Viscous Decretion Disk Research Articles

Long-term monitoring of the Oe star VES 735: Ope! not so quiet after all

ABSTRACT Only 3–4 per cent of Galactic O stars are observed to display the emission features representative of the OBe phenomenon, compared to Galactic B stars, which display these characteristics in 25–35 per cent of B0 and B1 stars. We present new observations of the high-mass O star, VES 735, which confirms its classification as one of these rare emission-line stars. These are its first recorded observations that display strong spectroscopic variations in nearly 30 yr of monitoring, with the H α profile exhibiting a 10-fold increase in emission compared to observations taken between 1996 and 2014 and having variations which show episodes of inflowing and outflowing material. These observations, coupled with photometric variations in the visible and infrared, show behaviour that is consistent with the mass reservoir effect for viscous decretion discs. We propose that in 2015 VES 735 began an approximately 3 yr event in which mass was being injected into the circumstellar environment followed by re-accretion towards the star. We also find evidence that the re-accretion may have been interrupted with another, smaller, mass-injection event based on observations in 2022 and 2023. Observational cadences ranging from hours to months show no evidence that VES 735 is part of a binary system, making it an ideal candidate for future observations to further investigate the evolution of high-mass stars and the OBe phenomenon as it pertains to their circumstellar environment.

Angular momentum loss rates in Be stars determined by the viscous decretion disc model

ABSTRACT Circumstellar discs around Be stars are formed by the material ejected by the central star. This process removes excess angular momentum from the star as viscosity facilitates the mass and angular momentum transfer within the disc and its growth. The angular momentum loss rates (AMLR) of Be stars is a subject of debate in the literature. Through the modelling of the disc formation and dissipation phases observed from Be stars, their average AMLR can be determined and this is the goal of this work. We use the viscous decretion disc (VDD) model to provide a range of the average AMLR for Be stars and compare these rates with predicted values from the literature. We explore the reasons for discrepancies between the predicted values of average AMLR, using the VDD and Geneva stellar evolution models that were previously reported in literature and find that the largest differences occur when Be stars are rotating below their critical speeds. We show that the time over which the mass reservoir builds up is inversely proportional to the average AMLR. Also, we determine a revised value of the average AMLR for the Galactic Be star ω CMa of $4.7\times 10^{36}\, \mathrm{g\, cm^2\, s^{-2}}$, which is in better agreement with the values expected for a typical B2-type star. Finally, the effect of disc truncation due to the presence of a companion star is investigated and we find that this has a minimal effect on the average AMLR.

3D MHD simulation of a pulsationally driven MRI decretion disc

ABSTRACT We explore the pulsationally driven orbital mass ejection mechanism for Be star disc formation using isothermal, 3D magnetohydrodynamic (MHD) and hydrodynamic simulations. Non-radial pulsations are added to a star rotating at 95 per cent of critical as an inner boundary condition that feeds gas into the domain. In MHD, the initial magnetic field within the star is weak. The hydrodynamics simulation has limited angular momentum transport, resulting in repeating cycles of mass accumulation into a rotationally supported disc at small radii followed by fall-back on to the star. The MHD simulation, conversely, has efficient (Maxwell αM ∼ 0.04) angular momentum transport provided by both turbulent and coherent magnetic fields: a slowly decreting midplane driven by the magnetorotational instability and a supersonic wind on the surface of the disc driven by global magnetic torques. The angle and time-averaged properties near the midplane agree reasonably well with a 1D viscous decretion disc model with a modified $\tilde{\alpha }=0.5$, in which the gas transitions from a subsonic thin disc to a supersonic spherical wind at the critical point. 1D models, however, cannot capture the multiphase decretion/angular structure seen in our simulations. Our results demonstrate that, at least under certain conditions, non-radial pulsations on the surface of a rapidly rotating, weakly magnetised star can drive a Keplerian disc with the basic properties of the viscous decretion disc paradigm, albeit coupled to a laminar wind away from the midplane. Future modelling of Be star discs should consider the possible existence of such a surface wind.

