Astrometric Method to Break the Photometric Degeneracy between Binary-source and Planetary Microlensing Perturbations

An extra-solar planet can be detected by microlensing because the planet can perturb the smooth lensing light curve created by the primary lens. However, it was shown by Gaudi that a subset of binary-source events can produce light curves that closely resemble those produced by a significant fraction of planet/star lens systems, causing serious contamination of a sample of suspected planetary systems detected via microlensing. In this paper, we show that if a lensing event is observed astrometrically, one can unambiguously break the photometric degeneracy between binary-source and planetary lensing perturbations. This is possible because while the planet-induced perturbation in the trajectory of the lensed source image centroid shifts points away from the opening of the unperturbed elliptical trajectory, while the perturbation induced by the binary source companion points always towards the opening. Therefore, astrometric microlensing observations by using future high-precision interferometers will be important for solid confirmation of microlensing planet detections.