On the link between energy equipartition and radial variation in the stellar mass function of star clusters
Bibliographic record
Abstract
We make use of N-body simulations to determine the relationship between two observable parameters that are used to quantify mass segregation and energy equipartition in star clusters. Mass segregation can be quantified by measuring how the slope of a cluster's stellar mass function α changes with clustercentric distance r, and then calculating | $\delta _\alpha = \frac{{\rm d} \alpha (r)}{{\rm d} ln(r/r_{\rm m})}$ |, where rm is the cluster's half-mass radius. The degree of energy equipartition in a cluster is quantified by η, which is a measure of how stellar velocity dispersion σ depends on stellar mass m via σ(m) ∝ m−η. Through a suite of N-body star cluster simulations with a range of initial sizes, binary fractions, orbits, black hole retention fractions, and initial mass functions, we present the co-evolution of δα and η. We find that measurements of the global η are strongly affected by the radial dependence of σ and mean stellar mass and the relationship between η and δα depends mainly on the cluster's initial conditions and the tidal field. Within rm, where these effects are minimized, we find that η and δα initially share a linear relationship. However, once the degree of mass segregation increases such that the radial dependence of σ and mean stellar mass become a factor within rm, or the cluster undergoes core collapse, the relationship breaks down. We propose a method for determining η within rm from an observational measurement of δα. In cases where η and δα can be measured independently, this new method offers a way of measuring the cluster's dynamical state.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".