SELF-LENSING BY A STELLAR DISK

I derive a general expression for the optical depth tau for gravitational lensing of stars in a disk by massive compact objects (MACHOS) in the same disk. For the more restricted case where the disk is self-gravitating and the stars and MACHOS have the same distribution function, I find tau = 2[upsilon2]/c2 sec2 i, where [upsilon2] is the mass-weighted vertical velocity dispersion and i is the angle of inclination. This result does not depend on any assumptions about the velocity distribution. As an example, if stars within the bar of the Large Magellanic Cloud (LMC) account for the observed optical depth tau approximately 8 x 10(-8) as has recently been suggested, then upsilon greater-than-or-similar-to 60 km s-1. This is substantially larger than the measured dispersions of known LMC populations.