Massive-star winds in the Tarantula Nebula

Transcription

1 Massive-star winds in the Tarantula Nebula T. Bagnoli Supervised by: Alex de Koter & Hugues Sana Astronomical Institute Anton Pannekoek August 30, 20

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3 i Abstract The role of stellar winds is of paramount importance in massive stars: it shapes their evolutionary tracks, it affects the upper limit to their mass, and it determines the end product of their lives (neutron stars, black holes, possibly LGRBs). A key unresolved issue is how to reconnect the relatively well understood winds of OB-type stars with those of more extreme objects: the Of, Of/WN and WN stars. Growing evidence seems to point at these high-luminosity objects having radiatively-driven winds just like their less massive counterparts, but a unified parametrization of mass loss over such a broad range of stars still lacks. Using VLT-FLAMES spectra of a sample of 3 of the brightest stars in the Tarantula Nebula, we investigated the possibility that the Eddington factor Γ e, which measures the importance of the radiation field, is the main parameter of a mass-loss recipe encompassing O, Of, Of/WN and Wolf-Rayet stars altogether, as well as the setter for the boundaries between these different stages. Our fastwind-based fitting method proved excellently in fitting O-type stars spectra and yielded acceptable results for the intermediate Of and Of/WN stages, but ultimately failed to reproduce WN spectra, which means that the highest Γ e regime could not be explored. Regarding the succesfully constrained Γ e range, we only observe a weak agreement with the theory, as a significant spread in mass-loss rates is present in our sample, although this may be due to the rather large photometric uncertainties that affect our estimate of the luminosity.

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5 Contents Introduction. Massive stars and their winds O-, Of- and slash stars Wolf-Rayet stars Wind diagnostics Winds of O-type and WR stars A Mass-loss recipe The metallicity dependence Ṁ(Γ e ) The data 9 2. The VLT-FLAMES Tarantula Survey Overview and scientific motivation Observations This sample Data selection Data reduction Spectral classification and v rad determination Automated fitting using a genetic algorithm 7 3. The fitting method fastwind The GA The fit parameters Fitness of a model Errors Results Degeneracies T eff and Y He Ṁ and β The fits - Results O stars Of and WN stars iii

6 iv CONTENTS 5 Discussion and Conclusions Mass determination The mass discrepancy Mass-Luminosity relation Wind properties Mass-loss and the wind-momentum-luminosity relation Mass loss and clumping The Ṁ(Γ e) relation Conclusions Appendices A Atlas 59 B Evolutionary tracks 9

7 Chapter Introduction. Massive stars and their winds Stars ending their lives in a core-collapse supernova explosion are referred to as massive stars. Roughly speaking, they have initial masses above 8 M (Kudritzki and Puls, 2000). They are extremely rare: for each 20 M star in the Galaxy there are almost a hundred thousand solar-type stars. Moreover, massive stars are comparatively short lived: due to enhanced nuclear burning thanks to their higher internal temperatures, their main-sequence lives are about a thousand times shorter than those of low-mass stars. Despite their rarity, they have properties of paramount importance for the interstellar medium (ISM), star formation and evolution of galaxies. Their powerful outputs, both in terms of gas flow and radiation fields, are responsible for ionizing the ISM and enriching it with nuclear-processed material, as well as for stopping further stellar formation in neighbouring clusters, dispersing the surrounding gas. In most cases their lives end in a supernova event, an explosion taking place after gravitational collapse of the iron core, where nuclear fusion can no longer provide the sustaining force. With typical energies of 0 5 erg (Woosley and Weaver, 986) supernovae can easily outshine their host galaxy for a few seconds, and they seem likely to power the most energetic phenomena in the universe, the gamma-ray bursts, when collapse happens in a sufficiently-fast rotating core that is only surrounded by a tiny envelope (Woosley, 993; Bloom et al., 2002; Price et al., 2002). The compact remnants they leave behind, neutron stars and black holes, are home to the most extreme physics in the universe. On cosmological scales, massive stars are thought of having reionized the early universe (Johnson et al., 2008), and even triggered initial galaxy formation. To assess the role played by massive stars in such a wide range of phenomena we need a careful determination of their behaviour during their evolution. However, unlike for their better-understood, less-massive counterparts, the evolution of a (single) massive star is complicated by the presence of strong winds resulting in very high mass-loss rates Ṁ (up to 0 4 M yr ) which can lead to shedding of a significant fraction of the initial mass and angular momentum, on such a drastically large scale (a very massive star may lose half its mass already during its main-sequence lifetime) that the evolution of a massive star is actually believed to be driven by its mass loss (De Loore et al., 977, 978; Chiosi et al., 978). The complications of mass loss are in fact the primary difficulty in modelling massive