Outbursts and stellar properties of the classical Be star HD 6226

ABSTRACT The bright and understudied classical Be star HD 6226 has exhibited multiple outbursts in the last several years during which the star grew a viscous decretion disc. We analyse 659 optical spectra of the system collected from 2017 to 2020, along with a ultraviolet spectrum from the Hubble Space Telescope and high cadence photometry from both Transiting Exoplanet Survey Satellite (TESS) and the Kilodegree Extremely Little Telescope (KELT) survey. We find that the star has a spectral type of B2.5IIIe, with a rotation rate of 74 per cent of critical. The star is nearly pole-on with an inclination of 13${_{.}^{\circ}}$4. We confirm the spectroscopic pulsational properties previously reported, and report on three photometric oscillations from KELT photometry. The outbursting behaviour is studied with equivalent width measurements of H α and H β, and the variations in both of these can be quantitatively explained with two frequencies through a Fourier analysis. One of the frequencies for the emission outbursts is equal to the difference between two photometric oscillations, linking these pulsation modes to the mass ejection mechanism for some outbursts. During the TESS observation time period of 2019 October 7 to 2019 November 2, the star was building a disc. With a large data set of H α and H β spectroscopy, we are able to determine the time-scales of dissipation in both of these lines, similar to past work on Be stars that has been done with optical photometry. HD 6226 is an ideal target with which to study the Be disc-evolution given its apparent periodic nature, allowing for targeted observations with other facilities in the future.

Hydrodynamic disk solutions for Be stars using HDUST

Abstract. In this work, we implemented a hydrodynamical solution for fast rotating stars, which leaves high values of mass-loss rates and low terminal velocities of the wind. This 1D density distribution adopts a viscosity mimicking parameter which simulates a quasi-Keplerian motion. Then, it is converted to a volumetric density considering vertical hydrostatic equilibrium using a power-law scale height, as usual in viscous decretion disk models. We calculate the theoretical hydrogen emission lines and the spectral energy distribution utilizing the radiative transfer code HDUST. Our disk-wind structures are in agreement with viscous decretions disk models.

A Multi–Observing Technique Study of the Dynamical Evolution of the Viscous Disk around the Be Star ω CMa

Abstract The observed emission lines of Be stars originate from a circumstellar Keplerian disk, which is generally well explained by the viscous decretion disk model. In an earlier work we performed modeling of the full light curve of the bright Be star ω CMa with the 1D time-dependent hydrodynamic code SINGLEBE and the Monte Carlo radiative transfer code HDUST. We used a V-band light curve that probes the inner disk through four disk formation and dissipation cycles. This new study compares predictions of the same set of model parameters with time-resolved photometry from the near-UV through the mid-IR, comprehensive series of optical spectra, and optical broadband polarimetry, which overall represent a larger volume of the disk. Qualitatively, the models reproduce the trends in the observed data due to the growth and decay of the disk. However, quantitative differences exist, e.g., an overprediction of flux increasing with wavelength, too slow decreases in Balmer emission line strength during disk dissipation, and a discrepancy between the range of polarimetric data and the model. We find that a larger value of the viscosity parameter alone or a disk truncated by a companion star reduces these discrepancies by increasing the dissipation rate in the outer regions of the disk.

Visible and near-infrared spectro-interferometric analysis of the edge-on Be star o Aquarii

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 Hα (VEGA) and Brγ (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 Hα and Brγ 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 Hα than in Brγ. We found that the inclination angle i derived from Hα is significantly lower (~15°) than the one derived from Brγ: 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 Brγ (β ~ −0.43), but not in Hα (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 Σ0 = 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, Hα and Brγ line profiles, and polarimetric quantities. Finally, our analysis of multi-epoch Hα 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 Brγ 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 Hα 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.

Be stars in the X-ray binary context

AbstractRapidly rotating B-type stars with gaseous mass-loss disks in Keplerian rotation are common central objects in X-Ray binaries. These disks are physically well understood in the framework of the viscous decretion disk, and their typical parameters have been established for a large number of single Be stars in the recent years. According to the current observational evidence, the Be stars and disks found in BeXRBs are well within the boundaries known from single Be stars, i.e., they are normal Be stars. New results have also been obtained on the orbital disk truncation and other tidal effects of the companion objects on the disk.

