Simulating cosmic ray physics on a moving mesh

Abstract

We discuss new methods to integrate the cosmic ray (CR) evolution equations coupled to magneto-hydrodynamics (MHD) on an unstructured moving mesh, as realised in the massively parallel arepo code for cosmological simulations. We account for diffusive shock acceleration of CRs at resolved shocks and at supernova remnants in the interstellar medium (ISM), and follow the advective CR transport within the magnetised plasma, as well as anisotropic diffusive transport of CRs along the local magnetic field. CR losses are included in terms of Coulomb and hadronic interactions with the thermal plasma. We demonstrate the accuracy of our formalism for CR acceleration at shocks through simulations of plane-parallel shock tubes that are compared to newly derived exact solutions of the Riemann shock tube problem with CR acceleration. We find that the increased compressibility of the post-shock plasma due to the produced CRs decreases the shock speed. However, CR acceleration at spherically expanding blast waves does not significantly break the self-similarity of the Sedov-Taylor solution; the resulting modifications can be approximated by a suitably adjusted, but constant adiabatic index. In first applications of the new CR formalism to simulations of isolated galaxies and cosmic structure formation, we find that CRs add an important pressure component to the ISM that increases the vertical scale height of disk galaxies, and thus reduces the star formation rate. Strong external structure formation shocks inject CRs into the gas, but the relative pressure of this component decreases towards halo centres as adiabatic compression favours the thermal over the CR pressure.

Shock-accelerated cosmic rays and streaming instability in the adaptive mesh refinement code Ramses

“…for γ CR = 4/3. In agreement with Pfrommer et al (2017), we find that for the same setup, an effective adiabatic index in the shock of γ e = 7/5 for the exact solution leads to a good recovering of the numerical solution in both total pressure and density, though the maximum values are less pronounced at the shock because of the limited resolution. Increasing the resolution naturally offers a more faithful capturing of the shock profile.…”

“…We use an adiabatic index for the thermal and CR components are respectively γ = 5/3 and γ CR = 4/3. The analytical solution with accelerated CRs is provided by Pfrommer et al 2017 (see their Appendix B). Figure 7 shows the result of the numerical calculation where the analytical solution is well reproduced with the correct Mach number of M 9.56 positioned at the shock front in one of the cell sampling the numerically broadened discontinuity.…”

Impact of Low-Energy Cosmic Rays on Star Formation

“…The typical gyroradii or scattering lengths of GeV protons with the magnetic field are significantly smaller than the scales under consideration, which allows for a fluid treatment of CRs. This high-energy fluid is then dynamically coupled to the MHD equation in a twofluid approach with an effective adiabatic index and a total pressure that includes the CR contributions (Hanasz and Lesch, 2003;Pfrommer et al, 2017). GeV protons are primarily produced in SN remnants (Ackermann et al, 2013), which are among the strongest and most abundant shocks in the ISM.…”

Probing Cosmic-Ray Transport with Radio Synchrotron Harps in the Galactic Center

“…The diffusion model assumes that the CRs diffuse along the magnetic flux tubes with a constant coefficient κ = 3 × 10 25 cm 2 s −1 , which was chosen to match NTF sizes with a diffusion length scale l = √ 2κt and t = 30 kyr. 1 We include Alfvén wave cooling of CRs (see Pfrommer et al 2017).…”