Electron-Ion Temperature Ratio in Transrelativistic Unmagnetized Shock Waves

TL;DR

This paper develops a unified model for the electron-ion temperature ratio in unmagnetized shock waves across a wide velocity spectrum, revealing electrons attain about 10% of ion kinetic energy regardless of shock speed.

Contribution

It introduces a comprehensive model for electron heating in unmagnetized shocks, applicable from Newtonian to relativistic regimes, including gamma-ray burst afterglows.

Findings

Electrons reach approximately 10% of ion kinetic energy in all shock regimes.

The model explains electron heating via ambipolar electric fields and turbulence.

Results are relevant for understanding energy distribution in astrophysical shocks.

Abstract

Weakly magnetized shock waves are paramount to a large diversity of environments, including supernova remnants, blazars, and binary-neutron-star mergers. Understanding the distribution of energy between electrons and ions within these astrophysical shock waves spanning a wide spectrum of velocities is a long-standing challenge. In this study, we present a unified model for the downstream electron temperature within unmagnetized shock waves. Encompassing velocities from Newtonian to relativistic, we probe regimes representative of the gradual deceleration of the forward shock in the late gamma-ray burst afterglow phase, such as GRB 170817A. In our model, heating results from an ambipolar electric field generated by the difference in inertia between electrons and ions, coupled with rapid electron scattering in the decelerating turbulence. Our findings demonstrate that the electron temperature consistently represents $10\%$ of the incoming ion kinetic energy in the shock front frame over the full range of shock velocities.