Wind Momentum-luminosity Relation Research Articles

Combined spectroscopy and intensity interferometry to determine the distances of the blue supergiants P Cygni and Rigel

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.

Intensity interferometry of P Cygni in the H α emission line: towards distance calibration of LBV supergiant stars

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.

Stellar population of the superbubble N 206 in the LMC

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 N 206 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 N 206 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. Methods. We observed the massive stars in the N 206 complex using the multi-object spectrograph FLAMES at ESO’s Very Large Telescope (VLT). Available ultra-violet (UV) spectra from archives are also used. The spectral analysis is performed with Potsdam Wolf–Rayet (PoWR) model atmospheres by reproducing the observations with the synthetic spectra. Results. We present the stellar and wind parameters of the OB stars and the two Wolf–Rayet (WR) binaries in the N 206 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 N 206 complex as well as for the cluster NGC 2018. The total ionizing photon flux produced by all massive stars in the N 206 complex is Q0 ≈ 5 × 1050 s−1, and the mechanical luminosity of their stellar winds amounts to Lmec = 1.7 × 1038 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 ≈ 2.3 × 1052 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 × 10−3 M⊙ 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.

Modeling the early evolution of massive OB stars with an experimental wind routine

Stellar evolution models of massive stars are very sensitive to the adopted mass-loss scheme. The magnitude and evolution of mass-loss rates significantly affect the main sequence evolution, and the properties of post-main sequence objects, including their rotational velocities. Driven by potential discrepancies between theoretically predicted and observationally derived mass-loss rates in the OB star range, we particularly aim to investigate the response to mass-loss rates that are lower than currently adopted, in parallel with the mass-loss behavior at the "first" bi-stability jump. We perform 1D hydrodynamical model calculations of single $20 - 60 \, M_{\odot}$ Galactic ($Z = 0.014$) stars where the effects of stellar winds are already significant during the main sequence phase. We develop an experimental wind routine to examine the behavior and response of the models under the influence of different mass-loss rates. This observationally guided, simple and flexible wind routine is not a new mass-loss description but a useful tool based on the Wind-momentum Luminosity Relation and other scaling relations, and provides a meaningful base for various tests and comparisons. The main result of this study indicates a dichotomy when accounting for currently debated problems regarding mass-loss rates of hot massive stars. In a fully diffusive approach, and for commonly adopted initial rotational velocities, lower mass-loss rates than theoretically predicted require to invoke an additional source of angular momentum loss (either due to bi-stability braking, or yet unidentified) to brake down surface rotational velocities. [...]

Analysis of Galactic late-type O dwarfs: more constraints on the weak wind problem

<i>Aims. <i/>We investigate the stellar and wind properties of a sample of late-type O dwarfs. Previous analyses of such stars have found very low mass-loss rates; rates much lower than predicted by theory (the weak wind problem).<i>Methods. <i/>Far-UV to optical spectra of five Galactic O stars were analyzed: HD 216898 (O9IV/O8.5V), HD 326329 (O9V), HD 66788 (O8V/O9V), <i>ζ<i/> Oph (O9.5Vnn), and HD 216532 (O8.5V((n))). We used a grid of TLUSTY models to obtain effective temperatures, gravities, rotational velocities, and to identify wind lines. Wind parameters for each object were obtained using expanding atmosphere models calculated with the CMFGEN code.<i>Results. <i/>The spectra of our sample have primarily a photospheric origin. A weak wind signature is seen in C iv 1548, 1551, from which mass-loss rates consistent with previous CMFGEN results for O8-O9V stars were derived ( yr<sup>-1<sup/>). A discrepancy of roughly two orders of magnitude is found between these mass-loss rates and the values predicted by theory (), confirming a breakdown or a steepening of the modified wind momentum-luminosity relation at log . We have estimated the carbon abundance for the stars of our sample and concluded that its value cannot be reduced to sufficiently small values to solve the <i>weak wind problem<i/>. Upper limits on were established for all objects using lines of different ions: P v 1118, 1128, C iii , N v 1239, 1243, Si iv 1394, 1403, and N iv <i>λ<i/>1718. All the values obtained are in disagreement with theoretical predictions, bringing support to the reality of <i>weak winds<i/>. Together with C iv 1548, 1551, the use of N v 1239, 1243 results in the lowest mass-loss rates: the upper limits indicate that must be <i>less<i/> than about -1.0 dex . Upper mass-loss rate limits obtained for other transitions are also low: they indicate that must be <i>less<i/> than about (-0.5 <i>±<i/> 0.2) dex . We studied the behavior of the H<i>α<i/> line with different mass-loss rates. For two stars, only models with very low 's provide the best fit to the UV and optical spectra. We also explored ways to fit the observed spectra with the theoretical mass-loss rates. By using large amounts of X-rays, we could reduce the predicted wind emission to the observed levels. However, unrealistic X-ray luminosities had to be used (log ). The validity of the models used in our analyses is discussed.

