What does FRB light-curve variability tell us about the emission mechanism?

A few fast radio bursts' (FRBs) light curves have exhibited large intrinsic modulations of their flux on extremely short time-scales, compared to pulse durations (tFRB ∼1 ms). Light-curve variability time-scales, the small ratio of rise time of the flux to pulse duration, and the spectro-temporal correlations in the data constrain the compactness of the source and the mechanism responsible for the powerful radio emission. The constraints are strongest when radiation is produced far 1010 from the compact object. We describe different physical set-ups that can account for the observed tr/tFRB 1 despite having large emission radii. The result is either a significant reduction in the radio production efficiency or distinct light-curve features that could be searched for in observed data. For the same class of models, we also show that due to high-latitude emission, if a flux f1(ν1) is observed at t1 then at a lower frequency ν2 < ν1 the flux should be at least (ν2/ν1)2f1 at a slightly later time (t2 = t1ν1/ν2) independent of the duration and spectrum of the emission in the comoving frame. These features can be tested, once light-curve modulations due to scintillation are accounted for. We provide the time-scales and coherence bandwidths of the latter for a range of possibilities regarding the physical screens and the scintillation regime. Finally, if future highly resolved FRB light curves are shown to have intrinsic variability extending down to time-scales, this will provide strong evidence in favour of magnetospheric models.