Saturn's rings: Particle size distributions for thin layer models

Zebker, H. A.; Marouf, E. A.; Tyler, G. L.

doi:10.1016/0019-1035(85)90074-0

Cited by 190 publications

(174 citation statements)

References 25 publications

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“…3 and 4 are shown for both limiting kernels [9] and [11], together with their simplified counterparts [12]. The stationary distributions for the systems with the complete kinetic coefficients [9] and [10] have exactly the same slope as the systems with the simplified kernel [12] of the same degree of homogeneity and hence quantitatively agree with the theoretical prediction [15]. Moreover, the numerical solutions demonstrate an exponential cutoff for large k, in agreement with the theoretical predictions.…”

Section: [4]supporting

confidence: 76%

“…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. In the case of complete decomposition into monomers we have γ = μ + 3=2 ( [15]). Hence the above criterion becomes α > 2.…”

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).…”

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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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: 76%

Section: [4]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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“…Furthermore, if ice balls could grow by continued agglomeration until disruptive tidal forces became stronger than the cohesive strength of crystalline ice, we should expect many icy particulates in Saturn's rings to acquire sizes of order $10-100 km. In fact, except for the occasional embedded moonlet (whose origin may lie in the fragmentation of yet larger bodies rather than from the assemblage of ordinary ring particles), the particulates in Saturn's rings have a maximum size $5 m (Zebker, Marouf, & Tyler 1985), intrigu-ingly close to the value implied if collective self-gravity were the only available force to assemble the largest bodies (Shu 1984).…”

Section: Introductionmentioning

confidence: 93%

Planetesimal Formation by Gravitational Instability

Youdin

Shu

2002

ApJ

465

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We investigate the formation of planetesimals via the gravitational instability of solids that have settled to the midplane of a circumstellar disk. Vertical shear between the gas and a subdisk of solids induces turbulent mixing that inhibits gravitational instability. Working in the limit of small, well-coupled particles, we find that the mixing becomes ineffective when the surface density ratio of solids to gas exceeds a critical value. Solids in excess of this precipitation limit can undergo midplane gravitational instability and form planetesimals. However, this saturation effect typically requires increasing the local ratio of solid to gaseous surface density by factors of 2-10 times cosmic abundances, depending on the exact properties of the gas disk. We discuss existing astrophysical mechanisms for augmenting the ratio of solids to gas in protoplanetary disks by such factors and investigate a particular process that depends on the radial variations of orbital drift speeds induced by gas drag. This mechanism can concentrate millimeter-sized chondrules to the supercritical surface density in few Â 10 6 yr, a suggestive timescale for the disappearance of dusty disks around T Tauri stars. We discuss the relevance of our results to some outstanding puzzles in planet formation theory-the size of the observed solar system and the rapid type I migration of Earth-mass bodies.

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“…Zebker et al (1985)). Recent observations by the spacecraft Cassini have shown that a large number of small moons (moonlets) are embedded in Saturn's dense rings being much larger than the usual ring particles (Tiscareno et al (2006); Sremčević et al (2007); Tiscareno et al (2008)).…”

Section: Introductionmentioning

confidence: 99%

Moonlet induced wakes in planetary rings: Analytical model including eccentric orbits of moon and ring particles

Seiß

Spahn

Schmidt

2010

Icarus

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Saturn's rings host two known moons, Pan and Daphnis, which are massive enough to clear circumferential gaps in the ring around their orbits. Both moons create wake patterns at the gap edges by gravitational deflection of the ring material (Cuzzi and Scargle (1985), Showalter et al. (1986)). New Cassini observations revealed that these wavy edges deviate from the sinusoidal waveform, which one would expect from a theory that assumes a circular orbit of the perturbing moon and neglects particle interactions. (2005)), which might be attributed to the neglect of particle interactions and vertical motion in our model.

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Saturn's rings: Particle size distributions for thin layer models

Cited by 190 publications

References 25 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

Planetesimal Formation by Gravitational Instability

Moonlet induced wakes in planetary rings: Analytical model including eccentric orbits of moon and ring particles

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