Impact of the frequency dependence of tidal Q on the evolution of planetary systems

¹ SYRTE, Observatoire de Paris, UMR 8630 du CNRS, UPMC, 77 Av. Denfert-Rochereau, 75014 Paris, France
e-mail: christophe.leponcin@obspm.fr; pierre.auclair-desrotour@obspm.fr
² Laboratoire AIM Paris-Saclay, CEA/DSM – CNRS – Université Paris Diderot, IRFU/SAp Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France
e-mail: stephane.mathis@cea.fr
³ IMCCE, Observatoire de Paris, UMR 8028 du CNRS, UPMC, 77 Av. Denfert-Rochereau, 75014 Paris, France
⁴ LESIA, Observatoire de Paris, CNRS UMR 8109, UPMC, Univ. Paris-Diderot, 5 place Jules Janssen, 92195 Meudon, France

Received: 2 October 2013
Accepted: 19 November 2013

Abstract

Context. Tidal dissipation in planets and in stars is one of the key physical mechanisms that drive the evolution of planetary systems.

Aims. Tidal dissipation properties are intrinsically linked to the internal structure and the rheology of the studied celestial bodies. The resulting dependence of the dissipation upon the tidal frequency is strongly different in the cases of solids and fluids.

Methods. We computed the tidal evolution of a two-body coplanar system, using the tidal-quality factor frequency-dependencies appropriate to rocks and to convective fluids.

Results. The ensuing orbital dynamics is smooth or strongly erratic, depending on the way the tidal dissipation depends upon frequency.

Conclusions. We demonstrate the strong impact of the internal structure and of the rheology of the central body on the orbital evolution of the tidal perturber. A smooth frequency-dependence of the tidal dissipation causes a smooth orbital evolution, while a peaked dissipation can produce erratic orbital behaviour.