On the astrometric behaviour of binary microlensing events

Despite the suspected binarity for a significant fraction of Galactic lenses, the current photometric surveys detected binary microlensing events only for a small fraction of the total events. The detection efficiency is especially low for non-caustic crossing events, which comprise the majority of the binary lensing events, as a result of the absence of distinctive features in their light curves combined with small deviations from the standard light curve of a single point-mass event. In addition, even if they are detected, it will be difficult to determine the solution of the binary lens parameters owing to the severe degeneracy problem. In this paper, we investigate the properties of binary lensing event expected when they are astrometrically observed by using high-precision interferometers. For this, we construct vector field maps of excess centroid shifts, which represent the deviations of the binary lensing centroid shifts from those of a single lensing event as a function of source position. From the analysis of the maps, we find that the excess centroid shifts are substantial in a considerably large area around caustics. In addition, they have characteristic sizes and directions depending strongly on the source positions with respect to the caustics and the resulting trajectories of the light centroid (astrometric trajectories) have distinctive features, which can be distinguished from the deviations caused by other reasons. We classify the types of the deviations and investigate where they occur. Because of the strong dependence of the centroid shifts on the lens system geometry combined with the distinctive features in the observed astrometric trajectories, astrometric binary lensing observations will provide an important tool that can probe the properties of the Galactic binary lens population.