Differential rotation in early type stars

Using 2D models of rotating stars, the interferometric measurements of alpha Eri and its fundamental parameters corrected for gravitational darkening effects we infer that the star might have a core rotating 2.7 times faster than the surface. We explore the consequences on spectral lines produced by surface differential rotation combined with the effects due to a kind of internal differential rotation with rotational energies higher than allowed for rigid rotation which induce geometrical deformations that do not distinguish strongly from those carried by the rigid rotation.Comment: 3 pages ; to appear in the proceedings of the Sapporo meeting on active OB stars ; ASP Conference Series ; eds: S. Stefl, S. Owocki and A. Okazak

Fast ray-tracing algorithm for circumstellar structures (FRACS). II. Disc parameters of the B[e] supergiant CPD-57° 2874 from VLTI/MIDI data

B[e] supergiants are luminous, massive post-main sequence stars exhibiting non-spherical winds, forbidden lines, and hot dust in a disc-like structure. The physical properties of their rich and complex circumstellar environment (CSE) are not well understood, partly because these CSE cannot be easily resolved at the large distances found for B[e] supergiants (typically \ga 1~kpc). From mid-IR spectro-interferometric observations obtained with VLTI/MIDI we seek to resolve and study the CSE of the Galactic B[e] supergiant CPD-57\degr\,2874. For a physical interpretation of the observables (visibilities and spectrum) we use our ray-tracing radiative transfer code (FRACS), which is optimised for thermal spectro-interferometric observations. Thanks to the short computing time required by FRACS ($<10$~s per monochromatic model), best-fit parameters and uncertainties for several physical quantities of CPD-57\degr\,2874 were obtained, such as inner dust radius, relative flux contribution of the central source and of the dusty CSE, dust temperature profile, and disc inclination. The analysis of VLTI/MIDI data with FRACS allowed one of the first direct determinations of physical parameters of the dusty CSE of a B[e] supergiant based on interferometric data and using a full model-fitting approach. In a larger context, the study of B[e] supergiants is important for a deeper understanding of the complex structure and evolution of hot, massive stars

Differential interferometric phases at high spectral resolution as a sensitive physical diagnostic of circumstellar disks

Context. The circumstellar disks ejected by many rapidly rotating B stars (so-called Be stars) offer the rare opportunity of studying the structure and dynamics of gaseous disks at high spectral as well as angular resolution. Aims. This paper explores a newly identified effect in spectro-interferometric phase that can be used for probing the inner regions of gaseous edge-on disks on a scale of a few stellar radii. Methods. The origin of this effect (dubbed central quasi-emission phase signature, CQE-PS) lies in the velocity-dependent line absorption of photospheric radiation by the circumstellar disk. At high spectral and marginal interferometric resolution, photocenter displacements between star and isovelocity regions in the Keplerian disk reveal themselves through small interferometric phase shifts. To investigate the diagnostic potential of this effect, a series of models are presented, based on detailed radiative transfer calculations in a viscous decretion disk. Results. Amplitude and detailed shape of the CQE-PS depend sensitively on disk density and size and on the radial distribution of the material with characteristic shapes in differential phase diagrams. In addition, useful lower limits to the angular size of the central stars can be derived even when the system is almost unresolved. Conclusions. The full power of this diagnostic tool can be expected if it can be applied to observations over a full life-cycle of a disk from first ejection through final dispersal, over a full cycle of disk oscillations, or over a full orbital period in a binary system

VLTI/MIDI observations of 7 classical Be stars

We measured the mid-infrared extension of the gaseous disk surrounding seven Be stars in order to constrain the geometry of their circumstellar environments and to try to infer physical parameters characterizing these disks. We used the VLTI/MIDI instrument with baselines up to 130 m to obtain an angular resolution of about 15 mas in the N band and compared our results with previous K band measurements obtained with the VLTI/AMBER instrument and/or the CHARA interferometer. We obtained one calibrated visibility measurement for each of the four stars, p Car, zeta Tau, kappa CMa, and alpha Col, two for delta Cen and beta CMi, and three for alpha Ara. Almost all targets remain unresolved even with the largest VLTI baseline of 130m, evidence that their circumstellar disk extension is less than 10 mas. The only exception is alpha Ara, which is clearly resolved and well-fitted by an elliptical envelope with a major axis a=5.8+-0.8mas and an axis ratio a/b=2.4+-1 at 8 microns. This extension is similar to the size and flattening measured with the VLTI/AMBER instrument in the K band at 2 microns. The size of the circumstellar envelopes for these classical Be stars does not seem to vary strongly on the observed wavelength between 8 and 12microns. Moreover, the size and shape of Alpha Ara's disk is almost identical at 2, 8, and 12microns

The environment of the fast rotating star Achernar - Thermal infrared interferometry with VLTI/MIDI and SIMECA modeling

