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The complex binary system β Lyr A has an extensive observational dataset: light curves (from far UV to far IR), interferometric squared visibility, closure phase, triple product measurements, spectral-energy distribution, high-resolution spectroscopy, differential visibility amplitude, and also a differential phase. In particular, we used spectra from the Ondřejov 2m telescope from 2013 to 2015 to measure the emission in H α , He  I , Si  II , Ne  I , or C  II lines, and differential interferometry by CHARA/VEGA from the 2013 campaign to measure wavelength-dependent sizes across H α and He  I 6678. This allowed us to constrain not only optically thick objects (primary, secondary, accretion disc), but also optically thin objects (disc atmosphere, jets, shell). We extended our modelling tool, Pyshellspec (based on Shellspec; a 1D local thermodynamical equilibrium radiative transfer code), to include all new observables, to compute differential visibilities/phases, to perform a Doppler tomography, and to determine a joint χ 2 metric. After an optimisation of 38 free parameters, we derived a robust model of the β Lyr A system. According to the model, the emission is formed in an extended atmosphere of the disc, two perpendicular jets expanding at ∼700 km s −1 , and a symmetric shell with the radius ∼70  R ⊙ . The spectroscopy indicates a low abundance of carbon, 10 −2 of the solar value. We also quantified systematic differences between datasets, and we discuss here alternative models with higher resolutions, additional asymmetries, or He-rich abundances. 

Context. The variety of physical processes at play in chemically peculiar stars makes it difficult to determine their fundamental parameters. In particular, for the magnetic ones, called Ap stars, the strong magnetic fields and the induced spotted stellar surfaces may lead to biased effective temperatures when these values are derived through spectro-photometry. Aims. We propose to benefit from the exquisite angular resolution provided by long-baseline interferometry in the visible to determine the accurate angular diameters of a number of Ap stars, and thus estimate their radii by a method that is as independent as possible of atmospheric models. Methods. We used the visible spectrograph VEGA at the CHARA interferometric array to complete the sample of Ap stars currently observable with this technique. We estimated the angular diameter and radius of six new targets. We estimated their bolometric flux based solely on observational spectroscopic and photometric data to derive nearly model-independent luminosities and effective temperatures. Results. We extend to 14 the number of Ap stars for which interferometric angular diameters have been measured. The fundamental parameters we derived for the complete Ap sample are compared with those obtained through a self-consistent spectroscopic analysis. Based on a model fitting approach of high-resolution spectra and spectro-photometric observations over a wide wavelength range, this method takes into account the anomalous chemical composition of the atmospheres and the inhomogeneous vertical distribution for different chemical elements. Regarding both the radii and the effective temperatures, the derived values from our interferometric observations and from self-consistent modelling are consistent within better than 2 σ for nine targets out of ten. We thus benchmark nine Ap stars for effective temperatures ranging from 7200 and 9100 K, and luminosities ranging between 7 L ⊙ and 86 L ⊙ . Conclusions. These results will be key for the future derivation of accurate radii and other fundamental parameters of fainter peculiar stars for which both the sensitivity and the angular resolution of the current interferometers are not sufficient. Within the context of the observations of Ap stars with the Transiting Exoplanet Survey Satellite (TESS), these interferometric measurements are crucial for testing the mechanism of pulsation excitation at work in these peculiar stars. In particular, our interferometric measurements provide accurate locations in the Hertzsprung-Russell diagram for hot Ap stars among which pulsations may be searched for with TESS, putting to test the blue edge of the theoretical instability strip. These accurate locations could be used to derive masses and ages of these stars through a specific grid of models, and to test correlations between the properties of these peculiar stars and their evolutionary state. 

