Stationary dynamics of planetary ring edge modes at Saturn’s B ring edge

Abstract

Recent analyses of the structure of the B ring edge have revealed the existence of a rather large number of mode-like features11In this work the expression mode-like features refers to sinusoidal in azimuth (at least in first approximation), variations of the edge shape. of azimuthal wavenumber ranging from m=1 to m=5. Several such mode-like features are associated with each m. The presence of so many features is a puzzle in itself.The present work investigates whether these features can all be associated with independent edge modes and develops to this effect a formal extension of the still embryonic theory of edge modes as trapped waves. Based on this formal extension, forced and free edge modes are explored in some detail. The analysis explicitly shows how edge mode properties such as their resonance location (for free modes) and edge amplitude (for the m=2 forced mode) are related to the ring surface density. Furthermore, the apsidal misalignment of the forced m=2 mode has been known for some time to be related to the ring viscous dissipation in the edge region.This investigation leads to a number of conclusions:i/ Only one mode-like structure associated with a given m can be associated with an edge mode, except possibly for m=1 modes where each of the three detected features can be interpreted as an independent edge mode.ii/ The ring surface density at the edge is in the 200 g/cm2 range under the assumption of dynamically independent edge modes, but a preliminary crude account of collective mode effects brings this down to a more realistic value of ∼100 g/cm2. This applies in the last 20 or 30 kilometers to the edge (m≠1). Further inside (one to two hundred kilometers), the surface density is somewhat more modest, ∼60 g/cm2 (m=1).iii/ The viscous dissipation at the edge is constrained by the observed misalignment between the mean longitude of Mimas and the forced edge mode. The implied level of dissipation at the edge is consistent with the now predominant idea that transport in the B ring, away from the edge, is dominated by self-gravity wakes.iv/ The m=2 mode forced by Mimas is never nonlinear enough by itself to produce the viscous angular flux momentum reversal required to make the edge effectively confined by the associated satellite torque. This explains the failure of Hahn et al. (2009) to explain the confinement of the edge by Mimas except for unrealistic stress tensor properties. It is argued that the presence of so many modes and mode-like features provides a way to restore in a somewhat different form the edge confinement process of Borderies et al. (1982), thereby resolving the conundrum raised by Hahn et al. (2009).