8 2 CHAPTER. INTRODUCTION star evolution. The parametrization of mass loss on physical parameters is still somewhat uncertain even during the main sequence (MS). The winds are likely being radiatively driven, i.e. they are due to momentum transfer through radiation pressure on spectral lines (first put forward by Lucy and Solomon, 970; for a recent review see Puls et al., 2008), which suggests metallicity would be of pivotal importance in determining the mass-loss rates of massive stars, as heavier elements absorb radiation more efficiently, thanks to a larger number of lines. However mass-loss seems to have a complicated and often counterintuitive interplay with other factors affecting stellar evolution as well. For example fast rotation, reducing the effective gravity, enhances mass loss, although this in turn spins down the star by mechanically removing angular momentum. Also, although iron (Fe) seems to be the most relevant element in line absorption thanks to the hundreds of thousands of spectral lines of its ions, other elements (e.g. CNO products like carbon and nitrogen) could be more relevant in metal-poor environments (Gräfener and Hamann, 2008), in fact reducing the Z-dependency of mass-loss rates. For evolved stars, characterizing the mass-loss rate becomes even more problematic. Luminous blue variables (LBVs) show episodic and huge mass-loss stages whose origin is poorly understood. Wolf-Rayet stars (WRs) show winds with the highest mass-loss rates of all highmass stars, but determining their physical properties relies heavily on the assumptions made in modelling their atmospheres. Despite the driving mechanism is still thought to be the same as in MS stars, it is uncertain to what extent the mass-loss rate would depend on Z in evolved stars, as their surface abundances are clearly the result of mixing of products of their own burning. The occurrence of these stages of extreme mass-loss in a massive star eventually leads to envelope-shedding as near-eddington luminosities are approached (Vink et al., 20), but a precise parametrization of the occurrence of these stages has not yet been achieved. Modelling the evolution of massive stars is an utterly complicated and still openly-debated problem in astrophysics, and a precise establishment of their mass-loss behaviour is a fundamental part of it... O-, Of- and slash stars Massive stars burn hydrogen into helium during the MS via the CNO cycle. The class of O-type stars is defined by the appearance of He ii absorption lines, particularly the Pickering series (λλ 4200, 4542, 54), distinguishing them from the colder B-type stars. Their effective temperatures T eff range from to K. Their atmospheric conditions, both in terms of temperature and density are such that non local-thermodynamic-equilibrium (NLTE) effects become important. Subclasses, ranging from O2 to O9.7, are further defined based on the ratio of the He ii λ 454 and He i λ 447 lines in the mid- and late-subtypes, while the relative strength of the N iii and N iv ions is the main criterion in the earliest subtypes (Walborn et al., 2002). The Of subclass is defined as showing the N iii λλ multiplet in emission. The further subcategories ((f)), (f) and f correspond respectively to strong He ii absorption with weak N iii emission, weak He ii absorption with strong N iii emission and both features strongly in emission. Analogous subdivisions apply to the f* class, which shows an N iv λ 4058 emission line stronger than the N iii emission. There is some evidence that the progression

9 .. MASSIVE STARS AND THEIR WINDS 3 from O- to Of-type stars is one in stellar wind densities, i.e. in mass-loss rates (assuming a constant wind terminal velocity v, see Sec...3). It is tempting to establish a further connection to a particular group of WR stars, the high-luminosity, narrow-line, (possibly) still young (i.e. H-rich) H-burning, late-type WN stars, with their increasingly extreme mass-loss rates and wind densities. An intermediate spectroscopic category in this progression is that of the so-called slash stars, showing both an Of-like absorption spectrum and WN-like emission features and therefore classified as e.g. O2If*/WN6. As Crowther and Walborn (20) proposed, O2-3.5If*, O2-3.5If*/WN5-7 and WN5-7 stars may be discerned using the morphology of Hβ to trace increasing wind densities: respectively purely in absorption, P-Cygni and purely in emission...2 Wolf-Rayet stars Wolf-Rayet (WR) stars have spectra dominated by bright, broad emission bands formed in a massive stellar wind. These reflect mass-loss rates as large as M yr, so that the wind is optically thick: photospheric features are not visible, and one merely observes lines superimposed on a hot continuum, both formed in the wind (Crowther, 2007). Clearly any classification system based on such emission lines is more loosely coupled to the stellar parameters. The broadness of the lines and the fact that they are forming out of hydrostatic equilibrium mean that the spectroscopic information on rotational velocity v rot and on surface gravity g is lost. The line shape is more heavily affected by T eff, Ṁ and the wind velocity law. In what has become known as the Conti scenario (Conti, 976; Crowther et al., 995), the most massive O-type stars evolve through intermediate stages as slash or LBV stars (possibly depending on their mass), eventually becoming Wolf-Rayet stars with extended, expanding atmospheres. Although the possible evolutionary paths to this stage are not entirely clear and may likely vary with the initial conditions in mass, metallicity and rotational velocity, WR stars must be fairly evolved objects that have shed off large parts of their envelopes, as shown by their surface chemical abundances. This actually allows for the definition of three subsequences of WR stars, the WN, WC and WO stars, the first featuring enriched abundances of the products of the CNO cycle (H burning) and the latter of triple-α processes (He burning). Hence, despite being exceptionally rare, these stars are greatly responsible for enriching the ISM with nuclear processed material (Gray and Corbally, 2009)...3 Wind diagnostics Mass loss in O and B stars is driven by radiation pressure: winds are initiated and then continuously accelerated by the absorption of photospheric photons in spectral lines until, at very large distances from the star, geometrical dilution of the radiation field progressively stops acceleration, and the terminal velocity v of the wind is reached (for a review, see Kudritzki and Puls, 2000). It has not entirely been secured whether this mechanism applies to LBV and WR stars as well. Obviously line-driven winds depend critically on the abundances of heavy elements, that thanks to their millions of spectral lines are far more efficient absorbers than the yet more

