Size and density of lunar core estimated using simulated annealing algorithm

Abstract

This study focuses on the size of composition of lunar core. To deal with this issue, we considered the lunar mean density and mean moment of inertia factor in our inversion. We used the degree-2 coefficients of lunar gravity field model GL990D and the lunar physical liberation parameters to compute mean moment of inertia factor, which is treated as an observed value. We also computed the observed value of the mean density according the total mass of the Moon. Based on the interior structure with various layers, we deduced the modeled expressions for the lunar mean density and mean moment of inertia factor. Summing squares of the difference between the observed and modeled values as an inversion criterion, we estimated the multi-parameters based on the simulated annealing algorithm. By considering the lunar interior structure with three layers, the estimated size of the lunar core is around 470 km, and the density of the core gets close to 5486 kg·m<sup>-3</sup>. The computed size and density of the lunar core are close to other studies, validating our algorithm. We then considered the scenarios that the lunar core differentiated with a solid inner and a liquid outer core. The good-inversed outer core is close to 385 km, while the inner core approaches to 350 km. By using the good-inversed sizes as fixed parameters, it is found that the inner core is quite denser to 7879 kg<teshuzifu>×m<sup>-</sup>³ than the outer core, which is estimated around 4618 kg<teshuzifu>×m<sup>-</sup>³. Our result indicates that the outer core is composed by ferrous sulfide (FeS), while the inner core is composed by ferrous or ferro-nickel at 3.56 billion years ago when the lunar core dynamo ended.