Context. Surface brightness–colour relations (SBCRs) are used to derive the stellar angular diameters from photometric observations. They have various astrophysical applications, such as the distance determination of eclipsing binaries or the determination of exoplanet parameters. However, strong discrepancies between the SBCRs still exist in the literature, in particular for early and late-type stars. Aims. We aim to calibrate new SBCRs as a function of the spectral type and the luminosity class of the stars. Our goal is also to apply homogeneous criteria to the selection of the reference stars and in view of compiling an exhaustive and up-to-date list of interferometric late-type targets. Methods. We implemented criteria to select measurements in the JMMC Measured Diameters Catalog. We then applied additional criteria on the photometric measurements used to build the SBCRs, together with stellar characteristics diagnostics. Results. We built SBCRs for F5/K7–II/III, F5/K7–IV/V, M–II/III and M–V stars, with respective rms of σ F V  = 0.0022 mag, σ F V  = 0.0044 mag, σ F V  = 0.0046 mag, and σ F V  = 0.0038 mag. This results in a precision on the angular diameter of 1.0%, 2.0%, 2.1%, and 1.7%, respectively. These relations cover a large V  −  K colour range of magnitude, from 1 to 7.5. Our work demonstrates that SBCRs are significantly dependent on the spectral type and the luminosity class of the star. Through a new set of interferometric measurements, we demonstrate the critical importance of the selection criteria proposed for the calibration of SBCR. Finally, using the Gaia photometry for our samples, we obtained ( G  −  K ) SBCRs with a precision on the angular diameter between 1.1% and 2.4%. Conclusions. By adopting a refined and homogeneous methodology, we show that the spectral type and the class of the star should be considered when applying an SBCR. This is particularly important in the context of PLATO. 

Context. 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%. Aims. 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. Methods. 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. Results. 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 σ 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). Conclusions. 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. 

Context. The harvest of exoplanet discoveries has opened the area of exoplanet characterisation. But this cannot be achieved without a careful analysis of the host star parameters. Aims. The system of HD 219134 hosts two transiting exoplanets and at least two additional non-transiting exoplanets. We revisit the properties of this system using direct measurements of the stellar parameters to investigate the composition of the two transiting exoplanets. Methods. We used the VEGA/CHARA interferometer to measure the angular diameter of HD 219134. We also derived the stellar density from the transits light curves, which finally gives a direct estimate of the mass. This allowed us to infer the mass, radius, and density of the two transiting exoplanets of the system. We then used an inference model to obtain the internal parameters of these two transiting exoplanets. Results. We measure a stellar radius, density, and mass of R ⋆ = 0.726 ± 0.014 R ⊙ , ρ ⋆ = 1.82 ± 0.19 ρ ⊙ , and M ⋆ = 0.696 ± 0.078 M ⊙ , respectively; there is a correlation of 0.46 between R ⋆ and M ⋆ . This new mass is lower than that derived from the C2kSMO stellar evolutionary model, which provides a mass range of 0.755−0.810 (±0.040) M ⊙ . Moreover, we find that planet b and c have smaller radii than previously estimated of 1.500 ± 0.057 and 1.415 ± 0.049 R ⊕ respectively; this clearly puts these planets out of the gap in the exoplanetary radii distribution and validates their super-Earth nature. Planet b is more massive than planet c , but the former is possibly less dense. We investigate whether this could be caused by partial melting of the mantle and find that tidal heating due to non-zero eccentricity of planet b may be powerful enough. Conclusions. The system of HD 219134 constitutes a very valuable benchmark for both stellar physics and exoplanetary science. The characterisation of the stellar hosts, and in particular the direct determination of the stellar density, radius, and mass, should be more extensively applied to provide accurate exoplanets properties and calibrate stellar models. 

