Atmospheric thermal tides and planetary spin

I. The complex interplay between stratification and rotation

¹ LAB, Université de Bordeaux, CNRS UMR 5804, Université de Bordeaux, Bât. B18N, Allée Geoffroy Saint-Hilaire CS50023, 33615 Pessac Cedex France
e-mail: pierre.auclair-desrotour@u-bordeaux.fr
² Laboratoire AIM Paris-Saclay, CEA/DRF, CNRS, Université Paris Diderot, IRFU/DAp Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France
e-mail: stephane.mathis@cea.fr
³ LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, UPMC Univ. Paris 6, Univ. Paris Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon, France
⁴ IMCCE, Observatoire de Paris, CNRS UMR 8028, PSL Research University, 77 Avenue Denfert-Rochereau, 75014 Paris, France
e-mail: jacques.laskar@obspm.fr

Received: 10 July 2017
Accepted: 28 September 2017

Abstract

Context. Thermal atmospheric tides can torque telluric planets away from spin-orbit synchronous rotation, as observed in the case of Venus. They thus participate in determining the possible climates and general circulations of the atmospheres of these planets.

Aims. The thermal tidal torque exerted on an atmosphere depends on its internal structure and rotation and on the tidal frequency. Particularly, it strongly varies with the convective stability of the entropy stratification. This dependence has to be characterized to constrain and predict the rotational properties of observed telluric exoplanets. Moreover, it is necessary to validate the approximations used in global modelings such as the traditional approximation, which is used to obtain separable solutions for tidal waves.

Methods. We wrote the equations governing the dynamics of thermal tides in a local vertically stratified section of a rotating planetary atmosphere by taking into account the effects of the complete Coriolis acceleration on tidal waves. This allowed us to analytically derive the tidal torque and the tidally dissipated energy, which we used to discuss the possible regimes of tidal dissipation and to examine the key role played by stratification.

Results. In agreement with early studies, we find that the frequency dependence of the thermal atmospheric tidal torque in the vicinity of synchronization can be approximated by a Maxwell model. This behavior corresponds to weakly stably stratified or convective fluid layers, as observed previously. A strong stable stratification allows gravity waves to propagate, and makes the tidal torque negligible. The transition is continuous between these two regimes. The traditional approximation appears to be valid in thin atmospheres and in regimes where the rotation frequency is dominated by the forcing or the buoyancy frequencies.

Conclusions. Depending on the stability of their atmospheres with respect to convection, observed exoplanets can be tidally driven toward synchronous or asynchronous final rotation rates. The domain of applicability of the traditional approximation is rigorously constrained by calculations.