A Multi-Parameter Degeneracy in Microlensing Events with Extreme Finite Source Effects

Abstract

For microlenses with sufficiently low mass, the angular radius of the source star can be much larger than the angular Einstein ring radius of the lens. For such extreme finite source effect (EFSE) events, finite source effects dominate throughout the duration of the event. Here, we demonstrate and explore a continuous degeneracy between multiple parameters of such EFSE events. The first component in the degeneracy arises from the fact that the directly-observable peak change of the flux depends on both the ratio of the angular source radius to the angular Einstein ring radius and the fraction of the baseline flux that is attributable to the lensed source star. The second component arises because the directly-observable duration of the event depends on both the impact parameter of the event and the relative lens-source proper motion. These two pairwise degeneracies become coupled when the detailed morphology of the light curve is considered, especially when including a limb-darkening profile of the source star. We derive these degeneracies mathematically through analytic approximations and investigate them further numerically with no approximations. We explore the likely physical situations in which these mathematical degeneracies may be realized and potentially broken. As more and more low-mass lensing events (with ever decreasing Einstein ring radii) are detected with improving precision and increasing cadence from microlensing surveys, one can expect that more of these EFSE events will be discovered. In particular, the detection of EFSE microlensing events could increase dramatically with the Roman Space Telescope Galactic Bulge Time Domain Survey.