Obliquity-driven sculpting of exoplanetary systems



NASA’s Kepler mission revealed that ~30% of Solar-type stars harbour planets with sizes between that of Earth and Neptune on nearly circular and coplanar orbits with periods less than 100 days1,2,3,4. Such short-period compact systems are rarely found with planet pairs in mean-motion resonances (MMRs)—configurations in which the planetary orbital periods exhibit a simple integer ratio—but there is a significant overabundance of planet pairs lying just wide of the first-order resonances5. Previous work suggests that tides raised on the planets by the host star may be responsible for forcing systems into these configurations by draining orbital energy to heat6,7,8. Such tides, however, are insufficient unless there exists a substantial and as-yet-unidentified source of extra dissipation9,10. Here we show that this cryptic heat source may be linked to ‘obliquity tides’ generated when a large axial tilt (obliquity) is maintained by secular resonance-driven spin–orbit coupling. We present evidence that typical compact, nearly coplanar systems frequently experience this mechanism, and we highlight additional features in the planetary orbital period and radius distributions that may be its signatures. Extrasolar planets that maintain large obliquities will exhibit infrared light curve features that are detectable with forthcoming space missions. The observed period ratio distribution can be explained if typical tidal quality factors for super-Earths and sub-Neptunes are similar to those of Uranus and Neptune.

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Fig. 1: Schematic of the excitation of planetary obliquities through secular spin–orbit resonant interaction.
Fig. 2: Intrinsic frequency commensurability for typical compact extrasolar systems.
Fig. 3: Capture into simultaneous mean-motion and spin–orbit resonances.
Fig. 4: Domain for the inner planet’s spin–orbit resonant capture during convergent inward migration.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Change history

  • 24 April 2019

    In the version of this Letter originally published, the following ‘Journal peer review information’ was missing: “Nature Astronomy thanks Jianghui Ji and the other anonymous reviewer(s) for their contribution to the peer review of this work.” This statement has now been added.


  1. 1.

    Batalha, N. M. et al. Planetary candidates observed by Kepler. III. Analysis of the first 16 months of data. Astrophys. J. Suppl. 204, 24 (2013).

    ADS  Article  Google Scholar 

  2. 2.

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

    ADS  Article  Google Scholar 

  3. 3.

    Petigura, E. A., Howard, A. W. & Marcy, G. W. Prevalence of Earth-size planets orbiting Sun-like stars. Proc. Natl Acad. Sci. USA 110, 19273–19278 (2013).

    ADS  Article  Google Scholar 

  4. 4.

    Zhu, W., Petrovich, C., Wu, Y., Dong, S. & Xie, J. About 30% of Sun-like stars have Kepler-like planetary systems: a study of their intrinsic architecture. Astrophys. J. 860, 101 (2018).

    ADS  Article  Google Scholar 

  5. 5.

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

    ADS  Article  Google Scholar 

  6. 6.

    Papaloizou, J. C. B. & Terquem, C. On the dynamics of multiple systems of hot super-Earths and Neptunes: tidal circularization, resonance and the HD 40307 system. Mon. Not. R. Astron. Soc. 405, 573–592 (2010).

    ADS  Google Scholar 

  7. 7.

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

    ADS  Article  Google Scholar 

  8. 8.

    Batygin, K. & Morbidelli, A. Dissipative divergence of resonant orbits. Astron. J. 145, 1 (2013).

    ADS  Article  Google Scholar 

  9. 9.

    Lee, M. H., Fabrycky, D. & Lin, D. N. C. Are the Kepler near-resonance planet pairs due to tidal dissipation? Astrophys. J. 774, 52 (2013).

    ADS  Article  Google Scholar 

  10. 10.

    Silburt, A. & Rein, H. Tides alone cannot explain Kepler planets close to 2:1 MMR. Mon. Not. R. Astron. Soc. 453, 4089–4096 (2015).

    ADS  Article  Google Scholar 

  11. 11.

    Petrovich, C., Malhotra, R. & Tremaine, S. Planets near mean-motion resonances. Astrophys. J. 770, 24 (2013).

    ADS  Article  Google Scholar 

  12. 12.

    Wang, S. & Ji, J. Near 3:2 and 2:1 mean motion resonance formation in the systems observed by Kepler. Astrophys. J. 795, 85 (2014).

