Electron Heating in Perpendicular Low-Beta Shocks

Collisionless shocks heat electrons in the solar wind, interstellar blast waves, and hot gas permeating galaxy clusters. How much shock heating goes to electrons instead of ions, and what plasma physics controls electron heating? We simulate 2-D perpendicular shocks with a fully kinetic particle-in-cell code. For magnetosonic Mach number $\mathcal{M}_\mathrm{ms} \sim 1$-$10$ and plasma beta $\beta_\mathrm{p} \lesssim 4$, the post-shock electron/ion temperature ratio $T_\mathrm{e}/T_\mathrm{i}$ decreases from $1$ to $0.1$ with increasing $\mathcal{M}_\mathrm{ms}$. In a representative $\mathcal{M}_\mathrm{ms}=3.1$, $\beta_\mathrm{p}=0.25$ shock, electrons heat above adiabatic compression in two steps: ion-scale $E_\parallel = \vec{E} \cdot \hat{b}$ accelerates electrons into streams along $\vec{B}$, which then relax via two-stream-like instability. The $\vec{B}$-parallel heating is mostly induced by waves; $\vec{B}$-perpendicular heating is mostly adiabatic compression by quasi-static fields.