© ESO, 2012

1. Introduction

One of the main products of the VLT-FLAMES survey of massive stars¹ (hereafter FLAMES I) was the determination of light element abundances from statistically significant samples of Galactic, Large and Small Magellanic Cloud (LMC, SMC) B-stars, covering a broad range of rotational velocities.

The inclusion of rotational mixing into massive star evolution (e.g., Heger & Langer 2000; Meynet & Maeder 2000; Brott et al. 2011a) brought better agreement with spectroscopic analyses that provide evidence for a characteristic enrichment of helium and nitrogen in many early-type stars (reviewed by, e.g., Herrero 2003; Herrero & Lennon 2004; and Morel 2009). Several recent studies based on the nitrogen diagnostics performed within the FLAMES I survey have severely challenged the predicted effects, though. In this context, nitrogen is a key element for testing the predictions of rotational mixing, because it should become strongly enriched at the stellar surface of rapidly rotating stars already in fairly early evolutionary phases, whilst for slow rotation almost no enhancement should occur before the red supergiant phase. Indeed, a significant number of both un-enriched fast rotators and highly enriched slow rotators have been found within the population of LMC core-hydrogen burning objects (Hunter et al. 2008a, 2009; Brott et al. 2011b)². These results imply that standard rotational mixing might not be dominant, and/or that other enrichment processes might be decisive as well (Brott et al. 2011b).

To further constrain these findings and to provide a general picture of massive star evolution, these studies need to be extended to O-type stars. Because of their shorter lifetimes, the time-range where this enrichment takes place can be narrowed down, and one might be able to constrain the mixing scenario even better than it is possible from B-stars alone. In this respect, the LMC is an ideal testbed, because the nitrogen baseline abundance is low and even a strong enrichment is easier to measure/confirm than, e.g., in the Milky Way.

Interestingly, most previous abundance studies of massive stars are strongly biased toward intermediate and early type B-stars. Indeed, when inspecting the available literature, metallic abundances, in particular of nitrogen, are scarcely found for O-stars. The situation for LMC objects is even worse, and data for only a few supergiants (Pauldrach et al. 1994; Crowther et al. 2002; Evans et al. 2004) and giants (Walborn et al. 2004) are available. One of the reasons for this lack of information is that the determination of nitrogen abundances is not trivial because of the complexity of N iii/N iv line formation, which is related to the impact of various processes that are absent or negligible at cooler spectral types where N ii is the dominant ion.

To provide more insight into this matter, we started a series of publications dealing with nitrogen spectroscopy in O-type stars. In the first paper of this series (Rivero Gonzalez et al. 2011, hereafter Paper I), we concentrated on the formation of the optical N iii emission lines at λλ4634 − 4640 − 4642, which are fundamental for the definition of the different morphological “f”-classes (Walborn 1971b). It turned out that the canonical explanation in terms of dielectronic recombination (Mihalas & Hummer 1973) no longer or only partly applies when modern atmosphere codes including line-blocking/blanketing and winds are used. The key role is now played by the stellar wind, which induces a (relative) overpopulation of the upper level of the transition, via pumping from the ground state rather than by dielectronic recombination as long as the wind-strength is powerful enough to enable a significantly accelerating velocity field already in the photospheric formation region.

The main goal of the present paper is to provide nitrogen abundances for a considerable number of O-stars in the LMC. For this purpose, we used the corresponding sample from Mokiem et al. (2007a, hereafter Mok07), mostly based on observations within the FLAMES I survey. So far, this is the most comprehensive sample of O-stars studied in the LMC by means of quantitative hydrogen and helium line spectroscopy, and allows us to determine nitrogen abundances for a significant number of objects. However, its size is still not comparable with the amount of corresponding B-stars, and does not allow us to extend the B-star results (that challenged rotational mixing) toward the O-star domain in a statistically sufficient way. Instead, it will yield a first impression on potential problems. A statistically significant analysis will become possible within the VLT-FLAMES Tarantula survey (Evans et al. 2011, “FLAMES II”), which provides an unprecedented sample of “normal” O-stars and emission-line stars.

This paper is organized as follows. In Sect. 2 we describe the tools used to determine nitrogen abundances, both the atmospheric code and the nitrogen model atom. In particular, we study the formation of the N ivλ4058 emission line in parallel with the N ivλ6380 absorption line. Section 3 presents the stellar sample and the observations used within this study. The procedure to determine stellar and wind parameters together with nitrogen abundances is outlined in Sect. 4. In Sect. 5 we comment in detail on the individual objects. Section 6 provides a discussion of our results, and Sect. 7 summarizes our findings and conclusions.

2. Prerequisites for nitrogen diagnostics

2.1. The code

We used a recently updated version (v10.1) of the atmosphere/line formation code fastwind (see Santolaya-Rey et al. 1997; and Puls et al. 2005, for previous versions). This code has been specifically designed for the optical and IR spectroscopic analysis of hot stars of spectral types early A to O, and accounts for NLTE conditions, spherical symmetry, and mass-loss. The current version incorporates a variety of updates and improvements compared with previous versions, which are briefly summarized in the following.

At first note that fastwind differentiates between so-called “explicit” and “background” elements, where the former are those used as diagnostic tools (in the present context: H, He, and N) and are treated with high precision, by means of detailed atomic models and comoving frame transport for the line transitions. The background elements (i.e., the rest) are used “only” for the line-blocking/blanketing calculations, and have been treated so far by means of the Sobolev approximation. Though this is reasonable in the wind regime, the Sobolev approximation becomes doubtful in regions where the velocity field is strongly curved, which is the case in the transition zone between photosphere and wind. We have checked that the induced errors are not important for the background radiation field, but they can have a certain influence on the temperature structure. Applying the Sobolev approximation in regions with a strong velocity field curvature results, on average, in too highly populated upper levels of line transitions (see, e.g., Santolaya-Rey et al. 1997). In turn, this leads to overestimated heating rates, which can result in too high temperatures in the transition region (and sometimes even below). To avoid this problem, the new fastwind version also treats the most important lines from the background elements in the comoving frame.

A second modification refers to the photospheric line acceleration. So far, this quantity (which is important for the photospheric density stratification – higher line acceleration, lower density) has been calculated from the Rosseland opacities, which is strictly justified only at high optical depths. In the new version, an additional iteration cycle for calculating the photospheric structure is performed, now by using the flux-weighted mean from the current NLTE opacities.

By calculating a large grid of OB-star models, and comparing with solutions from the previous fastwind version, it turned out that both improvements affect mostly dwarfs/giants in the effective temperature range 30 kK  ≤  T_eff  ≤  35 kK. In particular the optical He ii lines become stronger, mostly because of the somewhat lower (electron-) densities. Interestingly, this is just the domain where previous fastwind solutions showed the strongest deviations from other codes (Simón-Díaz & Stasińska 2008). The new structures excellently agree with results from tlusty. For dwarfs/giants with effective temperatures outside the “problematic” region, and for all supergiants, the differences to previous results from earlier fastwind versions are small.

The last major improvement concerns the implementation of dielectronic recombination, both for the background and the explicit elements, and was already described and successfully tested in Paper I.

2.2. The nitrogen model atom

To perform our analysis, we implemented a new nitrogen model atom into fastwind, consisting of the ionization stages N ii to N v, which has already been used for the calculations performed in Paper I. The level structures of both N iv and N v were taken from the wm-basic atomic database (Pauldrach et al. 1994).

N II

was adapted to fastwind from a previous model ion, developed by Becker & Butler (1989). We had no intention to develop a “perfect” N ii model, since most of our analyses deal with O-star spectra where N ii becomes invisible, and particularly because Przybilla and co-workers have already constructed such a model (based on an earlier version, see Przybilla & Butler 2001) which will be incorporated into our code after release. However, a series of tests were performed to ensure the goodness of the model ion, see Sect. 2.2.1.

For N ii, we considered 50 LS-coupled terms, up to principal quantum number n = 4 and angular momentum l = 3, where all fine-structure sublevels have been packed. Detailed information about the selected levels is provided in Table A.1 and Fig. A.1. We account for some hundred permitted electric dipole radiative transitions. For the bulk of the transitions, oscillator strengths were taken from calculations performed by Becker & Butler (1989), but for some transitions related to strong N ii lines oscillator strengths were taken from NIST³. Radiative intercombinations were neglected. Roughly one thousand collisional bound-bound transitions were considered, with corresponding rates using the van Regemorter (1962) approximation in the radiatively permitted case and following the semi-empirical expression by Allen (1973) in the forbidden one. Radiative ionization cross sections have been derived by Becker & Butler (1989), and were adapted to the representation suggested by Seaton (1958). Collisional ionization cross-sections were calculated using the Seaton (1962) formula in terms of the photoionization cross-section at threshold.

N III

has been already described in Paper I. In brief, it consists of 41 packed terms up to n = 6 and l = 4 (doublet and quartet system).

N IV.

This model ion also consists of 50 LS-coupled terms, up to principal quantum number n = 6 and angular momentum l = 4, with all fine-structure sublevels packed into one term. Table A.2 provides detailed information about the selected levels. Two spin systems (singlet and triplet) were treated simultaneously (Fig. A.2). All allowed electric dipole radiative transitions between the 50 levels were considered, as well as radiative intercombinations, with a total of 520 transitions. Corresponding oscillator strengths were drawn from either NIST when available or otherwise from the wm-basic database⁴. Furthermore, we considered roughly one thousand bound-bound collisional transitions between all levels, with effective collision strengths among the 12 lowest LS-states from R-matrix computations by Ramsbottom et al. (1994). Transitions without detailed data and collisional ionizations were treated as in N ii.

Photoionization cross-sections were taken from calculations by Tully et al. (1990), via TOPbase⁵, the OPACITY Project online database (Cunto & Mendoza 1992). For excited levels without available OPACITY Project data (5g ¹G, 5g ³G, 6s ¹S, and 6g ³G, see Table A.2), resonance-free cross-sections were used, provided in terms of the Seaton (1958) approximation with parameters from the wm-basic database. Finally, the most important dielectronic recombination and reverse ionization processes were implicitly accounted for by means of exploiting the OPACITY Project photo cross-sections. Only for the few levels without these data we applied the “explicit” method, using the stabilizing transitions on top of resonance-free photo cross-section (see, e.g., Paper I), with corresponding data from wm-basic.

N V.

Our model of this lithium-like ion (one doublet spin system) consists of 27 levels, including LS-coupled and packed terms up to n = 7 and l = 6 (see Table A.3 for details and Fig. A.3 for a Grotrian diagram). All allowed electric dipole radiative transitions were accounted for, with a total number of 102 radiative bound-bound transitions and oscillator strengths from wm-basic. Collisional excitations and ionizations were treated as in N ii, whilst photo cross-sections (in terms of the Seaton 1958 approximation) were taken from the wm-basic atomic database.

Our complete nitrogen model atom (from N ii to N v) comprises 178 LS-coupled levels, with more than 1100 radiative and more than 3800 collisional bound-bound transitions. To calculate the final synthetic profiles, we adopted Voigt profiles, with central wavelengths according to NIST, radiative damping parameters from the Kurucz database⁶, and collisional damping parameters (broadening by electron impact) computed according to Cowley (1971).

2.2.1. Testing the N II model ion

To test our somewhat simple N ii model ion⁷, we compared synthetic line profiles with corresponding ones from tlusty (Hubeny 1998) and detail/surface (Giddings 1981; Butler & Giddings 1985), the latter based on the newly developed N ii model by Przybilla et al. (see Sect. 2.2).

A summary of the various tests is provided in Table 1. We started by comparing with line profiles from the BSTAR2006 model grid (Lanz & Hubeny 2007). This grid has been calculated using the model atmosphere code tlusty (Hubeny 1988; Hubeny & Lanz 1995), a code that assumes plane-parallel geometry, hydrostatic and radiative equilibrium, and calculates line-blanketed NLTE model atmospheres and corresponding synthetic profiles. Owing to its restrictions, only objects with negligible winds can be analyzed.

