Ring dynamics around an oblate body with an inclined satellite: The case of Haumea

The recent discovery of rings and massive satellites around minor bodies and dwarf planets suggests that they may often coexist, as for example around Haumea. A ring perturbed by an oblate central body and by an inclined satellite may disperse on a short timescale. The conditions under which a ring may survive are explored both analytically and numerically. The trajectories of ring particles are integrated under the influence of the gravitational field of a triaxial ellipsoid and (a) massive satellite(s), including the effects of collisions. A ring initially formed in the equatorial plane of the central body will be disrupted if the satellite has an inclination in the Kozai Lidov regime (39.2 < i < 144.8). For lower inclinations, the ring may relax to the satellite orbital plane thanks to an intense collisional damping. On the other hand, a significant J2 term easily suppresses the perturbations of an inclined satellite within a critical semimajor axis, even in the case of Kozai Lidov cycles. However, if the ring is initially inclined with respect to the equatorial plane, the same J2 perturbations are not a protective factor but instead disrupt the ring on a short timescale. The ring found around Haumea is stable despite the rise in the impact velocities that is due to the asymmetric shape of the the body and the presence of a 3:1 resonance with the rotation of the central body. A ring close to an oblate central body should be searched for in the proximity of the equatorial plane, where the J2 perturbations protect it against the perturbations of an external inclined satellites. In an inclined configuration, the J2 term is itself disruptive.