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 factor p is 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 determine p , such as geometrical and hydrodynamical models or the inverse BW approach when the distance is known. Aims. We analyze new HARPS-N spectra of δ Cep 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 derive p directly from observations. The projection factor can be divided into three subconcepts: (1) a geometrical effect ( p 0 ); (2) the velocity gradient within the atmosphere ( f grad ); and (3) the relative motion of the optical pulsating photosphere with respect to the corresponding mass elements ( f o−g ). We then measure the f grad value of δ Cep for the first time. Results. When the HARPS-N mean cross-correlated line-profiles are fitted with a Gaussian profile, the projection factor is p cc−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 between f grad and the line depth measured when the Cepheid is at minimum radius. This relation is consistent with that obtained from our best hydrodynamical model of δ Cep and with our projection factor decomposition. Using the observational values of p and f grad found for the 17 spectral lines, we derive a semi-theoretical value of f o−g . We alternatively obtain f o−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 of δ Cep are consistent with our decomposition of the projection factor. The next step will be to measure p 0 directly from the next generation of visible interferometers. With these values in hand, it will be possible to derive f o−g directly from observations.
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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".