Periodic fine-scale structure in saturn's rings: A theory of self-gravity density waves

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A highly flattened, rapidly and differentially rotating disk of primarily large > cm size mutually gravitating and elastically colliding ice particles orbiting a central object is oftenly taken as an idealized model of Saturn's main A, B, and C rings. This article considers the problem of the stability of the Saturnian main ring system with special emphasis on its fine-scale of the order of 100 m density wave structure (almost regularly spaced, aligned cylindric density enhancements and rarefications). We attribute this periodic microstructure to the propagation of compression density waves in the ring plane. The wave propagation is a process of rotation as a solid about the center at a fixed phase velocity, despite the general differential rotation of the system; the structure consists of different material at different times. It seems likely that the key factor contributing to the generation of density waves is the classical Jeans instability of gravity perturbations (e.g., those produced by a spontaneous disturbance). This gravitational instability associated with small departures of macroscopic parameters from the dynamical equilibrium is hydrodynamical in nature and has nothing to do with any explicit resonant effects. We analyse Jeans' gravitational instability analytically through the use of hydrodynamic equations. It is shown that the instability in the rotating Saturnian ring layer may be stabilized by a peculiar particle motion, or "temperature" of a suitable magnitude. A stability criterion is given to suppress the instability of all perturbations including the most unstable spiral ones. We demonstrate that exclusively trailing spirals can be formed in Saturn's A nd B rings. The very existence and the value of the critical wavelength of the fine-scale structure is explained. Theoretical predictions are compared with numerical simulations. The stability analysis presented here would have to be regarded as an explanation of the almost regular periodic structure in the range of few tens to few hundreds meters in Saturn's A and Brings that has been recently revealed by Cassini spacecraft high-resolution measurements.

Original languageEnglish
Title of host publicationSpace Exploration Research
PublisherNova Science Publishers, Inc.
Number of pages64
ISBN (Electronic)9781616682125
ISBN (Print)9781606922644
StatePublished - 1 Jan 2009


  • Planetary rings-Saturn
  • Rings-planetary dynamics-instabilities and waves

ASJC Scopus subject areas

  • General Earth and Planetary Sciences
  • General Engineering
  • General Physics and Astronomy


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