Through stellar occultations, two narrow and well-defined rings were discovered encircling (10199) Chariklo at about 391km and 405km (Braga-Ribas et. al. 2014).
Sicardy et al. (2018a,b) showed that modest topographic features or elongations of Chariklo clear the region around the 1:1 resonance (corotation resonance) of an initial collisional disc. They showed that the particles outside the corotation radius are pushed beyond the 1:2 resonance, while the particles inside such radius fall toward the body.
A recent work by Morgado et al. (2021) showed that the main ring has width between 4.8 and 9.1 km, and the shape of Chariklo is well fitted by an ellipsoid with semi-axes of 143.8 km, 135.2 km and 99.1 km, generating a new, and significantly smaller value for the gravitational potential coefficient C22.
Adopting Poincaré Surface of Section technique, we explore the dynamics of the region near the location of the rings in light of the new results given by Morgado et al. (2021). The dynamical structure is divided into regular and chaotic regions, with their locations and sizes. The comprehension of these structures is made through the identification of periodic and quasi-periodic orbits. Of particular interest is try to understand the dynamical structure associated with the 1:3 resonance, which is supposed to be connected with the rings (Leiva et al. 2017).
From our results we obtained that the 1:3 resonant periodic orbits presented a relatively high value of eccentricity generating a radial range that is larger than the width of the rings, while the first kind periodic orbits exist for much lower eccentricity values. We found that the first kind periodic orbits family is responsible for a stable region whose location and size meet those of the Chariklo’s rings. However, in this analysis interactions between the ring particles were neglected.
Therefore, in order to assume interaction between the particles we made a sample of numerical simulations of the system formed by a disc of particles under the effects of Chariklo, with a spin period of 7.004 h, assuming new values of C20 and C22. Our results showed that the stable region is much interior to the inner edge of the main ring, corroborating the results derived from the Poincar'e Surface of Section Technique.
Acknowledgements: This work is supported by Fapesp (2018/23568- 6, 2016/24561-0), CNPq (313043/2020-5) and Capes Financial Code 001.