A gas-kinetic stability analysis of self-gravitating and collisional particulate disks with application to Saturn’s rings

Griv, Evgeny; Gedalin, M.; Eichler, David; Yuan, Chi

doi:10.1016/s0032-0633(00)00037-4

Cited by 13 publications

(19 citation statements)

References 109 publications

(209 reference statements)

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“…This paper reports on an investigation of the significance of self-excited (that is, intrinsic), off-resonant, almost aperiodic Jeans instability in Saturn's main rings to the formation of the fine-scale structures. I explored the linear regime of Jeans instabilities in Saturn's rings by means of sliding N -body patch model (e.g., Salo 1992Salo , 1995 and compared those numerical results with the quasi-linear kinetic stability theory by Griv et al (2000Griv et al ( , 2003aGriv et al ( , 2003b and Griv & Gedalin (2003). The aim of the work is to discuss specific astronomical implications of the study to Saturn's rings in view of the possibility of employing Cassini's experiments.…”

Section: Discussionmentioning

confidence: 99%

“…In turn, the "hot" model with c r ≡ 2c ϕ = 2c T is expected to be at best only marginally unstable to the growth of spiral waves. See Griv et al (2000Griv et al ( , 2003aGriv et al ( , 2003b and Griv & Gedalin (2003) for an explanation. In all experiments, initially c z = 0.2c r .…”

Section: Local Simulationsmentioning

confidence: 99%

“…The simulated wake structure rapidly at times t 0.6 reaches nonlinearity, and is thus beyond the scope of our theory (or any corresponding linear analysis of shearing modes). I then simulated a differentially rotating disk which is stable in accordance with the modified stability criterion (Griv et al 2000(Griv et al , 2003a(Griv et al , 2003bGriv & Gedalin 2003). Figure 4 shows the observed evolution of the dynamically hot model with c r = 2c T (or Q = 2, respectively).…”

Section: Fine-scale Structurementioning

confidence: 99%

“…Accordingly, a system of mutually gravitating particles of Saturn's rings exhibits collective, gravitationally unstable modes of motions. A quasi-linear kinetic theory of the almost aperiodic Jeans instability in Saturn's rings has been developed by Griv et al (2000Griv et al ( , 2003aGriv et al ( , 2003b and Griv & Gedalin (2003). The theory predicts that as a direct result of the instability of small-amplitude gravity disturbances the main parts of A, B, and C rings are divided into numerous irregular spiral ringlets of the order of 2π times the local thickness h = 5 − 30 m. Below I describe N -body simulations in order to verify the validities of the theory.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Local Simulationsmentioning

confidence: 99%

Section: Fine-scale Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Griv¹

2004

Proc. IAU

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“…However, below a length scale of a few kilometers, the Voyager's PPS data is too noisy to extract information about the structure: the finest structure observed by PPS is accurately descibed by models of statistical noise combined with stochastic variations resulting from large particles or clumps of particles (Showalter & Nicholson 1990). It was suggested numerically by Salo (1992Salo ( , 1995 and analytically by Griv (1998Griv ( , 2005a, Griv et al (2000Griv et al ( , 2003a, and that far more precise Cassini spacecraft observations would help us to resolve the question.…”

Section: Introductionmentioning

confidence: 99%

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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