DIFFUSIVE SHOCK ACCELERATION WITH MAGNETIC FIELD AMPLIFICATION AND ALFVÉNIC DRIFT

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), Alfv<TEX>$\acute{e}$</TEX>nic drift, thermal leakage injection, Bohm-like diffusion, and a free escape boundary are implemented. If the injection fraction of cosmic-ray (CR) particles is <TEX>${\xi}$</TEX> > <TEX>$2{\times}10^{-4}$</TEX>, 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 Alfv<TEX>$\acute{e}$</TEX>n 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 Alfv<TEX>$\acute{e}$</TEX>nic 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 <TEX>$20{\leq}M_s{\leq}100$</TEX>. 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 Alfv<TEX>$\acute{e}$</TEX>nic drift. For shocks with a moderate Alfv<TEX>$\acute{e}$</TEX>n Mach number (<TEX>$M_A$</TEX> < 10), the accelerated CR spectrum can become as steep as <TEX>$E^{-2.1}$</TEX> - <TEX>$E^{-2.3}$</TEX>, which is more consistent with the observed CR spectrum and gamma-ray photon spectrum of several young supernova remnants.