Self consistent modelling of the projection factor for interferometric distance determination

The distance of galactic Cepheids can be derived through the interferometric Baade-Wesselink method. The interferometric measurements lead to angular diameter estimations over the whole pulsation period, while the stellar radius variations can be deduced from the integration of the pulsation velocity. The latter is linked to the observational velocity deduced from line profiles by the so-called projection factor p. The knowledge of p is currently an important limiting factor for this method of distance determination. A self-consistent and time-dependent model of the star δ Cep is computed in order to study the dynamical structure of its atmosphere together with the induced line profile. Different kinds of radial and pulsation velocities are then derived. In particular, we compile a suitable average value for the projection factor related to different observational techniques, such as spectrometry, and spectral-line or wide-band interferometry. We show that the impact on the average projection factor and consequently on the final distance deduced from this method is of the order of 6%. We also study the impact of a constant or variable p-factor on the Cepheid distance determination. We conclude on this last point that if the average value of the projection factor is correct, then the influence of the time dependence is not significant as the error in the final distance is of the order of 0.2%.