The Metallicity Dependence of the Mass Loss of Early-Type Massive Stars

AbstractWe report on a comprehensive study of the wind properties of 115 O- and early B-type stars in the Galaxy and the Large Magellanic Clouds. This work is part of the VLT/FLAMES Survey of Massive Stars. The data is used to construct the empirical dependence of the mass-loss in stellar winds on the metal content of their atmospheres. The metal content of early-type stars in the Magellanic Clouds is discussed. Assuming a power-law dependence of mass loss on metal content, Ṁ ∝ Zm, we find m = 0.83 ± 0.16 from an analysis of the wind momentum luminosity relation (Mokiem et al. 2007b). This result is in good agreement with the prediction m = 0.69 ± 0.10 by Vink et al. (2001). Though the scaling agrees, the absolute empirical value of mass loss is found to be a factor of two higher than predictions. This may be explained by a modest amount of clumping in the outflows of the objects studied.

The most massive stars in the Arches cluster

Aims. We study a sample composed of 28 of the brightest stars in the Arches cluster. Our aim is to constrain their stellar and wind properties and to establish their nature and evolutionary status. Methods. We analyze K-band spectra obtained with the integral field spectrograph SINFONI on the VLT. Atmosphere models computed with the code CMFGEN are used to derive the effective temperatures, luminosities, stellar abundances, mass loss rates and wind terminal velocities. Results. We find that the stars in our sample are either H-rich WN7-9 stars (WN7-9h) or supergiants, where two are classified as OIf + . All stars are 2-4 Myr old. There is marginal evidence for a younger age among the most massive stars. The WN7-9h stars reach luminosities as high as 2 x 10 6 L ⊙ , consistent with initial masses of ∼120 M ⊙ . They are still quite H-rich, but show both N enhancement and C depletion. They are thus identified as core H-burning objects showing products of the CNO equilibrium on their surface. Their progenitors are most likely supergiants of spectral types earlier than 04-6 and initial masses >60 M ⊙ . Their winds follow a well-defined modified wind momentum - luminosity relation (WLR): this is a strong indication that they are radiatively driven. Stellar abundances tend to favor a slightly super-solar metallicity, at least for the lightest metals. We note, however, that the evolutionary models seem to under-predict the degree of N enrichment.

The empirical metallicity dependence of the mass-loss rate of O- and early B-type stars

[Abridged] We present a comprehensive study of the metallicity dependence of the mass-loss rates in stationary stellar winds of hot massive stars. Assuming a power-law dependence of mass loss on metallicity, Mdot \propto Z^{m}, and adopting a theoretical relation between the terminal velocity and metallicity, v_inf \propto Z^{0.13} (Leitherer et al.), we find m = 0.83 +/- 0.16 for non-clumped outflows from an analysis of the wind momentum luminosity relation (WLR) for stars more luminous than 10^{5.2} Lsun. Within the errors, this result agrees with the prediction of m = 0.69 +/- 0.10 from Vink et al. For the high luminosity stars we find the mass loss rates to be greater than the predictions, implying wind clumping factors in their line-forming regions of ~4. For lower luminosity stars, the winds are so weak that their strengths cannot be reliably derived from optical lines, and one must rely on analysis of UV lines. In the low-luminosity domain the Galactic WLR is found to be much steeper than expected from theory, leading to a discrepancy between UV mass-loss rates and the predictions by a factor 100 at luminosities of L ~ 10^{4.75} Lsun, the origin of which is unknown. We emphasize that even if the current mass-loss rates of hot luminous stars are overestimated as a result of wind clumping, the degree of clumping would likely to be independent of metallicity, so the scalings derived in this study are expected to remain correct.

