Correlations of Richness and Global Properties in Galaxy Clusters
Bibliographic record
Abstract
Richness is a key defining characteristic of a galaxy cluster. We measure the optical richness of galaxy clusters from the Canadian Network for Observational Cosmology Cluster Redshift Survey using the galaxy cluster center correlation amplitude B gc . We show that the B gc values measured using photometric catalogs are consistent with those derived from redshift catalogs, indicating that richness can be measured reliably from photometric data alone, even at moderate redshifts of ~0.6. We establish the correlations between optical richness and other important attributes of a galaxy cluster, such as velocity dispersion, mass, radius, and X-ray temperature and luminosity. We find that the scaling relations of these quantities with richness are entirely consistent with those derived by assuming a simple mass density profile at 0.5 h Mpc of ρ ~ r -1.8 . The excellent correlations between B gc and velocity dispersion and X-ray temperature allow one to use richness, an easily measurable quantity using relatively shallow optical imaging data alone, as a predictor of these quantities at moderate redshifts. The B gc parameter can be used to estimate the velocity dispersion of a cluster to a precision of approximately 15% (~±100 km s -1 ) and X-ray temperature to about 20%. Similar correlations, but with larger scatter, are also obtained between richness and the characteristic radius and mass of the clusters. We compare the relative merits of B gc , T X , and L X as predictors of the dynamical mass and find that they are comparable, providing estimates at an accuracy of ~30%. We also perform similar analyses of correlations between richness and velocity dispersion, T X , and L X with a sample of low-redshift Abell clusters and find consistent results, but with larger scatter, which may be the result of a less homogeneous database or sample-dependent effects.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".