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Electron acceleration to non-thermal energies is known to occur in low Machnumber (M<5) shocks in galaxy clusters and solar flares, but the electronacceleration mechanism remains poorly understood. Using two-dimensional (2D)particle-in-cell (PIC) plasma simulations, we showed in Paper I that electronsare efficiently accelerated in low Mach number (M=3) quasi-perpendicular shocksvia a Fermi-like process. The electrons bounce between the upstream region andthe shock front, with each reflection at the shock resulting in energy gain viashock drift acceleration. The upstream scattering is provided by obliquemagnetic waves, that are self-generated by the electrons escaping ahead of theshock. In the present work, we employ additional 2D PIC simulations to addressthe nature of the upstream oblique waves. We find that the waves are generatedby the shock-reflected electrons via the firehose instability, which is drivenby an anisotropy in the electron velocity distribution. We systematicallyexplore how the efficiency of wave generation and of electron accelerationdepend on the magnetic field obliquity, the flow magnetization (orequivalently, the plasma beta), and the upstream electron temperature. We findthat the mechanism works for shocks with high plasma beta (>20) at nearly allmagnetic field obliquities, and for electron temperatures in the range relevantfor galaxy clusters. Our findings offer a natural solution to the conflictbetween the bright radio synchrotron emission observed from the outskirts ofgalaxy clusters and the low electron acceleration efficiency usually expectedin low Mach number shocks.

astrophysical journal/the astrophysical journal

Non-Thermal Electron Acceleration in Low Mach Number Collisionless  Shocks. II. Firehose-Mediated Fermi Acceleration and its Dependence on  Pre-Shock Conditions