Shock Acceleration in the Intracluster Medium: Implications of Micromirror Confinement

TL;DR

This study investigates how micromirror confinement, produced by firehose and mirror instabilities in the high-$\beta$ intracluster medium, modifies cosmic-ray transport and the maximum energy achievable by diffusive shock acceleration at merger and accretion shocks. Analytic estimates show micromirror-induced diffusion suppression sets a baseline $E_{ m max}$ of roughly $\sim$100–130 GeV for protons in typical mergers, with accretion shocks potentially reaching $\sim$580 GeV and Bohm-like amplification capable of pushing to PeV scales if magnetic fluctuations grow to $\delta B/B_0\sim 1$. Cosmological simulations of a Coma-like cluster incorporating advective CR transport and micromirror-limited diffusion reveal CR energy densities $X_{\rm CR}\sim 10^{-4}-10^{-3}$ and $\,\gamma$-ray emission that remains compatible with Fermi-LAT upper limits, despite high $E_{ m max}$ at shocks. The results imply cluster CR transport is largely advection-dominated under micromirror confinement, reconcile efficient shock acceleration with current $\gamma$-ray non-detections, and suggest future TeV observations (e.g., CTA) could probe higher-energy CR components if CR-driven magnetic amplification occurs.

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 $γ$-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 $γ$-ray observations.

Figures (5)

• Figure 1: Allowed ratios of the maximum average CR pressure to the average ICM thermal pressure ($X_{\rm CR}$; shaded regions) as a function of the proton power-law slope, $q$, in the Coma cluster, based on Fermi-LAT upper limits ackermann+16. Colors correspond to different ambient densities, $n_{\rm ICM}$. To remain consistent with observations $X_{\rm CR}$ needs to be fairly small ($\lesssim 10^{-2}-10^{-3}$), depending on the average ambient density.
• Figure 2: Density (left panel), CR to thermal pressure ratio (center panels), and $\gamma$-ray luminosity (right panel) maps of our fiducial cluster simulation, a Coma-like cluster with a viral mass of $M_\mathrm{vir} \approx 2 \times 10^{15} M_\odot$. The circle illustrates $r_{200}$ of the cluster.
• Figure 3: Maximum energy of the shock accelerated protons, following Equation \ref{['eq:emax_mm']}.
• Figure 4: Average CR to thermal pressure ratio, $X_{\rm CR}$, as a function of radius for a simulated Coma analog. The blue line shows $X_{\rm CR}$ averaged over the entire shell at radius $r$, while the orange line only includes regions where the CR pressure ($P_{\rm CR}$) is nonzero. In both cases, $X_{\rm CR}$ generally falls well below the maximum allowed values illustrated in Figure \ref{['fig:pressureratio']}.
• Figure 5: Integrated $\gamma$-ray luminosity of our simulated Coma analog (purple point), compared to upper-limits from a sample of clusters measured with Fermi-LAT ackermann+14. The errorbar indicates the maximum impact of the ultra-relativistic approximation on our results. Our modeled cluster falls well below these upper-limits, implying that, while micromirror confinement can enhance the maximum proton energy, it does not yield a tension with observations.