A dynamical analysis of the 14 Her planetary system

Abstract

Precision radial velocity (RV) measurements of the Sun-like dwarf 14 Herculis published by Naef et. al (2004), Butler et. al (2006) and Wittenmyer et al (2007) reveal a Jovian planet in a 1760 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 ~13 AU. In this case, the mutual interactions between the Jovian planets are important for the long-term stability of the system. The best self-consistent and stable Newtonian fit to an edge-on configuration of Jovian planets has the outer planet in 9 AU 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 \Chi and persists over a wide range of the system inclination. Other stable configurations within 1σconfidence interval of the best fit are possible for the semi-major axis of the outer planet in the range of (6,13) AU and the eccentricity in the range of (0,0.3). The orbital inclination cannot yet be determined but when it decreases, both planetary masses approach ~10 Jupiter masses and for ~30 deg the hierarchy of the masses is reversed.