Cosmic Ray Drag and Damping of Compressive Turbulence

TL;DR

This paper investigates how cosmic rays damp and modify compressive turbulence, showing that CRs can significantly absorb turbulent energy, leading to a predominantly solenoidal small-scale turbulence and affecting interpretations of observed turbulence velocities.

Contribution

It demonstrates the impact of cosmic ray damping on turbulence spectra and energy transfer, supported by MHD simulations including CR transport effects.

Findings

CR damping steepens the turbulent power spectrum

Large-scale turbulence energy is largely absorbed by CRs

CR transport influences the solenoidal nature of turbulence

Abstract

While it is well-known that cosmic rays (CRs) can gain energy from turbulence via second order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping time $t_{\rm damp} \sim \rho v^{2}/\dot{E}_{\rm CR} \propto E_{\rm CR}^{-1}$ becomes comparable to the turbulent cascade time. Magnetohydrodynamic (MHD) simulations of stirred compressive turbulence in a gas-CR fluid with diffusive CR transport show clear imprints of CR-induced damping, saturating at $\dot{E}_{\rm CR} \sim \tilde{\epsilon}$, where $\tilde{\epsilon}$ is the turbulent energy input rate. In that case, almost all the energy in large scale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge-Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering small-scale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering of $E > 300$ GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp large scale motions, with kinetic energy reduced by up to to an order of magnitude in realistic $E_{\rm CR} \sim E_{\rm g}$ scenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such large scale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e. $\tilde{\epsilon} \gg \rho v^{3}/L$.