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Astron. Astrophys. 321, 776-790 (1997)

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4. Results

In the following sections we describe the CDs, HIDs and lightcurves we obtained for GS 2023+338 (Sect. 4.1), and the large changes in the low-energy absorption (Sect. 4.2). In Sect. 4.3 we will present the power spectra we have obtained, and in Sect. 4.4 we describe in some more detail the spectral changes which take place in the source spectrum on relatively short time scales. Finally we present the rms-spectra and phase-delay spectra we obtained in Sect. 4.5 and Sect. 4.6, respectively.

4.1. Light curve, CDs, and HIDs

The light curve of GS 2023+338 cannot be characterized by a simple smooth curve. In Fig. 1, which shows the sum of the count rates over the 4 energy bands (i.e. 2.3-23 keV), as a function of time, we see that the only trend visible is a long term decline as function of time. However, as we can see from Fig. 2, the variations on time scales shorter than a day are almost of the same order as the changes on time scales of a month. As we will discuss below this is largely due to large variations in the [FORMULA] column density.

[FIGURE] Fig. 1. The 2.3-23 keV light curve of all the corrected (see text) data of GS 2023+338. One point corresponds to 4s (occasionally 16 or 64s) of data; error bars are smaller than the size of the points. Note the large range of intrinsic variations within each observation. Data have been corrected for dead time, background, and collimator response.
[FIGURE] Fig. 2. The 2.3-23 keV light curves of all the corrected data of GS 2023+338. Note that the vertical scales are logarithmic and the same for all panels; the horizontal scale differs from panel to panel. Data have been corrected for dead time, background, and collimator response. Each point is 4s (occasionally 16s) of data, except in the last panel where each point is 64 s of data. Error bars are smaller than the size of the points

The soft colour (SC) as a function of time (which is, as we will show in Sect. 4.2 a good measure of the [FORMULA]), is very variable in the first month of the outburst, whereas the variations are substantially less in the later phases.

In the colour-colour diagram (Fig. 3) the following signatures are visible: there is a track which extends form SC [FORMULA] 3 to SC [FORMULA] 0.7, with a sharp bend at those low SC values. The observations which lies around the bend are obtained in the last stages of the outburst. There is another collection of points which lie above and partly to the left of the main track. Those points were obtained in the very early stages of the outburst (May 23 and 30, day 143 and 150), when the source was very bright. The CD seems more or less repeatable: the last (low intensity) observation falls on top of the observations obtained [FORMULA] 3 months earlier, at around the bend of the left-most tip of the extended branch. The width of the track gives an indication of the errors in the individual points; the errors in the points which lie above and to the left of this main track are smaller; real variations are thus present here (errors in both the soft and hard colour range from [FORMULA] 0.01 to 0.3).

[FIGURE] Fig. 3. The colour-colour diagram of GS 2023+338. Soft colour is the ratio of the 4.6-6.9 keV to the 2.3-4.6 keV band. Hard colour is the ratio of the 11.5-23.0 keV to the 6.9-11.5 keV band. Most points are 4s averages, some of them are 16s or 64 s averages. Errors in both colours range from [FORMULA] 0.01 to 0.3 (see text).

In the soft colour vs. intensity diagram (Fig. 4) several tracks are visible. They represent the data obtained during different observations. The errors can be estimated from the widths of these tracks. The data points at high count rates have been obtained early in the outburst. The errors in the points around intensity [FORMULA] 600 and SC [FORMULA] 2 are [FORMULA] 0.2-0.3 in SC. There seems to be a sharp cut-off at the bottom near soft colour [FORMULA] 0.6. This reflects (see Sect. 4.2) a minimum value of [FORMULA] viz. the extinction along the line of sight. However, two sharp tracks extend to lower values of SC; they are the result of real changes in the spectrum at low energies and occur during the May 23 and 30 observations (i.e, in the first phase of the outburst).