10 4 CHAPTER. INTRODUCTION abundant hydrogen. In the past years the establishment of an empirical mass-loss to metallicity relation has therefore become a fundamental point in spectroscopic studies of massive stars (see Kudritzki et al., 987; Puls et al., 2000; Vink et al., 200). The available methods to determine mass-loss rates rely on either the optical part of the spectrum (chiefly Hα and He ii 4686 Å) or on ultraviolet (UV) resonance lines (a third method, the measurement of the radio continuum flux, is only suitable for nearby stars, due to the detection limits in this band). Unfortunately the strongest UV lines start saturating at mass-loss rates of about 0 7 M yr, which is in turn the lower sensibility limit of Hα. This means these two diagnostics cannot be cross-checked in the regime where they are most sensitive. Furthermore, the ions responsible for UV resonance lines are affected by X-ray emission generating in non-thermal processes such as shock waves (Owocki et al., 994). The Hα and He ii 4686 Å recombination lines do not suffer from saturation or shock induced effects, and are thus normally held a more reliable diagnostic means. However, unlike in the UV, the line emission scales with the square of the density, meaning that density inhomogeneities will boost the line emission (see Puls et al., 2008)...4 Winds of O-type and WR stars Traditional models for radiatively-driven winds (Lucy and Solomon, 970; Castor et al., 975) have provided predictions for the mass-loss behaviour of O-type stars reasonably in agreement with observations. However, they heavily underestimated the mass-loss rates in Of stars, and even more dramatically so in WR stars, where the observed wind momentum seem to be well in excess of the radiation-field momentum. Rather than from fundamental differences in the nature of their outflows, this discrepancy could have arisen from the neglect of multiple line scattering (Puls et al., 996). Progressing from O- type to Of and WR stars, observations seem to point at a mechanical wind momentum in excess of the momentum of the radiation field (first noticed by Barlow et al., 98), with the wind efficiency parameter η = Ṁv /L/c describing the fraction of the momentum of the radiation that is transferred to the ions in the wind growing to values larger than one. In fact, theoretical modelling by Vink et al. (2000) shows that already for high luminosity OB stars the single-scattering treatment is no longer valid: η already exceeds unity for normal OB stars when L/L 6. If the winds are to be radiatively driven photon must start to be scattered multiple times in the increasingly optically-thick winds. This appeared to solve the wind momentum problem at least for the denser O-star winds (Vink et al., 2000)..2 A Mass-loss recipe.2. The metallicity dependence For O-type stars, a fairly good agreement between theoretical predictions of Ṁ(Z) and the analysis of large samples of spectra has been found and tested over a range of metallicities, although it appears to break down in the weak-wind regime (L < L ). Empirically, Mokiem et al. (2007a) have investigated O-type stars in the Galaxy, in the Large Magellanic Cloud (LMC) and in the Small Magellanic Cloud (SMC) finding that the mass-loss rate seems

11 .2. A MASS-LOSS RECIPE 5 to scale with metallicity as Ṁ(Z) Z8±. This is reasonably in agreement with previous theoretical predictions from Vink et al. (200), which put Ṁ(Z) Z 9. If the wind-driving mechanism is the same, a similar behaviour would be expected for WR stars. However, the situation becomes here far more complicated. Besides the aforementioned multiple line-scattering problem, the supposed analogy in the underlying physics would demand that mass-loss rates for WR stars show a similar metallicity dependency to OB stars (although saturation of the lines may in principle weaken the Z dependence). However claimed (Vink and de Koter, 2005), such a relation is yet to be secured, mainly because of a lack of observations spanning a wide range in metallicity. The progression from weaker to stronger wind regimes (O to Of/WN to WN types) is hence still unclear..2.2 Ṁ(Γ e ) A new theoretical approach in the quest for a unified mass-loss recipe for massive stars has started in recent years. This focusses on the role played by the Eddington factor Γ e, the ratio of the stellar luminosity L to the Eddington luminosity, the value of L at which the atmosphere becomes unbound due to the outward push of radiation pressure equalling the inward pull of gravity: Γ e = L L e = χ el 4πcGM. (.) Recent theoretical results (Gräfener and Hamann, 2008) while still agreeing on the importance of metallicity as a scaling factor, predict the Eddington factor to play the dominant role in the mass-loss behaviour of WR stars. The mass-loss rate seems to scale with Γ e (see Fig..). Apparently, for sufficiently large Γ e the mixing of the CNO products to the surface could be a powerful mean to radiatively drive the winds even at very low metallicities if the star is close enough to the Eddington limit. More extensive modelling by Vink et al. (20) has widened the studied mass range, in an attempt to study the behaviour of very massive stars as they approach the Eddington limit. Firstly, they shows that there is an additional mass-loss dependence on the mass, i.e. for fixed Γ e the mass-loss rates grows for increasing mass. Secondly, a smooth transition from O-type to WR-type mass-loss behaviour appears at Γ e (see Fig..2), which is also the point where the wind efficiency parameter η surpasses the single scattering limit, i.e. the threshold above which the wind becomes optically thick. The relations found are Ṁ M 8 Γ 2.2 e for 0.4 < Γ e < Ṁ M 8 Γ 4.77 e for < Γ e < 5. (.2) The much steeper Ṁ vs Γ e relation obtained in the latter regime is in agreement with the Wolf- Rayet model of Gräfener & Hamann (2008). When Γ e approaches unity, the wind efficiency number η smoothly rises to values as high as 3, confirming a natural transition between the mass-loss behaviour of O-type and WR stars. Uncertainties remain, particularly regarding the definition of the Eddington factor, which may be overly simplistic due to the aforementioned reasons. Now that predictions exist, they must be checked against observations. However, at present no homogeneous study of a sizeable sample has been done. Martins et al. (2008) have studied

12 6 CHAPTER. INTRODUCTION Figure.: Gräfener & Hamann (2008). WNL star mass loss from hydrodynamic models, plotted against the Eddington factor Γ e. Figure.2: Vink et al. (20). Predictions for O-type and WR stars mass-loss rates, divided by M, as a function of Γ e. The relation steepens at Γ e =.

