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.
Bibliographical noteFunding Information:
We thank Shami Chatterjee and Ziggy Pleunis for helpful conversations. B.D.M. acknowledges support from the National Science Foundation (grant No. GG016244). The research of P.B. was funded by the Gordon and Betty Moore Foundation through Grant GBMF5076. B.M. is supported by NASA through the NASA Hubble Fellowship grant #HST-HF2-51412.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. L.S. acknowledges support from the Cottrell Scholars Award and NASA 80NSSC18K1104.
© 2022. The Author(s). Published by the American Astronomical Society.