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Context. Spectroscopic analysis remains the most common method to derive masses of massive stars, the most fundamental stellar parameter. While binary orbits and stellar pulsations can provide much sharper constraints on the stellar mass, these methods are only rarely applicable to massive stars. Unfortunately, spectroscopic masses of massive stars heavily depend on the detailed physics of model atmospheres.
Aims. We demonstrate the impact of a consistent treatment of the radiative pressure on inferred gravities and spectroscopic masses of massive stars. Specifically, we investigate the contribution of line and continuum transitions to the photospheric radiative pressure. We further explore the effect of model parameters, e.g., abundances, on the deduced spectroscopic mass. Lastly, we compare our results with the plane-parallel TLUSTY code, commonly used for the analysis of massive stars with photospheric spectra.
Methods. We calculate a small set of O-star models with the Potsdam Wolf-Rayet (PoWR) code using different approaches for the quasi-hydrostatic part. These models allow us to quantify the effect of accounting for the radiative pressure consistently. We further use PoWR models to show how the Doppler widths of line profiles and abundances of elements such as iron affect the radiative pressure, and, as a consequence, the derived spectroscopic masses.
Results. Our study implies that errors on the order of a factor of two in the inferred spectroscopic mass are to be expected when neglecting the contribution of line and continuum transitions to the radiative acceleration in the photosphere. Usage of implausible microturbulent velocities, or the neglect of important opacity sources such as Fe, may result in errors of approximately 50% in the spectroscopic mass. A comparison with TLUSTY model atmospheres reveals a very good agreement with PoWR at the limit of low mass-loss rates.
The Galactic WC and WO stars
(2019)
Wolf-Rayet stars of the carbon sequence (WC stars) are an important cornerstone in the late evolution of massive stars before their core collapse. As core-helium burning, hydrogen-free objects with huge mass-loss, they are likely the last observable stage before collapse and thus promising progenitor candidates for type Ib/c supernovae. Their strong mass-loss furthermore provides challenges and constraints to the theory of radiatively driven winds. Thus, the determination of the WC star parameters is of major importance for several astrophysical fields. With Gaia DR2, for the first time parallaxes for a large sample of Galactic WC stars are available, removing major uncertainties inherent to earlier studies. In this work, we re-examine a previously studied sample of WC stars to derive key properties of the Galactic WC population. All quantities depending on the distance are updated, while the underlying spectral analyzes remain untouched. Contrasting earlier assumptions, our study yields that WC stars of the same subtype can significantly vary in absolute magnitude. With Gaia DR2, the picture of the Galactic WC population becomes more complex: We obtain luminosities ranging from log L/L-circle dot = 4.9-6.0 with one outlier (WR 119) having log L/L-circle dot = 4.7. This indicates that the WC stars are likely formed from a broader initial mass range than previously assumed. We obtain mass-loss rates ranging between log(M) over dot = -5.1 and -4.1, with (M) over dot proportional to L-0.68 and a linear scaling of the modified wind momentum with luminosity. We discuss the implications for stellar evolution, including unsolved issues regarding the need of envelope inflation to address the WR radius problem, and the open questions in regard to the connection of WR stars with Gamma-ray bursts. WC and WO stars are progenitors of massive black holes, collapsing either silently or in a supernova that most-likely has to be preceded by a WO stage.
Context. For more than two decades, stellar atmosphere codes have been used to derive the stellar and wind parameters of massive stars. Although they have become a powerful tool and sufficiently reproduce the observed spectral appearance, they can hardly be used for more than measuring parameters. One major obstacle is their inconsistency between the calculated radiation field and the wind stratification due to the usage of prescribed mass-loss rates and wind-velocity fields. Aims. We present the concepts for a new generation of hydrodynamically consistent non-local thermodynamical equilibrium (nonLTE) stellar atmosphere models that allow for detailed studies of radiation-driven stellar winds. As a first demonstration, this new kind of model is applied to a massive O star. Methods. Based on earlier works, the PoWR code has been extended with the option to consistently solve the hydrodynamic equation together with the statistical equations and the radiative transfer in order to obtain a hydrodynamically consistent atmosphere stratification. In these models, the whole velocity field is iteratively updated together with an adjustment of the mass-loss rate. Results. The concepts for obtaining hydrodynamically consistent models using a comoving-frame radiative transfer are outlined. To provide a useful benchmark, we present a demonstration model, which was motivated to describe the well-studied O4 supergiant zeta Pup. The obtained stellar and wind parameters are within the current range of literature values. Conclusions. For the first time, the PoWR code has been used to obtain a hydrodynamically consistent model for a massive O star. This has been achieved by a profound revision of earlier concepts used for Wolf-Rayet stars. The velocity field is shaped by various elements contributing to the radiative acceleration, especially in the outer wind. The results further indicate that for more dense winds deviations from a standard beta-law occur.
