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

5. The damped oscillator hypothesis

When we discovered that the DFT was unstable, we also tried to explain such apparent time dependence of the DFT with a completely different quasi-periodic approach. We considered the hypothesis that the DFT temporal instability was real and due to a very short life time of the oscillations, which were continuously excited and damped.

We therefore applied to the HS 2324 data the Linear State Space model developed by Michael König for the analysis of X-ray variability of AGN (König & Timmer 1997, König et al. 1997). The current version of this program requires uninterrupted and equally spaced datasets. Moreover, in order to provide reliable results, the time scales to be investigated must be sampled at least ten times. The only part of our light curve which fulfills these criteria (JD 94 - 94.9, after rebinning with 200 s) can be actually fitted with a period of 2134 s and a damping time of approximately 3.5 periods. A further attempt has been done using a larger nearly uninterrupted part of the light curve (JD 94 - 95.7), filling the small gaps with white noise or with synthetic data (both techniques give same results). The results are slightly different in this case: 2154 s and 3.1 periods. In both cases from a K-S test the residual is white noise with over 90 probability. If we try to find a secondary period the results are unreliable (damping time longer than the dataset), but in any case the inclusion of more frequencies does not improve the fit.

In Fig. 8 the fit from the Linear State Space model is compared with the multisinusoidal fit: the quality is comparably good. Despite this partial success, we cannot demonstrate that the damping time found is really a fundamental quantity, constant over at least some days. We would need several datasets (ideally, but not necessarily coherent) of at least one day length to reject or corroborate this hypothesis. Moreover, the excitation time-scale obtained from the Linear State Space model appears to be very short respect to the growth rates obtained from GW Vir non-adiabatic models. For these reasons the present results are not convincing enough to abandon the DFT results. On the other hand, the inviting advantage of the quasi-periodic approach is the small number of parameters required to describe the light curve. Unstable power spectra have been found also in other luminous PG 1159 stars (e.g. RXJ 2117+3412) and [WC] CSPN (e.g. NGC 1501) variables. Changes were observed down to the time resolution of several days (Bond et al. 1996, Table 6).

Fig. 8. Damped oscillator (up ) vs 19 sinusoids function (down ) in the best part of the light curve (BJD 94.0 - 95.7). Both the synthetic light curves (main panels) and DFTs (window panels) are shown and compared with the HS 2324 data (crosses).

© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999
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