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Astron. Astrophys. 329, 613-623 (1998)

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6. Discussion

The observed and theoretical spectra (presented in Figs. 3 and 4) indicate that there is better agreement when a non-zero microturbulence is adopted. This is apparent, for example, in the triplet lines at 4713 & 4471Å. Additionally, more consistent abundance estimates for different lines in a given stellar spectrum are obtained when microturbulence is included - see Table 2. For example, previously the most `problematic' line was probably that at 4713Å, whose theoretical line strengths were relatively insensitive to either effective temperature or gravity over the range of values considered here. As theory predicted it to be much weaker than is observed, the only way to obtain agreement was to invoke improbably large helium fractions. However, by including microturbulence, it now becomes possible to achieve acceptable fits for near-normal helium fractions. Other lines (such as 4026 & 4922Å), which had previously been fitted reasonably satisfactorily with zero microturbulence and enhanced helium fractions, can now also be reproduced with normal, or near-normal, values of y. Indeed, by assuming a zero microturbulence, helium fractions from 0.09 to well in excess of 0.4 are obtained for both stars. In contrast, by assuming a microturbulence deduced from the silicon lines, ten (out of sixteen) estimates are between 0.08 and 0.1 (i.e. effectively normal) with other values being 0.3 or less. Hence our principal conclusion is that the adoption of a realistic microturbulent velocity leads both to better and more consistent fits and to an approximately normal helium abundance in both stars.

We also believe that our other atmospheric parameters ([FORMULA], [FORMULA] and [FORMULA]) are improvements upon previously published values because of the high quality of the spectral data and the modifications introduced to the line profile computations. As discussed previously, the introduction of a microturbulent velocity has no direct effect on the estimates of effective temperature and logarithmic gravity. However, since the use of a non-zero microturbulence leads to a lower estimate of the helium fraction and since [FORMULA] and [FORMULA] are dependent upon y, there is an indirect dependence. In Table 3, we list our best estimates of the atmospheric parameters, together with error estimates. To aid the subsequent discussion, in Fig. 5 we show for [FORMULA] Ori, the points in the atmosphere where the line cores achieve an optical depth of unity.


Table 3. Adopted atmospheric parameters.

[FIGURE] Fig. 5. Plot of temperature versus mass (depth), showing the points at which the line cores of the lines of interest attain an optical depth of unity; the He I singlet lines (diamonds: 5047, 5015, 4922, 4437 and 4387), He I triplets (diamonds: 4713, 4471 and 4026), He II lines (asterisks: 4686, 4542 and 4200) and H I lines (crosses: 4340 and 4101). The depths of formation of the Si III triplet used to determine the microturbulence are also shown. These data are for our final [FORMULA] Ori model with [FORMULA]  = 27500 K, [FORMULA]  = 3.0, [FORMULA] and [FORMULA] =12 kms-1. The optical continuum forms only a little further out than the He II lines.

As we have already mentioned, Voels et al. (1989) proposed that the lines of He I may be subject to the generalized dilution effect, whereby various level populations are enhanced as a result of sphericity. They suggested that this is most significant for the 23 S level, followed by 21 S, 23 P and 21 P in order of decreasing importance, the effect also decreasing for higher lying states. They suggested that those He I lines forming deepest in the atmosphere should provide the most reliable y -estimates, and used this logic in selecting the He I lines with the lowest oscillator strengths for use as helium abundance indicators. Inspection of Table 2 shows that our results for zero microturbulence fit this general picture; 4437Å (21 P - 51 S) and 4387Å (21 P - 51 D) giving normal helium abundances, while 5015Å (21 S - 31 P) is very discrepant. We can also see that, at these temperatures, 4713Å (recommended by Voels et al. at higher temperatures), does not provide consistent y -estimates compared to 4387Å. Furthermore, the lines 5047 and 4387Å, used by Smith & Howarth, give significantly lower helium abundances than the triplets, and are not seriously affected by microturbulence. Whether or not the neglect of atmospheric extension and sphericity play a significant role in determining the perceived abundance pattern is unclear, since neither [FORMULA] Ori nor [FORMULA] Ori are particularly luminous supergiants, with pressure scale heights of order [FORMULA]. Nevertheless it is perhaps significant that 5015Å (21 S - 31 P) gives anomalously high helium abundances even when microturbulence is included.

Table 2 also demonstrates another problem not completely removed by the introduction of microturbulence, namely that the triplet transitions give systematically higher helium abundances than the singlets (we exclude 5015Å). This may be related to the neglect of line blocking in the n =2 continua of neutral helium, which would be most important for the metastable 23 S state as discussed by Lennon & Dufton (1989). It seems unlikely that blocking in the ground state continuum could be an important factor given the very low flux levels in this spectral region for B-type supergiants.

As pointed out in the introduction, the use of microturbulence is almost ubiquitous in spectroscopic stellar analyses. However, in spite of the evidence in support of the reality of microturbulent velocity fields in stellar atmospheres, one must remain cautious. B-type supergiants have appreciable mass loss rates (Prinja et al. 1990), and the resultant velocity fields above the stellar photosphere can affect line profiles in such a way as to mimic microturbulence if a simple hydrostatic analysis is applied (Kudritzki 1992 , Lamers & Achmad 1994). Indeed Lamers & Achmad show that velocity fields in the upper photosphere of an early B-type supergiant may lead to an apparent microturbulence of 10-15 kms-1. They argue that microturbulent velocity values such as those derived here are thus vastly overestimated, the derived values being the sum of a real (possibly zero) microturbulent velocity and a contribution due to the neglect of the dynamic nature of the supergiant photosphere. However, these calculations assumed LTE level populations and opacities and LTE analyses of such supergiants can result in much higher values of microturbulence (see Sect. 2). Additionally, main sequence B-type stars also exhibit evidence for significant microturbulent velocities and they have mass loss rates which are approximately 2 orders of magnitude lower than supergiants (Najarro et al 1996). [In terms of outflow velocity in the photosphere, one might expect the lower mass loss rate to be partly compensated for by the smaller radius, however this is in turn partially offset by the higher surface gravities and densities of main sequence stars.] We note that the star [FORMULA] CMa (B2 II) considered by Najarro et al., was also investigated by Gies & Lambert (1992) who derived a microturbulent velocity of 11.5 [FORMULA] 2.5 kms-1 from a non-LTE analysis of its metal lines.

