Stability analysis of three exoplanet systems

Abstract

The orbital solutions of published multi-planet systems are not necessarily dynamically stable on timescales comparable to the lifetime of the system as a whole. For this reason, dynamical tests of the architectures of proposed exoplanetary systems are a critical tool to probe the stability and feasibility of the candidate planetary systems, with the potential to point the way towards refined orbital parameters of those planets. Such studies can even help in the identification of additional companions in such systems. Here we examine the dynamical stability of three planetary systems, orbiting HD 67087, HD 110014, and HD 133131A. We use the published radial velocity measurements of the target stars to determine the best-fit orbital solutions for these planetary systems using the Systemic console. We then employ the n-body integrator Mercury to test the stability of a range of orbital solutions lying within 3-$\sigma$ of the nominal best-fit for a duration of 100 Myr. From the results of the n-body integrations, we infer the best-fit orbital parameters using the Bayesian package Astroemperor. We find that both HD 110014 and HD 133131A have long-term stable architectures that lie within the 1-$\sigma$ uncertainties of the nominal best-fit to their previously determined orbital solutions. However, the HD 67087 system exhibits a strong tendency toward instability on short timescales. We compare these results to the predictions made from consideration of the angular momentum deficit criterion, and find that its predictions are consistent with our findings.