The Moving Mirror model for Fast Radio Bursts

Abstract: Recent observations of coherent radiation from the Crab pulsar (Bij et al 2021) suggest the emission is driven by an ultra - relativistic ($\gamma \sim 10^4$), cold plasma flow. A relativistically expanding plasma shell can compress the ambient magnetic field, like a moving mirror, and thus produce coherent radiation whose wavelength is shorter than that of the ambient medium by $\gamma^2$. This mechanism has been studied in the past by Colgate and Noerdelinger (1971), in the context of radio loud supernova explosions. In this work we propose that a similar mechanism drives the coherent emission in fast radio bursts. The high Lorenz factors dramatically lower the implied energy and magnetic field requirements, allowing the spin down energy of regular (or even recycled), fast spinning pulsars, rather than slow spinning magnetars, to explain FRBs. We show that this model can explain the frequency and the time evolution of observed FRBs, as well as their duration, energetics and absence of panchromatic counterparts. We also predict that the peak frequency of sub pulses decline with observation time as $\omega_{\rm obs} \propto t_{\rm obs}^{-1/2}$. Unfortunately, with current capabilities it is not possible to constrain the shape of the curve $\omega_{\rm obs} \left(t_{\rm obs} \right)$. Finally, we find that a variation of this model can explain weaker radio transients, such as the one observed from a galactic magnetar. In this variant, the shock wave produces low frequency photons which are then Compton scattered to the GHz range.