Density Profiles of Collisionless Equilibria. I. Spherical Isotropic Systems
Bibliographic record
Abstract
We investigate the connection between collisionless equilibria and the phase-space relation between density ρ and velocity dispersion σ found in simulations of dark matter halo formation, F = ρ/σ 3 ∝ r -α . Understanding this relation will shed light on the physics relevant to collisionless collapse and on the subsequent structures formed. We show that empirical density profiles that provide good fits to N -body halos also happen to have nearly scale-free ρ/σ 3 distributions when in equilibrium. We have also done a preliminary investigation of variables other than r that may match or supersede the correlation with F . In the same vein, we show that ρ/σ m , where m = 3, is the most appropriate combination to use in discussions of the power-law relationship. Since the mechanical equilibrium condition that characterizes the final systems does not by itself lead to power-law F distributions, our findings prompt us to posit that dynamical collapse processes (such as violent relaxation) are responsible for the radial power-law nature of the ρ/σ 3 distributions of virialized systems.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".