HARPSN high spectral resolution observations of Cepheids I. The BaadeWesselink projection factor of δ Cep revisited
Abstract
Context. The projection factor p is the key quantity used in the BaadeWesselink (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 HARPSN spectra of δ Cep to measure its cycleaveraged 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_{og}). We then measure the f_{grad} value of δ Cep for the first time.
Results: When the HARPSN mean crosscorrelated lineprofiles are fitted with a Gaussian profile, the projection factor is p_{ccg} = 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 semitheoretical value of f_{og}. We alternatively obtain f_{og} = 0.975 ± 0.002 or 1.006 ± 0.002 assuming models using radiative transfer in planeparallel or spherically symmetric geometries, respectively.
Conclusions: The new HARPSN 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_{og} directly from observations. Table A.1 is also available at the CDS via anonymous ftp to http://cdsarc.ustrasbg.fr (http://130.79.128.5) or via http://cdsarc.ustrasbg.fr/vizbin/qcat?J/A+A/597/A73
 Publication:

Astronomy and Astrophysics
 Pub Date:
 January 2017
 DOI:
 10.1051/00046361/201629400
 arXiv:
 arXiv:1701.01589
 Bibcode:
 2017A&A...597A..73N
 Keywords:

 stars: oscillations;
 techniques: spectroscopic;
 stars: individual: delta Cep;
 stars: distances;
 stars: atmospheres;
 stars: variables: Cepheids;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 11 pages, accepted in A&