Microlensed Image Motions

Photometric monitoring of stars in the Galactic bulge and the Large Magellanic Cloud has revealed a number of clear gravitational microlensing events, but the nature of the lens population is currently uncertain. In this paper we point out that the apparent position of a lensed star traces out an ellipse during such events. The size of the ellipse is in direct proportion to the Einstein ring radius, the ellipticity yields the impact parameter of the event, and the orientation indicates the direction of relative motion of lens and source. This information in particular, the Einstein ring radius, in combination with the duration of the event permits a determination of the mass and distance of the lens, given a model velocity distribution for any putative lens population.

We show that regular observations of microlensing events with a space-based telescope could yield good measurements of the corresponding Einstein ring radii-except in cases where source and lens both lie in the LMC. Unfortunately, the current suite of Hubble Space Telescope instruments is not well suited to this experiment in differential astrometry, but a small, dedicated satellite ought to be able to do the job, thus going a long way to apprehending the nature of the lensing objects.