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For microlenses with sufficiently low mass, the angular radius of the sourcestar can be much larger than the angular Einstein ring radius of the lens. Forsuch extreme finite source effect (EFSE) events, finite source effects dominatethroughout the duration of the event. Here, we demonstrate and explore acontinuous degeneracy between multiple parameters of such EFSE events. Thefirst component in the degeneracy arises from the fact that thedirectly-observable peak change of the flux depends on both the ratio of theangular source radius to the angular Einstein ring radius and the fraction ofthe baseline flux that is attributable to the lensed source star. The secondcomponent arises because the directly-observable duration of the event dependson both the impact parameter of the event and the relative lens-source propermotion. These two pairwise degeneracies become coupled when the detailedmorphology of the light curve is considered, especially when including alimb-darkening profile of the source star. We derive these degeneraciesmathematically through analytic approximations and investigate them furthernumerically with no approximations. We explore the likely physical situationsin which these mathematical degeneracies may be realized and potentiallybroken. As more and more low-mass lensing events (with ever decreasing Einsteinring radii) are detected with improving precision and increasing cadence frommicrolensing surveys, one can expect that more of these EFSE events will bediscovered. In particular, the detection of EFSE microlensing events couldincrease dramatically with the Roman Space Telescope Galactic Bulge Time DomainSurvey.

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