A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067

A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067

  • R. Luque,
  • H. P. Osborn,
  • A. Leleu,
  • E. Pallé,
  • A. Bonfanti,
  • O. Barragán,
  • T. G. Wilson,
  • C. Broeg,
  • A. Collier Cameron,
  • M. Lendl,
  • P. F. L. Maxted,
  • Y. Alibert,
  • D. Gandolfi,
  • J.-B. Delisle,
  • M. J. Hooton,
  • J. A. Egger,
  • G. Nowak,
  • M. Lafarga,
  • D. Rapetti,
  • J. D. Twicken,
  • J. C. Morales,
  • I. Carleo,
  • J. Orell-Miquel,
  • V. Adibekyan,
  • T. Zingales

Nature  623, 932–937 (2023)Cite this article

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Planets with radii between that of the Earth and Neptune (hereafter referred to as ‘sub-Neptunes’) are found in close-in orbits around more than half of all Sun-like stars1,2. However, their composition, formation and evolution remain poorly understood3. The study of multiplanetary systems offers an opportunity to investigate the outcomes of planet formation and evolution while controlling for initial conditions and environment. Those in resonance (with their orbital periods related by a ratio of small integers) are particularly valuable because they imply a system architecture practically unchanged since its birth. Here we present the observations of six transiting planets around the bright nearby star HD 110067. We find that the planets follow a chain of resonant orbits. A dynamical study of the innermost planet triplet allowed the prediction and later confirmation of the orbits of the rest of the planets in the system. The six planets are found to be sub-Neptunes with radii ranging from 1.94R to 2.85R. Three of the planets have measured masses, yielding low bulk densities that suggest the presence of large hydrogen-dominated atmospheres.

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Data availability

The TESS observations used in this study are publicly available at the Mikulski Archive for Space Telescopes (https://archive.stsci.edu/missions-and-data/tess). The CHEOPS observations used in this study are available at the CHEOPS mission archive (https://cheops-archive.astro.unige.ch/archive_browser/). The ground-based photometry and high-resolution imaging observations are uploaded to ExoFOP (https://exofop.ipac.caltech.edu/tess/target.php?id=347332255) and are publicly available. CARMENES and HARPS-N reduced spectra, together with the derived CCF-based radial velocities and spectral indicators, are available at Zenodo (https://doi.org/10.5281/zenodo.8211589). All reduced transit photometry and radial velocity measurements used in this work are also provided at Zenodo (https://doi.org/10.5281/zenodo.8211589).

Code availability

We used the following publicly available codes, resources and Python packages to reduce, analyse and interpret our observations of HD 110067: numpy (ref. 155), matplotlib (ref. 156), astropy (ref. 157), lightkurve (ref. 44), PIPE (ref. 51,52), AstroImageJ (ref. 58), raccoon (ref. 73), serval (ref. 74), ARES (refs. 79,80), MOOG (ref. 81), ZASPE (ref. 83), emcee (ref. 158), CLES (ref. 96), exoplanet (ref. 99), MonoTools (ref. 106), pymc3 (ref. 117), ArviZ (ref. 120), GLS (ref. 121), MCMCI (ref. 132) and pyaneti (refs. 136,139). We can share the code used in the data reduction or data analysis on request.


  1. Howard, A. W. et al. Planet occurrence within 0.25 AU of solar-type stars from Kepler. Astrophys. J. Suppl. 201, 15 (2012).

    Article  ADS  Google Scholar

  2. Fressin, F. et al. The false positive rate of Kepler and the occurrence of planets. Astrophys. J. 766, 81 (2013).

    Article  ADS  Google Scholar

  3. Bean, J. L., Raymond, S. N. & Owen, J. E. The nature and origins of sub-Neptune size planets. J. Geophys. Res. Planets 126, e06639 (2021).

    Article  Google Scholar

  4. Ricker, G. R. et al. Transiting Exoplanet Survey Satellite (TESS). J. Astron. Telesc. Instrum. Syst. 1, 014003 (2015).

    Article  ADS  Google Scholar

  5. Jenkins, J. M. et al. in Software and Cyberinfrastructure for Astronomy IV (eds Chiozzi, G. & Guzman, J. C.) 99133E (SPIE, 2016).

  6. Benz, W. et al. The CHEOPS mission. Exp. Astron. 51, 109–151 (2021).

    Article  ADS  Google Scholar

  7. Sinclair, A. T. The orbital resonance amongst the Galilean satellites of Jupiter. Mon. Not. R. Astron. Soc. 171, 59–72 (1975).

    Article  ADS  MATH  Google Scholar

  8. Morbidelli, A. Modern Celestial Mechanics: Aspects of Solar System Dynamics(Taylor & Francis, 2002).

  9. Papaloizou, J. C. B. Three body resonances in close orbiting planetary systems: tidal dissipation and orbital evolution. Int. J. Astrobiol. 14, 291–304 (2015).

    Article  ADS  Google Scholar

  10. Leleu, A. et al. Six transiting planets and a chain of Laplace resonances in TOI-178. Astron. Astrophys. 649, A26 (2021).

    Article  CAS  Google Scholar

  11. Luger, R. et al. A seven-planet resonant chain in TRAPPIST-1. Nat. Astron. 1, 0129 (2017).

    Article  ADS  Google Scholar

  12. Goździewski, K., Migaszewski, C., Panichi, F. & Szuszkiewicz, E. The Laplace resonance in the Kepler-60 planetary system. Mon. Not. R. Astron. Soc. 455, L104–L108 (2016).

    Article  ADS  Google Scholar

  13. Agol, E. et al. Refining the transit-timing and photometric analysis of TRAPPIST-1: masses, radii, densities, dynamics, and ephemerides. Planet Sci. J. 2, 1 (2021).

    Article  Google Scholar

  14. Dai, F. et al. TOI-1136 is a young, coplanar, aligned planetary system in a pristine resonant chain. Astron. J. 165, 33 (2023).

    Article  ADS  Google Scholar

  15. Quirrenbach, A. et al. in Ground-based and Airborne Instrumentation for Astronomy VIII, (eds Evans, C. J., Bryant, J. J. & Motohara, K.) 114473C (SPIE, 2020).

  16. Cosentino, R. et al. in Ground-based and Airborne Instrumentation for Astronomy IV (eds McLean, I. S., Ramsay, S. K. & Takami, H.) 84461V (SPIE, 2012).

  17. Holman, M. J. & Murray, N. W. The use of transit timing to detect terrestrial-mass extrasolar planets. Science 307, 1288–1291 (2005).

    Article  ADS  CAS  PubMed  Google Scholar

  18. Fulton, B. J. et al. The California-Kepler survey. III. A gap in the radius distribution of small planets. Astron. J. 154, 109 (2017).

    Article  ADS  Google Scholar

  19. Van Eylen, V. et al. An asteroseismic view of the radius valley: stripped cores, not born rocky. Mon. Not. R. Astron. Soc. 479, 4786–4795 (2018).

    Article  ADS  Google Scholar

  20. Kasting, J. F., Whitmire, D. P. & Reynolds, R. T. Habitable zones around main sequence stars. Icarus 101, 108–128 (1993).

    Article  ADS  CAS  PubMed  Google Scholar

  21. Kopparapu, R. K. et al. Habitable zones around main-sequence stars: dependence on planetary mass. Astrophys. J. Lett. 787, L29 (2014).

    Article  ADS  Google Scholar

  22. Izidoro, A. et al. Formation of planetary systems by pebble accretion and migration. Hot super-Earth systems from breaking compact resonant chains. Astron. Astrophys. 650, A152 (2021).

    Article  Google Scholar

  23. Fabrycky, D. C. et al. Architecture of Kepler’s multi-transiting systems. II. New investigations with twice as many candidates. Astrophys. J. 790, 146 (2014).

    Article  ADS  Google Scholar

  24. Zeng, L. et al. Growth model interpretation of planet size distribution. Proc. Natl Acad. Sci. USA 116, 9723–9728 (2019).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar

  25. Kempton, E. M. R. et al. A framework for prioritizing the TESS planetary candidates most amenable to atmospheric characterization. Proc. Acad. Sci. Pac. 130, 114401 (2018).

    ADS  Google Scholar

  26. Otegi, J. F., Bouchy, F. & Helled, R. Revisited mass-radius relations for exoplanets below 120 M. Astron. Astrophys. 634, A43 (2020).