Aims. To gain a realistic picture of the donor star in Vela X-1, we constructed a hydrodynamically consistent atmosphere model describing the wind stratification while properly reproducing the observed donor spectrum. To investigate how X-ray illumination affects the stellar wind, we calculated additional models for different X-ray luminosity regimes. Methods. We used the recently updated version of the Potsdam Wolf-Rayet code to consistently solve the hydrodynamic equation together with the statistical equations and the radiative transfer. Results. The wind flow in Vela X-1 is driven by ions from various elements, with Fe III and S III leading in the outer wind. The model-predicted mass-loss rate is in line with earlier empirical studies. The mass-loss rate is almost unaffected by the presence of the accreting NS in the wind. The terminal wind velocity is confirmed at u(infinity) approximate to 600 km s(-1). On the other hand, the wind velocity in the inner region where the NS is located is only approximate to 100 km s(-1), which is not expected on the basis of a standard beta-velocity law. In models with an enhanced level of X-rays, the velocity field in the outer wind can be altered. If the X-ray flux is too high, the acceleration breaks down because the ionization increases. Conclusions. Accounting for radiation hydrodynamics, our Vela X-1 donor atmosphere model reveals a low wind speed at the NS location, and it provides quantitative information on wind driving in this important HMXB.
The Galactic WC stars Stellar parameters from spectral analyses indicate a new evolutionary sequence
(2012)
Context. The life cycles of massive stars from the main sequence to their explosion as supernovae or gamma ray bursts are not yet fully clear, and the empirical results from spectral analyses are partly in conflict with current evolutionary models. The spectral analysis of Wolf-Rayet stars requires the detailed modeling of expanding stellar atmospheres in non-LTE. The Galactic WN stars have been comprehensively analyzed with such models of the latest stage of sophistication, while a similarly comprehensive study of the Galactic WC sample remains undone.
Aims. We aim to establish the stellar parameters and mass-loss rates of the Galactic WC stars. These data provide the empirical basis of studies of (i) the role of WC stars in the evolution of massive stars, (ii) the wind-driving mechanisms, and (iii) the feedback of WC stars as input to models of the chemical and dynamical evolution of galaxies.
Methods. We analyze the nearly complete sample of un-obscured Galactic WC stars, using optical spectra as well as ultraviolet spectra when available. The observations are fitted with theoretical spectra, using the Potsdam Wolf-Rayet (PoWR) model atmosphere code. A large grid of line-blanked models has been established for the range of WC subtypes WC4 - WC8, and smaller grids for the WC9 parameter domain. Both WO stars and WN/WC transit types are also analyzed using special models.
Results. Stellar and atmospheric parameters are derived for more than 50 Galactic WC and two WO stars, covering almost the whole Galactic WC population as far as the stars are single, and un-obscured in the visual. In the Hertzsprung-Russell diagram, the WC stars reside between the hydrogen and the helium zero-age main sequences, having luminosities L from 10(4.9) to 10(5.6) L-circle dot. The mass-loss rates scale very tightly with L-0.8. The two WO stars in our sample turn out to be outstandingly hot (approximate to 200 kK) and do not fit into the WC scheme.
Conclusions. By comparing the empirical WC positions in the Hertzsprung-Russell diagram with evolutionary models, and from recent supernova statistics, we conclude that WC stars have evolved from initial masses between 20 solar masses and 45 M-circle dot. In contrast to previous assumptions, it seems that WC stars in general do not descend from the most massive stars. Only the WO stars might stem from progenitors that have been initially more massive than 45 M-circle dot.
In the last decades, stellar atmosphere codes have become a key tool in understanding massive stars, including precise calculations of stellar and wind parameters, such as temperature, massloss rate, and terminal wind velocity. Nevertheless, for these models the hydrodynamic equation is not solved in the wind. Motivated by the results of the CAK theory, the models typically use a beta velocity law, which however turns out not to be adequate for stars with very strong winds, and treat the mass-loss rate as a free parameter. In a new branch of the Potsdam Wolf-Rayet model atmosphere (PoWR) code, we solve the hydrodynamic equation consistently throughout the stellar atmosphere. The PoWR code performs the calculation of the radiative force without approximations (e.g. Sobolev). We show the impact of hydrodynamically consistent modelling on OB and WR stars in comparison to conventional models and discuss the obtained velocity fields and their impact on the observed spectral lines.
