Effects of Alfvenic Drift on Diffusive Shock Acceleration at Weak Cluster Shocks

Abstract

Non-detection of gamma-ray emission from galaxy clusters has challenged diffusive shock acceleration (DSA) of cosmic-ray (CR) protons at weak collisionless shocks that are expected to form in the intracluster medium. As an effort to address this problem, we here explore possible roles of Alfven waves self-excited via resonant streaming instability during the CR acceleration at parallel shocks. The mean drift of Alfven waves may either increase or decrease the scattering center compression ratio, depending on the postshock cross-helicity, leading to either flatter or steeper CR spectra. We first examine such effects at planar shocks, based on the transport of Alfven waves in the small amplitude limit. For the shock parameters relevant to cluster shocks, Alfvenic drift flattens the CR spectrum slightly, resulting in a small increase of the CR acceleration efficiency, eta. We then consider two additional, physically motivated cases: (1) postshock waves are isotropized via MHD and plasma processes across the shock transition, and (2) postshock waves contain only forward waves propagating along with the flow due to a possible gradient of CR pressure behind the shock. In these cases, Alfvenic drift could reduce eta by as much as a factor of five for weak cluster shocks. For the canonical parameters adopted here, we suggest eta similar to 10(-4)-10(-2) for shocks with sonic Mach number M-s approximate to 2-3. The possible reduction of. may help ease the tension between non-detection of gamma-rays from galaxy clusters and DSA predictions.