## 3. Oscillation frequencies and amplitudesWe use least squares Fourier decomposition to determine oscillation
spectra, applying the technique of Preliminary analysis of the full time-series for BT Cnc showed the presence of several outlying observations with excessive residuals. Removing 22 outliers we accept a time-series of 682 observations. In the following we first discuss this series. Fig. 1 shows the window function and four power spectra and Table 2 gives detailed information on the resulting four-frequency solution. The upper panel a) gives the window function centered on 10 cycles per day (c/d). Besides the 1 c/d alias's, considerably lower side-lobes separated by c/d are seen. Panels b) and c) uniquely identify the primary and secondary oscillations with main properties given in Table 2. The main oscillation has frequency c/d, amplitude 17.7 mmag and phase 2.61 radian with Epoch Feb. 14.8 1994 (HJD = 2449398.3054). Formal errors of both amplitude and phase are very small, 0.2 mmag and 0.01 radian, respectively. Due to the fact that our time-basis is only about 3 d, we cannot determine very accurate frequencies and are not able to separate e.g. close frequency pairs. Comparing results of many numerical experiments (see later) we estimate the uncertainty in our frequencies to be about c/d.
Panels c) - e) of Fig. 1 show S-spectra resulting from taking the already known frequencies as known constituents. From Panel c) it is seen that the S-value, S = 0.72, of the new frequency, c/d, is even higher than the value found for the frequency of the primary oscillation, . Closer inspection of Panel b) shows the presence of a top at about 7.0 c/d, which does not belong to the main pattern. Taking the primary oscillation as a known constituent, this top becomes the center of the -pattern, which also closely resembles the window function. While the primary and secondary oscillations are unambiguously identified, the following possible oscillations indicated in Table 2 have much smaller S-values and oscillation amplitudes, and no pattern in the S-spectrum resembling the window function can be identified. From Table 2 it is also seen that inclusion of the last two Fourier terms decrease the rms-scatter only marginally. The difficult problem of deciding whether Fourier terms of low
significance correspond to physical oscillations or are due to noise
has been studied extensively in the literature, e.g. recently by
Garrido & Rodríguez (1996) and Pardo & Poretti (1997).
They emphasize that before searching for low-amplitude modes, both
harmonics of the high-amplitude modes, i.e. 2 ,
3 , ... , etc., and the interaction modes with
frequencies ,
© European Southern Observatory (ESO) 1997 Online publication: April 28, 1998 |