13 .2. A MASS-LOSS RECIPE 7 a sample of 28 stars, including both late-type WN stars and O4-O6 stars, but they did not establish object masses. Attribution of mass ranges consistent with the given luminosities would yield values of Γ e about 0.2 for the O4-O6 stars and about 0.4 for the WN stars. High Γ e objects are hence very scarce. The main purpose of this master project is therefore to determine whether a Ṁ(Γ e) empirical relation can be established, whether it agrees with theoretical predictions and how large a luminosity range (O to Of/WN to WN types) can it encompass. Chapter 2 presents the dataset under study in the context of the VLT FLAMES Tarantula Survey and the details of data reduction. In Chapter 3, we explain our spectral analysis method to retrieve the stellar parameters and wind properties, presenting results with fits and comments on the individual targets in Chapter 4. Finally Chapter 5 discusses and summarizes our findings for the main problem under study.

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15 Chapter 2 The data 2. The VLT-FLAMES Tarantula Survey 2.. Overview and scientific motivation 30 Doradus (30 Dor) is the brightest H ii region in the Local Group, comprising at least five distinct generations of star formation (Walborn and Blades, 997). At the heart of 30 Dor resides the massive cluster Radcliffe 36 (R36), rich with young (-2 Myr, de Koter et al., 998) early O-type and WN stars, some of which seem to have masses larger than 50 M (Crowther et al., 200). The distance of 30 Dor is well constrained (distance modulus DM = 8.5, Gibson, 2000) as well as its metallicity (roughly half the solar value, Schaerer et al., 993). All in all, 30 Dor allows us to study a broad age and luminosity range of massive stars within a single complex of star formation. The VLT-FLAMES Tarantula Survey (VTFS, PI: Evans) is an ESO Large Programme that has obtained multi-epoch optical spectroscopy of over 800 massive stars in the 30 Dor region of the Large Magellanic Cloud (LMC). About 300 O-type stars spectra were obtained, together with about 20 slash and WR stars, massively sampling the upper part of the Hertzsprung- Russel diagram (HRD). The rest of the data include more than 400 B-type spectra, and about 50 cooler stars with spectral types A, F and later. I will here (briefly) summarize the scientific motivations for the survey. Stellar wind of the most massive stars As already explained in Sec..2, recent theoretical models seem to point at a dominant role of the Eddington factor Γ in determining mass-loss rates of the most massive stars. This work is a part of the larger effort within the survey atestablishing an empirical Ṁ(Γ) relation to investigate the progression of increasing wind strength from O-type to Of/WN to WN stars. Effects of rotationally induced mixing and rotational velocity distribution Rapid rotation could lead to quasi-chemically homogeneous evolution, giving rise to a rapidly rotating He-core surrounded by only a very tiny H envelope (Meynet and Maeder, 2000). Magnetic torques would then remove only very little angular momentum. Combined with a mass-loss rate hampered by a low metallicity, which would therefore less effectively spin the star 9

16 0 CHAPTER 2. THE DATA down, this might be a viable single-progenitor formation mechanism for long-duration gammaray bursts (LGRB, Yoon et al., 2006). Among other effects, it is predicted that rapid rotation should enhance the nitrogen surface abundance the most, up to a factor ten (Brott et al., 20). For the first time, the VFTS will provide nitrogen abundances and rotational velocities v sin i (where i is the inclination angle of the rotation axis) for a large observational sample of O stars, allowing the determination of the rotational velocity distribution and a thorough study of the effect of rotation on the surface abundances, with important consequences for the feasibility of the single-star LGRB channel at the LMC metallicity. B-type supergiants B-type supergiants rotate at much lower rates than their progenitor O-type dwarfs. It has been proposed that the braking takes place when the cooling star crosses the so-called by-stability jump at K (Vink et al., 999) where a change in the Fe ionization stage boosts the opacity and drives a much stronger wind, which spins down the star. This hypothesis will be tested thanks to the large sample of targets provided by the VFTS in this crucial temperature regime. Binary status and Cluster dynamics The multi-epoch approach of the survey allows for a determination of radial velocity (v rad ) variations down to km/s at best. This will allow a precise establishment of the binary fraction of the sample, a key ingredient for any theory of both star formation and cluster evolution. The v rad determination in the single-star sample will in fact yield a measurement of the velocity dispersion around R36, and thus of the dynamical mass of the cluster, as well as of its central potential and relaxation timescale, i.e. precious information in modelling the cluster dynamics in N-body simulations Observations Optical spectroscopy The VFTS comprises 60 hrs of VLT-FLAMES spectroscopy in the 30 Dor region, giving spectroscopy of 000 targets (reduced to 893 after rejection of foreground stars and insufficientquality spectra). Most of the observations took place between October 2008 and February 2009, with a last epoch obtained in October 2009 to increase chances of detecting intermediate- and long-period binaries (Evans et al., 20, from hereafter Paper I). The primary dataset was obtained feeding the GIRAFFE spectrograph by 32 MEDUSA fibres available for science (or sky) observations across a 25 field. Two other modes of the Fibre Large Array Multi- Element Spectrograph (FLAMES) were employed for R36, but are not discussed here as those observations are not a part of the sub-sample used here. For the description of these supplementary data see Paper I, which the star identifiers refer to. Nine MEDUSA configurations were observed, each of which at three wavelength settings (see Table 2.): LR02, LR03, HR5N. Each of these observational setups have been observed at least at 6, 3 and 2 epochs respectively (with some additional epochs due to operational