We used this grid of models as reference because it covers the parameter range at which N ii/N iii are the dominant ionization stages, and the N ii lines are clearly visible in the synthetic spectra. In addition, the BSTAR2006 grid has been used in numerous studies aiming at the determination of stellar abundances and parameters in B-stars (e.g., Lanz et al. 2008).

We calculated a grid of fastwind model, covering the temperature range 20 kK  ≤  T_eff  ≤  30 kK, using a typical step size of 2.5 kK, and gravities representative for dwarfs and giants. Because tlusty does not account for the presence of a wind, we used negligible mass-loss rates, Ṁ = 10^-9... 10^-10 M_⊙   yr^-1. Because fastwind allows for employing external photospheric structures, we created a second grid using the tlusty photospheric structure, smoothly connected to the wind structure as calculated by fastwind, with the usual β velocity law. For consistency with the tlusty grid, all models were calculated with the “older” solar nitrogen abundance, [N] = 7.92 (Grevesse & Sauval 1998), where [N] = log  N/H + 12 with respect to particle numbers. Note that all tests were performed with the complete nitrogen model atom involving the ions N ii to N v as described in Sect. 2.2.

We found substantial differences between the synthetic N ii line profiles calculated by tlusty (TL) and fastwind (FW), even though the hydrogen/helium lines agree very well (except for the forbidden component of He i which is stronger in FW-models). The latter code predicts stronger N ii profiles, which is also true for the fastwind results based on the tlusty photospheric structure (FW2, see Figs. B.2 to B.7).

For dwarfs, there are almost no differences between the profiles from the FW and FW2 models. This is readily understood, since the photospheric stratification of electron temperature, T_e, and electron density, n_e, are essentially the same (see Fig. B.1, panel 1, 3, 5), i.e., fastwind and tlusty predict the same structures.

On the other hand, models for giants at higher T_eff display (mostly) weak differences. At T_eff = 27.5 kK and log g = 3.0, e.g., there is a small disagreement of the electron densities in photospheric regions (τ_Ross ≤ 10^-5), even though the temperatures agree quite well (Fig. B.1, panel 6). In particular, the tlusty and thus the FW2 structure shows a lower electron density at optical depths where the photospheric lines are formed, because of a higher photospheric radiative line pressure in this model.

Because of the lower electron density, the lower recombination rates (at T_eff = 27.5 kK, N iii is the dominant ion) lead to somewhat weaker N ii profiles in the FW2 models compared to the FW ones, see Fig. B.7. Nevertheless, differences to the profiles as predicted by TL itself are still considerable, and we conclude that the photospheric structure is not the origin of the discrepancies.

As an independent check, we compared our results with spectra calculated by Przybilla (priv. comm.) for two of our grid models, denoted by Prz in the following. These spectra are based on the NLTE/line formation code detail/surface, and the N ii model ion recently developed by Przybilla et al. We consider this atomic model as the superior one in the present context, because the atomic data were successfully improved and tested, and the corresponding synthetic spectra perfectly match high-resolution/high-signal-to-noise observations from various B-stars (Przybilla et al. 2008).

Figures B.2 and B.4 show that the FW and Prz profiles agree excellently, which leaves us with the conclusion that there might be problems in the N ii atomic data used in the BSTAR2006 grid. Important studies using tlusty have been carried out during the past years (e.g., Dufton et al. 2006; Trundle et al. 2007; Hunter et al. 2009), including the determination of N ii abundances in LMC and SMC B-stars. These studies utilized a different model atom, developed by Allende Prieto et al. (2003), which has been tested by Przybilla at our request, with a positive outcome. Therefore these analyses should be free from uncertainties related to a potentially insufficient atomic model.

2.3. Diagnostic nitrogen lines in the optical

Table 2 presents a set of 51 nitrogen lines visible in the optical (and adjacent) spectra of OB-stars, along with the position of potential blends. Included are the connected levels (for corresponding term designations, see Appendix A) and multiplet numbers to provide an impression of how many independent lines are present.

Lines from N ii (visible in the spectra of B and late O-stars) have been selected after careful comparisons with profiles calculated by Przybilla (priv. comm., see Sect. 2.2.1). Only one of the suggested lines, N ii λ3995, is completely isolated and remains uncontaminated even at high rotation rates. Moreover, this is one of the strongest N ii lines located in the optical region, making it a good choice for deriving nitrogen abundances. Other useful lines are N iiλ5667 and λ5679, where the former is moderately strong and the latter has roughly the same strength as N iiλ3995.

The subset comprising lines from N iii has been discussed in Paper I. Prominent lines from N iii, N iv, and N v are among the most well-known features in O-stars and can be used to infer nitrogen abundances as well as effective temperatures for the earliest subtypes from the reaction of the N iv/N v ionization equilibrium⁸. In a similar line of reasoning, Walborn et al. (2002). used the N ivλ4058 emission line in combination with N iiiλλ4634 − 4640 − 4642 to split the degenerate O3 spectral type (Walborn 1971a) into three different types O2, O3, and O3.5, relying on the N iv/N iii emission line ratio⁹. Thus, a detailed understanding and modeling of N ivλ4058 (together with the N iii triplet, see Paper I) is mandatory to employ this powerful diagnostic safely.

N ivλ4058 and N ivλ6380 connect the “neighboring” levels of the singlet series 1s² 2s3l with l = s, p, d (levels #8, 9, and 12 in Table A.2). N ivλ4058 (if present) is observed in emission in the majority of stars, and has been suggested to be formed by photospheric NLTE processes (see below) rather than by emission in an extended atmosphere, in analogy to the N iii triplet emission. Note that there is no detailed analysis of the line formation process. So far, only Taresch et al. (1997) and Heap et al. (2006) simulated the behavior of this line as a function of effective temperature. Heap and collaborators found emission for this line at T_eff > 40 000 K for log g = 4.0 and [N] = 7.92, using the plane-parallel atmospheric code tlusty, which supports the idea that the emission is of photospheric origin and that velocity fields are not required to explain the basic effect. Other arguments for the photospheric origin of N ivλ4058 are the agreement with other, absorption line profiles as a function of v   sin   i, unshifted radial velocites, and lack of P Cygni profiles (Walborn, priv. comm.).

Interestingly, N ivλ6380 appears clearly in absorption in O-star spectra, and seems to play a similar role as the N iii absorption lines at λλ4097−4103 in the N iii emission line problem (see Paper I). We note that N ivλ6380 can be significantly affected by the presence of two diffuse interstellar bands (DIBs) at λλ6376.08,6379.32 (Herbig 1975; Krelowski et al. 1995), the latter of which is stronger if reddening is significant. Fortunately, the stars analyzed in this paper are subject to low reddening, and these DIBs only minorly affect some of the observed N ivλ6380 lines (e.g. N11-038, Fig. C.8).

As for the previous pair of N iv lines, N ivλ6380 and N iv λ4058, the N iv multiplets around 3480 Å and 7103−7129 Å are also formed between levels of the same series (here within the triplet system – levels #7, 10, and 11 in Table A.2), and seem to mimic the behavior of these lines: at least in the earliest O-star regime they are prominent features, where the former multiplet appears in absorption and the latter in emission. Both line complexes are widely used in WR-star analyses, and the emission in the latter multiplet is a strong feature in most WR spectra. The lack of emission at this multiplet and also at N ivλ4058 has been used for classification purposes in different WR-star studies (e.g., Negueruela & Clark 2005). Likewise, the multiplet around 3480 Å has been used by Walborn et al. (2004) to infer T_eff and nitrogen abundances for a set of O2 stars.

The remaining N iv lines listed, N ivλλ5200−5204−5205, also belong to the triplet system, and appear, if present, in absorption (for O-stars). Unfortunately, most spectra used within this study do not cover this spectral region. For the few field stars where this range is available to us (see Sect. 3.2), this multiplet is not visible.

Finally, N v lines at λλ4603 − 4619 are produced by transitions between the fine-structure components of 3s ²S and 3p ²P⁰ (levels #3 and 4 in Table A.3). These doublet lines are strong absorption features in the earliest O-stars, showing sometimes extended absorption in their blue wings or even pronounced P-Cygni profiles (e.g., N11-031, Fig. C.7), revealing that they can be formed in the wind. Therefore, mass-loss and wind-clumping will clearly influence the formation of these lines. Besides, we also list N vλλ4943−4945, which become important, (almost) isolated diagnostic lines in the spectra of very early, nitrogen rich O- and WNL-stars. Unfortunately, the corresponding wavelength range has not been observed for the bulk of our sample stars (see Sect. 3.2), whilst no features are visible in the few early-type spectra (field stars) where this range is available. Note that to use these lines, we would need to extend our N v model ion, including high-lying levels, to allow for cascading processes into the corresponding upper levels at n = 7 (which are our present uppermost ones).

2.4. Understanding the N IV λ4058/λ6380 line formation

In the following, we discuss the most important mechanisms that explain the presence of emission at N ivλ4058, in particular the decisive role of mass-loss. Our analysis is based on the model-grid as described in Sect. 4.2, and refers to LMC background abundances plus a solar (Asplund et al. 2005) nitrogen abundance, [N] = 7.78¹⁰, chosen to obtain pronounced effects.

All important levels and the corresponding transitions involved in the N iv emission problem are summarized in Fig. 1. A comparison with the analogous diagram for N iii (Fig. 1 in Paper I) shows a number of similarities, but also differences. In addition to what has already been outlined, the upper level of the emission line (3d  →  3p) is fed by only weak dielectronic recombination, with almost no influence on the population of 3d (contrasted to the N iii case), and there is no resonance line connected to 3d (which turned out to be crucial for N iii). Instead, the lower level of λ4058, 3p, is connected with the ground-state. Similar to N iii, on the other hand, there are two strong “two-electron” transitions able to drain 3p, via 3p ¹P⁰  →  2p^2 1S, ¹D.

2.4.1. Basic considerations

In agreement with the results from Heap et al. (2006), our simulations (see Fig. 2) show that N ivλ4058 turns from weak absorption (around T_eff ≈ 37 kK) into weak emission around T_eff ≈ 42 kK, for models with (very) low mass-loss rate and log g = 4.0. As usual, we define equivalent widths to be positive for absorption and to be negative for emission lines. We find a 2 kK difference w.r.t. the turning point, which can be attributed, to a major part, to the lower nitrogen content of our models and different background abundances. Toward hotter temperatures, the emission strength increases monotonically until a maximum around T_eff ≈ 53 kK has been reached, after which the emission stabilizes and finally decreases. For lower gravities and/or higher mass-loss rates, the line turns into emission at lower T_eff, so that, for a given T_eff, the emission strength increases with decreasing log g and increasing mass-loss rate, Ṁ. Since the absorption strength of N ivλ6380 increases in a similar way (though with a much weaker impact of Ṁ, and only until T_eff ≈ 50 kK), both lines appear (for a given T_eff) as anti-correlated, at least for a wide range of temperatures. In contrast, the corresponding transitions of N iii were found to be correlated (Paper I).

The behavior of both lines and the corresponding level structure implies an efficient drain of level 3p that enhances the emission at λ4058 and also prevents emission/increases absorption at λ6380, and is provided by the two “two-electron” transitions 3p  →  2p^2 1D, ¹S, similar to the case of N iii¹¹.

To investigate this mechanism in more detail and to avoid “contamination” by wind effects, we concentrated at first on a low-Ṁ model with decent emission at N ivλ4058, with T_eff = 45   000 K and log g = 4.0¹². In the upper panel of Fig. 3 we provide the NLTE departure coefficients, b, of involved levels, where black curves refer to our standard model. Obviously, level 3d is overpopulated with respect to 3p (b_3d > b_3p) over the complete line formation region. On the other hand, levels 2p^{2 1}D, 2p^2  1S, and 2p (the latter two not displayed) are (mostly collisionally) coupled to the ground state, which in itself is strongly depopulated, owing to fairly high ionizing fluxes (see below). This situation closely resembles the situation in N iii, where strongly depopulated draining levels (for non-blocked models) favored a depopulation of the analogous level 3p.

