On the 2 : 1 Orbital Resonance in the HD 82943 Planetary System

We present an analysis of the HD 82943 planetary system based on a radial velocity data set that combines new measurements obtained with the Keck telescope and the CORALIE measurements published in graphical form. We examine simultaneously the goodness of fit and the dynamical properties of the best-fit double-Keplerian model as a function of the poorly constrained eccentricity and argument of periapse of the outer planet's orbit. The fit with the minimum χ is dynamically unstable if the orbits are assumed to be coplanar. However, the minimum is relatively shallow, and there is a wide range of fits outside the minimum with reasonable χ . For an assumed coplanar inclination i = 30 ° (sin i = 0.5), only good fits with both of the lowest order, eccentricity-type mean-motion resonance variables at the 2 : 1 commensurability, θ 1 and θ 2 , librating about 0° are stable. For sin i = 1, there are also some good fits with only θ 1 (involving the inner planet's periapse longitude) librating that are stable for at least 10 8 yr. The libration semiamplitudes are about 6° for θ 1 and 10° for θ 2 for the stable good fit with the smallest libration amplitudes of both θ 1 and θ 2 . We do not find any good fits that are nonresonant and stable. Thus, the two planets in the HD 82943 system are almost certainly in 2 : 1 mean-motion resonance, with at least θ 1 librating, and the observations may even be consistent with small-amplitude librations of both θ 1 and θ 2 .