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Appendix A: Comments on individual stars

In this appendix we compile some additional information about individual stars of our sample, especially their distance and binary status:

WR 4 is a WC5 star that is listed as SB1 in van der Hucht (2001) owing to its short-periodic photometric variability measured by Rustamov & Cherepashchuk (1989), but it displays neither diluted emission nor absorption lines from a possible companion. Smith et al. (1990) discussed whether WR 4 belongs to an H i bubble, for which they estimate a distance of between 1.6 kpc and 2.73 kpc depending on the method. The smaller value is close to our spectroscopic distance of 1.64 kpc, based on the M_ν calibration.

WR 8 is classified as WN7/WCE. Its spectrum resembles a WN7 type star, but with stronger carbon lines than usual. Niemela (1991) measured large amplitude radial-velocity variations with a possible period of 38.4 d, where the carbon and nitrogen lines are in antiphase. This is indicative of a WN+WC binary system. We attempted to reproduce the spectrum using a single-star model, which resembles a hydrogen-free WN star with enhanced carbon, but failed to obtain a convincing fit (Fig. B.3). Lundström & Stenholm (1984) estimated the modulus to be D.M. = 12.7 mag based on a membership of the Anon Pup a association.

WR 14 is a WC7 star, for which photometric variability has been reported by various authors, and discussed by Shylaja (1990) in terms of a possible compact companion. It displays non-thermal radio emission (Chapman et al. 1999), which can normally be attributed to colliding winds in binary systems. We found that its spectrum can be reproduced with a typical WC model for single stars, and conclude that there is at least no bright companion that dilutes the WC emission lines. Lundström & Stenholm (1984) identified the star as a member of Anon Vel a, estimating a distance of D.M. = 11.5 mag.

WR 15 has the spectral type WC6. From the width of its lines, we estimated a terminal wind velocity of 2600 km s^-1, slightly higher values than typical for this subtype. The distance of D.M. = 12.0 mag is based on the possible membership of Anon Vel b suggested by Lundström & Stenholm (1984). We prefer to used this distance method over that used to calculate the spectroscopic parallaxes obtained by Conti & Vacca (1990), who derived a value of D.M. = 11.28 mag for WR 15.

WR 23 is another a WC6 star and belongs to the Car OB1 association, for which Smith (2006) obtained a distance modulus of D.M. = 11.8 mag for the Homunculus nebula around η   Car. Earlier distance calculations for Car OB1 were D.M. = 12.55 mag (Massey & Johnson 1993) and 12.1 mag (Lundström & Stenholm 1984).

WR 26 is classified as WN7/WCE. The spectrum contains a very strong C iv 5808 Å line, which requires a model with about a 20% carbon mass fraction to be reproduced. The fit to our single-star model is satisfactory. The high carbon abundance might indicate that WR 26 is undergoing a transition from a WN to a WC star.

WR 33 has the spectral type WC5. The UV spectrum is indicative of a high wind velocity of about 3000 km s^-1, but otherwise looks normal. The optical spectrum (from Torres & Massey 1987) shows very broad emission features between 4000 Å and 4600 Å that cannot be reproduced by any of our models.

WR 38 displays a WC4 spectrum. Our fit is not very consistent, possibly indicating that the lines are diluted by a companion’s continuum. From a weak cluster around WR 38, Shorlin et al. (2004) derived a very large distance of D.M. = 15.8 mag, which would imply a very high luminosity of this star. In contrast, Wallace et al. (2005) obtained a distance modulus of  mag from the HST photometry of the same cluster. Our photometric distance, based on the subtype calibration, yields D.M. = 15.1 mag, in perfect agreement with the latter work.

WR 39, classified as WC7+OB? (van der Hucht 2001), is an interesting test case for the “diluted emission-line” binarity criterion. When we analyze its line spectrum assuming that the star is single, the obtained parameters place the star distinctly above the sequence of single WC stars in the log    T_∗-log R_t-plane (see Fig. 6). Moreover, WR 39 shows non-thermal radio emission (Chapman et al. 1999), which is normally attributed to colliding winds in binary systems. We therefore conclude that WR 39 is indeed most likely a binary.

WR 45 is a WC6 star. Unfortunately, the only spectrum available to us is limited to 3410–4730 Å and does not cover many diagnostic lines. Therefore, the parameters we obtained for this star are uncertain.

