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Astron. Astrophys. 349, 553-572 (1999)

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6. Results

As this paper represents a first attempt to assign purely non-LTE atmospheric parameters to a large sample of B-type supergiants in a self-consistent and purely spectroscopic manner, we shall preface our results on chemical abundances with a discussion of the estimated atmospheric parameters. We shall compare our results (in particular the effective temperature scale) to the results published by other authors and shall discuss the errors, both systematic and random, which are present in our methods.

Because of the rather large number of supergiants in our dataset and the moderate quality of the spectroscopic data, we shall not attempt to chemically analyse each star independently. We shall instead examine the variations in linestrength as a function of effective temperature with the following aims:-

  • To investigate whether standard non-LTE methods can adequately reproduce the spectra of B-type supergiants.

  • Subject to the above, to estimate the non-LTE absolute abundances of the sample as a whole.

  • To quantify the linestrength variations in terms of abundance depletions or enrichments, focussing principally on those elements which are indicative of the presence of core-processed material in the photosphere.

6.1. Atmospheric parameters

Any chemical analysis depends upon the the reliability of the estimated atmospheric parameters, in particular that of the effective temperature scale ([FORMULA]). Many authors have ascribed temperature scales to early-type stars using a variety of empirical and more theoretical methods - a recent review is given by Crowther (1997). As well as the random errors associated with, e.g., errors in equivalent width measurements or line profile fitting, there are systematic offsets between the different scales due to the differing physical assumptions inherent in each method.

The [FORMULA]-[FORMULA] estimates, which are listed in Table 1, are reproduced in graphical form in the upper panel of Fig. 2. Also shown, in the lower panel, is a comparison of the [FORMULA]-scale derived here with the effective temperature versus spectral type scale used in Paper II, which was based upon that used by Barlow & Cohen (1977) and Lamers (1981). We emphasise that the temperature scale will be strongly dependent on the method used to obtain it. In particular the treatment of non-LTE effects and of line blocking may have significant effects. It is immediately apparent from the lower panel that the [FORMULA]-scale derived here is systematically hotter than that used in Paper II. This difference may be at least partly due to the lack of metal line-blocking in our non-LTE models and is not unexpected. However, whilst the systematic differences are real, they are probably not important for this analysis - the important point is that a consistent scale is used throughout.

[FIGURE] Fig. 2. Top: The estimated values of effective temperature and logarithmic gravity - as listed in Table 1. The symbols refer to the luminosity class as follows: cross - Ia+, triangle - Ia, diamond - Iab, circle - Ib, box - II and asterisk - III. Also shown is a linear fit, which excludes the luminosity class II and III objects. This fit then represents the average atmospheric parameters of the supergiant sample. Bottom: A comparison between the [FORMULA]-scale estimated here and that adopted in Paper II - see text for further discussion.

Despite the problems in applying Kurucz's LTE model atmospheres (1979, 1991) in the analysis of luminous stars such as are considered here, the Kurucz temperature scale is likely to be more physically realistic and closer to the empirical scale due to the fuller treatment of metal line blocking. Certainly, in the analysis of main sequence B-type stars, the Kurucz scale has been widely used (see, for example, Hibbins et al. 1998 and Smartt et al. 1996a , 1996b) and it would be useful to compare our scale with it. Recent analyses of early B-type supergiants (Smartt 1996) using both blanketed and unblanketed techniques have shown that the latter yield [FORMULA] estimates which are typically 10% higher than the former - this relationship has been recently confirmed by Hubeny et al. (1998) at higher effective temperatures.

In order to further investigate and confirm this relationship, we have examined the temperature-optical depth structures of our models and those of Kurucz. The aim is to derive a mapping between the temperature scale of Kurucz and that of our non-LTE unblanketed models. However, the task is made significantly more difficult as the gravity label of a model atmosphere may also depend on the physics included in the model. It has been shown recently (Lanz et al. 1996) that the derived stellar gravity may change significantly depending on whether or not line blocking is treated. Thus the correct mapping may not be purely along the temperature axis, but may also have a component in the [FORMULA] direction. The situation is further complicated as achieving convergence with Kurucz models at low gravities (such as may be appropriate for the supergiants analysed here) can be very difficult. For this reason, our grid of Kurucz models does not go to as low gravities as our TLUSTY grid. Hence, it would be a non-trivial effort to fully determine the nature of the mapping between the two scales, if such a simple relationship exists, and we have not attempted to rigorously define such a mapping.

