Constraints on the Engines of Fast Radio Bursts

Abstract: We model the sample of fast radio bursts (FRB), including the newly discovered CHIME repeaters, using the synchrotron blast wave model of Metzger, Margalit & Sironi (2019). This model postulates that FRBs are precursor radiation from ultra-relativistic magnetized shocks generated as flare ejecta from a central engine collide with an effectively stationary external medium. Downward drifting of the burst frequency structure naturally arises from deceleration of the blast-wave. The data are consistent with FRBs being produced by flares of energy $E_{\rm flare} \sim 10^{43}-10^{46}(f_{\xi}/10^{-3})^{-4/5}$ erg, where $f_{\xi}$ is the maser efficiency, and minimum bulk Lorentz factors $\Gamma \approx 10^2-10^3$, which generate the observed FRBs at shock radii $r_{\rm sh} \sim 10^{12}-10^{13}$ cm. We infer upstream densities $n_{\rm ext}(r_{\rm sh}) \sim 10^{2}-10^{4}$ cm$^{-3}$ and radial profiles $n_{\rm ext} \propto r^{-k}$ showing a range of slopes $k \approx [-2,1]$ (which are seen to evolve between bursts), broadly consistent with the upstream medium being the inner edge of an ion-loaded shell released by a recent energetic flare. The burst timescales, energetics, rates, and external medium properties are consistent with repeating FRBs arising from young, hyper-active flaring magnetars, but the methodology presented is generally applicable to any central engine which injects energy impulsively into a dense magnetized medium. Uncertainties and variations of the model are discussed, including the effects of the strong electric field of the FRB wave (strength parameter $a \gg 1$) on the upstream medium. One-dimensional particle-in-cell simulations of magnetized shocks into a pair plasma are presented which demonstrate that high maser efficiency can be preserved, even in the limit $a \gg 1$ in which the FRB wave accelerates the upstream electrons to ultra-relativistic speeds.