A Toy Model for the Time-Frequency Structure of Fast Radio Bursts: Implications for the CHIME/FRB Burst Dichotomy

We introduce a toy model for the time-frequency structure of fast radio bursts, in which the observed emission is produced as a narrowly peaked intrinsic spectral energy distribution sweeps down in frequency across the instrumental bandpass as a power law in time. Though originally motivated by emission models that invoke a relativistic shock, the model could in principle apply to a wider range of emission scenarios. We quantify the burst's detectability using the frequency bandwidth over which most of its signal-to-noise ratio is accumulated. We demonstrate that, by varying just a single parameter of the toy model - the power-law index β of the frequency drift rate - one can transform a long (and hence preferentially time-resolved) burst with a narrow time-integrated spectrum into a shorter burst with a broad power-law time-integrated spectrum. We suggest that source-to-source diversity in the value of β could generate the dichotomy between burst duration and frequency-bandwidth recently found by CHIME/FRB. In shock models, the value of β is related to the radial density profile of the external medium, which, in light of the preferentially longer duration of bursts from repeating sources, may point to diversity in the external environments surrounding repeating versus one-off FRB sources.