5. Determination of atmospheric parameters
The estimation of reliable atmospheric parameters for B-type supergiants is more fraught than for their main sequence counterparts. Photometric calibrations (such as those of Lester et al. 1986), which rely on the temperature dependence of the Balmer discontinuity, are useful for B-type dwarfs but are inappropriate here as they are generally based upon flux distributions calculated from the LTE model atmospheres of Kurucz (1979, 1991). A further problem is that such methods often neglect the gravity dependence of the stellar continuum, as they are calibrated using the spectra of near main sequence objects. Hence they may not fully account for the redder surface colours produced by the spherically extended supergiant atmospheres.
However, spectroscopic methods which allow for non-LTE effects, offer a possible alternative. There are a number of elements observed in B-type supergiant optical spectra which show more than one ionisation stage. For example, ionisation balances due to He I /II , Si III /IV and Si II /III are available as indicators of stellar effective temperature. A number of these spectroscopic indicators has been used, and the estimation of each of the atmospheric parameters are discussed separately below, with results listed in Table 1. As an example, Fig. 1 shows how the atmospheric parameters for Aurigae (B4 Iab) were estimated. Fits to the Balmer lines describe a locus in the - plane and the subsequent use of a temperature discriminant isolates one single point along this locus which represents the appropriate parameters. In this case the ionisation balance of Si II /III has been performed at three values of , and suggests an effective temperature of approximately 16 500 K.
The four atmospheric parameters (, , y, and ) are not independent and a degree of iteration is required. The method used - namely the - fitting diagram - gave simultaneous estimates for effective temperature and gravity. We have had to consider the possible effects of a varying helium fraction and microturbulence within our sample and our approach has been to initially assume a solar helium fraction for all our supergiants. Once the other parameters are estimated, the analysis of the He I lines provides a check on the validity of this assumption. The values estimated for the microturbulence are discussed separately.
5.1. Logarithmic gravity
Tests have shown that the Balmer lines are almost unaffected by microturbulent line-broadening, as they are dominated by both a large Stark effect and a relatively large Doppler broadening due to the high thermal velocities. Hence it was possible to estimate gravities for all supergiants with no prior knowledge of . The Balmer lines H and H have been used with a greater weighting being given to the former, as in some stars the core of H was slightly filled by wind emission. However, for the majority of the stars considered here, agreement between the two lines was good.
We have not used fits of H, which was available in all our spectra, due to blending with an interstellar line of calcium and a stellar He I line. Neither have we considered H or H as wind effects can be significant in these lines (see Paper I).
5.2. Effective temperature
The relatively wide range of spectral types in our sample precludes the use of a single temperature indicator. Here, the primary objective was to obtain atmospheric parameters across the large range of spectral types, whilst achieving a reasonable degree of consistency and our approach was as follows:
Late O-type and very early B-type supergiants. Where possible we have used He II features as indicators of effective temperature. It should be noted, however, that a strict ionisation balance has not been performed, as other authors have found that the temperature estimates derived in this way are strongly dependent upon of the choice of He I line used (see, for example, Lennon et al. 1991band Herrero et al. 1992). Indeed, the sensitivity of the He I lines to the adopted microturbulence may be partially responsible for the above inconsistencies in He I /II temperature estimates. Here, we have initially assumed a normal helium fraction, and having determined the locus of suitable values from the Balmer lines, have estimated effective temperatures by fitting the profiles of the He II lines alone.
It has been shown by MLD that the He II lines at 4200 and 4542 Å are almost unaffected by microturbulence at temperatures appropriate to early B-type supergiants. The He II line at 4686 Å was not used as it is strongly affected by stellar winds, as shown by Gabler et al. (1989). He II 4200 Å is blended with a N III feature and hence a greater weight was given to the line at 4542 Å.
Early B-type supergiants. For those objects having spectral types from B0 to B2, strong features due to Si III and Si IV were simultaneously observed. However, as was discussed in Sect. 4.1, the stronger Si III features are not well modelled for the low gravity models at effective temperatures greater than approximately 25 000 K (while discrepancies may well extend to lower temperatures). Hence, the weak Si III multiplet near H was used in conjunction with the Si IV feature near 4116 Å in order to obtain the effective temperature at which the predicted abundances from the two ionisation stages matched. The synthetic silicon profiles computed from the lowest gravity models have been rejected in favour of a modest extrapolation (over less than 0.25 dex) from the more reliable, higher gravity models. The luminosity class II/Ib objects in this spectral type range (whose silicon lines appear to be well modelled) have effective temperatures which support the validity of this approach.
The strengths of these lines are dependent on the microturbulent velocity and hence ionisation balances were performed for = 5, 10 & 15 kms-1. In most cases the temperature estimates were relatively insensitive to . The largest effects were (as expected) at spectral types where the line strengths from the two ionisation stages were significantly different. However, even then the effect was small and a subsequent estimation of allowed the effective temperature to be unambiguously defined.
