Predicting the Long-term Stability of Compact Multiplanet Systems

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TRAPPIST-1 System

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 multi-planet 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 multi-planet 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 (Hadden et al., 2019), SPOCK enables a powerful complementary method for precisely characterizing compact multi-planet systems. We publicly release SPOCK for community use.

Daniel Tamayo, Miles Cranmer, Samuel Hadden, Hanno Rein, Peter Battaglia, Alysa Obertas, Philip J. Armitage, Shirley Ho, David Spergel, Christian Gilbertson, Naireen Hussain, Ari Silburt, Daniel Jontof-Hutter, Kristen Menou
Comments: Published week of July 13th in Proceedings of the National Academy of Sciences: this https URL. Check out simple usage of package (and regenerate paper figures) at: this https URL
Subjects: Earth and Planetary Astrophysics (astro-ph.EP)
DOI: 10.1073/pnas.2001258117
Cite as: arXiv:2007.06521 [astro-ph.EP] (or arXiv:2007.06521v1 [astro-ph.EP] for this version)
Submission history
From: Daniel Tamayo
[v1] Mon, 13 Jul 2020 17:26:41 UTC (2,952 KB)
https://arxiv.org/abs/2007.06521
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