Maximally accreting supermassive stars: a fundamental limit imposed by hydrostatic equilibrium
Bibliographic record
Abstract
Context. Major mergers of gas-rich galaxies provide promising conditions for the formation of supermassive black holes (SMBHs; ≳105 M⊙) by direct collapse because they can trigger mass inflows as high as 104 − 105 M⊙ yr−1 on sub-parsec scales. However, the channel of SMBH formation in this case, either dark collapse (direct collapse without prior stellar phase) or supermassive star (SMS; ≳104 M⊙), remains unknown. Aims. Here, we investigate the limit in accretion rate up to which stars can maintain hydrostatic equilibrium. Methods. We compute hydrostatic models of SMSs accreting at 1–1000 M⊙ yr−1, and estimate the departures from equilibrium a posteriori by taking into account the finite speed of sound. Results. We find that stars accreting above the atomic cooling limit (≳10 M⊙ yr−1) can only maintain hydrostatic equilibrium once they are supermassive. In this case, they evolve adiabatically with a hylotropic structure, that is, entropy is locally conserved and scales with the square root of the mass coordinate. Conclusions. Our results imply that stars can only become supermassive by accretion at the rates of atomically cooled haloes (∼0.1 − 10 M⊙ yr−1). Once they are supermassive, larger rates are possible.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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".