[FIGURE] Fig. 4. The soft-colour vs. intensity diagram of GS 2023+338. Soft colour is the same as in Fig. 3, intensity is the count rate in the 2.3-23 keV band. Data have been corrected for dead time and collimator response.

Furthermore we can discern in the SC vs. intensity diagram that a track seems to be visible which is embedded in a cloud of points. The scatter in this cloud of points (which is roughly delimited by a triangle with coordinates: (I,SC) = (1000, 0.6),(6000, 0.6),(2000, 1.8)) is not statistical. The statistical scatter can be roughly estimated from the width of the tracks, which are visible in the CD. The extra scatter is a result of real changes in [FORMULA]. The regions where the statistical scatter is substantial are the left-most cloud of points (I,SC) = (70,0.8) and the cloud of points around (I,SC) = (500,2). In the first region the count rate is low, which increases the scatter. In the second region the count rate is relatively low, and more important, a lot of low-energy absorption is present, which decreases the count rate in the lowest energy band significantly, and thus the statistical scatter is increased.

The errors in the hard colour (HC) vs. intensity diagram (Fig. 5) are around [FORMULA] 0.01-0.05 in the hard colours (the errors in the count rates are very small), with the exception of the cloud of points around HC [FORMULA] 0.5 and a count rate of [FORMULA] 60 and around HC 0.7 and count rates of [FORMULA] 800, where the errors are up to a factor of five higher. This diagram is somewhat simpler than the CD and Soft-colour vs. Intensity diagram. The hard colour is mainly sensitive to changes in the intrinsic spectrum: i.e., a harder spectrum gives a higher value for the HC.

[FIGURE] Fig. 5. The hard-colour vs. intensity diagram of GS 2023+338. Hard colour is the same as in Fig. 3, intensity is the count rate in the 2.3-23 keV band.

4.2. Synthetic CDs and HIDs

In a first attempt to understand the complex behaviour of the source in the CDs and HIDs we made synthetic spectra, which we folded through the Ginga detector response. We then calculated the fluxes that would have been observed in the four energy bands that we used in our analysis. This enabled us to make CDs and HIDs for these simulated data. Varying one parameter of the model (which consisted of various combinations of a power law, blackbody component, Gaussian line and absorption) enabled us to see how a change in one parameter affected the position in the CD. We found from this that, almost independently of the assumed spectral shape, the effect of increasing [FORMULA] is to move a point along a line parallel to the main track we observe in the CD. We therefore conclude that the main determinant of the position in the CD is the value of the column density [FORMULA]. This column density has to be produced mainly locally, because of its large changes. This procedure we applied is functionally equivalent to the determination of the so-called "reddening line" (see Schulz et al. 1988).

To investigate the [FORMULA] variation in some more detail we have determined the location of points in the CD for an assumed power-law spectrum (photon index -1.35) and [FORMULA] between 5 [FORMULA] and 2 [FORMULA] cm-2, in steps of 5 [FORMULA] (Fig. 6). We find that the density of the points decreases to the right in the CD, in a similar way as is observed in the real data for GS 2023+338. This suggests that the distribution of the [FORMULA] values is more or less uniform between the two extremes. In order to test this we estimated the [FORMULA] from the soft colour in the following way: we selected points above soft colour 1.0 and belonging to the branch in the CD (i.e. hard colour below the line through (SC,HC) = (1.0,0.7) and (2.0,0.8)). We calculated the soft colours for an artificial spectrum with [FORMULA] ranging from 0.5 to 20 (1022 cm-2), with steps of 0.5. We then converted the measured soft colour to an [FORMULA] -value by a linear interpolation. In Fig. 7 we have plotted a histogram of these obtained [FORMULA] estimates. From this figure we see that between 5 [FORMULA] 1022 and 1.6 [FORMULA] 1023 the distribution is more or less uniform and starts to drop off above 1.6 [FORMULA] 1023.

