RAMSES-MCR: A consistent multi-group treatment of cosmic rays physics in momentum-space with the RAMSES code

Abstract

Cosmic rays (CRs) are known to play a key role in many astrophysical environments: they can modify shock dynamics, influence the thermochemistry and the ionization of the interstellar medium, regulate galaxy mass content by driving galactic winds, and be released by jets from active galactic nuclei. They also serve as important observational tracers through $\gamma$-ray emission, radio synchrotron, and secondary particle production. Since CR particles follow power-law distributions in momentum space spanning many decades in energy, and because diffusion and radiative losses further shape these spectra, it is crucial to model spectrally resolved CRs in numerical simulations and to assess the impact of this modeling on gas dynamics and observational signatures. We present a consistent multi-group spectral method in momentum space for CR protons called RAMSES-MCR in the adaptive mesh refinement code RAMSES, based on the two-moment formalism that evolves both CR energy and number density in momentum space, together with their associated flux. The modeled CR processes include advection, anisotropic/isotropic diffusion, streaming instability, Coulomb and hadronic losses, adiabatic changes, and feedback onto the gas. We also show that the method can be naturally extended to CR electrons (e.g. including synchrotron losses) and generalized to multiple CR species. The implementation is validated against a suite of standard multi-dimensional tests. We finally apply RAMSES-MCR to the three-dimensional expansion of a supernova remnant including CRs with anisotropic diffusion and energy losses, and demonstrate how CR energy redistributes in a momentum-dependent manner and modifies the gas momentum during the snowplough phase.