The life cycles of Be viscous decretion discs: The case of ω CMa

We analyzed V-band photometry of the Be star {\omega} CMa, obtained during the last four decades, during which the star went through four complete cycles of disc formation and dissipation. The data were simulated by hydrodynamic models based on a time-dependent implementation of the viscous decretion disc (VDD) paradigm, in which a disc around a fast-spinning Be star is formed by material ejected by the star and driven to progressively larger orbits by means of viscous torques. Our simulations offer a good description of the photometric variability during phases of disc formation and dissipation, which suggests that the VDD model adequately describes the structural evolution of the disc. Furthermore, our analysis allowed us to determine the viscosity parameter {\alpha}, as well as the net mass and angular momentum (AM) loss rates. We find that {\alpha} is variable, ranging from 0.1 to 1.0, not only from cycle to cycle but also within a given cycle. Additionally, build-up phases usually have larger values of {\alpha} than the dissipation phases. Furthermore, during dissipation the outward AM flux is not necessarily zero, meaning that {\omega} CMa does not experience a true quiescence but, instead, switches between a high to a low AM loss rate during which the disc quickly assumes an overall lower density but never zero. We confront the average AM loss rate with predictions from stellar evolution models for fast-rotating stars, and find that our measurements are smaller by more than one order of magnitude.

The life cycles of Be viscous decretion discs: fundamental disc parameters of 54 SMC Be stars

Be stars are main-sequence massive stars with emission features in their spectrum, which originates in circumstellar gaseous discs. Even though the viscous decretion disc (VDD) model can satisfactorily explain most observations, two important physical ingredients, namely the magnitude of the viscosity ($\alpha$) and the disk mass injection rate, remain poorly constrained. The light curves of Be stars that undergo events of disc formation and dissipation offer an opportunity to constrain these quantities. A pipeline was developed to model these events that uses a grid of synthetic light curves, computed from coupled hydrodynamic and radiative transfer calculations. A sample of 54 Be stars from the OGLE survey of the Small Magellanic Cloud (SMC) was selected for this study. Because of the way our sample was selected (bright stars with clear disc events), it likely represents the densest discs in the SMC. Like their siblings in the Galaxy, the mass of the disc in the SMC increases with the stellar mass. The typical mass and angular momentum loss rates associated with the disk events are of the order of $\sim$$10^{-10}\, M_\odot\,\mathrm{yr^{-1}}$ and $\sim$$5\times 10^{36}\, \mathrm{g\, cm^{2}\, s^{-2}}$, respectively. The values of $\alpha$ found in this work are typically of a few tenths, consistent with recent results in the literature and with the ones found in dwarf novae, but larger than current theory predicts. Considering the sample as a whole, the viscosity parameter is roughly two times larger at build-up ($\left\langle\alpha_\mathrm{bu}\right\rangle = 0.63$) than at dissipation ($\left\langle\alpha_\mathrm{d}\right\rangle = 0.26$). Further work is necessary to verify whether this trend is real or a result of some of the model assumptions.

Multitechnique testing of the viscous decretion disk model (Corrigendum)

Abstract : The viscous decretion disk (VDD) model is able to explain most of the currently observable properties of the circumstellar disks of Be stars. However, more stringent tests, focusing on reproducing multitechnique observations of individual targets via physical modeling, are needed to study the predictions of the VDD model under specific circumstances. In the case of nearby, bright Be star b CMi, these circumstances are a very stable low-density disk and a late-type (B8Ve) central star. Aims. The aim is to test the VDD model thoroughly, exploiting the full diagnostic potential of individual types of observations, in particular, to constrain the poorly known structure of the outer disk if possible, and to test truncation effects caused by a possible binary companion using radio observations. We use the Monte Carlo radiative transfer code HDUST to produce model observables, which we compare with a very large set of multitechnique and multiwavelength observations that include ultraviolet and optical spectra, photometry covering the interval between optical and radio wavelengths, optical polarimetry, and optical and near-IR (spectro) interferometry. A parametric VDD model with radial density exponent of n = 3.5, which is the canonical value for isothermal flaring disks is found to explain observables typically formed in the inner disk, while observables originating in the more extended parts favor a shallower, n = 3.0, density falloff. Theoretical consequences of this finding are discussed and the outcomes are compared with the predictions of a fully self-consistent VDD model. Modeling of radio observations allowed for the first determination of the physical extent of a Be disk (35[+10/-5] stellar radii), which might be caused by a binary companion. Finally, polarization data allowed for an indirect measurement of the rotation rate of the star, which was found to be W greater or equal 0:98, i.e., very close to critical.

