Ring dynamics around the Centaur Chariklo and the dwarf planet Haumea: effects of high-order resonances

Narrow and dense rings have been detected around the small Centaur body Chariklo (Braga-Ribas et al. 2014), as well as around the dwarf planet Haumea (Ortiz et al. 2017).

Both objects have non-axisymmetric shapes that induce strong resonant effects between the rotating central body with spin rate Ω and the radial epicyclic motion of the ring particles, κ. These resonances include the classical Eccentric Lindblad Resonances (ELR), where κ = m(n-Ω), with m integer, n being the particle mean motion. These resonances create an exchange of angular momentum between the body and the collisional ring, clearing the corotation zone, pushing the inner disk onto the body and repelling the outer part outside of the outermost 1/2 ELR, where the particles complete one orbital revolution while the body executes two rotations, i.e. n/Ω ~ 1/2 (Sicardy et al. 2019)

Here I will focus on higher-order resonances. They may appear either by considering other resonances such as n/Ω ~ 1/3, or the same resonance as above (n/Ω ~ 1/2), but with a body that has a triaxial shape. In this case, the invariance of the potential under a rotation of π radians transforms the 1st-order 1/2 Lindblad Resonance into a 2nd order 2/4 resonance.

Second-order resonances are of particular interest because they force a strong response of the particles near the resonance radius, in spite of the intrinsically small strength of their forcing terms. This stems from the topography of the associated resonant Hamiltonian, which possesses an unstable hyperbolic point at its origin.

The width of the region where this strong response is expected will be discussed for both Chariklo's and Haumea's rings. The special case of the second-order 1/3 resonance will be discussed, as it appears that both ring systems are close to that resonance.

This work is intended, among others, to pave the way for future collisional simulations of rings around non-axisymmetric bodies.

Braga-Ribas et al., 2014, Nature 508, 72
Ortiz et al., 2017, Nature 550, 219
Sicardy et al., 2019, Nature Astronomy 3, 146

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 n°669416 "Lucky Star"