Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

A high mutual inclination system around KOI-134 revealed by transit timing variations

Nature Astronomy (2025)Cite this article

Subjects

Abstract

Few planetary systems have measured mutual inclinations, and even fewer are found to be non-coplanar. Observing the gravitational interactions between exoplanets is an effective tool to detect non-transiting companions to transiting planets. Evidence of these interactions can manifest in the light curve through transit timing variations (TTVs) and transit duration variations (TDVs). Here, through analysis of Kepler photometry and joint TTV–TDV modelling, we confirm the detection of KOI-134 b, a transiting planet with mass and size similar to Jupiter on a period of ~67 days, and find that it exhibits high TTVs (20-h amplitude) and significant TDVs. We explain these signals with the presence of an innermost non-transiting planet in 2:1 resonance with KOI-134 b. KOI-134 c has a mass \(M=0.22{0}_{-0.011}^{+0.010}{M}_{{\rm{Jup}}}\) and a moderately high mutual inclination with KOI-134 b of \({i}_{{\rm{mut}}}=15.{4}_{-2.5}^{+2.{8}^{\circ }}\). Moreover, the inclination variations of KOI-134 b are so large that the planet is predicted to stop transiting in about 100 years. This system architecture cannot be easily explained by any one formation mechanism, with other dynamical effects needed to excite the planets’ mutual inclination while still preserving their resonance.

Access through your institution
Buy or subscribe

This is a preview of subscription content, access via your institution

Access options

Access through your institution

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Per-epoch Kepler light curves of KOI-134 b.
Fig. 2: TTVs and TDVs of KOI-134 b.
Fig. 3: Visualization of high versus low mutual inclination systems.
Fig. 4: Evolution of the KOI-134 system architecture.

Similar content being viewed by others

Data availability

The Kepler data used in this analysis can be accessed via the Kepler Data Search & Retrieval Tool (https://archive.stsci.edu/kepler/data_search/search.php). Any other datasets that were generated can be obtained from E.N. upon reasonable request.

Code availability

This study makes use of the following publicly available packages: astroARIADNE, batman, numpy, matplotlib, RadVel, REBOUND and scipy. The scripts used for this analysis are available via GitHub at https://github.com/enabbie/KOI134.

References

  1. Rivera, E. J. et al. The Lick-Carnegie Exoplanet Survey: a Uranus-mass fourth planet for GJ 876 in an extrasolar Laplace configuration. Astrophys. J. 719, 890–899 (2010).

    Article  ADS  Google Scholar 

  2. Sanchis-Ojeda, R. et al. Alignment of the stellar spin with the orbits of a three-planet system. Nature 487, 449–453 (2012).

    Article  ADS  Google Scholar 

  3. Nesvorný, D. et al. The detection and characterization of a nontransiting planet by transit timing variations. Science 336, 1133–1136 (2012).

    Article  ADS  Google Scholar 

  4. Huber, D. et al. Stellar spin–orbit misalignment in a multiplanet system. Science 342, 331–334 (2013).

    Article  ADS  Google Scholar 

  5. Almenara, J. M. et al. Absolute masses and radii determination in multiplanetary systems without stellar models. Mon. Not. R. Astron. Soc. 453, 2644–2652 (2015).

    Article  ADS  Google Scholar 

  6. Hamann, A., Montet, B. T., Fabrycky, D. C., Agol, E. & Kruse, E. K2-146: discovery of planet c, precise masses from transit timing, and observed precession. Astron. J. 158, 133 (2019).

    Article  ADS  Google Scholar 

  7. Johnson, M. C. et al. An aligned orbit for the young planet V1298 tau b. Astron. J. 163, 247 (2022).

    Article  ADS  Google Scholar 

  8. Feinstein, A. D. et al. H-alpha and Ca II infrared triplet variations during a transit of the 23 Myr planet V1298 tau c. Astron. J. 162, 213 (2021).