To further clarify the impact of the different processes, we investigated the corresponding net rates responsible for the population and depopulation of level 3p (Fig. 3, middle panel, black curves). As in Paper I, we display the dominating individual net rates (i.e., n_jR_ji − n_iR_ij > 0 for population, with index i the considered level) as a fraction of the total population rate. Indeed, the drain by level 2p^2 1D (dashed-dotted) and/or level 2p^2 1S (not displayed) are the most important processes that depopulate level 3p in the line formation region. In contrast, the resonance line does not contribute to any (de-)population of level 3p, because it is (almost) in detailed balance (long dashed line).

To check the validity of our scenario, we calculated an alternative model where the two draining transitions were suppressed, by using very low oscillator strengths. Indeed, the upper panel of Fig. 3 (red curves) shows that now b_3d is smaller than b_3p, and λ4058 becomes an absorption line (lower panel, red color). From the fractional net rates, we see that the preferred decay route has switched from 3p  →  2p² (standard model, black) to 3p  →  3s (red, dashed), though level 3p retains a much higher population.

The upper level of λ4058, 3d, is predominantly fed by cascading from 3d′ ¹F⁰, and also by pumping from level 2p, whilst dielectronic recombinations are negligible. Suppressing the population from level 2p leads to less emission (Fig. 3, lower panel, blue colors), owing to a less populated level 3d (upper panel).

Let us now consider the behavior of the absorption line at λ6380, resulting from the transition 3p  →  3s, again by means of Fig. 3. As mentioned earlier, this line shows an anti-correlation¹³ with N ivλ4058, in contrast to the behavior of the corresponding N iii lines, which appear to be correlated. In Paper I we argued that the latter correlation results from the proportionality of the level populations of 3p and 3s. That is, when b_3p decreases (e.g., due to increased “two-electron” drain), b_3s decreases in parallel due to less cascading, and the absorption at λ4097 becomes weaker in concert with an increase in the triplet emission. Vice versa, an increase of 3p implies less emission of the triplet lines and more absorption at λ4097, respectively.

This reaction requires the transition 3p  →  3s to be optically thin, dominated by spontaneous decays, which is no longer true for N ivλ6380. Owing to a mostly significant optical depth, the radiative net rate is no longer dominated by spontaneous decays, but also depends on absorption and induced emission processes. Now, an increased population of 3p leads to less increase of b_3s¹⁴, and the absorption becomes weaker because of an increased source function  ∝ b_3p/b_3s. Vice versa, a decrease in the population of 3p leads to more absorption at λ6380 in parallel with more emission at λ4058. This behavior becomes particularly obvious if we investigate the reaction of the absorption line when suppressing the draining transitions. In this case, 3p becomes strongly overpopulated (Fig. 3, upper panel, red color), and λ4058 goes into absorption whilst λ6380 becomes an emission line, due to a significantly increased source function (more pumping than in the original scenario). We checked that if the absorption and stimulated emission terms in the 3p  →  3s transitions are neglected, λ6380 displays more absorption instead, in accordance with our previous arguments.

Note, however, that this anti-correlation is not complete. If one changes processes that have an effect on 3d alone, e.g., the absorption strength of λ6380 remains unaltered. Thus, by suppressing 2p  →  3d, only b_3d is affected (upper panel, blue vs. black curves), and there is less emission at λ4058 while the absorption at λ6380 remains at the previous level (lower panel).

Summarizing, we interpret the different correlations between emission and absorption line-strength in N iii and N iv as caused by optical depth effects in the 3p  →  3s transition. As long as this is optically thin, cascade effects dominate, and both lines appear to be correlated (N iii). Higher optical depths introduce a counteracting “source-function effect”, and the lines become anti-correlated (N iv). The fairly high degree of such anti-correlation supports the importance of the draining transitions, because these are able to influence both the absolute population of the involved levels and their ratios in a very efficient way by providing additional decay channels for level 3p.

2.4.2. The impact of wind effects

So far, we discussed the possibility of obtaining emission at N ivλ4058 via solely photospheric NLTE processes. In Paper I, the presence of a wind (more accurately, a steep rise of the velocity field in the outer photosphere) turned out as crucial to explain the observed N iii triplet emission in Of-stars, enabling an efficient pumping of the upper level by the corresponding resonance line. To investigate how the presence of a wind affects the emission at N ivλ4058, we compared our previous model “A4540” with model “E4540”, which has the same stellar parameters but a considerably higher, supergiant-like mass-loss rate. Indeed, the inclusion of such a strong wind has a pronounced effect. Comparing Figs. 4 (lower panel) with 3, model “E4540” (black) results in much more emission than “A4540”, increasing the equivalent width of λ4058 from  −7 to  −114 mÅ. For higher T_eff the impact of Ṁ also remains significant. The absorption line N ivλ6380 is affected by the wind as well, though less pronounced. The absorption becomes slightly stronger (by 18% in the equivalent width), i.e., the anti-correlation discussed above is still present. This is valid not only for model “E4540”, but also for hotter models (Fig. 2), until the wind-emission begins to contaminate N ivλ6380.

The origin of this stronger emission at λ4058 becomes clear if one inspects the involved departure coefficients (Fig. 4, upper panel, black curves). Again, the onset of the wind is clearly visible (at τ_Ross ≈ 0.1), now much deeper than in the “A” model, and the line formation region is located in between τ_Ross ~ 0.40...0.04. Compared to the “A” model, “E4540” displays a more advanced ground-state depopulation, where the ground-state remains coupled with the draining levels 2p² as well as with level 2p (not displayed). This leads, particularly in the transition region between photosphere and wind, to an extreme depopulation of 3p. Because level 3d becomes strongly overpopulated mostly because of feeding by 3d′ ¹F⁰ (which is severely overpopulated as well), the resulting line source function is quite high and partly even in inversion, which explains the pronounced emission at N ivλ4058.

All these differences are caused by the onset of the wind. At first note that the N iv continuum (λ  <  160 Å) is strongly coupled with the He ii continuum. As already realized by Gabler et al. (1989), increasing mass-loss leads to more He ii ground-state depopulation, to higher fluxes in the He ii continuum and thus also to higher fluxes in the N iv continuum. Consequently, the N iv ground-state becomes strongly depopulated, and the nitrogen ionization equilibrium switches from N iv (which is the dominant stage in the deeper photosphere) toward N v from the transition region on. This also favors the overpopulation of 3d by means of increased recombinations to high-lying levels with subsequent cascades via 3d′ ¹F⁰.

One might now argue that the inclusion of the wind could amplify the impact of the resonance transition(s) by producing deviations from detailed balance which would lead to strong pumping, similar to the case of N iii. Unlike the situation in N iii, however, this effect would lead to less line emission or even absorption at N ivλ4058, because here the resonance line is connected to the lower level, 3p. But this effect is not present, however, because the resonance line is too strong (N iv is the dominant ion until the transition region) to leave detailed balance before the wind has reached a significant speed. Only then the resonance transition becomes dominant in populating level 3p, but this occurs already far beyond the formation region of N ivλ4058. Close to the formation region, there is only a moderate population of 3p by the resonance line, similar to the population from 3d itself. Even this additional population is counteracted (even slightly overcompensated) by enhanced drain toward 2p², not only in the formation region of λ4058 but also in those outer regions where the resonance line strongly pumps.

These arguments are supported by the fact that N ivλ6380 is only slightly affected by the wind, where the increased absorption results mostly from a diminished source function owing to a less populated 3p level. Performing the same tests as for the thin wind case, i.e., either suppressing the drain or suppressing the population of 3d via 2p  →  3d, leads to similar results, as can be seen from the red and blue curves and profiles in Fig. 4, respectively.

We conclude that Ṁ is a key parameter for modeling the N iv emission line, where in contrast to N iii the basic mechanism (for typical mass-loss rates and below) is always caused by the depopulation of the lower level by the “two-electron” transitions. This drain becomes stronger as a function of Ṁ, because of increasing ionizing fluxes that lead to more ground-state depopulation.

3. Stellar sample and observations

3.1. The stellar sample

Table 3 lists our stellar sample that was drawn from the analysis of LMC O-/early B-stars by Mok07.

Three of the 28 stars from the original sample were discarded from the present analysis for two reasons. First, from our analysis we suspect that N11-004 and N11-048 might be (SB1) binaries, where the former object shows discrepant line shifts and for the latter we were unable to reproduce the observed He lines accurately (shape and strength). A possible binarity of N11-048 was also suggested by Mok07 because of similar reasons. The other discarded star, Sk–67° 166, is the only object in the original sample that seems to be strongly evolved (helium content Y_He = N(He)/N(H) = 0.20...0.28, Crowther et al. 2002 and Mok07, respectively), and has a very dense wind, with both H_α and He ii4686 in strong emission. We confirm the stellar/wind parameters as derived by Mok07 (almost perfect fit quality of H/He lines), but did not succeed in a reasonable fit for the nitrogen lines. A comparison with the analysis by Crowther et al. (2002) shows similar discrepancies. Because of this problem and because of its highly evolved evolutionary status, which does not match with all other objects in our sample, we decided to discard this object from our present analysis and will reconsider it in a future attempt.

The remaining sample consists of 20 O-stars, mostly giants or dwarfs, and 5 early B-type supergiants or giants. All B-stars and 15 O-stars are associated with the cluster N11, and the others are field stars. The early B-stars were included in our sample to allow for a comparison with previous analyses of such stars (Hunter et al. 2009) and to check the consistency of different codes and methods in the transition region between O- and B-types (Sect. 6.2).

Table 3 gives information about spectral type, V-magnitude, interstellar extinction and absolute visual magnitude, and was taken from Mok07. Spectral types for N11 objects are based on Evans et al. (2006), slightly revised by Mok07 in collaboration with Evans (priv. comm.), and for the field stars from Walborn et al. (1995), and Massey et al. (1995, 2005). For the field star Sk–70° 69 we added the ((f)) designation because the present spectra show clear emission at N iiiλλ4634−4640−4642 and He iiλ4686 in absorption.

3.2. Observations

Most of the observations (for objects denoted by “N11-”) have been carried out within the FLAMES I survey, and are described in detail in Evans et al. (2006). In brief, the data were obtained using the Fibre Large Array Multi-Element Spectrograph (FLAMES) at the VLT, for six wavelengths settings with an effective resolving power of R  ≃  20 000. The S/N ratios are in the ranges 50−200 for LMC objects. After sky substraction, each wavelength range was co-added and normalized by means of a cubic spline¹⁵. The final merged spectra cover two spectral ranges, 3850−4750 Å and 6300−6700 Å.

To improve the sampling in luminosity and temperature, Mok07 augmented the N11 sample by LMC O-type field stars, which were observed using the UVES spectrograph at the VLT as part of the ESO programs 67.D-0238, 70.D-0164, and 074.D-0109 (P.I. P. Crowther). Spectra were obtained for four different wavelength settings at an effective resolving power of R ≃ 40   000. The final product provides coverage between 3300−5600 Å and 6300−10 400 Å for all stars except for Sk–70° 69, where “only” the region between 3300−5600 Å and 6300−6700 Å had been observed. The typical S/N ratios achieved for all spectra lie in the range 60−80.

4. Analysis

4.1. Methodology

In an ideal world, we could have used the stellar and wind parameters as obtained by Mok07 from H/He lines, and simply derived the nitrogen abundances from atmospheric models with these parameters. Unfortunately, there are reasons to reanalyze all program stars. First, the present fastwind version (see Sect. 2.1) is somewhat different from the version used by Mok07, and the parameters need certain (mostly small) alterations to reach a similar fit quality to the H/He lines. Second, we used a somewhat different fitting strategy with respect to the “free” parameters, which changes the optimum fit. In contrast to Mok07, we derived and fixed the projected rotational velocity, v   sin   i, independently from the actual fitting procedure (Sect. 4.3), whereas Mok07 included v   sin   i as a free parameter in their fitting algorithm. Moreover, during our fit procedure we allowed for the presence of extra line-broadening (“macro-turbulence”, v_mac), not considered by Mok07. Differences in v   sin   i and v_mac can lead to certain differences in the outcome of the fit, since the profile shapes might change (e.g., Fig. 4 in Puls 2008). Third, and most important, is that we now aim at a consistent fit for the H/He and nitrogen lines. Thus, and in the sense of a compromise solution (minimization of the differences between observed and synthetic spectra for all lines), different stellar parameters which result in a modest change of the fit quality of H/He alone¹⁶ can lead to a significant improvement with respect to the complete set of lines.

