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

8. Discussion

8.1. Validity of the non-LTE calculations

Figs. 3 to 8 show that, whilst problems remain, the hydrostatic non-LTE modelling used in this analysis can satisfactorily reproduce the optical spectra of B-type supergiants. The low gravities of some of the models have, however, led to difficulties in synthesising some spectral features - most notably, the He I triplet transitions, N II singlet transitions at high effective temperatures, the O II doublet transitions, and Si III triplet transitions at high effective temperatures and low gravities. Problems were also encountered in reproducing the strength of the C II feature at 4267 Å. However, this feature is difficult to model even in main sequence B-type stars (Eber & Butler 1988, Sigut 1996), and therefore the problems are not unique to our low gravity models. An exhaustive investigation into the reasons for these shortcomings has not been performed. However, the fact that the problems are often localised to the hotter models having low gravities and that photoionisation rates are extremely high in these models is highly suggestive of a problem in calculating the UV radiation field. The lack of metal line blocking in our model atmosphere calculations will lead to an overestimation of the radiation field and a first step towards the possible resolution of these problems would be the inclusion of some form of increased line-blanketing. Recent attempts at including metal line-blanketing within non-LTE models have been discussed by, for example, Hubeny et al. (1998).

The spectral features, which are not satisfactorily modelled, are often between levels, that are not radiatively coupled to the atomic or ionic ground state. So, for example, the singlet lines of neutral helium are better modelled than the triplets. It is also interesting to note that the only lines of Si III observed here are triplets (Si III has a singlet ground state) and that this may explain the difficulties encountered in the modelling. Unfortunately, the spectral data are not good enough to reliably measure any singlet Si III features, such as that at 4717 Å.

Hence, we recommend that when using unblanketed non-LTE models (particularly for hot, low gravity stars) greater weight is given to transitions that are radiatively connected to the appropriate ground state.

8.2. Microturbulence

It would appear that a non-zero value for the microturbulence parameter is required to reproduce the linestrengths in all atomic species. Whilst the errors associated with the estimation of atmospheric parameters are large, and systematic effects (e.g. variations of with chemical species) may be present, the requirement of a non-zero value is an interesting result, which supports the findings of numerous other authors (see references in Sect. 5.3). It is possible that mass loss (Lamers & Achmad 1994, Kudritzki 1992) may have a role in desaturating the lines in these luminous objects, although, from the analysis presented here, it is difficult to draw any useful conclusions. It is however, interesting to note that whilst supergiants have systematically higher microturbulences than are typically adopted for their main sequence counterparts (5 km s^-1 is often used - see, e.g., Smartt et al. 1996a and references therein), there is no evidence for any systematic difference in between the Ib and Ia supergiants.

8.3. Helium fractions, y

The findings of MLD - namely that the use of a non-zero microturbulence can lead to near-normal helium fractions in early B-type supergiants - is confirmed here, for the whole range of B-type supergiants. This is an important result as previous authors had found large helium fractions in many luminous OB-stars (see MLD and references therein). Additionally these results support our use of a normal helium abundance when deducing the atmospheric parameters. However, the moderate quality of our spectroscopic data does not preclude the possibility that our some of our sample may have moderate helium enhancements.

8.4. CNO abundances and stellar evolution

Fig. 12 shows the location of the supergiants in the - plane, along with the solar metallicity evolutionary tracks of Schaller et al. (1992). These tracks do not include effects due to stellar rotation, which may be important (see Sect. 8.5). However with this limitation, they constitute a complete and consistent theoretical grid and hence form a useful basis for comparison with our observations. Only the B-type supergiants, that have been assigned a CN status are included in the figure - hence the 3 hottest and 5 coolest objects have been omitted.

