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

TL;DR

This paper derives analytical formulas for tidal Love numbers of giant planets with solid cores and fluid envelopes, accounting for viscoelastic dissipation, improving previous models and applicable to diverse planetary types.

Contribution

It introduces a comprehensive analytical model for tidal Love numbers incorporating viscoelastic core properties, enhancing understanding of planetary tidal responses.

Findings

Derived explicit formulas for Love numbers of planets with solid cores.

Quantified how core properties influence tidal dissipation rates.

Extended the model to include viscoelastic behavior of planetary cores.

Abstract

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.