Measurement of the Rate Distribution of the Population of Repeating Fast Radio Bursts: Implications for Progenitor Models

The discovery of many repeating fast radio bursts (FRBs) by the Canadian Hydrogen Intensity Mapping Experiment, the high rate of individual bursts, and the observation of repeat bursts from a bright FRB initially detected by the Australian Square Kilometre Array Pathfinder (ASKAP) suggest a significant population of repeating FRBs. Here, we analyze the rate distribution of this population using results from follow-up observations of the Commensal Real-time ASKAP Fast Transients Survey. Characterizing a repeating FRB by its burst rate R0 above an energy of 1038 erg, we consider a volumetric density Φ(R0) with rate distribution $d{\rm{\Phi }}\propto {R}_{0}^{\zeta }{{dR}}_{0}$. We use maximum-likelihood methods to constrain ζ < −1.94 at 90% confidence. We discuss how this constraint can be used to limit different classes of progenitor models for repeating FRBs: it excludes FRBs with burst rate proportional to neutron star spin-down power with braking index n ≤ 14, i.e., magnetic dipole radiation (n = 3); and it excludes some scenarios for FRB emission from magnetars, and the magnetic field interactions of compact binaries.