Depletion of moderately volatile elements by pebble accretion in Earth-like planets

TL;DR

This study analyzes how pebble accretion in growing terrestrial planets generates hot, open nebular atmospheres that drive evaporation and exhaust of moderately volatile elements. By solving coupled pebble dynamics, vaporization kinetics, and 1D atmospheric structure across protoplanet masses, the authors show that Zn depletes around $0.4\,M_igoplus$ and Na, K around $0.6\,M_igoplus$ when the atmosphere exhaust timescale is a few hundred years. Including mantle–core partitioning and late impacts, they reproduce Earth-like depletion patterns most consistently with a ~0.7$\,M_igoplus$ target plus ~0.3$\,M_igoplus$ of impactors, highlighting the strong mass-dependence of volatile loss under pebble accretion. The results imply that Earth-like volatile depletion can emerge naturally from pebble-driven growth and emphasize the role of accretion history and atmosphere dynamics in shaping planetary volatile inventories.

Abstract

Protoplanets growing by pebble accretion capture massive hydrogen-helium atmospheres from the surrounding nebula. Pebbles settling through such atmospheres continuously release gravitational potential energy, heating both the atmosphere and the pebbles. Under these conditions, atmosphere temperatures above large protoplanets are sufficiently high to melt silicate pebbles, support long-lived magma oceans, and drive evaporation of volatile species. Because these atmospheres are open to the nebula, some amount of volatile loss is inevitable. Here we analyze the depletion of moderately volatile elements from terrestrial protoplanets undergoing pebble accretion. We consider chondrule-size silicate pebbles enriched in Si, Na, K, and Zn relative to Earth, settling through a hydrogen-helium-rich atmosphere containing these same volatiles. We show that volatile depletion depends critically on protoplanet mass, the timescale of atmosphere exhaust, and the pebble composition. The protoplanetary mass effect is especially strong. For exhaust timescales of a few centuries, we find that substantial depletion of Zn begins around 0.4 Earth mass, and for Na and K around 0.6 Earth mass, with negligible depletion of these elements at smaller masses. Using a pebble composition that matches Earth's major element abundances, broad agreement with Earth's depletion trend for moderately volatile elements is found by merging a large (approximately 0.7 Earth mass) volatile-depleted target protoplanet with one or more smaller, less-depleted impactors.

Figures (14)

• Figure 1: Element abundances normalized by Mg and CI chondrite abundances versus condensation temperature. Bulk Earth (diamonds), Bulk Mars (squares), CI chondrite (dashed line), and Pebble (triangles) abundances and 50% condensation temperatures are from Table 1.
• Figure 2: Schematic of the gas circulation around a terrestrial protoplanet growing by pebble accretion. Blue contours are disk plane gas streamlines in a reference frame orbiting with the protoplanet. Dotted circle denotes the Hill radius, solid circle the protoplanet surface (exaggerated in size), circular blue shading denotes the protoplanet atmosphere. Labeled shadings denote pathways for intake of volatile-bearing pebbles and exhaust of thermally-processed volatiles.
• Figure 3: Schematic of volatile fluxes into and out of a terrestrial protoplanet growing by pebble accretion. Blue, brown and gray shadings denote atmosphere, silicate mantle, and metallic core, respectively. Brown dots denote volatile-bearing silicate pebbles with size reduction indicating volatile loss to the atmosphere by evaporation. Gray dots denote metal pebbles, volatile-free in the atmosphere. Black arrows denote volatile addition by pebble influx. Short brown arrows denote volatile evaporation from the mantle; long curved brown arrows denote volatile loss from the atmosphere.
• Figure 4: Profiles of viscosity versus temperature for H$_{2}$, He, SiO vapor, and our volatile-free model H$_{2}$-He atmosphere.
• Figure 5: Atmosphere structure profiles around a 0.3$M_E$ protoplanet growing by pebble accretion. Model variables and properties are given in Tables 3-6. In (a)-(f) the solid curves correspond to the left axes, the dashed curves to the right axes. Flight time begins at altitude 9$r_{surf}$. Azimuthal winds labeled 2D and 3D are described in the Appendix. Stability is $N^2$ from equation (\ref{['Nsq']}).