[1] The recent determination of the gravity field of Mercury and new Earth-based radar observations of the planet's spin state afford the opportunity to explore Mercury's internal structure. These observations provide estimates of two measures of the radial mass distribution of Mercury: the normalized polar moment of inertia and the fractional polar moment of inertia of the solid portion of the planet overlying the liquid core. Employing Monte Carlo techniques, we calculate several million models of the radial density structure of Mercury consistent with its radius and bulk density and constrained by these moment of inertia parameters. We estimate that the top of the liquid core is at a radius of 2020 AE 30 km, the mean density above this boundary is 3380 AE 200 kg m À3 , and the density below the boundary is 6980 AE 280 kg m À3 . We find that these internal structure parameters are robust across a broad range of compositional models for the core and planet as a whole. Geochemical observations of Mercury's surface by MESSENGER indicate a chemically reducing environment that would favor the partitioning of silicon or both silicon and sulfur into the metallic core during core-mantle differentiation. For a core composed of Fe-S-Si materials, the thermodynamic properties at elevated pressures and temperatures suggest that an FeS-rich layer could form at the top of the core and that a portion of it may be presently solid.

[1] Earth-based radar observations of the spin state of Mercury at 35 epochs between 2002 and 2012 reveal that its spin axis is tilted by (2.04 AE 0.08) arc min with respect to the orbit normal. The direction of the tilt suggests that Mercury is in or near a Cassini state. Observed rotation rate variations clearly exhibit an 88-day libration pattern which is due to solar gravitational torques acting on the asymmetrically shaped planet. The amplitude of the forced libration, (38.5 AE 1.6) arc sec, corresponds to a longitudinal displacement of $450 m at the equator. Combining these measurements of the spin properties with second-degree gravitational harmonics (Smith et al., 2012) provides an estimate of the polar moment of inertia of Mercury C/MR 2 = 0.346 AE 0.014, where M and R are Mercury's mass and radius. The fraction of the moment that corresponds to the outer librating shell, which can be used to estimate the size of the core, is C m /C = 0.431 AE 0.025.

The present‐day thermal state, interior structure, composition, and rheology of Mars can be constrained by comparing the results of thermal history calculations with geophysical, petrological, and geological observations. Using the largest‐to‐date set of 3‐D thermal evolution models, we find that a limited set of models can satisfy all available constraints simultaneously. These models require a core radius strictly larger than 1,800 km, a crust with an average thickness between 48.8 and 87.1 km containing more than half of the planet's bulk abundance of heat producing elements, and a dry mantle rheology. A strong pressure dependence of the viscosity leads to the formation of prominent mantle plumes producing melt underneath Tharsis up to the present time. Heat flow and core size estimates derived from the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission will increase the set of constraining data and help to confine the range of admissible models.

Key Points:• We present models of the tidal deformation of Mercury based on MESSENGER results • Tides are sensitive to size and density of the core and rheology of outer shell • The presence of a FeS layer would increase the tidal response AbstractThe combination of the radio tracking of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft and Earth-based radar measurements of the planet's spin state gives three fundamental quantities for the determination of the interior structure of Mercury: mean density , moment of inertia C, and moment of inertia of the outer solid shell C m . This work focuses on the additional information that can be gained by a determination of the change in gravitational potential due to planetary tides, as parameterized by the tidal potential Love number k 2 . We investigate the tidal response for sets of interior models that are compatible with the available constraints ( , C, and C m ). We show that the tidal response correlates with the size of the liquid core and the mean density of material below the outer solid shell and that it is affected by the rheology of the outer solid shell of the planet, which depends on its temperature and mineralogy. For a mantle grain size of 1 cm, we calculate that the tidal k 2 of Mercury is in the range 0.45 to 0.52. Some of the current models for the interior structure of Mercury are compatible with the existence of a solid FeS layer at the top of the core. Such a layer, if present, would increase the tidal response of the planet.