Tidal constraints on the low-viscosity zone of the Moon

Abstract

In this paper, the effect on the tidal response of the low-viscosity zone in the deep interior of the Moon is investigated based on hypothetical temperature profiles. The tidal parameters are computed numerically to demonstrate their dependence on the low-viscosity zone and frequency. One of the calculated parameters is the tidal quality factor, to which energy dissipation is inversely proportional. The other parameters are the tidal Love numbers, which are normalized magnitudes of displacement and potential perturbation of tidal deformation. Unlike earlier considerations, the viscosity structure of the low-viscosity zone is no longer assumed to be fully uniform but linked with several temperature profiles such as a thermal boundary layer model or a convective layer model. The calculations show that the latest observational ranges of the frequency-dependent quality factors can be satisfied only by the convective layer model with some viscosity value for the middle layer but not by the thermal boundary layer model for any structure. The approximate viscosity solution is estimated to be 3 × 1016 Pa s. If considering also the observational ranges of the Love numbers together with those of the quality factors, the solution of the outer radius of the low-viscosity zone is approximately either 560 or 580 km. These solutions are almost identical to those based on the previous model where the low-viscosity zone has uniform viscosity. It is concluded that the thermal state of the bottom layer of the lunar mantle is predicted to be mainly controlled by local convection, and possibly maintained by the energy balance between convective cooling and tidal heating, as previously suggested.