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 radialvelocity data set that combines new measurements obtained with the Kecktelescope and the CORALIE measurements published in graphical form. We examinesimultaneously the goodness of fit and the dynamical properties of the best-fitdouble-Keplerian model as a function of the poorly constrained eccentricity andargument of periapse of the outer planet's orbit. The fit with the minimumchi_{nu}^2 is dynamically unstable if the orbits are assumed to be coplanar.However, the minimum is relatively shallow, and there is a wide range of fitsoutside the minimum with reasonable chi_{nu}^2. For an assumed coplanarinclination i = 30 deg. (sin i = 0.5), only good fits with both of the lowestorder, eccentricity-type mean-motion resonance variables at the 2:1commensurability, theta_1 and theta_2, librating about 0 deg. are stable. Forsin i = 1, there are also some good fits with only theta_1 (involving the innerplanet's periapse longitude) librating that are stable for at least 10^8 years.The libration semiamplitudes are about 6 deg. for theta_1 and 10 deg. fortheta_2 for the stable good fit with the smallest libration amplitudes of boththeta_1 and theta_2. We do not find any good fits that are non-resonant andstable. Thus the two planets in the HD 82943 system are almost certainly in 2:1mean-motion resonance, with at least theta_1 librating, and the observationsmay even be consistent with small-amplitude librations of both theta_1 andtheta_2.Comment: 24 pages, including 10 figures; accepted for publication in Ap