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An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System | | Benjamin E. Nelson
; Paul Robertson
; Matthew J. Payne
; Seth M. Pritchard
; Katherine M. Deck
; Eric B. Ford
; Jason T. Wright
; Howard Isaacson
; | | Date: |
29 Apr 2015 | | 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unpublished HIRES RVs.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 $Phi_{cb}=2.8pm^{1.7}_{1.3}$ degrees for
the "c" and "b" pair and $Phi_{be}=10.3pm^{6.3}_{5.1}$ degrees for the "b"
and "e" pair. We integrate the equations of motion of a sample of initial
conditions drawn from our posterior for $10^7$ years. We identify dynamically
unstable models and find that the GJ 876 planets must be roughly coplanar
($Phi_{cb}=1.41pm^{0.62}_{0.57}$ degrees and $Phi_{be} = 3.9pm^{2.0}_{1.9}$
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. | | Source: | arXiv, 1504.7995 | | Services: | Forum | Review | PDF | Favorites | |
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