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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 Markov Chain Monte Carlo 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 codemore »
Multiband light-curve analysis of the 40.5-min period eclipsing double-degenerate binary SDSS J082239.54+304857.19ABSTRACT We present the Apache Point Observatory BG40 broad-band and simultaneous Gemini r-band and i-band high-speed follow-up photometry observations and analysis of the 40.5-min period eclipsing detached double-degenerate binary SDSS J082239.54+304857.19. Our APO data spans over 318 d and includes 13 primary eclipses, from which we precisely measure the system’s orbital period and improve the time of mid-eclipse measurement. We fit the light curves for each filter individually and show that this system contains a low-mass DA white dwarf with radius RA = 0.031 ± 0.006 R⊙ and a RB = 0.013 ± 0.005 R⊙ companion at an inclination of i = 87.7 ± 0.2○. We use the best-fitting eclipsing light curve model to estimate the temperature of the secondary star as Teff = 5200 ± 100 K. Finally, while we do not record significant offsets to the expected time of mid-eclipse caused by the emission of gravitational waves with our 1-yr baseline, we show that a 3σ significant measurement of the orbital decay due to gravitational waves will be possible in 2023, at which point the eclipse will occur about 8 s earlier than expected.
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