Discovery of Small Ultra-short-period Planets Orbiting KG Dwarfs in Kepler Survey Using GPU Phase Folding and Deep Learning Detection System

Of over 5,000 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 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 days. Kepler-158d with a radius of $0.43 R_\oplus$ orbits a K dwarf star every 0.645088 days. Kepler-1489c with a radius of $0.51 R_\oplus$ orbits a G dwarf in 0.680741 days. Kepler-963c with a radius of $0.6 R_\oplus$ revolves around a G dwarf in 0.919783 days, and KOI-4978.02 with a radius of $0.7 R_\oplus$ circles a G dwarf in 0.941967 days. Among our findings, Kepler-879c, Kepler-158d and Kepler-963c rank as the first, the third, 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 photometry data from Kepler, TESS, and upcoming space transit missions, PLATO and ET.