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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2005.11.017 Byline: S.J. Weidenschilling Keywords: Solar nebula; Planetesimals Abstract: In the absence of global turbulence, solid particles in the solar nebula tend to settle into a thin layer in the central plane. Shear between this layer and pressure-supported gas produces localized turbulence in the midplane; the thickness of the particle layer is determined by balance between settling and turbulent diffusion. A numerical model is described, which allows computation of the vertical structure of a layer of particles of arbitrary size, with self-consistent distributions of particle density, turbulent velocity, and radial fluxes of particles and gas. Effects of varying particle size and the abundances of solids and gas are evaluated. If the surface density of solids is increased by an order of magnitude over nominal solar abundance, the peak density within a layer of small particles can approach the critical value needed for gravitational instability. However, depletion of the nebular gas is much less effective for raising the density of such a layer to the critical value, due to decreased coupling of particles to the gas as the density of the gas decreases. The variation of radial particle flux with surface density of the particle layer is not consistent with secular instability of the layer driven by gas drag. Author Affiliation: Planetary Science Institute, 1700 E. Fort Lowell Rd., Suite 106, Tucson, AZ 85719-2395, USA Article History: Received 4 August 2005; Revised 4 November 2005

For standard cosmic abundances of heavy elements, a layer of small particles in the central plane of the solar nebula cannot attain the critical density for gravitational instability. Youdin and Shu (2002, Astrophys. J. 580, 494--505) suggest that the local surface density of solids can be enhanced by radial migration of particles due to gas drag. However, they consider only motions of individual particles. Collective motion due to turbulent stress on the particle layer acts to inhibit such enhancement and may prevent gravitational instability. Keywords: Planetesimals; Solar nebula

The observed transneptunian binaries, with components of comparable mass and large separations, cannot be the result of collisions in the present dynamical environment of the Kuiper belt. They could be produced by collision of two planetesimals within the sphere of influence of a third body during low-velocity accretion in the solar nebula. Thus, they are primordial. Key Words: planetesimal; Kuiper belt; binaries; transneptunian objects.

Most extrasolar planets discovered to date are more massive than Jupiter, in surprisingly small orbits (semimajor axes less than 3 AU). Many of these have significant orbital eccentricities. Such orbits may be the product of dynamical interactions in multiplanet systems. We examine outcomes of such evolution in systems of three Jupiter-mass planets around a solar-mass star by integration of their orbits in three dimensions. Such systems are unstable for a broad range of initial conditions, with mutual perturbations leading to crossing orbits and close encounters. The time scale for instability to develop depends on the initial orbital spacing; some configurations become chaotic after delays exceeding [10.sup.8] y. The most common outcome of gravitational scattering by close encounters is hyperbolic ejection of one planet. Of the two survivors, one is moved closer to the star and the other is left in a distant orbit; for systems with equal-mass planets, there is no correlation between initial and final orbital positions. Both survivors may have significant eccentricities, and the mutual inclination of their orbits can be large. The inner survivor's semimajor axis is usually about half that of the innermost starting orbit. Gravitational scattering alone cannot produce the observed excess of 'hot Jupiters' in close circular orbits. However, those scattered planets with large eccentricities and small periastron distances may become circularized if tidal dissipation is effective. Most stars with a massive planet in an eccentric orbit should have at least one additional planet of comparable mass in a more distant orbit.

Chondrules are millimeter-scale igneous silicate spherules that constitute as much as half of the mass of chondrites, the most common type of meteorite. Many sources for chondrules have been proposed(1), [...], Isotopic dating indicates that chondrules were produced a few million years after the solar nebula formed. This timing is incompatible with dynamical lifetimes of small particles in the nebula and short time scales for the formation of planetesimals. Temporal and dynamical constraints can be reconciled if chondrules were produced by heating of debris from disrupted first-generation planetesimals. Jovian resonances can excite planetesimal eccentricities enough to cause collisional disruption and melting of dust by bow shocks in the nebular gas. The ages of chondrules may indicate the times of Jupiter's formation and dissipation of gas from the asteroidal region.

