A Reply to: Large Exomoons unlikely around Kepler-1625 b and Kepler-1708 b

Recently, Heller & Hippke argued that the exomoon candidates Kepler-1625 b-i and Kepler-1708 b-i were allegedly 'refuted'. In this Matters Arising, we address these claims. For Kepler-1625 b, we show that their Hubble light curve is identical to that previously published by the same lead author, in which the moon-like dip was recovered. Indeed, our fits of their data again recover the moon-like dip with improved residuals than that obtained by Heller & Hippke. Their fits therefore appear to have somehow missed this deeper likelihood maximum, as well producing apparently unconverged posteriors. Consequently, their best-fitting moon is the same radius as the planet, Kepler-1625 b; a radically different signal from that which was originally claimed. The authors then inject this solution into the Kepler data and remark, as a point of concern, how retrievals obtain much higher significances than originally reported. However, this issue stems from the injection of a fundamentally different signal. We demonstrate that their Hubble light curve exhibits ~20% higher noise and discards 11% of the useful data, which compromises its ability to recover the subtle signal of Kepler-1625 b-i. For Kepler-1708 b-i it was claimed that the exomoon model's Bayes factor is highly sensitive to detrending choices, yielding reduced evidence with a biweight filter versus the original claim. We use their own i) detrended light curve and ii) biweight filter code to investigate these claims. For both, we recover the original moon signal, to even higher confidence than before. The discrepancy is explained by comparing to their quoted fit metrics, where we again demonstrate that the Heller & Hippke regression definitively missed the deeper likelihood maximum corresponding to Kepler-1708 b-i. We conclude that both candidates remain viable but certainly demand further observations.