Photometric Microlens Parallaxes with theSpace Interferometry Mission

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Abstract
Astrometric measurements of microlensing events can in principle determine both the "parallax" E and the "proper motion" μ of an individual event, which (combined with the Einstein timescale tE) in turn yield the mass, distance, and transverse velocity of the lens. We show, however, that the parallax measurements are generically several orders of magnitude less precise than the proper-motion measurements. Fortunately, astrometric measurements by the Space Interferometry Mission (SIM) are simultaneously photometric measurements, and since SIM will be in solar orbit, these allow SIM to be used as a classical (photometric) parallax satellite. We show that SIM photometric parallaxes are of precision comparable to that of its astrometric proper-motion measurements. For I = 15 bulge stars, complete solutions with ~5% accuracy in mass, distance, and transverse velocity can be obtained from about 5 hr of observation, 100-10,000 times shorter than would be required for a purely astrometric solution of similar precision. Thus, it should be possible to measure directly the mass functions of both the bulge and the inner disk (including both dark and luminous objects) with only a few hundred hours of SIM observations.