Raw LC Cleaned LC Iterative prewhitening PU Learning Smoothed LC P: Known Hybrids U: A/F Stars PU Classifier 1.0015 1.001 0 1.00 05 1.0000 0.9995 0.999 0 0.99 85 0.9980 Normalized Flux 1.0015 1.0010 1.0005 1.0000 0.9995 0.9990 0.9985 Final LC Smoothed LC Normalized Flux Positive Unlabelled Learning to Discover Hybrid Pulsating Stars in the TESS Catalogue Mykyta Kliapets (1), Pablo Huijse Heise (1), Andrew Tkachenko (1), Conny Aerts (1, 2, 3) (1) Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001, Leuven, Belgium (2) Department of Astrophysics, IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands (3) Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany Correspondence email: nik.kliapets@gmail.com Problem Statement Data: TESS Light Curves (LCs) Methodology Results & Future Work δ Sct / γ Dor hybrid pulsating stars oscillating in both p- and g-modes are crucial for stella r astrophysics, yet not many of them are known. Large volumes of astronomical surveys (Kepler, TESS) make manual search impractical. Machine learning can help increase the available pool of hybrids with automated detection b y leveraging known ones. Known hybrids: 5,017 LCs of 522 known hybrid pulsators from 3 catalogues: Bowman et al (2016) , Li et al (2020), Skarka et al (2022). 1. Unlabelled stars: 122,137 LCs of A/F class stars from TESS Sectors 27 and 40 (Kunimoto et al 2021). 2. Labelled non-hybrids: 2,005 LCs of variable stars in 6 variability classes (Audenaert et al 2021). 3. Some hidden hybrids receive lower probabilities due to noisy data, requiring a cleaner training set (manual inspection of labelled LCs). Sources: Bowman, DM. et al. (2016). “Amplitude modulation in δ Sct stars: statistics from an ensemble study of Kepler targets”. In: Monthly Notices of the Royal Astronomical Society 460.2, pp. 1970–1989. Li, G. et al. (2020). “Gravity-mode period spacings and near-core rotation rates of 611 γ Doradus stars with Kepler”. In: Monthly Notices of the Royal Astronomical Society 491.3, pp. 3586–3605. Skarka, M. et al. (2022). “Periodic variable AF spectral type stars in the northern TESS continuous viewing zone-I. Identification and classification”. In: Astronomy & Astrophysics 666, A142. Kunimoto, M. et al. (2021). “Quick-look pipeline lightcurves for 9.1 million stars observed over the first year of the TESS Extended Mission”. In: Research Notes of the AAS 5.10, p. 234. Audenaert, J. et al. (2021). “TESS data for asteroseismology (T’DA) stellar variability classification pipeline: setup and application to the Kepler Q9 data”. In: The Astronomical Journal 162.5, p. 209. Bekker, J. and Davis, J. (2020). “Learning from positive and unlabeled data: a survey”. In: Machine Learning 109.4, pp. 719–760. New hybrid candidates: 112 LCs from TESS Sectors 27 and 40 with probabilities in [0.98, 1]. Acknowledgement: This Master’s Thesis research was funded with the 2023 Kavli Scholarship in machine learning for astrophysics, given by the Kavli Foundation. Each TESS LC is a separate training example. Using TESS quality flags and removing outliers. Subtracting the moving average to remove instrumental trend. Extracting up to 5 periods in both p- and g-mode regimes with an SNR check. Bagging ensemble outputs a probability of each unlabelled LC being a hybrid pulsator. We are only using extended mission data. Hundreds of millions of stars observed by space telescopes TESS Sectors 27 & 40. Remaining TESS Sectors (and Kepler data) contain hybrid pulsators and other variable phenomena waiting to be detected with PU Learning. 350 300 250 200 150 100 50 0 0 10 60 70 Periodogram p-mode g-mode 20 30 40 50 Frequency [1/d] Power [ppm] 1200 1000 800 600 400 200 0 0 10 20 30 40 Frequency [1/d] 50 Periodogram p-mode g-mode 60 70 Power [ppm] 1.0 0.8 2770 2775 2780 2790 2795 2785 Normalized Flux 0.9 0.7 0.6 Time [d] 2770 2775 2780 2790 2795 2785 Time [d] 2770 2775 2780 2790 2795 2785 Time [d] 10^4 10^3 10^2 10^1 10^0 0