Tidal interactions in spin-orbit misaligned systems

Abstract

Spin-orbit misalignments have been detected in exoplanetary systems and binary star systems. Tidal interactions may have played an important role in the evolution of the spin-orbit angle. In this study, we investigate the tidal interactions in spin-orbit misaligned systems. In particular, we focus on the tidal response of a rotating fluid body to the obliquity tide, which may be important for the evolution of the spin-orbit angle but hardly affects the orbital evolution. The obliquity tide also provides a torque for the mutual precession of the spin and orbital axes around the total angular momentum vector, which has not yet been considered in previous studies on the tidal interactions. In this paper, we first formulate a set of linearized equations describing the tidal response in spin-orbit misaligned systems, taking into account the precessional motion. Numerical solutions in a homogeneous fluid and in a polytrope of index 1 show that dissipative inertial waves can be excited on top of precession by the obliquity tide in the presence of a rigid core. The tidal quality factor associated with the obliquity tide $Q'_{210}$ can be several orders of magnitude smaller than those associated with other tidal components if their frequencies fall outside the frequency range of inertial waves. Therefore, it is possible that the spin-orbit misalignment undergoes much more rapid decay than the orbital decay in hot Jupiter systems owing to the enhanced dissipation of the obliquity tide.