Dynamical stability analysis of the HD202206 system and constraints to the planetary orbits

Abstract

Long-term precise Doppler measurements with the CORALIE spectrograph revealed the presence of two massive companions to the solar-type star HD202206. Although the three-body fit of the system is unstable, it was shown that a 5:1 mean motion resonance exists close to the best fit, where the system is stable. We present here an extensive dynamical study of the HD202206 system aiming at constraining the inclinations of the two known companions, from which we derive possible ranges of value for the companion masses. We study the long term stability of the system in a small neighborhood of the best fit using Laskar's frequency map analysis. We also introduce a numerical method based on frequency analysis to determine the center of libration mode inside a mean motion resonance. We find that acceptable coplanar configurations are limited to inclinations to the line of sight between 30 and 90 degrees. This limits the masses of both companions to roughly twice the minimum. Non coplanar configurations are possible for a wide range of mutual inclinations from 0 to 90 degrees, although $\Delta\Omega = 0 [\pi]$ configurations seem to be favored. We also confirm the 5:1 mean motion resonance to be most likely. In the coplanar edge-on case, we provide a very good stable solution in the resonance, whose $\chi^2$ does not differ significantly from the best fit. Using our method to determine the center of libration, we further refine this solution to obtain an orbit with a very low amplitude of libration, as we expect dissipative effects to have dampened the libration.Comment: 14 pages, 18 figure