Astrometric parallax measurements of gravitational microlensing events

The Einstein timescale, which is the only information obtained from current microlensing experiments, results from a combination of the lens parameter s that we want to determine. Of the methods for breaking the lens parameter degeneracy, the most promising and generally applicable method is to measu re the lens parallax from simultaneous photometric observations of a lensin g event from the ground and from a heliocentric satellite. However, the ele gant idea of lens parallax measurement, which was proposed to resolve the l ens parameter degeneracy, paradoxically suffers from another type of degene racy, which arises because a given set of light curves can have two possibl e values of parallax (parallax degeneracy). In this paper we show that one can break the parallax degeneracy either from the simultaneous astrometric observations of an event by using a high-precision ground-based interferome ter and a heliocentric satellite such as the Space Interferometry Mission o r from a combination of the astrometric observations on one site (either th e ground or the satellite) and the photometric observations on a different site. Since the proposed methods can measure both the lens parallax and pro per motion at the same time, one can completely break the lens parameter de generacy, and thus the physical parameters of individual lenses can be uniq uely determined.