A finite volume method for two-moment cosmic-ray hydrodynamics on a moving mesh

TL;DR

This paper introduces a novel finite volume numerical algorithm for two-moment cosmic-ray hydrodynamics implemented in the moving mesh Arepo code, accurately modeling anisotropic CR transport and interactions with magnetic fields.

Contribution

The paper presents a new finite volume method for two-moment CRHD on a moving mesh, including a semi-implicit integrator for CR-wave interactions, tested with diverse problems.

Findings

Robust and accurate coupling of CRs with MHD demonstrated.

Numerical convergence confirmed with analytic solutions.

Effective modeling of CR transport and interactions in various scenarios.

Abstract

We present a new numerical algorithm to solve the recently derived equations of two-moment cosmic ray hydrodynamics (CRHD). The algorithm is implemented as a module in the moving mesh Arepo code. Therein, the anisotropic transport of cosmic rays (CRs) along magnetic field lines is discretised using a path-conservative finite volume method on the unstructured time-dependent Voronoi mesh of Arepo. The interaction of CRs and gyroresonant Alfv\'en waves is described by short-timescale source terms in the CRHD equations. We employ a custom-made semi-implicit adaptive time stepping source term integrator to accurately integrate this interaction on the small light-crossing time of the anisotropic transport step. Both the transport and the source term integration step are separated from the evolution of the magneto-hydrodynamical equations using an operator split approach. The new algorithm is tested with a variety of test problems, including shock tubes, a perpendicular magnetised discontinuity, the hydrodynamic response to a CR overpressure, CR acceleration of a warm cloud, and a CR blast wave, which demonstrate that the coupling between CR and magneto-hydrodynamics is robust and accurate. We demonstrate the numerical convergence of the presented scheme using new linear and non-linear analytic solutions.