On the habitability of the OGLE-2006-BLG-109L planetary system

We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analog of the Solar System. Our work is inspired by the paper of Malhotra and Minton (2008). Using the linear Laplace– Lagrange (L–L) theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the system of jovian planets may be found in dynamically active region of the phase space spanned by low-order mean-motion resonances. To improve the L–L model, we construct a semi-analytical averaging method in terms of the restricted problem. The mean orbits of large planets are approximated by numerically averaged osculating elements. These mean elements are used to calculate the long-term motion of terrestrial planet by means of high-order analytic secular theory developed in our previous works. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian configurations. For some combinations of that angle, eccentricities and semi-major axes consistent with the observations, terrestrial planets may survive in low-eccentric, long-term stable orbits in large regions of HZ. We also study the effect of post-Newtonian gravity correction on the inner secular resonance in the HZ.