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

submitted to ApJ

References in corpus (11)

• Shocks and cold fronts in galaxy clusters
• Turbulence and Magnetic Fields in the Large Scale Structure of the Universe
• Particle Acceleration on Megaparsec Scales in a Merging Galaxy Cluster
• Simulations and Theory of Ion Injection at Non-relativistic Collisionless Shocks
• Diffusive Shock Acceleration with Magnetic Amplification by Non-resonant Streaming Instability in SNRs
• Cosmological Shock Waves in the Large Scale Structure of the Universe: Non-gravitational Effects
• Dynamical Feedback of Self-generated Magnetic Fields in Cosmic Ray Modified Shocks
• Cosmic ray physics in calculations of cosmological structure formation
• Turbulence and Vorticity in Galaxy Clusters Generated by Structure Formation
• Properties of Merger Shocks in Merging Galaxy Clusters
• Shock Acceleration Model with Postshock Turbulence for Giant Radio Relics

Cited by in corpus (13)

• Shock acceleration efficiency in radio relics
• Kinetic Simulations of Cosmic-Ray-Modified Shocks II: Particle Spectra
• Kinetic Simulations of Cosmic-Ray-Modified Shocks I: Hydrodynamics
• Exploring the spectral properties of radio relics I: Integrated spectral index and Mach number
• Shocks and non-thermal particles in clusters of galaxies
• Proton Acceleration in Weak Quasi-parallel Intracluster Shocks: Injection and Early Acceleration
• Polarisation of Radio Relics in Galaxy Clusters
• A Diffusive Shock Acceleration Model for Protons in Weak Quasi-parallel Intracluster Shocks
• Steep Cosmic Ray Spectra with Revised Diffusive Shock Acceleration
• Tempestuous life beyond R500: X-ray view on the Coma cluster with SRG/eROSITA. II. Shock & Relic
• Modeling of Cosmic-Ray Production and Transport and Estimation of Gamma-Ray and Neutrino Emissions in Starburst Galaxies
• On the Challenges of Cosmic-Ray Proton Shock Acceleration in the Intracluster Medium
• On the influence of supra-thermal particle acceleration on the morphology of low-Mach, high-$\beta$ shocks