    Article  ADS  CAS  Google Scholar

  27. Stassun, K. G. et al. The TESS input catalog and candidate target list. Astron. J.156, 102 (2018).

    Article  ADS  Google Scholar

  28. Stumpe, M. C. et al. Kepler Presearch Data Conditioning I—architecture and algorithms for error correction in Kepler light curves. Proc. Acad. Sci. Pac. 124, 985 (2012).

    ADS  Google Scholar

  29. Stumpe, M. C. et al. Multiscale systematic error correction via wavelet-based bandsplitting in Kepler data. Proc. Acad. Sci. Pac. 126, 100 (2014).

    ADS  Google Scholar

  30. Smith, J. C. et al. Kepler Presearch Data Conditioning II – a Bayesian approach to systematic error correction. Proc. Acad. Sci. Pac. 124, 1000 (2012).

    ADS  Google Scholar

  31. Jenkins, J. M. The impact of solar-like variability on the detectability of transiting terrestrial planets. Astrophys. J. 575, 493–505 (2002).

    Article  ADS  Google Scholar

  32. Jenkins, J. M. et al. in Software and Cyberinfrastructure for Astronomy (eds Radziwill, N. M. & Bridger, A.) 77400D (SPIE, 2010).

  33. Jenkins, J. M. et al. Kepler Data Processing Handbook: Transiting Planet Search. Kepler Science Document KSCI-19081-003 (2020).

  34. Twicken, J. D. et al. Kepler data validation I—architecture, diagnostic tests, and data products for vetting transiting planet candidates. Proc. Acad. Sci. Pac. 130, 064502 (2018).

    ADS  Google Scholar

  35. Li, J. et al. Kepler data validation II-transit model fitting and multiple-planet search. Proc. Acad. Sci. Pac. 131, 024506 (2019).

    ADS  Google Scholar

  36. Guerrero, N. M. et al. The TESS Objects of Interest Catalog from the TESS Prime Mission. Astrophys. J. Suppl. Ser. 254, 39 (2021).

    Article  ADS  Google Scholar

  37. Fausnaugh, M. M., Burke, C. J., Ricker, G. R. & Vanderspek, R. Calibrated full-frame images for the TESS Quick Look Pipeline. Res. Notes AAS 4, 251 (2020).

    Article  ADS  Google Scholar

  38. Hedges, C. et al. TOI-2076 and TOI-1807: two young, comoving planetary systems within 50 pc identified by TESS that are ideal candidates for further follow up. Astron. J. 162, 54 (2021).

    Article  ADS  CAS  Google Scholar

  39. Osborn, H. et al. Two warm Neptunes transiting HIP 9618 revealed by TESS & Cheops. Mon. Not. R. Astron. Soc. 523, 3069–3089 (2023).

    Article  ADS  Google Scholar

  40. Vanderburg, A. et al. TESS spots a compact system of super-Earths around the naked-eye star HR 858. Astrophys. J. Lett. 881, L19 (2019).

    Article  ADS  CAS  Google Scholar

  41. Deming, D. et al. Spitzer secondary eclipses of the dense, modestly-irradiated, giant exoplanet HAT-P-20b using pixel-level decorrelation. Astrophys. J. 805, 132 (2015).

    Article  ADS  Google Scholar

  42. Luger, R. et al. EVEREST: pixel level decorrelation of K2 light curves. Astron. J.152, 100 (2016).

    Article  ADS  Google Scholar

  43. Luger, R. et al. starry: analytic occultation light curves. Astron. J. 157, 64 (2019).

    Article  ADS  Google Scholar

  44. Lightkurve Collaboration et al. Lightkurve: Kepler and TESS time series analysis in Python. Astrophysics Source Code Library, record ascl:1812.013 (2018).

  45. Gilliland, R. L. et al. Kepler mission stellar and instrument noise properties. Astrophys. J. Suppl. Ser. 197, 6 (2011).

    Article  ADS  Google Scholar

  46. Van Cleve, J. E. et al. That’s how we roll: the NASA K2 mission science products and their performance metrics. Proc. Acad. Sci. Pac. 128, 075002 (2016).

    ADS  Google Scholar

  47. Schanche, N. et al. TOI-2257 b: a highly eccentric long-period sub-Neptune transiting a nearby M dwarf. Astron. Astrophys. 657, A45 (2022).

    Article  Google Scholar

  48. Ulmer-Moll, S. et al. Two long-period transiting exoplanets on eccentric orbits: NGTS-20 b (TOI-5152 b) and TOI-5153 b. Astron. Astrophys. 666, A46 (2022).

    Article  CAS  Google Scholar

  49. Osborn, A. et al. TOI-431/HIP 26013: a super-Earth and a sub-Neptune transiting a bright, early K dwarf, with a third RV planet. Mon. Not. R. Astron. Soc. 507, 2782–2803 (2021).

    Article  ADS  Google Scholar

  50. Tuson, A. et al. TESS and CHEOPS discover two warm sub-Neptunes transiting the bright K-dwarf HD 15906. Mon. Not. R. Astron. Soc. 523, 3090–3118 (2023).

    Article  ADS  Google Scholar

  51. Szabó, G. M. et al. The changing face of AU Mic b: stellar spots, spin-orbit commensurability, and transit timing variations as seen by CHEOPS and TESS. Astron. Astrophys. 654, A159 (2021).

    Article  Google Scholar

  52. Morris, B. M. et al. CHEOPS precision phase curve of the Super-Earth 55 Cancri e. Astron. Astrophys. 653, A173 (2021).

    Article  Google Scholar

  53. Hoyer, S. et al. Expected performances of the Characterising Exoplanet Satellite (CHEOPS). III. Data reduction pipeline: architecture and simulated performances. Astron. Astrophys. 635, A24 (2020).

    Article  Google Scholar

  54. Narita, N. et al. MuSCAT2: four-color simultaneous camera for the 1.52-m Telescopio Carlos Sánchez. J. Astron. Telesc. Instrum. Syst. 5, 015001 (2019).

    ADS  Google Scholar

  55. Parviainen, H. et al. MuSCAT2 multicolour validation of TESS candidates: an ultra-short-period substellar object around an M dwarf. Astron. Astrophys. 633, A28 (2020).

    Article  CAS  Google Scholar

  56. Brown, T. M. et al. Las Cumbres Observatory global telescope network. Proc. Acad. Sci. Pac. 125, 1031 (2013).

    ADS  Google Scholar

  57. McCully, C. et al. in Software and Cyberinfrastructure for Astronomy V (eds Guzman, J. C. & Ibsen, J.) 107070K (2018).

  58. Collins, K. A., Kielkopf, J. F., Stassun, K. G. & Hessman, F. V. AstroImageJ: image processing and photometric extraction for ultra-precise astronomical light curves. Astron. J. 153, 77 (2017).

    Article  ADS  Google Scholar

  59. Wheatley, P. J. et al. The Next Generation Transit Survey (NGTS). Mon. Not. R. Astron. Soc. 475, 4476–4493 (2018).

    Article  ADS  CAS  Google Scholar

  60. Garcia-Mejia, J. et al. in Ground-based and Airborne Telescopes VIII (eds Marshall, H. K., Spyromilio, J. & Usuda, T.) 114457R (SPIE, 2020).

  61. Demory, B. O. et al. A super-Earth and a sub-Neptune orbiting the bright, quiet M3 dwarf TOI-1266. Astron. Astrophys. 642, A49 (2020).

    Article  CAS  Google Scholar

  62. Narita, N. et al. in Ground-based and Airborne Instrumentation for Astronomy VIII(eds Evans, C. J., Bryant, J. J. & Motohara, K.) 114475K (SPIE, 2020).

  63. Fukui, A. et al. Measurements of transit timing variations for WASP-5b. Pub. Astron. Soc. Jpn. 63, 287–300 (2011).

    Article  ADS  Google Scholar

  64. Ciardi, D. R., Beichman, C. A., Horch, E. P. & Howell, S. B. Understanding the effects of stellar multiplicity on the derived planet radii from transit surveys: implications for Kepler, K2, and TESS. Astrophys. J. 805, 16 (2015).

    Article  ADS  Google Scholar

  65. Hayward, T. L. et al. PHARO: a near-infrared camera for the Palomar Adaptive Optics System. Proc. Acad. Sci. Pac. 113, 105–118 (2001).

    ADS  Google Scholar

  66. Dekany, R. et al. PALM-3000: exoplanet adaptive optics for the 5 m Hale telescope. Astrophys. J. 776, 130 (2013).

    Article  ADS  Google Scholar

  67. Furlan, E. et al. The Kepler follow-up observation program. I. A catalog of companions to Kepler stars from high-resolution imaging. Astron. J. 153, 71 (2017).

