Atmospheric tides in Earth-like planets

¹ IMCCE, Observatoire de Paris, CNRS UMR 8028, PSL, 77 Avenue Denfert-Rochereau, 75014 Paris, France
e-mail: pierre.auclair-desrotour@u-bordeaux.fr
² Laboratoire AIM Paris-Saclay, CEA/DSM – CNRS – Université Paris Diderot, IRFU/SAp Centre de Saclay, 91191 Gif-sur-Yvette, France
e-mail: stephane.mathis@cea.fr
³ LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon, France

Received: 4 February 2016
Accepted: 8 November 2016

Abstract

Context. Atmospheric tides can strongly affect the rotational dynamics of planets. In the family of Earth-like planets, which includes Venus, this physical mechanism coupled with solid tides makes the angular velocity evolve over long timescales and determines the equilibrium configurations of their spin.

Aims. Unlike the solid core, the atmosphere of a planet is subject to both tidal gravitational potential and insolation flux coming from the star. The complex response of the gas is intrinsically linked to its physical properties. This dependence has to be characterized and quantified for application to the wide variety of extrasolar planetary systems.

Methods. We develop a theoretical global model where radiative losses, which are predominant in slowly rotating atmospheres, are taken into account. We analytically compute the perturbation of pressure, density, temperature, and velocity field caused by a thermogravitational tidal perturbation. From these quantities, we deduce the expressions of atmospheric Love numbers and tidal torque exerted on the fluid shell by the star. The equations are written for the general case of a thick envelope and the simplified one of a thin isothermal atmosphere.

Results. The dynamics of atmospheric tides depends on the frequency regime of the tidal perturbation: the thermal regime near synchronization and the dynamical regime characterizing fast-rotating planets. Gravitational and thermal perturbations imply different responses of the fluid, i.e. gravitational tides and thermal tides, which are clearly identified. The dependence of the torque on the tidal frequency is quantified using the analytic expressions of the model for Earth-like and Venus-like exoplanets and is in good agreement with the results given by global climate models (GCM) simulations.Introducing dissipative processes such as radiation regularizes the tidal response of the atmosphere, otherwise it is singular at synchronization.

Conclusions. We demonstrate the important role played by the physical and dynamical properties of a super-Earth atmosphere (e.g. Coriolis, stratification, basic pressure, density, temperature, radiative emission) in its response to a tidal perturbation.  We point out the key parameters defining tidal regimes (e.g. inertia, Brunt-Väisälä, radiative frequencies, tidal frequency) and characterize the behaviour of the fluid shell in the dissipative regime, which cannot be studied without considering the radiative losses.