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

TL;DR

This work introduces GPFC, a GPU-accelerated phase folding + CNN pipeline, to detect ultra-short-period exoplanets in Kepler photometry without relying on pre-identified catalogs. By processing $10^{5}$ trial periods per star and leveraging synthetic-training data, GPFC achieves faster searches (≈15×) and improved detection metrics over traditional BLS, enabling the discovery of five new USPs around KG dwarfs: Kepler-158d, Kepler-963c, Kepler-879c, Kepler-1489c, and KOI-4978.02, with radii from $0.4$ to $0.7\,R_\oplus$ and periods from $0.6467$ to $0.94197$ days; these planets reside in multiplanet systems and push toward the smallest-known USPs, including the smallest USP around a K-dwarf. Comprehensive vetting (ten tests) and transit fitting via MCMC substantiate their planetary nature and yield precise orbital and stellar parameters, illustrating GPFC’s potential for upcoming missions (TESS, PLATO, ET) and broader applicability to photometric transit surveys. The results inform USP occurrence trends across stellar types and support formation scenarios where outer planets influence the inward migration of USPs.

Abstract

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.

Figures (23)

• Figure 1: Kepler-1409b completes an orbit around its host star, KIC 12405333, every 0.764863 days. This transit period was accurately identified using the GPFC method. The top panel illustrates a clear transit signal corresponding to the 0.764863-day period. The bottom panel shows a peak CNN score of 1.0000 aligning with this period, with another notable score of 0.9955 observed at the harmonic half-period of 0.382432 days.
• Figure 2: Depiction of the folded light curve for KIC 12068975, which has no known USP transits and serves as an example where no transit signal is detected within our search range of [0.2,1] days. The most prominent CNN score recorded is 0.2793 at a period of 0.761883 days, which is classified as a non-detection by the GPFC system.
• Figure 3: Folded light curve and CNN scores for candidate Kepler-963c orbiting host star KIC 8832512. A transit within the USP period range [0.2 1] days is detected at 0.919783 days, featuring a CNN score of 0.9309 and a transit SNR of 7.3. The detected transit is marked with a red line in the upper Flux plot. The CNN scores at the detected period and corresponding harmonics are marked in redlines in the lower Model Score plot.
• Figure 4: Folded light curve and CNN scores for Kepler-1489c orbiting KIC 8409295. A transit is detected within the USP period range [0.2 1] days at 0.680741 days, with a CNN score of 0.5599 and a transit SNR of 6.2. The detected transit is marked with a red line in the upper Flux plot. The CNN scores at the detected period and corresponding harmonics are marked in redlines in the lower Model Score plot.
• Figure 5: Folded light curve and CNN scores for Kepler-158d orbiting KIC 4633570. A transit is detected within the USP period range [0.2 1] days at 0.645088 days, with a CNN score of 0.8918 and a transit SNR of 6.5. The detected transit is marked with a red line in the upper Flux plot. The CNN scores at the detected period and corresponding harmonics are marked in redlines in the lower Model Score plot.