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.

A primordial origin for misalignments between stellar spin axes and planetary orbits

Abstract

The existence of gaseous giant planets whose orbits lie close to their host stars (‘hot Jupiters’) can largely be accounted for by planetary migration associated with viscous evolution of proto-planetary nebulae1. Recently, observations of the Rossiter–McLaughlin effect2 during planetary transits have revealed that a considerable fraction of hot Jupiters are on orbits that are misaligned with respect to the spin axes of their host stars3. This observation has cast doubt on the importance of disk-driven migration as a mechanism for producing hot Jupiters. Here I show that misaligned orbits can be a natural consequence of disk migration in binary systems whose orbital plane is uncorrelated with the spin axes of the individual stars4,5,6. The gravitational torques arising from the dynamical evolution of idealized proto-planetary disks under perturbations from massive distant bodies act to misalign the orbital planes of the disks relative to the spin poles of their host stars. As a result, I suggest that in the absence of strong coupling between the angular momentum of the disk and that of the host star, or of sufficient dissipation that acts to realign the stellar spin axis and the planetary orbits, the fraction of planetary systems (including systems of ‘hot Neptunes’ and ‘super-Earths’) whose angular momentum vectors are misaligned with respect to their host stars will be commensurate with the rate of primordial stellar multiplicity.

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

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Geometrical set-up of the problem.
Figure 2: Excitation of disk–star misalignment.
Figure 3: Timescales for excitation of spin-orbit misalignment.

References

  1. Lin, D. N. C., Bodenheimer, P. & Richardson, D. C. Orbital migration of the planetary companion of 51 Pegasi to its present location. Nature 380, 606–607 (1996)

    ADS  CAS  Article  Google Scholar 

  2. McLaughlin, D. B. Some results of a spectrographic study of the Algol system. Astrophys. J. 60, 22–31 (1924)

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  4. Ghez, A. M., Neugebauer, G. & Matthews, K. The multiplicity of T Tauri stars in the star forming regions Taurus-Auriga and Ophiuchus-Scorpius: a 2.2 micron speckle imaging survey. Astron. J. 106, 2005–2023 (1993)

    ADS  Article  Google Scholar 

  5. Kraus, A. L., Ireland, M. J., Martinache, F. & Hillenbrand, L. A. Mapping the shores of the brown dwarf desert. II. Multiple star formation in Taurus-Auriga. Astrophys. J. 731, 8 (2011)

    ADS  Article  Google Scholar 

  6. Marks, M. & Kroupa, P. Inverse dynamical population synthesis: constraining the initial conditions of young stellar clusters by studying their binary populations. Astron. Astrophys. 543, A8 (2012)

    ADS  Article  Google Scholar 

  7. Hébrard, G. 20 colleagues The retrograde orbit of the HAT-P-6b exoplanet. Astron. Astrophys. 527, L11 (2011)

    ADS  Article  Google Scholar 

  8. Wu, Y. & Murray, N. Planet migration and binary companions: the case of HD 80606b. Astrophys. J. 589, 605–614 (2003)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  10. Naoz, S., Farr, W. M., Lithwick, Y., Rasio, F. A. & Teyssandier, J. Hot Jupiters from secular planet–planet interactions. Nature 473, 187–189 (2011)

    ADS  CAS  Article  Google Scholar 

  11. Ford, E. B. & Rasio, F. A. Origins of eccentric extrasolar planets: testing the planet-planet scattering model. Astrophys. J. 686, 621–636 (2008)

    ADS  Article  Google Scholar 

  12. 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)

    ADS  Article  Google Scholar 

  13. Wu, Y. & Lithwick, Y. Secular chaos and the production of hot Jupiters. Astrophys. J. 735, 109 (2011)

    ADS  Article  Google Scholar 

  14. Guillochon, J., Ramirez-Ruiz, E. & Lin, D. Consequences of the ejection and disruption of giant planets. Astrophys. J. 732, 74 (2011)

    ADS  Article  Google Scholar 

  15. Morbidelli, A. & Crida, A. The dynamics of Jupiter and Saturn in the gaseous protoplanetary disk. Icarus 191, 158–171 (2007)

