Viscoelastic relaxation within the Moon and the phase lead of its Cassini state

TL;DR

This study models viscoelastic deformation within the Moon's inner core to explain the observed phase lead of its Cassini state, revealing significant contributions under specific viscosity and resonance conditions.

Contribution

It introduces a rotational dynamic model including an inner core with viscoelastic properties, exploring its effect on the Moon's Cassini state phase lead.

Findings

Inner core viscoelastic deformation can significantly influence the phase lead angle.

The contribution peaks when the inner core viscosity is between 10^{13} and 10^{14} Pa s.

Resonance with the free inner core nutation frequency enhances the effect.

Abstract

Analyses of Lunar Laser Ranging data show that the spin-symmetry axis of the Moon is ahead of its expected Cassini state by an angle of $\phi_p$ = 0.27 arcsec. This indicates the presence of one or more dissipation mechanisms acting on the lunar rotation. A combination of solid-body tides and viscous core-mantle coupling have been proposed in previous studies. Here, we investigate whether viscoelastic deformation within a solid inner core at the centre of the Moon can also account for a part of the observed phase lead angle $\phi_p$. We build a rotational dynamic model of the Cassini state of the Moon that comprises an inner core, a fluid core and a mantle, and where solid regions are allowed to deform viscoelastically in response to an applied forcing. We show that the presence of an inner core does not change the global monthly Q of the Moon and hence, that the contribution from solid-body tides to $\phi_p$ is largely unaffected by an inner core. However, we also show that viscoelastic deformation within the inner core, acting to realign its figure axis with that of the mantle, can contribute significantly to $\phi_p$ through inner core-mantle gravitational coupling. We show that the contribution to $\phi_p$ is largest when the inner core viscosity is in the range of $10^{13}$ to $10^{14}$ Pa s, when the inner core radius is large and when the free inner core nutation frequency approaches a resonance with the precession frequency of $2\pi/18.6$ yr$^{-1}$.