This is why we opted for an entire reanalysis, performed mostly by a simple “fit-by-eye” method where we aimed to accomplish the best fit to the strategic lines by visual inspection (for a discussion, see Mokiem et al. 2005). Because we started from the parameter set as provided by Mok07 (highest “fitness”¹⁷ with respect to their assumptions), our new solution should be located at or close to the global maximum of the corresponding merit function as well and not only at a local one. Note that our derivation of nitrogen abundance and micro-turbulence for most of the cooler sample stars relies on a more objective method (Sect. 4.4).

Mok07 themselves used an automated fitting method (developed by Mokiem et al. 2005) based on a genetic algorithm optimization routine to obtain the stellar/wind parameters by evolving a population of fastwind models over a course of generations, until the best fit to H/He is found. Seven free parameters were considered to obtain the highest “fitness”: effective temperature, T_eff, surface gravity, log g, helium content, Y_He, projected rotational velocity, v   sin   i (see above), micro-turbulent velocity, v_mic, mass-loss rate, Ṁ, and velocity-field exponent, β.

4.2. Model calculations and grids

All models used within this analysis were calculated with fastwind, augmented by a few cmfgen models for comparison purposes (Sect. 5). For these calculations, H, He, and N were treated as explicit elements. A description of our H/He model atoms can be found in Puls et al. (2005), and our nitrogen model atom is described in Sect. 2.2 and in Paper I.

To allow us to study the combined reaction of all diagnostic H/He/N lines on variations of the stellar/wind parameters and nitrogen abundances, and also for understanding the N ivλ4058 emission line process (Sect. 2.4), we generated a grid of models¹⁸. The grid was constructed using various nitrogen abundances centered at the solar value [N] = 7.78 (from [N] = 6.98 to 8.58 with step size 0.2 dex and including the LMC nitrogen baseline abundance, [N]_baseline = 6.9), and a background metallicity, Z = 0.5   Z_⊙, corresponding roughly to the global metallic abundance of the LMC (cf. Mokiem et al. 2007b). The individual abundances of the background elements (in terms of mass fractions) are scaled by the same factor with respect to the solar abundance pattern (see Massey et al. 2004).

For a given Z the grid is three-dimensional with respect to T_eff, log g, and log Q, where Q is the so-called wind-strength parameter (or optical depth invariant), Q = Ṁ/(v_∞R_∗)^1.5. This parameter allows us to condense the dependence on Ṁ, terminal velocity, v_∞, and stellar radius, R_∗, into one representative quantity¹⁹. The grids cover the temperature range from 25 to 55 kK (with increments of 1 kK), and a gravity range between 3.0 and 4.5 (with increments of 0.2 dex). For log Q, the different wind strengths are denoted by a letter (from “A” to “E”), with log Q =  −14.0,  −13.5,  −13.15,  −12.8,  −12.45, respectively, if Ṁ is calculated in M_⊙   yr^-1, v_∞ in km   s^-1, and R_∗ in R_⊙. Models with quantifier “A” correspond to thin winds, resulting in lines that are (almost) unaffected by the wind, whereas “E”-models correspond to a significant wind-strength typical for O-type supergiants. Other parameters were adopted as follows: a solar helium abundance, Y_He = 0.10; v_∞ as a function of the photospheric escape velocity, v_esc (see Kudritzki & Puls 2000); the stellar radius, R_∗, as a function of spectral type and luminosity class, corresponding to prototypical values; the velocity field exponent, β, from empirical values (Kudritzki & Puls 2000), with β = 0.8 for O-stars, and higher values toward later types; and the micro-turbulence, v_mic = 10 km   s^-1.

4.3. Determination of stellar and wind parameters

The different steps performed in our analysis can be summarized as follows, and are detailed in the next sections.

First, we determined v   sin   i for each object. Then we used the results from Mok07 in combination with our model grid to roughly constrain the stellar (T_eff, log g, [N]) and wind-strength parameters (log Q), by inspecting the synthetic and observed H/He and nitrogen line profiles (Y_He, β and v_mic already specified within the grid). During this step, we determined the extra line-broadening parameter, v_mac, by reproducing the profile shape of the weaker lines.

Subsequently, the stellar/wind parameters, now including Y_He and β, were fine-tuned by calculating a grid of much higher resolution around the initial guess and adopting v_∞ from Mok07. After the fundamental parameters were fixed and, in case, v_mac was adjusted, we fitted the nitrogen abundance using two different methods (for cooler and hotter objects, respectively), and also updated v_mic, which Mok07 solely derived from H/He lines. In certain cases, we needed to re-adapt the stellar/wind parameters to obtain the (almost) final solution. Now, we were able to calculate the stellar radius from M_V and the synthetic fluxes, and to update the mass-loss rate to its final value by scaling with the new radius. A final consistency check with the new Ṁ and R_∗ values was performed to ensure the stability of our results.

Tables 4 and 6 list all quantities derived in this way, and Table 5 yields the main differences between our and the Mok07 results. Note that these quantities refer to unclumped winds, whilst in Sect. 4.5.1 we discuss the impact of wind clumping.

Projected rotational velocities and macro-turbulence.

Before we were able to perform the actual (fine-)analysis, we needed to constrain the line broadening parameters, i.e., v   sin   i and v_mac (v_mic was – when possible – inferred in parallel with the nitrogen abundances, see Sect 4.4). As outlined above, Mok07 derived v   sin   i directly from their automated fitting method from the H/He lines. It is more suitable to use metal lines, because these are not affected by Stark-broadening. Only in case of high rotational velocities or high temperatures, where metallic lines are blended or are very weak, He i lines might be used. Therefore, we derived v   sin   i from scratch, employing the Fourier method (Gray 1976), as implemented and tested in the OB-star range by Simón-Díaz et al. (2006) and Simón-Díaz & Herrero (2007). This method has the advantage to easily discriminate the rotational contribution from other broadening mechanisms that affect the line shapes. In dependence of temperature and rotational velocity of the star, we used lines from O ii, N ii, C ii, and Si iii for B- and late O-type stars. For earlier O-types, higher ionization states are predominant, and mostly N iii/N iv and Si iv lines were considered, together with He i lines for the earliest types.

To finally reproduce the actual profile shape, some extra line-broadening was needed in most cases, conventionally called macro-turbulence. Though the physical origin of this broadening still remains to be proven, there are some strong indications that it is associated with (high order, non-radial) stellar pulsations (Aerts et al. 2009; Simón-Díaz et al. 2010). To account for this effect, we used a radial-tangential description of v_mac to fit the profile shapes of nitrogen (and partly helium) lines, using our first estimates on the stellar and wind parameters (see above) and the new v   sin   i values. For the fastest rotators of our sample, however, corresponding values could not been constrained, because high v   sin   i produce either too weak nitrogen lines, or these lines, together with He i lines, loose their sensitivity to distinct changes in v_mac.

As expected, most of our v   sin   i values turn out to be systematically lower than those provided by Mok07 (Table 5), by typically 30 − 40%. The derived range of v_mac values is consistent with results from similar investigations, e.g., Dufton et al. (2006); Simón-Díaz et al. (2006); Lefever et al. (2007); Markova & Puls (2008); Simón-Díaz et al. (2010). The uncertainty of our estimates is typically on the order of  ± 10   km   s^-1, being larger for stars with relatively low rotational speeds.

Effective temperatures.

This parameter is mostly constrained by the He i/He ii ionization equilibrium. For this purpose, we primarily used He i λλ 4471, 4713, 4387 and He ii λλ 4200, 4541. In most cases, we did not meet the so-called He i singlet problem (Najarro et al. 2006). As a consistency check on T_eff and especially for the hotter stars, where the He i lines can no longer serve as an efficient temperature indicator, we made additional use of the nitrogen ionization equilibrium by means of the lines listed in Table 2. For B- and late O-stars, we investigated N ii/N iii, for mid O-stars N iii/N iv, and for early O-stars N iv/N v or even – in a few cases – N iii/N iv/N v (see Table 4 for the specific diagnostics applied to a particular object). To this end, we either used our coarse grid or our specific “fine-grid” models, with a similar gridding of nitrogen abundances ([N] = 6.9...8.58). By exploiting this additional information, i.e., roughly “fitting” the nitrogen lines of different ions at a unique abundance, we were able to fine-tune T_eff (and also some of the other parameters, see below). For objects where only lines from one ionization stage are present (N11-033, 045, 061, 087, 123), this concistency check only allows for fairly weak constraints, if at all.

We estimate a typical uncertainty for T_eff according to the grid resolution, ΔT_eff ≈ 1 kK. For N11-066 and N11-068 we are only able to provide rough estimates on the stellar parameters, consistent with the nitrogen ionization equilibrium, and we adopt a larger error, ΔT_eff ≈ 2 kK. For some problematic stars, N11-026, N11-031, and N11-060, we consider an even larger error, about 4 kK, in agreement with Mok07 (see Sect. 5).

Surface gravities.

We derived log g using the classical approach from the Stark-broadened wings of the Balmer lines, basically H_γ and H_δ, which should be uncontaminated by wind-emission. As for T_eff, we used nitrogen lines as a final consistency check. These surface gravities need to be corrected for stellar rotation, applying a centrifugal correction (see Repolust et al. 2004, and references therein). The estimated error for log g is 0.1 dex.

Helium abundances.

To ensure the reliability of the final parameters, especially T_eff and and log g, and for our discussion on the abundance enrichment, we needed to revisit the helium line fits, because inconsistent helium abundances can influence these parameters. A small subgrid was constructed around the stellar parameters derived in previous steps, for different Y_He, from 0.08 (corresponding to the approximate LMC baseline abundance, see Sect. 6) to 0.14, in steps of 0.02. A rough estimate on the error is half this stepsize.

Terminal velocities

cannot be reliably derived from the optical, and were adopted from Mok07. For the field stars, values have been inferred from UV P Cygni profiles by Massa et al. (2003) and Massey et al. (2005). The terminal velocity of Sk–66° 18 was measured by Mok07 using UV O vi lines. For the FLAMES N11 stars, only N11-031 could be analyzed with respect to this parameter by Walborn et al. (2004). For all other stars, v_∞ has been estimated from v_esc, following Kudritzki & Puls (2000).

Velocity field exponent β.

The sample used in this study does not contain any star whose wind is so dense that H_α is in emission, therefore an accurate determination of this parameter is difficult²⁰ for optical spectroscopy. We applied the following philosophy. If the combination Ṁ-β provided by Mok07 resulted in reasonable H_α-fits, we kept β. Otherwise, we set β to prototypical values, β = 0.8...1.30, depending on spectral type and results from earlier analyses performed in our group. Moreover, for some of the sample stars, N11-008, N-029, N11-058, and N11-061, the automated fitting method used by Mok07 resulted in quite high values for β (e.g., N11-061: β = 1.8), whilst for N11-051 a rather low value, β = 0.6, was inferred. We consider these values as either unphysical or indicating a substantial amount of wind clumping. In all these cases, we modified β as outlined above (see also Sect. 5).

Mass-loss rates

were derived from fitting the synthetic H_α profiles to the observations, given β (see above). Usually He iiλ4686 was used as a consistency check. It turned out that for many sample stars we were unable to successfully fit both lines at the same Ṁ, because He iiλ4686 showed more absorption than consistent with the observations when H_α was fitting. This might indicate a certain problem regarding He iiλ4686 in the new fastwind version, or some impact of wind clumping. The problem needs to be investigated in the future, but has no impact on the present study.

