Glen R. Stewart

Accumulation of a swarm of small planetesimals

Abstract The stage of planetesimal accumulation in which ∼ 10-km planetesimals in the vicinity of 1 AU grow into “planetary embryos” greater than 10 25 to 10 27 g in mass has been studied using the methods of gas dynamics. Particular attention is given to identifying the circumstances for which runaway growth results in the formation of a relatively small number (e.g., 30) of massive (∼4 × 10 26 g) embryos in the terretrial planet region on a time scale of 10 5 to 10 6 years. It is found that under the assumptions made by the Moscow (Safronov and others) and Kyoto (Hayashi and others) “schools,” no runaways are found, in agreement with the conclusions of these investigators. In contrast, when more plausible physical processes are included, e.g., the importance of equipartition of energy in gravitational encounters, the presence of the “seeds” in the initial distribution, enhancement of the gravitational cross section above the two-body value at low velocity, and fragmentation, runaways in the terrestrial planet region are found to be very probable on a time scale of about 10 5 years. The final stage of planetary accumulation may then consist of the accumulation of these embryos into the present planets on a time scale of 10 7 to 10 8 years. At larger heliocentric distances the planetesimal evolution could be different; circumstances may have existed in which runaway growth of Jupiter prevented runaways in the asteroid belt.

Lunar accretion from an impact-generated disk

Although the mechanism by which the Moon was formed is currently unknown, several lines of evidence point to its accretion from a circumterrestrial disk of debris generated by a giant impact on the Earth. Theoretical simulations show that a single large moon can be produced from such a disk in less than a year, and establish a direct relationship between the size of the accreted moon and the initial configuration of the debris disk.

Evolution of planetesimal velocities

Abstract A self-consistent set of equations for the velocity evolution of a general planetesimal population is presented. The equations are given in a form convenient for calculations of the early stages of planetary accumulation, when it is necessary to model the planetesimal swarm by the methods of gas dynamics, rather than follow the orbital evolution of individual bodies. To illustrate the relative importance of the various terms of these equations, steady-state velocities of a simple planetesimal population, consisting of two different sizes of bodies, are calculated. Dynamical friction is found to be an important mechanism for transferring kinetic energy from the larger planetesimals to the smaller ones, providing an energy source for the small planetesimals that is comparable to that provided by the viscous stirring process. When small planetesimals are relatively abundant, gas drag and inelastic collisions among the smaller bodies are of comparable importance for dissipating energy from the population.

BAROCLINIC VORTICITY PRODUCTION IN PROTOPLANETARY DISKS. I. VORTEX FORMATION

The formation of vortices in protoplanetary disks is explored via pseudospectral numerical simulations of an anelastic-gas model. This model is a coupled set of equations for vorticity and temperature in two dimensions that includes baroclinic vorticity production and radiative cooling. Vortex formation is unambiguously shown to be caused by baroclinicity, because (1) these simulations have zero initial perturbation vorticity and a nonzero initial temperature distribution, and (2) turning off the baroclinic term halts vortex formation, as shown by an immediate drop in kinetic energy and vorticity. Vortex strength increases with larger background temperature gradients, warmer background temperatures, larger initial temperature perturbations, higher Reynolds number, and higher resolution. In the simulations presented here, vortices form when the background temperatures are ~200 K and vary radially as r-0.25, the initial vorticity perturbations are zero, the initial temperature perturbations are 5% of the background, and the Reynolds number is 109. A sensitivity study consisting of 74 simulations showed that as resolution and Reynolds number increase, vortices can form with smaller initial temperature perturbations, lower background temperatures, and smaller background temperature gradients. For the parameter ranges of these simulations, the disk is shown to be convectively stable by the Solberg-Hoiland criteria.

Origin of the Different Architectures of the Jovian and Saturnian Satellite Systems

The Jovian regular satellite system mainly consists of four Galilean satellites that have similar masses and are trapped in mutual mean-motion resonances except for the outer satellite, Callisto. On the other hand, the Saturnian regular satellite system has only one big icy body, Titan, and a population of much smaller icy moons. We have investigated the origin of these major differences between the Jovian and Saturnian satellite systems by semi-analytically simulating the growth and orbital migration of proto-satellites in an accreting proto-satellite disk. We set up two different disk evolution/structure models that correspond to Jovian and Saturnian systems, by building upon previously developed models of an actively supplied proto-satellite disk, the formation of gas giants, and observations of young stars. Our simulations extend previous models by including the (1) different termination timescales of gas infall onto the proto-satellite disk and (2) different evolution of a cavity in the disk, between the Jovian and Saturnian systems. We have performed Monte Carlo simulations and have shown that in the case of the Jovian systems, four to five similar-mass satellites are likely to remain trapped in mean-motion resonances. This orbital configuration is formed by type I migration, temporal stopping of the migration near the disk inner edge, and quick truncation of gas infall caused by Jupiter opening a gap in the solar nebula. The Saturnian systems tend to end up with one dominant body in the outer regions caused by the slower decay of gas infall associated with global depletion of the solar nebula. The total mass and compositional zoning of the predicted Jovian and Saturnian satellite systems are consistent with the observed satellite systems.

