Astron. Astrophys. 334, 618-632 (1998)

3. Spectral analysis

3.1. Model atmospheres and atomic data

For our spectral analyses homogeneous, plane-parallel model atmospheres in radiative and hydrostatic equilibrium were applied. Despite of the high gravity the ionization and excitation of the plasma is dominated by the intense radiation field due to the very high effective temperature (WHH). Non-LTE calculations are therefore required to obtain accurate results.

We used our non-LTE code which is based on the Accelerated Lambda Iteration method (Werner 1986, Dreizler & Werner 1993, Werner & Dreizler 1998) to calculate all atmospheric models presented here. We included the Hummer-Mihalas occupation probability formalism, generalized to non-LTE conditions by Hubeny et al. (1994), to ensure the pressure induced dissolution of the atomic levels. The influence on line profiles for hot helium-rich stars is demonstrated by Werner et al. (1995) and Werner (1996b). Without going into details we mention that in general profiles of He II lines become deeper and broader, most prominent is the change in the 4686 Å line. As demonstrated by Dreizler et al. (1994b [DWJH]), the broadening of the C IV resonance line as well as the lines contributing to the trough around 4670 Å has to be accounted for already in the calculation of the atmospheric structure. In order to make full use of the HST spectra we calculated an extended grid of NLTE model atmospheres taking into account most detailed model atoms. The great advantage of the HST spectra is the coverage of several ionization stages of carbon and oxygen. This, however, can only be exploited with very detailed model atoms since all these ionization stages have to be included simultaneously to ensure a consistent analysis of all detectable line transitions in the optical and UV spectra. Altogether we end up with 14 ionization stages, 351 levels and 1140 line transitions for 5 elements taking into account nearly all levels for C III/IV, N V, and O IV/V/VI listed by Bashkin & Stoner (1975). Atomic models are from WHH and DWJH partly updated with Opacity Project data (Seaton 1987).

Using these model atoms we calculated an extensive grid of 90 model atmospheres varying the effective temperature, surface gravity and surface composition. Due to the detailed model atoms included in the calculations an enormous amount of computer time was required. All models were calculated on CRAY Y-MP machines of the Computer Center of the University Kiel each one consuming roughly 5 days of CPU time. This effort is due to slow convergence especially caused by the detailed oxygen model atom. Finally, the emergent spectrum of each model was computed on Alpha workstations of the University Tübingen taking into account the best available broadening theories. Stark broadening of the C IV lines is the main source of uncertainty in our analysis since the observed lines are within the transition range of linear and quadratic Stark broadening regimes which is difficult to handle theoretically. We therefore still have to rely on the approximation introduced by WHH for these lines. Keeping this problem in mind it is not surprising that the profiles of the C IV lines around 1350 Å and 1315 Å can not be reproduced exactly (see Figs. 2a-d and 4). For the broadening of He II lines we used the tables of Schöning & Butler (1989) which are based on the Unified Theory of Vidal et al. (1970).

3.2. Spectral analysis of PG 1159 stars

Determination of the stellar parameters is performed by comparison of the observed spectrum with theoretical spectra. The fit procedure is demonstrated in Figs. 2a-d and 3a and b for the pulsator PG 2131 066 because of its importance for asteroseismology. Its spectral analysis is hampered, though, by a cool companion (Wesemael et al. 1985) whose continuum contribution has been subtracted here. The emission cores in the H and H lines (see Figs. 3a and b and 5) arising from the cool companion, however, cannot be corrected for (see also Paunzen et al. 1998). The final fits are displayed in Figs. 4 to 6, the results of the analyses are summarized in Table 3. The fitting procedure was performed by eye starting with the parameters determined from previous optical analyses (DWH, WHH). First we determined the interstellar column density of hydrogen by fitting the line wings of Ly and - using the standard Seaton law (1979) - the reddening by fitting the slope of the UV continuum which is, within the error limits for the effective temperature, only dependent on E(B-V). Varying the model parameters we then derived the best fitting model. The determination of the effective temperature is based on the strengths of the C III 1170 Å, O IV 1340 Å, and O V 1371 Å lines. All three temperature sensitive lines agree very well in the final model providing the expected low error range of . An additional O V line at 1418 Å confirms the results. Determination of the surface gravity is much more difficult since no particularly gravity sensitive line exists in the range of our HST spectra. Gravity determination is further hampered by the problem of line broadening (see above). We therefore calculated models only with two different surface gravities (log g=7.0 and 7.5) representing the typical (high gravity) PG 1159 star surface gravities. From HST spectra alone only a preference for one of the two gravities can be derived. No interpolation between the two values was therefore applied. Finally the chemical composition is determined by fitting the line strengths of the element in question (C, N and O). During the analysis it turned out that we could only determine the C/O ratio rather than their absolute values if the carbon abundance exceeds C/He=0.3 by number. Since the UV continuum is dominated by C and O opacities the line strengths of C and O lines are insensitive to changes in C and O abundances as long as the C/O ratio is kept fixed. Optical spectra are needed in addition to derive absolute values (see below). Finally we derived N abundances from the resonance doublet at N V 1240 Å for PG 0122 200, PG 2131 066, PG 1707 427, and PG 1159-035 or upper limits for the others which show only very weak N V 1240 Å lines. Since these weak lines could also include a contribution of interstellar matter these values are only upper limits. In the case of PG 0122 200, PG 2131 066, and PG 1707 427 the derived abundance is consistent with weak N IV lines at 1275 Å and 1296 Å.

