Transit timing variations in HIP 41378: CHEOPS and TESS confirm a non-transiting sixth planet in the system^★

¹ Dipartimento di Fisica, Università di Trento, Via Sommarive 14, 38123 Povo, Italy
² Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
³ INAF, Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁴ Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
⁵ Space Research and Planetary Sciences, Physics Institute, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
⁶ Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
⁷ Observatoire astronomique de l’Université de Genève, Chemin Pegasi 51, 1290 Versoix, Switzerland
⁸ Department of Astronomy, Stockholm University, AlbaNova University Center, 10691 Stockholm, Sweden
⁹ European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
¹⁰ Instituto de Astrofisica e Ciencias do Espaco, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
¹¹ Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
¹² Space sciences, Technologies and Astrophysics Research (STAR) Institute, Université de Liège, Allée du 6 Août 19C, 4000 Liège, Belgium
¹³ Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
¹⁴ Instituto de Astrofísica de Canarias, Vía Láctea s/n, 38200 La Laguna, Tenerife, Spain
¹⁵ Departamento de Astrofísica, Universidad de La Laguna, Astrofísico Francisco Sanchez s/n, 38206 La Laguna, Tenerife, Spain
¹⁶ Admatis, 5. Kandó Kálmán Street, 3534 Miskolc, Hungary
¹⁷ Depto. de Astrofísica, Centro de Astrobiología (CSIC-INTA), ESAC campus, 28692 Villanueva de la Cañada (Madrid), Spain
¹⁸ Departamento de Fisica e Astronomia, Faculdade de Ciencias, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal
¹⁹ Institute of Optical Sensor Systems, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany
²⁰ Centre for Exoplanet Science, SUPA School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
²¹ CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516 Coimbra, Portugal
²² Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany
²³ INAF, Osservatorio Astrofisico di Torino, Via Osservatorio, 20, 10025 Pino Torinese To, Italy
²⁴ Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden
²⁵ Aix Marseille Univ, CNRS, CNES, LAM, 38 rue Frédéric Joliot-Curie, 13388 Marseille, France
²⁶ ELTE Gothard Astrophysical Observatory, 9700 Szombathely, Szent Imre h. u. 112, Hungary
²⁷ SRON Netherlands Institute for Space Research, Niels Bohrweg 4, 2333 CA Leiden, The Netherlands
²⁸ Centre Vie dans l’Univers, Faculté des sciences, Université de Genève, Quai Ernest-Ansermet 30, 1211 Genève 4, Switzerland
²⁹ Leiden Observatory, University of Leiden, PO Box 9513, 2300 RA Leiden, The Netherlands
³⁰ Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden
³¹ Dipartimento di Fisica, Università degli Studi di Torino, via Pietro Giuria 1, 10125 Torino, Italy
³² National and Kapodistrian University of Athens, Department of Physics, University Campus, Zografos 157 84, Athens, Greece
³³ Astrobiology Research Unit, Université de Liège, Allée du 6 Août 19C, 4000 Liège, Belgium
³⁴ Department of Astrophysics, University of Vienna, Türkenschanzstrasse 17, 1180 Vienna, Austria
³⁵ Institute for Theoretical Physics and Computational Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austria
³⁶ Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, 1121 Budapest, Konkoly Thege Miklós út 15-17, Hungary
³⁷ ELTE Eötvös Loránd University, Institute of Physics, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
³⁸ Lund Observatory, Division of Astrophysics, Department of Physics, Lund University, Box 118, 22100 Lund, Sweden
³⁹ IMCCE, UMR8028 CNRS, Observatoire de Paris, PSL Univ., Sorbonne Univ., 77 av. Denfert-Rochereau, 75014 Paris, France
⁴⁰ Institut d’astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie, 98bis blvd. Arago, 75014 Paris, France
⁴¹ Astrophysics Group, Lennard Jones Building, Keele University, Staffordshire ST5 5BG, UK
⁴² European Space Agency, ESA – European Space Astronomy Centre, Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain
⁴³ INAF, Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123 Catania, Italy
⁴⁴ Weltraumforschung und Planetologie, Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
⁴⁵ ETH Zurich, Department of Physics, Wolfgang-Pauli-Strasse 2, 8093 Zurich, Switzerland
⁴⁶ Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, UK
⁴⁷ Institut fuer Geologische Wissenschaften, Freie Universitaet Berlin, Maltheserstrasse 74-100, 12249 Berlin, Germany
⁴⁸ Institut de Ciencies de l’Espai (ICE, CSIC), Campus UAB, Can Magrans s/n, 08193 Bellaterra, Spain
⁴⁹ Institut d’Estudis Espacials de Catalunya (IEEC), 08860 Castelldefels (Barcelona), Spain
⁵⁰ HUN-REN-ELTE Exoplanet Research Group, Szent Imre h. u. 112., Szombathely 9700, Hungary
⁵¹ Leiden Observatory, University of Leiden, Einsteinweg 55, 2333 CA Leiden, The Netherlands
⁵² Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

^★★ Corresponding author: pietro.leonardi.1@studenti.unipd.it

Received: 22 April 2025
Accepted: 11 September 2025

Abstract

In multiple-planet systems, gravitational interactions of exoplanets could lead to transit timing variations (TTVs), whose amplitude becomes significantly enhanced when planets are in or near mean-motion resonances (MMRs), making them more easily detectable. In cases where both TTVs and radial velocity (RV) measurements are available, combined analysis can break degeneracies and provide robust planetary and system characterization, even detecting non-transiting planets. In this context, HIP 41378 hosts five confirmed transiting planets with periods ranging from 15 to over 542 days, providing a unique dynamical laboratory for investigating wide multi-planet systems analogous to the Solar System. In this study, we present an intensive space-based photometric follow-up of HIP 41378, combining 15 new CHEOPS observations with eight TESS sectors, alongside data from K2, Spitzer, HST, and 311 HARPS spectra. We dynamically modeled the TTVs and RV signals of the two inner sub-Neptunes via N-body integration. These planets, HIP 41378 b (P_b = 15.57 days, R_b = 2.45 R_⊕) and HIP 41378 c (P_c = 31.71 days, R_c = 2.57 R_⊕), are close to (Δ ~ 1.8%) a 2:1 period commensurability. We report a clear detection of TTVs with amplitudes of 20 minutes for planet b and greater than 3 hours for planet c. We dynamically confirm the planetary nature of HIP 41378 g, a non-transiting planet with a period of about 64 days and a mass of about 7 M_⊕, close to a 2:1 commensurability with planet c, suggesting a possible mean-motion resonance chain in the inner system. Our precise determination of the masses, eccentricities, and radii of HIP 41378 b and c enabled us to investigate their possible volatile-rich compositions. Finally, by leveraging on the last TESS sectors we constrained the period of HIP 41378 d to three possible aliases (P_d = 278, 371, and 1113 days) suggesting that the system could be placed in a double quasi resonant chain, highlighting its complex dynamical architecture.