Microlensing of an elliptical source by a point mass

We present an efficient method for computing light curves of an elliptical source that is microlensed by a point mass. The amplification of an extended source involves a two-dimensional integral over its surface brightness distribution. We show that for a general surface brightness profile with an elliptical symmetry, this integral can be reduced to one dimension. We derive analytical results for the entire light curve in the limit of low-mass (e.g., planetary) lenses and for the wings of all microlensing light curves in general. In both cases, the light curve carries information about deviations of the source from elliptical symmetry, e.g., deviations caused by spots. The method is used to find the amplification of a circular red giant photosphere and an inclined accretion disk. We demonstrate that microlensing of an emission line from a disk can be used to infer the disk velocity structure and surface brightness profile.