Direct lens imaging of Galactic bulge microlensing events

Recently, from the Hubble Space Telescope (HST) images of one of the Large Magellanic Cloud (LMC) gravitational microlensing events taken 6.3 yr after the original lensing measurement, Alcock et al. were able to directly image the lens. Although the first resolved lens was identified for an LMC event, much more numerous lenses are expected to be resolved for Galactic bulge events. In this paper, we estimate the fraction of Galactic bulge events whose lenses can be directly imaged under the assumption that all bulge events are caused by normal stars. For this determination, we compute the distribution of lens proper motions of the currently detected Galactic bulge events based on standard models of the geometrical and kinematical distributions of lenses and their mass function. We then apply realistic criteria for lens resolution, and the result is presented as a function of the time elapsed after an original lensing measurement, Δf. If follow-up observations are performed by using an instrument with a resolving power of θ_PSF = 0.1 arcsec, which corresponds to that of HST equipped with the new Advanced Camera for Surveys, we estimate that lenses can be resolved for ∼3 and 22 per cent of disc-bulge events and for ∼0.3 and 6 per cent of bulge self-lensing events after Δt = 10 and 20 yr, respectively. The fraction increases substantially with the increase of the resolving power. If the instrument has a resolution of θ_PSF = 0.05 arcsec, which can be achieved by the Next Generation Space Telescope, we estimate that lenses can be resolved for ∼22 and 45 per cent of disc-bulge events and for ∼6 and 23 per cent of bulge self-lensing events after Δt = 10 and 20 yr, respectively.