Accretional Evolution of a Planetesimal Swarm

We use our multi-zone simulation code (D. Spaute, S. Weidenschilling, D. R. Davis, and F. Marzari,Icarus92,147–164, 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 andN-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 1.5 AU and spanning 106years 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 planetesimal 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.