Fig. 12. The positions of the B-type supergiants, and some comparison objects, in the - plane. The symbols are summarized in the figure, with indicates `highly processed', `processed?' and `moderate/normal' - see text for further discussion. Also shown are the evolutionary tracks of Schaller et al. (1992) together with their ZAMS masses. Note the -scale for the B-type supergiants has been uniformly reduced by 10 % to account for their expected offset relative to the other objects

Also shown in Fig. 12 are a sample of B-type (near) main sequence stars taken from Gies & Lambert (1992) and Kilian (1992) and a sample of A-type supergiants from Venn(1995a). For the main sequence stars, both studies implied that in general the atmospheric CNO abundances were normal apart from a few cases where there was evidence for moderate degrees of nuclear processing. The relationship between the A-type supergiants and their apparent progenitors, the B-type dwarfs, has been discussed in detail by Venn (1995b), who found that the [N/C] ratios of her supergiants were in general larger than those of the dwarfs, but less than the post-First Dredge-Up ratio predicted by evolutionary models. Hence, she concluded that her supergiants were pre-RSG objects which had suffered partial mixing during their main-sequence lifetimes.

There are a number of important caveats, which must be considered before any interpretation can be made of Fig. 12. Firstly, Gies & Lambert (1992) and Venn (1995a) used the model atmosphere structures of Kurucz (1991), and hence offer effective temperatures on an LTE, line-blanketed scale. Kilian (1992) used the model atmospheres of Gold (1984), which also include some blanketing. Therefore, their temperatures estimates are likely to be reasonably internally consistent but will differ from our scale based on unblanketed models. Hence the temperature scale for our B-type supergiants has been uniformly reduced by 10 % to allow for the effects of line blanketing as discussed in Sect. 6.1. Secondly, the estimation of gravity may be subject to errors due to the modelling assumptions made. Specifically, neglecting the dynamic effects of mass loss and also line-blanketing can lead to underestimates (see Gabler et al. 1989 and Lanz et al. 1996, respectively), with the effects likely to be greatest for the more luminous supergiants.

The principal implications from Fig. 12 are as follows

• There appears to be a mass segregation between the `highly processed' and `normal/moderate' B-type supergiants, with the former lying on the higher mass evolutionary tracks. The hotter supergiants, designated as `processed?', also lie on higher mass tracks.

• Practically all our B-type supergiants appear to be evolutionary distinct from either the B-type dwarfs or the A-type supergiants. The evolutionary calculations imply that their main sequence precursors would be O-type, whilst they would evolve into higher luminosity A-type supergiants than the predominantly Ib class discussed by Venn (1995b). A small number of our targets (approximately four) are on similar evolutionary tracks to the B-type main sequence and A-type supergiant stars but these all have approximately normal CNO abundances consistent with the other two samples.

Assuming that the non-rotating, single object, evolutionary tracks of Schaller et al. (1992) are appropriate, a possible evolutionary scenario to explain the observed abundance patterns would be as follows. Mixing has occurred on or near the main sequence and is strongly and positively correlated with the stellar mass. Then our lower mass B-type supergiants have suffered little or no atmospheric mixing and have retained near-normal surface compositions. These objects will eventually evolve into A-type supergiants, similar to those analysed by Venn (1995b). Although she found moderate CN anomalies, such relatively small chemical variations could be present within our `normal/moderate' stellar group but be masked by the quality of our observational data. The hotter `processed?' supergiants would then be the progenitors of the `highly processed' supergiants and significant changes in surface chemistry would be occurring in a short period of time (Schaller's computations suggest that the evolution from 4.65 to = 4.25 - i.e. from the the main sequence to the `highly processed' group - takes approximately 4.3 million years for a 40 model). However, it should be noted that the hotter `processed?' stellar sub-group lies in an effective temperature range for which there are difficulties in the modelling computations. Hence, it is possible that for these stars, the apparent surface chemical effects may simply be an artefact of our analytical approach.

8.5. Alternative evolutionary scenarios - rotation and binarity

As was discussed in the introduction, stellar rotation may have a role to play in the chemical mixing of stellar atmospheres. Massive main sequence stars are rapid rotators, having equatorial velocities of up to 400 km s^-1 (Penny 1996, Howarth et al. 1997) and these may be large enough to cause significant mixing in their atmospheres due to the effects of differential rotation and the subsequent instabilities which are introduced. They may also cause significant changes in the stellar evolutionary tracks themselves - even during the main sequence phase.

