Mercury's interior structure and tidal deformation

Abstract

Mercury is unique among the terrestrial planets for its comparatively low mass but high average density. Since polar orbit insertion in 2011, MESSENGER has been collecting altimetry and radio tracking data, from which the spherical harmonic expansion of Mercury’s low-degree gravity field is obtained. From the combined analysis of spacecraft and earth based observations, Margot et al. (2012) inferred the polar moment-of-inertia factor, C/MR2, together with the moment of inertia of the planet’s rigid outer shell relative to that of the planet, Cm/C. We have constructed four-layer spherically symmetric structural models, consisting of an iron-rich Fe-FeS liquid outer core, a pure iron solid inner core, and a silicate mantle overlain by a crust layer. The models have varying crustal thicknesses, silicate mantle compositions, core radii and sulfur contents and are required to satisfy the planet's mean density, C/MR2 and Cm/C within their observational uncertainties. Mercury’s response to solar tidal forcing is then described in terms of the surface body tide Love numbers k2 and h2, which strongly depend on the planet's interior structure and rheological properties. We employ the frequency-dependent Maxwell rheology to calculate the body tide Love numbers for the main tidal period (88 days) using the obtained density, rigidity and viscosity profiles of our structural models. We obtain values in the range 0.4 to 0.7 for k2 and between 0.7 and 1.1 for h2, respectively, indicating the planet's relatively strong tidal response in terms of potential variation and radial surface displacement. Furthermore, we find that both k2 and h2 are foremost dependent on the mantle composition and less affected by the details of the core structure. The peak-to-peak radial displacement amplitudes are predicted to range from a few tens of centimeters in the polar regions to several meters in the equatorial regions, sufficiently large to be detected by laser altimetry from the future BepiColombo spacecraft.