Acceleration and parallax effects in gravitational microlensing

To generate the standard microlensing light curve, we assume that the relative motion of the source, the lens and the observer is linear. In reality, the relative motion is likely to be more complicated due to accelerations of the observer, the lens and the source. The simplest approximation beyond the linear-motion assumption is to add a constant acceleration. Microlensing light curves due to accelerations can be symmetric or asymmetric depending on the angle between the acceleration and the velocity. We show that it is possible that some of the previously reported shorter marginal parallax events can be reproduced with constant-acceleration models, while the longer, multi-year parallax events are ill-fitted by such models. We find that there is a generic degeneracy inherent in constant-acceleration microlensing models. We also find that there is an equivalent degeneracy in parallax models, which manifests itself in short-duration events. The importance of this new parallax degeneracy is illustrated with an example, using one of these marginal parallax events. Our new analysis suggests that another of these previously suspected parallax candidate events may be exhibiting some weak binary-source signatures. If this turns out to be true, spectroscopic observations of the source could determine some parameters in the model and may also constrain or even determine the lens mass. We also point out that symmetric light curves with constant accelerations can mimic blended light curves, producing misleading Einstein-radius crossing time-scales when fitted by the standard 'blended' microlensing model; this may have some effect on the estimation of optical depth.