Dynamics Of Planetesimals Research Articles

Giant planet formation — a theoretical timeline

Low mass circumstellar disks are a result of the star formation process. The growth of dust and solid planets in such pre-planetary disks determines many properties of our solar system. Models of the Solar System giant planets indicate an enrichment of heavy elements and imply heavy element cores. Detailed models therefore describe giant planet formation as a consequence of the formation of solid planets that have grown sufficiently large to permanently bind gas from the protoplanetary nebula. The diversity of Solar System and extrasolar giant planets is explained by variations in the core growth rates caused by a coupling of the dynamics of planetesimals and the contraction of the massive envelopes they dive into, as well as by changes in the hydrodynamical accretion behavior of the envelopes resulting from differences in nebula density, temperature and orbital distance. Detailed formation models are able to determine observables as luminosities, radii and effective temperatures of young giant planets. Present observational techniques do now allow to probe star formation regions at ages covering all evolutionary stages of the giant planet formation process.

A tree code for planetesimal dynamics: comparison with a hybrid direct code

We present a tree code for simulations of collisional systems dominated by a central mass. We describe the implementation of the code and the results of some test runs with which the performance of the code was tested. A comparison between the behaviour of the tree code and a direct hybrid integrator is also presented. The main result is that tree codes can be useful in numerical simulations of planetary accretion, especially during intermediate stages, where possible runaway accretion and dynamical friction lead to a population with a few large bodies in low-eccentricity and low-inclination orbits embedded in a large swarm of small planetesimals in rather excited orbits. Some strategies to improve the performance of the code are also discussed.

Planetesimal clusters in a Keplerian disk

It was recently demonstrated by numerical simulations that a turbulent flow in a rotating system is capable of eciently concentrating passively advected particles - having a density larger than the fluid - inside anti-cyclonic vortices. This process has important consequences on the distribution of solid particles in protoplanetary disks, since dust surface densities 1-2 orders of magnitude higher than the background are rapidly reached in vortex cores. However, until now, the role of self-gravitation of captured solids has been neglected. In this work we study the action of mutual gravitational interactions - after the gas has dissipated - over the dynamics of planetesimals inside clusters similar to those created in vortex cores. A comparison is made between the behavior of idealized clusters of planetesimals characterized by ad-hoc velocity profiles, and more complex initial conditions such as those obtained in previous hydrodynamical simulations. We show here that, within the explored interval of parameters, mutual scattering of particles can quickly disperse the cluster. Our results are demonstrated to be not dependent on the resolution employed. It can be concluded that if large planetesimals were formed inside vortex cores, they would be ejected by mutual perturbations.

Symplectically Integrating Close Encounters with the Sun

We present a new symplectic algorithm that has the desirable property of being able to integrate close perihelion passages with the Sun. We have combined this algorithm with our fast and efficient algorithm for studying planetesimal dynamics and planet formation, known as SyMBA. The resulting code can symplectically integrate close encounters between all objects during a simulation, thus removing the main limitation of SyMBA (and related schemes). We believe that this algorithm will be a valuable tool for the study of the violent stages of planet formation.

Direct Large-Scale N-Body Simulations of Planetesimal Dynamics

We describe a new direct numerical method for simulating planetesimal dynamics in which N∼10 6 or more bodies can be evolved simultaneously in three spatial dimensions over hundreds of dynamical times. This represents several orders of magnitude improvement in resolution over previous studies. The advance is made possible through modification of a stable and tested cosmological code optimized for massively parallel computers. However, owing to the excellent scalability and portability of the code, modest clusters of workstations can treat problems with N∼10 5 particles in a practical fashion. The code features algorithms for detection and resolution of collisions and takes into account the strong central force field and flattened Keplerian disk geometry of planetesimal systems. We demonstrate the range of problems that can be addressed by presenting simulations that illustrate oligarchic growth of protoplanets, planet formation in the presence of giant planet perturbations, the formation of the jovian moons, and orbital migration via planetesimal scattering. We also describe methods under development for increasing the timescale of the simulations by several orders of magnitude.

Dynamical Evolution of Planetesimals in the Outer Solar System: I. The Jupiter/Saturn Zone

We report on numerical simulations designed to understand the distribution of small bodies in the Solar System and the winnowing of planetesimals accreted from the early solar nebula. The primordial planetesimal swarm evolved in a phase space divided into regimes by separatrices which define their trajectories and fate. This sorting process is driven by the energy and angular momentum and continues to the present day. We reconsider the existence and importance of stable niches in the Jupiter/Saturn zone using highly accurate numerical techniques based on high-order optimized multistep integration schemes coupled to roundoff error minimizing methods. We repeat the investigations of W. M. Weibel et al. (Icarus83, 382–390, 1990) with one hundred thousand massless particles—nearly 103 time more particles than our 1990 investigation. Previous studies of the Jupiter/Saturn zone have employed only hundreds of particles, usually starting on circular and zero inclination orbits. By employing 105 particles on both inclinded and eccentric orbits, we can perform a near-exhaustive search for test particle stability as a function of initial orbital elements. The increase in the numbers of test particles also facilitates robust statistical inference and comparison with analytic results. In our simulations, we observed three stages in the planetesimal dynamics. At the start of the simulation many planetesimals are quickly eliminated by close approaches to Jupiter or Saturn. Next there is a gravitational relaxation phase where the surviving particles are exponentially eliminated by random gravitational encounters with Jupiter or Saturn. Finally, the only long-lived particles in the simulation were initially located either at a Lagrange point or in an orbit nearly commensurable with Jupiter or Saturn. We conclude that although niches for planetesimal material are rare, extremely high-accuracy long-duration simulations employing many particles will be able to capture even the qualitative nature of early Solar System planetesimal evolution.

