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

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2. Observations and analysis

2.1. The satellite and the observations

Cygnus X-2 was observed with the Ginga satellite (Makino and the ASTRO-C team 1987) during 7 observations. For a log of the observations we refer to Table 1. Due to Earth occultations and the high background in the South Atlantic Anomaly (SAA) the observations were broken up into many pieces with a length of several tens of minutes.


Table 1. Log of the observations

The LAC instrument (Turner et al. 1989) on board Ginga was used in several different observation modes: the MPC1, MPC2, MPC3 and the PC mode. In the MPC1 and the MPC2 (hereafter MPC1/2) modes the source was observed in 48 photon energy channels and the time resolution ranged from 62.5 ms to 16 s. In the MPC3 mode the source was observed in 12 channels with a best high time resolution of 7.8 ms. In the PC mode only four overlapping channels were used and the time resolution was 1 or 2 ms. By manipulating the coarse gain (CG) amplifier, which had two levels, the energy range could be set to either 0.5-37 keV (low CG level) or to 0.3-18.7 keV (high CG level). By changing the high voltage (HV) levels the energy range could be extended to even higher energies (e.g. up to 60 keV). Due to these different CG amplifier settings, HV level settings and lower discriminator settings (see Turner et al. 1989) different sets of energy channels were used at different times.

Generally the satellite attitude control system kept the viewing direction within 30 arcmin from the position of Cygnus X-2 , which corresponds to a collimator transmission of [FORMULA] 70%. The systematic error in the observed count rates due to uncertainties in the collimator transmission is of the order of a few precent (Hertz et al. 1992). Due to, e.g., a long period without attitude control measurements the offset angle sometimes increased causing the collimator transmission to decrease to about 40%. The LAC collimator shows energy-dependent transmission effects due to reflection of soft X-rays (below [FORMULA] 6 keV) from the collimator walls at large offset angles (Turner et al. 1989). This low energy reflection was not taken into account when the intensities were corrected for collimator transmission (Sect. 2.2), which gives rise to an overestimation of the count rates for the lowest energy channels. When we encountered data with a collimator transmission below [FORMULA] 60 % we used Figs. 13 and 14 of Turner et al. (1989) in order to correct the count rates below 6 keV. Usually this means that the count rates were corrected for an overestimation of 3-4%. Sometimes the offset angle was even higher and the collimator transmission came below [FORMULA] 20%. At such high offset angle the collimator response is independent of incident photon energy (Turner et al. 1989). However, at these times the fractional uncertainty in the collimator transmission, and thus in the corrected count rates, due to aspect jitter is [FORMULA] 15% (Hertz et al. 1992). For this reason, we did not use any data with a collimator transmission [FORMULA] % in our analysis.

2.2. Colour-colour and hardness-intensity diagram analysis

For our studies of the CDs and the HIDs we used data rebinned to a time resolution of 4 seconds, which were background substracted and corrected for deadtime and aspect using the ISAS analysis system. The PC binned data were not corrected for background because no good background determinations are available for them. The 16 s resolution MPC1 data of the November 1990 and June 1991 observations had multiple register overflows and were left outside our analysis. The 4 s resolution MPC1 data of the June 1987, the October 1989, the May/June 1991 observations and the 2 s resolution MPC2 data of the June/October 1988 and the June 1991 observations had single overflows and the true count rates could be recovered.

In order to make CDs and HIDs we calculated the soft colour, the hard colour and the total intensity. The definitions of those quantities and the energy bands used in order to calculated them, are given in Table 2. Instead of the colours and intensities, usually used in the literature, we used the logarithmic value of those quantities. Any process which influences the intensity in the specified energy bands by multiplication, i.e. the instrumental response, produces only a shift in the CD and the HIDs. Using logarithmic values of the colours and the intensity therefore makes it easier to compare data of the same source obtained by different instruments, by simply shifting the diagrams. Also, the [FORMULA]  parametrization (Sect. 2.3) in this way does not depend on the actual values of the quantities or the count rates, but only on their changes. It can now be used not only for the CD but for the HIDs as well.


Table 2. The energy bands used to create colour-colour and hardness-intensity diagrams. We used the following definitions of the colours : Soft Colour  = 10 log(Band 2 / Band 1), Hard Colour = 10 log(Band 3 / Band 2). The intensity is the count rate in the energy range given in colum 6

Usually the total intensity was taken as the sum of the count rates in the same energy bands as were used to calculate the colours. However, for the PC data of the 1987 and the 1988 observations the total intensity was defined as the count rate in all four energy channels. For the 1989 PC data the count rates in the three lowest energy channels were summed, as the fourth channel only contained background photons. The lowest energy boundary of the 1987 PC data differs slightly from the lowest boundary in the 1988 PC data (Table 2). The effect on the Z in the CD and HID is negligible and therefore we discuss the 1987 and 1988 PC data together. The 1989 PC data is discussed seperately because of the different energy boundaries (see below).

In order to compare the MPC1/2 data with the MPC3 data we rebinned the MPC1/2 data to 12 channels using the same energy boundaries as the MPC3 data. Although in the 1991 observations the MPC3 data had slightly different energy boundaries compared to the MPC1/2 data (Table 2), the difference was small and had no significant effect on the place of the Z in the CD and HID.

