Highly siderophile elements in Earth’s mantle as a clock for the Moon-forming impact

Journal name:
Nature
Volume:
508,
Pages:
84–87
Date published:
DOI:
doi:10.1038/nature13172
Received
Accepted
Published online

According to the generally accepted scenario, the last giant impact on Earth formed the Moon and initiated the final phase of core formation by melting Earth’s mantle. A key goal of geochemistry is to date this event, but different ages have been proposed. Some1, 2, 3 argue for an early Moon-forming event, approximately 30 million years (Myr) after the condensation of the first solids in the Solar System, whereas others4, 5, 6 claim a date later than 50Myr (and possibly as late as around 100Myr) after condensation. Here we show that a Moon-forming event at 40Myr after condensation, or earlier, is ruled out at a 99.9 per cent confidence level. We use a large number of N-body simulations to demonstrate a relationship between the time of the last giant impact on an Earth-like planet and the amount of mass subsequently added during the era known as Late Accretion. As the last giant impact is delayed, the late-accreted mass decreases in a predictable fashion. This relationship exists within both the classical scenario7, 8 and the Grand Tack scenario9, 10 of terrestrial planet formation, and holds across a wide range of disk conditions. The concentration of highly siderophile elements (HSEs) in Earth’s mantle constrains the mass of chondritic material added to Earth during Late Accretion11, 12. Using HSE abundance measurements13, 14, we determine a Moon-formation age of 95±32Myr after condensation. The possibility exists that some late projectiles were differentiated and left an incomplete HSE record in Earth’s mantle. Even in this case, various isotopic constraints strongly suggest that the late-accreted mass did not exceed 1 per cent of Earth’s mass, and so the HSE clock still robustly limits the timing of the Moon-forming event to significantly later than 40Myr after condensation.

At a glance

Figures

  1. The late-accreted mass relative to each synthetic Earth-like planet/'s final mass as a function of the time of the last giant impact.
    Figure 1: The late-accreted mass relative to each synthetic Earth-like planet’s final mass as a function of the time of the last giant impact.

    Triangles represent Earth-like planets from the first category: classical simulations with Jupiter and Saturn near their contemporary orbits7, 8. Circles represent Earth-like planets from the second category: Grand Tack simulations with a truncated protoplanetary disk9, 10. The black line resembling a staircase is the moving geometric mean of the late-accreted masses in the Grand Tack simulations evaluated at logarithmic time intervals with a spacing parameter of 0.025 and a width parameter twice that. The blue region encloses the 1σ variance of the late-accreted mass, computed assuming that the latter is distributed log-normally about the geometric mean. Always predicting larger late-accreted masses for each last giant impact time, the dotted staircase is the geometric mean obtained by also considering the classical simulations, although those simulations do not fit Solar System constraints as well as the Grand Tack simulations do. The horizontal dashed line and enclosing darkened region are the best estimate and 1σ uncertainty of the late-accreted mass inferred from the HSE abundances in the mantle (chondritic mass): 4.8±1.6×10−3 . The best estimate for the intersection of the correlation and the chondritic mass is 95±32Myr after condensation. The dark and light red regions highlight Moon-formation times that are ruled out with 99.9% (40Myr) and 85% (63Myr) confidence or greater, respectively.

  2. The likelihood that a planet suffering a last giant impact within a specific range of times has a late-accreted mass less than or equal to the chondritic mass of 4.8[thinsp][plusmn][thinsp]1.6[thinsp][times][thinsp]10-3.
    Figure 2: The likelihood that a planet suffering a last giant impact within a specific range of times has a late-accreted mass less than or equal to the chondritic mass of 4.8±1.6×10−3 .

    The probability calculation uses the same bins as Fig. 1 but only includes the Grand Tack simulations, because they best reproduce the terrestrial planets9, 10, 18. The solid line shows this probability assuming perfect accretion and corresponds exactly to the late-accreted masses shown as circles in Fig. 1. The lower 1σ limit for the Moon formation age is 63Myr, which corresponds to a 15% probability that an Earth-like planet with a last giant impact at that age is characterized by a late-accreted mass equal or smaller than the chondritic mass. The dashed line shows the same calculation but for a late-accreted mass less than or equal to 0.01 , which is an upper limit established from a number of elemental and isotopic constraints (see Supplementary Information). The dotted line shows the same calculation as for the solid line—that is, using a chondritic mass—but assuming imperfect accretion during collisions. This decreases the late-accreted masses by a variable amount depending on the impact characteristics of the late-accreted projectiles onto each planet26. However, this calculation underestimates the late-accreted mass because a large fraction of the ejected material would be subsequently reaccreted27, 28 and projectile core material is less likely to be ejected post-impact29. Consequently, the dotted line overestimates the likelihood that a planet matches the chondritic mass constraint. A realistic estimate therefore lies between the solid and dotted curves (probably closer to the former).

