Dynamical evolution of planetesimals in the outer solar system - II. The Saturn/Uranus and Uranus/Neptune zones

We report on numerical simulations exploring the dynamical stability of planetesimals in the gaps between the outer Solar System planets. We search for stable niches in the Saturn/Uranus and Uranus/Neptune zones by employing 10,000 massless particles-many more than previous studies in these two zones-using high-order optimized multistep integration schemes coupled with roundoff error minimizing methods. An additional feature of this study differing from its predecessors, is the fact that our initial distributions contain particles on orbits which are both inclined and noncircular. These initial distributions were also Gaussian distributed such that the Gaussian peaks were at the midpoint between the neighboring perturbers, The simulations showed an initial transient phase where the bulk of the primordial planetesimal swarm was removed from the Solar System within 10(5) years. This is about 10 times longer than we observed in our previous Jupiter/Saturn studies. Next, there was a gravitational relaxation phase where the particles underwent a random walk in momentum space and were exponentially eliminated by random encounters with the planets. Unlike our previous Jupiter/Saturn simulation, the particles did not fully relax into a third Lagrangian niche phase where long-lived particles are at Lagrange points or stable niches. This is either because the Lagrangian niche phase never occurs or because these simulations did not have enough particles for this third phase to manifest. In these simulations, there was a general trend for the particles to migrate outward and eventually to be cleared out by the outermost planet in the zone. We confirmed that particles with higher eccentricities had shorter lifetimes and that the resonances between the jovian planets "pumped up" the eccentricities of the planetesimals with low-inclination orbits more than those with higher inclinations. We estimated the expected lifetime of particles using kinetic theory and even though the time scale of the Uranus/Neptune simulation was 380 times longer than our previous Jupiter/Saturn simulation, the planetesimals in the Uranus/Neptune zone were cleared out more quickly than those in the Saturn/Uranus zone because of the positions of resonances with the jovian planets. These resonances had an even greater effect than random gravitational stirring in the winnowing process and confirm that all the jovian planets are necessary in long simulations. Even though we observed several long-lived zones near 12.5, 14.4, 16, 24.5, and 26 AU, only two particles remained at the end of the 10(9)-year integration: one near the 2:3 Saturn resonance, and the other near the Neptune 1:1 resonance. This suggests that niches for planetesimal material in the jovian planets are rare and may exist either only in extremely narrow bands or in the neighborhoods of the triangular Lagrange points of the outer planets. (C) 1999 Academic Press.