Bringing closure to microlensing mass measurement

Interferometers offer multiple methods for studying microlensing events and determining the properties of the lenses. We investigate the study of microlensing events with optical interferometers, focusing on narrow-angle astrometry, visibility, and closure phase. After introducing the basics of microlensing and interferometry, we derive expressions for the signals in each of these three channels. For various forecasts of the instrumental performance, we discuss which method provides the best means of measuring the lens angular Einstein radius θ_E, a prerequisite for determining the lens mass. If the upcoming generation of large-aperture, AO-corrected long-baseline interferometers (e.g., VLTI or Keck) perform as well as expected, θ _E could be determined with signal-to-noise ratios greater than 10 for all bright events. We estimate that ∼5 events per year will be sufficiently bright and have long enough durations to allow the measurement of the lens mass and distance from the ground. We also consider the prospects for a VLTI survey of all bright lensing events using a Fisher matrix analysis, and find that even without individual masses, interesting constraints can be placed on the bulge mass function, although large numbers of events would be required.