Three-dimensional simulations of non-resonant streaming instability and particle acceleration near non-relativistic astrophysical shocks

TL;DR

This study compares 2-D and 3-D simulations of particle acceleration and magnetic field growth near non-relativistic shocks, finding qualitative similarities but notable differences in particle energy spectra.

Contribution

It demonstrates that 2-D simulations are adequate for studying gas instabilities but may overestimate particle acceleration compared to 3-D models.

Findings

2-D and 3-D models show similar gas behavior and instability growth rates.

2-D simulations accelerate more particles to higher velocities.

Spectral energy distributions differ significantly between 2-D and 3-D models.

Abstract

We use particle-in-magnetohydrodynamics-cells to model particle acceleration and magnetic field amplification in a high Mach, parallel shock in three dimensions and compare the result to 2-D models. This allows us to determine whether 2-D simulations can be relied upon to yield accurate results in terms of particle acceleration, magnetic field amplification and the growth rate of instabilities. Our simulations show that the behaviour of the gas and the evolution of the instabilities are qualitatively similar for both the 2-D and 3-D models, with only minor quantitative differences that relate primarily to the growth speed of the instabilities. The main difference between 2-D and 3-D models can be found in the spectral energy distributions (SEDs) of the non-thermal particles. The 2-D simulations prove to be more efficient, accelerating a larger fraction of the particles and achieving higher velocities. We conclude that, while 2-D models are sufficient to investigate the instabilities in the gas, their results have to be treated with some caution when predicting the expected SED of a given shock.