    Article  ADS  Google Scholar

  68. Scott, N. J. et al. Twin high-resolution, high-speed imagers for the Gemini telescopes: instrument description and science verification results. Front. Astron. Space Sci. 8, 138 (2021).

    Article  ADS  Google Scholar

  69. Howell, S. B., Everett, M. E., Sherry, W., Horch, E. & Ciardi, D. R. Speckle camera observations for the NASA Kepler Mission Follow-up Program. Astron. J. 142, 19 (2011).

    Article  ADS  Google Scholar

  70. Mugrauer, M. & Michel, K.-U. Gaia search for stellar companions of TESS Objects of Interest. Astron. Nachr. 341, 996–1030 (2020).

    Article  ADS  Google Scholar

  71. Mugrauer, M. & Michel, K.-U. Gaia search for stellar companions of TESS Objects of Interest II. Astron. Nachr. 342, 840–864 (2021).

    Article  ADS  Google Scholar

  72. Ziegler, C. et al. SOAR TESS survey. I. Sculpting of TESS planetary systems by stellar companions. Astron. J. 159, 19 (2020).

    Article  ADS  Google Scholar

  73. Lafarga, M. et al. The CARMENES search for exoplanets around M dwarfs. Radial velocities and activity indicators from cross-correlation functions with weighted binary masks. Astron. Astrophys. 636, A36 (2020).

    Article  Google Scholar

  74. Zechmeister, M. et al. Spectrum radial velocity analyser (SERVAL). High-precision radial velocities and two alternative spectral indicators. Astron. Astrophys. 609, A12 (2018).

    Article  Google Scholar

  75. Cosentino, R. et al. in Ground-based and Airborne Instrumentation for Astronomy V (eds Ramsay, S. K., McLean, I. S. & Takami, H.) 91478C (SPIE, 2014).

  76. Santos, N. C. et al. SWEET-Cat: a catalogue of parameters for Stars With ExoplanETs. I. New atmospheric parameters and masses for 48 stars with planets. Astron. Astrophys. 556, A150 (2013).

    Article  Google Scholar

  77. Sousa, S. G. ARES + MOOG: A Practical Overview of an Equivalent Width (EW) Method to Derive Stellar Parameters 297–310 (Springer, 2014).

  78. Sousa, S. G. et al. SWEET-Cat 2.0: The Cat just got SWEETer. Higher quality spectra and precise parallaxes from Gaia eDR3. Astron. Astrophys. 656, A53 (2021).

    Article  Google Scholar

  79. Sousa, S. G., Santos, N. C., Israelian, G., Mayor, M. & Monteiro, M. J. P. F. G. A new code for automatic determination of equivalent widths: Automatic Routine for line Equivalent widths in stellar Spectra (ARES). Astron. Astrophys. 469, 783–791 (2007).

    Article  ADS  Google Scholar

  80. Sousa, S. G., Santos, N. C., Adibekyan, V., Delgado-Mena, E. & Israelian, G. ARES v2: new features and improved performance. Astron. Astrophys. 577, A67 (2015).

    Article  ADS  Google Scholar

  81. Sneden, C. A. Carbon and Nitrogen Abundances in Metal-Poor Stars. PhD thesis, Univ. Texas at Austin (1973).

  82. Kurucz, R. L. SYNTHE spectrum synthesis programs and line data. Astrophysics Source Code Library (1993).

  83. Brahm, R., Jordán, A., Hartman, J. & Bakos, G. ZASPE: a code to measure stellar atmospheric parameters and their covariance from spectra. Mon. Not. R. Astron. Soc. 467, 971–984 (2017).

    ADS  CAS  Google Scholar

  84. Adibekyan, V. Zh. et al. Chemical abundances of 1111 FGK stars from the HARPS GTO planet search program. Galactic stellar populations and planets. Astron. Astrophys. 545, A32 (2012).

    Article  Google Scholar

  85. Adibekyan, V. et al. Identifying the best iron-peak and α-capture elements for chemical tagging: the impact of the number of lines on measured scatter. Astron. Astrophys. 583, A94 (2015).

    Article  Google Scholar

  86. Castelli, F. & Kurucz, R. L. in Modelling of Stellar Atmospheres, Proc. 210th Symposium of the International Astronomical Union (eds Piskunov, N., Weiss, W. W. & Gray, D. F.) A20 (Astronomical Society of the Pacific, 2003).

  87. Allard, F. in Exploring the Formation and Evolution of Planetary Systems, Proc. IAU Symposium No. 299 (eds Booth, M., Matthews, B. C. & Graham, J. R.) 271–272 (International Astronomical Union, 2014).

  88. Blackwell, D. E. & Shallis, M. J. Stellar angular diameters from infrared photometry. Application to Arcturus and other stars; with effective temperatures. Mon. Not. R. Astron. Soc. 180, 177–191 (1977).

    Article  ADS  Google Scholar

  89. Schanche, N. et al. WASP-186 and WASP-187: two hot Jupiters discovered by SuperWASP and SOPHIE with additional observations by TESS. Mon. Not. R. Astron. Soc. 499, 428–440 (2020).

    Article  ADS  CAS  Google Scholar

  90. Wilson, T. G. et al. A pair of sub-Neptunes transiting the bright K-dwarf TOI-1064 characterized with CHEOPS. Mon. Not. R. Astron. Soc. 511, 1043–1071 (2022).

    Article  ADS  CAS  Google Scholar

  91. Lindegren, L. et al. Gaia Early Data Release 3. Parallax bias versus magnitude, colour, and position. Astron. Astrophys. 649, A4 (2021).

    Article  Google Scholar

  92. Bonfanti, A. et al. CHEOPS observations of the HD 108236 planetary system: a fifth planet, improved ephemerides, and planetary radii. Astron. Astrophys. 646, A157 (2021).

    Article  CAS  Google Scholar

  93. Bonfanti, A., Ortolani, S., Piotto, G. & Nascimbeni, V. Revising the ages of planet-hosting stars. Astron. Astrophys. 575, A18 (2015).

    Article  ADS  Google Scholar

  94. Bonfanti, A., Ortolani, S. & Nascimbeni, V. Age consistency between exoplanet hosts and field stars. Astron. Astrophys. 585, A5 (2016).

    Article  ADS  Google Scholar

  95. Marigo, P. et al. A new generation of PARSEC-COLIBRI stellar isochrones including the TP-AGB phase. Astrophys. J. 835, 77 (2017).

    Article  ADS  Google Scholar

  96. Scuflaire, R. et al. CLÉS, Code Liégeois d’Évolution Stellaire. Astrophys. Space Sci. 316, 83–91 (2008).

    Article  ADS  Google Scholar

  97. Salmon, S. J. A. J., Van Grootel, V., Buldgen, G., Dupret, M. A. & Eggenberger, P. Reinvestigating α Centauri AB in light of asteroseismic forward and inverse methods. Astron. Astrophys. 646, A7 (2021).

    Article  Google Scholar

  98. Reddy, B. E., Lambert, D. L. & Allende Prieto, C. Elemental abundance survey of the Galactic thick disc. Mon. Not. R. Astron. Soc. 367, 1329–1366 (2006).

    Article  ADS  CAS  Google Scholar

  99. Foreman-Mackey, D. et al. dfm/exoplanet: exoplanet v0.2.1. Zenodo https://zenodo.org/record/3462740 (2019).

  100. Delrez, L. et al. Transit detection of the long-period volatile-rich super-Earth ν2Lupi d with CHEOPS. Nat. Astron. 5, 775–787 (2021).

    Article  ADS  Google Scholar

  101. Claret, A. A new method to compute limb-darkening coefficients for stellar atmosphere models with spherical symmetry: the space missions TESS, Kepler, CoRoT, and MOST. Astron. Astrophys. 618, A20 (2018).

    Article  ADS  Google Scholar

  102. Claret, A. Limb and gravity-darkening coefficients for the Space Mission CHEOPS. Res. Notes AAS 5, 13 (2021).

    Article  ADS  Google Scholar

  103. Van Eylen, V. & Albrecht, S. Eccentricity from transit photometry: small planets in Kepler multi-planet systems have low eccentricities. Astrophys. J. 808, 126 (2015).

    Article  ADS  Google Scholar

  104. Xie, J.-W. et al. Exoplanet orbital eccentricities derived from LAMOST–Kepler analysis. Proc. Natl Acad. Sci. USA 113, 11431–11435 (2016).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar

  105. Hadden, S. & Lithwick, Y. Kepler planet masses and eccentricities from TTV analysis. Astron. J. 154, 5 (2017).

    Article  ADS  Google Scholar

  106. Osborn, H. P. MonoTools: planets of uncertain periods detector and modeler. Astrophysics Source Code Library, record ascl:2204.020 (2022).