Context. SAO 244567, the exciting star of the Stingray nebula, is rapidly evolving. Previous analyses suggested that it has heated up from an effective temperature of about 21 kK in 1971 to over 50 kK in the 1990s. Canonical post-asymptotic giant branch evolution suggests a relatively high mass while previous analyses indicate a low-mass star.
Aims. A comprehensive model-atmosphere analysis of UV and optical spectra taken during 1988-2006 should reveal the detailed temporal evolution of its atmospheric parameters and provide explanations for the unusually fast evolution.
Methods. Fitting line profiles from static and expanding non-LTE model atmospheres to the observed spectra allowed us to study the temporal change of effective temperature, surface gravity, mass-loss rate, and terminal wind velocity. In addition, we determined the chemical composition of the atmosphere.
Results. We find that the central star has steadily increased its effective temperature from 38 kK in 1988 to a peak value of 60 kK in 2002. During the same time, the star was contracting, as concluded from an increase in surface gravity from log g = 4.8 to 6.0 and a drop in luminosity. Simultaneously, the mass-loss rate declined from log(M/M-circle dot yr(-1)) = -9.0 to -11.6 and the terminal wind velocity increased from v(infinity) = 1800 km s(-1) to 2800 km s(-1). Since around 2002, the star stopped heating and has cooled down again to 55 kK by 2006. It has a largely solar surface composition with the exception of slightly subsolar carbon, phosphorus, and sulfur. The results are discussed by considering different evolutionary scenarios.
Conclusions. The position of SAO 244567 in the log T-eff-log g plane places the star in the region of sdO stars. By comparison with stellar-evolution calculations, we confirm that SAO 244567 must be a low-mass star (M < 0.55 M-circle dot). However, the slow evolution of the respective stellar evolutionary models is in strong contrast to the observed fast evolution and the young planetary nebula with a kinematical age of only about 1000 years. We speculate that the star could be a late He-shell flash object. Alternatively, it could be the outcome of close-binary evolution. Then SAD 244567 would be a low-mass (0.354 M-circle dot) helium pre-white dwarf after the common-envelope phase, during which the planetary nebula was ejected.
The Magellanic Bridge, stretching between the Small and the Large Magellanic Cloud (SMC and LMC), is the nearest tidally stripped intergalactic environment. The Bridge has a significantly low average metallicity of Z less than or similar to 0.1 Z(circle dot). Here we report the first discovery of O-type stars in the Magellanic Bridge. Three massive O stars were identified thanks to the archival spectra obtained by the ESO's Very Large Telescope FLAMES instrument. We analyze the spectra of each star using the Potsdam Wolf-Rayet (PoWR) non-local thermodynamic equilibrium model atmosphere code, which provides the physical parameters, ionizing photon fluxes, and surface abundances. The ages of the newly discovered O stars suggest that star formation in the Bridge is ongoing. Furthermore, the discovery of O stars in the Bridge implies that tidally stripped galactic tails containing low-density but highly dynamical gas are capable of producing massive O stars. The multi-epoch spectra indicate that all three O stars are binaries. Despite their spatial proximity to one another, these O stars are chemically distinct. One of them is a fast-rotating giant with nearly LMC-like abundances. The other two are main-sequence stars that rotate extremely slowly and are strongly metal depleted. We discover the most nitrogen-poor O star known to date. Taking into account the previous analyses of B stars in the Bridge, we interpret the various metal abundances as the signature of a chemically inhomogeneous interstellar medium (ISM), suggesting that the Bridge gas might have accreted during multiple episodes of tidal interaction between the Clouds. Attributing the lowest derived metal content to the primordial gas, the time of the initial formation of the Bridge may date back several billion years. Using the Gaia and Galex color-magnitude diagrams, we roughly estimate the total number of O stars in the Bridge and their total ionizing radiation. Comparing this with the energetics of the diffuse ISM, we find that the contribution of the hot stars to the ionizing radiation field in the Bridge is less than 10% and conclude that the main sources of ionizing photons are leaks from the LMC and SMC. We estimate a lower limit for the fraction of ionizing radiation that escapes from these two dwarf galaxies.
