Lensing of fast radio bursts by binaries to probe compact dark matter

The possibility that a fraction of dark matter is comprised of massive compact halo objects (MACHOs) remains unclear, especially in the 20-100 M-circle dot 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 FRBs gravitational lensed by MACHO binaries to constrain their properties. Since lensing events could generate more than one image, 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 from approximately 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 a time interval larger than 1 ms and flux ratio less than 10(3) if the fraction of dark matter in MACHOs is f similar to 0.01. A null search of multiple-peak FRBs for time intervals 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.