Gravitational Microlensing near Caustics. I. Folds

We study the local behavior of gravitational lensing near fold catastrophes.Using a generic form for the lensing map near a fold, we determine theobservable properties of the lensed images, focusing on the case when theindividual images are unresolved, i.e., microlensing. Allowing for images notassociated with the fold, we derive analytic expressions for the photometricand astrometric behavior near a generic fold caustic. We show how this formreduces to the more familiar linear caustic, which lenses a nearby source intotwo images which have equal magnification, opposite parity, and are equidistantfrom the critical curve. In this case, the simplicity and high degree ofsymmetry allows for the derivation of semi-analytic expressions for thephotometric and astrometric deviations in the presence of finite sources witharbitrary surface brightness profiles. We use our results to derive some basicproperties of astrometric microlensing near folds, in particular we predict forfinite sources with uniform and limb darkening profiles, the detailed shape ofthe astrometric curve as the source crosses a fold. We find that theastrometric effects of limb darkening will be difficult to detect with thecurrently planned accuracy of the Space Interferometry Mission. We verify ourresults by numerically calculating the expected astrometric shift for thephotometrically well-covered Galactic binary lensing event OGLE-1999-BUL-23,finding excellent agreement with our analytic expressions. Our results can beapplied to any lensing system with fold caustics, including Galactic binarylenses and quasar microlensing.Comment: 37 pages, 7 figures. Revised version includes an expanded discussion of applications. Accepted to ApJ, to appear in the August 1, 2002 issue (v574