A machine learns to predict the stability of circumbinary planets

Long-period circumbinary planets appear to be as common as those orbiting single stars and have been found to frequently have orbital radii just beyond the critical distance for dynamical stability. Assessing the stability is typically done either through N-body simulations or using the classic stability criterion first considered by Dvorak and later developed by Holman and Wiegert: a second-order polynomial calibrated to broadly match numerical simulations. However, the polynomial is unable to capture islands of instability introduced by mean motion resonances, causing the accuracy of the criterion to approach that of a random coin-toss when close to the boundary. We show how a deep neural network (DNN) trained on Nbody simulations generated with REBOUND is able to significantly improve stability predictions for circumbinary planets on initially coplanar, circular orbits. Specifically, we find that the accuracy of our DNN never drops below 86 per cent, even when tightly surrounding the boundary of instability, and is fast enough to be practical for on-the-fly calls during likelihood evaluations typical of modern Bayesian inference. Our binary classifier DNN is made publicly available at https://github.com/CoolWorlds/orbital-stability.