    ADS  Article  Google Scholar 

  13. 13.

    Ramos, X. S., Charalambous, C., Bentez-Llambay, P. & Beaugé, C. Planetary migration and the origin of the 2:1 and 3:2 (near)-resonant population of close-in exoplanets. Astron. Astrophys. 602, A101 (2017).

    ADS  Article  Google Scholar 

  14. 14.

    Wang, S. & Ji, J. Near mean-motion resonances in the system observed by Kepler: affected by mass accretion and type I migration. Astron. J. 154, 236 (2017).

    ADS  Article  Google Scholar 

  15. 15.

    Hut, P. Tidal evolution in close binary systems. Astron. Astrophys. 99, 126–140 (1981).

    ADS  MATH  Google Scholar 

  16. 16.

    Fabrycky, D. C., Johnson, E. T. & Goodman, J. Cassini states with dissipation: why obliquity tides cannot inflate hot Jupiters. Astrophys. J. 665, 754–766 (2007).

    ADS  Article  Google Scholar 

  17. 17.

    Colombo, G. Cassini’s second and third laws. Astron. J. 71, 891 (1966).

    ADS  Article  Google Scholar 

  18. 18.

    Correia, A. C. M. Stellar and planetary Cassini states. Astron. Astrophys. 582, A69 (2015).

    ADS  Article  Google Scholar 

  19. 19.

    Levrard, B. et al. Tidal dissipation within hot Jupiters: a new appraisal. Astron. Astrophys. 462, L5–L8 (2007).

    ADS  Article  Google Scholar 

  20. 20.

    Wisdom, J. Tidal dissipation at arbitrary eccentricity and obliquity. Icarus 193, 637–640 (2008).

    ADS  Article  Google Scholar 

  21. 21.

    Lubow, S. H. & Ida, S. Planet Migration (ed. S. Seager) 347–371 (Univ. Arizona Press, Tucson, 1999).

  22. 22.

    Ward, W. R. & Hamilton, D. P. Tilting Saturn. I. Analytic model. Astron. J. 128, 2501–2509 (2004).

    ADS  Article  Google Scholar 

  23. 23.

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

    ADS  Article  Google Scholar 

  24. 24.

    Hamilton, D. P. & Ward, W. R. Tilting Saturn. II. Numerical model. Astron. J. 128, 2510–2517 (2004).

    ADS  Article  Google Scholar 

  25. 25.

    Delisle, J.-B. & Laskar, J. Tidal dissipation and the formation of Kepler near-resonant planets. Astron. Astrophys. 570, L7 (2014).

    ADS  Article  Google Scholar 

  26. 26.

    Ricker, G. R. et al. Transiting exoplanet survey satellite (TESS). J. Astron. Telesc. Instrum. Syst. 1, 014003 (2015).

    ADS  Article  Google Scholar 

  27. 27.

    Schwartz, J. C., Sekowski, C., Haggard, H. M., Pallé, E. & Cowan, N. B. Inferring planetary obliquity using rotational and orbital photometry. Mon. Not. R. Astron. Soc. 457, 926–938 (2016).

    ADS  Article  Google Scholar 

  28. 28.

    Tamayo, D., Rein, H., Petrovich, C. & Murray, N. Convergent migration renders TRAPPIST-1 long-lived. Astrophys. J. Lett. 840, L19 (2017).

    ADS  Article  Google Scholar 

  29. 29.

    Joshi, M. M., Haberle, R. M. & Reynolds, R. T. Simulations of the atmospheres of synchronously rotating terrestrial planets orbiting M dwarfs: conditions for atmospheric collapse and the implications for habitability. Icarus 129, 450–465 (1997).

    ADS  Article  Google Scholar 

  30. 30.

    Peale, S. J., Cassen, P. & Reynolds, R. T. Melting of Io by tidal dissipation. Science 203, 892–894 (1979).

    ADS  Article  Google Scholar 

  31. 31.

    Ragozzine, D. & Wolf, A. S. Probing the interiors of very hot Jupiters using transit light curves. Astrophys. J. 698, 1778–1794 (2009).

    ADS  Article  Google Scholar 

  32. 32.

    Kramm, U., Nettelmann, N., Redmer, R. & Stevenson, D. J. On the degeneracy of the tidal love number k 2 in multi-layer planetary models: application to Saturn and GJ 436b. Astron. Astrophys. 528, A18 (2011).

