A realistic two-dimensional model of Altair Bouchaud, K.; Domiciano de Souza, A.; Rieutord, M. ...
Astronomy and astrophysics (Berlin),
01/2020, Volume:
633
Journal Article
Peer reviewed
Open access
Context.
Fast rotation is responsible for important changes in the structure and evolution of stars and the way we see them. Optical long baseline interferometry now allows for the study of its ...effects on the stellar surface, mainly gravity darkening and flattening.
Aims.
We aim to determine the fundamental parameters of the fast-rotating star Altair, in particular its evolutionary stage (represented here by the core hydrogen mass fraction
X
c
), mass, and differential rotation, using state-of-the-art stellar interior and atmosphere models together with interferometric (ESO-VLTI), spectroscopic, and asteroseismic observations.
Methods.
We use ESTER two-dimensional stellar models to produce the relevant surface parameters needed to create intensity maps from atmosphere models. Interferometric and spectroscopic observables are computed from these intensity maps and several stellar parameters are then adjusted using the publicly available MCMC algorithm Emcee.
Results.
We determined Altair’s equatorial radius to be
R
eq
= 2.008 ± 0.006
R
⊙
, the position angle PA = 301.1 ± 0.3°, the inclination
i
= 50.7 ± 1.2°, and the equatorial angular velocity Ω = 0.74 ± 0.01 times the Keplerian angular velocity at equator. This angular velocity leads to a flattening of
ε
= 0.220 ± 0.003. We also deduce from the spectroscopically derived
v
sin
i
≃ 243 km s
−1
, a true equatorial velocity of ∼314 km s
−1
corresponding to a rotation period of 7h46m (∼3 cycles/day). The data also impose a strong correlation between mass, metallicity, hydrogen abundance, and core evolution. Thanks to asteroseismic data, and provided our frequencies identification is correct, we constrain the mass of Altair to 1.86 ± 0.03
M
⊙
and further deduce its metallicity
Z
= 0.019 and its core hydrogen mass fraction
X
c
= 0.71, assuming an initial solar hydrogen mass fraction
X
= 0.739. These values suggest that Altair is a young star ∼100 Myr old. Finally, the 2D ESTER model also gives the internal differential rotation of Altair, showing that its core rotates approximately 50% faster than the envelope, while the surface differential rotation does not exceed 6%.
ABSTRACT
We present intensity interferometry of the luminous blue variable P Cyg in the light of its H α emission performed with 1 m-class telescopes. We compare the measured visibility points to ...synthesized interferometric data based on the CMFGEN physical modelling of a high-resolution spectrum of P Cyg recorded almost simultaneously with our interferometry data. Tuning the stellar parameters of P Cyg and its H α linear diameter, we estimate the distance of P Cyg as 1.56 ± 0.25 kpc, which is compatible within 1σ with 1.36 ± 0.24 kpc reported by the Gaia DR2 catalogue of parallaxes recently published. Both the values are significantly smaller than the canonic value of 1.80 ± 0.10 kpc usually adopted in literature. Our method used to calibrate the distance of P Cyg can apply to very massive and luminous stars both in our Galaxy and neighbouring galaxies, and can improve the so-called wind momentum–luminosity relation that potentially applies to calibrate cosmological candles in the local Universe.
Future large arrays of telescopes, used as intensity interferometers, can be used to image the surfaces of stars with unprecedented angular resolution. Fast-rotating, hot stars are particularly ...attractive targets for intensity interferometry since shorter (blue) wavelength observations do not pose additional challenges. Starting from realistic surface brightness simulations of fast-rotating stars, we discuss the capabilities of future intensity interferometers for imaging effects such as gravity darkening and rotational deformation. We find that two-telescope intensity correlation data allow reasonably good imaging of these phenomena, but can be improved with additional higher order (e.g. three-telescope) correlation data, which contain some Fourier phase information.
ABSTRACT
In this paper, we report on spatial intensity interferometry measurements within the Hα line on two stars: the Luminous Blue Variable supergiant P Cygni and the late-type B supergiant ...Rigel. The experimental setup was upgraded to allow simultaneous measurement of two polarization channels, instead of one in our previous setup, and the zero baseline correlation function on-sky to validate independent estimates obtained from the stellar spectrum and the instrumental spectral throughput. Combined with simultaneous spectra measurements and based on radiative transfer models calculated with the code CMFGEN, we were able to fit our measured visibility curves to extract the stellar distances. Our distance determinations for both P Cygni (1.61 ± 0.18 kpc) and Rigel (0.26 ± 0.02 kpc) agree very well with the values provided by astrometry with the Gaia and Hipparcos missions, respectively. This result for Rigel was obtained by adopting a stellar luminosity of L⋆ = 123 000 L⊙, which is reported in the literature as being consistent with the Hipparcos distance to Rigel. However, due to the lack of consensus on Rigel’s luminosity, we also explore how the adoption of the stellar luminosity in our models affects our distance determination for Rigel. In conclusion, we support, in an independent way, the distance to Rigel as the one provided by the Hipparcos mission, when taking the luminosity of 123 000 L⊙ at face value. This study is the first successful step towards extending the application of the Wind Momentum Luminosity Relation method for distance calibration from an LBV supergiant to a more normal late-type B supergiant.