17 2.2. THIS SAMPLE GIRAFFE setting waveband (Å) R Exposures LR (2 85s) LR (2 85s) HR5N (2 2265s) Table 2.: Summary of MEDUSA-GIRAFFE observations. reasons). Intermediate resolution spectra were retrieved in the Å region, while a higher resolution of the Hα region was used to avoid contamination from nebular emission. Optical photometry For most targets in the central region (within a radius of 60 from the core) the UBV catalogue of Selman et al. (999) provided the photometric information and was used for the fibre configuration. Outside this regions, targets were identified by preliminary Wide- Field Imager (WFI) observations at the 2.2 m MPG/ESO telescope at La Silla. For these, a magnitude limit of V 7 mag was applied to ensure a good signal to noise ratio (S/N). The combination of the Selman catalogue and the WFI frames yielded photometry for over 700 targets. Whenever the two overlapped, Selman s data were preferred, due to the better seeing achieved. For the remaining targets, photometric data were available in the catalogues from Parker (993) for 68 stars and in the Magellanic Cloud Photometric Survey (MCPS, Zaritsky et al., 2004) for another 08 objects. While the Parker catalogue shows no systematic deviations in respect to the WFI photometry whenever a match between the two occurs, the residuals from the MCPS data appear to be biased towards brighter magnitudes (Paper I), which hints at unresolved blends in the MCPS data. This photometric source was therefore rejected, and in December 200 new imaging was acquired at the Cerro Tololo Inter-American Observatory (CTIO) for the remaining 9 stars. 2.2 This sample 2.2. Data selection To probe the mass-loss rates in the transitional (O to Of/WN to WN star) regime and get as close as possible to the Eddington limit, we must seek the most luminous targets in the sample. Although one may intuitively think that these correspond to the visually brightest stars, this needs not to be the case. Out of two stars with equal bolometric luminosity but different radii, the larger (and colder) one will be the visually brightest. In fact, as a star evolves and grows cooler and larger with time, its visual magnitude M V will increase. This does not correspond to an equal increase in its bolometric luminosity, which during MS evolution will only rise slightly due to the growing mean molecular weight. Furthermore, nebular emission may affect the optical brightness as well in heavily contaminated spectra. Thus optical photometry provides a first selection of the luminous, hot star population, and it is usually assisted by a spectral classification of the sources, which yields the bolometric correction (BC). However, given the size of the sample, a full spectral classification of all O- type stars in the VFTS would have been a disproportionate task for our study. We therefore

18 2 CHAPTER 2. THE DATA selected the 29 O-stars in the sample (see Table 2.2) simply choosing the visually brightest single objects, and as it will be shown, this provided indeed many massive and very luminous targets for our analysis (by single star it is here meant a target that does not show v rad variations). We need however to point out that, as no detailed information on the spatial variation of the extinction in the field was available, we adopted a uniform value for the total to selective extinction of R V = 3. (Schultz and Wiemer, 975). Unfortunately, as targets with peculiar values are expectable in the sample (see e.g. Bestenlehner et al., 20), this makes the error on the absolute magnitude and on related quantities somewhat large (see Sec. 3..5). The WR stars included in our list were chosen after the spectral classification of the emission-line targets had been completed (Crowther and Walborn, 20). We selected two late-type WN stars, likely to be the closest ones (in terms of wind properties) to the O-type star part of the sample, and hence the most suitable for the transitional regime we are here considering. Finally, two clarifications need to be made. Both the photometric properties of some targets as well as their binarity status changed at various stages and the sample had to be adjusted accordingly. New CTIO photometry replacing the MCPS one (see Sec.2..2) was only available in December 200, and the binarity study of the targets has been an ongoing task (Sana et al., in prep.) in the course of this project. The change in visual magnitudes for some of the targets was dealt with by adding to the initial list those that underwent such a decisive shift in M V as to have become part of the 20 visually brightest stars in the survey. Concerning binarity, seven targets initially classified as single stars were later proven to show modest line-profile variability, i.e. changes in v rad < 20 km/s, which may hint at binarity or photospheric effects. This could partly affect our results (see Sec.5.2) Data reduction Prior to the beginning of this work, the ESO Common Pipeline Library FLAMES reduction routines were used for the initial data reduction, including bias subtraction, flat-field normalization and wavelength calibration. The pipeline also produced an error spectrum for each fibre. The heliocentric corrections were applied with the IRAF packages RVCORRECT and DOPCOR. A median sky spectrum was subtracted from all fibres in an observations, a first correction for cosmic rays was performed and an estimate of the SNR was computed in line-free regions as the median ratio of the flux and error spectra. For more details on the early phase of the data reduction, see Paper I. Generally speaking, the SNR is higher at shorter wavelengths. The faintest spectra (V > 6 mag) show mean SNR of 50 for all wavelength settings, but given our selection criterion for the subsample here under study (see Sec. 2.2.) most targets exceed values of 200 and some peak to almost 500. A distinctively different response among different exposures is observed in the MEDUSA spectra, chiefly as an effect of atmospheric dispersion, resulting in different continuum shapes. We therefore normalized each spectrum individually, preferably with low-order polynomials, and only then combined them in a single LR02, LR03 and HR5N spectrum. While doing this, we rebinned the spectra to a common wavelength grid (with step sizes of 0.2 Å and 0.05 Å

