Algebraic and machine learning approach to hierarchical triple-star stability

We present two approaches to determine the dynamical stability of a hierarchical triple-star system. The first is an improvement on the semi-analytical stability criterion of Mardling & Aarseth (2001), where we introduce a dependence on inner orbital eccentricity and improve the dependence on mutual orbital inclination. The second involves a machine learning approach, where we use a multilayer perceptron (MLP) to classify triple-star systems as `stable' and `unstable'. To achieve this, we generate a large training data set of 10^6 hierarchical triples using the N-body code MSTAR. Both our approaches perform better than the original Mardling & Aarseth (2001) stability criterion, with the MLP model performing the best. The improved stability formula and the machine learning model have overall classification accuracies of 93 % and 95 % respectively. Our MLP model, which accurately predicts the stability of any hierarchical triple-star system within the parameter ranges studied with almost no computation required, is publicly available on Github in the form of an easy-to-use Python script.