  3. Four panels comparing the classical (triangles) and Grand Tack (circles) scenarios.
    Extended Data Fig. 1: Four panels comparing the classical (triangles) and Grand Tack (circles) scenarios.

    a, The mass of each planet in every simulated Solar System as a function of the semi-major axis. Planets within the grey zone are considered to be Earth-like. Planets at the distance of Mars from the Sun are too massive in classical simulations but are correct in Grand Tack simulations. b, c and d show the relative Late Accretion mass as a function of different parameters and the chondritic mass and its uncertainty MC = 4.8±1.6×10−3 as a dashed line and grey region. b is the same as Fig. 1 of the main text, but with a broader timescale. c and d show the relative Late Accretion mass and two orbital structure statistics: concentration37 Sc and angular momentum deficit37, 76 Sd. The Solar System has Sc = 89.9 and is marked with a vertical dashed line in c. Grand Tack simulations are as, or more, concentrated than classical simulations. The Solar System has Sd = 0.0018 and this is marked by a vertical dashed line in d. A late giant planet instability (about 500Myr after the condensation of the first solids in the Solar System) probably excites the inner Solar System; given that these simulations end before the instability, they should possess an angular momentum deficit that is only a fraction of the current value77. Grand Tack simulations are either as dynamically excited or colder than classical simulations, although they are in some cases hotter than the current terrestrial planets.

  4. Figure 1 of the main text is reproduced in each panel for each scenario within the classical category.
    Extended Data Fig. 2: Figure 1 of the main text is reproduced in each panel for each scenario within the classical category.

    For reference, the horizontal dashed line and enclosing darkened region are the best estimate and the 1σ uncertainty of the Late Veneer mass MC = 4.8±1.6×10−3 . Each panel shows the Earth-like planet’s relative late-accreted mass as a function of last giant impact time for different initial ratios of the total mass in embryos to planetesimals, as follows. 1:1 in a, 2:1 in b, 4:1 in c, and 8:1 in d. The mean time of the last giant impact increases and the relative Late Accretion mass decreases as the initial ratio of total embryo mass to planetesimal mass increases.

  5. The late-accreted mass MLA shown as greyscale contours of the two parameters X and Y.
    Extended Data Fig. 3: The late-accreted mass MLA shown as greyscale contours of the two parameters X and Y.

    The blue dashed contours indicate the location of a few specific late-accreted masses and are labelled in the framed boxes. For this figure, we assumed that Earth receives 52 times as much mass in small projectiles than the Moon (σ = 52). The red region is inaccessible, given that the measured chondritic mass in the lunar mantle requires a minimum flux of small planetesimals onto Earth's mantle.

  6. Each panel is like Extended Data Fig. 3 but showing additional constraints.
    Extended Data Fig. 4: Each panel is like Extended Data Fig. 3 but showing additional constraints.

    The constraint X0.53, deduced by a reanalysis of Rudge et al.23 with the Hf/W ratio updated from Konig et al.15, is shown in light red in each panel. In bd, the solid green contours indicate the set of X, Y parameters that reproduce the nominal difference in W-isotope composition between the Moon and Earth (0.09 in units; see Touboul et al.4). The difference among these panels is in the assumed Hf/W and W-isotope composition for the mantle of the differentiated projectiles: b assumes values typical of eucrites; c is for aubrites and d is for Mars. The green dashed contours are the 1σ uncertainties on X, Y related to the uncertainty on the difference between the W-isotope composition between the Moon and Earth: ±0.1 in units. The areas exterior to these 1σ uncertainties have been coloured red.

Tables

  1. Chondritic concentrations for different HSEs in Earth's mantle 13 and chondritic meteorites14 and the ratio of the two
    Extended Data Table 1: Chondritic concentrations for different HSEs in Earth's mantle 13 and chondritic meteorites14 and the ratio of the two
  2. Tungsten abundances nature13172-m43jpg20K7317 and nature13172-m44jpg22K6838 ratios for the mantle materials: basaltic eucrites75, aubrites78, and Mars75
    Extended Data Table 2: Tungsten abundances and ratios for the mantle materials: basaltic eucrites75, aubrites78, and Mars75

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Author information

Affiliations

  1. Observatoire de la Côte d’Azur, Laboratoire Lagrange, Boulevard de l’Observatoire, BP 4229, 06304 Nice Cedex 4, France

    • Seth A. Jacobson &
    • Alessandro Morbidelli
  2. Universität Bayreuth, Bayerisches Geoinstitut, 95440 Bayreuth, Germany

