The kinetic-energy bottleneck in Fast Radio Burst models

Abstract

Most Fast Radio Burst (FRB) models invoke a two-step process in which energy released by the central engine is converted into particle kinetic energy and only subsequently radiated as coherent GHz emission. We derive model-independent constraints on FRB emission mechanisms and use them to infer the density, size, and particle Lorentz factor of the emitting region. We assess the implications for the three main classes of FRB models. (i) Inner-magnetospheric models violate brightness-temperature and kinetic-luminosity constraints unless particles are continuously re-accelerated in situ. Magnetar-strength magnetic fields can supply the required parallel electric field out to $R\lesssim10^{10} \mathrm{cm}$ with additional, model-dependent constraints. The monster-shock scenario provides such continuous acceleration, but requires particle densities exceeding the Goldreich-Julian value by $\gtrsim 10^{12}$, shifting the maser peak to $\gtrsim10^3$ GHz for typical FRB luminosities. (ii) Light-cylinder-scale forced-reconnection provides continuous particle acceleration but the radio energy emitted from the compressed reconnection layer is typically only $\lesssim10^{-6}$ of the injected energy. (iii) External-shock maser models satisfy kinetic-luminosity and brightness-temperature constraints. However, we show that the upstream wind is unavoidably optically thick to induced Compton scattering, independent of the model's principal parameters. Proposed escape routes - emission above the maser peak or upstream magnetization $σ_{\rm w}\gtrsim30$ - lead to tiny efficiencies, while the former also conflicts with narrow FRB spectra. We conclude that magnetospheric models operating near the neutron-star surface and incorporating continuous particle acceleration remain the most promising FRB emission scenario, subject to successful wave escape from the magnetosphere (discussed in the Introduction).