Many differentiated planetary bodies are characterised by a depletion in moderately volatile elements (MVEs) and their light isotopes relative to chondrites. We investigate numerically whether hydrodynamic escape of transient atmospheres from planetesimals and planetary embryos in the aftermath of accretional impacts can viably cause this characteristic. Focusing on the case of potassium, we obtain a mass window between about 3⋅1021 and 1023 kg (5⋅10−4 to 1.7⋅10−2 Earth masses) in which hydrodynamic vapour escape is energetically possible. The lower bound most likely arises from inadequate impact energy. The upper bound of 1023 kg arises from the gravitational energy precluding escape. We tracked cumulative impact effects in Grand Tack N-body simulations. Consistent with observations comparing meteorites and terrestrial samples, our simulation results display a lack of correlation between K depletion and body isotopic composition due to mixing of objects with variable K depletion. We find that about one in six bodies that grow beyond 1022 kg display significant K loss and isotopic fractionation, and bodies above the maximum loss threshold of ∼1023 kg inherit the depletion signatures from smaller precursors. Our simulations do not produce a correlation between K isotope fractionation and final body mass. Impact-driven loss may have significantly contributed to MVE depletion among differentiated bodies more massive than 3⋅1021 kg. If this lower mass bound is not substantially affected by the limitations of the simulation data, then the depletion of smaller objects such as the eucrite parent body must have had a different heat source than impacts, or experienced depletion by a different mechanism than hydrodynamic escape.
Calogero et al. (Wed,) studied this question.