    ADS  Article  Google Scholar 

  33. 33.

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

    Google Scholar 

  34. 34.

    Correia, A. C. M. et al. The HARPS search for southern extra-solar planets. XIX. Characterization and dynamics of the GJ 876 planetary system. Astron. Astrophys. 511, A21 (2010).

    Article  Google Scholar 

  35. 35.

    Mardling, R. A. & Lin, D. N. C. Calculating the tidal, spin, and dynamical evolution of extrasolar planetary systems. Astrophys. J. 573, 829–844 (2002).

    ADS  Article  Google Scholar 

  36. 36.

    Darwin, G. H., Darwin, F., Brown, E. W., Stratton, F. J. M. & Jackson, J. Scientific Papers (Cambridge Univ. Press, Cambridge, 1907).

  37. 37.

    Singer, S. F. The origin of the moon and geophysical consequences. Geophys. J. R. Astron. Soc. 15, 205–226 (1968).

    Article  Google Scholar 

  38. 38.

    Mignard, F. The evolution of the lunar orbit revisited. I. Moon Planets 20, 301–315 (1979).

    ADS  Article  Google Scholar 

  39. 39.

    Eggleton, P. P., Kiseleva, L. G. & Hut, P. The equilibrium tide model for tidal friction. Astrophys. J. 499, 853–870 (1998).

    ADS  Article  Google Scholar 

  40. 40.

    Efroimsky, M. & Williams, J. G. Tidal torques: a critical review of some techniques. Celest. Mech. Dyn. Astron. 104, 257–289 (2009).

    ADS  MathSciNet  Article  Google Scholar 

  41. 41.

    Efroimsky, M. Bodily tides near spin-orbit resonances. Celest. Mech. Dyn. Astron. 112, 283–330 (2012).

    ADS  MathSciNet  Article  Google Scholar 

  42. 42.

    Ferraz-Mello, S. Tidal synchronization of close-in satellites and exoplanets. A rheophysical approach. Celest. Mech. Dyn. Astron. 116, 109–140 (2013).

    ADS  MathSciNet  Article  Google Scholar 

  43. 43.

    Correia, A. C. M., Boué, G., Laskar, J. & Rodrguez, A. Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology. Astron. Astrophys. 571, A50 (2014).

    ADS  Article  Google Scholar 

  44. 44.

    Storch, N. I. & Lai, D. Viscoelastic tidal dissipation in giant planets and formation of hot Jupiters through high-eccentricity migration. Mon. Not. R. Astron. Soc. 438, 1526–1534 (2014).

    ADS  Article  Google Scholar 

  45. 45.

    Boué, G., Correia, A. C. M. & Laskar, J. Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology. Celest. Mech. Dyn. Astron. 126, 31–60 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  46. 46.

    Alibert, Y. et al. Theoretical models of planetary system formation: mass vs. semi-major axis. Astron. Astrophys. 558, A109 (2013).

    Article  Google Scholar 

  47. 47.

    Lee, M. H. & Peale, S. J. Dynamics and origin of the 2:1 orbital resonances of the GJ 876 planets. Astrophys. J. 567, 596–609 (2002).

    ADS  Article  Google Scholar 

  48. 48.

    Leconte, J., Chabrier, G., Baraffe, I. & Levrard, B. Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity. Astron. Astrophys. 516, A64 (2010).

    ADS  Article  Google Scholar 

  49. 49.

    Eggleton, P. P. & Kiseleva-Eggleton, L. Orbital evolution in binary and triple stars, with an application to SS lacertae. Astrophys. J. 562, 1012–1030 (2001).

    ADS  Article  Google Scholar 

  50. 50.

    Correia, A. C. M. Secular evolution of a satellite by tidal effect: application to triton. Astrophys. J. Lett. 704, L1–L4 (2009).

    ADS  Article  Google Scholar 

  51. 51.

    Ward, W. R. & Canup, R. M. The obliquity of Jupiter. Astrophys. J. Lett. 640, L91–L94 (2006).

    ADS  Article  Google Scholar 

  52. 52.

    Correia, A. C. M., Laskar, J. & de Surgy, O. N. Long-term evolution of the spin of Venus. I. Theory. Icarus 163, 1–23 (2003).

