Self-Lensing By A Stellar Disk

I derive a general expression for the optical depth τ 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 τ = 2 〈 v 〉 /c sec i where 〈 v 〉 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 τ ∼ 8× 10 as has recently been suggested, then v > ∼ 60 km s . This is substantially larger than the measured dispersions of known LMC populations. Subject Headings: dark matter – gravitational lensing submitted to The Astrophysical Journal: August 1, 1994 Preprint: OSU-TA-13/94