Context: As is the case of several other Be stars, Achernar is surrounded by an envelope, recently detected by near-IR interferometry. Aims: We search for the signature of circumstellar emission at distances of a few stellar radii from Achernar, in the thermal IR domain. Methods: We obtained interferometric observations on three VLTI baselines in the N band (8-13 mic), using the MIDI instrument. Results: From the measured visibilities, we derive the angular extension and flux contribution of the N band circumstellar emission in the polar direction of Achernar. The interferometrically resolved polar envelope contributes 13.4 +/- 2.5 % of the photospheric flux in the N band, with a full width at half maximum of 9.9 +/- 2.3 mas (~ 6 Rstar). This flux contribution is in good agreement with the photometric IR excess of 10-20% measured by fitting the spectral energy distribution. Due to our limited azimuth coverage, we can only establish an upper limit of 5-10% for the equatorial envelope. We compare the observed properties of the envelope with an existing model of this star computed with the SIMECA code. Conclusions: The observed extended emission in the thermal IR along the polar direction of Achernar is well reproduced by the existing SIMECA model. Already detected at 2.2mic, this polar envelope is most probably an observational signature of the fast wind ejected by the hot polar caps of the star.Comment: A&A Letter, in pres

Understanding the dynamical structure of pulsating stars: The Baade-Wesselink projection factor of the delta Scuti stars AI Vel and beta Cas

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 aimed 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

VLTI/PIONIER images the Achernar disk swell

Context. The mechanism of disk formation around fast-rotating Be stars is not well understood. In particular, it is not clear which mechanisms operate, in addition to fast rotation, to produce the observed variable ejection of matter. The star Achernar is a privileged laboratory to probe these additional mechanisms because it is close, presents B-Be phase variations on timescales ranging from 6 yr to 15 yr, a companion star was discovered around it, and probably presents a polar wind or jet. Aims. Despite all these previous studies, the disk around Achernar was never directly imaged. Therefore we seek to produce an image of the photosphere and close environment of the star. Methods. We used infrared long-baseline interferometry with the PIONIER/VLTI instrument to produce reconstructed images of the photosphere and close environment of the star over four years of observations. To study the disk formation, we compared the observations and reconstructed images to previously computed models of both the stellar photosphere alone (normal B phase) and the star presenting a circumstellar disk (Be phase). Results. The observations taken in 2011 and 2012, during the quiescent phase of Achernar, do not exhibit a disk at the detection limit of the instrument. In 2014, on the other hand, a disk was already formed and our reconstructed image reveals an extended H-band continuum excess flux. Our results from interferometric imaging are also supported by several H-alpha line profiles showing that Achernar started an emission-line phase sometime in the beginning of 2013. The analysis of our reconstructed images shows that the 2014 near-IR flux extends to 1.7 - 2.3 equatorial radii. Our model-independent size estimation of the H-band continuum contribution is compatible with the presence of a circumstellar disk, which is in good agreement with predictions from Be-disk models

Fast ray-tracing algorithm for circumstellar structures (FRACS) I. Algorithm description and parameter-space study for mid-IR interferometry of B[e] stars

The physical interpretation of spectro-interferometric data is strongly model-dependent. On one hand, models involving elaborate radiative transfer solvers are too time consuming in general to perform an automatic fitting procedure and derive astrophysical quantities and their related errors. On the other hand, using simple geometrical models does not give sufficient insights into the physics of the object. We propose to stand in between these two extreme approaches by using a physical but still simple parameterised model for the object under consideration. Based on this philosophy, we developed a numerical tool optimised for mid-infrared (mid-IR) interferometry, the fast ray-tracing algorithm for circumstellar structures (FRACS) which can be used as a stand-alone model, or as an aid for a more advanced physical description or even for elaborating observation strategies. FRACS is based on the ray-tracing technique without scattering, but supplemented with the use of quadtree meshes and the full symmetries of the axisymmetrical problem to significantly decrease the necessary computing time to obtain e.g. monochromatic images and visibilities. We applied FRACS in a theoretical study of the dusty circumstellar environments (CSEs) of B[e] supergiants (sgB[e]) in order to determine which information (physical parameters) can be retrieved from present mid-IR interferometry (flux and visibility). From a set of selected dusty CSE models typical of sgB[e] stars we show that together with the geometrical parameters (position angle, inclination, inner radius), the temperature structure (inner dust temperature and gradient) can be well constrained by the mid-IR data alone. Our results also indicate that the determination of the parameters characterising the CSE density structure is more challenging but, in some cases, upper limits as well as correlations on the parameters characterising the mass loss can be obtained. Good constraints for the sgB[e] central continuum emission (central star and inner gas emissions) can be obtained whenever its contribution to the total mid-IR flux is only as high as a few percents. Ray-tracing parameterised models such as FRACS are thus well adapted to prepare and/or interpret long wavelengths (from mid-IR to radio) observations at present (e.g. VLTI/MIDI) and near-future (e.g. VLTI/MATISSE, ALMA) interferometers

AMBER/VLTI observations of the B[e] star MWC 300

Aims. We study the enigmatic B[e] star MWC 300 to investigate its disk and binary with milli-arcsecond-scale angular resolution. Methods. We observed MWC 300 with the VLTI/AMBER instrument in the H and K bands and compared these observations with temperature-gradient models to derive model parameters. Results. The measured low visibility values, wavelength dependence of the visibilities, and wavelength dependence of the closure phase directly suggest that MWC 300 consists of a resolved disk and a close binary. We present a model consisting of a binary and a temperature-gradient disk that is able to reproduce the visibilities, closure phases, and spectral energy distribution. This model allows us to constrain the projected binary separation (~4.4 mas or ~7.9 AU), the flux ratio of the binary components (~2.2), the disk temperature power-law index, and other parameters.Comment: 4 pages, 1 figure, accepted by A&