Hf/w Isotopic Evolution from N-body Accretion Simulations: Constraints on Equilibra- Tion Processes during Large Impacts

Introduction The hafnium-tungsten (Hf-W) isotopic system provides a powerful constraint on accretion and core formation timescales [1-3]. However, most estimates of these timescales 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 [4-6]. Such giant impacts have significant thermal and isotopic consequences. We have developed a framework [7], similar to that of [3], for calculating the Hf-W isotope evolution of individual bodies based on the results of N-body accretion simulations. We find the closest agreement between model results and observations if even the largest impactors undergo re-equilibration with the mantle of the target body. Methods Two physical processes are responsible for the isotopic anomalies generated during core formation [7,8]. The first is fractionation; the second is radioactive decay. If fractionation occurs while the radioactive parent element (e.g. Hf) is still extant (t1/2=9 Myr for the Hf-W system), isotopic anomalies result due to the subsequent ingrowth of the daughter element (e.g. W ) in the mantle (which has high Hf/W). Such anomalies may be detected at the present day. Regarding fractionation, some elements partition into silicates during differentiation (e.g. Hf), others prefer metals (e.g. W). For the case of an initially homogeneous object which differentiates into core and mantle, mass balance considerations and the definition of the partition coefficient D give