The aim of this work is to improve the SBC relation for early-type stars in the $-1 leq V-K leq 0$ color domain, using optical interferometry. Observations of eight B- and A-type stars were secured with the VEGA/CHARA instrument in the visible. The d
erived uniform disk angular diameters were converted into limb darkened angular diameters and included in a larger sample of 24 stars, already observed by interferometry, in order to derive a revised empirical relation for O, B, A spectral type stars with a V-K color index ranging from -1 to 0. We also took the opportunity to check the consistency of the SBC relation up to $V-K simeq 4$ using 100 additional measurements. We determined the uniform disk angular diameter for the eight following stars: $gamma$ Ori, $zeta$ Per, $8$ Cyg, $iota$ Her, $lambda$ Aql, $zeta$ Peg, $gamma$ Lyr, and $delta$ Cyg with V-K color ranging from -0.70 to 0.02 and typical precision of about $1.5%$. Using our total sample of 132 stars with $V-K$ colors index ranging from about $-1$ to $4$, we provide a revised SBC relation. For late-type stars ($0 leq V-K leq 4$), the results are consistent with previous studies. For early-type stars ($-1 leq V-K leq 0$), our new VEGA/CHARA measurements combined with a careful selection of the stars (rejecting stars with environment or stars with a strong variability), allows us to reach an unprecedented precision of about 0.16 magnitude or $simeq 7%$ in terms of angular diameter.
High-resolution spectroscopy is a powerful tool to study the dynamical structure of pulsating stars atmosphere. We aim at comparing the line asymmetry and velocity of the two delta Sct stars rho Pup and DX Cet with previous spectroscopic data obtaine
d on classical Cepheids and beta Cep stars. We obtained, analysed and discuss HARPS high-resolution spectra of rho Pup and DX Cet. We derived the same physical quantities as used in previous studies, which are the first-moment radial velocities and the bi-Gaussian spectral line asymmetries. The identification of f=7.098 (1/d) as a fundamental radial mode and the very accurate Hipparcos parallax promote rho Pup as the best standard candle to test the period-luminosity relations of delta Sct stars. The action of small-amplitude nonradial modes can be seen as well-defined cycle-to-cycle variations in the radial velocity measurements of rho Pup. Using the spectral-line asymmetry method, we also found the centre-of-mass velocities of rho Pup and DX Cet, V_gamma = 47.49 +/- 0.07 km/s and V_gamma = 25.75 +/- 0.06 km/s, respectively. By comparing our results with previous HARPS observations of classical Cepheids and beta Cep stars, we confirm the linear relation between the atmospheric velocity gradient and the amplitude of the radial velocity curve, but only for amplitudes larger than 22.5 km/s. For lower values of the velocity amplitude (i.e., < 22.5 km/s), our data on rho Pup seem to indicate that the velocity gradient is null, but this result needs to be confirmed with additional data. We derived the Baade-Wesselink projection factor p = 1.36 +/- 0.02 for rho Pup and p = 1.39 +/- 0.02 for DX Cet. We successfully extended the period-projection factor relation from classical Cepheids to delta Scuti stars.
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.
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
med 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.
High-precision interferometric measurements of pulsating stars help to characterize their close environment. In 1974, a close companion was discovered around the pulsating star beta Cep using the speckle interferometry technique and features at the l
imit of resolution (20 milli-arcsecond or mas) of the instrument were mentioned that may be due to circumstellar material. Beta Cep has a magnetic field that might be responsible for a spherical shell or ring-like structure around the star as described by the MHD models. Using the visible recombiner VEGA installed on the CHARA long-baseline interferometer at Mt. Wilson, we aim to determine the angular diameter of beta Cep and resolve its close environment with a spatial resolution up to 1 mas level. Medium spectral resolution (R=6000) observations of beta Cep were secured with the VEGA instrument over the years 2008 and 2009. These observations were performed with the S1S2 (30m) and W1W2 (100m) baselines of the array. We investigated several models to reproduce our observations. A large-scale structure of a few mas is clearly detected around the star with a typical flux relative contribution of 0.23 +- 0.02. Our best model is a co-rotational geometrical thin ring around the star as predicted by magnetically-confined wind shock models. The ring inner diameter is 8.2 +- 0.8 mas and the width is 0.6 +- 0.7 mas. The orientation of the rotation axis on the plane of the sky is PA = 60 +- 1 deg, while the best fit of the mean angular diameter of beta Cep gives UD[V] = 0.22 +- 0.05 mas. Our data are compatible with the predicted position of the close companion of beta Cep. These results bring additional constraints on the fundamental parameters and on the future MHD and asteroseismological models of the star.
Galactic Cepheids in the vicinity of the Sun have a residual line-of-sight velocity, or gamma-velocity, which shows a systematic blueshift of about 2 km/s compared to an axisymmetric rotation model of the Milky Way. This term is either related to the
space motion of the star and, consequently, to the kinematic structure of our Galaxy, or it is the result of the dynamical structure of the Cepheids atmosphere. We aim to show that these residual gamma-velocities are an intrinsic property of Cepheids. We observed nine galactic Cepheids with the HARPS spectroscope, focusing specifically on 17 spectral lines. For each spectral line of each star, we computed the gamma-velocity (resp. gamma-asymmetry) as an average value of the interpolated radial velocity (resp. line asymmetry) curve. For each Cepheid in our sample, a linear relation is found between the gamma-velocities of the various spectral lines and their corresponding gamma-asymmetries, showing that residual gamma-velocities stem from the intrinsic properties of Cepheids. We also provide a physical reference to the stellar gamma-velocity: it should be zero when the gamma-asymmetry is zero. Following this definition, we provide very precise and physically calibrated estimates of the gamma-velocities for all stars of our sample. To understand this very subtle gamma-asymmetry effect, further numerical studies are needed. Cepheids atmosphere are strongly affected by pulsational dynamics, convective flows, nonlinear physics, and complex radiative transport. Hence, all of these effects have to be incorporated simultaneously and consistently into the numerical models to reproduce the observed line profiles in detail.
The ratio of pulsation to radial velocity (the projection factor) is currently limiting the accuracy of the interferometric Baade-Wesselink method. This work aims at establishing a link between the line asymmetry evolution over the Cepheids pulsation
cycles and their projection factor, with the final objective to improve the accuracy of the Baade-Wesselink method for distance determinations. We present HARPS high spectral resolution observations of nine galactic Cepheids having a good period sampling. We fit spectral line profiles by an asymmetric bi-Gaussian to derive radial velocity, Full-Width at Half-Maximum in the line (FWHM) and line asymmetry for all stars. We then extract correlations curves between radial velocity and asymmetry. A geometric model providing synthetic spectral lines, including limb-darkening, a constant FWHM (hereafter sigma_c) and the rotation velocity is used to interpret these correlations curves. For all stars, comparison between observations and modelling is satisfactory, and we were able to determine the projected rotation velocities and sigma_c for all stars. We also find a correlation between the rotation velocity (Vrot sin i) and the period of the star: Vrot sin i = (11.5 +- 0.9) log(P) + (19.8 +- 1.0) [km/s]. Moreover, we observe a systematic shift in observational asymmetry curves (noted gamma_O), related to the period of the star, which is not explained by our static model: gamma_O = (10.7+-0.1) log(P) + (9.7+-0.2) [in %] . For long-period Cepheids, in which velocity gradients, compression or shock waves seem to be large compared to short- or medium period Cepheids we observe indeed a greater systematic shift in asymmetry curves. (abridged)
