University of Oulu

Lehmann, M., Schmidt, J., Salo, H. (2017) Viscous Overstability in Saturn’s Rings: Influence of Collective Self-gravity. Astrophysical Journal, 851 (2), 125.

Viscous overstability in Saturn’s rings : influence of collective self-gravity

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Author: Lehmann, Marius1; Schmidt, Jürgen1; Salo, Heikki1
Organizations: 1Astronomy Research Unit, University of Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 9.2 MB)
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Language: English
Published: IOP Publishing, 2017
Publish Date: 2019-02-22


We investigate the influence of collective self-gravity forces on the nonlinear, large-scale evolution of the viscous overstability in Saturn’s rings. We numerically solve the axisymmetric nonlinear hydrodynamic equations in the isothermal and non-isothermal approximation, including radial self-gravity and employing transport coefficients derived by Salo et al. We assume optical depths τ = 1.5–2 to model Saturn’s dense rings. Furthermore, local N-body simulations, incorporating vertical and radial collective self-gravity, are performed. Vertical self-gravity is mimicked through an increased frequency of vertical oscillations, while radial self-gravity is approximated by solving the Poisson equation for an axisymmetric thin disk with a Fourier method. Direct particle–particle forces are omitted, which prevents small-scale gravitational instabilities (self-gravity wakes) from forming, an approximation that allows us to study long radial scales and to compare directly the hydrodynamic model and the N-body simulations. Our isothermal and non-isothermal hydrodynamic model results with vanishing self-gravity compare very well with results of Latter & Ogilvie and Rein & Latter, respectively. In contrast, for rings with radial self-gravity we find that the wavelengths of saturated overstable waves settle close to the frequency minimum of the nonlinear dispersion relation, i.e., close to a state of vanishing group velocities of the waves. Good agreement is found between non-isothermal hydrodynamics and N-body simulations for moderate and strong radial self-gravity, while the largest deviations occur for weak self-gravity. The resulting saturation wavelengths of viscous overstability for moderate and strong self-gravity (λ ~ 100–300 m) agree reasonably well with the length scales of axisymmetric periodic microstructure in Saturn’s inner A ring and the B ring, as found by Cassini.

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Series: Astrophysical journal
ISSN: 0004-637X
ISSN-E: 1538-4357
ISSN-L: 0004-637X
Volume: 851
Issue: 2
Article number: 125
DOI: 10.3847/1538-4357/aa97de
Type of Publication: A1 Journal article – refereed
Field of Science: 115 Astronomy and space science
Funding: We acknowledge support from the Academy of Finland and the University of Oulu Graduate School.
Copyright information: © 2017. The American Astronomical Society.