Gliese 876 has a 3D Laplace Resonant Exoplanetary System

An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System

Authors:

Nelson et al

Abstract:

We report constraints on the three-dimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 876 (=GJ 876) based solely on Doppler measurements and demanding long-term orbital stability. Our dataset incorporates publicly available radial velocities taken with the ELODIE and CORALIE spectrographs, HARPS, and Keck HIRES as well as previously unpublished HIRES RVs. We first quantitatively assess the validity of the planets thought to orbit GJ 876 by computing the Bayes factors for a variety of different coplanar models using an importance sampling algorithm. We confirm that a four-planet model is indeed preferred over a three-planet model. Next, we apply a Newtonian MCMC algorithm (RUNDMC, Nelson et al. 2014) to perform a Bayesian analysis of the planet masses and orbits using an n-body model that allows each planet to take on its own orbit in three-dimensional space. Based on the radial velocities alone, the mutual inclinations for the outer three resonant planets are constrained to Φcb=2.8±1.71.3 degrees for the "c" and "b" pair and Φbe=10.3±6.35.1 degrees for the "b" and "e" pair. We integrate the equations of motion of a sample of initial conditions drawn from our posterior for 107 years. We identify dynamically unstable models and find that the GJ 876 planets must be roughly coplanar (Φcb=1.41±0.620.57 degrees and Φbe=3.9±2.01.9 degrees), indicating the amount of planet-planet scattering in the system has been low. We investigate the distribution of the respective resonant arguments of each planet pair and find that at least one resonant argument for each planet pair and the Laplace argument librate. The libration amplitudes in our three-dimensional orbital model supports the idea of the outer-three planets having undergone significant past disk migration.