Surface brightness–colour relations of Cepheids calibrated by optical interferometry
Bibliographic record
Abstract
Context. Surface brightness–colour relations (SBCRs) are widely used to determine the angular diameters of stars. They are in particular used in the Baade-Wesselink (BW) method of distance determination of Cepheids. However, the impact of the SBCR on the BW distance of Cepheids is about 8%, depending on the choice of SBCR considered in the literature. Aims. We aim to calibrate a precise SBCR dedicated to Cepheids using the best quality interferometric measurements available as well as different photometric bands, including the Gaia bands. Methods. We selected interferometric and photometric data in the literature for seven Cepheids covering different pulsation periods. From the phased photometry in the different bands (VJHKGGBP GRP) corrected from extinction and the interferometric limb-darkened angular diameters, we calculated the SBCR associated with each combination of colours. Results. We first find that the seven Cepheids have consistent SBCRs as long as the two magnitudes considered are not too close in wavelengths. For the SBCR (FV, V − K): FV = −0.1336±0.0009(V − K)0 + 3.9572±0.0015, we obtain a root mean square (RMS) of 0.0040 mag, which is three times lower than the latest estimate from 2004. Also, for the first time, we present an SBCR dedicated to Cepheids based on Gaia bands only: FGBP = −0.3001±0.0030(GBP − GRP)0 + 3.9977±0.0029, with an excellent RMS of 0.0061 mag. However, using theoretical models, we show that this SBCR is highly sensitive to metallicity. From this empirical multi-wavelength approach, we also show that the impact of the CircumStellar Environment (CSE) of Cepheids emission is not negligible and should be taken into account in the future. Conclusions. With this study, we improve the calibration and our understanding of the SBCR of Cepheids. The overall goal of this project is to provide a purely empirical SBCR version of the BW method that takes into account the metallicity and the CSE emission of Cepheids and that could be applied to individual Cepheids in the local group in the context of JWST and ELT.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.002 |
| 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".