  107. Kipping, D. The orbital period prior for single transits. Res. Notes AAS 2, 223 (2018).

    Article  ADS  Google Scholar

  108. Van Eylen, V. et al. The orbital eccentricity of small planet systems. Astron. J.157, 61 (2019).

    Article  ADS  Google Scholar

  109. Osborn, H. P. et al. Uncovering the true periods of the young sub-Neptunes orbiting TOI-2076. Astron. Astrophys. 664, A156 (2022).

    Article  Google Scholar

  110. Mills, S. M. et al. A resonant chain of four transiting, sub-Neptune planets. Nature 533, 509–512 (2016).

    Article  ADS  CAS  PubMed  Google Scholar

  111. Siegel, J. C. & Fabrycky, D. Resonant chains of exoplanets: libration centers for three-body angles. Astron. J. 161, 290 (2021).

    Article  ADS  Google Scholar

  112. Lopez, T. A. et al. Exoplanet characterisation in the longest known resonant chain: the K2-138 system seen by HARPS. Astron. Astrophys. 631, A90 (2019).

    Article  CAS  Google Scholar

  113. Rein, H. & Liu, S. F. REBOUND: an open-source multi-purpose N-body code for collisional dynamics. Astron. Astrophys. 537, A128 (2012).

    Article  ADS  Google Scholar

  114. Delisle, J.-B. samsam: Scaled Adaptive Metropolis SAMpler. Astrophysics Source Code Library, record ascl:2207.011 (2022).

  115. Leleu, A. et al. Removing biases on the density of sub-Neptunes characterised via transit timing variations. Update on the mass-radius relationship of 34 Kepler planets. Astron. Astrophys. 669, A117 (2023).

    Article  CAS  Google Scholar

  116. Parviainen, H. & Aigrain, S. ldtk: Limb Darkening Toolkit. Mon. Not. R. Astron. Soc. 453, 3821–3826 (2015).

    Article  ADS  Google Scholar

  117. Salvatier, J., Wiecki, T. V. & Fonnesbeck, C. Probabilistic programming in Python using PyMC3. PeerJ Comput. Sci. 2, e55 (2016).

    Article  Google Scholar

  118. Watanabe, S. & Opper, M. Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J. Mach. Learn. Res. 11, 3571–3594 (2010).

    MathSciNet  MATH  Google Scholar

  119. Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat. Comput. 27, 1413–1432 (2017).

    Article  MathSciNet  MATH  Google Scholar

  120. ArviZ Developers. ArviZ: exploratory analysis of Bayesian models. Astrophysics Source Code Library, record ascl:2004.012 (2020).

  121. Zechmeister, M. & Kürster, M. The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms. Astron. Astrophys. 496, 577–584 (2009).

    Article  ADS  Google Scholar

  122. Saar, S. H. & Donahue, R. A. Activity-related radial velocity variation in cool stars. Astrophys. J. 485, 319–327 (1997).

    Article  ADS  Google Scholar

  123. Hatzes, A. P. Starspots and exoplanets. Astron. Nachr. 323, 392–394 (2002).

    Article  ADS  CAS  Google Scholar

  124. Meunier, N., Desort, M. & Lagrange, A. M. Using the Sun to estimate Earth-like planets detection capabilities. II. Impact of plages. Astron. Astrophys. 512, A39 (2010).

    Article  ADS  Google Scholar

  125. Dumusque, X., Boisse, I. & Santos, N. C. SOAP 2.0: a tool to estimate the photometric and radial velocity variations induced by stellar spots and plages. Astrophys. J. 796, 132 (2014).

    Article  ADS  Google Scholar

  126. Queloz, D. et al. No planet for HD 166435. Astron. Astrophys. 379, 279–287 (2001).

    Article  ADS  CAS  Google Scholar

  127. Boisse, I. et al. Stellar activity of planetary host star HD 189 733. Astron. Astrophys. 495, 959–966 (2009).

    Article  ADS  CAS  Google Scholar

  128. Dumusque, X. Radial velocity fitting challenge. I. Simulating the data set including realistic stellar radial-velocity signals. Astron. Astrophys. 593, A5 (2016).

    Article  ADS  Google Scholar

  129. Simola, U., Dumusque, X. & Cisewski-Kehe, J. Measuring precise radial velocities and cross-correlation function line-profile variations using a Skew Normal density. Astron. Astrophys. 622, A131 (2019).

    Article  ADS  CAS  Google Scholar

  130. Simola, U. et al. Accounting for stellar activity signals in radial-velocity data by using change point detection techniques. Astron. Astrophys. 664, A127 (2022).

    Article  Google Scholar

  131. Bonfanti, A. et al. TOI-1055 b: Neptunian planet characterised with HARPS, TESS, and CHEOPS. Astron. Astrophys. 671, L8 (2023).

  132. Bonfanti, A. & Gillon, M. MCMCI: a code to fully characterise an exoplanetary system. Astron. Astrophys. 635, A6 (2020).

    Article  ADS  CAS  Google Scholar

  133. Schwarz, G. Estimating the dimension of a model. Ann. Stat. 6, 461–464 (1978).

    Article  MathSciNet  MATH  Google Scholar

  134. Gelman, A. & Rubin, D. B. Inference from iterative simulation using multiple sequences. Stat. Sci. 7, 457–472 (1992).

    Article  MATH  Google Scholar

  135. Rajpaul, V., Aigrain, S., Osborne, M. A., Reece, S. & Roberts, S. A Gaussian process framework for modelling stellar activity signals in radial velocity data. Mon. Not. R. Astron. Soc. 452, 2269–2291 (2015).

    Article  ADS  CAS  Google Scholar

  136. Barragán, O., Aigrain, S., Rajpaul, V. M. & Zicher, N. PYANETI – II. A multidimensional Gaussian process approach to analysing spectroscopic time-series. Mon. Not. R. Astron. Soc. 509, 866–883 (2022).

    Article  ADS  Google Scholar

  137. Barragán, O. et al. The young HD 73583 (TOI-560) planetary system: two 10-Mmini-Neptunes transiting a 500-Myr-old, bright, and active K dwarf. Mon. Not. R. Astron. Soc. 514, 1606–1627 (2022).

    Article  ADS  Google Scholar

  138. Zicher, N. et al. One year of AU Mic with HARPS – I. Measuring the masses of the two transiting planets. Mon. Not. R. Astron. Soc. 512, 3060–3078 (2022).

    Article  ADS  CAS  Google Scholar

  139. Barragán, O., Gandolfi, D. & Antoniciello, G. PYANETI: a fast and powerful software suite for multiplanet radial velocity and transit fitting. Mon. Not. R. Astron. Soc. 482, 1017–1030 (2019).

    Article  ADS  Google Scholar

  140. Cale, B. L. et al. Diving beneath the sea of stellar activity: chromatic radial velocities of the young AU Mic planetary system. Astron. J. 162, 295 (2021).

    Article  ADS  CAS  Google Scholar

  141. Blunt, S. et al. Overfitting affects the reliability of radial velocity mass estimates of the V1298 Tau planets. Astron. J. 166, 62 (2023).

  142. Dorn, C. et al. Can we constrain the interior structure of rocky exoplanets from mass and radius measurements? Astron. Astrophys. 577, A83 (2015).

    Article  Google Scholar

  143. Dorn, C. et al. A generalized Bayesian inference method for constraining the interiors of super Earths and sub-Neptunes. Astron. Astrophys. 597, A37 (2017).

    Article  Google Scholar

  144. Haldemann, J., Alibert, Y., Mordasini, C. & Benz, W. AQUA: a collection of H2O equations of state for planetary models. Astron. Astrophys. 643, A105 (2020).

    Article  ADS  CAS  Google Scholar

  145. Hakim, K. et al. A new ab initio equation of state of hcp-Fe and its implication on the interior structure and mass-radius relations of rocky super-Earths. Icarus313, 61–78 (2018).

    Article  ADS  CAS  Google Scholar

  146. Sotin, C., Grasset, O. & Mocquet, A. Mass radius curve for extrasolar Earth-like planets and ocean planets. Icarus 191, 337–351 (2007).

    Article  ADS  CAS  Google Scholar

  147. Lopez, E. D. & Fortney, J. J. Understanding the mass–radius relation for sub-Neptunes: radius as a proxy for composition. Astrophys. J. 792, 1 (2014).

