The tidal deformation and atmosphere of WASP-12 b from its phase curve^★,★★

¹ Observatoire astronomique de l’Université de Genève, Chemin Pegasi 51, 1290 Versoix, Switzerland
e-mail: tunde.akinsanmi@unige.ch
² Instituto de Astrofisica e Ciencias do Espaco, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
³ Departamento de Fisica e Astronomia, Faculdade de Ciencias, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal
⁴ Space Research Institute, Austrian Academy of Sciences, Schmiedl-strasse 6, 8042 Graz, Austria
⁵ INAF, Osservatorio Astrofisico di Torino, Via Osservatorio, 20, 10025 Pino Torinese To, Italy
⁶ Weltraumforschung und Planetologie, Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
⁷ Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
⁸ Department of Astronomy, Stockholm University, AlbaNova University Center, 10691 Stockholm, Sweden
⁹ Centre for Exoplanet Science, SUPA School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
¹⁰ IMCCE, UMR8028 CNRS, Observatoire de Paris, PSL Univ., Sorbonne Univ., 77 av. Denfert-Rochereau, 75014 Paris, France
¹¹ INAF, Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123 Catania, Italy
¹² Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
¹³ Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, UK
¹⁴ Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany
¹⁵ Instituto de Astrofisica de Canarias, Via Lactea s/n, 38200 La Laguna, Tenerife, Spain
¹⁶ Departamento de Astrofisica, Universidad de La Laguna, Astrofísico Francisco Sanchez s/n, 38206 La Laguna, Tenerife, Spain
¹⁷ European Space Agency (ESA), ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
¹⁸ Admatis, 5. Kandó Kálmán Street, 3534 Miskolc, Hungary
¹⁹ Depto. de Astrofisica, Centro de Astrobiologia (CSIC-INTA), ESAC campus, 28692 Villanueva de la Cañada (Madrid), Spain
²⁰ Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
²¹ INAF, Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
²² Institute of Optical Sensor Systems, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany
²³ Université de Paris Cité, Institut de physique du globe de Paris, CNRS, 1 Rue Jussieu, 75005 Paris, France
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 Astrobiology Research Unit, Université de Liège, Allée du 6 Août 19C, 4000 Liège, Belgium
²⁷ Space sciences, Technologies and Astrophysics Research (STAR) Institute, Université de Liège, Allée du 6 Août 19C, 4000 Liège, Belgium
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 Department of Astrophysics, University of Vienna, Türkenschanzs-trasse 17, 1180 Vienna, Austria
³³ Institute for Theoretical Physics and Computational Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austria
³⁴ Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, 1121 Budapest, Konkoly Thege Miklós út 15–17, Hungary
³⁵ ELTE Eötvös Loránd University, Institute of Physics, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
³⁶ Institut d’astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie, 98bis blvd. Arago, 75014 Paris, France
³⁷ Astrophysics Group, Lennard Jones Building, Keele University, Staffordshire ST5 5BG, UK
³⁸ Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
³⁹ Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
⁴⁰ ETH Zurich, Department of Physics, Wolfgang-Pauli-Strasse 2, 8093 Zurich, Switzerland
⁴¹ Zentrum für Astronomie und Astrophysik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
⁴² Institut fuer Geologische Wissenschaften, Freie Universitaet Berlin, Maltheserstrasse 74-100, 12249 Berlin, Germany
⁴³ Institut de Ciencies de l’Espai (ICE, CSIC), Campus UAB, Can Magrans s/n, 08193 Bellaterra, Spain
⁴⁴ Institut d’Estudis Espacials de Catalunya (IEEC), Gran Capità 2–4, 08034 Barcelona, Spain
⁴⁵ ELTE Eötvös Loránd University, Gothard Astrophysical Observatory, 9700 Szombathely, SzentImre h. u. 112, Hungary
⁴⁶ HUN-REN-ELTE Exoplanet Research Group, Szent Imre h. u. 112, Szombathely, 9700, Hungary
⁴⁷ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁴⁸ CFisUC, Departamento de Fisica, Universidade de Coimbra, 3004516 Coimbra, Portugal

Received: 6 November 2023
Accepted: 5 February 2024

Abstract

Context. Ultra-hot Jupiters present a unique opportunity to understand the physics and chemistry of planets, their atmospheres, and interiors at extreme conditions. WASP-12 b stands out as an archetype of this class of exoplanets, with a close-in orbit around its star that results in intense stellar irradiation and tidal effects.

Aims. The goals are to measure the planet’s tidal deformation, atmospheric properties, and also to refine its orbital decay rate.

Methods. We performed comprehensive analyses of the transits, occultations, and phase curves of WASP-12b by combining new CHEOPS observations with previous TESS and Spitzer data. The planet was modeled as a triaxial ellipsoid parameterized by the second-order fluid Love number of the planet, h₂, which quantifies its radial deformation and provides insight into the interior structure.

Results. We measured the tidal deformation of WASP-12b and estimated a Love number of h₂ = 1.55_−0.49^+0.45 (at 3.2σ) from its phase curve. We measured occultation depths of 333 ± 24 ppm and 493 ± 29 ppm in the CHEOPS and TESS bands, respectively, while the nightside fluxes are consistent with zero, and also marginal eastward phase offsets. Our modeling of the dayside emission spectrum indicates that CHEOPS and TESS probe similar pressure levels in the atmosphere at a temperature of ~2900 K. We also estimated low geometric albedos of A_g = 0.086 ± 0.017 and A_g = 0.01 ± 0.023 in the CHEOPS and TESS passbands, respectively, suggesting the absence of reflective clouds in the high-temperature dayside of the planet. The CHEOPS occultations do not show strong evidence for variability in the dayside atmosphere of the planet at the median occultation depth precision of 120 ppm attained. Finally, combining the new CHEOPS timings with previous measurements refines the precision of the orbital decay rate by 12% to a value of −30.23 ± 0.82 ms yr⁻¹, resulting in a modified stellar tidal quality factor of Q′_★ = 1.70 ± 0.14 × 10⁵.

Conclusions. WASP-12 b becomes the second exoplanet, after WASP-103b, for which the Love number has been measured from the effect of tidal deformation in the light curve. However, constraining the core mass fraction of the planet requires measuring h₂ with a higher precision. This can be achieved with high signal-to-noise observations with JWST since the phase curve amplitude, and consequently the induced tidal deformation effect, is higher in the infrared.