Spectrally resolved cosmic ray hydrodynamics -- I. Spectral scheme

TL;DR

This paper introduces a novel numerical scheme for accurately simulating the spectral evolution of cosmic ray protons in astrophysical plasmas, improving precision and efficiency in hydrodynamical models.

Contribution

The paper presents a low-diffusion, spectral scheme solving the Fokker-Planck equation with piecewise power laws, enabling accurate cosmic ray spectrum modeling in simulations.

Findings

Reduces numerical errors by orders of magnitude compared to classical methods.

Efficiently computes spectral evolution with only 10-20 spectral bins.

Allows for detailed modeling of cosmic ray impact on astrophysical environments.

Abstract

Cosmic ray (CR) protons are an important component in many astrophysical systems. Processes like CR injection, cooling, adiabatic changes as well as active CR transport through the medium strongly modify the CR momentum distribution and have to be taken into account in hydrodynamical simulations. We present an efficient novel numerical scheme to accurately compute the evolution of the particle distribution function by solving the Fokker-Planck equation with a low number of spectral bins (10 - 20), which is required to include a full spectrum for every computational fluid element. The distribution function is represented by piecewise power laws and is not forced to be continuous, which enables an optimal representation of the spectrum. The Fokker-Planck equation is solved with a two-moment approach evolving the CR number and energy density. The low numerical diffusion of the scheme reduces the numerical errors by orders of magnitude in comparison to classical schemes with piecewise constant spectral representations. With this method not only the spectral evolution of CRs can be computed accurately in magnetohydrodynamic simulations but also their dynamical impact as well as CR ionisation. This allows for more accurate models for astrophysical plasmas, like the interstellar medium, and direct comparisons with observations.