Fig. 13 shows the dependence of projected rotational velocity, , on effective temperature. The values are taken from Howarth et al. (1997) and omit a number of the B-type supergiants considered here, most notably the `highly processed' stars HD 14956 & HD 194279. However, the values estimated here (see Table 1) for these objects (75 & 70 km s<sup>-1</sup> respectively) would put them in a similar position to the other `highly processed' supergiants. Despite the small number statistics, the `highly processed' supergiants appear, on average, to have larger projected rotational velocities than the `normal/moderate supergiants' and could imply a connection between chemical mixing and stellar rotation rate.

Fig. 13. The figure shows the projected rotational velocity, , as a function of effective temperature for some of the B-type supergiant sample. The `highly processed' stars clearly have larger values than the `normal/moderate' objects. The symbols represent the CN status of the supergiants as follows:  - `moderate/normal',  - `processed?',  - `highly processed'.

However the projected rotational velocities estimated by Howarth et al. are observational parameters which may correlate with but are unlikely to equate to the physical projected equatorial rotational velocity. For example, other physical mechanisms, such as macroturbulence, may contribute to the observed broadening; then the greater line broadening in the `highly processed' group could simply reflect their higher luminosities and hence greater atmospheric macroturbulence. Indeed as discussed by Howarth et al., the absence of early-B-type supergiants with low projected rotational velocities indicates that another broadening mechanism (as well as rotation) must be present. Hence we conclude that there is some evidence for our `highly processed' supergiants having broader spectral lines but it is unclear whether this is a signature of enhanced rotational velocities.

In Fig. 14, the positions of our B-type supergiants in the - plane are shown (see Sect. 2 for sources of luminosity estimates).

Fig. 14. The positions of the B-type supergiants in the - plane. The -scale for the B-type supergiants has been uniformly reduced by 10%. The stellar luminosities are taken from Lennon (1994). The evolutionary tracks of Schaller et al. are shown, along with their ZAMS masses. The differing chemical sub-groups are plotted using the same symbols as in Fig. 12.

It is notable that the stellar masses in Figs. 12 and 14 are not coincident. This is a manifestation of the well-known mass discrepancy problem (see, e.g. Herrero et al. 1992), whereby stellar masses derived from non-LTE spectroscopic methods and those based on evolutionary calculations, typically do not agree. Specific areas which may lead to a resolution of this discrepancy are improvements in the calculation of gravities (e.g. using hydrodynamic atmosphere codes) and proper treatment of line blocking effects (Lanz et al. 1996). However, the discrepancy is not crucial to this discussion as Fig. 14 supports the broad conclusions drawn from Fig. 12 - namely that the two sub-groups which appear to have processed material in their atmospheres are generally more massive than the chemically normal supergiants.

An uncertain fraction of luminous stars may be members of binary or indeed multiple systems. In the case of close binaries, interactions may occur which have a very important effect on the evolution of the individual stars. Mass transfer is predicted between the components and the changing stellar masses lead to complex changes in the evolutionary tracks. Langer et al. (1999) have recently considered the evolution of a close 20 + 18 pair, where mass transfer during the core hydrogen burning phase of the primary is included. They have shown that the primary in such a system may evolve into a helium star while the secondary may evolve into a luminous blue supergiant - such as is considered here. During the main sequence lifetime of the primary, mass transfer leads to a deposition of helium enriched matter onto the surface of the secondary. This generates an inversion in the mean molecular weight gradient in the secondary and leads to significant atmospheric mixing (so-called thermohaline mixing) with changes in the abundances of carbon and nitrogen, by factors of 2-3, being predicted. Although these are smaller than the values estimated in Sect. 7.1, the uncertainties in these estimates are such that they may well be consistent with the predictions. The evolutionary calculations also imply that during the accretion of the extra mass, the luminosity of the secondary may increase substantially. In the case of their 18 (ZAMS) object, Langer et al. predict that after the mass transfer, log 5.4-5.5 and log 4.3-4.5; both consistent with the position of our `highly processed' group of B-type supergiants. Clearly, their calculations are preliminary and need to be extended to include other initial masses. However, binarity is clearly an important evolutionary mechanism which may reproduce the observed abundance patterns in some supergiants, including our `highly processed' group.

© European Southern Observatory (ESO) 1999

Online publication: September 2, 1999
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