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

5. Discussion

In this section we will make a comparison between the behaviour as found for GS 2023+338 with the behaviour found in other BHCs.

5.1. Comparison of the power spectra with those of other Black Hole Candidates

The overal power spectral shape of GS 2023+338 (see Fig. 8 and 9) is somewhat like that of Cyg X-1, GX 339-4, and GS1124-68 in the low (hard) state (see Miyamoto et al. 1992). It can be described by an (almost) flat part below frequencies of 0.05 Hz, while above this frequency the power drops off steeply. In two sources, the part of the spectrum above this frequency has been observed to stay approximately the same, while the part below this cut-off frequency changes. This has been observed in Cyg X-1 (Belloni & Hasinger 1990) and GX 339-4 (Miyamoto et al. 1991). The part above the cut-off frequency has been described in different ways by different authors: as a power law with different indices in three different frequency regimes (Belloni and Hasinger 1990), or as composed of different Lorentzians (Miyamoto et al. 1991).

However, there are some differences: GS 2023+338 does not show the above-described Belloni-Hasinger effect as seen in data from Cyg X-1. There is no clear change visible in the power spectra of GS 2023+338 with respect to the level or cut-off frequency of the flat top, although the intensities are different by a large factor (see also Miyamoto et al. 1993a). Another difference with respect to Cyg X-1 is that the power spectrum is steeper at higher frequencies (above 5 Hz). In Cyg X-1 the power spectrum above these frequencies can be described with a power law with an index of 1.5, while in GS 2023+338 the description with a Lorentzian with a FWHM of 3 Hz seems satisfactory. At frequencies higher than a few FWHM ( 6 Hz) this corresponds to power law with index 2. It should, however, be noted that the steepness of the spectrum of Cyg X-1 above a few Hz can be described with a power law with an index changing between 1.4-2 (Belloni and Hasinger 1990). In 4U 1705-44 (a burst source, Berger and Van der Klis, 1996) the steepness of the power spectrum at frequencies just above the flat part can be described with a power law with an index of 0.9. A possible relation between the mass of the compact object and the steepness of the power spectrum might exist, but currently not enough data on different sources are available to draw conclusions.

From Belloni and Hasinger (1990) it appears that in the power spectrum of Cyg X-1 a bump around 4 Hz is present. A similar component is also visible in the power spectra of GX 339-4 presented by Miyamoto et al. (1992) at around 2 Hz. In GS 2023+338 this bump is also present and we modelled it with the zero-centered Lorentzian component with a FWHM of 3 Hz, and its frequency thus is 1.5 Hz. In atoll sources, which show similar behaviour to black holes in their low states when they are dim (e.g. 4U 1705-44) additional power is present at frequencies of 3 Hz (Berger and Van der Klis 1996).

Summarizing we can say that we are beginning to see small differences (e.g. the frequency of the "bumps" or the steepness of the spectra) in the power spectra of different BHCs. It will be interesting to study those subtle differences between these sources in more detail.

The power spectra observed during the early stages of the outburst (and thus at high count rates) (PC spectrum 1A, and both MPC3 spectra) differ from the power spectra observed in other black-hole candidates. They contain a large amount of variability ( 35% between 0.001 and 1 Hz) and can be described as a steep () power law. They do not resemble the power spectra of other BHCs in their high or very high state (see Miyamoto et al. 1991, 1992, 1993b, 1994a, b). A plausible explanation for this additional steep component in the power spectra of GS 2023+338 is the effect of the variations in which occur below 1 Hz (see Sect. 4.5).

The power spectrum observed at the highest peak of the outburst (May 30 data), shows an additional component near 0.04 Hz (Fig. 11). This power spectrum looks similar to that of Cyg X-1 as obtained with Sigma data (Vikhlinin et al. 1994). This power spectrum of Cyg X-1 has been obtained in its low state and shows a peak around 0.05 Hz. This peak can either be labeled broad low-frequency QPO or "peaked" low-state noise. Since in GS 2023+338 the peak is only observed once we can not study its behaviour in more detail.

