Thermal Electrons in Mildly-relativistic Synchrotron Blast-waves

TL;DR

This paper develops a comprehensive synchrotron emission model including thermal and non-thermal electrons in mildly-relativistic shocks, explaining observed features in transients like AT2018cow and predicting their spectral signatures.

Contribution

It introduces a complete thermal plus non-thermal synchrotron model for sub-relativistic shocks, clarifying the role of thermal electrons in transient emissions.

Findings

Thermal electrons significantly influence peak emission at shock velocities above 0.2c.

Thermal electron synchrotron spectra exhibit steep optically-thin and ν^2 optically-thick features.

Model explains spectral and light-curve characteristics of AT2018cow-like events.

Abstract

Numerical models of collisionless shocks robustly predict an electron distribution comprised of both thermal and non-thermal electrons. Here, we explore in detail the effect of thermal electrons on the emergent synchrotron emission from sub-relativistic shocks. We present a complete `thermal + non-thermal' synchrotron model and derive properties of the resulting spectrum and light-curves. Using these results we delineate the relative importance of thermal and non-thermal electrons for sub-relativistic shock-powered synchrotron transients. We find that thermal electrons are naturally expected to contribute significantly to the peak emission if the shock velocity is $\gtrsim 0.2c$, but would be mostly undetectable in non-relativistic shocks. This helps explain the dichotomy between typical radio supernovae and the emerging class of `AT2018cow-like' events. The signpost of thermal electron synchrotron emission is a steep optically-thin spectral index and a $\nu^2$ optically-thick spectrum. These spectral features are also predicted to correlate with a steep post-peak light-curve decline rate, broadly consistent with observed AT2018cow-like events. We expect that thermal electrons may be observable in other contexts where mildly-relativistic shocks are present, and briefly estimate this effect for gamma-ray burst afterglows and binary neutron star mergers. Our model can be used to fit spectra and light-curves of events and accounts for both thermal and non-thermal electron populations with no additional physical degrees of freedom.