Periodic Fast Radio Bursts as a Probe of Extragalactic Asteroid Belts

The periodic activity of the repeating fast radio burst (FRB) 180916.J0158+65 was recently reported by the CHIME/FRB Collaboration team. From this source 28 bursts not only show a ∼16 day period with an active phase of ∼4.0 days, but they also exhibit a broken power law in differential energy distribution. In this Letter, we suggest that FRB 180916.J0158+65-like periodic FRBs could provide a unique probe of extragalactic asteroid belts (EABs), based on our previously proposed pulsar-EAB impact model, in which repeating FRBs arise from an old-aged, slowly spinning, moderately magnetized pulsar traveling through an EAB around another stellar-mass object. These two objects form a binary, and thus the observed period is in fact the orbital period. We show that this model can be used to well interpret all of the observed data of FRB 180916.J0158+65. Furthermore, we constrain the EAB's physical properties and find that (1) the outer radius of the EAB is at least an order of magnitude smaller than that of its analog in the solar system, (2) the differential size distribution of the EAB's asteroids at small diameters (large diameters) is shallower (steeper) than that of solar system small objects, and (3) the two belts have a comparable mass.