Due to the HV and CG levels of 1989 and 1990 observations (energy range 1-60 keV) the energy boundaries of their spectral channels differ from those of the other five observations. Due to the broad energy channels the energy boundaries of these observations could not be succesfully interpolated to the boundaries of the others. Therefore, we discuss the 1989 and 1990 observations seperately from the other observations. In order to get an approximately uniform analysis we took for the MPC1 mode data colours which resembles the colours used in the other observations.

2.3. [FORMULA]   parametrization

Hasinger et al. (1990) introduced the concept of rank number of the Z track in the CD. This concept was refined by Hertz et al. (1992) and by Dieters & van der Klis (1996). Here we use the method described by Dieters & van der Klis (1996) for the measurement of the position along the Z, with the difference that we perform all operations on the logarithmic colours and intensity values (see Sect. 2.2). We therefore transform the two logarithmic colour coordinates (hard colour and soft colour) into the coordinates [FORMULA]   (the distance along the Z track) and [FORMULA]   (the distance perpendicular to the Z track). We also calculated the velocity ([FORMULA]) and the acceleration ([FORMULA]) along the Z track, as defined as


where [FORMULA] (i) is the position in the Z track on time T(i), and


respectively (see also Dieters & van der Klis (1996)). The length of the NB is scaled to 1 and positions on the HB and FB are normalised to the length of the NB. The hard vertex corresponds to [FORMULA] = 1, and the soft vertex to [FORMULA] = 2. We applied the [FORMULA]  parametrization also on the Z tracks in the HID. We obtained a different set of [FORMULA]   and [FORMULA]   values which we call [FORMULA]   and [FORMULA].

The distribution of [FORMULA]   or [FORMULA]   is a measure for the thickness of the branches in the CD or HID, respectively. To quantify the thickness of the branches we calculated the sample standard deviation of the [FORMULA]   and [FORMULA]   distributions using the method discribed in the Appendix. As a measure of the overall velocity and acceleration in the CD the standard deviations of the [FORMULA]   and [FORMULA]   distribution were used, again using the method outlined in the Appendix.

2.4. Power-spectral analysis

For the power-spectral analysis we used the MPC3 and PC data. We made FFTs of 128s data segments which resulted in a frequency range of 0.0078-64 Hz (MPC3 7.8 ms resolution data) or 0.0078-256 Hz (PC 1.95 ms resolution data) in the power spectra. We calculated the FFTs for the energy interval 1.2-18.6 keV (June 1987, June/October 1988 and May/June 1991 MPC3 observations) or 1.2-19.0 keV (November 1990 MPC3 observation). For the PC mode we used the sum of the energy intervals 0.8-12.3 keV and 0.6-9.1 keV (June 1987), or 0.8-12.3 keV and 0.8-9.1 keV (June and October 1988), or 1.2-17.9 keV and 1.2-15.7 keV (October 1989).

The average level of the photon counting noise, modified by deadtime processes (the Poisson level), was estimated and subtracted using a counter deadtime of 206 µs (MPC3 data) and 16.5 µs (PC data) (see Mitsuda & Dotani 1989). In the resulting power spectra several components can be identified:

  • very low frequency noise (VLFN), which we fitted with [FORMULA], where [FORMULA] is the frequency, [FORMULA] is the power-law index and [FORMULA] the normalization constant.
  • low frequency noise (LFN) and a high frequency noise (HFN), are fitted with [FORMULA], where [FORMULA] is the power-law index, [FORMULA] the cut-off frequency, and [FORMULA] the normalization constant, for the LFN (L) and HFN (H), respectively.
  • HBO, its harmonic, NBO and FBO, are fitted with Lorentzians: [FORMULA], where [FORMULA] the centroid frequency, [FORMULA] the full width at half maximum (FWHM) of the QPO and [FORMULA] the normalization constant.

The fractional rms amplitudes of the various noise components were determined by integrating their contribution over the following frequency ranges ; VLFN: 0.001-1 Hz, LFN: 0.01-100 Hz, HFN: 0.01-100 Hz. We note that variations in the collimator transmission could influences the VLFN (see e.g. the EXOSAT data of GX 17+2 [Kuulkers et al. 1996b]). The errors in the parameter values were calculated using an error scan through [FORMULA] space using [FORMULA]. Due to the poor statistics it was not always possible to fit a HFN component. When HFN was fitted we used [FORMULA] because in Z sources this index was found to be consistent with zero (Hasinger & van der Klis 1989, Dieters & van der Klis 1996). The best way to examine the correlations between the timing behaviour and the position on the Z track is to select a small part of the Z track, using the [FORMULA]   parametrization and determine what the corresponding timing properties are for that segment. However, our data did not allow this procedure as we did not have enough data at high time resolution for this procedure to give sufficient statistics. Therefore we first selected parts of the data that covered a relatively small [FORMULA]   range and afterwards determined an average [FORMULA]   value and range for each data set.

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Online publication: June 5, 1998