HARPS-N high spectral resolution observations of Cepheids I. The Baade-Wesselink projection factor of δ Cep revisited⋆
1 Université Côte d’Azur, OCA, CNRS, Lagrange, France
2 INAF–Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate (LC), Italy
3 Institute of Astronomy of the Russian Academy of Sciences, 48 Pjatnitskaya Str., 109017 Moscow, Russia
4 Université de Toulouse, UPS-OMP, Institut de Recherche en Astrophysique et Planétologie, 31400 Toulouse, France
5 CNRS, UMR 5277, Institut de Recherche en Astrophysique et Planétologie, 14 avenue Édouard Belin, 31400 Toulouse, France
6 Department of Physics and Astronomy, The Johns Hopkins University, 3400 N. Charles St, Baltimore, MD 21218, USA
7 European Southern Observatory, Alonso de Córdova 3107, Casilla 19001, Santiago 19, Chile
8 Departamento de Astronomía, Universidad de Concepción, Casilla 160-C, Concepción, Chile
9 Millenium Institute of Astrophysics, Santiago, Chile
10 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warszawa, Poland
11 LESIA (UMR 8109), Observatoire de Paris, PSL, CNRS, UPMC, Univ. Paris-Diderot, 5 place Jules Janssen, 92195 Meudon, France
12 Unidad Mixta Internacional Franco-Chilena de Astronomía, CNRS/INSU, France (UMI 3386) and Departamento de Astronomía, Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile
13 Department of Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON, M5S 3H4, Canada
14 Leibniz Institute for Astrophysics, An der Sternwarte 16, 14482 Potsdam, Germany
Received: 26 July 2016
Accepted: 21 October 2016
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 (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 the fgrad 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 pcc−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 fgrad 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 fgrad found for the 17 spectral lines, we derive a semi-theoretical value of fo−g. We alternatively obtain fo−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 p0 directly from the next generation of visible interferometers. With these values in hand, it will be possible to derive fo−g directly from observations.
Key words: stars: oscillations / techniques: spectroscopic / stars: individual: delta Cep / stars: distances / stars: atmospheres / stars: variables: Cepheids
Table A.1 is also available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (220.127.116.11) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/597/A73
© ESO, 2017