Complete Parallax and Proper‐Motion Solutions for Halo Binary‐Lens Microlensing Events

A major problem in the interpretation of microlensing events is that the onlymeasured quantity, the Einstein time scale t_E, is a degenerate combination ofthe three quantities one would like to know, the mass, distance, and speed ofthe lens. This degeneracy can be partly broken by measuring either a "parallax"or a "proper motion" and completely broken by measuring both. Proper motionscan easily be measured for caustic-crossing binary-lens events. Here we examinethe possibility (first discussed by Hardy & Walker) that one could also measurea parallax for some of these events by comparing the light curves of thecaustic crossing as seen from two observatories on Earth. We derive analyticexpressions for the signal-to-noise ratio of the parallax measurement in termsof the characteristics of the source and the geometry of the event. ForGalactic halo binary lenses seen toward the LMC, the light curve is delayedfrom one continent to another by a seemingly minuscule 15 seconds (compared tot_E ~ 40 days). However, this is sufficient to cause a difference inmagnification of order 10%. To actually extract complete parallax information(as opposed to merely detecting the effect) requires observations from threenon-collinear observatories. Parallaxes cannot be measured for binary lenses inthe LMC but they can be measured for Galactic halo binary lenses seen towardM31. Robust measurements are possible for disk binary lenses seen toward theGalactic bulge, but are difficult for bulge binary lenses.Comment: Revised to take account of important work by Hardy & Walker (1995