On the mechanisms for instabilities in compact multiplanet systems

The fact that we often only observe solar system and extrasolar bodies after billions to trillions of dynamical timescales of orbital evolution motivates understanding their long-term stability in order to meaningfully interpret their histories and formation. Criteria for the long-term stability of co-planar, compact two-planet systems are now well understood analytically, both for initially circular orbits and for the general eccentric case. The dynamical behavior in such cases separates quite sharply into long-lived configurations and ones that quickly destabilize. By contrast, there is a qualitative change for compact systems of higher planet multiplicity, which have been found numerically to exhibit a much broader dynamic range of instability timescales, over a significantly wider range of interplanetary separations. Overlap of three-body resonances has been identified as a promising route to chaos in these higher multiplicity systems, which is clearly inaccessible in two-planet systems. Analytic modeling of the diffusion due to the overlap of such resonances can accurately predict instability times in initially circular, compact systems, though the dominant dynamics in the general eccentric case remains unclear. At these higher eccentricities, we investigate the role of secular dynamics in modulating the widths of two-body MMRs and causing them to overlap. Additionally, we identify a near symmetry that prevents strong secular driving in the two-planet case, but is broken at higher multiplicities, providing a separate explanation for the dichotomy between the two-planet and higher-multiplicity cases.