Picolensing as a probe of primordial black hole dark matter

The gravitational-lensing parallax of gamma-ray bursts (GRBs) is an intriguing probe of primordial black hole (PBH) dark matter in the asteroid-mass window, $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}{M}_{\ensuremath{\bigodot}}\ensuremath{\lesssim}{M}_{\mathrm{PBH}}\ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{M}_{\ensuremath{\bigodot}}$. Recent work in the literature has shown exciting potential reach for this ``picolensing'' signal if a future space mission were to fly two x-/$\ensuremath{\gamma}$-ray detectors in the Swift/BAT class, with interspacecraft separation baselines on the order of the Earth--Moon distance. We revisit these projections with a view to understanding their robustness to various uncertainties related to GRBs. Most importantly, we investigate the impact of uncertainties in observed GRB angular sizes on reach projections for a future mission. Overall, we confirm that picolensing shows great promise to explore the asteroid-mass window; however, we find that previous studies may have been too optimistic with regard to the baselines required. Detector baselines on the order of at least the Earth--L2 distance would make such a mission more robust to GRB size uncertainties; baselines on the order of an astronomical unit (AU) would additionally enable reach that equals or exceeds existing microlensing constraints up to ${M}_{\mathrm{PBH}}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}{M}_{\ensuremath{\bigodot}}$.