Implications of CHIME repeating fast radio bursts

CHIME has now detected 18 repeating fast radio bursts (FRBs). We explore what can be learned about the energy distribution and activity level of the repeaters by fitting realistic FRB population models to the data. For a power-law energy distribution dN/dE ~ E^{-\gamma} for the repeating bursts, there is a critical index \gamma_c that controls whether the dispersion measure (DM, a proxy for source distance) distribution of repeaters is bottom or top-heavy. We find \gamma_c = 7/4 for Poisson wait-time distribution of repeaters in Euclidean space and further demonstrate how it is affected by temporal clustering of repetitions and cosmological effects. It is especially interesting that two of the CHIME repeaters (FRB 181017 and 190417) have large DM ~ 1000 pc/cm^3. These can be understood if: (i) the energy distribution is shallow \gamma = 1.7^{+0.3}_{-0.1} (68% confidence) or (ii) a small fraction of sources are extremely active. In the second scenario, these two high-DM sources should be repeating more than 100 times more frequently than FRB 121102, and the energy index is constrained to be \gamma = 1.9^{+0.3}_{-0.2} (68% confidence). In either case, this \gamma is consistent with the energy dependence of the non-repeating ASKAP sample, which suggests that they are drawn from the same population. Finally, our model predicts how the CHIME repeating fraction should decrease with redshift, and this can be compared with observations to infer the distribution of activity level in the whole population.