A dynamical analysis of the 14 Her planetary system

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Abstract
Precision radial velocity (RV) measurements of the Sun-like dwarf 14 Herculis in Naef et. al (2004), Butler et. al (2006) and Wittenmyer et al (2007) reveal a Jovian planet in a 1700 day orbit and a trend indicating the second distant object. On the grounds of dynamical considerations, we test a hypothesis that the trend can be explained by the presence of an additional giant planet. We derive dynamical limits to th orbital parameters of the putative outer Jovian companion in an orbit within ~12AU. In this case, the mutual interactions between the Jovian planets are important for the long-term stability of the system. Hence the kinematic model is not adequate to model the RV data. The best self-consistent and stable Newtonian fit corresponds to an edge-on configuration of Jovian planets in about 9AU orbit with a moderate eccentricity ~0.2 and confined to a zone spanned by the low-order mean motion resonances 5:1 and 6:1. This solution lies in a shallow minimum of Chi2 and persists over a wide range of the system inclination. Because the data cover roughly a half of the period (~27 yr) of the orbital solution, the semi-major axis of the outer planet cannot be well constrained. Other stable configurations within 1\sigma confidence interval of the best fit are possible and correspond to the semi-major axis of the outer planet in the range of (6,12) AU. The orbital inclination cannot yet be determined but when it decreases, both planetary masses approach ~10m_J and for i ~30 deg the hierarchy of the masses is reversed. Simultaneously, the border of dynamical stability is shifted beyond 8--9~AU.

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