Improving the surface brightness-color relation for early-type stars using optical interferometry

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 derived 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.Comment: 13 pages, 5 figures, accepted for publication in A&

The fundamental parameters of the roAp star γ\gamma Equulei

Physical processes working in the stellar interiors as well as the evolution of stars depend on some fundamental stellar properties, such as mass, radius, luminosity, and chemical abundances. A classical way to test stellar interior models is to compare the predicted and observed location of a star on theoretical evolutionary tracks in a H-R diagram. This requires the best possible determinations of stellar mass, radius, luminosity and abundances. To derive its fundamental parameters, we observed the well-known rapidly oscillating Ap star, $\gamma$ Equ, using the visible spectro-interferometer VEGA installed on the optical CHARA array. We computed the calibrated squared visibility and derived the limb-darkened diameter. We used the whole energy flux distribution, the parallax and this angular diameter to determine the luminosity and the effective temperature of the star. We obtained a limb-darkened angular diameter of 0.564~$\pm$~0.017~mas and deduced a radius of $R$~=~2.20~$\pm$~0.12~${\rm R_{\odot}}$. Without considering the multiple nature of the system, we derived a bolometric flux of $(3.12\pm 0.21)\times 10^{-7}$ erg~cm$^{-2}$~s$^{-1}$ and an effective temperature of 7364~$\pm$~235~K, which is below the effective temperature that has been previously determined. Under the same conditions we found a luminosity of $L$~=~12.8~$\pm$~1.4~${\rm L_{\odot}}$. When the contribution of the closest companion to the bolometric flux is considered, we found that the effective temperature and luminosity of the primary star can be, respectively, up to $\sim$~100~K and up to $\sim$~0.8~L$_\odot$ smaller than the values mentioned above.These new values of the radius and effective temperature should bring further constraints on the asteroseismic modelling of the star.Comment: Accepted by A&

Differential rotation in rapidly rotating early-type stars : I. Motivations for combined spectroscopic and interferometric studies

Context. Since the external regions of the envelopes of rapidly rotating early-type stars are unstable to convection, a coupling may exist between the convection and the internal rotation. Aims. We explore what can be learned from spectroscopic and interferometric observations about the properties of the rotation law in the external layers of these objects. Methods. Using simple relations between the entropy and specific rotational quantities, some of which are found to be efficient at accounting for the solar differential rotation in the convective region, we derived analytical solutions that represent possible differential rotations in the envelope of early-type stars. A surface latitudinal differential rotation may not only be an external imprint of the inner rotation, but induces changes in the stellar geometry, the gravitational darkening, the aspect of spectral line profiles, and the emitted spectral energy distribution. Results. By studying the equation of the surface of stars with non-conservative rotation laws, we conclude that objects undergo geometrical deformations that are a function of the latitudinal differential rotation able to be scrutinized both spectroscopically and by interferometry. The combination of Fourier analysis of spectral lines with model atmospheres provides independent estimates of the surface latitudinal differential rotation and the inclination angle. Models of stars at different evolutionary stages rotating with internal conservative rotation laws were calculated to show that the Roche approximation can be safely used to account for the gravitational potential. The surface temperature gradient in rapid rotators induce an acceleration to the surface angular velocity. Although a non-zero differential rotation parameter may indicate that the rotation is neither rigid nor shellular underneath the stellar surface, still further information, perhaps non-radial pulsations, is needed to determine its characteristics as a function of depth.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

Time, spatial, and spectral resolution of the Halpha line-formation region of Deneb and Rigel with the VEGA/CHARA interferometer

