Atmospheric thermal tides and planetary spin I. The complex interplay between stratification and rotation

Thermal atmospheric tides can torque telluric planets away from spin-orbit synchronous rotation, as observed in the case of Venus. They thus participate to determine the possible climates and general circulations of the atmospheres of these planets. In this work, we write 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 allows us to derive analytically the tidal torque and the tidally dissipated energy, which we use to discuss the possible regimes of tidal dissipation and examine the key role played by stratification. 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 behaviour corresponds to weakly stably stratified or convective fluid layers, as observed in ADLM2016a. A strong stable stratification allows gravity waves to propagate, which makes the tidal torque become 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. 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.