Turbulent Reacceleration of Streaming Cosmic Rays

TL;DR

This study investigates how subsonic turbulence influences cosmic ray reacceleration and energy losses, highlighting the roles of streaming, plasma beta, and magnetic field alignment through MHD simulations.

Contribution

It provides new insights into the impact of CR streaming and plasma beta on reacceleration rates and quantifies streaming energy losses, advancing understanding beyond diffusive transport models.

Findings

CR reacceleration rates agree with analytic predictions for diffusion-only cases.

Streaming slows reacceleration in low-beta environments but not in high-beta environments.

Streaming energy losses are resolution-dependent and less affected by magnetic field strength.

Abstract

Subsonic, compressive turbulence transfers energy to cosmic rays (CRs), a process known as non-resonant reacceleration. It is often invoked to explain observed ratios of primary to secondary CRs at $\sim \rm GeV$ energies, assuming wholly diffusive CR transport. However, such estimates ignore the impact of CR self-confinement and streaming. We study these issues in stirring box magnetohydrodynamic (MHD) simulations using Athena++, with field-aligned diffusive and streaming CR transport. For diffusion only, we find CR reacceleration rates in good agreement with analytic predictions. When streaming is included, reacceleration rates depend on plasma $\beta$. Due to streaming-modified phase shifts between CR and gas variables, they are slower than canonical reacceleration rates in low-$\beta$ environments like the interstellar medium (ISM) but remain unchanged in high-$\beta$ environments like the intracluster medium (ICM). We also quantify the streaming energy loss rate in our simulations. For sub-Alfv\'{e}nic turbulence, it is resolution-dependent (hence unconverged in large scale simulations) and heavily suppressed -- by an order of magnitude -- compared to the isotropic loss rate $v_{A} \cdot \nabla P_{\rm CR} / P_{\rm CR} \sim v_{A}/L_{0}$, due to misalignment between the mean field and isotropic CR gradients. Counterintuitively, and unlike acceleration efficiencies, CR losses are almost independent of magnetic field strength over $\beta \sim 1-100$ and are, therefore, not the primary factor behind lower acceleration rates when streaming is included. While this paper is primarily concerned with how turbulence affects CRs, in a follow-up paper (Bustard and Oh, in prep), we consider how CRs affect turbulence by diverting energy from the MHD cascade, altering the pathway to gas heating and steepening the turbulent power spectrum.