19 2.2. THIS SAMPLE 3 for the LR and HR setups respectively), and with a 5σ clipping at each pixel around the median spectrum we efficiently refined the cosmic-ray removal. By means of the Time Variance Spectrum (TVS, see Fullerton et al., 996)we could highlight binarity effects, amplitude variations, and unremoved cosmic rays. Finally, the averaged LR02, LR03 and HR5N spectra were merged. The data come from LR02 below 4500 Å, from LR03 above 4525 Å and from an average of the two in between, with the error spectrum giving the weights. No overlap is present with HR5N. The final set of normalized spectra is reported in Sec. A. We dealt with the removal of nebular emission manually, as the error spectrum provided an insufficient criterion for an automatized clean-up Spectral classification and v rad determination As far as possible, we dealt with the spectral classification of the targets in a quantitative approach. This relies on the ratio of the equivalent widths (EW) of the He i 447 Å and He ii 454 Å for the spectral type (Conti & Frost, 977). Luminosity classes were obtained from the Si iv 4089 Å and He i 443 Å EW ratio in mid- to late-type O stars (Conti & Alschuter, 97) and from the absolute strength of He ii 4686 Å in early O-type stars (Mathys, 988). Only when nebular emission was severely hampering these measurements, or to discern among the earliest types (e.g. to tell O2- from O3-types) our classification relied on a qualitative comparison with spectra taken at a comparable resolution. The results from these two approaches agree within half magnitude for almost all targets. Ultimately, we performed the v rad measurement in MIDAS. For almost the whole sample, these mainly rely on the Doppler correction computed from the He ii 4200 and 454 Å lines to avoid nebular contamination. The only exceptions are the Of-type and the two WN targets, for which no coherent v rad information could be extracted from the spectra. The average value for the sample was instead used. The results are listed in Table 2.2.

20 4 CHAPTER 2. THE DATA (a) (b) Figure 2.: Left: Map of the sample stars. Right: The core region. Identifiers are as in Paper I.

21 2.2. THIS SAMPLE 5 Table 2.2: The sample. (a) Spectral types are derived from the quantitative analysis unless otherwise indicated in the last column. When a quantitative result could not be determined (see Sec ), the result from the morphological analysis is reported in this column. For each spectral type, the (b) appropriate calibration (B V )0 was applied (Martins et al., 2005) in computing the absolute magnitude MV. The given error is the standard (c) deviation of the mean of the vrad values derived from different lines (see Sec ). When missing, no variability is detected. (d) The three values (e) given for the SNR correspond to the three different settings (LR02, LR03 and HN5R, see Sec. 2..2). M indicates the spectral type comes from the morphological classification, or a disagreement between the quantitative and morphological analysis (in this case, the morphological result follows). (f) Unknown calibration, value for a O3I spectral type adopted. (g) From Paper I. (h) Refers to the average value of the sample. star V B-V B-V0 MV Sp. Type (a) vrad [km/s] (b) vrad [km/s] (c) SNR (d) notes (e) O2III(f*) 85± - 386,229,227 M O2III(n)(f*) 269± - 369,98,7 M O9.5III 276± ,324, (f) 6.48 WN7h (g) 268 (h) - 250,20, O8.5V 302±0.4-45,03,94 M O3III(f*) 265±.0-269,86, O7IIInn 292± ,62, O9.7III 283± ,464, O3If* 268 (h) 9. 38,329,54 M O8.5III(n)(f) 264±.5-228,60, O4V((fc)) 259± - 267,88, O5III(n)(fc) 239± ,23, O9III(f) 299± ,227,7 M: B O4V((fc)) 296± - 38,74, O5V((f)) 260± - 22,86, O5.5If 303± ,90,63 M: O6.5If, but fast rotator O3-4V 253±2.7-29,93, (f) 6.48 WN8(h) (g) 268 (h) - 36,254, O8V 250±4.3-54,4,3 low SNR O6.5III(f) 246± ,280,20 M: O7.5III(f) (f) 7.2 O2If/WN6 248± ,24, O5.5Vn 254±5.4-68,55,65 low SNR B0III 263± ,296,22 M O8V 249±3.4-32,99,54 M O9.7III(n) 264±4.2-60,99,72 M O2III(f*) 264± - 379,208,53 M O2III(f*) 262± - 360,269,28 M O2V((f*)) 278±.3-42,0,94 M O5.5III((f)) 276± - 298,20, O7.5III(f) 262± - 268,203, O9.5III 286±3.8-6,36,45 low SNR

