4. Computation of non-LTE line profiles
Line formation calculations were performed using the codes DETAIL and SURFACE (Giddings 1981and Butler 1984respectively). DETAIL calculates level populations whilst allowing for departures from LTE, and SURFACE computes the emergent line profiles and fluxes. Such calculations assume that the model atmosphere structure is fixed, and hence may be used to examine second order effects in H/He line formation or to treat impurity elements i.e. the metals. Microturbulent velocities, which are close to the speed of sound, have been found for B-type supergiants. However, this parameter is not well-understood and its magnitude can vary from star to star. Therefore, in the calculation of line profiles, microturbulence has been included as an extra free parameter, and estimates for our sample will be discussed below.
The successful execution of DETAIL & SURFACE over such a large range of atmospheric parameters was not trivial. For these calculations, the model hydrogen and helium atoms were more complex (containing 10 levels of H I , 27 levels of He I and 14 levels of He II ), and therefore the first step has been to recalculate the populations using those from the model atmospheres as a starting point. This improvement is important for the computation of line profiles of H I and He I /II and also improves the evaluation of background continuum opacities in the case of the metal lines. In calculating metal ion populations and line-profiles, atomic data were similar to previously published analyses: C II - Eber & Butler (1988), N II - Becker & Butler (1989), O II - Becker & Butler (1988), Si II /III /IV - Becker & Butler (1990) and Mg II - Mihalas (1972). As the model atmospheres do not include metals, LTE populations were used as a starting point.
To realistically compare observed and theoretical line profiles, it is necessary to have reliable estimates of the projected rotational velocities of the stellar sample. Values of have been estimated from the metal line profiles as follows; unbroadened Gaussian profiles having equivalent widths which match the observed widths of prominent metal-line features were convolved with a Gaussian function to account for instrumental broadening, and a rotational broadening function (see Lennon et al. 1991afor more details). The amount of rotational broadening was varied until reasonable agreement with the observed profile was achieved. Typically three prominent metallic features were used for each star, with different features offering reasonable internal consistency. The estimates of , which are included in Table 1, do not include the effects of macro- and microturbulence; hence, they should be considered as upper limits.
4.1. Convergence problems associated with low gravity models
Significant difficulties were encountered in running DETAIL and SURFACE for the silicon model ion at the lowest gravities. For models with effective temperatures greater than that for the peak in Si III linestrength (i.e. 25 000 K), convergence could only be achieved by performing preliminary runs where the resonant transitions of Si III & Si IV were set into radiative detailed balance. The resultant populations were then used as starting points in runs which treated the silicon ions fully, which led to convergence in all cases.
Having successfully converged all silicon populations throughout the grid, the silicon line profiles at 4128, 4131 (Si II ), 4552, 4567, 4575, 4813, 4820, 4829 (Si III ) and 4088, 4116 Å (Si IV ) were computed. However an examination of the line profiles showed that for the lowest gravity models having 22 500 K, significant difficulties remain. For any given effective temperature, the Si III linestrengths would be expected to increase with decreasing logarithmic gravity and indeed this occurred in most cases. However, in models having the lowest gravities, the linestrengths in both Si III multiplets decreased. Examination of the line profiles indicated that this was caused by either emission or `filling in' of the profiles. Indeed the DETAIL calculations showed an overpopulation of the upper levels in the atmospheric regions where the lines were formed. This was coupled with large photoionisation rates (and subsequent cascades) in these low density models. We do not believe that this effect is real as it leads to anomalous effective temperature estimates compared with other methods (e.g. the He II profiles). Rather, we postulate that the emission is an artefact of our exclusion of line blanketing which leads to an overestimate of the UV flux and hence an overestimate of the photoionisation rates. At these temperatures, the weaker Si III multiplet near 4813 Å, appears to be more reliably modelled than the multiplet near 4552 Å, as it is formed deeper in the atmosphere and is thus less affected by low particle densities and departures from LTE. Indeed its linestrengths appear well-behaved for effective temperatures up to 25 000 K.
The problems which were encountered in the synthesis of the silicon features also seem to be present (but to a lesser extent) in the other elements, where they manifest themselves as chemical abundance anomalies in certain lines. These difficulties, which may be symptomatic of unblanketed, non-LTE models at high effective temperatures and low gravities are discussed further below.
© European Southern Observatory (ESO) 1999
Online publication: September 2, 1999