It is clear that around maximum intensities the shape of the power spectrum changes, but it does not develop into a very-high-state spectrum (which is characterized by very strong band-limited noise with a cut-off frequency in the range from 1 to 10 Hz and QPO with a frequency between 2-10 Hz and sometimes harmonics), since no evidence for 2-10 Hz QPO is present (we estimate an upper-limit of 4% in the 2-10 Hz range). The upper limit is not very strict since a lot of variability is present in this source and small deviations from the global shape of the power spectrum have to be fitted with a relatively strong QPO component. This upper limit is not very different from the observed strength of the QPO in e.g., GX 339-4: 4-5% (Miyamoto et al. 1991).

It is remarkable that although GS 2023+338 reaches very high count rates and high luminosities (Tanaka [1989] concluded from the saturation of the light curve near the peak that the Eddington luminosity was reached) the power spectrum is remarkably similar to that of other BHCs in the low-state (spectrally hard). Only when the source is at its peak the power spectrum (and also the energy spectrum) changes, but certainly does not resemble a power spectrum of other BHCs in either the high (soft) or very-high state. Tanaka (1989) reached a similar conclusion from a spectral analysis which showed that the intrinsic spectrum of GS 2023+338 was always a power law, and did not show the ultra-soft component usually seen in the high and very-high states of BHCs. There are two possible differences with other sources which could explain this behaviour. The first is that GS 2023+338 is known to have a very massive compact object ( 6 , and probably 12 , see Shahbaz et al., 1994), possibly more massive than that of other BHCs. However, it is not clear how the high mass of the compact object (which is after all probably of the same order of the masses of other BHCs) could prevent the source from exhibiting high- or very-high- state behaviour, especially since the main determinant of the behaviour would likely be the fraction of the Eddington luminosity at which the source is radiating. The source may reach the Eddington limit for a 10 compact object (Tanaka 1989).

The other possibility is at different inclination of the source. It could well be that a different viewing geometry is present, and therefore a different part of the region around the compact object is observed. However, although there are suggestions (see Van der Klis 1995b), little is known about the effects of inclination on the observed variability behaviour. An inclination of 42- is allowed from optical observations (Casares & Charles 1994); from modelling of the ellipsoidal variations Shahbaz et al. (1994) find a lower limit of .

5.2. Energy dependence of the variability

From Fig. 13 (panel "1 non-high") we conclude that during the early stages of the outburst the variability below 7 keV diminishes (see also Oosterbroek et al. 1995), which is explained by Tanaka (1991) as caused by the presence of a diluting soft component which is not variable itself.

From the rms spectra (Fig. 13 and 14) we conclude that changes in affect the fast variability behaviour of GS 2023+338. At low variability frequencies the contribution of changes in is evident. At frequencies above 1 Hz there is almost no extra variability below 5 keV. This suggest that changes in take place on a time scale of 1 s.

Since we find that the -changes play an important role on time scales longer than 1 s, we consider here a model where clumps of cold gas move in front of the compact object on a Keplerian time scale. Whenever such a cloud (or any other geometry, e.g. filaments) passes through the line of sight it introduces an additional and a temporal variation in the flux. The clouds which cause the absorption should not be completely ionized. In the next part we make an estimation at which radii, partially ionized clouds could be present. Below we denote the time scale of the variability with , and the characteristic size of the clouds with l. The clouds are at a distance a from the compact object. Then:

Where is the orbital period at a distance a. For a 12 solar mass black hole this can be written as:

If we take as the change in 10²² cm^-2 (which is high for variation on a time scale of 1 s, but reasonable for the slower variations), then where n is the density of hydrogen atoms (in cm^-3) and thus:

The ionization parameter is defined as: (Hatchett, Buff & McCray 1975), where L is the luminosity of the central source (we take L as 10% of the Eddington luminosity for a 12 compact object). This can be written as:

Low-energy absorption takes place for (Hatchett et al. 1975), which leads to:

this leads to a radius of 6-40 light seconds, as the minimal radius where enough absorbing material can be orbiting the compact object. This is well inside the system since the semi-major axis equals 90 light seconds. A site where this orbiting material can be naturally found is the rim of the accretion disk. At the high accretion rates present in GS 2023+338 we expect that the accretion disk is thick, and together with the inclination of 42- it could be that we are just looking through the edge of the accretion disk and, if the disk is slightly irregular, see the observed variations in the column density. The large -values in the large changes in this value could result from a special viewing geometry (i.e., just through the rim of the disk).

If the above is a correct interpretation of the rapid changes of the column-density, then the opening angle of the disk must be at least , but less than .

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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