Unique Determination of the Physical Parameters of Individual MACHOs from Astrometric Parallax Measurements

Abstract

The Einstein time scale, which is the only information obtained from current microlensing experiments, results from a complicated 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 observations of a lensing event from the ground and a heliocentric satellite (Gould 1994). However, the elegant idea of parallax measurement, which was proposed to resolve the lens parameter degeneracy, paradoxically suffers from its own degeneracy due to the ambiguity of the source star trajectory. In this paper, we propose to measure the lens parallax astrometrically by mounting an interferometer instead of a photometer in the proposed parallax satellite. By simultaneously measuring the source star centroid shifts from a geocentric and an additional heliocentric satellite, one can determine the lens parallax without ambiguity. If the already planned {\it Space Interferometry Mission} will be used as one of the satellites, one simply needs to replace the photometer in the parallax satellite with an instrument for astrometric observation. In addition, since the proposed method can measure both the lens parallax and the proper motion at the same time, one can completely break the lens parameter degeneracy, and therefore uniquely determine the physical parameters of individual lenses.