Saturn's Rings II Particle Sizes Inferred from Stellar Occultation Data

French, R. G.

doi:10.1006/icar.2000.6357

Cited by 149 publications

(142 citation statements)

References 26 publications

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“…This is in excellent agreement with observations, where values for q in the range from 2.70 to 3.11 were reported (15,17). Fitting the theory to the particle size distribution of Saturn's A ring inferred from data obtained by the Voyager Radio Science Subsystem (RSS) during a radio occultation of the spacecraft by Saturn's A ring (15), we find R c = 5.5 m (Fig.…”

Section: [4]supporting

confidence: 90%

“…If the additional terms [16] and [17] were negligible, compared with the terms [18] that arise for both models, the emergent steady-state size distributions would be the same. For k 1, one can neglect [16] and [17] compared with [18] if α > γ − μ and α > 1.…”

Section: [4]mentioning

confidence: 99%

“…For k 1, one can neglect [16] and [17] compared with [18] if α > γ − μ and α > 1. Taking into account that the equations for the monomers for the two models coincide when α > 2, we arrive at the following criterion for universality of the steady-state distribution: α > maxfγ − μ, 2g.…”

Section: [4]mentioning

confidence: 99%

“…Rather, ring particles are believed to be involved in active accretion-destruction dynamics (5-13) and their sizes vary over a few orders of magnitude as a power law (14)(15)(16)(17), with a sharp cutoff for large sizes (18)(19)(20)(21). Moreover, tidal forces fail to explain the abrupt decay of the size distribution for house-sized particles (22).…”

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Size distribution of particles in Saturn’s rings from aggregation and fragmentation

Brilliantov

Krapivsky

Bodrova

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

135

129

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Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, ∼ r −q with q ≈ 3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75 ≤ q ≤ 3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn's rings. (1-3) and the observation of rapid processes in the ring system (4) indicate that the shape of the particle size distribution is likely not primordial or a direct result of the ring-creating event. Rather, ring particles are believed to be involved in active accretion-destruction dynamics (5-13) and their sizes vary over a few orders of magnitude as a power law (14-17), with a sharp cutoff for large sizes (18-21). Moreover, tidal forces fail to explain the abrupt decay of the size distribution for house-sized particles (22). One wishes to understand the following: (i) Can the interplay between aggregation and fragmentation lead to the observed size distribution? And (ii) is this distribution peculiar for Saturn's rings, or is it universal for planetary rings in general? To answer these questions quantitatively, one needs to elaborate a detailed model of the kinetic processes in which the ring particles are involved. Here we develop a theory that quantitatively explains the observed properties of the particle size distribution and show that these properties are generic for a steady state, when a balance between aggregation and fragmentation holds. Our model is based on the hypothesis that collisions are binary and that they may be classified as aggregative, restitutive, or disruptive (including collisions with erosion); which type of collision is realized depends on the relative speed of colliding particles and their masses. We apply the kinetic theory of granular gases (23, 24) for the multicomponent system of ring particles to quantify the collision rate and the type of collision. Results and DiscussionModel. Ring particles may be treated as aggregates built up of primary grains (9) of a certain size r 1 and mass m 1 . [Observations indicate that particles below a certain radius are absent in dense rings (16).] Denote by m k = km 1 the mass of rin...

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Section: [4]supporting

confidence: 90%

Section: [4]mentioning

confidence: 99%

Section: [4]mentioning

confidence: 99%

mentioning

confidence: 99%

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Size distribution of particles in Saturn’s rings from aggregation and fragmentation

Brilliantov

Krapivsky

Bodrova

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

135

129

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“…This is a region with optical depth (∼0.075; e.g., Collins et al 1984) such that the assumptions of our model meet reality more closely than, for instance, in the denser B ring. We also note that Porco et al (2005) report, from analysis of the damping length of Atlas' 5:4 and Pan's 7:6 density waves, a characteristic particle size in the Cassini division to be 0.4−0.6 m, an order of magnitude smaller than in the B and A rings (see also French & Nicholson 2000;and Tiscareno et al 2007) and closer to the size range susceptible to radiative perturbations. A typical timescale of a centimetre to decimetre size particle to drift across the Cassini division is surprisingly short from our work 3−10 My only.…”