Another consistency check for Ṁ is provided by the nitrogen lines, particularly by the N iii and N iv emission lines (and sometimes also by the N v doublet), which are strongly affected by the wind strength. In the case of two stars, N11-058 and N11-065, which showed quite good line fits to H, He and N, the synthetic N ivλ4058 profile displayed weak emission, whereas the observed one was clearly in weak absorption. Consistency could be achieved by lowering Ṁ until this line could be acceptably fitted, leaving the remaining nitrogen lines and H_α almost unaltered. In both cases it turned out that H_α was already almost insensitive to reductions in Ṁ. Other stars that showed a similar problem, N11-051, Sk–66° 18, and Sk–66° 100, could not be “cured” by this approach because there a reduced value of Ṁ was no longer consistent with (unclumped!, see Sect. 4.5.1) H_α.

Because H_α is in absorption in all our objects, which leads to the well-known Ṁ-β degeneracy, we estimated quite a large error on Ṁ, namely plus/minus a factor of two, which is typical in this situation (e.g., Markova et al. 2004). The impact of the error in R _∗  is negligible here, as outlined in the next paragraph.

Stellar radii.

Because the effective temperatures derived within this work are different from those of Mok07 (overall, these differences are modest, except for N11-026, N11-031, and N11-068, see Table 5), this leads to different theoretical fluxes and thus to different stellar radii. Similar to Mok07, we followed Kudritzki (1980) and Herrero et al. (1992), and calculated the “new” radii from the theoretical Eddington fluxes and the (de-reddened) absolute magnitudes from Table 3.

Once the radii were redetermined, Ṁ needed to be modified as well to preserve the fit quality of H_α, which depends on the optical depth invariant Q (see above). Contrasted to the case of Galactic objects, where the error of M_V (because of unknown distances) dominates the error budget of Ṁ, this plays a secondary role in our sample, owing to sufficiently well-known distances and the fairly large error introduced by the Ṁ-β degeneracy.

4.4. Nitrogen abundances and micro-turbulences

After determining the stellar and wind parameters and their uncertainties (some fine-tuning may still be necessary), we are now in a position to derive the nitrogen abundances and the corresponding micro-turbulent velocities, v_mic. Because the latter parameter significantly affects the strength of both He and metal lines and thus the implied abundances, it is useful to determine both quantities in parallel.

To carry out this analysis, we calculated a fine grid of typically 25 models by combining different abundances centered at the rough estimates derived in Sect. 4.3 with five different values for v_mic = 0,5,10,15,20 km   s^-1.

When possible (see below), we used a “curve of growth” method based on the equivalent widths of the lines, which has been applied in the past years to different sets of B-stars to obtain various metallic abundances (e.g., Urbaneja 2004; Simón-Díaz et al. 2006; Markova & Puls 2008). In brief, this method uses synthetic and observed equivalent widths including uncertainties from all considered lines to derive a unique pair of abundance and v_mic (incl. errors). Results from these analyses are indicated by an asterisk in the v_mic-column of Table 4.

Unfortunately, this procedure was not applicable to the bulk of the sample stars because of various reasons, e.g., blending and diluted lines owing to fast rotation, almost invisible lines owing to low nitrogen content, and peculiarities in the observed lines from some of the stars with highly ionized nitrogen. All these problems will be commented on in Sect. 5, and we opted for a determination of the nitrogen abundance/micro-turbulence pair by means of a visual inspection of the fit quality, using the same fine grid as described above.

We estimated the errors in v_mic to be 3 − 5 km   s^-1, both for the equivalent width and the visual method. To provide an impression of the impact of these errors on the derived nitrogen abundances, we note that a decrease in v_mic by 5 km   s^-1 leads to an increase of [N] by 0.05 − 0.07 dex. For the error associated to [N] when derived by “visual” fitting, we decided to be quite conservative. Even though we are able to obtain quite good fits for the bulk of the stars implying an uncertainty of 0.1 dex, we instead adopt a higher value of 0.15 dex to roughly account for the additional dependence on the stellar and wind parameters. For two stars, N11-033 and N11-087, we can only provide an upper limit on the abundance, with an estimated uncertainty of 0.20 dex. This value is also adopted for N11-066, N11-068, and N11-045, N11-051. We were able to obtain only rough estimates for the stellar parameters of the first two stars and could only use one nitrogen multiplet for the latter two. Even larger uncertainties were derived for two “problematic” stars, N11-026 and N11-060, see Sect. 5.

Table 6 lists the obtained nitrogen abundances together with their estimated errors. When available, corresponding literature values were added.

4.5. Additional considerations

4.5.1. Wind clumping

So far, we neglected wind clumping in our analysis. Because most of the nitrogen lines are formed in the intermediate or outer photosphere²¹, at least for not too extreme winds as considered here, they should remain quite unaffected by direct clumping effects, though indirect effects could be important (see Paper I). Clumped winds have lower mass-loss rates compared to their unclumped counterparts by a factor of  if the clumping factor f_cl is radially constant, which could influence both the N iii and the N iv emission lines, because of their sensitivity on Ṁ. Given the multitude of evidence for wind-clumping (e.g., Puls 2008, and references therein), it is necessary to examine the impact of clumping on our abundance determinations.

We adopted the parametrization as used by Hillier & Miller (1999) and Hillier et al. (2003), (1)where f(r) is the volume filling factor²², f_∞ its asymptotic value (if v_∞ ≫ v_cl) and v_cl the velocity where the volume filling factor reaches values close to e^-1, if f_∞ ≪ 1. To allow for maximum effects, we set v_cl = 30   km   s^-1, close to the sonic speed for O-stars, and concentrated on models with f_∞ = 0.1, corresponding to Ṁ reductions by a factor of roughly 0.3 (consistent with recent investigations allowing for macro-clumping, see Sundqvist et al. 2011).

Because most of our sample stars display thin winds, no major reaction due to clumping is to be expected. Indeed, a value of f_∞ = 0.1 did not induce any noticeable change in the spectrum for the bulk of the stars.

For stars N11-038, 032, BI237, N11-060, 065, 066, and 068, mostly the N iii triplet is affected (for BI237, also N v), requiring 0.05 to 0.1 dex more nitrogen to preserve the previous fit quality of these lines. Because on the other hand the other nitrogen lines remain unmodified, the inclusion of clumping did not change our [N]-values for these stars, but only improved or deteriorated the particular representation of the triplet lines.

For BI253 and Sk–70° 69, clumping of the considered amount has a stronger effect, particularly on the N iii triplet, N ivλ4058 and the N v doublet. Here, a clumping factor of f_∞ = 0.1 requires [N] to be increased by 0.15...0.20 dex.

Finally, for N11-026 and N11-031, the inclusion of clumping affects the stellar parameters as well. Owing to the lower Ṁ, a hotter temperature (by 1 to 2 kK) is needed to preserve the He i fit. For N11-026, [N] needs to be considerably increased, by 0.25 to 0.3 dex. This is the only case where we encountered a significant effect. For N11-031, on the other hand, at least the “cool solution” (see Sect. 5) remained at the previous nitrogen abundance.

In addition to these general effects, for a few stars, Sk–66° 100, Sk–70° 69, N11-051, Sk–66° 18 and N11-065, the inclusion of clumping (of a lesser degree than f_∞ = 0.1) favors a better fit to N ivλ4058, see Sect. 5.

4.5.2. Background abundances

One of the central results of Paper I was that the N iii triplet emission increases with decreasing background metallicity, Z, due to reduced line-blocking. In this investigation we assume, following Mokiem et al. (2007b), a global Z of the LMC, Z = 0.5   Z_⊙. Because this value is somewhat controversial, and a Z = 0.4   Z_⊙ might be appropriate as well (e.g., Dufour 1984), we need to test the impact of this difference on the derived nitrogen abundances.

Overall, the lower background Z does not produce any extreme changes. As expected, the triplet emission increases, requiring a roughly 0.05 dex lower abundance to recover the previous fits. Interestingly, we also found that N ivλ4058 and the N iii quartet lines tend to more emission and weaker absorption, respectively, but to a lesser extent. The effect on the remaining nitrogen lines is marginal. Note that a lower [N] value owing to lower background abundances would partly cancel the corresponding increase in the derived [N] because of moderately clumped winds.

5. Comments on the individual objects

In the following, we give specific comments on the individual objects, regarding peculiarities and problems found during our analysis. We distinguish between B-/late O-stars and (hotter) O-stars, and sort by luminosity class and spectral type, starting at the hotter side. All nitrogen line fits (including corresponding limits according to Table 6) are displayed in Appendix C, except for the objects N11-072, N11-032, and BI237 which were included in the main paper, because they are exemplary for objects with different features. All spectra were corrected for radial velocity shifts.

We selected those lines that were clearly visible, at least in most cases. In particular, for T_eff ≤ 35 kK, we used N iiλλ 3995, 4447, 4601, 4607, 4621, 4630 and N iiiλλ 4003, 4097, 4195, 4379, λλ4634−4640−4642, and λλ4510−4514−4518. For T_eff  > 35 kK, we analyzed the lines from N iii/N iv/N v: N iii as before, N ivλλ 4058, 6380, and N vλλ4603−4619 (see Table 2). Additionally, the N iv multiplets around 3480 Å and 7103−7129 Å were used for the field stars observed with UVES (except for Sk–70° 69 where only N ivλ3480 is available).

5.1. Late O- and B-supergiants/giants

5.1.1. Supergiants

N11-029 – O9.7 Ib.

This is the only O-supergiant within our sample. Because of its late nature, we discuss it here together with the B-supergiants. No major problem was encountered, and the largest difference with respect to Mok07 concerns the high β = 1.63 derived in their analysis. We opted for a lower value, β = 1.23, still at the limit of prototypical values. To compensate for this modification, Ṁ needs to be somewhat increased.

Figure C.1 shows the best fit for the nitrogen lines. An abundance of [N] = 7.43  ±  0.15 was inferred mainly from N iiλ3995 and the N iii quartet lines. The bulk of the N ii lines are not helpful because they are blended by O ii (Table 2). This is also the case for most of the N iii lines.

The most interesting feature, however, is the discrepancy for N iiiλ4634²³, which shows an almost completely refilled profile but is predicted to be in absorption. To synthesize a profile with EW  ≈  0 would require a higher T_eff or a lower log g, inconsistent with the He ionization equilibrium. This seems to be the first observational evidence for one of the problems discussed in Paper I. For a certain temperature range (around 30 to 35 kK), fastwind spectra predict too little emission in the N iii triplet compared to results from cmfgen, because of the (still) missing overlap effects between the N iii and O iii resonance lines around 374 Å (which are treated consistently in cmfgen; for details, see Paper I).

For additional tests, we calculated a cmfgen model at the same stellar/wind parameters and abundances as derived in the present analysis. As expected, the corresponding synthetic profiles are closer to the observations (though still not as refilled as observed). To check whether the oxygen abundance plays a significant role, two different abundances were considered, [O] = 8.66 and 8.30 dex (solar and factor two lower). In agreement with our theoretical argumentation from Paper I, this difference did not affect the predicted N iii triplet emission strength.

N11-036 – B0.5 Ib.

The largest difference to Mok07 is that we derive a lower value for log g (by 0.2 dex) as well as a lower T_eff (by 500 K), by exploiting He i/He ii in parallel with the N ii/N iii ionization equilibrium.

The nitrogen lines are well fitted, both for N ii and N iii (Fig. C.2). The only discrepancy found relates to an underprediction of absorption strength in N iiλ4607, whereas the discrepancy at N iiλ4601 is caused by an O ii blend. Quite a large enrichment is found, [N] = 7.85  ±  0.17.

N11-008 – B0.7 Ia.

Again, we adapted the fairly high velocity field exponent derived by Mok07, β = 1.87, to a more typical value of β = 1.30. We derived v   sin   i = 46 km   s^-1, which is approximately half the value obtained by Mok07, and compensated by invoking a v_mac = 60 km   s^-1.

