Dynamics and stability of telluric planets within the habitable zone of extrasolar planetary systems : Numerical simulations of test particles within the HD 4208 and HD 70642 systems

Aims. We study gravitational perturbation effects of observed giant extrasolar planets on hypothetical Earth-like planets in the context of the three-body problem. This paper considers a large parameter survey of different orbital configuration of two extrasolar giant planets (HD 70642b and HD 4208b) and compares their dynamical effect on Earth-mass planetary orbits initially located within the respective habitable terrestrial region. We are interested in determining giant-planet orbit (and mass) parameters that favor the condition to render an Earth-mass planet to remain on a stable and bounded orbit within the continuous habitable zone. Methods. We applied symplectic numerical integration techniques to studying the short and long term time evolution of hypothetical Earth-mass planets that are treated as particles. In addition, we adopt the MEGNO technique to obtain a complete dynamical picture of the terrestrial phase space environment. Both multi-particle and single-particle simulations were performed to follow an Earth-mass planet in the habitable region and its subsequent long term evolution. Results. Our numerical simulations show that giant planets should be on circular orbits to minimize the perturbative effect on terrestrial orbits. The orbit eccentricity (and hence proximity) is the most important orbital parameter of dynamical significance. The most promising candidate for maintaining an Earth-mass planet on a stable and bounded orbit well-confined to the continuous habitable zone is HD 70642b. Even the large planetary mass of HD 70642b renders an Earth-mass planet habitable during the complete lifetime of the host star. The results allow us to extrapolate similar observed systems and points the necessity further constraining the uncertainty range in giant planet orbital eccentricity by future follow-up observations.