A SPECTROSCOPIC METHOD TO MEASURE MACHO PROPER MOTIONS

A massive compact halo object (MACHO) that lenses a background star will magnify different parts of the rotating stellar disk by varying amounts. The differential magnification will cause a shift in the centroid of the spectral lines of the star during the lensing event. The shift is proportional to the projected rotation velocity of the star and to the ratio of the stellar radius to the projected separation of the MACHO from the star. It therefore provides a direct measure of the Einstein ring radius, and so also a measure of the proper motion (angular speed) of the MACHO. This measurement can remove some of the degeneracy between mass, distance to the lens, and transverse velocity that exists in the interpretation of results from ongoing microlensing experiments, and it is an independent test of the lensing nature of the event. The accuracy of the measurement depends on how well the projected rotation speed (v sin i) and stellar radius can be determined, as well as the accuracy of the line-shift measurement. We show that using the high precision attainable by stellar radial velocity measurements, it may be possible to measure proper motions for similar to 10% of MACHOs that lens A stars in the Large Magellanic Cloud (LMC), i.e., about 7% of the type of relatively high-magnification events that have been reported to date. The shift can be measured for similar to 40% of the high-magnification A-star events generated by MACHOs in the dark halo of the LMC itself. This, in turn, would provide a measurement of the fraction of LMC versus Galactic MACHO events. If this proper-motion measurement were combined with a parallax measurement of the ''reduced velocity,'' then the MACHO mass, distance, speed, and direction could each be separately determined.