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.