An empirically derived threedimensional Laplace resonance in the Gliese 876 planetary system
Abstract
We report constraints on the threedimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 876 based solely on Doppler measurements and demanding longterm orbital stability. Our data set incorporates publicly available radial velocities taken with the ELODIE and CORALIE spectrographs, High Accuracy Radial velocity Planet Searcher (HARPS), and Keck HIgh Resolution Echelle Spectrometer (HIRES) as well as previously unpublished HIRES velocities. 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 find that a fourplanet model is preferred over a threeplanet model. Next, we apply a Newtonian Markov chain Monte Carlo algorithm to perform a Bayesian analysis of the planet masses and orbits using an Nbody model in threedimensional space. Based on the radial velocities alone, we find that a 99 per cent credible interval provides upper limits on the mutual inclinations for the three resonant planets (Φ_{cb} < 6.20° for the {c} and {b} pair and Φ_{be} < 28.5° for the {b} and {e} pair). Subsequent dynamical integrations of our posterior sample find that the GJ 876 planets must be roughly coplanar (Φ_{cb} < 2.60° and Φ_{be} < 7.87°, suggesting that the amount of planetplanet 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 argument for each planet pair and the Laplace argument librate. The libration amplitudes in our threedimensional orbital model support the idea of the outer three planets having undergone significant past disc migration.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 January 2016
 DOI:
 10.1093/mnras/stv2367
 arXiv:
 arXiv:1504.07995
 Bibcode:
 2016MNRAS.455.2484N
 Keywords:

 methods: numerical;
 methods: statistical;
 techniques: radial velocities;
 planets and satellites: dynamical evolution and stability;
 planets and satellites: formation;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 19 pages, 11 figures, 8 tables. Accepted to MNRAS. Posterior samples available at https://github.com/benelson/GJ876