The dynamics of particle disks

Araki, Suguru

doi:10.1016/0019-1035(88)90150-9

Cited by 47 publications

(10 citation statements)

References 6 publications

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“…b) Ring stability curves in β − e plane at τ = 0.1 (circles) and τ = 1.0 (squares); the dotted line represents the limit curve τ → 0 obtained by Araki (1991). β = 1 (perfectly rough spheres), where the former method predicts a lower critical e, which, however, turns out to be in agreement with a previous calculation (Araki 1988) where non-local collisions effects were neglected. Particular attention has been devoted to reproducing the MD results described in the paper (Wisdom & Tremaine 1988) (hereafter WT), in the case of smooth spheres (β = −1) and constant normal restitution coefficient e = 0.5.…”

Section: Simulations Without Self-gravity Effectssupporting

confidence: 83%

DSMC simulation of the vertical structure of planetary rings

Frezzotti

2001

A&A

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Section: Simulations Without Self-gravity Effectssupporting

confidence: 83%

DSMC simulation of the vertical structure of planetary rings

Frezzotti

2001

A&A

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“…At these densities the applicability of Goldreich and Tremaine's (1978) standard model we are interesting in becomes questionable (Araki 1991a). The collisional dynamics of such very dense rings has been studied by Shukhman (1984), Borderies, Goldreich & Tremaine (1985), Araki & Tremaine (1986), Araki (1988, 1991a,b), Schmit & Tscharnuter (1995, 1999), Salo et al (2001) and Tremaine (2003).…”

Section: Introductionmentioning

confidence: 99%

On the stability of Saturn's rings: a quasi-linear kinetic theory

Griv

Gedalin

Yuan

2003

Monthly Notices of the Royal Astronomical Society

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A self‐consistent system of the Boltzmann kinetic equation and the Poisson equation is used to study the dynamical evolution of Saturn's main A, B and C rings composed of discrete mutually gravitating particles. The simplified case of relatively rare collisions between identical particles, when the collision frequency is smaller than (compared with) the orbital frequency, is examined. Equations describing the quasi‐linear stage of Jeans instability of small‐amplitude gravity perturbations in Saturn's rings are derived and solved analytically. Conditions under which the quasi‐linearization of the Boltzmann equation can be used to describe a wave–particle interaction are calculated with reference to the excitation of Jeans‐type perturbations. The theory, as applied to Saturn's rings, predicts for several features, such as numerous irregular Jeans‐unstable wakes, with size and spacing between them of the order of 2πh≤ 100 m, where h is the typical thickness of the system. The interaction of particles with these almost aperiodically growing gravity perturbations increases both the radial spread of the disc and random velocities of particles in a very short time‐scale of only two to three disc orbital revolutions. The latter leads to an eventual stabilization of the system, unless some effective cooling mechanism exists, reducing the magnitude of the relative velocity of particles. It is suggested that inelastic (dissipative) interparticle impacts provide such a cooling mechanism, leading to the recurrent density waves activity. We predict that the high‐resolution images from the forthcoming (2004) Cassini spacecraft will reveal this fine‐scale recurrent ∼100 m or even less spiral structure in low and moderately high optical depth regions (τ≤ 1, where τ is the normal optical depth) of Saturn's main rings.

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“…Salo (1987b) performed global N-body simulations of collisional evolution of a narrow ring of spinning particles, but gravitational attraction between particles was not taken into account. Analytic studies related to spinning particles included particle gravity only in an approximate manner (Salo 1987a;Araki 1988Araki , 1991Hämeen-Anttila & Salo 1993). Some previous N-body simulations of self-gravitating planetary rings studied the cases with rotation of particles.…”

Section: Introductionmentioning

confidence: 99%

LocalN-Body Simulations for the Rotation Rates of Particles in Planetary Rings

Ohtsuki

Toyama

2005

Astron J

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Using N-body simulations, we examine rotation rates caused by mutual collisions of particles in planetary rings. In the case of particles with a power-law size distribution, we find that the size-dependence of the rms rotation rates can be well approximated by a power law. The overall rotation rates increase for a smaller tangential coefficient of restitution, an increased size of the largest particles, and /or a shallower size distribution of particles. However, the slope of the size dependence of the rotation rates is rather insensitive to these parameter values. This size dependence of the particles' rotation rates needs to be taken into account when developing energy balance models that are used to interpret observations of thermal emission from Saturn's rings.

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The dynamics of particle disks

Cited by 47 publications

References 6 publications

DSMC simulation of the vertical structure of planetary rings

DSMC simulation of the vertical structure of planetary rings

On the stability of Saturn's rings: a quasi-linear kinetic theory

LocalN-Body Simulations for the Rotation Rates of Particles in Planetary Rings

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