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.

  • Letter
  • Published:

Ring dynamics around non-axisymmetric bodies with application to Chariklo and Haumea

Nature Astronomy volume 3, pages 146–153 (2019)Cite this article

Subjects

Abstract

Dense and narrow rings have been discovered recently around the small Centaur object Chariklo1 and the dwarf planet Haumea2, while being suspected around the Centaur Chiron3, although this point is debated4. They are the first rings observed in the Solar System elsewhere than around giant planets. In contrast to giant planets, gravitational fields of small bodies may exhibit large non-axisymmetric terms that create strong resonances between the spin of the object and the mean motion of ring particles. Here we show that modest topographic features or elongations of Chariklo and Haumea explain why their rings are relatively far away from the central body, when scaled to those of the giant planets5. Resonances actually clear on decadal timescales an initial collisional disk that straddles the corotation resonance (where the particles' mean motion matches the spin rate of the body). Quite generically, the disk material inside the corotation radius migrates onto the body, while the material outside the corotation radius is pushed outside the 1/2 resonance, where the particles complete one revolution while the body completes two rotations. Consequently, the existence of rings around non-axisymmetric bodies requires that the 1/2 resonance resides inside the Roche limit of the body, favouring faster rotators for being surrounded by rings.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Fig. 1: Corotation and LRs around Chariklo.
Fig. 2: Torque strengths at LRs around Chariklo and migration timescales.
Fig. 3: Migration of ring particles around Chariklo.

Similar content being viewed by others

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.

References

  1. Braga-Ribas, F. et al. A ring system detected around the Centaur (10199) Chariklo. Nature 508, 72–75 (2014).

    Article  ADS  Google Scholar 

  2. Ortiz, J. L. et al. The size, shape, density and ring of the dwarf planet Haumea from a stellar occultation. Nature 550, 219–223 (2017).

    Article  ADS  Google Scholar 

  3. Ortiz, J. L. et al. Possible ring material around Centaur (2060) Chiron. Astron. Astrophys. 576, A18 (2015).

    Article  Google Scholar 

  4. Ruprecht, J. D. et al. 29 November 2011 stellar occultation by 2060 Chiron: symmetric jet-like features. Icarus 252, 271–276 (2015).

    Article  ADS  Google Scholar 

  5. Esposito, L. W. Planetary rings. Rep. Prog. Phys. 65, 1741–1783 (2002).

    Article  ADS  Google Scholar 

  6. Sicardy, B. et al. in Planetary Ring Systems (eds Tiscareno, M. S. & Murray, C. D.) 135–153 (Cambridge Univ. Press, Cambridge, 2018).

  7. Pan, M. & Wu, Y. On the mass and origin of Chariklo’s rings. Astrophys. J. 821, 18 (2016).

    Article  ADS  Google Scholar 

  8. Hyodo, R., Charnoz, S., Genda, H. & Ohtsuki, K. Formation of Centaurs’ rings through their partial tidal disruption during planetary encounters. Astrophys. J. Lett. 828, L8 (2016).

    Article  ADS  Google Scholar 

  9. Araujo, R. A. N., Sfair, R. & Winter, O. C. The rings of Chariklo under close encounters with the giant planets. Astrophys. J. 824, 80 (2016).

    Article  ADS  Google Scholar 

  10. Wood, J., Horner, J., Hinse, T. C. & Marsden, S. C. The dynamical history of Chariklo and its rings. Astron. J. 153, 245 (2017).

    Article  ADS  Google Scholar 

  11. Melita, M. D., Duffard, R., Ortiz, J. L. & Campo-Bagatin, A. Assessment of different formation scenarios for the ring system of (10199) Chariklo. Astron. Astrophys. 602, A27 (2017).

    Article  ADS  Google Scholar 

  12. Leiva, R. et al. Size and shape of Chariklo from multi-epoch stellar occultations. Astron. J. 154, 159 (2017).

    Article  ADS  Google Scholar 

  13. Hedman, M. M. & Nicholson, P. D. More kronoseismology with saturn’s rings. Mon. Not. R. Astron. Soc. 444, 1369–1388 (2014).

    Article  ADS  Google Scholar 

  14. Morais, M. H. M. & Giuppone, C. A. Stability of prograde and retrograde planets in circular binary systems. Mon. Not. R. Astron. Soc. 424, 52–64 (2012).

    Article  ADS  Google Scholar 

  15. Goldreich, P. & Tremaine, S. The excitation of density waves at the Lindblad and corotation resonances by an external potential. Astrophys. J. 233, 857–871 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  16. Hopkins, P. F. & Quataert, E. An analytic model of angular momentum transport by gravitational torques: from galaxies to massive black holes. Mon. Not. R. Astron. Soc. 415, 1027–1050 (2011).

    Article  ADS  Google Scholar 

  17. Lin, D. N. C. & Papaloizou, J. Tidal torques on accretion discs in binary systems with extreme mass ratios. Mon. Not. R. Astron. Soc. 186, 799–812 (1979).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  19. Goldreich, P. & Tremaine, S. The dynamics of planetary rings. Ann. Rev. Astron. Astro. 20, 249–283 (1982).

