Dynamical selection of the 1:3 spin-orbit resonance within the rings systems of Haumea, Chariklo, Quaoar

The discovery of rings surrounding small celestial bodies has been a recent advancement made possible through ground-based stellar occultations. Notably, dense and narrow rings have been identified encircling the dwarf planet (136108) Haumea, the Centaur (10199) Chariklo, the trans-Neptunian object (50000) Quaoar. These rings are observed in a specific dynamical configuration known as the 1:3 resonance, which correlates the orbit of a ring particle with the rotation of the central body, wherein their periods maintain a 1/3 ratio. In this study, we provide dynamical arguments in strong support to the preference shown by the small bodies for the 1:3 resonance over alternative resonances. Our findings are exclusively based on the consideration of the potential of the central body, without invoking other effects, such as those potentially induced by satellites of the small bodies.