Einstein Radii from Binary‐Source Lensing Events

We show that the Einstein ring radius and transverse speed of a lensprojected on the source plane, $\hat{r}_{\rm e}$ and $\hat{v}$, can bedetermined from the light curve of a binary-source event, followed by thespectroscopic determination of the orbital elements of the source stars. Thedetermination makes use of the same principle that allows one to measure theEinstein ring radii from finite-source effects. For the case when the orbitalperiod of the source stars is much longer than the Einstein time scale, $P\ggt_{\rm e}$, there exists a single two-fold degeneracy in determining$\hat{r}_{\rm e}$. However, when $P \lesssim t_{\rm e}$ the degeneracy canoften be broken by making use of the binary-source system's orbital motion.%Once $\hat{r}_{\rm e}$, and thus $\hat{v}$ are determined, one can%distinguish self-lensing events in the Large Magellanic Cloud %from Galactichalo events. For an identifiable 8\% of all lensing events seen toward theLarge Magellanic Cloud (LMC), one can unambiguously determine whether thelenses are Galactic, or whether they lie in the LMC itself. The requiredobservations can be made after the event is over and could be carried out forthe $\sim 8$ events seen by Alcock et al.\ and Aubourg et al.. In addition, wepropose to include eclipsing binaries as sources for gravitational lensingexperiments.Comment: 18 pages, revised version, submitted to Ap