Lensing of Fast Radio Bursts by Binaries to Probe Compact Dark Matter

Abstract

The possibility that a fraction of the dark matter is comprised of massive compact halo objects (MACHOs) remains unclear, especially in the 20-100 $M_{\odot}$ window. MACHOs could make up binaries, whose mergers may be detected by LIGO as gravitational wave events. On the other hand, the cosmological origin of fast radio burst (FRBs) has been confirmed. We investigate the possibility of detecting fast radio bursts (FRBs) gravitational lensed by MACHO binaries to constrain their properties. Since lensing events could generate more than one images, lensing by binaries could cause multiple-peak FRBs. The angular separation between these images is roughly $10^{-3}$ mas, which is too small to be resolved. The typical time interval between different images is roughly 1 millisecond (ms). The flux ratio between different images is roughly from 10 to $10^3$. With the expected detection rate of $10^4$ FRBs per year by the upcoming experiments, we could expect five multi-peak FRBs observed per year with time interval larger than 1 ms and flux ratio less than $10^3$ if the fraction of dark matter in MACHOs is $f\sim0.01$. A null search multiple-peak FRBs for time interval larger than 1 ms and flux ratio less than $10^3$ with $10^4$ FRBs would constrain the fraction $f$ of dark matter in MACHOs to $f<0.001$.