    Article  ADS  Google Scholar

  148. Thiabaud, A. et al. From stellar nebula to planets: the refractory components. Astron. Astrophys. 562, A27 (2014).

    Article  Google Scholar

  149. Marboeuf, U., Thiabaud, A., Alibert, Y., Cabral, N. & Benz, W. From planetesimals to planets: volatile molecules. Astron. Astrophys. 570, A36 (2014).

    Article  ADS  Google Scholar

  150. Venturini, J., Guilera, O. M., Haldemann, J., Ronco, M. P. & Mordasini, C. The nature of the radius valley. Hints from formation and evolution models. Astron. Astrophys. 643, L1 (2020).

    Article  ADS  Google Scholar

  151. Emsenhuber, A. et al. The New Generation Planetary Population Synthesis (NGPPS). II. Planetary population of solar-like stars and overview of statistical results. Astron. Astrophys. 656, A70 (2021).

    Article  CAS  Google Scholar

  152. Izidoro, A. et al. The exoplanet radius valley from gas-driven planet migration and breaking of resonant chains. Astrophys. J. 939, L19 (2022).

    Article  ADS  Google Scholar

  153. Hu, R. et al. Unveiling shrouded oceans on temperate sub-Neptunes via transit signatures of solubility equilibria versus gas thermochemistry. Astrophys. J. 921, L8 (2021).

    Article  ADS  CAS  Google Scholar

  154. Tsai, S.-M. et al. Inferring shallow surfaces on sub-Neptune exoplanets with JWST. Astrophys. J. 922, L27 (2021).

    Article  ADS  CAS  Google Scholar

  155. Harris, C. R. et al. Array programming with NumPy. Nature 585, 357–362 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar

  156. Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007).

    Article  Google Scholar

  157. The Astropy Collaboration et al. The Astropy Project: sustaining and growing a community-oriented open-source project and the latest major release (v5.0) of the core package. Astrophys. J. 935, 167 (2022).

    Article  ADS  Google Scholar

  158. Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC hammer. Proc. Acad. Sci. Pac. 125, 306 (2013).

    ADS  Google Scholar

  159. MacDonald, M. G., Shakespeare, C. J. & Ragozzine, D. A five-planet resonant chain: reevaluation of the Kepler-80 system. Astron. J. 162, 114 (2021).

    Article  ADS  Google Scholar

  160. Cannon, A. J. & Pickering, E. C. The Henry Draper catalogue 0h, 1h, 2h, and 3h. Ann. Harvard College Observatory 91, 1–290 (1918).

    ADS  Google Scholar

  161. Gaia Collaboration et al. Gaia Early Data Release 3. Summary of the contents and survey properties. Astron. Astrophys. 649, A1 (2021).

    Article  Google Scholar

  162. Yoss, K. M. & Griffin, R. F. Radial velocities and DDO, BV photometry of Henry Draper G5-M stars near the North Galactic Pole. J. Astrophys. Astron. 18, 161–227 (1997).

    Article  ADS  Google Scholar

  163. Skrutskie, M. F. et al. The Two Micron All Sky Survey (2MASS). Astron. J. 131, 1163–1183 (2006).

    Article  ADS  Google Scholar

  164. Delisle, J. B. Analytical model of multi-planetary resonant chains and constraints on migration scenarios. Astron. Astrophys. 605, A96 (2017).