[FIGURE] Fig. 6. The observed colour-colour diagram of GS 2023+338 (small dots), and the synthetic points (large dots) calculated from a power law spectrum (photon-index -1.35) absorbed by different amounts of column density. The column density ([FORMULA]) ranges from 5 [FORMULA] and 2 [FORMULA] cm-2, in steps of 5 [FORMULA]. Column density increases from the left to the right.
[FIGURE] Fig. 7. The number distribution of the obtained [FORMULA] -values (see text). From this figure we conclude that [FORMULA] -values between roughly 500 and 1600 (1020 cm-2) are distributed approximately uniformly.

Only in the parts of the CD where the source gets very bright (i.e., points above and to the left of the main track) and the left most tip (i.e., the bend around (SC,HC)=0.7,0.5) the intrinsic source spectrum has to change. In the other parts of the CD the behaviour in this diagram can be reasonably well described by a fixed underlying spectrum, that is only modified by variable absorption.

4.3. Power spectra

In Fig. 8 we present the power spectra as obtained with the PC-data. From this figure it is clear that the power spectra are remarkebly similar to each other during most of the outburst. Only the power spectra obtained on May 30 (day 150, 1A) are different. Here there is clearly less power above [FORMULA] 0.1 Hz. The spectrum is much steeper than the other power spectra. From the fits to the power spectrum it can be concluded that in our power spectral decomposition (see Sect. 3), the difference is mainly caused by the absence of the component with a FWHM of 2-3 Hz. While these power spectra were obtained the source occupied a different region in the CD. We concluded this from data with high-energy resolution, which were obtained just before and after (but not simultaneously with) the high-time resolution data. In Fig. 10 we can see which region in the CD was approximately occupied by the source when the power spectra were obtained.

[FIGURE] Fig. 8. The power spectra data with a Nyquist frequency of 64 Hz or greater (MPC3 and PC data). The approximate start times (MJD - 47000) at which the power spectra are obtained are plotted in the top-right corners of the panels. For the power spectra which have been fitted with a model consisting of three Lorentzians the fit (drawn line, mostly invisible), and the individual Lorentzian components (dashed, dot-dashed, and dotted for resp. Lorentzian 1, 2, 3) have been drawn in order to show their relative contribution in the different frequency regimes.
[FIGURE] Fig. 9. The power spectra for the MPC2 data. Approximate start times (MJD - 47000) for the power spectra are plotted in the top-right corners of the panels.
[FIGURE] Fig. 10. In this figure the (approximate) regions are plotted where the power-spectra are obtained. In the left panel the place where the power spectra with the high Nyquist frequencies (MPC3 and PC data) are plotted. In the right panel the positions where the power spectra with low Nyquist frequency (MPC2 data) are obtained have been plotted. The horizontal line labelled with 3A indicates where (at the main branch) the power spectra have been obtained. The regions indicated in the left panel for the PC data are only very approximate, since no spectral data are available when PC data is obtained.


Table 3. In this table the times can be read at which the different power spectra and rms spectra are obtained. The labels mentioned in the first column are also used in the figures.

In Fig. 11 we show the power spectrum obtained when the source was very bright (MJD=47676.25). In this power spectrum additional power is visible around frequencies of 0.05 Hz.

[FIGURE] Fig. 11. The power spectrum obtained when the source is very bright. This spectrum has been obtained between MJD = 47676.2139004630 and 47676.314519676

We have fitted all power spectra with a model consisting of Lorentzians (see Sect. 3). We note that the inclusion of a third Lorentzian decreases the [FORMULA] by [FORMULA] 40 (from [FORMULA] to [FORMULA] 100) for [FORMULA] 80 degrees of freedom and is therefore statistically significant. However, the shape of the additional component is not well constrained.

We conclude from our fits (see Table 4) that the changes in the shape of the power spectrum over a period of 60 days are very small. The only systematic change which might be present is a shift toward lower frequencies of the Lorentzian component with a full width at half maximum (FWHM) of [FORMULA] 3 Hz, although it is a relatively small change (see Table 4). This width changes from [FORMULA] 3.4 Hz on MJD 47676 to [FORMULA] 2.5 on MJD 47728. There are some additional significant, seemingly random, changes in the power spectra, which are reflected in the obtained fit parameters. The overall shape, however, remains fairly constant.