However at gravities appropriate to (near) main-sequence stars ([FORMULA] = 4.0), a shift in effective temperature of approximately 10% yields reasonable agreement between the temperatures in the line forming region - the sense of this shift in going from the TLUSTY scale to the Kurucz scale is a decrease in the effective temperature label of the corresponding model. Whether this shift can be assumed to be appropriate for supergiants is unclear. The situation is complicated further by the possible effect of a stellar wind on the Balmer line profiles, which might lead to a further error in our estimated gravities. For these reasons, we tentatively suggest that a reduction of approximately 10% in our [FORMULA]-scale may be appropriate to allow for the effects of line blanketing.

A clear separation between the luminosity classes is evident in the upper panel of Fig. 2. In particular, the luminosity class II/III objects are distinct from the other supergiants. For example, a large range in gravity is present at [FORMULA] 4.3 (spectral type B2 on our scale) and simply reflects the increased range in luminosity classes observed at this spectral type. There is also evidence that effective temperature is a function of gravity at fixed spectral type, in the sense that stars having lower gravities also have lower [FORMULA] (see Table 1). This `shear' effect has been examined by Voels et al. (1989) for a sequence of stars having spectral type O9.5, who found a monotonic dependence of [FORMULA] on [FORMULA] - for Ia to V; [FORMULA] = 30 000 K to 35 000 K - in qualitative agreement with our results.

In the syntheses of helium and metal line linestrengths, the effect of these gravity variations has been included in the following manner: The straight line in Fig. 2 (upper panel) shows a least-squares fit through the [FORMULA]-[FORMULA] plane - this fit excludes the luminosity class II & III objects and hence represents the average parameters of the luminous supergiant sample. In generating theoretical linestrengths as a function of [FORMULA], we have used the appropriate [FORMULA] values given by this fit. Thus, the loci of non-LTE linestrengths which are used below, might be expected to reproduce the general behaviour of the spectral features as a function of temperature, but will not allow for any variations in the gravity of individual stars from this least squares fit.

6.2. Helium fractions, y

In Fig. 3 the observed and predicted strengths of He I lines are compared. The singlet and triplet series lines (in order of increasing oscillator strength) are shown on the left and right respectively, for two helium fractions, y = 0.09 (solar) and y = 0.20. MLD have previously shown that it is important to use a non-zero microturbulence when modelling these features in early B-type supergiant spectra. Hence in order to confirm this conclusion, we included non-LTE results for two values of the microturbulent velocity, [FORMULA] = 0, 10 km s-1.

[FIGURE] Fig. 3. Measured He I linestrengths with non-LTE predictions. The plots on the left show representative singlet lines, whereas those on the right show triplet lines. Both are plotted in order of increasing oscillator strength. The non-LTE loci are for helium fractions, y = 0.09 (solid lines) and y = 0.20 (dashed lines) and are each shown for two values of the microturbulence, [FORMULA] = 0, 10 kms-1. The symbols are the same as those in Fig. 2.

From inspection of Fig. 3, it is obvious that there are a number of unresolved problems in reproducing the He I spectra of B-type supergiants. Considering first the question of microturbulence, we confirm our previous finding that a non-zero value for [FORMULA] leads to improved agreement between theory and observation - this improvement is apparent in all lines except 4437 Å (the weakest line under consideration here). In all cases, the trivial result is found that using an increased microturbulence leads to a reduction in the estimated value of the helium fraction and apart from the line at 4437 Å, this brings the y-estimates closer to the solar value. The effect is most obvious, perhaps, in the cases of the lines at 4471 Å and 4713 Å (both triplets), which for [FORMULA] = 0 km s-1 imply that a helium fraction, [FORMULA] 0.2, for most of the supergiant sample. More importantly, as was shown by MLD, microturbulent line broadening leads to an improvement in the quality of the He I line profile fits.