Revealing the structure of the outer disks of Be stars

Context. The structure of the inner parts of Be star disks (20 stellar radii) is well explained by the viscous decretion disk (VDD) model, which is able to reproduce the observable properties of most of the objects studied so far. The outer parts, on the ther hand, are not observationally well-explored, as they are observable only at radio wavelengths. A steepening of the spectral slope somewhere between infrared and radio wavelengths was reported for several Be stars that were previously detected in the radio, but a convincing physical explanation for this trend has not yet been provided. Aims. We test the VDD model predictions for the extended parts of a sample of six Be disks that have been observed in the radio to address the question of whether the observed turndown in the spectral energy distribution (SED) can be explained in the framework of the VDD model, including recent theoretical development for truncated Be disks in binary systems. Methods. We combine new multi-wavelength radio observations from the Karl. G. Jansky Very Large Array (JVLA) and Atacama Pathfinder Experiment (APEX) with previously published radio data and archival SED measurements at ultraviolet, visual, and infrared wavelengths. The density structure of the disks, including their outer parts, is constrained by radiative transfer modeling of the observed spectrum using VDD model predictions. In the VDD model we include the presumed effects of possible tidal influence from faint binary companions. Results. For 5 out of 6 studied stars, the observed SED shows strong signs of SED turndown between far-IR and radio wavelengths. A VDD model that extends to large distances closely reproduces the observed SEDs up to far IR wavelengths, but fails to reproduce the radio SED. ... (abstract continues but did not fit here)

The outer disk of the classical Be star ψ Per

AbstractTo this date ψ Per is the only classical Be star that was angularly resolved in radio (by the VLA at λ = 2 cm). Gaussian fit to the azimuthally averaged visibility data indicates a disk size (FWHM) of ~500 stellar radii (Dougherty & Taylor 1992). Recently, we obtained new multi-band cm flux density measurements of ψ Per from the enhanced VLA. We modeled the observed spectral energy distribution (SED) covering the interval from ultraviolet to radio using the Monte Carlo radiative transfer code HDUST (Carciofi & Bjorkman 2006). An SED turndown, that occurs between far-IR and radio wavelengths, is explained by a truncated viscous decretion disk (VDD), although the shallow slope of the radio SED suggests that the disk is not simply cut off, as is assumed in our model. The best-fit size of a truncated disk derived from the modeling of the radio SED is 100+5−15 stellar radii, which is in striking contrast with the result of Dougherty & Taylor (1992). The reasons for this discrepancy are under investigation.

Tidal tearing of circumstellar disks in Be/X-ray and gamma-ray binaries

AbstractAbout one half of high-mass X-ray binaries host a Be star [an OB star with a viscous decretion (slowly outflowing) disk]. These Be/X-ray binaries exhibit two types of X-ray outbursts (Stella et al. 1986), normal X-ray outbursts (LX~1036−37 erg s−1) and occasional giant X-ray outbursts (LX > 1037 erg s−1). The origin of giant X-ray outbursts is unknown. On the other hand, a half of gamma-ray binaries have a Be star as the optical counterpart. One of these systems [LS I +61 303 (Porb = 26.5 d)] shows the superorbital (1,667 d) modulation in radio through X-ray bands. No consensus has been obtained for its origin. In this paper, we study a possibility that both phenomena are caused by a long-term, cyclic evolution of a highly misaligned Be disk under the influence of a compact object, by performing 3D hydrodynamic simulations. We find that the Be disk cyclically evolves in mildly eccentric, short-period systems. Each cycle consists of the following stages: 1)As the Be disk grows with time, the initially circular disk becomes eccentric by the Kozai-Lidov mechanism.2)At some point, the disk is tidally torn off near the base and starts precession.3)Due to precession, a gap opens between the disk base and mass ejection region, which allows the formation of a new disk in the stellar equatorial plane (see Figure 1).4)The newly formed disk finally replaces the precessing old disk. Such a cyclic disk evolution has interesting implications for the long-term behavior of high energy emission in Be/X-ray and gamma-ray binaries.

