Analytical Model of Tidal Distortion and Dissipation for a Giant Planet with a Viscoelastic Core

We present analytical expressions for the tidal Love numbers of a giant planet with a solid core and a fluid envelope. We model the core as a uniform, incompressible, elastic solid, and the envelope as a non-viscous fluid satisfying the \(n=1\) polytropic equation of state. We discuss how the Love n...

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Bibliographic Details
Published in:arXiv.org 2015-02
Main Authors: Storch, Natalia I, Lai, Dong
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Distortion
Equations of state
Exact solutions
Extrasolar planets
Fluid flow
Incompressible flow
Jupiter
Love number
Mathematical analysis
Mathematical models
Rheological properties
Saturn
Shear modulus
Viscoelasticity
Viscous fluids
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Summary:We present analytical expressions for the tidal Love numbers of a giant planet with a solid core and a fluid envelope. We model the core as a uniform, incompressible, elastic solid, and the envelope as a non-viscous fluid satisfying the \(n=1\) polytropic equation of state. We discuss how the Love numbers depend on the size, density, and shear modulus of the core. We then model the core as a viscoelastic Maxwell solid and compute the tidal dissipation rate in the planet as characterized by the imaginary part of the Love number \(k_2\). Our results improve upon existing calculations based on planetary models with a solid core and a uniform (\(n=0\)) envelope. Our analytical expressions for the Love numbers can be applied to study tidal distortion and viscoelastic dissipation of giant planets with solid cores of various rheological properties, and our general method can be extended to study tidal distortion/dissipation of super-earths.
ISSN:2331-8422
DOI:10.48550/arxiv.1502.06550