Extended Data Fig. 8: Variation of the average stable isotopic fractionation (expressed in log ‰) across all elements as a function of the three randomised variables in 1000 Monte Carlo simulations.
The four N-body simulations are organised by row, in which the logarithm of the mean isotope fractionation is plotted on the ordinate axis and the value of the random variable on the abscissa, organised by column; mass accretion rate (\(\dot M\)) (in solar masses/yr), mean atmospheric mass (mi) (in g/mol) and embryo feeding zone (σembryo) (in K). The degree of isotopic fractionation in the fully accreted Earth analogue is only mildly dependent on \(\dot M\) and σembryo, but shows a strong negative correlation with the mean atmospheric mass, mi, reflecting the scaling between atmospheric loss rate and atmosphere scale height with its molar mass. Changes in slope reflect the participation of different, major atmospheric loss events (hydrodynamic escape) engendered by multiple collisions.
