A Multiparameter Degeneracy in Microlensing Events with Extreme Finite Source Effects

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