ACCRETIONAL EVOLUTION OF A PLANETESIMAL SWARM .2. THE TERRESTRIAL ZONE

We use our multi-zone simulation code (D. Spaute, S. Weidenschilling, D. R. Davis, and F. Marzari, Icarus 92, 147-164, 1991) to model numeri cally the accretion of a swarm of planetesimals in the region of the t errestrial planets, The hybrid code allows interactions between a cont inuum 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 coll isional and gravitational interactions among the embryos are treated s tochastically 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-stag e models and N-body calculations of the final stage of planetary accre tion. The code has been tested for a variety of assumptions for stirri ng of eccentricities and inclinations by gravitational perturbations a nd the presence or absence of damping by gas drag. Viscous stirring, w hich acts to increase relative velocities of bodies in crossing orbits , produces so-called ''orderly'' growth, with a power-law size distrib ution having most of the mass in the largest bodies. Addition of dynam ical friction, which tends to equalize kinetic energies and damp the v elocities of the more massive bodies, produces rapid ''runaway'' growt h of a small number of embryos. Their later evolution is affected by d istant perturbations between bodies in non-crossing orbits. Distant pe rturbations increase eccentricities while allowing inclinations to rem ain low, promoting collisions between embryos and reducing their tende ncy to become dynamically isolated. Growth is aided by orbital decay o f smaller bodies due to gas drag, which prevents them from being stran ded between orbits of the embryos. We report results of a large-scale simulation of accretion in the region of terrestrial planets, employin g 100 zones spanning the range 0.5 to 1.5 AU and spanning 10(6) years of model time. The final masses of the largest bodies are several time s 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. Longe r time scales, additional physical phenomena, and/or a more massive sw arm may be needed to produce Earth-like planets. (C) 1997 Academic Pre ss.