HEK. VI. on the Dearth of Galilean Analogs in Kepler, and the Exomoon Candidate Kepler-1625b i

Exomoons represent an outstanding challenge in modern astronomy, with the potential to provide rich insights into planet formation theory and habitability. In this work, we stack the phase-folded transits of 284 viable moon hosting Kepler planetary candidates, in order to search for satellites. These planets range from Earth- to Jupiter-sized and from ∼0.1 to 1.0 au in separation - so-called "warm" planets. Our data processing includes two-pass harmonic detrending, transit timing variations, model selection, and careful data quality vetting to produce a grand light curve with an rms of 5.1 ppm. We find that the occurrence rate of Galilean analog moon systems for planets orbiting between ∼0.1 and 1.0 au can be constrained to be to 95% confidence for the 284 KOIs considered, with a 68.3% confidence interval of . A single-moon model of variable size and separation locates a slight preference for a population of short-period moons with radii ∼0.5 R orbiting at 5-10 planetary radii. However, we stress that the low Bayes factor of just 2 in this region means it should be treated as no more than a hint at this time. Splitting our data into various physically motivated subsets reveals no strong signal. The dearth of Galilean analogs around warm planets places the first strong constraint on exomoon formation models to date. Finally, we report evidence for an exomoon candidate Kepler-1625b I, which we briefly describe ahead of scheduled observations of the target with the Hubble Space Telescope.