THE SIZES AND LUMINOSITIES OF MASSIVE STAR CLUSTERS
Bibliographic record
Abstract
The masses of star clusters range over seven decades, from ten up to one hundred million solar masses. Remarkably, clusters with masses in the range 10 4 –10 6 M ☉ show no systematic variation of radius with mass. However, recent observations have shown that clusters with M cl ≳ 3 × 10 6 M ☉ do show an increase in size with increasing mass. We point out that clusters with M cl ≳ 10 6 M ☉ were optically thick to far-infrared radiation when they formed, and explore the hypothesis that the size of clusters with M cl ≳ 3 × 10 6 M ☉ is set by a balance between accretion powered radiation pressure and gravity when the clusters formed, yielding a mass–radius relation r cl ∼ 0.3( M cl /10 6 M ☉ ) 3/5 pc. We show that the Jeans mass in optically thick objects increases systematically with cluster mass. We argue, by assuming that the break in the stellar initial mass function (IMF) is set by the Jeans mass, that optically thick clusters are born with top heavy IMFs; it follows that they are overluminous compared to optically thin clusters when young, and have a higher mass-to-light ratio ϒ V = M cl / L V when older than ∼1 Gyr. Old, optically thick clusters have ϒ V ∼ M 0.1−0.3 cl . It follows that L V ∼ σ β , where σ is the cluster velocity dispersion, and 3.6 ≲ β ≲ 4.5. It appears that ϒ V is an increasing function of cluster mass for compact clusters and ultracompact dwarf galaxies. We show that this is unlikely to be due to the presence of nonbaryonic dark matter, by comparing clusters to Milky Way satellite galaxies, which are dark matter dominated. The satellite galaxies appear to have a fixed mass inside a fiducial radius, M ( r = r 0 ) = constant.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".