N-body Simulations of the Ring Formation Process around the Dwarf Planet Haumea

Haumea is the only known trans-Neptunian object with a ring. The ring is in a position that causes a 3:1 spin-orbit resonance with the rotational period of Haumea, which has a triaxial shape. The non-axisymmetric gravitational field around Haumea is thought to affect the dynamics of the ring; however, the process of ring formation has not been elucidated. In this study, we analyze in some detail a potential ring formation scenario for Haumea. We first calculated the gravitational field around the triaxial ellipsoid and estimated the distance at which an object revolving around Haumea can exist stably using a simulation that incorporated the time-varying gravitational field. The results of this simulation showed that the trajectory of the object became unstable just inside its current ring position. Next, we analytically derived the Roche radius for a rigid body revolving around a triaxial ellipsoid and showed that the Roche radius could be near the current ring position. Furthermore, as a parameter study, we performed N-body simulations using the coefficient of rubble-pile restitution as a variable. Results demonstrated that, according to numerous parameters, the position of the Roche radius was near the current position of Haumea's ring. Based on these findings, we can assume that there is a high possibility that the ring formed in the region between the boundary of the unstable region of the orbit and the Roche radius. The scenario presented in this study could help explain the process by which Haumea's ring formed.