Table 4. Fits to the power spectra obtained from the PC and MPC3 data.

A problem in the interpretation of the obtained fit parameters is the correlation between the parameters. Especially the obtained width of the first Lorentzian is strongly correlated with the obtained width of the second Lorentzian. This is evident from Table 5 in which we see that whenever a small value for the width of the first Lorentzian is obtained also a small value for the width of the second Lorentzian is obtained.


Table 5. Fits to the power spectra obtained from the MPC2 data.

Additionally we also have tried to estimate an upper limit for Lorentzian shaped peaks in the power spectrum between 2 and 10 Hz. This is relevant, because in other BHCs QPOs with these frequencies have been observed. We only tried to fit the spectra where the count rates are high (PC1A, PC1B, MPC3A) to determine this upper limit. We included a Lorentzian component in our fit model in which the frequency was allowed to vary between 2 and 10 Hz, and the FWHM was constrained to be smaller than [FORMULA] 0.5 times the frequency of this component. We note that the results of the procedure depend on the assumed underlying spectral shape and the results are therefore only approximate. However, from a visual inspection of the power spectra no indications of the presence of QPO are obtained, while in other BHCs in the "very-high" state, these QPO peaks are immediately obvious. We can set a firm (1 [FORMULA]) upper limit of 4% to the strength of the QPO in this frequency region.


Table 6. Fits to the power spectra obtained during the first 8 days of the observations.

4.4. X-ray spectral changes

From our analysis of the X-ray spectral changes we draw the following conclusions: (i) The influence of changes in [FORMULA] on the spectral shape (and thus the colours) is very large. To first order the behaviour in the colour-colour diagram for a large fraction of the data can be described reasonably well by changes in the (local) column density ([FORMULA]). We find that in the later observations the inferred column density is less, and also less variable, which suggests that the source is getting clear of matter which is local to the source. (ii) A different type of change in the colours occurs near the peak of the outburst. This tells us that the intrinsic spectrum is then changing. When this happens also a different power spectrum is obtained.

The results of the analysis of the ratios of spectra obtained at the intensity peaks and valleys are summarized in Fig. 12, from which we learn that there is large difference in the energy-dependent variability. Especially during the maximum of the outburst (the panels marked with a 1 I-V) we see that there is a large variation of shapes. In the first panel we see a lot of variability around 5 keV and a signature of an iron line with less variability (see Oosterbroek et al. 1995). In the second and third panel we see the presence of a soft component which is relatively invariable.

[FIGURE] Fig. 12. The PHA-ratios for the different data sets. Note that the vertical scale for the first three panels is different from the scale of the other panels. Start times at which these ratios are determined are plotted in the panels (MJD - 47000). In panels 1 II and 1 III the ratio at low photon-eneries (below [FORMULA] 7 keV) is small compared to that at higher energies. This is interpreted as a relatively invariable soft component. In panel 2 an increase of the ratio towards low photon-energies (below [FORMULA] 4 keV) is visible; this is interpreted as the effect of a change in the absorbing column density (see text). The single panel at the bottom has a different energy range.

The later ratio plots (2, 3, 4 I) show differences caused by the variation in cold-matter absorption. If the [FORMULA] -value is high (and thus the variatons in [FORMULA]), we see this as increased variability towards the lowest energies. Since the spectra are obtained using a moving average over 64 seconds, which effectively filters out all the faster variations, this confirms that there are large changes in the column-density on long time scales.

4.5. Rms-spectra

The rms-spectra we obtained during the observations with enough time- and spectral resolution are plotted in Fig. 13. A remarkable rms spectrum in Fig. 13 is that presented in panel "1 B+C"; a decrease is visible below [FORMULA] 7 keV. This is probably associated with the presence of a soft-component in the spectrum which is not (or less) variable and dilutes the variability (see Tanaka, 1991).

