Velocity distribution in stellar disks: Are higher order moments negligible?
Bibliographic record
Abstract
Abstract We analysed the structure of the velocity space in galactic disks which are subject to a rotating spiral perturbation. A key assumption of the Boltzmann moment equation approach is the zero‐heat flux approximation, i.e. the neglection of third order velocity terms. We tested this assumption by performing test particle simulations for stars in a disk galaxy subject to a rotating spiral perturbation. The third order velocity moments were typically small (normalized values reach 25% of the initial velocity dispersion) and uncorrelated over almost all of the disk with the exception of the 4:1 resonance region (UHR). Even there, the values are smaller than the initial velocity dispersion. Far outside the resonance position a bimodal distribution characterizes the 3rd order moments. A qualitatively similar distribution is found for the 5th order terms. Contrary to these odd moments, the 4th order terms exceed almost everywhere the initial velocity dispersion. Therefore, an extension of the Boltzmann moment equations by only one moment, i.e. up to the third order, is not reasonable without including the fourth order terms. For all moments a large‐scale structure (either two‐armed or four‐armed) is clearly visible inside the UHR. The odd moments show a patchy irregular pattern outside the UHR, whereas the fourth order moments show also a clear large‐scale pattern. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".