Composition of Earth's initial atmosphere and fate of accreted volatiles set by core formation and magma ocean redox evolution

The origins of volatile depletion in the Bulk Silicate Earth (BSE) remain controversial due to the numerous processes during accretion and differentiation that can alter volatile abundances. Here, we integrate realistic impact histories from N-body simulations to determine the distribution of H, C, and N between Earth's core, mantle, and atmosphere, including loss to space, during the giant impact stage of accretion. Estimates of the BSE's volatile abundances can be matched if accreting materials were depleted similar to 1-2 orders of magnitude relative to CI chondrite volatile abundances, indicating early volatile loss on planetesimals and embryos prior to terrestrial accretion. We find the proto-Earth's atmosphere to be dominated by CO (>97%), which leads to the preferential erosion of C relative to H and N by subsequent impacts. Erosion can remove significant C (similar to 18-45% of accreted C), and potentially substantial N as well (similar to 12-23%), if N is not extremely siderophile at high pressures and temperatures. Out of the accreted volatiles, the majority are sequestered in the core, which is the largest reservoir of H (similar to 57-75%), C (similar to 54%-98%), and N (similar to 69%-99.9%) in the bulk Earth after accretion. Our results show that the BSE's volatile depletion relative to chondrites is dominated by loss on precursor bodies (>92%), followed by core formation (similar to 77-99% of remaining <8%), while atmosphere erosion accounts for the rest. Formation scenarios that source more material from the outer Solar System, such as Classical and Grand Tack, result in Earth analogs that have higher total volatile concentrations, lower proportions of volatiles stored in Earth analog cores, and have lost a larger fraction of their accreted C due to atmosphere erosion. The BSE's superchondritic C/N ratio can be matched or exceeded, even if Earth's building blocks have CI chondritic C/N, if N is more strongly siderophile at high pressures and temperatures. If N does not become sufficiently siderophile at high pressures and temperatures, however, Earth's building blocks must have accreted with superchondritic C/N ratios.