Equilibrium Tides on Planets and Stars

• Autor(a) principal: Gabriel de Oliveira Gomes
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://doi.org/10.11606/T.14.2022.tde-20062022-170909

Most applications currently made using equilibrium tidal theories are based on the use of ad-hoc tidal lags. In the case of applications made with Darwin\'s classical theory, for example, the prediction for the final stage of rotational evolution is synchronism for the case of circular orbits and supersynchronism for eccentric orbits (where the excess of rotation in relation to the synchronism is given by 6ne2, where n is the mean orbital motion and is the orbital eccentricity). Recently, a formulation for equilibrium tides that considers a linearized solution of the Navier-Stokes equation was made at the IAG (see Ferraz-Mello 2013, 2015). The theory allows the description of equilibrium tides in both rigid bodies (such as super-Earths) and gaseous bodies (such as mini-Neptunes and hot Jupiters) by adjusting just one parameter, which is the uniform viscosity coefficient. The first version of the tidal creep theory (ie the version proposed in Ferraz-Mello 2013, 2015) was based on a series expansion of the so-called creep equation. In this structure, the rate of rotation of the tidal deformed body was considered constant when solving the creep equation. Then, the rotation rate was evolved considering the torque expression related to tidal interactions. This method is not consistent when it comes to the evolution of the rotation rate of the tidal deformed body. One of the consequences of considering the rotation rate constant for the body when solving the creep equation is that the rotation rate librations in the synchronous rotation regime are very small for rigid bodies. This result is inconsistent with the libration amplitude of the rotation rate and the tidal lag angle of the Solar System\'s planetary satellites. A new formulation of the tidal creep theory was proposed in Folonier et al. (2018). The new version of the theory leads to a consistent treatment of the rotational dynamics of the tidally deformed body, where forced librations around the synchronous solution (which are characteristic in the case of rigid bodies such as super-Earths and planetary satellites) are reproduced. Furthermore, the new version of the tidal creep theory allows a study of the equilibrium figure of the tidal deformed body in a much simpler way than the previous version of the theory. In this thesis, we present applications of the tidal creep theory to several cases, where both gas giant planets and Earth-like rigid planets are considered. We also discuss in detail the differences between the first version of the creep tide theory (see Ferraz-Mello 2013, 2015) and the new version (see Folonier et al. 2018).