    Article  ADS  Google Scholar 

  20. Meyer-Vernet, N. & Sicardy, B. On the physics of resonant disk-satellite interaction. Icarus 69, 157–175 (1987).

    Article  ADS  Google Scholar 

  21. Marley, M. S. & Porco, C. C. Planetary acoustic mode seismology: Saturn’s rings. Icarus 106, 508–524 (1993).

    Article  ADS  Google Scholar 

  22. Michikoshi, S. & Kokubo, E. Simulating the smallest ring world of Chariklo. Astrophys. J. Lett. 837, L13 (2017).

    Article  ADS  Google Scholar 

  23. Gupta, A., Nadkarni-Ghosh, S. & Sharma, I. Rings of non-spherical, axisymmetric bodies. Icarus 199, 97–116 (2018).

    Article  ADS  Google Scholar 

  24. Tiscareno, M. S., Hedman, M. M., Burns, J. A. & Castillo-Rogez, J. Compositions and origins of outer planet systems: insights from the Roche critical density. Astrophys. J. Lett. 765, L28 (2013).

    Article  ADS  Google Scholar 

  25. Porco, C. C., Thomas, P. C., Weiss, J. W. & Richardson, D. C. Saturn’s small inner satellites: clues to their origins. Science 318, 1602 (2007).

    Article  ADS  Google Scholar 

  26. Thomas, P. C. Sizes, shapes, and derived properties of the saturnian satellites after the Cassini nominal mission. Icarus 208, 395–401 (2010).

    Article  ADS  Google Scholar 

  27. Ip, W.-H. On a ring origin of the equatorial ridge of Iapetus. Geophys. Res. Lett. 33, L16203 (2006).

    Article  ADS  Google Scholar 

  28. Levison, H. F., Walsh, K. J., Barr, A. C. & Dones, L. Ridge formation and de-spinning of Iapetus via an impact-generated satellite. Icarus 214, 773–778 (2011).

    Article  ADS  Google Scholar 

  29. Dombard, A. J., Cheng, A. F., McKinnon, W. B. & Kay, J. P. Delayed formation of the equatorial ridge on Iapetus from a subsatellite created in a giant impact. J. Geophys. Res. 117, E03002 (2012).

    Article  ADS  Google Scholar 

  30. Balmino, G. Gravitational potential harmonics from the shape of an homogeneous body. Celest. Mech. Dyn. Astr. 60, 331–364 (1994).

    Article  ADS  Google Scholar 

  31. Boyce, W. Comment on a formula for the gravitational harmonic coefficients of a triaxial ellipsoid. Celest. Mech. Dyn. Astron. 67, 107–110 (1997).

    Article  ADS  MathSciNet  Google Scholar 

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

  33. Dermott, S. F. & Murray, C. D. The dynamics of tadpole and horseshoe orbits. I. Theory. Icarus 48, 1–11 (1981).

    Article  ADS  Google Scholar 

  34. Schmidt, J. et al. in Saturn from Cassini-Huygens (eds Dougherty, M. K., Esposito, L. W. & Krimigis S. M.) 413–458 (Springer, Dordrecht, 2009).

  35. Fornasier, S. et al. The Centaur 10199 Chariklo: investigation into rotational period, absolute magnitude, and cometary activity. Astron. Astrophys. 568, L11 (2014).

    Article  ADS  Google Scholar 

  36. Lellouch, E. et al. ‘TNOs are cool’: a survey of the trans-Neptunian region. II. The thermal lightcurve of (136108) Haumea. Astron. Astrophys. 518, L147 (2010).

    Article  ADS  Google Scholar 

  37. Ragozzine, D. & Brown, M. E. Orbits and masses of the satellites of the dwarf planet Haumea (2003 EL61). Astron. J. 137, 4766–4776 (2009).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The work leading to these results has received funding from the European Research Council under the European Community’s H2020 2014-2020 ERC Grant Agreement No. 669416 ‘Lucky Star’. P.S.-S. acknowledges financial support by the European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement No. 687378 ('SBNAF'). We thank F. Combes for discussions on corotation and Lindblad resonances in the context of galactic dynamics, and T. Vaillant for comments on satellite formations and migrations.

Author information

Authors and Affiliations

  1. LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Meudon, France

    B. Sicardy, F. Roques & J. Desmars

  2. Department of Space Studies, Southwest Research Institute, Boulder, CO, USA

    R. Leiva

  3. IMCCE, Observatoire de Paris, CNRS UMR 8028, Université de Lille, Observatoire de Lille, Lille, France

    S. Renner

  4. Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca, NY, USA

    M. El Moutamid

  5. Carl Sagan Institute, Cornell University, Ithaca, NY, USA

    M. El Moutamid

  6. Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía S/N, Granada, Spain

    P. Santos-Sanz

Authors
  1. B. Sicardy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Leiva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Renner
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. Roques
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. El Moutamid
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. P. Santos-Sanz
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. J. Desmars
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

B.S., R.L. and M.E.M. contributed to the analytical calculations that describe the resonance dynamics around a non-axisymmetric body. B.S. wrote the paper and made the figures, with contributions from R.L., S.R., F.R. and P.S.-S. and J.D. F.R. provided insights for the application of this work to the formation of satellites around small bodies. Numerical integrations were independently performed by B.S, S.R. and F.R.

Corresponding author

Correspondence to B. Sicardy.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Table 1, Supplementary Figures 1–2

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sicardy, B., Leiva, R., Renner, S. et al. Ring dynamics around non-axisymmetric bodies with application to Chariklo and Haumea. Nat Astron 3, 146–153 (2019). https://doi.org/10.1038/s41550-018-0616-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-018-0616-8

This article is cited by

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