The applicability of the astrometric method for determining the physical parameters of gravitational microlenses

In this paper, we investigate the applicability of the astrometric method to the determination of the lens parameters for gravitational microlensing events towards both the LMC and the Galactic bulge. For this analysis, we investigate the dependence of the uncertainty of astrometrically determined angular Einstein ring radius, δθE/ θE,0), on the lens parameters by testing various types of events. In addition, by computing δ (θE/θE,0) for events with lensing parameters that are the most probable for a given lens mass under the standard models of Galactic matter density and velocity distributions, we determine the expected distribution of the uncertainties as a function of lens mass. From this study, we find that the values of the angular Einstein ring radius are expected to be measured with uncertainties δ (θE/θE,0) ≅ 10 per cent up to a lens mass of M ∼ 0.1 M⊙for both Galactic disc—bulge and halo—LMC events with a moderate observational strategy. The uncertainties are relatively large for Galactic bulge—bulge self-lensing events, δ (θE/ θE,0) ∼ 25 per cent for M ∼ 0.1 M⊙, but they can be substantially reduced by adopting more aggressive observational strategies. We also find that although astrometric observations can be performed for most photometrically detected Galactic bulge events, a significant fraction (∼ 45 per cent) of LMC events cannot be astrometrically observed owing to the faintness of their source stars.