Bibliographic record
Abstract
Context. Stellar limb darkening, I(μ = cosθ), is an important constraint for microlensing, eclipsing binary, planetary transit, and interferometric observations, but is generally treated as a parameterized curve, such as a linear-plus-square-root law. Many analyses assume limb-darkening coefficients computed from model stellar atmospheres. However, previous studies, using I(μ) from plane-parallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common μ location on the stellar disk, for all values of Teff, log g and wavelength. Aims. We study this fixed μ-point to determine if it is a property of the model stellar atmospheres or a property of the limb-darkening laws. Furthermore, we use this limb-darkening law as a tool to probe properties of stellar atmospheres for comparison to limb-darkening observations. Methods. Intensities computed with plane-parallel and spherically-symmetric Atlas models (characterized by the three fundamental parameters L⋆, M⋆ and R⋆) are used to reexamine the existence of the fixed μ-point for the parametrized curves. Results. We find that the intensities from our spherical models do not have a fixed point, although the curves do have a minimum spread at a μ-value similar to the parametrized curves. We also find that the parametrized curves have two fixed points, μ1 and μ2, although μ2 is so close to the edge of the disk that it is missed using plane-parallel atmospheres. We also find that the spherically-symmetric models appear to agree better with published microlensing observations relative to plane-parallel models. Conclusions. The intensity fixed point results from the choice of the parametrization used to represent the limb darkening and from the correlation of the coefficients of the parametrization, which is a consequence of their dependence on the angular moments of the intensity. For spherical atmospheres, the coefficients depend on the three fundamental parameters of the atmospheres, meaning that limb-darkening laws contain information about stellar atmospheres. This suggests that limb-darkening parameterizations fit with spherically-symmetric model atmospheres are powerful tools for comparing to observations of red giant stars.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| 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".