Abstract
Electron acceleration to non-thermal energies is known to occur in low Mach number (M<5) shocks in galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Using two-dimensional (2D) particle-in-cell (PIC) plasma simulations, we showed in Paper I that electrons are efficiently accelerated in low Mach number (M=3) quasi-perpendicular shocks via a Fermi-like process. The electrons bounce between the upstream region and the shock front, with each reflection at the shock resulting in energy gain via shock drift acceleration. The upstream scattering is provided by oblique magnetic waves, that are self-generated by the electrons escaping ahead of the shock. In the present work, we employ additional 2D PIC simulations to address the nature of the upstream oblique waves. We find that the waves are generated by the shock-reflected electrons via the firehose instability, which is driven by an anisotropy in the electron velocity distribution. We systematically explore how the efficiency of wave generation and of electron acceleration depend on the magnetic field obliquity, the flow magnetization (or equivalently, the plasma beta), and the upstream electron temperature. We find that the mechanism works for shocks with high plasma beta (>20) at nearly all magnetic field obliquities, and for electron temperatures in the range relevant for galaxy clusters. Our findings offer a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.
Highlights
There is considerable observational evidence that electrons are efficiently accelerated in low Mach number collisionless shocks in astrophysical sources
We found that most of the shock physics is well captured by 2D simulations in the xy plane, if the magnetic field lies in the simulation plane, i.e., φB = 0◦
In Paper I, we studied a reference shock that propagates in a high-temperature plasma (Te = 109 K) carrying a quasi-perpendicular magnetic field
Summary
There is considerable observational evidence that electrons are efficiently accelerated in low Mach number collisionless shocks in astrophysical sources. In the first paper of this series (Guo et al 2014, Paper I hereafter), we focused on the particle energy spectra and the acceleration mechanism in a reference PIC run with Mach number Ms = 3 and a quasi-perpendicular magnetic field. In Paper I, we did not investigate the nature of the upstream waves, which are essential for sustaining the Fermi-like process. In addition to clarifying the nature of the upstream waves, another goal of this paper is to explore the dependence of the efficiency of firehose-mediated electron acceleration on pre-shock conditions. The magnetic field strength and obliquity cannot be constrained, though we expect a range of strengths and obliquities With this as motivation, we explore here the dependence of the electron acceleration mechanism on various pre-shock parameters.
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