    Article  ADS  Google Scholar 

  9. Goldreich, P. & Tremaine, S. Disk–satellite interactions. Astrophys. J. 241, 425–441 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  10. Lissauer, J. J. et al. Architecture and dynamics of Kepler’s candidate multiple transiting planet systems. Astrophys. J. Suppl. Ser. 197, 8 (2011).

    Article  ADS  Google Scholar 

  11. Steffen, J. H. et al. Five Kepler target stars that show multiple transiting exoplanet candidates. Astrophys. J. 725, 1226–1241 (2010).

    Article  ADS  Google Scholar 

  12. Fang, J. & Margot, J.-L. Are planetary systems filled to capacity? A study based on Kepler results. Astrophys. J. 767, 115 (2013).

    Article  ADS  Google Scholar 

  13. 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 

  14. Marzari, F. & Weidenschilling, S. J. Eccentric extrasolar planets: the jumping Jupiter model. Icarus 156, 570–579 (2002).

    Article  ADS  Google Scholar 

  15. Chatterjee, S., Ford, E. B., Matsumura, S. & Rasio, F. A. Dynamical outcomes of planet–planet scattering. Astrophys. J. 686, 580–602 (2008).

    Article  ADS  Google Scholar 

  16. Jurić, M. & Tremaine, S. Dynamical origin of extrasolar planet eccentricity distribution. Astrophys. J. 686, 603–620 (2008).

    Article  ADS  Google Scholar 

  17. Dawson, R. I. & Chiang, E. A class of warm Jupiters with mutually inclined, apsidally misaligned close friends. Science 346, 212–216 (2014).

    Article  ADS  Google Scholar 

  18. McArthur, B. E. et al. New observational constraints on the υ Andromedae system with data from the Hubble Space Telescope and Hobby–Eberly Telescope. Astrophys. J. 715, 1203–1220 (2010).

    Article  ADS  Google Scholar 

  19. Dawson, R. I. et al. Large eccentricity, low mutual inclination: the three-dimensional architecture of a hierarchical system of giant planets. Astrophys. J. 791, 89 (2014).

    Article  ADS  Google Scholar 

  20. Mills, S. M. & Fabrycky, D. C. Kepler-108: a mutually inclined giant planet system. Astron. J. 153, 45 (2017).

    Article  ADS  Google Scholar 

  21. 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 

  22. Korth, J. et al. TOI-1130: a photodynamical analysis of a hot Jupiter in resonance with an inner low-mass planet. Astron. Astrophys. 675, A115 (2023).

    Article  Google Scholar 

  23. Korth, J. et al. TOI-1408: discovery and photodynamical modeling of a small inner companion to a hot Jupiter revealed by transit timing variations. Astrophys. J. Lett. 971, L28 (2024).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. Dawson, R. I. et al. TOI-216b and TOI-216 c: two warm, large exoplanets in or slightly wide of the 2:1 orbital resonance. Astron. J. 158, 65 (2019).

    Article  ADS  Google Scholar 

  26. Dawson, R. I. et al. Precise transit and radial-velocity characterization of a resonant pair: the warm Jupiter TOI-216c and Eccentric Warm Neptune TOI-216b. Astron. J. 161, 161 (2021).

    Article  ADS  Google Scholar 

  27. Nesvorný, D., Chrenko, O. & Flock, M. TOI-216: resonant constraints on planet migration. Astrophys. J. 925, 38 (2022).

    Article  ADS  Google Scholar 

  28. Nesvorný, D. et al. KOI-142, the king of transit variations, is a pair of planets near the 2:1 resonance. Astrophys. J. 777, 3 (2013).

    Article  ADS  Google Scholar 

  29. Lithwick, Y., Xie, J. & Wu, Y. Extracting planet mass and eccentricity from TTV data. Astrophys. J. 761, 122 (2012).

    Article  ADS  Google Scholar 

  30. Deck, K. M., Payne, M. & Holman, M. J. First-order resonance overlap and the stability of close two-planet systems. Astrophys. J. 774, 129 (2013).

