Spatial patterns of tidal heating

TL;DR

This paper develops a mathematical framework to predict the spatial distribution of tidal heating within spherically stratified planetary bodies, illustrating its application to moons like Europa, Titan, and Io.

Contribution

It introduces a linear combination model of angular functions to efficiently compute 3D dissipation patterns from 1D internal structure data without assuming specific rheology.

Findings

Dissipation peaks at poles in mantle with liquid core.

Maximum heating occurs in equatorial soft layers for certain structures.

Tidal heating patterns fall into three main types based on internal layering.

Abstract

In a body periodically strained by tides, heating produced by viscous friction is far from homogeneous. I show here that the distribution of the dissipated power within a spherically stratified body is a linear combination of three angular functions. These angular functions depend only on the tidal potential whereas the radial weights are specified by the internal structure of the body. The 3D problem of predicting spatial patterns of dissipation at all radii is thus reduced to the 1D problem of computing weight functions. I compute spatial patterns in various toy models without assuming a specific rheology: a viscoelastic thin shell stratified in conductive and convective layers, an incompressible homogeneous body and a two-layer model of uniform density with a liquid or rigid core. For a body in synchronous rotation undergoing eccentricity tides, dissipation in a mantle surrounding a liquid core is highest at the poles. Within a softer layer (asthenosphere or icy layer), the same tides generate maximum heating in the equatorial region with a significant degree-four structure if the layer is thin. Tidal heating patterns are thus of three main types: mantle dissipation (including the case of a floating icy crust), dissipation in a thin soft layer and dissipation in a thick soft layer. I illustrate the method with applications to Europa, Titan and Io. The formalism described in this paper applies to dissipation within solid layers of planets and satellites for which internal spherical symmetry and viscoelastic linear rheology are good approximations.