    Article  ADS  Google Scholar

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We acknowledge the use of public TESS data from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center (SPOC). Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products. The CHaracterising ExOPlanets Satellite (CHEOPS) is a European Space Agency (ESA) mission in partnership with Switzerland with important contributions to the payload and the ground segment from Austria, Belgium, France, Germany, Hungary, Italy, Portugal, Spain, Sweden and the United Kingdom. The CHEOPS Consortium would like to gratefully acknowledge the support received by all the agencies, offices, universities and industries involved. Their flexibility and willingness to explore new approaches were essential to the success of this mission. CARMENES acknowledges financial support from the Agencia Estatal de Investigación of the Ministerio de Ciencia e Innovación MCIN/AEI/10.13039/501100011033 and the European Regional Development Fund (ERDF) ‘A way of making Europe’ through projects PID2019-107061GB-C61, PID2019-107061GB-C66, PID2021-125627OB-C31 and PID2021-125627OB-C32, from the Centre of Excellence ‘Severo Ochoa’ award to the Instituto de Astrofísica de Canarias (IAC; CEX2019-000920-S), from the Centre of Excellence ‘María de Maeztu’ award to the Institut de Ciències de l’Espai (CEX2020-001058-M) and from the Generalitat de Catalunya/CERCA programme. Based on observations made with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundación Galileo Galilei of the Istituto Nazionale di Astrofisica (INAF) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. This article is based on observations made with the MuSCAT2 instrument, developed by the Astrobiology Center (ABC), at Telescopio Carlos Sánchez operated on the island of Tenerife by the IAC in the Spanish Observatorio del Teide. This paper is based on observations made with the MuSCAT3 instrument, developed by ABC and under financial supports by JSPS KAKENHI (JP18H05439) and JST PRESTO (JPMJPR1775), at Faulkes Telescope North on Maui, Hawaii, operated by the Las Cumbres Observatory. Tierras is supported by grants from the John Templeton Foundation and the Harvard Origins of Life Initiative. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. The Next Generation Transit Survey (NGTS) facility is operated by the consortium institutes with support from the UK Science and Technology Facilities Council (STFC) under projects ST/M001962/1 and ST/S002642/1. Some of the observations presented in this paper were carried out at the Observatorio Astronómico Nacional on the Sierra de San Pedro Mártir (OAN-SPM), Baja California, México. This work makes use of observations from the Las Cumbres Observatory global telescope network. Some of the observations in this paper made use of the High-Resolution Imaging instrument Alopeke and were obtained under Gemini LLP Proposal Number GN-S-2021A-LP-105. Alopeke was funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by S. B. Howell, N. Scott, E. P. Horch and E. Quigley. Alopeke was mounted on the Gemini North telescope of the international Gemini Observatory, a programme of NSF OIR Lab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. On behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil) and Korea Astronomy and Space Science Institute (Republic of Korea). This work was supported by the KESPRINT collaboration, an international consortium devoted to the characterization and research of exoplanets discovered with space-based missions. R.Lu. thanks D. Fabrycky for helpful discussions about the orbital dynamics of the HD 110067 system. R.Lu. acknowledges funding from University of La Laguna through the Margarita Salas Fellowship from the Spanish Ministry of Universities ref. UNI/551/2021-May 26 and under the EU Next Generation funds. This work has been carried out within the framework of the National Centre for Competence in Research (NCCR) PlanetS supported by the Swiss National Science Foundation (SNSF) under grants 51NF40_182901 and 51NF40_205606. A.C.Ca. and T.G.Wi. acknowledge support from STFC consolidated grant numbers ST/R000824/1 and ST/V000861/1 and UKSA grant number ST/R003203/1. O.Ba. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 865624). M.Le. acknowledges support of the SNSF under grant number PCEFP2_194576. P.F.L.Ma. acknowledges support from STFC research grant number ST/M001040/1. Y.Al. acknowledges support from the SNSF under grant 200020_192038. D.Ga. gratefully acknowledges financial support from the CRT foundation under grant no. 2018.2323 ‘Gaseous or rocky? Unveiling the nature of small worlds’. J.A.Eg. acknowledges support from the SNSF under grant 200020_192038. G.No. is grateful for the research funding from the Ministry of Education and Science programme ‘The Excellence Initiative – Research University’ conducted at the Centre of Excellence in Astrophysics and Astrochemistry of the Nicolaus Copernicus University in Torun, Poland. D.Ra. was supported by NASA under award number NNA16BD14C for NASA Academic Mission Services. M.La. acknowledges funding from a UKRI Future Leader Fellowship, grant number MR/S035214/1. V.Ad. is supported by Fundação para a Ciência e a Tecnologia (FCT) through national funds by grants UIDB/04434/2020, UIDP/04434/2020 and 2022.06962.PTDC. P.J.Am. acknowledges financial support from grants CEX2021-001131-S and PID2019-109522GB-C52, both funded by MCIN/AEI/ 10.13039/501100011033 and by the ERDF ‘A way of making Europe’. S.C.C.Ba. acknowledges support from FCT through FCT contract no. IF/01312/2014/CP1215/CT0004. X.Bo., S.Ch., D.Ga., M.Fr. and J.La. acknowledge their role as ESA-appointed CHEOPS science team members. L.Bo., V.Na., I.Pa., G.Pi., R.Ra., G.Sc., and T.Zi. acknowledge support from CHEOPS ASI-INAF agreement no. 2019-29-HH.0. A.Br. was supported by the Swedish National Space Agency (SNSA). Contributions at the Mullard Space Science Laboratory by E.M.Br. were supported by STFC through the consolidated grant ST/W001136/1. S.C.-G. acknowledges support from UNAM PAPIIT-IG101321. D.Ch. and J.G.-M. thank the staff at the F. L. Whipple Observatory for their assistance in the refurbishment and maintenance of the 1.3-m telescope. W.D.Co. acknowledges support from NASA grant 80NSSC23K0429. This is University of Texas Center for Planetary Systems Habitability Contribution 0063. K.A.Co. acknowledges support from the TESS mission through subaward s3449 from MIT. H.J.De. acknowledges support from the Spanish Research Agency of the Ministry of Science and Innovation (AEI-MICINN) under grant PID2019-107061GB-C66, doi:10.13039/501100011033. This project was supported by the CNES. The Belgian participation to CHEOPS has been supported by the Belgian Federal Science Policy Office (BELSPO) in the framework of the PRODEX Program and by the University of Liège through an ARC grant for Concerted Research Actions financed by the Wallonia-Brussels Federation. L.De. is an F.R.S.-FNRS Postdoctoral Researcher. This work was supported by FCT through national funds and by FEDER through COMPETE2020 – Programa Operacional Competitividade e Internacionalizacão by these grants: UID/FIS/04434/2019, UIDB/04434/2020, UIDP/04434/2020, PTDC/FIS-AST/32113/2017 and POCI-01-0145-FEDER-032113, PTDC/FIS-AST/28953/2017 and POCI-01-0145-FEDER-028953, PTDC/FIS-AST/28987/2017 and POCI-01-0145-FEDER-028987. O.D.S.De. is supported in the form of work contract (DL 57/2016/CP1364/CT0004) funded by national funds through FCT. B.-O.De. acknowledges support from the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number MB22.00046. This project has received funding from the ERC under the European Union’s Horizon 2020 research and innovation programme (project Four Aces grant agreement no. 724427). It has also been carried out in the frame of the NCCR PlanetS supported by the SNSF. D.Eh. acknowledges financial support from the SNSF for project 200021_200726. E.E.-B. acknowledges financial support from the European Union and the State Agency of Investigation of the Spanish Ministry of Science and Innovation (MICINN) under the grant PRE2020-093107 of the Pre-Doc Program for the Training of Doctors (FPI-SO) through FSE funds. M.Fr. gratefully acknowledges the support of the Swedish National Space Agency (DNR 65/19, 174/18). J.G.-M. acknowledges support by the National Science Foundation through a Graduate Research Fellowship under grant no. DGE1745303 and by the Ford Foundation through a Ford Foundation Predoctoral Fellowship, administered by the National Academies of Sciences, Engineering, and Medicine. The contributions at the University of Warwick by S.Gi. have been supported by STFC through consolidated grants ST/L000733/1 and ST/P000495/1. M.Gi. is F.R.S.-FNRS Research Director. Y.G.M.Ch. acknowledges support from UNAM PAPIIT-IG101321. E.Go. acknowledges support by the Thueringer Ministerium füër Wirtschaft, Wissenschaft und Digitale Gesellschaft. M.N.Gu. is the ESA CHEOPS Project Scientist and Mission Representative and, as such, is also responsible for the Guest Observers (GO) Programme. M.N.Gu. does not relay proprietary information between the GO and Guaranteed Time Observation (GTO) Programmes, and does not decide on the definition and target selection of the GTO Programme. A.P.Ha. acknowledges support by DFG grant HA 3279/12-1 within the DFG Schwerpunkt SPP 1992. Ch.He. acknowledges support from the European Union H2020-MSCA-ITN-2019 under grant agreement no. 860470 (CHAMELEON). S.Ho. gratefully acknowledges CNES funding through the grant 837319. This work is partly supported by JST CREST grant number JPMJCR1761. K.G.Is. is the ESA CHEOPS Project Scientist and is responsible for the ESA CHEOPS GO Programme. She does not participate in, or contribute to, the definition of the Guaranteed Time Programme of the CHEOPS mission through which observations described in this paper have been taken nor to any aspect of target selection for the programme. J.Ko. gratefully acknowledges the support of the SNSA (DNR 2020-00104) and of the Swedish Research Council (VR: Etableringsbidrag 2017-04945). K.W.F.La. was supported by Deutsche Forschungsgemeinschaft grants RA714/14-1 within the DFG Schwerpunkt SPP 1992, Exploring the Diversity of Extrasolar Planets. This work was granted access to the HPC resources of MesoPSL financed by the Region Ile de France and the project Equip@Meso (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir supervised by the Agence Nationale pour la Recherche. A.L.desE. acknowledges support from the CNES (Centre national d’études spatiales, France). This work is partly supported by Astrobiology Center SATELLITE Research project AB022006. This work is partly supported by JSPS KAKENHI grant number JP18H05439 and JST CREST grant number JPMJCR1761. H.L.M.Os. acknowledges funding support by STFC through a PhD studentship. H.Pa. acknowledges the support by the Spanish Ministry of Science and Innovation with the Ramon y Cajal fellowship number RYC2021-031798-I. This work was also partially supported by a grant from the Simons Foundation (PI: Queloz, grant number 327127). S.N.Qu. acknowledges support from the TESS mission through subaward s3449 from MIT. S.N.Qu. acknowledges support from the TESS GI Program under award 80NSSC21K1056 (G03268). L.Sa. acknowledges support from UNAM PAPIIT project IN110122. N.C.Sa. acknowledges funding by the European Union (ERC, FIERCE, 101052347). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the ERC. Neither the European Union nor the granting authority can be held responsible for them. N.Sc. acknowledges support from the SNSF (PP00P2-163967 and PP00P2-190080) and NASA under award number 80GSFC21M0002. S.G.So. acknowledges support from FCT through FCT contract no. CEECIND/00826/2018 and POPH/FSE (EC). Gy.M.Sz. acknowledges the support of the Hungarian National Research, Development and Innovation Office (NKFIH) grant K-125015, a PRODEX Experiment Agreement no. 4000137122, the Lendület LP2018-7/2021 grant of the Hungarian Academy of Science and the support of the city of Szombathely. A.Tu. acknowledges funding support from the STFC through a PhD studentship. V.V.Ey. acknowledges support by the STFC through the consolidated grant ST/W001136/1. V.V.Gr. is an F.R.S.-FNRS Research Associate. J.Ve. acknowledges support from the SNSF under grant PZ00P2_208945. N.A.Wa. acknowledges UKSA grant ST/R004838/1. N.Wa. is partly supported by JSPS KAKENHI grant number JP21K20376.

Author information

  1. These authors contributed equally: H. P. Osborn, A. Leleu, E. Pallé

Authors and Affiliations

  1. Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL, USA

    R. Luque & J. L. Bean

  2. Space Research and Planetary Sciences, Physics Institute, University of Bern, Bern, Switzerland

    H. P. Osborn, A. Leleu, C. Broeg, Y. Alibert, J. A. Egger, T. Beck, W. Benz, B.-O. Demory, A. Fortier, C. Mordasini, A. E. Simon & N. Thomas

  3. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    H. P. Osborn, K. M. Hesse, G. R. Ricker, A. Rudat, S. Seager, A. Shporer & A. M. Vanderburg

  4. Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA

    H. P. Osborn, K. M. Hesse, G. R. Ricker, A. Rudat, S. Seager, A. Shporer & A. M. Vanderburg

  5. Observatoire Astronomique de l’Université de Genève, Versoix, Switzerland

    A. Leleu, M. Lendl, J.-B. Delisle, M. Beck, N. Billot, A. Deline, D. Ehrenreich, S. Salmon, D. Ségransan, S. Udry & J. Venturini

  6. Instituto de Astrofisica de Canarias, La Laguna, Tenerife, Spain

    E. Pallé, G. Nowak, I. Carleo, J. Orell-Miquel, R. Alonso, H. J. Deeg, E. Esparza-Borges, A. Fukui, F. Murgas, N. Narita & H. Parviainen

