THE EFFECT OF DENSITY ON THE THERMAL STRUCTURE OF GRAVITATIONALLY DARKENED Be STAR DISKS
Bibliographic record
Abstract
The effects of gravitational darkening on the thermal structure of Be star disks of differing densities are systematically examined. Gravitational darkening is the decrease of the effective temperature near the equator and the corresponding increase near the poles of a star caused by rapid rotation. We also include the rotational distortion of the star using the Roche model. Increasing the disk density increases the optical depths in the equatorial plane, resulting in the formation of an inner cool region near the equatorial plane of the disk. High rotation rates result in disks that have temperatures similar to those of a denser disk, namely cooler overall. However, the effect of increasing rotation produces additional heating in the upper disk due to the hotter stellar pole. Cool regions in the equatorial plane normally associated with high density are seen in low-density models at high rotation rates. Gravitational darkening increases the amount of very cool and very hot material in the disk and decreases the amount of disk material at moderate temperatures. We also present models that study the effect of gravitational darkening on hydrostatically converged disks, in which the temperature structure is consistent with vertical hydrostatic equilibrium. Because the equatorial regions become cooler, hydrostatically converged models that include gravity darkening have smaller vertical scale heights, and H / R is smaller by as much as 56% near v crit . Finally, we explore differences in disk temperatures when alternate formulations of gravitational darkening, which lower the temperature difference between the pole and the equator, are used.
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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 | 0.000 | 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".