An Analytical Model for Transit Light Curves

Abstract

Transits and secondary eclipses of an exoplanet orbiting a host star generate dips in the light curve. This article proposes a new class of mathematical functions that provide simple and computationally efficient models for such light curves. The transit and secondary eclipse functions account for ingress/egress, and the transit function incorporates curvilinear limb darkening. Their parameters are estimated using least squares methods. These models can be used to test for the statistical significance of dips, potentially revealing the existence of an exoplanet. In addition, they can be used to estimate features such as duration and depth of a transit or a secondary eclipse, limb darkening curvature and ingress/egress slope, and the orbital period. Examples using publicly available light curve data are presented, demonstrating the accuracy and efficiency of the proposed functions as fast analytical models for transits and/or secondary eclipses.