Mid and late B-type supergiants. For supergiants of spectral type later than approximately B2.5, strong absorption features due to Si II and Si III are observed. At the lower effective temperatures applicable to these objects, the silicon lines are believed to be well modelled and hence it was possible to assign each star a temperature based on the ionisation balance of the features at 4552/4567/4574Å (Si III ) and 4128/4131 Å (Si II ). Again microturbulent velocities between 5 and 15 kms-1 were considered.
Using the temperature indicators listed above allowed the estimation of atmospheric parameters for 39 out of the 46 target stars. For four of the remaining objects ( Cas, HD 193183, 9 Cep & HD 13866) effective temperatures were adopted based on those found for other stars with the same spectral type - logarithmic gravities were still available from the fits to H /H . As these objects occupy small `gaps' in our spectral type- scale, this should not lead to significant error.
However, the three objects having the latest spectral types in our sample have no spectroscopic temperature indicators. In these cases we have used Strömgren uvby photometry (obtained from the General Catalogue of Photometric Data - see Mermilliod et al. 1997) and the calibration of Lester et al. (1986). As discussed above, the temperature scales of the Kurucz line-blanketed model atmospheres and those used here may not necessarily be the same. Hence, photometric temperatures were assigned to the bottom 10 stars in the list. Those having effective temperatures from both spectroscopic and photometric indicators suggest that, at around spectral types B6-B8, the two scales are similar. Hence, we have adopted the photometric temperatures for the three coolest stars. Whilst this may lead to inconsistencies with the rest of the sample, the errors are likely to be small and should not affect the main conclusions of this paper, which are principally based on the stars of spectral type earlier than B7.
5.3. The microturbulent velocity,
Previous work on luminous blue stars has consistently produced rather large values for the microturbulent velocity. Lennon et al. (1991b) analysed three B0.5 Ia supergiants (in the Galaxy, the LMC and the SMC respectively) using non-LTE techniques similar to those used here, and they adopted a value of = 10 km s-1, noting however that this value was not sufficiently large to remove the slope in abundance. Gies & Lambert (1992) analysed a large number of B-type stars, of which three were supergiants, in both LTE and non-LTE. They found for their supergiants, that by assuming LTE a high value of 30 km s-1 was obtained, and that by moving to a non-LTE analysis, this value was reduced to 15 kms-1. More recently Smartt et al. (1997) analysed the spectra of four supergiants near the Galactic Centre using both LTE and non-LTE techniques and in both cases deduced microturbulences of 30 kms-1.
MLD have shown that in the case of the early B-type supergiants & Ori (also analysed in this work), the lines of Si III indicate a smaller microturbulence than do the lines of O II ( 12 kms-1 as compared to 30 kms-1) - this effect has been independently discovered by Vrancken (1998) in her analyses of early B-type giants in h & Persei. Whilst O II has the advantage that it shows many absorption lines with a great range in equivalent width, the Si III lines at 4552, 4567 & 4574 Å offer a reasonable range in linestrength and are from the same multiplet . Hence they are likely to be less affected by such problems as errors in the atomic data and the inadequate treatment of non-LTE effects. For these reasons, the Si III lines have been used to estimate microturbulent velocities where possible and these are listed in Table 1.
By using the Si III features, microturbulences have been estimated for supergiants having spectral types between approximately B0 and B5. Within this range in effective temperature, seems to remain essentially constant at 10-15 kms-1 and there seems little dependence on luminosity class (to within the errors). There is some tentative evidence that this value may decline for later spectral types, as the ionisation balance diagrams provide some indication of the appropriate microturbulence. For example, in the case of Aurigae (see Fig. 1), the `tightness' of the lines suggests that 10-15 km s-1 may be appropriate. For stars later than B5, equivalent diagrams indicate that values of between 5 and 10 km s-1 may be correct. However, at these temperatures the Si III lines are weak and hence are both less reliably measured and have a smaller dependence on . Therefore, the information on microturbulence is essentially derived from the Si II features which have very similar linestrengths. Unfortunately, other suitable spectral indicators for the microturbulent velocity were not available at these spectral types. Whilst the suggestion that may decline towards 5 km s-1 for late B-type supergiants is a tentative one, it is in agreement with the work of others; for example, Venn (1995a) finds LTE microturbulences of 5-8 kms-1 for her A-type supergiants.
For the analyses of element abundances which follow, the value = 10 km s-1 has been assumed throughout. It is possible that may be a function of effective temperature or of gravity and any errors present in our analysis due to this simplification will be considered below.
© European Southern Observatory (ESO) 1999
Online publication: September 2, 1999