Discovery of small ultra-short-period planets orbiting <i>Kepler</i> KG dwarfs with GPU phase folding and deep learning

ABSTRACT Of over 5000 exoplanets identified so far, only a few hundred possess sub-Earth radii. The formation processes of these sub-Earths remain elusive, and acquiring additional samples is essential for investigating this unique population. In our study, we employ the GPFC method, a novel GPU phase folding algorithm combined with a convolutional neural network, on the Kepler photometry data. This method enhances the transit search speed significantly over the traditional Box-fitting Least Squares method, allowing a complete search of the known Kepler KOI data within days using a commercial GPU card. To date, we have identified five new ultra-short-period planets (USPs): Kepler-158d, Kepler-963c, Kepler-879c, Kepler-1489c, and KOI-4978.02. Kepler-879c with a radius of 0.4 R$_{\oplus }$ completes its orbit around a G dwarf in 0.646716 d, Kepler-158d with a radius of 0.43 R$_{\oplus }$ orbits a K dwarf star every 0.645088 d, Kepler-1489c with a radius of 0.51 R$_{\oplus }$ orbits a G dwarf in 0.680741 d, Kepler-963c with a radius of 0.6 R$_{\oplus }$ revolves around a G dwarf in 0.919783 d, and KOI-4978.02 with a radius of 0.7 R$_{\oplus }$ circles a G dwarf in 0.941967 d. Among our findings, Kepler-879c, Kepler-158d, and Kepler-963c rank as the first, the third, and the fourth smallest USPs identified to date. Notably, Kepler-158d stands as the smallest USP found orbiting K dwarfs, while Kepler-963c, Kepler-879c, Kepler-1489c, and KOI-4978.02 are the smallest USPs found orbiting G dwarfs. Kepler-879c, Kepler-158d, Kepler-1489c, and KOI-4978.02 are among the smallest planets that are closest to their host stars, with orbits within 5 stellar radii. In addition, these discoveries highlight GPFC’s promising capability in identifying small, new transiting exoplanets within the photometry data from Kepler, TESS, and upcoming space transit missions PLATO and ET.