Implementation of CR Energy SPectrum (CRESP) algorithm in PIERNIK MHD code. I. Spectrally resolved propagation of CR electrons on Eulerian grids

TL;DR

This paper introduces an efficient spectral evolution algorithm for cosmic ray transport in MHD simulations, featuring adaptive momentum bin boundaries and validated through tests and galactic wind modeling.

Contribution

The paper presents a novel extension of the CGMV method with variable momentum bin boundaries that adapt to spectral cutoffs, improving CR spectral evolution modeling.

Findings

Algorithm accurately reproduces analytical solutions in tests.

Results in galactic wind simulations align with theoretical expectations.

Adaptive bins effectively capture spectral cutoff dynamics.

Abstract

We present an efficient algorithm to follow spectral evolution of Cosmic Rays (CR) coupled with an MHD system on Eulerian grids. The algorithm is designed for studies of CR energy spectrum evolution in MHD simulations of a galactic interstellar medium. The base algorithm for CR transport relies on the two-moment piece-wise power-law method, known also as Coarse Grained Momentum Final Volume (CGMV), for solving the Fokker-Planck CR transport equation, with a low number of momentum-bins extending over several decades of the momentum coordinate. We propose an extension of the CGMV with a novel feature which allows momentum boundaries to change in response to CR momentum gains or losses near the extremes of the population distribution. Our extension involves a special treatment of momentum bins containing spectral cutoff. Contrary to the regular bins of fixed width, those bins have variable-width, and their outer edges coincide with spectral cutoffs. The cutoff positions are estimated from the particle number density and energy density in the outer bins for an assumed small value of an additional parameter representing the smallest physically significant level of CR spectral energy density. We performed a series of elementary tests to validate the algorithm and demonstrated, whenever possible, that results of the test simulations correspond, with a reasonable accuracy, to the results of analogous analytical solutions. In a more complex test of galactic CR-driven wind problem we obtained results consistent with expectations regarding the effects of advection, diffusion, adiabatic, and synchrotron cooling of a CR population.