On tidal theories and the rotation of viscous bodies

Abstract

Celestial bodies are complex systems with the ability to get deformed by tides. Modelling accurately this process is a difficult task even for the planets of our own solar system. This is why tidal theories applied to exoplanets are often reduced to a simple formula accounting for our lack of knowledge. In this work, we identify the three minimal assumptions leading to this level of simplification. We then compare different rheologies compatible with these hypotheses and discuss their qualitative behaviour. Finally, we apply the viscous model to close-in planets and describe their rotation evolution, emphasising the apparition of spin-orbit resonances as the viscous timescale increases.