Title: HARPS-N high spectral resolution observations of Cepheids I. The Baade-Wesselink projection factor of δ Cep revisited,
Abstract: 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. We
analyze new HARPS-N spectra of delta Cep to measure its cycle-averaged
atmospheric velocity gradient in order to better constrain the projection
factor. 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 delta Cep for the first time. 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 delta 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. The new
HARPS-N observations of delta Cep are consistent with our decomposition of the
projection factor.