Detectability of the Parallax-induced Deviations in the Astrometric Centroid Shift Trajectories of Gravitational Microlensing Events

The uncertainty of the lens mass can be substantially reduced if it is determined from the lens proper motion obtained from astrometric measurements of the source image centroid shifts, \(\vdelta\vtheta_c\), by using high precision interferometers. However, for the complete resolution of the lens parameter degeneracy it is required to determine the lens parallax by measuring the parallax-induced deviations in the centroid shifts trajectory, \(\vDelta \vdelta \vtheta_c\). In this paper, we investigate the detectabilities of \(\vdelta\vtheta_c\) and \(\vDelta\vdelt\vtheta_c\) by determining the distributions of the maximum centroid shifts and the average maximum deviations expected for different types of Galactic microlensing events caused by various masses. From this investigation, we find that as long as sources are bright enough for astrometric observations it is expected that \(\vdeltavxtheta_c\) for most events caused by masses greater than 0.1 M_\odot regardless of the event types can be easily detected from observations by using not only the Space Interfeormetry Mission (SIM, with a detection threshold ~ 3 \mu-as) but also the ground-based interferometers (with a threshold ~30 \mu-as). However, detection of \(\vDelta\vdelta\vtheta_c\) from ground-based observations will be difficult for nearly all Galactic bulge self-lensing events, and will be restricted only for small fractions of disk-bulge and halo-LMC events, for which the deviations are relatively large. From observations by using the SIM, on the other hand, detecting \(\vDelta\vdelta\vtheta_c\) will be possible for majority of disk-bulge and halo-LMC events and even for some fraction of bulge self-lensing events. For the complete resolution of the lens parameter degeneracy, therefore, SIM observations (or equivalent) will be essential.