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Astron. Astrophys. 342, 745-755 (1999)

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6. Summary and discussion

The results of our multisite campaign clearly show that the power spectrum of HS 2324 contains several periodic signals (about 20 or more). We therefore may exclude binarity to explain its variability, as already suggested by Handler et al. (1997). The frequencies and amplitudes are comparable with those of the GW Vir stars. If we consider also that HS 2324 is spectroscopically classified as a PG 1159 star, the immediate interpretation is that its variability is due to high overtone g-mode pulsations.

The high H abundance detected in HS 2324, about 17% in mass (Dreizler 1998), is a very interesting and unique (up to now) element, which might help to shed light upon the driving mechanisms of the GW Vir stars. As discussed in the introduction, the presence of H was generally considered as an inhibitor of pulsations (Stanghellini et al. 1991). But this result was rather speculative because, until a few years ago, no H-rich PG 1159 stars were known. With HS 2324 this question has gained importance. Presently the real effects of the presence of H appear to be less severe from preliminary models of H-rich GW Vir stars (Saio 1996, Gautschy 1997). On the other hand, the detection of hydrogen in the atmosphere of HS 2324 does not necessarily imply that hydrogen is present also in the driving regions. However, HS 2324 belongs to the subclass of luminous PG 1159 stars which still show mass loss effects in strong UV/FUV lines (Koesterke & Werner 1998, Koesterke et al. 1998). It is highly probable that HS 2324 is also affected by mass loss which would inhibit an abundance gradient due to gravitational settling. It is therefore plausible that the atmospheric composition is also representative for the driving region. An unambiguous detection of mass loss and the determination of the mass loss rate has to await FUSE (Far Ultraviolet Spectroscopic Explorer) observations of the O VI resonance lines.

However, the asteroseismological analysis is hampered by the fact that the DFT appears to be unstable in time. In principle this is not a new phenomenon: it has been observed in the light curve of all luminous PG 1159 and [WC] variables (the term "variable variables" was therefore coined by S. D. Kawaler). But in our case, as discussed in Sect. 3.1, this fact is probably due to a poor frequency resolution caused by an insufficient coverage.

If this interpretation is correct, it is not possible to obtain definite precision asteroseismology results from our data set. Nevertheless a spacing of the signals is probably present in the DFT and can be explained in two different ways. The most likely hypothesis is that we see the frequency spacing produced by the stellar rotation with a period [FORMULA] days. The second possibility, which can not be completely excluded, is that we see the period spacing between successive overtones. In this case the period spacings, equal to 18.8 (l=1) and 10.4 (l=2) s, would imply a stellar mass of 0.67 (l=1) and 0.70 [FORMULA] (l=2) using the interpolation formula of Winget et al. (1991). This asteroseismological mass would be higher than the 0.59 [FORMULA] value, found from spectroscopy plus evolutionary tracks (Dreizler et al. 1996). But this discrepancy would not be very significant as it is possible that the interpolation formula of Winget et al. (1991) needs some adjustment because of the peculiar composition of HS 2324.

In an alternative interpretation we assumed that the DFT instability was real and we applied the Linear State Space model (König & Timmer 1997) to investigate the quasi-periodic nature of these variations. As discussed in Sect. 5, this approach is also partially successful, but it also requires new longer observations to be confirmed. At the moment we can only speculate about the physical interpretation. Do we see the coupling time between different g-modes or the damping of a single mode? In principle, the quasi-periodic nature of HS 2324 could even endanger the interpretation as g-mode pulsations.

In conclusion both possible interpretations of the apparent DFT instability need a new bigger observational effort, which could be realized only with a larger number of telescopes in a WET-like campaign. If we adopt the hypothesis that the DFT instability is only apparent, it is also possible to estimate the duration needed for such a campaign in order to be able to separate all the frequencies. If all the l=1 and l=2 frequencies were excited in the region between 450 and 500 µHz, where most power is concentrated, the average frequency separation would be about 0.4 µHz. In a more realistic case, if only 50% of the frequencies were excited (as in PG 1159, which is the GW Vir star with the largest number of detected modes), a frequency resolution of about 0.8 µHz would be enough. Therefore we would require a data set with a time base of about 1.7 times the data set analyzed in this paper.

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999