Global N-body Simulation of Gap Edge Structures Created by Perturbations from a Small Satellite Embedded in Saturn's Rings

Observations by the Voyager and Cassini spacecrafts have revealed various striking features of the gap structure in Saturn's ring, such as the density waves, sharp edge, and vertical wall structure. In order to explain these features in a single simulation, we perform a high-resolution (N~10^6-10^7) global full N-body simulation of gap formation by an embedded satellite considering gravitational interactions and inelastic collisions among all ring particles and the satellite, while these features have been mostly investigated separately with different theoretical approaches: the streamline models, 1D diffusion models, and local N-body simulation. As a first attempt of a series of papers, we here focus on the gap formation by separating satellite migration with fixing the satellite orbit in a Keplerian circular orbit. We reveal how the striking gap features - the density waves, sharp edge, and vertical wall structure - are simultaneously formed by an interplay of the satellite-ring and ring particle-particle interactions. In particular, we propose a new mechanism to quantitatively explain the creation of the vertical wall structure at the gap edge. Inelastic collisions between ring particles damp their eccentricity excited by the satellite's perturbations to enhance the surface density at the gap edge, making its sharp edges more pronounced. We find the eccentricity damping process inevitably raises the vertical wall structures the most effectively in the second epicycle waves. Particle-particle collisions generally convert their lateral epicyclic motion into vertical motion. Because the excited epicyclic motion is the greatest near the ring edge and the epicycle motions are aligned in the first waves, the conversion is the most efficient in the gap edge of the second waves and the wall height is scaled by the satellite Hill radius, which are consistent with the observations.