Microlensing of Elliptical Sources by Fold Caustics

We consider the problem of an elliptical background source crossing a linear gravitational lensing fold caustic. We derive a simple expression for the light curve of a source with a uniform surface brightness that is accurate to third order in the ellipticity e (yielding brightness errors of . 1% for e . 0.3). We then consider caustic crossings of a rotating star, an oblate giant extrasolar planet, and an inclined standard thin accretion disk around a quasar black hole, 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, in general, 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 to their parent star), or because they are too faint for detection (if they are farther away from the parent star). However, a close-in planet with a large ellipticity could cause a detectable distortion, especially if the caustic crossing occurs in the direction parallel to the major or minor axis of the planet’s surface. (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 caustic-crossing quasar microlensing event in passbands probing the outer parts of the disk. More precise or higher-frequency observations can reduce this uncertainty. Subject headings: gravitational lensing – stars:atmospheres – planetary systems