Puzzling wind properties of young massive stars in SMC-N81

We present a quantitative study of massive stars in the High Excitation Blob N81, a compact star forming region in the SMC. The stellar content was resolved by HST, and STIS was used to obtain medium resolution spectra. The qual- itative analysis of the stellar properties presented in Heydari-Malayeri et al. (2002a) is extended using non-LTE spherically extended atmosphere models including line-blanketing computed with the code CMFGEN (Hillier & Miller 1998), and the wind properties are investigated. The main results are the following: - The SMC-N81 components are young (∼0-4 Myrs) O stars with effective temperatures compatible with medium to late subtypes and with luminosities lower than those of average Galactic O dwarfs, rendering them possible ZAMS candidates. - The winds are extremely weak: with values of the order of 10 −8 /10 −9 Myr −1 the mass loss rates are lower than observed so far for Galactic dwarfs. Only the recent study of SMC stars by Bouret et al. (2003) show the same trend. The modified wind momenta ( u M v∞ √ R) are also 1 to 2 orders of magnitude lower than observed for Galactic stars. Both the mass loss rates and the modified wind momenta are lower than the predictions of the most recent hydrodynamical models. The accuracy of the UV based mass loss rate determination, relying in particular on the predicted ionisation fractions, are carefully examined. We find that u M could be underestimated by a factor of up to 10. Even in this unlikely case, the above conclusions remain valid qualitatively. The reasons for such weak winds are investigated with special emphasis on the modified wind momenta: - There may be a break-down of the wind momentum-luminosity relation (WLR) for dwarf stars at low luminosity (log L/L� < 5.5). However, reasons for such a breakdown remain unknown. - The slope of the WLR may be steeper at low metallicity. This is predicted by the radiation driven wind theory, but the current hydrodynamical simulations do not show any change of the slope at SMC metallicity. Moreover, there are indications that some Galactic objects have wind momenta similar to those of the SMC stars. - Decoupling may take place in the atmosphere of the SMC-N81 stars, leading to multicomponent winds. However, various tests indicate that this is not likely to be the case. The origin of the weakness of the wind observed in the SMC-N81 stars remains unknown. We suggest that this weakness may be linked with the youth of these stars and represents possibly the onset of stellar winds in recently formed massive stars.

Stellar and wind parameters of Galactic O-stars

We have re-analyzed the Galactic O-star sample from Puls et al. (1996) by means of line-blanketed NLTE model atmospheres in order to investigate the influence of line-blocking/blanketing on the derived parameters. The analysis has been carried out by fitting the photospheric and wind lines from H and He. In most cases we obtained a good fit, but we have also found certain inconsistencies which are probably related to a still inadequate treatment of the wind structure. These inconsistencies comprise the line cores of H γ and H β in supergiants (the synthetic profiles are too weak when the mass-loss rate is determined by matching H α ) and the generalized dilution effect (cf. Voels et al. 1989) which is still present in He I 4471 of cooler supergiants and giants. Compared to pure H/He plane-parallel models we found a decrease in effective temperatures which is largest at earliest spectral types and for supergiants (with a maximum shift of roughly 8000 K). This finding is explained by the fact that line-blanketed models of hot stars have photospheric He ionization fractions similar to those from unblanketed models at higher T eff and higher log g. Consequently, any line-blanketed analysis based on the He ionization equilibrium results in lower T eff -values along with a reduction of either log g or helium abundance (if the reduction of log g is prohibited by the Balmer line wings). Stellar radii and mass-loss rates, on the other hand, remain more or less unaffected by line-blanketing. We have calculated new spectroscopic masses and compared them with previous results. Although the former mass discrepancy (Herrero et al. 1992) becomes significantly reduced, a systematic trend for masses below 50 M ○. seems to remain: The spectroscopically derived values are smaller than the evolutionary masses by roughly 10 M ○. . Additionally, a significant fraction of our sample stars stays over-abundant in He, although the actual values were found to be lower than previously determined. Also the wind-momentum luminosity relation (WLR) changes because of lower luminosities and almost unmodified wind-momentum rates. Compared to previous results, the separation of the WLR as a function of luminosity class is still present but now the WLR for giants/dwarfs is consistent with theoretical predictions. We argue that the derived mass-loss rates of stars with H α in emission are affected by clumping in the lower wind region. If the predictions from different and independent theoretical simulations (Vink et al. 2000; Pauldrach et al. 2003; Puls et al. 2003a) that the WLR should be independent of luminosity class were correct, a typical clumping factor / 2 5 should be derived by unifying the different WLRs.

