A New Application of the Astrometric Method to Break Severe Degeneracies in Binary Microlensing Events

TL;DR

This paper proposes a new astrometric method to resolve close/wide degeneracies in binary microlensing events by detecting centroid shifts caused by the secondary star, especially effective for wide binaries within 20 AU.

Contribution

It introduces a novel application of astrometric follow-up observations to break degeneracies in binary microlensing, with probability estimates and detection timelines.

Findings

Degeneracy can be resolved if the source passes near the Einstein ring of the secondary.

Detection of centroid shifts is feasible within 100 days for typical Galactic events.

The method is effective for binary separations up to approximately 20 AU.

Abstract

When a source star is microlensed by one stellar component of a widely separated binary stellar components, after finishing the lensing event, the event induced by the other binary star can be additionally detected. In this paper, we investigate whether the close/wide degeneracies in binary lensing events can be resolved by detecting the additional centroid shift of the source images induced by the secondary binary star in wide binary lensing events. From this investigation, we find that if the source star passes close to the Einstein ring of the secondary companion, the degeneracy can be easily resolved by using future astrometric follow-up observations with high astrometric precision. We determine the probability of detecting the additional centroid shift in binary lensing events with high magnification. From this, we find that the degeneracy of binary lensing events with a separation of $\lesssim 20.0$ AU can be resolved with a significant efficiency. We also estimate the waiting time for the detection of the additional centroid shift in wide binary lensing events. We find that for typical Galactic lensing events with a separation of $\lesssim 20.0$ AU, the additional centroid shift can be detected within 100 days, and thus the degeneracy of those events can be sufficiently broken within a year.