Rings around irregular bodies

II. Numerical simulations of the 1/3 spin-orbit resonance confinement and applications to Chariklo

¹ Space Physics and Astronomy Research unit, University of Oulu, 90014 Oulu, Finland
² Laboratoire Temps Espace (LTE), Observatoire de Paris, Université PSL, CNRS UMR 8255, Sorbonne Université, LNE, 61 Av. de l’Observatoire, 75014 Paris, France

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 22 August 2025
Accepted: 2 January 2026

Abstract

Aims. Our goal was to understand how collisional rings can be confined near second-order SORs in spite of the fact that they force self-intersecting streamlines.

Methods. We used full 3D numerical simulations that treat rings of inelastically colliding particles orbiting nonaxisymmetric central bodies, characterized by a dimensionless mass anomaly parameter µ. While most of our simulations ignore self-gravity, a few runs include gravitational interactions between particles, providing preliminary results on the effect of self-gravity on the ring confinement.

Results. The 1/3 SOR can confine ring material, by transferring the forced resonant mode into free Lindblad modes. We derived a criterion ensuring that the 1/3 SOR counteracts viscous spreading. It reads kµ² ≳ τR², where k is a dimensionless coefficient, τ is the ring optical depth, and R is the particle radius. Expressing R in terms of the radius of the synchronous orbit, we obtain k ∼ 4 × 10⁻⁵ for the 1/3 SOR acting on nongravitating rings. Assuming meter-sized ring particles, and τ ∼ 1, this requires a threshold value µ ≳ 10⁻³ in Chariklo’s case. The confinement is not permanent as a slow outward leakage of particles is observed in our simulations. This leakage can be halted by an outside moonlet with a mass of ∼10⁻⁷–10⁻⁶ relative to Chariklo, corresponding to subkilometer-sized objects. With self-gravity, the ring viscosity increases by a factor of a few in low-τ rings due to gravitational encounters. For large τ, self-gravity wakes enhance the viscosity ν by a factor of ∼100 compared to a nongravitating ring, requiring ∼tenfold larger µ values since the threshold value increases proportionally to v.