The best fitting abundance, [N] = 8.08  ±  0.11 (Fig. C.3), was obtained by the “curve of growth method”, and yielded reasonable fits except for N iiλλ4447, 4621, and N iiiλ4003, which are slightly overpredicted.

5.1.2. Giants

N11-042 – B0 III.

We derive a lower projected velocity than Mok07, v   sin   i = 21 km   s^-1, as well as a lower T_eff, together with a corresponding decrease of log g, for consistency with the N ii/N iii ionization equilibrium. For this cooler solution, the helium abundance needs to be lowered as well, Y_He = 0.08, close to the LMC He baseline abundance (see Sect. 6).

Owing to the low rotational speed, we were able to clearly inspect all N ii and N iii lines (Fig. C.4) which are fitted almost perfectly. The only discrepancy occurs at N iiiλ4097, caused by a coincident O ii line. We were able to see two strong O ii absorption lines at both sides of N iiiλ4640, and to the left of N iiiλ4379 (where the former cannot be used for the diagnostics of similar stars with rapid rotation, N11-008, N11-029, N11-036, and N11-045).

A low nitrogen content was derived, [N] = 7.00  ±  0.15, consistent with the low helium abundance.

N11-033 – B0 IIIn.

We find a slightly cooler T_eff compared to Mok07, and our helium line fits suggest Y_He = 0.10.

Owing to its rapid rotation, all nitrogen lines are severely diluted and almost “vanish” from the spectrum (Fig. C.5), implying an upper limit of [N] = 7.28 from the N ii lines.

N11-072 – B0.2 III.

This object shows a very sharp-lined spectrum, with the lowest v   sin   i value within our sample. A consistent solution for nitrogen and helium suggests a slightly cooler T_eff (by 1 kK) and lower log g (by 0.1 dex). Our best fit indicates Y_He = 0.10.

As for the similar object N11-042, we were able to obtain a good fit from the “curve of growth” method, with [N] = 7.68  ±  0.15, and a rather low v_mic = 2.7 km   s^-1. Thus, and in contrast to N11-042, this object is clearly enriched. Note that N11-072 and N11-042 belong to different associations, LH-10 and LH-9, respectively.

5.2. O-stars

5.2.1. Giants

N11-026 – O2 III(f ^∗ ).

This star is one of the four O2 stars in our sample, together with N11-031, BI237, and BI253, comprising the hottest objects. Unlike Mok07, we favor a cooler solution, T_eff = 49 kK (Mok07: 53 kK), and a somewhat lower Ṁ. This comparably large difference for T_eff relies both on the better reproduction of He iλ4471 and on the fit to the nitrogen lines, with three ionization stages visible (Fig. C.6). Mokiem et al. (2007a) considered this cooler solution as well (almost included in their error bars), which would have improved their fit to He iλ4471, but argued in favor of the hotter one, accounting for the global fit quality. By considering nitrogen now, we find support for a lower T_eff, since for T_eff ≥ 50 kK the N iii lines vanish from the spectrum (cf. BI237 and BI253).

The derived nitrogen abundance results from a compromise solution, [N] = 7.80, where this value is also the lower limit. Moreover, we estimate quite a large uncertainty (upper limit) of 0.4 dex, arising from our difficulties to fit all three ionization stages in parallel. We favor a solution that provides a good fit for the N iii quartet and the N iv lines, whereas a larger abundance, [N] = 8.20, is needed to fit the N v doublet. From Fig. C.6 it is clear that this large abundance (red) disagrees with the remaining nitrogen lines. Of course, we also tried a fit at hotter temperatures. At T_eff = 52 kK (close to the result by Mok07), log g = 4.1 (which is still consistent with the Balmer line wings) and Ṁ = 1.5    ×    10^-6   M_⊙   yr^-1, it is possible to fit both N iv and N v, for quite a similar abundance, [N] = 7.75. At this temperature, however, all N iii lines have vanished. To recover them we would need to increase the abundance again, also by 0.4 dex. Because of the poorer prediction of He iλ4471 we opted for the cooler solution. Since in both cases the implied nitrogen abundances are similar, this does not lead to severe problems for our subsequent analysis, but requires larger error bars than typical.

N11-031 – ON2 III(f^∗).

This star raised the most severe difficulties in our sample when trying to fit the nitrogen lines (Fig. C.7). Already its “ON” designation indicates strong nitrogen features in its spectra, in this case N ivλλ4058,3480 (for the latter, see Walborn et al. 2004), and the N v doublet lines. We were unable to consistently fit these strong features together with the remaining nitrogen lines. In contrast, N ivλ6380 has almost the same strength as in N11-026.

When we tried to reproduce the (rather weak, but clearly visible) He iλ4471 in parallel with N iii and N ivλ6380, we obtained T_eff = 47.8 kK, slightly cooler than N11-026, whilst Mok07 derived T_eff = 45 kK, excluding T_eff values higher than 47 kK based on the helium ionization analysis.

When, on the other hand, we tried to fit the problematic lines, we needed a much higher T_eff. A consistent fit for all N iv lines (including N ivλ6380) together with those from N v requires T_eff = 56 kK, log g = 4.00, and Ṁ = 2.2  ×  10^-6   M_⊙   yr^-1, together with a very high abundance, [N] = 8.30. Clearly, this set of stellar parameters neither reproduces the N iii lines nor the weak He iλ4471. N11-031 has been previously analyzed by Walborn et al. (2004) and Doran & Crowther (2011) using the N iv/N v lines (without discussion of He i and N iii). The former authors obtained quite similar parameters, T_eff = 55 kK, log g = 4.00, and a somewhat lower Ṁ  =  1.0  ×  10^-6   M_⊙   yr^-1, presumably because of a clumped wind (though clumping has not been mentioned). At these parameters, they derived [N] = 8.00  ±  0.18, which for our models would be still too low. Doran & Crowther (2011) only provided T_eff within their analysis, deriving T_eff = 54.7 kK for this object.

Because of the similarities with N11-026 (except for the two strong features), the fact that N ivλ6380²⁴ behaves “normally” and that He iλ4471 is clearly visible, the cooler solution with [N] = 7.83  ±  0.15 cannot be discarded so far. We checked our synthetic spectra by independent cmfgen calculations. The results are quite similar, in particularly the predicted N iii emission lines are even slightly weaker than those produced by fastwind, again pointing to a cooler solution.

We also tried to attribute the problematic feature to the presence of X-rays by means of cmfgen calculations including typical X-ray strengths and distribution, but almost no effect on these lines was found (basically because the line forming region is still inside or close to the photosphere).

Of course, it would be helpful to consider N ivλ3480 as well, which unfortunately is not included in our dataset. A by-eye comparison with the corresponding profile displayed in Walborn et al. (2004, their Fig. 1 showed that both our cooler and hotter solutions are compatible with this spectrum²⁵.

Consequently, the nature of the strong N ivλ4058 and N v doublet features remains open. Of course, binarity could be a plausible solution, where a cooler component could be responsible for He i and N iii, and a hotter one for the intense N iv and N v lines. We note that this is the brightest (M_V =  −5.78) object of the O-star sample and that other, previously thought single early O-stars, displaying both strong N v lines as well as the presence of He i in their optical spectra such as CygOB2-22 and HD 93129A, were subsequently resolved as binaries (Walborn et al. 2002; Nelan et al. 2004). Therefore, the binarity scenario for N11-031 needs to be clarified in future investigations.

Note, however, that the other ON-stars discussed by Walborn et al. (2004), LH64-16 and NGC 346-3, seem to display very similar features, though the presence of He i is not as clearly visible as in our spectrum for N11-031. Similar, but less dramatic, problems are also found for those other sample stars where we were able to analyze N iii/N iv/N v in parallel, namely N11-026 and N11-060 (see below). While the presence of these discrepancies in all these objects may point toward a less likely binary scenario for N11-031, we note that the differences in T_eff for the two alternative solutions reach 8000 K in N11-031, and remain at moderate 3000 K for the other two objects analyzed here.

We will reconsider N11-031 and other ON-stars in future investigation to clarify how it is possible to have weak He i and N iii in parallel with strong N iv and N v. For the remainder of this paper, however, we discuss the results for N11-031 in terms of both the cool and the hot solution, without preferring either of them.

N11-038 – O5 II(f⁺).

The parameter set derived for this star is quite similar to that of Mok07, with only slightly lower Y_He = 0.08 and v   sin   i = 100 km   s^-1. This star displays a peculiar He iλ4471 profile of triangular shape that could not be reproduced, even if invoking macro-turbulent broadening (as speculated by Mok07).

We obtained [N] = 7.85  ±  0.15, similar to the case of N11-032, by means of quite a good fit to all lines from three ionization stages. Besides the peculiar He iλ4471 profile, N ivλ6380 shows contamination by the DIBs at λλ 6376.08, 6379.32, and the N vλ4603 absorption is much stronger than predicted, contrasted to the other component.

Sk–66° 100 – O6 II(f)

is one of the field stars within our sample. The inspection of the H/He fits suggests no major revision of the values provided by Mok07.

Figure C.9 shows the best fit to the nitrogen lines. An abundance of [N] = 8.48  ±  0.15 was needed to obtain a consistent fit. This high value agrees well with the high He content found for this object, Y_He = 0.19. However, we also found some problems regarding the N iv fits, except for the multiplet around 3480 Å, where the fit is perfect. Interestingly, we were able to “cure” these problems by invoking a clumped wind with f_∞ = 0.2, with no significant changes in the remaining nitrogen lines.

N11-032 – O7 II(f).

No major problems were found for this star. Our solution is slightly hotter than in Mok07, and we preferred a typical β value for O-stars, β = 0.80.

An excellent fit is obtained for this star of the (f) category (Fig. 6), resulting in [N] = 7.87  ±  0.15 for both the N iii triplet and the quartet lines. The fit quality of N iiiλ4097 is remarkable as well. Note that for this star N iiiλ4003 has not been observed. Since the N iv lines are weak and quite noisy, we can only state that our simulations are consistent with the observations.

N11-045 – O9 III.

Our analysis agrees well with that of Mok07. We confirm that a low He abundance (lower than the estimated LMC He baseline abundance) matches the observations.

The only clear N-abundance indicators are the N iii quartet lines, since most other lines are weak and the spectrum is noisy (Fig. C.10). N iiiλ4097 is also weakly visible, and consistent with the quartet lines. Around this T_eff, the N iii triplet turns from absorption to emission, and thus this object does not belong to the “f” category. The absence of lines, the fact that the star does not display a fast (projected) rotation, and the very low helium content is consistent with the very low nitrogen abundance, [N] = 6.98  ±  0.20. These findings suggest that this object is of unevolved nature.

5.2.2. Dwarfs

BI253 – O2 V((f^∗)).

This was one of the stars that were used by Walborn et al. (2002) to define the O2 spectral type. A slightly hotter solution (by 1 kK, T_eff = 54.8 kK) than in Mok07 was obtained by using the N iv/N v ionization equilibrium. This star was also analyzed by Massey et al. (2005) and Doran & Crowther (2011). The former authors provide only a lower limit on T_eff and a consistently lower log g (T_eff ≥ 48 kK and log g = 3.9), both in agreement with the error bars by Mok07, whilst Doran & Crowther (2011) derive a somewhat cooler solution (by 2 kK) compared to our findings.

Figure C.11 shows that N ivλ6380, N ivλ3480, the N iv multiplet around 7120 Å (where we reproduce the observed emission), and the N v lines are nicely fitted, with [N] = 7.90  ±  0.15. At this T_eff and Ṁ, no N iii is visible in the spectrum (see also our discussion on N11-031). The feature located around N iiiλ4634 corresponds to O ivλ4632. On the other hand, we were unable to reproduce the fairly broad emission of N ivλ4058 (a higher v   sin   i is inconsistent with the remaining lines). For this star, we compared again with a cmfgen model at similar parameters, in particular with the same [N]. Contrasted to our solution, the width of the N iv emission line could be fitted, whilst the other lines indicated either a hotter temperature or a higher abundance.