A Multiple Time Step Symplectic Algorithm for Integrating Close Encounters

We present a new symplectic algorithm that has the desirable properties of the sophisticated but highly efficient numerical algorithms known as mixed variable symplectic (MVS) methods and that, in addition, can handle close encounters between objects. This technique is based on a variant of the standard MVS methods, but it handles close encounters by employing a multiple time step technique. When the bodies are well separated, the algorithm has the speed of MVS methods, and whenever two bodies suffer a mutual encounter, the time step for the relevant bodies is recursively subdivided to whatever level is required. We demonstrate the power of this method using several tests of the technique. We believe that this algorithm will be a valuable tool for the study of planetesimal dynamics and planet formation.

Gas drag effects on planetesimals in the 2:1 resonance with proto-Jupiter

The combined effects are studied of gas drag and gravitational perturbations by a proto-Jupiter on the orbital evolution of a swarm of planetesimals in the primordial asteroid belt in the 2:1 mean motion resonance region. The gas drag in the primordial nebula causes planetesimals to spiral towards the Sun and, therefore, to cross mean motion resonances with proto-Jupiter. The dynamics of planetesimals are numerically investigated while passing through an inner resonance in a planar model. It is found that eccentricities are drastically increased and the maximum value reached by each planetesimal depends only on the resonance argument ψ at the resonance entry. The higher average eccentricity of the swarm within the resonance borders induces a faster spiralling rate of planetesimals and a consequent decrease of their number density, in particular at the 2:1, the most relevant resonance in the asteroid belt. This phenomenon causes the formation of a gap in the swarm at the resonance location. By intergrating a large number of planetesimal orbits, the gap formation process is analysed; it is found that the planetesimal number density near the resonance centre is reduced to 10–40% of its average value, depending on the free eccentricity assumed for the proto-Jupiter. Relative velocities between planetesimals are increased by a factor of four by resonant perturbations, favouring fragmentation at impacts; higher impact velocities and the reduced planetesimal density slow down the planetesimal accretion process and inhibit the formation of big bodies in the resonance region.

Nebular Gas Drag and Planetary Accretion

We have studied the orbital dynamics of planetesimals whose decay due to gas drag in the primordial solar nebula causes them to spiral sunward and approach a growing planet. The planet is assumed to be on a circular orbit unaffected by gas drag. Particles (planetesimals) originate in circular orbits external to the planet's orbit and are usually coplanar with it. The trajectories of these particles are studied using three-body numerical simulations. Trapping of particles at mean motion resonances with the planet sets a maximum size on the particles which can reach the planet's orbit (Weidenschilling and Davis 1985, Icarus 62, 16-29). We find that the stability of resonance locks depends on a variety of factors, including the strength of the resonance in question, the proximity of other resonances and in some cases a period-doubling transition to chaos as the drag rate is increased.When the particles are small enough to pass through all of the resonances and approach the planet, we find that for realistic solid planet densities only a small fraction (typically 10 to 40%) of the material not trapped in resonances hits the planet. The remainder is transferred into inferior orbits. A planet with a dense extended atmosphere capable of trapping planetesimals may be able to accrete a much larger fraction of the approaching planetesimals. At large orbital decay rates, the impact probability varies as the inverse of the drag parameter. For particles whose vertical motions relative to the plane of the planet's orbit are large compared to the planet's radius, the impact probability varies inversely with the inclination of the particle's orbit.The axial rotation induced by those particles which hit the planet is dependent on the rate of orbital decay. Particles with low orbital decay rates (i.e., the particle semimajor axes evolve by less than a planetary Hill sphere radius in a synodic period when they are 23 Hill spheres from the planet's orbit) produce prograde rotation, as expected for particles accreted from the edge of the planet's accretion zone (Lissauer and Kary 1991, Icarus 94, 126-159). Particles whose orbits decay rapidly produce retrograde rotation, since these particles can approach the planet from anywhere in the accretion zone, and their eccentricities are damped down to near zero on a synodic time scale.

A new tree code method for simulation of planetesimal dynamics

A new tree code method for simulation of planetesimal dynamics is presented. A self-similarity argument is used to restrict the problem to a small patch of a ring of planetesimals at 1 au from the Sun. The code incorporates a sliding box model with periodic boundary conditions and surrounding ghost particles. The tree is self-repairing and exploits the flattened nature of Keplerian discs to maximize efficiency. The code uses a fourth-order force polynomial integration algorithm with individual particle time-steps. Collisions and mergers, which play an important role in planetesimal evolution, are treated in a comprehensive manner