Aims. We present a detailed visible and near-infrared spectro-interferometric analysis of the Be-shell star o Aquarii from quasi-contemporaneous CHARA/VEGA and VLTI/AMBER observations. Methods. We analyzed spectro-interferometric data in the H α (VEGA) and Br γ (AMBER) lines using models of increasing complexity: simple geometric models, kinematic models, and radiative transfer models computed with the 3D non-LTE code HDUST. Results. We measured the stellar radius of o Aquarii in the visible with a precision of 8%: 4.0 ± 0.3 R ⊙ . We constrained the circumstellar disk geometry and kinematics using a kinematic model and a MCMC fitting procedure. The emitting disk sizes in the H α and Br γ lines were found to be similar, at ~10–12 stellar diameters, which is uncommon since most results for Be stars indicate a larger extension in H α than in Br γ . We found that the inclination angle i derived from H α is significantly lower (~15°) than the one derived from Br γ : i ~ 61.2° and 75.9°, respectively. While the two lines originate from a similar region of the disk, the disk kinematics were found to be near to the Keplerian rotation (i.e., β = −0.5) in Br γ ( β ~ −0.43), but not in H α ( β ~ −0.30). After analyzing all our data using a grid of HDUST models (BeAtlas), we found a common physical description for the circumstellar disk in both lines: a base disk surface density Σ 0 = 0.12 g cm −2 and a radial density law exponent m = 3.0. The same kind of discrepancy, as with the kinematic model, is found in the determination of i using the BeAtlas grid. The stellar rotational rate was found to be very close (~96%) to the critical value. Despite being derived purely from the fit to interferometric data, our best-fit HDUST model provides a very reasonable match to non-interferometric observables of o Aquarii: the observed spectral energy distribution, H α and Br γ line profiles, and polarimetric quantities. Finally, our analysis of multi-epoch H α profiles and imaging polarimetry indicates that the disk structure has been (globally) stable for at least 20 yr. Conclusions. Looking at the visible continuum and Br γ emission line only, o Aquarii fits in the global scheme of Be stars and their circumstellar disk: a (nearly) Keplerian rotating disk well described by the viscous decretion disk (VDD) model. However, the data in the H α line shows a substantially different picture that cannot fully be understood using the current generation of physical models of Be star disks. The Be star o Aquarii presents a stable disk (close to the steady-state), but, as in previous analyses, the measured m is lower than the standard value in the VDD model for the steady-state regime ( m = 3.5). This suggests that some assumptions of this model should be reconsidered. Also, such long-term disk stability could be understood in terms of the high rotational rate that we measured for this star, the rate being a main source for the mass injection in the disk. Our results on the stellar rotation and disk stability are consistent with results in the literature showing that late-type Be stars are more likely to be fast rotators and have stable disks. 

Context. Rapid rotation is a common feature for massive stars, with important consequences on their physical structure, flux distribution and evolution. Fast-rotating stars are flattened and show gravity darkening (non-uniform surface intensity distribution). Another important and less studied impact of fast-rotation in early-type stars is its influence on the surface brightness colour relation (hereafter SBCR), which could be used to derive the distance of eclipsing binaries. Aims. The purpose of this paper is to determine the flattening of the fast-rotating B-type star δ Per using visible long-baseline interferometry. A second goal is to evaluate the impact of rotation and gravity darkening on the V − K colour and surface brightness of the star. Methods. The B-type star δ Per was observed with the VEGA/CHARA interferometer, which can measure spatial resolutions down to 0.3 mas and spectral resolving power of 5000 in the visible. We first used a toy model to derive the position angle of the rotation axis of the star in the plane of the sky. Then we used a code of stellar rotation, CHARRON, in order to derive the physical parameters of the star. Finally, by considering two cases, a static reference star and our best model of δ Per, we can quantify the impact of fast rotation on the surface brightness colour relation (SBCR). Results. We find a position angle of 23 ± 6 degrees. The polar axis angular diameter of δ Per is θ p = 0.544 ± 0.007 mas, and the derived flatness is r = 1.121 ± 0.013. We derive an inclination angle for the star of i = 85 + 5 -20 degrees and a projected rotation velocity V sin i = 175 + 8 -11 km s -1 (or 57% of the critical velocity). We find also that the rotation and inclination angle of δ Per keeps the V − K colour unchanged while it decreasing its surface-brightness by about 0.05 mag. Conclusions. Correcting the impact of rotation on the SBCR of early-type stars appears feasible using visible interferometry and dedicated models.