WR 50 is a double-lined spectroscopic binary WC7+OB (van der Hucht 2001) with a light-curve period of 1d (van Genderen et al. 1991). We analyzed its spectrum as if it were from a single star, and obtained parameters that are obviously affected by the d.e.l. effect (cf. Fig. 6). The distance modulus is D.M. = 12.8 mag according to Vázquez et al. (2005).

WR 52 is one of only five known Galactic WC4 stars, and does not show indications of binarity. The spectral fit Fig. B.16) requires models with higher oxygen abundances (10–15% by mass) than we used for our standard WC grid (5%). This agrees with our findings of higher oxygen abundances for WC4 and WO stars. As discussed by Chu & Treffers (1981), a kinematic distance of 2 kpc and a photometric distance of 4 kpc were derived from the associated nebula. From our subtype calibration, we obtained a distance modulus of D.M. = 12.67 mag, corresponding to 3.4 kpc.

WR 53 is classified as WC8 with the “d" indicating persistent dust. In contrast to the WC9 stars, dust formation is uncommon for this subtype, and might indicate colliding winds. The fit to our models, calculated with the full C ii ion, remains remarkably poor (Fig. B.17) for unknown reasons. Martín et al. (2007) found an expanding H i shell probably associated with this star, encircling an optical emission nebula, and estimated the distance of the shell to be 4 ± 1 kpc. From our subtype calibration, we obtained 2.9 kpc.

WR 58 is a transition-type star, classified as WN4/WC. For this star, a carbon mass fraction of 0.1% is enough to reproduce the C iv 5808 Å-line.

WR 59 is classified as WC9d. The star might be a binary, as Williams et al. (2005) found Balmer absorption features by comparing the spectral lines to those of a non-dusty WC9 star.

WR 64 is classified as WC7. The only spectrum available to us is that of Torres & Massey (1987) and covers only a short wavelength range, making our analysis less precise.

WR 65, classified as WC9d, shows variable X-ray emission. According to Oskinova & Hamann (2008), the emission originates from the wind-wind collision in a massive binary system, and the variability is caused by the different absorption columns along the orbit. Williams et al. (2005) detected absorption features from the Balmer lines of hydrogen. We analyzed the spectrum as if it were from a single WC star and found no indication of a composite nature. However, if WR 65 were a member of the Cir OB1 association as suggested by Lortet et al. (1987), it would be by far the brightest WC star in our sample (M_ν = −7.02   mag adopting a distance modulus from Turner 1996 of 12.57 mag). As this seems unlikely, we conclude that WR 65 is located in the foreground of Cir OB1, or it has a companion that contributes significantly to its total brightness. In any case, we cannot employ this star for our M_ν versus subtype calibration.

WR 68 is of subtype WC7 and a possible member of the Cir OB1 association. Turner (1996) deduced a distance of D.M. = 12.57 mag, based on the cluster Pismis 20, which is part of Cir OB1. Adopting this number leads to a plausible luminosity and HRD position. However, the distance of Cir OB1 has been debated in the past with distance moduli ranging from 11.58 mag (Moffat & Vogt 1973) to 12.8 mag (Vazquez et al. 1995), 13.00 mag (Lortet et al. 1987), and 13.22 mag (Lynga 1968).

WR 69 is one of the few WC9d stars for which a useful IUE spectrum exists, since the reddening for this star is relatively moderate. Williams et al. (2005) measured differences in the radial velocities between different observations, possibly indicating binarity.

WR 81 is another WC9 star, but one of the few Galactic examples without dust emission. Our line fit is remarkably much more consistent than for the dusty WC9d stars.

WR 86 is a visual binary classified as WC7 that has a B0 companion. The star is another example that helps to demonstrate which model parameters are obtained when a composite spectrum is fitted with a single-star model. We again find that the “diluted emission-line" effect places the results from this pseudo-fit in the characteristic domain of the log    T_∗-log R_t-plane (Fig. 6).

WR 88 is classified as WC9 and does not show dust emission. Thus it resembles WR 81. Williams et al. (2005) attribute a couple of emission lines to nitrogen, and conclude that WR 88 is either a WC+WN binary or belongs to a previously unobserved transitional WN/WC9 subtype. We fitted the spectrum with our WC models, and obtained parameters that agree with those of other WC9 stars (Fig. 6). Given the poor quality of the Torres & Massey (1987) spectrum we use, we refrain from test calculations with enhanced nitrogen abundances.

