MACHO PROPER MOTIONS FROM OPTICAL INFRARED PHOTOMETRY/

Optical/infrared photometry can double the number of proper-motion mea surements of massive compact objects (MACHOs) relative to single-band photometry. The proper motion of a MACHO can be measured by finding th e ratio q of the (known) radius of the source star to the Einstein rad ius of the MACHO q = theta(s)/theta(e). A classic method for doing thi s is to look for the effect on the light curve of the finite size of t he source. A modification of this method proposed by Witt is to look f or color changes in the light curve due to the fact that the limb dark ening of the source is different in different bands. We demonstrate th at the ''classical'' method is not feasible unless the MACHO actually transits the source: if the MACHO passes at, say, 1.5 source radii, th ere is still a sizable similar to 5% effect, but the light curve canno t be distinguished from point-source light curves with different param eters. However, color measurements in V (0.55 mu m) and H (1.65 mu m) reduce the errors by a factor similar to 120 and permit proper-motion measurements at impact parameters of up to 2 source radii. Color maps in V - H are also useful in the detection of planetary systems. Giant stars have a ''red ring'' in such maps. A planet which transits this r ing gives rise to a distinctive signature which can help in the measur ement of the planetary system's proper motion.