A SPECTROSCOPIC METHOD TO MEASURE MACHO PROPER MOTIONS

A massive compact halo object (MACHO) that lenses a background star wi ll magnify different parts of the rotating stellar disk by varying amo unts. The differential magnification will cause a shift in the centroi d of the spectral lines of the star during the lensing event. The shif t is proportional to the projected rotation velocity of the star and t o the ratio of the stellar radius to the projected separation of the M ACHO from the star. It therefore provides a direct measure of the Eins tein ring radius, and so also a measure of the proper motion (angular speed) of the MACHO. This measurement can remove some of the degenerac y between mass, distance to the lens, and transverse velocity that exi sts in the interpretation of results from ongoing microlensing experim ents, and it is an independent test of the lensing nature of the event . The accuracy of the measurement depends on how well the projected ro tation speed (v sin i) and stellar radius can be determined, as well a s the accuracy of the line-shift measurement. We show that using the h igh precision attainable by stellar radial velocity measurements, it m ay 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 rep orted to date. The shift can be measured for similar to 40% of the hig h-magnification A-star events generated by MACHOs in the dark halo of the LMC itself. This, in turn, would provide a measurement of the frac tion of LMC versus Galactic MACHO events. If this proper-motion measur ement were combined with a parallax measurement of the ''reduced veloc ity,'' then the MACHO mass, distance, speed, and direction could each be separately determined.