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Register a new userVEGA/CHARA interferometric observations of Cepheids. I. A resolved structure around the prototype classical Cepheid delta Cep in the visible spectral range
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The B-W method is used to determine the distance of Cepheids and consists in combining the angular size variations of the star, as derived from infrared surface-brightness relations or interferometry, with its linear size variation, as deduced from visible spectroscopy using the projection factor. While many Cepheids have been intensively observed by infrared beam combiners, only a few have been observed in the visible. This paper is part of a project to observe Cepheids in the visible with interferometry as a counterpart to infrared observations already in hand. Observations of delta Cep itself were secured with the VEGA/CHARA instrument over the full pulsation cycle of the star. These visible interferometric data are consistent in first approximation with a quasi-hydrostatic model of pulsation surrounded by a static circumstellar environment (CSE) with a size of theta_cse=8.9 +/- 3.0 mas and a relative flux contribution of f_cse=0.07+/-0.01. A model of visible nebula (a background source filling the field of view of the interferometer) with the same relative flux contribution is also consistent with our data at small spatial frequencies. However, in both cases, we find discrepancies in the squared visibilities at high spatial frequencies (maximum 2sigma) with two different regimes over the pulsation cycle of the star, phi=0.0-0.8 and phi=0.8-1.0. We provide several hypotheses to explain these discrepancies, but more observations and theoretical investigations are necessary before a firm conclusion can be drawn. For the first time we have been able to detect in the visible domain a resolved structure around delta~Cep. We have also shown that a simple model cannot explain the observations, and more work will be necessary in the future, both on observations and modelling.
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We obtained spectro-interferometric observations in the visible of $beta$ Lyrae and $upsilon$ Sgr using the instrument VEGA of the CHARA interferometric array. For $beta$ Lyrae, the dispersed fringe visibilities and differential phases were obtained in spectral regions containing the H$alpha$ and HeI 6678 lines and the H$beta$ and HeI 4921 lines. Whereas the source is unresolved in the continuum, the source of the emission lines is resolved and the photocenter of the bulk of the H$alpha$ emission exhibits offsets correlated with the orbital phase. For $upsilon$ Sgr, both the continuum and H$alpha$ sources are resolved, but no clear binary signal is detected. The differential phase shift across the line reveals that the bulk of the H$alpha$ emission is clearly offset from the primary.
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 models 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.
We used new HARPS-N spectra to revisitate the projection factor of Delta Cep and to directly measure the specific contribution of the velocity gradient within the atmosphere. By introducing an hydrodynamical model we could also determine the semi-theoretical values of the correction factor between the gas movement and the optical continuum by assuming radiative transfer in plane-parallel or sherically symmetric geometries, respectively.
The surface brightness - color relationship (SBCR) is a poweful tool for determining the angular diameter of stars from photometry. It was for instance used to derive the distance of eclipsing binaries in the Large Magellanic Cloud (LMC), which led to its distance determination with an accuracy of 1%. We calibrate the SBCR for red giant stars in the 2.1 < V-K < 2.5 color range using homogeneous VEGA/CHARA interferometric data secured in the visible domain, and compare it to the relation based on infrared interferometric observations, which were used to derive the distance to the LMC. Observations of eight G-K giants were obtained with the VEGA/CHARA instrument. The derived limb-darkened angular diameters were combined with a homogeneous set of infrared magnitudes in order to constrain the SBCR. The average precision we obtain on the limb-darkened angular diameters of the eight stars in our sample is 2.4%. For the four stars in common observed by both VEGA/CHARA and PIONIER/VLTI, we find a 1 sigma agreement for the angular diameters. The SBCR we obtain in the visible has a dispersion of 0.04 magnitude and is consistent with the one derived in the infrared (0.018 magnitude). The consistency of the infrared and visible angular diameters and SBCR reinforces the result of 1% precision and accuracy recently achieved on the distance of the LMC using the eclipsing-binary technique. It also indicates that it is possible to combine interferometric observations at different wavelengths when the SBCR is calibrated.
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 limit 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.
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