Thermal Electrons in Mildly Relativistic Synchrotron Blast Waves

Numerical models of collisionless shocks robustly predict an electron distribution composed of both thermal and nonthermal electrons. Here, we explore in detail the effect of thermal electrons on the emergent synchrotron emission from subrelativistic shocks. We present a complete "thermal + nonthermal" synchrotron model and derive properties of the resulting spectrum and light curves. Using these results, we delineate the relative importance of thermal and nonthermal electrons for subrelativistic shock-powered synchrotron transients. We find that thermal electrons are naturally expected to contribute significantly to the peak emission if the shock velocity is ≳0.2c, but would be mostly undetectable in nonrelativistic 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 ν2 optically-thick spectrum. These spectral features are also predicted to correlate with a steep postpeak 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 nonthermal electron populations with no additional physical degrees of freedom.