The neutral helium lines may be subject to the `generalised dilution effect' (as discussed by Voels et al. 1989), whereby various He I level populations are enhanced due to sphericity, leading to a strengthening of the triplet lines relative to the singlets. Voels et al. suggested that the He I lines forming deepest in the atmosphere should be least affected and should therefore provide more reliable y-estimates. This logic has been used by a number of other authors (e.g. Smith & Howarth 1994) and it is noticeable that these papers estimate smaller helium fractions than those which use all available He I lines (e.g. Lennon et al. 1991b). As formation depth is primarily determined by the intrinsic strength of the line, the weakest lines should be the more reliable. Indeed, Fig. 3 does seem to confirm this result - the singlet and triplet systems do suggest that the estimated y-value increases with oscillator strength.

Finally, as was noted by MLD, the triplet lines appear to indicate higher helium fractions than the singlets. In the above paper this was attributed to the lack of metal line blocking, which leads to a spurious calculation of the ultraviolet radiation field. As has been discussed by Lennon & Dufton (1989), this could be particularly important in calculating the photoionisation rates from the n=2 levels in He I , especially for the metastable 23S state - it is unlikely to be as important for photoionisation from the ground state, as the flux in this spectral region for B-type supergiants is very low. This may explain the well-known difficulties in reproducing the triplet features at 5876 and 10 830 Å in non-LTE calculations such as these. If this hypothesis were correct, we might expect that the problem would be less important for the late B-type supergiants due to the reduced flux in the n = 2 continua of He I and there is tentative evidence that this is the case (e.g. the 4471 Å line). In any case, the singlet lines seem to be more reliably modelled over the whole temperature range, with the line at 4387 Å giving the most satisfactory fits.

Given the problems associated with modelling the lines of He I , it is difficult to unambiguously identify any supergiants which may be helium rich. The dependence of the linestrengths on gravity, which is not explicitly included in Fig. 3, is an added complication. It seems that the only reliable way to examine the helium fractions is to perform individual examinations of the line profiles, which is beyond the scope of this paper. However, we will further discuss the possibility of a variation in helium fraction in our sample below.

6.3. Absolute metal abundances

As was explained above, we shall not give absolute elemental abundances for individual objects in our supergiant sample, but shall instead give a broader based analysis of the targets as a whole. Such an approach requires that we make comparisons with previously published abundances in early-type stars. However, the different analytical methods which have been used and the sensitivity of the results to such methods mean that it is not immediately obvious which analyses represent the most suitable comparisons. We shall therefore begin with a discussion of recent abundance analyses performed on B-type stars, limiting our discussion to those analyses which used non-LTE techniques applied to optical spectra.

Gies & Lambert (1992) and also Cunha & Lambert (1992, 1994) have examined a significant number of B-type stars and give pseudo-non-LTE abundances. The overlap between their work and ours is somewhat limited in the sense that their target lists comprise mostly main sequence or near main sequence objects and only include a small number of B-type supergiants. They have also concentrated on objects in the spectral type range B0-B3 (which covers the peaks in strength of lines due to CNO). However, each of their papers uses a consistent (and reliable) philosophy in obtaining abundances - essentially an LTE methodology. In obtaining the atmospheric parameters (effective temperature and gravity), they have used profile fits to the pressure-sensitive Balmer lines (typically H [FORMULA]) and a published calibration of the temperature-sensitive [[FORMULA]] photometric index. They derive LTE atmospheric parameters and element abundances and then use a sophisticated mapping procedure to allow for non-LTE effects in individual lines. Aside from the limited overlap between their stellar sample and ours, their reliance on `photometric' temperatures, which use Kurucz's LTE model fluxes as a calibration, may mean that their work does not provide suitable material for comparison with our results which omit the effect of line-blocking and use ionisation equilibria as the temperature indicator.

