Analytic Light Curve for Mutual Transits of Two Bodies Across a Limb-darkened Star

TL;DR

This paper introduces an analytic model for the light curves of two bodies mutually transiting a star with limb darkening, including derivatives for efficient inference, aiding exomoon detection and other multi-body transit studies.

Contribution

It provides a novel analytic solution for mutual transits with derivatives, enabling fast, gradient-based inference methods for complex multi-body transit systems.

Findings

Analytic light curve model for mutual transits with limb darkening.

Code implementation supporting hierarchical and confocal systems.

Facilitates efficient inference for exomoon and multi-planet systems.

Abstract

We present a solution for the light curve of two bodies mutually transiting a star with polynomial limb darkening. The term "mutual transit" in this work refers to a transit of the star during which overlap occurs between the two transiting bodies. These could be an exoplanet with an exomoon companion, two exoplanets, an eclipsing binary and a planet, or two stars eclipsing a third in a triple star system. We include analytic derivatives of the light curve with respect to the positions and radii of both bodies. We provide code that implements a photodynamical model for a mutual transit. We include two dynamical models, one for hierarchical systems in which a secondary body orbits a larger primary (e.g. an exomoon system) and a second for confocal systems in which two bodies independently orbit a central mass (e.g. two planets in widely separated orbits). Our code is fast enough to enable inference with MCMC algorithms, and the inclusion of derivatives allows for the use of gradient-based inference methods such as Hamiltonian Monte Carlo. While applicable to a variety of systems, this work was undertaken primarily with exomoons in mind. It is our hope that making this code publicly available will reduce barriers for the community to assess the detectability of exomoons, conduct searches for exomoons, and attempt to validate existing exomoon candidates. We also anticipate that our code will be useful for studies of planet-planet transits in exoplanetary systems, transits of circumbinary planets, and eclipses in triple-star systems.