Diffusive Shock Acceleration at Cosmological Shock Waves

TL;DR

This paper investigates nonlinear diffusive shock acceleration at cosmological shocks, incorporating wave-particle interactions, magnetic field amplification, and Alfv'enic drift, revealing how these factors influence cosmic-ray acceleration efficiency and energy spectra.

Contribution

It introduces a kinetic DSA model that includes magnetic field amplification and Alfv'enic drift effects, providing new insights into cosmic-ray acceleration at cosmological shocks.

Findings

CR acceleration efficiency depends mainly on sonic Mach number

Magnetic field amplification depends on Alfv'enic Mach number

CR pressure saturates at about 20% of shock ram pressure for strong shocks

Abstract

We reexamine nonlinear diffusive shock acceleration (DSA) at cosmological shocks in the large scale structure of the Universe, incorporating wave-particle interactions that are expected to operate in collisionless shocks. Adopting simple phenomenological models for magnetic field amplification (MFA) by cosmic-ray (CR) streaming instabilities and Alfv'enic drift, we perform kinetic DSA simulations for a wide range of sonic and Alfv'enic Mach numbers and evaluate the CR injection fraction and acceleration efficiency. In our DSA model the CR acceleration efficiency is determined mainly by the sonic Mach number Ms, while the MFA factor depends on the Alfv'enic Mach number and the degree of shock modification by CRs. We show that at strong CR modified shocks, if scattering centers drift with an effective Alfv'en speed in the amplified magnetic field, the CR energy spectrum is steepened and the acceleration efficiency is reduced significantly, compared to the cases without such effects. As a result, the postshock CR pressure saturates roughly at ~ 20 % of the shock ram pressure for strong shocks with Ms>~ 10. In the test-particle regime (Ms<~ 3), it is expected that the magnetic field is not amplified and the Alfv'enic drift effects are insignificant, although relevant plasma physical processes at low Mach number shocks remain largely uncertain.