Microlensing of Elliptical Sources by Fold Caustics

We consider microlensing of an elliptical source crossing a fold caustic. We derive a simple expression for the light curve of a source with uniform surface brightness that is accurate to third order in the ellipticity e (yielding errors of <1% for e<0.3). We consider caustic crossings of a rotating star, an oblate giant extrasolar planet, and an inclined standard thin accretion disk, and find the following results. (1) If most stars have rotation periods similar to chromospherically-active (i.e. spotted) giant stars in the bulge, than ~15% should be sufficiently oblate (e>0.25) to produce detectable (>1%) deviations with current observations. The form of the deviation due to ellipticity is qualitatively similar to that due to limb-darkening. Thus stellar oblateness may have to be taken into account in interpretations of precise limb-darkening measurements with microlensing. (2) Giant planets will generally not produce a detectable oblateness signal, either because they rotate too slowly (if they are close-in and tidally locked), or because they are too faint (if they are farther away from the parent star). (3) There is a near-degeneracy between ellipticity and position angle for equal-area sources with scale-free intensity profiles and elliptical isophotes. This degeneracy results in a factor of ~2 uncertainty in the measurement of the scale-length of a standard thin accretion disk using observations of a single, linear fold crossing quasar microlensing event in passbands probing the outer parts of the disk. Higher-frequency observations can reduce this uncertainty.