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

Using numerical methods we thoroughly investigate the dynamical stability in the region between the two planets found in HD 74156. The two planets with minimum masses 1.56 M_JUP (HD 74156b) and 7.5 M_JUP (HD 74156c), semimajor axes 0.276 AU and 3.47 AU move on quite eccentric orbits (e=0.649 and 0.395). There is a region between 0.7 and 1.4 AU which may host additional planets which we checked via numerical integrations using different dynamical models. Besides the orbital evolution of several thousands of massless regarded planets in a three-dimensional restricted 4-body problem (host star, two planets + massless bodies) we also have undertaken test computation for the orbital evolution for fictive planets with masses of 0.1, 0.3 and 1 M_JUP in the region between HD74156b and HD74156c. For direct numerical integrations up to 10^7 years we used the Lie-integrator, a method with adaptive stepsize; additionally we used the Fast Lyapunov Indicators as tool for detecting chaotic motion in this region. We emphasize the important role of the inner resonances (with the outer planet) and the 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 very unstable probably due to three-body-resonances acting there. Our results do not strictly "forbid" planets to move there, but the existence of a planet on a stable orbit between 0.8 and 1.3 AU is unlikely