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

TL;DR

This study analyzes the potential for Earth-mass planets to exist in the habitable zone of the OGLE-2006-BLG-109L system, using advanced secular theory and numerical methods to identify stable orbital configurations.

Contribution

We develop a semi-analytical averaging method and apply high-order secular theory to identify stable, low-eccentricity orbits in the habitable zone of the system.

Findings

Stable, quasi-circular orbits are possible in the habitable zone.

Eccentricity excitation depends on the jovian orbital apsidal angle.

Post-Newtonian gravity effects influence secular resonance behavior.

Abstract

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 work of Malhotra and Minton (2008). Using the linear Laplace-Lagrange 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 sub-system of Jupiters may be found in dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular model, we construct a semi-analytical averaging method in terms of the restricted problem. The secular orbits of large planets are approximated by numerically averaged osculating elements. They are used to calculate the mean orbits of terrestrial planets by means of a high-order analytic secular theory developed in our previous works. We found regions in the parameter space of the problem in which stable, quasi-circular orbits in the HZ are permitted. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian orbits. For some combinations of that angle, eccentricities and semi-major axes consistent with the observations, a terrestrial planet may survive in low eccentric orbits. We also study the effect of post-Newtonian gravity correction on the innermost secular resonance.