Advances in radiatively driven wind models

We report on a re-analysis of the Galactic O-type star sample presented by Puls et al. (1996) by means of non-LTE model atmospheres including line-blocking and line-blanketing. In particular, we concentrate on the question concerning the dependence of the wind-momentum luminosity relation (WLR) on luminosity class. Owing to the line-blanketing, the derived effective temperatures become significantly lower when compared to previous results, whereas the so-called ‘modified wind-momentum rates’ remain roughly at their former values. Therefore, we obtain a new WLR for O-type stars. By comparing these ‘observational’ results with new theoretical predictions and simulations, we conclude that the Hα forming region for objects with Hα in emission might be considerably clumped and thus a larger mass-loss rate than actually present is mimicked. We suggest that the previously found dependence of the WLR on luminosity class is an artefact.

High Dynamic Imaging of Luminous Massive Stars

Hot massive stars constitute an important class of objects among stellar populations. Diffraction limited high dynamic imaging (HDI) with 8-10 m class telescopes of fine structures which often characterize their extended nebulosities can trace back the history of their mass-loss, therefore the evolution of the central star across the HRD. Since these stars are among the most luminous stars and display unique emission spectral features in galaxies at high redshift, they can serve as natural candles to estimate cosmological distances through the Wind-momentum Luminosity Relation (WLR, Kudritzki et al. 2000). In this paper I develop the context of massive stars HDI and derive some general instrumental specifications for coronagraphic adaptive optics.

Spectroscopic analysis of new-born massive stars in SMC N 81

We present the first results of a spectroscopic study of young massive stars in the SMC high excitation blob N 81. These stars have Mv values which are ~ 2 mag smaller than those of normal dwarf stars. Their UV HST-stis spectra reveal features typical of O-type stars, but surprisingly weak wind components. The preliminary modeling of these spectra with the code cmfgen (Hillier &amp; Miller 1998) indicates mass loss rates of the order of 10–9 M⊙ yr–1. If confirmed, such a weak wind may indicate either a breakdown of the wind-momentum luminosity relation at low luminosity, or a steeper slope of this relation at low metallicity.

Rotation and the wind momentum-luminosity relation for extragalactic distances

The effects of axial stellar rotation on the wind-momentum relation (WLR) for determining the extragalactic distances are investigated. Despite the fact that the mass loss rates grow quite a lot with rotation, remarkably the effects on the WLR are found to be very small on average. As an example, for an average orientation angle between the rotation axis and the line of sight, the luminosity would be overestimated by 5.9% for a star rotating at 90% of its break-up rotational velocity. Different orientation angles between the rotation axis and the line of sight produce some limited scatter.

Mass‐Loss Rates and Stellar Wind Momenta of A‐Supergiants in M31: First Results from the Keck HIRES Spectrograph

High-quality Keck HIRES echelle spectra of two A-supergiants in M31, designated 41-3654 (spectral type A2 Ia-O) and 41-3712 (A3 Ia-O), at 10.2 kpc galactocentric distance are analyzed by means of NLTE unified model atmospheres to determine the properties of their stellar winds, in particular the wind momenta. We obtain mass-loss rates of 1.9 × 10-6 and 1.1 × 10-6 M☉ yr-1 for 41-3654 and 41-3712, respectively, with an accuracy of 15% from the fit of the Hα profiles. The terminal velocities are 200 ± 25 km s-1. In addition, the exponents of the wind velocity fields are determined (β = 2 and 3, respectively) and microturbulent velocities of the order of 20 km s-1 are found. The wind momenta of the two targets are in excellent agreement with the wind momentum-luminosity relation (WLR) for galactic A- and B-supergiants. We discuss the potential of the WLR for extragalactic distance determinations and conclude that it may allow independent distance moduli to be obtained with an accuracy of 10%.