BI237 – O2 V((f^∗)).

As for BI253, the nitrogen ionization equilibrium favours the hotter solution proposed by Mok07 (T_eff = 53.2 kK) rather than the cooler limit derived by Massey et al. (2005). Our result is also consistent with the work by Doran & Crowther (2011). This object is quite similar to BI253 with a somewhat thinner wind.

Figure 7 displays a good fit for the nitrogen lines. N ivλ4058 does not show a broad profile as in BI253, and we are able to perform an excellent fit to this line. We derive a lesser enrichment than for BI253, with [N] = 7.38  ±  0.15.

N11-060 – O3 V((f^∗)).

With T_eff = 48 kK, which is about 2 kK hotter than in Mok07, we found a consistent description of H/He and nitrogen. As argued by Mok07, He iλ4471 is similar to N11-031, and they derived a similar T_eff around 45 kK for both stars. Our findings indicate a higher value for both stars, indicating the internal consistency.

Again, we encountered the problem already met for N11-026 and N11-031, i.e., it is quite difficult to fit the lines from three different nitrogen ionization stages in parallel, see Fig. C.12. We opted for a compromise solution with [N] = 8.20 + 0.30, which is quite high but in line with the helium enrichment. Note that we also estimate quite a high upper limit, motivated by the following reasoning.

As for N11-026, we considered the impact of a hotter solution. With T_eff = 51 kK and log g = 4.1, we are able to fit both N iv and N v at a similar abundance, [N] = 8.15. To recover the N iii triplet lines at these hot temperatures, however, requires an increase of [N] by roughly 0.3 dex. Thus, we are able to derive a quite similar nitrogen abundance for different T_eff, either using the N iii/N iv or N iv/N v ionization equilibrium. The upper limit results from the condition to match either N v or N iii, respectively.

Sk–70° 69 – O5 V((f)).

For this field star, we had some problems to reconcile H/He and N at the parameters provided by Mok07. Our final solution is cooler by 1 kK, and we derived Y_He = 0.14 which is lower than the Y_He = 0.17 estimated by Mok07.

Figure C.13 presents the best fit for all nitrogen lines, for [N] = 8.05  ±  0.15. There are only two disagreements: the “right” wing of N iiiλ4634 is predicted a bit too narrow, and N ivλ4058 is predicted to be in very weak emission, contrasted to the observations. We consider the fit acceptable, particularly since in a clumped wind this weak emission becomes almost suppressed.

N11-051 – O5 Vn((f)).

This star is the fastest rotator in our sample, and we derived a slightly higher v   sin   i and cooler T_eff. We also used a prototypical value of β = 0.8 instead of the rather low β = 0.6 derived by Mok07, implying also a lower Ṁ.

Unlike N11-033, where the fast rotation removes almost all information, this object shows the N iii triplet in emission, which is quite well reproduced by our model, with [N] = 7.58  ±  0.20 (Fig. C.14). At such high v   sin   i, these lines are blended with C iiiλλ4647 − 4650 − 4652. Since carbon is not included in our calculations, it is not possible to predict the right wing of the blended profile. That the carbon triplet has the same strength as the N iii one indicates that this star could belong to the newly defined Ofc category (Walborn et al. 2010; Sota et al. 2011), which seems to be strongly peaked at spectral type O5 for all luminosity classes.

The only problem of our fitting procedure is found for N ivλ4058, predicted to be in slight emission and actually not present in the observed spectra. In contrast to N11-058 and N11-065, it was not possible to circumvent this discrepancy by lowering Ṁ, since the fit to H_α becomes inacceptable then. By means of a clumped wind with lower Ṁ, on the other hand, we can fit both H_α and obtain a better result for N ivλ4058, whilst not compromising the remaining nitrogen lines.

N11-058 – O5.5 V((f)).

To find a consistent solution for all H, He, and N lines, a very low Ṁ = 0.01    ×    10^-6   M_⊙   yr^-1 is required (similar to the case of N11-065), and also a low log g (0.14 dex lower than Mok07), which is still consistent with the Balmer line wings but appears to be fairly low for a dwarf.

This was the only O-star that could be analyzed by the “curve growth method” with respect to [N] and v_mic. The derived value of v_mic = 6  ±  3 km   s^-1is lower than for the other O-stars, though such a difference does not drastically affect the derived abundance, as argued in Sect. 4.4. Quite a large abundance, [N] = 8.09  ±  0.15, was determined which fits all the lines (Fig. C.15).

Sk–66° 18 – O6 V((f)).

Our estimates agree well with those from Mok07. As for Sk–66° 100, we found a very large nitrogen abundance, [N] = 8.48  ±  0.15 (Fig. C.16). Note that the N ivλ4058 line is predicted in weak emission but appears in absorption. Again, lowering Ṁ was not sufficient to cure this problem. A somewhat better fit to the this line was obtained for a weakly clumped wind with f_cl = 2.3, included in the figure.

N11-065 – O6.5 V((f)).

Our best fit to the He lines indicates Y_He = 0.13, lower than the value derived by Mok07, Y_He = 0.17. As already discussed in Sect. 4.3, a satisfactory reproduction of N ivλ4058 requires a very low Ṁ = 0.05    ×    10^-6   M_⊙   yr^-1. Since this line clearly appears in absorption, whereas our model with Ṁ from Mok07 predicts much too less absorption, we lowered Ṁ, but were able to preserve the fit to H_α and the remaining nitrogen lines. By the inclusion of clumping we obtained an even better fit quality, with [N] = 8.17  ±  0.15 from N iii and N iv.

N11-066 – O7 V((f)).

T_eff and log g as derived by Mok07 turned out to be inconsistent with the N iii/N iv ionization equilibrium. We had considerable problems to fit both N iii and N iv lines at the same abundance, and particularly to reproduce the absorption within N ivλ4058 and the N iii quartet lines. To this end, a lower T_eff was mandatory, but only rough estimates using our coarse grid could be obtained, resulting in T_eff = 37 kK and log g = 3.7 dex, which are 2.3 kK and 0.17 dex lower than the values provided by Mok07, respectively. The gravity is somewhat low for a dwarf but still inside the error bars assigned by Mok07. With these values, we determined [N] = 8.17  ±  0.20, see Fig. C.18, which seems rather large for Y_He = 0.1.

N11-068 – O7 V((f)).

As for N11-066, we were only able to fit the H/He and N lines by means of the coarse grid. The differences to the results by Mok07 are significant, but still consistent with the observations and identical to those of N11-066 which has the same spectral type.

In contrast to N11-066, however, particularly the N iii triplet shows weaker emission, and thus a lower [N] = 7.85  ±  0.20 has been found, see Fig. C.19.

N11-061 – O9 V.

In contrast to Mok07, we chose a prototypical value for the velocity field exponent, β = 0.8, together with a higher value for Ṁ. All H/He lines could be reproduced without difficulties.

The nitrogen analysis is quite similar to the case of N11-045, and we derived [N] = 7.18  ±  0.15 from N iii alone (Fig. C.20).

N11-123 – O9.5 V((f)).

Our parameters are very similar to Mok07, and Fig. C.21 shows our solution for N ii/N iii. Even though the rotation is not extreme, almost no nitrogen is visible, and the features overlapping with the “non-existent” N iiλ4630 and N iiiλ4640 are blends by O iii and Si iii, respectively. Thus, we infer a very low nitrogen content, [N] = 7.00  ±  0.15, roughly corresponding to the LMC baseline abundance.

N11-087 – O9.5 Vn.

For this rapid rotator we also found good agreement with Mok07. Because of rotation, all nitrogen lines are diluted into the continuum (Fig. C.22), and only an upper limit for [N] could be estimated, [N] = 7.38.

6. Discussion

6.1. Comparison with results from Mok07

In our discussion of the derived results we first concentrate on a brief comparison with the findings by Mok07 (see Table 5). Except for a few cases, we derive somewhat cooler T_eff. To a certain extent, this might be attributed to the improved temperature structure in the new fastwind version, and also to the possibility to exploit the nitrogen ionization equilibrium. The most substantial changes concern N11-026 (4.3 kK cooler), and N11-031 (already the cooler solution is 2.8 kK hotter). For the earliest stars in our sample (two O2 dwarfs and two O2 giants), we determine a temperature range of 47.8  ≤  T_eff ≤ 54.8, quite similar to Mok07, but now including N11-031, since we infer hotter solutions for this object. Massey et al. (2005) found a similar range, using two dwarfs and two giants. Gravities changed in parallel for most of the cases, with 0.10 and  −0.43 dex as largest positive and negative difference, respectively. Stellar radii agree very well, even for the two stars with the most extreme changes in T_eff (less than 5% difference in R_∗).

We derive Ṁ values that are typically lower by less than a factor of two (Δlog Ṁ  ≈   −0.1 ...  −0.4 dex), with a maximum change of  −1.2 dex for N11-058 based on our analysis of the nitrogen lines. The resulting Y_He values agree well, except for two stars with differences considerably larger than the adopted errors. For both stars (Sk–70° 69 and N11-065) we find a lower helium content.

The largest differences relate to v   sin   i and v_mic. Differences around 30 − 40% in v   sin   i stress the importance of obtaining this parameter in a separate step, when using an automated fitting method. The substantial differences in v_mic, on the other hand, should not be taken too seriously. To a major part, v_mic has not been literally derived during this work, but was only adopted (as v_mic = 10 km   s^-1), where the resulting fit quality did not indicate any problems with this value, within  ±5 km   s^-1. Only for four mostly cooler stars we were indeed able to infer more robust estimates, indicating quite a low v_mic  ≈  5 km   s^-1. Note, however, that the latter value refers to nitrogen lines only, and inconsistencies in v_mic from H/He (used by Mok07) and metal lines have been found already in various studies.

Because the topic of a potential relation between v_mic and stellar type (log g!) is of recent interest²⁶ because it might indicate (together with other evidence) the presence of sub-surface convection (Cantiello et al. 2009), a more thorough investigation is certainly required. A derivation from light elements will become difficult for the hotter O-stars though, because of the restricted number of visible lines and the complex formation mechanism of the ubiquitous (photospheric) emission lines. Here, it will become advantageous to exploit the information contained in the numerous UV Fe and Ni lines (e.g., Haser et al. 1998).

6.2. Overlap with B-star nitrogen analyses

To ensure the consistency between O-star nitrogen abundances from this (and upcoming) work and previous results from B-stars (using different codes, model atoms and analysis methods), a more thorough inspection of the cooler objects is certainly required. Indeed, we are able to compare with alternative nitrogen abundances from some overlapping objects (compiled by Hunter et al. 2009, see Table 6), which are based on stellar parameters obtained by means of tlusty and using the Si iii/Si iv ionization equilibrium (Hunter et al. 2007).

Hunter et al. (2007) already realized that their T_eff-values were somewhat lower than corresponding results from Mok07 (who used exclusively H and He), but also pointed out that T_eff estimates based on He iiλ4541 would agree much closer. This is even more true regarding our “new” values, which lie in between the Hunter et al. estimates from Si and those from Mok07. These differences in T_eff derived either from metals or from H/He are somewhat disturbing because of their influence on the metallic abundances when using lines from one ionization stage only.

Still, Hunter et al. (2007) decided to keep their cooler solution to preserve the internal consistency of their analysis. Consequently, the nitrogen abundances derived in the present study are systematically higher because of our higher T_eff (leading to intrinsically weaker N ii lines), with ΔT_eff ≈ 1kK for N11-008 and N11-072, and  ≈ 2 kK for N11-036. For N11-042, the T_eff is quite similar, and for this object the derived [N]-values indeed overlap by better than 0.1 dex. For N11-029 our T_eff is quite similar as well, but we derive a 0.1 dex lower log g, which leads to weaker N ii lines.

