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Astronomy and Astrophysics 541, A165 (2012) 17 p.
Anelastic tidal dissipation in multi-layer planets
Françoise Remus 1, 2, 3, Stephane Mathis 3, 4, Jean -Paul Zahn 1, Valery Lainey 2

Earth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic cores. The tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on their rheology and on the tidal frequency. Therefore, modelling tidal interactions presents a high interest to provide constraints on planets' properties and to understand their history and their evolution, in our Solar System or in exoplanetary systems. We examine the equilibrium tide in the anelastic parts of a planet whatever the rheology, taking into account the presence of a fluid envelope of constant density. We show how to obtain the different Love numbers that describe its tidal deformation. Thus, we discuss how the tidal dissipation in solid parts depends on the planet's internal structure and rheology. Finally, we show how the results may be implemented to describe the dynamical evolution of planetary systems. The first manifestation of the tide is to distort the shape of the planet adiabatically along the line of centers. Then, the response potential of the body to the tidal potential defines the complex Love numbers whose real part corresponds to the purely adiabatic elastic deformation, while its imaginary part accounts for dissipation. This dissipation is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which we derive the characteristic evolution times. The rate at which the system evolves depends on the physical properties of tidal dissipation, and specifically on how the shear modulus varies with tidal frequency, on the radius and also the rheological properties of the solid core. The quantification of the tidal dissipation in solid cores of giant planets reveals a possible high dissipation which may compete with dissipation in fluid layers.
1 :  Laboratoire Univers et Théories (LUTH)
CNRS : UMR8102 – INSU – Observatoire de Paris – Université Paris VII - Paris Diderot
2 :  Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE)
CNRS : UMR8028 – INSU – Observatoire de Paris – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Lille I - Sciences et technologies
3 :  Astrophysique Interactions Multi-échelles (AIM - UMR 7158)
CNRS : UMR7158 – INSU – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
4 :  Laboratoire d'études spatiales et d'instrumentation en astrophysique (LESIA)
CNRS : UMR8109 – INSU – Observatoire de Paris – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot
Physique/Astrophysique/Planétologie et astrophysique de la terre

Planète et Univers/Astrophysique/Planétologie et astrophysique de la terre
planets and satellites: general – planets and satellites: physical evolution – planets and satellites: individual: Jupiter – planets and satellites: dynamical evolution and stability – planets and satellites: individual: Saturn – planet-star interactions
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