Stars that start their lives with spectral types O and early B are the progenitors of core-collapse supernovae, long gamma-ray bursts, neutron stars, and black holes. These massive stars are the primary sources of stellar feedback in star-forming galaxies. At low metallicities, the properties of massive stars and their evolution are not yet fully explored. Here we report a spectroscopic study of 320 massive stars of spectral types O (23 stars) and B (297 stars) in the Wing of the Small Magellanic Cloud (SMC). The spectra, which we obtained with the ESO Very Large Telescope, were analyzed using state-of-the-art stellar atmosphere models, and the stellar parameters were determined. We find that the stellar winds of our sample stars are generally much weaker than theoretically expected. The stellar rotation rates show broad, tentatively bimodal distributions. The upper Hertzsprung-Russell diagram (HRD) is well populated by the stars of our sample from a specific field in the SMC Wing. A few very luminous O stars are found close to the main sequence, while all other, slightly evolved stars obey a strict luminosity limit. Considering additional massive stars in evolved stages, with published parameters and located all over the SMC, essentially confirms this picture. The comparison with single-star evolutionary tracks suggests a dichotomy in the fate of massive stars in the SMC. Only stars with an initial mass below similar to 30 M-circle dot seem to evolve from the main sequence to the cool side of the HRD to become a red supergiant and to explode as type II-P supernova. In contrast, stars with initially more than similar to 30 M-circle dot appear to stay always hot and might evolve quasi chemically homogeneously, finally collapsing to relatively massive black holes. However, we find no indication that chemical mixing is correlated with rapid rotation. We measured the key parameters of stellar feedback and established the links between the rates of star formation and supernovae. Our study demonstrates that in metal-poor environments stellar feedback is dominated by core-collapse supernovae in combination with winds and ionizing radiation supplied by a few of the most massive stars. We found indications of the stochastic mode of massive star formation, where the resulting stellar population is fully capable of producing large-scale structures such as the supergiant shell SMC-SGS 1 in the Wing. The low level of feedback in metal-poor stellar populations allows star formation episodes to persist over long timescales.
Context. Clusters or associations of early-type stars are often associated with a "superbubble" of hot gas. The formation of such superbubbles is caused by the feedback from massive stars. The complex N206 in the Large Magellanic Cloud (LMC) exhibits a superbubble and a rich massive star population. Aims. Our goal is to perform quantitative spectral analyses of all massive stars associated with the N206 superbubble in order to determine their stellar and wind parameters. We compare the superbubble energy budget to the stellar energy input and discuss the star formation history of the region. Results. We present the stellar and wind parameters of the OB stars and the two Wolf-Rayet (WR) binaries in the N206 complex. Twelve percent of the sample show Oe/Be type emission lines, although most of them appear to rotate far below critical. We found eight runaway stars based on their radial velocity. The wind-momentum luminosity relation of our OB sample is consistent with the expectations. The Hertzsprung-Russell diagram (HRD) of the OB stars reveals a large age spread (1-30 Myr), suggesting different episodes of star formation in the complex. The youngest stars are concentrated in the inner part of the complex, while the older OB stars are scattered over outer regions. We derived the present day mass function for the entire N206 complex as well as for the cluster NGC2018. The total ionizing photon flux produced by all massive stars in the N206 complex is Q(0) approximate to 5 x 10(50) s(-1), and the mechanical luminosity of their stellar winds amounts to L-mec = 1.7 x 10(38) erg s(-1). Three very massive Of stars are found to dominate the feedback among 164 OB stars in the sample. The two WR winds alone release about as much mechanical luminosity as the whole OB star sample. The cumulative mechanical feedback from all massive stellar winds is comparable to the combined mechanical energy of the supernova explosions that likely occurred in the complex. Accounting also for the WR wind and supernovae, the mechanical input over the last five Myr is approximate to 2.3 x 10(52) erg. Conclusions. The N206 complex in the LMC has undergone star formation episodes since more than 30 Myr ago. From the spectral analyses of its massive star population, we derive a current star formation rate of 2.2 x 10(-3) M-circle dot yr(-1). From the combined input of mechanical energy from all stellar winds, only a minor fraction is emitted in the form of X-rays. The corresponding input accumulated over a long time also exceeds the current energy content of the complex by more than a factor of five. The morphology of the complex suggests a leakage of hot gas from the superbubble.