Mercury’s Low-Degree Geoid and Topography from Insolation-Driven Elastic Deformation

Abstract:

Because of Mercury’s high eccentricity, nearly zero obliquity, and 3:2 spin-orbit resonance, the planet’s surface is characterized by an average insolation pattern resulting in longitudinal and latitudinal temperature variations that can be expressed in terms of the (2,0), (2,2) and (4,0) harmonics [Vasavada et al., 1999]. We show that the temperature anomalies that propagate from the surface into the deep mantle can be used to interpret the above harmonics of the geoid and topography spectra in terms of the elastic response of the lithosphere and mantle. Using 3D numerical simulations of thermal evolution constrained by MESSENGER observations [Tosi et al., 2013], we first demonstrate that mantle convection either ceased in the past or, at most, is very weak at present, implying that the mantle is in a conductive or nearly-conductive state. As a consequence, the power spectra of the geoid and topography due to present-day mantle convection only are orders of magnitude smaller than the observed ones. We assume therefore that present-day heat transport in the mantle occurs primarily via thermal conduction and numerically solve the diffusion equation in a 3D spherical shell with variable surface temperature and internal heat sources partitioned between the mantle and a crust of variable thickness according to different enrichment factors. We obtain a set of temperature distributions that are employed to calculate the deformation of a compressible elastic layer overlying a quasi-hydrostatic mantle in which shear stresses are assumed to be relaxed and deformation solely induced by thermal and mechanical compressibility. The surface displacements calculated with this model are then compared against the observed topography, while the internal density anomalies and the displacements of the surface and core-mantle boundary are used to calculate Mercury’s geoid. We thoroughly explore the parameter space by varying the thickness of the boundary between the elastic and quasi-hydrostatic layers, the lithosphere’s elastic parameters and the coefficient of thermal expansion. Our model can reproduce more than 90% of the observed low-degree geoid and topography thereby allowing us to constrain the effective thickness of Mercury’s elastic lithosphere.