WR 90 shows non-thermal radio emission (Chapman et al. 1999), but otherwise no indications of binarity. Our single-star fit and the derived parameters are typical of its WC7 type.

WR 95 has the spectral subtype WC9d. According to Moffat et al. (1977), it belongs to the open cluster Trumpler 27 and has a distance of 2.1 ± 0.2   kpc implying a distance modulus of D.M. = 11.61 mag. Thé & Stokes (1970) and Bakker & Thé (1983) obtained lower values of 10.17 mag and 11.09 mag, which would lead to very low luminosities.

WR 98 was originally classified as a single star of WN8/WC7 transition type. Gamen & Niemela (2003) detected O8-9 type absorption lines superimposed on its spectrum. From the SB2 radial velocity curves, they derived the orbital elements. We tried to fit the spectrum with our single-star models. According to the WN/WC transition type of the spectrum, the best-fitting model is basically a hydrogen-free WN model with enhanced carbon (5% by mass). However, some spectral features cannot be reproduced by any of our single-star models, most likely because the contribution of the O-star companion cannot be neglected. We therefore consider Fig. B.34 as a “pseudo fit” that is in fact unsuitable for this composite spectrum, and omit WR 98 from our single-star analysis.

WR 102, also known as Sand 4, is one of two WO stars analyzed in this work. Classified as WO2, it has the same subtype as WR 142. To reproduce its spectrum, we needed to use models with an enhanced oxygen abundance and very high wind velocities. Moreover, the observed emission line profiles of WR 142 have a round top, which differs from the Gaussian-like shape usually encountered in WR spectra. Our models can only reproduce this round shape when we convolve the synthetic spectrum for rotational broadening with a νsini of about 1000 km s^-1. (For wind spectra, flux convolution is only a rough approximation to account for rotation.) We note that the WO stars are very compact, since their radius is smaller than the solar radius. Interestingly, the same effect has also been found for the most compact WN star in our Galaxy, the WN2 star WR 2 (Hamann et al. 2006). This rapidly rotating, bare, and compact stellar core is certainly a gamma-ray burst candidate. For the distance of WR 102, we adopt 3 ± 1   kpc from Dopita et al. (1990), which is based on the nebula G2.4+1.4 that was originally classified as a supernova remnant, but is now considered to be stellar ejecta from WR 102 despite this star not being located in its center. Drew et al. (2004) calculated a distance of 4.6 kpc based on an IR photometry scaling relative to WR 142. We did not use this distance as it does not rely on an independent measurement. Using a value of 4.6 kpc would infer an extremely high luminosity of log L/L_⊙ = 6.1.

WR 104 is well known for its pinwheel nebula. It is a binary system consisting of a WC9d and a B0.5V star. The latter is visually brighter than the WC star (Williams et al. 1987). A third, fainter component was resolved with HST (Wallace et al. 2002), hence the WC emission lines are expected to be “diluted”. Nevertheless, an acceptable fit can still be achieved for WR 104 with a single-star model that has quite “typical” WC9 parameters (cf. Fig. 6). The distance (D.M. = 11.0 mag) is adopted from Lundström & Stenholm (1984), who assigned WR 104 as a possible member to the association Sgr OB1.

WR 111 is a prototypical WC5 star, which has been frequently studied. Gräfener et al. (2002) basically used the same models as the present study, and therefore obtained similar results. Gräfener & Hamann (2005) constructed a hydrodynamically consistent model for WR 111, thus showed for the first time that WC winds can be explained in terms of radiation-driven mass loss. Their model provided a more consistent fit of the line spectrum than the semi-empirical models used in the present paper. The hydrodynamical model of Gräfener & Hamann (2005) has a much higher stellar temperature T_∗ = 140 kK than our present study (89 kK). This mainly reflects the different radial structures of the two respective models in the deepest zones of the wind – we recall that T_∗ is defined as the effective temperature corresponding to the radius R_∗, where the Rosseland optical depth reaches 20 (cf. Eq. (1)).