22 6 CHAPTER 2. THE DATA

23 Chapter 3 Automated fitting using a genetic algorithm 3. The fitting method To investigate the stellar parameters and the wind properties of our sample, we fit synthetic profiles of hydrogen and helium lines to our continuum-normalized data. The fast-performance atmospheric code fastwind (first introduced by Santolaya-Rey et al., 997) forms the fundamental brick of our approach. Spectral fitting is an optimisation problem: one pursues the best fit, i.e. the global optimum in parameter space. However this is an intrinsically multidimensional problem, in which line profiles depend (although obviously to different extents) on all the fit parameters simultaneously. Clearly a by eye fit offers no sound guarantee that the proposed fit is the one that actually best matches the observed spectrum, and a certain degree of arbitrariness would be unavoidable. We therefore turn to an automated fitting method, i.e. one employing a well-defined fitting criterion (see Sec. 3..4) that can work in a systematic and reproducible way. Such an approach has been developed by Mokiem et al. (2005), combining fastwind with the genetic algorithm (GA) based optimization routine pikaia (Charbonneau, 995) and has proven an excellent means to fit massive star spectra (Mokiem et al., 2006, 2007b). 3.. fastwind fastwind has been designed to reproduce optical and IR spectra of OBA stars of all luminosity classes. We use here the latest 0. version (Puls et al., 2005). fastwind implements the idea of a unified model atmosphere, i.e. one in which there is a smooth transition from a pseudo-hydrostatic photosphere to the stellar wind, along with an appropriate treatment of line-broadening (Stark and pressure broadening). The photospheric density follows from hydrostatic equilibrium and consistently accounts for both the temperature stratification, using a flux-correction method in the lower atmosphere and the thermal balance of electrons in the outer atmosphere, and the radiation pressure, as given by both the explicit and the background elements (see below). 7

24 8 CHAPTER 3. AUTOMATED FITTING USING A GENETIC ALGORITHM The velocity field corresponds to quasi-hydrostatic equilibrium in the photosphere and to a standard β velocity law in the sonic point region and beyond, i.e. ( v(r) = v r ) β 0 (3.) r where the acceleration parameter β sets the steepness of the acceleration, v is the wind terminal velocity and r 0 allows for a smooth transition between the two regimes (Lamers et al., 987). The code s priority is a fast performance: it was designed for the analysis of large samples of massive stars within a reasonable time-scale, to cope with the large dataset introduced by the advent of new telescopes and multi-object spectrographs. Basically, appropriate physical approximations are made anytime this would not impair accuracy. The most time-consuming part of the computation of realistic stellar atmospheres is the calculation of the radiation field. fastwind is not an exact code as e.g. cmfgen (Hillier and Miller, 998), in which all lines (including the hundreds of thousands of lines from the iron-group elements) are treated in the comoving frame (CMF), a very time-consuming task. The code distinguishes instead between the explicit elements, H and He, and background ones (most importantly: C, N, O, Ne, Si, Mg, S, Ar, Fe, Ni). The former are actively used as diagnostic tools, with highly detailed atomic models and by means of CMF transport for the bound-bound transitions. The current version of the code includes atomic models for H and He ii, consisting of 20 levels each, and for He i, with a 0-levels atomic model. The background ions are those allowing for the effects of line-blocking and -blanketing, for which on the other hand only an approximate NLTE solution is applied (see Abbott and Lucy, 985). A restricted number of about lines is used to solve the rate equations, while several millions are approximated in terms of a pseudo continuum (hence the approximate lineblocking) to derive the background opacities. The abundances of the background elements are taken from the solar values (Grevesse and Sauval, 998) and scaled to the desired metallicity (for the LMC, Z 0.008, Schaerer et al., 993). These simplifications make fastwind an extremely fast code (a typical model runs in about fifteen minutes, against the several hours needed for cmfgen) and therefore is the most efficient for an automated search of the global optimum The GA The Genetic Algorithms (GA) have been proposed as an alternative to the grid approach, which becomes too time consuming when a fine exploration of a sizeable multi-parameter space is required. In a nutshell, they are a class of optimization techniques which translate the notion of evolution by means of natural selection into a numerical method. GAs are given the desired parameter ranges, discretized in a grid in which each value is associated with a real number between 0 and, a so-called phenotype. This is further encoded in an integer, a gene, using a certain base (2,4,0..). Genes are then glued together into one sequence of integers, a genotype, where the parameter set distinguishing a specific model, an individual, is encoded. A GA first simultaneously generates a series of individuals with random phenotypes (in our case, a series of fastwind models corresponding to random positions in parameter space).

