Inclination Dynamics of Resonant Planets under the Influence of an Inclined External Companion

Abstract

Recent observations suggest that a large fraction of Kepler super-Earth systems have external giant planet companions (cold Jupiters), which can shape the architecture of the inner planets, in particular their mutual inclinations. The dynamical perturbation from cold Jupiters may account for the population of misaligned planets in the Kepler data. The effectiveness of this mechanism can be hindered by a strong planet--planet coupling in the inner system. In this paper, we study how mean-motion resonances (MMRs) affect this coupling and the expected misalignment. We derive approximate analytical expressions for the mutual inclination excitations in the inner planet system induced by an inclined companion, for various period ratios and perturber properties. In most cases, the mutual inclination is proportional to a dimensionless parameter that characterizes the strength of the perturber relative to the coupling in the inner system. We show that the MMR strengthens the inner coupling, reducing the mutual inclination induced by the perturber by a factor of a few. We find that the resonance is resilient to the perturbation, and derive a criterion for the libration of the resonant angle. Our results have applications for constraining unseen planetary perturbers, and for understanding the architecture of multiplanet systems.