  7. Departamento de Astrofisica, Universidad de La Laguna, La Laguna, Tenerife, Spain

    E. Pallé, G. Nowak, J. Orell-Miquel, R. Alonso, H. J. Deeg, E. Esparza-Borges, F. Murgas & H. Parviainen

  8. Space Research Institute, Austrian Academy of Sciences, Graz, Austria

    A. Bonfanti, W. Baumjohann, P. E. Cubillos, L. Fossati & Ch. Helling

  9. Sub-department of Astrophysics, Department of Physics, University of Oxford, Oxford, UK

    O. Barragán

  10. Centre for Exoplanet Science, SUPA School of Physics and Astronomy, University of St Andrews, St Andrews, UK

    T. G. Wilson & A. Collier Cameron

  11. Department of Physics, University of Warwick, Coventry, UK

    T. G. Wilson, M. Lafarga, D. R. Anderson, D. Bayliss, E. M. Bryant, S. Gill & D. Pollacco

  12. Centre for Exoplanets and Habitability, University of Warwick, Coventry, UK

    T. G. Wilson, M. Lafarga & D. R. Anderson

  13. Center for Space and Habitability, University of Bern, Bern, Switzerland

    C. Broeg, Y. Alibert, W. Benz, B.-O. Demory, A. Fortier, C. Mordasini & N. Schanche

  14. Astrophysics Group, Lennard Jones Building, Keele University, Keele, UK

    P. F. L. Maxted

  15. Dipartimento di Fisica, Universita degli Studi di Torino, Torino, Italy

    D. Gandolfi & E. Goffo

  16. Cavendish Laboratory, University of Cambridge, Cambridge, UK

    M. J. Hooton, D. Queloz & A. Tuson

  17. Institute of Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Toruń, Poland

    G. Nowak

  18. NASA Ames Research Center, Moffett Field, CA, USA

    D. Rapetti, J. D. Twicken, S. B. Howell & J. M. Jenkins

  19. Research Institute for Advanced Computer Science, Universities Space Research Association, Washington, DC, USA

    D. Rapetti

  20. SETI Institute, Mountain View, CA, USA

    J. D. Twicken

  21. Institut de Ciencies de l’Espai (ICE-CSIC), Bellaterra, Spain

    J. C. Morales, G. Anglada-Escudé & I. Ribas

  22. Institut d’Estudis Espacials de Catalunya (IEEC), Barcelona, Spain

    J. C. Morales, G. Anglada-Escudé & I. Ribas

  23. INAF – Osservatorio Astrofisico di Torino, Pino Torinese, Italy

    I. Carleo & P. E. Cubillos

  24. Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, Porto, Portugal

    V. Adibekyan

  25. Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Porto, Portugal

    V. Adibekyan

  26. Mullard Space Science Laboratory, University College London, Dorking, UK

    A. Alqasim, E. M. Bryant, H. L. M. Osborne & V. Van Eylen

  27. Instituto de Astrofísica de Andalucía (IAA-CSIC), Granada, Spain

    P. J. Amado

  28. European Space Research and Technology Centre (ESTEC), European Space Agency (ESA), Noordwijk, The Netherlands

    T. Bandy, M. N. Günther, K. G. Isaak, N. Rando & F. Ratti

  29. Admatis, Miskolc, Hungary

    T. Bárczy

  30. Depto. de Astrofisica, Centro de Astrobiología (INTA-CSIC), Madrid, Spain

    D. Barrado Navascues

  31. Instituto de Astrofisica e Ciencias do Espaco, Universidade do Porto, Porto, Portugal

    S. C. C. Barros, O. D. S. Demangeon, N. C. Santos & S. G. Sousa

  32. Departamento de Fisica e Astronomia, Faculdade de Ciencias, Universidade do Porto, Porto, Portugal

    S. C. C. Barros, O. D. S. Demangeon & N. C. Santos

  33. Université Grenoble Alpes, CNRS, IPAG, Grenoble, France

    X. Bonfils

  34. INAF – Osservatorio Astronomico di Padova, Padova, Italy

    L. Borsato, D. Magrin, V. Nascimbeni, G. Piotto & R. Ragazzoni

  35. Department of Astronomy, California Institute of Technology, Pasadena, CA, USA

    A. W. Boyle, D. R. Ciardi & F. Dai

  36. Department of Astronomy, Stockholm University, AlbaNova University Center, Stockholm, Sweden

    A. Brandeker & G. Olofsson

  37. Institute of Planetary Research, German Aerospace Center (DLR), Berlin, Germany

    J. Cabrera, Sz. Csizmadia, A. Erikson, K. W. F. Lam, H. Rauer & A. M. S. Smith

  38. Instituto de Astronomía, Universidad Nacional Autónoma de México, Ciudad de México, Mexico

    S. Carrazco-Gaxiola & Y. Gómez Maqueo Chew

  39. Department of Physics and Astronomy, Georgia State University, Atlanta, GA, USA

    S. Carrazco-Gaxiola

  40. RECONS Institute, Chambersburg, PA, USA

    S. Carrazco-Gaxiola

  41. Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA

    D. Charbonneau, K. A. Collins, J. Garcia-Mejia, D. W. Latham & S. N. Quinn

  42. Université de Paris Cité, Institut de Physique du Globe de Paris, CNRS, Paris, France

    S. Charnoz

  43. McDonald Observatory, The University of Texas, Austin, TX, USA

    W. D. Cochran

  44. Center for Planetary Systems Habitability, The University of Texas, Austin, TX, USA

    W. D. Cochran

  45. Department of Physics and Astronomy, University of Kansas, Lawrence, KS, USA

    I. J. M. Crossfield

  46. Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA

    F. Dai

  47. Centre for Mathematical Sciences, Lund University, Lund, Sweden

    M. B. Davies

  48. Aix Marseille Univ., CNRS, CNES, LAM, Marseille, France

    M. Deleuil & S. Hoyer

  49. Astrobiology Research Unit, Université de Liège, Liège, Belgium

    L. Delrez & M. Gillon

  50. Space sciences, Technologies and Astrophysics Research (STAR) Institute, Université de Liège, Liège, Belgium

    L. Delrez, M. Stalport & V. Van Grootel

  51. Centre Vie dans l’Univers, Faculté des sciences, Université de Genève, Genève 4, Switzerland

    D. Ehrenreich

  52. Space Telescope Science Institute, Baltimore, MD, USA

    B. Falk

  53. Leiden Observatory, University of Leiden, Leiden, The Netherlands

    M. Fridlund

  54. Onsala Space Observatory, Department of Space, Earth and Environment, Chalmers University of Technology, Onsala, Sweden

