A Caltech Library Service

An empirically derived three-dimensional Laplace resonance in the Gliese 876 planetary system

Nelson, Benjamin E. and Robertson, Paul M. and Payne, Matthew J. and Pritchard, Seth M. and Deck, Katherine M. and Ford, Eric B. and Wright, Jason T. and Isaacson, Howard T. (2015) An empirically derived three-dimensional Laplace resonance in the Gliese 876 planetary system. Monthly Notices of the Royal Astronomical Society, 455 (3). pp. 2484-2499. ISSN 0035-8711.

[img] PDF - Published Version
See Usage Policy.

[img] Archive (ZIP) - Supplemental Material
See Usage Policy.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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 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Radial velocity Planet Searcher (HARPS), and Keck HIgh Resolution Echelle Spectrometer (HIRES) as well as previously unpublished HIRES velocities.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 four-planet model is preferred over a three-planet model. Next, we apply a Newtonian Markov chain Monte Carlo algorithm to perform a Bayesian analysis of the planet masses and orbits using an N-body model in three-dimensional 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 cc and bb 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 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 argument for each planet pair and the Laplace argument librate. The libration amplitudes in our three-dimensional orbital model support the idea of the outer three planets having undergone significant past disc migration.

Item Type:Article
Related URLs:
URLURL TypeDescription Information Paper
Payne, Matthew J.0000-0001-5133-6303
Ford, Eric B.0000-0001-6545-639X
Wright, Jason T.0000-0001-6160-5888
Isaacson, Howard T.0000-0002-0531-1073
Additional Information:© 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2015 October 8. Received 2015 October 5. In original form 2015 April 24. First published online November 23, 2015. PR acknowledges support from NSF grant AST-1126413 and the Center for Exoplanets and Habitable Worlds. MJP gratefully acknowledges the NASA Origins of Solar Systems Program grant NNX13A124G. EBF and JTW acknowledge NASA Keck PI Data Awards, administered by the NASA Exoplanet Science Institute, including awards 2007B N095Hr, 2010A N147Hr, 2011A&B N141Hr, and 2012A N129Hr. This research was supported by NASA Origins of Solar Systems grant NNX09AB35G. We acknowledge the University of Florida High Performance Computing Center and the Pennsylvania State Research Computing and Advanced Cyberinfrastructure Group for providing computational resources and support that have contributed to the results reported within this paper. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. We extend special thanks to those of Hawaiian ancestry on whose sacred mountain of Mauna Kea we are privileged to be guests. Without their generous hospitality, the Keck observations presented herein would not have been possible.
Group:Infrared Processing and Analysis Center (IPAC)
Funding AgencyGrant Number
Center for Exoplanets and Habitable WorldsUNSPECIFIED
NASA2007B N095Hr
NASA2010A N147Hr
NASA2011A&B N141Hr
NASA2012A N129Hr
Pennsylvania State UniversityUNSPECIFIED
Eberly College of ScienceUNSPECIFIED
Pennsylvania Space Grant ConsortiumUNSPECIFIED
Subject Keywords:methods: numerical methods: statistical techniques: radial velocities planets and satellites: dynamical evolution and stability planets and satellites: formation
Issue or Number:3
Record Number:CaltechAUTHORS:20160204-143735754
Persistent URL:
Official Citation:Benjamin E. Nelson, Paul M. Robertson, Matthew J. Payne, Seth M. Pritchard, Katherine M. Deck, Eric B. Ford, Jason T. Wright, and Howard T. Isaacson An empirically derived three-dimensional Laplace resonance in the Gliese 876 planetary system MNRAS (January 21, 2016) Vol. 455 2484-2499 doi:10.1093/mnras/stv2367 First published online November 23, 2015
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64239
Deposited By: Ruth Sustaita
Deposited On:05 Feb 2016 16:58
Last Modified:09 Mar 2020 13:19

Repository Staff Only: item control page