    ADS  Article  Google Scholar 

  16. Marquis de Laplace, P.-S. Traite de Mecanique Celeste, 1 and 2 Vol. 1, Ch. VII, 569–634, http://ia600303.us.archive.org/19/items/mcaniquecles01laplrich/mcaniquecles01laplrich.pdf (Hillard, Gray, Little and Wilkins, 1799)

    Google Scholar 

  17. Gauss, C. F. Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium (eds Perthes, F. & Besser, I. H. ) (Sumtibus, 1809); in Werke Vol. 3, 331–355, http://resolver.sub.uni-goettingen.de/purl?PPN235999628 (Dieterich, Gottinger, 1866)

    Google Scholar 

  18. Murray, C. D. & Dermott, S. F. Solar System Dynamics Ch. 7 (Cambridge University Press, 1999)

    MATH  Google Scholar 

  19. Touma, J. R., Tremaine, S. & Kazandjian, M. V. Gauss’s method for secular dynamics, softened. Mon. Not. R. Astron. Soc. 394, 1085–1108 (2009)

    ADS  Article  Google Scholar 

  20. Batygin, K., Morbidelli, A. & Tsiganis, K. Formation and evolution of planetary systems in presence of highly inclined stellar perturbers. Astron. Astrophys. 533, A7 (2011)

    ADS  Article  Google Scholar 

  21. Morbidelli, A. Modern Celestial Mechanics: Aspects of Solar System Dynamics Chs 4 and 8 (Taylor and Francis, 2002)

    MATH  Google Scholar 

  22. Herbst, W., Bailer-Jones, C. A. L., Mundt, R., Meisenheimer, K. & Wackermann, R. Stellar rotation and variability in the Orion nebula cluster. Astron. Astrophys. 396, 513–532 (2002)

    ADS  Article  Google Scholar 

  23. Calvet, N. et al. Disk evolution in the Orion OB1 association. Astron. J. 129, 935–946 (2005)

    ADS  CAS  Article  Google Scholar 

  24. Kaib, N. A., Raymond, S. N. & Duncan, M. J. 55 Cancri: a coplanar planetary system that is likely misaligned with its star. Astrophys. J. 742, L24 (2011)

    ADS  Article  Google Scholar 

  25. Kraus, A. L. & Hillenbrand, L. A. The role of mass and environment in multiple-star formation: a 2MASS survey of wide multiplicity in three young associations. Astrophys. J. 662, 413–430 (2007)

    ADS  CAS  Article  Google Scholar 

  26. Adams, F. C. The birth environment of the Solar System. Annu. Rev. Astron. Astrophys. 48, 47–85 (2010)

    ADS  CAS  Article  Google Scholar 

  27. Bate, M. R., Lodato, G. & Pringle, J. E. Chaotic star formation and the alignment of stellar rotation with disc and planetary orbital axes. Mon. Not. R. Astron. Soc. 401, 1505–1513 (2010)

    ADS  Article  Google Scholar 

  28. Lai, D. Tidal dissipation in planet-hosting stars: damping of spin-orbit misalignment and survival of hot Jupiters. Mon. Not. R. Astron. Soc. 423, 486–492 (2011)

    ADS  Article  Google Scholar 

  29. Terquem, C. & Papaloizou, J. C. B. Migration and the formation of systems of hot super-Earths and Neptunes. Astrophys. J. 654, 1110–1120 (2007)

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

Download references

Acknowledgements

I thank A. Morbidelli, P. Golreich, H. Knutson, S. Tremaine, J. Winn and F. Adams for numerous conversations and D. Stevenson and G. Laughlin for carefully reading the manuscript. I am greatly indebted to M. Kazandjian and J. Touma for providing me with the softened analytical Gaussian averaging algorithm used in this work and help with implementation. Finally, I am grateful to D. Fabrycky for careful examination of the paper and numerous suggestions, which resulted in a substantial improvement of the manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Konstantin Batygin.

Ethics declarations

Competing interests

The author declares no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data 1-4, Supplementary Figures 1-6 and additional references. (PDF 1408 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Batygin, K. A primordial origin for misalignments between stellar spin axes and planetary orbits. Nature 491, 418–420 (2012). https://doi.org/10.1038/nature11560

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature11560

Further reading

Comments

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.

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