Detecting Extragalactic Exoplanets With Fast Radio Burst Nanolensing

Fast Radio Bursts (FRBs) are spatially and temporally compact sources at cosmological distances. As background sources, they will be uniquely sensitive to the gravitational lensing of exoplanets outside of our own galaxy. We present a method to detect extragalactic exoplanets using planetary echo nanolensing-periodic, nanosecond-scale variations in the relative time of arrival (ToA) between an initial FRB and its microlensed echo as the planet orbits its host star. For a simple binary lens model, we demonstrate that measuring the amplitude and period of these ToA fluctuations enables a determination of the exoplanet mass and orbital parameters. FRBs will be most sensitive to echo nanolensing by lenses within ten megaparsecs of the Milky Way as well as within ten megaparsecs of the FRB host, opening the door to detections of planets at a range of redshifts. We estimate that at least one in a million FRBs will exhibit this phenomenon (i.e. an optical depth of τ l = 10-6). While current burst rates and low repeating-FRB fractions make a detection challenging in the immediate term, upcoming high-volume surveys and next-generation arrays (such as the SKA Phase 2) will bring the unambiguous detection of extragalactic exoplanets across cosmological redshifts into possibility.