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 accr eted from the early solar nebula. The primordial planetesimal swarm evolved in a phase space divided into regimes by separatrices which define their t rajectories and fate. This sorting process is driven by the energy and angu lar momentum and continues to the present day. We reconsider the existence and importance of stable niches in the Jupiter/Saturn zone using highly acc urate numerical techniques based on high-order optimized multistep integrat ion schemes coupled to roundoff error minimizing methods. We repeat the inv estigations of W.M. Weibel et al. (Icarus 83, 382-390, 1990) with one hundr ed thousand massless particles-nearly 10(3) time more particles than our 19 90 investigation. Previous studies of the Jupiter/Saturn zone have employed only hundreds of particles, usually starting on circular and zero inclinat ion orbits. By employing 10(5) particles on both inclinded and eccentric or bits, we can perform a near-exhaustive search for test particle stability a s a function of initial orbital elements. The increase in the numbers of te st particles also facilitates robust statistical inference and comparison w ith analytic results. In our simulations, we observed three stages in the p lanetesimal 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 exponen tially eliminated by random gravitational encounters with Jupiter or Saturn . Finally, the only long-lived particles in the simulation were initially l ocated either at a Lagrange point or in an orbit nearly commensurable with Jupiter or Saturn. We conclude that although niches for planetesimal materi al are rare, extremely high-accuracy long-duration simulations employing ma ny particles will be able to capture even the qualitative nature of early S olar System planetesimal evolution. (C) 1999 Academic Press.