tokens: of all bodies to zero. We also fixed the orbital period of the planet–moon barycenter to 287.378949 days (the best fit from TK18 ). We elected not to vary the period of the planet–moon barycenter because it is poorly constrained from a single transit observation. A longer period would cause a longer transit duration for the planet, but this could equivalently result from a smaller impact parameter, a larger star, or a massive moon that significantly perturbs the planetary orbit. We used the following priors: the stellar radius was normally distributed, R * ∼ N (1.81, 0.17) R ⊙ (see the next section). The planet radius was uniform from 8 to 14 R ⊕ . The planet transit time was uniform over the timespan of the observations, and inclination was uniform from 0° to 90°. The planet mass was log-normally distributed, M p ∼ 10 2.5±0.5 M ⊕ , based on the expectation for Jupiter-radius objects from Ning et al. ( 2018 ). For the moon model, we allowed the transit time to vary uniformly over the entire visit. The moon period was uniform between 1.6 and 260 days. These limits span the duration of the HST observations (so there is one possible moon occultation event), to the orbit at 0.5 the Hill radius, based on the stability limit for prograde moon orbits (Domingos et al. 2006 ). The Hill radius calculation assumed that the planet and stellar masses are 1 M Jup and 1.37 M ⊙ . The moon mass varied uniformly from 0 to 30 M ⊕ . The longitude of the ascending node was also uniform from 0° to 360°. The moon inclination was uniform from 0° to 90°, and was defined relative to the line of sight. We assigned zero prior probability to scenarios where the moon did not transit or experienced a grazing transit. We made this choice to put an upper limit on the radius of a fully transiting moon; for grazing transits or non-transits the moon radius could be arbitrarily large. 3.1.1. Stellar Parameters For both the moon and no-moon scenarios, we used a quadratic stellar limb-darkening law and fixed the coefficients to the prediction for a 5700 K, solar metallicity PHOENIX model from Espinoza Jordán ( 2015 ); u 1 , u 2 = [0.216, 0.183]. We estimated the host star parameters using the Gaia second data release (DR2) parallax (Gaia Collaboration et al. 2016 , 2018 ) along with UBV photometry from Everett et al. ( 2012 ) and JHK photometry from the Two Micron All-Sky Survey (Skrutskie et al. 2006 ). We employed the isochrone python package (Morton 2015 ) with the Dartmouth isochrone grid (Dotter et al. 2008 ) to obtain posterior constraints on the stellar parameters. The resulting parameters indicate that Kepler-1625 has stellar mass M ⊙ , radius R ⊙ , and age Gyr. In our analysis, we fixed the stellar mass to the best-fit value (1.37 M ⊙ ), and used a Gaussian prior on the radius, R * ∼ N (1.81, 0.17). 3.2. Instrument Systematics Model There are two systematic trends in the data. One is the orbit-long ramp, attributed to charge traps in the detector filling up over the orbit
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