Kepler Rotation Effects on the Binary-Lens Microlensing Events

We investigate the effects of the Kepler rotation of lens binaries on the binary-microlensing events towards the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC). It is found that the rotation effects cannot always be neglected when the lens binaries are in the LMC disk or the SMC disk, i.e., when they are self-lensing. Therefore we suggest that it will be necessary to consider the rotation effects in the analyses of the coming binary events if the microlensing events towards the halo are self-lensing. As an example, we reexamine the MACHO LMC-9 event, in which the slow transverse velocity of the lens binary suggests a microlensing event in the LMC disk. From a simple analysis, it is shown that the lens binary with total mass $sim 1M_{odot}$ rotates by more than $sim 60^{circ}$ during the Einstein radius crossing time. However, the fitting of MACHO LMC-9 with an additional parameter, the rotation period, shows that the rotation effects are small, i.e., the projected rotation angle is only $sim 5.9^{circ} (M/M_{odot})^{1/4}$ during the Einstein radius crossing time. This contradiction can be settled if the physical parameters, such as the mass and the velocity, are different in this event, the binary is nearly edge-on, or the binary is very eccentric, though definite conclusions cannot be drawn from this single event. If the microlensing events towards the halo are due to self-lensing, binary-events for which the rotation effects are important will increase and stronger constraints on the nature of the lenses will be obtained.