The architecture of the GJ 876 planetary system Masses and orbital coplanarity for planets b and c ⋆

We present a combined analysis of previously published high-precision radial velocities and astrometry for the GJ 876 planetary system using a self-consistent model that accounts for the planet-planet interactions. Assuming the three planets so far identified in the system are coplanar, we find that including the astrometry in the analysis does not result in a best-fit inclination significantly different than that found by Rivera and collaborators from analyzing the radial velocities alone. In this unique case, the planet-planet interactions are of such significance that the radial velocity data set is more sensitive to the inclination of the system through the dependence of the interactions on the true masses of the two gas giant planets in the system (planets b and c). The astrometry does allow determination of the absolute orbital inclination (i.e. distinguishing between i and 180 − i) and longitude of the ascending node for planet b, which allows us to quantify the mutual inclination angle between its orbit and planet c's orbit when combined with the dynamical considerations. We find that the planets have a mutual inclination Φ bc = 5.0 • +3.9 • −2.3 •. This result constitutes the first determination of the degree of coplanarity in an exoplanetary system around a normal star. That we find the two planets' orbits are nearly coplanar, like the orbits of the Solar System planets, indicates that the planets likely formed in a circumstellar disk, and that their subsequent dynamical evolution into a 2:1 mean motion resonance only led to excitation of a small mutual inclination. This investigation demonstrates how the degree of coplanarity for other exoplanetary systems could also be established using data obtained from existing facilities.