A Machine Learns to Predict the Stability of Tightly Packed Planetary Systems

The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We show that characterizing the complicated and multi-dimensional stability boundary of tightly packed systems is amenable to machine-learning methods. We find that training an XGBoost machine-learning algorithm on physically motivated features yields an accurate classifier of stability in packed systems. On the stability timescale investigated (107 orbits), it is three orders of magnitude faster than direct N-body simulations. Optimized machine-learning classifiers for dynamical stability may thus prove useful across the discipline, e.g., to characterize the exoplanet sample discovered by the upcoming Transiting Exoplanet Survey Satellite. This proof of concept motivates investing computational resources to train algorithms capable of predicting stability over longer timescales and over broader regions of phase space

Statistics, Formation and Stability of Exoplanetary Systems

Over the past two decades scientists have detected thousands of exoplanets, and their collective properties are now emerging. This thesis contributes to the exoplanet field by analyzing the statistics, formation and stability of exoplanetary systems. The first part of this thesis conducts a statistical reconstruction of the radius and period distributions of Kepler planets. Accounting for observation and detection biases, as well as measurement errors, we calculate the occurrence of planetary systems, including the prevalence of Earth-like planets. This calculation is compared to related works, finding both similarities and differences. Second, the formation of Kepler planets near mean motion resonance (MMR) is investigated. In particular, 27 Kepler systems near 2:1 MMR are analyzed to determine whether tides are a viable mechanism for transporting Kepler planets from MMR. We find that tides alone cannot transport near-resonant planets from exact 2:1 MMR to their observed locations, and other mechanisms must be invoked to explain their formation. Third, a new hybrid integrator HERMES is presented, which is capable of simulating N-bodies undergoing close encounters. HERMES is specifically designed for planets embedded in planetesimal disks, and includes an adaptive routine for optimizing the close encounter boundary to help maintain accuracy. We find the performance of HERMES comparable to other popular hybrid integrators. Fourth, the longterm stability of planetary systems is investigated using machine learning techniques. Typical studies of longterm stability require thousands of realizations to acquire statistically rigorous results, which can take weeks or months to perform. Here we find that a trained machine is capable of quickly and accurately classifying longterm planet stability. Finally, the planetary system HD155358, consisting of two Jovian-sized planets near 2:1 MMR, is investigated using previously collected radial velocity data. New orbital parameters are derived using a Bayesian framework, and we find a high likelihood that the planets are in MMR. In addition, formation and stability constraints are placed on the HD155358 system.Ph.D