    Article  ADS  Google Scholar 

  31. Murray, C. D. & Dermott, S. F. Solar System Dynamics (Cambridge Univ. Press, 1999).

  32. Thommes, E. W. & Lissauer, J. J. Resonant inclination excitation of migrating giant planets. Astrophys. J. 597, 566–580 (2003).

    Article  ADS  Google Scholar 

  33. Cresswell, P. & Nelson, R. P. Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc. Astron. Astrophys. 482, 677–690 (2008).

    Article  ADS  Google Scholar 

  34. Jenkins, J. M. et al. Overview of the Kepler Science Processing Pipeline. Astrophys. J. Lett. 713, L87 (2010).

    Article  ADS  Google Scholar 

  35. Coughlin, J. L. et al. Planetary candidates observed by Kepler. VII. The first fully uniform catalog based on the entire 48-month data set (Q1–Q17 DR24). Astrophys. J. Suppl. Ser. 224, 12 (2016).

    Article  ADS  Google Scholar 

  36. Borucki, W. J. et al. Characteristics of planetary candidates observed by Kepler. II. Analysis of the first four months of data. Astrophys. J. 736, 19 (2011).

    Article  ADS  Google Scholar 

  37. Thompson, S. E. et al. Planetary candidates observed by Kepler. VIII. A fully automated catalog with measured completeness and reliability based on Data Release 25. Astrophys. J. Suppl. Ser. 235, 38 (2018).

    Article  ADS  Google Scholar 

  38. Bryson, S. T. et al. in The Kepler Certified False Positive Table. Kepler Science Document KSCI-19093-003 (eds Haas, M. R. & Batalha, N. M.) 12 (Kepler Office at NASA Ames, 2017).

  39. Vanderburg, A. et al. A habitable-zone Earth-sized planet rescued from false positive status. Astrophys. J. Lett. 893, L27 (2020).

    Article  ADS  Google Scholar 

  40. Fűrész, G., Szentgyorgyi, A. H. & Meibom, S. Precision of radial velocity surveys using multiobject spectrographs—experiences with hectochelle. In Precision Spectroscopy in Astrophysics (eds Santos, N. C. et al.) 287–289 (Springer, 2008).

  41. Zhou, G. et al. A well-aligned orbit for the 45 Myr-old transiting Neptune DS Tuc Ab. Astrophys. J. Lett. 892, L21 (2020).

    Article  ADS  Google Scholar 

  42. Vogt, S. S. et al. HIRES: the high-resolution echelle spectrometer on the Keck 10-m telescope. In Proc. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Instrumentation in Astronomy VIII (eds Crawford, D. L. & Craine, E. R.) 362–375 (SPIE, 1994).

  43. Tull, R. G., MacQueen, P., Sneden, C. & Lambert, D. L. The McDonald 2.7-in echelle spectrometer. In Proc. Astronomical Society of the Pacific Conference Series (eds Pyper, D. M. & Angione, R. J.) 148 (ASP, 1994).

  44. Buchhave, L. A. et al. An abundance of small exoplanets around stars with a wide range of metallicities. Nature 486, 375–377 (2012).

    Article  ADS  Google Scholar 

  45. Valenti, J. A. & Piskunov, N. Spectroscopy Made Easy: a new tool for fitting observations with synthetic spectra. Astron. Astrophys. Suppl. 118, 595–603 (1996).

    Article  ADS  Google Scholar 

  46. Baranec, C. et al. Bringing the visible universe into focus with Robo-AO. J. Vis. Exp. 12, 50021 (2013).

    Google Scholar 

  47. Baranec, C. et al. High-efficiency autonomous laser adaptive optics. Astrophys. J. Lett. 790, L8 (2014).

    Article  ADS  Google Scholar 

  48. Ziegler, C. et al. Robo-AO Kepler Planetary Candidate Survey. III. Adaptive optics imaging of 1629 Kepler exoplanet candidate host stars. Astron. J. 153, 66 (2017).

