On models of Mars’ interior and amplitudes of forced nutations: 1. The effects of deviation of Mars from its equilibrium state on the flattening of the core–mantle boundary

Abstract

In a static approach the effects of deviation of Mars from its equilibrium state on the flattening of the core–mantle boundary (CMB) are studied. The calculations are performed for a set of interior structure models with 50- and 100-km thick crust and averaged crustal density varying in the range of 2700–3200 kg m −3, which are based on new values for the moment of inertia and the elastic tidal Love number k 2 s defined by Konopliv et al. [Konopliv, A.S., Yoder, C.F., Standish, E.M., Yuan, D.-N., Sjorgen, W.L., 2006. A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris. Icarus, 182, 23–50]. The models differ in density contrast at the crust–mantle boundary and the core radius. The observational data constrain the radius of a liquid core to be within 1700–1800 km. For joint interpretation of gravity and topography data an outer surface of a hydrostatical model is chosen as a reference surface. The Green's functions (or loading factors) technique for the case of a single anomalous density wave located at two depth level is used to compute the second-degree CMB deformation, and then the CMB flattening. Two types of models have been calculated: an elastic model and a model with an elastic lithosphere and weakened layers below it (relaxed values of shear modulus); the effective shear modulus of the mantle is reduced in comparison with an elastic one and in extreme case it is approaching zero everywhere except the elastic lithosphere. Non-equilibrium state of Mars results in three-axiality of the core–mantle boundary. For an elastic case the deformation of CMB leads to the large decrease of the semiaxis b, going through the central region of Tharsis rise, by 660–780 m, and the increase of the equatorial semiaxis a by 240–300 m, and the polar axis c by 400–490 m. Tharsis rise plays a constitutive role for the CMB deformation. The second-degree harmonics in the expansion of non-equilibrium part of gravity field and topography are sensitive, first of all, to the properties of the crust in the Tharsis region. Non-hydrostatic contributions decrease the flattening of the CMB by about 5–6%. The effect of loading increases when the value of shear modulus decreases by a factor of 10, but as the shear modulus is decreasing up to zero the flattening is approaching its hydrostatic value.