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 pla netesimals in the gaps between the outer Solar System planets. We search fo r stable niches in the Saturn/Uranus and Uranus/Neptune zones by employing 10,000 massless particles-many more than previous studies in these two zone s-using high-order optimized multistep integration schemes coupled with rou ndoff error minimizing methods. An additional feature of this study differi ng from its predecessors, is the fact that our initial distributions contai n particles on orbits which are both inclined and noncircular. These initia l distributions were also Gaussian distributed such that the Gaussian peaks were at the midpoint between the neighboring perturbers, The simulations s howed an initial transient phase where the bulk of the primordial planetesi mal swarm was removed from the Solar System within 10(5) years. This is abo ut 10 times longer than we observed in our previous Jupiter/Saturn studies. Next, there was a gravitational relaxation phase where the particles under went a random walk in momentum space and were exponentially eliminated by r andom encounters with the planets. Unlike our previous Jupiter/Saturn simul ation, the particles did not fully relax into a third Lagrangian niche phas e 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 migra te outward and eventually to be cleared out by the outermost planet in the zone. We confirmed that particles with higher eccentricities had shorter li fetimes and that the resonances between the jovian planets "pumped up" the eccentricities of the planetesimals with low-inclination orbits more than t hose with higher inclinations. We estimated the expected lifetime of partic les using kinetic theory and even though the time scale of the Uranus/Neptu ne simulation was 380 times longer than our previous Jupiter/Saturn simulat ion, the planetesimals in the Uranus/Neptune zone were cleared out more qui ckly than those in the Saturn/Uranus zone because of the positions of reson ances with the jovian planets. These resonances had an even greater effect than random gravitational stirring in the winnowing process and confirm tha t 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, onl y 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. Th is suggests that niches for planetesimal material in the jovian planets are rare and may exist either only in extremely narrow bands or in the neighbo rhoods of the triangular Lagrange points of the outer planets. (C) 1999 Aca demic Press.