Modeling transit and reflected light curves for non-spherical exoplanets

Abstract Newton was the first to provide a mathematical framework to describe the oblateness of the Earth, a framework later expended by Maclaurin, Jacobi, and Poincare and applied to other astronomical objects. In the Solar System, the Jacobi triaxial ellipsoid has successfully described the shape of Haumea and Chariklo, while Ceres appears to be an oblate spheroid of the Maclaurin type. Beyond the Solar System, new exoplanets are being discovered almost daily showing vastly different characteristics (e.g. mass, temperature, eccentricity, radius, orbital period). Recently, Kepler-427b was shown to be a moderately oblate spheroid, and it is possible to imagine that certain exoplanets could be triaxial ellipsoids. Considering the wealth of data now available from the current and past missions whose aim is to hunt for new extra-solar systems, it has become vital to broaden the range of parameters to be estimated for a single exoplanet. In this paper, we present a new algorithm to model variations in transit light curves induced by ellipsoidal exoplanets, which will be ultimately released to the community as a MATLAB-based package. Most variations happen during the ingress and egress phase of the transit. Combining several transits can lead to the detection of oblateness by measuring the precession of the obliquity angle of the exoplanet over time. For the first time, we also attempt to model reflected light curves for ellipsoidal exoplanets.