Limits on Protoplanet Growth by Accretion of Small Solids
Bibliographic record
Abstract
Abstract This paper identifies constraints on the growth of a small planetary core (0.3 M ⊕ ) that accretes millimeter-sized pebbles from a gaseous disk. We construct time-dependent spherical envelope models that capture physical processes that are 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 resticking. Therefore the high pebble accretion rate needed to build a core of mass > M ⊕ leads to a high envelope metallicity and grain opacity. Above yr −1 , 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 ≳ 1 near the lower convective boundary, the core growth rate is limited to 1 × 10 −7 f turb M ⊕ yr −1 and the e-folding time 3/ f turb 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 H 2 /He and metals. We interpret our results using simpler steady models and semianalytical estimates. Future global simulations incorporating the processes modeled here are needed to understand the influence of rotation and vertical disk structure.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".