Constraints on the Engines of Fast Radio Bursts

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 $E_{\rm flare} \sim 10^{43}-10^{46}(f_ξ/10^{-3})^{-4/5}$ erg, where $f_ξ$ is the maser efficiency, and minimum bulk Lorentz factors $Γ\approx 10^2-10^3$, 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.

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