An analytical framework for atmospheric tides on rocky planets. II. Semidiurnal thermotidal torque

The thermodynamic acceleration induced by atmospheric thermal tides has a major impact on the rotation of temperate rocky planets, where gravitational and radiative tidal forcings are of comparable strength. This acceleration drives planets away from synchronous rotation, thereby affecting their climate, large-scale circulation, and surface conditions. These implications underline the need to better constrain the dependence of thermotidal torque on tidal frequency and on the physical parameters characterising a star-planet system, as this relationship remains insufficiently understood. In particular, the role of resonantly excited Lamb waves requires clarification due to its potential impact on Earth's length of day (LOD) during the Precambrian. A LOD length of the day Building on a previous work that provided a fully analytical formulation of the atmospheric tidal response of rocky planets, we applied this framework to isentropic and isothermal atmospheres. We performed a comprehensive functional analysis of the resulting torque and compared the analytical predictions with numerical solutions from earlier general circulation model (GCM) studies. A GCM general circulation model The analytical model reproduces the present-day thermotidal bulge and torque inferred from barometric observations when direct absorption is assumed. It also agrees well with GCM results, accurately capturing the frequency dependence of both surface-pressure oscillation amplitudes and tidal torque for paleo-Earth as well as that of the torque for present-day Earth. More generally, the solutions capture the torque peak near synchronous rotation and the amplification associated with Lamb-wave resonance, although incomplete GCM spectra limit some quantitative comparisons. Near resonance, the GCM results exhibit a braking torque of a larger amplitude than the accelerating torque. This asymmetry was reproduced by allowing tidal heating to lag behind insolation. The agreement with GCM spectra constrains the free parameters of our model. It further suggests that thermal tides in the benchmark simulations are driven predominantly by an indirect thermal forcing characterised by a substantial time delay, in contrast to the direct absorption of sunlight that dominates semidiurnal tides on present-day Earth.