The Stability Analysis of the HD 82943 and HD 37124 Planetary Systems

Abstract

We carry out numerical simulations to explore the dynamical evolution of the HD 82943 and HD 37124 planetary systems,which both have two Jupiter-like planets. By simulating various planetary configurations in the neighborhood of the fitting orbits, we find three mechanisms to maintain the stability of these systems: For HD 82943,we find that the 2:1 mean motion resonance can act as the first mechanism for all the stable orbits. The second mechanism is the alignment of the periastron of the two planets of HD 82943 system. In the paper,we show one case is simultaneously maintained by the two mechanisms. Additionally,we also use the corresponding analytical models successfully to explain the different numerical results for the system. The third mechanism is the Kozai resonance which takes place in the mutual highly orbits of HD 37124. In the simulations,we discover that the argument of periastron $ω$ of the inner planet librates about $90^{\circ}$ or $270^{\circ}$ for the whole time span. The Kozai mechanism can explain the stable configuration of large eccentricity of the inner planet.