Limits on Protoplanet Growth by Accretion of Small Solids

Abstract

This paper identifies constraints on the growth of a small planetary core (0.3 M${}_{\oplus }$) that accretes millimeter-sized pebbles from a gaseous disk. We construct time-dependent spherical envelope models that capture physical processes not included in existing global hydrodynamic simulations, including particle size evolution, dust transport, and realistic gas equations of state. We assume a low enough disk density that pebbles are marginally coupled to the gas and are trapped efficiently near the core Bondi radius. Pebbles then drift rapidly enough to experience erosion by sandblasting, mutual collisions, and sublimation of water ice. We find that pebble fragmentation is more efficient than dust re-sticking. Therefore the large pebble accretion rate ${\dot{M}}_p$ needed to build a core of mass > M${}_{\oplus }$ leads to a high envelope metallicity and grain opacity. Above ${\dot{M}}_p$ $\sim 10^{-7}$ M${}_{\oplus }$/yr, and without other luminosity sources, convective motions expand near the Bondi radius. The warm, dusty, and turbulent envelope buffers the inward drift of pebble debris: given a turbulent concentration factor $f_{turb}\ge$ 1 near the lower convective boundary, the core growth rate is limited to $1\times 10^{-7}{f}_{turb}$ M${}_{\oplus }$/yr and the e-folding time 3$f_{turb}^{-1}$ Myr. The remainder of the solid debris is expelled as highly processed silicates. Pebble ice never reaches the core, and the envelope contains comparable amounts of H2/He and metals. We interpret our results using simpler steady models and semi-analytical estimates. Future global simulations incorporating the processes modelled here are needed to understand the influence of rotation and vertical disk structure.

41 pages, 17 figures. Accepted for publication in the Astrophysical Journal. Expanded analytic treatment of threshold for refluxing. Corrected treatment of ice sublimation in the envelope. Effect added of heating due to the accretion of a fraction of pebble debris onto the core

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• Sublimation of refractory minerals in the gas envelopes of accreting rocky planets
• Transport, destruction and growth of pebbles in the gas envelope of a protoplanet
• Turbulent Disk Viscosity and the Bifurcation of Planet Formation Histories
• Solid Accretion onto Neptune-Mass Planets I: In-Situ Accretion and Constraints from the metallicity of Uranus and Neptune
• Dust processing in protoplanetary envelopes as the origin of hot minerals in comets
• Compositional Turbulence and Layering in the Gaseous Envelopes of Forming Planets
• Interior dynamics of envelopes around disk-embedded planets
• The effect of late giant collisions on the atmospheres of protoplanets and the formation of cold sub-Saturns