Structure, stability and evolution of Saturn's rings

Bridges, F.; Hatzes, A. P.; Lin, D. N. C.

doi:10.1038/309333a0

Cited by 346 publications

(282 citation statements)

References 15 publications

Supporting

Mentioning

259

Contrasting

Unclassified

Order By: Relevance

“…While the stresses in solid/solid collisions have been embodied in a range of planetesimal studies through examination of, among other things, the restitution coefficient (Chokshi et al 1993;Bridges et al 1996;Higa et al 1998;Güttler et al 2010), their influence on the bulk and interfacial phase behavior has heretofore received little attention. Due to a combination of accessibility and the dual role of relevance to both the formation of the gas giants and the dynamics of Saturn's rings, there have been a number of experiments on the collisions of ice particles under various conditions (e.g., Bridges et al 1984Bridges et al , 1996Higa et al 1998;Dominik et al 2007;Blum & Wurm 2008), but none at the very high pressures and low temperatures where this new mechanism is operative. Depending on the temperature and pressure, many materials can take on multiple equilibrium crystal structures (polymorphs) and moreover, under other conditions the crystalline order of one of the polymorphs can be lost and the system becomes amorphous such as the case with glass.…”

Section: Overview Of Resultsmentioning

confidence: 99%

Accretion in Protoplanetary Disks by Collisional Fusion

Wettlaufer

2010

ApJ

View full text Add to dashboard Cite

The formation of a solar system such as ours is believed to have followed a multi-stage process around a protostar and its associated accretion disk. Whipple first noted that planetesimal growth by particle agglomeration is strongly influenced by gas drag, and Cuzzi and colleagues have shown that when midplane particle mass densities approach or exceed those of the gas, solid-solid interactions dominate the drag effect. The size dependence of the drag creates a "bottleneck" at the meter scale with such bodies rapidly spiraling into the central star, whereas much smaller or larger particles do not. Independent of whether the origin of the drag is angular momentum exchange with gas or solids in the disk, successful planetary accretion requires rapid planetesimal growth to kilometer scales. A commonly accepted picture is that for collisional velocities V c above a certain threshold value, V th ∼ 0.1-10 cm s −1 , particle agglomeration is not possible; elastic rebound overcomes attractive surface and intermolecular forces. However, if perfect sticking is assumed for all ranges of interparticle collision speeds the bottleneck can be overcome by rapid planetesimal growth. While previous work has dealt with the influences of collisional pressures and the possibility of particle fracture or penetration, the basic role of the phase behavior of matter-phase diagrams, amorphs, and polymorphs-has been neglected. Here, it is demonstrated for compact bodies that novel aspects of surface phase transitions provide a physical basis for efficient sticking through collisional melting/amorphization/ polymorphization and subsequent fusion/annealing to extend the collisional velocity range of primary accretion to ΔV c ∼ 1-100 m s −1 V th , which encompasses both typical turbulent rms speeds and the velocity differences between boulder-sized and small grains ∼1-50 m s −1 . Therefore, as inspiraling meter-sized bodies collide with smaller particles in this high velocity collisional fusion regime they grow sufficiently rapidly to ∼0.1-1 km scale and settle into stable Keplerian orbits in ∼10 5 years before photoevaporative wind clears the disk of source material. The basic theory applies to low and high melting temperature materials and thus to the inner and outer regions of a nebula.

show abstract

Section: Overview Of Resultsmentioning

confidence: 99%

Accretion in Protoplanetary Disks by Collisional Fusion

Wettlaufer

2010

ApJ

View full text Add to dashboard Cite

show abstract

“…The simulation box is located at a distance of 100,000 km of a mass point of one saturnian mass. For the inelasticity of the particles we take the standard formula of Bridges et al (1984) for an impact velocity dependent coefficient of restitution. For a description of the simulation method see Salo (1991Salo ( , 1995.…”

Section: Comparison Of Theory and Simulationmentioning

confidence: 99%

Viscous Overstability in Saturn's B-Ring II. Hydrodynamic Theory and Comparison to Simulations

Schmidt¹

2001

Icarus

View full text Add to dashboard Cite

We investigate the viscous oscillatory instability (overstability) of an unperturbed dense planetary ring, an instability that might play a role in the formation of radial structure in Saturn's B-ring. We generalize existing hydrodynamic models by including the heat flow equation in the analysis and compare our results to the development of overstable modes in local particle simulations. With the heat flow, in addition to the balance equations for mass and momentum, we take into account the balance law for the energy of the random motion; i.e., we allow for a thermal mode in a stability analysis of the stationary Keplerian flow. We also incorporate the effects of nonlocal transport of momentum and energy on the stability of the ring. In a companion paper (Salo, H., J. Schmidt, and F. Spahn 2001. Icarus, doi:10.1006/icar.2001.6680) we describe the determination of the local and nonlocal parts of the viscosity, the heat conductivity, the pressure, as well as the collisional cooling, together with their dependences on temperature and density, in local event-driven simulations of a planetary ring. The ring's self-gravity is taken into account in these simulations by an enhancement of the frequency of vertical oscillations z > . We use these values as parameters in our hydrodynamic model for the comparison to overstability in simulated rings of meter-sized inelastic particles of large optical depth with z / = 3.6. We find that the inclusion of the energy-balance equation has a stabilizing influence on the overstable modes, shifting the stability boundary to higher optical depths, and moderating the growth rates of the instability, as compared to a purely isothermal treatment. The non-isothermal model predicts correctly the growth rates and oscillation frequencies of overstable modes in the simulations, as well as the phase shifts and relative amplitudes of the perturbations in density and radial and tangential velocity.

show abstract

“…[14,15,16]) nor with basic mechanics of particle collisions [17]. The coefficient of restitution depends on the impact velocity g and tends to unity for very small g. As a consequence, particles behave more and more elastically as the average velocity of the grains decreases.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamics and transport coefficients for dilute granular gases

Brilliantov

Pöschel

2003

Phys. Rev. E

View full text Add to dashboard Cite

The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, is developed using a modified ChapmanEnskog approach. We derive the hydrodynamic equations and the according transport coefficients with the assumption that the shape of the velocity distribution function follows adiabatically the decaying temperature. We show numerically that this approximation is justified up to intermediate dissipation. The transport coefficients and the coefficient of cooling are expressed in terms of the elastic and dissipative parameters of the particle material and by the gas parameters. The dependence of these coefficients on temperature differs qualitatively from that obtained with the simplifying assumption of a constant coefficient of restitution which was used in previous studies. The approach formulated for gases of viscoelastic particles may be applied also for other impactvelocity dependencies of the restitution coefficient.

show abstract

Structure, stability and evolution of Saturn's rings

Cited by 346 publications

References 15 publications

Accretion in Protoplanetary Disks by Collisional Fusion

Accretion in Protoplanetary Disks by Collisional Fusion

Viscous Overstability in Saturn's B-Ring II. Hydrodynamic Theory and Comparison to Simulations

Hydrodynamics and transport coefficients for dilute granular gases

Contact Info

Product

Resources

About