Collective processes in planetary rings

Osterbart, R.; Willerding, E.

doi:10.1016/0032-0633(94)00201-2

Cited by 20 publications

(14 citation statements)

References 19 publications

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“…In low and moderately high optical depth regions of the A and B rings, c ⊥ ∼ 0.1 cm s −1 and σ 0 = 30−100 g cm −2 , thus λ crit = 30−100 m, that is, the wavelength assumes a value of roughly several tens of particle diameters. These values of Q ∼ 2 and λ crit < ∼ 100 m predicted in our analysis are close to Salo (1992Salo ( , 1995, Richardson (1994), Osterbart & Willerding (1995), Griv (1998Griv ( , 2005a, , , Griv & Gedalin (2005), and Griv et al (2006a) numerical results. These fine waves were indeed found in data obtained by the Cassini spacecraft.…”

Section: Fine-scale Structuresupporting

confidence: 88%

“…The free kinetic energy associated with the differential rotation of the system is one possible source for the growth of the energy of these spiral gravity perturbations, and appears to be released when angular momentum is transferred outward. Vandervoort (1970), Yue (1982), Shu (1984), Morozov (1981), Romeo (1992Romeo ( , 1994, and Osterbart & Willerding (1995) already obtained somewhat similar stabilizing factors ∝h by using simplified theories.…”

Section: A3 Dispersion Relationmentioning

confidence: 85%

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Fine-scale density wave structure of Saturn's rings: A hydrodynamic theory

Griv

Gedalin

2010

A&A

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Aims. We examine the linear stability of the Saturnian ring disk of mutually gravitating and physically colliding particles with special emphasis on its fine-scale ∼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. Methods. We analyze the Jeans' instabilities of gravity perturbations (e.g., those produced by a spontaneous disturbance) analytically by using the Navier-Stokes dynamical equations of a compressible fluid. The theory is not restricted by any assumptions about the thickness of the system. We consider a simple model of the system consisting of a three-dimensional ring disk that is weakly inhomogeneous and whose structure is analyzed by making a horizontally local short-wave approximation. Results. We demonstrate that the disk is probably unstable and that gravity perturbations grow effectively within a few orbital periods. We find that self-gravitation plays a key role in the formation of the fine structure. The predictions of the theory are compared with observations of Saturn's rings by the Cassini spacecraft and are found to be in good agreement. In particular, it appears very likely that some of the quasi-periodic microstructures observed in Saturn's A and B rings -both axisymmetric and nonaxisymmetric onesare manifestations of these effects. We argue that the quasi-periodic density enhancements revealed in Cassini data are flattened structures, with a height to width ratio of about 0.3. One should analyze high-resolution of the order of 10 m data acquired for the A and B rings (and probably C ring as well) to confirm this prediction. We also show that the gravitational instability is a potential cluster-forming mechanism leading to the formation of porous 100-m-diameter moonlets of preferred mass ∼10 7 g each embedded in the outer A ring, although this has yet to be directly measured.

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Section: Fine-scale Structuresupporting

confidence: 88%

Section: A3 Dispersion Relationmentioning

confidence: 85%

Fine-scale density wave structure of Saturn's rings: A hydrodynamic theory

Griv

Gedalin

2010

A&A

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“…46 E. Griv, M. Gedalin, E. Liverts, & C. Yuan predict the recurrent structure of order of 100 m (or even less) to be observed in the low and moderately high optical depth regions of the rings A, B, and C. In fact, it should be made clear right from the start that the suggestion of fine-scale~100 m structure in Saturn's rings due to the effect of self-gravity is not an entirely new idea. Apparently, the microstructure in Saturn's rings has already been predicted by local simulations (Salo 1992;Osterbart & Willerding 1995;Richardson 1994;Griv 1998;Daisaka & Ida 1999). Earlier, the so-called quadrupole asymmetry observed in the A ring has been explained in terms of numerous unresolved spiral density "wakes" by Colombo et al (1976) and Franklin et al (1978).…”

Section: Introductionmentioning

confidence: 84%

Modeling of the Saturnian Ring System

Griv

Liverts

Gedalin

et al. 2003

Symp. - Int. Astron. Union

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Abstract. A self-consistent system of the Boltzmann equation and the Poisson equation is used to study the dynamical evolution of Saturn's main A, B, and C rings. The theory, as applied to the Saturnian ring system, predicts for several features, such as numerous irregular density wakes, with size and spacing between them of the order 41rp~21rh, where p is the mean epicycle radius of the particle and h is the typical thickness of the system under study. In Saturn's rings, p~10 m. Computer N-body experiments are desribed which test the validities of the theory. Use of the 112-processor SGI Origin 2000 supercomputer is enabled us to make long runs using a large number of particles in the direct simulation code and thus simulate phenomena not previously studied numerically. We predict that forthcoming in 2004 Cassini spacecraft high-resolution images will reveal this recurrent fine-scale rv 100 m or so structure in low and moderately high optical depth regions of the rings.

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“…4 establishes experimental evidence to support the stability theory developed by Griv and co-workers. Note that Salo (1995), Richardson (1994), Osterbart & Willerding (1995), Sterzik et al (1995), and Daisaka & Ida (1999) number Q of Toomre in relaxed equilibrium disks does not fall below a critical value, which lies about Q crit = 2− 2.5. However, no adequate explanation of the latter has been presented.…”

Section: Fine-scale Structurementioning

confidence: 95%

“…The dynamical behavior of planetary rings has already studied via simplified N -body simulations of an orbiting patch of the ring by Salo (1992Salo ( , 1995, Richardson (1994), Osterbart & Willerding (1995), Sterzik et al (1995), Griv (1998), Daisaka & Ida (1999), and others. See Griv & Gedalin (2003) as a review of the problem.…”

Section: Local Simulationsmentioning

confidence: 99%

Fine-scale density wave structure of Saturn's A, B, and C rings

Griv¹

2004

Proc. IAU

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Abstract. In view of the possibility of employing Cassini's experiments for the diagnosis of the Saturnian ring system, local N -body simulations of low and moderately high optical depth regions of Saturn's main rings are presented. A special emphasis is made on fine-scale spiral structures (irregular cylindric wave-type structures of the order of 100 m or so) of Saturn's A, B, and C rings. It is predicted that Cassini spacecraft high-resolution images of Saturn's rings will reveal this kind of small-scale irregular density wave structure.

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Collective processes in planetary rings

Cited by 20 publications

References 19 publications

Fine-scale density wave structure of Saturn's rings: A hydrodynamic theory

Fine-scale density wave structure of Saturn's rings: A hydrodynamic theory

Modeling of the Saturnian Ring System

Fine-scale density wave structure of Saturn's A, B, and C rings

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