The model of Gräfener & Hamann (2005) has nearly the same luminosity as we obtain from our empirical fit. The mass-loss rate of the hydrodynamically consistent model (log Ṁ = −5.14) is considerably lower than that of our empirical model (–4.67). This difference is mainly due to the much higher clumping contrast assumed by Gräfener & Hamann (2005) (D = 50 in the outer parts instead of 10 in this work). Such strong clumping is probably unrealistic, but was needed to compensate for the incomplete line opacities and achieve sufficient radiative driving. A minor part of the mass-loss rate differences is due to the terminal wind velocity, which was slightly smaller in the hydrodynamic model (2050 km s^-1) than the value adopted in the present paper (2398 km s^-1). For the model of Gräfener & Hamann (2005), a much higher stellar temperature (T_∗ = 140 kK) was assumed than the 89 kK given in the present paper. Different stellar radii R_∗ compensate for the effect of luminosity. The similarity of the emergent spectra demonstrate again the parameter degeneracy for very dense winds discussed in Sect. 5.1. The star WR 111 is assumed to be a member of the Sgr OB1 association (Lundström & Stenholm 1984) with a distance modulus of D.M. = 11.0 mag.

WR 113 is a WC8d+O8-9 binary system (Cherepashchuk & Karetnikov 2003), which has an excess in its 2MASS K-band magnitude most probably caused by dust emission. The pseudo-fit of its spectrum obtained from our single-star models leads to parameters in the binary domain of the log    T_∗-log R_t-plane (Fig. 6), obviously due to the dilution of the emission lines.

WR 114, classified as WC5, is a member of the Ser OB1 association (Lundström & Stenholm 1984) with a distance modulus of D.M. = 11.5 mag. The spectrum was found to have diluted emission lines, and the star was therefore listed as a binary candidate in van der Hucht (2001). However, our spectral fit and the obtained parameters are normal for a single WC5 star.

WR 117 is a “dusty” WC9d star. Williams et al. (2005) did not find any evidence of an OB companion, and our single-star model also fits most features in the observed spectrum with typical parameters. The lines are significantly stronger than in other WC9 stars. The best-fitting model has a stellar temperature of T_∗ = 56   kK, which is relatively high for the WC9 subclass. The position of WR 117 in the log    T_∗-log R_t-plane, as well as the high terminal wind velocity, are close to or maybe already in the WC8 parameter region. Some previous papers (e.g. Conti & Vacca 1990) have indeed classified WR 117 as type WC8. Unfortunately, our available spectrum does not comprise any C ii-lines, which would provide the criterion to distinguish the subtype WC8 from WC9.

WR 121 is another “dusty” WC9d star that is apparently single. Williams et al. (2005) could not find any evidence of an OB companion, and our single-star model fits most features in the observed spectrum with typical parameters.

WR 125 is an SB2 binary system (WC7ed+O9III, Williams et al. 1994), where the letters “ed” stand for episodic dust formation. Our pseudo fit with a single-star model gives parameters that are characteristic of composite spectra (cf. Fig. 6).

WR 126 shows a unique spectrum that differs from those of all other Wolf-Rayet subtypes. Its designation as WC5/WN indicates that it has predominantly a WC-type spectrum (albeit the emission lines are unusually weak), but also relatively strong nitrogen. We tentatively fit the spectrum with a WC-type model from our low-carbon (20% mass fraction) grid (Fig. B.46). The N iv lines at 7005–7031 Å reveal obviously a significant abundance of nitrogen, which is not included in our WC models. The mass-loss rate is much lower than those typically found for WC5 stars. A thorough spectral analysis of this transition-type star is beyond the scope of the present paper. Following Radoslavova (1989), the star is probably a member of the Vul OB2 association, which has a distance modulus of D.M. = 13.2 mag.

WR 132 is classified as WC6 and might be associated with an H i-bubble. Based on that bubble, Arnal (1992) estimated a kinematic distance of 4.3 kpc, which we adopt for our luminosity scaling.

WR 135 is one of only four WC8 stars analyzed in this work. The star is a possible member of Cyg OB3, leading to a distance of D.M. = 11.2 mag (Garmany & Stencel 1992). The earlier calculations of Lundström & Stenholm (1984) obtained a slightly higher value of 11.6 mag. WR 135 is the only WC8 single star with an independent distance estimate.

WR 137 is a binary system (WC8pd+O9) showing periodic dust (“pd”) formation. Under the assumption that the O star is a main-sequence star, Williams et al. (2001) estimated a distance modulus of D.M. = 11.1 mag. The pseudo-fit with a single-star model yields parameters that are typical for composite spectra (cf. Fig. 6).