The collisional dynamics of particulate disks

Abstract We use a Krook equation, modified to allow collisions to be inelastic, to describe the dynamics of a particulate disk. By a simple heuristic argument, we compute the effective collision rate in a disk of spherical particles with a power-law distribution of sizes. For Saturns rings, the effective collision rate for momentum transport is substantially lower than that conventionally estimated on the basis of an observed optical depth at visual wavelengths. We then discuss how the vertically integrated set of moment equations may be closed without the need to discard the third-order moments at the outset; our formulation allows for the possibility of a bent disk. In the limit that the collision frequency is much larger than the orbit frequency, we recover the usual Navier-Stokes equations of viscous hydrodynamics for a thin disk, with an explicit expression for the shear viscosity. For an unperturbed disk, we can solve the krook equation directly, without any assumptions about the magnitude of the collision frequency. Our analytical results, for an unperturbed disk, are in good agreement with the treatments of Hameen-Anttila, of Goldreich and Tremaine , and of Borderies, Goldreich, and Tremaine, using a Boltzmann description for a collection of identical spheres (assumed to be smooth so that the rotational and translational degrees of freedom do not couple). As a final application of the method, we generalize the formation to include the effects of gravitational scattering. This generalization is not crucial for many applications in planetary rings, but it may be important for the discussion of gas clouds in the disk of a spiral galaxy, and it is probably central to the accumulation of planets from smaller bodies in the primitive solar nebula.

BAROCLINIC VORTICITY PRODUCTION IN PROTOPLANETARY DISKS. II. VORTEX GROWTH AND LONGEVITY

The factors affecting vortex growth in convectively stable protoplanetary disks are explored using numerical simulations of a two-dimensional anelastic-gas model that includes baroclinic vorticity production and radiative cooling. The baroclinic feedback, in which anomalous temperature gradients produce vorticity through the baroclinic term and vortices then reinforce these temperature gradients, is found to be an important process in the rate of growth of vortices in the disk. Factors that strengthen the baroclinic feedback include fast radiative cooling, high thermal diffusion, and large radial temperature gradients in the background temperature. When the baroclinic feedback is sufficiently strong, anticyclonic vortices form from initial random perturbations and maintain their strength for the duration of the simulation, for over 600 orbital periods. Based on both simulations and a simple vortex model, we find that the local angular momentum transport due to a single vortex may be inward or outward, depending on its orientation. The global angular momentum transport is highly variable in time and is sometimes negative and sometimes positive. This result is for an anelastic-gas model and does not include shocks that could affect angular momentum transport in a compressible-gas disk.

The role of orbital dynamics and cloud-cloud collisions in the formation of giant molecular clouds in global spiral structures

The role of orbit crowding and cloud-cloud collisions in the formation of GMCs and their organization in global spiral structure is investigated. Both N-body simulations of the cloud system and a detailed analysis of individual particle orbits are used to develop a conceptual understanding of how individual clouds participate in the collective density response. Detailed comparisons are made between a representative cloud-particle simulation in which the cloud particles collide inelastically with one another and give birth to and subsequently interact with young star associations and stripped down simulations in which the cloud particles are allowed to follow ballistic orbits in the absence of cloud-cloud collisions or any star formation processes. Orbit crowding is then related to the behavior of individual particle trajectories in the galactic potential field. The conceptual picture of how GMCs are formed in the clumpy ISMs of spiral galaxies is formulated, and the results are compared in detail with those published by other authors. 68 references.

A gravitational kinetic theory for planetesimals

An analytical theory is developed for the velocity evolution of nonaccreting planetesimal populations, based on the Boltzmann and Fokker-Planck equations. Adapting Shkarofskys calculation of plasma viscosities, the rate of increase in random velocities due to gravitational encounters between planetesimals of equal mass is found to be one-third to one-half Safronovs result. Comparison with Wetherills numerical experiments suggests that the Fokker-Planck equation underestimates the effectiveness of encounters and that Safronovs value is approximately correct. For populations of nonuniform sizes, the Fokker-Planck equation indicates an efficient redistribution of energy from the largest bodies to the smaller ones. By conserving angular momentum, the rate of radial spreading of orbits is also derived.

Evolution of a Terrestrial Multiple-Moon System

The currently favored theory of lunar origin is the giant-impact hypothesis. Recent work that has modeled accretional growth in impact-generated disks has found that systems with one or two large moons and external debris are common outcomes. In this paper we investigate the evolution of terrestrial multiple-moon systems as they evolve due to mutual interactions (including mean motion resonances) and tidal interaction with Earth, using both analytical techniques and numerical integrations. We find that multiple-moon configurations that form from impact-generated disks are typically unstable: these systems will likely evolve into a single-moon state as the moons mutually collide or as the inner moonlet crashes into Earth.