    Article  ADS  Google Scholar 

  49. Tayar, J., Claytor, Z. R., Huber, D. & van Saders, J. A guide to realistic uncertainties on the fundamental properties of solar-type exoplanet host stars. Astrophys. J. 927, 31 (2022).

    Article  ADS  Google Scholar 

  50. Eastman, J. D. et al. EXOFASTv2: a public, generalized, publication-quality exoplanet modeling code. Preprint at https://arxiv.org/abs/1907.09480 (2019).

  51. Fulton, B. J., Petigura, E. A., Blunt, S. & Sinukoff, E. RadVel: the radial velocity modeling toolkit. Publ. Astron. Soc. Pac. 130, 044504 (2018).

    Article  ADS  Google Scholar 

  52. Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: The MCMC Hammer. Publ. Astron. Soc. Pac. 125, 306 (2013).

    Article  ADS  Google Scholar 

  53. Kreidberg, L. batman: BAsic Transit Model cAlculatioN in Python. Publ. Astron. Soc. Pac. 127, 1161 (2015).

    Article  ADS  Google Scholar 

  54. Murphy, S. J. An examination of some characteristics of Kepler short- and long-cadence data. Mon. Not. R. Astron. Soc. 422, 665–671 (2012).

    Article  ADS  Google Scholar 

  55. Choi, J. et al. Mesa Isochrones and Stellar Tracks (MIST). I. Solar-scaled models. Astrophys. J. 823, 102 (2016).

    Article  ADS  Google Scholar 

  56. Green, G. M. dustmaps: a Python interface for maps of interstellar dust. J. Open Source Softw. 3, 695 (2018).

    Article  ADS  Google Scholar 

  57. Schlegel, D. J., Finkbeiner, D. P. & Davis, M. Maps of dust infrared emission for use in estimation of reddening and cosmic microwave background radiation foregrounds. Astrophys. J. 500, 525–553 (1998).

    Article  ADS  Google Scholar 

  58. Schlafly, E. F. & Finkbeiner, D. P. Measuring reddening with Sloan Digital Sky Survey stellar spectra and recalibrating SFD. Astrophys. J. 737, 103 (2011).

    Article  ADS  Google Scholar 

  59. Kipping, D. M. Efficient, uninformative sampling of limb darkening coefficients for two-parameter laws. Mon. Not. R. Astron. Soc. 435, 2152–2160 (2013).

    Article  ADS  Google Scholar 

  60. Seager, S. & Mallén-Ornelas, G. A unique solution of planet and star parameters from an extrasolar planet transit light curve. Astrophys. J. 585, 1038–1055 (2003).

    Article  ADS  Google Scholar 

  61. Rein, H. & Spiegel, D. S. IAS15: a fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits. Mon. Not. R. Astron. Soc. 446, 1424–1437 (2015).

    Article  ADS  Google Scholar 

  62. Kipping, D. M. Investigations of approximate expressions for the transit duration. Mon. Not. R. Astron. Soc. 407, 301–313 (2010).

    Article  ADS  Google Scholar 

  63. Korth, J. Characterization of Extrasolar Multi-planet Systems by Transit Timing Variation. PhD thesis, Universität zu Köln (2020); https://kups.ub.uni-koeln.de/11289/

  64. Nesvorný, D. & Vokrouhlický, D. Dynamics and transit variations of resonant exoplanets. Astrophys. J. 823, 72 (2016).

    Article  ADS  Google Scholar 

  65. Lithwick, Y. & Wu, Y. Resonant repulsion of Kepler planet pairs. Astrophys. J. Lett. 756, L11 (2012).

    Article  ADS  Google Scholar 

  66. Aarseth, S. J. Gravitational N-Body Simulations (Cambridge Univ. Press, 2003).

  67. Faridani, T. H., Naoz, S., Li, G. & Inzunza, N. Let’s sweep: the effect of evolving J2 on the resonant structure of a three-planet system. Astrophys. J. 956, 90 (2023).