Section: High Contrast In Optical and Infrared Absorptivitiesmentioning

confidence: 58%

Thermal forces on planetary ring particles: application to the main system of Saturn

Vokrouhlický

Nesvorný

Dones

et al. 2007

A&A

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Context. The motion of small particles in planetary rings is affected in the long-term by radiation forces. While the PoyntingRobertson effect has been extensively discussed and applied to the dynamics of micron-sized ring particles, studies of thermal selfacceleration of particles are only in their infancy. Aims. We extend the pioneering work of Rubincam (2006, Icarus 184, 532) by a more thorough analytical formulation of both planetary and solar thermal forces on ring particles. Methods. Within a sparse disk model we analytically compute both seasonal and diurnal variants of the thermal forces and we demonstrate that the diurnal effect components vanish for a sample of rapidly rotating particles with randomly oriented spin axes. For sufficiently slowly rotating ring particles, though, these diurnal components might significantly modify the expected planetocentric secular drift rates of their orbits. We also take into account the orbital effects of Poynting-Robertson drag that begin to dominate the thermal forces for particles with sizes ≤5 mm. Our formulation of the Poynting-Robertson drag is the first to account properly for the influence of the planetary shadow. Results. We critically review the previous suggestion that Saturn's A and B ring boundaries might correlate with radiative null-torque orbits of small particles. Using the best estimates of optical and thermal parameters of Saturn's ring particles, we show that the millimetre to several centimetre size particles mostly drift inward to the planet with a characteristic radial speed ν r ∼ 3 × 10 −6 cm/s, corresponding to drift across the whole main ring system in ∼(1−5) × 10 8 years if the effects of inter-particle collisions are neglected. The radial speed is comparable to, or even larger than, the effective radial drift rate of small particles due to redistribution of collisional ejecta from micrometeoroid impacts. Therefore, radiation forces may be important for estimating the evolution timescales of Saturn's rings as derived from the ballistic transport theory. We propose that, in addition to collisional coagulation, radiation forces may efficiently remove centimetre-sized particles and thus help explain the observed paucity of these particles in Saturn's rings. A population of particles with spin axes aligned with normal to the disk plane, if it exists, would experience a net outward drift provided their rotation rate is larger than their orbital frequency.

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Hydrodynamic Description of Planetary Rings

Spahn

Schmidt

2006

GAMM-Mitteilungen

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We demonstrate the suitability of a hydrodynamic description of the dynamics of a dense planetary ring considering as an example the viscous oscillatory instability. For the successful application of hydrodynamics the transport coefficients must be known as functions of surface mass density σ and the granular temperature T of the ring material. We arrange scaling laws for these quantities and use parameters determined from particle simulations of a planetary ring. With such a preparation, the theory predicts an oscillatory instability of a dense ring: waves of radial wavelengths λ ≈ 100m...200m evolve, driven by the combined effects of viscous momentum flux and Coriolis force. These predictions are confirmed by direct particle simulations: wavelengths of the unstable modes, their growth rates, as well as the properties of the eigenfunctions of the perturbations. This success bears the hope to explain a class of so-called fine-structure in Saturn's rings, which are poorly understood to date. The experiments of the Cassini-spacecraft in orbit around Saturn offer the unique chance to identify the predicted density features by analyzing the imaging and occultation data.

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Saturn's Rings II Particle Sizes Inferred from Stellar Occultation Data

Cited by 149 publications

References 26 publications

Size distribution of particles in Saturn’s rings from aggregation and fragmentation

Size distribution of particles in Saturn’s rings from aggregation and fragmentation

Thermal forces on planetary ring particles: application to the main system of Saturn

Hydrodynamic Description of Planetary Rings

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