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H. Latter, G. Ogilvie (DAMTP, University of Cambridge)
Irregular structure in planetary rings, in particular Saturn's B-ring, has often been attributed to instabilities of a homogeneous state, which have previously been analysed in the context of simple hydrodynamic models. We examine the effects of velocity anisotropy and a non-Newtonian viscous stress on the linear stability of a dilute planetary ring using a kinetic model, solving the linearised moment equations derived by Shu and Stewart [\emph{Icarus} \textbf{62} (1985) 360 ]. These admit analytic stability criteria for the viscous overstability and viscous instability. The criteria are compared with those of a hydrodynamic model incorporating the viscosity and cooling function computed from the kinetic steady state. We find the two agree in the `hydrodynamic limit', (i.e. many collisions per orbit) but disagree in the intermediate range, where we expect the viscous stress to become non-Newtonian and anisotropy to increase. In particular hydrodynamics predicts viscous overstability for a larger section of parameter space. In addition we also numerically solve the linearised equations of the more accurate Goldreich and Tremaine kinetic model [\emph{Icarus} \textbf{34} (1978) 227] and discover its linear stability to be qualitatively the same as that of Shu and Stewart. Thus the simple Krook collision operator employed in the latter appears to be an adequate approximation, at least in the linear regime. We discuss the consequences of this analysis for future nonlinear studies of instabilities in dilute and dense planetary rings
The author(s) of this abstract have provided an email address for comments about the abstract: hl278@damtp.cam.ac.uk
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Bulletin of the American Astronomical Society, 37 #3
© 2004. The American Astronomical Soceity.