Constraints on the lunar core viscosity from tidal deformation

We use the tidal deformations of the Moon induced by the Earth and the Sun as a tool for studying the inner structure of our satellite. Based on measurements of the degree-two tidal Love numbers k2 and h2 and dissipation coefficients from the GRAIL mission, Lunar Laser Ranging and Laser Altimetry on board of the LRO spacecraft, we perform Monte Carlo samplings for 120,000 possible combinations of thicknesses and viscosities for two classes of the lunar models. The first one includes a uniform core, a low viscosity zone (LVZ) at the core-mantle boundary, a mantle and a crust. The second one has an additional inner core. All models are consistent with the lunar total mass as well as its moment of inertia. By comparing predicted and observed parameters for the tidal deformations we find that the existence of an inner core cannot be ruled out. Furthermore, by deducing temperature profiles for the LVZ and an Earth-like mantle, we obtain stringent constraints on the radius (500 +- 1) km, viscosity,21 (4.5 +- 0.8) x 10^16 Pa.s and the density (3400 +- 10) kg/m^3 of the LVZ. We also infer the first estimation for the outer core viscosity, (2.07 +- 1.03) x 10^17 Pa.s, for two different possible structures: a Moon with a 70 km thick outer core and a large inner core (290 km radius with a density of 6000 kg/m3), and a Moon with a thicker outer core (169 km thick) but a denser and smaller inner core (219 km radius for 8000 kg/m^3).