DIFFUSIVE SHOCK ACCELERATION AT COSMOLOGICAL SHOCK WAVES

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 Alfvenic drift, we perform kinetic DSA simulations for a wide range of sonic and Alfvenic 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 M-s, while the MFA factor depends on the Alfvenic 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 Alfven 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 similar to 20% of the shock ram pressure for strong shocks with M-s greater than or similar to 10. In the test-particle regime (M-s less than or similar to 3), it is expected that the magnetic field is not amplified and the Alfvenic drift effects are insignificant, although relevant plasma physical processes at low Mach number shocks remain largely uncertain.