Global N-body simulation of gap edge structures created by perturbations from a small satellite embedded in Saturn’s rings II: The effect of satellite’s orbital eccentricity and inclination

Small satellites, Pan and Daphnis, are embedded in Saturn’s rings and opening a clear gap with satellite wakes at the gap edges. Furthermore, in the case of Daphnis, pronounced vertical wall structures casting shadows on the rings are also observed in the satellite wakes. In our previous paper (Torii, N., Ida, S., Kokubo, E., Michikoshi, S. [2024]. Icarus, 425, 116029), we found through global 3D N-body simulation that the ring particles’ lateral epicycle motions excited by an encounter with a satellite are converted to the vertical motions through oblique physical collisions between the particles at the wavefronts of satellite wakes. In order to highlight this dynamics, Torii et al., (2024) considered the circular ($e_s=0$) and coplanar ($i_s=0$) satellite orbit, where $e_s$ and $i_s$ are the satellite orbital eccentricity and inclination, respectively. However, Daphnis has non-negligible eccentricity and inclination. In this paper, we perform a global 3D N-body simulation with non-zero $e_s$ or non-zero $i_s$ of the satellite orbit to investigate how they affect the gap edge structures. We found that the effect of satellite eccentricity is important both in the satellite wakes and the vertical walls at the gap edges. The non-sinusoidal sawtooth-like satellite wakes and azimuthally more localized vertical walls observed by Cassini are simultaneously reproduced in the detailed structures and spatial scales. Both of them periodically vary due to the satellite excursions between the apocenter and the pericenter. The ring particles in outer (inner) rings that undergo closest encounters with the satellite near the apocenter (pericenter) are excited the most highly. Because the excited eccentricities of the ring particles are converted to the inclinations through physical collisions, the conversion is the most active for the particles that acquire the highest eccentricities, resulting in the azimuthally more localized vertical wall structures. The predicted height of the tallest vertical walls is $\sim 0.2$ times the satellite Hill radius in the case of the satellite eccentricity comparable to Daphnis when adopting Hill scaling, which is twice as much as the height obtained in the case of the circular satellite orbit and is quantitatively more consistent with the Cassini observation. The simulation with the inclined satellite orbit reveals that the local vertical walls created by the particle–particle collisions persist at the satellite wavefronts and are superposed with the global bending waves induced by the satellite out-of-plane perturbations. These results show that the observed vertical walls are actually formed by the satellite wakes followed by their conversion to the vertical motions through inter-particle collisions, rather than by the out-of-plane perturbation from the satellite in an inclined orbit.