## 4. "Classical" seismological interpretation## 4.1. Frequency splittingIn the power spectrum of HS 2324 there is not any clear direct sign of frequency splitting. This may be due to different reasons. A very small rotation rate, with secondary (m0) modes below the frequency resolution, seems quite unlikely because it would require a rotation period longer than about 9 days. A more realistic possibility is that the star has a low inclination, so that the amplitudes of the m0 modes are near the level of the noise. A third possibility is that the concentration of the peaks is so high that we are simply not able to recognize the modes splitted by the rotation. If a direct identification of the rotational splitting is not
possible, the high number of peaks allows one to make use of
statistical methods. First we constructed an histogram of the
frequency separations between the signals listed in Table 2,
excluding the linear combinations. The result was not significant: no
preferred frequency spacings appeared. Another attempt was done using
all the peaks of the power spectrum higher than a fixed level; we
selected 49 frequencies and made the histogram. Here also we did not
get any significant result apart that all the peaks were never higher
than the one day alias near 10-11 At this point we invoked a third method: we computed the DFT of the
amplitude spectrum, using two different subsets spanning
350-1000
Looking now at the peak near 10 In this context we can also try to estimate the inclination of the
star using the l=1 modes. Following Pesnell
(1985) ## 4.2. Period spacing and mode trappingThe two peaks in the amplitude spectrum DFT, described in the previous section, could also be due to the period spacing between modes with successive overtones. In Fig. 7 (left panels) we show the DFT of the period spectrum (amplitude spectrum in the period domain). For the upper panel we used a subset of the period spectrum with periods between 1000 and 2857 s, while for the lower panel we used a narrower part with periods spanning 2000 - 2273 s. Excluding the peak at about 46 s, which is related to the one day alias as discussed in the previous section, the most significant period spacings are 18.8 s and 10.4 s (at least in the lower graph; in the upper graph the 10.4 s peak appears more uncertain). Their ratio is close (accuracy better than 5%) to the asymptotic value of , suggesting that 18.8 and 10.4 s might correspond to the l=1 and l=2 period spacings. In this hypothesis, the differences between the two left panels of Fig. 7 suggest that the l=2 modes might be present only (or mainly) in the high-amplitude region between 2000 and 2273 s.
An attempt to confirm the hypothesis that the modes of HS 2324 are
equally spaced in period (and not in frequency) has been done applying
the Kolmogorov-Smirnov (K-S) test (Kawaler 1988) and the Inverse
Variance technique (O'Donoghue 1994) to the first 12 periods listed in
Table 2 (excluding the linear combinations). The results,
reported in Fig. 7 (right panels), do not confirm that the modes are
equally spaced in period. Moreover, the lack of any significant period
spacing further indicates that the period list is not
complete Nothing may be said about the trapped modes phenomenon apart the
following. The ratio between the frequencies of the highest peaks in
the 380 and 475 © European Southern Observatory (ESO) 1999 Online publication: February 23, 1999 |