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

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4. Discussion

We want to discuss our results in the context of asteroseismology and post-AGB evolution. Our analyses provide several interesting implications for both fields.

4.1. Effective temperatures and the boundary of the GW Vir instability strip

The main motivation for the HST observations was a precise determination of [FORMULA]. The better access of [FORMULA] from UV spectra now provides a reliably defined instability strip in the HRD (Fig. 8). The pair PG 1159-035 and PG 1520 [FORMULA] 525 defines the blue edge of the GW Vir instability strip since PG 1159-035 is variable and PG 1520 [FORMULA] 525 is stable. Due to a better determination of [FORMULA] these stars are separated by 10 000 K now. However, from preliminary analyses NGC 650 (the stable star next to PG 1159-035 in Fig. 8) has parameters similar to PG 1159-035 but is stable. A more elaborated analysis of NGC 650, however, is required for more detailed conclusions. So, the puzzle remains that stable and instable PG 1159 stars can have very similar effective temperatures and gravities. An upcoming detailed analysis of NGC 650 might reveal differences between these two stars. The red edge seems to be in accordance with the low temperature limit of the spectroscopic class of PG 1159 stars. HS 0704 [FORMULA] 6153 and PG 0122 [FORMULA] 200 are now defining the cool end of PG 1159 stars, the former is stable the latter is pulsating. This clearly indicates that the pulsations stop due to abundance evolution effects: Around the position of HS 0704 [FORMULA] 6153 and PG 0122 [FORMULA] 200 the transition from PG 1159 stars towards white dwarfs seems to be completed. Heavier elements are then removed from the outer envelope due to gravitational settling making the star appear as a hot DO (or DA if a sufficient amount of H remained in the envelope) white dwarf and destroying the C/O driving mechanism.

[FIGURE] Fig. 8. [FORMULA] - log g diagram with observed locations of PG 1159 stars. Different symbols are used to distinguish pulsators and non-pulsators (squares: pulsators, circles: non-pulsators, triangles: no photometric data available). Big symbols represent our programme stars. The parameters for the other PG 1159 stars are taken from Werner et al. (1997a). Post-AGB stellar evolutionary tracks of Wood & Faulkner (1986, He burners, mass loss type B) are plotted with long dashed lines: Masses are from right to left 0.6, 0.7 and 0.76 [FORMULA]. Solid lines are used for tracks of O'Brien & Kawaler (in prep.). Models of 0.550, 0.573, 0.600, and 0.630 [FORMULA] have a helium and carbon rich surface similar to the observed atmospheric abundances. Evolutionary tracks which have started from homogeneous He main sequence with 0.57, 0.63, and 0.70 [FORMULA] (Gautschy 1997) are marked with short dashed lines, thick parts denote phases where pulsational instability occurs.

4.2. Masses and the width of the GW Vir strip

One important point is that the instability strip becomes considerably narrower compared to previous results (Werner et al. 1996b). In the regime of the GW Vir stars the instability seems to be confined to a very small mass range around 0.55 [FORMULA] in contrast to the PNNV instability strip which is much wider. Predictions of the strip position from pulsational models are still not satisfactory as mentioned in Sect. 1.2. They either require a steep abundance gradient to obtain a pure C and O mixture in the driving region (Bradley & Dziembowski 1996) or predict much less luminous or cooler GW Vir stars (Gautschy 1997, Fig. 8). The latter problem is probably due to the initial conditions of the evolutionary sequences of Gautschy.

It is therefore important to compare our results with asteroseismological analyses (which are independent from the models concerning the position of the GW Vir strip). One common parameter is the stellar mass which can be determined with high precision from asteroseismology. In order to circumvent systematic effects we derive our spectroscopic masses from a comparison with the evolutionary tracks also applied for the asteroseismologic analyses (O'Brien & Kawaler in prep., calculated with input physics similar to Dehner & Kawaler 1995; tracks are kindly provided by these authors). This is necessary as can be clearly seen from Fig. 8 where we included different evolutionary tracks. Previously we used the ones of Wood & Faulkner (1986), which have however a hydrogen rich surface. There is a systematic offset of 0.03 [FORMULA] compared to the tracks of O'Brien & Kawaler which are hydrogen deficient and have a surface composition similar to our spectroscopic results. The main uncertainty of the spectroscopic mass determination is the uncertainty of the surface gravity. An error of 0.3 dex translates into an error of 0.1 [FORMULA]. In Table 4 we compare our spectroscopic masses with those from asteroseismology. In the two cases of WET observations the values are in reasonable agreement (PG 1159-035, PG 2131 [FORMULA] 066) within our error limits, in the two cases of single site observations (PG 1707 [FORMULA] 427, PG 0122 [FORMULA] 200) the spectroscopic mass is significantly lower. Upcoming analyses of the latest WET runs will hopefully clarify this discrepancy. Another parameter which can be compared is the effective temperature. This in very good agreement between spectroscopy and asteroseismology, e.g. for PG 1159-035 140 000 K (this paper) versus 136 000 K (Kawaler & Bradley 1994). Asteroseismology also corroborates the surface composition determined from spectroscopy (Kawaler & Bradley 1994). Together, this can be regarded as good mutual confirmation of both approaches. Future spectroscopic work will concentrate on more precise gravity determinations.


