ON THE PERSISTENCE OF SMALL REGIONS OF VORTICITY IN THE PROTOPLANETARY NEBULA

The fate of small regions of vorticity in a barotropic model of the protoplanetary nebula is investigated over thousands of years using a finite difference model. It is found that the coherence time for a small island of vorticity depends on its size, strength, orientation, and radial location in the nebula. Anticyclonic vorticity retains its coherence for longer times than cyclonic vorticity due to favorable interactions with the Keplerian shear flow. Rossby waves are generated as a result of mean vorticity gradients across the disk. The two-dimensional nebula evolves from discrete vortices into an axisymmetric flow consisting of small-amplitude vortex sheets at the radial locations of the initial vorticity. These vortex sheets induce an additional small, potential flow velocity superimposed on the Keplerian rotation curve

Inhomogeneous models of the Venus clouds containing sulfur

Based on the suggestion that elemental sulfur is responsible for the yellow color of Venus, calculations are compared at 3.4 microns of the reflectivity phase function of two sulfur containing inhomogeneous cloud models with that of a homogeneous model. Assuming reflectivity observations with 25% or less total error, comparison of the model calculations leads to a minimum detectable mass of sulfur equal to 7% of the mass of sulfuric acid for the inhomogeneous drop model. For the inhomogeneous cloud model the comparison leads to a minimum detectable mass of sulfur between 17% and 38% of the mass of the acid drops, depending upon the actual size of the large particles. It is concluded that moderately accurate 3.4 microns reflectivity observations are capable of detecting quite small amounts of elemental sulfur at the top of the Venus clouds

Accretion in Protoplanetary Disks by Collisional Fusion

The formation of a solar system is believed to have followed a multi-stage process around a protostar. Whipple first noted that planetesimal growth by particle agglomeration is strongly influenced by gas drag; there is a "bottleneck" at the meter scale with such bodies rapidly spiraling into the central star, whereas much smaller or larger particles do not. Thus, successful planetary accretion requires rapid planetesimal growth to km scale. A commonly accepted picture is that for collisional velocities $V_c$ above a certain threshold collisional velocity, ${V_{th}} \sim$ 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 collisions the bottleneck can be overcome by rapid planetesimal growth. While previous work has dealt explicitly 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 that novel aspects of surface phase transitions provide a physical basis for efficient sticking through collisional melting or amphorph-/polymorphization and fusion to extend the collisional velocity range of primary accretion to $\Delta V_c \sim$ 1-100 m s$^{-1}$, which bound both turbulent RMS speeds and the velocity differences between boulder sized and small grains $\sim$ 1-50 m s$^{-1}$. Thus, as inspiraling meter sized bodies collide with smaller particles in this high velocity collisional fusion regime they grow rapidly to km scales and hence settle into stable Keplerian orbits in $\sim$ 10$^5$ years before photoevaporative wind clears the disk of source material.Comment: 11 pages, 7 figures, 1 tabl

The effect of the Coriolis force on Kelvin-Helmholtz-driven mixing in protoplanetary disks

We study the stability of proto-planetary disks with vertical velocity gradients in their equilibrium rotation rates; such gradients are expected to develop when dust settles into the midplane. Using a linear stability analysis of a simple three-layer model, we show that the onset of instability occurs at a larger value of the Richardson number, and therefore for a thicker layer, when the effects of Coriolis forces are included. This analysis also shows that even-symmetry (midplane-crossing) modes develop faster than odd-symmetry ones. These conclusions are corroborated by a large number of nonlinear numerical simulations with two different parameterized prescriptions for the initial (continuous) dust distributions. Based on these numerical experiments, the Richardson number required for marginal stability is more than an order of magnitude larger than the traditional 1/4 value. The dominant modes that grow have horizontal wavelengths of several initial dust scale heights, and in nonlinear stages mix solids fairly homogeneously over a comparable vertical range. We conclude that gravitational instability may be more difficult to achieve than previously thought, and that the vertical distribution of matter within the dust layer is likely globally, rather than locally, determined.Comment: Accepted for publication in Ap

Charging and coagulation of dust in protoplanetary plasma environments

Combining a particle-particle, particle-cluster and cluster-cluster agglomeration model with an aggregate charging model, the coagulation and charging of dust particles in various plasma environments relevant for proto-planetary disks have been investigated. The results show that charged aggregates tend to grow by adding small particles and clusters to larger particles and clusters, leading to greater sizes and masses as compared to neutral aggregates, for the same number of monomers in the aggregate. In addition, aggregates coagulating in a Lorentzian plasma (containing a larger fraction of high-energy plasma particles) are more massive and larger than aggregates coagulating in a Maxwellian plasma, for the same plasma densities and characteristic temperature. Comparisons of the grain structure, utilizing the compactness factor, {\phi}{\sigma}, demonstrate that a Lorentzian plasma environment results in fluffier aggregates, with small {\phi}{\sigma}, which exhibit a narrow compactness factor distribution. Neutral aggregates are more compact, with larger {\phi}{\sigma}, and exhibit a larger variation in fluffiness. Measurement of the compactness factor of large populations of aggregates is shown to provide information on the disk parameters that were present during aggregation