In a series of recent papers, Kilian has also made substantial efforts in the area of non-LTE B-type star abundance estimations (see Kilian 1992, 1994 and references therein). Again, her sample primarily consists of near main sequence objects. However, her non-LTE methods are very similar to those used here - her spectroscopic approach in estimating atmospheric parameters (Kilian 1991) and non-LTE philosophy is closely mirrored by ours. Kilian has used the LTE line-blanketed model atmosphere structures of Gold (1984), but her treatment of the non-LTE problem is similar to ours in that line blocking is not treated in her statistical equilibrium and line transfer computations. Of particular importance is that our atomic datasets are effectively identical to those used by Kilian. Therefore, whilst differences are likely between the [FORMULA]-scale derived by Kilian and that derived here, element abundances are likely to be comparable. For these reasons we have elected to compile representative non-LTE B-type main sequence stellar abundances from the results of Kilian.

Within her sample of 21 near main sequence B-type stars, Kilian identifies three stars as having anomalously high nitrogen abundances and four stars as having anomalously low silicon abundances. The nitrogen enrichments are attributed to chemical processing effects and the apparent silicon depletions are likely to be due to difficulties in modelling her cooler stars' silicon spectra. In compiling the `normal' abundances, listed in Table 2, we have excluded these results - our rationale being that we wish to make comparisons with unprocessed stellar material. However, the slightly higher value for the standard deviation, [FORMULA], in the case of nitrogen may indicate a larger intrinsic scatter in the nitrogen abundances within Kilian's sample.


[TABLE]

Table 2. Mean non-LTE abundances for main sequence B-type stars (on the logarithmic scale with hydrogen being 12), as compiled from the work of Kilian. Also shown are the number of stars used in determining the average, n, and the standard deviation in the mean, [FORMULA] (see text for further details).


Rather than discuss the chemical elements in order of their atomic number, as is conventional, we shall deal first with those elements which are likely to have a unique abundance throughout the stellar sample (i.e. Mg & Si). We shall then discuss those elements whose linestrengths may be affected by abundance variations (i.e. CNO).

6.3.1. Magnesium

Our spectral data provided only one feature due to Mg II , namely the close doublet at 4481 Å, whose observed equivalent widths are shown in Fig. 4. As this line is used as a primary indicator in the spectral typing of B-type stars, any large discontinuities would call our temperature scale into question. Therefore the observed smooth monotonic variation with effective temperature is reassuring. A greater range in observed linestrengths at [FORMULA] [FORMULA] 4.3 is most probably due to the larger range in surface gravities at this temperature (see Fig. 2).

[FIGURE] Fig. 4. Observed Mg II equivalent widths compared with the non-LTE predictions. The non-LTE locus is for a magnesium abundance of 7.38 dex with [FORMULA] = 10 kms-1 (full line). Also shown are loci for magnesium abundances at [FORMULA] 0.2 dex (dotted). The symbols are the same as those in Fig. 2.

Also shown are non-LTE results for the representative B-type stellar magnesium abundance of 7.38 dex (full line) with additional loci at [FORMULA]0.2 dex - all for [FORMULA] = 10 km s-1. Our non-LTE calculations suggest that the abundance for our supergiant sample may be constant at [FORMULA] 7.58 dex. This is slightly higher than the magnesium abundance implied by results of Kilian, but the agreement is still relatively good given the different luminosity classes of the two samples.

6.3.2. Silicon

In Paper II, equivalent widths were given for 11 spectral features due to silicon, covering three ionisation stages and 5 multiplets. For Si II , we have elected to show the line at 4128 Å - the other component of this doublet is at 4131 Å and shows a qualitatively similar behaviour. A second doublet was also measured at 6347 & 6371 Å but was not well modelled by our non-LTE computations and has not been included here. There are two multiplets due to Si III which were measured in Paper II, viz. the triplets at 4552, 4567 & 4574 Å and 4813, 4819 & 4829 Å. The second of these multiplets is not illustrated as it is inherently quite weak, while the feature at 4552 Å has been selected as representative of the first multiplet. Only one spectral feature due to Si IV is shown, that is the line at 4116 Å. The other component of this doublet (at 4088 Å) suffers blending problems due to a nearby line of O II .

