Predicting the long-term stability of compact multiplanet systems

Significance Observations of planets beyond our solar system (exoplanets) yield uncertain orbital parameters. Particularly in compact multiplanet systems, a significant fraction of observationally inferred orbital configurations can lead to planetary collisions on timescales that are short compared with the age of the system. Rejection of these unphysical solutions can thus sharpen our view of exoplanetary orbital architectures. Long-term stability determination is currently performed through direct orbital integrations. However, this approach is computationally prohibitive for application to the full exoplanet sample. By speeding up this process by up to five orders of magnitude, we enable precise exoplanet characterization of compact multiplanet systems and our ability to examine the stability properties of the multiplanet exoplanet sample as a whole. We combine analytical understanding of resonant dynamics in two-planet systems with machine-learning techniques to train a model capable of robustly classifying stability in compact multiplanet systems over long timescales of 109 orbits. Our Stability of Planetary Orbital Configurations Klassifier (SPOCK) predicts stability using physically motivated summary statistics measured in integrations of the first 104 orbits, thus achieving speed-ups of up to 105 over full simulations. This computationally opens up the stability-constrained characterization of multiplanet systems. Our model, trained on ∼100,000 three-planet systems sampled at discrete resonances, generalizes both to a sample spanning a continuous period-ratio range, as well as to a large five-planet sample with qualitatively different configurations to our training dataset. Our approach significantly outperforms previous methods based on systems’ angular momentum deficit, chaos indicators, and parametrized fits to numerical integrations. We use SPOCK to constrain the free eccentricities between the inner and outer pairs of planets in the Kepler-431 system of three approximately Earth-sized planets to both be below 0.05. Our stability analysis provides significantly stronger eccentricity constraints than currently achievable through either radial velocity or transit-duration measurements for small planets and within a factor of a few of systems that exhibit transit-timing variations (TTVs). Given that current exoplanet-detection strategies now rarely allow for strong TTV constraints [S. Hadden, T. Barclay, M. J. Payne, M. J. Holman, Astrophys. J. 158, 146 (2019)], SPOCK enables a powerful complementary method for precisely characterizing compact multiplanet systems. We publicly release SPOCK for community use.