Fig. 2. Sample fit of PG 2131 066. Observations are plotted with thin, theoretical spectra with thick lines. Stellar lines are marked at the bottom, interstellar lines at the top. The temperature sensitive C III, O IV and O V lines allow a determination with 5% accuracy (a, b). The gravity determination is hampered by the poorly known broadening of the C IV lines. A systematic error lower than 0.3 dex is therefore impossible to achieve (c). The C/O ratio can be determined with an uncertainty of a factor of three (d top two). The C/He abundance can only be determined in the less carbon rich stars with an uncertainty of a factor of two (d lower three). In the more carbon rich stars the derived C/He abundances from the HST spectra are only lower limits. Optical spectra are needed to improve the results (Fig. 3a and b).

Fig. 3. Sample fit of He II 4860 Å in the optical spectrum of PG 2131 066. Observations are plotted with thin, theoretical spectra with thick lines. The emission reversal in the He II line core is due to H emission from the cool companion (see Paunzen et al. 1998) . We subtracted its continuum contribution but could not correct for the emission components. Gravity determination is also difficult in the optical. Spectra with higher signal/noise and resolution are required to reduce the error bar (a). The He II lines are most sensitive to changes in the C/He ratio. While a higher ratio than C/He=0.3 could not be excluded from the HST spectra (Fig. 2a-d), the He II lines become too weak in this case (b).

Fig. 4. Final fits of de-reddened HST spectra from PG 1159 stars. Observation thin, theoretical spectra thick lines. Top five: non-pulsating, bottom four: pulsating PG 1159 stars. Note the strong N V doublet at 1238/1242 Å in the cool pulsators indicated by vertical lines at the bottom. The nitrogen abundances in the stable PG 1159 stars are upper limits as derived from the HST spectra. In the case of PG 1520 525 a tighter limit can be derived from the optical spectrum. Also indicated at the bottom are the strategic lines for determinations, the interstellar lines originating from low ionization stages (e.g. N I, O I, Si II, S II) are marked at the top. A contribution of high ionization interstellar lines is possible only in the case of the N V resonance doublet (see text). Abundances are given as number ratios. For identification of the spectral lines and possible interstellar contamination see Table 2.

Fig. 5. Final fits to normalized optical spectra. Observation thin, theoretical spectra thick lines. Top five: non-pulsating, bottom four: pulsating PG 1159 stars.

Fig. 6. Final model spectra from HST fitting compared to de-reddened IUE low resolution spectra. In addition to the HST spectra IUE covers the C IV lines at 1550 Å and 1585 Å and the He II line 1640 Å. Top four: non-pulsating, bottom four pulsating PG 1159 stars. For line identification see WHH.

Table 3. Results of the analyses. Top: non-pulsating, bottom: pulsating PG 1159 stars. Abundances are given in number ratios.

The parameters of the final models are then checked by a comparison with optical and IUE spectra. The IUE spectra cover the C IV 1550 Å resonance doublet and the He II 1640 Å line, which are both outside the GHRS range. In all cases except for PG 1520 525 both lines are well reproduced with the HST parameters. A further confirmation of our results comes from a fit to HUT spectra of PG 1424 535 and PG 1707 427 with our HST parameters (Kruk & Werner 1998).

With the effective temperature fixed by the UV analysis we hoped to improve the gravity and the He abundance determined from optical spectra. Too high a carbon abundance results in too shallow optical He II lines. Thereby the C/He ratio was constrained to within a factor of two. The gravity determination, however, could not be improved significantly. Although the broadening of the He II lines is more reliable the precision of the gravity determination is limited by the available spectra and is not better than from the UV metal lines ( dex, see Fig. 3a and b). At least, we find no discrepancy between both gravity indicators, lending some support to our approximate treatment of CIV/OVI line broadening.