BA-type supergiants are amongst the most optically-bright stars. They are observable in extragalactic environments, hence potential accurate distance indicators. Emission activity in the Halpha line of the BA supergiants Rigel (B8Ia) and Deneb (A2Ia) is indicative of presence of localized time-dependent mass ejections. Here, we employ optical interferometry to study the Halpha line-formation region in these stellar environments. High spatial- (0.001 arcsec) and spectral- (R=30 000) resolution observations of Halpha were obtained with the visible recombiner VEGA installed on the CHARA interferometer, using the S1S2 array-baseline (34m). Six independent observations were done on Deneb over the years 2008 and 2009, and two on Rigel in 2009. We analyze this dataset with the 1D non-LTE radiative-transfer code CMFGEN, and assess the impact of the wind on the visible and near-IR interferometric signatures, using both Balmer-line and continuum photons. We observe a visibility decrease in Halpha for both Rigel and Deneb, suggesting that the line-formation region is extended (1.5-1.75 R*). We observe a significant visibility decrease for Deneb in the SiII6371 line. We witness time variations in the differential phase for Deneb, implying an inhomogeneous and unsteady circumstellar environment, while no such variability is seen in differential visibilities. Radiative-transfer modeling of Deneb, with allowance for stellar-wind mass loss, accounts fairly well for the observed decrease in the Halpha visibility. Based on the observed differential visibilities, we estimate that the mass-loss rate of Deneb has changed by less than 5%

An investigation of the close environment of beta Cep with the VEGA/CHARA interferometer

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.Comment: Paper accepted for publication in A&A (in press

Chromosphere of K giant stars Geometrical extent and spatial structure detection

We aim to constrain the geometrical extent of the chromosphere of non-binary K giant stars and detect any spatial structures in the chromosphere. We performed observations with the CHARA interferometer and the VEGA beam combiner at optical wavelengths. We observed seven non-binary K giant stars. We measured the ratio of the radii of the photosphere to the chromosphere using the interferometric measurements in the Halpha and the Ca II infrared triplet line cores. For beta Ceti, spectro-interferometric observations are compared to an non-local thermal equilibrium (NLTE) semi-empirical model atmosphere including a chromosphere. The NLTE computations provide line intensities and contribution functions that indicate the relative locations where the line cores are formed and can constrain the size of the limb-darkened disk of the stars with chromospheres. We measured the angular diameter of seven K giant stars and deduced their fundamental parameters: effective temperatures, radii, luminosities, and masses. We determined the geometrical extent of the chromosphere for four giant stars. The chromosphere extents obtained range between 16% to 47% of the stellar radius. The NLTE computations confirm that the Ca II/849 nm line core is deeper in the chromosphere of ? Cet than either of the Ca II/854 nm and Ca II/866 nm line cores. We present a modified version of a semi-empirical model atmosphere derived by fitting the Ca II triplet line cores of this star. In four of our targets, we also detect the signature of a differential signal showing the presence of asymmetries in the chromospheres. Conclusions. It is the first time that geometrical extents and structure in the chromospheres of non-binary K giant stars are determined by interferometry. These observations provide strong constrains on stellar atmosphere models.Comment: 10 pages, 12 figure

Differential rotation in rapidly rotating early-type stars : I. Motivations for combined spectroscopic and interferometric studies

Context. Since the external regions of the envelopes of rapidly rotating early-type stars are unstable to convection, a coupling may exist between the convection and the internal rotation. Aims. We explore what can be learned from spectroscopic and interferometric observations about the properties of the rotation law in the external layers of these objects. Methods. Using simple relations between the entropy and specific rotational quantities, some of which are found to be efficient at accounting for the solar differential rotation in the convective region, we derived analytical solutions that represent possible differential rotations in the envelope of early-type stars. A surface latitudinal differential rotation may not only be an external imprint of the inner rotation, but induces changes in the stellar geometry, the gravitational darkening, the aspect of spectral line profiles, and the emitted spectral energy distribution. Results. By studying the equation of the surface of stars with non-conservative rotation laws, we conclude that objects undergo geometrical deformations that are a function of the latitudinal differential rotation able to be scrutinized both spectroscopically and by interferometry. The combination of Fourier analysis of spectral lines with model atmospheres provides independent estimates of the surface latitudinal differential rotation and the inclination angle. Models of stars at different evolutionary stages rotating with internal conservative rotation laws were calculated to show that the Roche approximation can be safely used to account for the gravitational potential. The surface temperature gradient in rapid rotators induce an acceleration to the surface angular velocity. Although a non-zero differential rotation parameter may indicate that the rotation is neither rigid nor shellular underneath the stellar surface, still further information, perhaps non-radial pulsations, is needed to determine its characteristics as a function of depth.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