The additional broadening introduced by the use of a non-zero microturbulence might affect the estimation of projected rotational velocities. This effect would be particularly interesting in the case of early O-type stars where slow rotators are rarely observed (see, for example, Penny 1996). However, the effect would only be significant for slowly rotating stars observed at high spectral resolution (i.e. with an instrumental width less than or approximately equal to the inferred microturbulence) and hence we do not believe that this possible additional intrinsic broadening should significantly affect previous investigations of stellar rotational velocities.

Whether our results can be explained solely by a macroscopic velocity field (wind) or whether some microturbulent contribution is still required, is unclear. It is an issue however which has obvious and potentially far-reaching implications for stellar atmospheres and the winds of hot stars (for example see Hubeny et al. 1991). If microturbulence is present then it will have greatest impact in the transition region between the near hydrostatic layers in the atmosphere and the sonic point, where the thermal Doppler width is decreasing and before the wind outflow velocity begins to dominate (see Fig. 6). Should such microturbulent velocities be comparable to either ion thermal velocities or the sound speed in this region, then there will clearly be a significant effect on the line formation, structure and even the line force. We cannot address these issues in the present paper, using as we do hydrostatic equilibrium models. Certainly one can estimate an outflow velocity for a given mass loss rate and stellar radius, just using the equation of continuity, and this is also plotted in Fig. 6. However the low velocities implied by this procedure (for example 1 kms-1 for the line core of 4471Å), are certainly unreliable as the density structure will be drastically altered by the velocity field (see Najarro et al. 1996 , Santolaya-Ray et al. 1997 and Kudritzki 1997). Test calculations for a model applicable to [FORMULA] Ori indicate that outflow velocities in the He I line formation regions may in fact be of order 10 kms-1, but detailed analysis of the spectrum using non-LTE calculations and hydrodynamical models are required to investigate the full implications for the implied properties of supergiants. However, whatever the physical origin of the additional broadening (and hence line desaturation) that is incorporated here via a microturbulent velocity, we do not believe that it significantly affects the main conclusions of this paper regarding the derived helium abundances.

[FIGURE] Fig. 6. For the same model as in Fig. 5 we plot some relevant velocities as follows; hydrogen thermal velocity (v [FORMULA]), helium thermal velocity (v [FORMULA]), silicon thermal velocity (v [FORMULA]), adiabatic sound speed (v [FORMULA]), microturbulent velocity (v [FORMULA]). For illustration, we also show the outflow velocity (v [FORMULA]) implied by the continuity equation and assuming a radius of 30 solar radii for [FORMULA] Ori and a mass loss rate of [FORMULA] /yr.

The main conclusion of this paper is that helium abundances of hot supergiants are over-estimated when the results of non-LTE hydrostatic equilibrium model atmosphere analyses are indiscriminately applied to all available He I lines. Contrary to previous results (Lennon et al. 1991 , Kudritzki et al. 1987), we find close to solar helium abundances for the two Galactic supergiants [FORMULA] Ori and [FORMULA] Ori. This is an important result (which must of course be verified) since these two stars are often considered to be normal supergiants (but see below). If these objects did have significant helium overabundances then an obvious explanation would be that they are post-RSG (red supergiant) core helium burning stars. This scenario now appears to be ruled out, which agrees with the results of Venn (1995) who finds that slightly less massive Galactic A-supergiants have CNO abundances which are also inconsistent with the blue loop scenario for massive star evolution at solar metallicity. In addition, from Table 2, we note that there is some slight evidence that [FORMULA] Ori is marginally enhanced in helium compared to [FORMULA] Ori. While the difference is well within our error bars this may be significant since [FORMULA] Ori belongs to a class of supergiants with morphologically moderate anomalies, being nitrogen weak (Walborn 1976). We would interpret this as implying that [FORMULA] Ori is in fact slightly nitrogen, and helium, rich. This would also be consistent with Venn's results since moderate CN anomalies were found for some A-supergiants, and is attributed to mixing processes occuring on the main sequence.

One can also speculate that the helium enrichments in O-type stars discussed by Herrero et al. (1992) may be due, at least partly, to the neglect of velocity fields. This possibility was also suggested by Schaerer & Schmutz (1994) and is well worth investigating since there is a general trend of increasing helium abundance with luminosity class in the Herrero et al. sample. These authors considered only the He I lines at 4471, 4922 to 4387Å but, recognising that the dilution effect was present in their results, they concentrated on 4922 and 4387Å. However, they gave greatest weight to the former which, if our results can be extended to O-type stars, would imply that helium abundances may still be overestimated. Indeed, since submission of this paper, we have become aware of work by Smith (1997) which shows that the inclusion of microturbulence in the non-LTE analysis of late O-type supergiants does lead to improvements in line profile fits and a reduction in the estimated helium fractions for these stars.

Finally, we emphasize that for those stars with microturbulent values of the order discussed here (which may include some main-sequence stars), it is important to include this parameter in the calculation of the level populations.

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© European Southern Observatory (ESO) 1998

Online publication: December 8, 1997