http://arxiv.org/abs/2301.04156
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. This “divergence-cleaning” should render small-scale turbulence largely solenoidal and could suppress fluctuations important for thermal instability. The lack of small-scale compressive modes is also problematic for hypothesized resonant scattering of $E > 300$ GeV CRs, when self-confinement is inefficient. 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 the turbulent forcing rate, i.e. $\tilde{\epsilon} \gg \rho v^{3}/L$. These findings motivate future, higher resolution simulations with a mixture of turbulent driving modes.
C. Bustard and S. Oh
Thu, 12 Jan 23
56/68
Comments: Submitted to ApJ, 21 pages, 12 figures