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Astron. Astrophys. 323, 399-414 (1997)

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4. Results: the fast timing behaviour

The results of the power spectra analysis are shown in Tables 4 and 5.

4.1. Very-low frequency noise (VLFN)

Since in the HB the VLFN is low (e.g. Hasinger & van der Klis 1989), we were in some cases unable to measure the VLFN, at the left end of the HB. In the June 1987 and June 1988 observations we fixed the power law index of the VLFN when Cygnus X-2 is on the HB.

We have high time resolution data of the same part of the Z track (especially near the soft vertex) but during different overall intensity levels. The comparison of these data reveals a very significant difference of the VLFN properties between the medium and high overall intensity levels in the lower part of the NB. During the medium overall intensity observations (June 1988 and May 1991) we detect a weak (0.5-1% rms amplitude) and flat (power law index of [FORMULA] 1) VLFN on the lower NB and near the soft vertex. The rms amplitude and power law index increase to [FORMULA] 5.3% and [FORMULA] 1.4, respectively, on the upper FB in the June 1988 observation. However, during the high overall intensity observations (October 1988 and June 1991) we detect a very strong (8.5% and 4.5% rms, respectively) and steep (index of 1.4-1.7) VLFN on the lower NB and near the soft vertex. The VLFN decreases in strength to about 6.7 % rms amplitude on the FB in the October 1988 observation. We note that this strong VLFN near the soft vertex can not be caused by changing collimator response. During the intermediate overall intensity observation (June 1987) we see VLFN with a strength of [FORMULA] % rms and power law index of [FORMULA] 1.1 near the soft vertex, which increases to [FORMULA] 4.2% and [FORMULA] 1.4, respectively, on the FB. This gradual change in the strength and steepness of the VLFN as a function of overall intensity level is clearly visible in Figs. 8a-i. This figure shows the power spectra in the medium level, the intermediate level and the high level at approximately the same [FORMULA]   values.

[FIGURE] Fig. 8. Power spectra of different observations at about the same [FORMULA], the power spectra in the column indicated with NB, SV and FB, are taken on the lower normal branch, the soft vertex, and the flaring branch, respectively: a, b and c are the May 1991 power spectra at [FORMULA] =1.79 [FORMULA] 0.07, 1.97 [FORMULA] 0.10 and 2.05 [FORMULA] 0.06, respectively, d, e and f are the June 1987 power spectra at [FORMULA] =1.83 [FORMULA] 0.02, 1.97 [FORMULA] 0.07 and 2.10 [FORMULA] 0.03, respectively, and g, h and i are the October 1988 power spectra at [FORMULA] =1.856 [FORMULA] 0.008, 2.00 [FORMULA] 0.02 and 2.10 [FORMULA] 0.01, respectively

It is remarkable that when Cygnus X-2 is in the high level the VLFN near the soft vertex is strong and steep and that when the source is in the medium level the VLFN at the same [FORMULA]   values is much weaker and less steep. During intermediate levels the VLFN is weak and flat on the NB but strong and steep on the FB. The correlation of the amplitude and steepness of the VLFN near the soft vertex with mean overall intensity level is not strict. At the highest overall intensities (1991 June) the amplitude is about the half of the one at the second highest overall intensity (1988 October), and the spectrum is less steep.

4.2. Low-frequency noise (LFN) and high-frequency noise (HFN)

Due to the scarcity of high time resolution data when Cygnus X-2   was on the HB or near the hard vertex and the difficulty in determining [FORMULA], comparisons of the LFN between the observations are difficult. The June 1987 and 1988 observations show a LFN with an rms of [FORMULA] 4.7 % on the HB which decreases to [FORMULA] 3.0 % on the hard vertex and upper NB. The November 1990 observation shows that the rms of the LFN increases from the beginning of the HB to the hard vertex (from [FORMULA] 5.8 % to [FORMULA] 6.5 % rms). The same is seen in the October 1989 observation (LFN rms from 4.5 % to 5.5 %), but in this observation the rms decreases to 3.8 % when the source moves into the upper NB. No clear correlation between the power law index (0.0-0.3) or the cut-off frequency (4.0-13 Hz) with [FORMULA]   is seen.

When LFN or NBO were fitted it was difficult to fit the HFN simultaneously, possibly due to interference between them (see also Kuulkers et al. 1994a). When it was necessary to fit a HFN component it had an rms between 1-2% and cut-off frequencies between 10 and 20 Hz. The October 1989 PC data show a strong HFN ([FORMULA] 6% rms) with a high cut-off frequency between 30 and 50 Hz.

4.3. Normal branch QPO (NBO)

Normal branch QPOs (NBOs) were detected in the medium and intermediate level observations. To our suprise, none were detected in the high level observations (see Fig. 8), although we had high timing data in the lower NB for them. The rms 2 [FORMULA] upper limits ([FORMULA] %) are significantly lower than the rms (1-2.5%) of the NBOs in the medium and intermediate levels. This also shows that during different overall intensity levels the rapid X-ray variability at the same position on the Z track differs significantly from each other.

When NBOs are seen no clear relation is detected between the amplitude of the NBO and [FORMULA]. However, the FWHM and the centroid frequency seems to increase from the middle of the NB to the FB. The FWHM increases from [FORMULA] 2.4 Hz to [FORMULA] 13 Hz and the centroid frequency from [FORMULA] 5 Hz to [FORMULA] 8 Hz. In the June 1987, the June 1988 and May 1991 observations it was impossible to make a distinction between a broad NBO or a HFN on the lower FB, although a NBO provided a better fit (e.g. for the June 1987 observation [FORMULA] /dof = 27.5/29 for the NBO versus 31.0/30 for the HFN).

4.4. Horizontal branch QPO (HBO)

Horizontal branch QPOs are seen during all overall intensity levels, on the HB as well as in the upper NB. Taking all data into account, we find that the frequency of the HBO increases from [FORMULA] 31 Hz at the left end of the HB to [FORMULA] 55 Hz at the hard vertex. The PC data of the June 1987 and October 1989 observations indicate that when the source moves down the NB the HBO frequency decreases again to [FORMULA] 47 Hz. The rms amplitude decreases from the HB to the upper NB, from [FORMULA] 4% to [FORMULA] 1%.

As already mentioned in Sect. 3.2.3, the PC data of October 1989 show several points at low intensities and high soft colour. Those points are placed in the CD near the hard vertex but in the HID near the left end of the HB. The power spectrum corresponding to these points is shown in Fig. 9. A HBO at 25 Hz is clearly visible (3.8% rms amplitude) and indicates that Cygnus X-2 was indeed at the left end of the HB (see Fig. 6a and b, the points marked H). A second QPO is visible at [FORMULA] 49 Hz with a rms amplitude of 2.5%. Hasinger et al. (1985a) and Hasinger (1987) found already evidence for the harmonic of the HBO in the EXOSAT data of Cygnus X-2. However, the frequency ratio was smaller (1.85 [FORMULA] 0.03) than expected for a second harmonic. Our frequency ratio (1.96 [FORMULA] 0.05) indicates that this feature is indeed the second harmonic of the HBO.

[FIGURE] Fig. 9. The power spectrum of the beginning of the horizontal branch taken in the October 1989 observation. A harmonic of the HBO is visible at about 50 Hz
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Online publication: June 5, 1998