HARPS-N high spectral resolution observations of Cepheids I. The Baade-Wesselink projection factor of<i>δ</i>Cep revisited
Bibliographic record
Abstract
Context.The projection factorpis the key quantity used in the Baade-Wesselink (BW) method for distance determination; it converts radial velocities into pulsation velocities. Several methods are used to determinep, such as geometrical and hydrodynamical models or the inverse BW approach when the distance is known. Aims.We analyze new HARPS-N spectra ofδCep to measure its cycle-averaged atmospheric velocity gradient in order to better constrain the projection factor. Methods.We first apply the inverse BW method to derivepdirectly from observations. The projection factor can be divided into three subconcepts: (1) a geometrical effect (p0); (2) the velocity gradient within the atmosphere (fgrad); and (3) the relative motion of the optical pulsating photosphere with respect to the corresponding mass elements (fo−g). We then measure thefgradvalue ofδCep for the first time. Results.When the HARPS-N mean cross-correlated line-profiles are fitted with a Gaussian profile, the projection factor ispcc−g= 1.239 ± 0.034(stat.) ± 0.023(syst.). When we consider the different amplitudes of the radial velocity curves that are associated with 17 selected spectral lines, we measure projection factors ranging from 1.273 to 1.329. We find a relation betweenfgradand the line depth measured when the Cepheid is at minimum radius. This relation is consistent with that obtained from our best hydrodynamical model ofδCep and with our projection factor decomposition. Using the observational values ofpandfgradfound for the 17 spectral lines, we derive a semi-theoretical value offo−g. We alternatively obtainfo−g= 0.975 ± 0.002 or 1.006 ± 0.002 assuming models using radiative transfer in plane-parallel or spherically symmetric geometries, respectively. Conclusions.The new HARPS-N observations ofδCep are consistent with our decomposition of the projection factor. The next step will be to measurep0directly from the next generation of visible interferometers. With these values in hand, it will be possible to derivefo−gdirectly from observations.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".