THE CLUSTER AGES EXPERIMENT (CASE). V. ANALYSIS OF THREE ECLIPSING BINARIES IN THE GLOBULAR CLUSTER M4
Bibliographic record
Abstract
We use photometric and spectroscopic observations of the eclipsing binaries V65, V66, and V69 in the field of the globular cluster M4 to derive masses, radii, and luminosities of their components. The orbital periods of these systems are 2.29, 8.11, and 48.19 days, respectively. The measured masses of the primary and secondary components ( M p and M s ) are 0.8035 ± 0.0086 and 0.6050 ± 0.0044 M ☉ for V65, 0.7842 ± 0.0045 and 0.7443 ± 0.0042 M ☉ for V66, and 0.7665 ± 0.0053 and 0.7278 ± 0/0048 M ☉ for V69. The measured radii ( R p and R s ) are 1.147 ± 0.010 and 0.6110 ± 0.0092 R ☉ for V66, 0.9347 ± 0.0048 and 0.8298 ± 0.0053 R ☉ for V66, and 0.8655 ± 0.0097 and 0.8074 ± 0.0080 R ☉ for V69. The orbits of V65 and V66 are circular, whereas that of V69 has an eccentricity of 0.38. Based on systemic velocities and relative proper motions, we show that all three systems are members of the cluster. We find that the distance to M4 is 1.82 ± 0.04 kpc—in good agreement with recent estimates based on entirely different methods. We compare the absolute parameters of V66 and V69 with two sets of theoretical isochrones in mass–radius and mass–luminosity diagrams, and for assumed [Fe/H] = −1.20, [α/Fe] = 0.4, and Y = 0.25 we find the most probable age of M4 to be between 11.2 and 11.3 Gyr. Color–magnitude diagram (CMD) fitting with the same parameters yields an age close to, or slightly in excess of, 12 Gyr. However, considering the sources of uncertainty involved in CMD fitting, these two methods of age determination are not discrepant. Age and distance determinations can be further improved when infrared eclipse photometry is obtained.
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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 | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.015 | 0.003 |
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".