[FIGURE] Fig. 13. The 0.01-8 Hz rms variability spectra for four data sets. Labels refer to the same data as were used for the power spectra in Fig. 9. Note the increase towards lower energies of the variability which is present in rms-spectra 2 and 3, but much less in rms-spectrum 4.

In the other rms spectra we see that the average 0.01-8 Hz rms-variability is [FORMULA] 30 %, while in some rms-spectra an increase towards lower photon energies below [FORMULA] 4 keV is visible (rms-spectra 2 and 3). In the panels labeled 4A+B, 4C, 4D this increase at low photon energies is much less prominent. This favours an interpretation where an underlying [FORMULA] 30%variability that is roughly constant with photon energy is, at low photon energies, increased by additional changes in the [FORMULA] column density. The changes in the column density introduce additional variability in the flux only below [FORMULA] 4 keV. The additional variability below [FORMULA] 4 keV is not present in the last observation (rms-spectra 4A+B, 4C, 4D), which is consistent with a lower [FORMULA] -value (and changes of this value) as derived from the CD at that time. In Fig. 14 we have plotted the rms-spectra as obtained from integrating the variability between 0.01-0.1, 0.1-1, and 1-8 Hz, and from 0.01 to 8 Hz. From this figure we can conclude that the changes in the [FORMULA] column density only occur on time scales longer than 1 second, since the variability in the 1-8 Hz band is almost constant with photon energy.

[FIGURE] Fig. 14. The frequency dependence of the rms spectra. From top to bottom the rms-spectra in the frequency range 0.01-8, 0.01-0.1, 0.1-1, and 1-8 Hz are plotted. The data used in this figure are the same as used for panel 2A and 2B in Fig. 13.

The result from the analysis of the rms spectra and the spectral ratios are consistent; on time scales longer than 1 s variations in the absorbing column play an important role in the variability of GS 2023+338.

4.6. Phase delays

The phase delays as a function of photon energy are plotted in Fig. 15. We have plotted the phase delays (for certain frequency bands) as a function of energy, because we are interested in possible dependencies on photon energy. We see that phase changes occur, but that they are generally modest: no phase delays with an amplitude larger than 0.1 radians are detected. In general, the phase delay increases monotonically with photon energy. Between 0 and 1 Hz a delay is present at energies below [FORMULA] 4 keV (panel 3). It should be noted that this occurs when the increase towards low energies in the rms-spectrum (interpreted as the effect of changes in [FORMULA]) is most prominent.

[FIGURE] Fig. 15. The phase delay spectra. Both the delays in the 0-1 Hz, and the 1-2 Hz band have been plotted (indicated in top right of the panels). The channel with an energy of [FORMULA] 6 keV has been choosen as a reference channel and has therefore by definition a phase delay of zero. Typical errors are 0.02 to 0.05 radians (in observation 1 the errors are 2 to 3 times larger). The observed scatter in the plots is smaller due to correlations between the points.

From the phase delays plotted in panels labeled 2 and 3 it seems that the phase delays are somewhat larger in the 1-2 Hz band than in the 0-1 Hz band. This is also present in the data presented by Miyamoto et al. (1992) for Cyg X-1. However, it is difficult to compare our results with those of Miyamoto et al. (1992) since we have plotted the phase delays in two selected frequency bands against photon energy, while Miyamoto et al. (1992) have plotted the phase delays between two energy bands against frequency. A comparison of our results with the results of Miyamoto et al. (1992) for GX339-4 show that the phase delays might be similar.

We conclude from this is that only small phase-differences are present in the variations at different energies of the X-ray flux; those phase delays seem to be roughly comparable to those found in Cyg X-1 (and possibly GX339-4), however the quite large statistical errors inherent to the determination of small phase delays make a accurate comparison difficult.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998