Table 4. Comparison between spectroscopic and asteroseismologic masses in [FORMULA] (top four). Spectroscopic masses are derived from the comparison with tracks of O'Brien & Kawaler (in prep.). In the case of PG 1424 [FORMULA] 535 and HS 1517 [FORMULA] 7403 the extrapolation is quite large and the masses can only be guessed. HS 0704 [FORMULA] 6153 is probably not an AGB descendant as discussed in DWJH. The error in the spectroscopic mass determination is 0.1 [FORMULA].

Finally, it is worthwhile to note that PG 1520 [FORMULA] 525 is more massive (0.65 [FORMULA]) than any other programme star (0.5 ... 0.55 [FORMULA]). It is also the only star in the sample known to reside in a PN.

4.3. Abundances and driving mechanism

4.3.1. Nitrogen abundance

A surprising result of our analysis is the detection of nitrogen in four of the programme stars. Only one PG 1159 star with detectable amount of N was known previously (PG 1144 [FORMULA] 005, Werner & Heber 1991). In the other stars the optical N lines were below the detection limit of older spectra. The result is also extremely interesting in view of the driving mechanism of the GW Vir pulsations. In all analyzed stars of this sample the existence of N is strongly correlated with pulsations. All stable PG 1159 stars of the sample have a N/He abundance below 1 [FORMULA] while pulsators have a N/He abundance at the 1% level. PG 1159-035 seems to fit into this correlation also. It needs, however, confirmation by future observations. Since our sample contains all GW Vir variables we conclude that a high N abundance is necessary to drive oscillations in this parameter range or directly traces the necessary driving process. Compared to the high C and O abundances, the N abundance (1%) in the pulsating stars is relatively low. Whether this is too low to drive pulsations remains to be seen. It should be noted, though, that the derivatives of the opacity with respect to the local temperature and densities are important for the driving, not the total opacity. The other PG 1159 star with ni- trogen, PG 1144 [FORMULA] 005, is somewhat hotter ([FORMULA] =150 000 K) and of lower gravity (log g=6.5) than PG 1159-035. Despite of its nitrogen-richness no variability has been detected (Grauer et al. 1987). Admittedly this is at odds with our proposed correlation.

It is worthwhile to notice that previously Vauclair (1990) suspected nitrogen to be responsible for the GW Vir pulsations. He found from diffusion calculations that N should dominate in the driving region. Since however, the abundance pattern of PG 1159 stars is impossible to explain in the context of diffusion and radiative levitation and due to the fact that only one PG 1159 star with atmospheric N abundance was known at that time this explanation was abandoned again.

Does a correlation of the N abundance with pulsations exist in the PNNVs? No N could be detected in any of the PG 1159 stars of lgE subclass (e.g. RX J 2117 [FORMULA] 3412, Werner et al. 1996a) so far, whether pulsating or not. In the case of the [WC] stars some show nitrogen and some don't with no correlation to pulsations. Additionally, the two stable PG 1159-[WC] transition objects (A 30 and A 78) show nitrogen. The PNNV pulsators, though, differ from the GW Vir stars with respect to their stellar winds. Fast winds ([FORMULA] 3000 km/s) have been detected in UV spectra of the central stars of NGC 246 (Heap, 1982) and K 1-16 (Patriarchi & Perinotto, 1996) and are likely to be present in the other PG 1159 lgE stars as well. The existence of the stellar wind might strongly influence the pulsations. Both the PG 1159 stars among the PNNVs and the pulsating [WC] stars have pulsation frequencies around 1 mHz while GW Vir stars have frequencies between 2 and 2.5 mHz. Furthermore the frequency pattern of the former group is variable (Steven Kawaler coined the term "variable variables") while it is much more stable in the case of the latter group. In the light of the results regarding the N abundances we conjecture that also the driving mechanism is (slightly) different between the PNNVs and GW Vir stars despite of otherwise very similar spectroscopic and evolutionary properties.

4.3.2. Carbon and oxygen abundances

Another important point is that we could derive O abundances for the cooler ([FORMULA] [FORMULA] 100 000 K) PG 1159 stars, which was impossible from previous optical analyses. It was one of the main motivations for the HST proposal to find differences in the C and O abundance between pulsators and non-pulsators since these elements are believed to cause the instabilities due to cyclic ionization (e.g. Starrfield et al. 1984). Indeed, the non-variable HS 1517 [FORMULA] 7403 has considerably less C and O than the GW Vir stars. The other non-variables have also C, O and O/C on average lower than the pulsating stars, but the difference is small (less than a factor of two) and therefore only marginally significant. Hence, we conclude that a correlation between pulsation and C and O abundances might exist, however, considerably weaker than in the case of the N abundance.

