W-shaped occultation signatures: Inference of entwined particle orbits in charged planetary ringlets

Observed W-shaped occultation signatures of certain narrow ringlets in the ring systems of Saturn and Uranus imply a concentration of material near their inner and outer radial edges. A model is proposed where edge bunching is a natural consequence of particles in entwined elliptical orbits, with the same particles alternately defining both edges. While such orbits cross over in radius, collisions would not occur if they have small inclinations, the same fixed argument of periapse ω, and other parameters whereby the particles would “fly in formation” along compressed helical paths relative to the core of the ringlet, which is taken to be a circle in the equatorial plane. For this model to match the observed ring thickness and ringlet widths, orbit inclinations i must be much smaller than their eccentricities e, which themselves would be very small compared to unity. Thus, the meridional cross section of the resultant torus would be a very thin ellipse of thickness proportional to i∣cos ω∣, tilted slightly from the equatorial plane by (i/e)∣sin ω∣ radians. However, gravitational perturbations due to the oblateness of the planet would cause a secular change in ω so that this cross section would collapse periodically to a tilted line, and collisions would then occur. If this collapse could be prevented, the torus could remain in a continuous state of nearly zero viscosity. Stabilization against collapse appears possible due to several remarkable characteristics that are added to the model when the particles are electrically charged. First, because of inherent features of the torus structure, a weak electric force could counter the key effect of the vastly larger oblateness force. Second, because the electric perturbation also affects i, there is a large region in ω,i space where stability against cross-sectional collapse is automatic. For this region, the thickness of the elliptical cross section would expand and contract in concert with the way that the major axis of the ellipse rocks back and forth relative to the equatorial plane. The period of these “rocking and breathing” changes would be from 1 to 3 weeks for a torus in the C ring of Saturn, for example. The electric effects could change considerably without driving the parameters of the torus from the stable domain where cross-sectional collapse does not occur. While specialized and in several important ways still incomplete, the proposed model could account for the W-shaped patterns and explain how very dense ringlets might endure without energy loss due to collisions. It also appears to be capable of explaining the observed sorting of particles by size within a ringlet. Several characteristics of the model suggest definitive tests of its applicability, including its prediction that a nonsymmetrical W-shaped occultation signature could be reversed a half orbit away, and that grazing solar illumination of tilted ringlets might cast shadows that change with time in a prescribed way.