    Article  ADS  Google Scholar 

  68. Faridani, T., Naoz, S., Li, G., Rice, M. & Inzunza, N. More likely than you think: inclination-driving secular resonances are common in known exoplanet systems. Astrophys. J. 978, 18 (2024).

    Article  Google Scholar 

  69. Nagasawa, M., Lin, D. N. C. & Ida, S. Eccentricity evolution of extrasolar multiple planetary systems due to the depletion of nascent protostellar disks. Astrophys. J. 586, 1374–1393 (2003).

    Article  ADS  Google Scholar 

  70. Petrovich, C., Muñoz, D. J., Kratter, K. M. & Malhotra, R. A disk-driven resonance as the origin of high inclinations of close-in planets. Astrophys. J. Lett. 902, L5 (2020).

    Article  ADS  Google Scholar 

  71. Huang, C. X. et al. Photometry of 10 million stars from the first two years of TESS full frame images: part II. Res. Notes AAS 4, 206 (2020).

    Article  ADS  Google Scholar 

  72. Kovács, G., Zucker, S. & Mazeh, T. A box-fitting algorithm in the search for periodic transits. Astron. Astrophys. 391, 369–377 (2002).

    Article  ADS  Google Scholar 

  73. Hartman, J. VARTOOLS: Light Curve Analysis Program record ascl:1208.016 (Astrophysics Source Code Library, 2012).

  74. Holczer, T. et al. Transit timing observations from Kepler. IX. Catalog of the full long-cadence data set. Astrophys. J. Suppl. Ser. 225, 9 (2016).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank R. Dawson for helpful discussions throughout our analysis. E.N. acknowledges the PhD scholarship provided by the ARC Discovery Project DP220100365. C.X.H. and A.V. thank the support of the ARC DECRA project DE200101840. A.V. thanks M. Omohundro, K. Deck, A. Vanderburg and J. Becker for helpful comments during the inception of this study. G.Z. thanks the support of the Australian Research Council project FT230100517. We acknowledge support from the Swiss NCCR PlanetS and the Swiss National Science Foundation. This work has been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation under grant numbers 51NF40182901 and 51NF40205606. J.K. acknowledges support from the Swedish Research Council (project grants 2017-04945 and 2022-04043) and of the Swiss National Science Foundation under grant number TMSGI2_211697. H.P. acknowledges support by the Spanish Ministry of Science and Innovation with the Ramon y Cajal fellowship number RYC2021-031798-I. Funding from the University of La Laguna and the Spanish Ministry of Universities is acknowledged.

