Unveiling Mercury’s interior with dynamical Love numbers

Mercury will soon be visited by the BepiColombo mission, whose scientific objectives span a wide range of topics in physics and planetary science. Investigating its interior and origin is crucial for understanding the formation and evolution of the Solar System. To this aim, the Mercury Orbiter Radio science Experiment (MORE) will enable the determination of the static gravity field and Mercury’s potential Love number k₂, which quantifies the response of a planetary body’s gravity potential to tidal forcing.

In many studies, a static tide approximation is adopted, leading to the determination of a single k₂ value. This approach is appropriate when the planet is treated as purely elastic, so that the tidal response is instantaneous and in phase with the tidal forcing. A more physically consistent description of the interior, however, requires viscoelastic rheologies, which induce a lag in the tidal response. Under these conditions, the static tide approximation is more adequate when the orbit is circular and the planet is in synchronous rotation (tidally locked). Mercury, however, is in a 3:2 spin-orbit resonance and has an eccentric orbit (e = 0.2056), making a dynamical tide description required. To implement it, the tidal potential is expanded as a Fourier series over multiple tidal modes. The main consequence of this approach is the emergence of a frequency-dependent Love number, k₂(Ιω_2mpqΙ) , evaluated at the specific forcing frequencies Ιω_2mpqΙ.

The aim of this work is to investigate the scientific insights that could be gained from measuring k₂(Ιω_2mpqΙ). Since not all tidal modes contribute equally, we focus on those expected to account for the largest fraction to the tidal signal. We then consider different internal models of Mercury and compute the Love numbers associated to the selected modes using ALMA3 and assess their sensitivity to various parameters of the planet’s interior. The main variables examined are the thickness and rigidity of the elastic lithosphere, the size of the liquid outer core, and the viscosity and rheology of the mantle. We demonstrate that the measurement of the dynamical Love number could significantly improve our understanding of Mercury’s mantle relaxation timescales, providing new and essential constraints on its internal structure.

Finally, we performed accurate numerical simulations to verify the feasibility of these measurements with MORE, showing that its sensitivity is adequate to explore the admissible region of the parameter space considered in our models.