Uranian ring dynamics: An analysis of multimode motions

Abstract

The purpose of this paper is to present an extension of the standard streamline formalism which allows us to discuss the dynamics of a narrow ring in the presence of several modes. The ring is supposed to be perturbed by its self-gravity only, and nonlinear coupling between the modes is neglected. It is shown that self-gravity is able to enforce the rigid precession of all modes. Also, special attention is paid to the response of the ring width to the presence of several modes. In particular, it is shown that the m = 1 mode of the γ ring should have no influence on its width, and that extreme cases for which the mean shape is purely elliptical (m = 1 mode) while the width is controlled by a different mode are possible. This last result might help explain the apparent incoherence of the width-longitude relations of the narrowest Uranian rings.

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