Stability of Compact Exoplanet Systems

A central question is whether planetary orbital configurations get set at formation and remain largely, or whether dynamical instabilities are common through planetary systems' Gyr lifetimes, leading to a sequence of collisions and orbital rearrangements. Such questions have been largely studied through computationally expensive N-body integrations, but it has been challenging to extract a clear picture without a theoretical understanding of the dynamics driving such instabilities.

A long-standing numerical result is that instabilities in compact 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 due to the overlap of mean motion resonances (MMRs), 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 secular (long-term) evolution, which causes MMRs to slowly expand and contract, and modulates the boundary at which they overlap with one another.

We will present an overview of this theoretical picture, and show how the community can evaluate the stability of compact exoplanet orbital architectures with our open-source Stability of Planetary Orbital Configurations Klassifier (SPOCK) package. This can provide complementary theoretical constraints on uncertain orbital parameters, and opens up new paths to understanding the early phases of planetary systems.