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

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3. Results: the spectral variations

The CDs and HIDs for all observations are presented in Figs. 1-6a and b. Each point represents a time interval of 120 seconds of which [FORMULA] % contained data.

[FIGURE] Fig. 1. The June 1987, June 1988, and October 1988 observations. MPC modes: a, c, and e are the colour-colour diagrams and b, d, and f are the hardness-intensity diagrams for the June 1987, June 1988 and October 1988 observation, respectively. For the definitions of the colours and the intensity see text and Table 2. The position of the I, II and the II (c) indicate the position in the Z track were the three June 1988 burst occurred. The position of the IV (e) indicates were in the Z the October 1988 burst occurred
[FIGURE] Fig. 2. The May 1991 and June 1991 observations. MPC modes: a and d are the colour-colour diagrams, b and e are the hardness-intensity diagrams, and c and f are the hard colour curves for the May and June observations, respectively
[FIGURE] Fig. 3. The October 1989 and November 1990 observations. MPC1 modes: a is the colour-colour diagram and b is the hardness-intensity diagram. The dots ([FORMULA]) are the October 1989 data, the crosses (x) are the November 1990 data. The position of the V indicates where in the Z the October 1989 burst occured
[FIGURE] Fig. 4. The October 1989 and November 1990 observation. MPC1 and MPC3 modes: a is the colour-colour diagram and b is the hardness-intensity diagram. The dots ([FORMULA]) are the October 1989 data, the crosses (x) are the November 1990 data. The definitions of colours differ from the ones used in Fig. 3, see text and Table 2
[FIGURE] Fig. 5. The June 1987, June 1988 and October 1988 observations. PC mode: a, c, and e are the colour-colour diagrams and b, d, and f are the hardness-intensity diagrams for the June 1987, June 1988 and October 1988 observation, respectively. Most likely the parts of the Z in the CD of the October 1988 observation (e) indicated by HV and SV belong to the hard vertex and soft vertex, respectively. The state of the area indicated by E is unclear. See further text
[FIGURE] Fig. 6. October 1989 observation. PC mode: a is the colour-colour diagram and b is the hardness-intensity diagram. An harmonic of the HBO was seen in the part of the Z in the HID (b) which is indicated by the H. See also text

3.1. The 1987, 1988 and 1991 observations

3.1.1. June 1987

In both the CD and HID of the MPC-data (Figs. 1a and b) a NB can be seen. No HB is present. The FB is only just seen in the CD, but it is clearly visible in the HID. The count rate decreases as soon as the source enters this FB. In the HID, the upper NB is approximately twice as broad as the middle and lower NB. This broadening of the upper NB is not seen in the CD. The PC data (Figs. 5a and b) only show a NB. The June 1987 data were previously discussed by Mitsuda & Dotani (1989), however, they used 16-second data points. Due to the scatter induced by Poisson statistics they could not detect the broadening of the upper NB in the HID.

3.1.2. June 1988

This observation was already discussed by Hasinger et al. (1990). Parts of the data (from 1988 June 12 02:16 to 1988 June 13 08:49 UT and from 1988 June 14 01:29 to 03:59 UT) were obtained when the offset angle was about [FORMULA], giving a collimator transmission of 40-60%. We corrected these data for the overestimation of the count rates in the low photon energy bands (Sect. 2.1). In the CDs of the MPC and PC data (Figs. 1c and 5c, respectively) clearly a HB, a NB and an extended FB are visible. The horizontal branch is not horizontal but diagonal. The HIDs of the MPC and PC data (Figs. 1d and 5d, respectively) also show all three branches. When the source moves into the FB, the count rate first slightly increases and then decreases.

3.1.3. October 1988

The CD and HID of the MPC data (Figs. 1e and f) were reported before by Hasinger et al. (1990). In the CD and HID all three branches are visible. The HB is really horizontal and when the source enters the FB the count rate decreases immediately. In the CD and HID of the PC data (Figs. 5e and f, not previously reported) three seperate areas of points are visible. Comparing these figures with the MPC data of this observation, the upper and the middle area (indicated by HV and SV, respectively) are probably near the hard and soft vertices, respectively. This is confirmed by the fast timing analysis (see Sect. 4). The status of the third, lowest area (indicated by E) is unclear. The fast timing properties (see Sect. 4 and Table 5) suggest that Cygnus X-2 was near the soft vertex, either on the NB, or on the FB.

