Proper motions of MACHOs

If a Massive Compact Halo Object (MACHO) passes over the face of the star that it is lensing, then one can measure the MACHO's proper motion. Since the proper motions of MACHOs in the LMC are 15 times smaller than those of Galactic MACHOs, this measurement allows one to distinguish unambiguously between the two populations. The fraction of events where a MACHO of mass M passes directly over the star is 1/550 (M/0.1 M_sun_)^- 1/2 for Galactic MACHOs and 8 times larger for LMC MACHOs. The optical depth of LMC MACHOs can be measured with a fractional accuracy N^-1/2^, where N is the number of LMC MACHOs with measured proper motions. The recent detection of MACHO events may be due to a maximal MACHO thick disk rather than a MACHO halo. Proper motion measurements of MACHOs toward the Galactic bulge could distinguish between the thick-disk and halo models.