A Spectral Method to Compute the Tides of Laterally-Heterogeneous Bodies

TL;DR

This paper introduces a new spectral method for efficiently computing the tidal response of bodies with lateral heterogeneities, revealing significant signals that could be measured by future space missions.

Contribution

The paper presents a novel spectral approach that handles large lateral variations in planetary interiors, improving upon previous methods in accuracy and computational efficiency.

Findings

Lateral heterogeneities can produce tidal signals up to 10% of the main response.

Shell-thickness variations of 50% cause 1-10% additional tidal signals.

Future missions may detect these heterogeneity-induced signals.

Abstract

Body tides reveal information about planetary interiors and affect their evolution. Most models to compute body tides rely on the assumption of a spherically-symmetric interior. However, several processes can lead to lateral variations of interior properties. We present a new spectral method to compute the tidal response of laterally-heterogeneous bodies. Compared to previous spectral methods, our approach is not limited to small-amplitude lateral variations; compared to finite element codes, the approach is more computationally-efficient. While the tidal response of a spherically-symmetric body has the same wave-length as the tidal force; lateral heterogeneities produce an additional tidal response with an spectra that depends on the spatial pattern of such variations. For Mercury, the Moon and Io the amplitude of this signal is as high as $1\%-10\%$ the main tidal response for long-wavelength shear modulus variations higher than $\sim 10\%$ the mean shear modulus. For Europa, Ganymede and Enceladus, shell-thickness variations of $50\%$ the mean shell thickness can cause an additional signal of $\sim 1\%$ and $\sim 10\%$ for the Jovian moons and Encelaudus, respectively. Future missions, such as $ \textit{BepiColombo}$ and $\textit{JUICE}$, might measure these signals. Lateral variations of viscosity affect the distribution of tidal heating. This can drive the thermal evolution of tidally-active bodies and affect the distribution of active regions.