Astrometric Observation of MACHO Gravitational Microlensing

Following previous suggestions of other researchers, this paper discusses theprospects for astrometric observation of MACHO gravitational microlensingevents. We derive the expected astrometric observables for a simplemicrolensing event with either a dark or self-luminous lens, and demonstratethat accurate astrometry can determine the lens mass, distance, and propermotion in a very general fashion. In particular we argue that in limitedcircumstances ground-based, narrow-angle differential astrometric techniquesare sufficient to measure the lens mass directly, and other lens properties(distance, transverse motion) by applying an independent model for the sourcedistance and motion. We investigate the sensitivity of differential astrometryin determining lens parameters by Monte Carlo methods, and derive aquasi-empirical relationship between astrometric accuracy and mass uncertainty.Comment: 28 p, 12 fig, To appear in the Ap