Context. Among intermediate-mass and massive stars, Be stars are the fastest rotators in the main sequence (MS) and, as such, these stars are a cornerstone to validate models of structure and ...evolution of rotating stars. Several phenomena, however, induce under- or overestimations either of their apparent V sini, or true velocity V. Aims. In the present contribution we aim at obtaining distributions of true rotational velocities corrected for systematic effects induced by the rapid rotation itself, macroturbulent velocities, and binarity. Methods. We study a set of 233 Be stars by assuming they have inclination angles distributed at random. We critically discuss the methods of Cranmer and Lucy-Richardson, which enable us to transform a distribution of projected velocities into another distribution of true rotational velocities, where the gravitational darkening effect on the V sini parameter is considered in different ways. We conclude that iterative algorithm by Lucy-Richardson responds at best to the purposes of the present work, but it requires a thorough determination of the stellar fundamental parameters. Results. We conclude that once the mode of ratios of the true velocities of Be stars attains the value V/V sub(c)Asymp totically = to 0.77 in the main-sequence (MS) evolutionary phase, it remains unchanged up to the end of the MS lifespan. The statistical corrections found on the distribution of ratios V/V sub(c) for overestimations of V sini, due to macroturbulent motions and binarity, produce a shift of this distribution toward lower values of V/V sub(c) when Be stars in all MS evolutionary stages are considered together. The mode of the final distribution obtained is at V/V sub(c)Asymp totically = to 0.65. This distribution has a nearly symmetric distribution and shows that the Be phenomenon is characterized by a wide range of true velocity ratios 0.3 <, ~ V/V sub(c)<, ~ 0.95. It thus suggests that the probability that Be stars are critical rotators is extremely low. Conclusions. The corrections attempted in the present work represent an initial step to infer indications about the nature of the Be-star surface rotation that will be studied in the second paper of this series.
Context.
The infrared (IR) excess of classical Cepheids is seldom studied and poorly understood despite observational evidence and the potential for its contribution to induce systematics on the ...period-luminosity (PL) relation used in the calibration of the extragalactic distance scale.
Aims.
This study aims to understand the physical origin of the IR excess found in the spectral energy distribution (SED) of 5 Cepheids: RS Pup (
P
= 41.46d),
ζ
Gem (
P
= 10.15d),
η
Aql (
P
= 7.18d), V Cen (
P
= 5.49d) and SU Cyg (
P
= 3.85d).
Methods.
A time series of atmospheric models along the pulsation cycle were fitted to a compilation of data, including optical and near-IR photometry,
Spitzer
spectra (secured at a specific phase), interferometric angular diameters, effective temperature estimates, and radial velocity measurements.
Herschel
images in two bands were also analyzed qualitatively. In this fitting process, based on the SPIPS algorithm, a residual was found in the SED, whatever the pulsation phase, and for wavelengths larger than about 1.2
μ
m, which corresponds to the so-determined infrared excess of Cepheids. This IR excess was then corrected from interstellar medium absorption in order to infer the presence (or absence) of dust shells and was, ultimately, used in order to fit a model for a shell of ionized gas.
Results.
For all Cepheids, we find a continuum IR excess increasing up to approximately −0.1 magnitudes at 30
μ
m, which cannot be explained by a hot or cold dust model of CircumStellar Environment (CSE). However, a weak but significant dust emission at 9.7
μ
m is found for
ζ
Gem,
η
Aql and RS Pup, while clear interstellar clouds are seen in the
Herschel
images for V Cen and RS Pup. We show, for the first time, that the IR excess of Cepheids can be explained by free–free emission from a thin shell of ionized gas, with a thickness of ≃15% of the star radius, a mass of 10
−9
−10
−7
M
⊙
and a temperature ranging between 3500 and 4500 K.
Conclusions.
The presence of a thin shell of ionized gas around Cepheids must be tested with interferometers operating in the visible or mid-IR, or using radio telescopes. The impact of such CSEs of ionized gas on the PL relation of Cepheids also calls for further investigation.
ABSTRACT
Classical B emission (Be) stars are fast rotating, near-main-sequence B-type stars. The rotation and the presence of circumstellar discs profoundly modify the observables of active Be stars. ...Our goal is to infer stellar and disc parameters, as well as distance and interstellar extinction, using the currently most favoured physical models for these objects. We present BeAtlas, a grid of $61\, 600$ non-local thermodynamic equilibrium radiative transfer models for Be stars, calculated with the hdust code. The grid was coupled with a Monte Carlo Markov chain (MCMC) code to sample the posterior distribution. We test our method on two well-studied Be stars, α Eri and β CMi, using photometric, polarimetric, and spectroscopic data as input to the code. We recover literature determinations for most of the parameters of the targets, in particular the mass and age of α Eri, the disc parameters of β CMi, and their distances and inclinations. The main discrepancy is that we estimate lower rotational rates than previous works. We confirm previously detected signs of disc truncation in β CMi and note that its inner disc seems to have a flatter density slope than its outer disc. The correlations between the parameters are complex, further indicating that exploring the entire parameter space simultaneously is a more robust approach, statistically. The combination of BeAtlas and Bayesian-MCMC techniques proves successful, and a powerful new tool for the field: The fundamental parameters of any Be star can now be estimated in a matter of hours or days.