    M. Fridlund

  55. Komaba Institute for Science, The University of Tokyo, Tokyo, Japan

    A. Fukui, T. Kodama & N. Narita

  56. Thüringer Landessternwarte Tautenburg, Tautenburg, Germany

    E. Goffo, E. W. Guenther & A. P. Hatzes

  57. Department of Astrophysics, University of Vienna, Vienna, Austria

    M. Güdel & R. Ottensamer

  58. Department of Multi-Disciplinary Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan

    K. Ikuta, T. Kagetani, J. P. D. Leon, M. Mori & N. Watanabe

  59. Konkoly Observatory, HUN-REN Research Centre for Astronomy and Earth Sciences, Budapest, Hungary

    L. L. Kiss

  60. Institute of Physics, ELTE Eötvös Loránd University, Budapest, Hungary

    L. L. Kiss

  61. Lund Observatory, Division of Astrophysics, Department of Physics, Lund University, Lund, Sweden

    J. Korth

  62. IMCCE, UMR8028 CNRS, Observatoire de Paris, PSL Univ., Sorbonne Univ., Paris, France

    J. Laskar

  63. Institut d’Astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie, Paris, France

    A. Lecavelier des Etangs

  64. Astrobiology Center, Tokyo, Japan

    J. H. Livingston & N. Narita

  65. National Astronomical Observatory of Japan, Tokyo, Japan

    J. H. Livingston

  66. Department of Astronomical Science, The Graduate University for Advanced Studies, SOKENDAI, Tokyo, Japan

    J. H. Livingston

  67. United States Naval Observatory, Washington, DC, USA

    R. A. Matson

  68. Max Planck Institute for Astronomy, Heidelberg, Germany

    E. C. Matthews

  69. Instituto de Astronomía, Universidad Católica del Norte, Antofagasta, Chile

    M. Moyano

  70. INAF – Osservatorio Astrofisico di Catania, Catania, Italy

    M. Munari, I. Pagano & G. Scandariato

  71. Institute of Optical Sensor Systems, German Aerospace Center (DLR), Berlin, Germany

    G. Peter & I. Walter

  72. Dipartimento di Fisica e Astronomia “Galileo Galilei”, Universita degli Studi di Padova, Padova, Italy

    G. Piotto, R. Ragazzoni & T. Zingales

  73. Department of Physics, ETH Zurich, Zurich, Switzerland

    D. Queloz

  74. Landessternwarte, Zentrum für Astronomie der Universität Heidelberg, Heidelberg, Germany

    A. Quirrenbach

  75. Zentrum für Astronomie und Astrophysik, Technische Universität Berlin, Berlin, Germany

    H. Rauer

  76. Institut für Geologische Wissenschaften, Freie Universität Berlin, Berlin, Germany

    H. Rauer

  77. Astronomy Department, Wesleyan University, Middletown, CT, USA

    S. Redfield

  78. Van Vleck Observatory, Wesleyan University, Middletown, CT, USA

    S. Redfield

  79. Instituto de Astronomía, Universidad Nacional Autónoma de México, Ensenada, Mexico

    L. Sabin

  80. Department of Astronomy, University of Maryland, College Park, MD, USA

    N. Schanche

  81. NASA Goddard Space Flight Center, Greenbelt, MD, USA

    J. E. Schlieder

  82. Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

    S. Seager

  83. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA

    S. Seager

  84. Gothard Astrophysical Observatory, ELTE Eötvös Loránd University, Szombathely, Hungary

    Gy. M. Szabó

  85. HUN-REN-ELTE Exoplanet Research Group, Szombathely, Hungary

    Gy. M. Szabó

  86. Institute of Astronomy, University of Cambridge, Cambridge, UK

    N. A. Walton

  87. Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA

    J. N. Winn


R.Lu., H.P.Os., A.Le., E.Pa., A.Bo., O.Ba. and T.G.Wi. conceived the project and contributed notably to the writing of this manuscript. R.Lu. and H.P.Os. led the analysis of the photometric data. A.Le. led the dynamical analysis of the system and developed the method with J.-B.De. to predict the orbits of the planets based on their resonant state within the chain. R.Lu., A.Bo. and O.Ba. led the analysis of the radial velocity data and the stellar activity mitigation. T.G.Wi. led the stellar characterization with the help of V.Ad., S.G.So., A.Bo., V.V.Gr., S.Sa. and W.D.Co. Y.Al. and J.A.Eg. led the analysis of the internal structures and L.Fo. and A.Bo. performed the atmospheric evolution simulations. D.Ra., J.D.Tw. and J.M.Je. improved the TESS data reduction to recover the missing cadences affected by reflected light and high background. R.Lu., E.Pa. and G.No. planned and obtained the time for the observations with CARMENES and HARPS-N. CARMENES observations were made possible by M.La., J.C.Mo., P.J.Am., A.Qu. and I.Ri. HARPS-N observations were made possible by I.Ca., J.O.-M., F.Mu., H.J.De., J.Ko., D.Ga., J.H.Li., W.D.Co., E.W.Gu., V.V.Ey., H.L.M.Os., S.Re., E.Go., F.Da. and K.W.F.La. High-resolution imaging observations from Palomar and Gemini North were made possible by A.W.Bo., D.R.Ci., I.J.M.Cr., S.B.Ho., E.Ma. and J.E.Sc. Ground-based photometric observations to catch the transit of planet f were made possible by the MuSCAT2 (R.Lu., E.Pa., N.Na., J.H.Li., K.Ik., E.E.-B., J.O.-M., N.Wa., F.Mu., G.No., A.Fu., H.Pa., M.Mo., T.Ka., J.P.D.Le. and T.Ko.), LCO (T.G.Wi., R.Lu., H.P.Os., E.Pa., A.Le., A.Tu., M.J.Ho., Y.Al. and D.Ga.), NGTS (H.P.Os., S.Gi., D.Ba., D.R.An., M.Mo., A.M.S.Sm., E.M.Br. and S.Ud.), Tierras (J.G.-M. and D.Ch.), SAINT-EX (N.Sc., Y.G.M.Ch., L.Sa., S.C.-G. and B.-O.De.) and MuSCAT3 (N.Na., J.H.Li., K.Ik., N.Wa., A.Fu., M.Mo., T.Ka., J.P.D.Le. and T.Ko.) instruments. The remaining authors provided key contributions to the development of the TESS and CHEOPS mission. All authors read and commented on the manuscript and helped with its revision.

Corresponding author

Correspondence to R. Luque.

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Extended data figures and tables

Extended Data Fig. 1 Transit duration versus transit depth for all unassigned transits in the TESS data.

TESS Sector 23 and Sector 49 are shown as different colours. The numbers above each transit denote the mid-transit time in TJD. Contours represent percentile levels, the innermost one corresponding to the 50th percentile and the outermost to the 99th percentile by increments of 10%. The transit of planet f in PLD photometry is marked with * to indicate that its properties are heavily affected by pretransit systematic noise.

Extended Data Fig. 2 Generalized three-body Laplace angles for known systems in resonant chains.

Included are the Galilean satellites Kepler-60 (refs. 12,115), Kepler-80 (ref. 159), K2-138 (ref. 112), Kepler-223 (ref. 110), TRAPPIST-1 (ref. 13) and TOI-178 (ref. 10). Measurements belonging to the same system are marked with the same colour. The line marks the observed distance to the theorized equilibrium (marked with a circle). The distances are estimated at the zeroth order in eccentricity110,111. For most systems, a single estimation of the generalized Laplace angle is made, whereas ref. 110 made an estimation for each Kepler quarter.

Extended Data Fig. 3 Observed distance from the equilibrium for all the simulated scenarios in which planets f and g continue the resonant chain.

The y axis is converted to the mean peak-to-peak amplitude from the generalized three-body Laplace angle using the following expression: mean \(({\mathcal{A}}({\varPsi }_{i}))=C/4\). Case A2 remains the one that has the potential to be the closest to an equilibrium.

Extended Data Fig. 4 Results from the ground-based campaign to detect HD 110067 f.

a, ΔWAIC for each of the constrained period bins when compared with a transit-free model. b,c, Best-fit decorrelated photometry with (b) and without (c) a transit model. Each light curve from each telescope has been offset for clarity. Error bars represent 1σ uncertainties.

Extended Data Fig. 5 Results from the two radial velocity analyses to measure the mass of each of the planets in the HD 110067 system.

Each histogram represents the posterior density function (pdf) of the radial velocity semiamplitudes as inferred from method I (red) and method II (blue). The area underneath each histogram is normalized to unity.

Extended Data Fig. 6 Gas mass fraction of the HD 110067 planets as a function of their equilibrium temperature.

We infer two values per planet by assuming the different planetary masses from our method I (red) and method II (blue) radial velocity analyses. The boxes, orange lines, green triangles and red stars represent, respectively, the 25th and 75th percentiles, medians, means and modes of the posterior distributions. The opacity of the vertical lines is proportional to the posterior distribution.

Extended Data Table 1 CHEOPS observing log
Extended Data Table 2 Ground-based photometric campaign observing log
Extended Data Table 3 Stellar parameters of HD 110067
Extended Data Table 4 Distance of the estimated generalized three-body Laplace angle Ψe=0 to the closest equilibrium for all period ratios that are not excluded by available observations

Supplementary information

Supplementary Information

The file includes Supplementary Figs. 1–12 and Supplementary Tables 1–5. The figures include: full detrended CHEOPS photometry of all visits (Fig. S1); high-resolution imaging of HD 110067 excluding nearby stellar companions (Fig. S2); potential orbital solutions from the analysis of the two duo transit and the two mono transit events (Fig. S3); properties of known resonant chains in terms of their period ratios (Fig. S4); a numerical integration of the best-fit solution of the full six-body resonant chain demonstrating the dynamical stability of the system (Fig. S5); original and reprocessed TESS Sector 23 data confirming the existence of planets f and g (Fig. S6); periodograms of the radial velocity and derived spectral indicators of the CARMENES and HARPS-N data (Figs. S7 and S8); best-fit solution of the radial velocity model from method I (Fig. S9); cross-validation analysis of the GP fit used in the radial velocity model from method II (Fig. S10); periodogram of radial velocity residuals after the fit demonstrating the absence of further signals in the data (Fig. S11); and corner plots of the most relevant parameters from the photometric fit (Fig. S12). The tables include the parameters, priors and posterior distributions of our photometric model (Table S1), radial velocity models using method I (Tables S2 and S3) and method II (Table S4), and internal structure model (Table S5).

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Luque, R., Osborn, H.P., Leleu, A. et al. A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067. Nature 623, 932–937 (2023). https://doi.org/10.1038/s41586-023-06692-3

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