The life cycles of Be viscous decretion discs: time-dependent modelling of infrared continuum observations

We apply the viscous decretion disc (VDD) model to interpret the infrared disc continuum emission of 80 Be stars observed in different epochs. In this way, we determined 169 specific disc structures, namely their density scale, $\rho_0$, and exponent, $n$. We found that the $n$ values range mainly between $1.5$ and $3.5$, and $\rho_0$ varies between $10^{-12}$ and $10^{-10}\,\mathrm{g\,cm^{-3}}$, with a peak close to the lower value. Our large sample also allowed us to firmly establish that the discs around early-type stars are denser than in late-type stars. Additionally, we estimated the disc mass decretion rates and found that they range between $10^{-12}$ and $10^{-9}\,\mathrm{M_{\odot}\,yr^{-1}}$. These values are compatible with recent stellar evolution models of fast-rotating stars. One of the main findings of this work is a correlation between the $\rho_0$ and $n$ values. In order to find out whether these relations can be traced back to the evolution of discs or have some other origin, we used the VDD model to calculate temporal sequences under different assumptions for the time profile of the disc mass injection. The results support the hypothesis that the observed distribution of disc properties is due to a common evolutionary path. In particular, our results suggest that the timescale for disc growth, during which the disc is being actively fed by mass injection episodes, is shorter than the timescale for disc dissipation, when the disc is no longer fed by the star and dissipates as a result of the viscous diffusion of the disc material.

On the relationship between circumstellar disc size and X-ray outbursts in Be/X-ray binaries

We present long term H$\alpha$ monitoring results of five Be/X-ray binaries to study the Be disc size variations and their influence on Type II (giant) X-ray outbursts. The work is done in the context of the viscous decretion disc model which predicts that Be discs in binary systems are truncated by resonant torques induced by the neutron star in its orbit. Our observations show that type II outbursts are not correlated(nor anti-correlated) with the disc size, as they are seen to occur both at relatively small and large Be disc radii. We discuss these observations in context of alternate interpretation of Be disc behaviour, such as precession, elongation and density effects, and with cognisance of the limitations of our disc size estimates.

INVESTIGATING THE CIRCUMSTELLAR DISK OF THE Be SHELL STAR 48 LIBRAE

ABSTRACT A global disk oscillation implemented in the viscous decretion disk (VDD) model has been used to reproduce most of the observed properties of the well known Be star ζ Tau. 48 Librae shares several similarities with ζ Tau—they are both early-type Be stars, display shell characteristics in their spectra, and exhibit cyclic V/R variations—but has some marked differences as well, such as a much denser and more extended disk, a much longer V/R cycle, and the absence of the so-called triple-peak features. We aim to reproduce the photometric, polarimetric, and spectroscopic observables of 48 Librae with a self-consistent model, and to test the global oscillation scenario for this target. Our calculations are carried out with the three-dimensional NLTE radiative transfer code HDUST. We employ a rotationally deformed, gravity-darkened central star surrounded by a disk whose unperturbed state is given by the VDD model. A two-dimensional global oscillation code is then used to calculate the disk perturbation and superimpose it on the unperturbed disk. A very good, self-consistent fit to the time-averaged properties of the disk is obtained with the VDD. The calculated perturbation has a period P = 12 years, which agrees with the observed period, and the behavior of the V/R cycle is well reproduced by the perturbed model. The perturbed model improves the fit to the photometric data and reproduces some features of the observed spectroscopic data. Some suggestions to improve the synthesized spectroscopy in a future work are given.

