Parameterised by the Love number k2 and the tidal quality factor Q, and inferred from lunar laser ranging (LLR), tidal dissipation in the Moon follows an unexpected frequency dependence often interpreted as evidence for a highly dissipative, melt-bearing layer encompassing the core-mantle boundary. Within this, more or less standard interpretation, the basal layer’s viscosity is required to be of order 1015 to 1016 Pa.s and its outer radius is predicted to extend to the zone of deep moonquakes. While the reconciliation of those predictions with the mechanical properties of rocks might be challenging, alternative lunar interior models without the basal layer are said to be unable to fit the frequency dependence of tidal Q. The purpose of our paper is to illustrate under what conditions the frequency-dependence of lunar tidal Q can be interpreted without the need for deep-seated partial melt. Devising a simplified lunar model, in which the mantle is described by the Sundberg-Cooper rheology, we predict the relaxation strength and characteristic timescale of elastically-accommodated grain boundary sliding in the mantle that would give rise to the desired frequency dependence. Along with developing this alternative model, we test the traditional model with basal partial melt; and we show that the two models cannot be distinguished from each other by the available selenodetic measurements. Additional insight into the nature of lunar tidal dissipation can be gained either by measurements of higher-degree Love numbers and quality factors or by farside lunar seismology.

Free nutation is excited if the rotational equilibrium of a planetary body is disturbed. When viewed from space, it is expressed as a wobble of the planet around its rotation pole, and the duration of one cycle is referred to as the Chandler period. Because planets are not rigid, their free nutation period differs from their Euler period by the factor 1-kX/kf, where kX/kf is a ratio of two Love numbers. Here, we perform direct numerical simulations of free nutation and show that kX is not the Love number at the frequency of the Chandler wobble itself, as is commonly assumed, but rather that it is close to ke, the elastic Love number. This result is important when the Chandler periods of Earth and Mars are interpreted, because the measured frequency is related to the internal rheological structure in a different way than previously thought.

The anelastic reaction of planet-forming materials is successfully described by the Andrade rheological model, which presents an extension of the simple Maxwell rheology. In addition to the instantaneous elastic deformation and the long-term viscous creep, the Andrade rheology incorporates the transient creep in metals, ices, and silicates, and is able to explain the tidal parameters of planets even in cases, where the Maxwell model requires the assumption of unrealistically low mantle viscosities. In this work, we discuss the applications of the Andrade model in planetary science, the parameters used in the literature, and their justification by material science and geodesy. We also examine the topic of relating the empirical tidal parameters to the mantle viscosity of moons and terrestrial planets and assess the limitations resulting from the uncertainties in the rheological parameters. Our study illustrates the necessity for future measurements that would help to better calibrate the rheological models to conditions relevant to the deep interiors of planets and moons.

A document by Aymeric Fleury. Click on the document to view its contents.