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Astron. Astrophys. 359, 1085-1106 (2000)

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5. The impact of velocity fields on the line formation

As we have shown in the previous sections, abundances determined from the strong near-infrared lines are not entirely consistent with the results from the weak lines in the visible. The fitting of line profiles for the near-infrared lines in supergiants and to a smaller degree in the main sequence star Vega still poses a problem. There has been some indication that the problems might not result from a possible weakness in our OI non-LTE model atom but from the inadequacy of the standard assumptions in the model atmosphere description. In particular, plane-parallel geometry, stationarity, the assumption of LTE and hydrostatic equilibrium have to be questioned for the atmospheric models of supergiants and deviations from these will become noticeable in the strong lines first as they are formed over a large part of the geometrical extent of the stellar atmosphere. Limitations of the available codes mean that we can only address the influence of velocity fields on the line formation, but as we will see, significant progress can be achieved by taking them into account.

5.1. Microturbulence

Microturbulence has been introduced as a parameter to bring model calculations into better agreement with observation. The concept of some additional non-thermal line-broadening is not out of the question physically despite the lack of a comprehensive theoretical explanation for it at present. In the following we investigate its impact on our line formation calculations.

First, a rather technical question has to be addressed. McErlean et al. (1998) include microturbulence explicitly in the statistical equilibrium calculations (with DETAIL ) for helium in OB stars and find significantly different profiles as compared to the standard procedure of including microturbulence only in the final step of the spectrum synthesis (with SURFACE ) for microturbulent velocities in excess of 10 km s-1. In the OB-type supergiants thermal velocities [FORMULA] (k being the Boltzmann constant, T the temperature and m the mass of the ionic species) for helium are of the same order as the microturbulent velocities ([FORMULA]10 km s-1). Given the larger mass of the oxygen atom and the lower temperatures this ratio becomes approximately 1:3 ([FORMULA]:[FORMULA]) in A-type supergiants. A pronounced effect should therefore be expected for the statistical equilibrium calculations from Eq. (1). We find no profile changes for oxygen as the level populations are only marginally affected. Still, the classical effects of adopting a microturbulent velocity apply in the final spectrum synthesis.

This unexpected finding is related to the behaviour of the occupation numbers [FORMULA] throughout the line formation region for the energy levels involved. The [FORMULA] (N being the total particle density) for the terms [FORMULA], [FORMULA], [FORMULA] and [FORMULA] are nearly constant. Thus the line opacity remains almost constant as an increased microturbulence pushes the formation depth of the line centre deeper into the atmosphere but simultaneously broadens the frequency bandwidth for absorption. Only for cases where the occupation numbers vary strongly on small geometrical scales do the effects of microturbulence as proposed by McErlean et al. (1998) come into operation.

More recent studies for stellar abundances (among others e.g. Venn 1995b) favour the application of a depth independent microturbulent velocity to bring abundances from weak and strong lines into agreement. The bulk of the metallic lines in the spectra of our test stars can be satisfactorily reproduced by this assumption, the remaining discrepancies attributed to inaccuracies in the gf values and to unaccounted non-LTE effects. For the strong OI lines these explanations can be quite probably excluded as discussed above.

We investigate what can be achieved if a depth dependent microturbulence is invoked. For Vega, a depth dependent [FORMULA] is derived by Gigas (1986) from a non-LTE study of FeI/II lines varying from [FORMULA] km s-1 through the atmosphere (bottom to top). The abundances derived from the individual lines are displayed in Table 3. A remarkably small scatter around the mean oxygen abundance is found for all lines. In Fig. 16 the resulting line profiles for the mean value are presented for [FORMULA] 6155-8, 7771-5, 8446 and 9260-5 in comparison with the profiles for a depth independent [FORMULA] of 2 km s-1 for the same elemental abundance. Lines weaker than [FORMULA] 6155-8 are virtually insensitive to the change in the microturbulence parameter. For [FORMULA] 6155-8 a slightly better concordance for the single components is achieved while the fit for the stronger lines is significantly improved as can be expected from their position on the curve of growth.

[FIGURE] Fig. 16. The impact of a depth dependent microturbulence in the case of Vega. Displayed are the observed profiles (full line) of the stronger OI lines and theoretical profiles for a constant microturbulence of [FORMULA]=2 km s-1 as in the last section (dashed) and for a depth dependent [FORMULA] (0...3.5 km s-1 throughout the atmosphere, dotted) as derived by Gigas (1986). The weaker lines remain virtually unaffected, cf. Fig. 13 for profile fits.

