The architecture of the GJ 876 planetary system

Abstract

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.

The HARPS search for southern extra-solar planets

“…The best-fit orbit for planet d is also eccentric, in contrast to previous determinations in which its value was constrained to be zero (Rivera et al 2005;Bean & Seifahrt 2009). We can also fix this parameter and our revised solution corresponds to an adjustment with χ 2 = 1.40 and rms = 2.34 m s −1 .…”

“…Rivera et al (2005) re-examined the dynamical interactions with many additional Keck radial velocity measurements, and found an intermediate inclination of ∼50 • . Bean & Seifahrt (2009) reconciled the astrometry and radial velocities by performing a joint adjustment to the Keck and HST datasets, and showed that both are consistent with ∼50 • . Early inclination determinations were, in retrospect, affected by smallnumber statistics (for astrometry) and by a modest signal-tonoise ratio in the radial velocity residuals.…”

Planetary Phase Variations of the 55 Cancri System

“…Theoretical modeling performed by Tremaine & Dong (2011) independently supports the claim by Lissauer et al (2011) that near-zero mutual inclinations are favored for multiplanet systems. Stability analyses of RV systems have also been used to determine coplanarity, such as the cases of the HD 10180 system (Lovis et al 2011) and GJ 876 system (Bean & Seifahrt 2009). It should be noted however that dynamical stability over long timescales can be achieved through interaction of giant planets or the influence of an external perturber (Guillochon et al 2011;Malmberg et al 2002).…”

Exoplanet Observations

“…If the dynamical perturbations are large enough, and occurring on a short enough timescale, then study of radial velocity data can yield constraints on the interacting planets' true masses and degree of coplanarity [37,38,42]. The key to the additional insight is that the planet-planet perturbations discernible in radial velocity data are dependent on the true masses and three-dimensional orbital orientations of the interacting bodies.…”

“…Therefore, if the perturbations can be characterized well enough, then the planet masses and orbits can be constrained. To date, this kind of analysis has only been applied to one system (GJ 876, [2,42]), but this should also be possible for some other known systems when enough data have been collected.…”