Fast radio bursts as synchrotron maser emission from decelerating relativistic blast waves

Abstract: Fast radio bursts (FRB) can arise from synchrotron maser emission at ultra-relativistic magnetized shocks, such as produced by flare ejecta from young magnetars. We combine PIC simulation results for the synchrotron maser with the dynamics of self-similar shock deceleration, as commonly applied to GRBs, to explore the implications for FRB emission. We assume the upstream environment into which the ultra-relativistic ejecta collides is a mildly relativistic baryon-loaded shell released following a previous flare, motivated by the high electron-ion injection rate Mdot ~ 1e19-1e21 g/s needed on larger scales to power the persistent radio nebula coincident with the repeating burster FRB 121102 and its high inferred rotation measure. The observed radio fluence peaks once the optical depth ahead of the shock to induced Compton scattering decreases to <~ few, a condition which places a GHz observer on the high frequency tail of the maser SED. Given intervals between ion shell ejection events ~1e5 s similar to the occurrence rate of the most powerful bursts from FRB 121102, we demonstrate the production of FRBs of frequency ~ 0.1-10 GHz, isotropic radiated energies ~1e37-1e40 erg and durations ~0.1-10 ms for flares of energy ~1e43-1e45 erg. Deceleration of the blast wave, and increasing transparency of the upstream medium, generates a temporal decay of the peak frequency, similar to the downward drift seen in the sub-bursts of FRB 121102 and FRB 180814.J0422+73. The delay >~ 1e5 s between major ion-injection events needed to clear sufficiently low densities around the engine for FRB emission could explain prolonged "dark" periods and clustered burst arrival times, and lead to stochastic variation in the dispersion measure. Thermal electrons heated at the shock generate a short-lived <~ 1 ms (1 s) synchrotron transient at gamma-ray (X-ray) energies, analogous to a GRB afterglow.