When the core ate the atmosphere
The initial volatile element inventories in a planet's atmosphere, mantle, and core are established by delivery and transport during planetary growth. Conversely, the volatile abundances of Earth's planetary reservoirs record its accretion pathway. We model here volatile transport during planet formation for two different delivery scenarios, via pebble and planetesimal accretion, to predict the volatile inventories of proto-Earth at the end of its main accretion phase. We find that the distributions of volatiles between the atmosphere, mantle, and core exhibit strong sensitivity to volatile delivery timing, metal-silicate partition coefficients, atmosphere-magma solubilities, and planet mass. In particular, the early volatile delivery expected in pebble accretion scenarios substantially enhances core sequestration of hydrogen and carbon relative to continuous delivery during incremental planetesimal accretion. With our fiducial partition coefficients, the pebble accretion model produces a 760 bar carbon-dominated atmosphere with 39 bar of hydrogen and water and a few bars of nitrogen, consistent with volatile concentration estimates for bulk silicate Earth including the atmosphere. The corresponding planetesimal accretion model produces a more massive ($\sim$$1350$ bar) atmosphere with similar composition. The core stores $\sim$$70$% of both the H and the C budget in the early-delivery scenario, but $\lesssim$$50$% in the corresponding continuous delivery scenario. Overall our results demonstrate that substantial amounts of volatiles are sequestered into rocky planet cores during planet formation and that the volatile inventory of bulk silicate Earth was likely established already during the magma ocean phase of planet formation.