The observed and predicted equivalent widths for these lines are shown in Fig. 5. The synthetic line strengths are for a silicon abundance of 7.28 dex (with [FORMULA]0.2 dex) and a microturbulence of 10 km s-1. However, as some difficulties remain with the non-LTE modelling of these lines, the predictions are only plotted for restricted ranges of effective temperature.

[FIGURE] Fig. 5. Observed Si II /III /IV linestrengths compared with non-LTE predictions. The non-LTE loci are for silicon abundances of 7.28 dex [FORMULA] 0.2 dex and [FORMULA] = 10 km s-1. The symbols are as in Fig. 2.

The silicon lines are believed to be well modelled in the temperature range where Si II is strong and indeed agreement between theory and observation for the Si II feature is good. There may be a decline (relative to the theoretical calculations) in the observed linestrengths at later spectral types, possibly due to a decrease in the microturbulence in these objects.

The Si III line at 4552 Å is observed from spectral types B0 to approximately B8, but is not well modelled above [FORMULA] [FORMULA] 22500 K and hence the non-LTE locus in Fig. 5 is restricted. Below this temperature, the feature appears to be predicted well by our non-LTE computations and agreement is excellent. This line is particularly sensitive to gravity and it is interesting to note that the lines from the luminosity class II objects appear weaker than those of their more luminous counterparts. The agreement in abundance between Si II and Si III is expected due to the ionisation balances performed for these stars.

In the case of the Si IV feature at 4116 Å, the non-LTE locus is again restricted by problems in the computations. For effective temperatures above 27 500 K, the profiles are filled in or are entirely in emission. As was the case for some of the Si III profiles, we do not believe these effects to be real and suggest that they may again reflect our neglect of line blanketing. For the reduced range in effective temperature for which the silicon computations are believed to be realistic, the general behaviour of the 4116 Å feature is reproduced satisfactorily.

There is perhaps a suggestion that the 4116 Å feature indicates a slightly lower silicon abundance than the features due to Si III and Si II . However, when one notes the extreme luminosity sensitivity of the Si IV feature, coupled with the range in luminosities within the sample, it becomes difficult to confirm this. Certainly, to within the errors, all three silicon ionisation stages are consistent with a silicon abundance of approximately 7.28 dex, in excellent agreement with the results of Kilian.

6.3.3. Carbon

Paper II gave linestrength measurements for 3 C II features - the close doublet at 4267 Å, and the doublet components at 6578 & 6582 Å. We have elected to plot the equivalent widths of 4267 Å and of 6578 Å.

The feature at 4267 Å is the strongest C II feature in the classical blue region of B-type stellar spectra but is notoriously difficult to model successfully. An early attempt to do so was made by Lennon (1983) whose non-LTE calculations overestimated the observed strength in main sequence B-type stars by a factor of two for a solar abundance. Later attempts by Eber & Butler (1988) and Sigut (1996), have increased the complexity of the model ion (notably by including quartet terms which were omitted by Lennon), and the latter paper demonstrates that the non-LTE line strengths have now converged with respect to model ion complexity. As can be seen from Fig. 6, our non-LTE calculations (which use the same atomic dataset as Eber & Butler) again overestimate the strength of the 4267 Å line for a normal B-type star abundance. However, for a reduced abundance of 7.80 dex, the shape of the distribution of linestrengths is satisfactorily reproduced. There are a number of supergiants which have linestrengths significantly less than their nearest neighbours in effective temperature. Whether this reflects variations in gravity or the carbon abundances in these stars will be discussed below.

[FIGURE] Fig. 6. Observed C II linestrengths compared with non-LTE predictions. The non-LTE loci are as follows: 4267 Å - [C/H]=7.80 and 6578 Å - [C/H]=8.20. Each plot shows predictions for [FORMULA]=10 kms-1 and includes loci at [FORMULA]0.2 dex. The symbols are the same as those in Fig. 2.

