Constructing Earth Formation History Using Deep Mantle Noble Gas Reservoirs

TL;DR

This paper develops a coupled envelope–mantle framework to connect primordial solar-nebula gas accretion onto Earth embryos with the deep-mantle noble gas inventory, focusing on neon dissolution into magma oceans. By adapting a 1D quasi-hydrostatic gas-accretion model and applying Henry's law dissolution, the authors show that embryos of about $0.2$–$0.3\,M_\oplus$ forming during nebular dispersal in a depleted disk can reproduce the present-day deep-mantle $^{22}$Ne concentration after rapid dissolution, implying late-stage, gas-poor conditions at $1$ au. The results support a cohesive Earth-formation scenario in which three $\sim0.3\,M_\oplus$ embryos assemble in the dispersed nebula, merge to form a proto-Earth, and undergo Moon-forming giant impacts post-dispersal; to account for heavy noble gases, CI carbonaceous chondrites and subducted atmospheric components are invoked. The work highlights that light noble gases trace nebular accretion, while heavy noble gases reflect solid accretion and later processing, providing a nuanced timeline for Earth's formation and interior volatile budgets.

Abstract

Noble gases are powerful probes of the Earth's early history, as they are chemically inert. Neon isotopic ratios in deep mantle plumes suggest that nebular gases were incorporated into the Earth's interior. This evidence implies the Earth's formation began when there was still gas around, with Earth embryos accreting primordial gas and a fraction of that gas dissolved into molten magma. In this work, we examine these implications, simulating the growth of primordial envelopes using modern gas accretion schemes, and computing the dissolution of nebular Ne into magma oceans following chemical equilibrium. We find that the embryo mass that reproduces the deep mantle concentration of primordial Ne is tightly constrained to $\sim 0.3 M_\oplus$, within a solar nebula depleted by $\geq 100 \times$ in gas density. Embryos of smaller masses cannot accrete enough gas to allow the mantle to reach the melting temperature of basalt. Embryos of larger masses accrete way too much gas, producing excessive Ne concentrations in the deep mantle. Based on our calculations, we suggest that the Earth's formation began with the assembly of $\sim 0.3 M_\oplus$ embryos during the dispersal of the solar nebula. Light noble gases (He, Ne) in the deep mantle reflect the primordial gas accretion history of the Earth, while heavy noble gases (Ar, Kr, Xe) probe early solid accretion processes. Our results are consistent with the final assembly of the Earth through at least two giant impacts after the dispersal of the nebula.

Figures (9)

