The HARPS search for southern extra-solar planets XIX. Characterization and dynamics of the GJ 876 planetary system

Precise radial-velocity measurements for data acquired with the HARPS spectrograph infer that three planets orbit the M 4 dwarf star GJ 876. In particular, we confirm the existence of planet d, which orbits every 1.93785 days. We find that its orbit may have significant eccentricity (e = 0.14), and deduce a more accurate estimate of its minimum mass of 6.3 M(circle plus). Dynamical modeling of the HARPS measurements combined with literature velocities from the Keck Observatory strongly constrain the orbital inclinations of the b and c planets. We find that i(b) = 48.9 degrees +/- 1.0 degrees and i(c) = 48.1 degrees +/- 2.1 degrees, which infers the true planet masses of M(b) = 2.64 +/- 0.04 M(Jup) and M(c) = 0.83 +/- 0.03 M(Jup), respectively. Radial velocities alone, in this favorable case, can therefore fully determine the orbital architecture of a multi-planet system, without the input from astrometry or transits. The orbits of the two giant planets are nearly coplanar, and their 2: 1 mean motion resonance ensures stability over at least 5 Gyr. The libration amplitude is smaller than 2 degrees, suggesting that it was damped by some dissipative process during planet formation. The system has space for a stable fourth planet in a 4: 1 mean motion resonance with planet b, with a period around 15 days. The radial velocity measurements constrain the mass of this possible additional planet to be at most that of the Earth.