Orbital motion effects in astrometric microlensing

Abstract

We investigate lens orbital motion in astrometric microlensing and its detectability. In microlensing events, the light centroid shift in the source trajectory (the astrometric trajectory) falls offmuch more slowly than the light amplification as the source distance from the lens position increases. As a result, perturbations developed with time such as lens orbital motion can make considerable deviations in astrometric trajectories. The rotation of the source trajectory due to lens orbital motion produces a more detectable astrometric deviation because the astrometric cross-section ismuch larger than the photometric one. Among binarymicrolensing events with detectable astrometric trajectories, those with stellar-mass black holes have most likely detectable astrometric signatures of orbitalmotion. Detecting lens orbitalmotion in their astrometric trajectories helps to discover further secondary components around the primary even without any photometric binarity signature as well as resolve close/wide degeneracy. For these binary microlensing events, we evaluate the efficiency of detecting orbital motion in astrometric trajectories and photometric light curves by performing Monte Carlo simulation. We conclude that astrometric efficiency is 87.3 per cent whereas the photometric efficiency is 48.2 per cent. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.