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


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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.

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.


  1. 1.

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

  2. 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).

  3. 3.

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

  4. 4.

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

  5. 5.

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

  6. 6.

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

  7. 7.

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

  8. 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).

  9. 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).

  10. 10.

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

  11. 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).

  12. 12.

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

  13. 13.

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

  14. 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).

  15. 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).

  16. 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).

  17. 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).

  18. 18.

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

  19. 19.

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

  20. 20.

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

  21. 21.

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

  22. 22.

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

  23. 23.

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

  24. 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).

  25. 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).

  26. 26.

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

  27. 27.

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

  28. 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).

  29. 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).

  30. 30.

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

  31. 31.

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

  32. 32.

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

  33. 33.

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

  34. 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. 35.

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

  36. 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).

  37. 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).

Download references


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

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.

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

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

Further reading