Type I Planet Migration in Nearly Laminar Disks

We describe 2D hydrodynamic simulations of the migration of low-mass planets ($\leq 30 M_{\oplus}$) in nearly laminar disks (viscosity parameter $\alpha < 10^{-3}$) over timescales of several thousand orbit periods. We consider disk masses of 1, 2, and 5 times the minimum mass solar nebula, disk thickness parameters of $H/r = 0.035$ and 0.05, and a variety of $\alpha$ values and planet masses. Disk self-gravity is fully included. Previous analytic work has suggested that Type I planet migration can be halted in disks of sufficiently low turbulent viscosity, for $\alpha \sim 10^{-4}$. The halting is due to a feedback effect of breaking density waves that results in a slight mass redistribution and consequently an increased outward torque contribution. The simulations confirm the existence of a critical mass ($M_{cr} \sim 10 M_{\oplus}$) beyond which migration halts in nearly laminar disks. For \alpha \ga 10^{-3}, density feedback effects are washed out and Type I migration persists. The critical masses are in good agreement with the analytic model of Rafikov (2002). In addition, for \alpha \la 10^{-4} steep density gradients produce a vortex instability, resulting in a small time-varying eccentricity in the planet's orbit and a slight outward migration. Migration in nearly laminar disks may be sufficiently slow to reconcile the timescales of migration theory with those of giant planet formation in the core accretion model.Comment: 3 figures, accepted to ApJ

Material enhancement in protoplanetary nebulae by particle drift through evaporation fronts

Solid material in a protoplanetary nebula is subject to vigorous redistribution processes relative to the nebula gas. Meter-sized particles drift rapidly inwards near the nebula midplane, and material evaporates when the particles cross a condensation/evaporation boundary. The material cannot be removed as fast in its vapor form as it is being supplied in solid form, so its concentration increases locally by a large factor (more than an order of magnitude under nominal conditions). As time goes on, the vapor phase enhancement propagates for long distances inside the evaporation boundary (potentially all the way in to the star). Meanwhile, material is enhanced in its solid form over a characteristic lengthscale outside the evaporation boundary. This effect is applicable to any condensible (water, silicates, {\it etc.}). Three distinct radial enhancement/depletion regimes can be discerned by use of a simple model. Meteoritics applications include oxygen fugacity and isotopic variations, as well as isotopic homogenization in silicates. Planetary system applications include more robust enhancement of solids in Jupiter's core formation region than previously suggested. Astrophysical applications include differential, time-dependent enhancement of vapor phase CO and H$_2$O in the terrestrial planet regions of actively accreting protoplanetary disks.Comment: To appear in Astrophys. J., vol 614, Oct 10 2004 issu

The discovery and dynamical evolution of an object at the outer edge of Saturn's A ring

This work was supported by the Science and Technology Facilities Council (Grant No. ST/F007566/1) and we are grateful to them for financial assistance. C.D.M. is also grateful to the Leverhulme Trust for the award of a Research Fellowshippublisher PDF not permitted, withdraw

Rapid planetesimal formation in turbulent circumstellar discs

The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies (Safronov 1969). How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem (Dominik et al. 2007): boulders stick together poorly (Benz 2000), and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas (Weidenschilling 1977). Gravitational collapse of the solid component has been suggested to overcome this barrier (Safronov 1969, Goldreich & Ward 1973, Youdin & Shu 2002). Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer (Weidenschilling & Cuzzi 1993, Dominik et al. 2007), but turbulence must be present to explain observed gas accretion in protostellar discs (Hartmann 1998). Here we report the discovery of efficient gravitational collapse of boulders in locally overdense regions in the midplane. The boulders concentrate initially in transient high pressures in the turbulent gas (Johansen, Klahr, & Henning 2006), and these concentrations are augmented a further order of magnitude by a streaming instability (Youdin & Goodman 2005, Johansen, Henning, & Klahr 2006, Johansen & Youdin 2007) driven by the relative flow of gas and solids. We find that gravitationally bound clusters form with masses comparable to dwarf planets and containing a distribution of boulder sizes. Gravitational collapse happens much faster than radial drift, offering a possible path to planetesimal formation in accreting circumstellar discs.Comment: To appear in Nature (30 August 2007 issue). 18 pages (in referee mode), 3 figures. Supplementary Information can be found at 0708.389