## 3. Temporal spectroscopy## 3.1. Spectral window and power spectrumWe computed a single sine function with unit amplitude at the same sample times of the entire data set (window function). The discrete Fourier transform of the window function gives the spectral window, which is shown in Fig. 2. For more completeness, both the amplitude and the power (amplitude squared) spectra of the window function are presented. The only structures which may give troubles for the unambiguous identification of the modes are the 1 cycle/day aliases, with a relative amplitude of about 0.3 (relative power of 0.09).
Using the same discrete Fourier transform (DFT), based on the
Deeming (1975) method and Kurtz (1985) algorithm, we computed the
transform of the entire reduced data set. In Fig. 2 both amplitude and
power spectrum are shown in units of millimodulation amplitude (mma)
and micromodulation power (
Looking at Fig. 3, some structures appear to be not completely resolved, suggesting that the light curve could be too short that we can resolve all the present frequencies. To test this crucial point, we divided the data set into two equal parts and computed the Fourier transform of each part. The two power spectra, presented in Fig. 4, show strong differences not only in amplitude, but also in frequency. The first interpretation of such differences is simply that the data set is not long enough to "stabilize" the Fourier transform. In other words, the light curve is not completely resolved. The reliability of this hypothesis is increased by the fact that our best multisinusoidal fit of the entire data set (see next section and Table 2) gives good results also when applied only to the first or the second half of data (Fig. 4). If the DFT apparent instability is actually due to the insufficient coverage, most of the analyses reported in Sects. 3.2, 4.1 and 4.2, and based on the assumption that the DFT of HS 2324 is not time dependent on time scales shorter than our run, will need further confirmation from a new longer observational campaign.
On the other hand, if the DFT time instability was real, we would need a different explanation for such peculiar behaviour. An alternative hypothesis of a fast damped oscillator has been considered and is reported in Sect. 5. ## 3.2. Frequency identificationLooking at Figs. 2 and 3, it is immediately evident that determining the active frequencies from the power spectrum of HS 2324 will be more difficult than in most other GW Vir stars for several reasons: the power is concentrated in only 3 crowded regions; the amplitudes are very low; the low frequencies imply that the frequency and the period spacing expected may have about same values. The high frequency region does not help much because it seems to be constituted only by linear combinations of the low-frequency peaks. Moreover we know that the frequencies are not completely resolved and therefore we certainly have errors both in frequency and in amplitude. To distinguish the real frequencies present in the HS 2324 data
from the artifacts introduced by the spectral window, we proceeded as
follows. First we selected the highest peak in each of the three
"active regions" near 390, 470 and 950
© European Southern Observatory (ESO) 1999 Online publication: February 23, 1999 |