WR 142, classified as WO2, is the other WO star analyzed in this work. It has the same subtype as WR 102. The spectra of both stars are very similar, hence so are the results of their analyses. We achieved the best fit with a very high terminal wind velocity (ν_∞ = 5000 km s^-1) and a very high stellar temperature of T_∗ = 200 kK. As for WR 102, we had to convolve the emergent spectrum with a high rotational broadening velocity of 1000 km s^-1 in order to reproduce the round shape of the emission lines. Oskinova et al. (2009) detected weak but hard X-rays from this object. These X-rays cannot be attributed to colliding stellar winds since there is apparently no companion. WR 142 is a member of the Berkeley 87 cluster. The distance of this cluster has been disputed in the past. Turner & Forbes (1982) derived a cluster distance of 946 ± 26 pc, which would imply log    L/L_⊙ = 5.5. Massey et al. (2001) and Knödlseder et al. (2002) obtained 1.58 kpc and 1.8 kpc, raising the luminosity to 5.9 or even 6.0 for the latter distance. In our work, we used the latest value of Turner et al. (2006) of a distance of 1230 ± 40 pc leading to log    L/L_⊙ = 5.7.

WR 143 was revealed as a binary (WC4+Be) by Varricatt & Ashok (2006). The analysis with our single-star models yields parameters that closely fit to the WC sequence, possibly indicating that the contribution of the Be-type companion to the composite spectrum is relatively weak.

WR 144 is one of two Galactic WC4 stars that are not suspected to be binaries. According to Lundström & Stenholm (1984), the star is a possible member of the Cyg OB2 association with a distance modulus of 11.3 mag, which we adopt for our luminosity scaling. This distance implies a luminosity of log L/L_⊙ = 5.22. An alternative distance modulus of D.M. = 9.8 mag for Cyg OB2 claimed by Linder et al. (2009) would lead to an implausibly low luminosity of log L/L_⊙ = 4.6.

WR 145 is of the transition type WN7/WC. Its spectrum is nicely fitted by a WN-type model with enhanced carbon. The distance modulus of 11.3 mag is taken from Lundström & Stenholm (1984) based on the possible membership of WR 145 in the Cyg OB2 association. The star is located in a nebula (Miller & Chu 1993).

WR 146 is a visual binary system consisting of a WC5 star with an O8 companion. Dougherty et al. (1996) also resolved two components with a high-spatial-resolution radio observation and classified WR 146 as a colliding wind binary due to its non-thermal radio emission. Dougherty et al. (2000) performed an in-depth analysis of the different types of radio emission from both components and their colliding wind region. They suggested that the companion might actually not be a single O8 star, but a composite system itself, possibly consisting of an O8 and another WC star to explain the high mass-loss rate. The poor pseudo fit that can be achieved with single-star models yields parameters which are typical of binaries if the d.e.l. effect is neglected (cf. Fig. 6). Dessart et al. (2000) tried to account for the companion’s continuum when they analyzed this WR star, but still arrived at parameters that are atypical of a WC5 star. WR 146 is also listed as a possible member of the Cyg OB2 association with D.M. = 11.3 mag (Lundström & Stenholm 1984), although this membership has since been questioned. Dougherty et al. (1996) obtained D.M. = 10.4 mag, which would place WR 146 in front of Cyg OB2 and is the value that we used in our pseudo fit.

WR 154 is a WC6 single star and a possible member of the Cep OB1 association, for which Garmany & Stencel (1992) give a distance modulus of 12.2 mag. Earlier calculations obtained D.M. = 13.7 mag (Smith et al. 1990) and 12.53 mag (Conti & Vacca 1990).

Appendix B: Spectral fits

This section lists the spectral fits of all stars analyzed in this work. For each star, a composite plot is available that consists of an SED fit (top panel, similar to Fig. 4) and several panels that show the best-fitting grid model together with the normalized UV and visual spectra when available. In all panels, the observed spectra are plotted in blue, while the model is printed in red. The flux of the SED has been decreased according to the distance and reddened with E_b−ν as given in the figures. The applied reddening law is indicated by the keywords seaton, cardelli, or fitzpatrick. The parameters R_V is also given as the last two laws use it as a free parameter.

In most cases, the best-fitting model was taken from the standard WC grid described in Sect. 3. If a special model was required to reproduce the observed spectrum, this is clearly noted in the corresponding figure.

© ESO, 2012