HARPS-N high spectral resolution observations of Cepheids I. The Baade-Wesselink projection factor of δ Cep revisited

摘要

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.