The Lower Main Sequence and Mass Function of the Globular Cluster Messier 4
Bibliographic record
Abstract
The deepest optical image ever in a globular star cluster, a Hubble Space Telescope 123 orbit exposure in a single field of Messier 4, was obtained in two filters (F606W, F814W) over a 10 week period in early 2001. A somewhat shallower image obtained in 1995 allowed us to select out cluster and field objects via their proper-motion displacement, resulting in remarkably clean color-magnitude diagrams that reach to V = 30, I = 28. The cluster main-sequence luminosity function contains very few stars fainter than M V = 15.0, M I = 11.8, which, in both filters, is more than 2 mag brighter than our limit. This is about the faintest luminosity seen among field Population II subdwarfs of the same metallicity. However, there remains a sprinkling of potential cluster stars to lower luminosity all the way down to our limiting magnitudes. These latter objects are significantly redder than any known metal-poor field subdwarf. Comparison with the current generation of theoretical stellar models implies that the masses of the lowest luminosity cluster stars observed are near 0.09 M ☉ . We derive the mass function of the cluster in our field and find that it is very slowly rising toward the lowest masses with no convincing evidence of a turnover even below 0.1 M ☉ . The formal slope between 0.65 and 0.09 M ☉ is α = 0.75 (Salpeter of 2.35) with a 99% confidence interval of 0.55-1.05. A consistency check between these slopes and the number of observed cluster white dwarfs yields a range of possible conclusions, one of which is that we have indeed seen the termination of the white dwarf cooling sequence in M4.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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) | 0.005 | 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".