Detectability of orbital motion in stellar binary and planetary microlenses

A standard binary microlensing event light curve allows just two parameters of the lensing system to be measured: the mass ratio of the companion to its host and the projected separation of the components in units of the Einstein radius. However, other exotic effects can provide more information about the lensing system. Orbital motion in the lens is one such effect, which, if detected, can be used to constrain the physical properties of the lens. To determine the fraction of binary-lens light curves affected by orbital motion (the detection efficiency), we simulate light curves of orbiting binary star and star-planet (planetary) lenses and simulate the continuous, high-cadence photometric monitoring that will be conducted by the next generation of microlensing surveys that are beginning to enter operation. The effect of orbital motion is measured by fitting simulated light-curve data with standard static binary microlensing models; light curves that are poorly fitted by these models are considered to be detections of orbital motion. We correct for systematic false positive detections by also fitting the light curves of static binary lenses. For a continuous monitoring survey without intensive follow-up of high-magnification events, we find the orbital motion detection efficiency for planetary events with caustic crossings to be 0.061 � 0.010, consistent with observational results, and 0.0130 � 0.0055 for events without caustic crossings (smooth events). Similarly, for stellar binaries, the orbital motion detection efficiency is 0.098 � 0.011 for events with caustic crossings and is 0.048 � 0.006 for smooth events. These result in combined (caustic-crossing and smooth) orbital motion detection efficiencies of 0.029 � 0.005 for planetary lenses and 0.070 � 0.006 for stellar binary lenses. We also investigate how various microlensing parameters affect the orbital motion detectability. We find that the orbital motion detection efficiency increases as the binary mass ratio and event time-scale increase, and as the impact parameter and lens distance decrease. For planetary caustic-crossing events, the detection efficiency is highest at relatively large values of semimajor axis ?4 au, due to the large size of the resonant caustic at this orbital separation. Effects due to the orbital inclination are small and appear to significantly affect only smooth stellar binary events. We find that, as suggested by Gaudi, many of the events that show orbital motion can be classified into one of the following two classes. The first class, separational events, typically show large effects due to subtle changes in resonant caustics, caused by changes in the projected binary separation. The second class, rotational events, typically show much smaller effects, which are due to the magnification patterns of close lenses exhibiting large changes in angular orientation over the course of an event; these changes typically cause only subtle changes to the light curve.