We use our multi-zone simulation code (D. Spaute, S. Weidenschilling, D. R. Davis, and F. Marzari, Icarus 92, 147-164, 1991) to model numerically the accretion of a swarm of planetesimals in the region of the terrestrial planets. The hybrid code allows interactions between a continuum distribution of small bodies in a series of orbital zones and a population of large, discrete planetary embryos in individual orbits. Orbital eccentricities and inclinations evolve independently, and collisional and gravitational interactions among the embryos are treated stochastically by a Monte Carlo approach. The spatial resolution of our code allows modeling of the intermediate stage when particle-in-a-box methods lose validity due to nonuniformity in the planetesimal swarm. The simulations presented here bridge the gap between such early-stage models and N-body calculations of the final stage of planetary accretion. The code has been tested for a variety of assumptions for stirring of eccentricities and inclinations by gravitational perturbations and the presence or absence of damping by gas drag. Viscous stirring, which acts to increase relative velocities of bodies in crossing orbits, produces so-called 'orderly' growth, with a power-law size distribution having most of the mass in the largest bodies. Addition of dynamical friction, which tends to equalize kinetic energies and damp the velocities of the more massive bodies, produces rapid 'runaway' growth of a small number of embryos. Their later evolution is affected by distant perturbations between bodies in non-crossing orbits. Distant perturbations increase eccentricities while allowing inclinations to remain low, promoting collisions between embryos and reducing their tendency to become dynamically isolated. Growth is aided by orbital decay of smaller bodies due to gas drag, which prevents them from being stranded between orbits of the embryos. We report results of a large-scale simulation of accretion in the region of terrestrial planets, employing 100 zones spanning the range 0.5 to .5 AU and spanning [10.sup.6] years of model time. The final masses of the largest bodies are several times larger than predicted by a simple analytic model of runaway growth, but a minimal-mass planetisimal swarm still yields smaller bodies, in more closely spaced orbits, than the actual terrestrial planets. Longer time scales, additional physical phenomena, and/or a more massive swarm may be needed to produce Earth-like planets.

Comets originated as icy planetesimals in the outer Solar System, as shown by dynamical studies and direct observation of objects in the Kuiper disk. Their nuclei have low strength consistent with 'rubble pile' structure and inhomogeneities on scales of tens to hundreds of meters. These properties can be explained by their formation process in the solar nebula. I present results of numerical simulation of the growth of cometesimals, beginning with a uniform mixture of microscopic grains in the nebular gas. Coagulation and settling yield a thin, dense layer of small aggregates in the central plane of the nebula. Shear between this layer and the pressure-supported gas produces turbulence that initially inhibits gravitational instability. Particles grow by collisional coagulation; relative velocities are dominated by radial motion due to orbital decay induced by gas drag. The radial velocity dispersion further delays gravitational instability until the mean particle size reaches tens of meters. Lack of damping in the swarm of macroscopic particles limits gravitational instability to large scales that do not allow collapse to solid bodies. Collisional coagulation is responsible for growth even after instability occurs. The size distribution of cometesimals growing by drag-induced collisions develops a narrow peak in the range tens to hundreds of meters. This occurs because drag-induced velocities decrease with size in this range, while gravitational focusing is negligible. Impact velocities have a minimum at the transition from drag-driven to gravitational accretion at approximately kilometer sizes. Bodies accreted in this manner should have low mechanical strength and macroscopic voids in addition to small-scale porosity. They will be composed of structural elements having a variety of scales, but with some tendency for preferential sizes in the range [approximately]10-100 m. These properties are in good agreement with inferred properties of comets, which may preserve a physical record of their accretion.

Poynting-Robertson drag causes an orbital decay in the grains orbiting a star and they behave like planets, in resonance with planetary motions. The conditions for trapping such grains in a circular restricted three-body problem is examined, and a criterion for trapping in terms of the radiation pressure factor, beta, is derived. The derivation of the criterion in terms of planetary mass, resonance location and grain's orbital velocity are also performed. The criteria determined are in perfect agreement with the results of multiplanet simulations and three-body orbital integrations.

Gravitational instability occurs only in a layer of macroscopic bodies that are greater than tens of meters in size because the presence of nebular gas prevents instabilities in smaller bodies. A decrease in velocity dispersion, due to particle growth, initiates instability rather than critical densities as previously proposed. Gravitational instability does not play any role in planetesimal formation rather planetesimals are formed by collisional coagulation.

Studies of the origin of cometary nuclei suggest the involvement of a two stage process involving collisional coagulation in the solar nebula and macroscopic body layer gravitational instability. The data from comet Shoemaker-Levy reveal that fragment size of 10 square to 10 cube m may suggest a composite of about 20 primary nuclei. The disappearance of each fragment behind the planet may reveal details of mass and energy deposition in Jupiter's atmosphere.

N. J. S. Stacy et al.[1] have dealt a blow to the hypothesis that ice deposits may exist in permanently shadowed regions at the lunar poles. Their ground-based radar observations [...]

Argues that the observed sizes and structure of comet nuclei are better explained by a two-stage process. Involvement of elements of models; Collisional coagulation in the solar nebula; Gravitational instability of a layer of macroscopic bodies.