CLASSICAL Oe STARS IN THE FIELD OF THE SMALL MAGELLANIC CLOUD*

ABSTRACT We present 29 ± 1 classical Oe stars from RIOTS4 (the Runaways and Isolated O Type Star Spectroscopic Survey of the SMC), a spatially complete, spectroscopic survey of Small Magellanic Cloud (SMC) field OB stars. The two earliest are O6e stars, and four are earlier than any Milky Way (MW) Oe stars. We also find ten Ope stars, showing He i infill and/or emission; five appear to be at least as hot as ∼O7.5e stars. The hottest, star 77616, shows He ii disk emission, suggesting that even the hottest O stars can form decretion disks, and offers observational support for theoretical predictions that the hottest, fastest rotators can generate He+-ionizing atmospheres. Our data also demonstrate that Ope stars correspond to Oe stars earlier than O7.5e with strong disk emission. We find that in the SMC, Oe stars extend to earlier spectral types than in the MW, and our SMC Oe/O frequency, 0.26 ± 0.04, is much greater than the MW value, 0.03 ± 0.01. These results are consistent with angular momentum transport by stronger winds suppressing decretion disk formation at higher metallicity. In addition, the Oe star frequency in the SMC field is indistinguishable from that for clusters, which is consistent with the similarity between rotation rates in these environments, and contrary to the pattern for MW rotation rates. Thus, our findings strongly support the viscous decretion disk model and confirm that Oe stars are the high-mass extension of the Be phenomenon. Additionally, we find that Fe ii emission occurs among Oe stars later than O7.5e with massive disks, and we revise a photometric criterion for identifying Oe stars to J − [ 3.6 ] ≥ 0.1 ?> .

Multitechnique testing of the viscous decretion disk model

The viscous decretion disk (VDD) model is able to explain most of the currently observable properties of the circumstellar disks of Be stars. However, more stringent tests, focusing on reproducing multitechnique observations of individual targets via physical modeling, are needed to study the predictions of the VDD model under specific circumstances. In the case of nearby, bright Be star $\beta$ CMi, these circumstances are a very stable low-density disk and a late-type (B8Ve) central star. The aim is to test the VDD model thoroughly, exploiting the full diagnostic potential of individual types of observations, in particular, to constrain the poorly known structure of the outer disk if possible, and to test truncation effects caused by a possible binary companion using radio observations. We use the Monte Carlo radiative transfer code HDUST to produce model observables, which we compare with a very large set of multitechnique and multiwavelength observations that include ultraviolet and optical spectra, photometry covering the interval between optical and radio wavelengths, optical polarimetry, and optical and near-IR (spectro)interferometry. Due to the absence of large scale variability, data from different epochs can be combined into a single dataset. A parametric VDD model with radial density exponent of $n$ = 3.5, which is the canonical value for isothermal flaring disks, is found to explain observables typically formed in the inner disk, while observables originating in the more extended parts favor a shallower, $n$ = 3.0, density falloff. Modeling of radio observations allowed for the first determination of the physical extent of a Be disk (35$^{+10}_{-5}$ stellar radii), which might be caused by a binary companion. Finally, polarization data allowed for an indirect measurement of the rotation rate of the star, which was found to be $W \gtrsim 0.98$, i.e., very close to critical.

The pseudo-photosphere model for the continuum emission of gaseous discs

We investigate the continuum emission of viscous decretion discs around Be stars in this paper. The results obtained from non-LTE (local thermodynamic equilibrium) radiative transfer models show two regimes in the disc surface brightness profile: an inner optically thick region, which behaves as a pseudo-photosphere with a wavelength-dependent size, and an optically thin tenuous outer part, which contributes with about a third of the total flux. The isophotal shape of the surface brightness is well described by elliptical contours with an axial ratio $b/a=\cos i$ for inclinations $i<75^{\circ}$. Based on these properties, a semi-analytical model was developed to describe the continuum emission of gaseous discs. It provides fluxes and spectral slopes at the infrared within an accuracy of $10\%$ and $5\%$, respectively, when compared to the numerical results. The model indicates that the infrared spectral slope is mainly determined by both the density radial slope and the disc flaring exponent, being practically independent of disc inclination and base density. As a first application, the density structure of 15 Be stars was investigated, based on the infrared flux excess, and the results compared to previous determinations in the literature. Our results indicate that the decretion rates are in the range of $10^{-12}$ to $10^{-9}\,{\rm M_{\odot}\,yr^{-1}}$, which is at least two orders of magnitude smaller than the previous outflowing disc model predictions.