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تسجيل مستخدم جديدUnderstanding the dynamical structure of pulsating stars: The center-of-mass velocity and the Baade-Wesselink projection factor of the beta-Cephei star alpha-Lupi
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High-resolution spectroscopy of pulsating stars is a powerful tool to study the dynamical structure of their atmosphere. Lines asymmetry is used to derive the center-of-mass velocity of the star, while a direct measurement of the atmospheric velocity gradient helps determine the projection factor used in the Baade-Wesselink method of distance determination. We aim at deriving the center-of-mass velocity and the projection factor of the beta-Cephei star alpha-Lup. We present HARPS high spectral resolution observations of alpha-Lup. We calculate the first-moment radial velocities and fit the spectral line profiles by a bi-Gaussian to derive line asymmetries. Correlations between the gamma-velocity and the gamma-asymmetry (defined as the average values of the radial velocity and line asymmetry curves respectively) are used to derive the center-of-mass velocity of the star. By combining our spectroscopic determination of the atmospheric velocity gradient with a hydrodynamical modelof the photosphere of the star, we derive a semi-theoretical projection factor for alpha Lup. We find a center-of-mass velocity of Vgamma = 7.9 +/- 0.6 km/s and that the velocity gradient in the atmosphere of alpha Lup isnull. We apply to alpha Lup the usual decomposition of the projection factor into three parts, p = p0 fgrad fog (originally developed for Cepheids), and derive a projection factor of p = 1.43 +/-0.01. By comparing our results with previous HARPS observations of classical Cepheids, we also point out a linear relation between the atmospheric velocity gradient and the amplitude of the radial velocity curve. Moreover, we observe a phase shift (Van Hoof effect), whereas alpha Lup has no velocity gradient.
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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 ai
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Cepheids play a key role in astronomy as standard candles for measuring intergalactic distances. Their distance is usually inferred from the Period-Luminosity relationship, calibrated using the semi-empirical Baade-Wesselink method. Using this method
, the distance is known to a multiplicative factor, called the projection factor. Presently, this factor is computed using numerical models - it has hitherto never been measured directly. Based on our new interferometric measurements obtained with the CHARA Array and the already published parallax, we present a geometrical measurement of the projection factor of a Cepheid, delta Cep. The value we determined, p = 1.27$pm$0.06, confirms the generally adopted value of p = 1.36 within 1.5 sigmas. Our value is in line with recent theoretical predictions of Nardetto et al. (2004).
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 m
odels 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.
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