Conditions of Dynamical Stability for the HD 160691 Planetary System
Abstract
This paper presents a global dynamics analysis in the 3-D orbital parameter space related to the HD 160691 planetary system whose orbital parameters of the outer planet are yet uncertain. We make into evidence a stabilizing mechanism that could be the key to its existence. We show that the orbital parameters may allow the existence of a rather wide stability zone in the semi-major axes parameter space. This stability zone is only possible as the result of a 2:1 mean motion resonance coupled with adequate relative positions of the planets on their orbits avoiding close approaches in the closeness of their periastron. The mechanism itself is preserved by librations of the mean motion resonance variables while the longitudes of periapse on average precess at the same rate. We conclude that in order to be dynamically stable, the HD 160691 planetary system has to satisfy the following conditions: (1) a 2:1 mean motion resonance combined with (2) an apsidal secular resonance in (3) a configuration where the two apsidal lines are anti-aligned, and (4) high eccentricity for the outer orbit. In this orbital topology, the HD 160691 system and its mechanism have revealed resources of the 2:1 orbital resonances that have not been observed nor analyzed before. We also show that there is an upper limit for planetary masses due to the dynamical stability mechanism. We obtained our results using a new technique called MEGNO and verified them with the Fast Lyapunov Indicator technique (FLI).Keywords
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