The Lick-Carnegie Exoplanet Survey: A Uranus-mass Fourth Planet for GJ 876 in an Extrasolar Laplace Configuration

Abstract

(Abreviated) Continued radial velocity monitoring of the nearby M4V red dwarf star GJ~876 with Keck/HIRES has revealed the presence of a Uranus-mass fourth planetary companion in the system. The new planet has a mean period of $P_e=126.6$ days (over the 12.6-year baseline of the radial velocity observations), and a minimum mass of $m_e\sin i_e=12.9\pm 1.7M_{\oplus }$. Self-consistent, N-body fits to the radial velocity data set show that the four-planet system has an invariable plane with an inclination relative to the plane of the sky of $i=59.5^{\circ }$. The fit is not significantly improved by the introduction of a mutual inclination between the planets ``b'' and ``c,'' but the new data do confirm a non-zero eccentricity, $e_d=0.207\pm 0.055$ for the innermost planet, ``d.'' In our best-fit coplanar model, the mass of the new component is $m_e=14.6\pm 1.7M_{\oplus }$. Our best-fitting model places the new planet in a 3-body resonance with the previously known giant planets (which have mean periods of $P_c=30.4$ and $P_b=61.1$ days). The critical argument, ${\phi }_{\mathrm{Laplace}}={\lambda }_c-3{\lambda }_b+2{\lambda }_e$, for the Laplace resonance librates with an amplitude of $\Delta {\phi }_{\mathrm{Laplace}}=40\pm 13^{\circ }$ about ${\phi }_{\mathrm{Laplace}}=0^{\circ }$. Numerical integration indicates that the four-planet system is stable for at least a billion years (at least for the coplanar cases). This resonant configuration of three giant planets orbiting an M-dwarf primary differs from the well-known Laplace configuration of the three inner Galilean satellites of Jupiter, which are executing very small librations about ${\phi }_{\mathrm{Laplace}}=180^{\circ }$, and which never experience triple conjunctions. The GJ~876 system, by contrast, comes close to a triple conjunction between the outer three planets once per every orbit of the outer planet, ``e.''

41 pages, 7 figures, 4 tables, accepted for publication in ApJ

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