A Simulation Study of Particle Acceleration in High-beta Shocks Via Weibel Amplification: Implications for Galaxy Cluster Outskirts

Abstract

Cosmological structure formation simulations predict that external accretion shocks form in the outer region of galaxy clusters owing to supersonic gas infall from filaments and voids in the cosmic web. These shocks are characterized by high Mach numbers and propagate into an almost unmagnetized medium. Using 2D particle-in-cell simulations, we show that collisionless shocks could form via the Weibel-amplified magnetic fields, and that electrons can be pre-accelerated via the stochastic Fermi process to be injected into diffusive shock acceleration. Based on these findings, we propose analytic models for the energy spectra of shock-accelerated cosmic-ray (CR) protons and electrons that utilize conventional thermal leakage injection concept. Applying these model CR spectra to numerical shock zones in structure formation simulations, we estimated nonthermal emissions, including synchrotron and inverse Compton radiation due to CR electrons and pi^0-decay gamma-rays due to CR protons, around simulated clusters. The synthetic synchrotron maps produced by our model calculations are consistent with recent radio observations of the Coma Cluster. However, detecting nonthermal X-rays and gamma-rays from accretion shocks in the outer region of galaxy clusters with current observational facilities would be challenging.