Rings of Uranus - Dynamics and Origin

Dynamics and Origin

An outstanding problem concerning the physics governing the narrow Uranian rings is their confinement. Without some mechanism to hold their particles together, the rings would quickly spread out radially. The lifetime of the Uranian rings without such a mechanism cannot be more than 1 million years. The most widely cited model for such confinement, proposed initially by Goldreich and Tremaine, is that a pair of nearby moons, outer and inner shepherds, interact gravitationally with a ring and act like sinks and donors, respectively, for excessive and insufficient angular momentum (or equivalently, energy). The shepherds thus keep ring particles in place, but gradually move away from the ring themselves. To be effective, the masses of the shepherds should exceed the mass of the ring by at least a factor of two to three. This mechanism is known to be at work in the case of the ε ring, where Cordelia and Ophelia serve as shepherds. Cordelia is also the outer shepherd of the δ ring, and Ophelia is the outer shepherd of the γ ring. However no moon larger than 10 km is known in the vicinity of other rings. The current distance of Cordelia and Ophelia from the ε ring can be used to estimate the ring’s age. The calculations show that the ε ring cannot be older than 6 × 108 years.

Since the rings of Uranus appear to be young, they must be continuously renewed by the collisional fragmentation of larger bodies. The estimates show that the lifetime against collisional disruption of a moon with the size like that of Puck is a few billion years. The lifetime of a smaller satellite is much shorter. Therefore all current inner moons and rings can be products of disruption of several Puck-sized satellites during the last four and half billion years. Every such disruption would have started a collisional cascade that quickly ground almost all large bodies into much smaller particles, including dust. Eventually the majority of mass was lost, and particles survived only in positions that were stabilized by mutual resonances and shepherding. The end product of such a disruptive evolution would be a system of narrow rings. However, a few moonlets must still be embedded within the rings at present. The maximum size of such moonlets is probably around 10 km.

The origin of the dust bands is less problematic. The dust has a very short lifetime, 100–1000 years, and should be continuously replenished by collisions between larger ring particles, moonlets and meteoroids from outside the Uranian system. The belts of the parent moonlets and particles are themselves invisible due to their low optical depth, while the dust reveals itself in forward-scattered light. The narrow main rings and the moonlet belts that create dust bands are expected to differ in particle size distribution. The main rings have more centimeter to meter-sized bodies. Such a distribution increases the surface area of the material in the rings, leading to high optical density in back-scattered light. In contrast, the dust bands have relatively few large particles, which results in low optical depth.