Research Note

The surface signature of the tidal dissipation of the core in a two-layer planet

¹ IMCCE, Observatoire de Paris – UMR 8028 du CNRS – Université Pierre et Marie Curie, 77 avenue Denfert-Rochereau, 75014 Paris, France
e-mail: francoise.remus@obspm.fr, lainey@imcce.fr
² LUTH, Observatoire de Paris – CNRS – Université Paris Diderot, 5 place Jules Janssen, 92195 Meudon Cedex, France
e-mail: jean-paul.zahn@obspm.fr
³ 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
⁴ LESIA, Observatoire de Paris – CNRS – Université Paris Diderot – Université Pierre et Marie Curie, 5 place Jules Janssen, 92195 Meudon, France

Received: 25 June 2014
Accepted: 30 September 2014

Abstract

Context. Tidal dissipation, which is directly linked to internal structure, is one of the key physical mechanisms that drive the evolution of systems and govern their architecture. A robust evaluation of its amplitude is thus needed to predict the evolution time for spins and orbits and their final states.

Aims. The purpose of this paper is to refine a recent model of the anelastic tidal dissipation in the central dense region of giant planets, which are commonly assumed to retain a large amount of heavy elements, which constitute an important source of dissipation.

Methods. The previous paper evaluated the impact of the static fluid envelope on the tidal deformation of the core and on the associated anelastic tidal dissipation through the tidal quality factor Q_c. We examine here its impact on the corresponding effective anelastic tidal dissipation through the effective tidal quality factor Q_p.

Results. We show that the strength of this mechanism mainly depends on mass concentration. In the case of Jupiter- and Saturn-like planets, it can increase their effective tidal dissipation by, around, factors 2.4 and 2, respectively. In particular, the range of the rheologies compatible with the observations is enlarged compared to the results issued from previous formulations.

Conclusions. We derive here an improved expression of the tidal effective factor Q_p in terms of the tidal dissipation factor of the core Q_c, without assuming the commonly used assumptions. When applied to giant planets, the formulation obtained here allows a better match between the anelastic core’s tidal dissipation of a two-layer model and the observations.