An Efficient Fokker-Planck Solver and its Application to Stochastic Particle Acceleration in Galaxy Clusters

TL;DR

This paper introduces a computationally efficient Fokker-Planck solver for modeling cosmic-ray electron spectra in galaxy clusters, enabling large-scale simulations of particle acceleration and radio emission over cosmic timescales.

Contribution

The authors develop a novel, memory-efficient Fokker-Planck solver for cosmic-ray spectra that can be integrated into large astrophysical simulations, with a focus on galaxy cluster environments.

Findings

The code accurately models relativistic electron spectra evolution.

Application to galaxy clusters demonstrates realistic radio emission predictions.

Spectral compression reduces memory use by a factor of ten.

Abstract

Particle acceleration by turbulence plays a role in many astrophysical environments. The non- linear evolution of the underlying cosmic-ray spectrum is complex and can be described by a Fokker-Planck equation, which in general has to be solved numerically. We present here an implementation to compute the evolution of a cosmic-ray spectrum coupled to turbulence considering isotropic particle pitch-angle distributions and taking into account the relevant particle energy gains and losses. Our code can be used in run time and post-processing to very large astrophysical fluid simulations. We also propose a novel method to compress cosmic- ray spectra by a factor of ten, to ease the memory demand in very large simulations. We show a number of code tests, which firmly establish the correctness of the code. In this paper we focus on relativistic electrons, but our code and methods can be easily extended to the case of hadrons. We apply our pipeline to the relevant problem of particle acceleration in galaxy clusters. We define a sub-grid model for compressible MHD-turbulence in the intra- cluster-medium and calculate the corresponding reacceleration timescale from first principles. We then use a magneto-hydrodynamic simulation of an isolated cluster merger to follow the evolution of relativistic electron spectra and radio emission generated from the system over several Gyrs.