Effect of a non-hydrostatic core-mantle boundary on the nutations of Mars

Abstract. Dynamic loads in planetary mantles have the potential to deform the core-mantle boundary (CMB). On Earth, subducting slabs primarily induce a degree 2–order 2 deformation of the CMB in the spherical harmonic (SH) reference system. On Mars, the presence of the dichotomy and of the Tharsis region could produce loading across multiple degrees and orders, including degree-1, degree 2–order 2, degree 2–order 0, and degree 3–order 3 components. Thanks to the InSight (Interior exploration using Seismic Investigations, Geodesy, and Heat Transport) mission’s radio science experiment, observations of Mars' nutations are now available. Periodic length-of-day (LOD) variations of Mars have been detected first by radio tracking the Viking landers, and InSight data have indicated the presence of a secular trend in LOD. In the case of nutations, the Martian core’s non-hydrostatic flattening plays a first-order role in determining nutation amplitudes. In this study, we explore second-order effects arising from dynamic topography at the CMB. We compute the pressure exerted on the CMB topography inside Mars' liquid core and evaluate the resulting topographic pressure torque acting on the boundary, which can influence both nutations and LOD variations. Our results show that, albeit at microarcsecond level—well below current observational thresholds, the most significant contribution to nutations arises from degree 2–order 2 component. As for LOD variations, while Earth exhibits notable contributions from inertial wave resonances, the situation on Mars is different. The planet’s tidal LOD variations have periods that are either too long or too far apart from those of inertial waves. Consequently, the associated contributions fall below the level of detectability.