New criteria for evaluating the orbital stability of circumbinary planets

Many stars are found in pairs. An interesting problem in stellar binary systems is how to assess whether a planetary orbit is dynamically stable or not.  Besides being a theoretical puzzle, the solution to that problem has many applications in topics such as for example in planet detection, planet formation, habitability, and the evolution of planetary systems off the  Main Sequence. Here, we present the latest developments in the problem of the stability of circumbinary planetary orbits.  With the aim of identifying stable and unstable orbits in such systems, we carry out more than 3x10⁸ numerical simulations of planets between the size of Mercury and the lower fusion boundary (13 Jupiter masses) which revolve around the center of mass of a stellar binary over long timescales. For the first time, three dimensional and eccentric planetary orbits are considered. Based on the results of our numerical simulations, we determine two critical borders: an outer border beyond which all planetary orbits are stable and an inner border closer to the binary below which all planetary orbits are unstable. In between the two borders, a mixture of stable and unstable planetary orbits is observed. We provide empirical expressions in the form of multidimensional, parameterized fits for the two borders that separate the three dynamical regimes. Moreover, we train a machine learning model on our data set in order to have an additional tool for predicting stable and unstable motion. Both the empirical fits and the machine learning model are tested for their predictive capabilities against randomly generated circumbinary planetary systems. The parameterized fits are also applied to the Kepler and TESS circumbinary systems, confirming the stability of the planets in these systems. Finally, the empirical fits are compared against previously derived stability criteria.