Radius of lunar core estimated by GRAIL results

Internal structure and composition of the Moon provide important clue and constraints on theories for how the Moon formed and evolved. The Apollo seismic network has contributed to the internal structure modeling. Efforts have been made to detect the lunar core from the noisy Apollo data (e.g., [1], [2]), but there is scant information about the structure below the deepest moonquakes at about 1000 km depth. On the other hand, there have been geodetic studies to infer the deep structure of the Moon. For example, LLR (Lunar Laser Ranging) data analyses detected a displacement of the lunar pole of rotation, indicating that dissipation is acting on the rotation arising from a fluid core [3]. Bayesian inversion using geodetic data (such as mass, moments of inertia, tidal Love numbers k₂ and h₂, and quality factor Q) also suggests a fluid core and partial melt in the lower mantle region [4]. Recent analyses of GRAIL data have achieved the improved k₂ accuracy; JPL solution is 0.02405 × 0.00018 [5], and GSFC solution is 0.02427 × 0.00026 [6]. The two solutions are consistent with each other within their error bounds, and the accuracy of k₂ is now about 1 %. Such an accurately-determined Love number will contribute to constrain the structure of the lunar deep interior, such as the radius of the possible liquid core. We used geodetic data of the mass, the mean moment of inertia, the Love numbers h₂ and k₂ to infer the size of liquid core. It is difficult to tightly constrain the internal structure from the geodetic data only because there are trade-offs among the structures of crust, mantle, and core. In our preliminary analysis we used a 5-layer model and the mantle structure was constrained by VPREMOON [2] with 5 % error for density and 10 % error for shear and bulk moduli being assumed. An inversion using Markov chain Monte Carlo method indicates that the core radius is 480 × 50 km, but the density values were sampled around the assumed lower limit of 3600 kg/m³. When the lower limit of the core density is raised to 5000 kg/m³, the estimated core radius gets smaller to be 380 × 50 km. A better estimate of the core parameters is expected by including Apollo seismic data into the analysis. References [1] Weber et al. (2011), Science, 331, 309-312, doi:10.1126/science.1199375 [2] Garcia et al. (2011), PEPI, doi:10.1016/j.pepi.2011.06.015 [3] Williams et al. (2001), JGR, 106, E11, 27,933-27,968 [4] Khan and Mosegaard (2005), GRL, 32, L22203, doi:10.1029/2005GL023985 [5] Konopliv et al (2013), JGR, 118, doi:10.1002/jgre.20097 [6] Taken from the PDS label of GRAIL Derived Data Products