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

Abstract

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 the thermotidal torque on the tidal frequency and on the physical parameters characterising the 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. Building on a previous work, which provided a fully analytical formulation of the atmospheric tidal response of rocky planets, we apply this framework to isentropic and isothermal atmospheres. We perform a comprehensive functional analysis of the resulting torque and compare the analytical predictions with numerical solutions from earlier general circulation model (GCM) studies. The analytical model agrees well with GCM results, accurately capturing the frequency dependence of tidal torque both for paleo-Earth and present-day Earth. More generally, the solutions capture the torque peak near synchronous rotation and the amplification associated with Lamb-wave resonance. Near resonance, the GCM results exhibit a stronger braking torque than accelerating torque. This asymmetry is reproduced by allowing tidal heating to lag behind insolation. The agreement with GCM spectra 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.