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

Abstract

Rings have been found around Chariklo, Haumea and Quaoar, three small objects of the Solar System. All these rings are observed near the second-order spin-orbit resonances (SORs) 1/3 or 5/7 with the central body, suggesting an active confinement mechanism by these resonances. Our goal is to understand how collisional rings can be confined near second-order SORs in spite of the fact that they force self-intersecting streamlines.We use full 3D numerical simulations that treat rings of inelastically colliding particles orbiting non-axisymmetric central bodies, characterized by a dimensionless mass anomaly parameter mu. 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. The 1/3 SOR can confine ring material, by transferring the forced resonant mode into free Lindblad modes. We derive a criterion ensuring that the 1/3 SOR counteracts viscous spreading. Assuming meter-sized ring particles, and tau~1, this requires a threshold value mu > 1e-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 ~1e-7 - 1e-6 relative to Chariklo, corresponding to subkilometer-sized objects. With self-gravity, the ring viscosity nu increases by a factor of few in low-tau rings due to gravitational encounters. For large tau, self-gravity wakes enhance nu by a factor of ~100 compared to a non-gravitating ring, requiring ~10-fold larger mu since the threshold value increases proportional to square-root of nu.