25 3.. THE FITTING METHOD 9 This is what is called a generation, the amount of individuals in it being the population size. Once the corresponding models are confronted with the data (i.e. the observed line profiles), selection pressure ensues, i.e. the models closest to the solution (see Sec. 3..4) are picked, hence acting towards convergence. Reproduction of the chosen genotypes to form the next generation is simulated by two genetic operators, the cross-over and the mutation operator. The former simulates sexual reproduction by testing different combinations of parameters, and while not affecting convergence it ensures the griding of parameter space, which will be the finest in the regions where convergence grows. The latter simulates random errors in copying a gene, and although acting against convergence it allows for the exploration of new paths in parameters space introducing new genes in the population, hence ensuring the solution found is actually a global, and not a local optimum. Obviously the ability of the GA to find a global optimum will improve with the number of generations being computed. This is usually achieved after more than a hundred generations. For our choice of population size (76 individuals) this translates into running several thousands of fastwind models, a clearly impossible task in a sequential approach. The PIKAIA routine has therefore been parallelized as to work on several processors simultaneously (Mokiem et al., 2005). Each fastwind model within a generation runs on one of 76 cores, which allow us to compute between one and three hundred generations (depending on the individual models) in 70 to 00 hours The fit parameters The parameters playing a role in a fit are the effective temperature T eff, the surface gravity g, the mass-loss rate Ṁ, the exponent of the velocity law β, the helium to hydrogen fractional abundance Y He, the rotational velocity v rot and the microturbulent velocity v turb. The stellar radius is not a free parameter, as it is constrained by the observed absolute visual magnitude M V and the T eff of the model (Kudritzki, 980; Herrero et al., 992): where the theoretical visual magnitude is 5 log(r/r ) = (V theo M V ), (3.2) V theo = 2.5 log 0 4H λ S λ dλ, (3.3) with H λ the theoretical Eddington flux from the calculated model and S λ the transmission function as given by Matthews and Sandage (963). It has been noted that for ρ 2 -dependent line processes (such as Hα and He ii 4686 Å) the quantity to which the wind diagnostics are sensitive is not the mere mass-loss rate but rather the invariant wind-strength parameter Q (Puls et al., 996): Q Ṁ R 3/2 (3.4) We thank SARA Computing and Networking Services ( for their support in using the Lisa Compute Cluster.

26 20 CHAPTER 3. AUTOMATED FITTING USING A GENETIC ALGORITHM line weight H Balmer.0 He i 4026 Å.0 He i 4387 Å 0.25 He i 447 Å.0 He i 473 Å.0 He ii 4200 Å 0.5 He ii 454 Å.0 He ii 4686 Å 0.5 Table 3.: Adopted line-weighting scheme. (for a detailed discussion on Q, particularly its dependency on v, see Puls et al., 996; de Koter et al., 998). Adjustments in the radius therefore imply a rescaling of the mass-loss rate as well. Lastly, the wind terminal velocity is assumed to scale directly with the escape velocity (Lamers et al., 995): v = 2.6 v esc = 2.6 2GM R. (3.5) 3..4 Fitness of a model As to what criterion defines how well a model fits an observed spectrum, several options are available. Following Mokiem et al. (2005), we define the fitness of a model as ( N F w i χred,i) 2, (3.6) i where χ 2 red,i (x obs,j x com,j ) 2 j j σ 2 j σ 2 j (3.7) is the reduced chi squared of each of the N fitted lines, with x com,j the computed intensity at the j -th data point x obs,j, and σ j the corresponding value from the error spectrum. F is therefore the quantity being maximized within this optimization problem. Weights w i are assigned to the different lines as to account for line blends with unmodeled species, lacking physics and/or potential problems in the model atmosphere code (see Table 3.). Commenting briefly on the lower weights, the He i singlet line at 4387 Å is very weak in early-type stars, and differences between the synthetic profiles of this line and He ii 4686 Å modelled by fastwind and cmfgen for the same input parameters have been reported (Puls et al., 2005). He ii 4200 Å is sometimes blended with an N iii line at the same wavelength, and is not always completely consistent with the other He ii lines. Note that nonetheless in our bestfitting models all synthetic profiles match remarkably the observed spectra.

27 3.. THE FITTING METHOD Errors Mokiem et al. (2005) also defined an error-estimate method based on the distribution of the fitnesses of the models in parameter space. Summarizing, the error on a given parameter is its maximum variation among the (user-defined) best-fitting models. A look at Fig. 3. can help clarify what we here mean. In the lower-right panel the distribution of models according to their fitness is shown, normalized such that the maximum fitness is equal to unity. The peak at F 5 and the surrounding region, between and, identify the width of the global optimum. The maximum variation of each parameter within the optimum, shown in the previous seven boxes, defines the errors on such parameters. Obviously, error bars defined as such need not be symmetric around the bestfit parameter values. As for the errors in the parameters derived from those actively explored from the GA, we follow the treatment from Repolust et al. (2004), which has already been applied to the GA by Mokiem et al. (2005, 2006, 2007b). Here, we only summarize the main points briefly. The error in the stellar radius is dominated by the uncertainty on the absolute visual magnitude, and is defined as log R 0.2 ( M V ) 2 + (2.5 log T eff ) 2, (3.8) with The absolute magnitude is ( log T eff log + T ) eff. (3.9) T eff M V = V R V [(B V ) obs (B V ) 0 ] DM (3.0) with total to selective extinction R V = 3.±0. (Schultz and Wiemer, 975), (B V ) 0 = 0.3, and distance modulus DM = 8.5 ± 0.3 (Panagia et al., 99). From error propagation it follows that M V = σv 2 + [(B V ) obs (B V ) 0 ] 2 σr 2 V + RV 2 σ2 (B V) + σ2 DM (3.) = ( + 2R 2V )σ2v + [(B V ) obs (B V ) 0 ] 2 σ 2RV + σ 2DM, since σb V 2 = σ2 V + σ2 B = 2σ2 V as the dispersion in the two photometric bands is the same for each photometric source, varying between 0. and 0.2 (see Paper I). The error in luminosity is given by Then, the modified wind-momentum rate is given by log L (4 log T eff ) 2 + (2 log R) 2. (3.2) ( R D mom = Ṁv R ) 0.5 ( ) 2 R Q, (3.3) R where the error has to be computed from the second equality, since Q = Ṁ/R.5 (and not Ṁ) is the actual fit quantity (see Puls et al., 996). Thus