Upper row: long-term evolution of a 1/3 SOR ringlet perturbed by a mass anomaly µ = 0.03, using 30 000 particles with radius R = 5 × 10⁻⁴ (corresponds to 100 m for Chariklo rings). Although the ringlet maintains a well-defined core, a slow outward leakage of particles appears, forming a faint tail. For better viewing, the width of the ring has been expanded by a factor of 10. Lower left panel: effect of a satellite located at 2.3 ≈ 1.1a_1/3, with a mass µ_s = 2 × 10⁻⁶ relative to the central body. Without the 1/3 SOR, the ring spreads inward under the effects of spiral density perturbations forced by Lindblad resonances, shown here at T=100 000. Lower right panel: when both the satellite and the 1/3 SOR are present, the outward leakage of particles is prevented by the 8/7 Lindblad resonance with the satellite. Two movies generated from simulation snapshots stored every 360 Chariklo rotations (about 105 days) are available online.

Movie8

displays the evolution of eccentricity versus semi-major axis in the simulation without an external satellite: after T ∼ 60 000 (about 50 years for Chariklo), the particles start to leak outwards due to a small torque associated with the 1/3 SOR.

Movie9

shows the same for the simulation with the moonlet: the leakage observed when only the 1/3 SOR is acting on the ring is prevented, and the ring ends up being confined between the 1/3 SOR and the 8/7 inner Lindblad resonance with the satellite.