How do External Companions Affect Spin-Orbit Misalignment of Hot Jupiters?

Abstract

Consider a planet with its orbital angular momentum axis aligned with the spin axis of its host star. To what extent does an inclined distant companion (giant planet or binary star) affect this alignment? We provide an analytic, quantitative answer and apply it to hot Jupiter systems, for which misalignments between the orbital axis and the stellar spin axis have been detected. We also show how similar consideration can be applied to multi-planet systems with distant companions (such as Kepler-56). The result of this paper provides a simple method to assess the dynamical role played by external companions on spin-orbit misalignments in exoplanetary systems.