Fine-Scale Density Wave Structure of Saturn's Main Rings: A Hydrodynamic Theory

Evgeny Griv, Michael Gedalin

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The theoretical studies of Maxwell (1859) have showed that the rings around Saturn could not be solid or liquid, but rather a swarm of millions of individual particles rotating in separate concentric orbits at different speeds. A modern very popular model of the particles in Saturn's rings is a smooth ice sphere, whose restitution coefficient is quite high (exceeding 0.63) and decreases as the collision velocity increases. In this work, the linear stability of the Saturnian ring disk of mutually gravitating and physically colliding particles is examined with special emphasis on its fine-scale of the order of 100 m density wave structure, that is, almost regularly spaced, aligned cylindric density enhancements and optically-thin zones with the width and the spacing between them of roughly several tens particle diameters. Jeans' instabilities of small-amplitude gravity perturbations (e.g., those produced by a spontaneous disturbance) are analyzed analytically through the use of Navier-Stokes dynamical equations of a compressible fluid. An essential feature of this study is that the theory is not restricted by any assumptions regarding the thickness of the system. The simple model of the system is considered: the ring disk is considered to be thin, a weakly spatially inhomogeneous, and its structure is considered in a horizontally local short-wave approximation. We show that the disk is probably unstable and gravity perturbations grow effectively within a few orbital periods; self-gravitation plays a key role in the formation of the fine-scale structure while particle collisions play a secondary role. The predictions of the theory are compared with recent observations of Saturn's rings by the Cassini spacecraft and are found to be in good agreement. Particulary, it appears very likely that some of the microstructures observed in Saturn's A and B rings -both axisymmetric and nonaxisymmetric ones -are manifestations of these effects produced by Jeans' gravitational instability. We argue that the quasi-periodic density enhancements revealed by Cassini obser-vations are flattened structures, with height/width ratio of about 0.3 or even less. A separate investigation based on high-resolution of the order of 10 m observations of Saturn's A and B rings (and probably C ring as well) should be done to confirm this prediction. It is also shown that the gravitational instability might be proposed as potential clusters-forming mechanism leading to formation of porous 100-meter-diameter moonlets ("clumpy moons") embedded in the mid and outer A ring, and this has also yet to be directly measured. This work was supported in part by the Israel Science Foundation.
Original languageEnglish GB
Title of host publication38th COSPAR Scientific Assembly. Held 18-15 July 2010, in Bremen, Germany
StatePublished - 2010

Publication series

Name38th COSPAR Scientific Assembly. Held 18-15 July 2010, in Bremen, Germany


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