Primordial protostars accreting beyond the ΩΓ-limit: radiation effect around the star–disc boundary
Bibliographic record
Abstract
We consider whether the maximum mass of first stars is imposed by the protostellar spin (i.e. by the so-called ΩΓ-limit), which requires the sum of the radiation and centrifugal forces at the stellar surface to be smaller than the inward pull of the gravity. Once the accreting protostar reaches such a marginal state, the star cannot spin up more and is not allowed to accrete more gas with inward angular momentum flux. So far, however, the effect of stellar radiation on the structure of the accretion disc has not been properly taken into account in discussing the effect of the ΩΓ-limit on the formation of the first stars. Here, we obtain a series of steady accretion-disc solutions considering such an effect, and we find solutions without net angular momentum influx to the stars with arbitrary rotation rates, in addition to those with finite angular momentum flows. The accretion of positive angular momentum flows pushes the star beyond the ΩΓ-limit, which is allowed only with the external pressure provided by the circumstellar disc. However, the accretion with no net angular momentum influx does not result in the spin-up of the star. Thus, the existence of the solution with no net angular momentum influx indicates that protostars can keep growing in mass by accretion, even after they reach the ΩΓ-limit.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".