Fig. 3: The probability of an Earth-like lunar ε_182W.

The cumulative probability of a range of Earth–Moon ε_182W differences is shown, given an Earth-like terrestrial ε_182W of 2.2 ± 0.15 (see ref. ⁵). Vertical dotted lines indicate the maximum Earth–Moon ε_182W difference allowed based on calculations of the Earth’s pre-late veneer composition, ±0.15 ε units (see ref. ⁵), and the gray shaded rectangles indicate the corresponding maximum probability of forming an Earth–Moon pair with an ε_182W difference no larger than this. Results for various fractions of equilibrating metal k (in the range 0.1–1) are combined. a Results for four combinations of accretion scenarios and lunar W metal–silicate partition coefficient D_W, with the Moon made entirely of Theia materials (no terrestrial component). Blue lines: Circular Jupiter and Saturn (CJS) and Eccentric Jupiter and Saturn (EJS) simulations, combined. Green lines: Grand Tack simulations. Solid lines: D_W = 30. Dashed lines: D_W = 150. With the Moon made entirely from Theia materials, <1.6–4.7% of Earth–Moon pairs have ε_182W differences of <0.15 ε units. b The effect of mixing Earth and Theia materials to form the Moon, with 0–50% of the mass of the Moon coming from the Earth (indicated by color). Results are shown for CJS/EJS simulations and D_W = 30. In this case, the probability of an Earth–Moon pair having an ε_182W difference of <0.15 ε units ranges from 1.9% (0% Earth materials) to 9.4% (20–30% Earth materials) to 17.0% (50% Earth materials). These probabilities are for W isotopes alone, and may be significantly lower when also considering stable isotopes.