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

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.