Identification of Bright Lenses from the Astrometric Observations of Gravitational Microlensing Events

Abstract

When a source star is gravitationally microlensed by a dark lens, the centroid of the source star image is displaced relative to the position of the unlensed source star with an elliptical trajectory. Recently, routine astrometric follow-up measurements of these source star image centroid shifts by using high precision interferometers are proposed to measure the lens proper motion which can resolve the lens parameter degeneracy in the photometrically determined Einstein time scale. When an event is caused by a bright lens, on the other hand, the astrometric shift is affected by the light from the lens, but one cannot identify the existence of the bright lens from the observed trajectory because the resulting trajectory of the bright lens event is also an ellipse. As results, lensing parameters determined from the trajectory differ from those of a dark lens event, causing wrong identification of lens population. In this paper, we show that although the shape and size of the astrometric centroid shift trajectory are changed due to the bright lens, the angular speed of centroid shifts around the apparent position of the unlensed source star is not affected by the lens brightness. Then, one can identify the existence of the bright lens and determine its brightness by comparing the lens parameters determined from the angular speed curve with those determined from the trajectory of observed centroid shifts. Once the lens brightness is determined, one can correct for the lens proper motion. Since the proposed method provides both information about the lens brightness (dark or bright) and the corrected values of the physical parameters of the lens, one can significantly better constrain the nature of MACHOs.