A study of the stable regions in the planetary system HD 74156 - Can it host earthlike planets in habitable zones?

Using numerical methods we thoroughly investigate dynamical stability in the region between the two planets found in HD 74156. The two planets with semimajor axes 0.28 AU and 3.82 AU move on quite eccentric orbits ( e=0.649 and 0.354). There is a region between 0.7 and 1.4 AU which may host additional planets which we checked via numerical integrations for different dynamical models. Besides the orbital evolution of several thousands of massless planets in a three-dimensional restricted 4-body problem (host star, two planets + massless bodies) we also have undertaken test computations of the orbital evolution of fictitious planets with masses of 0.1, 0.3 and 1 M JUP in the region between HD 74156b and HD 74156c. For direct numerical integrations up to 10^7 years we used the Lie-integrator, a method with adaptive step-size. We also computed the Fast Lyapunov Indicators to detect chaotic motion in this region. We emphasize the important rôle of the inner resonances (with the outer planet) and outer resonances (with the inner planet) with test bodies located inside the resonances. In these two "resonance" regions almost no orbits survive. The region between the 1:5 outer resonance (0.8 AU) and the 5:1 inner resonance (1.3 AU), just in the right position for habitability, is also not very likely to host planets. Our results do not strictly "forbid" planets to move in the habitable zone, but their existence is unlikely.