Power Laws and Non–Power Laws in Dark Matter Halos
Bibliographic record
Abstract
Simulated dark matter profiles are often modeled as an NFW density profile rather than a single power law. Recently, attention has turned to the rather rigorous power-law behavior exhibited by the "pseudo-phase-space density" of the dark matter halo, which is defined dimensionally in terms of the local density and velocity dispersion of the dark matter particles. The non-power-law behavior of the density profile is generally taken to exclude simple scale-free infall models; however, the power-law behavior of the "pseudodensity" is a counter indication. We argue in this paper that both behaviors may be at least qualitatively understood in terms of a dynamically evolving self-similarity, rather than as the form for self-similar infall that is fixed by cosmological initial conditions. The evolution is likely due to collective relaxation such as that provided by the radial-orbit instability on large scales. We deduce, from a distribution function given by first-order coarse-graining, both the NFW-type density profile and the power-law pseudodensity profile. The results are not greatly sensitive to variations of about 3 in the power of the velocity dispersion used in the definition of the phase-space pseudodensity. We suggest that the power 2 may create the more physical quantity, whose deviations from a power law are a diagnostic of incomplete relaxation.
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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 | 0.015 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| 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".