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

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.

29 pages, 18 figures. Code available at https://github.com/tagordon/gefera

References in corpus (16)

• Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
• The Transiting Circumbinary Planets Kepler-34 and Kepler-35
• emcee v3: A Python ensemble sampling toolkit for affine-invariant MCMC
• KOI-126: A Triply-Eclipsing Hierarchical Triple with Two Low-Mass Stars
• exoplanet: Gradient-based probabilistic inference for exoplanet data & other astronomical time series
• Analytic Approximations for Transit Light Curve Observables, Uncertainties, and Covariances
• The Featureless Transmission Spectra of Two Super-Puff Planets
• An Exomoon Survey of 70 Cool Giant Exoplanets and the New Candidate Kepler-1708 b-i
• Transit Light Curves with Finite Integration Time: Fisher Information Analysis
• Planet-Planet Occultations in TRAPPIST-1 and Other Exoplanet Systems
• The Compact Triply Eclipsing Triple Star TIC 209409435 Discovered with TESS
• Triply eclipsing triple stars in the northern TESS fields: TICs 193993801, 388459317 and 52041148
• TIC 278825952: a triply eclipsing hierarchical triple system with the most intrinsically circular outer orbit
• Transits of Inclined Exomoons - Hide and Seek and an Application to Kepler-1625
• Pandora: A fast open-source exomoon transit detection algorithm
• Accurate modeling of grazing transits using umbrella sampling

Cited by in corpus (5)

• Large Exomoons unlikely around Kepler-1625 b and Kepler-1708 b
• A full transit of ${\nu }^2$ Lupi d and the search for an exomoon in its Hill sphere with CHEOPS
• The "Drake equation" of exomoons -- a cascade of formation, stability and detection
• Analytic auto-differentiable $\Lambda$CDM cosmography
• A differentiable N-body code for transit timing and dynamical modelling -- II. Photodynamics