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The recent paper Thermal Emission from the Uranian Ring System has been in the news recently. The introduction mentions:

The ε ring, the brightest and most massive of the narrow rings, was shown to maintain an appreciable eccentricity (e = 0.00794) and an azimuthally-varying width; the ring is five times wider and ∼2.5 times brighter in reflected sunlight at apoapsis than at periapsis (French et al. 19881; Karkoschka 2001a2). However, many fundamental parameters about the ring system remain unknown, including the filling factor, composition, thickness,

1French, R. G., Elliot, J. L., French, L. M., et al. 1988, Icarus, 73, 349, doi: 10.1016/0019-1035(88)90104-2

2Karkoschka, E. 2001a, Icarus, 151, 51, doi: 10.1006/icar.2001.6596

I've read in Wikipedia's Rings of Uranus that several rings are expected to be fairly young, and there may be interaction with some small moons, but I am surprised that the rings could maintain a significant eccentricity, and do not circularize or smear out due to collisions.

Question: What kind of dynamical effects can maintain Uranus' rings' eccentricities?

Uranus itself has a huge J2 and so any ring that isn't perfectly equatorial should have an eccentricity-dependent precession. The paper states that the apoapsis of the rings is five times wider than the periapsis, so there's definitely a population of different eccentricities and semi-major axes within the ε ring.

List of rings and their orbital parameters

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A relevant paper is Papaloizou & Melita (2004) "Structuring eccentric-narrow planetary rings" which starts off promisingly with the following:

The nature of the dynamical mechanism that maintains the apse alignment of narrow-eccentric planetary rings is one of the most interesting and challenging problems of Celestial Mechanics.

According to the leading model (Goldreich and Tremaine 1979) the self-gravity of the ring counter-acts the differential precession induced by the oblateness of the central planet. Using this hypothesis, a prediction of the total mass of the ring can be made, which, in general, is not in good agreement with the inferred mass of the observed eccentric rings in the Uranus system

It then goes on to describe subsequent refinements taking account of additional effects including particle interactions and perturbations that bring the predictions more in line. The approach described is given in the introduction:

In this work we build, from first principles, a simple general continuum or fluid like model of a narrow-eccentric ring. The eccentric pattern in the ring can be described as being generated by a normal mode of oscillation of wave-number m = 1 which may be considered to be a standing wave. Dissipation can be allowed to occur due to inter-particle collisions leading to a viscosity which would lead to damping of the mode. However, this global m = 1 mode can also be perturbed by neighboring-shepherd satellites which can inject energy and angular momentum through resonances. In this way losses due to particle collisions may be balanced. It is that process that is the focus of this paper. Other possible mechanisms, such as mode excitation through self-excitation through viscous overstability, that could arise with an appropriate dependence of viscosity on physical state variables (see Papaloizou and Lin 1988, Longaretti & Rappaport 1995), are beyond the scope of this paper and accordingly not investigated here.

The specific case of the ε-ring of Uranus is described in section 10.2, where the main satellite forcing considered is due to the 47:49 second-order mean-motion resonance between the ring and Cordelia.

The paper goes into quite a bit of mathematical detail on the various processes involved.

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  • $\begingroup$ "...47:49 second-order mean-motion resonance between the ring and Cordelia." Wow, this is a pretty elaborate theory! I understand that it's a potential explanation and not necessarily conclusive, but I get the idea that it's going to turn out to be something complicated one way or the other. Thanks! $\endgroup$ – uhoh Jun 23 at 0:57

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