Cosmological Simulations of Weakly Collisional Plasmas with Braginskii Viscosity in Galaxy Clusters

TL;DR

This work tackles the challenge of modeling anisotropic momentum transport in the weakly collisional intracluster medium by implementing Braginskii viscosity within the SPH-based MHD code OpenGadget3. The authors validate the approach against a benchmark suite of analytical solutions (sound waves, Alfvén waves, fast magnetosonic waves, and Kelvin–Helmholtz instability) and demonstrate alignment with established results, including a parallel with Braginskii treatments in other codes. They then apply the solver to cosmological zoom-in simulations of a galaxy cluster, revealing how anisotropic viscosity and microinstability limiters alter turbulence, dynamo action, and magnetic-field amplification compared with isotropic viscosity and inviscid runs. The findings underscore the importance of anisotropic transport physics for realistic ICM modeling and establish OpenGadget3 as a practical tool for exploring weakly collisional plasmas in cosmological contexts.

Abstract

We present the implementation of an anisotropic viscosity solver within the magnetohydrodynamics (MHD) framework of the TreeSPH code OpenGadget3. The solver models anisotropic viscous transport along magnetic field lines following the Braginskii formulation and includes physically motivated limiters based on the mirror and firehose instability thresholds, which constrain the viscous stress in weakly collisional plasmas. To validate the implementation, we performed a suite of standard test problems -- including two variants of the sound-wave test, circularly and linearly polarized Alfven waves, fast magnetosonic wave, and the Kelvin-Helmholtz instability -- both with and without the plasma-instability limiters. The results show excellent agreement with the AREPO implementation of a similar anisotropic viscosity model (Berlok et al. 2019), confirming the accuracy and robustness of our method. Our formulation integrates seamlessly within the individual adaptive timestepping framework of OpenGadget3, avoiding the need for subcycling. This provides efficient and stable time integration while maintaining physical consistency. Finally, we applied the new solver to a cosmological zoom-in simulation of a galaxy cluster, demonstrating its capability to model anisotropic transport and plasma microphysics in realistic large-scale environments. Our implementation offers a versatile and computationally efficient tool for studying anisotropic viscosity in magnetized astrophysical systems.

Figures (17)

• Figure 1: Velocity and viscous heating profiles of the soundwave described by eq. \ref{['eqn:soundwave']} after $ct/L=1$ with the hydro solver off. The data points show the velocity profile for the different numerical simulations (green for the inviscid case, red for the isotropic viscosity case, and blue for the anisotropic case), while the dashed lines indicate the analytical solutions following the same color code as the data points. In this case, the magnetic field has only $x$-component, i.e., parallel to the velocity gradient. Top panel: $v_x$ profile. Bottom panel: Cumulative viscous heating.
• Figure 2: Velocity profile of the soundwave described by eq. \ref{['eqn:soundwave']} after $ct/L=1$ with the hydro solver on. The data points show the velocity profile for the different numerical simulations (green for the inviscid case, red for the isotropic viscosity case, and blue for the anisotropic case), while the dashed lines indicate the analytical solutions following the same color code as the data points. Top panel: Magnetic field in the $\hat{x}$ direction, parallel to the velocity gradient. Bottom panel: Magnetic field in the $\hat{y}$ direction, perpendicular to the velocity gradient.
• Figure 3: Cumulative viscous heating profile of the soundwave described by eq. \ref{['eqn:soundwave']} after $ct/L=1$. The data points are the results from the simulations, and the dashed lines indicate the analytical solution (red for the isotropic viscosity case, and blue for the anisotropic case). Top panel: Magnetic field parallel to the velocity gradient. Bottom panel: Magnetic field perpendicular to the velocity gradient.
• Figure 4: Velocity profiles of the soundwave described in eq. \ref{['eqn:ICs_soundwaveII']} and \ref{['eqn:ICs_soundwaveII_q']} after $ct/L=1$ for the anisotropic case. The black-dashed lines show the initial conditions and the solid lines the evolution after $t\gg1$. We compare our results (blue dots) with the exact analytical solution (blue-dashed lines). Top panel: $v_y$ profile. Bottom panel: $v_x$ profile triggered by $\Delta p$ due to the misalignment between the magnetic field and the wave propagation.
• Figure 5: Evolution of $\Delta p$ profile of the soundwave described by eq. \ref{['eqn:ICs_soundwaveII']} and \ref{['eqn:ICs_soundwaveII_q']} after $ct/L=1$ for the anisotropic case (blue dots). Black-dashed line shows the initial conditions, and the solid line shows the evolution after $t\gg1$. The exact analytical solution is given by the blue-dashed line.