A Criterion for the Onset of Chaos in Compact, Eccentric Multiplanet Systems

In the last few years, there has been significant progress in elucidating the dynamics that can drive instabilities in compact planetary systems with low mutual inclinations. A long-standing numerical result is that instabilities in two-planet systems are a special case, compared with general systems with three or more planets. The edge of stability for two eccentric planets was recently analytically understood as the boundary where mean motion resonances (MMRs) overlap, but this criterion fails in general for higher multiplicity systems.

We show that in the general compact, multi-planet case, the chaotic boundary can still be understood through MMR overlap, but only if one additionally accounts for the long-term secular evolution, which causes MMRs to slowly expand and contract, and modulates the boundary at which they overlap with one another. We demonstrate that for closely spaced two-planet systems, a near-symmetry strongly suppresses this secular modulation, explaining why the chaotic boundaries for two-planet systems are qualitatively different from cases with more than two planets.

Finally, I will demonstrate how the community can evaluate our semi-analytic chaotic boundary with the open-source Stability of Planetary Orbital Configurations Klassifier (SPOCK) package, in order to help constrain and understand new multiplanet system discoveries.