Abstract
Context. Thermal atmospheric tides have a strong impact on the rotation of terrestrial planets. They can lock these planets into an asynchronous rotation state of equilibrium. Aims. We aim to characterize the dependence of the tidal torque resulting from the semidiurnal thermal tide on the tidal frequency, the planet orbital radius, and the atmospheric surface pressure. Methods. The tidal torque was computed from full 3D simulations of the atmospheric climate and mean flows using a generic version of the LMDZ general circulation model in the case of a nitrogen-dominated atmosphere. Numerical results are discussed with the help of an updated linear analytical framework. Power scaling laws governing the evolution of the torque with the planet orbital radius and surface pressure are derived. Results. The tidal torque exhibits (i) a thermal peak in the vicinity of synchronization, (ii) a resonant peak associated with the excitation of the Lamb mode in the high frequency range, and (iii) well defined frequency slopes outside these resonances. These features are well explained by our linear theory. Whatever the star–planet distance and surface pressure, the torque frequency spectrum – when rescaled with the relevant power laws – always presents the same behaviour. This allows us to provide a single and easily usable empirical formula describing the atmospheric tidal torque over the whole parameter space. With such a formula, the effect of the atmospheric tidal torque can be implemented in evolutionary models of the rotational dynamics of a planet in a computationally efficient, and yet relatively accurate way.
Highlights
Understanding the evolution of planetary systems has become a crucial question with the rapidly growing number of exoplanets discovered up to now
We introduce two new models for the thermally generated atmospheric tidal torque: an ab initio analytical model based upon the linear theory of atmospheric tides (e.g. Chapman & Lindzen 1970), and a parametrized semi-analytical model derived from results obtained using general circulation models (GCM) simulations
Discussion on the Maxwell model Analytic ab initio approaches based on a linear analysis of the atmospheric tidal response – including this work – predict that the imaginary part of surface pressure variations can be expressed as a function of the forcing frequency σ = 2 (Ω − n ) as (e.g. Ingersoll & Dobrovolskis 1978; Auclair-Desrotour et al 2017a)
Summary
Understanding the evolution of planetary systems has become a crucial question with the rapidly growing number of exoplanets discovered up to now. Characterizing the atmospheric dynamics and climate of these planets is a topic that motivated numerous theoretical works, both analytical and numerical (e.g. Pierrehumbert 2011; Heng & Kopparla 2012; Leconte et al 2013; Heng & Workman 2014; Wolf et al 2017; Wolf 2017; Turbet et al 2018) This tendency will be reinforced in the future by the rise of forthcoming space observatories such as the James Webb Space Telescope (JWST), which will unravel features of the planetary atmospheric structure by performing high resolution spectroscopy over the infrared frequency range (Lagage 2015). In the low-frequency range, the behaviour of the torque appears to be a little bit more complex than that predicted by the model, which reduces to a simple Maxwell function This is not surprising since the atmospheric tidal response at low tidal frequencies involves complex non-linear mechanisms, interactions with mean flows, and dissipative processes, which are clearly outside of the scope of the classical tidal theory used to establish the solution given by Eqs. As they treat the full non-linear 3D dynamics of the atmosphere in a selfconsistent way, GCM simulations are useful in this prospect
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