The formation of rings around small bodies: an overview

Rings are observed around several small bodies of the solar systems: the Centaur Chariklo, the dwarf planet Haumea, the large trans-Neptunian object Quaoar and possibly the active Centaur Chiron. In spite of large differences in sizes and heliocentric distances, these rings share common properties. First, they are dense, in the sense that their dynamics is dominated by collisions, meaning optical depths from a percent or so to essentially opaque. Secondly, they are narrow, thus calling for confining mechanisms. Such features are also observed around the giant planets, with the nine narrow Uranus' rings, the two Adams and Le Verrier rings of Neptune, or the numerous ringlets of Saturn.

Thus, even though their physical parameters and origins are very diverse (Sicardy et al. 2025), these rings show some "convergent evolution", implying that some common mechanisms are at work. Here, we examine the role of spin-orbit resonances (SORs) between the central body and its ring(s), which involve commensurabilities between the rotation rate of a non-asymmetric central body and the mean motion of the ring particles. This non-axisymmetry of the body can take the form of a mass anomaly μ at the surface of the body, or an elongation of the body (or a combination of both). Resonances can also stem from a satellite. However, due to their expected small sizes, there resonance  are expected  to be much weaker than those stemming from SORs.

We have already explored through numerical simulations the fate of a collisional ring orbiting an irregular body, see the dynamical  study  and the numerical  results of Sicardy and Salo (2024) and Salo and Sicardy (2024).

Here, we placed a ring initially close to the second-order 5/7 SOR with Chariklo, meaning that the ring particles complete five revolutions while the central body complete seven rotations. This SOR lies just beyond the synchronous orbit, where the particle mean motion matches the central body spin rate, see Fig.1. The left panel illustrates the main characteristics of the ring evolution: (i) the general outwards migration caused by the positive torque exerted by the mass anomaly and (ii) the temporary capture of the ring in successive first- (aka Lindblad) and second-order SORs 2/3, 3/5, 1/2. The right panel of Fig. 1 shows the same simulation, where the particle dynamical states are plotted in a diagram showing the eccentricities as a function semi-major axis. It illustrates again the temporary capture of the ring in first- and second-order SORs.

In this example, the torque exerted by the mass anomaly eventually pushes the ring outside the SOR. We will examine in the talk the role of a small satellite that may halt this outward migration, in particular at the 1/3 SOR (not visible in Fig. 1). The general view that emerges from this work is that the strong SORs caused by irregularities in the body potential (mass anomaly, elongation or more complex non-axisymmetric features) cause a rapid  confinement of the ring, while a small satellite balances the positive torque from the SOR, thus stabilizing the ring on the long term. This behavior may be generic to rings around small bodies, irrespective to the origin of this material.

Fig. 1 – Left: A density plot showing the evolution of a Chariklo ring with initial optical depth τ₀=0.075, composed of 7,500 inelastically colliding particles with radius 200 m (without self-gravity) orbiting a central body with mass anomaly μ=0.003. The time is expressed in terms of revolutions of the central body and the y-axis show the particle angular momenta L_z, normalized to its value at synchronous orbit. The red curve is the average value of L_z. Right: The green dots show the orbital eccentricities of the particles  shown in Fig. 1 as a function of semi-major axes. The black (resp. red) curves are the theoretical responses of test particles to the corresponding first-order (resp. second-order) SORs.

Acknowledgements  - This work has been supported by the French ANR project Roche, number ANR-23-CE49-0012.

References:
- Salo & Sicardy, "Collisional confinement of 1:3 resonance ringlets around non-spherical bodies",  EPSC Abstracts 17,, EPSC2024-534 (2024), doi: 10.5194/epsc2024-534
- Sicardy & Salo, "The dense resonance meshes around the ringed Chariklo, Haumea and Quaoar", EPSC Abstracts 17, EPSC2024-123 (2024), doi: 10.5194/epsc2024-123
- Sicardy et al., "Origins of rings in the Solar System", Phil. Trans. R. Soc. A 383 (2025): 20240193