Rotation significantly impacts on the structure and life of stars. In phases of high rotation velocity (close to critical), the photospheric structure can be highly modified, and present in ...particular geometrical deformation (rotation flattening) and latitudinal-dependent flux (gravity darkening). The fastest known rotators among the nondegenerate stars close to the main sequence, Be stars, are key targets for studying the effects of fast rotation on stellar photospheres. We seek to determine the purely photospheric parameters of Achernar based on observations recorded during an emission-free phase (normal B phase). The analysis did not reveal any important circumstellar contribution, so that Achernar was essentially in a normal B phase at least from mid-2009 to end-2012, and the model parameters derived in this work provide a fair description of its photosphere. This model offers a promising explanation to the fact that the measured Beta parameter decreases with flattening and shows significantly lower values than the classical prediction of von Zeipel.
Context. The interpretation of stellar apparent fundamental parameters (viewing-angle dependent) requires that they be treated consistently with the characteristics of their surface rotation law. ...Aims. We aim to develop a model to determine the distribution of the effective temperature and gravity, which explicitly depend on the surface differential rotation law and on the concomitant stellar external geometry. Methods. The basic assumptions in this model are: a) the external stellar layers are in radiative equilibrium; b) the emergent bolometric flux is anti-parallel with the effective gravity; c) the angular velocity in the surface obeys relations like Ω(θ) = Ωo 1 + αΥ(θ,k) where Υ(θ,k) = coskθ or sinkθ, and where (α,k) are free parameters. Results. The effective temperature varies with co-latitude θ, with amplitudes that depend on the differential-rotation law through the surface effective gravity and the gravity-darkening function (GDF). Although the derived expressions can be treated numerically, for some low integer values of k, analytical forms of the integral of characteristic curves, on which the determination of the GDF relies, are obtained. The effects of the quantities (η,α,k) (η = ratio between centrifugal and gravitational accelerations at the equator) on the determination of the Vsini parameter and on the gravity-darkening exponent are studied. Depending on the values of (η,α,k) the velocity V in the derived Vsini may strongly deviate from the equatorial rotational velocity. It is shown that the von Zeipel’s-like gravity-darkening exponent β1 depends on all parameters (η,α,k) and that its value also depends on the viewing-angle i. Hence, there no unique interpretation of this exponent determined empirically in terms of (i,α). Conclusions. We stress that the data on rotating stars should be analyzed by taking into account the rotational effects through the GDF, by assuming k = 2 as a first approximation. Instead of the classic pair (η,β1), it would be more useful to determine the quantities (η,α,i) to characterize stellar rotation.
The evolved fast rotator Sargas Domiciano de Souza, A.; Bouchaud, K.; Rieutord, M. ...
Astronomy and astrophysics (Berlin),
11/2018, Volume:
619
Journal Article
Peer reviewed
Open access
Context.
Gravity darkening (GD) and flattening are important consequences of stellar rotation. The precise characterization of these effects across the Hertzsprung–Russell (H-R) diagram is crucial to ...a deeper understanding of stellar structure and evolution.
Aims.
We seek to characterize such important effects on Sargas (
θ
Scorpii), an evolved, fast-rotating, intermediate-mass (∼5
M
⊙
) star, located in a region of the H-R diagram where they have never been directly measured as far as we know.
Methods.
We use our numerical model CHARRON to analyze interferometric (VLTI/PIONIER) and spectroscopic (VLT/UVES) observations through a MCMC model-fitting procedure. The visibilities and closure phases from the PIONIER data are particularly sensitive to rotational flattening and GD. Adopting the Roche approximation, we investigate two GD models: (1) the
β
-model (
T
eff
∝
g
eff
β
), which includes the classical von Zeipel’s GD law, and (2) the
ω
-model, where the flux is assumed to be anti-parallel to
g
eff
.
Results.
Using this approach we measure several physical parameters of Sargas, namely, equatorial radius, mass, equatorial rotation velocity, mean
T
eff
, inclination and position angle of the rotation axis, and
β
. In particular, we show that the measured
β
leads to a surface flux distribution equivalent to the one given by the
ω
-model. Thanks to our results, we also show that Sargas is most probably located in a rare and interesting region of the H-R diagram: within the Hertzsprung gap and over the hot edge of the instability strip (equatorial regions inside it and polar regions outside it because of GD).
Conclusions.
These results show once more the power of optical/infrared long-baseline interferometry, combined with high-resolution spectroscopy, to directly measure fast-rotation effects and stellar parameters, in particular GD. As was the case for a few fast rotators previously studied by interferometry, the
ω
-model provides a physically more profound description of Sargas’ GD, without the need of a
β
exponent. It will also be interesting to further investigate the implications of the singular location of such a fast rotator as Sargas in the H-R diagram.
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