Detection Rates for Close Binaries Via Microlensing

Microlensing is one of the most promising methods of reconstructing the stellar mass function down to masses even below the hydrogen-burning limit. The fundamental limit to this technique is the presence of unresolved binaries, which can in principle significantly alter the inferred mass function. Here we quantify the fraction of binaries that can be detected using microlensing, considering specifically the mass ratio and separation of the binary. We find that almost all binary systems with separations greater than $b \sim 0.4$ of their combined Einstein ring radius are detectable assuming a detection threshold of $3\%$. For two M dwarfs, this corresponds to a limiting separation of $\gsim 1 \au$. Since very few observed M dwarfs have companions at separations $\lsim 1 \au$, we conclude that close binaries will probably not corrupt the measurements of the mass function. We find that the detectability depends only weakly on the mass ratio. For those events for which individual masses can be determined, we find that binaries can be detected down to $b \sim 0.2$.