Author information

Authors and Affiliations

  1. Centre for Astrophysics, University of Southern Queensland, Toowoomba, Queensland, Australia

    Emma Nabbie, Chelsea X. Huang, Alexander Venner, Robert Wittenmyer & George Zhou

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

    Judith Korth

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

    Judith Korth

  4. Departamento de Astrofísica, Universidad de La Laguna, San Cristóbal de La Laguna, Spain

    Hannu Parviainen

  5. Instituto de Astrofísica de Canarias, Santa Cruz de Tenerife, Spain

    Hannu Parviainen

  6. CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, People’s Republic of China

    Su Wang

  7. CAS Center for Excellence in Comparative Planetology, Hefei, People’s Republic of China

    Su Wang

  8. Center for Astrophysics, Harvard and Smithsonian, Cambridge, MA, USA

    Allyson Bieryla & David W. Latham

  9. Center for Relativistic Astrophysics, School of Physics, Georgia Institute of Technology, Atlanta, GA, USA

    Gongjie Li

  10. Department of Astronomy and Astrophysics, University of California, Santa Cruz, Santa Cruz, CA, USA

    Douglas N. C. Lin

  11. Institute for Advanced Study, Tsinghua University, Beijing, People’s Republic of China

    Douglas N. C. Lin

Authors
  1. Emma Nabbie
    View author publications

    Search author on:PubMed Google Scholar

  2. Chelsea X. Huang
    View author publications

    Search author on:PubMed Google Scholar

  3. Judith Korth
    View author publications

    Search author on:PubMed Google Scholar

  4. Hannu Parviainen
    View author publications

    Search author on:PubMed Google Scholar

  5. Su Wang
    View author publications

    Search author on:PubMed Google Scholar

  6. Alexander Venner
    View author publications

    Search author on:PubMed Google Scholar

  7. Robert Wittenmyer
    View author publications

    Search author on:PubMed Google Scholar

  8. Allyson Bieryla
    View author publications

    Search author on:PubMed Google Scholar

  9. David W. Latham
    View author publications

    Search author on:PubMed Google Scholar

  10. Gongjie Li
    View author publications

    Search author on:PubMed Google Scholar

  11. Douglas N. C. Lin
    View author publications

    Search author on:PubMed Google Scholar

  12. George Zhou
    View author publications

    Search author on:PubMed Google Scholar

Contributions

E.N. led the light curve and N-body analyses, interpretation of the results and preparation of the paper. C.X.H. supervised the project, conducted N-body simulations, facilitated analysis of the system’s TDVs and contributed to the writing of the paper. J.K. and H.P. performed the photodynamical analyses. S.W. conducted disk migration simulations to investigate the system’s formation and evolution. A.V. identified the system and contributed to the analysis of the Kepler observations and mid-transit times. R.W. supervised the project and contributed to the analysis. G.L. contributed to the theoretical dynamical analyses. D.N.C.L. contributed to analysis and interpretation of disk migration simulations. A.B., D.W.L. and G.Z. were responsible for the TRES radial velocity observations and data reduction.

Corresponding author

Correspondence to Emma Nabbie.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Astronomy thanks Daniel Fabrycky, Melissa Hobson and Michael Ireland for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Direct imaging observations of KOI-134.

Panel (a): 5σ sensitivity curve depicting the difference in magnitude versus orbital separation. Panel (b): High resolution i-band direct imaging of KOI-134 observed with the P60 telescope’s Robo-AO instrument. The 8" square image cutout is centered on the star, with a pixel scale of 0.021" per pixel.

Extended Data Fig. 2 KOI-134 b in context with other Kepler TTV systems.

The histogram shows the distribution of TTV amplitudes from Kepler systems with significant TTVs, taken from Table 5 of the Kepler TTV catalog by74. The dashed line shows the position of KOI-134 b in comparison to this population.

Extended Data Fig. 3 The proximity of KOI-134 to an exact 2:1 resonance.

The position of KOI-134 within the 2:1 resonant ___domain, re-parametrized to a 1-degree of freedom model30. Randomly-sampled points from the planet parameter posterior distribution are shown in red circles. X measures the system’s separatrices and stable/unstable fixed points, and γ quantifies how close the system is to an exact resonance. The shaded region denotes the formally-defined resonant ___domain.

Extended Data Fig. 4 Trajectories of the resonant angles of KOI-134 b and c.

Trajectories of the resonant angles (Θe,b and Θe,c) and the secular apsidal angle Δω, as they evolve over a time scale of 1 million years. Panel (a) shows these trajectories for KOI-134 b, while panel (b) shows those for KOI-134 c. The color scheme is shared with Fig. 4.

Extended Data Fig. 5 The population of near-MMR multi-planet systems with giant planets.

Confirmed multi-planet systems with a giant planet, where at least one pair of orbital periods are near a first-order resonance. The empty circles represent non-transiting planets. Marker size corresponds to relative planet radius.

Extended Data Table 1 Stellar and Planet Parameters for KOI-134
Full size table
Extended Data Table 2 High-Precision System Parameters for N-body Integration
Full size table

Supplementary information

Supplementary Information

Supplementary text, Figs. 1–4, Tables 1–3 and references.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nabbie, E., Huang, C.X., Korth, J. et al. A high mutual inclination system around KOI-134 revealed by transit timing variations. Nat Astron (2025). https://doi.org/10.1038/s41550-025-02594-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41550-025-02594-8

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing