Isotopic outcomes of N-body accretion simulations: Constraints on equilibration processes during large impacts from Hf/W observations

Most estimates of planetary core formation timescales using hafnium–tungsten (Hf–W) isotopes employ analytical expressions assuming either continuous planetary growth or instantaneous core formation. In contrast, dynamical modelling of planetary accretion suggests that the final stage of terrestrial planet formation is punctuated by multiple large and stochastic impacts. Such giant impacts have significant thermal and isotopic consequences. We present a framework for calculating the Hf–W isotope evolution of individual bodies based on the results of an N-body accretion simulation and assuming constant partition coefficients. The results show that smaller bodies exhibit a larger range in isotopic values than larger bodies, because the latter have suffered more impacts. The analytical core formation timescales calculated using these isotopic values can differ very significantly from the timing of the final giant impact each planet actually experiences. Simulations in which 1) even the largest impactors undergo re-equilibration with the targetʹs mantle, rather than the cores merging directly, and 2) the original planetary embryos possessed radially variable iron : silicate ratios, produce results which are consistent with the observed physical and isotopic characteristics of inner solar system bodies. Varying W partition coefficients (due to changing mantle oxidation state) or initial planetesimal Hf / W ratios might produce similar isotopic outcomes, and potentially permit core mergers without violating the isotopic constraints. The style of re-equilibration required suggests that magma oceans were present on Mars-sized and larger bodies; an alternative for bodies of Mars-size and smaller is that the bulk of the mass was delivered as impactors much smaller than the target. For Mars we conclude that a prolonged (∼10 Myr) accretion process is both dynamically and isotopically plausible. We also predict likely Pd–Ag isotopic anomalies for Vesta-, Mars- and Earth-size bodies.