Skip to main content

Thank you for visiting 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.

Hot Jupiters from secular planet–planet interactions



About 25 per cent of ‘hot Jupiters’ (extrasolar Jovian-mass planets with close-in orbits) are actually orbiting counter to the spin direction of the star1. Perturbations from a distant binary star companion2,3 can produce high inclinations, but cannot explain orbits that are retrograde with respect to the total angular momentum of the system. Such orbits in a stellar context can be produced through secular (that is, long term) perturbations in hierarchical triple-star systems. Here we report a similar analysis of planetary bodies, including both octupole-order effects and tidal friction, and find that we can produce hot Jupiters in orbits that are retrograde with respect to the total angular momentum. With distant stellar mass perturbers, such an outcome is not possible2,3. With planetary perturbers, the inner orbit's angular momentum component parallel to the total angular momentum need not be constant4. In fact, as we show here, it can even change sign, leading to a retrograde orbit. A brief excursion to very high eccentricity during the chaotic evolution of the inner orbit allows planet–star tidal interactions to rapidly circularize that orbit, decoupling the planets and forming a retrograde hot Jupiter.

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

Access options

Rent or buy this article

Get just this article for as long as you need it


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

Figure 1: Dynamical evolution of a representative planet and brown dwarf system.
Figure 2: Dynamical evolution of a representative two-planet system with tidal dissipation included.


  1. Triaud, A. H. M. J. et al. Spin-orbit angle measurements for six southern transiting planets. New insights into the dynamical origins of hot Jupiters. Astron. Astrophys. 524, A25 (2010)

    Article  Google Scholar 

  2. Fabrycky, D. & Tremaine, S. Shrinking binary and planetary orbits by Kozai cycles with tidal friction. Astrophys. J. 669, 1298–1315 (2007)

    Article  ADS  CAS  Google Scholar 

  3. Wu, Y., Murray, N. W. & Ramsahai, J. M. Hot Jupiters in binary star systems. Astrophys. J. 670, 820–825 (2007)

    Article  ADS  Google Scholar 

  4. Ford, E. B., Kozinsky, B. & Rasio, F. A. Secular evolution of hierarchical triple star systems. Astrophys. J. 535, 385–401 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  6. Lai, D., Foucart, F. & Lin, D. N. C. Evolution of spin direction of accreting magnetic protostars and spin-orbit misalignment in exoplanetary systems. Mon. Not. R. Astron. Soc. (submitted); preprint at 〈〉 (2011)

  7. Nagasawa, M., Ida, S. & Bessho, T. Formation of hot planets by a combination of planet scattering, tidal circularization, and the Kozai mechanism. Astrophys. J. 678, 498–508 (2008)

    Article  ADS  Google Scholar 

  8. Schlaufman, K. C. Evidence of possible spin-orbit misalignment along the line of sight in transiting exoplanet systems. Astrophys. J. 719, 602–611 (2010)

    Article  ADS  Google Scholar 

  9. Takeda, G., Kita, R. & Rasio, F. A. Planetary systems in binaries. I. Dynamical classification. Astrophys. J. 683, 1063–1075 (2008)

    Article  ADS  Google Scholar 

  10. Winn, J. N., Fabrycky, D., Albrecht, S. & Johnson, J. A. Hot stars with hot Jupiters have high obliquities. Astrophys. J. 718, L145–L149 (2010)

    Article  ADS  Google Scholar 

  11. Wu, Y. & Lithwick, Y. Secular chaos and the production of hot Jupiters. Preprint at 〈〉 (2010)

  12. Lin, D. N. C. & Papaloizou, J. On the tidal interaction between protoplanets and the proto-planetary disk. III — Orbital migration of protoplanets. Astrophys. J. 309, 846–857 (1986)

    Article  ADS  Google Scholar 

  13. Masset, F. S. & Papaloizou, J. Runaway migration and the formation of hot Jupiters. Astrophys. J. 588, 494–508 (2003)

    Article  ADS  Google Scholar 

  14. Gaudi, B. S. & Winn, J. N. Prospects for the characterization and confirmation of transiting exoplanets via the Rossiter-McLaughlin effect. Astrophys. J. 655, 550–563 (2007)

    Article  ADS  Google Scholar 

  15. Holman, M., Touma, J. & Tremaine, S. Chaotic variations in the eccentricity of the planet orbiting 16 Cygni B. Nature 386, 254–256 (1997)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Kozai, Y. Secular perturbations of asteroids with high inclination and eccentricity. Astron. J. 67, 591–598 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  18. Lidov, M. L. The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Planet. Space Sci. 9, 719–759 (1962)

    Article  ADS  Google Scholar 

  19. Mazeh, T. & Shaham, J. The orbital evolution of close triple systems — the binary eccentricity. Astron. Astrophys. 77, 145–151 (1979)

    ADS  Google Scholar 

  20. Harrington, R. S. The stellar three-body problem. Celest. Mech. 1, 200–209 (1969)

    Article  ADS  Google Scholar 

  21. Krymolowski, Y. & Mazeh, T. Studies of multiple stellar systems — II. Second-order averaged Hamiltonian to follow long-term orbital modulations of hierarchical triple systems. Mon. Not. R. Astron. Soc. 304, 720–732 (1999)

    Article  ADS  Google Scholar 

  22. Kiseleva, L. G., Eggleton, P. P. & Mikkola, S. Tidal friction in triple stars. Mon. Not. R. Astron. Soc. 300, 292–302 (1998)

    Article  ADS  Google Scholar 

  23. Zdziarski, A. A., Wen, L. & Gierlin´ski, M. The superorbital variability and triple nature of the X-ray source 4U 1820–303. Mon. Not. R. Astron. Soc. 377, 1006–1016 (2007)

    Article  ADS  Google Scholar 

  24. Mikkola, S. & Tanikawa, K. Does Kozai resonance drive CH Cygni? Astron. J. 116, 444–450 (1998)

    Article  ADS  Google Scholar 

  25. Ford, E. B. & Rasio, F. A. On the relation between hot Jupiters and the Roche limit. Astron. J. 638, L45–L48 (2006)

    Article  ADS  Google Scholar 

  26. Kalas, P. et al. Optical images of an exosolar planet 25 light-years from Earth. Science 322, 1345–1348 (2008)

    Article  ADS  CAS  Google Scholar 

  27. Marois, C. et al. Direct imaging of multiple planets orbiting the star HR 8799. Science 322, 1348–1352 (2008)

    Article  ADS  CAS  Google Scholar 

  28. Pollack, J. B. et al. Formation of the giant planets by concurrent accretion of solids and gas. Icarus 124, 62–85 (1996)

    Article  ADS  Google Scholar 

  29. Matsumura, S., Peale, S. J. & Rasio, F. A. Formation and evolution of close-in planets. Astrophys. J. 725, 1995–2016 (2010)

    Article  ADS  CAS  Google Scholar 

Download references


We thank D. Fabrycky and H. Perets for discussions. S.N. acknowledges support from a Gruber Foundation Fellowship and from the National Post Doctoral Award Program for Advancing Women in Science (Weizmann Institute of Science). Simulations for this project were performed on the HPC cluster fugu funded by an NSF MRI award.

Author information

Authors and Affiliations



S.N. performed numerical calculations with help from J.T. All authors developed the mathematical model, discussed the physical interpretation of the results and jointly wrote the manuscript.

Corresponding author

Correspondence to Smadar Naoz.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Notes and Data , Supplementary Figure 1 and legend and additional references. (PDF 112 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Naoz, S., Farr, W., Lithwick, Y. et al. Hot Jupiters from secular planet–planet interactions. Nature 473, 187–189 (2011).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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