Shepherding of the Uranian Rings. II. Dynamics

We explore the dynamical significance of the orbital resonances, identified in Paper I (Porco and Goldreich 1987), involving the satellites l986U7 and 1986U8, and the ɛ, δ, and γ rings. We demonstrate that these satellites are capable of exerting torques on the ɛ ring which supply at the inner edge, and remove at the outer edge, the unperturbed angular-momentum luminosity transported by viscous stresses outward across the ring, provided that the ring has a mass which is comparable to the predicted value M_ɛ = 6.1 x 10¹⁸ g, and that it is not more than a few meters thick. Thus there is no compelling reason to question the applicability of the standard theory of shepherding to the ɛ ring. However, the standard theory does place rather stringent requirements on the ring's properties, suggesting that confinement might be due to the reduction of the angular-momentum luminosity by flux reversal. Flux reversal could be associated either with the ring's eccentricity gradient or with nonlinear density waves in its interior. The drag due to the planet's extended neutral hydrogen atmosphere probably has only a minor effect on the dynamics of the ɛ, δ, and γ rings. However, it poses a severe problem for the shepherding of the α and β rings unless their masses have been seriously underestimated. This problem, and the large s-band optical depths of these rings, lead us to question the proposal that self-gravity is responsible for enforcing rigid precession in narrow rings.