Arxiv:1504.07995V2 [Astro-Ph.EP] 12 Oct 2015 Lee86(G 7)I 0.37 a Is 876) (=GJ 876 Gliese INTRODUCTION 1
Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 5 June 2021 (MN LATEX style file v2.2) An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System Benjamin E. Nelson1,2, Paul M. Robertson1,2, Matthew J. Payne3, Seth M. Pritchard4, Katherine M. Deck5, Eric B. Ford1,2, Jason T. Wright1,2, Howard T. Isaacson6 1Center for Exoplanets and Habitable Worlds, The Pennsylvania State University, 525 Davey Laboratory, University Park, PA, 16802, USA 2Department of Astronomy & Astrophysics, The Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802, USA 3Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA 4Department of Physics & Astronomy, University of Texas San Antonio, UTSA Circle, San Antonio, TX 78249, USA 5Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91101, USA 6Department of Astronomy, University of California, Berkeley, Berkeley, California 94720, USA 5 June 2021 ABSTRACT We report constraints on the three-dimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 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radial velocities taken with the ELODIE and CORALIE spectrographs, HARPS, and Keck HIRES as well as previously unpublished HIRES velocities. We first quantita- tively 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 four-planet model is preferred over a three-planet model. Next, we apply a Newtonian MCMC algorithm to perform a Bayesian analysis of the planet masses and orbits using an n-body model in three-dimensional space.
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