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

TL;DR

This paper investigates how Alfvénic drift influences diffusive shock acceleration efficiency at weak galaxy cluster shocks, potentially explaining the lack of observed gamma-ray emissions by modifying cosmic-ray spectra.

Contribution

It introduces a detailed analysis of Alfvénic drift effects on CR acceleration at weak shocks, considering various wave postshock configurations, and quantifies how these effects alter acceleration efficiency.

Findings

Alfvénic drift slightly flattens CR spectra, increasing efficiency.

In certain wave configurations, Alfvénic drift can reduce efficiency by up to a factor of 5.

Estimated efficiency range for weak shocks is $ ext{10}^{-4}$ to $ ext{10}^{-2}$.

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 Alfv\'en waves self-excited via resonant streaming instability during the CR acceleration at parallel shocks. The mean drift of Alfv\'en 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 Alfv\'en waves in the small amplitude limit. For the shock parameters relevant to cluster shocks, Alfv\'enic 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, Alfv\'enic drift could reduce $\eta$ by as much as a factor of 5 for weak cluster shocks. For the canonical parameters adopted here, we suggest $\eta\sim10^{-4}-10^{-2}$ for shocks with sonic Mach number $M_{\rm s}\approx2-3$. The possible reduction of $\eta$ may help ease the tension between non-detection of $\gamma$-rays from galaxy clusters and DSA predictions.