Bibliographic record
Abstract
Abstract How rapidly a planet grows in mass and how far it may park from the host star depend sensitively on two nondimensional parameters: Stokes number St and turbulent α. Yet these parameters remain highly uncertain, being difficult or impossible to measure directly. Here, we demonstrate how the ringed disks can be leveraged to obtain St and α separately by constructing a simple toy model that combines the dust radial equation of motion under aerodynamic drag and coupling to gas motion with the measured distribution of dust masses in Class 0/I disks. Focusing on known systems with well-resolved dust rings, we find that the ranges of St and α that are consistent with the measured properties of the rings are small: 10−4 ≲ St ≲ 10−2 and 10−5 ≲ α ≲ 10−3. These low St and α ensure the observed rings are stable against clumping. Even in one marginal case where the formation of bound clumps is possible, further mass growth by pebble accretion is inhibited. Furthermore, the derived low α is consistent with the nearly inviscid regime where type I migration can be prematurely halted. Our analysis predicts a minimal planet population beyond ∼tens of au, where we observe dust rings and significantly more vigorous planet formation inside ∼10 au, consistent with current exo-giant statistics. We close with discussions on the implications of our results on small planet statistics at large orbital distances.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".