    ADS  Article  Google Scholar 

  53. 53.

    Correia, A. C. M. & Laskar, J. Long-term evolution of the spin of Venus. II. Numerical simulations. Icarus 163, 24–45 (2003).

    ADS  Article  Google Scholar 

  54. 54.

    Touma, J. & Wisdom, J. The chaotic obliquity of Mars. Science 259, 1294–1297 (1993).

    ADS  Article  Google Scholar 

  55. 55.

    Tassoul, J.-L. Stellar Rotation (Cambridge Univ. Press, Cambridge, 2000).

    Google Scholar 

  56. 56.

    Bouvier, J. et al. in Protostars and Planets VI (eds Beuther, H. et al.) 433–450 (Univ. Arizona Press, Tucson, 2014).

  57. 57.

    Batygin, K. & Adams, F. C. Magnetic and gravitational disk-star interactions: an interdependence of PMS stellar rotation rates and spin-orbit misalignments. Astrophys. J. 778, 169 (2013).

    ADS  Article  Google Scholar 

  58. 58.

    Spalding, C. & Batygin, K. A secular resonant origin for the loneliness of hot Jupiters. Astron. J. 154, 93 (2017).

    ADS  Article  Google Scholar 

  59. 59.

    Tittemore, W. C. & Wisdom, J. Tidal evolution of the Uranian satellites. III — evolution through the Miranda-Umbriel 3:1, Miranda-Ariel 5:3, and Ariel-Umbriel 2:1 mean-motion commensurabilities. Icarus 85, 394–443 (1990).

    ADS  Article  Google Scholar 

  60. 60.

    Zhang, K. & Hamilton, D. P. Orbital resonances in the inner neptunian system. II. Resonant history of proteus, Larissa, Galatea, and Despina. Icarus 193, 267–282 (2008).

    ADS  Article  Google Scholar 

  61. 61.

    Morley, C. V. et al. Forward and inverse modeling of the emission and transmission spectrum of GJ 436b: investigating metal enrichment, tidal heating, and clouds. Astron. J. 153, 86 (2017).

    ADS  Article  Google Scholar 

  62. 62.

    Puranam, A. & Batygin, K. Chaotic excitation and tidal damping in the GJ 876 system. Astron. J. 155, 157 (2018).

    ADS  Article  Google Scholar 

  63. 63.

    Gavrilov, S. V. & Zharkov, V. N. Love numbers of the giant planets. Icarus 32, 443–449 (1977).

    ADS  Article  Google Scholar 

  64. 64.

    Lainey, V., Arlot, J.-E., Karatekin, Ö. & van Hoolst, T. Strong tidal dissipation in Io and Jupiter from astrometric observations. Nature 459, 957–959 (2009).

    ADS  Article  Google Scholar 

  65. 65.

    Goldreich, P. Inclination of satellite orbits about an oblate precessing planet. Astron. J. 70, 5 (1965).

    ADS  Article  Google Scholar 

  66. 66.

    Teachey, A., Kipping, D. M. & Schmitt, A. R. HEK. VI. On the dearth of galilean analogs in Kepler, and the exomoon candidate Kepler-1625b I. Astron. J. 155, 36 (2018).

    ADS  Article  Google Scholar 

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We thank K. Batygin, D. Fabrycky and Y. Wu for inspiring conversations. S.M. is supported by the National Science Foundation Graduate Research Fellowship Program under grant number DGE-1122492. This material is also based on work supported by the National Aeronautics and Space Administration through the NASA Astrobiology Institute under Cooperative Agreement Notice NNH13ZDA017C issued through the Science Mission Directorate. We acknowledge support from the NASA Astrobiology Institute through a cooperative agreement between NASA Ames Research Center and Yale University.

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S.M. performed the simulations, calculated the resonant proximity diagnostics and made the resonant capture parameter space map. G.L. conceived of and derived the constraints on the tidal quality factors, the radius distribution observations and the predictions regarding satellites. Both authors wrote the paper and made figures.

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Correspondence to Sarah Millholland.

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Journal peer review information: Nature Astronomy thanks Jianghui Ji and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Millholland, S., Laughlin, G. Obliquity-driven sculpting of exoplanetary systems. Nat Astron 3, 424–433 (2019). https://doi.org/10.1038/s41550-019-0701-7

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