• Figure 1: Layered structure of Earth embryos considered in this work. Embryos are divided into a rocky interior and a surrounding gas envelope accreted from the primordial nebula of the solar system. We assume that the rocky interior is made of an innermost iron core and an outer silicate mantle, analogous to the Earth's current internal structure. As argued in Section \ref{['subsec:gas_accretion']}, the energy transport within the inner and outer atmospheric layers is set by convection and radiation, respectively, which follows from the Schwarzschild criterion. Note that the figure is not to scale. In reality, the envelope dominates the volume despite its small contribution to the total embryo mass.
• Figure 2: Formation of primordial gas envelopes atop rocky interiors embedded at 1 au in the minimum-mass solar nebula of Hayashi_1981, with gas density depleted by a factor of $f_{\rm dep} = 10^{-2}$ (see Equation \ref{['eq:rho_MMSN']}). Top: Radial profiles (solid) of the temperature and pressure $(T,P)$ of the envelope with mass $M_{\rm env}$ for a rocky interior of mass $M_{\rm rock}=0.2M_\oplus$, extending from the radius of the rocky interior $R_{\rm rock}$ to the Bondi radius $R_B$. Each color represents a hydrostatic snapshot of the envelope for specific values of $M_{\rm env}/M_{\rm rock}$. The dotted line indicates the melting temperature $T_{\rm melt} \approx 1600 \mathrm{K}$ of the surface of the basaltic mantle Solomatov_2000. Center: Same as top, but for $M_{\rm rock}=0.3M_\oplus$. Bottom: Time evolution of $M_{\rm env}/M_{\rm rock}$ for rocky interiors of mass $M_{\rm rock}=0.2M_\oplus$ (solid) and $M_{\rm rock}=0.3M_\oplus$ (dashed). The expected maximal disk lifetime Mamajek_2009 is shown with a dotted vertical line. A horizontal dotted line denotes the isothermal endstate of the $M_{\rm rock}=0.2M_\oplus$ case.
• Figure 3: Dissolution calculation of the concentration of primordial $^{22}$Ne captured at the molten surface of magma oceans on Earth embryos embedded in the solar nebula. Subfigures (a), (b), (c) and (d) present our results for protocore masses of $0.1,0.2,0.3,0.4M_\oplus$, respectively. For each case, the upper panel shows the temperature $T_0$ of the envelope-mantle boundary as a function of time and the lower panel the resulting concentration of primordial $^{22}$Ne dissolved in the silicate interior $c_{\rm ^{22}Ne,p}$ before the surface of the mantle solidifies at a melting temperature $T_{\rm melt}\approx 1600{\rm K}$Solomatov_2000. The shaded areas represent the target concentration required to explain the present-day budget of the deep mantle, as constrained by Marty_2012 and corrected by a factor of $\approx 18.7$ to account for mantle outgassing Parai_2022. The solid black line indicates the temperature $T_{\rm disk}$ of the minimum-mass solar nebula (MMSN) of Hayashi_1981 and the black dashed line the melting temperature $T_{\rm melt}$ of the basaltic mantle Solomatov_2000, required at the surface for the dissolution of primordial gas in the interior. The upper bound on the lifetime of the disk Mamajek_2009 is indicated with a dotted vertical line, corresponding to the maximal possible time after which primordial accretion must come to an end. Different colors account for different depletion factors $f_{\rm dep} \leq 1$ of the gas density of the MMSN disk.
• Figure 4: Schematic illustration of the favored Earth formation scenario implied by our results. Top: From left to right, we show the different formation stages of the Earth from a side-view of a truncated solar nebula, which is initially rich in gas (yellow) and dust (gray dots). As the disk progressively dissipates, the coagulation of solids (see Section \ref{['subsubsec:late_stage_formation']}) leads to the formation of a set of three $\sim 0.3 M_\oplus$ embryos, displayed with cyan, orange and red circles representing the layered embryo structure of Figure \ref{['fig:structure_diagram']}. Following the dispersal of the disk, embryo mergers are enabled, resulting in the formation of the proto-Earth via the doubling (orange arrow) of two $\sim 0.3 M_\oplus$ embryos. The proto-Earth later collides (blue arrow) with the remaining embryo (i.e. Theia) to form the final Earth-Moon system. Bottom: Time evolution (yellow curve) of the volume gas density $\rho_{\rm disk}$ of the solar nebula beginning from a full minimum-mass solar nebula density $\rho_{\rm MMSN}$, as parametrized by the parameter $f_{\rm dep}$ of Equation (\ref{['eq:rho_MMSN']}). Key values of $f_{\rm dep} = 10^{-2}$ and $f_{\rm dep} = 10^{-4}$ setting the boundaries between the gas-rich, gas-poor and dispersed stages of the disk are shown with dash horizontal lines.
• Figure 5: Orbit crossing time $t_X$ of $0.3M_\oplus$ embryos assembled at $a\sim 1$ au with eccentricity $e=0.001$, as a function of orbital spacing $k$. The eccentricity damping timescale $t_{\rm damp}$ of the embryos in a gaseous nebular depleted by factors $f_{\rm dep}=[10^{-2},10^{-3},10^{-4}]$ are displayed with cyan, yellow and magenta dashed horizontal lines, respectively. The damping times are multiplied by 10 to assess the merger criterion $t_X < 10 t_{\rm damp}$ of Papaloizou_2000. As a reference, the orbital spacing $k_{\rm E-V}$ between the Earth and its nearest neighbor Venus is indicated with a red dotted vertical line.