3.1.4. May 1991

Part of the data of this observation (from 1991 May 15 01:16 to 04:53 UT) was obtained when the offset angle was large and the collimator transmission low (40-60%). We attempted a correction to the low photon energy channels for the count rate overestimation (Sect. 2.1). During the time of low transmission, Cygnus X-2 seemed to be on the NB, as judged from the CD, but in the HID the same data points were displaced from the NB. Correcting the count rates for the low-energy flux overestimation was not enough to place the points exactly on the NB in the HID. In order to show more clearly the soft vertex and the beginning of the FB (see below) we did not include these points in the HID, and did not use them in our further analysis. In the CD (Fig. 2a) the HB is short and diagonal. No clear FB can be seen, but a full NB can. In the HID (Fig. 2b) the beginning of a FB can be seen, which is not made up of the points with the low collimator transmission. The count rate increases when the source enters the FB.

3.1.5. June 1991

During part of this observation (from 1991 June 10 10:06 to 16:02 UT) Cygnus X-2 was observed with a very large offset angle and a collimator transmission of 10-20%. We did not include these data in our analysis because of the large uncertainties in the count rates (Sect. 2.1). The remaining data (Figs. 2d and e) show a clear NB, and a hint for a FB, which is most clearly seen in the HID. When examining the data at higher time resolution we see a more developed FB. No HB is observed. When the source moves onto the FB the count rate decreases immediately. The FB is approximately horizontal. Notice that the very broad NB in the HID corresponds to a narrow NB in the CD.

3.1.6. Comparison of the 1987, 1988 and 1991 observations

Comparing the five observations we find the following. The overall intensity level, defined as the mean count rate on the NB, changed by a factor of 1.34 between the observations. The lowest intensities were observed in June 1988 and May 1991, the highest intensities in October 1988 and June 1991. Intermediate intensities were observed in June 1987. Following the classification of Kuulkers et al. (1996a) our lowest overall intensities correspond to their "medium level" and our highest overall intensities to their "high level". We shall adopt this terminology in what follows. As we also observe a level intermediate between these two, it is obvious from our data that the medium and high levels are probably part of a continuous range instead of a discrete set. We did not observe Cygnus X-2 when it was in the so-called "low level" (Kuulkers et al. 1996a). We confirm the previously reported (Hasinger et al. 1990; Kuulkers et al. 1996a and references therein) correlation between the shape of the Z in the CDs and HIDs and the overall intensity level.

In the medium level the HB is not horizontal but oriented under an [FORMULA] angle in the CD. It is less steep in the HID. In the CD the HB is quite short compared to the NB. In the HID the HB and NB are of the same length. The NB is nearly exactly vertical in the HID, with almost no changes in intensity. The FB is very well developed in the CD, with large colour changes. In the HID, when the source enters the FB the count rate first increases, then, further up the FB, decreases. In the high level the HBs in both CD and HID are nearly horizontal. In the CD the HB is again short compared to the NB, while in the HID it is approximately the same length as the NB. The NB in the HID shows a positive correlation between hard colour and intensity. The FB in the CD is hardly visible, with hardly any colour changes. In the HID the FB is well developed and horizontal (little colour changes), and when the source moves onto the FB the count rate immediately decreases. The "intermediate" level shows characteristics of both the medium and the high level. Due to lack of data nothing can be said about the orientation of the HB during the intermediate level. The hard colour of the NB in the HID shows a positive correlation with intensity, similar to the high level, although not as clear. The FB in the CD is hardly visible, with small colour changes, also similar to the high level. When the source moves on the FB in the HID, which is not horizontal, this is similar to the medium level, the count rate immediately decreases (like in the high level). In the CD and HIDs, the Z-track shifts downward (to softer colours), parallel to the NB in the CD, when the overall intensity level increases. In the medium level it is at its highest position (hard colour), in the intermediate level it is lower, and in the high level it is lowest.

When we compare the NBs in the HIDs we see that the branch width changes with overall intensity. In the high level the NB is broader than in the medium level. The NB in the intermediate level is only broad in its upper part. Comparing the hard colour curves (Figs. 2c and f), we see that the character of the motion through the NB depends on intensity level. In the medium level the colours change slower than in the high level. These two new results are discussed in the next section.

3.1.7. The motion through the Z using [FORMULA]

The [FORMULA]   parametrization makes it possible to investigate the kinematics of the motion along the Z track in more detail (see Dieters & van der Klis 1996). When examining [FORMULA]   as a function of time it is evident that the source does not jump through the branches, but moves smoothly along the Z track. In the high level Cygnus X-2 seems to move faster up and down the normal branch than when the overall intensities are lower (compare Figs. 2c and f). In order to investigate this we calculated the velocity ([FORMULA]) and acceleration ([FORMULA]) distributions (Sect. 2.3; Dieters & van der Klis 1996). We find that the distributions are symmetric about zero: there is no difference in the motion up and down the Z track. The scatter of [FORMULA]   and [FORMULA]   increases from the HB, through the NB, to the FB indicating that the source moves through the Z most slowly on the HB, faster on the NB and fastest on the FB. On the NB the scatter of [FORMULA]   and [FORMULA]   increases when the overall intensity increases. In order to quantify this we determined the standard deviations of [FORMULA]   ([FORMULA]) and [FORMULA]   ([FORMULA]).