Also in the case of supergiants a significant improvement can be achieved, with the necessary microturbulent velocities not exceeding the speed of sound. But, by adopting a depth dependent microturbulence the quality of the (LTE) fits for lines from other elements is worsened and different velocity fields for various elements are required, as found in other studies (e.g. Rosendhal 1970; Aydin 1972). A definite statement cannot be made in this context as non-LTE calculations especially for the iron group elements (the microturbulence indicators) are not available, although work on this is in progress.

5.2. Wind outflow velocity fields

An alternative explanation for the large ([FORMULA] speed of sound) microturbulent velocities observed in supergiants is provided by Kudritzki (1992), cf. also Lamers & Achmad (1994) for the case of A-type supergiants. The subsonic outflow velocity field at the base of the stellar wind in supergiants will strengthen lines saturated just in their line cores even for the moderate mass-loss observed in the latter types. Desaturation of the lines due to the Doppler shifts experienced by the moving medium is the driving mechanism for the strengthening of the spectral features. For higher mass-loss rates even weak lines can be affected. This might be interpreted as a large "microturbulent" velocity in the hydrostatic approach. A macroscopic velocity field will also result in: a blue-shift of the central wavelength (increasing with equivalent width) and an asymmetry in the line profile with extra absorption in the blue wing. A-type supergiants offer an opportunity to verify these predictions due to the comparatively small rotational velocities observed for these stars. At earlier spectral types the effects of the wind on the weak lines are likely to be masked by the higher [FORMULA].

For the galactic supergiant HD 92207 the following parameters are used for fitting the [FORMULA]/[FORMULA]/[FORMULA] features with the SPH code (Kudritzki et al. 1999):

[EQUATION]

(with Y being the ratio of He to H by number, [FORMULA] the stellar radius, [FORMULA] the mass loss rate, [FORMULA] the terminal velocity and [FORMULA] the velocity law coefficient).

Based on this SPH model atmosphere we investigate the impact of the implementation of a ([FORMULA]-type) velocity field in the non-LTE radiative transfer calculations on the computed line profiles. In Fig. 17 the results are displayed for the OI lines [FORMULA] 7771-5 and 6155-8 for [FORMULA]=8.78. For comparison, the line profiles resulting from the hydrostatic approach with an ATLAS9 atmosphere are also included. Despite the differences in the stellar parameters used (needed to compensate the absence of metal line blanketing in the SPH model) the profiles for the weak lines from the ATLAS9 and the SPH model - neglecting the velocity field - are almost identical. The strong lines on the other hand are weakened due to the lower local densities in the outer atmosphere of the SPH model. Taking the velocity field into account results in the effects described above. Both strong and weak lines strengthen, but only in the strong features do the blueward shift of the line centre and the line profile asymmetry become noticeable. The strengthening of [FORMULA] 7771-5 is not large enough to explain the strength of the observed feature - it is not even sufficient to reproduce the hydrostatic calculations - and for [FORMULA] 6155-8 the theory produces lines that are too strong. An explanation for this behaviour might be a too steep velocity gradient. Reducing the slope would diminish the velocities at the formation depth of the weak lines and would also shift the position of the sonic point further out in the atmosphere, thus expanding the formation depth of the strong lines. As the density drops rapidly beyond the sonic point, the medium becomes optically thin at the line frequencies and the feature appears too weak. In addition, the shift of the line centre is too large compared with the observation, also implying a too large value of the local velocity.

[FIGURE] Fig. 17. The impact of a hydrodynamic outflow velocity field on the line formation. Displayed are theoretical line profiles of OI [FORMULA] 7771-5 (top) and 6155-8 (bottom) calculated for the stellar parameters of HD 92207 in the hydrostatic approach (ATLAS9 model, full line) and broadened according to the observations. The other two profiles are based on a hydrodynamic model (SPH) with the velocity field accounted for in the line formation calculation (dashed) and with the velocity field neglected (dotted).

Certainly, this topic deserves further attention as it offers the opportunity to study the velocity stratification in detail at the base of the stellar wind. But, due to the large number of parameters involved the theoretical description of the unified model atmospheres has to be refined first. In particular, line blanketing has to be accounted for in the models to give a realistic description of the atmospheric stratification, presently the subject of extensive work at the Universitätssternwarte München.

Finally, a last point concerning supergiants has to be mentioned here. In addition to the macroscopic velocity field the spherical extension of the atmosphere will also strengthen the near-infrared OI lines: the probability for photon escape is increased in the extended atmosphere thus the line source function is further depressed resulting in a stronger spectral feature. It is our hope that by accounting for all these effects we will be able to determine consistent abundances from all OI lines in supergiants with the present model atom.

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© European Southern Observatory (ESO) 2000

Online publication: July 13, 2000
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