Self consistent modelling of the projection factor for interferometric distance determination

Abstract

Abstract. 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%.

Cepheid limb darkening, angular diameter corrections, and projection factor from static spherical model stellar atmospheres

“…These results suggest that Kervella et al (2004) relations measured by Kervella et al (2004) and Fouqué & Gieren (1997). The result is also consistent with the results of Sasselov & Karovska (1994) and Nardetto et al (2004).…”

New Baade-Wesselink distances and radii for four metal-rich Galactic Cepheids

“…This approach was applied to δ Cep by Mérand et al (2005) using the new optical interferometric measurements obtained with the CHARA Array, the FGS@HST trigonometric parallax by Benedict et al (2007) and the radial velocities available in the literature. The p-factor they foundp=1.27 ± 0.06-agrees quite well with theoretical predictions by Nardetto et al (2004). More recently, G07 found that the use of a constant p-factor (p=1.27 ± 0.05) for six Galactic Cepheids, with interferometrically measured angular diameter variations and known distances, agrees quite well with HST parallaxes.…”

The Baade–Becker–Wesselink technique and the fundamental astrophysical parameters of Cepheids

“…Variations of P F have also been reported by, e.g. Nardetto et al (2004). We provide useful analytic approximation for the projection factor, P F , as a three-parameter exponential expression, based on 10,000 numerical experiments (Rastorguev 2010):…”

“…There is yet no consensus as to which projection factor (PF) should be used for Cepheid variables (Nardetto et al 2004, Groenewegen 2007, Nardetto et al 2007, Nardetto et al 2009). Different approaches (constant or period-dependent P F values) lead to systematic differences in the inferred Cepheid parameters, first and foremost in the radii.…”