On the NB, [FORMULA]   and [FORMULA]   show a strong correlation with overall intensity (see Figs. 7a and b). They increase by a factor [FORMULA] 1.4 and [FORMULA] 1.5, respectively, when the overall intensity increases by a factor of 1.34. No correlations between [FORMULA]   and [FORMULA]   on the FB and the overall intensity were found. For the HB the data do not allow a conclusion on this point.

[FIGURE] Fig. 7. Standard deviation of [FORMULA]   (a), [FORMULA]   (b) and [FORMULA]   (c) on the NB against the log mean intensity (c/s) on the NB during the different observations

In order to examine the width of the NB in the HID we applied the [FORMULA]   parametrization on the Z track in the HID (Sect. 2.3). The [FORMULA]   time series are symmetric around zero. The lack of points on the HBs and FBs makes a definitive conclusion about the evolution of the width of the Z from the HB, via the NB to the FB, impossible. However, when two or more branches are present the Z width seems to increase from the HB to the NB, and further on the FB. As mentioned earlier (Sect. 3.1.6) we find that the NB width in the HID increases when the overall intensity increases. This effect is visible as a strong increase in the standard deviation of [FORMULA] on the NB, with overall intensity (Fig. 7c). When the overall intensity increases by a factor [FORMULA] 1.34, the standard deviation of [FORMULA]   on the NB increases by a factor [FORMULA] 1.75. On the other branches the standard deviation of [FORMULA]   stays approximately the same at all overall intensities. When we examine the NB width in the CDs we do not find any increase in the standard deviation of [FORMULA]   with overall intensity: the NB has approximately the same width at all intensity levels in the CDs.

3.2. The 1989 and the 1990 observations

3.2.1. The MPC1 mode data

In order to be able to compare these observations roughly with the other observations, and because of the very broad photon energy channels of the MPC3 mode (see Sect. 2.2), we made CDs and HIDs of the MPC 1 data only. Because during the November 1990 observation the MPC1 mode was used only very briefly, we combined the October 1989 (dots) and November 1990 (crosses) data in Fig. 3. In both the CD and the HID the HB and the NB are clearly visible. No FB is present. An upward curve can be seen at the beginning of the HB during the October 1989 observation. Such an upward curve of the HB was previously reported by Kuulkers et al. (1996a) in the 1985 EXOSAT observation on day 301/302. The colour points of the November 1990 observation are displaced with respect to the October 1989 data.

3.2.2. The MPC3 mode data

In order to include the MPC3 data and to find out on wich part of the Z track the source was in during the November 1990 observation, we had to use different colours, with broader energy bands. For comparison we did the same for the October 1989 data. The energy bands used are given in Table 2. Fig. 4 shows a clear HB and NB for the October 1989 data (dots), as before, and the curve upwards of the HB, although less pronounced. The November 1990 data (crosses) show only a HB which is shifted in colour with respect to the October 1989 data. No upward curve is visible in the November 1990 data.

3.2.3. The PC mode data

The October 1989 PC data CD and the HID (Fig. 6a and b) show a NB, the hard vertex and parts of the HB. In the HID, the points (indicated by the H) on the HB with the lowest intensity and low hard colour are not on the HB in the CD. They are placed on the hard vertex in the CD. The fast timing behaviour would suggest that those points are at the left end of the HB (see Sect. 4.4)

3.2.4. Comparison of the 1989 and 1990 observations to the other observations

The 1989 and 1990 observations were performed using different energy bands as compared to the other observations. Therefore, we can not directly compare their overall intensity levels. However, if we assume that the difference in the total count rate between 2.3-18.6 keV and 2.9-19.0 keV is minor we see that the overall intensity of the October 1989 observation is about the same as for the June 1987 observations. There is no NB available for the November 1990 observation so no direct comparison with the other observations of the mean NB intensity can be made. However, the shift of the HB during this observation with respect to the October 1989 HB indicates that the overall intensity of the November 1990 observation was higher than the overall intensity of the October 1989 observation. Therefore, we conclude that the October 1989 observation was taken at an overall intensity level in between the medium and high level, and the November 1990 observation during a high level episode.

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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