Predicting the long-term stability of compact multi-planet systems

We present our Stability of Planetary Orbital Configurations Klassifier (SPOCK), a machine learning model capable of robustly determining the long-term stability of compact multiplanet architectures up to 10⁵ times faster than direct integration (Tamayo et al., accepted). We find that our model, trained only on near-resonant 3-planet configurations, readily generalizes to higher multiplicities and uniform period sampling, and significantly outperforms previous stability criteria. At a fixed false-positive rate of 10%, SPOCK correctly predicts 94% of systems in our test set, as compared to 74% using the Angular Momentum Deficit stability criterion, and 39% using Hill sphere separations. This computationally opens up several applications, including the efficient rejection of unstable configurations when fitting the orbits of newly discovered systems. As an example, we present a stability analysis of Kepler 431, a compact system of 3 approximately Earth-mass planets. We find that stability constrains free eccentricities to be approximately less than 0.05. Given that no transit timing variations have been observed, such tight eccentricity constraints on rocky planets around a distant star are far beyond the reach of current observations. SPOCK thus holds the promise of significantly sharpening our view of compact multiplanet systems, and we release it as an open-source package for community use (https://github.com/dtamayo/spock).