Diffusive shock acceleration with magnetic field amplification and Alfvenic drift

TL;DR

This study uses kinetic simulations to analyze how magnetic field amplification and Alfvenic drift influence diffusive shock acceleration at astrophysical shocks, revealing effects on CR spectra and acceleration efficiency.

Contribution

It introduces a comprehensive model combining MFA, Alfvenic drift, and other effects into DSA simulations, providing new insights into shock precursor development and CR spectrum shaping.

Findings

CR feedback leads to magnetic amplification up to 20 times.

Alfvenic drift steepens CR energy spectra and reduces acceleration efficiency.

CR pressure saturates at about 10% of shock ram pressure for strong shocks.

Abstract

We explore how wave-particle interactions affect diffusive shock acceleration (DSA) at astrophysical shocks by performing time-dependent kinetic simulations, in which phenomenological models for magnetic field amplification (MFA), Alfvenic drift, thermal leakage injection, Bohm-like diffusion, and a free escape boundary are implemented. If the injection fraction of cosmic-ray (CR) particles is greater than 2x10^{-4}, for the shock parameters relevant for young supernova remnants, DSA is efficient enough to develop a significant shock precursor due to CR feedback, and magnetic field can be amplified up to a factor of 20 via CR streaming instability in the upstream region. If scattering centers drift with Alfven speed in the amplified magnetic field, the CR energy spectrum can be steepened significantly and the acceleration efficiency is reduced. Nonlinear DSA with self-consistent MFA and Alfvenic drift predicts that the postshock CR pressure saturates roughly at 10 % of the shock ram pressure for strong shocks with a sonic Mach number ranging 20< M_s< 100. Since the amplified magnetic field follows the flow modification in the precursor, the low energy end of the particle spectrum is softened much more than the high energy end. As a result, the concave curvature in the energy spectra does not disappear entirely even with the help of Alfvenic drift. For shocks with a moderate Alfven Mach number (M_A<10), the accelerated CR spectrum can become as steep as E^{-2.1}-E^{-2.3}, which is more consistent with the observed CR spectrum and gamma-ray photon spectrum of several young supernova remnants.