The Concentric Maclaurin Spheroid method with tides and a rotational enhancement of Saturn's tidal response

TL;DR

This paper extends the Concentric Maclaurin Spheroid method to include tides and planetary rotation, revealing significant effects on tidal response in gas giants like Saturn and Jupiter, with results matching observational data.

Contribution

The paper introduces a 3D extension of the Concentric Maclaurin Spheroid method that incorporates tides and rotation, providing more accurate models of gas giant gravitational responses.

Findings

Rotation significantly affects tidal Love numbers in gas giants.

The Saturn model's Love number matches Cassini observations.

The method is validated against existing test cases.

Abstract

We extend to three dimensions the Concentric Maclaurin Spheroid method for obtaining the self-consistent shape and gravitational field of a rotating liquid planet, to include a tidal potential from a satellite. We exhibit, for the first time, the important effect of the planetary rotation rate on tidal response of gas giants. Simulations of planets with fast rotation rates like those of Jupiter and Saturn, exhibit significant changes in calculated tidal love numbers $k_{nm}$ when compared with non-rotating bodies. A test model of Saturn fitted to observed zonal gravitational multipole harmonics yields $k_2=0.413$, consistent with a recent observational determination from Cassini astrometry data (Lainey et al., 2016). The calculated love number is robust under reasonable assumptions of interior rotation rate, satellite parameters, and details of Saturn's interior structure. The method is benchmarked against several published test cases.