Semidiurnal thermal tides in asynchronously rotating hot Jupiters

Abstract

Context. Thermal tides can torque the atmosphere of hot Jupiters into asynchronous rotation, while these planets are usually assumed to be locked into spin-orbit synchronization with their host star. Aims. In this work, our goal is to characterize the tidal response of a rotating hot Jupiter to the tidal semidiurnal thermal forcing of its host star, by identifying the structure of tidal waves responsible for variation of mass distribution, their dependence on the tidal frequency and their ability to generate strong zonal flows. Methods. We develop an ab initio global modeling that generalizes the early approach of Arras & Socrates (2010) to rotating and non-adiabatic planets. We derive analytically the torque exerted on the body and the associated timescales of evolution, as well as the equilibrium tidal response of the atmosphere in the zero-frequency limit. Finally, we integrate numerically the equations of thermal tides for three cases including dissipation and rotation step by step.Results. The resonances associated with tidally generated gravito-inertial waves amplify significantly the resulting tidal torque in the range 1-30 days. This torque can drive globally the atmosphere into asynchronous rotation, as its sign depends on the tidal frequency. The resonant behaviour of the tidal response is enhanced by rotation, which couples the forcing to several Hough modes in the general case, while the radiative cooling tends to regularize it and diminish its amplitude.

Tidal oscillations of rotating hot Jupiters

“…We calculate small amplitude gravitational and thermal tides of uniformly rotating hot Jupiters, composed of a thin radiative envelope and a convective core (see, e.g., Arras & Socrates 2010;Auclair-Desrotour & Leconte 2018;Lee & Murakami 2019), taking account of viscous dissipations in the core and radiative dissipations in the envelope. We linearize the basic equations for the fluid dynamics to describe small amplitude tidal responses.…”

“…thermal tides (e.g., Arras & Socrates 2010;Socrates 2013, Auclair-Desrotour & Leconte 2018. See also, e.g., Jermyn et al (2017) and Lee (2019) for other possibilities.…”

“…Thermal tides in hot Jupiters were discussed by Arras & Socrates (2010), Auclair-Desrotour & Leconte (2018), and Lee & Murakami (2019) as a mechanism that keeps the rotation of hot Jupiters asynchronous to the orbital motion so that tidal heatings in the interior can be operative to inflate the radii of the planets. Arras & Socrates (2010), for non-rotating hot Jupiters, computed tidal responses to semi-diurnal insolation of the hosting star.…”

Modeling the Thermal Bulge of a Hot Jupiter with the Two-stream Approximation

“…Indeed recently, Auclair-Desrotour & Leconte (2018) included the effect of Newtonian damping in the framework of AS to determine how the non-adiabatic effect reduces the quadrupole moment in the atmosphere. The Newtonian damping/cooling is commonly referred to as a linear damping process on the temperature perturbation T ′ over the radiative timescale t th ; i.e., the entropy exchange rate between a wave and its environment is proportional to −T ′ /t th (e.g., Holton 2004).…”

“…MESA has been built to incorporate the atmospheric model with the two-stream approximation formulated by Guillot (2010). In this undertaking, we concentrate on the parameters of the hot Jupiter HD 209458 b as a fiducial study to develop a theoretical model that allows us to draw comparisons with the previous works of Arras & Socrates (2010) and Auclair-Desrotour & Leconte (2018). Given that T eq ∼ 1500 K, the atmosphere of HD 209458 b was postulated to be the boundary between the presence of temperature inversion on hotter planets and the absence of the inversion feature on colder planets (Fortney et al 2008).…”