The amount of helium (and hydrogen) in the driving region are critical parameters to match the observed instability strip and pulsation frequencies. The results of Bradley & Dziembowski (1996) and all former work require a nearly pure C-O driving region which would require a steep abundance gradient from the photosphere towards the driving region in order to increase the oxygen abundance to about 50%. A higher O/C ratio in the case of pulsators is therefore favorable. It should, however, be noted that the models of Saio (1996) and Gautschy (1997) do not require such a high O abundance to drive pulsations. We conclude that our results in principle corroborate the ideas about the driving mechanism. However, our result on the N abundance might lead to modifications. We conjecture that adding nitrogen could steepen the opacity gradient with respect to temperature and density and, therefore, enforce the driving. This might be necessary to compensate for the damping effect from traces of He and H in the driving region. We therefore strongly encourage the pulsation theorist to test this hypothesis.

4.4. Evolutionary status of PG 1159 stars

The positions of most programme stars in the ([FORMULA], log g)-plane are well reproduced by post-AGB tracks of low masses (see Fig. 8 and Table 4). PG 1424 [FORMULA] 535 and HS 1517 [FORMULA] 7403 and, as already discussed by DWJH, HS 0704 [FORMULA] 6153 are not matched by post-AGB tracks due to the lower surface gravity of these stars. The alternative that these stars are AGB manqué stars is very likely for HS 0704 [FORMULA] 6153, however, the large error of the gravity determination still allows PG 1424 [FORMULA] 535 and HS 1517 [FORMULA] 7403 to be identified with post-AGB stars. Only a better gravity determination can provide further constraints.

The very high carbon and oxygen abundances indicate the presence of 3 [FORMULA] processed material on the surface of PG 1159 stars (see also WHH). The nitrogen abundance in this context is very interesting for the evolutionary status of PG 1159 stars, because the existence of N in a C and O dominated surrounding is difficult to explain by nuclear evolution. All N is destroyed in the 3 [FORMULA] process. Mixing processes leading to ingestion of H during a He shell flash into the 3 [FORMULA] burning shell is required to explain this result. Due to the complex modeling of the time dependent mixing only one evolutionary calculation for this scenario exists (Iben & MacDonald 1995). We hope that the larger number of PG 1159 stars with high N abundances will be a motivation to extend these evolutionary calculations. It is very interesting to note that this picture seems to be supported by recent observations: Sakurai's object, probably a star just undergoing a late He shell flash, shows spectroscopic evidence for H ingestion (Asplund et al. 1997). The H abundance dropped by 0.7 dex over half a year but the N abundance is still unaffected.

The larger number of PG 1159 stars with N raises the question what parameter decides whether mixing occurs during a late He flash. Iben & MacDonald (1995) identified five different scenarios for post-AGB evolution. Their Case 4 and Case 5 lead to a late He flash and are therefore relevant to the PG 1159 stars. In Case 4 the flash occurs during H burning, which prevents mixing due to the entropy barrier at the H/He discontinuity. In Case 5 the flash occurs when all nuclear processes have ceased and the star has evolved into a white dwarf for the first time. In this case the flash induced mixing can transport H into the He burning shell. As pointed out by Werner et al. (1998) this idea can be tested by a comparison between the Case 4/5 ratio with the ratio of N depleted/enhanced PG 1159 stars. This comparison seems not convincing (3/2 versus 22/5), but this is not surprising. The theoretical ratio is determined under the assumption that the likelihood of the first departure from the AGB is independent of the thermal pulse phase on the AGB as well as of the mass. The observational value is still uncertain since only the minority of the PG 1159 stars have been searched for N because that requires very good optical or UV spectra. Further efforts on the theoretical and observational side are therefore necessary.

For the evolutionary connection between DO white dwarfs and PG 1159 stars the carbon and oxygen abundances are of special interest. The majority of our sample has carbon abundances of C/He=0.3 and oxygen abundances of O/He=0.1. This is by far more than in any DO white dwarf. It is therefore believed that gravitational settling removes the heavier elements leaving a helium-rich atmosphere (assuming the star to be hydrogen free) when the star evolves further into a DO star. As discussed above this transition seems to be completed at the position of the coolest PG 1159 stars (PG 0122 [FORMULA] 200 and HS 0704 [FORMULA] 6153). The transition process is however not yet understood since determined abundances in DOs (and also in PG 1159 stars) are not in agreement with present predictions of the diffusion theory (Dreizler & Werner 1996, Unglaub & Bues 1996, 1997). As pointed out above, three PG 1159 stars (HS 1517 [FORMULA] 7403, HS 0704 [FORMULA] 6153, and MCT 0130-1937) have lower carbon and oxygen abundances. In the most extreme case of HS 1517 [FORMULA] 7403 the carbon abundance is only C/He=0.05. The most carbon rich DO (RE 0503-289) has a carbon abundance of C/He=0.007 (Dreizler & Werner 1996). It can be speculated that these two stars represent transition objects between PG 1159 stars and DO white dwarfs.

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© European Southern Observatory (ESO) 1998

Online publication: May 15, 1998