Particle Acceleration and Heating in Low Mach Number Collisionless Shocks

Abstract

Low Mach number collisionless shocks occur during the mergers of galaxy clusters. Radio and X-ray observations reveal that particles are accelerated and heated in these shocks. However, exactly how the particles, especially the electrons whose radiative signature we directly observe, are actually energized has been poorly understood. In this thesis, I use multi-dimensional first-principles numerical simulations to elucidate the microphysics of particle acceleration and heating in low Mach number collisionless shocks. The first part of the thesis focuses on particle acceleration. I show via simulations that electrons are efficiently accelerated in low Mach number quasi-perpendicular shocks, while protons are not. I identify a Fermi-like electron acceleration mechanism in which particle injection operates via shock drift acceleration, and long term evolution is sustained by electron self-generated waves driven by the oblique electron firehose instability. I then explore how the efficiency of electron acceleration depends on pre-shock conditions of the plasma. I find that the mechanism I have identified works for shocks with high plasma beta, at nearly all magnetic field obliquities, and for electron temperatures in the range relevant for galaxy clusters. My findings offer a natural explanation for the bright radio synchrotron emission observed in the outskirts of galaxy clusters. Previously, this radiation was considered problematic since electron acceleration was believed to be inefficient in low Mach number shocks. In the second part of the thesis I focus on particle heating in low Mach number shocks. I show that protons are heated to higher temperatures than electrons in perpendicular shocks. However, electrons still experience a non-trivial amount of irreversible heating, i.e., their entropy increases as they travel through the shock. I develop a model for particle irreversible heating which requires the presence of two elements: (i) temperature anisotropy between field-parallel and field-perpendicular directions, and (ii) a mechanism to break the adiabatic dynamics of particles. For electrons in shocks, the temperature anisotropy is induced by field amplification via compression, while adiabaticity is broken by the action of electron whistler waves which are triggered by the same anisotropy. I successfully validate the model through detailed comparisons with first-principles numerical simulations. I then explore how the efficiency of electron heating depends on pre-shock conditions of the plasma. I provide an empirical fitting formula for the irreversible heating of electrons in low Mach number shocks and use it to predict the post-shock electron-to-proton temperature ratio as a function of two key parameters, the sonic Mach number of the shock and the plasma beta of the upstream gas. The model predictions compare favorably with observational data.