Astron. Astrophys. 363, 1040-1050 (2000)

3. Spectral analysis

3.1. Models

In order to derive effective temperatures the observed spectra have been fitted to model spectra of nearly pure helium atmospheres with a small admixture of hydrogen ( relative to helium by number) covering a temperature range from 10000 K to 35000 K in 250 K steps up to 16000 K, in 500 K steps between 16000 K and 20000 K, and 1000 K steps above 20000 K. was given between 7.75 and 8.5 in 0.25 dex increments. Between 16500 K and 20000 K we extended the grid to . HeI line profiles were calculated with our LTE atmosphere codes (see Finley et al. 1997for a recent description) in which the improved HeI line broadening theory of Beauchamp et al. (1997) was implemented. These Stark profiles have been calculated for temperatures ranging from 10000 K to 40000 K and consider broadening by ions and electrons. Line broadening by neutral perturbers, which becomes important at lower temperatures, was not included in our calculation of line profiles. This might lead to some uncertainties. However, a temperature determination from the continuum slopes of HE 0446-2531 and HE 0449-2554, for which we have absolutely calibrated flux spectra, showed the deviation in to be less than 1000 K at temperatures of about 12000 K.

3.2. Determination of

Effective temperature and were determined in a fitting procedure based on a Levenberg-Marquard algorithm (cf. Press et al. 1992) by comparison of HeI line profiles with synthetic spectra from the He/H atmospheres. The method is very similar to that described in detail in Homeier et al. (1998).

We started the fitting procedure with both temperature and as a free parameter. However, at the given data quality the dependence on turned out to be rather small, and it was thus not possible to determine it unambiguously. In most cases a higher could be compensated by a higher temperature, and vice versa, with roughly the same value. Furthermore, systematic effects like small differences in the starting values for and might change the solution by much more than the statistical errors. We therefore determined for fixed to 8, too. Comparison of temperatures derived from fits with as free parameter and fixed to 8 only revealed small differences, which could often be regarded as equal within their statistical errors. This is reflected by the mean of all fitted values of 8.150.24. In Table 3 we have compiled the results of our analysis. The given errors for temperatures and are formal statistical errors from the covariance matrix of the fit, which do not reflect any systematic errors. As it has been discussed by many authors using similar methods (see e.g. Homeier et al. 1998; Napiwotzki et al. 1999), external errors can be higher by a large factor.

Table 3. Results from the temperature and determination and derived spectral types for the analyzed stars. Equivalent widths are given in Å ngström

3.3. Determination of hydrogen and metal abundances

As for the DB stars, was determined for DBA and DBAZ white dwarfs by comparing HeI line profiles with those from synthetic spectra of our He/H atmospheres. We did not perform selfconsistent calculations with hydrogen and metal lines already included in the atmospheres. In the next step model atmospheres for the derived effective temperatures were calculated which contain calcium and/or hydrogen in estimated amounts for the respective star. The resulting temperature and pressure stratification was then used to compute detailed synthetic spectra with varying calcium and/or hydrogen abundances. For HE 0446-2531 also magnesium and iron were considered. Abundances were then obtained by comparison of observed equivalent widths and line profiles to those from the synthetic spectra. Unless otherwise mentioned, equivalent widths of H, H, and H were determined between 6543 Å and 6583 Å, 4841 Å and 4881 Å, and 4310 Å and 4370 Å, respectively; equivalent widths of the CaII doublet were determined between 3890 Å and 3990 Å.

When comparing HE 0446-2531 and HE 0449-2554, the great difference in calcium abundances (approximately a factor of 30) is surprising because temperatures are similar, and equivalent widths differ only by a factor of 2. However, their hydrogen abundances also differ by about a factor of 20. This affects the atmospheric structure since hydrogen contributes electrons, and changes the opacity. In turn the changed atmospheric structure does influence the line spectrum.

© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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