Nebular Atmosphere to Magma Ocean: Early Mantle Acquisition of Hydrogen and Helium

The origin and abundance of mantle volatiles present major unresolved questions for Earth's evolution. Here we quantify amounts of mantle volatiles acquired by ingassing from a dense hydrogen-helium atmosphere derived from the solar nebula in the first few million years of Earth history. We model nebular atmosphere-mantle evolution during Earth's accretion, coupling a boundary layer representation of magma ocean dynamics to a one-dimensional nebular atmosphere model. We include atmosphere winds based on scaling laws for rotating fluid convection in deep spherical shells, plus gas transfer between the magma and the nebular atmosphere based on the systematics of air-sea CO2 transfer. The two key phases of system evolution we focus on are (1) nebular atmosphere growth during the first part of accretion, with ingassing of hydrogen and helium into the magma ocean, the hydrogen combining with oxygen to form water, followed by (2) dissipation of the nebular atmosphere with partial degassing during late accretion. We show that gas transfer to the magma depends on the solubility and diffusivity of each volatile phase, the mean age of the magma surface, plus astrophysical timescales including the lifetime of the solar nebula, the dissipation timescale of the nebular atmosphere, and the planet accretion time. Our model predicts that during accretion the surface pressure at the base of Earth's nebular atmosphere may have exceeded 0.5 kb, the surface temperature may have approached 3000 K, with the core-mantle boundary temperature approaching 7000 K. Once the Earth grew beyond a quarter of its final mass, the combination of high surface temperature, strong atmospheric winds and frequent impacts would maintain a super-heated turbulent magma ocean. Calculations show that, under these conditions, the magma ocean would have acquired multiple ocean masses of water and hundreds of petagrams of primordial helium-3 from its nebular atmosphere, far exceeding present-day mantle abundances. Our model also predicts partial degassing of helium and hydrogen during the late stages of accretion, leading Fe+3 production and oxidized conditions in the magma ocean.