Semianalytical Dark Matter Halos and the Jeans Equation
Bibliographic record
Abstract
Although N -body studies of dark matter halos show that the density profiles, ρ( r ), are not simple power laws, the quantity ρ/σ 3 , where σ( r ) is the velocity dispersion, is in fact a featureless power law over ~3 decades in radius. In the first part of the paper we demonstrate, using the semianalytic Extended Secondary Infall Model (ESIM), that the nearly scale-free nature of ρ/σ 3 is a robust feature of virialized halos in equilibrium. By examining the processes in common between numerical N -body and semianalytic approaches, we argue that the scale-free nature of ρ/σ 3 cannot be the result of hierarchical merging; rather it must be an outcome of violent relaxation. The empirical results of the first part of the paper motivate the analytical work of the second part of the paper, where we use ρ/σ 3 ∝ r -α as an additional constraint in the isotropic Jeans equation of hydrostatic equilibrium. Our analysis shows that the constrained Jeans equation has different types of solutions, and in particular, it admits a unique "periodic" solution with α = 1.9444. We derive the analytic expression for this density profile, which asymptotes to inner and outer profiles of ρ ~ r -0.78 and ρ ~ r -3.44 , respectively.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.001 | 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".