# Tidal interactions in spin-orbit misaligned systems

## TL;DR

This paper investigates how tidal interactions, especially obliquity tides and inertial waves, influence the evolution of spin-orbit misalignments in exoplanetary and binary systems, revealing potential rapid decay of misalignments.

## Contribution

It introduces a linearized model for tidal response in misaligned systems considering precession and inertial waves, highlighting the significance of obliquity tide dissipation.

## Key findings

- Dissipative inertial waves can be excited by obliquity tides in rotating fluid bodies.
- The tidal quality factor for obliquity tide can be significantly lower than other components.
- Spin-orbit misalignments may decay faster than orbital parameters in hot Jupiter 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.