  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.