To check our model atom and our diagnostic approach, we performed an additional analysis by reproducing the conditions adopted by Hunter et al. (2007), i.e., we used their stellar parameters (with negligible Ṁ to mimic tlusty models) and N ii lines only, within the “curve of growth” method and adopting their N ii equivalent widths and uncertainties. For N11-029 and N11-042, we could only perform a “by eye” estimate because Hunter et al. considered one N ii line alone. Corresponding results are compared in Table 7, and the agreement is almost excellent.

Therefore we conclude that the consistency of nitrogen abundances in the overlapping B- and O-star regime is satisfactory, and that the different codes and methods reasonably agree. However, there is a slight offset on the order of 0.1 to 0.2 dex, which we attribute mostly to different effective temperatures. Because our analysis is based on both N ii and N iii lines (in contrast to Hunter et al.), and was performed in parallel with the analysis of H/He, we prefer our values.

6.3. Nitrogen abundances

Figure 8 summarizes the basic outcome of our analysis by displaying the derived nitrogen abundances as a function of spectral type and helium content together with the LMC baseline abundance from Hunter et al. (2007). Evidently, there are only few cooler objects located close to the baseline, whereas the majority of the objects (independent of luminosity class!) is strongly enriched, with [N] in between 7.5 and 8.1²⁷. Five objects display extreme enrichment, with [N] from 8.17 to 8.5, which is close to the maximum nitrogen content given by the CNO equilibrium value for nitrogen, [N]_max  ≈  8.5. However, this is well above the enrichment reached for a 40 M_⊙ star with an initial rotational velocity of 275 km   s^-1 (Brott et al. 2011a).

The lower panel of Fig. 8 is more promising. There seems to be a strong correlation between the nitrogen and the helium enrichment, here displayed logarithmically. The LMC helium abundance should be located, in terms of number fraction, around Y_He = 0.08 − 0.094 corresponding to [He] = 10.90 − 10.97 (Russell & Dopita 1990; Maeder & Meynet 2001; Vermeij & van der Hulst 2002; Peimbert 2003; Tsamis et al. 2003), and agrees quite well with our minimum values for the derived helium abundance. We found only five stars with considerably enriched nitrogen close to this value, three (super-)giants and two dwarfs, but note also the attributed uncertainty in helium content. Except for these objects, the correlation is almost perfect, and there is a certain clustering around the pair [He] = 11.0/[N] = 8.0.

A somewhat different view is provided in Fig. 9, which displays the so-called “Hunter-plot”, nitrogen-abundance vs. projected rotational speed, for all our sample stars with T_eff ≥ 29 kK. N-11 stars are indicated in black, field stars in blue. Circles, diamonds, and squares correspond to objects with low (Y_He  <  0.1), intermediate (Y_He = 0.1), and strong (Y_He  >  0.1) helium enrichment, respectively.

The background of this figure consists of results from the recent population synthesis by Brott et al. (2011b), for all objects with T_eff ≥ 29 kK, and a magnitude limit (corresponding to our sample) of V ≤ 15.29, shown as a density plot. The underlying simulation assumes a fairly broad Gaussian rotational velocity distribution as derived for LMC early-type stars, peaking at 100 km   s^-1 with a standard deviation of σ = 140 km   s^-1 (Hunter et al. 2008b, 2009)²⁸, and random inclinations.

Such diagrams ([N] vs. v   sin   i, compared with evolutionary calculations) have been presented the first time by Hunter et al. (2008a), to summarize the outcome of the B-star analyses within the FLAMES-I survey, and to investigate the predicted effects of rotational mixing. One of their major findings was the unexpected presence of a significant number of objects with slow rotation and high enrichment, not predicted by (single-star) theory, so-called “group 2” objects.

In the O-star case now this problem becomes even more severe. We refrain here from a detailed statistical analysis, because there are too few investigated objects, and postpone this until the results from the FLAMES Tarantula survey (with more than 200 “useful” O-stars) have become available.

Nevertheless, the trend is obvious. Roughly one third of the objects are located at positions where they should be expected (those at the baseline and the “diagonal”), another one-third is located at the predicted upper limit, and the last one-third (beyond [N] = 8.0) extends to very high values where the predicted population density is almost zero. We note that the two objects with the highest [N] enrichment ( ≈ 8.5 dex, which is (incidentally?) just the maximum nitrogen content given by the CNO equilibrium value) are two field stars, Sk–66° 100 and Sk–66° 18, one O6 giant and another O6 dwarf. Both stars did not present any difficulties in the nitrogen analysis, which indicates a reasonable quality.

In terms of the original Hunter et al. sample, roughly two-thirds of our objects would be denoted by “group 2”²⁹. The corresponding number of objects is so large that inclination effects w.r.t. v   sin   i should be irrelevant. Interestingly, however, the corresponding He-abundances are in line with our findings. The first group has a low abundance (Fig. 9, circles), the second group mostly consists of enriched objects (diamonds), and the third one comprises objects with considerable He enrichment (squares). Accordingly, in parallel with the derived correlation between observed nitrogen and helium content, the discrepancy between observations and theory becomes the stronger the larger the He-abundance is.

In evolutionary models the amount of He transported to the surface is strongly controlled by the parameter f_μ, which describes the inhibiting effect of mean molecular weight gradients (in this case, the H-He gradient) on the transport of elements (see Heger & Langer 2000). The models of Brott et al. (2011a) have adopted f_μ = 0.1, from an earlier calibration of Yoon et al. (2006). Lowering the sensitivity to the mean molecular weight barrier would increase mixing of nitrogen and helium to the surface, but would also reduce the minimum mass and velocity required for chemical homogeneous evolution in the models (see also the discussion in Heger & Langer 2000). Given the present values of [N] and Y_He, it might be possible to derive tighter constraints on f_μ in future work.

7. Summary

We investigated the N ivλ4058 emission line formation, determined the nitrogen abundance of a sample of 25 LMC O- and early B-stars, and performed a first comparison with corresponding predictions from stellar evolution including rotational mixing. The results of this work can be summarized as follows.

• 1.

  The dominating process responsible for theN iv line emission in O-stars isthe strong depopulation of the lower level by the “two-electron”transitions 3p  →  2p², of (mostly) photospheric origin. This drain increases as a function of Ṁ because of increasing ionizing fluxes (which are coupled to the He ii continuum), which leads to more depopulation of the ground and the coupled 2p² states. Resonance lines (as for the N iii emission triplet) do not play a role for typical O-star mass-loss rates and below. Because in addition to nitrogen there are many other elements that display optical line emission in the hot star regime (C, O, Si), it might be suspected that similar processes might be invoked because of similar electronic configurations/transitions.

• 2.

  To infer the nitrogen abundances, we redetermined the stellar and wind parameters by means of “by eye” fits, starting with the values provided by Mok07, but exploiting in parallel the nitrogen ionization equilibrium and deriving v   sin   i in a first, separate step. Moreover, we accounted for extra line-broadening expressed in terms of v_mac. In addition to systematically lower v   sin   i, we also derived mostly lower T_eff (partly because of using an improved fastwind version) and thus log g, but differences to Mok07 are generally small, except for few objects.

• 3.

  Based on these parameters, we derived nitrogen abundances mostly by varying the abundance and comparing with all nitrogen lines present in the spectrum. In a few cases, we were able to estimate [N] and v_mic in parallel, by means of a curve-of-growth method.

• 4.

  Again in most cases, we found no problems in fitting the nitrogen lines, and reproduced the “f” features quite well. Only for some of the (hotter) objects where lines from all three stages, N iii, N iv and N v, are visible, we needed to aim at a compromise solution. Considerable problems were encountered for one star, N11-031 (ON2 III(f^∗)), where only either He i, N iii and N ivλ6380 (at cooler T_eff) or N iv and N v (at higher T_eff) could be fitted in parallel. The difference in the derived T_eff amounts to 8000 K, which is far from satisfactory, and requires future effort to resolve the problem. A solution in terms of binarity, though somewhat unlikely, cannot be ruled out so far.

• 5.

  For some cooler objects already analyzed by Hunter et al. (2007) by means of tlusty using N ii lines alone, we found differences in [N] on the order of 0.1 to 0.3 dex, with higher values from our analysis. These differences could be exclusively attributed to different stellar parameters, mostly T_eff. Overall, however, the nitrogen abundances in the overlapping B- and O-star domain are consistent within a reasonable error.

• 6.

  Within our sample, we found only three cooler objects close to the LMC nitrogen baseline abundance, [N]_baseline = 6.9. The majority of the analyzed O-stars (independent of luminosity class) seems to be strongly enriched, with [N] = 7.5 to 8.1. Five objects indicate an extreme enrichment, with [N] = 8.17 to 8.5.

• 7.

  There is a fairly good correlation between the derived nitrogen and helium surface abundances.

• 8.

  Comparing the nitrogen abundances as a function of v   sin   i with tailored evolutionary calculations, we found a significant number of highly enriched, low v   sin   i (“group 2”) objects. Interestingly, the correlation between He and N becomes also visible in this comparison: whilst most objects with unenriched He are located just in the region where the predicted population density is highest (accounting for selection effects), objects with enriched He are located at the upper limit of this distribution and above, and particularly those with the highest He enrichment lie well above this limit.

Owing to the low initial (baseline) nitrogen abundance, the detection of strong nitrogen enrichment in the bulk of O-stars might indicate that efficient mixing takes place already during the very early phases of stellar evolution of LMC O-stars. Nevertheless, it would be premature to draw firm conclusions from our results, because the sample size is still small. Upcoming results from the VLT-FLAMES Tarantula survey (which will be derived in a similar way as presented here, drawing from our experience) will enable a more complete view. In particular, the determination of O-star nitrogen abundances in the LMC will place very tight constraints on the early evolutionary phases of O-stars and thus on the theory of massive star evolution.

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Acknowledgments

We like to thank our anonymous referee and N. Walborn for valuable comments and suggestions. Many thanks to P. Crowther for providing us with the UVES spectra for the LMC field stars, and N. Przybilla for synthetic spectra based on his N ii model ion and for performing test calculations with the N ii data set developed by C. Allende Prieto. Many thanks also to John Hillier for providing the cmfgen code, and particularly to Keith Butler for his advice and help on the nitrogen atomic data. J.G.R.G. gratefully acknowledges financial support from the German DFG, under grant 418 SPA 112/1/08 (agreement between the DFG and the Instituto de Astrofísica de Canarias). J.P and F.N. acknowledge financial support from the Spanish Ministerio de Ciencia e Innovación under projects AYA2008-06166-C03-02 and AYA2010-21697-C05-01.

References

Online material

Appendix A: Details of the nitrogen model atom

This section provides some details of our N ii, N iv and N v model ions (corresponding material for N iii has been already presented in Paper I). Configurations and term designations are outlined in Tables A.1−A.3, whilst Figs. A.1−A.3 display the Grotrian diagrams for the N ii singlet and triplet system (the quintet system comprises five levels only), the N iv singlet and triplet system, and the N v doublet system, respectively. In these figures, important optical transitions as given in Table 2 are indicated as well.

Appendix B: Tests of the N II model ion

Figures B.1 to B.7 refer to tests of our N ii model ion, as described in Sect. 2.2.1. Figure B.1 compares electron temperatures and densities for B-star parameters calculated by fastwind and tlusty, whilst Figs. B.2 to B.7 compare corresponding synthetic N ii line profiles from these two codes and from calculations by Przybilla et al. (priv. comm.).

Appendix C: Line fits for individual objects

Figures C.1 to C.22 display the observed (green) and best-fitting optical nitrogen spectra (black) for all our objects, except for N11-072, N11-032, and BI237, which are contained in the main section. Blue and red spectra show corresponding synthetic line profiles with [N] at the lower and upper limit, respectively. For N11-031 (Fig. C.7), we show the fits corresponding to the two alternative solutions for this star (see Sect. 5). For details on the line fits, see Sect. 5, and for adopted stellar parameters and derived nitrogen abundances inspect Tables 4 and 6, respectively. All fits are based on unclumped winds except when explicitly stated.

All Tables

All Figures