Improved Detection Rates for Close Binaries via Astrometric Observations of Gravitational Microlensing Events

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Abstract
In addition to constructing a Galactic matter mass function free from the bias induced by the hydrogen-burning limit, gravitational microlensing allows one to construct a mass function that is less affected by the problem of unresolved binaries. However, even with the method of microlensing, the photometric detection of binaries is limited to binary systems with relatively large separations, b 0.4, of their combined Einstein ring radius, and thus the mass function is still not totally free from the problem of unresolved binaries. In this paper, we show that by detecting distortions of the astrometric ellipse of a microlensing event with high-precision instruments such as the future Space Interferometry Mission, one can detect close binaries at a much higher rate than with the photometric method. We find that by astrometrically observing microlensing events, ~50% of binaries with separations of 0.1rE can be detected with a detection threshold of 3%. The proposed astrometric method is especially efficient at detecting very close binaries. With a detection threshold of 3% and a rate of 10%, one can astrometrically detect binaries with separations down to ~0.01rE.