The C II feature at 6578 Å is only satisfactorily modelled for effective temperatures below 20 000 K, with the hotter models predicting that this multiplet should be in emission. As this is not confirmed by the observations, we attribute this disagreement to a failing of our non-LTE computations for this multiplet at high effective temperature and note the similarity with the behaviour of some silicon features mentioned in Sect. 4.1. Again, large photoionisation rates and subsequent cascades are causing the emission and the lack of line-blanketing may mean our photoionisation rates are overestimated. It is however, interesting to note that the observed equivalent widths in the feature at 6578 Å do decrease sharply with increasing stellar effective temperature.

6.3.4. Nitrogen

Paper II gave linestrength measurements for 9 N II features which cover five multiplets. Three lines (at 3995, 4228 & 4447 Å) arise from transitions between singlet levels, with the others (at 4236 & 4241 and 4601, 4607, 4621 & 4630 Å) being from triplet levels.

We show in Fig. 7 linestrengths for the N II features at 3995, 4241, 4447 & 4630 Å, with the singlet and triplet N II features being shown on the left and right respectively. There is a qualitative difference in the behaviour of these two series, as the calculations of the singlet transitions exhibit a sharp increase in predicted linestrength at [FORMULA] [FORMULA] 4.4, which is absent from the triplet transitions. The cause of this discrepancy is unclear and it is not seen in the observed linestrength patterns.

[FIGURE] Fig. 7. Observed N II linestrengths compared with non-LTE predictions. Each plot shows predictions for[N/H] = 7.49, 7.69, 7.89 dex and for [FORMULA] = 10km s-1. The features shown on the left are singlets, whilst those on the right are triplets. There are clearly problems in modelling the singlets - see text for further discussion. The symbols are the same as those in Fig. 2.

We note that a normal B-type star nitrogen abundance of 7.69 dex provides satisfactory fits to the lower envelope of most of the observations. At effective temperatures below the `bump' in the predicted singlet linestrengths, agreement is reasonable. In the case of the triplet features, the non-LTE predictions fit the observed lower envelope reasonably well throughout the temperature range.

The tendency for most of the observed linestrengths to lie above the non-LTE locus is contrary to the behaviour of the C II features, while the particularly large spread in linestrength at [FORMULA] [FORMULA] 4.3 mirrors the behaviour of the C II features. These effects may be due to differing nitrogen abundances across our stellar sample and this will be discussed further below.

6.3.5. Oxygen

Paper II gave linestrength estimates for 11 O II spectral lines covering 4 multiplets. In Fig. 8 we show one representative feature from each multiplet, namely the lines at 4075, 4317, 4596 & 4661 Å. The feature at 4596 Å is between doublet levels, whilst the rest are for quartet levels. For the latter, the general shape of the observed linestrengths is reproduced satisfactorily. In the case of the doublet feature at 4596 Å the agreement between theory and observation is limited to temperatures below [FORMULA] [FORMULA] 4.3 and this behaviour is replicated by the other line of this multiplet at 4590 Å. Hence we conclude that our computations do not successfully model this multiplet and again there is a discrepancy between the different spin series.

[FIGURE] Fig. 8. Observed O II linestrengths compared with non-LTE predictions. Each plot shows predictions for [O/H] = 8.35, 8.55 & 8.75 dex and for [FORMULA] = 10 km s-1. The shaded area shows the effect of increasing [FORMULA] to 20 km s-1 for an abundance of 8.55 dex. The symbols are the same as those in Fig. 2.

The effect of increasing the microturbulence to 20 km s-1, whilst retaining a normal oxygen abundance is shown by the grey shaded areas. It appears that a [FORMULA]10 km s-1 may be appropriate for the oxygen lines, in agreement with other studies (MLD, Vrancken 1998), where a higher microturbulent velocity was estimated from lines of O II .

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© European Southern Observatory (ESO) 1999

Online publication: September 2, 1999
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