A long-lived magma ocean on a young Moon

Abstract

A giant impact onto Earth led to the formation of the Moon, resulted in a lunar magma ocean (LMO), and initiated the last event of core segregation on Earth. However, the timing and temporal link of these events remain uncertain. Here, we demonstrate that the low thermal conductivity of the lunar crust combined with heat extraction by partial melting of deep cumulates undergoing convection results in an LMO solidification time scale of 150 to 200 million years. Combining this result with a crystallization model of the LMO and with the ages and isotopic compositions of lunar samples indicates that the Moon formed 4.425 ± 0.025 billion years ago. This age is in remarkable agreement with the U-Pb age of Earth, demonstrating that the U-Pb age dates the final segregation of Earth's core.

Fig. 1. Sketch of the thermal evolution model with its four reservoirs.

Black arrows indicate heat exchanges between different reservoirs. The gray arrow symbolizes solid-state convection in the cumulates, causing decompression melting (orange dots), melt migration, and heat piping. The radii of the interfaces between the reservoirs are represented on the inclined right axis.

Fig. 2. Time evolution of the LMO and crust’s bottom depth.

(A) Evolution of the bottom radii of the LMO (lower curves) and of the crust (upper curves) for different values of the crustal thermal conductivity k_crust, assuming purely conductive heat transfer through both the crust and the cumulates underlying the magma ocean. The protracted tail of solidification is due to the strong final drop in the crystallization temperature (see Materials and Methods). (B) As in (A) but for k_crust = 2 W m⁻¹ K⁻¹, taking into account thermal convection in the cumulates and the heat piping effect for different values of the reference viscosity of the cumulates η_ref. The black dashed line corresponds to the same case on both panels. In the inset in (B), the vertical dotted lines in the inset indicate the time at which crystallization ends for different reference viscosities.

Fig. 3. Thermal state of the Moon at 100 Ma.

(A) Snapshot of the temperature field in the cumulates after 100 Ma for our fiducial case using k_crust = 2 W m⁻¹ K⁻¹ and η_ref = 10²¹ Pa s (Fig. 2, blue curve). Convection in the cumulates occurs while the magma ocean (yellow area) is still solidifying and the plagioclase crust (gray area) is still growing. (B) Corresponding laterally averaged temperature profile (blue line). In hot upwellings, the temperature exceeds the solidus [red dashed line in (B)], causing partial melting [pale areas in (A)] that results in heat piping.

Fig. 4. Isotopic systematics of the evolving LMO and KREEP.

(A) Evolution of ε¹⁷⁶Hf, ε¹⁴³Nd (B) in the LMO and KREEP, and (C) distribution of Moon formation time (t₀) and KREEP isolation time (t_KREEP). Light gray curves represent the evolution in the magma ocean before KREEP formation; dark gray lines represent the subsequent KREEP decay lines obtained from Monte Carlo models that fitted at least 11 of the 12 data points for Lu-Hf and Sm-Nd systems used in (22) and plotted in orange (circles for KREEP basalts and diamonds for Mg-suite rocks). One KREEP basalt sample used for the Sm-Nd system (NWA773) has an age of 2.993 Ga and falls out of plot (B). The model ages of KREEP from (22) for the two systems [corresponding to the intercept of the orange solid lines, with the x axis corresponding to the extremes of the orange shaded area in (C)]. The age of FAN 60025 is represented by a black dashed line in (C). Among the cases shown on the histograms in (C), those compatible with Kal009 data are highlighted on the brighter subhistograms.

Fig. 5. Distribution of Moon (t₀, red points) and KREEP (t_KREEP, blue points) formation times computed for the various initial LMO depths investigated.

The red shaded area corresponds to our estimate range (4.40 to 4.45 Ga) for the Moon formation event. The black dashed line represents the age of FAN 60025 (21), consistent with the crust formation time span obtained for a 1000-km-deep LMO or a whole-mantle LMO.