Algebraic and machine learning approach to hierarchical triple-star stability
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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 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.
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