Where is the Second Planet in the HD 160691 Planetary System?

The set of radial velocity measurements of the HD 160691 has been recentlypublished by Jones et.al 2002 (MNRAS). It reveals a linear trend that indicatesa presence of the second planet in this system. The preliminarydouble-Keplerian orbital fit to the observations, announced by the discoveryteam, describes a highly unstable, self-disrupting configuration. Because theobservational window of the HD 160691 system is narrow, the orbital parametersof the hypothetical second companion are unconstrained. In this paper we try tofind out whether a second giant planet can exist up to the distance of Jupiterand search for the dynamical constraints on its orbital parameters. Ouranalysis employs a combination of fitting algorithms and simultaneousexamination of the dynamical stability of the obtained orbital fits. It revealsthat if the semi-major axis of the second planet is smaller than $\simeq 5.2$AU, the observations are consistent with quasi-periodic, regular motions of thesystem confined to the islands of various low-order mean motion resonances,e.g., 3:1, 7:2, 4:1, 5:1, or to their vicinity. In such cases the second planethas smaller eccentricity $\simeq 0.2-0.5$ than estimated in the previous works.We show that the currently available Doppler data rather preclude the 2:1 meanmotion resonance expected by some authors to be present in the HD 160691planetary system. We also demonstrate that the MEGNO-penalty method, developedin this paper, which is a combination of the genetic minimization algorithm andthe MEGNO analysis, can be efficiently used for predicting stable planetaryconfigurations when only a limited number of observations is given or the datado not provide tight constraints on the orbital elements.