Photo-dynamical characterisation of the TOI-178 resonant chain

Exploring the robustness of transit-timing variations and radial velocity mass characterisations^★,★★

¹ Observatoire astronomique de l’Université de Genève, Chemin Pegasi 51, 1290 Versoix, Switzerland
e-mail: adrien.leleu@unige.ch
² Space Research and Planetary Sciences, Physics Institute, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
³ Astrobiology Research Unit, Université de Liège, Allée du 6 Août 19C, 4000 Liège, Belgium
⁴ Space sciences, Technologies and Astrophysics Research (STAR) Institute, Université de Liège, Allée du 6 Août 19C, 4000 Liège, Belgium
⁵ Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
⁶ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
⁷ Department of Astronomy, Stockholm University, AlbaNova University Center, 10691 Stockholm, Sweden
⁸ Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
⁹ Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
¹⁰ Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
¹¹ Centre Vie dans l’Univers, Faculté des sciences, Université de Genève, Quai Ernest-Ansermet 30, 1211 Genève 4, Switzerland
¹² Observatoire Astronomique de l’Université de Genève, Chemin Pegasi 51, CH-1290 Versoix, Switzerland
¹³ European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
¹⁴ Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, UK
¹⁵ Instituto de Astrofísica de Canarias, Vía Láctea s/n, 38200 La Laguna, Tenerife, Spain
¹⁶ Departamento de Astrofísica, Universidad de La Laguna, Astrofísico Francisco Sanchez s/n, 38206 La Laguna, Tenerife, Spain
¹⁷ Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile
¹⁸ Instituto de Astronomía, Universidad Católica del Norte, Angamos 0610, Antofagasta 1270709, Chile
¹⁹ Admatis, 5. Kandó Kálmán Street, 3534 Miskolc, Hungary
²⁰ Depto. de Astrofísica, Centro de Astrobiología (CSIC-INTA), ESAC campus, 28692 Villanueva de la Cañada (Madrid), Spain
²¹ Instituto de Astrofisica e Ciencias do Espaco, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
²² Departamento de Fisica e Astronomia, Faculdade de Ciencias, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal
²³ Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
²⁴ INAF, Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
²⁵ Centre for Exoplanet Research, School of Physics and Astronomy, University of Leicester, Leicester LE1 7RH, UK
²⁶ Centre for Exoplanet Science, SUPA School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
²⁷ CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516 Coimbra, Portugal
²⁸ Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany
²⁹ INAF, Osservatorio Astrofisico di Torino, Via Osservatorio, 20, 10025 Pino Torinese To, Italy
³⁰ Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden
³¹ Aix-Marseille Université, CNRS, CNES, LAM, 38 rue Frédéric Joliot-Curie, 13388 Marseille, France
³² ELTE Gothard Astrophysical Observatory, 9700 Szombathely, Szent Imre h. u. 112, Hungary
³³ SRON Netherlands Institute for Space Research, Niels Bohrweg 4, 2333 CA Leiden, The Netherlands
³⁴ Leiden Observatory, University of Leiden, PO Box 9513, 2300 RA Leiden, The Netherlands
³⁵ Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden
³⁶ Dipartimento di Fisica, Università degli Studi di Torino, via Pietro Giuria 1, 10125, Torino, Italy
³⁷ National and Kapodistrian University of Athens, Department of Physics, University Campus, Zografos 157 84, Athens, Greece
³⁸ Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK
³⁹ Department of Astrophysics, University of Vienna, Türkenschanzstrasse 17, 1180 Vienna, Austria
⁴⁰ Institute for Theoretical Physics and Computational Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austria
⁴¹ Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejército Libertador 441, Santiago, Chile
⁴² NASA Ames Research Center, Moffett Field, CA 94035, USA
⁴³ Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, 1121 Budapest, Konkoly Thege Miklós út 15-17, Hungary
⁴⁴ ELTE Eötvös Loránd University, Institute of Physics, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
⁴⁵ Lund Observatory, Division of Astrophysics, Department of Physics, Lund University, Box 118, 22100 Lund, Sweden
⁴⁶ IMCCE, UMR8028 CNRS, Observatoire de Paris, PSL Univ., Sorbonne Univ., 77 av. Denfert-Rochereau, 75014 Paris, France
⁴⁷ Center for Astrophysics, Harvard and Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
⁴⁸ Institut d’Astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie, 98bis blvd. Arago, 75014 Paris, France
⁴⁹ Astrophysics Group, Lennard Jones Building, Keele University, Staffordshire ST5 5BG, UK
⁵⁰ Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4L8, UK
⁵¹ INAF, Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123 Catania, Italy
⁵² Institute of Optical Sensor Systems, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany
⁵³ Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
⁵⁴ ETH Zurich, Department of Physics, Wolfgang-Pauli-Strasse 2, 8093 Zurich, Switzerland
⁵⁵ Institut fuer Geologische Wissenschaften, Freie Universitaet Berlin, Maltheserstrasse 74-100, 12249 Berlin, Germany
⁵⁶ Institut de Ciencies de l’Espai (ICE, CSIC), Campus UAB, Can Magrans s/n, 08193 Bellaterra, Spain
⁵⁷ Institut d’Estudis Espacials de Catalunya (IEEC), 08860 Castelldefels (Barcelona), Spain
⁵⁸ Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
⁵⁹ Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
⁶⁰ HUN-REN-ELTE Exoplanet Research Group, Szent Imre h. u. 112., Szombathely 9700, Hungary
⁶¹ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶² Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
⁶³ Centro de Astrofísica y Tecnologías Afines (CATA), Casilla 36-D, Santiago, Chile

Received: 2 April 2024
Accepted: 23 May 2024

Abstract

Context. The TOI-178 system consists of a nearby, late-K-dwarf with six transiting planets in the super-Earth to mini-Neptune regime, with radii ranging from to 2.9 R_⊕ and orbital periods between 1.9 and 20.7 days. All the planets, but the innermost one, form a chain of Laplace resonances. The fine-tuning and fragility of such orbital configurations ensure that no significant scattering or collision event has taken place since the formation and migration of the planets in the protoplanetary disc, thereby providing important anchors for planet formation models.

Aims. We aim to improve the characterisation of the architecture of this key system and, in particular, the masses and radii of its planets. In addition, since this system is one of the few resonant chains that can be characterised by both photometry and radial velocities, we propose to use it as a test bench for the robustness of the planetary mass determination with each technique.

Methods. We performed a global analysis of all the available photometry from CHEOPS, TESS and NGTS, and radial velocity from ESPRESSO, using a photo-dynamical modelling of the light curve. We also tried different sets of priors on the masses and eccentricity, as well as different stellar activity models, to study their effects on the masses estimated by transit-timing variations (TTVs) and radial velocities (RVs).

Results. We demonstrate how stellar activity prevents a robust mass estimation for the three outer planets using radial velocity data alone. We also show that our joint photo-dynamical and radial velocity analysis has resulted in a robust mass determination for planets c to 𝑔, with precision of ~ 12% for the mass of planet c, and better than 10% for planets d to 𝑔. The new precisions on the radii range from 2 to 3%. The understanding of this synergy between photometric and radial velocity measurements will be valuable for the PLATO mission. We also show that TOI-178 is indeed currently locked in the resonant configuration, librating around an equilibrium of the chain.