Astrometric Parallax Measurements of Gravitational Microlensing Events

Abstract

The Einstein timescale, which is the only information obtained from current microlensing experiments, results from a combination of the lens parameters that we want to determine. Of the methods for breaking the lens parameter degeneracy, the most promising and generally applicable method is to measure the lens parallax from simultaneous photometric observations of a lensing event from the ground and from a heliocentric satellite. However, the elegant idea of lens parallax measurement, which was proposed to resolve the lens parameter degeneracy, paradoxically suffers from another type of degeneracy, which arises because a given set of light curves can have two possible 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 interferometer and a heliocentric satellite such as the Space Interferometry Mission or from a combination of the astrometric observations on one site (either the ground or the satellite) and the photometric observations on a different site. Since the proposed methods can measure both the lens parallax and proper motion at the same time, one can completely break the lens parameter degeneracy, and thus the physical parameters of individual lenses can be uniquely determined.