Made-to-measure modelling of globular clusters
Bibliographic record
Abstract
ABSTRACT We present the first application of the made-to-measure method for modelling dynamical systems to globular clusters. Through the made-to-measure algorithm, the masses of individual particles within a model cluster are adjusted while the system evolves forward in time via a gravitational N-body code until the model cluster is able to reproduce select properties of an observed cluster. The method is first applied to observations of mock isotropic and anisotropic clusters while fitting against the cluster’s 3D or projected density profile, density weighted mean-squared velocity profile, or its density profile with individual mean-squared velocity profiles assuming $10 {{\ \rm per\ cent}}$ uncertainty in each of these observables. We find that a cluster’s 3D density profile can easily be reproduced by the made-to-measure method, with minor discrepancies in the outer regions if fitting against a cluster’s projected surface density or projected kinematic properties. If an observed cluster is anisotropic, only fitting against the cluster’s density profile and individual mean-squared velocity profiles will fully recover the full degree of anisotropy. Partial anisotropy can be recovered as long as two kinematic properties are included in the fit. We further apply the method to observations of the Galactic globular cluster M4 and generate a complete 6D representation of the cluster that reproduces observations of its surface density profile, mean-squared proper motion velocity profile, and mean-squared line of sight velocity profile. The M2M method predicts M4 is primarily isotropic with a mass of $9.2\pm 0.4\times 10^4\, \mathrm{ M}_{\odot }$ and a half-mass radius of 3.7 ± 0.1 pc.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".