Constraining the Theia and proto-Earth in the Moon-forming giant impact

The currently accepted model for the origin of the Moon is that of a giant impact between a proto-Earth and a Mars-sized body, Theia, that produced an initial protolunar disk that later accreted into the Earth and Moon couple [1-5].

Here, we employ the smoothed particle hydrodynamic method to investigate how varying Theia’s mass, γ, and its core mass fraction (CMF) affect the giant-impact process and the post-impact compositions of the proto-Earth and the protolunar disk. We fix the total system mass at 1.02 Earth mass and explore impactor mass ratios γ of 0.13, 0.16, and 0.20 total mass, each at an oblique impact angle of ~45°, while varying Theia’s CMF from 10% to 70%.

Our dynamical results show that, under the constraint of reproducing the present Earth-Moon angular momentum, Theia’s mass must not exceed ~0.15 Earth mass, as larger impactors produce too much angular momentum. Furthermore, Theia’s CMF strongly controls the post-impact material: an increased CMF yields higher iron concentrations in both the post-impact proto-Earth and the protolunar disk, while simultaneously diminishing the fraction of Theia-derived silicates in each.

Using the results of our SPH simulations, we obtain the mass distribution in the resulting protolunar disk, from which we can try to derive some characteristics of Theia and proto-Earth. To translate these findings into geochemical features, we combine elemental (Fe, Si, Mg) and isotopic (Δ¹⁷O, ε⁵⁰Ti, ε⁵⁴Cr) data for Earth’s and Moon’s mantles with mass-balance modeling. Under both end-member scenarios—complete iron–silicate equilibration and zero equilibration—we find that Theia’s CMF must be <35% to satisfy dual Earth-Moon constraints. Correspondingly, Theia’s mantle would have Fe < 11%, Si ≈ 20-21%, Mg ≈ 18-21%, Δ¹⁷O×C_O ≈ -2.61~-1.96, ε⁵⁰Ti×C_Ti ≈ -0.01~0, and ε⁵⁴Cr×C_Cr ≈ 0~0.04. The proto-Earth’s mantle, in contrast, would be characterized by Fe ≈ 5-7%, Si ≈ 21~22%, Mg ≈ 22-23%, Δ¹⁷O×C_O ≈ -2.86~-2.61, ε⁵⁰Ti×C_Ti ≈ 0.002~0.004, and ε⁵⁴Cr×C_Cr ≈ 0.01~0.05.

Comparing these modeled compositions to those of planetary models and measurements on different meteorite groups indicates that Theia's mantle closely resembles Earth's in both elemental abundances and isotopic characteristics, with only a slight difference in Si and Mg content, while proto-Earth's mantle exhibits an even stronger resemblance to present-day Earth. Furthermore, from the O, Ti, and Cr data covering both differentiated and undifferentiated meteorite samples, Aubrites exhibit the closest match to the predicted composition of Theia’s mantle. The isotopic signatures of proto-Earth and Theia also closely resemble those of EH and EL chondrites; however, the undifferentiated nature of EH and EL accounts for the pronounced differences in Fe, Si, and Mg compositions. This suggests both bodies originated from highly reduced, enstatite-chondrite-rich material in the inner Solar System.

In summary, by integrating SPH modeling with Earth–Moon geochemical data, we provide quantitative pre-impact constraints on Theia’s mass (~0.13–0.15 Earth mass), CMF (< 35%), and reduced, Aubrite-like mantle composition [6], as well as confirmation that the proto-Earth mantle closely resembles that of today. These findings alleviate the lunar isotope conundrum and offer new pathways for tracing Theia’s provenance and the early evolution of the Earth–Moon system.

REFERENCES

[1] Asphaug, E. Annu. Rev. Earth Planet. Sci. 42, 551-578 (2014).

[2] Cameron, A. G. W. & Ward, W. R. Abstr. Lunar Planet. Sci. Conf. 7, 120-122 (1976).

[3] Canup, R. M. et al. Rev. Mineral. Geochem. 89, 53-102 (2023).

[4] Ćuk, M. & Stewart, S. T., Science 338, 1047-1052 (2012).

[5] Caracas, R. & Stewart, S. T., Earth Planet. Sci. Lett. 608, 118014(2023).

[6] Dauphas, N., Burkhardt, C., Warren, P. H. & Teng, F. Phil. Trans. R. Soc. A. 372, 20130244 (2014).