4 Characteristic frequencies

Figure 3: Histogram similar to Fig. 2 ( S/N ratio = 3.25), but with the data separated according to spectral type (upper panel) and luminosity class (lower panel).

For the stars analysed by us, the four highest peaks above a S/N ratio higher than 3.25, 3.6, and 4.0 were used to produce a histogram. Kuschnig et al. (1997) demonstrated that a S/N ratio larger than 4 corresponds to a probability of more than 99.9% that a peak in the amplitude spectrum can be considered significant. A S/N ratio of more than 3.6 and 3.25 corresponds to a probability of more than 99% and 95%, respectively. The histogram (Fig. 2) illustrates how often at least one of the up to four highest peaks (above a chosen S/N ratio level) in the amplitude spectra of our presumably constant stars falls into a given frequency bin of 0.5 ${\rm d}^{\,-1}$ width for the high-frequency domain and 0.05 ${\rm d}^{\,-1}$ width for the low-frequency domain. We compared this number with the number of cases we would expect if all the frequencies were uniformly distributed over all the bins in the histogram and plotted the corresponding ratio. Because of the minimum distance of the 4 peaks per star, a number we have chosen for our extraction routine (see Sect. 2) an individual star can appear only once in a given bin.

Figure 2 shows, e.g., that in the frequency bin ranging from 11 to 11.5 ${\rm d}^{\,-1}$ we found 4 times more frequencies with an amplitude exceeding the noise level than expected for an uniform distribution. These are 6.25% of 816 stars with a peak exceeding a S/N ratio of 4 and a 4.5 times higher incidence than expected from a uniform distribution. Some of the frequencies listed in Table 1 are also indicated in Fig. 2.

In the low-frequency domain (0 to 2 ${\rm d}^{\,-1}$) we found a total of 228 peaks exceeding a S/N ratio of 4. The highest bin from 0 to 0.05 ${\rm d}^{\,-1}$ corresponds to the typically 3 to 5 week data gaps in the lightcurves. A comparison with spectral windows does not show correlations with other bins in the histogram. Aliasing therefore should not contribute significantly to the low frequency peaks. Our result seems to confirm what Kerschbaum et al. (2001) have found for the AGB star RVCam. Whereas Koen & Laney (2000) reported on the discovery of a period of 7.67 days (0.13 ${\rm d}^{\,-1}$), based on HIPPARCOS photometry, Kerschbaum et al. do not find such a periodicity in ground based photometric data with a 10 times lower noise level. Our Fig. 2 illustrates the verbal description of aliases and spurious periods by Eyer & Grenon (2000), who report on a poor detection capability of HIPPARCOS photometry in the frequency range from 0.05 to 0.2 ${\rm d}^{\,-1}$ and at 0.0017 ${\rm d}^{\,-1}$.

In a further step we investigated possible effects due to luminosity and spectral types. No such dependency was found on either of these astrophysical parameters (Fig. 3). Figure 4 illustrates the uniform distribution of our program stars in the HR-diagram and shows that stars with "significant'' periods are found everywhere.