Stability of Minor-Body Orbits in Systems with Two Giant Planets

Abstract

We have performed a large ensemble of long-term numerical integrations to study the stability of the orbits of minor bodies in systems containing a solar-mass star and two giant planets. Given the large parameter space involved, we have focused on systems in which the inner planet has the mass of Jupiter (MJ) and the outer planet has a mass equal to either MJ or MJ, and where we use an initially dynamically cold (e = 0) minor-body population. We investigated the effects of the planetary semimajor-axis ratio, eccentricity, and inclination on the stability of orbits distributed throughout the system. We show that the behavior of the particles varies from region to region as the result of a complex interplay of the two major types of resonances: resonances associated with commensurabilities of orbital frequencies, and resonances associated with commensurabilities of orbital precession frequencies. In the region inward of the inner planet, mean motion resonances produce instabilities and secular resonances induce high eccentricities in the particles. Between the planets, the mean motion resonances are dominant and generally induce instability. Beyond the outer planet, secular and mean motion resonances overlap and produce wide-scale instability. In this last region, many stable particles are associated with mean motion resonances in various kinds of protective mechanisms. We also show that increased planetary eccentricity generally results in increased instability and that high initial inclination of both planet and test particles greatly changes the final structure of the system. Overall, our results show trends that make it possible to predict the general features of the minor-body distribution for a given set of orbital elements of the planets. We demonstrate this with two examples drawn from the set of observed extrasolar planetary systems.