## Understanding the dynamical structure of pulsating stars: The
center-of-mass velocity and the Baade-Wesselink projection factor of the
*β* Cephei star *α* Lupi^{⋆}

^{1}
Laboratoire Lagrange, UMR7293, Université de Nice Sophia-Antipolis, CNRS,
Observatoire de la Côte d’Azur,
Nice,
France

e-mail:
Nicolas.Nardetto@oca.eu

^{2}
Institut de Recherche en Astrophysique et Planétologie, CNRS, 14
avenue Edouard Belin, Université de Toulouse, UPS-OMP, IRAP, 31400
Toulouse,
France

^{3}
Institute of Astronomy of the Russian Academy of Sciences,
48 Pjatnitskaya
Str., 109017
Moscow,
Russia

^{4}
Universidad de Concepcíon, Departamento de
Astronomía, Casilla
160-C, Concepcíon,
Chile

^{5}
Warsaw University Observatory, Al. Ujazdowskie 4, 00-478
Warsaw,
Poland

Received:
29
October
2012

Accepted:
24
March
2013

*Context. *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.

*Aims. *We aim at deriving the center-of-mass velocity and the projection
factor of the *β* Cephei star *α* Lup.

*Methods. *We present HARPS high spectral resolution observations of
*α* 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 *γ*-velocity and the *γ*-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 model of the
photosphere of the star, we derive a semi-theoretical projection factor for
*α* Lup.

*Results. *We find a center-of-mass velocity of
*V*_{γ} = 7.9 ± 0.6 km s^{-1} and that
the velocity gradient in the atmosphere of *α* Lup is null. We apply to
*α* Lup the usual decomposition of the projection factor into three
parts,
*p* = *p*_{0}*f*_{grad}*f*_{og}
(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 *α* Lup has no velocity
gradient. New HARPS data of a short-period *β* Cephei star,
*τ*^{1} Lup, are also presented in this paper.

*Conclusions. *By comparing Cepheids and *β* Cephei stars,
these results bring insight into the dynamical structure of pulsating star atmospheres,
which helps to better understand the k-term problem and the Baade-Wesselink p-factor for
Cepheids.

Key words: stars: oscillations / stars: atmospheres / line: profiles / stars: individual:*τ*^{1}Lup / stars: individual:*α*Lup / stars: distances

*© ESO, 2013*