Planetary Ring Dynamics -- The Streamline Formalism -- 2. Theory of Narrow Rings and Sharp Edges

TL;DR

This paper develops a comprehensive theoretical framework for large-scale ring dynamics, focusing on modes, eccentricities, and confinement in planetary rings, complementing previous work on density waves and small-scale structures.

Contribution

It extends the streamline formalism to cover all ring modes, origin of eccentricities, and confinement mechanisms, providing a self-contained theoretical approach.

Findings

Detailed analysis of ring mode dynamics

Insights into ring eccentricity origins

Mechanisms of ring and gap confinement

Abstract

The present material covers the features of large scale ring dynamics in perturbed flows that were not addressed in part 1 (astro-ph/1606.00759); this includes an extensive coverage of all kinds of ring modes dynamics (except density waves which have been covered in part 1), the origin of ring eccentricities and mode amplitudes, and the issue of ring/gap confinement. This still leaves aside a number of important dynamical issues relating to the ring small scale structure, most notably the dynamics of self-gravitational wakes, of local viscous overstabilities and of ballistic transport processes. As this material is designed to be self-contained, there is some 30% overlap with part 1. This work constitutes a preprint of Chapter 11 of the forthcoming Cambridge University book on rings (Planetary Ring Systems, Matt Tiscareno and Carl Murray, eds).