Dense planetary rings and the viscous overstability

Abstract

This paper examines the onset of the viscous overstability in dense particulate rings. First, we formulate a dense gas kinetic theory that is applicable to the Saturnian system. Our model is essentially that of Araki and Tremaine (1986), which we show can be both simplified and generalised. Second, we put this model to work computing the equilibrium properties of dense planetary rings, which we subsequently compare with the results of N-body simulations, namely those of Salo (1991). Finally, we present the linear stability analyses of these equilibrium states, and derive criteria for the onset of viscous overstability in the self-gravitating and non-self-gravitating cases. These are framed in terms of particle size, orbital frequency, optical depth, and the parameters of the collision law. Our results compare favourably with the simulations of Salo et al. (2001). The accuracy and practicality of the continuum model we develop encourages its general use in future investigations of nonlinear phenomena.

Accepted in Icarus; 58 pages; 15 figures

References in corpus (4)

• The World of the Complex Ginzburg-Landau Equation
• On the origin of irregular structure in Saturn's rings
• Violation of Molecular Chaos in dissipative gases
• The linear stability of dilute particulate rings

Cited by in corpus (11)

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• Hydrodynamical simulations of viscous overstability in Saturn's rings
• The ballistic transport instability in Saturn's rings I: formalism and linear theory
• Density Waves and the Viscous Overstability in Saturn's Rings
• Viscous Overstability in Saturn's Rings: Influence of Collective Self-gravity
• The stress-pressure lag in MRI turbulence and its implications for thermal instability in accretion discs
• Filament formation due to diffusive instabilities in dusty protoplanetary disks
• Planetary Ring Dynamics -- The Streamline Formalism -- 2. Theory of Narrow Rings and Sharp Edges
• Developing a Non-Newtonian Fluid Model for Dust, for Application to Astrophysical Flows
• Thermal hysteresis and front propagation in dense planetary rings