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

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.

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• Turbulence and Particle Acceleration in Giant Radio Haloes: the Origin of Seed Electrons
• The Matryoshka Run (II): Time Dependent Turbulence Statistics, Stochastic Particle Acceleration and Microphysics Impact in a Massive Galaxy Cluster
• Second order Fermi reacceleration mechanisms and large scale synchrotron radio emission in intra-cluster bridges
• Testing cosmic-ray acceleration with radio relics: a high-resolution study using MHD and tracers
• The Coma cluster at LOFAR frequencies I: insights into particle acceleration mechanisms in the radio bridge
• Shocks and non-thermal particles in clusters of galaxies
• MeerKAT's View of the Bullet Cluster 1E 0657-55.8
• A numerical study of the interplay between Fermi acceleration mechanisms in radio lobes of FR-II radio galaxies
• On the Challenges of Cosmic-Ray Proton Shock Acceleration in the Intracluster Medium
• Contribution of Radio Halos to the Foreground for SKA EoR Experiments
• Electron transport with re-acceleration and radiation in the jets of X-ray binaries
• Simulations of the merging cluster of galaxies Cygnus A