Journal
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 509, Issue 3, Pages 3779-3797Publisher
OXFORD UNIV PRESS
DOI: 10.1093/mnras/stab2635
Keywords
MHD; plasmas; methods: numerical; cosmic rays; ISM: structure; galaxies: evolution
Categories
Funding
- NSF [1911233, 20009234]
- NSF CAREER grant [1455342]
- NASA [80NSSC18K0562, HST-AR-15800.001-A]
- NASA HEC [SMD-16-7592]
- Rutherford Discovery Fellowship [RDF-U001804]
- Marsden Fund [UOO1727]
- Division Of Astronomical Sciences
- Direct For Mathematical & Physical Scien [1911233] Funding Source: National Science Foundation
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We derive a consistent set of moment equations for cosmic ray magnetohydrodynamics, which are valid in various regimes and allow for anisotropic scattering and transport/magnetic field structure. We discuss the differences between this set of equations and previous treatments, as well as the similarities and differences with the analog M1-RHD equations.
We derive a consistent set of moment equations for cosmic ray (CR)-magnetohydrodynamics, assuming a gyrotropic distribution function (DF). Unlike previous efforts, we derive a closure, akin to the M1 closure in radiation hydrodynamics (RHD), that is valid in both the nearly isotropic DF and/or strong-scattering regimes, and the arbitrarily anisotropic DF or free-streaming regimes, as well as allowing for anisotropic scattering and transport/magnetic field structure. We present the appropriate two-moment closure and equations for various choices of evolved variables, including the CR phase space DF f, number density n, total energy e, kinetic energy epsilon, and their fluxes or higher moments, and the appropriate coupling terms to the gas. We show that this naturally includes and generalizes a variety of terms including convection/fluid motion, anisotropic CR pressure, streaming, diffusion, gyro-resonant/streaming losses, and re-acceleration. We discuss how this extends previous treatments of CR transport including diffusion and moment methods and popular forms of the Fokker-Planck equation, as well as how this differs from the analogous M1-RHD equations. We also present two different methods for incorporating a reduced speed of light (RSOL) to reduce time-step limitations: In both, we carefully address where the RSOL (versus true c) must appear for the correct behaviour to be recovered in all interesting limits, and show how current implementations of CRs with an RSOL neglect some additional terms.
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