Astron. Astrophys. 363, 1013-1018 (2000)

3. Results

We adopted the noise level model described in the previous section for the subsequent analysis of the Cyg X-1 data. Since the Cyg X-1 observations were performed with time resolution coarser than sec, the photon dead time and duration of the VLE window are not constrained by the data. We fixed them at the best fit values determined from the Sco X-1 data: s and s. As mentioned above, at the count rates typical for Cyg X-1, 1000-1500 cnts/s, the noise level does not depend on the count rate. We therefore fixed the parameter at the averaged observed value. The only free parameter of the noise level model was . Similarly to the procedure applied to the Sco X-1 data, we included the source component into the model. The source component was represented by a power law . We used the high frequency part of the power spectra, from 100 Hz up to the Nyquist frequency, for the fits.

The high frequency part of the observed power spectra of Cyg X-1 before subtraction of the noise level , the best fit model and the residuals of the data from the model are shown in Fig. 4, Fig. 5 and Fig. 6. The overall power spectra in a broad frequency range from 1 mHz to kHz after subtraction of the best fit noise level model are shown in Fig. 7. One can see that the model describes the data points reasonably well: 38/55 dof for observations P10236 (Fig. 4), 56/49 dof for observations P30157 (Fig. 5) and 46/49 for observations P10512 (soft state, Fig. 6). The best fit values of the slope of the source power spectrum are: for P10236, for P30157 and for P10512. The intrinsic variability of the source has been statistically significantly detected up to frequencies of 150-300 Hz (Fig. 4 -Fig. 6) with the fractional rms amplitude in frequency band 100-400 Hz of % (hard spectral state) and 2% (soft state).

Fig. 4. The power spectrum of Cyg X-1 (observations 15-17 Dec., 1996; proposal P10236). Total exposure time ksec. Dashed line shows the instrumental noise level.

Fig. 5. The same as Fig. 4 but for observations from proposal P30157 (Dec. 1997-Dec. 1998, hard spectral state). Total exposure 110 ksec.

Fig. 6. The same as Fig. 4 but for observations from proposal P10512 (4-18 June, 1996, soft spectral state). Exposure 10 ksec.

Fig. 7. The broad band ( Hz) power spectrum of Cyg X-1 in the hard and soft spectral states averaged over different data sets used for the analysis. The power spectra were multiplied by the frequency.

In order to increase statistics we averaged all the hard state data increasing the total exposure time up to ksec. The power law approximation of the averaged power spectrum above 100 Hz gives the power law index of . The power law approximation of the same data in the 20-60 Hz frequency range results in , although the PDS clearly has a more complicated shape than a power law (Fig. 8). We therefore conclude that we detected statistically significant steepening of the power spectrum of Cyg X-1 in the hard state at the frequency of 40-80 Hz. Note, that some indication of such steepening can be found in Nowak et al. 1999, although short duration of the used observations ( ksec) was not sufficient to study the high frequencies in detail. In order to illustrate the high frequency behaviour of the power spectra, we plot in Fig. 8 the power spectra multiplied by . As it can be seen from Fig. 8 the particular shape of the rollover above 100 Hz is not significantly constrained by the data. Assuming that power spectrum continues with the same slope to the higher frequencies an observatory of the EXTRA/LASTE class (effective area m², Barret 2000) would be able to detect statistically significant signal up to several kHz in tens of ksec exposure time and help us to say something more about the exact shape of the rollover of the PDS.

Fig. 8. The power density spectrum of Cyg X-1 at high frequencies. Note, that the power spectrum has been multiplied by .

The 2 upper limit on the amplitude of a possible QPO component (Lorentz profile with quality Q) in the 500-2000 Hz frequency range in the hard state power spectrum is 2% for and 0.9% for . These upper limits were obtained using the observations from the propsal P10236 performed on 15-17 Dec. 1996 in which the shape of the power density at the lower frequency did not vary significantly. The upper limit on the continuum noise component at the high frequency is somewhat more difficult to estimate. A statistical () error on the fractional rms in the 500-2000 Hz for the sum of all hard state observations is . Assuming that the noise level model is exact the upper limit on the fractional rms would coincide with the above number. However, as we mentioned in the previous section a weak and very flat source power spectrum component might be not detected given the procedure used to determine the instrumental noise level.

© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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