viscosity or magnetic tension suppresses them. We perform cluster merger simulations incorporating four ICM viscosity models: (A) inviscid, (B) isotropic Spitzer viscosity, (C) anisotropic Braginskii viscosity, and (D) Braginskii viscosity limited by microinstabilities. The isotropic Spitzer viscosity (case B) strongly suppresses KHI, producing smooth cold front surfaces, while the inviscid (A) and microinstability-limited (D) cases show prominent ripples. The Braginskii case (C) yields intermediate suppression. We also vary the plasma $β$ parameter ($β\approx$ 100 and 1600) to examine how a changing magnetic field strength affects the results. Stronger magnetic fields further suppress KHI, leading to smoother fronts and reduced differences between different viscosity models, while also widening the range of permitted pressure anisotropies when microinstability-based limiters are present. These results indicate that both viscosity and magnetic fields play crucial roles in stabilising sloshing cold fronts in galaxy clusters.

Figures (13)

• Figure 1: Density slice plots for high plasma $\beta$ ($\beta \sim 1600$) simulations at $t=2.2$ Gyr. The simulations are still in the early phase of the cluster merger. At this epoch, the cold fronts are already beginning to form, though there are no significant differences among the four models.
• Figure 2: Density slice plots for high plasma $\beta$ ($\beta \sim 1600$) simulations at $t=4.0$ Gyr. Spiral-shaped cold fronts are apparent at this stage. The apparently stability of the cold front surfaces follows this order: $\rm{B}1600>\rm{C}1600>\rm{D}1600\gtrsim\rm{A}1600$. The black lines represent line integral convolution of the velocity field in the $x$–$y$ plane, used to visualise the gas velocity structure.
• Figure 3: Temperature slice plots for high plasma $\beta$ ($\beta \sim 1600$) simulations at $t=4.0$ Gyr. Due to the sloshing motions induced by the merger, the cool-core region becomes disturbed, with hot outer gas intruding inward and forming temperature discontinuities. These structures, known as cold fronts, are characterized by the inner regions being cooler than the outer regions.
• Figure 4: Magnetic field strength slice plots for high $\beta$ ($\beta \sim 1600$) simulations at $t=4.0$ Gyr. Velocity shear across the cold fronts stretches the magnetic field lines, leading to magnetic field amplification and the formation of magnetized layers aligned along the cold front surfaces.
• Figure 5: Angle between the magnetic field and velocity slice plots for high $\beta$ ($\beta \sim 1600$) simulations at $t=4.0$ Gyr. Because of the weaker magnetic tension in the high $\beta$ environment, the magnetic fields are more easily stretched by sloshing motions, enhancing their alignment (yellow regions).