Abstract
Aims. The Baade-Wesselink method of distance determination is based on the oscillations of pulsating stars. The key parameter of this method is the projection factor used to convert the radial velocity into the pulsation velocity. Our analysis was aimed at deriving for the first time the projection factor of delta Scuti stars, using high-resolution spectra of the high-amplitude pulsator AI Vel and of the fast rotator beta Cas. Methods. The geometric component of the projection factor (i.e. p0) was calculated using a limb-darkening model of the intensity distribution for AI Vel, and a fast-rotator model for beta Cas. Then, using SOPHIE/OHP data for beta Cas and HARPS/ESO data for AI Vel, we compared the radial velocity curves of several spectral lines forming at different levels in the atmosphere and derived the velocity gradient associated to the spectral-line-forming regions in the atmosphere of the star. This velocity gradient was used to derive a dynamical projection factor p. Results. We find a flat velocity gradient for both stars and finally p = p0 = 1.44 for AI Vel and p = p0 = 1.41 for beta Cas. By comparing Cepheids and delta Scuti stars, these results bring valuable insights into the dynamical structure of pulsating star atmospheres. They suggest that the period-projection factor relation derived for Cepheids is also applicable to delta Scuti stars pulsating in a dominant radial mode.
Highlights
Determining distances in the Universe is not a trivial task
Using SOPHIE/OHP data for β Cas and HARPS/ESO data for AI Vel, we compared the radial velocity curves of several spectral lines forming at different levels in the atmosphere and derived the velocity gradient associated to the spectral-line-forming regions in the atmosphere of the star
We find p = 1.44 ± 0.05 for AI Vel and p = 1.41 ± 0.25 for β Cas
Summary
From our Galaxy to the Virgo Cluster, distances can be derived using the period-luminosity relation (PL) of Cepheids (Riess et al 2009a,b) This relation has to be calibrated, using the Baade-Wesselink method of distance determination for instance (Storm et al 2011a,b). This paper is part of the international Araucaria Project, whose purpose is to provide an improved local calibration of the extragalactic distance scales out to distances of a few megaparsecs (Gieren et al 2005) In this context, δ Scuti stars are extremely interesting since it has been shown recently that they follow a PL relation (McNamara et al 2007; Poretti et al 2008)
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