Conditions of Dynamical Stability for the HD 160691 Planetary System

Abstract

The orbits in the HD 160691 planetary system at first appeared highly unstable, but using the MEGNO and FLI techniques of global dynamics analysis in the orbital parameter space we have found a stabilizing mechanism that could be the key to its existence. 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 $P_c(ap)-S-P_b(ap)$ where the two apsidal lines are anti-aligned, and (4) specific conditions on the respective sizes of the eccentricities (high eccentricity for the outer orbit is in particular the most probable necessary condition). More generally, in this original orbital topology, where the resonance variables ${\theta }_1$ and ${\theta }_3$ librate about $180^{\circ }$ while ${\theta }_2$ librates about $0^{\circ }$, the HD 160691 system and its mechanism have revealed aspects of the 2:1 orbital resonances that have not been observed nor analyzed before. The present topology combined with the 2:1 resonance is indeed more wide-ranging than the particular case of the HD 160691 planetary system. It is a new theoretical possibility suitable for a stable regime despite relatively small semi-major axes with respect to the important masses in interactions.

arXiv comment21 pages, 8 figures, 1 table, accepted version to ApJ (31 Jul 2003)

References in corpus (4)

• Short-Term Dynamical Interactions Among Extrasolar Planets
• The Apsidal Antialignment of the HD 82943 System
• Global dynamics and stability limits for planetary systems around HD 12661, HD 38529, HD 37124 and HD 160691
• Effects of perturbing forces on the orbital stability of planetary systems

Cited by in corpus (14)

• Evolution of Planetary Systems in Resonance
• Application of the MEGNO technique to the dynamics of Jovian irregular satellites
• Where is the second planet in the HD 160691 planetary system?
• Multiple Companions to HD 154857 and HD 160691
• Stability and Formation of the Resonant System HD 73526
• What is a planet?
• The Successful Prediction of the Extrasolar Planet HD 74156 d
• Dynamics of planets in retrograde mean motion resonance
• Are retrograde resonances possible in multi-planet systems?
• Testing a Fast Dynamical Indicator: The MEGNO
• Planetary Dynamics and Habitable Planet Formation In Binary Star Systems
• On the oscillations in Mercury's obliquity
• Stable chaos in the 55Cnc exoplanetary system?
• Retrograde resonances in compact multi-planetary systems: a feasible stabilizing mechanism