Occultation and Microlensing

Abstract

Occultation and microlensing are different limits of the same phenomenon of one body passing in front of another body. We derive a general exact analytic expression that describes both microlensing and occultation in the case of spherical bodies with a source of uniform brightness and a nonrelativistic foreground body. We also numerically compute the case of a source with quadratic limb darkening. In the limit that the gravitational deflection angle is comparable to the angular size of the foreground body, both microlensing and occultation occur as the objects align. Such events can be used to constrain the size ratio of the lens and source stars, the limb-darkening coefficients of the source star, and the surface gravity of the lens star (if the lens and source distances are known). Application of these results to microlensing during transits in binaries and giant-star microlensing is discussed. These results unify the microlensing and occultation limits and should be useful for rapid model fitting of microlensing, eclipse, and ``micro-occultation'' events.