Viscoelastic Tides of Mercury and the Determination of its Inner Core Size

Abstract

We computed interior structure models of Mercury and analyzed their viscoelastic tidal response. The models are consistent with MErcury Surface, Space Environment, GEochemistry, and Ranging mission inferences of mean density, mean moment of inertia, moment of inertia of mantle and crust, and tidal Love number k2. Based on these constraints we predict the tidal Love number h2 to be in the range from 0.77 to 0.93. Using an Andrade rheology for the mantle the tidal phase‐lag is predicted to be 4° at maximum. The corresponding tidal dissipation in Mercury's silicate mantle induces a surface heat flux smaller than 0.16 mW/m2. We show that, independent of the adopted mantle rheological model, the ratio of the tidal Love numbers h2 and k2 provides a better constraint on the maximum inner core size with respect to other geodetic parameters (e.g., libration amplitude or a single Love number), provided it responds elastically to the solar tide. For inner cores larger than 700 km, and with the expected determination of h2 from the upcoming BepiColombo mission, it may be possible to constrain the size of the inner core. The measurement of the tidal phase‐lag with an accuracy better than ≈0.5° would further allow constraining the temperature at the core‐mantle boundary for a given grain size and therefore improve our understanding of the physical structure of Mercury's core.

Geodetic Evidence That Mercury Has A Solid Inner Core

“…For this reason, we did not include in our internal model determination the Love number k 2 , which provides information more sensitive to the outer silicate layers than the solid inner core (Padovan et al, 2014). Knowledge of k 2 and the radial displacement Love number h 2 , the latter of which is still unknown in value, may enable a better characterization of the deep interior (Steinbrügge et al, 2018). We adapted a Markov chain Monte Carlo (MCMC) algorithm to generate ensembles of interior models that satisfy these geophysical constraints.…”

Prospects for measuring Mercury’s tidal Love numberh2with the BepiColombo Laser Altimeter

“…Measurements of tides (Mazarico et al 2014b;Verma & Margot 2016;Genova et al 2019) and global contraction (Byrne et al 2014) can further constrain interior models (Padovan et al 2014;Knibbe & van Westrenen 2015). Recent modeling efforts are in agreement on Mercury's being composed of a solid outer shell of about 400 km thickness and a large metallic liquid core (Hauck et al 2013;Padovan et al 2014;Knibbe & van Westrenen 2015;Margot et al 2018;Steinbrügge et al 2018a;Genova et al 2019). However, the existence and size of a potential solid inner core is still uncertain (Margot et al 2018, and references therein).…”

“…The Love number h 2 is a bulk quantity that can be computed from radial profiles of density, shear modulus, and viscosity (Segatz et al 1988;Moore & Schubert 2000). Model calculations predict 0.77 < h 2 < 0.93 (Steinbrügge et al 2018a). For h 2 = 0.85, the peak-to-peak amplitude of the resulting surface displacement u r reaches the maximum of 2.13 m at (θ = 90…”

“…Both h 2 and the Love number k 2 , which describes the change of the gravitational potential due to tides, are highly sensitive to the thickness and rheology of the mantle and only weakly depend on the properties of the core. However, forming the ratio h 2 /k 2 and the linear combination 1 + k 2 − h 2 , also called the diminishing factor, alleviates the resulting tradeoffs (Wu et al 2001;Wahr et al 2006;van Hoolst et al 2007;Steinbrügge et al 2018a). These derived quantities are rather sensitive to the inner core size, which could be inferred to ±100 km given error-free measurements of k 2 and h 2 if the inner core radius exceeds 800 km (Steinbrügge et al 2018a).…”

Measuring Ganymede’s Librations with Laser Altimetry

“…However, these studies also show that the tidal Love numbers h 2 and k 2 further depend on the ice shell rheology and to some extent on the deeper interior. Also, a linear combination of both Love numbers [2,13,19] still shows a wide range of ambiguities and is highly model dependent. Hence, the analysis of the libration amplitudes may impose additional independent constraints, as demonstrated recently by Thomas et al [20] for Saturn's moon Enceladus.…”