The caustic crossing microlensing event by binary MACHOs and the timescale bias

Caustic crossing microlensing events provide us a unique opportunity to measure the relative proper motion of the lens to the source, and so those caused by binary MACHOs are of great importance for understanding the structure of the Galactic halo and the nature of MACHOs. The microlensing event 98-SMC-01, which occurred in 1998 June, is the first event for which the proper motion is ever measured through the caustic crossing, and this event may be caused by binary MACHOs, as I argue in this Letter. Motivated by the possible existence of binary MACHOs, I have performed the Monte Carlo simulations of caustic crossing events by binary MACHOs and investigated the properties and detectability of the events. My calculation shows that typical caustic crossing events have the interval between two caustic crossings (t(cc)) of about 5 days. I argue that with the current strategy of binary event searches, the proper motions of these typical events are not measurable because of the short timescale. Therefore, the proper-motion distribution that is measured from caustic crossing events suffers significantly from "timescale bias," which is a bias toward finding long timescale events and hence slowly moving lenses. I predict that there are 2 times more short timescale events (t(cc) less than or equal to 10 days) than long timescale events (t(cc) greater than or equal to 10 days), and I propose an hourly monitoring observation instead of the nightly monitoring currently undertaken to detect caustic crossing events by binary MACHOs more efficiently.