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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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).
Fressin, F. et al. The false positive rate of Kepler and the occurrence of planets. Astrophys. J. 766, 81 (2013).
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).
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).
Lissauer, J. J. et al. Architecture and dynamics of Kepler’s candidate multiple transiting planet systems. Astrophys. J. Suppl. 197, 8 (2011).
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).
Lithwick, Y. & Wu, Y. Resonant repulsion of Kepler planet pairs. Astrophys. J. Lett. 756, L11 (2012).
Batygin, K. & Morbidelli, A. Dissipative divergence of resonant orbits. Astron. J. 145, 1 (2013).
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).
Silburt, A. & Rein, H. Tides alone cannot explain Kepler planets close to 2:1 MMR. Mon. Not. R. Astron. Soc. 453, 4089–4096 (2015).
Petrovich, C., Malhotra, R. & Tremaine, S. Planets near mean-motion resonances. Astrophys. J. 770, 24 (2013).
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).
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).
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).
Hut, P. Tidal evolution in close binary systems. Astron. Astrophys. 99, 126–140 (1981).
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).
Colombo, G. Cassini’s second and third laws. Astron. J. 71, 891 (1966).
Correia, A. C. M. Stellar and planetary Cassini states. Astron. Astrophys. 582, A69 (2015).
Levrard, B. et al. Tidal dissipation within hot Jupiters: a new appraisal. Astron. Astrophys. 462, L5–L8 (2007).
Wisdom, J. Tidal dissipation at arbitrary eccentricity and obliquity. Icarus 193, 637–640 (2008).
Lubow, S. H. & Ida, S. Planet Migration (ed. S. Seager) 347–371 (Univ. Arizona Press, Tucson, 1999).
Ward, W. R. & Hamilton, D. P. Tilting Saturn. I. Analytic model. Astron. J. 128, 2501–2509 (2004).
Hadden, S. & Lithwick, Y. Kepler planet masses and eccentricities from TTV analysis. Astron. J. 154, 5 (2017).
Hamilton, D. P. & Ward, W. R. Tilting Saturn. II. Numerical model. Astron. J. 128, 2510–2517 (2004).
Delisle, J.-B. & Laskar, J. Tidal dissipation and the formation of Kepler near-resonant planets. Astron. Astrophys. 570, L7 (2014).
Ricker, G. R. et al. Transiting exoplanet survey satellite (TESS). J. Astron. Telesc. Instrum. Syst. 1, 014003 (2015).
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).
Tamayo, D., Rein, H., Petrovich, C. & Murray, N. Convergent migration renders TRAPPIST-1 long-lived. Astrophys. J. Lett. 840, L19 (2017).
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).
Peale, S. J., Cassen, P. & Reynolds, R. T. Melting of Io by tidal dissipation. Science 203, 892–894 (1979).
Ragozzine, D. & Wolf, A. S. Probing the interiors of very hot Jupiters using transit light curves. Astrophys. J. 698, 1778–1794 (2009).
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).
Murray, C. D. & Dermott, S. F. Solar System Dynamics (Cambridge Univ. Press, Cambridge, 1999).
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).
Mardling, R. A. & Lin, D. N. C. Calculating the tidal, spin, and dynamical evolution of extrasolar planetary systems. Astrophys. J. 573, 829–844 (2002).
Darwin, G. H., Darwin, F., Brown, E. W., Stratton, F. J. M. & Jackson, J. Scientific Papers (Cambridge Univ. Press, Cambridge, 1907).
Singer, S. F. The origin of the moon and geophysical consequences. Geophys. J. R. Astron. Soc. 15, 205–226 (1968).
Mignard, F. The evolution of the lunar orbit revisited. I. Moon Planets 20, 301–315 (1979).
Eggleton, P. P., Kiseleva, L. G. & Hut, P. The equilibrium tide model for tidal friction. Astrophys. J. 499, 853–870 (1998).
Efroimsky, M. & Williams, J. G. Tidal torques: a critical review of some techniques. Celest. Mech. Dyn. Astron. 104, 257–289 (2009).
Efroimsky, M. Bodily tides near spin-orbit resonances. Celest. Mech. Dyn. Astron. 112, 283–330 (2012).
Ferraz-Mello, S. Tidal synchronization of close-in satellites and exoplanets. A rheophysical approach. Celest. Mech. Dyn. Astron. 116, 109–140 (2013).
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).
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).
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).
Alibert, Y. et al. Theoretical models of planetary system formation: mass vs. semi-major axis. Astron. Astrophys. 558, A109 (2013).
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).
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).
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).
Correia, A. C. M. Secular evolution of a satellite by tidal effect: application to triton. Astrophys. J. Lett. 704, L1–L4 (2009).
Ward, W. R. & Canup, R. M. The obliquity of Jupiter. Astrophys. J. Lett. 640, L91–L94 (2006).
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).
Correia, A. C. M. & Laskar, J. Long-term evolution of the spin of Venus. II. Numerical simulations. Icarus 163, 24–45 (2003).
Touma, J. & Wisdom, J. The chaotic obliquity of Mars. Science 259, 1294–1297 (1993).
Tassoul, J.-L. Stellar Rotation (Cambridge Univ. Press, Cambridge, 2000).
Bouvier, J. et al. in Protostars and Planets VI (eds Beuther, H. et al.) 433–450 (Univ. Arizona Press, Tucson, 2014).
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).
Spalding, C. & Batygin, K. A secular resonant origin for the loneliness of hot Jupiters. Astron. J. 154, 93 (2017).
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).
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).
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).
Puranam, A. & Batygin, K. Chaotic excitation and tidal damping in the GJ 876 system. Astron. J. 155, 157 (2018).
Gavrilov, S. V. & Zharkov, V. N. Love numbers of the giant planets. Icarus 32, 443–449 (1977).
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).
Goldreich, P. Inclination of satellite orbits about an oblate precessing planet. Astron. J. 70, 5 (1965).
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).
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.
The authors declare no competing interests.
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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