Characterizing the orbital and dynamical state of extrasolar multiple-planet systems with radial velocity measurements

Abstract

Extrasolar planetary surveys have discovered about 780 extrasolar planets and more than 100 multiple planetary systems to date, with the largest fraction of them being confirmed by the radial velocity detection method. Multiple planetary systems, especially those contain pairs of planets in mean-motion resonances, are particularly interesting because their current orbital architectures provide constraints for orbital evolution of planetary systems. Precisely determining the orbital and dynamical state of multiple planetary systems with radial velocity measurements is important.

New results from an analysis of radial velocity data of the HD 82943 planetary system based on 10 years of measurements obtained with the Keck telescope is presented in this thesis. Previous studies have shown that the HD 82943 system has two planets that are likely in 2:1 MMR, with the orbital periods about 220 and 440 days (Lee et al. 2006). However, alternative fits that are qualitatively different have also been suggested, with the two planets in 1:1 resonance or the addition of a third planet possibly in a Laplace 4:2:1 resonance with the other two (Goździewski & Konacki 2006; Beaugé et al. 2008). Here based on the X^2 minimization method combined with parameter grid search, the orbital parameters and dynamical states of the qualitatively different types of fits have been investigated. The results support the coplanar 2:1 MMR configuration for this system and fits of the 1:1 resonance and the 3-planet Laplace resonance are ruled out according to X^2 statistic and dynamical instability. The inclination of the HD 82943 system is well constrained at about 20°C. The system contains two planets with masses of about 4.64 MJ and 4.66 MJ and orbital periods of about 219 and 442 days for the inner and outer planet, respectively. The best fit is dynamically stable with two resonance angles θ 1 = λ1 - 2λ2 + ϖ1 and θ 2 = λ1 - 2λ2 + ϖ 2 librating around 0°. Based on the best fit, the origin of the 2:1 MMR of the HD 82943 planetary system has been explored by N-body simulations with forced inward migration of the outer planet.

This research has demonstrated the importance of dynamical fitting for multiple planetary systems with radial velocity measurements. It also fulfills the cases of planetary systems in mean-motion resonances such that more generic understanding of the orbital evolution of planetary systems can be obtained.