# Reconstructing the late-accretion history of the Moon

## Abstract

The importance of highly siderophile elements (HSEs; namely, gold, iridium, osmium, palladium, platinum, rhenium, rhodium and ruthenium) in tracking the late accretion stages of planetary formation has long been recognized. However, the precise nature of the Moon’s accretional history remains enigmatic. There is a substantial mismatch in the HSE budgets of the Earth and the Moon, with the Earth seeming to have accreted disproportionally more HSEs than the Moon1. Several scenarios have been proposed to explain this conundrum, including the delivery of HSEs to the Earth by a few big impactors1, the accretion of pebble-sized objects on dynamically cold orbits that enhanced the Earth’s gravitational focusing factor2, and the ‘sawtooth’ impact model, with its much reduced impact flux before about 4.10 billion years ago3. However, most of these models assume a high impactor-retention ratio (the fraction of impactor mass retained on the target) for the Moon. Here we perform a series of impact simulations to quantify the impactor-retention ratio, followed by a Monte Carlo procedure considering a monotonically decaying impact flux4, to compute the impactor mass accreted into the lunar crust and mantle over their histories. We find that the average impactor-retention ratio for the Moon’s entire impact history is about three times lower than previously estimated1,3. Our results indicate that, to match the HSE budgets of the lunar crust and mantle5,6, the retention of HSEs should have started 4.35 billion years ago, when most of the lunar magma ocean was solidified7,8. Mass accreted before this time must have lost its HSEs to the lunar core, presumably during lunar mantle crystallization9. The combination of a low impactor-retention ratio and a late retention of HSEs in the lunar mantle provides a realistic explanation for the apparent deficit of the Moon’s late-accreted mass relative to that of the Earth.

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## Data availability

The data that support the findings of this study are available from the corresponding author on request.

## Code availability

At present, the iSALE code is not fully open source. It is distributed on a case-by-case basis to academic users in the impact community, strictly for non-commercial use. Scientists interested in using or developing iSALE should see http://www.isale-code.de for a description of application requirements. The Monte Carlo code used here is available from the corresponding author on request.

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## Acknowledgements

We thank J. M. D. Day and R. J. Walker for useful discussions. We acknowledge the developers of iSALE (www.isale-code.de), in particular D. Elbeshausen, who developed iSALE-3D. M.-H.Z. is supported by the Science and Technology Development Fund of Macau (079/2018/A2). K.W., H.B., N.A. and M.-H.Z. are funded by Deutsche Forschungsgeimenschaft (DFG) grant SFB-TRR 170 (A4, C2), TRR-170 Pub. No. 55. Q.-Z.Y. is funded by the NASA Emerging Worlds Program (NNX16AD34G).

### Peer review information

Nature thanks James Day and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

Authors

### Contributions

M.-H.Z. conceived the idea and performed the impact simulations. N.A. performed the Monte Carlo modelling. M.-H.Z., A.M., Q.-Z.Y, H.B. and K.W. interpreted the results. All authors contributed to the discussion of the results and wrote the manuscript.

### Corresponding author

Correspondence to Meng-Hua Zhu.

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### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 Thermal profiles of the Moon.

Two possible thermal profiles (TP1 and TP2) for the Moon, which we use in this study to test the effects of temperature on the impactor-retention ratio.

### Extended Data Fig. 2 Effects of lunar thermal profiles on the impactor-retention ratio.

We calculated impactor-retention ratios for oblique impacts of impactors with diameters (d) of 210 km and velocities (v) of 15 km s−1. The impact angles were varied from 15° to 90°. TP1 and TP2 represent the temperature profiles used here (Extended Data Fig. 1).

### Extended Data Fig. 3 Fraction of retained impactor material deposited within the transient crater in all simulations.

In our simulations, this fraction is between 0.9 and 1.0 for impact angles greater than 20° (relative to the lunar surface). For large impactors (d > 100 km) with impact angles smaller than 20°, the fraction of retained material within the transient cavity is less than 0.9. The dashed line represents the fraction of 0.96 that we use in our calculations (see Fig. 3) for simplicity. The dotted line represents the fraction of 0.90 used in Extended Data Fig. 6. The numbers in the key represent the impactor diameter (D) and impact velocity (V).

### Extended Data Fig. 4 Lunar impact fluxes.

The differential number of lunar craters larger than 20 km as a function of time for the production functions discussed in the text4,9.

### Extended Data Fig. 5 Two scenarios involving a differentiated impactor hitting the Moon.

The arrows represent the impact direction and the lines show the extent of interaction of the impactor core with the Moon. When the core of a differentiated impactor is accreted to the Moon (a), we record the total mass of impactors accreted to the Moon. However, when the impactor’s core is not accreted to the Moon (b), we do not record any accreted mass.  This simplification is justified because in reality the HSEs of a differentiated impactor should almost entirely be dominated by its core.

### Extended Data Fig. 6 Cumulative impactor masses that hit and are accreted into the Moon.

a, b, The total impactor masses hitting the Moon (blue) and being accreted to the Moon (purple) from different starting times (between 4.5 Gyr to 3.5 Gyr ago) to the present day, for assumed crustal thicknesses of 34 km (a) and 43 km (b). The cumulative masses accreted to the lunar crust (orange) and mantle (green) are estimated separately. This figure is similar to Fig. 3, except that we assume that around 10% of the retained impactor material is deposited beyond the transient crater and mixed with the crust.

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Zhu, MH., Artemieva, N., Morbidelli, A. et al. Reconstructing the late-accretion history of the Moon. Nature 571, 226–229 (2019). https://doi.org/10.1038/s41586-019-1359-0

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