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Thermal atmospheric tides have a strong impact on the rotation of terrestrialplanets. They can lock these planets into an asynchronous rotation state ofequilibrium. We aim at characterizing the dependence of the tidal torqueresulting from the semidiurnal thermal tide on the tidal frequency, the planetorbital radius, and the atmospheric surface pressure. The tidal torque iscomputed from full 3D simulations of the atmospheric climate and mean flowsusing a generic version of the LMDZ general circulation model (GCM) in the caseof a nitrogen-dominated atmosphere. Numerical results are discussed with thehelp of an updated linear analytical framework. Power scaling laws governingthe evolution of the torque with the planet orbital radius and surface pressureare derived. The tidal torque exhibits i) a thermal peak in the vicinity ofsynchronization, ii) a resonant peak associated with the excitation of the Lambmode in the high frequency range, and iii) well defined frequency slopesoutside these resonances. These features are well explained by our lineartheory. Whatever the star-planet distance and surface pressure, the torquefrequency spectrum -- when rescaled with the relevant power laws -- alwayspresents the same behaviour. This allows us to provide a single and easilyusable empirical formula describing the atmospheric tidal torque over the wholeparameter space. With such a formula, the effect of the atmospheric tidaltorque can be implemented in evolutionary models of the rotational dynamics ofa planet in a computationally efficient, and yet relatively accurate way.

A generic frequency dependence for the atmospheric tidal torque of terrestrial planets