The Hα\alpha line forming region of AB Aur spatially resolved at sub-AU with the VEGA/CHARA spectro-interferometer

A crucial issue in star formation is to understand the physical mechanism by which mass is accreted onto and ejected by a young star. The visible spectrometer VEGA on the CHARA array can be an efficient means of probing the structure and the kinematics of the hot circumstellar gas at sub-AU. For the first time, we observed the Herbig Ae star AB Aur in the H$\alpha$ emission line, using the VEGA low spectral resolution on two baselines of the array. We computed and calibrated the spectral visibilities between 610 nm and 700 nm. To simultaneously reproduce the line profile and the visibility, we used a 1-D radiative transfer code that calculates level populations for hydrogen atoms in a spherical geometry and synthetic spectro-interferometric observables. We clearly resolved AB Aur in the H$\alpha$ line and in a part of the continuum, even at the smallest baseline of 34 m. The small P-Cygni absorption feature is indicative of an outflow but could not be explained by a spherical stellar wind model. Instead, it favors a magneto-centrifugal X-disk or disk-wind geometry. The fit of the spectral visibilities could not be accounted for by a wind alone, so we considered a brightness asymmetry possibly caused by large-scale nebulosity or by the known spiral structures, inducing a visibility modulation around H$\alpha$. Thanks to the unique capabilities of VEGA, we managed to simultaneously record for the first time a spectrum at a resolution of 1700 and spectral visibilities in the visible range on a target as faint as $m_{V}$ = 7.1. It was possible to rule out a spherical geometry for the wind of AB Aur and provide realistic solutions to account for the H$\alpha$ emission compatible with magneto-centrifugal acceleration. The study illustrates the advantages of optical interferometry and motivates observations of other bright young stars to shed light on the accretion/ejection processes

Spectrally resolved interferometric observations of α Cephei and physical modeling of fast rotating stars

This is the final version of the article. Available from the publisher via the DOI in this record.Context. When a given observational quantity depends on several stellar physical parameters, it is generally very difficult to obtain observational constraints for each of them individually. Therefore, we studied under which conditions constraints for some individual parameters can be achieved for fast rotators, knowing that their geometry is modified by the rapid rotation which causes a non-uniform surface brightness distribution. Aims. We aim to study the sensitivity of interferometric observables on the position angle of the rotation axis (PA) of a rapidly rotating star, and whether other physical parameters can influence the determination of PA, and also the influence of the surface differential rotation on the determination of the β exponent in the gravity darkening law that enters the interpretation of interferometric observations, using α Cep as a test star. Methods. We used differential phases obtained from observations carried out in the Hα absorption line of α Cep with the VEGA/CHARA interferometer at high spectral resolution, R = 30 000 to study the kinematics in the atmosphere of the star. Results. We studied the influence of the gravity darkening effect (GDE) on the determination of the PA of the rotation axis of α Cep and determined its value, PA = −157-10°+17°. We conclude that the GDE has a weak influence on the dispersed phases. We showed that the surface differential rotation can have a rather strong influence on the determination of the gravity darkening exponent. A new method of determining the inclination angle of the stellar rotational axis is suggested. We conclude that differential phases obtained with spectro-interferometry carried out on the Hα line can in principle lead to an estimate of the stellar inclination angle i. However, to determine both i and the differential rotation parameter α, lines free from the Stark effect and that have collision-dominated source functions are to be preferred.VEGA is a collaboration between CHARA and OCA/LAOG/CRAL/LESIA that has been supported by the French programs PNPS and ASHRA, by INSU and by the Région PACA. The project has obviously benefitted from the strong support of the OCA and CHARA technical teams. The CHARA Array is operated with support from the National Science Foundation through grant AST-0908253, the W. M. Keck Foundation, the NASA Exoplanet Science Institute, and from Georgia State University. This work has made use of the BeSS database, operated at GEPI, Observatoire de Meudon, France: http://basebe.obspm.fr, use of the Jean-Marie Mariotti Center SearchCal service1 co-developed by FIZEAU and LAOG, and of CDS Astronomical Databases SIMBAD and VIZIER2. We are grateful to an anonymous referee for her/his valuable suggestions that helped to improve the presentation of our results