Shock Acceleration in the Intracluster Medium: Implications of Micromirror Confinement

Abstract

Merging galaxy clusters exhibit strong observational evidence for efficient particle acceleration in the intracluster medium (ICM), particularly in the form of synchrotron-emitting radio relics and halos. Cosmic ray (CR) electrons are likely accelerated (or re-accelerated) at merger and accretion shocks via diffusive shock acceleration (DSA). However, in the presence of the large diffusion coefficients one would naively expect in the rarefied, relatively unmagnetized ICM, this acceleration--in particular, the maximum proton energy ($E_{\rm max}$)--is limited by long acceleration times. On the other hand, recent work on CR transport suggests that the diffusion coefficient can be suppressed in ICM-like environments. In this picture, deviations from local thermodynamic equilibrium can trigger the mirror instability, creating plasma-scale magnetic structures, or "micromirrors," that efficiently scatter CRs. In this paper, we investigate the implications of micromirror confinement for shock acceleration in the ICM. We demonstrate that micromirrors enforce a minimum value of $E_{\rm max} \gtrsim 100$ GeV that does not rely on CR-driven magnetic field amplification. We also discuss micromirror confinement in the context of cosmological simulations and $\gamma$-ray observations, and present a simulation of a Coma-like merging cluster that self-consistently includes CR acceleration at shocks, with an effective diffusion coefficient set by micromirrors. We show that the introduction of micromirrors yields simulated galaxy clusters that remain consistent with $\gamma$-ray observations.