Late Orbital Instabilities in the Outer Planets Induced by Interaction with a Self-gravitating Planetesimal Disk

We revisit the issue of the cause of the dynamical instability during the so-called Nice model, which describes the early dynamical evolution of the giant planets. In particular, we address the problem of the interaction of planets with a distant planetesimal disk in the time interval between the dispersal of the proto-solar nebula and the instability. In contrast to previous works, we assume that the inner edge of the planetesimal disk is several AUs beyond the orbit of the outermost planet, so that no close encounters between planets and planetesimals occur. Moreover, we model the disk's viscous stirring, induced by the presence of embedded Pluto-sized objects. The four outer planets are assumed to be initially locked in a multi-resonant state that most likely resulted from a preceding phase of gas-driven migration. We show that viscous stirring leads to an irreversible exchange of energy between a planet and a planetesimal disk even in the absence of close encounters between the planet and disk particles. The process is mainly driven by the most eccentric planet, which is the inner ice giant in the case studied here. In isolation, this would cause this ice giant to migrate inward. However, because it is locked in resonance with Saturn, its eccentricity increases due to adiabatic invariance. During this process, the system crosses many weak secular resonances--many of which can disrupt the mean motion resonance and make the planetary system unstable. We argue that this basic dynamical process would work in many generic multi-resonant systems--forcing a good fraction of them to become unstable. Because the energy exchange proceeds at a very slow pace, the instability manifests itself late, on a timescale consistent with the epoch of the late heavy bombardment (~700 Myr). In the migration mechanism presented here, the instability time is much less sensitive to the properties of the planetesimal disk (particularly the location of its inner edge) than in the classic Nice model mechanism.