Terrestrial Planet Formation Surrounding Close Binary Stars

Disk material has been observed around both components of some young close binary star systems. It has been shown that if planets form at the right places within such disks, they can remain dynamically stable for very long times. Herein, we numerically simulate the late stages of terrestrial planet growth in circumbinary disks around 'close' binary star systems with stellar separations between 0.05 AU and 0.4 AU and binary eccentricities up to 0.8. In each simulation, the sum of the masses of the two stars is 1 solar mass, and giant planets are included. Our results are statistically compared to a set of planet formation simulations in the Sun-Jupiter-Saturn system that begin with essentially the same initial disk of protoplanets. The planetary systems formed around binaries with apastron distances less than ~ 0.2 AU are very similar to those around single stars, whereas those with larger maximum separations tend to be sparcer, with fewer planets, especially interior to 1 AU. We also provide formulae that can be used to scale results of planetary accretion simulations to various systems with different total stellar mass, disk sizes, and planetesimal masses and densities.Comment: 60 pages, 4 tables, and 11 low resolution eps figures. Article with high resolution figures is available at http://www-personal.umich.edu/~equintan/publications.html . Accepted for publication in Icaru

A scaling law for accretion zone sizes

Current theories of runaway planetary accretion require small random velocities of the accreted particles. Two body gravitational accretion cross sections which ignore tidal perturbations of the Sun are not valid for the slow encounters which occur at low relative velocities. Wetherill and Cox have studied accretion cross sections for rocky protoplanets orbiting at 1 AU. Using analytic methods based on Hill's lunar theory, one can scale these results for protoplanets that occupy the same fraction of their Hill sphere as does a rocky body at 1 AU. Generalization to bodies of different sizes is achieved here by numerical integrations of the three-body problem. Starting at initial positions far from the accreting body, test particles are allowed to encounter the body once, and the cross section is computed. A power law is found relating the cross section to the radius of the accreting body (of fixed mass)

Composition of Massive Giant Planets

The two current models for giant planet formation are core accretion and disk instability. We discuss the core masses and overall planetary enrichment in heavy elements predicted by the two formation models, and show that both models could lead to a large range of final compositions. For example, both can form giant planets with nearly stellar compositions. However, low-mass giant planets, enriched in heavy elements compared to their host stars, are more easily explained by the core accretion model. The final structure of the planets, i.e., the distribution of heavy elements, is not firmly constrained in either formation model.Comment: 6 pages, Proceedings of IAU Symposium 276 (Invited talk), The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution. Turin, Italy, Oct. 201

Formation of Giant Planets and Brown Dwarves

According to the prevailing core instability model, giant planets begin their growth by the accumulation of small solid bodies, as do terrestrial planets. However, unlike terrestrial planets, the growing giant planet cores become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. Models predict that rocky planets should form in orbit about most stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large enough to gravitationally trap substantial quantities of gas. Ongoing theoretical modeling of accretion of giant planet atmospheres, as well as observations of protoplanetary disks, will help decide this issue. Observations of extrasolar planets around main sequence stars can only provide a lower limit on giant planet formation frequency . This is because after giant planets form, gravitational interactions with material within the protoplanetary disk may cause them to migrat~ inwards and be lost to the central star. The core instability model can only produce planets greater than a few jovian masses within protoplanetary disks that are more viscous than most such disks are believed to be. Thus, few brown dwarves (objects massive enough to undergo substantial deuterium fusion, estimated to occur above approximately 13 jovian masses) are likely to be formed in this manner. Most brown dwarves, as well as an unknown number of free-floating objects of planetary mass, are probably formed as are stars, by the collapse of extended gas/dust clouds into more compact objects

Collision probabilities in the presence of nebular gas drag

We are developing a model to determine what fraction of the planetesimals would have hit a protoplanet on their sunward journey as opposed to having a close approach and passing into an inferior orbit. The model involves direct numerical integration of restricted-three-body orbits using a predictor-corrector integrator. A simple gas drag law with a v(exp 2) dependence was also included in the equations of motion. Runs of 100 to 500 particles were already performed, while some future runs may require several times this number in order to get good impact statistics. All planetesimals start in superior orbits with semi-major axes 5 to 10 R(sub H) from the protoplanets, where R(sub H) is the protoplanet's Hill Sphere radius. The orbit is followed until the planetesimal passed into an inferior orbit at least 10 R(sub H) from the protoplanet. This process typically requires 10(exp 4) to 10(exp 5) orbits

Long-term evolution of a planetesimal swarm in the vicinity of a protoplanet

Many models of planet formation involve scenarios in which one or a few large protoplanets interact with a swarm of much smaller planetesimals. In such scenarios, three-body perturbations by the protoplanet as well as mutual collisions and gravitational interactions between the swarm bodies are important in determining the velocity distribution of the swarm. We are developing a model to examine the effects of these processes on the evolution of a planetesimal swarm. The model consists of a combination of numerical integrations of the gravitational influence of one (or a few) massive protoplanets on swarm bodies together with a statistical treatment of the interactions between the planetesimals. Integrating the planetesimal orbits allows us to take into account effects that are difficult to model analytically or statistically, such as three-body collision cross-sections and resonant perturbations by the protoplanet, while using a statistical treatment for the particle-particle interactions allows us to use a large enough sample to obtain meaningful results