Electron acceleration at rippled low Mach number shocks in merging galaxy clusters

Shock waves are ubiquitous in cosmic plasmas wherein they accelerate particles. In particular, X-ray and radio observations of so-called radio relics indicate electron acceleration at large-scale merger shocks in galaxy clusters. These shocks are also candidate sites for ultra-high-energy cosmic ray production. Merger shocks have low Mach numbers and propagate in hot plasmas with plasma beta ß » 1. Particle energization and especially electron injection mechanisms are poorly understood in such conditions. Recent studies show that shock drift acceleration (SDA) accompanied by particle-wave interactions can provide electron acceleration, albeit a multi-scale shock structure in the form of ion-scale shock rippling may significantly alter the injection mechanisms. Here we study the effects of the shock rippling with large-scale 2D PIC simulations of low Mach number cluster shocks. We find that the electron acceleration rate increases considerably after the appearance of wave-rippling modes. The main acceleration process is stochastic SDA, in which electrons are confined in the shock transition region by pitch-angle scattering off magnetic turbulence and gain energy from motional electric field. The presence of multi-scale turbulence in the shock is essential for particle energization. Wide-energy non-thermal electron distributions are formed both upstream and downstream of the shock. We show for the first time that the downstream electron spectrum has a power-law form with index p = 2.4, in agreement with observations.