    • Seth A. Jacobson &
    • David C. Rubie
  3. Universite Bordeaux, Laboratoire d'Astrophysique de Bordeaux, UMR 5804, 33270 Floirac, France

    • Sean N. Raymond
  4. CNRS, Laboratoire d’Astrophysique de Bordeaux, UMR 5804, 33270 Floirac, France

    • Sean N. Raymond
  5. Planetary Science Institute, 1700 East Fort Lowell, Suite 106, Tucson, Arizona 85719, USA

    • David P. O'Brien
  6. Southwest Research Institute, Planetary Science Directorate, 1050 Walnut Street, Suite 300, Boulder, Colorado 80302, USA

    • Kevin J. Walsh

Contributions

A.M., K.J.W., S.N.R. and D.P.O’B. initiated a study of numerically simulating terrestrial planet formation. A.M., S.A.J., S.N.R., D.P.O’B. and K.J.W. ran N-body simulations and provided reduced data. S.A.J. analysed results. S.A.J., A.M. and D.C.R. discussed the meaning of the discovered relationship. S.A.J. wrote the paper with guidance from A.M. All authors commented on the manuscript.

Competing financial interests

The authors declare no competing financial interests.

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Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: Four panels comparing the classical (triangles) and Grand Tack (circles) scenarios. (284 KB)

    a, The mass of each planet in every simulated Solar System as a function of the semi-major axis. Planets within the grey zone are considered to be Earth-like. Planets at the distance of Mars from the Sun are too massive in classical simulations but are correct in Grand Tack simulations. b, c and d show the relative Late Accretion mass as a function of different parameters and the chondritic mass and its uncertainty MC = 4.8±1.6×10−3 as a dashed line and grey region. b is the same as Fig. 1 of the main text, but with a broader timescale. c and d show the relative Late Accretion mass and two orbital structure statistics: concentration37 Sc and angular momentum deficit37, 76 Sd. The Solar System has Sc = 89.9 and is marked with a vertical dashed line in c. Grand Tack simulations are as, or more, concentrated than classical simulations. The Solar System has Sd = 0.0018 and this is marked by a vertical dashed line in d. A late giant planet instability (about 500Myr after the condensation of the first solids in the Solar System) probably excites the inner Solar System; given that these simulations end before the instability, they should possess an angular momentum deficit that is only a fraction of the current value77. Grand Tack simulations are either as dynamically excited or colder than classical simulations, although they are in some cases hotter than the current terrestrial planets.

  2. Extended Data Figure 2: Figure 1 of the main text is reproduced in each panel for each scenario within the classical category. (187 KB)

    For reference, the horizontal dashed line and enclosing darkened region are the best estimate and the 1σ uncertainty of the Late Veneer mass MC = 4.8±1.6×10−3 . Each panel shows the Earth-like planet’s relative late-accreted mass as a function of last giant impact time for different initial ratios of the total mass in embryos to planetesimals, as follows. 1:1 in a, 2:1 in b, 4:1 in c, and 8:1 in d. The mean time of the last giant impact increases and the relative Late Accretion mass decreases as the initial ratio of total embryo mass to planetesimal mass increases.

  3. Extended Data Figure 3: The late-accreted mass MLA shown as greyscale contours of the two parameters X and Y. (282 KB)

    The blue dashed contours indicate the location of a few specific late-accreted masses and are labelled in the framed boxes. For this figure, we assumed that Earth receives 52 times as much mass in small projectiles than the Moon (σ = 52). The red region is inaccessible, given that the measured chondritic mass in the lunar mantle requires a minimum flux of small planetesimals onto Earth's mantle.

  4. Extended Data Figure 4: Each panel is like Extended Data Fig. 3 but showing additional constraints. (568 KB)

    The constraint X0.53, deduced by a reanalysis of Rudge et al.23 with the Hf/W ratio updated from Konig et al.15, is shown in light red in each panel. In bd, the solid green contours indicate the set of X, Y parameters that reproduce the nominal difference in W-isotope composition between the Moon and Earth (0.09 in units; see Touboul et al.4). The difference among these panels is in the assumed Hf/W and W-isotope composition for the mantle of the differentiated projectiles: b assumes values typical of eucrites; c is for aubrites and d is for Mars. The green dashed contours are the 1σ uncertainties on X, Y related to the uncertainty on the difference between the W-isotope composition between the Moon and Earth: ±0.1 in units. The areas exterior to these 1σ uncertainties have been coloured red.

Extended Data Tables

  1. Extended Data Table 1: Chondritic concentrations for different HSEs in Earth's mantle 13 and chondritic meteorites14 and the ratio of the two (280 KB)
  2. Extended Data Table 2: Tungsten abundances and ratios for the mantle materials: basaltic eucrites75, aubrites78, and Mars75 (79 KB)

Additional data