The formation of rocky planets involves accretion, leading to the potential capture of gases like helium and hydrogen from the solar nebula. Some gases are trapped internally, while others contribute to primordial atmospheres, potentially eroded after nebula dissipation. Extensive melting, from impacts or radiogenic heat, results in magma oceans (MOs). Volatiles are continuously delivered and dissolved in MOs or outgassed into secondary atmospheres. Large impacts, such as the one forming the Moon, cause extensive melting and atmospheric resets. For Earth, volatiles survived this impact and mixed within the silicate liquid. Heavier volatiles, like noble gases and carbon, became part of the early Earth, either dissolved or in the atmosphere. This volatile-rich atmosphere was thick and insulating, delaying MO solidification and prolonging devolatilization. The rate of devolatilization depends on the thermochemical evolution at the MO surface. Initially, vaporization was unhindered, but as crystallization progressed, melt percolation formed a surface lid, limiting degassing. Understanding volatile degassing is crucial to constrain the budget of primitive volatiles and the conditions and timescales of Earth's crystallization. This study examines carbon's influence on helium degassing from the early Earth's global MO, using ab initio molecular dynamics simulations on pyrolite melt (simulating Bulk Silicate Earth composition), with added helium and CO2 molecules. Noble gases (especially helium) are excellent tracers of physical processes due to their lack of chemical bonding, and carbon's devolatilization behavior is well-studied. This study is the first to examine their concurrent vaporization.

Previous research has examined helium and carbon vaporization independently from pyrolite, but not concurrently. Studies have shown CO and CO2 dominated the early atmosphere. Noble gases, being undersaturated in the MO, couldn't nucleate bubbles alone; instead, they partitioned into bubbles filled with CO2 or other volatiles. Existing work on helium and carbon vaporization from pyrolite provided a foundation for this study, which explores the interactive effects of these two elements.

Ab initio molecular dynamics simulations were performed on a pyrolite melt (simulating Bulk Silicate Earth composition) with added helium and CO2. The interatomic forces were computed using the projector-augmented wave method of density functional theory (DFT) as implemented within the Vienna Ab initio Simulation Package (VASP). The Perdew-Burke-Ernzerhof (PBE) form of the generalized gradient approximation was used for electron exchange and correlation. Simulations were conducted at various temperatures (2000-5000 K) and pressures (0.5-256 kb) to cover conditions from early MOs to present-day magmas. Multiple starting configurations were used to ensure wide sampling of configurational space. The formation of nanoscale cavities (nanobubbles) containing vaporized species was observed at pressures below ~25 kb. The time spent by each volatile in the liquid versus vapor phases was measured to determine solubility. Helium vaporization was quantified by analyzing the coordination number to oxygen, with a coordination number of 2 or less classifying helium as vapor. For carbon, a bonding matrix analysis, identifying small atomic clusters as vapor species, was used. Speciation analysis was conducted using the UMD package. The pressure of the gas phase was computed using a modified Van der Waals equation of state, considering intermolecular interactions. Bader charge analysis was employed to approximate the volume of the gas phase. To distinguish between bulk and adsorbed carbon, the local bonding environments of non-vaporized carbon atoms were analyzed. Carbon atoms bonded to a single anion were classified as adsorbed, while those with more than one bond were classified as part of the bulk melt.

Above ~25 kbar, carbon and helium are completely dissolved in the melt. Below this pressure, nanoscale cavities (nanobubbles) form, populated by vaporized species. Helium devolatilization is very efficient at low pressures (totally degassed below 1 kb) and increases with temperature. CO2 enhances helium degassing, likely by increasing melt porosity and creating escape pathways. Carbon devolatilization is also controlled by pressure and temperature, with higher temperatures and lower pressures favoring devolatilization. Helium enhances carbon vaporization. At lower temperatures (2000 and 3000 K), helium and carbon have similar devolatilization rates, while at higher temperatures, helium becomes more volatile. Carbon vapor is predominantly CO2 and CO. Below ~5 kb, CO2 dominates, while above ~5 kb, CO is favored at higher temperatures. With decreasing pressure, the abundance of non-vaporized carbon decreases exponentially in the bulk, while it increases in the vapor phase. At mid-pressures (3-8 kb), adsorbed, bulk, and vaporized carbon abundances are roughly equal. At lower pressures, most non-vaporized carbon is adsorbed. Helium and carbon vaporization increase with temperature at all pressures examined (1, 3, and 5 kb). CO2 enhances helium degassing significantly, especially at high temperatures. At conditions simulating the early MO (~5000 K and 5 kb), about half of the helium and 40% of the carbon degassed. As the MO cooled (~3000-4000 K and 3 kb), slightly more than half degassed. In final-stage melts (~2000 K and 1 kb), degassing was efficient (~65-70% loss). These results agree with estimates from present-day degassing of mixed volatile-bearing melts. The abundance of CO2 increases with decreasing pressure and temperature, creating a feedback loop where more efficient CO2 degassing prolongs MO cooling. The presence of additional volatiles significantly increases devolatilization.

The study's findings address the research question of carbon's influence on helium degassing from the early Earth's magma ocean. The results show a synergistic effect where the presence of CO2 significantly enhances helium degassing, indicating that the early Earth's atmosphere was likely much richer in helium than previously assumed. This has significant implications for models of early Earth's atmospheric evolution and composition. The observed enhanced devolatilization of noble gases in the presence of carbon necessitates a revision of existing models for Earth's noble gas budget. The significant CO2 content likely created a strong greenhouse effect, prolonging the cooling of the magma ocean. The methodology, utilizing ab initio molecular dynamics simulations, provides a detailed microscopic understanding of the degassing processes. The results are also applicable to other planetary bodies, suggesting that the composition of a star influences the extent of degassing and atmospheric thickness of its orbiting planets.

This study demonstrates that the concurrent degassing of CO2 and helium from a magma ocean is a highly efficient process, leading to significant loss of both volatiles. This finding implies a significantly different early Earth atmosphere, thicker and richer in carbon and helium than previously estimated. The synergistic effect between CO2 and helium degassing should be considered in future models of planetary formation and evolution. Future research could explore the impact of other volatiles and the role of convection in influencing the efficiency of degassing.

The simulations are limited by the size of the computational cells, leading to uncertainties in the vaporization values due to surface effects. The number of helium and carbon atoms included in the simulations is also limited due to computational constraints. While the results show clear trends, the quantitative values have uncertainties associated with these limitations. The nanoscale bubbles observed in the simulation represent the initial stages of degassing; the actual degassing process involves bubble coalescence and migration on a larger scale.