TY  - JOUR
A1  - Pohl, Martin
T1  - Time-dependent treatment of cosmic-ray spectral steepening due to turbulence driving
T2  - The astrophysical journal : an international review of spectroscopy and astronomical physics
N2  - Cosmic-ray acceleration at non-relativistic shocks relies on scattering by turbulence that the cosmic rays drive upstream of the shock. We explore the rate of energy transfer from cosmic rays to non-resonant Bell modes and the spectral softening it implies. Accounting for the finite time available for turbulence driving at supernova-remnant shocks yields a smaller spectral impact than found earlier with steady-state considerations. Generally, for diffusion scaling with the Bohm rate by a factor eta, the change in spectral index is at most eta divided by the Alfvenic Mach number of the thermal sub-shock. For M (A) less than or similar to 50 it is well below this limit. Only for very fast shocks and very efficient cosmic-ray acceleration can the change in spectral index reach 0.1. For standard SNR parameters, it is negligible. Independent confirmation is derived by considering the synchrotron energy losses of electrons: if intense nonthermal multi-keV emission is produced, the energy loss, and hence the spectral steepening, is very small for hadronic cosmic rays that produce TeV-band gamma-ray emission.
Y1  - 2021
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/61384
SN  - 1538-4357
VL  - 921
IS  - 2
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -