Geochemical Constraints on the Origin of the Moon and Preservation of Ancient Terrestrial Heterogeneities

Abstract

The Moon forming giant impact marks the end of the main stage of Earth’s accretion and sets the stage for the subsequent evolution of our planet. The giant impact theory has been the accepted model of lunar origin for 40 years, but the parameters of the impact and the mechanisms that led to the formation of the Moon are still hotly debated. Here we review the principal geochemical observations that constrain the timing and parameters of the impact, the mechanisms of lunar formation, and the contemporaneous evolution of Earth. We discuss how chemical and isotopic studies on lunar, terrestrial and meteorite samples relate to physical models and how they can be used to differentiate between lunar origin models. In particular, we argue that the efficiency of mixing during the collision is a key test of giant impact models. A high degree of intra-impact mixing is required to explain the isotopic similarity between the Earth and Moon but, at the same time, the impact did not homogenize the whole terrestrial mantle, as isotopic signatures of pre-impact heterogeneity are preserved. We summarize the outlook for the field and highlight the key advances in both measurements and modeling needed to advance our understanding of lunar origin.

Appendix

1.1 A.1 Data Sources for Figs. 5 and 6

Data for Figs. 5 and 6 were taken from a compilation by Dauphas (2017) with the exception that the lunar value for $\epsilon$⁵⁴Cr was taken from Mougel et al. (2018). Below, we give the original data sources for this compilation.

1.1.1 A.1.1 $\Delta$¹⁷O

$\Delta$¹⁷O data was compiled by Dauphas (2017) with the aid of MetBase (Meteorite Information Database, http://www.metbase.org/). $\Delta$¹⁷O data were taken from Bischoff et al. (1991, 1993, 1998), Bischoff (1994), Bridges et al. (1997, 1999), Brearley et al. (1989), Burkhardt et al. (2017), Buchanan et al. (1993), Clayton and Mayeda (1978, 1981, 1984, 1985, 1989, 1990, 1996), Clayton et al. (1976, 1977, 1983, 1984a,b, 1991, 1997a,b), Connolly et al. (2007), Franchi et al. (1992, 1999), Grossman and Zipfel (2001), Grossman et al. (1987), Grossman (1999), Grady et al. (1987), Gooding et al. (1983), Goodrich et al. (1987), Halbout et al. (1984, 1986), Ivanov et al. (1987), Jabeen et al. (1998), Jackel et al. (1996), Kallemeyn et al. (1996), Keller et al. (1994), McCoy et al. (1995, 1996, 1997), Mayeda and Clayton (1980, 1983, 1989a,b), Mayeda et al. (1987, 1995), Moroz et al. (1988), Nehru et al. (1996), Olsen et al. (1987, 1994), Onuma et al. (1978, 1983), Petaev et al. (1988), Prinz et al. (1991), Pun et al. (1991), Romanek et al. (1998), Rowe et al. (1994), Russell et al. (1998, 2005), Ruzicka et al. (1995), Recca et al. (1986), Sears et al. (1990), Simon et al. (1995), Schulze et al. (1994), Stepniewski et al. (1998), Weber et al. (1996, 1997), Weisberg et al. (1991, 1993, 1995, 1996, 1997), Zolensky et al. (1989, 1997); and Young et al. (2016).

1.1.2 A.1.2 $\epsilon$⁵⁰Ti

$\epsilon$⁵⁰Ti data were taken from Zhang et al. (2011, 2012), Trinquier et al. (2009); and Burkhardt et al. (2017).

1.1.3 A.1.3 $\epsilon$⁵⁴Cr

$\epsilon$⁵⁴Cr data were taken from Trinquier et al. (2007), Qin et al. (2010a,b), Shukolyukov and Lugmair (2006a,b), Shukolyukov et al. (2009), Schiller et al. (2014), Yamashita et al. (2005, 2010), Yamakawa et al. (2010), Larsen et al. (2011), Göpel and Birck (2010), Burkhardt et al. (2017); and Mougel et al. (2018).

1.2 A.2 Details of Mixing Model

In Sect. 6 we present the results of a mixing model to investigate the requirements for mixing during and after the Moon-forming giant impact imposed by the isotopic similarity between the Earth and Moon. Here we provide the details of that model.

We divide the post-impact body into two regions: the Moon-forming region and an isolate region that does not communicate with the Moon forming region during the period of Moon formation. The mass of these two regions are $M_{1}$ and $M_{2}$ respectively, where 1 denotes the Moon-forming region and 2 the isolated region (Fig. 8). The masses of the two regions are such that

$$ M_{1}+M_{2}=M_{\mathrm{Earth}} + M_{\mathrm{Moon}} \;, $$

(1)

where $M_{\mathrm{Moon}}$ and $M_{\mathrm{Earth}}$ are the mass of the present-day Moon and Earth respectively.

The two regions are made up of a different mass fraction of impactor material, $f_{\mathrm{imp}}^{i}$, and so have different average $\Delta$¹⁷O isotopic compositions, $c_{i}$. Note that both these regions can be internally heterogeneous and the only requirement is that the Moon inherits the average composition of the Moon-forming region. For simplicity, we assume that the majority of Earth mixes after the impact and that the present-day observable mantle is a mixture of the isolated region and the fraction of the Moon-forming region that was not incorporated into the Moon such that

$$ (M_{1}-M_{\mathrm{Moon}})c_{1}+M_{2}c_{2}=M_{\mathrm{Earth}}c_{\mathrm{Earth}}=0 \; , $$

(2)

where $c_{\mathrm{Earth}}$ is the composition of the present-day Earth’s mantle which is zero by definition. The composition of each region is related to the composition of the target and impactor by

$$ c_{i}=f_{\mathrm{imp}}^{i} c_{\mathrm{imp}} + (1-f_{\mathrm{imp}}^{i}) c_{\mathrm{tar}} \; , $$

(3)

where $c_{\mathrm{imp}}$ and $c_{\mathrm{tar}}$ are the $\Delta$¹⁷O isotopic composition of the impactor and target respectively.

We can determine an expression for the mass fraction of the post-impact structure that must be mixed in to the Moon-forming region ($F_{\mathrm{mix}}=M_{1}/(M_{1}+M_{2})=M_{1}/(M_{ \mathrm{Earth}}+M_{\mathrm{Moon}})$) given a present-day difference in $\Delta$¹⁷O between the Moon and Earth ($\varDelta c_{\mathrm{M-E}}=c_{1}$ by definition), a specified $\Delta$¹⁷O offset between the impactor and target ($\varDelta c_{\mathrm{imp-tar}}=c_{\mathrm{imp}}-c_{\mathrm{tar}}$), and a difference in the mass fraction of impactor in the two regions ($\varDelta f_{\mathrm{imp}} = f_{\mathrm{imp}}^{1} - f_{\mathrm{imp}}^{2}$). By substituting for $M_{2}$ in equation (2) using equation (1) we can find an expression for $M_{1}$ as a function of the composition of the two regions:

$$ M_{1}= \frac{M_{\mathrm{Moon}}c_{1}-(M_{\mathrm{Earth}}+M_{\mathrm{Moon}})c_{2}}{(c_{1}-c_{2})} \; . $$

(4)

Independently we can re-express equation 2 for the isolated region ($i=2$) to give an expression for $c_{2}$ in terms of the composition of the impactor and target:

$$ c_{2}=c_{\mathrm{imp}} - (1-f_{\mathrm{imp}}^{2}) \varDelta c_{\mathrm{imp-tar}}\; . $$

(5)

Similarly, rearranging equation (2) for the Moon-forming region ($i=1$) we obtain an expression for $c_{\mathrm{imp}}$:

$$ c_{\mathrm{imp}}=\varDelta c_{M-E} + (1-f_{\mathrm{imp}}^{1})\varDelta c_{\mathrm{imp-tar}} \; . $$

(6)

Substituting for $c_{\mathrm{imp}}$ in equation (5) using equation (6) we obtain

$$ c_{2}=\varDelta c_{M-E} - \varDelta f_{\mathrm{imp}} \varDelta c_{\mathrm{imp-tar}}\; . $$

(7)

Substituting for $c_{2}$ in equation (4) using equation (7) and rearranging we find that

$$ F_{\mathrm{mix}}= \frac{\varDelta f_{\mathrm{imp}} \varDelta c_{\mathrm{imp-tar}} (M_{\mathrm{Earth}}-M_{\mathrm{Moon}}) - \varDelta c_{\mathrm{M-E}} M_{\mathrm{Earth}}}{\varDelta f_{\mathrm{imp}} \varDelta c_{\mathrm{imp-tar}} (M_{\mathrm{Earth}}+M_{\mathrm{Moon}})} \; , $$

(8)

or alternatively:

$$ F_{\mathrm{mix}}=1- \frac{\varDelta c_{\mathrm{M-E}} M_{\mathrm{Earth}}}{\varDelta f_{\mathrm{imp}} \varDelta c_{\mathrm{imp-tar}} (M_{\mathrm{Earth}}+M_{\mathrm{Moon}})} \; . $$

(9)

The expression given in equation (9) is significant as it relates the degree of post-impact mixing that is required to explain the Earth-Moon isotopic similarity for a given degree of intra-impact mixing and compositional difference between impactor and target. We can therefore use it to understand the trade offs between mixing during and after the impact (Sect. 6).