The N V 4604/4620 Å doublet provides an independent check of the N abundance. In the case of PG 1520 525 the upper limit could be reduced significantly compared to the HST value. In the case of PG 1159-035 the determination of the N abundance is inconclusive since the doublet is just in the transition from absorption to emission in the parameter range of PG 1159-035 (Fig. 7). While the resonance line in the HST spectrum indicates an N abundance of the optical N V lines are much too strong at the parameters derived previously ( =140 000 K, log g=7.0). However, slight changes within the error limits weaken the emission line of the 140 000/7.0 model to an undetectable strength in the 135 000/7.5 model, in accordance with the observation. A slightly lower effective temperature would then turn the line into an absorption line. Due to this sensitive dependence of the N abundance on other parameters the optical spectrum of PG 1159-035 does not constrain it further. Because of the high effective temperature of PG 1159-035 the resonance doublet in the UV is weak and an interstellar origin can not be excluded. However, we have two independent hints that it is more likely of stellar origin. First, the N V lines in PG 1159-035 are significantly stronger than in PG 1520 525 which has otherwise very similar stellar parameters but a higher interstellar hydrogen column density. Second, the IUE high-resolution spectra of PG 1159-035 allow a separation of the stellar and interstellar lines (Liebert et al. 1989). While the interstellar lines have a mean velocity of -28.2 km/s the N V lines have 33.8 km/s in reasonable agreement with other stellar features (O V 1371 Å, C IV 1548/1550 Å). The separation of 60 km/s, however, is only marginally above the limit of the spectral resolution of the IUE Echelle spectrum. For a conclusive determination we therefore need additional spectra in another wavelength range to corroborate our result. One possibility is the FUV where further N V lines can be found. An existing HUT spectrum of PG 1159-035 (Kruk & Werner 1998) indicates the presence of N at the 1% level, however, the resolution is not sufficient for a safe statement. The problem can only be solved after the launch of FUSE (Far Ultraviolet Spectroscopic Explorer) which will obtain a high resolution FUV spectrum of PG 1159-035.

Fig. 7. Determination of the nitrogen abundance of PG 1159-035. Comparison of the optical, HST and HUT spectra with theoretical spectra. Positions of the nitrogen lines are marked in the HST and HUT spectrum. While the HST and HUT data can be fitted with the 140 000 K/log=7.0 model, the N V lines in the optical are too strong. A reduction of the effective temperature to 135 000 K and an increase of log g to 7.5 provides a good fit, however. See text for detailed discussion.

A progress in the determination of the hydrogen abundance is only possible with high resolution spectra ( 0.1 Å). Such spectra are not yet available for all programme stars except PG 1159-035. Werner (1996a) could derive an upper limit of 5% in this case. It should be noted that a hydrogen abundance of 5% would still be sufficient to transform a PG 1159 star into DA white dwarf during the further evolution.

As is obvious from Figs. 4 to 6 the fits of the observed UV and optical spectra are excellent in most cases. Slight discrepancies occur only in the C IV 1350 Å and 1315 Å lines as well as in the He II/H line in few cases. The former problem is probably due to inaccurately known broadening theory (see Sect. 3.1). Several lines in the UV spectra are not matched by our theoretical models. All these lines are of interstellar origin. The resolution of the employed gratings, however, does not allow a detailed analysis of the interstellar clouds, except for the hydrogen column density (see Table 1 for results).

3.3. Results

The resulting atmospheric parameters and C, N and O abundances are summarized in Table 3. Effective temperatures range from 75 000 K to 150 000 K at gravities of either 7.0 or 7.5. The atmospheric parameters of PG 1159-035 derived by WHH are confirmed. The former twins (PG 1159-035/PG 1520 525 and PG 1424 535/PG 1707 427), however, are disrupted by the new analysis, indicating that PG 1520 525 is slightly hotter and has a higher gravity than PG 1159-035 corroborating earlier results of Werner et al. (1996b) which were based on the analysis of an EUVE spectrum. In the other twin pair PG 1424 535 turns out to be hotter than found by WHH, whereas PG 1707 427 is cooler and has a higher gravity. HS 0704 6153 is also hotter than found by DWJH. The changes in and log g are within the error limits of previous analyses (10-15%, 0.5 dex, respectively). While the programme stars (except HS 1517 7403, see Sect. 4.4) have very similar C and O abundances, surprisingly four stars are N rich (all with the same abundance of 1% by number relative to He) while no nitrogen can be detected in the others indicating that N/He is below the solar abundance. The derived C and O abundances agree also with previous results to within their error limits. Changes are due to (i) the modified effective temperatures and gravities and (ii) the improvements in the model atmospheres described in Sect. 3.1.

© European Southern Observatory (ESO) 1998

Online publication: May 15, 1998

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