Conditions of Dynamical Stability for the HD 160691 Planetary System

The orbits in the HD 160691 planetary system at first appeared highlyunstable, but using the MEGNO and FLI techniques of global dynamics analysis inthe orbital parameter space we have found a stabilizing mechanism that could bethe key to its existence. In order to be dynamically stable, the HD 160691planetary system has to satisfy the following conditions: (1) a 2:1 mean motionresonance, combined with (2) an apsidal secular resonance in (3) aconfiguration $P_{c}(ap) - S - P_{b}(ap)$ where the two apsidal lines areanti-aligned, and (4) specific conditions on the respective sizes of theeccentricities (high eccentricity for the outer orbit is in particular the mostprobable necessary condition). More generally, in this original orbitaltopology, where the resonance variables $\theta_{1}$ and $\theta_{3}$ librateabout $180^{\circ}$ while $\theta_{2}$ librates about $0^{\circ}$, the HD160691 system and its mechanism have revealed aspects of the 2:1 orbitalresonances that have not been observed nor analyzed before. The presenttopology combined with the 2:1 resonance is indeed more wide-ranging than theparticular case of the HD 160691 planetary system. It is a new theoreticalpossibility suitable for a stable regime despite relatively small semi-majoraxes with respect to the important masses in interactions.Comment: 21 pages, 8 figures, 1 table, accepted version to ApJ (31 Jul 2003